diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..3e3461a --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +*.asv diff --git a/README.md b/README.md new file mode 100644 index 0000000..6ec8c0d --- /dev/null +++ b/README.md @@ -0,0 +1,25 @@ +[![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=symbiotic-engineering/IFAC_CAMS_2024) + +# Force Saturation Analysis + +This repository can replicate the plots in the IFAC-CAMS paper, showing the effect of an impedance mismatch on electrical power production of a wave energy converter, and especially the effect of an impedance mismatch caused by nonlinear actuator force saturation. + +Note that it is intended for showing relationships, and is not intended for real-time execution in an optimization. Optimization-suited code for the effect of force saturation on mechanical power exists [Here](https://github.com/symbiotic-engineering/MDOcean/blob/49bee41511abcb8873273ba0ff210978d67bb053/mdocean/simulation/modules/dynamics/dynamics.m#L90), and for the effect of force saturation on electrical power will be developed soon. + +Citation: McCabe and Haji, "Force-Limited Control of Wave Energy Converters using a Describing Function Linearization," IFAC Conference on Control Applications in Marine Systems, Robotics, and Vehicles 2024. + +# How to replicate results +- Use `electrical_impedance_match.mlx` to derive equations 3, 4, and 5. This script also contains some plots that served as early inspiration for figures 2, 3, and 4. +- Use `elec_impedance_match_plots.m` to display figures 2, 3, and 4. +- Use [this](https://github.com/symbiotic-engineering/MDOcean/blob/main/mdocean/plots/sin_saturation_demo.m) script from another repository to display figure 6. +- Use `describing_fcn_fsat_graphs.mlx` to derive equation 16 and display figure 8. +- Use `sensitivity_plot.m` to display figure 9. + +# Dependencies +- MATLAB (tested in R2023b) +- Symbolic math toolbox +- RF toolbox (for smith plots) +- the paretoFront function can be found [here](https://github.com/symbiotic-engineering/MDOcean/blob/main/mdocean/optimization/multiobjective/paretoFront.m) + +# Funding Acknowledgement +This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE–2139899. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation. diff --git a/describing_fcn_fsat_graphs.mlx b/describing_fcn_fsat_graphs.mlx new file mode 100644 index 0000000..d433e5e Binary files /dev/null and b/describing_fcn_fsat_graphs.mlx differ diff --git a/elec_impedance_match_plots.m b/elec_impedance_match_plots.m new file mode 100644 index 0000000..7531c77 --- /dev/null +++ b/elec_impedance_match_plots.m @@ -0,0 +1,263 @@ +clear all +clc +close all + +%% Power equation on Smith Plot + +mag_delta = 0.01; +phase_delta = pi/90; + +[MagGamma,PhaseGamma] = meshgrid(0:mag_delta:1, 0:phase_delta:2*pi); +ReGamma = MagGamma .* cos(PhaseGamma); +ImGamma = MagGamma .* sin(PhaseGamma); +gamma = ReGamma + 1i * ImGamma; +z = -(gamma + 1) ./ (gamma - 1); +m1 = real(z); +m2 = imag(z); + +power_ratio = 1-MagGamma.^2; +mySmithPlot(ReGamma, ImGamma, power_ratio, 'Power Ratio', true) +colormap(flipud(copper)) + +%% Current ratio on smith plot +sq_coeff = m2.^2 + (1-m1).^2; +lin_coeff = 4*m2; +const_coeff = m2.^2 + (1+m1).^2; +b_over_a = [-20, -5, -2, -1, 0, 1, 2, 5, 20]; + +figure(2) +clf +hold on + +markers = {'-',':','--','-.','--*'}; + +for i = 1:length(b_over_a) + b_a = b_over_a(i); + sqrt_term = b_a^2 * sq_coeff + b_a * lin_coeff + const_coeff; + sqrt_term(sqrt_term<0) = 1e-16; + currentRatio = 2 ./ sqrt(sqrt_term); + currentTitle = ['Current Ratio $\frac{|I_L|}{|I_L^m|}$, for $\alpha = ', num2str(b_a), '$']; + showColorbar = b_a == b_over_a(end); % only show colorbar on last plot + [Z1_non_dom, Z2_non_dom] = mySmithPlot(ReGamma, ImGamma, currentRatio, currentTitle, showColorbar, power_ratio, 'm'); + if b_a >= 0 % only plot positive because pos and neg are the same + figure(2) + plot(Z1_non_dom,Z2_non_dom,['m',markers{i-4}],'DisplayName',['|\alpha|=',num2str(b_a)]) + end +end + +figure(2) +xlabel('Current Ratio |I_L|/|I_L^m|') +ylabel('Power Ratio P_L/P_L^m') +title('Pareto Front') +legend +improvePlot + +%% Voltage Ratio on smith plot + +for i = 1:length(b_over_a) + b_a = b_over_a(i); + complex_term = z * (1 - b_a * 1i) ./ (1 + z + (1 - z)*b_a*1i); + voltageRatio = 2/sqrt(1 + b_a^2) * abs(complex_term); + voltageTitle = ['Voltage Ratio $\frac{|V_L|}{|V_L^m|}$, for $\alpha = ', num2str(b_a),'$']; + showColorbar = b_a == b_over_a(end); % only show colorbar on last plot + [Z1_non_dom, Z2_non_dom] = mySmithPlot(ReGamma, ImGamma, voltageRatio, voltageTitle, showColorbar, power_ratio, 'g'); + if b_a >= 0 % only plot positive because pos and neg are the same + figure(2) + plot(Z1_non_dom,Z2_non_dom,['g',markers{i-4}],'DisplayName',['|\alpha|=',num2str(b_a)]) + end +end + +figure(2) +xlabel('Voltage Ratio |V_L|/|V_L^m|') +ylabel('Power Ratio P_L/P_L^m') +title('Pareto Front') +legend +improvePlot + +%% Optimal voltage and current, but symbolic instead of numerical optimum +syms P_ratio real positive +syms alpha real +GamMag = sqrt(1-P_ratio); +num = alpha^2 * GamMag^2 - sqrt( (alpha^2+1)*(alpha^2*GamMag^4 + 1) ) + 1; +den_V = alpha * (1 - GamMag)^2; +den_I = alpha * (1 + GamMag)^2; +V_ratio_opt = 2*atan(num/den_V); +I_ratio_opt = 2*atan(num/den_I); + +figure +for i=1:length(b_over_a) + b_a = b_over_a(i); + V = subs(V_ratio_opt,alpha,b_a); + I = subs(I_ratio_opt,alpha,b_a); + fplot(V,[0 1],'-','DisplayName',['voltage',num2str(b_a)]) + hold on + fplot(I,[0 1],'--','DisplayName',['current',num2str(b_a)]) + legend + xlabel('Power Ratio') + ylabel('Current/Voltage Ratio') +end + +%% Pareto tradeoff of voltage and current and power +close all +b_a_pos = [0, 1, 2, 5, 20]; + +sq_coeff = m2.^2 + (1-m1).^2; +lin_coeff = 4*m2; +const_coeff = m2.^2 + (1+m1).^2; + +Gammas = unique(MagGamma); +for j = 1:length(b_a_pos) + b_a = b_a_pos(j); + + sqrt_term = b_a^2 * sq_coeff + b_a * lin_coeff + const_coeff; + sqrt_term(sqrt_term<0) = 1e-16; + currentRatio = 2 ./ sqrt(sqrt_term); + + complex_term = z * (1 - b_a * 1i) ./ (1 + z + (1 - z)*b_a*1i); + voltageRatio = 2/sqrt(1 + b_a^2) * abs(complex_term); + + p = [-voltageRatio(:), -currentRatio(:), power_ratio(:)]; % assumes max Z is better + [~, non_dom_idxs] = paretoFront(p); + + vol_opt_path = zeros(length(Gammas),2); + cur_opt_path = zeros(length(Gammas),2); + + figure + hold on + + % pink, green shaded patches + patch([0,2,2,0],[1,1,2,2],'m','FaceAlpha',0.2,'DisplayName','Current Exceeds z=1 Baseline'); + hold on + patch([1,2,2,1],[0,0,2,2],'g','FaceAlpha',0.2,'DisplayName','Voltage Exceeds z=1 Baseline'); + + % Pareto plots for different gamma + colors = copper(length(Gammas)); + for i=1:length(Gammas) + idx = non_dom_idxs(ismember(non_dom_idxs, find(MagGamma == Gammas(i)))); + vol = voltageRatio(idx); + cur = currentRatio(idx); + [vol_sorted, sort_idx] = sort(vol); + cur_sorted = cur(sort_idx); + vol_opt_path(i,:) = [vol_sorted(1), cur_sorted(1)]; + cur_opt_path(i,:) = [vol_sorted(end), cur_sorted(end)]; + plot(vol_sorted,cur_sorted,'HandleVisibility','off','Color',colors(i,:),'LineWidth',1.5) + end + + % optimal paths + plot(vol_opt_path(:,1),vol_opt_path(:,2),'g:','DisplayName','Voltage Optimal Path','LineWidth',2.5) + plot(cur_opt_path(:,1),cur_opt_path(:,2),'m-.','DisplayName','Current Optimal Path','LineWidth',2.5) + + % dummy pareto for legend + middleIdx = round(length(Gammas)/2); + plot(NaN,NaN,'DisplayName','Pareto front','Color',colors(middleIdx,:)) + + xlabel('Voltage Ratio') + ylabel('Current Ratio') + title(['|\alpha| = ',num2str(b_a)]) + + xlim([0 2]) + ylim([0 2]) + % plot([0 1],[1 1],'k--','HandleVisibility','off') + % plot([1 1],[0 1],'k--','HandleVisibility','off') + legend + + showColorbar = j == length(b_a_pos); % only show colorbar on last plot + if showColorbar + % color bar for gamma + cb = colorbar; + colormap('copper') + + % second color bar for power ratio + % see https://www.mathworks.com/matlabcentral/answers/475762-colormap-utility-two-axes-in-colorbar + power_ratio_evenly_spaced = 1 : -0.1 : 0; + gamma_for_equally_spaced_power_ratio = sqrt(1 - power_ratio_evenly_spaced); + ax = gca; + cb2 = axes('Position',cb.Position,'color','none'); % add new axes at same posn + cb2.XAxis.Visible = 'off'; % hide the x axis of new + posn = ax.Position; % get main axes location + posn(3) = 0.8 * posn(3); % cut down width + ax.Position = posn; % resize main axes to make room for colorbar labels + yticks(cb2,gamma_for_equally_spaced_power_ratio); + yticklabels(cb2, cellstr(string(power_ratio_evenly_spaced)) ); + + ylabel(cb,'Reflection Coefficient Magnitude |\Gamma|') + ylabel(cb2,'Power Ratio P_L/P_L^m') + cb.Position = cb2.Position; % put the colorbar back to overlay second axeix + end + + improvePlot + + if showColorbar + set(cb2,'FontWeight','normal','LineWidth',0.5) + box off + set(gcf,'Pos',[100 100 850 600]) % make plot wider + end +end + +%% smith plot function +function [Z1_nondom_sorted, Z2_nondom_sorted] = mySmithPlot(X,Y,Z,titleString,showColorbar,Z_pareto_compare,col) +% Z pareto compare and col (color) are optional arguments to trace out an optimal path + + figure('Color',[1 1 1]) + smithplot('TitleTop',titleString,'TitleTopTextInterpreter','latex', ... + 'TitleTopFontSizeMultiplier',1.5) + hold on + levs = 0:0.1:1; + Z_capped = Z; + Z_capped(Z>1) = NaN; + contour(X, Y, Z_capped, levs, 'HandleVisibility','off','LineWidth',3); + + grey = [.3 .3 .3]; + red = [.5 .1 .1]; + + % colored shading where Z>1 + if max(Z,[],'all') > 1 + Z_caps = Z; + Z_caps(Z<=1) = NaN; + contourf(X, Y, Z_caps,0,'FaceColor',col,'FaceAlpha',0.2,'HandleVisibility','off') + patch(NaN,NaN,col,'FaceAlpha',0.2,'DisplayName','Exceeds z=1 Baseline') % dummy patch for legend + end + + if showColorbar + cb = colorbar; + scale = 0.8; % smaller colorbar to fit smith chart + cb.Position = [cb.Position(1), cb.Position(2)+0.1, ... + cb.Position(3)*scale cb.Position(4)*scale]; + end + + if nargin>5 + Z_capped(X==1) = NaN; % don't include far right point because it has + % the same value as the far left point (0,0) and will mess up the optimum curve + p = [-Z_capped(:), Z_pareto_compare(:)]; % assumes max Z is better + [~, non_dom_idxs] = paretoFront(p); + non_dom_idxs(ismember(non_dom_idxs, find(isnan(Z_capped)))) = []; % remove nans from pareto front + Z1_nondom = Z_capped(non_dom_idxs); + Z2_nondom = Z_pareto_compare(non_dom_idxs); + [Z1_nondom_sorted,sort_idxs] = sort(Z1_nondom); + Z2_nondom_sorted = Z2_nondom(sort_idxs); + + % red shading where dominated +% Z_dom = Z_capped; +% Z_dom(non_dom_idxs) = NaN; +% contourf(X,Y,Z_dom,0,'FaceColor',red,'HandleVisibility','off') +% patch(NaN,NaN,red, 'DisplayName','Dominated by other z') % dummy patches for the sake of legend + + % trace out nondominated points + X_opt = X(non_dom_idxs); + Y_opt = Y(non_dom_idxs); + plot(X_opt(sort_idxs),Y_opt(sort_idxs),[col '--'],'DisplayName','Optimal','LineWidth',3) + legend('location','southeast') + + % pareto front with dom and non dom points + % figure + % scatter(Z_capped(:),Z_pareto_compare(:),'HandleVisibility','off') + % hold on + % + % scatter(Z1_nondom, Z2_nondom,'s','Filled','DisplayName',titleString) + % xlabel(titleString) + % ylabel('Power Ratio') + % title('Pareto Front') + % legend('Interpreter','latex') + end +end + diff --git a/electrical_impedance_match.mlx b/electrical_impedance_match.mlx new file mode 100644 index 0000000..ca5da77 Binary files /dev/null and b/electrical_impedance_match.mlx differ diff --git a/ifacconf_latex/README.txt b/ifacconf_latex/README.txt new file mode 100644 index 0000000..cbdc4bb --- /dev/null +++ b/ifacconf_latex/README.txt @@ -0,0 +1,30 @@ +INSTALLING THE IFACCONF LATEX PACKAGE +===================================== + +1. Unzip the ifacconf_latex.zip archive into a folder (directory) of your convenience. + +2. Copy the ifaconf.cls file to a directory where latex can find it (see your local installation documentation for the details). + +3. Test the class file by processing the sample file twice: + +pdflatex ifaconf.tex +pdflatex ifaconf.tex # run twice to solve cross-references + +You should obtain as a result a file named ifaconf.pdf. It should look the same as the provided ifaconf_sample.pdf. This file also contains some guidelines about using the ifaconf.cls LaTeX class. + +Alternatively, you can generate a PDF file using latex and ghostscript: + +latex ifacconf.tex +latex ifacconf.tex # run twice to solve cross-references +dvips -Ppdf -G0 -ta4 ifacconf +ps2pdf -dCompatibilityLevel=1.4 -dMaxSubsetPct=100 -dSubsetFonts=true \ + -dEmbedAllFonts=true -sPAPERSIZE=a4 ifacconf.ps ifaconf.pdf + +4. 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made (SP) + +%SP 2001/01/23 +% Changed the pages output for inproceedings +%SP 2003/07/25 +% Add the leading space in format.vol.num.pages only if there is a volume +%SP 2005/01/21 +% Add volume and number to incollection with cross-reference +% Capitalize No., as Ch. and Vol. + +%% ---------------------------------------- +%% *** Author-date reference style for elsart *** +%% $Id: elsart-harv.bst,v 1.3 2005/01/21 11:23:24 spepping Exp $ +%% +%% Copyright 1994-1999 Patrick W Daly + % =============================================================== + % IMPORTANT NOTICE: + % This bibliographic style (bst) file has been generated from one or + % more master bibliographic style (mbs) files, listed above. + % + % This generated file can be redistributed and/or modified under the terms + % of the LaTeX Project Public License Distributed from CTAN + % archives in directory macros/latex/base/lppl.txt; either + % version 1 of the License, or any later version. + % =============================================================== + % Name and version information of the main mbs file: + % \ProvidesFile{merlin.mbs}[1999/03/18 3.88 (PWD)] + % For use with BibTeX version 0.99a or later + %------------------------------------------------------------------- + % This bibliography style file is intended for texts in ENGLISH + % This is an author-year citation style bibliography. As such, it is + % non-standard LaTeX, and requires a special package file to function properly. + % Such a package is natbib.sty by Patrick W. Daly + % The form of the \bibitem entries is + % \bibitem[Jones et al.(1990)]{key}... + % \bibitem[Jones et al.(1990)Jones, Baker, and Smith]{key}... + % The essential feature is that the label (the part in brackets) consists + % of the author names, as they should appear in the citation, with the year + % in parentheses following. There must be no space before the opening + % parenthesis! + % With natbib v5.3, a full list of authors may also follow the year. + % In natbib.sty, it is possible to define the type of enclosures that is + % really wanted (brackets or parentheses), but in either case, there must + % be parentheses in the label. + % The \cite command functions as follows: + % \citet{key} ==>> Jones et al. (1990) + % \citet*{key} ==>> Jones, Baker, and Smith (1990) + % \citep{key} ==>> (Jones et al., 1990) + % \citep*{key} ==>> (Jones, Baker, and Smith, 1990) + % \citep[chap. 2]{key} ==>> (Jones et al., 1990, chap. 2) + % \citep[e.g.][]{key} ==>> (e.g. Jones et al., 1990) + % \citep[e.g.][p. 32]{key} ==>> (e.g. Jones et al., p. 32) + % \citeauthor{key} ==>> Jones et al. + % \citeauthor*{key} ==>> Jones, Baker, and Smith + % \citeyear{key} ==>> 1990 + %--------------------------------------------------------------------- + +ENTRY + { address + author + booktitle + chapter + edition + editor + howpublished + institution + journal + key + month + note + number + organization + pages + publisher + school + series + title + type + url + volume + year + } + {} + { label extra.label sort.label short.list } + +INTEGERS { output.state before.all mid.sentence after.sentence after.block } + +FUNCTION {init.state.consts} +{ #0 'before.all := + #1 'mid.sentence := + #2 'after.sentence := + #3 'after.block := +} + +STRINGS { s t } + +FUNCTION {output.nonnull} +{ 's := + output.state mid.sentence = + { ", " * write$ } + { output.state after.block = + { add.period$ write$ + newline$ + "\newblock " write$ + } + { output.state before.all = + 'write$ + { add.period$ " " * write$ } + if$ + } + if$ + mid.sentence 'output.state := + } + if$ + s +} + +FUNCTION {output} +{ duplicate$ empty$ + 'pop$ + 'output.nonnull + if$ +} + +FUNCTION {output.check} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} + +FUNCTION {fin.entry} +{ add.period$ + write$ + newline$ +} + +FUNCTION {new.block} +{ output.state before.all = + 'skip$ + { after.block 'output.state := } + if$ +} + +FUNCTION {new.sentence} +{ output.state after.block = + 'skip$ + { output.state before.all = + 'skip$ + { after.sentence 'output.state := } + if$ + } + if$ +} + +%SP 2003/07/25 +% No longer used +FUNCTION {add.blank} +{ " " * before.all 'output.state := +} + +FUNCTION {date.block} +{ + new.sentence +} + +FUNCTION {not} +{ { #0 } + { #1 } + if$ +} + +FUNCTION {and} +{ 'skip$ + { pop$ #0 } + if$ +} + +FUNCTION {or} +{ { pop$ #1 } + 'skip$ + if$ +} + +FUNCTION {new.block.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.block + if$ +} + +FUNCTION {field.or.null} +{ duplicate$ empty$ + { pop$ "" } + 'skip$ + if$ +} + +FUNCTION {emphasize} +{ skip$ } + +FUNCTION {capitalize} +{ "u" change.case$ "t" change.case$ } + +FUNCTION {space.word} +{ " " swap$ * " " * } + + % Here are the language-specific definitions for explicit words. + % Each function has a name bbl.xxx where xxx is the English word. + % The language selected here is ENGLISH +FUNCTION {bbl.and} +{ "and"} + +FUNCTION {bbl.etal} +{ "et~al." } + +FUNCTION {bbl.editors} +{ "Eds." } + +FUNCTION {bbl.editor} +{ "Ed." } + +FUNCTION {bbl.edby} +{ "edited by" } + +FUNCTION {bbl.edition} +{ "Edition" } + +FUNCTION {bbl.volume} +{ "Vol." } + +FUNCTION {bbl.of} +{ "of" } + +%SP 2005/01/21 +% capitalize, as Ch. and Vol. +FUNCTION {bbl.number} +{ "No." } + +FUNCTION {bbl.nr} +{ "no." } + +FUNCTION {bbl.in} +{ "in" } + +FUNCTION {bbl.pages} +{ "pp." } + +FUNCTION {bbl.page} +{ "p." } + +FUNCTION {bbl.chapter} +{ "Ch." } + +FUNCTION {bbl.techrep} +{ "Tech. Rep." } + +FUNCTION {bbl.mthesis} +{ "Master's thesis" } + +FUNCTION {bbl.phdthesis} +{ "Ph.D. thesis" } + +FUNCTION {bbl.first} +{ "1st" } + +FUNCTION {bbl.second} +{ "2nd" } + +FUNCTION {bbl.third} +{ "3rd" } + +FUNCTION {bbl.fourth} +{ "4th" } + +FUNCTION {bbl.fifth} +{ "5th" } + +FUNCTION {bbl.st} +{ "st" } + +FUNCTION {bbl.nd} +{ "nd" } + +FUNCTION {bbl.rd} +{ "rd" } + +FUNCTION {bbl.th} +{ "th" } + +MACRO {jan} {"Jan."} + +MACRO {feb} {"Feb."} + +MACRO {mar} {"Mar."} + +MACRO {apr} {"Apr."} + +MACRO {may} {"May"} + +MACRO {jun} {"Jun."} + +MACRO {jul} {"Jul."} + +MACRO {aug} {"Aug."} + +MACRO {sep} {"Sep."} + +MACRO {oct} {"Oct."} + +MACRO {nov} {"Nov."} + +MACRO {dec} {"Dec."} + +FUNCTION {eng.ord} +{ duplicate$ "1" swap$ * + #-2 #1 substring$ "1" = + { bbl.th * } + { duplicate$ #-1 #1 substring$ + duplicate$ "1" = + { pop$ bbl.st * } + { duplicate$ "2" = + { pop$ bbl.nd * } + { "3" = + { bbl.rd * } + { bbl.th * } + if$ + } + if$ + } + if$ + } + if$ +} + +MACRO {acmcs} {"ACM Comput. Surv."} + +MACRO {acta} {"Acta Inf."} + +MACRO {cacm} {"Commun. ACM"} + +MACRO {ibmjrd} {"IBM J. Res. Dev."} + +MACRO {ibmsj} {"IBM Syst.~J."} + +MACRO {ieeese} {"IEEE Trans. Softw. Eng."} + +MACRO {ieeetc} {"IEEE Trans. Comput."} + +MACRO {ieeetcad} + {"IEEE Trans. Comput.-Aided Design Integrated Circuits"} + +MACRO {ipl} {"Inf. Process. Lett."} + +MACRO {jacm} {"J.~ACM"} + +MACRO {jcss} {"J.~Comput. Syst. Sci."} + +MACRO {scp} {"Sci. Comput. Programming"} + +MACRO {sicomp} {"SIAM J. Comput."} + +MACRO {tocs} {"ACM Trans. Comput. Syst."} + +MACRO {tods} {"ACM Trans. Database Syst."} + +MACRO {tog} {"ACM Trans. Gr."} + +MACRO {toms} {"ACM Trans. Math. Softw."} + +MACRO {toois} {"ACM Trans. Office Inf. Syst."} + +MACRO {toplas} {"ACM Trans. Prog. Lang. Syst."} + +MACRO {tcs} {"Theoretical Comput. Sci."} + +FUNCTION {write.url} +{ url empty$ + { skip$ } + { "\newline\urlprefix\url{" url * "}" * write$ newline$ } + if$ +} + + +INTEGERS { nameptr namesleft numnames } + +FUNCTION {format.names} +{ 's := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv~}{ll}{, jj}{, f.}" format.name$ + 't := + nameptr #1 > + { + namesleft #1 > + { ", " * t * } + { + "," * + s nameptr "{ll}" format.name$ duplicate$ "others" = + { 't := } + { pop$ } + if$ + t "others" = + { + " " * bbl.etal * + } + { " " * t * } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} +FUNCTION {format.names.ed} +{ format.names } +FUNCTION {format.key} +{ empty$ + { key field.or.null } + { "" } + if$ +} + +FUNCTION {format.authors} +{ author empty$ + { "" } + { author format.names } + if$ +} + +FUNCTION {format.editors} +{ editor empty$ + { "" } + { editor format.names + editor num.names$ #1 > + { " (" * bbl.editors * ")" * } + { " (" * bbl.editor * ")" * } + if$ + } + if$ +} + +FUNCTION {format.in.editors} +{ editor empty$ + { "" } + { editor format.names.ed + editor num.names$ #1 > + { " (" * bbl.editors * ")" * } + { " (" * bbl.editor * ")" * } + if$ + } + if$ +} + +FUNCTION {format.note} +{ + note empty$ + { "" } + { note #1 #1 substring$ + duplicate$ "{" = + 'skip$ + { output.state mid.sentence = + { "l" } + { "u" } + if$ + change.case$ + } + if$ + note #2 global.max$ substring$ * + } + if$ +} + +FUNCTION {format.title} +{ title empty$ + { "" } + { title "t" change.case$ + } + if$ +} + +FUNCTION {format.full.names} +{'s := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv~}{ll}" format.name$ + 't := + nameptr #1 > + { + namesleft #1 > + { ", " * t * } + { + numnames #2 > + { "," * } + 'skip$ + if$ + s nameptr "{ll}" format.name$ duplicate$ "others" = + { 't := } + { pop$ } + if$ + t "others" = + { + " " * bbl.etal * + } + { bbl.and + space.word * t * + } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {author.editor.key.full} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.full.names } + if$ + } + { author format.full.names } + if$ +} + +FUNCTION {author.key.full} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { author format.full.names } + if$ +} + +FUNCTION {editor.key.full} +{ editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.full.names } + if$ +} + +FUNCTION {make.full.names} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.full + { type$ "proceedings" = + 'editor.key.full + 'author.key.full + if$ + } + if$ +} + +FUNCTION {output.bibitem} +{ newline$ + "\bibitem[{" write$ + label write$ + ")" make.full.names duplicate$ short.list = + { pop$ } + { * } + if$ + "}]{" * write$ + cite$ write$ + "}" write$ + newline$ + "" + before.all 'output.state := +} + +FUNCTION {n.dashify} +{ + 't := + "" + { t empty$ not } + { t #1 #1 substring$ "-" = + { t #1 #2 substring$ "--" = not + { "--" * + t #2 global.max$ substring$ 't := + } + { { t #1 #1 substring$ "-" = } + { "-" * + t #2 global.max$ substring$ 't := + } + while$ + } + if$ + } + { t #1 #1 substring$ * + t #2 global.max$ substring$ 't := + } + if$ + } + while$ +} + +FUNCTION {word.in} +{ bbl.in capitalize + ":" * + " " * } + +FUNCTION {format.date} +{ year duplicate$ empty$ + { "empty year in " cite$ * "; set to ????" * warning$ + pop$ "????" } + 'skip$ + if$ + month empty$ + 'skip$ + { month + " " * swap$ * + } + if$ + extra.label * + before.all 'output.state := + ", " swap$ * +} + +FUNCTION {format.btitle} +{ title +} + +FUNCTION {tie.or.space.connect} +{ duplicate$ text.length$ #3 < + { "~" } + { " " } + if$ + swap$ * * +} + +FUNCTION {either.or.check} +{ empty$ + 'pop$ + { "can't use both " swap$ * " fields in " * cite$ * warning$ } + if$ +} + +FUNCTION {format.bvolume} +{ volume empty$ + { "" } + { bbl.volume volume tie.or.space.connect + series empty$ + 'skip$ + { bbl.of space.word * series emphasize * } + if$ + "volume and number" number either.or.check + } + if$ +} + +FUNCTION {format.number.series} +{ volume empty$ + { number empty$ + { series field.or.null } + { output.state mid.sentence = + { bbl.number } + { bbl.number capitalize } + if$ + number tie.or.space.connect + series empty$ + { "there's a number but no series in " cite$ * warning$ } + { bbl.in space.word * series * } + if$ + } + if$ + } + { "" } + if$ +} + +FUNCTION {is.num} +{ chr.to.int$ + duplicate$ "0" chr.to.int$ < not + swap$ "9" chr.to.int$ > not and +} + +FUNCTION {extract.num} +{ duplicate$ 't := + "" 's := + { t empty$ not } + { t #1 #1 substring$ + t #2 global.max$ substring$ 't := + duplicate$ is.num + { s swap$ * 's := } + { pop$ "" 't := } + if$ + } + while$ + s empty$ + 'skip$ + { pop$ s } + if$ +} + +FUNCTION {convert.edition} +{ edition extract.num "l" change.case$ 's := + s "first" = s "1" = or + { bbl.first 't := } + { s "second" = s "2" = or + { bbl.second 't := } + { s "third" = s "3" = or + { bbl.third 't := } + { s "fourth" = s "4" = or + { bbl.fourth 't := } + { s "fifth" = s "5" = or + { bbl.fifth 't := } + { s #1 #1 substring$ is.num + { s eng.ord 't := } + { edition 't := } + if$ + } + if$ + } + if$ + } + if$ + } + if$ + } + if$ + t +} + +FUNCTION {format.edition} +{ edition empty$ + { "" } + { output.state mid.sentence = + { convert.edition "l" change.case$ " " * bbl.edition * } + { convert.edition "t" change.case$ " " * bbl.edition * } + if$ + } + if$ +} + +INTEGERS { multiresult } + +FUNCTION {multi.page.check} +{ 't := + #0 'multiresult := + { multiresult not + t empty$ not + and + } + { t #1 #1 substring$ + duplicate$ "-" = + swap$ duplicate$ "," = + swap$ "+" = + or or + { #1 'multiresult := } + { t #2 global.max$ substring$ 't := } + if$ + } + while$ + multiresult +} + +FUNCTION {format.pages} +{ pages empty$ + { "" } + { pages multi.page.check + { bbl.pages pages n.dashify tie.or.space.connect } + { bbl.page pages tie.or.space.connect } + if$ + } + if$ +} + +FUNCTION {format.journal.pages} +{ pages empty$ + 'skip$ + { duplicate$ empty$ + { pop$ format.pages } + { + ", " * + pages n.dashify * + } + if$ + } + if$ +} + +%SP 2001/01/23 +% Only used in articles +FUNCTION {format.vol.num.pages} +{ +%SP 2001/01/23 +% Add the leading space only if there is a volume + % volume field.or.null + " " + volume empty$ + { pop$ "" } + { volume * } + if$ + number empty$ + 'skip$ + { + "~(" number * ")" * * + volume empty$ + { "there's a number but no volume in " cite$ * warning$ } + 'skip$ + if$ + } + if$ +} + +FUNCTION {format.chapter.pages} +{ chapter empty$ + { "" } + { type empty$ + { bbl.chapter } + { type "l" change.case$ } + if$ + chapter tie.or.space.connect + } + if$ +} + +FUNCTION {format.in.ed.booktitle} +{ booktitle empty$ + { "" } + { editor empty$ + { word.in booktitle * } + { word.in format.in.editors * ", " * + booktitle * } + if$ + } + if$ +} + +FUNCTION {format.thesis.type} +{ type empty$ + 'skip$ + { pop$ + type "t" change.case$ + } + if$ +} + +FUNCTION {format.tr.number} +{ type empty$ + { bbl.techrep } + 'type + if$ + number empty$ + { "t" change.case$ } + { number tie.or.space.connect } + if$ +} + +FUNCTION {format.article.crossref} +{ + word.in + " \cite{" * crossref * "}" * +} + +FUNCTION {format.book.crossref} +{ volume empty$ + { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ + word.in + } + { bbl.volume capitalize + volume tie.or.space.connect + bbl.of space.word * + } + if$ + " \cite{" * crossref * "}" * +} + +FUNCTION {format.incoll.inproc.crossref} +{ + word.in + " \cite{" * crossref * "}" * +} + +FUNCTION {format.org.or.pub} +{ 't := + "" + address empty$ t empty$ and + 'skip$ + { + t empty$ + { address empty$ + 'skip$ + { address * } + if$ + } + { t * + address empty$ + 'skip$ + { ", " * address * } + if$ + } + if$ + } + if$ +} + +FUNCTION {format.publisher.address} +{ publisher empty$ + { "empty publisher in " cite$ * warning$ + "" + } + { publisher } + if$ + format.org.or.pub +} + +FUNCTION {format.organization.address} +{ organization empty$ + { "" } + { organization } + if$ + format.org.or.pub +} + +FUNCTION {article} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.sentence + crossref missing$ + { journal + "journal" output.check +%SP 2001/01/23 +% Add the space in format.vol.num.pages + % add.blank + before.all 'output.state := + format.vol.num.pages output + } + { format.article.crossref output.nonnull + format.pages output + } + if$ + format.journal.pages + format.note output + fin.entry + write.url +} + +FUNCTION {book} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + format.date "year" output.check + date.block + format.btitle "title" output.check + crossref missing$ + { format.edition output + new.sentence + format.bvolume output + format.number.series output + new.sentence + format.publisher.address output + } + { + new.sentence + format.book.crossref output.nonnull + } + if$ + format.note output + fin.entry + write.url +} + +FUNCTION {booklet} +{ output.bibitem + format.authors output + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.sentence + howpublished output + address output + format.note output + fin.entry + write.url +} + +FUNCTION {inbook} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + format.date "year" output.check + date.block + format.btitle "title" output.check + crossref missing$ + { + format.edition output + new.sentence + format.bvolume output + format.number.series output + new.sentence + format.publisher.address output + format.chapter.pages "chapter and pages" output.check + } + { + format.chapter.pages "chapter and pages" output.check + new.sentence + format.book.crossref output.nonnull + } + if$ + format.pages "pages" output.check + format.note output + fin.entry + write.url +} + +FUNCTION {incollection} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.sentence + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.edition output + new.sentence + format.bvolume output + format.number.series output + new.sentence + format.publisher.address output + format.chapter.pages output + } + { format.incoll.inproc.crossref output.nonnull +%SP 2005/01/21 +% Add volume and number + format.bvolume output + format.number.series output + format.chapter.pages output + } + if$ + format.pages "pages" output.check + format.note output + fin.entry + write.url +} + +FUNCTION {inproceedings} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.sentence + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.edition output + new.sentence + format.bvolume output + format.number.series output + new.sentence + publisher empty$ + { format.organization.address output } + { organization output + format.publisher.address output + } + if$ +%SP 2001/01/23 +% format.pages output + } + { format.incoll.inproc.crossref output.nonnull +%SP 2001/01/23 +% format.pages output + } + if$ +%SP 2001/01/23 + format.pages "pages" output.check + format.note output + fin.entry + write.url +} + +FUNCTION {conference} { inproceedings } + +FUNCTION {manual} +{ output.bibitem + format.authors output + author format.key output + format.date "year" output.check + date.block + format.btitle "title" output.check + new.sentence + organization output + address output + format.edition output + format.note output + fin.entry + write.url +} + +FUNCTION {mastersthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.sentence + bbl.mthesis format.thesis.type output.nonnull + school "school" output.check + address output + format.note output + fin.entry + write.url +} + +FUNCTION {misc} +{ output.bibitem + format.authors output + author format.key output + format.date "year" output.check + date.block + format.title output + new.sentence + howpublished output + format.note output + fin.entry + write.url +} + +FUNCTION {phdthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.sentence + bbl.phdthesis format.thesis.type output.nonnull + school "school" output.check + address output + format.note output + fin.entry + write.url +} + +FUNCTION {proceedings} +{ output.bibitem + format.editors output + editor format.key output + format.date "year" output.check + date.block + format.btitle "title" output.check + new.sentence + format.bvolume output + format.number.series output + new.sentence + publisher empty$ + { format.organization.address output } + { organization output + format.publisher.address output + } + if$ + format.note output + fin.entry + write.url +} + +FUNCTION {techreport} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.sentence + format.tr.number output.nonnull + institution "institution" output.check + address output + format.note output + fin.entry + write.url +} + +FUNCTION {unpublished} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + format.note "note" output.check + fin.entry + write.url +} + +FUNCTION {default.type} { misc } + +READ + +FUNCTION {sortify} +{ purify$ + "l" change.case$ +} + +INTEGERS { len } + +FUNCTION {chop.word} +{ 's := + 'len := + s #1 len substring$ = + { s len #1 + global.max$ substring$ } + 's + if$ +} + +FUNCTION {format.lab.names} +{ 's := + s #1 "{vv~}{ll}" format.name$ + s num.names$ duplicate$ + #2 > + { pop$ + " " * bbl.etal * + } + { #2 < + 'skip$ + { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = + { + " " * bbl.etal * + } + { bbl.and space.word * s #2 "{vv~}{ll}" format.name$ + * } + if$ + } + if$ + } + if$ +} + +FUNCTION {author.key.label} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.editor.key.label} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.lab.names } + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {editor.key.label} +{ editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.lab.names } + if$ +} + +FUNCTION {calc.short.authors} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.label + { type$ "proceedings" = + 'editor.key.label + 'author.key.label + if$ + } + if$ + 'short.list := +} + +FUNCTION {calc.label} +{ calc.short.authors + short.list + "(" + * + year duplicate$ empty$ + { pop$ "????" } + 'skip$ + if$ + * + 'label := +} + +FUNCTION {sort.format.names} +{ 's := + #1 'nameptr := + "" + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" + format.name$ 't := + nameptr #1 > + { + " " * + namesleft #1 = t "others" = and + { "zzzzz" * } + { t sortify * } + if$ + } + { t sortify * } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {sort.format.title} +{ 't := + "A " #2 + "An " #3 + "The " #4 t chop.word + chop.word + chop.word + sortify + #1 global.max$ substring$ +} + +FUNCTION {author.sort} +{ author empty$ + { key empty$ + { "to sort, need author or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.editor.sort} +{ author empty$ + { editor empty$ + { key empty$ + { "to sort, need author, editor, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {editor.sort} +{ editor empty$ + { key empty$ + { "to sort, need editor or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ +} + +FUNCTION {presort} +{ calc.label + label sortify + " " + * + type$ "book" = + type$ "inbook" = + or + 'author.editor.sort + { type$ "proceedings" = + 'editor.sort + 'author.sort + if$ + } + if$ + #1 entry.max$ substring$ + 'sort.label := + sort.label + * + " " + * + title field.or.null + sort.format.title + * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {presort} + +SORT + +STRINGS { last.label next.extra } + +INTEGERS { last.extra.num number.label } + +FUNCTION {initialize.extra.label.stuff} +{ #0 int.to.chr$ 'last.label := + "" 'next.extra := + #0 'last.extra.num := + #0 'number.label := +} + +FUNCTION {forward.pass} +{ last.label label = + { last.extra.num #1 + 'last.extra.num := + last.extra.num int.to.chr$ 'extra.label := + } + { "a" chr.to.int$ 'last.extra.num := + "" 'extra.label := + label 'last.label := + } + if$ + number.label #1 + 'number.label := +} + +FUNCTION {reverse.pass} +{ next.extra "b" = + { "a" 'extra.label := } + 'skip$ + if$ + extra.label 'next.extra := + extra.label + duplicate$ empty$ + 'skip$ + { "{\natexlab{" swap$ * "}}" * } + if$ + 'extra.label := + label extra.label * 'label := +} + +EXECUTE {initialize.extra.label.stuff} + +ITERATE {forward.pass} + +REVERSE {reverse.pass} + +FUNCTION {bib.sort.order} +{ sort.label + " " + * + year field.or.null sortify + * + " " + * + title field.or.null + sort.format.title + * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {bib.sort.order} + +SORT + +FUNCTION {begin.bib} +{ preamble$ empty$ + 'skip$ + { preamble$ write$ newline$ } + if$ + "\begin{thebibliography}{" number.label int.to.str$ * "}" * + write$ newline$ + "\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi" + write$ newline$ + "\expandafter\ifx\csname url\endcsname\relax" + write$ newline$ + " \def\url#1{\texttt{#1}}\fi" + write$ newline$ + "\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi" + write$ newline$ +} + +EXECUTE {begin.bib} + +EXECUTE {init.state.consts} + +ITERATE {call.type$} + +FUNCTION {end.bib} +{ newline$ + "\end{thebibliography}" write$ newline$ +} + +EXECUTE {end.bib} +%% End of customized bst file +%% +%% End of file `elsart-harv.bst'. diff --git a/ifacconf_latex/ifacconf.bst b/ifacconf_latex/ifacconf.bst new file mode 100644 index 0000000..306dcde --- /dev/null +++ b/ifacconf_latex/ifacconf.bst @@ -0,0 +1,1537 @@ +%% +%% This is file `ifacconf.bst', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% merlin.mbs (with options: `ay,nat,nm-rvvc,keyxyr,dt-beg,yr-par,note-yr,volp-com,num-xser,doi,edpar,ppx,ed,xedn,url,url-blk,nfss,') +%% ---------------------------------------- +%% *** Bibliography style for IFAC Proceedings *** +%% +%% Copyright 1994-2007 Patrick W Daly + % =============================================================== + % IMPORTANT NOTICE: + % This bibliographic style (bst) file has been generated from one or + % more master bibliographic style (mbs) files, listed above. + % + % This generated file can be redistributed and/or modified under the terms + % of the LaTeX Project Public License Distributed from CTAN + % archives in directory macros/latex/base/lppl.txt; either + % version 1 of the License, or any later version. + % =============================================================== + % Name and version information of the main mbs file: + % \ProvidesFile{merlin.mbs}[2007/04/24 4.20 (PWD, AO, DPC)] + % For use with BibTeX version 0.99a or later + %------------------------------------------------------------------- + % This bibliography style file is intended for texts in ENGLISH + % This is an author-year citation style bibliography. As such, it is + % non-standard LaTeX, and requires a special package file to function properly. + % Such a package is natbib.sty by Patrick W. Daly + % The form of the \bibitem entries is + % \bibitem[Jones et al.(1990)]{key}... + % \bibitem[Jones et al.(1990)Jones, Baker, and Smith]{key}... + % The essential feature is that the label (the part in brackets) consists + % of the author names, as they should appear in the citation, with the year + % in parentheses following. There must be no space before the opening + % parenthesis! + % With natbib v5.3, a full list of authors may also follow the year. + % In natbib.sty, it is possible to define the type of enclosures that is + % really wanted (brackets or parentheses), but in either case, there must + % be parentheses in the label. + % The \cite command functions as follows: + % \citet{key} ==>> Jones et al. (1990) + % \citet*{key} ==>> Jones, Baker, and Smith (1990) + % \citep{key} ==>> (Jones et al., 1990) + % \citep*{key} ==>> (Jones, Baker, and Smith, 1990) + % \citep[chap. 2]{key} ==>> (Jones et al., 1990, chap. 2) + % \citep[e.g.][]{key} ==>> (e.g. Jones et al., 1990) + % \citep[e.g.][p. 32]{key} ==>> (e.g. Jones et al., p. 32) + % \citeauthor{key} ==>> Jones et al. + % \citeauthor*{key} ==>> Jones, Baker, and Smith + % \citeyear{key} ==>> 1990 + %--------------------------------------------------------------------- + +ENTRY + { address + author + booktitle + chapter + doi + edition + editor + eid + howpublished + institution + journal + key + month + note + number + organization + pages + publisher + school + series + title + type + url + volume + year + } + {} + { label extra.label sort.label short.list } +INTEGERS { output.state before.all mid.sentence after.sentence after.block } +FUNCTION {init.state.consts} +{ #0 'before.all := + #1 'mid.sentence := + #2 'after.sentence := + #3 'after.block := +} +STRINGS { s t} +FUNCTION {output.nonnull} +{ 's := + output.state mid.sentence = + { ", " * write$ } + { output.state after.block = + { add.period$ write$ + newline$ + "\newblock " write$ + } + { output.state before.all = + 'write$ + { add.period$ " " * write$ } + if$ + } + if$ + mid.sentence 'output.state := + } + if$ + s +} +FUNCTION {output} +{ duplicate$ empty$ + 'pop$ + 'output.nonnull + if$ +} +FUNCTION {output.check} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} +FUNCTION {fin.entry} +{ add.period$ + write$ + newline$ +} + +FUNCTION {new.block} +{ output.state before.all = + 'skip$ + { after.block 'output.state := } + if$ +} +FUNCTION {new.sentence} +{ output.state after.block = + 'skip$ + { output.state before.all = + 'skip$ + { after.sentence 'output.state := } + if$ + } + if$ +} +FUNCTION {add.blank} +{ " " * before.all 'output.state := +} + +FUNCTION {date.block} +{ + new.block +} + +FUNCTION {not} +{ { #0 } + { #1 } + if$ +} +FUNCTION {and} +{ 'skip$ + { pop$ #0 } + if$ +} +FUNCTION {or} +{ { pop$ #1 } + 'skip$ + if$ +} +FUNCTION {new.block.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.block + if$ +} +FUNCTION {field.or.null} +{ duplicate$ empty$ + { pop$ "" } + 'skip$ + if$ +} +FUNCTION {emphasize} +{ duplicate$ empty$ + { pop$ "" } + { "\emph{" swap$ * "}" * } + if$ +} +FUNCTION {tie.or.space.prefix} +{ duplicate$ text.length$ #3 < + { "~" } + { " " } + if$ + swap$ +} + +FUNCTION {capitalize} +{ "u" change.case$ "t" change.case$ } + +FUNCTION {space.word} +{ " " swap$ * " " * } + % Here are the language-specific definitions for explicit words. + % Each function has a name bbl.xxx where xxx is the English word. + % The language selected here is ENGLISH +FUNCTION {bbl.and} +{ "and"} + +FUNCTION {bbl.etal} +{ "et~al." } + +FUNCTION {bbl.editors} +{ "eds." } + +FUNCTION {bbl.editor} +{ "ed." } + +FUNCTION {bbl.edby} +{ "edited by" } + +FUNCTION {bbl.edition} +{ "edition" } + +FUNCTION {bbl.volume} +{ "volume" } + +FUNCTION {bbl.of} +{ "of" } + +FUNCTION {bbl.number} +{ "number" } + +FUNCTION {bbl.nr} +{ "no." } + +FUNCTION {bbl.in} +{ "in" } + +FUNCTION {bbl.pages} +{ "" } + +FUNCTION {bbl.page} +{ "" } + +FUNCTION {bbl.chapter} +{ "chapter" } + +FUNCTION {bbl.techrep} +{ "Technical Report" } + +FUNCTION {bbl.mthesis} +{ "Master's thesis" } + +FUNCTION {bbl.phdthesis} +{ "Ph.D. thesis" } + +MACRO {jan} {"January"} + +MACRO {feb} {"February"} + +MACRO {mar} {"March"} + +MACRO {apr} {"April"} + +MACRO {may} {"May"} + +MACRO {jun} {"June"} + +MACRO {jul} {"July"} + +MACRO {aug} {"August"} + +MACRO {sep} {"September"} + +MACRO {oct} {"October"} + +MACRO {nov} {"November"} + +MACRO {dec} {"December"} + +MACRO {acmcs} {"ACM Computing Surveys"} + +MACRO {acta} {"Acta Informatica"} + +MACRO {cacm} {"Communications of the ACM"} + +MACRO {ibmjrd} {"IBM Journal of Research and Development"} + +MACRO {ibmsj} {"IBM Systems Journal"} + +MACRO {ieeese} {"IEEE Transactions on Software Engineering"} + +MACRO {ieeetc} {"IEEE Transactions on Computers"} + +MACRO {ieeetcad} + {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"} + +MACRO {ipl} {"Information Processing Letters"} + +MACRO {jacm} {"Journal of the ACM"} + +MACRO {jcss} {"Journal of Computer and System Sciences"} + +MACRO {scp} {"Science of Computer Programming"} + +MACRO {sicomp} {"SIAM Journal on Computing"} + +MACRO {tocs} {"ACM Transactions on Computer Systems"} + +MACRO {tods} {"ACM Transactions on Database Systems"} + +MACRO {tog} {"ACM Transactions on Graphics"} + +MACRO {toms} {"ACM Transactions on Mathematical Software"} + +MACRO {toois} {"ACM Transactions on Office Information Systems"} + +MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"} + +MACRO {tcs} {"Theoretical Computer Science"} +FUNCTION {bibinfo.check} +{ swap$ + duplicate$ missing$ + { + pop$ pop$ + "" + } + { duplicate$ empty$ + { + swap$ pop$ + } + { swap$ + pop$ + } + if$ + } + if$ +} +FUNCTION {bibinfo.warn} +{ swap$ + duplicate$ missing$ + { + swap$ "missing " swap$ * " in " * cite$ * warning$ pop$ + "" + } + { duplicate$ empty$ + { + swap$ "empty " swap$ * " in " * cite$ * warning$ + } + { swap$ + pop$ + } + if$ + } + if$ +} +FUNCTION {format.url} +{ url empty$ + { "" } + { "\urlprefix\url{" url * "}" * } + if$ +} + +INTEGERS { nameptr namesleft numnames } + + +STRINGS { bibinfo} + +FUNCTION {format.names} +{ 'bibinfo := + duplicate$ empty$ 'skip$ { + 's := + "" 't := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv~}{ll}{, jj}{, f{.}.}" + format.name$ + bibinfo bibinfo.check + 't := + nameptr #1 > + { + namesleft #1 > + { ", " * t * } + { + s nameptr "{ll}" format.name$ duplicate$ "others" = + { 't := } + { pop$ } + if$ + numnames #2 > + { "," * } + 'skip$ + if$ + t "others" = + { + " " * bbl.etal * + } + { + bbl.and + space.word * t * + } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ + } if$ +} +FUNCTION {format.names.ed} +{ + 'bibinfo := + duplicate$ empty$ 'skip$ { + 's := + "" 't := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{f{.}.~}{vv~}{ll}{ jj}" + format.name$ + bibinfo bibinfo.check + 't := + nameptr #1 > + { + namesleft #1 > + { ", " * t * } + { + s nameptr "{ll}" format.name$ duplicate$ "others" = + { 't := } + { pop$ } + if$ + numnames #2 > + { "," * } + 'skip$ + if$ + t "others" = + { + + " " * bbl.etal * + } + { + bbl.and + space.word * t * + } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ + } if$ +} +FUNCTION {format.key} +{ empty$ + { key field.or.null } + { "" } + if$ +} + +FUNCTION {format.authors} +{ author "author" format.names +} +FUNCTION {get.bbl.editor} +{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ } + +FUNCTION {format.editors} +{ editor "editor" format.names duplicate$ empty$ 'skip$ + { + " " * + get.bbl.editor + "(" swap$ * ")" * + * + } + if$ +} +FUNCTION {format.doi} +{ doi "doi" bibinfo.check + duplicate$ empty$ 'skip$ + { + new.block + "\doi{" swap$ * "}" * + } + if$ +} +FUNCTION {format.note} +{ + note empty$ + { "" } + { note #1 #1 substring$ + duplicate$ "{" = + 'skip$ + { output.state mid.sentence = + { "l" } + { "u" } + if$ + change.case$ + } + if$ + note #2 global.max$ substring$ * "note" bibinfo.check + } + if$ +} + +FUNCTION {format.title} +{ title + duplicate$ empty$ 'skip$ + { "t" change.case$ } + if$ + "title" bibinfo.check +} +FUNCTION {format.full.names} +{'s := + "" 't := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv~}{ll}" format.name$ + 't := + nameptr #1 > + { + namesleft #1 > + { ", " * t * } + { + s nameptr "{ll}" format.name$ duplicate$ "others" = + { 't := } + { pop$ } + if$ + t "others" = + { + " " * bbl.etal * + } + { + numnames #2 > + { "," * } + 'skip$ + if$ + bbl.and + space.word * t * + } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {author.editor.key.full} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.full.names } + if$ + } + { author format.full.names } + if$ +} + +FUNCTION {author.key.full} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { author format.full.names } + if$ +} + +FUNCTION {editor.key.full} +{ editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.full.names } + if$ +} + +FUNCTION {make.full.names} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.full + { type$ "proceedings" = + 'editor.key.full + 'author.key.full + if$ + } + if$ +} + +FUNCTION {output.bibitem} +{ newline$ + "\bibitem[{" write$ + label write$ + ")" make.full.names duplicate$ short.list = + { pop$ } + { * } + if$ + "}]{" * write$ + cite$ write$ + "}" write$ + newline$ + "" + before.all 'output.state := +} + +FUNCTION {n.dashify} +{ + 't := + "" + { t empty$ not } + { t #1 #1 substring$ "-" = + { t #1 #2 substring$ "--" = not + { "--" * + t #2 global.max$ substring$ 't := + } + { { t #1 #1 substring$ "-" = } + { "-" * + t #2 global.max$ substring$ 't := + } + while$ + } + if$ + } + { t #1 #1 substring$ * + t #2 global.max$ substring$ 't := + } + if$ + } + while$ +} + +FUNCTION {word.in} +{ bbl.in capitalize + " " * } + +FUNCTION {format.date} +{ year "year" bibinfo.check duplicate$ empty$ + { + "empty year in " cite$ * "; set to ????" * warning$ + pop$ "????" + } + 'skip$ + if$ + extra.label * + before.all 'output.state := + " (" swap$ * ")" * +} +FUNCTION {format.btitle} +{ title "title" bibinfo.check + duplicate$ empty$ 'skip$ + { + emphasize + } + if$ +} +FUNCTION {either.or.check} +{ empty$ + 'pop$ + { "can't use both " swap$ * " fields in " * cite$ * warning$ } + if$ +} +FUNCTION {format.bvolume} +{ volume empty$ + { "" } + { bbl.volume volume tie.or.space.prefix + "volume" bibinfo.check * * + series "series" bibinfo.check + duplicate$ empty$ 'pop$ + { swap$ bbl.of space.word * swap$ + emphasize * } + if$ + "volume and number" number either.or.check + } + if$ +} +FUNCTION {format.number.series} +{ volume empty$ + { number empty$ + { series field.or.null } + { series empty$ + { number "number" bibinfo.check } + { output.state mid.sentence = + { bbl.number } + { bbl.number capitalize } + if$ + number tie.or.space.prefix "number" bibinfo.check * * + bbl.in space.word * + series "series" bibinfo.check * + } + if$ + } + if$ + } + { "" } + if$ +} + +FUNCTION {format.edition} +{ edition duplicate$ empty$ 'skip$ + { + output.state mid.sentence = + { "l" } + { "t" } + if$ change.case$ + "edition" bibinfo.check + " " * bbl.edition * + } + if$ +} +INTEGERS { multiresult } +FUNCTION {multi.page.check} +{ 't := + #0 'multiresult := + { multiresult not + t empty$ not + and + } + { t #1 #1 substring$ + duplicate$ "-" = + swap$ duplicate$ "," = + swap$ "+" = + or or + { #1 'multiresult := } + { t #2 global.max$ substring$ 't := } + if$ + } + while$ + multiresult +} +FUNCTION {format.pages} +{ pages duplicate$ empty$ 'skip$ + { duplicate$ multi.page.check + { + n.dashify + } + { + } + if$ + "pages" bibinfo.check + } + if$ +} +FUNCTION {format.journal.pages} +{ pages duplicate$ empty$ 'pop$ + { swap$ duplicate$ empty$ + { pop$ pop$ format.pages } + { + ", " * + swap$ + n.dashify + "pages" bibinfo.check + * + } + if$ + } + if$ +} +FUNCTION {format.journal.eid} +{ eid "eid" bibinfo.check + duplicate$ empty$ 'pop$ + { swap$ duplicate$ empty$ 'skip$ + { + ", " * + } + if$ + swap$ * + } + if$ +} +FUNCTION {format.vol.num.pages} +{ volume field.or.null + duplicate$ empty$ 'skip$ + { + "volume" bibinfo.check + } + if$ + number "number" bibinfo.check duplicate$ empty$ 'skip$ + { + swap$ duplicate$ empty$ + { "there's a number but no volume in " cite$ * warning$ } + 'skip$ + if$ + swap$ + "(" swap$ * ")" * + } + if$ * + eid empty$ + { format.journal.pages } + { format.journal.eid } + if$ +} + +FUNCTION {format.chapter.pages} +{ chapter empty$ + 'format.pages + { type empty$ + { bbl.chapter } + { type "l" change.case$ + "type" bibinfo.check + } + if$ + chapter tie.or.space.prefix + "chapter" bibinfo.check + * * + pages empty$ + 'skip$ + { ", " * format.pages * } + if$ + } + if$ +} + +FUNCTION {format.booktitle} +{ + booktitle "booktitle" bibinfo.check + emphasize +} +FUNCTION {format.in.ed.booktitle} +{ format.booktitle duplicate$ empty$ 'skip$ + { + editor "editor" format.names.ed duplicate$ empty$ 'pop$ + { + " " * + get.bbl.editor + "(" swap$ * "), " * + * swap$ + * } + if$ + word.in swap$ * + } + if$ +} +FUNCTION {format.thesis.type} +{ type duplicate$ empty$ + 'pop$ + { swap$ pop$ + "t" change.case$ "type" bibinfo.check + } + if$ +} +FUNCTION {format.tr.number} +{ number "number" bibinfo.check + type duplicate$ empty$ + { pop$ bbl.techrep } + 'skip$ + if$ + "type" bibinfo.check + swap$ duplicate$ empty$ + { pop$ "t" change.case$ } + { tie.or.space.prefix * * } + if$ +} +FUNCTION {format.article.crossref} +{ + word.in + " \cite{" * crossref * "}" * +} +FUNCTION {format.book.crossref} +{ volume duplicate$ empty$ + { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ + pop$ word.in + } + { bbl.volume + capitalize + swap$ tie.or.space.prefix "volume" bibinfo.check * * bbl.of space.word * + } + if$ + " \cite{" * crossref * "}" * +} +FUNCTION {format.incoll.inproc.crossref} +{ + word.in + " \cite{" * crossref * "}" * +} +FUNCTION {format.org.or.pub} +{ 't := + "" + address empty$ t empty$ and + 'skip$ + { + t empty$ + { address "address" bibinfo.check * + } + { t * + address empty$ + 'skip$ + { ", " * address "address" bibinfo.check * } + if$ + } + if$ + } + if$ +} +FUNCTION {format.publisher.address} +{ publisher "publisher" bibinfo.warn format.org.or.pub +} + +FUNCTION {format.organization.address} +{ organization "organization" bibinfo.check format.org.or.pub +} + +FUNCTION {article} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.block + crossref missing$ + { + journal + "journal" bibinfo.check + emphasize + "journal" output.check + format.vol.num.pages output + } + { format.article.crossref output.nonnull + format.pages output + } + if$ + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} +FUNCTION {book} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + format.date "year" output.check + date.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + new.block + format.number.series output + new.sentence + format.publisher.address output + } + { + new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} +FUNCTION {booklet} +{ output.bibitem + format.authors output + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.block + howpublished "howpublished" bibinfo.check output + address "address" bibinfo.check output + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} + +FUNCTION {inbook} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + format.date "year" output.check + date.block + format.btitle "title" output.check + crossref missing$ + { + format.bvolume output + format.chapter.pages "chapter and pages" output.check + new.block + format.number.series output + new.sentence + format.publisher.address output + } + { + format.chapter.pages "chapter and pages" output.check + new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} + +FUNCTION {incollection} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.chapter.pages output + new.sentence + format.publisher.address output + format.edition output + } + { format.incoll.inproc.crossref output.nonnull + format.chapter.pages output + } + if$ + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} +FUNCTION {inproceedings} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.pages output + new.sentence + publisher empty$ + { format.organization.address output } + { organization "organization" bibinfo.check output + format.publisher.address output + } + if$ + } + { format.incoll.inproc.crossref output.nonnull + format.pages output + } + if$ + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} +FUNCTION {conference} { inproceedings } +FUNCTION {manual} +{ output.bibitem + format.authors output + author format.key output + format.date "year" output.check + date.block + format.btitle "title" output.check + organization address new.block.checkb + organization "organization" bibinfo.check output + address "address" bibinfo.check output + format.edition output + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} + +FUNCTION {mastersthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.btitle + "title" output.check + new.block + bbl.mthesis format.thesis.type output.nonnull + school "school" bibinfo.warn output + address "address" bibinfo.check output + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} + +FUNCTION {misc} +{ output.bibitem + format.authors output + author format.key output + format.date "year" output.check + date.block + format.title output + new.block + howpublished "howpublished" bibinfo.check output + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} +FUNCTION {phdthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.btitle + "title" output.check + new.block + bbl.phdthesis format.thesis.type output.nonnull + school "school" bibinfo.warn output + address "address" bibinfo.check output + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} + +FUNCTION {proceedings} +{ output.bibitem + format.editors output + editor format.key output + format.date "year" output.check + date.block + format.btitle "title" output.check + format.bvolume output + format.number.series output + new.sentence + publisher empty$ + { format.organization.address output } + { organization "organization" bibinfo.check output + format.publisher.address output + } + if$ + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} + +FUNCTION {techreport} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title + "title" output.check + new.block + format.tr.number output.nonnull + institution "institution" bibinfo.warn output + address "address" bibinfo.check output + format.doi output + new.block + format.url output + new.block + format.note output + fin.entry +} + +FUNCTION {unpublished} +{ output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + format.doi output + new.block + format.url output + new.block + format.note "note" output.check + fin.entry +} + +FUNCTION {default.type} { misc } +READ +FUNCTION {sortify} +{ purify$ + "l" change.case$ +} +INTEGERS { len } +FUNCTION {chop.word} +{ 's := + 'len := + s #1 len substring$ = + { s len #1 + global.max$ substring$ } + 's + if$ +} +FUNCTION {format.lab.names} +{ 's := + "" 't := + s #1 "{vv~}{ll}" format.name$ + s num.names$ duplicate$ + #2 > + { pop$ + " " * bbl.etal * + } + { #2 < + 'skip$ + { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = + { + " " * bbl.etal * + } + { bbl.and space.word * s #2 "{vv~}{ll}" format.name$ + * } + if$ + } + if$ + } + if$ +} + +FUNCTION {author.key.label} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.editor.key.label} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.lab.names } + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {editor.key.label} +{ editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.lab.names } + if$ +} + +FUNCTION {calc.short.authors} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.label + { type$ "proceedings" = + 'editor.key.label + 'author.key.label + if$ + } + if$ + 'short.list := +} + +FUNCTION {calc.label} +{ calc.short.authors + short.list + "(" + * + year duplicate$ empty$ + short.list key field.or.null = or + { pop$ "" } + 'skip$ + if$ + * + 'label := +} + +FUNCTION {sort.format.names} +{ 's := + #1 'nameptr := + "" + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv{ } }{ll{ }}{ ff{ }}{ jj{ }}" + format.name$ 't := + nameptr #1 > + { + " " * + namesleft #1 = t "others" = and + { "zzzzz" * } + { t sortify * } + if$ + } + { t sortify * } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {sort.format.title} +{ 't := + "A " #2 + "An " #3 + "The " #4 t chop.word + chop.word + chop.word + sortify + #1 global.max$ substring$ +} +FUNCTION {author.sort} +{ author empty$ + { key empty$ + { "to sort, need author or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { author sort.format.names } + if$ +} +FUNCTION {author.editor.sort} +{ author empty$ + { editor empty$ + { key empty$ + { "to sort, need author, editor, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ + } + { author sort.format.names } + if$ +} +FUNCTION {editor.sort} +{ editor empty$ + { key empty$ + { "to sort, need editor or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ +} +FUNCTION {presort} +{ calc.label + label sortify + " " + * + type$ "book" = + type$ "inbook" = + or + 'author.editor.sort + { type$ "proceedings" = + 'editor.sort + 'author.sort + if$ + } + if$ + #1 entry.max$ substring$ + 'sort.label := + sort.label + * + " " + * + title field.or.null + sort.format.title + * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {presort} +SORT +STRINGS { last.label next.extra } +INTEGERS { last.extra.num number.label } +FUNCTION {initialize.extra.label.stuff} +{ #0 int.to.chr$ 'last.label := + "" 'next.extra := + #0 'last.extra.num := + #0 'number.label := +} +FUNCTION {forward.pass} +{ last.label label = + { last.extra.num #1 + 'last.extra.num := + last.extra.num int.to.chr$ 'extra.label := + } + { "a" chr.to.int$ 'last.extra.num := + "" 'extra.label := + label 'last.label := + } + if$ + number.label #1 + 'number.label := +} +FUNCTION {reverse.pass} +{ next.extra "b" = + { "a" 'extra.label := } + 'skip$ + if$ + extra.label 'next.extra := + extra.label + duplicate$ empty$ + 'skip$ + { "{\natexlab{" swap$ * "}}" * } + if$ + 'extra.label := + label extra.label * 'label := +} +EXECUTE {initialize.extra.label.stuff} +ITERATE {forward.pass} +REVERSE {reverse.pass} +FUNCTION {bib.sort.order} +{ sort.label + " " + * + year field.or.null sortify + * + " " + * + title field.or.null + sort.format.title + * + #1 entry.max$ substring$ + 'sort.key$ := +} +ITERATE {bib.sort.order} +SORT +FUNCTION {begin.bib} +{ preamble$ empty$ + 'skip$ + { preamble$ write$ newline$ } + if$ + "\begin{thebibliography}{" number.label int.to.str$ * "}" * + write$ newline$ + "\providecommand{\natexlab}[1]{#1}" + write$ newline$ + "\providecommand{\url}[1]{\texttt{#1}}" + write$ newline$ + "\providecommand{\urlprefix}{URL }" + write$ newline$ + "\expandafter\ifx\csname urlstyle\endcsname\relax" + write$ newline$ + " \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else" + write$ newline$ + " \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup \urlstyle{rm}\Url}\fi" + write$ newline$ +} +EXECUTE {begin.bib} +EXECUTE {init.state.consts} +ITERATE {call.type$} +FUNCTION {end.bib} +{ newline$ + "\end{thebibliography}" write$ newline$ +} +EXECUTE {end.bib} +%% End of customized bst file +%% +%% End of file `ifacconf.bst'. diff --git a/ifacconf_latex/ifacconf.cls b/ifacconf_latex/ifacconf.cls new file mode 100644 index 0000000..beac7e4 --- /dev/null +++ b/ifacconf_latex/ifacconf.cls @@ -0,0 +1,1732 @@ +%% +%% This is file `ifacconf.cls', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% pergamon.dtx (with options: `oxford,ifacmtg,cep,uppercasesection,uppercasetitle,specialfront') +%% +%% IMPORTANT NOTICE: +%% +%% For the copyright see the source file. +%% +%% You are *not* allowed to modify this file. +%% +%% You are *not* allowed to distribute this file. +%% For distribution of the original source see the terms +%% for copying and modification in the file pergamon.dtx. +%% +\def\filedate{2008/04/14} +\def\fileversion{3.2ModD} +\def\@journal{IFAC conferences} +\def\@shortjnl{ifacconf} +\def\@issn{} +\def\@shortjid{ifacconf} +\def\@company{IFAC} +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesClass{\@shortjid} +[\filedate, \fileversion: \@journal] +\DeclareOption{a4paper} + {\setlength\paperheight {297mm}% + \setlength\paperwidth {210mm}} +\DeclareOption{letterpaper} + {\setlength\paperheight {11in}% + \setlength\paperwidth {8.5in}} +\ExecuteOptions{a4paper} +\ProcessOptions +%% +%% This is file `public.cls', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% esl.dtx (with options: `package,bare,pergamon,PUBLIC,SL5,TWOCOL,QUOTEABS,MCS,NOTEFIRSTPAGE') +%% +%% IMPORTANT NOTICE: +%% +%% For the copyright see the source file. +%% +%% You are *not* allowed to modify this file. +%% +%% You are *not* allowed to distribute this file. +%% For distribution of the original source see the terms +%% for copying and modification in the file esl.dtx. +%% +\def\esp@fileversion{2.16} +\def\esp@filedate{1998/12/16} +%% esl.dtx Copyright (C) 1994-1998 Elsevier Science +\def\@shortjnl{\relax} +%% \typeout{} +%% \typeout{} +%% \typeout{** IMPORTANT NOTICE:} +%% \typeout{** This is modified version on ifacmtg.cls} +%% \typeout{** All future IFAC meetings must use this class} +%% \typeout{** to prepare papers for Elsevier.} +%% \typeout{** Original notice: The TeX code in this package} +%% \typeout{** is NOT being placed in the public domain.} +%% \typeout{** Copyright 1995 Elsevier Science Ltd} +%% \typeout{} +\typeout{} + +\newif\if@TwoColumn +\newif\if@seceqn +\newif\if@secthm +\newif\if@nameyear +\newif\if@Elproofing +\@Elproofingfalse +\def\@pagenumprefix{} +\def\author@font{} +\def\partname{Part} +\def\appendixname{Appendix} +\def\contentsname{Contents} +\def\listfigurename{List of Figures} +\def\listtablename{List of Tables} +\def\refname{References} +\def\indexname{Index} +\def\figurename{Fig.} +\def\tablename{Table} +\def\abstractname{} +\lineskip 1\p@ +\normallineskip 1\p@ +\def\baselinestretch{1} +\frenchspacing +\def\@xiiipt{12} +\newdimen\@frontmatterwidth +\def\@overtitleskip{0\p@} % WAS 69 PMISRA +\def\@overhistoryskip{\z@} +\def\@undertitleskip{\z@} +\def\@overkeywordskip{6\p@} % WAS 12 PMISRA 2007-05-30 +\def\@overabstractskip{6\p@} +\def\@overcaptionskip{8\p@} +\def\@preabstractskip{4\p@ \@plus 2\p@ \@minus 2\p@} %WAS 24 PMISRA +\def\@belowfmskip{6\p@} % WAS 12 PMISRA 2007-05-30 +\def\@bibliosize{\small} +\def\@historysize{\small} +\def\@keywordsize{\small} +\def\@overaddressskip{2pt} +\def\@titlesize{\Large} +\def\@authorsize{\large} +\def\@keywordheading{{\it Key words: \ }} +\def\@addressstyle{\small\itshape} +\def\@captionsize{\small} +\def\@tablecaptionsize{\@captionsize} +\def\@figurecaptionsize{\@captionsize} +\def\captionwidth{.8\linewidth} +\def\@tablesize{\small} +\def\@keywordwidth{.8\textwidth} +\def\@abstractwidth{.8\textwidth} +\def\@fignumfont#1{#1} +% SP 2001/08/07 subsections with italic numbers +\def\@secnumfont#1{\ifcase#1\upshape\or\upshape\else\itshape\fi} +\def\@catchlinesize{\footnotesize} +\def\@pergamonsize{\@catchlinesize} +\def\@runheadsize{\normalsize} +\def\etal{et al.} +\def\AND{\&} +\def\@Colofonheight{1cm} +%% \def\@abstractsize{\fontsize{\@ixpt}{11pt}\selectfont} +%% \def\@articletypesize{\fontsize{\@xiiipt}{13pt}\selectfont} +%% \def\normalsize{\@setfontsize\normalsize\@xpt{12}% +%% \abovedisplayskip 5.75\p@ \@plus 2\p@ \@minus 2\p@% +%% \belowdisplayskip \abovedisplayskip +%% \abovedisplayshortskip \z@ \@plus 2\p@% +%% \belowdisplayshortskip 3.5\p@ \@plus 2\p@ \@minus 2\p@ +%% \let\@listi\@listI} +%% \def\small{\@setfontsize\small\@viiipt{10}% +%% \abovedisplayskip 7\p@ \@plus 2\p@ \@minus 4\p@% +%% \belowdisplayskip \abovedisplayskip +%% \abovedisplayshortskip \z@ \@plus 1\p@% +%% \belowdisplayshortskip 3\p@ \@plus 1\p@ \@minus 2\p@ +%% \def\@listi{\topsep 0.5\@bls \parsep\z@ \itemsep\parsep}} +%% \let\footnotesize=\small +%% \let\@xviiipt\@xviipt +%% \def\scriptsize{\@setfontsize\scriptsize\@viipt{8}} +%% \def\tiny{\@setfontsize\tiny\@vipt{7}} +%% \def\large{\@setfontsize\large\@xiiipt{14}} +%% \def\Large{\@setfontsize\Large\@xviipt{20}} +%% \def\LARGE{\@setfontsize\LARGE\@xviiipt{22}} +%% \def\huge{\@setfontsize\huge\@xxpt{22}} +%% \def\Huge{\@setfontsize\Huge\@xxvpt{27}} +%% \def\baselinestretch{1} +%% \normalsize % Choose the normalsize font. + +\def\@abstractsize{\fontsize{\@ixpt}{10pt}\selectfont} +\def\@articletypesize{\fontsize{\@xiiipt}{13pt}\selectfont} +\def\normalsize{\@setfontsize\normalsize\@xpt{10}% +\abovedisplayskip 3\p@ \@plus 1\p@ \@minus 1\p@% +\belowdisplayskip \abovedisplayskip +\abovedisplayshortskip \z@ \@plus 2\p@% +\belowdisplayshortskip 2\p@ \@plus 1\p@ \@minus 1\p@ +\let\@listi\@listI} +\def\small{\@setfontsize\small\@viiipt{9}% +\abovedisplayskip 4\p@ \@plus 1\p@ \@minus 1\p@% +\belowdisplayskip \abovedisplayskip +\abovedisplayshortskip \z@ \@plus 1\p@% +\belowdisplayshortskip 3\p@ \@plus 1\p@ \@minus 1\p@ +\def\@listi{\topsep 0.5\@bls \parsep\z@ \itemsep\parsep}} +\let\footnotesize=\small +\let\@xviiipt\@xviipt +\def\scriptsize{\@setfontsize\scriptsize\@viipt{8}} +\def\tiny{\@setfontsize\tiny\@vipt{7}} +\def\large{\@setfontsize\large\@xiiipt{14}} +\def\Large{\@setfontsize\Large\@xviipt{20}} +\def\LARGE{\@setfontsize\LARGE\@xviiipt{22}} +\def\huge{\@setfontsize\huge\@xxpt{22}} +\def\Huge{\@setfontsize\Huge\@xxvpt{27}} +\def\baselinestretch{1.1} +\normalsize % Choose the normalsize font. + +\newdimen\@bls % Several dimensions are +\@bls=\baselineskip % expressed in terms of this. +%\if@twoside +% \oddsidemargin \z@ % Commented out 2007-05-30 PMISRA +% \evensidemargin \z@ % Commented out 2007-05-30 PMISRA +% \marginparwidth 10\p@ % Commented out 2007-05-30 PMISRA +%\else % Commented out 2007-05-30 PMISRA +% \oddsidemargin \z@ % Commented out 2007-05-30 PMISRA +% \evensidemargin \z@ % Commented out 2007-05-30 PMISRA +% \marginparwidth 2pc % Commented out 2007-05-30 PMISRA +%\fi + +\if@twoside % Values for two-sided printing: % Added + \oddsidemargin -11mm % Left margin on odd-numbered pages. % by PMISRA + \evensidemargin -11mm % Left margin on even-numbered pages. % 2007-05-30 + \marginparwidth 1pc % \@Width of marginal notes. % +\else % Values for one-sided printing: % + \oddsidemargin -11mm % Left margin on odd-numbered pages. % + \evensidemargin -11mm % Left margin on even-numbered pages. % + \marginparwidth 1pc +\fi + +\marginparsep 10\p@ % Horizontal space between outer margin and WAS 20 PMISRA + % marginal note +\topmargin 2mm % Nominal distance from top of page to top of + % box containing running head. +\headheight 10\p@ % + \headsep 20\p@ % + \footskip 10\p@ % Changed to 10 from 23 PMISRA 2007-05-30 +\bigskipamount=\@bls \@plus 0.3\@bls \@minus 0.3\@bls % 1/1 line +\medskipamount=0.5\bigskipamount % 1/2 line +\smallskipamount=0.25\bigskipamount % 1/4 line +\textheight 54\baselineskip % \@Height of text (incl. footnotes and figures, +\advance\textheight\topskip % excl. running head and foot). +\textwidth 180mm % \@Width of text line. + % For two-column mode: +\columnsep 5mm % Space between columns +\columnseprule \z@ % \@Width of rule between columns. + \footnotesep 6.65\p@ +\skip\footins 6\p@ \@plus 8\p@ % Space between last line of text and % was 12 PMISRA 2007-05-30 + % top of first footnote. +\floatsep 8\p@ \@plus 4\p@ \@minus 2\p@ % Space between adjacent floats moved + % to top or bottom of text page. +\textfloatsep 8\p@ \@plus 4\p@ \@minus 2\p@ % Space between main text and floats + % at top or bottom of page. +\intextsep 8\p@ \@plus 4\p@ \@minus 2\p@ % Space between in-text figures and + % text. +\dblfloatsep 8\p@ \@plus 4\p@ \@minus 4\p@ % Same as \floatsep for double-column + % figures in two-column mode. +\dbltextfloatsep 12\p@ \@plus 4\p@ \@minus 4\p@ % \textfloatsep for double-column + % floats. +\@fptop \z@ \@plus 1fil % Stretch at top of float page/column. (Must be + % \z@ \@plus ...) +\@fpsep 8\p@ \@plus 2fil % Space between floats on float page/column. +\@fpbot \z@ \@plus 1fil % Stretch at bottom of float page/column. (Must be + % \z@ \@plus ... ) +\@dblfptop \z@ \@plus 1fil % Stretch at top of float page. (Must be \z@ \@plus ...) +\@dblfpsep 8\p@ \@plus 2fil % Space between floats on float page. +\@dblfpbot \z@ \@plus 1fil % Stretch at bottom of float page. (Must be + % \z@ \@plus ... ) +\marginparpush 5\p@ % Minimum vertical separation between two marginal + % notes. +\parskip \z@ +\parindent 1em +\newskip\eqntopsep % Extra vertical space, in addition to + \eqntopsep 4\p@ \@plus 2\p@ \@minus 2\p@ %\parskip, added above and below % WAS 8 PMISRA 2007-05-30 +\newdimen\eqnarraycolsep % Half the space between columns +\eqnarraycolsep 1\p@ % in an \eqnarray. +\@lowpenalty 51 % Produced by \nopagebreak[1] or \nolinebreak[1] +\@medpenalty 151 % Produced by \nopagebreak[2] or \nolinebreak[2] +\@highpenalty 301 % Produced by \nopagebreak[3] or \nolinebreak[3] +\@beginparpenalty -\@lowpenalty % Before a list or paragraph environment. +\@endparpenalty -\@lowpenalty % After a list or paragraph environment. +\@itempenalty -\@lowpenalty % Between list items. +\def\part{\@startsection{part}{1}{\z@}{0.8\@bls \@plus + 0.4\@bls}{\@bls}{\normalsize}} +\def\partmark#1{} +\def\section{\@startsection{section}{1}{\z@}{0.5\@bls + \@plus .2\@bls \@minus .1\@bls}{0.5\@bls}{\normalsize\bfseries + \boldmath}} % WAS 1.8\@bls PMISRA 2007-05-30 +\def\subsection{\@startsection{subsection}{2}{\z@}{0.3\@bls + \@plus .2\@bls \@minus .1\@bls}{0.3\@bls}{\normalsize\itshape}} % WAS \@bls and .3\@bls PMISRA 2007-05-30 +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{0.3\@bls + \@plus .1\@bls}{0.0001pt}{\normalsize\itshape}} % WAS \@bls PMISRA 2007-05-30 +\def\paragraph{\@startsection{paragraph}{4}{\z@}{3.25ex \@plus + 2ex \@minus 0.2ex}{-1em}{\normalfont\normalsize\itshape}} +\def\subparagraph{\@startsection{subparagraph}{5}{1em}{3.25ex \@plus + 2ex \@minus 0.2ex}{-1em}{\normalfont\normalsize\itshape}} +\setcounter{secnumdepth}{4} +\def\half@em{\hskip 0.5em} +\def\lb@part{PART \thepart.\half@em} + \def\lb@empty@part{PART \thepart} +\def\lb@section{\thesection.\half@em} + \def\lb@empty@section{\thesection} +\def\lb@subsection{\thesubsection.\half@em} + \def\lb@empty@subsection{\thesubsection} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% The point of this change is to make tertiary section numbers go away. +%\def\lb@subsubsection{\thesubsubsection.\half@em} +% \def\lb@empty@subsubsection{\thesubsubsection} +\def\lb@subsubsection{} + \def\lb@empty@subsubsection{} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\def\lb@paragraph{\theparagraph.\half@em} + \def\lb@empty@paragraph{\theparagraph} +\def\lb@subparagraph{\thesubparagraph.\half@em} + \def\lb@empty@subparagraph{\thesubparagraph} +\def\head@format#1#2{#2} +\def\head@style{\interlinepenalty\@M + \hyphenpenalty\@M \exhyphenpenalty\@M + \rightskip \z@ \@plus 0.5\hsize \relax + } +\def\@sect#1#2#3#4#5#6[#7]#8{% + \ifnum #2>\c@secnumdepth + \let\@svsec\@empty + \else + \refstepcounter{#1}\def\@tempa{#8}% + \ifx\@tempa\@empty + \edef\@svsec{\csname lb@empty@#1\endcsname}% + \else + \edef\@svsec{\csname lb@#1\endcsname}\fi\fi + \@tempskipa #5\relax + \ifdim \@tempskipa>\z@ + \begingroup #6\relax +\noindent \hskip #3\relax{\@secnumfont{#2}\@svsec}% + {\head@style\head@format{#2}{#8}\par}% + \endgroup + \csname #1mark\endcsname{#7}% + \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi #7}% + \else + \def\@svsechd{#6\hskip #3\relax {\@secnumfont{#2}\@svsec }% + {\head@style\head@format{#2}{#8}}\csname #1mark\endcsname{#7}% + \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi #7}}% + \fi + \@xsect{#5}} +\def\@ssect#1#2#3#4#5#6{% + \@tempskipa #4\relax + \ifdim \@tempskipa>\z@ + \begingroup + #5{% + \@hangfrom{\hskip #2}% + \interlinepenalty \@M \head@format{#1}{#6}\@@par}% + \endgroup + \else + \def\@svsechd{#5{\hskip #2\relax \head@format{#1}{#6}}}% + \fi + \@xsect{#4}} +\def\@startsection#1#2#3#4#5#6{% + \if@noskipsec \leavevmode \fi + \par + \@tempskipa #4\relax + \@afterindenttrue + \ifdim \@tempskipa <\z@ + \@tempskipa -\@tempskipa \@afterindentfalse + \fi + \if@nobreak + \everypar{}% + \else + \addpenalty\@secpenalty\addvspace\@tempskipa + \fi + \@ifstar + {\@ssect{#2}{#3}{#4}{#5}{#6}}% + {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}} + +\def\app@number#1{\setcounter{#1}{0}% + \@addtoreset{#1}{section}% + \@namedef{the#1}{\thesection.\arabic{#1}}} +\def\appendix{\@ifstar{\appendix@star}{\appendix@nostar}} +\def\appendix@nostar{% + \def\lb@section{\appendixname\ \thesection.\half@em} + \def\lb@empty@section{\appendixname\ \thesection} + \setcounter{section}{0}\def\thesection{\Alph{section}}% + \setcounter{subsection}{0}% + \setcounter{subsubsection}{0}% + \setcounter{paragraph}{0}% + \app@number{equation}\app@number{figure}\app@number{table}} +\def\appendix@star{% + \def\lb@section{\appendixname}\let\lb@empty@section\lb@section + \setcounter{section}{0}\def\thesection{\Alph{section}}% + \setcounter{subsection}{0}% + \setcounter{subsubsection}{0}% + \setcounter{paragraph}{0}% + \app@number{equation}\app@number{figure}\app@number{table}} +\def\ack{\section*{Acknowledgements}% + \addtocontents{toc}{\protect\vspace{6pt}}% + \addcontentsline{toc}{section}{Acknowledgements}% +} +\@namedef{ack*}{\par\vskip 3.0ex \@plus 1.0ex \@minus 1.0ex} +\let\endack\par +\@namedef{endack*}{\par} +\newdimen\labelwidthi +\newdimen\labelwidthii +\newdimen\labelwidthiii +\newdimen\labelwidthiv +\def\normal@labelsep{0.5em} +\labelsep\normal@labelsep +\settowidth{\labelwidthi}{(iii)} +\settowidth{\labelwidthii}{(d)} +\settowidth{\labelwidthiii}{(iii)} +\settowidth{\labelwidthiv}{(M)} +\leftmargini\labelwidthi \advance\leftmargini\labelsep +\leftmarginii\labelwidthii \advance\leftmarginii\labelsep +\leftmarginiii\labelwidthiii \advance\leftmarginiii\labelsep +\leftmarginiv\labelwidthiv \advance\leftmarginiv\labelsep +\def\setleftmargin#1#2{\settowidth{\@tempdima}{#2}\labelsep\normal@labelsep + \csname labelwidth#1\endcsname\@tempdima + \@tempdimb\@tempdima \advance\@tempdimb\labelsep + \csname leftmargin#1\endcsname\@tempdimb} +\def\@listI{\leftmargin\leftmargini + \labelwidth\labelwidthi \labelsep\normal@labelsep + \topsep \z@ \partopsep\z@ \parsep\z@ \itemsep\z@ + \listparindent 1em} +\def\@listii{\leftmargin\leftmarginii + \labelwidth\labelwidthii \labelsep\normal@labelsep + \topsep\z@ \partopsep\z@ \parsep\z@ \itemsep\z@ + \listparindent 1em} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\labelwidthiii \labelsep\normal@labelsep + \topsep\z@ \partopsep\z@ \parsep\z@ \itemsep\z@ + \listparindent 1em} +\def\@listiv{\leftmargin\leftmarginiv + \labelwidth\labelwidthiv \labelsep\normal@labelsep + \topsep\z@ \partopsep\z@ \parsep\z@ \itemsep\z@ + \listparindent 1em} +\let\@listi\@listI +\@listi +\def\left@label#1{{#1}\hss} +\def\right@label#1{\hss\llap{#1}} +\def\thick@label#1{\hspace\labelsep #1} +\newcount\@maxlistdepth +\@maxlistdepth=4 +\def\labelitemi{$\bullet$} \def\labelitemii{$\cdot$} +\def\labelenumi{(\theenumi)} \def\theenumi{\arabic{enumi}} +\def\labelenumii{(\alph{enumii})} \def\theenumii{\theenumi\alph{enumii}} +\def\labelenumiii{(\roman{enumiii})}\def\theenumiii{\theenumii.\roman{enumiii}} +\def\labelenumiv{(\Alph{enumiv})} \def\theenumiv{\theenumiii.\Alph{enumiv}} +\def\enumerate{% + \ifnum \@enumdepth >\@maxlistdepth + \@toodeep + \else + \advance\@enumdepth \@ne + \edef\@enumctr{enum\romannumeral\the\@enumdepth}% + \list{\csname label\@enumctr\endcsname}% + {\usecounter{\@enumctr} + \let\makelabel=\right@label} + \fi} +\def\itemize{% + \ifnum \@itemdepth >\@maxlistdepth + \@toodeep + \else + \advance\@itemdepth \@ne + \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}% + \list{\csname\@itemitem\endcsname}% + {\let\makelabel\right@label} + \fi} +\def\verse{\let\\=\@centercr + \list{}{\itemsep\z@ + \itemindent \z@ + \listparindent\z@ + \rightmargin 1em + \leftmargin \rightmargin}\item[]} +\let\endverse\endlist +\def\quotation{\list{}{\itemindent\z@ + \leftmargin 4em \rightmargin 1em + \parsep \z@ \@plus 1pt}\item[]} +\let\endquotation=\endlist +\def\quote{\list{}{\itemindent\z@ + \@topsep \eqntopsep + \leftmargin 4em \rightmargin 1em}% +\item[]} +\let\endquote=\endlist +\def\descriptionlabel#1{\hspace\labelsep \bfseries #1} +\def\description{\list{}{\labelwidth\z@ + \leftmargin 1em \itemindent-\leftmargin + \let\makelabel\descriptionlabel}} +\let\enddescription\endlist +\def\@atfmtname{atlplain} +\ifx\fmtname\@atfmtname + \def\neq{\not\nobreak\mkern -2mu =}% + \let\ne\neq +\fi +\def\operatorname#1{\mathop{\mathrm{#1}}\nolimits} +\def\lefteqn#1{\hbox to\z@{$\displaystyle {#1}$\hss}} +\def\newdelim{\delimiterfactor=750 \delimitershortfall=7pt} +\def\olddelim{\delimiterfactor=901 \delimitershortfall=0pt} +\newskip\eqnbaselineskip % Standard interline spacing in an {eqnarray} +\jot=2\p@ +\newskip\eqnlineskip % Minimal space between the bottom of + % a line and the top of the next line. +\eqnbaselineskip=14\p@ \eqnlineskip=2\p@ +\newdimen\mathindent +\if@TwoColumn + \mathindent 0em +\else + \mathindent 2em +\fi +\def\[{\relax\ifmmode\@badmath + \else%\bgroup removed on request from BW (1993-05-17) + \@beginparpenalty\predisplaypenalty + \@endparpenalty\postdisplaypenalty + \begin{trivlist}\@topsep \eqntopsep % used by first \item + \@topsepadd \eqntopsep % used by \@endparenv + \item[]\leavevmode + \hbox to\linewidth\bgroup\hfil $ \displaystyle + \hskip\mathindent\bgroup\fi} +\def\]{\relax\ifmmode \egroup $\hfil \egroup + \end{trivlist}% \egroup removed on request from BW (1993-05-17) + \else \@badmath \fi} +\def\equation{\@beginparpenalty\predisplaypenalty + \@endparpenalty\postdisplaypenalty +\refstepcounter{equation}\trivlist + \@topsep \eqntopsep % used by first \item + \@topsepadd \eqntopsep % used by \@endparenv + \item[]\leavevmode + \hbox to\linewidth\bgroup \hfil $ \displaystyle \hskip\mathindent\bgroup} +\def\endequation{\egroup$\hfil \displaywidth\linewidth + \@eqnnum\egroup \endtrivlist} +\def\eqnarray{% + \par %BW + \noindent %BW + \baselineskip\eqnbaselineskip\lineskip\eqnlineskip %BW + \lineskiplimit\eqnlineskip %BW + \stepcounter{equation}% + \let\@currentlabel=\theequation + \global\@eqnswtrue + \global\@eqcnt\z@ + \tabskip\@centering + \let\\=\@eqncr + \abovedisplayskip\eqntopsep\ifvmode\advance\abovedisplayskip\partopsep\fi + \belowdisplayskip\abovedisplayskip + \belowdisplayshortskip\abovedisplayskip + \abovedisplayshortskip\abovedisplayskip + $$\halign to \displaywidth\bgroup\@eqnsel + \pre@coli$\displaystyle\tabskip\z@{##}$\post@coli + &\global\@eqcnt\@ne + \pre@colii$\displaystyle{##}$\post@colii + &\global\@eqcnt\tw@ + \pre@coliii $\displaystyle\tabskip\z@{##}$\post@coliii + \tabskip\@centering&\llap{##}\tabskip\z@\cr +} +\def\endeqnarray{\@@eqncr\egroup + \global\advance\c@equation\m@ne$$\global\@ignoretrue } +\def\pre@coli{\hskip\@centering} \def\post@coli{} +\def\pre@colii{\hskip 2\eqnarraycolsep \hfil} \def\post@colii{\hfil} +\def\pre@coliii{\hskip 2\eqnarraycolsep} \def\post@coliii{\hfil} +\arraycolsep 2\p@ % Half the space between columns in array environment. + \tabcolsep 6\p@ % idem in tabular environment. +\arrayrulewidth 0.4\p@ % \@Width of rules and space between adjacent +\doublerulesep 2\p@ % rules in any of these two environments. +\def\@arrayclassz{\ifcase \@lastchclass \@acolampacol \or \@ampacol \or + \or \or \@addamp \or \@acolampacol \or \@firstampfalse \@acol \fi + \edef\@preamble{\@preamble + \ifcase \@chnum + \hfil$\relax\displaystyle\@sharp$\hfil \or + $\relax\displaystyle\@sharp$\hfil \or + \hfil$\relax\displaystyle\@sharp$\fi}} +\newdimen\rulepreskip \newdimen\rulepostskip +\rulepreskip=4\p@ \rulepostskip=6\p@ +\newdimen\Arrayrulewidth \Arrayrulewidth=1.0\p@ +\def\Hline{\noalign{\ifnum0=`}\fi\hrule \@height \Arrayrulewidth \futurelet + \@tempa\@xhline} +\newdimen\crulepostskip \crulepostskip -7\p@ +\def\ccline#1{% + \noalign{\vskip\rulepreskip}% + \do@ccline(#1,1-0)\cr + \noalign{\vskip\crulepostskip}} +\def\do@ccline(#1-#2,#3){% + \ifnum#1>#2\else\@cline[#1-#2]\do@ccline(#3,1-0)\fi + \ignorespaces} +\newdimen\@Ldec \newdimen\@Rdec +\def\dec #1.#2 {\hbox to\@Ldec{\hss#1}\def\@tempb{#2}% +\ifx\@tempb\empty\hbox to\@Rdec{\hfill}\else\hbox to\@Rdec{.#2\hss}\fi} +\def\setdec #1.#2 {\relax + \bgroup + \setbox0\hbox{\kern1pt\relax#1}\setbox1\hbox{\kern1pt\relax#2}% + \global\@Ldec\wd0\global\@Rdec\wd1 + \egroup} +\setdec 000.000 % default 3 digits on each side +\newdimen\@Lpmdec \newdimen\@Rpmdec +\def\pmdec #1.#2 {\hbox to\@Lpmdec{\hss#1}\def\@tempb{#2}% +\ifx\@tempb\empty\hbox to\@Rpmdec{\hfill}\else\hbox to\@Rpmdec{.#2\hss}\fi} +\def\setpmdec #1.#2 {\relax + \bgroup + \setbox0\hbox{\kern1pt\relax#1}\setbox1\hbox{\kern1pt\relax#2}% + \global\@Lpmdec\wd0\global\@Rpmdec\wd1 + \egroup} +\setpmdec 0.0 % default 1 digit on each side +\tabbingsep \labelsep % Space used by the \' command. (See LaTeX{} manual.) +\skip\@mpfootins = 6\p@ \@plus 2\p@ % Space between last line of text and + % top of first footnote. +\fboxsep = 7\p@ % Space left between box and text by \fbox and \framebox. +\fboxrule = 0.4\p@ % \@Width of rules in box made by \fbox and \framebox. +\newcounter{section} +\newcounter{subsection}[section] +\newcounter{subsubsection}[subsection] +\newcounter{paragraph}[subsubsection] +\newcounter{subparagraph}[paragraph] +\if@seceqn + \@addtoreset{equation}{section} + \def\theequation{\arabic{section}.\arabic{equation}} +\else + \def\theequation{\arabic{equation}} +\fi +\def\thesection {\arabic{section}} +\def\thesubsection {\thesection.\arabic{subsection}} +\def\thesubsubsection{\thesubsection.\arabic{subsubsection}} +\def\theparagraph {\thesubsubsection.\arabic{paragraph}} +\def\thesubparagraph {\theparagraph.\arabic{subparagraph}} +\@addtoreset{section}{part} % reset section numbers at beginning of part + + \RequirePackage{theorem} + \RequirePackage{newlfont} +\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} +\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} +\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} +\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} +\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} +\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl} +\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc} +\def\qed{\relax\ifmmode\hskip2em \Box\else\unskip\nobreak\hskip1em $\Box$\fi} +\def\proof@headerfont{\upshape\bfseries} + \gdef\th@plain{\itshape + \def\@begintheorem##1##2{\item[\hskip\labelsep + {\theorem@headerfont ##1\ ##2.}]}% + \def\@opargbegintheorem##1##2##3{\item[\hskip\labelsep + {\theorem@headerfont ##1\ ##2}\ {\upshape (##3).}]}} +\gdef\th@definition{\upshape + \def\@begintheorem##1##2{\item[\hskip\labelsep + {\theorem@headerfont ##1\ ##2.}]}% + \def\@opargbegintheorem##1##2##3{\item[\hskip\labelsep + {\theorem@headerfont ##1\ ##2}\ {\upshape(}{\it ##3\/}{\upshape).}]}} +\gdef\theorem@headerfont{\itshape} +\gdef\th@plain{\upshape + \def\@begintheorem##1##2{\item[\hskip\labelsep + {\theorem@headerfont ##1\ ##2.}]}% + \def\@opargbegintheorem##1##2##3{\item[\hskip\labelsep + {\theorem@headerfont ##1\ ##2.}\ {\upshape (##3).}]}} +\gdef\th@definition{\upshape + \def\@begintheorem##1##2{\item[\hskip\labelsep + {\theorem@headerfont ##1\ ##2.}]}% + \def\@opargbegintheorem##1##2##3{\item[\hskip\labelsep + {\theorem@headerfont ##1\ ##2.}\ {\upshape (##3).}]}} + +\def\rom#1{\leavevmode\skip@\lastskip\unskip\/% + \ifdim\skip@=\z@\else\hskip\skip@\fi + {\upshape#1}} +\theorempreskipamount=3\p@ \@minus 1\p@ % WAS 12 PMISRA 2007-05-30 +\theorempostskipamount=\theorempreskipamount +\newenvironment{pf}% + {\par\addvspace{\theorempreskipamount}\noindent + {\proof@headerfont\Elproofname}\enspace\ignorespaces}% + {\par\addvspace{\theorempreskipamount}} +\def\Elproofname{Proof.} +\@namedef{pf*}#1{\par\begingroup\def\Elproofname{#1}\pf\endgroup\ignorespaces} +\expandafter\let\csname endpf*\endcsname=\endpf + \theoremstyle{plain} +\if@secthm + \newtheorem{thm}{Theorem}[section] + \@addtoreset{thm}{section} +\else + \newtheorem{thm}{Theorem} +\fi +\newtheorem{cor}[thm]{Corollary} +\newtheorem{lem}[thm]{Lemma} +\newtheorem{claim}[thm]{Claim} +\newtheorem{axiom}[thm]{Axiom} +\newtheorem{conj}[thm]{Conjecture} +\newtheorem{fact}[thm]{Fact} +\newtheorem{hypo}[thm]{Hypothesis} +\newtheorem{assum}[thm]{Assumption} +\newtheorem{prop}[thm]{Proposition} +\newtheorem{crit}[thm]{Criterion} + \theoremstyle{definition} +\newtheorem{defn}[thm]{Definition} +\newtheorem{exmp}[thm]{Example} +\newtheorem{rem}[thm]{Remark} +\newtheorem{prob}[thm]{Problem} +\newtheorem{prin}[thm]{Principle} +\newtheorem{alg}{Algorithm} +\long\def\@makealgocaption#1#2{\vskip 2ex \small + \hbox to \hsize{\parbox[t]{\hsize}{{\bfseries #1.} #2}}} +\newcounter{algorithm} +\def\thealgorithm{\@arabic\c@algorithm} +\def\fps@algorithm{tbp} +\def\ftype@algorithm{4} +\def\ext@algorithm{lof} +\def\fnum@algorithm{Algorithm \thealgorithm} +\def\algorithm{\let\@makecaption\@makealgocaption\@float{algorithm}} +\let\endalgorithm\end@float +\newtheorem{note}{Note} +\newtheorem{summ}{Summary} +\newtheorem{case}{Case} +\def\@pnumwidth{2.55em} +\def\@tocrmarg{2.55em \@plus 5em} +\def\@dotsep{-2.5} +\setcounter{tocdepth}{2} +\newcommand\listoffigures{% + \section*{\listfigurename + \@mkboth{\MakeUppercase\listfigurename}% + {\MakeUppercase\listfigurename}}% + \@starttoc{lof}% + } +\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}} +\newcommand\listoftables{% + \section*{\listtablename + \@mkboth{% + \MakeUppercase\listtablename}{\MakeUppercase\listtablename}}% + \@starttoc{lot}% + } +\let\l@table\l@figure +\def\tableofcontents{% + \begin{small} + \leftline {{\bfseries \contentsname\/}} + \setcounter{secnumdepth}{4}% + \setcounter{tocdepth}{2}% + {\@starttoc{toc}}% +\end{small} +} +\newcommand*\l@section{\@dottedtocline{1}{1.5em}{2.3em}} +\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}} +\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}} +\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}} +\newcommand*\l@subparagraph{\@dottedtocline{5}{10em}{5em}} +\def\@dotsep{2000} +\def\thebibliography{% +\section*{\refname} + \@thebibliography} +\let\endthebibliography=\endlist +\def\@thebibliography#1{\@bibliosize + \list{\@biblabel{\arabic{enumiv}}}{\settowidth\labelwidth{\@biblabel{#1}} + \if@nameyear + \labelwidth\z@ \labelsep\z@ \leftmargin\parindent + \itemindent-\parindent + \else + \labelsep 3\p@ \itemindent\z@ + \leftmargin\labelwidth \advance\leftmargin\labelsep +\fi + \itemsep \z@ \@plus 0.5\p@ \@minus 0.5\p@ + \usecounter{enumiv}\let\p@enumiv\@empty + \def\theenumiv{\arabic{enumiv}}}% + \tolerance\@M + \hyphenpenalty=50 + \hbadness5000 \sfcode`\.=1000\relax} +\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em} +\@namedef{thebibliography*}{\section*{}\@thebibliography} +\@namedef{endthebibliography*}{\endlist} +\if@nameyear + \def\@biblabel#1{} +\else + \def\@biblabel#1{[#1]\hskip \z@ \@plus 1filll} +\fi +\newcount\@tempcntc +\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi + \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do + {\@ifundefined + {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries ?}\@warning + {Citation `\@citeb' on page \thepage \space undefined}}% + {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}% + \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne + \@citea\def\@citea{,}\hbox{\csname b@\@citeb\endcsname}% + \else + \advance\@tempcntb\@ne + \ifnum\@tempcntb=\@tempcntc + \else\advance\@tempcntb\m@ne\@citeo + \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}} +\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else\@citea\def\@citea{,}% + \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else + {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else \def\@citea{--}\fi + \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi} +\@namedef{cv*}{\section*{Curriculum Vitae}\cv} + \def\cv{\hangindent=7pc \hangafter=-12 \parskip\bigskipamount \small} +\def\footnote{\@ifnextchar[{\@xfootnote}{\refstepcounter + {\@mpfn}\protected@xdef\@thefnmark{\thempfn}\@footnotemark\@footnotetext}} +\def\footnotemark{\@ifnextchar[{\@xfootnotemark + }{\refstepcounter{footnote}\xdef\@thefnmark{\thefootnote}\@footnotemark}} +\def\footnoterule{\kern-3\p@ + \hrule \@width 3pc % The \hrule has default \@height of 0.4pt. + \kern 2.6\p@} +\def\thempfootnote{\fnsymbol{mpfootnote}} +\def\mpfootnotemark{% + \@ifnextchar[{\@xmpfootnotemark}{\stepcounter{mpfootnote}% + \begingroup + \let\protect\noexpand + \xdef\@thefnmark{\thempfootnote}% + \endgroup + \@footnotemark}} +\def\@xmpfootnotemark[#1]{% + \begingroup + \c@mpfootnote #1\relax + \let\protect\noexpand + \xdef\@thefnmark{\thempfootnote}% + \endgroup + \@footnotemark} +\def\@mpmakefnmark{\,\hbox{$^{\mathrm{\@thefnmark}}$}} +\long\def\@mpmakefntext#1{\noindent + \hbox{$^{\mathrm{\@thefnmark}}$} #1} +\def\@iiiminipage#1#2[#3]#4{% + \leavevmode + \@pboxswfalse + \setlength\@tempdima{#4}% + \def\@mpargs{{#1}{#2}[#3]{#4}}% + \setbox\@tempboxa\vbox\bgroup + \color@begingroup + \hsize\@tempdima + \textwidth\hsize \columnwidth\hsize + \@parboxrestore + \def\@mpfn{mpfootnote}\def\thempfn{\thempfootnote}\c@mpfootnote\z@ + \let\@footnotetext\@mpfootnotetext + \let\@makefntext\@mpmakefntext + \let\@makefnmark\@mpmakefnmark + \let\@listdepth\@mplistdepth \@mplistdepth\z@ + \@minipagerestore\global\@minipagetrue %% \global added 24 May 89 + \everypar{\global\@minipagefalse\everypar{}}} +\def\fn@presym{} +\long\def\@makefntext#1{\noindent\hbox to 1em + {$^{\fn@presym\mathrm{\@thefnmark}}$\hss}#1} +\def\@makefnmark{\,\hbox{$^{\fn@presym\mathrm{\@thefnmark}}$}\,} +\def\patched@end@dblfloat{% + \if@twocolumn + \par\vskip\z@skip %% \par\vskip\z@ added 15 Dec 87 + \global\@minipagefalse + \outer@nobreak + \egroup %% end of vbox + \color@endbox + \ifnum\@floatpenalty <\z@ + \@largefloatcheck + \@cons\@dbldeferlist\@currbox + \fi + \ifnum \@floatpenalty =-\@Mii \@Esphack\fi + \else + \end@float + \fi +} +\setcounter{topnumber}{5} +\def\topfraction{0.99} +\def\textfraction{0.05} +\def\floatpagefraction{0.9} +\setcounter{bottomnumber}{5} +\def\bottomfraction{0.99} +\setcounter{totalnumber}{10} +\def\dbltopfraction{0.99} +\def\dblfloatpagefraction{0.8} +\setcounter{dbltopnumber}{5} +\long\def\@maketablecaption#1#2{\@tablecaptionsize + \global \@minipagefalse + \hbox to \hsize{\parbox[t]{\hsize}{#1 \\ #2}}} +\long\def\@makefigurecaption#1#2{\@figurecaptionsize + \vskip \@overcaptionskip + \setbox\@tempboxa\hbox{#1. #2} + \ifdim \wd\@tempboxa >\hsize % IF longer than one line THEN + \unhbox\@tempboxa\par % set as justified paragraph + \else % ELSE + \global \@minipagefalse + \hbox to\hsize{\hfil\box\@tempboxa\hfil}% center single line. + \fi} +\def\@makecaption{\@makefigurecaption} +\def\conttablecaption{\par \begingroup \@parboxrestore \normalsize + \@makecaption{\fnum@table\,---\,continued}{}\par + \vskip-1pc \endgroup} +\def\contfigurecaption{\vskip-1pc \par \begingroup \@parboxrestore + \@captionsize + \@makecaption{\fnum@figure\,---\,continued}{}\par + \endgroup} +\newcounter{figure} +\def\thefigure{\@arabic\c@figure} +\def\fps@figure{tbp} +\def\ftype@figure{1} +\def\ext@figure{lof} +\def\fnum@figure{\figurename~\thefigure} +\def\figure{% + \let\@makecaption\@makefigurecaption + \let\contcaption\contfigurecaption \@float{figure}} +\let\endfigure\end@float +\@namedef{figure*}{% + \let\@makecaption\@makefigurecaption + \let\contcaption\contfigurecaption \@dblfloat{figure}} +\@namedef{endfigure*}{\end@dblfloat} +\newcounter{table} +\def\thetable{\@arabic\c@table} +\def\fps@table{tbp} +\def\ftype@table{2} +\def\ext@table{lot} +\def\fnum@table{\tablename~\thetable} +\let\old@floatboxreset\@floatboxreset +\def\table{% +\let\@makecaption\@maketablecaption +\def\@floatboxreset{% + \old@floatboxreset + \@tablesize +}% + \let\footnoterule\relax + \let\contcaption\conttablecaption \@float{table}} +\let\endtable\end@float +\@namedef{table*}{% +\let\@makecaption\@maketablecaption +\def\@floatboxreset{% + \old@floatboxreset + \@tablesize +}% + \let\footnoterule\relax + \let\contcaption\conttablecaption \@dblfloat{table}} +\@namedef{endtable*}{\end@dblfloat} +\newtoks\t@glob@notes % List of all notes +\newtoks\t@loc@notes % List of notes for one element +\newcount\note@cnt % Number of notes per element +\newcounter{author} % Author counter +\newcount\n@author % Total number of authors +\def\n@author@{1} % idem, read from .aux file +\newcounter{collab} % Collaboration counter +\newcount\n@collab % Total number of collaborations +\def\n@collab@{} % idem, read from .aux file +\newcounter{address} % Address counter +\def\theHaddress{\arabic{address}}% for hyperref +\newdimen\sv@mathsurround % Dimen register to save \mathsurround +\newcount\sv@hyphenpenalty % Count register to save \hyphenpenalty +\newcount\prev@elem \prev@elem=0 % Variables to keep track of +\newcount\cur@elem \cur@elem=0 % types of elements that are processed +\chardef\e@title=1 +\chardef\e@subtitle=1 +\chardef\e@author=2 +\chardef\e@collab=3 +\chardef\e@address=4 +\newif\if@newelem % Switch to new type of element? +\newif\if@firstauthor % First author or collaboration? +\newif\if@preface % If preface: omit history and abstract +\newif\if@hasabstract % If abstract / keywords: do not omit rules +\newif\if@haskeywords % If abstract / keywords: do not omit rules +\newbox\fm@box % Box for collected front matter +\newdimen\fm@size % Total height of \fm@box +\newbox\t@abstract % Box for abstract +\newbox\t@keyword % Box for keyword abstract +\newcount\rep@mod \rep@mod=10 +\def\report@elt#1{% +} +\def\add@tok#1#2{\global#1\expandafter{\the#1#2}} +\def\add@xtok#1#2{\begingroup + \no@harm + \xdef\@act{\global\noexpand#1{\the#1#2}}\@act +\endgroup} +\def\beg@elem{\global\t@loc@notes={}\global\note@cnt\z@} +\def\@xnamedef#1{\expandafter\xdef\csname #1\endcsname} +\def\no@harm{% + \let\\=\relax \let\rm\relax + \let\ss=\relax \let\ae=\relax \let\oe=\relax + \let\AE=\relax \let\OE=\relax + \let\o=\relax \let\O=\relax + \let\i=\relax \let\j=\relax + \let\aa=\relax \let\AA=\relax + \let\l=\relax \let\L=\relax + \let\d=\relax \let\b=\relax \let\c=\relax + \let\bar=\relax + \def\protect{\noexpand\protect\noexpand}} +\def\proc@elem#1#2{\begingroup + \no@harm % make a few instructions harmless + \let\thanksref\@gobble % remove \thanksref from element + \@xnamedef{@#1}{#2}% % and store as \@#1 + \endgroup + \prev@elem=\cur@elem % keep track of type of previous + \cur@elem=\csname e@#1\endcsname % and current element + \expandafter\elem@nothanksref#2\thanksref\relax} +\def\elem@nothanksref#1\thanksref{\futurelet\@peektok\elem@thanksref} +\def\elem@thanksref{\ifx\@peektok\relax % No more \thanksref, so now exit + \else \expandafter\elem@morethanksref \fi} +\def\elem@morethanksref#1{\add@thanksref{#1}\elem@nothanksref} +\def\add@thanksref#1{% + \global\advance\note@cnt\@ne + \def\@tempa{*}\def\@tempb{#1}% + \ifx\@tempa\@tempb + \ifnum\note@cnt>\@ne \add@xtok\t@loc@notes{\note@sep}\fi + \add@tok\t@loc@notes{*}% + \else + \ifnum\note@cnt>\@ne \add@xtok\t@loc@notes{\note@sep}\fi + \add@tok\t@loc@notes{% + \if@Elproofing#1\else\ref{#1}\fi + }% + \fi} +\def\note@sep{,} +\def\thanks{\@ifnextchar[{\@tempswatrue + \thanks@optarg}{\@tempswafalse\thanks@optarg[]}} +\def\thanks@optarg[#1]#2{% + \def\@tempa{*}\def\@tempb{#1}% + \ifx\@tempa\@tempb + \@tempcnta=\c@footnote \c@footnote=-1 \label{#1}\c@footnote=\@tempcnta + \gdef\@corresp@note{\footnotetext[-1]{#2}}% + \else + \add@tok\t@glob@notes{\footnotetext}% + \refstepcounter{footnote}% + \if@Elproofing\else\if@tempswa\label{#1}\else\relax\fi\fi + \add@xtok\t@glob@notes{[\the\c@footnote]}% + \add@tok\t@glob@notes{{#2}}% + \fi} +\let\real@refstepcounter\refstepcounter +\def\footnote{\@ifnextchar[{\@xfootnote}{\real@refstepcounter + {\@mpfn}\protected@xdef\@thefnmark{\thempfn}\@footnotemark\@footnotetext}} +\def\footnotemark{\@ifnextchar[{\@xfootnotemark + }{\real@refstepcounter{footnote}\xdef\@thefnmark{\thefootnote}\@footnotemark}} +\def\footnoterule{\kern-3\p@ + \hrule \@width 3pc % The \hrule has default \@height of 0.4pt. + \kern 2.6\p@} +\newenvironment{NoHyper}{}{} +\def\frontmatter{% + \NoHyper + \let\@corresp@note\relax + \global\t@glob@notes={}\global\c@author\z@ + \global\c@collab\z@ \global\c@address\z@ + \sv@mathsurround\mathsurround \m@th + \global\n@author=0\n@author@\relax + \global\n@collab=0\n@collab@\relax + \global\advance\n@author\m@ne % In comparisons later on we need + \global\advance\n@collab\m@ne % n@author-1 and n@collab-1 + \global\@firstauthortrue % set to false by first \author or \collab + \global\@hasabstractfalse % Default: no abstract or keywords + \global\@haskeywordsfalse % Default: no abstract or keywords + \global\@prefacefalse % not preface + \ifnum\c@firstpage=\c@lastpage + \gdef\@pagerange{\@pagenumprefix\ESpagenumber{firstpage}} + \else + \gdef\@pagerange{\@pagenumprefix + \ESpagenumber{firstpage}--\@pagenumprefix\ESpagenumber{lastpage}}% + \fi + \@ifundefined{RIfM@}{\global\let\vec\@bfvec}{\undo@AMS}% + \open@fm \ignorespaces} +\def\preface{\@prefacetrue} +\def\endfrontmatter{% + \ifx\@runauthor\relax + \global\let\@runauthor\@runningauthor + \fi + \global\n@author=\c@author + \global\n@collab=\c@collab \@writecount + \global\@topnum\z@ + \thispagestyle{copyright}% % Format rest of front matter: + \if@preface \else % IF not preface THEN + \vskip \@overhistoryskip + \history@fmt % print history (received, ...) + \newcount\c@sv@footnote + \global\c@sv@footnote=\c@footnote % save current footnote number +\if@TwoColumn\else + \output@glob@notes % Put notes at bottom of 1st page +\fi + + + \if@hasabstract % IF abstract/ keywords THEN + \vskip \@preabstractskip % Space above rule + \nointerlineskip + \moveright 0.1\textwidth \vbox{\hrule width 0.8\textwidth height 0.4\p@} % Rule above abstract/keywords + \nointerlineskip + \vskip 8\p@ + \unvbox\t@abstract % print abstract, if any + \fi + \if@haskeywords % IF keywords THEN + \vskip \@overkeywordskip + \unvbox\t@keyword % Keyword abstract, if any + \fi % FI + \vskip \@preabstractskip % Space above rule + \nointerlineskip + \moveright 0.1\textwidth \vbox{\hrule width 0.8\textwidth height 0.4\p@} % Rule above abstract/keywords + \nointerlineskip + \dedicated@fmt % print dedication + \vskip \@belowfmskip % Vertical space below frontmatter +\fi % FI + \close@fm % Close front matter material. + \if@TwoColumn + \output@glob@notes % Put notes at bottom of 1st page + \fi + \global\c@footnote=\c@sv@footnote % restore footnote number + \global\@prefacefalse + \global\leftskip\z@ % Restore the normal values of + \global\@rightskip\z@ % \leftskip, + \global\rightskip\@rightskip % \rightskip and + \global\mathsurround\sv@mathsurround % \mathsurround. + \let\title\relax \let\author\relax + \let\collab\relax \let\address\relax + \let\frontmatter\relax \let\endfrontmatter\relax + \let\@maketitle\relax \let\@@maketitle\relax + \normal@text +} +\let\maketitle\relax +\newdimen\t@xtheight +\t@xtheight\textheight \advance\t@xtheight-\splittopskip +\def\open@fm{\global\setbox\fm@box=\vbox\bgroup + \hsize=\@frontmatterwidth % Front matter is page-wide by default + \centering % and centered + \sv@hyphenpenalty\hyphenpenalty % (save \hyphenpenalty) + \hyphenpenalty\@M} % and not hyphenated +\def\close@fm{\egroup % close \vbox (\fm@box) + \fm@size=\dp\fm@box \advance\fm@size by \ht\fm@box + \@whiledim\fm@size>\t@xtheight \do{% + \global\setbox\@tempboxa=\vsplit\fm@box to \t@xtheight + \unvbox\@tempboxa \newpage + \fm@size=\dp\fm@box \advance\fm@size by \ht\fm@box} + \if@TwoColumn + \emergencystretch=1pc \twocolumn[\unvbox\fm@box] + \else + \unvbox\fm@box + \fi} +\def\output@glob@notes{\bgroup + \the\t@glob@notes + \egroup} +\def\justify@off{\let\\=\@normalcr + \leftskip\z@ \@rightskip\@flushglue \rightskip\@rightskip} +\def\justify@on{\let\\=\@normalcr + \leftskip\z@ \@rightskip\z@ \rightskip\@rightskip} +\def\normal@text{\global\let\\=\@normalcr + \global\leftskip\z@ \global\@rightskip\z@ \global\rightskip\@rightskip + \global\parfillskip\@flushglue} +\def\@writecount{\write\@mainaux{\string\global + \string\@namedef{n@author@}{\the\n@author}}% + \write\@mainaux{\string\global\string + \@namedef{n@collab@}{\the\n@collab}}} +\def\title#1{% + \beg@elem + \title@note@fmt % formatting instruction + \add@tok\t@glob@notes % for \thanks commands + {\title@note@fmt}% + \proc@elem{title}{#1}% + \def\title@notes{\the\t@loc@notes}% % store the notes of the title, + \title@fmt{\@title}{\title@notes}% % print the title + \ignorespaces} +\def\subtitle#1{% + \beg@elem + \proc@elem{subtitle}{#1}% + \def\title@notes{\the\t@loc@notes}% % store the notes of the title, + \subtitle@fmt{\@subtitle}{\title@notes}% print the title + \ignorespaces} +\newdimen \@logoheight \@logoheight 5pc +\def\@Lhook{\vrule \@height \@logoheight \@width \z@ \vrule \@height 10\p@ \@width 0.2\p@ \vrule \@height 0.2\p@ \@width 10pt} +\def\@Rhook{\vrule \@height 0.2\p@ \@width 10\p@ \vrule \@height 10\p@ \@width 0.2\p@ \vrule \@height \@logoheight \@width \z@} +\def\title@fmt#1#2{% +\@ifundefined{@runtitle}{\global\def\@runtitle{#1}}{}% + %\vspace*{\@overtitleskip} % Vertical space above article type, + \@articletypesize % Size for article type + \leavevmode\vphantom{Aye!} + \@articletype + \vskip12\p@ + {\@titlesize #1\,\hbox{$^{#2}$}\par}% + \vskip\@undertitleskip + } +\def\subtitle@fmt#1#2{% % No vertical space above sub-title + {\@titlesize #1\,\hbox{$^{#2}$}}\par} +\def\title@note@fmt{\def\thefootnote{\fnstar{footnote}}} +\def\author{\@ifnextchar[{\author@optarg}{\author@optarg[]}} +\def\author@optarg[#1]#2{\stepcounter{author}% + \beg@elem + \@for\@tempa:=#1\do{\expandafter\add@thanksref\expandafter{\@tempa}}% + \report@elt{author}\proc@elem{author}{#2}% + \ifnum0\n@collab@=\z@ \runningauthor@fmt \fi + \author@fmt{\the\c@author}{\the\t@loc@notes}{\@author}% +} +\def\runningauthor@fmt{% + \begingroup\no@harm + \if@firstauthor + \ifnum0\n@author@ > 2 + \global\edef\@runningauthor{\@author\ et al.}% + \else + \global\let\@runningauthor\@author% + \fi + \else % \c@author > 1 + \ifnum0\n@author@ = 2 + \global\edef\@runningauthor{\@runningauthor\ \& \noexpand\@author}% + \fi + \fi + \endgroup +} +\def\author@fmt#1#2#3{\@newelemtrue + \if@firstauthor + \first@author \global\@firstauthorfalse \fi + \ifnum\prev@elem=\e@author \global\@newelemfalse \fi + \if@newelem \author@fmt@init \fi + \edef\@tempb{#2}\ifx\@tempb\@empty + \hbox{{\author@font #3}}\else + \hbox{{\author@font #3}\,$^{\mathrm{#2}}$}% + \fi} +\def\first@author{\author@note@fmt % re-define \thefootnote as + % appropriate for author/address + \add@tok\t@glob@notes + {\author@note@fmt\@corresp@note}}% +\def\author@fmt@init{% + \par + \vskip 8\p@ \@plus 4\p@ \@minus 2\p@ + \@authorsize + \leavevmode} % Vertical space above author list + \let\and\relax \let\And\and +\def\collab{\@ifstar{\collab@arg}{\collab@arg}} +\let\collaboration=\collab +\def\collab@arg#1{\stepcounter{collab}% + \if@firstauthor \first@collab \global\@firstauthorfalse \fi + \gdef\@runningauthor{#1}% + \beg@elem + \proc@elem{collab}{#1}% + \collab@fmt{\the\c@collab}{\the\t@loc@notes}{\@collab}% + \ignorespaces} +\def\collab@fmt#1#2#3{\@newelemtrue + \ifnum\prev@elem=\e@collab \global\@newelemfalse \fi + \if@newelem \collab@fmt@init \fi + \par % Start new paragraph + {\large #3\,$^{\mathrm{#2}}$}} +\def\first@collab{ + \collab@note@fmt % re-define \thefootnote as + \add@tok\t@glob@notes % appropriate for collab/address + {\collab@note@fmt}}% +\def\collab@fmt@init{\vskip 1em} % Vertical space above list +\def\author@note@fmt{\setcounter{footnote}{0}% + \def\thefootnote{\xarabic{footnote}}} +\let\collab@note@fmt=\author@note@fmt +\def\xarabic#1{% + \expandafter\expandafter\expandafter\ifnum\expandafter\the\@nameuse{c@#1}<0 + *\else\arabic{#1} \fi} +\def\xalph#1{% + \expandafter\expandafter\expandafter\ifnum\expandafter\the\@nameuse{c@#1}<0 + *\else\alph{#1} \fi} +\def\xfnsymbol#1{% + \expandafter\expandafter\expandafter\ifnum\expandafter\the\@nameuse{c@#1}<0 + *\else\fnsymbol{#1} \fi} +\def\address{\@ifstar{\address@star}% + {\@ifnextchar[{\address@optarg}{\address@noptarg}}} +\def\address@optarg[#1]#2{\real@refstepcounter{address}% + \beg@elem + \report@elt{address}\proc@elem{address}{#2}% + \address@fmt{\c@address}{\the\t@loc@notes}{\@address}{#1}% + \if@Elproofing\else\label{#1}\fi + \ignorespaces} +\def\address@noptarg#1{\real@refstepcounter{address}% + \beg@elem + \proc@elem{address}{#1}% + \address@fmt{\z@}{\the\t@loc@notes}{\@address}{\theaddress}% + \ignorespaces} +\def\address@star#1{% + \beg@elem + \proc@elem{address}{#1}% + \address@fmt{\m@ne}{\the\t@loc@notes}{\@address}{*}% + \ignorespaces} +\def\theaddress{\fnsymbol{address}} +\def\address@fmt#1#2#3#4{\@newelemtrue + \if@Elproofing\def\@eltag{#4}\else\def\@eltag{\theaddress}\fi + \ifnum\prev@elem=\e@address \@newelemfalse \fi + \if@newelem \address@fmt@init \fi + \noindent \bgroup \@addressstyle + \ifnum#1=\z@ + #3\,$^{\mathrm{#2}}$\space% + \else + \ifnum#1=\m@ne + $^{\phantom{\mathrm{\@eltag}}}$\space #3\,$^{\mathrm{#2}}$% + \else + $^{\mathrm{\@eltag}}\,$#3\,$^{\mathrm{#2}}$% + \fi + \fi + \par \egroup} +\def\address@fmt@init{% + \par % Start new paragraph + \vskip \@overaddressskip} % Vertical space before addresses +\def\abstract{\@ifnextchar[{\@abstract}{\@abstract[]}} +\def\@abstract[#1]{% + \global\@hasabstracttrue + \hyphenpenalty\sv@hyphenpenalty % restore \hyphenpenalty + \global\setbox\t@abstract=\vbox\bgroup + \@abstractsize % Text in 9/11 + \hbox to \textwidth\bgroup\hfill\begin{minipage}{\@abstractwidth} + \abstractname +\noindent\ignorespaces +} + \def\endabstract{\end{minipage}\hfill\egroup\egroup} +\def\keyword{% + \global\@haskeywordstrue % Implies rules are to be printed + \hyphenpenalty\sv@hyphenpenalty % restore \hyphenpenalty + \def\sep{\unskip, } % separator for multiple keywords + \def\MSC{\par\leavevmode\hbox {\it 1991 MSC:\ }}% + \def\PACS{\par\leavevmode\hbox {\it PACS:\ }}% + \global\setbox\t@keyword=\vbox\bgroup + \hbox to \textwidth\bgroup\hfill\begin{minipage}{\@keywordwidth} + \@keywordsize + \parskip\z@ + \vskip 10\p@ \@plus 2\p@ \@minus 2\p@ % One line of space above keywords. + \noindent\@keywordheading + \justify@off % Keywords are not justified. + \ignorespaces} + \def\endkeyword{\end{minipage}\hfill\egroup\egroup} +\def\runtitle#1{\gdef\@runtitle{#1}} +\def\runauthor#1{\gdef\@runauthor{#1}} +\let\@runauthor\relax +\let\@runtitle\relax +\let\@runningauthor\relax +\def\RUNDATE{} +\def\RUNJNL{} +\def\RUNART{} +\def\volume#1{\gdef\@volume{#1}} \def\@volume{0} +\def\issn#1{\gdef\@issn{#1}} % defined earlier in this file +\def\issue#1{\gdef\@issue{#1}} \def\@issue{0} +\newcount\@pubyear +\@pubyear=\number\year +\def\company#1{\def\@company{#1}} +\def\@copyrightyear{\number\year} +\def\@shortenyear#1#2#3#4\\{\global\def\@shortyear{#3#4}} +\expandafter\@shortenyear\the\@pubyear\\ +\def\pubyear#1{\global\@pubyear#1 + \expandafter\@shortenyear\the\@pubyear\\% + \ignorespaces} +\def\copyear#1{% + \gdef\@copyrightyear{#1}% + \ignorespaces} +\let\copyrightyear\copyear +\newcounter{firstpage} +\newcounter{lastpage} +\let\ESpagenumber\arabic +\def\firstpage#1{\def\@tempa{#1}\ifx\@tempa\@empty\else + \setcounter{firstpage}{#1}% + \global\c@page=#1 \ignorespaces\fi} +\setcounter{firstpage}{1} +\let\realpageref\pageref +\setcounter{lastpage}{0} +\def\lastpage#1{\def\@tempa{#1}\ifx\@tempa\@empty\else + \setcounter{lastpage}{#1}\ignorespaces\fi + } +\AtEndDocument{% + \clearpage + \addtocounter{page}{-1}% + \immediate\write\@auxout{% + \string\global\string\c@lastpage=\the\c@page}% + \addtocounter{page}{1}% +} + \def\price#1{\gdef\@price{#1}} + \def\@price{ - see front matter} % +\def\ssdi#1#2{% + \gdef\@piiname{PII }% + \gdef\@pubid{S\expandafter\@@ssdi\@issn(#1)#2\end}% +} +\def\SSDI#1{\gdef\@pubid{\@@ssdi#1\end}} +\def\@@ssdi#1{\ifx#1\end \let\next=\relax + \else#1\hskip 1\p@ \let\next=\@@ssdi\fi \next} +\def\@pubid{\relax} +\def\PII#1{% + \gdef\@piiname{PII: }% + \gdef\@piinum{\@@pii#1\end}} +\def\pii#1#2{% + \gdef\@piiname{PII: }% + \gdef\@piinum{S\@issn(#1)#2}% +} +\def\piitrail{\@piiname: \@piinum} +\def\piiname#1{% + \gdef\spaced@piiname{\protect\letterspace to 1.2\naturalwidth{#1}}% + \gdef\@piiname{#1}} +\def\piinum#1{% + \gdef\spaced@piinum{\protect\letterspace to 1.2\naturalwidth{#1}}% + \gdef\@piinum{#1}} +\def\@piiname{} +\def\@piinum{} +\def\@pubid{\piitrail} +\let\corresp\@gobble +\def\jid#1{% + \def\@tempa{#1}% + \ifx\@tempa\@empty + \else + \gdef\@jid{#1}% + \fi +} +\def\@jid{\relax} +\def\convertas#1#2{#2} +\def\aid#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@aid{#1}\fi} + \def\@aid{\relax} +\def\received#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@received{#1}\fi} + \def\@received{\relax} +\def\revised#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@revised{#1}\fi} + \def\@revised{\relax} +\def\accepted#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@accepted{#1}\fi} + \def\@accepted{\relax} +\def\communicated#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@communicated{#1}\fi} + \def\@communicated{\relax} +\def\dedicated#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@dedicated{#1}\fi} + \def\@dedicated{\relax} +\def\presented#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@presented{#1}\fi} + \def\@presented{\relax} +\def\articletype#1{\gdef\@articletype{#1}} + \@ifundefined{@articletype}{\def\@articletype{}}{} +\def\received@prefix{Received~} +\def\revised@prefix{; revised~} +\def\accepted@prefix{; accepted~} +\def\communicated@prefix{; communicated~by~} +\def\history@prefix{} +\def\received@postfix{} +\def\revised@postfix{} +\def\accepted@postfix{} +\def\communicated@postfix{} +\def\history@postfix{} +\def\receivedprefix#1{\gdef\received@prefix{#1}} +\def\revisedprefix#1{\gdef\revised@prefix{#1}} +\def\acceptedprefix#1{\gdef\accepted@prefix{#1}} +\def\communicatedprefix#1{\gdef\communicated@prefix{#1}} +\def\historyprefix#1{\gdef\history@prefix{#1}} +\def\receivedpostfix#1{\gdef\received@postfix{#1}} +\def\revisedpostfix#1{\gdef\revised@postfix{#1}} +\def\acceptedpostfix#1{\gdef\accepted@postfix{#1}} +\def\communicatedpostfix#1{\gdef\communicated@postfix{#1}} +\def\historypostfix#1{\gdef\history@postfix{#1}} +\def\empty@data{\relax} +\def\history@fmt{% + \bgroup + \@historysize + \vskip 6\p@ \@plus 2\p@ \@minus 1\p@ % Vertical space above history + \ifx\@received\empty@data \else % If there is no \received, + % do not print anything + \leavevmode + \history@prefix + \received@prefix\@received \received@postfix% + \ifx\@revised\empty@data \else + \revised@prefix\@revised \revised@postfix% + \fi + \ifx\@accepted\empty@data \else + \accepted@prefix\@accepted \accepted@postfix% + \fi + \ifx\@communicated\empty@data \else + \communicated@prefix\@communicated \communicated@postfix% + \fi + \history@postfix + \fi + \par \egroup} +\def\dedicated@fmt{% + \ifx\@dedicated\empty@data \else + \vskip 4\p@ \@plus 3\p@ + \normalsize\it\centering \@dedicated + \fi} +\def\@alph#1{\ifcase#1\or a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or +k\or \ell\or m\or n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or +y\or z\or aa\or ab\or ac\or ad\or ae\or af\or ag\or ah\or ai\or aj\or +ak\or a\ell\or am\or an\or ao\or ap\or aq\or ar\or as\or at\or au\or av\or +aw\or ay\or az\or ba\or bb\or bc\or bd\or be\or bf\or bg\or bh\or bi\or +bj\or bk\or b\ell\or bm\or bn\or bo\or bp\or bq\or br\or bs\or bt\or +bu\or bw\or bx\or by\or bz\or ca\or cb\or cc\or cd\or ce\or cf\or cg\or +ch\or ci\or cj\or ck\or c\ell\or cm\or cn\or co\or cp\or cq\or cr\or +cs\or ct\or cu\or cw\or cx\or cy\or cz\or da\or db\or dc\or dd\or de\or df\or dg\or dh\or di\or dj\or dk\or +d\ell\or dm\or dn\or do\or dp\or dq\or dr\or ds\or dt\or du\or dw\or +dx\or dy\or dz\or ea\or eb\or ec\or ed\or ee\or ef\or eg\or eh\or +ei\or ej\or ek\or e\ell\or em\or en\or eo\or ep\or eq\or er\or es\or +et\or eu\or ew\or ex\or ey\or ez\else\@ctrerr\fi} +\def\fnstar#1{\@fnstar{\@nameuse{c@#1}}} +\def\@fnstar#1{\ifcase#1\or + \hbox{$\star$}\or + \hbox{$\star\star$}\or + \hbox{$\star\star\star$}\or + \hbox{$\star\star\star\star$}\or + \hbox{$\star\star\star\star\star$}\or + \hbox{$\star\star\star\star\star\star$} + \else + \@ctrerr + \fi + \relax} +\mark{{}{}} % Initializes TeX's marks +\def\ps@plain{\let\@mkboth\@gobbletwo + \def\@oddhead{}% + \def\@evenhead{}% + \def\@oddfoot{\hfil {\rmfamily\thepage} \hfil}% + \let\@evenfoot\@oddfoot} +\def\@triple#1#2#3{\vtop{% + \hbox to \textwidth{\strut \rlap{#1} \hfil {#2} \hfil \llap{#3}}}} +\def\@nonuple#1#2#3#4#5#6#7#8#9{\vtop{% + \hbox to \textwidth{\strut \rlap{#1} \hfil {#2} \hfil \llap{#3}}% + \hbox to \textwidth{\strut \rlap{#4} \hfil {#5} \hfil \llap{#6}}% + \hbox to \textwidth{\strut \rlap{#7} \hfil {#8} \hfil \llap{#9}}}} +\def\@copyright{\@issn/\@shortyear/\$\@price\ $\copyright$\ \the\@pubyear\ + \@company{} All rights reserved} +\def\@jou@vol@pag{\@journal\ \@volume\ (\the\@pubyear)\ \@pagerange} +\def\sectionmark#1{} +\def\subsectionmark#1{} +\let\@j@v@p\@jou@vol@pag % long journal title appears in reprint line +\let\@@j@v@p\@jou@vol@pag % long journal title appears in running headline +\def\sectionmark#1{} +\def\subsectionmark#1{} +\def\ps@headings{% + \let\@mkboth\@gobbletwo + \def\@oddhead{\hfill \@runtitle \hfill \thepage}% + \def\@evenhead{\thepage\hfill \@runauthor\hfill}% + \def\@oddfoot{}% + \def\@evenfoot{}} +\def\ps@copyright{\let\@mkboth\@gobbletwo + \def\@oddhead{\@logohead} + \let\@evenhead\@oddhead + \def\@oddfoot{\hfill{\fontsize{8}{9\p@}\selectfont\@pagenumprefix\thepage}\hfill} + \let\@evenfoot\@oddfoot +} +\def\@logohead{% +\bgroup +\@catchlinesize +\savebox{\@tempboxa}{\vbox {% +\hbox to \textwidth{\hfill +\emph{\@shortjnl}, Vol.\ \@volume, No.\ \@issue, + pp.\ \@pagerange, \the\@pubyear}% +\hbox to \textwidth{\hspace{1.5cm}{\@pergamonsize\textbf{Pergamon}} +\hfill \FullCopyrightText}% +\hbox to \textwidth{% +\raisebox{0pt}[0pt][0pt]{\includegraphics[height=\@Colofonheight]{colofon}}% +\hfill Printed in Great Britain}% +\hbox to \textwidth{\hfill {\small\bfseries + \@pubid \hfill}\llap{\@issn/\@shortyear\ \$\@price}}% +}}% +\box\@tempboxa +\egroup +} +\def\ps@pergamon{% + \let\@mkboth\@gobbletwo + \def\@oddhead{{\@runheadsize\hfill \@runtitle \hfill \thepage}}% + \def\@evenhead{{\@runheadsize\thepage\hfill \@runauthor \hfill}}% + \def\@oddfoot{}% + \def\@evenfoot{}} +\pagestyle{pergamon} +\def\today{\number\day\space\ifcase\month\or + January\or February\or March\or April\or May\or June\or + July\or August\or September\or October\or November\or December\fi + \space\number\year} +\def\nuc#1#2{\relax\ifmmode{}^{#1}{\protect\text{#2}}\else${}^{#1}$#2\fi} +\def\itnuc#1#2{\setbox\@tempboxa=\hbox{\scriptsize\it #1} + \def\@tempa{{}^{\box\@tempboxa}\!\protect\text{\it #2}}\relax + \ifmmode \@tempa \else $\@tempa$\fi} +\let\old@vec\vec % save old definition of \vec +\def\pol#1{\old@vec{#1}} +\def\@bfvec#1{\boldsymbol{#1}} +\def\@pmbfvec#1{\pmb{#1}} +\def\undo@AMS{\global\let\vec\@bfvec} +\def\half{{\textstyle\frac{1}{2}}} +\def\threehalf{{\textstyle\frac{3}{2}}} +\def\quart{{\textstyle\frac{1}{4}}} + \def\espfrac#1#2{\frac{\displaystyle #1}{\displaystyle #2}} +\def\d{\,\mathrm{d}} +\def\e{\mathop{\mathrm{e}}\nolimits} +\def\int{\intop} +\def\oint{\ointop} +\newbox\slashbox \setbox\slashbox=\hbox{$/$} +\newbox\Slashbox \setbox\Slashbox=\hbox{\large$/$} +\def\pFMslash#1{\setbox\@tempboxa=\hbox{$#1$} + \@tempdima=0.5\wd\slashbox \advance\@tempdima 0.5\wd\@tempboxa + \copy\slashbox \kern-\@tempdima \box\@tempboxa} +\def\pFMSlash#1{\setbox\@tempboxa=\hbox{$#1$} + \@tempdima=0.5\wd\Slashbox \advance\@tempdima 0.5\wd\@tempboxa + \copy\Slashbox \kern-\@tempdima \box\@tempboxa} +\def\FMslash{\protect\pFMslash} +\def\FMSlash{\protect\pFMSlash} + \def\Cset{\mathbb{C}} + \def\Hset{\mathbb{H}} + \def\Nset{\mathbb{N}} + \def\Qset{\mathbb{Q}} + \def\Rset{\mathbb{R}} + \def\Zset{\mathbb{Z}} +\if@TwoColumn + \adjdemerits=100 + \linepenalty=100 + \doublehyphendemerits=5000 % experimental (1993-12-14) + \emergencystretch=1.6pc + \spaceskip=0.3em \@plus 0.17em \@minus 0.12em +\fi +\binoppenalty=300 +\relpenalty=100 +\clubpenalty=5000 % 'Club line' at bottom of page. +\widowpenalty=2000 % 'Widow line' at top of page. +\displaywidowpenalty=1000 % Math display widow line. +\predisplaypenalty=150 % Breaking before a math display. +\postdisplaypenalty=50 % Breaking after a math display. +\hfuzz=1\p@ +\hbadness=3000 +\@frontmatterwidth\textwidth + \let\pldots\dots +\ps@headings % 'headings' page style +\pagenumbering{arabic} % Arabic page numbers +\def\thepage{\@pagenumprefix\ESpagenumber{page}} % preceded by \@pagenumprefix +\InputIfFileExists{\@shortjid.cfg}{}{} +%% +%% End of file `public.cls'. +\setcounter{secnumdepth}{5} +\pretolerance=700 +\tolerance=2000 +\hbadness=4000 +\vbadness=4000 +\hyphenpenalty=400 +\relpenalty=500 +\widowpenalty=10000 +\clubpenalty=10000 +\def\@Point#1#2{% + \fontsize{#1}{#2\p@}\selectfont +} +\long\def\@maketablecaption#1#2{\@tablecaptionsize + \sbox\@tempboxa{\@fignumfont{#1}. #2}% + \ifdim \wd\@tempboxa > \captionwidth + \begin{center} + \begin{minipage}{\captionwidth} + \leftskip 0pt plus 0.5fil + \rightskip 0pt plus -0.5fil + \parfillskip 0pt plus 1fil + \@fignumfont{#1}. #2\par + \end{minipage} + \end{center} + \else + \hbox to\hsize{\hfil\box\@tempboxa\hfil}% + \fi + \vskip8\p@ +} +\long\def\@makefigurecaption#1#2{\@figurecaptionsize + \vskip \@overcaptionskip + \sbox\@tempboxa{\@fignumfont{#1}. #2}% + \ifdim \wd\@tempboxa > \captionwidth + \begin{center} + \begin{minipage}{\captionwidth} + \leftskip 0pt plus 0.5fil + \rightskip 0pt plus -0.5fil + \parfillskip 0pt plus 1fil + \@fignumfont{#1}. #2\par + \end{minipage} + \end{center} + \else + \hbox to\hsize{\hfil\box\@tempboxa\hfil}% + \fi + \vskip8\p@ +} +\def\AND{ \& } +\def\author@mark#1{$^{\mathrm{#1}}$} +\def\author@fudge#1{#1} +\def\etal{et al.} +\def\l@paragraph{\@dottedtocline{4}{4.0em}{3.5em}} +\def\l@subparagraph{\@dottedtocline{5}{5em}{3.5em}} +\def\@dotsep{2000} +\def\@fnsymbol#1{\ifcase#1\or *\or \dagger\or \ddagger\or + \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger + \or \ddagger\ddagger \else\@ctrerr\fi} +\def\newblock{} +\let\printhistory\relax +\textwidth182mm % WAS 159 PMISRA +\textheight245mm % WAS 252 PMISRA +% SP 2001/08/07 text vertically centered on the page +\voffset=-12.5mm % VOFFSET +% SP 2001/08/07 new value: 125mm +%\def\@abstractwidth{146mm} % WAS 125 PMISRA +\def\@abstractwidth{.8\textwidth} +\@frontmatterwidth\@abstractwidth +\def\@keywordwidth{\@abstractwidth} +\columnsep5mm % WAS .3 IN PMISRA +\def\@captionsize{\normalsize} +\def\@abstractsize{\normalsize} +\def\@articletypesize{\normalsize} +\def\@historysize{\normalsize} +\def\@keywordsize{\normalsize} +\def\@keywordheading{{\itshape Keywords: }} +\def\abstractname{{\bfseries {Abstract: }}} % Abstract Bold PMISRA 2007-05-30 +\def\@bibliosize{\normalsize} +\historyprefix{(\bgroup \itshape} +\historypostfix{\egroup)} +\def\@titlesize{\@Point{14}{16}\bfseries} +\def\@addressstyle{\normalsize\itshape} +\def\@authorsize{\normalsize} +\def\author@font{\upshape\bfseries} +\def\@overtitleskip{0in} % WAS 1IN PMISRA +% SP 2001/08/07 new value: 4\@bls - 10\p@ + 4\p@ +\def\@belowfmskip{12\p@} %WAS 42 PMISRA 2007-05-30 +% SP 2001/08/07 new value: 1\@bls - 10\p@ + 4\p@ +\def\@overkeywordskip{6pt} +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{0.3\@bls + \@plus .2\@bls}{-1em}{\normalsize\itshape}} % WAS \@bls PMISRA 2007-05-30 +\def\section{\@startsection{section}{1}{\z@} + {6\p@ \@plus 0.5\@bls \@minus 4\p@} % WAS 18 PMISRA 2007-05-30 + {6\p@ \@plus 1\p@ \@minus 2\p@} + {\centering}} +\def\subsection{\@startsection{subsection}{2}{\z@} + {6\p@ \@plus 0.5\@bls \@minus 4\p@} % WAS 18 PMISRA 2007-05-30 + {6\p@ \@plus 1\p@ \@minus 2\p@} + {\itshape}} +\parindent0em +\parskip 6pt +\def\head@style{\interlinepenalty\@M + \hyphenpenalty\@M \exhyphenpenalty\@M + } +% SP 2001/08/07 use the previous definition +% \def\thebibliography{\section{REFERENCES}\@thebibliography} +\long\def\@makefigurecaption#1#2{% + \vskip 8\p@ + \par\hangindent2em\@fignumfont{#1}. #2\par +} +\def\lb@subsection{\thesubsection\half@em} +\def\@fnsymbol#1{\ifcase#1\or *\or **\or *** \or **** \or \dagger\or \ddagger +\or\S\or| \or \ddagger\ddagger \else\@ctrerr\fi\relax} +\def\@price{09.50 $+$ 0.00} +\def\footnoterule{\kern-3\p@ + \hrule \@width 2in + \kern 3\p@} % WAS 12 PMISRA 2007-05-30 +\let\oldaddress@fmt\address@fmt +\def\address@fmt#1#2#3#4{% +\bgroup +\parskip\z@ +\oldaddress@fmt{#1}{#2}{#3}{#4}% +\egroup +} +\def\address@fmt@init{% + \par + \vskip 12\p@} %WAS 24 PMISRA +\advance\topskip by -8mm +\@twocolumntrue\@TwoColumntrue +% SP 2002/04/18 set the mathindent right after specifying twocolumn output +\mathindent=0em +\def\ps@ifacconf{% + \let\@mkboth\@gobbletwo + \def\@oddhead{}% + \def\@evenhead{}% + \def\@oddfoot{}% + \def\@evenfoot{}} +\pagestyle{ifacconf} +\def\ps@copyright{\let\@mkboth\@gobbletwo + \def\@oddhead{\@logohead} + \let\@evenhead\@oddhead + \def\@oddfoot{}\let\@evenfoot\@oddfoot +} +\newif\ifNAT@numbers +\AtBeginDocument{% +\@ifpackageloaded{harvard}{}{ + \RequirePackage{natbib} + %\bibliographystyle{plainnat} + \bibliographystyle{ifacconf} +}} +\@bsphack +\AtEndDocument + {\immediate\write\@auxout{\string\global\string\NAT@numbersfalse}} +\def\@logohead{% +\bgroup +\footnotesize +\savebox{\@tempboxa}{\vtop {% +\hbox to \textwidth{}% +\hbox to \textwidth{}% +\hbox to \textwidth{}% +\hbox to \textwidth{}% +\hbox to \textwidth{}% +}}% +\box\@tempboxa +\egroup +} +\let\oldtitle@fmt\title@fmt +\def\title@fmt#1#2{% + % SP 2000/03/16 use LaTeX's \MakeUppercase + % \oldtitle@fmt{\MakeUppercase{#1}}{#2}% + \oldtitle@fmt{#1}{#2}% +} +\def\head@format#1#2{% + % SP 2000/03/16 use LaTeX's \MakeUppercase + \ifnum #1>1 #2 \else \MakeUppercase{#2}\fi +} +\newdimen\@frontindent +\@frontindent\textwidth +\advance\@frontindent by -\@frontmatterwidth +\def\open@fm{% +\global\setbox\fm@box=\vbox\bgroup + \centering + \leftskip\@frontindent \@plus 1fil + \hsize\@frontmatterwidth + \sv@hyphenpenalty\hyphenpenalty % (save \hyphenpenalty) + \hyphenpenalty\@M} % and not hyphenated +% SP 2001/08/07 Removed the new definition of \close@fm +\endinput +%% +%% End of file `ifacconf.cls'. diff --git a/ifacconf_latex/ifacconf.pdf b/ifacconf_latex/ifacconf.pdf new file mode 100644 index 0000000..8a39ced Binary files /dev/null and b/ifacconf_latex/ifacconf.pdf differ diff --git a/ifacconf_latex/references.bib b/ifacconf_latex/references.bib new file mode 100644 index 0000000..d262428 --- /dev/null +++ b/ifacconf_latex/references.bib @@ -0,0 +1,2770 @@ + +@article{coe_useful_2023, + title = {Useful {Power} {Maximization} for {Wave} {Energy} {Converters}}, + volume = {16}, + copyright = {http://creativecommons.org/licenses/by/3.0/}, + issn = {1996-1073}, + url = {https://www.mdpi.com/1996-1073/16/1/529}, + doi = {10.3390/en16010529}, + abstract = {Wave energy converters (WECs) have enormous potential in providing clean renewable energy with high levels of predictability [...]}, + language = {en}, + number = {1}, + urldate = {2024-02-11}, + journal = {Energies}, + author = {Coe, Ryan G. and Bacelli, Giorgio}, + month = jan, + year = {2023}, + note = {Number: 1 +Publisher: Multidisciplinary Digital Publishing Institute}, + keywords = {n/a}, + pages = {529}, +} + +@article{faedo_optimal_2017, + title = {Optimal control, {MPC} and {MPC}-like algorithms for wave energy systems: {An} overview}, + volume = {1}, + issn = {2468-6018}, + shorttitle = {Optimal control, {MPC} and {MPC}-like algorithms for wave energy systems}, + url = {https://www.sciencedirect.com/science/article/pii/S2468601817301104}, + doi = {10.1016/j.ifacsc.2017.07.001}, + abstract = {Model predictive control (MPC) has achieved considerable success in the process industries, with its ability to deal with linear and nonlinear models, while observing system constraints and considering future behaviour. Given these characteristics, against the backdrop of the energy maximising control problem for Wave Energy Converters (WECs), with physical constraints on system variables and a non-causal optimal control solution it is, perhaps, natural to consider the application of MPC to the WEC problem. However, the WEC energy maximisation problem requires a significant modification of the traditional MPC objective function, resulting in a potentially non-convex optimisation problem. A variety of MPC formulations for WECs have been proposed, with variations in the WEC model, discretisation method, objective function and optimisation algorithm employed. This paper attempts to provide a critical comparison of the various WEC MPC algorithms, while also presenting WEC MPC algorithms within the broader context of other WEC “optimal” control schemes.}, + urldate = {2024-02-10}, + journal = {IFAC Journal of Systems and Control}, + author = {Faedo, Nicolás and Olaya, Sébastien and Ringwood, John V.}, + month = sep, + year = {2017}, + keywords = {Constrained optimisation, Model predictive control, Optimal control, Receding horizon, Wave energy conversion, Wave energy device}, + pages = {37--56}, +} + +@article{nuij_higher-order_2006, + title = {Higher-order sinusoidal input describing functions for the analysis of non-linear systems with harmonic responses}, + volume = {20}, + issn = {0888-3270}, + url = {https://www.sciencedirect.com/science/article/pii/S088832700500083X}, + doi = {10.1016/j.ymssp.2005.04.006}, + abstract = {For high-precision motion systems, modelling and control design specifically oriented at friction effects is instrumental. The sinusoidal input describing function theory represents an approximative mathematical framework for analysing non-linear system behaviour. This theory, however, limits the description of the non-linear system behaviour to a quasi-linear amplitude-dependent relation between sinusoidal excitation and sinusoidal response. In this paper, an extension to higher-order describing functions is realised by introducing the concept of the harmonics generator. The resulting higher-order sinusoidal input describing functions (HOSIDFs) relate the magnitude and phase of the higher harmonics of the periodic response of the system to the magnitude and phase of a sinusoidal excitation. Based on this extension two techniques to measure HOSIDFs are presented. The first technique is FFT based. The second technique is based on IQ (in-phase/quadrature-phase) demodulation. In a simulation, the measurement techniques have been tested by comparing the simulation results to analytically derived results from a known (backlash) non-linearity. In a subsequent practical case study both techniques are used to measure the changes in dynamic behaviour as a function of drive level due to friction in an electric motor. Both methods prove successful for measuring HOSIDFs.}, + number = {8}, + urldate = {2024-02-10}, + journal = {Mechanical Systems and Signal Processing}, + author = {Nuij, P. W. J. M. and Bosgra, O. H. and Steinbuch, M.}, + month = nov, + year = {2006}, + keywords = {Describing function, Frequency domain analysis, Harmonic distortion, Non-linear systems, System identification}, + pages = {1883--1904}, +} + +@article{merigaud_geometrical_2023, + title = {Geometrical {Framework} for {Hydrodynamics} and {Control} of {Wave} {Energy} {Converters}}, + volume = {2}, + url = {https://link.aps.org/doi/10.1103/PRXEnergy.2.023003}, + doi = {10.1103/PRXEnergy.2.023003}, + abstract = {This article presents a simple geometrical approach to visualize the hydrodynamic properties of wave energy converters (WECs), in terms of wave reflection, transmission, and absorption, and how those properties are governed by the WEC control parameters. The problem is modeled as an array of periodic rows of WECs parallel to the wave front, which is representative of WEC farms located along the shoreline, and allows for a straightforward two-dimensional analysis of energy fluxes. The WECs are assumed to be symmetric with respect to the plane perpendicular to the wave propagation direction, and they operate in a single degree of freedom. Under those assumptions, fundamental hydrodynamic relationships allow the WEC operation at a given frequency to be mapped to a single complex number, {\textasciicircum}T, which represents the WEC (complex) transmission coefficient, located in a circle with center 1/2 and radius 1/2. The WEC hydrodynamic and control parameters (added mass, stiffness, damping) govern the precise location of {\textasciicircum}T within the circle. The distance of {\textasciicircum}T to the center of the circle determines the hydrodynamic efficiency, between 0 (when {\textasciicircum}T is on the circle border) and 1/2 (which is achieved when {\textasciicircum}T is at the center of the circle). Therefore, the representation of {\textasciicircum}T provides an immediate insight into the balance between reflection, transmission, and absorption. The proposed unified representation reflects, in a didactic way, some fundamental wave energy concepts, common to all WECs, such as the Haskind relationship, or the impedance matching condition for optimal wave power absorption. Two numerical examples illustrate how the locus of {\textasciicircum}T, across a prescribed frequency range, provides a distinctive “signature” specific to the WEC geometry, mode of operation, and control strategy. Finally, the proposed representation shows many similarities to the Smith chart and, as such, is but one additional analogy between wave energy conversion and electrical engineering.}, + number = {2}, + urldate = {2024-02-07}, + journal = {PRX Energy}, + author = {Mérigaud, Alexis and Thiria, Benjamin and Godoy-Diana, Ramiro}, + month = may, + year = {2023}, + note = {Publisher: American Physical Society}, + pages = {023003}, +} + +@inproceedings{gaebele_incorporating_2023, + title = {Incorporating {Empirical} {Nonlinear} {Efficiency} {Into} {Control} {Co}-{Optimization} of a {Real} {World} {Heaving} {Point} {Absorber} {Using} {WecOptTool}}, + url = {https://dx.doi.org/10.1115/OMAE2023-103899}, + doi = {10.1115/OMAE2023-103899}, + abstract = {Abstract. The open-source WecOptTool was developed to make wave energy converter (WEC) control co-design accessible. WecOptTool is based on the pseudo-spectral method which is capable of efficiently dealing with any linear or nonlinear constraints and nonlinear dynamics by solving the WEC optimal control problem in the time domain using a gradient based optimization algorithm. This work1 presents a control co-optimization study of the AquaHarmonics Inc. heaving point absorber WEC sized for ocean deployment to solve practical industry design problems. Components such as the specific type of generator, the hull shape, and the displaced volume are pre-determined. We co-optimize the WEC’s mass versus mooring line pretension in conjunction with the controller. The optimization is subject to the power-take-off (PTO) dynamics and the rated constraints of the components. In particular, the continuous torque rating is implemented as an explicit constraint, a novel approach for WEC optimization. The PTO dynamics are incorporated into the optimization algorithm via a combination of first principle methods (linear drivetrain model) and empirical efficiency maps (electrical generator) represented as a power loss map. This is a practical method applicable to a variety of PTO architectures and transferable to other WECs. A discussion between using an efficiency coefficient versus a power loss map and their implication for the optimization method is presented. This application of WecOptTool represents a real world WEC by combining simplified models with empirical efficiency data. The WEC, as a dynamically coupled, oscillatory system, requires consideration of the time trajectory dependent power loss for optimizing the average electrical power. This objective function, the modelling approach, and the realistic loss terms makes the common practice of artificially penalizing the reactive power needless.}, + language = {en}, + urldate = {2024-02-06}, + publisher = {American Society of Mechanical Engineers Digital Collection}, + author = {Gaebele, Daniel T. and Michelén Ströfer, Carlos A. and Devin, Michael C. and Grasberger, Jeff T. and Coe, Ryan G. and Bacelli, Giorgio}, + month = sep, + year = {2023}, +} + +@article{strofer_control_2023, + title = {Control {Co}-{Design} of {Power} {Take}-{Off} {Systems} for {Wave} {Energy} {Converters} {Using} {WecOptTool}}, + volume = {14}, + issn = {1949-3037}, + url = {https://ieeexplore.ieee.org/document/10114969}, + doi = {10.1109/TSTE.2023.3272868}, + abstract = {Improved power take-off (PTO) controller design for wave energy converters is considered a critical component for reducing the cost of energy production. However, the device and control design process often remains sequential, with the space of possible final designs largely reduced before the controller has been considered. Control co-design, whereby the device and control design are considered concurrently, has resulted in improved designs in many industries, but remains rare in the wave energy community. In this paper we demonstrate the use of a new open-source code, WecOptTool, for control co-design of wave energy converters, with the aim to make the co-design approach more accessible and accelerate its adoption. Additionally, we highlight the importance of designing a wave energy converter to maximize electrical power, rather than mechanical power, and demonstrate the co-design process while modeling the PTO's components (i.e., drive-train and generator, and their dynamics). We also consider the design and optimization of causal fixed-structure controllers. The demonstration presented here considers the PTO design problem and finds the optimal PTO drive-train that maximizes annual electrical power production. The results show a 22\% improvement in the optimal controller and drive-train co-design over the optimal controller for the nominal, as built, device design.}, + number = {4}, + urldate = {2024-01-29}, + journal = {IEEE Transactions on Sustainable Energy}, + author = {Ströfer, Carlos A. Michelén and Gaebele, Daniel T. and Coe, Ryan G. and Bacelli, Giorgio}, + month = oct, + year = {2023}, + note = {Conference Name: IEEE Transactions on Sustainable Energy}, + keywords = {Control design, Mathematical models, Optimal control, Optimization, Software tools, Wave energy conversion, Wave energy converter (WEC), co-design, optimal control, optimization, power take-off (PTO)}, + pages = {2157--2167}, +} + +@article{bacelli_geometric_2013, + title = {A geometric tool for the analysis of position and force constraints in wave energy converters}, + volume = {65}, + issn = {0029-8018}, + url = {https://www.sciencedirect.com/science/article/pii/S0029801813001200}, + doi = {10.1016/j.oceaneng.2013.03.011}, + abstract = {Most wave energy devices are subject to finite constraints on both the power take-off (PTO) stroke length and the maximum force that the PTO can tolerate. It is also often the case that greater stroke lengths can reduce the maximum force in the PTO and vice versa. Ultimately, some informed choice of PTO constraints must be made in order to ensure that PTO constraints are not violated and that the trade-off between position and force constraints is made in such as way that maximum energy is captured by the converter. This paper presents a tool to allow device developers to check the satisfaction of constraints for a given hydrodynamic model and set of sea conditions and, where constraints are not satisfied, shows how to relax the constraints to maximize energy capture. The tool is algebraic, requiring no simulation and the results are presented through intuitive geometrical constructs. Sample application results are presented for single- and two-body wave energy systems.}, + urldate = {2024-01-29}, + journal = {Ocean Engineering}, + author = {Bacelli, Giorgio and Ringwood, John V.}, + month = jun, + year = {2013}, + keywords = {Constraints, Discretization, Power take-off, Wave energy}, + pages = {10--18}, +} + +@article{zou_optimal_2017, + title = {Optimal control of wave energy converters}, + volume = {103}, + issn = {0960-1481}, + url = {https://www.sciencedirect.com/science/article/pii/S0960148116310059}, + doi = {10.1016/j.renene.2016.11.036}, + abstract = {Optimal control theory is applied to compute control for a single-degree-of-freedom heave wave energy converter. The goal is to maximize the energy extraction per cycle. Both constrained and unconstrained optimal control problems are presented. Both periodic and non-periodic excitation forces are considered. In contrast to prior work, it is shown that for this non-autonomous system, the optimal control, in general, includes both singular arc and bang-bang modes. Conditions that determine the switching times to/from the singular arc are derived. Simulation results show that the proposed optimal control solution matches the solution obtained using the complex conjugate control. A generic linear dynamic model is used in the simulations. The main advantage of the proposed control is that it finds the optimal control without the need for wave prediction; it only requires the knowledge of the excitation force and its derivatives at the current time.}, + urldate = {2024-01-29}, + journal = {Renewable Energy}, + author = {Zou, Shangyan and Abdelkhalik, Ossama and Robinett, Rush and Bacelli, Giorgio and Wilson, David}, + month = apr, + year = {2017}, + keywords = {Bang-bang control, Optimal control, Singular arc control, Wave energy conversion}, + pages = {217--225}, +} + +@article{abdulkadir_optimal_2024, + title = {Optimal {Constrained} {Control} of {Arrays} of {Wave} {Energy} {Converters}}, + volume = {12}, + copyright = {http://creativecommons.org/licenses/by/3.0/}, + issn = {2077-1312}, + url = {https://www.mdpi.com/2077-1312/12/1/104}, + doi = {10.3390/jmse12010104}, + abstract = {Wave Energy Converters (WECs) are designed to be deployed in arrays, usually in a limited space, to minimize the cost of installation, mooring, and maintenance. Control methods that attempt to maximize the harvested power often lead to power flow from the WEC to the ocean, at times, to maximize the overall harvested power from the ocean over a longer period. The Power Take-Off (PTO) units that can provide power to the ocean (reactive power) are usually more expensive and complex. In this work, an optimal control formulation is presented using Pontryagin’s minimum principle that aims to maximize the harvested energy subject to constraints on the maximum PTO force and power flow direction. An analytical formulation is presented for the optimal control of an array of WECs, assuming irregular wave input. Three variations of the developed control are tested: a formulation without power constraints, a formulation that only allows for positive power, and finally, a formulation that allows for finite reactive power. The control is compared with optimally tuned damping and bang–bang control.}, + language = {en}, + number = {1}, + urldate = {2024-01-29}, + journal = {Journal of Marine Science and Engineering}, + author = {Abdulkadir, Habeebullah and Abdelkhalik, Ossama}, + month = jan, + year = {2024}, + note = {Number: 1 +Publisher: Multidisciplinary Digital Publishing Institute}, + keywords = {Pontryagin’s minimum principle, constrained control, optimal control, reactive power, wave energy converter}, + pages = {104}, +} + +@article{sun_stochastic_2019, + title = {Stochastic control of wave energy converters for optimal power absorption with constrained control force}, + volume = {87}, + issn = {0141-1187}, + url = {https://www.sciencedirect.com/science/article/pii/S0141118718303122}, + doi = {10.1016/j.apor.2019.03.002}, + abstract = {This paper presents an analytical solution derived for optimal control of the power take-off of a single-degree of freedom heave point absorber with constraints on the control force. The optimal control law turns out to be noncausal with a functional dependence on future velocities. To handle this problem, an algorithm for predicting future velocities is derived. Based on the solution the mean (time-averaged) absorbed power in a given sea-state is calculated. The performance of the indicated controller in terms of the mean absorbed power is close to the optimal value obtained by nonlinear programming and better than a controller with feedback from the present displacement, velocity and acceleration, and with optimized gain factors.}, + urldate = {2024-01-29}, + journal = {Applied Ocean Research}, + author = {Sun, Tao and Nielsen, Søren R. K.}, + month = jun, + year = {2019}, + keywords = {Actuator force constraints, Heave point absorber, Optimal power take-off, Wave energy}, + pages = {130--141}, +} + +@article{sichani_constrained_2014, + title = {Constrained optimal stochastic control of non-linear wave energy point absorbers}, + volume = {47}, + issn = {0141-1187}, + url = {https://www.sciencedirect.com/science/article/pii/S0141118714000546}, + doi = {10.1016/j.apor.2014.06.005}, + abstract = {The paper deals with the stochastic optimal control of a wave energy point absorber with strong nonlinear buoyancy forces using the reactive force from the electric generator on the absorber as control force. The considered point absorber has only one degree of freedom, heave motion, which is used to extract energy. Constrains are enforced on the control force to prevent large structural stresses in the floater at specific hot spots with the risk of inducing fatigue damage, or because the demanded control force cannot be supplied by the actuator system due to saturation. Further, constraints are enforced on the motion of the floater to prevent it from hitting the bottom of the sea or to make unacceptable jumps out of the water. The applied control law, which is of the feedback type with feedback from the displacement, velocity, and acceleration of the floater, contains two unprovided gain parameters, which are chosen so the mean (expected value) of the power outtake in the stationary state is optimized. In order to ensure accuracy of the results for each configuration of the controller Monte Carlo simulations have been carried out for various sea-states and the final results have been presented in the paper. The effect of nonlinear buoyancy force – in comparison to linear buoyancy force – and constraints of the controller on the power outtake of the device have been studied in details and supported by numerical simulations.}, + urldate = {2024-01-29}, + journal = {Applied Ocean Research}, + author = {Sichani, M. T. and Chen, J. B. and Kramer, M. M. and Nielsen, S. R. K.}, + month = aug, + year = {2014}, + keywords = {Constrained optimal stochastic control, Irregular sea state, Nonlinear buoyancy force, Wave energy point converter}, + pages = {255--269}, +} + +@article{tedeschi_effect_2011, + title = {Effect of {Control} {Strategies} and {Power} {Take}-{Off} {Efficiency} on the {Power} {Capture} {From} {Sea} {Waves}}, + volume = {26}, + issn = {1558-0059}, + url = {https://ieeexplore.ieee.org/abstract/document/6026916}, + doi = {10.1109/TEC.2011.2164798}, + abstract = {The choice of the most suitable control strategy for wave energy converters (WECs) is often evaluated with reference to the sinusoidal assumption for incident waves. Under this hypothesis, linear techniques for the control of the extracted power, as passive loading and optimum control, are well known and widely analyzed. It can be shown, however, how their performances are fundamentally different when irregular waves are considered and the theoretical superiority of optimum control is questionable under real wave conditions. Moreover, the global optimization of WECs implies a rational design of the power electronics equipment. This requires the analysis of the instantaneous extracted power in addition to the average one. In this paper, the impact of irregular waves on the power extraction when using different control techniques is analyzed in the case of a point absorber in heave. It is also shown how a convenient tradeoff between high average power extraction and limited power electronics overrating can be obtained by applying simple power saturation techniques. Moreover, the impact of power conversion efficiency on the control strategy is analyzed.}, + number = {4}, + urldate = {2024-01-29}, + journal = {IEEE Transactions on Energy Conversion}, + author = {Tedeschi, Elisabetta and Carraro, Matteo and Molinas, Marta and Mattavelli, Paolo}, + month = dec, + year = {2011}, + note = {Conference Name: IEEE Transactions on Energy Conversion}, + keywords = {Analytical models, Control strategies, Hydrodynamics, Load modeling, Mathematical model, Power electronics, Time domain analysis, Wave energy, irregular waves, power take-off (PTO), wave energy}, + pages = {1088--1098}, +} + +@article{babarit_numerical_2012, + title = {Numerical benchmarking study of a selection of wave energy converters}, + volume = {41}, + issn = {0960-1481}, + url = {https://www.sciencedirect.com/science/article/pii/S0960148111005672}, + doi = {10.1016/j.renene.2011.10.002}, + abstract = {The aim of this study is to estimate the mean annual power absorption of a selection of eight Wave Energy Converters (WECs) with different working principles. Based on these estimates a set of power performance measures that can be related to costs are derived. These are the absorbed energy per characteristic mass [kWh/kg], per characteristic surface area [MWh/m2], and per root mean square of Power Take Off (PTO) force [kWh/N]. The methodology relies on numerical modelling. For each device, a numerical Wave-to-Wire (W2W) model is built based on the equations of motion. Physical effects are modelled according to the state-of-the-art within hydrodynamic modelling practise. Then, the W2W models are used to calculate the power matrices of each device and the mean annual power absorption at five different representative wave sites along the European Coast, at which the mean level of wave power resource ranges between 15 and 88 kW per metre of wave front. Uncertainties are discussed and estimated for each device. Computed power matrices and results for the mean annual power absorption are assembled in a summary sheet per device. Comparisons of the selected devices show that, despite very different working principles and dimensions, power performance measures vary much less than the mean annual power absorption. With the chosen units, these measures are all shown to be of the order of 1.}, + urldate = {2024-01-29}, + journal = {Renewable Energy}, + author = {Babarit, A. and Hals, J. and Muliawan, M. J. and Kurniawan, A. and Moan, T. and Krokstad, J.}, + month = may, + year = {2012}, + keywords = {Comparison, Mean annual power, Power matrix, Wave energy converter}, + pages = {44--63}, +} + +@article{pena-sanchez_control_2022, + series = {9th {IFAC} {Symposium} on {Mechatronic} {Systems} {MECHATRONICS} 2022}, + title = {Control co-design of power take-off parameters for wave energy systems}, + volume = {55}, + issn = {2405-8963}, + url = {https://www.sciencedirect.com/science/article/pii/S2405896322025848}, + doi = {10.1016/j.ifacol.2022.10.531}, + abstract = {A key component of wave energy converters (WECs), which determines the technical and economic performance of WECs, is the power take-off (PTO) system. This WEC subsystem converts the hydrodynamic excitation of the WEC into useful mechanical and, typically, electrical energy. It is well known that WEC control systems have the capability to significantly enhance the performance of WECs, but are limited in scope by the physical PTO displacement and force constraints. A variety of WEC control algorithms have the capacity to include the PTO constraints within the (constrained) optimal control formulation, delivering performance which takes maximum advantage of the available operational space, but avoiding exceedance of device/PTO specifications. However, little consideration is given to the interplay between the constraint levels and the maximum achievable performance. This paper examines, from an economic perspective, the trade-off between energy receipts and the capital cost of force and displacement constraints in a typical heaving point absorber WEC.}, + number = {27}, + urldate = {2024-01-27}, + journal = {IFAC-PapersOnLine}, + author = {Peña-Sanchez, Yerai and García-Violini, Demián and Ringwood, John V.}, + month = jan, + year = {2022}, + keywords = {Power take-off, constraints, control co-design, energy maximisation, wave energy}, + pages = {311--316}, +} + +@article{mavrakos_hydrodynamic_2004, + title = {Hydrodynamic coefficients in heave of two concentric surface-piercing truncated circular cylinders}, + volume = {26}, + issn = {0141-1187}, + url = {https://www.sciencedirect.com/science/article/pii/S0141118705000076}, + doi = {10.1016/j.apor.2005.03.002}, + abstract = {The paper aims at presenting a solution of the linearized hydrodynamic radiation problem for two concentric, free surface-piercing truncated vertical cylinders that are forced to independently oscillate in heave in finite depth waters. For the solution of the problem, the flow field around the two bodies is subdivided into ring-shaped fluid regions, in each of which axisymmetric eigenfunction expansions for the velocity potential are made. By implementing Galerkin's method, the various potential solutions are matched and extensive numerical results concerning the hydrodynamic and interaction coefficients in heave for various geometrical configurations presented and discussed.}, + number = {3}, + urldate = {2023-12-13}, + journal = {Applied Ocean Research}, + author = {Mavrakos, Spyros A.}, + month = may, + year = {2004}, + keywords = {Concentric cylinders, Hydrodynamic parameters, Wave energy devices}, + pages = {84--97}, +} + +@article{kokkinowrachos_behaviour_1986, + title = {Behaviour of vertical bodies of revolution in waves}, + volume = {13}, + issn = {0029-8018}, + url = {https://www.sciencedirect.com/science/article/pii/0029801886900375}, + doi = {10.1016/0029-8018(86)90037-5}, + abstract = {This paper presents the so-called macroelement method by means of which the complete linear hydromechanic analysis of arbitrarily shaped bodies of revolution with vertical axis can be carried out. The development of a special method for this wide class of structures which are common in offshore designs is of great advantage for the engineering work. The method described here is based on the discretization of the flow field around the structure by means of ring-shaped macroelements, the velocity potential in each element being approximated with Fourier series. For the matching of the solution between neighbouring elements Galerkin's method is applied. Both the diffraction and the radiation problems are solved.}, + number = {6}, + urldate = {2023-12-12}, + journal = {Ocean Engineering}, + author = {Kokkinowrachos, Konstantin and Mavrakos, Spyridon and Asorakos, Sampson}, + month = jan, + year = {1986}, + pages = {505--538}, +} + +@article{zhang_hydrodynamic_2016, + title = {Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters}, + volume = {30}, + issn = {2191-8945}, + url = {https://doi.org/10.1007/s13344-016-0062-2}, + doi = {10.1007/s13344-016-0062-2}, + abstract = {The absorber is known to be vertical axisymmetric for a single-point wave energy converter (WEC). The shape of the wetted surface usually has a great influence on the absorber’s hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method (BDM) which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.}, + language = {en}, + number = {6}, + urldate = {2023-12-12}, + journal = {China Ocean Engineering}, + author = {Zhang, Wan-chao and Liu, Heng-xu and Zhang, Liang and Zhang, Xue-wei}, + month = dec, + year = {2016}, + keywords = {astringency, complex wetted surface, geometrical shape, semi-analytical method, vertical axisymmetric}, + pages = {954--966}, +} + +@inproceedings{chau_inertia_2013, + title = {Inertia, {Damping}, and {Wave} {Excitation} of {Heaving} {Coaxial} {Cylinders}}, + url = {https://dx.doi.org/10.1115/OMAE2012-83987}, + doi = {10.1115/OMAE2012-83987}, + abstract = {The method of matched eigenfunction expansions is applied in this paper to obtain the hydrodynamic coefficients of a pair of coaxial cylinders, each of which can have independent movement. The geometry idealizes a device for extracting ocean wave energy in the heave mode. The effects of geometric variations and the interaction between cylinders on the hydrodynamic properties are discussed. Analytical expressions for the low-frequency behavior of the hydrodynamic coefficients are also derived. The wave-exciting force on the bottom surface of either one of the cylinders is derived using the radiation solutions, with a generalized form of the Haskind relation developed for this geometry. The presented results are immediately applicable to examine free motion of coaxial cylinders in a wave field.}, + language = {en}, + urldate = {2023-12-12}, + publisher = {American Society of Mechanical Engineers Digital Collection}, + author = {Chau, Fun Pang and Yeung, Ronald W.}, + month = aug, + year = {2013}, + pages = {803--813}, +} + +@article{de_la_torre-castro_combined_2023, + title = {Combined impact of power take-off capping and of wave resource description on wave energy converter performance}, + volume = {134}, + issn = {0141-1187}, + url = {https://www.sciencedirect.com/science/article/pii/S014111872300038X}, + doi = {10.1016/j.apor.2023.103494}, + abstract = {Wave energy converters (WECs) energy production estimates are key metrics for performance predictions. This study compares four methods for energy production assessment: power matrix, interpolated power matrix, capture length matrix, and a reference method based on the exact omnidirectional spectra for every sea state. Two deployment sites are considered and their wave resource is derived from hindcast databases. The WEC chosen for this study is a two-body self-referenced heaving device characterised using a boundary element method (BEM) numerical model run in time-domain and accounting for some non-linearities. The model also includes power take-off capping, in terms of power capacity and a force cap, independently. A novel metric is introduced to assess the shape similarity between two spectra and it is used to assess the impact of approximating raw spectra with standard ones on energy production estimates. The study shows that the power take-off capping approaches and values and the way the exact resource spectra are approximated have a significant impact WEC energy estimation methods accuracy. Indeed, relative differences in yearly production estimates with respect to the benchmark method vary from 2.4\% to 8.3\% across capping values and estimation methods. It also shows that there is little difference in yearly averaged energy production estimates between the different “matrix based” methods. These differences are of the order of tens of percent for a given power take-off capping configuration and a given site.}, + urldate = {2023-12-12}, + journal = {Applied Ocean Research}, + author = {de la Torre-Castro, L. M. and Pascal, R. C. R. and Perignon, Y. and Babarit, A. and Payne, G. S.}, + month = may, + year = {2023}, + keywords = {Energy production estimates, Power take-off capping, Wave energy, Wave resource characterisation}, + pages = {103494}, +} + +@article{liu_analysis_2014, + title = {Analysis of orthogonal wave reflection by a caisson with open front chamber filled with sloping rubble mound}, + volume = {91}, + issn = {0378-3839}, + url = {https://www.sciencedirect.com/science/article/pii/S0378383914000994}, + doi = {10.1016/j.coastaleng.2014.05.002}, + abstract = {A new combined caisson, including an open window on the front wall and an internal rubble mound with a slope, has been proposed and used in Italy. This study presents a semi-analytical solution to estimate the wave absorbing performance of the new combined caisson with regard to orthogonal wave attack. The internal slope of the rubble mound is assumed to be a series of horizontal steps. Then the matched eigenfunction expansions are used to develop the semi-analytical solution. The square-root singularity of fluid velocity at the upper tip of the front submerged wall is incorporated into the solution to enhance the convergence of calculated results. The new semi-analytical solution is confirmed by an independently developed multi-domain boundary element method solution. Also the predictions of the semi-analytical solution agree reasonably well with experimental data. Based on both the calculations and the experimental data, some useful results are presented for practical engineering.}, + urldate = {2023-12-09}, + journal = {Coastal Engineering}, + author = {Liu, Yong and Faraci, Carla}, + month = sep, + year = {2014}, + keywords = {Combined caisson, Reflection coefficient, Rubble mound, Semi-analytical solution, Slope}, + pages = {151--163}, +} + +@article{chittick_asymmetric_2009, + title = {An asymmetric suboptimization approach to aerostructural optimization}, + volume = {10}, + issn = {1573-2924}, + url = {https://doi.org/10.1007/s11081-008-9046-2}, + doi = {10.1007/s11081-008-9046-2}, + abstract = {An asymmetric suboptimization method for performing multidisciplinary design optimization is introduced. The objective of the proposed method is to improve the overall efficiency of aerostructural optimization, by simplifying the system-level problem, and thereby reducing the number of calls to a potentially costly aerodynamics solver. To guide a gradient-based optimization algorithm, an extension of the coupled sensitivity equations is developed to include post-optimality information from the structural suboptimization. The optimization of an aircraft wing is performed using linear aerodynamic and structural analyses, and a thorough performance comparison is made between the new approach and the conventional multidisciplinary feasible method. The asymmetric suboptimization method is found to be the more efficient approach when it adequately simplifies the system-level problem, or when there is a large enough discrepancy between disciplinary solution times.}, + language = {en}, + number = {1}, + urldate = {2023-12-04}, + journal = {Optimization and Engineering}, + author = {Chittick, Ian R. and Martins, Joaquim R. R. A.}, + month = mar, + year = {2009}, + keywords = {Asymmetric suboptimization, Coupled post-optimality sensitivity analysis, Multidisciplinary design optimization}, + pages = {133--152}, +} + +@article{martins_multidisciplinary_2013, + title = {Multidisciplinary {Design} {Optimization}: {A} {Survey} of {Architectures}}, + volume = {51}, + issn = {0001-1452}, + shorttitle = {Multidisciplinary {Design} {Optimization}}, + url = {https://doi.org/10.2514/1.J051895}, + doi = {10.2514/1.J051895}, + abstract = {Multidisciplinary design optimization is a field of research that studies the application of numerical optimization techniques to the design of engineering systems involving multiple disciplines or components. Since the inception of multidisciplinary design optimization, various methods (architectures) have been developed and applied to solve multidisciplinary design-optimization problems. This paper provides a survey of all the architectures that have been presented in the literature so far. All architectures are explained in detail using a unified description that includes optimization problem statements, diagrams, and detailed algorithms. The diagrams show both data and process flow through the multidisciplinary system and computational elements, which facilitate the understanding of the various architectures, and how they relate to each other. A classification of the multidisciplinary design-optimization architectures based on their problem formulations and decomposition strategies is also provided, and the benefits and drawbacks of the architectures are discussed from both theoretical and experimental perspectives. For each architecture, several applications to the solution of engineering-design problems are cited. The result is a comprehensive but straightforward introduction to multidisciplinary design optimization for nonspecialists and a reference detailing all current multidisciplinary design-optimization architectures for specialists.}, + number = {9}, + urldate = {2023-12-04}, + journal = {AIAA Journal}, + author = {Martins, Joaquim R. R. A. and Lambe, Andrew B.}, + year = {2013}, + note = {Publisher: American Institute of Aeronautics and Astronautics +\_eprint: https://doi.org/10.2514/1.J051895}, + pages = {2049--2075}, +} + +@inproceedings{sundarrajan_towards_2021, + title = {Towards a {Fair} {Comparison} between the {Nested} and {Simultaneous} {Control} {Co}-{Design} {Methods} using an {Active} {Suspension} {Case} {Study}}, + url = {https://ieeexplore.ieee.org/abstract/document/9482687}, + doi = {10.23919/ACC50511.2021.9482687}, + abstract = {This paper tackles perhaps the two most common control co-design coordination strategies: simultaneous analysis and design and the nested control problem formulation. Many practical insights into the two strategies are presented using the literature and comprehensive numerical results from a detailed and challenging CCD problem of an active vehicle suspension. The study conducted attempts to provide a fair comparison and discussion between the control co-design coordination implementations. The results indicate a substantial reduction in computational costs over the existing implementations and conclusions on method selection contrary to common assumptions in the literature. However, additional work is needed to provide a robust set of CCD implementation guidelines.}, + urldate = {2023-12-04}, + booktitle = {2021 {American} {Control} {Conference} ({ACC})}, + author = {Sundarrajan, Athul K. and Herber, Daniel R.}, + month = may, + year = {2021}, + note = {ISSN: 2378-5861}, + pages = {358--365}, +} + +@article{bacelli_numerical_2015, + title = {Numerical {Optimal} {Control} of {Wave} {Energy} {Converters}}, + volume = {6}, + issn = {1949-3037}, + url = {https://ieeexplore.ieee.org/abstract/document/6987295}, + doi = {10.1109/TSTE.2014.2371536}, + abstract = {Energy maximizing control for wave energy converters (WECs) is a nonstandard optimal control problem. While the constrained optimal control problem for WECs has been addressed by model-predictive control strategies, such strategies need to employ cost function modifications due to convexity problems and the algorithms are computationally complex, making real-time implementation difficult. The recently developed family of direct transcription methods offer a promising alternative, since they are computationally efficient and a convex problem results. Moreover, constraints on both the device displacement and velocity, and power take off force, are easily incorporated. Both single-body and multibody device models can be used, as well as arrays of single-body or multibody devices.}, + number = {2}, + urldate = {2023-11-27}, + journal = {IEEE Transactions on Sustainable Energy}, + author = {Bacelli, Giorgio and Ringwood, John V.}, + month = apr, + year = {2015}, + note = {Conference Name: IEEE Transactions on Sustainable Energy}, + pages = {294--302}, +} + +@article{coe_maybe_2021, + title = {Maybe less is more: {Considering} capacity factor, saturation, variability, and filtering effects of wave energy devices}, + volume = {291}, + issn = {0306-2619}, + shorttitle = {Maybe less is more}, + url = {https://www.sciencedirect.com/science/article/pii/S0306261921002701}, + doi = {10.1016/j.apenergy.2021.116763}, + abstract = {While a great deal of research has been performed to quantify and characterize the wave energy resource, there are still open questions about how a wave energy developer should use this wave resource information to design a wave energy converter device to suit a specific environment or, alternatively, to assess potential deployment locations. It is natural to focus first on the impressive magnitudes of power available from ocean waves, and to be drawn to locations where mean power levels are highest. However, a number of additional factors such as intermittency and capacity factor may be influential in determining economic viability of a wave energy converter, and should therefore be considered at the resource level, so that these factors can influence device design decisions. This study examines a set of wave resource metrics aimed towards this end of bettering accounting for variability in wave energy converter design. The results show distinct regional trends that may factor into project siting and wave energy converter design. Although a definitive solution for the optimal size of a wave energy converter is beyond the reaches of this study, the evidence presented does support the idea that smaller devices with lower power ratings may merit closer consideration.}, + urldate = {2023-11-27}, + journal = {Applied Energy}, + author = {Coe, Ryan G. and Ahn, Seongho and Neary, Vincent S. and Kobos, Peter H. and Bacelli, Giorgio}, + month = jun, + year = {2021}, + keywords = {Practical resource, Wave energy converter (WEC), Wave power resource}, + pages = {116763}, +} + +@article{grossmann_systematic_2013, + title = {Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming}, + volume = {59}, + copyright = {Copyright © 2013 American Institute of Chemical Engineers}, + issn = {1547-5905}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/aic.14088}, + doi = {10.1002/aic.14088}, + abstract = {Discrete-continuous optimization problems are commonly modeled in algebraic form as mixed-integer linear or nonlinear programming models. Since these models can be formulated in different ways, leading either to solvable or nonsolvable problems, there is a need for a systematic modeling framework that provides a fundamental understanding on the nature of these models. This work presents a modeling framework, generalized disjunctive programming (GDP), which represents problems in terms of Boolean and continuous variables, allowing the representation of constraints as algebraic equations, disjunctions and logic propositions. An overview is provided of major research results that have emerged in this area. Basic concepts are emphasized as well as the major classes of formulations that can be derived. These are illustrated with a number of examples in the area of process systems engineering. As will be shown, GDP provides a structured way for systematically deriving mixed-integer optimization models that exhibit strong continuous relaxations, which often translates into shorter computational times. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3276–3295, 2013}, + language = {en}, + number = {9}, + urldate = {2023-11-27}, + journal = {AIChE Journal}, + author = {Grossmann, Ignacio E. and Trespalacios, Francisco}, + year = {2013}, + note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/aic.14088}, + keywords = {logic-based optimization, mixed-integer programming, optimization}, + pages = {3276--3295}, +} + +@misc{sundarrajan_open-loop_2023, + title = {Open-{Loop} {Control} {Co}-{Design} of {Semisubmersible} {Floating} {Offshore} {Wind} {Turbines} using {Linear} {Parameter}-{Varying} {Models}}, + url = {http://arxiv.org/abs/2310.13647}, + doi = {10.48550/arXiv.2310.13647}, + abstract = {This paper discusses a framework to design elements of the plant and control systems for floating offshore wind turbines in an integrated manner using linear parameter-varying models. Multiple linearized models derived from aeroelastic simulation software in different operating regions characterized by the incoming wind speed are combined to construct an approximate low-fidelity model of the system. The combined model is then used to generate open-loop, optimal control trajectories as part of a nested control co-design strategy that explores the system's power production and stability using the platform pitch tilt as a proxy in the context of crucial plant and control design decisions. The radial distance between the central and outer columns and the diameter of the outer columns of the semisubmersible platform are the plant design variables. The platform stability and power production are studied for different plant design decisions. The effect of plant decisions on subsequent power production and stability response of the floating wind turbine is quantified in terms of the levelized cost of energy. The results show that the inner-loop constraints and the plant design decisions affect the turbine's power and, subsequently, the cost of the system.}, + urldate = {2023-11-01}, + publisher = {arXiv}, + author = {Sundarrajan, Athul Krishna and Lee, Yong Hoon and Allison, James T. and Zalkind, Daniel and Herber, Daniel}, + month = oct, + year = {2023}, + note = {arXiv:2310.13647 [cs, eess]}, + keywords = {Electrical Engineering and Systems Science - Systems and Control}, +} + +@article{herber_advances_2017, + title = {Advances in combined architecture, plant, and control design}, + url = {https://www.ideals.illinois.edu/items/105359}, + urldate = {2023-11-01}, + author = {Herber, Daniel Ronald}, + year = {2017}, +} + +@article{herber_nested_2018, + title = {Nested and {Simultaneous} {Solution} {Strategies} for {General} {Combined} {Plant} and {Control} {Design} {Problems}}, + volume = {141}, + issn = {1050-0472}, + url = {https://doi.org/10.1115/1.4040705}, + doi = {10.1115/1.4040705}, + abstract = {In this paper, general combined plant and control design or co-design problems are examined. The previous work in co-design theory imposed restrictions on the type of problems that could be posed. This paper lifts many of those restrictions. The problem formulations and optimality conditions for both the simultaneous and nested solution strategies are given. Due to a number of challenges associated with the optimality conditions, practical solution considerations are discussed with a focus on the motivating reasons for using direct transcription (DT) in co-design. This paper highlights some of the key concepts in general co-design including general coupling, the differences between the feasible regions for each strategy, general boundary conditions, inequality path constraints, system-level objectives, and the complexity of the closed-form solutions. Three co-design test problems are provided. A number of research directions are proposed to further co-design theory including tailored solution methods for reducing total computational expense, better comparisons between the two solution strategies, and more realistic test problems.}, + number = {011402}, + urldate = {2023-10-30}, + journal = {Journal of Mechanical Design}, + author = {Herber, Daniel R. and Allison, James T.}, + month = oct, + year = {2018}, +} + +@article{abbas_control_2024, + title = {Control co-design of a floating offshore wind turbine}, + volume = {353}, + issn = {0306-2619}, + url = {https://www.sciencedirect.com/science/article/pii/S0306261923014009}, + doi = {10.1016/j.apenergy.2023.122036}, + abstract = {Several control co-design (CCD) optimizations of floating offshore wind turbines are presented in this work using the newly introduced Wind Energy with Integrated Servo-Control (WEIS) framework. Three methods for parameterizing the primary tuning inputs to the Reference Open-Source Controller are presented and optimized, including a sensitivity-margin constrained controller. WEIS, a detailed, open-source floating offshore wind turbine design optimization tool is then used to conduct CCD optimizations on the International Energy Agency (IEA) 15MW wind turbine on the University of Maine VolturnUS-S semisubmersible platform. The results from optimizations are shown to reduce the levelized cost of energy (LCOE) by approximately 1\% and 4\% when optimizing the tower and platform, respectively. It is also found that the coupling between the tower and control system parameters is weaker than the coupling between the floating system and control system parameters, showing that CCD may not be advantageous for certain problems. Finally, a subset of operational design load cases is run to verify the optimized controller and turbine models.}, + urldate = {2023-10-30}, + journal = {Applied Energy}, + author = {Abbas, Nikhar J. and Jasa, John and Zalkind, Daniel S. and Wright, Alan and Pao, Lucy}, + month = jan, + year = {2024}, + keywords = {Control systems, Floating wind turbines, Multidisciplinary design, Optimization}, + pages = {122036}, +} + +@article{mowers_evaluation_2021, + title = {An evaluation of electricity system technology competitiveness metrics: {The} case for profitability}, + volume = {34}, + issn = {1040-6190}, + shorttitle = {An evaluation of electricity system technology competitiveness metrics}, + url = {https://www.sciencedirect.com/science/article/pii/S1040619021000221}, + doi = {10.1016/j.tej.2021.106931}, + abstract = {In this work we develop standardized functional forms for electricity technology competitiveness metrics and show how the mathematical relationship between value and cost can affect the robustness of the metric. We make the case to replace established metrics with economic profitability metrics – including a new profitability-based adjustment to LCOE. These profitability metrics are shown to be more robust for evaluating technology competitiveness by keeping comparisons on an equivalent monetary basis.}, + number = {4}, + urldate = {2023-10-30}, + journal = {The Electricity Journal}, + author = {Mowers, Matthew and Mai, Trieu}, + month = may, + year = {2021}, + keywords = {Competitiveness metrics, Electricity technology competitiveness, Levelized cost of electricity, Profitability, Renewable energy, System value}, + pages = {106931}, +} + +@article{michele_theory_2016, + title = {Theory of the synchronous motion of an array of floating flap gates oscillating wave surge converter}, + volume = {472}, + url = {https://royalsocietypublishing.org/doi/10.1098/rspa.2016.0174}, + doi = {10.1098/rspa.2016.0174}, + abstract = {We consider a finite array of floating flap gates oscillating wave surge converter (OWSC) in water of constant depth. The diffraction and radiation potentials are solved in terms of elliptical coordinates and Mathieu functions. Generated power and capture width ratio of a single gate excited by incoming waves are given in terms of the radiated wave amplitude in the far field. Similar to the case of axially symmetric absorbers, the maximum power extracted is shown to be directly proportional to the incident wave characteristics: energy flux, angle of incidence and wavelength. Accordingly, the capture width ratio is directly proportional to the wavelength, thus giving a design estimate of the maximum efficiency of the system. We then compare the array and the single gate in terms of energy production. For regular waves, we show that excitation of the out-of-phase natural modes of the array increases the power output, while in the case of random seas we show that the array and the single gate achieve the same efficiency.}, + number = {2192}, + urldate = {2023-10-22}, + journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, + author = {Michele, Simone and Sammarco, Paolo and d’Errico, Michele}, + month = aug, + year = {2016}, + note = {Publisher: Royal Society}, + keywords = {floating flap gate energy, resonance, wave-body interaction}, + pages = {20160174}, +} + +@phdthesis{andre_sustainable_2022, + title = {Sustainable {Design} of {Electric} {Vertical} {Take}-{Off} and {Landing} {Aircraft} for {Urban} {Air} {Mobility}}, + url = {https://mediatum.ub.tum.de/1618545}, + abstract = {The thesis assesses the environmental impact of electric vertical take-off and landing (eVTOL) aircraft. It develops a methodology for the integrated conceptual design and life cycle assessment of eVTOL that facilitates evaluating different configurations, electrochemical energy carriers, and scenarios. It is shown that eVTOLs can provide a sustainable transportation mode under appropriate circumstances. Sensitivity analyses, case studies, and a novel regression-based conceptual design approach analyze those circumstances and discuss implications of uncertainties.}, + urldate = {2023-10-07}, + school = {Technische Universität München}, + author = {André, Nicolas}, + year = {2022}, +} + +@article{noauthor_reflection_2014, + title = {Reflection of oblique ocean water waves by a vertical porous structure placed on a multi-step impermeable bottom}, + volume = {47}, + issn = {0141-1187}, + url = {https://www.sciencedirect.com/science/article/pii/S0141118714000595}, + doi = {10.1016/j.apor.2014.07.001}, + abstract = {Based on linear water wave theory, wave reflection by a vertical porous structure placed on an elevated impermeable seabed, assumed to consist of a nu…}, + language = {en-US}, + urldate = {2023-10-07}, + journal = {Applied Ocean Research}, + month = aug, + year = {2014}, + note = {Publisher: Elsevier}, + pages = {373--385}, +} + +@article{edwards_optimisation_2022, + title = {Optimisation of the geometry of axisymmetric point-absorber wave energy converters}, + volume = {933}, + issn = {0022-1120, 1469-7645}, + url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/optimisation-of-the-geometry-of-axisymmetric-pointabsorber-wave-energy-converters/EE6FAE12B0F2F9C4DC607C301406411F}, + doi = {10.1017/jfm.2021.993}, + abstract = {, +We propose a scientifically rigorous framework to find realistic optimal geometries of wave energy converters (WECs). For specificity, we assume WECs to be axisymmetric point absorbers in a monochromatic unidirectional incident wave, all within the context of linearised potential theory. We consider separately the problem of a WEC moving and extracting wave energy in heave only and then the more general case of motion and extraction in combined heave, surge and pitch. We describe the axisymmetric geometries using polynomial basis functions, allowing for discontinuities in slope. Our framework involves ensuring maximum power, specifying practical motion constraints and then minimising surface area (as a proxy for cost). The framework is robust and well-posed, and the optimisation produces feasible WEC geometries. Using the proposed framework, we develop a systematic computational and theoretical approach, and we obtain results and insights for the optimal WEC geometries. The optimisation process is sped up significantly by a new theoretical result to obtain roots of the heave resonance equation. For both the heave-only, and the heave-surge-pitch combined problems, we find that geometries which protrude outward below the waterline are generally optimal. These optimal geometries have up to 73 \% less surface area and 90 \% less volume than the optimal cylinders which extract the same power.}, + language = {en}, + urldate = {2023-10-07}, + journal = {Journal of Fluid Mechanics}, + author = {Edwards, Emma C. and Yue, Dick K.-P.}, + month = feb, + year = {2022}, + note = {Publisher: Cambridge University Press}, + keywords = {surface gravity waves, wave–structure interactions}, + pages = {A1}, +} + +@article{garrett_bottomless_1970, + title = {Bottomless harbours}, + volume = {43}, + issn = {1469-7645, 0022-1120}, + url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/bottomless-harbours/37CE36DBABFD3726B04474AD6039E96F}, + doi = {10.1017/S0022112070002495}, + abstract = {Does the harbour of an artificial island need a bottom? The excitation of waves inside a partially immersed open circular cylinder is considered. An incident plane wave is expanded in Bessel functions and for each mode the problem is formulated in terms of the radial displacement on the cylindrical interface below the cylinder. The solution is obtainable either from an infinite set of simultaneous equations or from an integral equation. It is shown that the phase of the solution is independent of depth and resonances are found at wave-numbers close to those of free oscillations in a cylinder extending to the bottom. If the resonances of the cylinder are made sharper (by increasing the depth of immersion) the peak response of the harbour increases, but the response to a continuous spectrum remains approximately constant. Numerical results are obtained by minimizing the least squares error of a finite number N of simultaneous equations. Convergence is slow, but the error is roughly proportional to 1/N and this is exploited. The solution obtained from a variational formulation using the incoming wave as a trial function is found to give a very good approximation for small wave-numbers, but is increasingly inaccurate for large wave-numbers. Away from resonance the amplitude of the harbour oscillation is less than 10\% of the amplitude of the incoming wave provided the depth of the cylinder is greater than about ¼ wavelength, and it is argued that in practice at the resonant wave-number oscillations excited through the bottom of the harbour will leak out through the entrance before they can reach large amplitudes. In an appendix the excitation of harbour oscillations through the harbour entrance is discussed, and some results of Miles \& Munk (1961) on an alleged harbour paradox are re-interpreted.}, + language = {en}, + number = {3}, + urldate = {2023-10-06}, + journal = {Journal of Fluid Mechanics}, + author = {Garrett, C. J. R.}, + month = sep, + year = {1970}, + note = {Publisher: Cambridge University Press}, + pages = {433--449}, +} + +@article{mavrakos_hydrodynamic_1997, + title = {Hydrodynamic characteristics of floating toroidal bodies}, + volume = {24}, + issn = {0029-8018}, + url = {https://www.sciencedirect.com/science/article/pii/S0029801896000200}, + doi = {10.1016/S0029-8018(96)00020-0}, + abstract = {The paper deals with the linearized exciting wave forces and hydrodynamic coefficients of a toroidal body floating in water of finite depth. For the solution of the diffraction and the radiation problems the flow field around the body is subdivided into ring-shaped fluid regions, in each of which axisymmetric eigenfunction expansions for the velocity potential is made. By implementing Galerkin's method the various potential solutions are matched and numerical results concerning the exciting wave forces and the hydrodynamic coefficients in all modes of motion are obtained.}, + number = {4}, + urldate = {2023-10-04}, + journal = {Ocean Engineering}, + author = {Mavrakos, S. A.}, + month = apr, + year = {1997}, + pages = {381--399}, +} + +@article{garrett_wave_1971, + title = {Wave forces on a circular dock}, + volume = {46}, + issn = {1469-7645, 0022-1120}, + url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/wave-forces-on-a-circular-dock/467202A9E4D8385F6ECFABC253B6EC80}, + doi = {10.1017/S0022112071000430}, + abstract = {The scattering of surface gravity waves by a circular dock is considered in order to determine the horizontal and vertical forces and torque on the dock. An incident plane wave is expanded in Bessel functions, and for each mode the problem is formulated in terms of the potential on the cylindrical surface containing the dock and extending to the bottom. The solution is shown to have phase independent of depth and so may be obtained from an infinite set of real equations, which are solved numerically by Galerkin's method. The convergence of the solution is discussed, and some numerical results are presented.This problem has been investigated previously by Miles \& Gilbert (1968) by a different method, but their work contained errors.}, + language = {en}, + number = {1}, + urldate = {2023-09-28}, + journal = {Journal of Fluid Mechanics}, + author = {Garrett, C. J. R.}, + month = mar, + year = {1971}, + note = {Publisher: Cambridge University Press}, + pages = {129--139}, +} + +@book{chatjigeorgiou_analytical_2018, + address = {Cambridge}, + title = {Analytical {Methods} in {Marine} {Hydrodynamics}}, + isbn = {978-1-107-17969-1}, + url = {https://www.cambridge.org/core/books/analytical-methods-in-marine-hydrodynamics/FA575866CF4838EE370460746C304B55}, + abstract = {The value of analytical solutions relies on the rigorous formulation, and a strong mathematical background. This comprehensive volume unifies the most important geometries, which allow for the development of analytical solutions for hydrodynamic boundary value problems. It offers detailed explanations of the Laplance domain and numerical results associated with such problems, providing deep insight into the theory of hydrodynamics. Extended numerical calculations are provided and discussed, allowing the reader to use them as benchmarks for their own computations and making this an invaluable resource for specialists in in various disciplines, including hydrodynamics, acoustics, optics, electrostatics, and brain imaging.}, + urldate = {2023-09-28}, + publisher = {Cambridge University Press}, + author = {Chatjigeorgiou, Ioannis K.}, + year = {2018}, + doi = {10.1017/9781316838983}, +} + +@inproceedings{chau_inertia_2013-1, + title = {Inertia, {Damping}, and {Wave} {Excitation} of {Heaving} {Coaxial} {Cylinders}}, + url = {https://dx.doi.org/10.1115/OMAE2012-83987}, + doi = {10.1115/OMAE2012-83987}, + abstract = {The method of matched eigenfunction expansions is applied in this paper to obtain the hydrodynamic coefficients of a pair of coaxial cylinders, each of which can have independent movement. The geometry idealizes a device for extracting ocean wave energy in the heave mode. The effects of geometric variations and the interaction between cylinders on the hydrodynamic properties are discussed. Analytical expressions for the low-frequency behavior of the hydrodynamic coefficients are also derived. The wave-exciting force on the bottom surface of either one of the cylinders is derived using the radiation solutions, with a generalized form of the Haskind relation developed for this geometry. The presented results are immediately applicable to examine free motion of coaxial cylinders in a wave field.}, + language = {en}, + urldate = {2023-09-28}, + publisher = {American Society of Mechanical Engineers Digital Collection}, + author = {Chau, Fun Pang and Yeung, Ronald W.}, + month = aug, + year = {2013}, + pages = {803--813}, +} + +@article{yeung_inertia_2010, + title = {Inertia and {Damping} of {Heaving} {Compound} {Cylinders} {Fun}}, + url = {https://www.academia.edu/73219479/Inertia_and_Damping_of_Heaving_Compound_Cylinders_Fun}, + abstract = {for The 25th International Workshop on Water Waves and Floating Bodies, Harbin, China, May 9-13, 2010. Inertia and Damping of Heaving Compound Cylinders Fun Pang Chau∗ and Ronald W. Yeung† Department of Mechanical Engineering University of California}, + language = {en}, + urldate = {2023-09-28}, + author = {Yeung, Ronald W.}, + month = jan, + year = {2010}, +} + +@article{yeung_added_1981, + title = {Added mass and damping of a vertical cylinder in finite-depth waters}, + volume = {3}, + issn = {0141-1187}, + url = {https://www.sciencedirect.com/science/article/pii/0141118781901012}, + doi = {10.1016/0141-1187(81)90101-2}, + abstract = {A comprehensive set of theoretical added masses and wave damping data for a floating circular cylinder in finite-depth water is presented. The hydrodynamic problem is solved by matching eigen functions of the interior and exterior problems. The resulting infinite system is solved directly and found to have excellent truncation characteristics. Added mass and damping are given for heave, sway, and roll motion, as well as coupling coefficients for sway and roll. It is shown that the heave added mass is logarithmic singular and the damping approaches a constant in the low-frequency limit. Transition of the behaviour in finite-depth water to deep water is also discussed.}, + number = {3}, + urldate = {2023-09-28}, + journal = {Applied Ocean Research}, + author = {Yeung, Ronald W.}, + month = jul, + year = {1981}, + pages = {119--133}, +} + +@misc{mccabe_multidisciplinary_2022, + title = {Multidisciplinary {Optimization} to {Reduce} {Cost} and {Power} {Variation} of a {Wave} {Energy} {Converter}}, + copyright = {MIT}, + url = {https://github.com/symbiotic-engineering/MDOcean}, + abstract = {Multidisciplinary Design Optimization (MDO) to optimize an ocean wave energy converter}, + urldate = {2023-09-14}, + author = {McCabe, Rebecca and Murphy, Olivia and Haji, Maha N.}, + year = {2022}, + note = {Series: ["name"={\textgreater}"International Design Engineering Technical Conferences \& Computers and Information in Engineering Conference", "city"={\textgreater}"St. Louis", "region"={\textgreater}"MO", "date-start"={\textgreater}Sun, 14 Aug 2022, "date-end"={\textgreater}Wed, 17 Aug 2022] +original-date: 2021-09-25T03:02:03Z}, +} + +@article{bacelli_control_2011, + series = {18th {IFAC} {World} {Congress}}, + title = {A control system for a self-reacting point absorber wave energy converter subject to constraints}, + volume = {44}, + issn = {1474-6670}, + url = {https://www.sciencedirect.com/science/article/pii/S1474667016454443}, + doi = {10.3182/20110828-6-IT-1002.03694}, + abstract = {The problem of the maximization of the energy produced by a self reacting point absorber subject to motion restriction is addressed. The main objective is to design a control system suitable for real-time implementation. The method presented for the solution of the optimization problem is based on the approximation of the motion of the device and of the force exerted by the power take off unit by means of a linear combination of basis functions. The result is that the optimal control problem is reformulated as a non linear program where the properties of the cost function and of the constraint are affected by the choice of the basis functions. An example is described where the motion and the force are approximated using Fourier series; an optimization algorithm for the solution of the non linear program is also presented. The control system is implemented and simulated using a real sea profile measured by a waverider buoy.}, + number = {1}, + urldate = {2023-09-13}, + journal = {IFAC Proceedings Volumes}, + author = {Bacelli, Giorgio and Ringwood, John V. and Gilloteaux, Jean-Christophe}, + month = jan, + year = {2011}, + pages = {11387--11392}, +} + +@article{fukui_impedance_2021, + title = {Impedance {Control} {Considering} {Velocity} {Saturation} of a {Series} {Elasticity} {System} with a {Motor}}, + volume = {33}, + doi = {10.20965/jrm.2021.p0833}, + abstract = {Human-machine cooperative robots are required to drive their arms with low impedance and high torque. As a compact mechanism that generates a large torque and has low impedance characteristics, the series elastic drive system, in which an elastic element is inserted between the motor and driving unit, has been proposed. In this paper, we propose a method of applying impedance control to a series elasticity system with a torque-compensating motor that uses a torsion bar as an elastic body that enables its use under high loads. The stability of the system was verified via simulation and experiment by considering the allowable speed and maximum torque of the motor. The experimental results from the conventional system and the proposed system were compared. The proposed system was confirmed to be superior to the conventional system in terms of both stability and tracking performance. Consequently, the effectiveness of our proposed system was confirmed.}, + number = {4}, + journal = {Journal of Robotics and Mechatronics}, + author = {Fukui, Ren and Kusakabe, Yasuhito and Ikeura, Ryojun and Hayakawa, Soichiro}, + year = {2021}, + keywords = {human-robot cooperation, impedance control, robot arm, series elasticity system, velocity saturation}, + pages = {833--842}, +} + +@article{flower_describing-function_1980, + title = {Describing-function method for estimating the performance of a dynamic system having nonlinear-power take-off, with application to wave-power conversion}, + volume = {20}, + issn = {0196-8904}, + url = {https://www.sciencedirect.com/science/article/pii/0196890480900175}, + doi = {10.1016/0196-8904(80)90017-5}, + abstract = {This work reports part of a programme aimed at stimulating the use of control engineering methods and techniques in the wave-power arena. Here we use the Describing-Function method to estimate the performance of a dynamical energy-conversion system (a second-order system in this particular case) with nonlinear damping. The Describing-Function is used to model the nonlinearity, and the system is conceptually re-arranged to appear in closed-loop form; this arrangement is particularly convenient for the application of a graphical method of solution. By this means the motion and the mean-rate of energy conversion of the system can be rapidly evaluated. The method is primarily directed towards solving problems of wave-power conversion by nonlinear devices.}, + number = {2}, + urldate = {2023-08-27}, + journal = {Energy Conversion and Management}, + author = {Flower, J. O. and Knott, G. F.}, + month = jan, + year = {1980}, + keywords = {Describing-Function, Nonlinear, Power conversion, Wave-power}, + pages = {127--134}, +} + +@inproceedings{herber_wave_2014, + title = {Wave {Energy} {Extraction} {Maximization} in {Irregular} {Ocean} {Waves} {Using} {Pseudospectral} {Methods}}, + url = {https://dx.doi.org/10.1115/DETC2013-12600}, + doi = {10.1115/DETC2013-12600}, + abstract = {Energy extraction from ocean waves and conversion to electrical energy is a promising form of renewable energy, yet achieving economic viability of wave energy converters (WECs) has proven challenging. In this article, the design of a heaving cylinder WEC will be explored. The optimal plant (i.e. draft and radius) design space with respect to the design’s optimal control (i.e. power take-off trajectory) for maximum energy production is characterized. Irregular waves based on the Bretschneider wave spectrum are considered. The optimization problem was solved using a pseudospectral method, a direct optimal control approach that can incorporate practical design constraints, such as power flow, actuation force, and slamming. The results provide early-stage guidelines for WEC design. Results show the resonance frequency required for optimal energy production with a regular wave is quite different than the resonance frequency found for irregular waves; specifically, it is much higher.}, + language = {en}, + urldate = {2023-08-27}, + publisher = {American Society of Mechanical Engineers Digital Collection}, + author = {Herber, Daniel R. and Allison, James T.}, + month = feb, + year = {2014}, +} + +@article{tom_pseudo-spectral_2017, + title = {Pseudo-spectral control of a novel oscillating surge wave energy converter in regular waves for power optimization including load reduction}, + volume = {137}, + issn = {0029-8018}, + url = {https://www.sciencedirect.com/science/article/pii/S0029801817301403}, + doi = {10.1016/j.oceaneng.2017.03.027}, + abstract = {The aim of this paper is to describe a procedure to maximize the power-to-load ratio of a novel wave energy converter (WEC) that combines an oscillating surge wave energy converter with variable structural components. The control of the power-take-off torque will be on a wave-to-wave timescale, whereas the structure will be controlled statically such that the geometry remains the same throughout the wave period. Linear hydrodynamic theory is used to calculate the upper and lower bounds for the time-averaged absorbed power and surge foundation loads while assuming that the WEC motion remains sinusoidal. Previous work using pseudo-spectral techniques to solve the optimal control problem focused solely on maximizing absorbed energy. This work extends the optimal control problem to include a measure of the surge foundation force in the optimization. The objective function includes two competing terms that force the optimizer to maximize power capture while minimizing structural loads. A penalty weight was included with the surge foundation force that allows control of the optimizer performance based on whether emphasis should be placed on power absorption or load shedding. Results from pseudo-spectral optimal control indicate that a unit reduction in time-averaged power can be accompanied by a greater reduction in surge-foundation force.}, + urldate = {2023-08-27}, + journal = {Ocean Engineering}, + author = {Tom, N. M. and Yu, Y. H. and Wright, A. D. and Lawson, M. J.}, + month = jun, + year = {2017}, + keywords = {Convex optimization, Load shedding, Oscillating surge wave energy converter, Psuedo-spectral control, Variable structures}, + pages = {352--366}, +} + +@misc{mit_energy_initiative_genx_nodate, + title = {{GenX}: a configurable power system capacity expansion model for studying low-carbon energy futures}, + url = {https://github.com/GenXProject/GenX}, + author = {{MIT Energy Initiative} and {Princeton University ZERO lab}}, +} + +@article{sepulveda_design_2021, + title = {The design space for long-duration energy storage in decarbonized power systems}, + volume = {6}, + copyright = {2021 The Author(s), under exclusive licence to Springer Nature Limited}, + issn = {2058-7546}, + url = {https://www.nature.com/articles/s41560-021-00796-8}, + doi = {10.1038/s41560-021-00796-8}, + abstract = {Long-duration energy storage (LDES) is a potential solution to intermittency in renewable energy generation. In this study we have evaluated the role of LDES in decarbonized electricity systems and identified the cost and efficiency performance necessary for LDES to substantially reduce electricity costs and displace firm low-carbon generation. Our findings show that energy storage capacity cost and discharge efficiency are the most important performance parameters. Charge/discharge capacity cost and charge efficiency play secondary roles. Energy capacity costs must be ≤US\$20 kWh–1 to reduce electricity costs by ≥10\%. With current electricity demand profiles, energy capacity costs must be ≤US\$1 kWh–1 to fully displace all modelled firm low-carbon generation technologies. Electrification of end uses in a northern latitude context makes full displacement of firm generation more challenging and requires performance combinations unlikely to be feasible with known LDES technologies. Finally, LDES systems with the greatest impact on electricity cost and firm generation have storage durations exceeding 100 h.}, + language = {en}, + number = {5}, + urldate = {2023-05-22}, + journal = {Nature Energy}, + author = {Sepulveda, Nestor A. and Jenkins, Jesse D. and Edington, Aurora and Mallapragada, Dharik S. and Lester, Richard K.}, + month = may, + year = {2021}, + note = {Number: 5 +Publisher: Nature Publishing Group}, + keywords = {Climate-change mitigation, Energy and society, Energy economics, Energy policy, Energy science and technology}, + pages = {506--516}, +} + +@article{schwartz_value_2023, + title = {The value of fusion energy to a decarbonized {United} {States} electric grid}, + volume = {7}, + issn = {2542-4785, 2542-4351}, + url = {https://www.cell.com/joule/abstract/S2542-4351(23)00075-2}, + doi = {10.1016/j.joule.2023.02.006}, + language = {English}, + number = {4}, + urldate = {2023-05-22}, + journal = {Joule}, + author = {Schwartz, Jacob A. and Ricks, Wilson and Kolemen, Egemen and Jenkins, Jesse D.}, + month = apr, + year = {2023}, + note = {Publisher: Elsevier}, + keywords = {capacity expansion, macro-energy systems, nuclear fusion, technology assessment, tokamaks}, + pages = {675--699}, +} + +@inproceedings{mccabe_system_2023, + address = {Boston, MA, USA}, + title = {System {Level} {Techno}-{Economic} and {Environmental} {Design} {Optimization} for {Ocean} {Wave} {Energy}}, + author = {McCabe, Rebecca and Dietrich, Madison and Liu, Alan and Haji, Maha}, + month = aug, + year = {2023}, +} + +@article{gray_openmdao_2019, + title = {{OpenMDAO}: an open-source framework for multidisciplinary design, analysis, and optimization}, + volume = {59}, + issn = {1615-1488}, + shorttitle = {{OpenMDAO}}, + url = {https://doi.org/10.1007/s00158-019-02211-z}, + doi = {10.1007/s00158-019-02211-z}, + abstract = {Multidisciplinary design optimization (MDO) is concerned with solving design problems involving coupled numerical models of complex engineering systems. While various MDO software frameworks exist, none of them take full advantage of state-of-the-art algorithms to solve coupled models efficiently. Furthermore, there is a need to facilitate the computation of the derivatives of these coupled models for use with gradient-based optimization algorithms to enable design with respect to large numbers of variables. In this paper, we present the theory and architecture of OpenMDAO, an open-source MDO framework that uses Newton-type algorithms to solve coupled systems and exploits problem structure through new hierarchical strategies to achieve high computational efficiency. OpenMDAO also provides a framework for computing coupled derivatives efficiently and in a way that exploits problem sparsity. We demonstrate the framework’s efficiency by benchmarking scalable test problems. We also summarize a number of OpenMDAO applications previously reported in the literature, which include trajectory optimization, wing design, and structural topology optimization, demonstrating that the framework is effective in both coupling existing models and developing new multidisciplinary models from the ground up. Given the potential of the OpenMDAO framework, we expect the number of users and developers to continue growing, enabling even more diverse applications in engineering analysis and design.}, + language = {en}, + number = {4}, + urldate = {2023-03-01}, + journal = {Structural and Multidisciplinary Optimization}, + author = {Gray, Justin and Hwang, John and Martins, Joaquim and Moore, Kenneth and Naylor, Bret}, + year = {2019}, + pages = {1075--1104}, +} + +@techreport{bhatnagar_grid_2021, + address = {Richland, WA (United States)}, + title = {Grid {Value} {Proposition} of {Marine} {Energy}}, + url = {https://www.osti.gov/biblio/1833512}, + abstract = {Marine energy technologies convert the energy of ocean waves, and tidal, river, and ocean currents into electricity and other forms of usable energy. The marine energy resource potential in the United States is significant and geographically diverse, with a study commissioned by the U.S. Department of Energy estimating that the nation’s annual marine energy potential is approximately 2,300 TWh/year across the 50 states, or greater than 57 percent of U.S. electricity generation in 2019. However, the marine energy industry still faces hurdles to commercialization. While high costs relative to wind and solar remain a key challenge, other hurdles relate to marine energy’s value streams not being well characterized and not captured by traditional energy comparison metrics like the levelized cost of energy. To address this challenge, this project undertakes several types of analyses to identify and illustrate value propositions for marine energy resources. It provides a fresh framework for considering electric system benefits based on unique marine energy attributes, and provides analyses illustrating and quantifying those benefits. The authors find many opportunities for the deployment of marine energy technologies both in the near term and within typical utility planning timeframes (i.e. up to 20 years). From a resource and technology perspective, marine energy resources can deliver distinct and valuable benefits to different configurations of the grid, whether the bulk system, isolated distribution systems, or remote communities, islands, and microgrids. Marine energy resources can be valuable in increasing technology diversity in a generation portfolio, providing energy where it is otherwise difficult to come by, supporting local resiliency, complementing and being complemented by other resources including solar, wind, and energy storage, and avoiding land constraints.}, + language = {English}, + number = {PNNL-31123}, + urldate = {2023-03-07}, + institution = {Pacific Northwest National Lab}, + author = {Bhatnagar, Dhruv and Bhattacharya, Saptarshi and Preziuso, Danielle and Hanif, Sarmad and O'Neil, Rebecca and Alam, Md and Chalishazar, Vishvas and Newman, Sarah and Lessick, Jennifer and Medina, Gabriel Garcia and Douville, Travis and Robertson, Bryson and Busch, Jason and Kilcher, Levi and Yu, Y}, + year = {2021}, + doi = {10.2172/1833512}, +} + +@techreport{previsic_future_2012, + title = {The {Future} {Potential} of {Wave} {Power} in the {United} {States}}, + abstract = {The theoretical ocean wave energy resource potential exceeds 50\% of the annual domestic energy demand of the United States, is located close to coastal population centers, and, although variable in nature, may be more consistent and predictable than some other renewable generation technologies. As a renewable electricity generation technology, ocean wave energy offers a low air pollutant option for diversifying the +U.S. electricity generation portfolio. Furthermore, the output characteristics of these technologies may complement other renewable technologies. + +This study addresses the following: +(1) The theoretical, technical and practical potential for electricity generation from wave energy +(2) The present lifecycle cost profile (Capex, Opex, and Cost of Electricity) of wave energy conversion +technology at a reference site in Northern California at different plant scales +(3) Cost of electricity variations as a function of deployment site, considering technical, geo-spatial and +and electric grid constraints +(4) Technology cost reduction pathways +(5) Cost reduction targets at which the technology will see significant deployment within US markets, explored through a series of deployment scenarios}, + author = {Previsic, Mirko and Eppler, Jeff and Hand, Mohammed and Heimiller, Donna and Short, Walter and Eurek, Kelly}, + month = aug, + year = {2012}, + doi = {10.13140/RG.2.2.24238.05444}, +} + +@inproceedings{coe_minimizing_2022, + title = {Minimizing {Cost} in a 100\% {Renewable} {Electricity} {Grid}: {A} {Case} {Study} of {Wave} {Energy} in {California}}, + shorttitle = {Minimizing {Cost} in a 100\% {Renewable} {Electricity} {Grid}}, + url = {https://asmedigitalcollection.asme.org/OMAE/proceedings-abstract/OMAE2022/85932/1148047}, + doi = {10.1115/OMAE2022-80731}, + abstract = {Abstract. Wave energy converters have yet to reach broad market viability. Traditionally, levelized cost of energy has been considered the ultimate stage gate through which wave energy developers must pass in order to find success (i.e., the levelized cost of wave energy must be less than that of solar and wind). However, real world energy decisions are not based solely on levelized cost of energy. In this study, we consider the energy mix in California in the year 2045, upon which the state plans to achieve zero carbon energy production. By considering temporal electricity production and consumption, we are able to perform a more informed analysis of the decision process to address this challenge. The results show that, due to high level of ocean wave energy in the winter months, wave energy provides a valuable complement to solar and wind, which have higher production in the summer. Thus, based on this complementary temporal aspect, wave energy appears cost-effective, even when the cost of installation and maintenance is twice that of solar and wind.}, + language = {en}, + urldate = {2023-03-01}, + publisher = {American Society of Mechanical Engineers Digital Collection}, + author = {Coe, Ryan and Lavidas, George and Bacelli, Giorgio and Kobos, Peter and Neary, Vincent}, + month = oct, + year = {2022}, +} + +@incollection{roy_mixed_nodate, + title = {A {Mixed} {Integer} {Efficient} {Global} {Optimization} {Algorithm} with {Multiple} {Infill} {Strategy} - {Applied} to a {Wing} {Topology} {Optimization} {Problem}}, + urldate = {2023-03-13}, + booktitle = {{AIAA} {Scitech} 2019 {Forum}}, + publisher = {American Institute of Aeronautics and Astronautics}, + author = {Roy, Satadru and Crossley, William and Stanford, Bret and Moore, Kenneth and Gray, Justin}, +} + +@article{sobieszczanski-sobieski_multidisciplinary_1997, + title = {Multidisciplinary aerospace design optimization: survey of recent developments}, + volume = {14}, + issn = {1615-1488}, + shorttitle = {Multidisciplinary aerospace design optimization}, + url = {https://doi.org/10.1007/BF01197554}, + doi = {10.1007/BF01197554}, + abstract = {The increasing complexity of engineering systems has sparked rising interest in multidisciplinary optimization (MDO). This paper surveys recent publications in the field of aerospace, in which the interest in MDO has been particularly intense. The primary c hallenges in MDO are computational expense and organizational complexity. Accordingly, this survey focuses on various methods used by different researchers to address these challenges. The survey is organized by a breakdown of MDO into its conceptual components, reflected in sections on mathematical modelling, approximation concepts, optimization procedures, system sensitivity, and human interface. Because the authors' primary area of expertise is in the structures discipline, the majority of the references focus on the interaction of this discipline with others. In particular, two sections at the end of this review focus on two interactions that have recently been pursued with vigour: the simultaneous optimization of structures and aerodynamics and the simultaneous optimization of structures with active control.}, + language = {en}, + number = {1}, + urldate = {2021-10-20}, + journal = {Structural optimization}, + author = {Sobieszczanski-Sobieski, J. and Haftka, R.}, + month = aug, + year = {1997}, + pages = {1--23}, +} + +@techreport{kilcher_marine_2021, + title = {Marine {Energy} in the {United} {States}: {An} {Overview} of {Opportunities}}, + shorttitle = {Marine {Energy} in the {United} {States}}, + url = {https://www.osti.gov/servlets/purl/1766861/}, + language = {en}, + number = {NREL/TP-5700-78773}, + urldate = {2021-10-19}, + institution = {NREL}, + author = {Kilcher, Levi and Fogarty, Michelle and Lawson, Michael}, + month = feb, + year = {2021}, + doi = {10.2172/1766861}, +} + +@book{sterman_business_2000, + title = {Business {Dynamics}: {Systems} {Thinking} and {Modeling} for a {Complex} {World}}, + isbn = {978-0-07-231135-8}, + shorttitle = {Business {Dynamics}}, + abstract = {Today's leading authority on the subject of this text is the author, MIT Standish Professor of Management and Director of the System Dynamics Group, John D. Sterman. Sterman's objective is to explain, in a true textbook format, what system dynamics is, and how it can be successfully applied to solve business and organizational problems. System dynamics is both a currently utilized approach to organizational problem solving at the professional level, and a field of study in business, engineering, and social and physical sciences.}, + language = {en}, + publisher = {Irwin/McGraw-Hill}, + author = {Sterman, John}, + year = {2000}, +} + +@article{ricks_value_2022, + title = {The value of in-reservoir energy storage for flexible dispatch of geothermal power}, + volume = {313}, + issn = {0306-2619}, + url = {https://www.sciencedirect.com/science/article/pii/S0306261922002537}, + doi = {10.1016/j.apenergy.2022.118807}, + abstract = {Geothermal systems making use of advanced drilling and well stimulation techniques have the potential to provide tens to hundreds of gigawatts of clean electricity generation in the United States by 2050. With near-zero variable costs, geothermal plants have traditionally been envisioned as providing “baseload” power, generating at their maximum rated output at all times. However, as variable renewable energy sources (VREs) see greater deployment in energy markets, baseload power is becoming increasingly less competitive relative to flexible, dispatchable generation and energy storage. Herein we conduct an analysis of the potential for future geothermal plants to provide both of these services, taking advantage of the natural properties of confined, engineered geothermal reservoirs to store energy in the form of accumulated, pressurized geofluid and provide flexible load-following generation. We develop a linear optimization model based on multi-physics reservoir simulations that captures the transient pressure and flow behaviors within a confined, engineered geothermal reservoir. We then optimize the investment decisions and hourly operations of a power plant exploiting such a reservoir against a set of historical and modeled future electricity price series. We find that operational flexibility and in-reservoir energy storage can significantly enhance the value of geothermal plants in markets with high VRE penetration, with energy value improvements of up to 60\% relative to conventional baseload plants operating under identical conditions. Across a range of realistic subsurface and operational conditions, our modeling demonstrates that confined, engineered geothermal reservoirs can provide large and effectively free energy storage capacity, with round-trip storage efficiencies comparable to those of leading grid-scale energy storage technologies. Optimized operational strategies indicate that flexible geothermal plants can provide both short- and long-duration energy storage, prioritizing output during periods of high electricity prices. Sensitivity analysis assesses the variation in outcomes across a range of subsurface conditions and cost scenarios.}, + language = {en}, + urldate = {2023-05-15}, + journal = {Applied Energy}, + author = {Ricks, Wilson and Norbeck, Jack and Jenkins, Jesse}, + month = may, + year = {2022}, + keywords = {EGS, Flexibility, Geothermal, Solar, Storage, Wind}, + pages = {118807}, +} + +@article{lopez-garza_fuzzy_2022, + title = {Fuzzy {Logic} and {Linear} {Programming}-{Based} {Power} {Grid}-{Enhanced} {Economical} {Dispatch} for {Sustainable} and {Stable} {Grid} {Operation} in {Eastern} {Mexico}}, + volume = {15}, + copyright = {http://creativecommons.org/licenses/by/3.0/}, + issn = {1996-1073}, + url = {https://www.mdpi.com/1996-1073/15/11/4069}, + doi = {10.3390/en15114069}, + abstract = {Sustainable, stable, and cost-optimized operation of power grids must be the main objectives of power grid operators and electric utilities. The energy transition towards a preponderant green energy economy requires innovative solutions to enhance the power grid economic dispatches looking for a better allocation of the energy demand among the diverse renewable and fossil fuel energy plants. Green renewable energy systems must be preferred over fossil fuel generators when they are available. However, fossil plants are still required to be kept operational due to the variability and uncertainty of renewable energy plants. This study proposes a hybrid rational economic dispatch model that combines a cost minimization linear model enhanced with a fuzzy logic system for decision-making on wind and hydropower minimum and maximum generation levels. The model considers the intermittency of wind energy and recognizes the strategic value of hydropower as energy storage. The results of the model with real data taken from wind, hydroelectric, geothermal, nuclear, bioenergy, and fossil fuel power plants in the eastern region of Mexico show that a fairer, rational, and cost-optimized power grid economic dispatch can be achieved with the proposed approach.}, + language = {en}, + number = {11}, + urldate = {2023-03-27}, + journal = {Energies}, + author = {López-Garza, Esmeralda and Domínguez-Cruz, René Fernando and Martell-Chávez, Fernando and Salgado-Tránsito, Iván}, + month = jan, + year = {2022}, + note = {Number: 11 +Publisher: Multidisciplinary Digital Publishing Institute}, + keywords = {economic dispatch, optimization of generation grids, reliability power grid}, + pages = {4069}, +} + +@techreport{united_nations_transforming_2015, + title = {Transforming our {World}: {The} 2030 {Agenda} for {Sustainable} {Development}}, + url = {https://sdgs.un.org/publications/transforming-our-world-2030-agenda-sustainable-development-17981}, + number = {A/RES/70/1}, + urldate = {2023-03-25}, + institution = {United Nations Department of Economic and Social Affairs}, + author = {{United Nations}}, + year = {2015}, +} + +@article{wu_dynamic_2014, + title = {Dynamic economic dispatch of a microgrid: {Mathematical} models and solution algorithm}, + volume = {63}, + issn = {0142-0615}, + shorttitle = {Dynamic economic dispatch of a microgrid}, + url = {https://www.sciencedirect.com/science/article/pii/S0142061514003482}, + doi = {10.1016/j.ijepes.2014.06.002}, + abstract = {Dynamic economic dispatch of a microgrid is better suited to the requirements of a system in actual operation because it not only considers the lowest cost in a scheduling cycle but also coordinates between different distribution generations (DGs) over many periods. So it is very significant to research the dynamic economic dispatch of a microgrid. Since wind energy and solar energy are subject to random variations and intervals, there is great difficulty in solving the dynamic economic dispatch. In this paper, we establish a combined heat and power (CHP) microgrid system which includes wind turbines (WT), photovoltaic arrays (PV), diesel engines (DE), a micro-turbine (MT), a fuel cell (FC) and a battery (BS). Comprehensively considering the operation cost and the pollutant treatment cost of the microgrid system, we choose the maximum comprehensive benefits as the objective function for the dynamic economic dispatch. At the same time, we establish the spinning reserve probability constraints of the microgrid considering the influence of uncertainty factors such as the fluctuation of the renewable energy, load fluctuation error, and fault shutdown of the unit. Also researched are four different operation scheduling strategies under grid-connected mode and island mode of the microgrid. An improved particle swarm optimization (PSO) algorithm combined with Monte Carlo simulation is used to solve the objective function. With the example system, the proposed models and improved algorithm are verified. When the microgrid is running under the grid-connected mode, we discuss the influence of different scheduling strategies, optimization goals and reliability indexes on the dynamic economic dispatch. And when the microgrid is running under the island mode, we discuss the influence of the uncertainty factors and the capacityof the battery on the dynamic economic dispatch. The presented research can provide some reference for dynamic economic dispatch of microgrid on making full use of renewable energy and improving the microgrid system reliability.}, + language = {en}, + urldate = {2023-03-16}, + journal = {International Journal of Electrical Power \& Energy Systems}, + author = {Wu, Hongbin and Liu, Xingyue and Ding, Ming}, + month = dec, + year = {2014}, + keywords = {Dynamic economic dispatch, Improved particle swarm optimization, Microgrid, Monte Carlo simulation, Operation scheduling strategies, Uncertainty}, + pages = {336--346}, +} + +@techreport{yang_reliability_2020, + type = {Deliverable}, + title = {Reliability, {Availability}, {Maintainability} and {Survivability} {Assessment} {Tool} – {Alpha} version}, + url = {https://www.dtoceanplus.eu/content/download/5623/file/DTOceanPlus_D6.3_Systems%20RAMS%20Tools_alpha_AAU_20200430_v1.0.pdf}, + number = {D6.3}, + institution = {Aalborg University}, + author = {Yang, Yi and Nambiar, Amup and Luxcey, Neil and Fonseca, Francisco and Amaral, Luis}, + month = apr, + year = {2020}, +} + +@techreport{correia_da_fonseca_system_2019, + type = {Deliverable}, + title = {System {Lifetime} {Costs} {Tools} - alpha version}, + url = {https://www.dtoceanplus.eu/content/download/4457/file/DTOceanPlus_D6.4_System_Lifetime_Costs_WavEC_20191219_v1.0.pdf%20citation%20link%20for%20dtoceanslc}, + number = {D6.4}, + institution = {WavEC}, + author = {Correia da Fonseca, F. X. and Amaral, Luis and González Armayor, Amorina and Cândido, José and Arede, Filipe and Henderson, Jillian and Hudson, Ben and Nava, Vincenzo and Tunga, Ines and Petrov, Alexey}, + month = dec, + year = {2019}, +} + +@article{pan_technological_2007, + series = {Sustainability and {Cost}-{Benefit} {Analysis}}, + title = {Technological change in energy systems: {Learning} curves, logistic curves and input–output coefficients}, + volume = {63}, + issn = {0921-8009}, + shorttitle = {Technological change in energy systems}, + url = {https://www.sciencedirect.com/science/article/pii/S0921800907000912}, + doi = {10.1016/j.ecolecon.2007.01.013}, + abstract = {Learning curves have recently been widely adopted in climate-economy models to incorporate endogenous change of energy technologies, replacing the conventional assumption of an autonomous energy efficiency improvement. However, there has been little consideration of the credibility of the learning curve. The current trend that many important energy and climate change policy analyses rely on the learning curve means that it is of great importance to critically examine the basis for learning curves. Here, we analyse the use of learning curves in energy technology, usually implemented as a simple power function. We find that the learning curve cannot separate the effects of price and technological change, cannot reflect continuous and qualitative change of both conventional and emerging energy technologies, cannot help to determine the time paths of technological investment, and misses the central role of R\&D activity in driving technological change. We argue that a logistic curve of improving performance modified to include R\&D activity as a driving variable can better describe the cost reductions in energy technologies. Furthermore, we demonstrate that the top-down Leontief technology can incorporate the bottom-up technologies that improve along either the learning curve or the logistic curve, through changing input–output coefficients. An application to UK wind power illustrates that the logistic curve fits the observed data better and implies greater potential for cost reduction than the learning curve does.}, + language = {en}, + number = {4}, + urldate = {2023-03-14}, + journal = {Ecological Economics}, + author = {Pan, Haoran and Köhler, Jonathan}, + month = sep, + year = {2007}, + keywords = {Input–output coefficients, Learning curve, Logistic curve, Technological change, UK wind power}, + pages = {749--758}, +} + +@book{simpson_product_2006, + address = {New York, NY}, + title = {Product {Platform} and {Product} {Family} {Design}}, + isbn = {978-0-387-25721-1 978-0-387-29197-0}, + url = {http://link.springer.com/10.1007/0-387-29197-0}, + language = {en}, + urldate = {2023-03-13}, + publisher = {Springer US}, + editor = {Simpson, Timothy W. and Siddique, Zahed and Jiao, Jianxin Roger}, + year = {2006}, + doi = {10.1007/0-387-29197-0}, + keywords = {architecture, capacity, design, development, innovation, management, manufacturing, mass customization, platform design, product design, product development, product family design, production, pruduction efficiency, technology roadmap}, +} + +@techreport{noauthor_system_2023, + title = {The system benefits of ocean energy to {European} power systems}, + url = {https://evolveenergy.eu/wp-content/uploads/2023/01/EVOLVE-technical-note-The-system-benefits-of-ocean-energy-to-European-power-systems.pdf}, + institution = {EVOLVE Consortium}, + month = jan, + year = {2023}, +} + +@book{crawley_system_2016, + title = {System {Architecture}: {Strategy} and {Product} {Development} for {Complex} {Systems}}, + isbn = {978-0-13-397534-5}, + shorttitle = {System {Architecture}}, + abstract = {For courses in engineering and technical management Architecture and Function of Complex Systems System architecture is the study of early decision making in complex systems. This text teaches how to capture experience and analysis about early system decisions, and how to choose architectures that meet stakeholder needs, integrate easily, and evolve flexibly. With case studies written by leading practitioners, from hybrid cars to communications networks to aircraft, this text showcases the science and art of system architecture.}, + language = {en}, + publisher = {Pearson}, + author = {Crawley, Edward and Cameron, Bruce and Selva, Daniel}, + year = {2016}, + note = {Google-Books-ID: 67TuoQEACAAJ}, +} + +@techreport{costello_wavesparc_2019, + title = {{WaveSPARC}: {Evaluation} of {Innovation} {Techniques} for {Wave} {Energy}.}, + shorttitle = {{WaveSPARC}}, + url = {https://www.osti.gov/biblio/1641798}, + abstract = {Abstract not provided.}, + language = {English}, + number = {SAND2019-10104C}, + urldate = {2023-03-07}, + institution = {Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)}, + author = {Costello, Ronan and Nielsen, Kim and Weber, Jochem and Tom, Nate and Roberts, Jesse D.}, + month = aug, + year = {2019}, +} + +@inproceedings{trueworthy_set-based_2019, + address = {Naples, Italy}, + title = {A {Set}-{Based} {Design} approach for the design of high-performance wave energy converters}, + abstract = {The objective of this paper is to introduce an approach for designing wave energy converters (WECs) that can be implemented early during the conceptual design phase, enabling downstream convergence on higher performance concepts. Currently, WEC concepts span a wide design space which includes a high number of functionally dissimilar devices. The concept-agnostic assessment of WEC techno-economic performance, the Technology Performance Level (TPL) metric [1], provides designers with a set of customer requirements upon which devices can be assessed. Those requirements were translated to functional requirements using a systems engineering approach [2]. Despite the framework that TPL and the functional requirements provide, WEC designers have limited guidance in approach to conceptual design. This often results in premature commitment to a single functional concept that can limit device performance, even if later-stage design optimization techniques are used [3]. TPL has made significant strides in helping designers understand the requirements of WEC design. This work aims to guide designers toward design processes which can help them meet those requirements. This paper proposes a Set-Based Design approach to WEC conceptual design which could enable the generation of high-performance concepts faster and with less expense. Set-Based Design is a design process in which engineers ideate a large set of potential solutions and work with critical stakeholders to ensure convergence on an optimal concept [4]. The process was chosen specifically due to its ability to directly facilitate design decision making. We tested the design method through a design workshop in which participants were given design requirements and asked to generate WEC concepts. Though the workshop was constrained by time, number of participants, and background of participants, it was a good proof of concept for the applicability of this design methodology and provided insight on how to continue developing WEC design methodologies. SBD is a methodology that can help designers understand and design to the conflicting requirements of WEC design. SBD also allows designers to avoid making decisions based on imprecise information, which may ultimately lead to more efficient generation of +high-performance concepts.}, + author = {Trueworthy, Ali and DuPont, Bryony and Maurer, Benjamin and Cavagnaro, Robert}, + year = {2019}, +} + +@misc{noauthor_ali_nodate, + title = {Ali {TRUEWORTHY} {\textbar} {PhD} {Student} {\textbar} {Oregon} {State} {University}, {Oregon} {\textbar} {OSU} {\textbar} {School} of {Mechanical}, {Industrial} and {Manufacturing} {Engineering} {\textbar} {Research} profile}, + url = {https://www.researchgate.net/profile/Ali-Trueworthy-2}, + abstract = {I work in wave energy from both the engineering and the humanities disciplines. Currently, I am doing work related to WEC design methodologies and the relationships between wave energy and climate change.}, + language = {en}, + urldate = {2023-03-07}, + journal = {ResearchGate}, +} + +@article{bubbar_method_2018, + title = {A method for comparing wave energy converter conceptual designs based on potential power capture}, + volume = {115}, + issn = {0960-1481}, + url = {https://www.sciencedirect.com/science/article/pii/S0960148117308674}, + doi = {10.1016/j.renene.2017.09.005}, + abstract = {The design space for ocean wave energy converters is notable for its divergence. To facilitate convergence, and thereby support commercialization, we present a new simple method for analysis and comparison of alternative device architectures at an early stage of the design process. Using Thévenin's theorem, Falnes crafted an ingenious solution for the monochromatic optimal power capture of heaving point absorber devices by forming a mechanical impedance matching problem between the device and the power take-off. However, his solutions are limited by device architecture complexity. In this paper, we use the mechanical circuit framework to extend Falnes' method to form and solve the impedance matching problem and calculate the optimal power capture for converter architectures of arbitrary complexity. The new technique is first applied to reprove Falnes' findings and then to assess a complex converter architecture, proposed by Korde. This work also provides insight into a master-slave relationship between the geometry and power take-off force control problems that are inherent to converter design, and it reveals a hierarchy of distinct design objectives unbeknownst to Korde for his device. Finally, we show how application of the master-slave principle leads to the reduction in the dimensionality of the associated design space.}, + language = {en}, + urldate = {2023-03-07}, + journal = {Renewable Energy}, + author = {Bubbar, K. and Buckham, B. and Wild, P.}, + month = jan, + year = {2018}, + keywords = {Design convergence, Geometry control, Impedance matching, Mechanical circuits, Optimal PTO force control, Optimal power capture, Thévenin's theorem, WEC canonical form}, + pages = {797--807}, +} + +@book{vogtlander_lca-based_2010, + address = {Oegetgeest, The Netherlands}, + series = {Sustainable {Design} {Series} of {Delft} {University} of {Technology}}, + title = {{LCA}-based assessment of sustainability: the {Eco}-costs/{Value} {Ratio} ({EVR})}, + url = {https://www.ecocostsvalue.com/EVR/img/references%20ecocosts/Book_EVR.pdf}, + publisher = {Sustainability Impact Metrics}, + author = {Vogtlander, Joost G and Baetens, Bianca and Bijma, Arianne and Brandjes, Eduard and Lindeijer, Erwin and Segers, Merel and Witte, Flip and Brezet, J.C. and Hendriks, Ch.F.}, + year = {2010}, +} + +@techreport{araignous_environmental_2020, + type = {Deliverable}, + title = {Environmental and {Social} {Acceptance} {Tools} - alpha version}, + url = {https://www.dtoceanplus.eu/content/download/4813/file/DTOceanPlus_D6.5_ESA_alpha_FEM_20200227_v1.0.pdf}, + number = {D6.5}, + institution = {France Energies Marines}, + author = {Araignous, E and Safi, G}, + month = feb, + year = {2020}, +} + +@article{de_faria_optimizing_2022, + title = {Optimizing offshore renewable portfolios under resource variability}, + volume = {326}, + issn = {0306-2619}, + url = {https://www.sciencedirect.com/science/article/pii/S0306261922012697}, + doi = {10.1016/j.apenergy.2022.120012}, + abstract = {The deployment of offshore wind, wave, and ocean current technologies can be coordinated to provide maximum economic benefit. We develop a model formulation based on Mean-Variance portfolio theory to identify the optimal site locations for a given number of wind, wave, and ocean current turbines subject to constraints on their energy collection system and the maximum number of turbines per site location. A model relaxation is also developed to improve the computational efficiency of the optimization process, allowing the inclusion of more than 5000 candidate generation sites. The model is tested using renewable resource estimates from the coast of North Carolina, along the eastern US coast. Different combinations of technology-specific offshore technologies are compared in terms of their levelized cost of electricity and energy variability. The optimal portfolio results are then included in a capacity expansion model to derive economic targets that make the offshore portfolios cost-competitive with other generating technologies. Results of this work indicate that the integration of different offshore technologies can help to decrease the energy variability associated with marine energy resources. Furthermore, this research shows that substantial cost reductions are still necessary to realize the deployment of these technologies in the region investigated.}, + language = {en}, + urldate = {2023-03-07}, + journal = {Applied Energy}, + author = {de Faria, Victor A. D. and de Queiroz, Anderson R. and DeCarolis, Joseph F.}, + month = nov, + year = {2022}, + keywords = {Energy economics, Energy system planning, Ocean current energy, Offshore renewable energy, Portfolio optimization, Wave energy, Wind energy}, + pages = {120012}, +} + +@article{guerra_value_2020, + title = {The value of seasonal energy storage technologies for the integration of wind and solar power}, + volume = {13}, + issn = {1754-5706}, + url = {https://pubs.rsc.org/en/content/articlelanding/2020/ee/d0ee00771d}, + doi = {10.1039/D0EE00771D}, + abstract = {Energy storage at all timescales, including the seasonal scale, plays a pivotal role in enabling increased penetration levels of wind and solar photovoltaic energy sources in power systems. Grid-integrated seasonal energy storage can reshape seasonal fluctuations of variable and uncertain power generation by reducing energy curtailment, replacing peak generation capacity, and providing transmission benefits. Most current literature focuses on technology cost assessments and does not characterize the potential grid benefits of seasonal storage to capture the most cost-effective solutions. We propose a model-based approach for comprehensive techno-economic assessments of grid-integrated seasonal storage. The approach has two major advantages compared to those presented in the literature. First, we do not make assumptions about the operation of the storage device, including annual cycles, asset utilization or depth of discharge. Rather, a model is used to calculate optimal storage operation profiles. Second, the model-based approach accounts for avoided power system costs, which allows us to estimate the cost effectiveness of different types of storage devices. We assess the cost competitiveness of three specific storage technologies including pumped hydro, compressed air, and hydrogen seasonal storage and explore the conditions (cost, storage duration, and efficiency) that encourage cost competitiveness for seasonal storage technologies. This study considers the Western U.S. power system with 24\% to 61\% of variable renewable power sources on an annual energy basis (up to 83.5\% of renewable energy including hydro, geothermal, and biomass power sources). Our results indicate that for the Western U.S. power system, pumped hydro and compressed air energy storage with 1 day of discharge duration are expected to be cost-competitive in the near future. In contrast, hydrogen storage with up to 1 week of discharge duration could be cost-effective in the near future if power and energy capacity capital costs are equal to or less than ∼US\$1507 kW−1 and ∼US\$1.8 kWh−1 by 2025, respectively. However, based on projected power and energy capacity capital costs for 2050, hydrogen storage with up to 2 weeks of discharge duration is expected to be cost-effective in future power systems. Moreover, storage systems with greater discharge duration could be cost-competitive in the near future if greater renewable penetration levels increase arbitrage or capacity value, significant energy capital cost reductions are achieved, or revenues from additional services and new markets—e.g., reliability and resiliency—are monetized.}, + language = {en}, + number = {7}, + urldate = {2023-03-07}, + journal = {Energy \& Environmental Science}, + author = {Guerra, Omar J. and Zhang, Jiazi and Eichman, Joshua and Denholm, Paul and Kurtz, Jennifer and Hodge, Bri-Mathias}, + month = jul, + year = {2020}, + note = {Publisher: The Royal Society of Chemistry}, + pages = {1909--1922}, +} + +@article{galparsoro_new_2021, + title = {A new framework and tool for ecological risk assessment of wave energy converters projects}, + volume = {151}, + issn = {1364-0321}, + url = {https://www.sciencedirect.com/science/article/pii/S1364032121008170}, + doi = {10.1016/j.rser.2021.111539}, + abstract = {Marine renewable energy has considerable potential for enhancing the diversity of renewable sources, to reduce our reliance on fossil fuels and combat climate change. While the technological development of wave energy converters is progressing rapidly, their environmental impacts are still largely unknown, which is a barrier that could hinder their deployment. This research contributes to the state-of-the-art by introducing a framework for quantifying and analysing the ecological risks of three technologies (oscillating water columns, oscillating wave surge converters, and wave turbines). Based on a literature review, expert consultation process, and the development of a web tool, the potential pressures and the ecosystem elements that might be affected during the life cycle of a generic wave farm (an array of wave energy converters) are investigated. The main pressures are found to be physical disturbance, physical loss, hydrological change, and noise. The ecosystem elements sustaining the largest number of pressures and, therefore, at higher ecological risk are fish and cephalopods species, and benthic and pelagic habitats. The ecological risk assessment framework is operationalized into a free-access web tool (https://aztidata.es/wec-era/) for the interactive assessment and visualisation of the pressures and ecological risks. The tool is intended to be used by managers, decision makers, scientists or promoters during the Strategic Environmental Assessment and Environmental Impact Assessment of wave energy projects. The novel approach presented in this work is more sophisticated than previous risk assessment matrices, enabling to better capture the complexity of the interactions between a wave farm and the environment.}, + language = {en}, + urldate = {2023-03-07}, + journal = {Renewable and Sustainable Energy Reviews}, + author = {Galparsoro, I. and Korta, M. and Subirana, I. and Borja, Á. and Menchaca, I. and Solaun, O. and Muxika, I. and Iglesias, G. and Bald, J.}, + month = nov, + year = {2021}, + keywords = {Blue growth, Decision support tool, Environmental impact, Marine renewable energy, Marine spatial planning, Ocean energy}, + pages = {111539}, +} + +@techreport{mai_competitiveness_2021, + title = {Competitiveness {Metrics} for {Electricity} {System} {Technologies}}, + url = {https://www.osti.gov/biblio/1765599}, + abstract = {The relative economic competitiveness of power generation technologies is a topic of much interest to diverse electric industry participants. However, assessing competitiveness can be challenging as it requires considering both total costs and total system value of each technology, which are complicated by the (1) numerous and diverse grid services needed to operate a reliable power system; (2) variations in the economic value of the grid services with system state and location, and over multiple timescales, due to the challenges of transporting and storing electricity; and (3) the unique characteristics of different electric system assets. Ideally, metrics designed or used to convey technology competitiveness must consider these complexities, but existing metrics often fall short. For example, the levelized cost of energy does not consider the system economic value of the various technologies nor does it consider services beyond electricity production. Various other metrics have been designed with the purpose of more-accurately communicating the economic viability of electric system technologies. In this report, we summarize the primary sources and components of costs and value and review the known competitiveness metrics by presenting their definitions, applications, advantages, and disadvantages. We also introduce a new set of competitiveness metrics, which we refer to as System Profitability metrics, that more-directly applies the economic principles of return-on-investment to electric system technologies. We use conceptual examples to show how the System Profitability metrics better reflect economic viability and relative technology competitiveness compared with existing metrics. We also describe how competitiveness metrics can be quantified using optimization-based models and demonstrate this capability using a U.S. electric sector capacity expansion model.}, + language = {English}, + number = {NREL/TP-6A20-72549}, + urldate = {2023-03-07}, + institution = {National Renewable Energy Lab. (NREL), Golden, CO (United States)}, + author = {Mai, Trieu and Mowers, Matthew and Eurek, Kelly}, + month = feb, + year = {2021}, + doi = {10.2172/1765599}, +} + +@techreport{jenne_powering_2021, + title = {Powering the {Blue} {Economy}: {Economics} of {Marine} {Renewable} {Energy} {Systems}}, + shorttitle = {Powering the {Blue} {Economy}}, + url = {https://www.osti.gov/biblio/1811994}, + abstract = {This presentation, part of the Policy and Innovation Drivers Shaping the Market for Marine Renewable Energy panel of the 2020 Marine Renewable Energy Conference: On and Off the Grid, moderated by Leslie-Ann McGee, Assistant Director of the Consortium for Marine Robotics at the Woods Hole Oceanographic Institution and Program Manager, Cape Cod Blue Economy Foundation, delves into government policies incentivizing technological advances, collaborative models for technology development, market trends, and permitting hurdles. Panelists include: Jennifer Garson, Senior Advisor, U.S. Dept. of Energy Lead for the Powering the Blue Economy Initiative; Henry Jeffrey, Chairman of the Technology Collaboration Programme for Ocean Energy Systems, University of Edinburgh; Alf Carroll, SBIR Blackbelt and Ocean Energy SME, Raytheon Technologies; Walter Schurtenberger, Founder, Hydrokinetic Energy Corp.; and Dale "Scott" Jenne, Engineer, National Renewable Energy Laboratory.}, + language = {English}, + number = {NREL/PR-5700-78328}, + urldate = {2023-03-07}, + institution = {National Renewable Energy Lab. (NREL), Golden, CO (United States)}, + author = {Jenne, Scott}, + month = jul, + year = {2021}, +} + +@techreport{driscoll_methodology_2018, + title = {Methodology to {Calculate} the {ACE} and {HPQ} {Metrics} {Used} in the {Wave} {Energy} {Prize}}, + url = {https://www.osti.gov/biblio/1426063}, + abstract = {The U.S. Department of Energy's Wave Energy Prize Competition encouraged the development of innovative deep-water wave energy conversion technologies that at least doubled device performance above the 2014 state of the art. Because levelized cost of energy (LCOE) metrics are challenging to apply equitably to new technologies where significant uncertainty exists in design and operation, the prize technical team developed a reduced metric as proxy for LCOE, which provides an equitable comparison of low technology readiness level wave energy converter (WEC) concepts. The metric is called 'ACE' which is short for the ratio of the average climate capture width to the characteristic capital expenditure. The methodology and application of the ACE metric used to evaluate the performance of the technologies that competed in the Wave Energy Prize are explained in this report.}, + language = {English}, + number = {NREL/TP-5000-70592}, + urldate = {2023-03-07}, + institution = {National Renewable Energy Lab. (NREL), Golden, CO (United States)}, + author = {Driscoll, Frederick R. and Weber, Jochem W. and Jenne, Dale S. and Thresher, Robert W. and Fingersh, Lee J. and Bull, Dianna and Dallman, Ann and Gunawan, Budi and Ruehl, Kelley and Newborn, David and Quintero, Miguel and LaBonte, Alison and Karwat, Darshan and Beatty, Scott}, + month = mar, + year = {2018}, + doi = {10.2172/1426063}, +} + +@article{sykes_flexible_2022, + title = {A {Flexible}, {Multi}-fidelity {Levelised} {Cost} of {Energy} {Model} for {Floating} {Offshore} {Wind} {Turbines} {Multidisciplinary} {Design}, {Analysis} and {Optimisation} {Approaches}}, + volume = {2265}, + issn = {1742-6596}, + url = {https://dx.doi.org/10.1088/1742-6596/2265/4/042029}, + doi = {10.1088/1742-6596/2265/4/042029}, + abstract = {As the UK takes a step towards a greener, cleaner future aiming to be net zero by 2050, continuous development of the power network is required. A clear solution is offshore wind, having already proved its feasibility and success in nearshore sites. However, a large majority of near shore sites in the UK are already being utilised. The next step is to move into deeper waters and utilise the stronger, more consistent wind resources. A solution could be floating offshore wind which is still in its infancy, with only a few operational floating wind farms installed. Building upon the multidisciplinary design, analysis, and optimisation framework (MDAO) for floating offshore wind turbines (FOWT) being developed at the University of Strathclyde, called FEDORA, the aim of this work is to refine the LCoE model adopted by FEDORA, and applying it to perform the optimisation of the floating offshore OC3 SPAR. There is limited data on cost, therefore Hywind Scotland Pilot Park will be used as a basis for the LCoE model, allowing the results to be validated. This model is not restricted to SPARs, as it establishes a general methodology to calculate the life cycle cost of floating offshore wind farms. Utilising the improved cost model this work finds four optimised SPAR structures for four different maximum angles of inclination which can be experienced in the wind turbines operation. The improved cost model has a much higher accuracy, highlighting the initial cost model underestimates the cost of the SPAR structure by around half.}, + language = {en}, + number = {4}, + urldate = {2023-03-07}, + journal = {Journal of Physics: Conference Series}, + author = {Sykes, V. and Collu, M. and Coraddu, A.}, + month = may, + year = {2022}, + note = {Publisher: IOP Publishing}, + pages = {042029}, +} + +@inproceedings{bilgen_openturbinecode_2022, + address = {University of Delaware, DE}, + title = {{OpenTurbineCoDe} ({OTCD}): {An} {Open}-{Source} {Floating} {Offshore} {Wind} {Turbine} {Multidisciplinary} {Control} {Co}-{Design} {Optimization} {Framework}}, + url = {https://dial.uclouvain.be/pr/boreal/en/object/boreal%3A269524/datastreams}, + urldate = {2023-03-01}, + author = {Bilgen, Onur and Martins, Joaquim R. R. A. and Ning, Andrew and Burlion, Laurent and Platt, Andy and Caprace, Denis–Gabriel and Du, Xianping and Mangano, Marco and Lopez Muro, Juan Francisco and Wright, Cody and Zhang, Kai}, + month = sep, + year = {2022}, +} + +@book{sartori_research_2020, + title = {A {Research} {Framework} for the {Multidisciplinary} {Design} and {Optimization} of {Wind} {Turbines}}, + isbn = {978-1-78984-408-5}, + url = {https://www.intechopen.com/chapters/70217}, + abstract = {The design of very large wind turbines is a complex task which requires the development of dedicated tools and techniques. In this chapter, we present a system-level design procedure based on the combination of multi-body numerical models of the turbine and a multilevel optimization scheme. The overall design aims at the minimization of the cost of energy (COE) through the optimization of all the characteristics of the turbine, and the procedure automatically manages all the simulations required to compute relevant loads and displacements. This unique setup allows the designer to conduct trade-off studies in a highly realistic virtual environment and is an ideal test bench for advanced research studies in which it is important to assess the economic impact of specific design choices. Examples of such studies include the impact of stall-induced vibrations on fatigue, the development of active/passive control laws for large rotors, and the complete definition of 10–20 MW reference turbines.}, + language = {en}, + urldate = {2023-03-07}, + publisher = {IntechOpen}, + author = {Sartori, Luca and Cacciola, Stefano and Croce, Alessandro and Riboldi, Carlo Emanuele Dionigi and Sartori, Luca and Cacciola, Stefano and Croce, Alessandro and Riboldi, Carlo Emanuele Dionigi}, + month = apr, + year = {2020}, + doi = {10.5772/intechopen.90172}, + note = {Publication Title: Design Optimization of Wind Energy Conversion Systems with Applications}, +} + +@article{jasa_effectively_2022, + title = {Effectively using multifidelity optimization for wind turbine design}, + volume = {7}, + issn = {2366-7443}, + url = {https://wes.copernicus.org/articles/7/991/2022/}, + doi = {10.5194/wes-7-991-2022}, + abstract = {Wind turbines are complex multidisciplinary systems that are challenging to design because of the tightly coupled interactions between different subsystems. Computational modeling attempts to resolve these couplings so we can efficiently explore new wind turbine systems early in the design process. Low-fidelity models are computationally efficient but make assumptions and simplifications that limit the accuracy of design studies, whereas high-fidelity models capture more of the actual physics but with increased computational cost. This paper details the use of multifidelity methods for optimizing wind turbine designs by using information from both low- and high-fidelity models to find an optimal solution at reduced cost. Specifically, a trust-region approach is used with a novel corrective function built from a nonlinear surrogate model. We find that for a diverse set of design problems – with examples given in rotor blade geometry design, wind turbine controller design, and wind power plant layout optimization – the multifidelity method finds the optimal design using 38 \%–58 \% of the computational cost of the high-fidelity-only optimization. The success of the multifidelity method in disparate applications suggests that it could be more broadly applied to other wind energy or otherwise generic applications.}, + language = {English}, + number = {3}, + urldate = {2023-03-07}, + journal = {Wind Energy Science}, + author = {Jasa, John and Bortolotti, Pietro and Zalkind, Daniel and Barter, Garrett}, + month = may, + year = {2022}, + note = {Publisher: Copernicus GmbH}, + pages = {991--1006}, +} + +@article{oconnell_review_2023, + title = {A review of geographic information system ({GIS}) and techno economic ({TE}) software tools for renewable energy and methodology to develop a coupled {GIS}-{TE} software tool for marine renewable energy ({MRE})}, + issn = {1475-0902}, + url = {https://doi.org/10.1177/14750902221150050}, + doi = {10.1177/14750902221150050}, + abstract = {Accurate and up-to-date Geographic Information System (GIS) and Techno Economic (TE) tools are pertinent to helping to develop the renewable energy sector. This paper reviews the state of the art in existing GIS and TE tools for renewable energy and proposes a methodology to develop a coupled GIS-TE software tool that is geared specifically to Marine Renewable Energy (MRE) applications and bespoke to Irish and Western UK waters. Methods for approaching GIS and TE analysis within existing tools for renewable energy are presented and compared. Many existing tools of this nature have some interesting functionalities, but most are unsuitable for MRE; are limited by a lack of information on both the technology and the site; and focus solely either on GIS or TE aspects of analysis. Additionally, almost all of those with a TE focus are not open access. The proposed tool aims to incorporate increased resolution and site relevance of resource data; the most up-to-date geospatial data for site selection; and will provide site specific TE indicators and recommendations for contemporary MRE devices. The result will be the development an open-access GIS-TE software tool for MRE.}, + language = {en}, + urldate = {2023-03-07}, + journal = {Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment}, + author = {O’Connell, Ross and Murphy, Jimmy and Devoy McAuliffe, Fiona and Dalton, Gordon}, + month = jan, + year = {2023}, + note = {Publisher: SAGE Publications}, + pages = {14750902221150050}, +} + +@misc{noauthor_exfin_nodate, + title = {Exfin {Software} {\textbar} {Your} {Single} {Source} of {Digital} {Truth}}, + url = {https://exfinsoftware.com/product/}, + abstract = {Exfin financial modelling software for the renewable industry, creates a centralised, single source of digital truth in 4 simple steps.}, + language = {en-US}, + urldate = {2023-03-07}, + journal = {exfinsoftware.com}, +} + +@article{roberts_bringing_2021, + title = {Bringing {Structure} to the {Wave} {Energy} {Innovation} {Process} with the {Development} of a {Techno}-{Economic} {Tool}}, + volume = {14}, + copyright = {http://creativecommons.org/licenses/by/3.0/}, + issn = {1996-1073}, + url = {https://www.mdpi.com/1996-1073/14/24/8201}, + doi = {10.3390/en14248201}, + abstract = {Current wave energy development initiatives assume that available designs have the potential for success through continuous learning and innovation-based cost reduction. However, this may not be the case, and potential winning technologies may have been overlooked. The scenario creation tool presented in this paper provides a structured method for the earliest stages of design in technology development. The core function of the scenario creation tool is to generate and rank scenarios of potential Wave Energy Converter (WEC) attributes and inform the user on the areas of the parameter space that are most likely to yield commercial success. This techno-economic tool uses a structured innovation approach to identify commercially attractive and technically achievable scenarios, with a scoring system based on their power performance and costs. This is done by leveraging performance and cost data from state-of-the-art wave energy converters and identifying theoretical limits to define thresholds. As a result, a list of scored solutions is obtained depending on resource level, wave energy converter hull shape, size, material, degree of freedom for power extraction, and efficiency. This scenario creation tool can be used to support private and public investors to inform strategy for future funding calls, and technology developers and researchers in identifying new avenues of innovation.}, + language = {en}, + number = {24}, + urldate = {2023-03-07}, + journal = {Energies}, + author = {Roberts, Owain and Henderson, Jillian Catherine and Garcia-Teruel, Anna and Noble, Donald R. and Tunga, Inès and Hodges, Jonathan and Jeffrey, Henry and Hurst, Tim}, + month = jan, + year = {2021}, + note = {Number: 24 +Publisher: Multidisciplinary Digital Publishing Institute}, + keywords = {commercial attractiveness, scenario creation, structured innovation, technical achievability, wave energy}, + pages = {8201}, +} + +@article{tunga_addressing_2021, + title = {Addressing {European} {Ocean} {Energy} {Challenge}: {The} {DTOceanPlus} {Structured} {Innovation} {Tool} for {Concept} {Creation} and {Selection}}, + volume = {14}, + copyright = {http://creativecommons.org/licenses/by/3.0/}, + issn = {1996-1073}, + shorttitle = {Addressing {European} {Ocean} {Energy} {Challenge}}, + url = {https://www.mdpi.com/1996-1073/14/18/5988}, + doi = {10.3390/en14185988}, + abstract = {The whole energy system requires renewables that scale and produce reliable, valuable energy at an acceptable cost. The key to increasing the deployment of ocean energy is bringing down development and operating costs. This paper proposes a structured approach to innovation in ocean energy systems that would spur innovation and expand the market for ocean energy. This approach can be used by a wide range of stakeholders—including technology and project developers and investors—when considering creating or improving designs. The Structured Innovation design tool within the DTOceanPlus suite is one of a kind beyond the current state-of-the-art. It enables the adaptation and integration of systematic problem-solving tools based on quality function deployment (QFD), the theory of inventive thinking (TRIZ), and the failure modes and effects analysis (FMEA) methodologies for the ocean energy sector. In obtaining and assessing innovative concepts, the integration of TRIZ into QFD enables the designers to define the innovation problem, identifies trade-offs in the system, and, with TRIZ as a systematic inventive problem-solving methodology, generates potential design concepts for the contradicting requirements. Additionally, the FMEA is used to assess the technical risks associated with the proposed design concepts. The methodology is demonstrated using high-level functional requirements for a small array of ten tidal turbines to improve the devices layout and power cabling architecture. The Structured Innovation design tool output comprises critical functional requirements with the highest overall impact and the least organisational effort to implement, along with appropriate alternative solutions to conflicting requirements.}, + language = {en}, + number = {18}, + urldate = {2023-03-07}, + journal = {Energies}, + author = {Tunga, Inès and Garcia-Teruel, Anna and Noble, Donald R. and Henderson, Jillian}, + month = jan, + year = {2021}, + note = {Number: 18 +Publisher: Multidisciplinary Digital Publishing Institute}, + keywords = {DTOceanPlus, FMEA, fundamental relationships, innovation, ocean energy, quality function deployment, structured innovation tool, theory of inventive problem solving}, + pages = {5988}, +} + +@inproceedings{weber_wec_2012, + title = {{WEC} {Technology} {Readiness} and {Performance} {Matrix} – finding the best research technology development trajectory}, + abstract = {The paper identifies and discusses the need for techno-economic performance improvements at early stages of the wave energy converter (WEC) technology development process. Technology Readiness Levels (TRLs) for wave energy projects provide a valuable metric of technology readiness and deliver useful guidance for the development process. This paper describes the complementary metric of Technology Performance Levels (TPLs) characterised by a set of quantified performance criteria aimed at identifying and classifying the techno-economic performance of wave energy technology. These TPLs are broadly inversely related to cost of energy (CoE) and provide a combined measure for capital expenditure (CapEx), lifecycle operational expenditure (OpEx), energy conversion efficiency and technology availability. Less quantifiable performance aspects such as acceptability and safety are also considered in the definition of the TPLs. +A 2-dimensional representation of technology readiness and performance levels is introduced. This TRL–TPL–Matrix visualisation provides a useful means for the evaluation, comparison and discussion of different research technology development trajectories over the technology readiness and performance levels plane. The paper identifies the need for technology performance trajectories with high technology performance levels at low readiness levels and gives valuable advice on the development strategy and tools required to achieve successful WEC technology development outcome at reduced development time, total development cost and encountered risk.}, + author = {Weber, Jochem}, + month = oct, + year = {2012}, +} + +@inproceedings{noauthor_notitle_nodate, +} + +@article{clark_reliability-based_2018, + title = {Reliability-based design optimization in offshore renewable energy systems}, + volume = {97}, + issn = {1364-0321}, + url = {https://www.sciencedirect.com/science/article/pii/S1364032118306154}, + doi = {10.1016/j.rser.2018.08.030}, + abstract = {Offshore wind farm operations and maintenance costs currently total 6 m€/year, or 25–28\% of total costs. For wave and tidal energy converters, this cost is projected to be twice that of offshore wind, but has high levels of uncertainty. As the wave and tidal energy industries mature, decreasing O\&M costs through reliability-based design optimization is critical to increasing feasibility and competitiveness with other energy technologies. In this paper, we will synthesize existing information on reliability-based optimization in systems analogous to offshore renewable energy systems. We will conclude by highlighting opportunities for future work in this field.}, + language = {en}, + urldate = {2023-03-07}, + journal = {Renewable and Sustainable Energy Reviews}, + author = {Clark, Caitlyn E. and DuPont, Bryony}, + month = dec, + year = {2018}, + keywords = {Offshore renewable energy, Offshore wind energy, Reliability-based design optimization, Tidal energy, Wave energy}, + pages = {390--400}, +} + +@article{macgillivray_innovation_2014, + title = {Innovation and cost reduction for marine renewable energy: {A} learning investment sensitivity analysis}, + volume = {87}, + issn = {0040-1625}, + shorttitle = {Innovation and cost reduction for marine renewable energy}, + url = {https://www.sciencedirect.com/science/article/pii/S0040162513003041}, + doi = {10.1016/j.techfore.2013.11.005}, + abstract = {Using learning curves as an analytical tool for technology forecasting involves making assumptions over a range of key uncertainties, often implicitly. In this paper, we present an explicit treatment of the key uncertainties involved in learning rates' analyses of marine energy innovation (wave and tidal stream) — technology fields attracting considerable interest, but whose commercial prospects depends on substantial learning and cost reduction. Taking a simple single factor learning rate model, we describe a range of plausible learning investments required so that marine energy technologies become cost-competitive with their ‘benchmark’ technology: offshore wind. Our analysis highlights the sensitivity of marine energy to three key parameters: the capital cost of first devices, the level of deployment before sustained cost reduction emerges, and the average rate of cost reduction with deployment (learning rate). Figures often quoted within the marine energy sector for the parameters of starting cost, learning rate, and capacity at which sustained cost reduction occurs (metrics conventionally used for learning rate analysis) can be seen to represent very attractive scenarios. The intention of this paper is to display that even small changes to input assumptions can have a dramatic effect on the overall investment required for a sector to reach parity with benchmark technologies. In the short term, reaching cost competitiveness with offshore wind is a necessity if marine energy is to reach commercialisation. Additionally, an assessment of the plausible total investment (and inherent uncertainties) in a global wave and tidal deployment scenario will be presented. The paper also considers the implications of these uncertainties for marine energy innovation management. While the benchmark against offshore wind will generally be used as a performance indicator, in order to achieve similar and sustained cost reductions to other, more mature, renewable energy technologies (and thus achieve a competitive price for marine technologies, securing their place within the energy mix), the marine energy sector needs a targeted innovation focus to fulfil the desired objectives, and a development pathway very different to offshore wind must be used.}, + language = {en}, + urldate = {2023-03-05}, + journal = {Technological Forecasting and Social Change}, + author = {MacGillivray, Andrew and Jeffrey, Henry and Winskel, Mark and Bryden, Ian}, + month = sep, + year = {2014}, + keywords = {Experience curve, Learning curve, Learning investment, Marine energy, Technology innovation}, + pages = {108--124}, +} + +@article{tassey_standardization_2000, + title = {Standardization in technology-based markets}, + volume = {29}, + issn = {0048-7333}, + url = {https://www.sciencedirect.com/science/article/pii/S0048733399000918}, + doi = {10.1016/S0048-7333(99)00091-8}, + abstract = {The complexity of modern technology, especially its system character, has led to an increase in the number and variety of standards that affect a single industry or market. Standards affect the R\&D, production, and market penetration stages of economic activity and therefore have a significant collective effect on innovation, productivity, and market structure. Standards are classified into product-element and nonproduct categories because the two types arise from different technologies and require different formulation and implementation strategies. Because standards are a form of technical infrastructure, they have considerable public good content. Research policy must therefore include standardization in analyses of technology-based growth issues.}, + language = {en}, + number = {4}, + urldate = {2023-03-05}, + journal = {Research Policy}, + author = {Tassey, Gregory}, + month = apr, + year = {2000}, + keywords = {Economic growth, Industry structure, Innovation, R\&D, Standardization}, + pages = {587--602}, +} + +@article{moni_life_2020, + title = {Life cycle assessment of emerging technologies: {A} review}, + volume = {24}, + copyright = {© 2019 by Yale University}, + issn = {1530-9290}, + shorttitle = {Life cycle assessment of emerging technologies}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/jiec.12965}, + doi = {10.1111/jiec.12965}, + abstract = {In recent literature, prospective application of life cycle assessment (LCA) at low technology readiness levels (TRL) has gained immense interest for its potential to enable development of emerging technologies with improved environmental performances. However, limited data, uncertain functionality, scale up issues and uncertainties make it very challenging for the standard LCA guidelines to evaluate emerging technologies and requires methodological advances in the current LCA framework. In this paper, we review published literature to identify major methodological challenges and key research efforts to resolve these issues with a focus on recent developments in five major areas: cross-study comparability, data availability and quality, scale-up issues, uncertainty and uncertainty communication, and assessment time. We also provide a number of recommendations for future research to support the evaluation of emerging technologies at low technology readiness levels: (a) the development of a consistent framework and reporting methods for LCA of emerging technologies; (b) the integration of other tools with LCA, such as multicriteria decision analysis, risk analysis, technoeconomic analysis; and (c) the development of a data repository for emerging materials, processes, and technologies.}, + language = {en}, + number = {1}, + urldate = {2023-03-04}, + journal = {Journal of Industrial Ecology}, + author = {Moni, Sheikh Moniruzzaman and Mahmud, Roksana and High, Karen and Carbajales-Dale, Michael}, + year = {2020}, + note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/jiec.12965}, + keywords = {emerging technology, ex ante LCA, industrial ecology, life cycle assessment (LCA), technoeconomic analysis (TEA), technology readiness level (TRL)}, + pages = {52--63}, +} + +@article{pennock_life_2022, + title = {Life cycle assessment of a point-absorber wave energy array}, + volume = {190}, + issn = {0960-1481}, + url = {https://www.sciencedirect.com/science/article/pii/S0960148122004712}, + doi = {10.1016/j.renene.2022.04.010}, + abstract = {Wave energy has a large global resource and thus a great potential to contribute to low-carbon energy systems. This study quantifies the environmental impacts of a 10 MW array of 28 point-absorber wave energy converters, by means of a process-based life cycle assessment (LCA). Midpoint and Cumulative Energy Demand LCA results are presented over 19 impact categories, representing impacts encompassing human health, ecosystems and resource availability. Three scenarios are undertaken to represent the use phase of the array, identified as a particularly uncertain input, with very little long-term operation of wave energy arrays available to validate assumptions. The resultant global warming potential of the array ranges from 25.1 to 46.0 gCO2e/kWh over a 95\% confidence interval, 23–43 times lower than conventional fossil fuel electricity generation. The Energy Payback Time of the array ranges between 2.6 and 5.2 years. LCA results are found to be particularly sensitive to annual energy production across all impact categories, and to assumptions associated with the frequency of marine operations over a number of categories quantifying the production of greenhouse gases. This LCA has been undertaken at an early stage in the WEC product development and will inform innovative research focused on further reducing the environmental impacts of electricity generation.}, + language = {en}, + urldate = {2023-03-04}, + journal = {Renewable Energy}, + author = {Pennock, Shona and Vanegas-Cantarero, María M. and Bloise-Thomaz, Tianna and Jeffrey, Henry and Dickson, Matthew J.}, + month = may, + year = {2022}, + keywords = {Carbon footprint, Environmental impact, Life cycle assessment, Operations and maintenance, Wave energy}, + pages = {1078--1088}, +} + +@article{galparsoro_new_2021-1, + title = {A new framework and tool for ecological risk assessment of wave energy converters projects}, + volume = {151}, + issn = {1364-0321}, + url = {https://www.sciencedirect.com/science/article/pii/S1364032121008170}, + doi = {10.1016/j.rser.2021.111539}, + abstract = {Marine renewable energy has considerable potential for enhancing the diversity of renewable sources, to reduce our reliance on fossil fuels and combat climate change. While the technological development of wave energy converters is progressing rapidly, their environmental impacts are still largely unknown, which is a barrier that could hinder their deployment. This research contributes to the state-of-the-art by introducing a framework for quantifying and analysing the ecological risks of three technologies (oscillating water columns, oscillating wave surge converters, and wave turbines). Based on a literature review, expert consultation process, and the development of a web tool, the potential pressures and the ecosystem elements that might be affected during the life cycle of a generic wave farm (an array of wave energy converters) are investigated. The main pressures are found to be physical disturbance, physical loss, hydrological change, and noise. The ecosystem elements sustaining the largest number of pressures and, therefore, at higher ecological risk are fish and cephalopods species, and benthic and pelagic habitats. The ecological risk assessment framework is operationalized into a free-access web tool (https://aztidata.es/wec-era/) for the interactive assessment and visualisation of the pressures and ecological risks. The tool is intended to be used by managers, decision makers, scientists or promoters during the Strategic Environmental Assessment and Environmental Impact Assessment of wave energy projects. The novel approach presented in this work is more sophisticated than previous risk assessment matrices, enabling to better capture the complexity of the interactions between a wave farm and the environment.}, + language = {en}, + urldate = {2023-03-04}, + journal = {Renewable and Sustainable Energy Reviews}, + author = {Galparsoro, I. and Korta, M. and Subirana, I. and Borja, Á. and Menchaca, I. and Solaun, O. and Muxika, I. and Iglesias, G. and Bald, J.}, + month = nov, + year = {2021}, + keywords = {Blue growth, Decision support tool, Environmental impact, Marine renewable energy, Marine spatial planning, Ocean energy}, + pages = {111539}, +} + +@inproceedings{apolonia_developing_2019, + address = {Universitá degli Studi della Campania “Luigi Vanvitelli”, Italy}, + title = {Developing an {Environmental} {Impact} {Assessment} model for nearshore wave energy devices}, + booktitle = {Proceedings of the {Thirteenth} {European} {Wave} and {Tidal} {Energy} {Conference}}, + publisher = {EWTEC}, + author = {Apolonia, Maria and Silva, Ana and Simas, Teresa}, + editor = {Vicinanza, D.}, + month = sep, + year = {2019}, +} + +@article{zhang_optimization_2022, + title = {Optimization of energy-capture performance of point-absorber wave energy converter}, + volume = {46}, + issn = {1099-114X}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/er.7816}, + doi = {10.1002/er.7816}, + abstract = {An optimization process is proposed for improving the energy-harvesting efficiency of the point-absorber wave energy converter (WEC) and thus enhancing the utilization of wave energy resources. The multidisciplinary design optimization integration system ISIGHT is adopted to establish an optimization design flow for the shape parameters of the point-absorber WEC. The motion equations of the point-absorber WEC are established according to the potential flow theory, and the wave energy capture capacity per unit is calculated. Considering it as the objective, the point-absorber WEC is modified to improve the energy-capture efficiency by using an optimization function in an approximation model. A comparison indicates that a cylindrical-bottom point-absorber WEC with a diameter of 7 m, draft of 1.8 m, and damping factor of 31 150 Ns·m−1 has the optimal performance and the maximum energy capture capacity. The energy-capture performance of the WEC can be significantly enhanced through this optimization method.}, + language = {en}, + number = {7}, + urldate = {2023-03-03}, + journal = {International Journal of Energy Research}, + author = {Zhang, Baocheng and Deng, Ziwei and Miao, Yu and Zhao, Bo and Wang, Qiang and Zhang, Kaisheng}, + year = {2022}, + note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/er.7816}, + keywords = {hydrodynamic, optimization design, parameterization, point absorber, wave energy}, + pages = {9444--9455}, +} + +@article{herber_dynamic_2014, + title = {Dynamic system design optimization of wave energy converters utilizing direct transcription}, + copyright = {Copyright 2014 Daniel Ronald Herber}, + url = {https://hdl.handle.net/2142/49463}, + abstract = {Dynamics are playing an increasingly important role in many engineering +domains as these systems become more active and autonomous. Designing +a dynamic engineering system can be challenging. In this thesis, both the problem formulation and solution methods will be discussed for designing a dynamic engineering system. A case is made for the inclusion of both the physical and control system design into a single design formulation. A particular class of numerical methods known as direct transcription is identified as promising solution method. These principles are then demonstrated on the design of a wave energy converter, a device that captures energy present in ocean waves. This system is of particular interest since a successful design hinges on exploiting the natural dynamics of the interaction between the ocean waves and the physical wave energy converter. A number of numerical studies are presented that identify both novel and previously observed strategies for the maximizing energy production of a ocean wave energy converter.}, + urldate = {2023-03-03}, + author = {Herber, Daniel Ronald}, + month = may, + year = {2014}, +} + +@inproceedings{caio_tackling_2019, + title = {Tackling the {Wave} {Energy} {Paradox} - {Stepping} {Towards} {Commercial} {Deployment}}, + url = {https://onepetro.org/ISOPEIOPEC/proceedings-abstract/ISOPE19/All-ISOPE19/21575}, + abstract = {ABSTRACT. For the wave energy industry, the leap from R\&D to commercial deployment remains considerable and arises as part of the ‘wave energy paradox’, defined here as a negative reinforcement cycle involving a lack of investment, deployment, learning and returns. In this context, we review performance metrics set by funding bodies, industry standards and developers, examining how existing practices can result in sub-optimal design targets due to current specifications and misalignment of metrics between developers and external stakeholders. This paper offers initial insights - via a case study - to demonstrate how the integration of meaningful and aligned metrics throughout the design process represents a key lever in overcoming the paradox.INTRODUCTION. The vast potential of wave energy as a renewable source of power has been advocated for several decades (Isaacs \& Seymour, 1973), (Cruz, 2008). Although nearshore wave energy potential has been estimated to be in the TW range, e.g. (Gunn \& Stock-Williams, 2012), global deployed capacity as of 2017 was lagging at only 8MW (Ocean Energy Systems, 2017). Many observers argue that the shortfall is a result of the failure of wave energy converters (WECs) to converge to a single optimal design, though this can be viewed as both a cause and an effect (see following section). In 2016, O'Hagan et al. highlighted that}, + language = {en}, + urldate = {2023-03-03}, + publisher = {OnePetro}, + author = {Caio, Andrea and Davey, Thomas and McNatt, Cameron}, + month = jun, + year = {2019}, +} + +@misc{noauthor_triton_nodate, + title = {Triton {\textbar} {PNNL}}, + url = {https://www.pnnl.gov/projects/triton}, + urldate = {2023-03-01}, +} + +@article{li_quantitative_2022, + title = {Quantitative sustainable design ({QSD}) for the prioritization of research, development, and deployment of technologies: a tutorial and review}, + volume = {8}, + issn = {2053-1419}, + shorttitle = {Quantitative sustainable design ({QSD}) for the prioritization of research, development, and deployment of technologies}, + url = {https://pubs.rsc.org/en/content/articlelanding/2022/ew/d2ew00431c}, + doi = {10.1039/D2EW00431C}, + abstract = {The pursuit of sustainability has catalyzed broad investment in the research, development, and deployment (RD\&D) of innovative water, sanitation, and resource recovery technologies, yet the lack of transparent and agile methodologies to navigate the expansive landscape of technology development pathways remains a critical challenge. This challenge is further complicated by the higher levels of uncertainty that are intrinsic to early-stage technologies. In this work, we review and synthesize published literature on the sustainability analyses of water and related technologies to present quantitative sustainable design (QSD) – a methodology to expedite and support technology RD\&D. With a shared lexicon and a structured approach, QSD facilitates interdisciplinary communication and research consistency. In introducing QSD, we review existing studies to highlight best practices and discuss them in the context of the specific steps of QSD, which include defining the problem space, establishing simulation algorithms, and characterizing system sustainability across economic, environmental, human health, and social dimensions. Next, we summarize tools for QSD execution and provide recommendations to account for uncertainty in this process. We further discuss applications of QSD in the fields of water/wastewater and beyond (e.g., renewable fuels, circular economy) in combination with uncertainty, sensitivity, and scenario analyses to generate the desired types of insight. Finally, we identify future research needs for sustainability analyses to advance technology RD\&D. Ultimately, QSD can be used to elucidate the complex and intertwined connections among design decisions, technology characteristics, contextual factors, and sustainability indicators, thereby supporting transparent, consistent, and agile RD\&D.}, + language = {en}, + number = {11}, + urldate = {2023-03-01}, + journal = {Environmental Science: Water Research \& Technology}, + author = {Li, Yalin and Trimmer, John T. and Hand, Steven and Zhang, Xinyi and Chambers, Katherine G. and Lohman, Hannah A. C. and Shi, Rui and Byrne, Diana M. and Cook, Sherri M. and Guest, Jeremy S.}, + month = oct, + year = {2022}, + note = {Publisher: The Royal Society of Chemistry}, + pages = {2439--2465}, +} + +@article{mahmud_integration_2021, + title = {Integration of techno-economic analysis and life cycle assessment for sustainable process design – {A} review}, + volume = {317}, + issn = {0959-6526}, + url = {https://www.sciencedirect.com/science/article/pii/S0959652621024641}, + doi = {10.1016/j.jclepro.2021.128247}, + abstract = {For sustainable design, technology developers need to consider not only technical and economic aspects but also potential environmental impacts while developing new technologies. Techno economic analysis (TEA) evaluates the technical performance and economic feasibility of a technology. Life cycle assessment (LCA) evaluates the potential environmental impacts associated with a product system throughout its life cycle from raw material extraction to disposal. Generally, TEA and LCA performed separately for technology assessment. Understanding of the trade-off between economic and environmental performance is crucial for sustainable process design, which is not fully available if TEA and LCA is performed separately. In contrast, integration of TEA and LCA enables systematic analysis of the relationships between technical, economic, and environmental performance and provides more information to technology developers for trade-off analysis. Integrated TEA-LCA tool can also reduce inconsistency between system boundaries, functional units, and assumptions that can arise from using standalone TEA and LCA findings in decision making. There is also growing interest of prospective application of integrated TEA-LCA tool to evaluate emerging technologies at early technology readiness level (TRL). Integration of TEA and LCA is still an evolving area and requires further exploration to develop a consistent methodological guideline. The goal of this study is to review the current state-of-the-art in TEA and LCA to identify the methodological challenges of TEA-LCA integration approaches. This study also identifies major challenges to perform integrated TEA-LCA analysis of emerging technologies at low TRLs. Lack of consistent methodological guidelines and compatible software tools, inconsistent system boundary and functional unit selection, limited data availability and uncertainty are key methodological challenges for integration of LCA and TEA. Future research should focus on developing integrated TEA-LCA tool, formulating approach to incorporate optimization method with integrated TEA-LCA tool, and developing strategy of proper communication of results from integrated LCA-TEA tool to broad range of stakeholders.}, + language = {en}, + urldate = {2023-03-01}, + journal = {Journal of Cleaner Production}, + author = {Mahmud, Roksana and Moni, Sheikh Moniruzzaman and High, Karen and Carbajales-Dale, Michael}, + month = oct, + year = {2021}, + keywords = {Emerging technology, Integration, Life cycle assessment (LCA), Sustainable process design, Techno-economic analysis (TEA), Technology readiness level (TRL)}, + pages = {128247}, +} + +@article{li_quantitative_2022-1, + title = {Quantitative sustainable design ({QSD}) for the prioritization of research, development, and deployment of technologies: a tutorial and review}, + volume = {8}, + issn = {2053-1419}, + shorttitle = {Quantitative sustainable design ({QSD}) for the prioritization of research, development, and deployment of technologies}, + url = {https://pubs.rsc.org/en/content/articlelanding/2022/ew/d2ew00431c}, + doi = {10.1039/D2EW00431C}, + abstract = {The pursuit of sustainability has catalyzed broad investment in the research, development, and deployment (RD\&D) of innovative water, sanitation, and resource recovery technologies, yet the lack of transparent and agile methodologies to navigate the expansive landscape of technology development pathways remains a critical challenge. This challenge is further complicated by the higher levels of uncertainty that are intrinsic to early-stage technologies. In this work, we review and synthesize published literature on the sustainability analyses of water and related technologies to present quantitative sustainable design (QSD) – a methodology to expedite and support technology RD\&D. With a shared lexicon and a structured approach, QSD facilitates interdisciplinary communication and research consistency. In introducing QSD, we review existing studies to highlight best practices and discuss them in the context of the specific steps of QSD, which include defining the problem space, establishing simulation algorithms, and characterizing system sustainability across economic, environmental, human health, and social dimensions. Next, we summarize tools for QSD execution and provide recommendations to account for uncertainty in this process. We further discuss applications of QSD in the fields of water/wastewater and beyond (e.g., renewable fuels, circular economy) in combination with uncertainty, sensitivity, and scenario analyses to generate the desired types of insight. Finally, we identify future research needs for sustainability analyses to advance technology RD\&D. Ultimately, QSD can be used to elucidate the complex and intertwined connections among design decisions, technology characteristics, contextual factors, and sustainability indicators, thereby supporting transparent, consistent, and agile RD\&D.}, + language = {en}, + number = {11}, + urldate = {2023-03-01}, + journal = {Environmental Science: Water Research \& Technology}, + author = {Li, Yalin and Trimmer, John T. and Hand, Steven and Zhang, Xinyi and Chambers, Katherine G. and Lohman, Hannah A. C. and Shi, Rui and Byrne, Diana M. and Cook, Sherri M. and Guest, Jeremy S.}, + month = oct, + year = {2022}, + note = {Publisher: The Royal Society of Chemistry}, + pages = {2439--2465}, +} + +@article{mccabe_constrained_2013, + title = {Constrained optimization of the shape of a wave energy collector by genetic algorithm}, + volume = {51}, + issn = {0960-1481}, + url = {https://www.sciencedirect.com/science/article/pii/S0960148112006258}, + doi = {10.1016/j.renene.2012.09.054}, + abstract = {Wave energy extraction requires the conversion of the energy within the waves to drive the power take off system, often by means of a principal interface, or collector. This paper describes part of the development of a robust, systematic method of optimizing the collector shape to improve energy extraction using a genetic algorithm. The collector geometry uses a parametric description based upon bi-cubic B-spline surfaces, generated from a relatively small number of control points to reduce the dimensionality of the search space. The collector shapes that are optimized have one plane of symmetry and move in one degree of freedom (surge). Each candidate shape is assessed in a wave climate based upon data from a site in the North-East Atlantic Ocean. Three cost functions, distinguished by the severity of the penalty put on the size of the candidate collectors, and four constraint regimes, defined by two displacement and two power rating limits, are the governing influences on the twelve optimization procedures described. The selected collector shapes from each optimization run are appraised in terms of size, complexity and their performance compared to that of ‘benchmark’ box-shaped collectors.}, + language = {en}, + urldate = {2023-03-01}, + journal = {Renewable Energy}, + author = {McCabe, A. P.}, + month = mar, + year = {2013}, + keywords = {Genetic algorithms, Marine energy conversion, Optimization methods, Wave energy converter design}, + pages = {274--284}, +} + +@inproceedings{mccabe_multidisciplinary_2022, + title = {Multidisciplinary {Optimization} to {Reduce} {Cost} and {Power} {Variation} of a {Wave} {Energy} {Converter}}, + url = {https://asmedigitalcollection.asme.org/IDETC-CIE/proceedings-abstract/IDETC-CIE2022/86229/1150407}, + doi = {10.1115/DETC2022-90227}, + abstract = {Abstract. Wave energy converters (WECs) can advance the global energy transition by producing clean power for utility grids and offshore technologies. This paper provides a multidisciplinary, dual objective optimization of the Reference Model 3 (RM3), a two-body point absorber WEC design benchmark. The simulation model employs linear hydrodynamics with force saturation and probabilistic waves. The RM3 geometry and controller parameters are optimized using sequential quadratic programming to minimize the levelized cost of energy (LCOE) and the coefficient of variation of power. The minimum-LCOE design produces a power variation of 205\% and an LCOE of \$0.08/kWh, a seven-fold cost reduction and 23\% lower variation from the RM3 baseline of \$0.75/kWh and 255\% variation. Parameter sensitivities show that LCOE depends more strongly on site and economic parameters than geometric or material parameters, while power variation is largely insensitive to all parameters. A Pareto trade-offbetween cost and power variation reveals different optimal designs depending on which objective is prioritized, suggesting application-specific design heuristics. Three representative optimal designs are investigated: a minimum-LCOE design for cost-sensitive operations like utility power, a minimum-variation design for cost-insensitive installations like small offshore systems, and a balanced design for intermediate applications. Power probability distributions are shown for each.}, + language = {en}, + urldate = {2023-03-01}, + publisher = {American Society of Mechanical Engineers Digital Collection}, + author = {McCabe, Rebecca and Murphy, Olivia and Haji, Maha}, + month = nov, + year = {2022}, +} + +@article{sykes_flexible_2022, + title = {A {Flexible}, {Multi}-fidelity {Levelised} {Cost} of {Energy} {Model} for {Floating} {Offshore} {Wind} {Turbines} {Multidisciplinary} {Design}, {Analysis} and {Optimisation} {Approaches}}, + volume = {2265}, + issn = {1742-6596}, + url = {https://dx.doi.org/10.1088/1742-6596/2265/4/042029}, + doi = {10.1088/1742-6596/2265/4/042029}, + abstract = {As the UK takes a step towards a greener, cleaner future aiming to be net zero by 2050, continuous development of the power network is required. A clear solution is offshore wind, having already proved its feasibility and success in nearshore sites. However, a large majority of near shore sites in the UK are already being utilised. The next step is to move into deeper waters and utilise the stronger, more consistent wind resources. A solution could be floating offshore wind which is still in its infancy, with only a few operational floating wind farms installed. Building upon the multidisciplinary design, analysis, and optimisation framework (MDAO) for floating offshore wind turbines (FOWT) being developed at the University of Strathclyde, called FEDORA, the aim of this work is to refine the LCoE model adopted by FEDORA, and applying it to perform the optimisation of the floating offshore OC3 SPAR. There is limited data on cost, therefore Hywind Scotland Pilot Park will be used as a basis for the LCoE model, allowing the results to be validated. This model is not restricted to SPARs, as it establishes a general methodology to calculate the life cycle cost of floating offshore wind farms. Utilising the improved cost model this work finds four optimised SPAR structures for four different maximum angles of inclination which can be experienced in the wind turbines operation. The improved cost model has a much higher accuracy, highlighting the initial cost model underestimates the cost of the SPAR structure by around half.}, + language = {en}, + number = {4}, + urldate = {2023-03-01}, + journal = {Journal of Physics: Conference Series}, + author = {Sykes, V. and Collu, M. and Coraddu, A.}, + month = may, + year = {2022}, + note = {Publisher: IOP Publishing}, + pages = {042029}, +} + +@article{patryniak_multidisciplinary_2022, + title = {Multidisciplinary design analysis and optimisation frameworks for floating offshore wind turbines: {State} of the art}, + volume = {251}, + issn = {0029-8018}, + shorttitle = {Multidisciplinary design analysis and optimisation frameworks for floating offshore wind turbines}, + url = {https://www.sciencedirect.com/science/article/pii/S0029801822004267}, + doi = {10.1016/j.oceaneng.2022.111002}, + abstract = {Meeting climate and air quality targets, while preserving the focus on the reliability and cost-effectiveness of energy, became a central issue for offshore wind turbine engineers. Floating offshore wind turbines, which allow harnessing the large untapped wind resources in deep waters, are highly complex and coupled systems. Subsystem-level optimisations result in suboptimal designs, implying that an integrated design approach is important. Literature saw a few attempts on multidisciplinary design analysis and optimisation of floating wind turbines, with varying results, proving the need for an efficient, and sufficiently accurate, integrated approach. This paper reviews the state-of-the-art approaches to multidisciplinary design analysis and optimisation of floating support structures. The choice of the optimisation framework architecture, support platform design variables, constraints and objective functions are investigated. The techno-economic analysis models are closely examined, focusing on the approaches to achieving the optimum accuracy–efficiency balance. It is shown that the representation of the fully coupled system within the optimisation framework requires the introduction of a more complex multidisciplinary analysis workflow. Methods to increase the efficiency of such frameworks are indicated. Non-conventional support structure configurations can be conceived through the application of more advanced parametrisation schemes, which is feasible together with design space size reduction techniques. The set of design criteria should be extended by operation and maintenance cost, and power production metrics. The main technical limitations of the frameworks adopted so far include the inability to accurately analyse a diverse range of support structure topologies in multiple design load cases within a common framework. The cost approximation models should be extended by the chosen aspects of pre-operational phases, to better explore the benefits of the floating platforms.}, + language = {en}, + urldate = {2023-03-01}, + journal = {Ocean Engineering}, + author = {Patryniak, Katarzyna and Collu, Maurizio and Coraddu, Andrea}, + month = may, + year = {2022}, + keywords = {Coupled dynamics, Floating offshore wind turbine, MDAO, Multidisciplinary optimisation, Offshore wind, Support structure}, + pages = {111002}, +} + +@article{giannini_wave_2022, + title = {Wave energy converters design combining hydrodynamic performance and structural assessment}, + volume = {249}, + issn = {0360-5442}, + url = {https://www.sciencedirect.com/science/article/pii/S0360544222005448}, + doi = {10.1016/j.energy.2022.123641}, + abstract = {The design of a wave energy converter (WEC) is a many-sided and important assignment that determines its future technical and economic viability. Presently, there is a lack of structured design methodologies that take into account both the hydrodynamic performance, structural reliability and economic data from early development stages. Therefore, a new methodology is proposed, aiming for a viable predesign solution for avoiding major setbacks at later stages. It includes a series of steps related to the initial design definition, hydrodynamic analysis, yield strength investigation and early-stage economic assessment. For demonstration, the methodology is applied to progress a sloped motion WEC for near-shore locations. The original WEC configuration is also assessed and the novel design, which allows reducing the mass of floating elements by 70\%, is developed. It is found that: for recurrent sea states, the capture width ratio of the new design (20–40\%) is similar to the one of the original design (20–50\%), the estimated cost of the device is reduced by 28.6\% and the payback period is reduced by 2.4 years. Overall, the results obtained for the case study demonstrated the interest in the proposed methodology that can assist in the development and analysis of early-stage WEC concepts.}, + language = {en}, + urldate = {2023-03-01}, + journal = {Energy}, + author = {Giannini, Gianmaria and Rosa-Santos, Paulo and Ramos, Victor and Taveira-Pinto, Francisco}, + month = jun, + year = {2022}, + keywords = {Economic analysis, Hydrodynamic structural analysis, Multi-scope design development, Pivoting wave energy converter, Wave loads, marine Energy}, + pages = {123641}, +} + +@misc{noauthor_dtocean_nodate, + title = {{DTOcean}+}, + url = {https://www.dtoceanplus.eu/Tools/DTOcean}, + language = {en-GB}, + urldate = {2023-03-01}, + journal = {DTOceanPlus - Design tools for ocean energy systems}, +} + +@article{garcia-teruel_geometry_2020, + title = {Geometry optimisation of wave energy converters}, + url = {https://era.ed.ac.uk/handle/1842/36912}, + doi = {10.7488/era/213}, + abstract = {Given the large energy resource available in ocean waves, wave energy +converters have been developed over the last decades for power extraction. +Various concepts exist, and research efforts are now focussed on reducing their +levelised cost of energy. The device structure has been identified to have the +highest cost reduction potential. For this reason, a number of hull geometry +optimisation studies have been performed in recent years. In these studies, +costs have been mostly represented through the device size or weight, and +devices have been optimised for specific sea conditions, based generally on +simple shapes such as spheres or cylinders. However, there is no consensus in +the employed methodology and resulting shapes might be difficult to manu +facture or unable to survive in high energetic seas. The goal of this thesis is, +therefore, to develop a device-agnostic methodology for geometry optimisation +of wave energy converters, which enables the generation of improved hull shapes +that reduce the levelised cost of electricity. An existing approach for single +body floating point-absorbers, exhibiting some of the best practices found in +this field, is re-implemented and extended to improve its robustness for its +application to different case studies. Each of the elements composing this +approach (how the geometry is defined, the choice of objective function and +the choice of optimisation algorithm and set-up) are then evaluated and their +suitability is assessed through comparison to other strategies. The method is +then applied to a range of study cases, such as to study the effect of location +and of the choice of modes-of-motion for power extraction on the optimal hull +shape. Further extensions of the method to include manufacturability and +reliability considerations, as well as to include the effect of mass distribution +are investigated. As a result, recommendations are formulated for the set-up of +an early stage WEC design geometry optimisation process. Additionally, trends +for the hull shape design are identified for the considered cases - depending +on, location, the choice of the modes of motion for power extraction, and how +costs are accounted for.}, + language = {en}, + urldate = {2023-03-01}, + author = {Garcia-Teruel, Anna}, + month = jul, + year = {2020}, + note = {Accepted: 2020-03-31T10:31:18Z +Publisher: The University of Edinburgh}, +} + +@misc{noauthor_system_2020, + address = {Golden, CO}, + title = {System {Advisor} {Model} ({SAM})}, + copyright = {BSD-3-Clause}, + url = {https://github.com/NREL/SAM/}, + abstract = {System Advisor Model (SAM)}, + urldate = {2022-05-13}, + publisher = {National Renewable Energy Laboratory}, + month = nov, + year = {2020}, + note = {original-date: 2013-01-10T02:52:47Z}, +} + +@misc{noauthor_proteusds_nodate, + title = {{ProteusDS} {\textbar} {A} flexible {Dynamic} {Analysis} {Tool} for {Ocean} {Industries} {\textbar} {DSA}}, + url = {https://dsaocean.com/proteusds/overview/}, + abstract = {ProteusDS is a full-featured dynamic analysis software capable of simulating vessels, flexible structures, lines and technologies in harsh marine environments. It is modern, customizable and validated.}, + language = {en-CA}, + urldate = {2023-03-01}, + journal = {DSA Ocean}, +} + +@misc{ruehl_wec-simwec-sim_2022, + title = {{WEC}-{Sim}/{WEC}-{Sim}: {WEC}-{Sim} v5.0.1}, + shorttitle = {{WEC}-{Sim}/{WEC}-{Sim}}, + url = {https://zenodo.org/record/7121186}, + abstract = {New Features This is a bug fix release. New features since the previous release are not included. Bug Fixes Fix saveViz by @jtgrasb in https://github.com/WEC-Sim/WEC-Sim/pull/866 Fix typo in docs. by @mancellin in https://github.com/WEC-Sim/WEC-Sim/pull/898 Update documentation tutorials to fix OSWEC inertia by @jtgrasb in https://github.com/WEC-Sim/WEC-Sim/pull/894 CI: Split docs jobs {\textbar} Add color to docs logs {\textbar} Cancel runs on new push {\textbar} Add 2021b to MATLAB versions by @H0R5E in https://github.com/WEC-Sim/WEC-Sim/pull/862 Mac path fixes and make outputDir public by @ahmedmetin in https://github.com/WEC-Sim/WEC-Sim/pull/874 wecSimPCT Fix (Master) by @yuyihsiang in https://github.com/WEC-Sim/WEC-Sim/pull/870 Fix image bug in PTO-Sim in Library Browser by @jleonqu in https://github.com/WEC-Sim/WEC-Sim/pull/896 update to v5.0 citation by @akeeste in https://github.com/WEC-Sim/WEC-Sim/pull/911 fix non-linear hydro by @dforbush2 in https://github.com/WEC-Sim/WEC-Sim/pull/910 Pull dev bugfixes into master by @akeeste @jtgrasb in https://github.com/WEC-Sim/WEC-Sim/pull/950 (includes https://github.com/WEC-Sim/WEC-Sim/pull/929 https://github.com/WEC-Sim/WEC-Sim/pull/917 https://github.com/WEC-Sim/WEC-Sim/pull/884 by @jtgrasb) New Contributors @mancellin made their first contribution in https://github.com/WEC-Sim/WEC-Sim/pull/898 @ahmedmetin made their first contribution in https://github.com/WEC-Sim/WEC-Sim/pull/874 Issues and Pull Requests {\textgreater}52 issues closed since v5.0 {\textgreater}23 PRs merged since v5.0 Full Changelog: https://github.com/WEC-Sim/WEC-Sim/compare/v5.0...v5.0.1}, + urldate = {2023-03-01}, + publisher = {Zenodo}, + author = {Ruehl, Kelley and Keester, Adam and Ströfer, Carlos A. Michelén and nathanmtom and Topper, Mathew and Lawson, Michael and dforbush2 and Ling, Bradley A. and jtgrasb and j-vanrij and Sal and jhbates and Ogden, David and Nguyen, Lily and Jeffalo1 and Leon, Jorge and sedwardsand and Alves, Erick F. and crobarcro and emiliofa and ratanakso and Rashid, Ahmed and Aquaharmonics and Sauer, Filip and Ancellin, Matthieu and NREL-Jim-McNally and SiHeTh and gparisella and Hall, Matt and yuyihsiang}, + month = sep, + year = {2022}, + doi = {10.5281/zenodo.7121186}, +} + +@article{balitsky_analyzing_2018, + title = {Analyzing the {Near}-{Field} {Effects} and the {Power} {Production} of an {Array} of {Heaving} {Cylindrical} {WECs} and {OSWECs} {Using} a {Coupled} {Hydrodynamic}-{PTO} {Model}}, + volume = {11}, + copyright = {http://creativecommons.org/licenses/by/3.0/}, + issn = {1996-1073}, + url = {https://www.mdpi.com/1996-1073/11/12/3489}, + doi = {10.3390/en11123489}, + abstract = {The Power Take-Off (PTO) system is the key component of a Wave Energy Converter (WEC) that distinguishes it from a simple floating body because the uptake of the energy by the PTO system modifies the wave field surrounding the WEC. Consequently, the choice of a proper PTO model of a WEC is a key factor in the accuracy of a numerical model that serves to validate the economic impact of a wave energy project. Simultaneously, the given numerical model needs to simulate many WEC units operating in close proximity in a WEC farm, as such conglomerations are seen by the wave energy industry as the path to economic viability. A balance must therefore be struck between an accurate PTO model and the numerical cost of running it for various WEC farm configurations to test the viability of any given WEC farm project. Because hydrodynamic interaction between the WECs in a farm modifies the incoming wave field, both the power output of a WEC farm and the surface elevations in the ‘near field’ area will be affected. For certain types of WECs, namely heaving cylindrical WECs, the PTO system strongly modifies the motion of the WECs. Consequently, the choice of a PTO system affects both the power production and the surface elevations in the ‘near field’ of a WEC farm. In this paper, we investigate the effect of a PTO system for a small wave farm that we term ‘WEC array’ of 5 WECs of two types: a heaving cylindrical WEC and an Oscillating Surge Wave Energy Converter (OSWEC). These WECs are positioned in a staggered array configuration designed to extract the maximum power from the incident waves. The PTO system is modelled in WEC-Sim, a purpose-built WEC dynamics simulator. The PTO system is coupled to the open-source wave structure interaction solver NEMOH to calculate the average wave field η in the ‘near-field’. Using a WEC-specific novel PTO system model, the effect of a hydraulic PTO system on the WEC array power production and the near-field is compared to that of a linear PTO system. Results are given for a series of regular wave conditions for a single WEC and subsequently extended to a 5-WEC array. We demonstrate the quantitative and qualitative differences in the power and the ‘near-field’ effects between a 5-heaving cylindrical WEC array and a 5-OSWEC array. Furthermore, we show that modeling a hydraulic PTO system as a linear PTO system in the case of a heaving cylindrical WEC leads to considerable inaccuracies in the calculation of average absorbed power, but not in the near-field surface elevations. Yet, in the case of an OSWEC, a hydraulic PTO system cannot be reduced to a linear PTO coefficient without introducing substantial inaccuracies into both the array power output and the near-field effects. We discuss the implications of our results compared to previous research on WEC arrays which used simplified linear coefficients as a proxy for PTO systems.}, + language = {en}, + number = {12}, + urldate = {2023-03-01}, + journal = {Energies}, + author = {Balitsky, Philip and Quartier, Nicolas and Verao Fernandez, Gael and Stratigaki, Vasiliki and Troch, Peter}, + month = dec, + year = {2018}, + note = {Number: 12 +Publisher: Multidisciplinary Digital Publishing Institute}, + keywords = {BEM, NEMOH, PTO system, PTO system tuning, PTO-sim, WEC array, WEC farm, WEC-sim, hydraulic, linearization, model coupling}, + pages = {3489}, +} + +@article{de_andres_adaptability_2015, + title = {Adaptability of a generic wave energy converter to different climate conditions}, + volume = {78}, + issn = {0960-1481}, + url = {https://www.sciencedirect.com/science/article/pii/S0960148115000270}, + doi = {10.1016/j.renene.2015.01.020}, + abstract = {This study evaluates the influence of wave climate tunability on the performance of a generic Wave Energy Converter (WEC) for different climate scenarios. The generic WEC is assumed to be composed of an array of heaving, floating cylinders. In this study, two natural periods for the cylinders of 4 s and 8 s (typical of enclosed seas and the mean Atlantic swell, respectively) and a location-tunable cylinder are considered to evaluate the influence of tuning on the power performance of the cylinder. The WEC power matrix is computed using a frequency domain model, and the performance of the WEC is evaluated along the global coasts; the met-ocean data originated from the global reanalysis database (GOW) from Reguero et al. (2012). The performance of the WEC is evaluated using two parameters: the capture width ratio (CWR), which evaluates the efficiency of the converter at each location, and the kW/Ton (KWT) parameter, which evaluates the efficiency of the converter using “economic” terms. Tuning a converter for each location displayed a positive CWR; however, the KWT was low after WEC tuning because of the weight of the structures required to tune the converter that experiences high peak periods.}, + language = {en}, + urldate = {2023-03-01}, + journal = {Renewable Energy}, + author = {de Andres, A. and Guanche, R. and Vidal, C. and Losada, I. J.}, + month = jun, + year = {2015}, + keywords = {Adaptability, Capture width ratio, Resonance, Tuning, Wave energy converter}, + pages = {322--333}, +} + +@article{zhang_ocean_2021, + title = {Ocean wave energy converters: {Technical} principle, device realization, and performance evaluation}, + volume = {141}, + issn = {1364-0321}, + shorttitle = {Ocean wave energy converters}, + url = {https://www.sciencedirect.com/science/article/pii/S1364032121000605}, + doi = {10.1016/j.rser.2021.110764}, + abstract = {As a renewable energy with immense development potential, ocean wave energy has abundant storage. The utilizations of wave energy technology to exploit wave energy resources have broad application prospects and an important realistic meaning. The researchers worldwide have designed many wave energy converters (WEC) with varied and structures based on different concepts. In this paper, the principle of wave energy power generation technology is reviewed and analyzed from basic structure and power take-off (PTO). Some typical WEC and multi-degree of freedom WEC (MDWEC) and their realization are introduced. The analytic hierarchy process (AHP) is employed to construct a comprehensive multi-index model and evaluate the present WEC from five perspectives: energy capture, technology cost economic, reliability, environmental friendliness and adaptability. Results show that in the field of wave energy utilization and development, the MDWEC has a good comprehensive performance and a wide application range. Qualitative and quantitative methods are adopted to find the optimal WEC technical scheme based on the review and analysis of technology principles of wave energy power generation and realization of devices, which can be used for the development of WEC.}, + language = {en}, + urldate = {2023-03-01}, + journal = {Renewable and Sustainable Energy Reviews}, + author = {Zhang, Yongxing and Zhao, Yongjie and Sun, Wei and Li, Jiaxuan}, + month = may, + year = {2021}, + keywords = {Device realization, Ocean wave energy, Performance evaluation, Technical principles, Wave energy converters}, + pages = {110764}, +} + +@misc{noauthor_small_nodate, + title = {Small {WEC}}, + url = {https://apps.openei.org/swec/}, + urldate = {2023-03-01}, +} + +@article{trueworthy_wave_2020, + title = {The {Wave} {Energy} {Converter} {Design} {Process}: {Methods} {Applied} in {Industry} and {Shortcomings} of {Current} {Practices}}, + volume = {8}, + copyright = {http://creativecommons.org/licenses/by/3.0/}, + issn = {2077-1312}, + shorttitle = {The {Wave} {Energy} {Converter} {Design} {Process}}, + url = {https://www.mdpi.com/2077-1312/8/11/932}, + doi = {10.3390/jmse8110932}, + abstract = {Wave energy is among the many renewable energy technologies being researched and developed to address the increasing demand for low-emissions energy. The unique design challenges for wave energy converter design—integrating complex and uncertain technological, economic, and ecological systems, overcoming the structural challenges of ocean deployment, and dealing with complex system dynamics—have lead to a disjointed progression of research and development. There is no common design practice across the wave energy industry and there is no published synthesis of the practices that are used by developers. In this paper, we summarize the methods being employed in WEC design as well as promising methods that have yet to be applied. We contextualize these methods within an overarching design process. We present results from a survey of WEC developers to identify methods that are common in industry. From the review and survey results, we conclude that the most common methods of WEC design are iterative methods in which design parameters are defined, evaluated, and then changed based on evaluation results. This leaves a significant space for improvement of methods that help designers make better-informed decisions prior to sophisticated evaluation, and methods of using the evaluation results to make better design decisions during iteration. Despite the popularity of optimization methods in academic research, they are less common in industry development. We end this paper with a summary of the areas of WEC design in which the testing and development of new methods is necessary, and where more research is required to fully understand the influence of design decisions on WEC performance.}, + language = {en}, + number = {11}, + urldate = {2023-03-01}, + journal = {Journal of Marine Science and Engineering}, + author = {Trueworthy, Ali and DuPont, Bryony}, + month = nov, + year = {2020}, + note = {Number: 11 +Publisher: Multidisciplinary Digital Publishing Institute}, + keywords = {conceptual design, design methods, industry survey, stakeholder requirements, wave energy converter}, + pages = {932}, +} + +@article{guerra_value_2020, + title = {The value of seasonal energy storage technologies for the integration of wind and solar power}, + volume = {13}, + issn = {1754-5706}, + url = {https://pubs.rsc.org/en/content/articlelanding/2020/ee/d0ee00771d}, + doi = {10.1039/D0EE00771D}, + abstract = {Energy storage at all timescales, including the seasonal scale, plays a pivotal role in enabling increased penetration levels of wind and solar photovoltaic energy sources in power systems. Grid-integrated seasonal energy storage can reshape seasonal fluctuations of variable and uncertain power generation by reducing energy curtailment, replacing peak generation capacity, and providing transmission benefits. Most current literature focuses on technology cost assessments and does not characterize the potential grid benefits of seasonal storage to capture the most cost-effective solutions. We propose a model-based approach for comprehensive techno-economic assessments of grid-integrated seasonal storage. The approach has two major advantages compared to those presented in the literature. First, we do not make assumptions about the operation of the storage device, including annual cycles, asset utilization or depth of discharge. Rather, a model is used to calculate optimal storage operation profiles. Second, the model-based approach accounts for avoided power system costs, which allows us to estimate the cost effectiveness of different types of storage devices. We assess the cost competitiveness of three specific storage technologies including pumped hydro, compressed air, and hydrogen seasonal storage and explore the conditions (cost, storage duration, and efficiency) that encourage cost competitiveness for seasonal storage technologies. This study considers the Western U.S. power system with 24\% to 61\% of variable renewable power sources on an annual energy basis (up to 83.5\% of renewable energy including hydro, geothermal, and biomass power sources). Our results indicate that for the Western U.S. power system, pumped hydro and compressed air energy storage with 1 day of discharge duration are expected to be cost-competitive in the near future. In contrast, hydrogen storage with up to 1 week of discharge duration could be cost-effective in the near future if power and energy capacity capital costs are equal to or less than ∼US\$1507 kW−1 and ∼US\$1.8 kWh−1 by 2025, respectively. However, based on projected power and energy capacity capital costs for 2050, hydrogen storage with up to 2 weeks of discharge duration is expected to be cost-effective in future power systems. Moreover, storage systems with greater discharge duration could be cost-competitive in the near future if greater renewable penetration levels increase arbitrage or capacity value, significant energy capital cost reductions are achieved, or revenues from additional services and new markets—e.g., reliability and resiliency—are monetized.}, + language = {en}, + number = {7}, + urldate = {2023-03-01}, + journal = {Energy \& Environmental Science}, + author = {Guerra, Omar J. and Zhang, Jiazi and Eichman, Joshua and Denholm, Paul and Kurtz, Jennifer and Hodge, Bri-Mathias}, + month = jul, + year = {2020}, + note = {Publisher: The Royal Society of Chemistry}, + pages = {1909--1922}, +} + +@book{bazilian_analytical_2009, + title = {Analytical {Methods} for {Energy} {Diversity} and {Security}: {Portfolio} {Optimization} in the {Energy} {Sector}: {A} {Tribute} to the work of {Dr}. {Shimon} {Awerbuch}}, + isbn = {978-0-08-091531-9}, + shorttitle = {Analytical {Methods} for {Energy} {Diversity} and {Security}}, + abstract = {Analytical Methods for Energy Diversity and Security is an ideal volume for professionals in academia, industry and government interested in the rapidly evolving area at the nexus between energy and climate change policy. The cutting-edge international contributions allow for a wide coverage of the topic. Analytical Methods for Energy Diversity and Security focuses on the consideration of financial risk in the energy sector. It describes how tools borrowed from financial economic theory, in particular mean-variance portfolio theory, can provide insights on the costs and benefits of diversity, and thus inform investment decision making in conditions of uncertainty. It gives the reader an in-depth understanding of how to manage risk at a time when the world’s focus is on this area. The book provides insights from leading authorities in the area of energy security. It gives readers abundant, rigorous analysis and guidance at a critical time in facing the twin challenges of energy security and climate change. The book also highlights the role of clean energy technology in moving towards future diverse and intelligent electricity systems. It will be a trusted, first point of reference for decision-makers in the field of energy policy. The book includes a foreword by the 2007 Nobel Peace Prize winner. All royalties from sale of this book will be donated to charities working in the energy sector in the developing world. Theoretical underpinning and applied use of Portfolio theory in the energy sector In-depth consideration of risk Contributions from leading international energy economists Innovative methodologies for thinking about energy security and diversity}, + publisher = {Elsevier}, + author = {Bazilian, Morgan and Roques, Fabien}, + month = mar, + year = {2009}, + note = {Google-Books-ID: iV1qIPxGM4wC}, + keywords = {Business \& Economics / Industries / Energy, Technology \& Engineering / Power Resources / General}, +} + +@article{jurasz_review_2020, + title = {A review on the complementarity of renewable energy sources: {Concept}, metrics, application and future research directions}, + volume = {195}, + issn = {0038-092X}, + shorttitle = {A review on the complementarity of renewable energy sources}, + url = {https://www.sciencedirect.com/science/article/pii/S0038092X19311831}, + doi = {10.1016/j.solener.2019.11.087}, + abstract = {Global and regional trends indicate that energy demand will soon be covered by a widespread deployment of renewable energy sources. However, the weather and climate driven energy sources are characterized by a significant spatial and temporal variability. One of the commonly mentioned solutions to overcome the mismatch between demand and supply provided by renewable generation is a hybridization of two or more energy sources into a single power station (like wind-solar, solar-hydro or solar-wind-hydro). The operation of hybrid energy sources is based on the complementary nature of renewable sources. Considering the growing importance of such systems and increasing number of research activities in this area this paper presents a comprehensive review of studies which investigated, analyzed, quantified and utilized the effect of temporal, spatial and spatiotemporal complementarity between renewable energy sources. The review starts with a brief overview of available research papers, formulates detailed definition of major concepts, summarizes current research directions and ends with prospective future research activities. The review provides a chronological and spatial information with regard to the studies on the complementarity concept.}, + language = {en}, + urldate = {2023-03-01}, + journal = {Solar Energy}, + author = {Jurasz, J. and Canales, F. A. and Kies, A. and Guezgouz, M. and Beluco, A.}, + month = jan, + year = {2020}, + keywords = {Complementarity index, Non-dispatchable energy sources, Reliability, Variability, Weather-driven}, + pages = {703--724}, +} + +@techreport{livecchi_powering_2019, + title = {Powering the {Blue} {Economy}: {Exploring} {Opportunities} for {Marine} {Renewable} {Energy} in {Maritime} {Markets}}, + urldate = {2022-05-16}, + institution = {US Department of Energy}, + author = {LiVecchi, Al and Copping, A and Jenne, Dale and Gorton, A}, + month = apr, + year = {2019}, +} + +@misc{noauthor_system_2022, + title = {System {Advisor} {Model} ({SAM})}, + copyright = {BSD-3-Clause}, + url = {https://github.com/NREL/SAM}, + abstract = {System Advisor Model (SAM)}, + urldate = {2022-05-13}, + publisher = {National Renewable Energy Laboratory}, + month = apr, + year = {2022}, + note = {original-date: 2013-01-10T02:52:47Z}, +} + +@book{franklin2014feedback, + series = {Always learning}, + title = {Feedback control of dynamic systems}, + isbn = {978-1-292-06890-9}, + url = {https://books.google.com/books?id=yO2hoAEACAAJ}, + publisher = {Pearson}, + author = {Franklin, G.F. and Powell, J.D. and Emami-Naeini, A.}, + year = {2014}, +} + +@incollection{FPE, + edition = {7}, + title = {Equivalent {Gain} {Analysis} {Using} {Frequency} {Response}: {Describing} {Functions}}, + isbn = {978-1-292-06890-9}, + url = {https://books.google.com/books?id=yO2hoAEACAAJ}, + booktitle = {Feedback control of dynamic systems}, + publisher = {Pearson}, + author = {Franklin, G.F. and Powell, J.D. and Emami-Naeini, A.}, + year = {2015}, + pages = {678--682}, +} + +@misc{noauthor_feedback_nodate, + title = {Feedback {Control} of {Dynamic} {Systems}, 7th {Edition}}, + url = {https://www.pearson.com/content/one-dot-com/one-dot-com/us/en/higher-education/program.html}, + abstract = {Feedback Control of Dynamic Systems, 7th Edition}, + language = {en}, + urldate = {2022-05-12}, +} + +@misc{noauthor_paretosearch_nodate, + title = {paretosearch {Algorithm} - {MATLAB} \& {Simulink}}, + url = {https://www.mathworks.com/help/gads/paretosearch-algorithm.html}, + urldate = {2022-02-21}, +} + +@article{agte_mdo_2009, + title = {{MDO}: assessment and direction for advancement—an opinion of one international group}, + volume = {40}, + issn = {1615-1488}, + shorttitle = {{MDO}}, + url = {https://doi.org/10.1007/s00158-009-0381-5}, + doi = {10.1007/s00158-009-0381-5}, + abstract = {This paper is a summary of topics presented and discussed at the 2006 European–U.S. Multidisciplinary Optimization (MDO) Colloquium in Goettingen, Germany, attended by nearly seventy professionals from academia, industry, and government. An attempt is made to accurately reflect the issues discussed by this diverse group, qualified by interest, experience, and accomplishment to present an opinion about the state-of-the-art, trends, and developments in Multidisciplinary Design Optimization. As such, its main purpose is to provide suggestions and stimulus for future research in the field. The predominant content of the colloquium was centered on aerospace, with a few contributions from the automotive industry, and this is reflected in the article. Due to the timeframe that has passed since the conclusion of the workshop, the authors have updated topics where appropriate to reflect observed developments over the past 3 years. Finally, rather than dwelling extensively on past accomplishments and current capabilities in MDO we focus on the needs and identified shortcomings from the colloquium which lead to potential future research directions. A brief MDO background is provided to set the discussion in its proper context.}, + language = {en}, + number = {1}, + urldate = {2022-02-14}, + journal = {Structural and Multidisciplinary Optimization}, + author = {Agte, Jeremy and de Weck, Olivier and Sobieszczanski-Sobieski, Jaroslaw and Arendsen, Paul and Morris, Alan and Spieck, Martin}, + month = apr, + year = {2009}, + pages = {17}, +} + +@article{goteman_methods_2014, + title = {Methods of reducing power fluctuations in wave energy parks}, + volume = {6}, + url = {https://aip.scitation.org/doi/10.1063/1.4889880}, + doi = {10.1063/1.4889880}, + number = {4}, + urldate = {2022-02-14}, + journal = {Journal of Renewable and Sustainable Energy}, + author = {Göteman, Malin and Engström, Jens and Eriksson, Mikael and Isberg, Jan and Leijon, Mats}, + month = jul, + year = {2014}, + note = {Publisher: American Institute of Physics}, + pages = {043103}, +} + +@article{gaudin_single_2021, + title = {From single to multiple wave energy converters: {Cost} reduction through location and configuration optimisation}, + shorttitle = {From single to multiple wave energy converters}, + journal = {Final Report. The University of Western Australia}, + author = {Gaudin, C. and David, D. R. and Cai, Y. and Hansen, J. E. and Bransby, M. F. and Rijnsdorp, D. P. and Lowe, R. J. and O’Loughlin, C. D. and Lu, T. and Uzielli, M.}, + year = {2021}, +} + +@article{herber_dynamic_nodate, + title = {Dynamic {System} {Design} {Optimization} of {Wave} {Energy} {Converters} {Utilizing} {Direct} {Transcription}}, + language = {en}, + author = {Herber, Daniel Ronald}, + pages = {153}, +} + +@article{al_shami_parameter_2019, + title = {A parameter study and optimization of two body wave energy converters}, + volume = {131}, + issn = {0960-1481}, + url = {https://www.sciencedirect.com/science/article/pii/S0960148118307833}, + doi = {10.1016/j.renene.2018.06.117}, + abstract = {This paper studies the multidisciplinary nature of two body wave energy converters by a parametric study based on the Taguchi method which helps to understand the effect of different dependent parameters on the wave energy conversion performance. Seven different parameters are analyzed and their effect on the maximum captured power, resonance frequency and bandwidth is studied. An interesting comparison between a cylindrical submerged body and a spherical one was made in terms of the system's viscous damping and hydrodynamics. The best system parameter combinations based on the maximum output power, best resonant frequency and frequency bandwidth were identified from the outcomes of the Taguchi method and optimized to capture the maximum power to operate in the specific (Australian) sea regions where the waves' frequencies are relatively low. This paper should provide a guideline for designers to tune their parameters based on the desired performance and sea state.}, + language = {en}, + urldate = {2022-02-14}, + journal = {Renewable Energy}, + author = {Al Shami, Elie and Wang, Xu and Zhang, Ran and Zuo, Lei}, + month = feb, + year = {2019}, + keywords = {Bandwidth, Optimization, Parameter, Power, Taguchi method, Two body wave energy converters}, + pages = {1--13}, +} + +@article{martins_multidisciplinary_2013, + title = {Multidisciplinary {Design} {Optimization}: {A} {Survey} of {Architectures}}, + volume = {51}, + issn = {0001-1452}, + shorttitle = {Multidisciplinary {Design} {Optimization}}, + url = {https://arc.aiaa.org/doi/10.2514/1.J051895}, + doi = {10.2514/1.J051895}, + abstract = {Multidisciplinary design optimization is a field of research that studies the application of numerical optimization techniques to the design of engineering systems involving multiple disciplines or components. Since the inception of multidisciplinary design optimization, various methods (architectures) have been developed and applied to solve multidisciplinary design-optimization problems. This paper provides a survey of all the architectures that have been presented in the literature so far. All architectures are explained in detail using a unified description that includes optimization problem statements, diagrams, and detailed algorithms. The diagrams show both data and process flow through the multidisciplinary system and computational elements, which facilitate the understanding of the various architectures, and how they relate to each other. A classification of the multidisciplinary design-optimization architectures based on their problem formulations and decomposition strategies is also provided, and the benefits and drawbacks of the architectures are discussed from both theoretical and experimental perspectives. For each architecture, several applications to the solution of engineering-design problems are cited. The result is a comprehensive but straightforward introduction to multidisciplinary design optimization for nonspecialists and a reference detailing all current multidisciplinary design-optimization architectures for specialists.}, + number = {9}, + urldate = {2022-02-14}, + journal = {AIAA Journal}, + author = {Martins, Joaquim R. R. A. and Lambe, Andrew B.}, + month = sep, + year = {2013}, + note = {Publisher: American Institute of Aeronautics and Astronautics}, + keywords = {Aerodynamic Loads, Aircraft Design, Computing, Lagrange Multipliers, MDO, Numerical Optimization, Sequential Linear Programming, Sequential Quadratic Programming, Structural Analysis, Structural Optimization}, + pages = {2049--2075}, +} + +@article{aderinto_ocean_2018, + title = {Ocean {Wave} {Energy} {Converters}: {Status} and {Challenges}}, + volume = {11}, + copyright = {http://creativecommons.org/licenses/by/3.0/}, + issn = {1996-1073}, + shorttitle = {Ocean {Wave} {Energy} {Converters}}, + url = {https://www.mdpi.com/1996-1073/11/5/1250}, + doi = {10.3390/en11051250}, + abstract = {Wave energy is substantial as a resource, and its potential to significantly contribute to the existing energy mix has been identified. However, the commercial utilization of wave energy is still very low. This paper reviewed the background of wave energy harvesting technology, its evolution, and the present status of the industry. By covering the theoretical formulations, wave resource characterization methods, hydrodynamics of wave interaction with the wave energy converter, and the power take-off and electrical systems, different challenges were identified and discussed. Solutions were suggested while discussing the challenges in order to increase awareness and investment in wave energy industry as a whole.}, + language = {en}, + number = {5}, + urldate = {2022-02-14}, + journal = {Energies}, + author = {Aderinto, Tunde and Li, Hua}, + month = may, + year = {2018}, + note = {Number: 5 +Publisher: Multidisciplinary Digital Publishing Institute}, + keywords = {challenges, design, wave energy, wave energy converters}, + pages = {1250}, +} + +@article{franzitta_desalination_2016, + title = {The {Desalination} {Process} {Driven} by {Wave} {Energy}: {A} {Challenge} for the {Future}}, + volume = {9}, + copyright = {http://creativecommons.org/licenses/by/3.0/}, + issn = {1996-1073}, + shorttitle = {The {Desalination} {Process} {Driven} by {Wave} {Energy}}, + url = {https://www.mdpi.com/1996-1073/9/12/1032}, + doi = {10.3390/en9121032}, + abstract = {The correlation between water and energy is currently the focus of several investigations. In particular, desalination is a technological process characterized by high energy consumption; nevertheless, desalination represents the only practicable solution in several areas, where the availability of fresh water is limited but brackish water or seawater are present. These natural resources (energy and water) are essential for each other; energy system conversion needs water, and electrical energy is necessary for water treatment or transport. Several interesting aspects include the study of saline desalination as an answer to freshwater needs and the application of renewable energy (RE) devices to satisfy electrical energy requirement for the desalination process. A merge between renewable energy and desalination is beneficial in that it is a sustainable and challenging option for the future. This work investigates the possibility of using renewable energy sources to supply the desalination process. In particular, as a case study, we analyze the application of wave energy sources in the Sicilian context.}, + language = {en}, + number = {12}, + urldate = {2022-02-14}, + journal = {Energies}, + author = {Franzitta, Vincenzo and Curto, Domenico and Milone, Daniele and Viola, Alessia}, + month = dec, + year = {2016}, + note = {Number: 12 +Publisher: Multidisciplinary Digital Publishing Institute}, + keywords = {desalination, renewable energy, water, wave}, + pages = {1032}, +} + +@inproceedings{driscol_wave-powered_2019, + title = {Wave-{Powered} {AUV} {Recharging}: {A} {Feasibility} {Study}}, + shorttitle = {Wave-{Powered} {AUV} {Recharging}}, + url = {https://asmedigitalcollection.asme.org/OMAE/proceedings/OMAE2019/58899/V010T09A023/1068258}, + doi = {10.1115/OMAE2019-95383}, + language = {en}, + urldate = {2022-02-14}, + publisher = {American Society of Mechanical Engineers Digital Collection}, + author = {Driscol, Blake P. and Gish, Andrew and Coe, Ryan G.}, + month = nov, + year = {2019}, +} + +@inproceedings{ramudu_ocean_2011, + title = {Ocean {Wave} {Energy}-{Driven} {Desalination} {Systems} for {Off}-grid {Coastal} {Communities} in {Developing} {Countries}}, + doi = {10.1109/GHTC.2011.38}, + abstract = {Resolute Marine Energy, Inc. (RME) is based in Boston, MA and is developing ocean wave energy converters (WECs) to benefit remote off-grid communities in developing nations. Our two WEC technologies are based on the heaving and surging motion of a buoy on the ocean surface (the 3-D WEC) and on a bottom-mounted hinged paddle that oscillates in the full water column (the Surge WEC). Our computer models and wave tank tests have revealed conversion efficiencies as high as 31\% in random sea states for the 3-D WEC and 40\% for the Surge WEC. Our objective is to complete all the testing and prototyping of both WECs by the end of 2012. RME plans to use the Surge WEC in conjunction with a reverse osmosis seawater desalination system in order to provide fresh water to coastal communities in developing countries. The proposed system will operate completely off-grid and will represent a clean and low-cost solution to the water scarcity problem commonly faced by remote communities. The fresh water production process comprises three stages: energy extraction from waves, process water acquisition and pressure regulation, and reverse osmosis. We estimate that an array of about 25 Surge WECs can produce 0.9 million m3 of fresh water per year, which is enough to meet the water needs of about 30,000 people while eliminating about 104 thousand tons of carbon dioxide emissions per year. RME has identified a municipality in South Africa as its launch customer and has the support of the South African Department of Water Affairs to develop the project. In South Africa, 1.97 million people live on the coast where wave energy is abundant and each person needs an additional 700 m3 of water per person per year to comply with United Nations Millennium Development Goals. After the first deployment, RME will expand to other remote communities in South Africa.}, + booktitle = {2011 {IEEE} {Global} {Humanitarian} {Technology} {Conference}}, + author = {Ramudu, Eshwan}, + month = oct, + year = {2011}, + keywords = {Communities, Desalination, Ocean waves, Oceans, Sea measurements, Surges, coastal communities, desalination, ocean wave energy, renewable energy, water}, + pages = {287--289}, +} + +@inproceedings{polinder_wave_2005, + title = {Wave energy converters and their impact on power systems}, + doi = {10.1109/FPS.2005.204210}, + abstract = {The objective of this paper is to give an introduction into ocean wave energy converters and their impact on power systems. The potential of wave energy is very large. There are a lot of different methods and systems for converting this power into electrical power, such as oscillating water columns, hinged contour devices as the Pelamis, overtopping devices as the wave dragon and the Archimedes wave swing. The main characteristics of these wave energy converters are discussed. A lot of research, development and engineering work is necessary to develop the experimental systems into reliable and cost-effective power stations. The wide variety of systems makes it difficult to say general things about power quality. However, the large variations of output power are a common problem. Whether this can be solved by using wave farms has to be investigated further}, + booktitle = {2005 {International} {Conference} on {Future} {Power} {Systems}}, + author = {Polinder, H. and Scuotto, M.}, + month = nov, + year = {2005}, + keywords = {Archimedes Wave Swing, Energy conversion, Ocean wave energy, Ocean waves, Petroleum, Power engineering and energy, Power generation, Power quality, Power system reliability, Power systems, Reliability engineering, Renewable energy resources, oscillating water column, power quality, power systems, renewable energy, wave energy conversion}, + pages = {9 pp.--9}, +} + +@article{borettiSolar, + title = {High-frequency standard deviation of the capacity factor of renewable energy facilities: {Part} 1—{Solar} photovoltaic}, + volume = {2}, + issn = {2578-4862}, + shorttitle = {High-frequency standard deviation of the capacity factor of renewable energy facilities}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/est2.101}, + doi = {10.1002/est2.101}, + abstract = {It is important to secure for every solar photovoltaic energy installation the highest-possible average (mean) capacity factor, as well as the lowest-possible SD, this latter computed with high frequency. High-frequency data of solar photovoltaic energy facilities are, however, very hard to be found. There are no estimations in the literature of the SD of the capacity factor of solar photovoltaic energy installations sampled with high frequency. Here, we show the data sampled every 5 minutes for the solar photovoltaic energy facilities connected to the Australian National Electricity Market grid during the year 2018. The average capacity factors are about 27\%-28\% flat panel, and 31\%-32\% tracking flat panel. The SDs have larger values at about 37\%-38\%, for coefficients of variation 120\%-130\%. As solar photovoltaic energy facilities only produce electricity during the daylight time, that is predictable, the statistic analysis is also applied to the daylight times only. While average daylight-only capacity factors are about twice the previous values, SDs are slightly less, for coefficients of variations more than halved at 55\%-65\%. The analysis highlights the extreme variability of solar energy helping the design of the energy storage needed for making possible an efficient, resilient, renewable energy-only grid. The collected and interpreted information and the provided analysis are filing a gap in the area of renewable energy and energy harvesting technology based on wind and solar photovoltaics where variability has been so far underevaluated.}, + language = {en}, + number = {1}, + urldate = {2022-01-26}, + journal = {Energy Storage}, + author = {Boretti, Alberto}, + year = {2020}, + keywords = {Australia, energy storage, renewable energy, solar energy, variability analysis, variability measures}, + pages = {e101}, +} + +@article{falcaoHydro, + title = {Wave energy utilization: {A} review of the technologies}, + volume = {14}, + issn = {1364-0321}, + shorttitle = {Wave energy utilization}, + url = {https://www.sciencedirect.com/science/article/pii/S1364032109002652}, + doi = {10.1016/j.rser.2009.11.003}, + abstract = {Sea wave energy is being increasingly regarded in many countries as a major and promising resource. The paper deals with the development of wave energy utilization since the 1970s. Several topics are addressed: the characterization of the wave energy resource; theoretical background, with especial relevance to hydrodynamics of wave energy absorption and control; how a large range of devices kept being proposed and studied, and how such devices can be organized into classes; the conception, design, model-testing, construction and deployment into real sea of prototypes; and the development of specific equipment (air and water turbines, high-pressure hydraulics, linear electrical generators) and mooring systems.}, + language = {en}, + number = {3}, + urldate = {2022-01-26}, + journal = {Renewable and Sustainable Energy Reviews}, + author = {Falcão, António F. de O.}, + month = apr, + year = {2010}, + keywords = {Equipment, Power take-off, Renewable energy, Review, Wave energy, Wave power}, + pages = {899--918}, +} + +@techreport{RM3, + address = {Albuquerque, New Mexico}, + title = {Methodology for {Design} and {Economic} {Analysis} of {Marine} {Energy} {Conversion} ({MEC}) {Technologies}}, + shorttitle = {{RM3}}, + url = {https://energy.sandia.gov/wp-content/gallery/uploads/SAND2014-9040-RMP-REPORT.pdf}, + language = {en}, + number = {SAND2014-9040}, + institution = {Sandia National Laboratories}, + author = {Neary, Vincent S and Previsic, Mirko and Jepsen, Richard A and Lawson, Michael J and Yu, Yi-Hsiang and Copping, Andrea E and Fontaine, Arnold A and Hallett, Kathleen C and Murray, Dianne K}, + month = mar, + year = {2014}, + pages = {262}, +} + +@book{newman, + title = {Marine {Hydrodynamics}}, + shorttitle = {newman}, + url = {https://direct.mit.edu/books/book/2693/Marine-Hydrodynamics}, + abstract = {Marine Hydrodynamics was specifically designed to meet the need for an ocean hydrodynamics text that is up-to-date in terms of both content and approach. The bo}, + language = {en}, + urldate = {2022-01-26}, + author = {Newman, J. N.}, + month = aug, + year = {1977}, +} + +@article{boretti_high-frequency_2020, + title = {High-frequency standard deviation of the capacity factor of renewable energy facilities: {Part} 1—{Solar} photovoltaic}, + volume = {2}, + issn = {2578-4862}, + shorttitle = {High-frequency standard deviation of the capacity factor of renewable energy facilities}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/est2.101}, + doi = {10.1002/est2.101}, + abstract = {It is important to secure for every solar photovoltaic energy installation the highest-possible average (mean) capacity factor, as well as the lowest-possible SD, this latter computed with high frequency. High-frequency data of solar photovoltaic energy facilities are, however, very hard to be found. There are no estimations in the literature of the SD of the capacity factor of solar photovoltaic energy installations sampled with high frequency. Here, we show the data sampled every 5 minutes for the solar photovoltaic energy facilities connected to the Australian National Electricity Market grid during the year 2018. The average capacity factors are about 27\%-28\% flat panel, and 31\%-32\% tracking flat panel. The SDs have larger values at about 37\%-38\%, for coefficients of variation 120\%-130\%. As solar photovoltaic energy facilities only produce electricity during the daylight time, that is predictable, the statistic analysis is also applied to the daylight times only. While average daylight-only capacity factors are about twice the previous values, SDs are slightly less, for coefficients of variations more than halved at 55\%-65\%. The analysis highlights the extreme variability of solar energy helping the design of the energy storage needed for making possible an efficient, resilient, renewable energy-only grid. The collected and interpreted information and the provided analysis are filing a gap in the area of renewable energy and energy harvesting technology based on wind and solar photovoltaics where variability has been so far underevaluated.}, + language = {en}, + number = {1}, + urldate = {2021-12-14}, + journal = {Energy Storage}, + author = {Boretti, Alberto}, + year = {2020}, + keywords = {Australia, energy storage, renewable energy, solar energy, variability analysis, variability measures}, + pages = {e101}, +} + +@article{renzi_hydrodynamics_2013, + title = {Hydrodynamics of the oscillating wave surge converter in the open ocean}, + doi = {10.1016/j.euromechflu.2013.01.007}, + abstract = {A potential flow model is derived for a large flap-type oscillating wave energy converter in the open ocean. Application of Green’s integral theorem in the fluid domain yields a hypersingular integral equation for the jump in potential across the flap. The solution is found via a series expansion in terms of the Chebyshev polynomials of the second kind and even order. Several relationships are then derived between the hydrodynamic parameters of the system. Comparison is made between the behaviour of the converter in the open ocean and in a channel. The degree of accuracy of wave tank experiments aiming at reproducing the performance of the device in the open ocean is quantified. A parametric analysis of the system is then undertaken. In particular, it is shown that increasing the flap width has the beneficial effect of broadening the bandwidth of the capture factor curve. This phenomenon can be exploited in random seas to achieve high levels of efficiency.}, + author = {Renzi, E. and Dias, F.}, + year = {2013}, +} + +@article{noauthor_notitle_nodate, +} + +@inproceedings{du_control_2021, + title = {Control {Co}-{Design} for {Rotor} {Blades} of {Floating} {Offshore} {Wind} {Turbines}}, + url = {https://asmedigitalcollection.asme.org/IMECE/proceedings/IMECE2020/84546/V07AT07A052/1099255}, + doi = {10.1115/IMECE2020-24605}, + language = {en}, + urldate = {2021-10-20}, + publisher = {American Society of Mechanical Engineers Digital Collection}, + author = {Du, Xianping and Burlion, Laurent and Bilgen, Onur}, + month = feb, + year = {2021}, +} + +@article{mwasilu_potential_2019, + title = {Potential for power generation from ocean wave renewable energy source: a comprehensive review on state-of-the-art technology and future prospects}, + volume = {13}, + issn = {1752-1424}, + shorttitle = {Potential for power generation from ocean wave renewable energy source}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1049/iet-rpg.2018.5456}, + doi = {10.1049/iet-rpg.2018.5456}, + abstract = {This study presents a comprehensive review of the ocean wave technology and prospects of the wave energy penetration to cater to clean global energy demand. An ocean wave is a remarkable energy resource, but it presents a very small share in the global energy mix because of various challenges and limitations encountered to unleash its potential. This study evaluates intensively the complex barriers to the ocean energy technology deployment. The existing and prospective major wave energy projects are extensively examined to identify the learned lessons and optimise possible technological solutions to close the gap in the energy market. Furthermore, limiting and motivating factors to foster the global wave energy potential growth are deeply discussed to ignite new research directions and promising solutions. In particular, the wave energy converters as the underpinning enabling technology are fully investigated regarding their technical readiness, reliability, competitiveness and critical challenges. To complete the power equation, possible energy conversion stages, grid connection and integration issues are dealt with in a broad view of the wave energy power system. Eventually, this study aims at providing an updated ocean wave technology review and progress while introducing new research gap to fast-track contributions in the global energy mix.}, + language = {en}, + number = {3}, + urldate = {2021-10-20}, + journal = {IET Renewable Power Generation}, + author = {Mwasilu, Francis and Jung, Jin-Woo}, + year = {2019}, + keywords = {clean global energy demand, energy market, global energy mix, global wave energy potential growth, hydroelectric power, ocean energy technology deployment, ocean wave renewable energy source, ocean waves, power generation, renewable energy sources, underpinning enabling technology, wave energy converters, wave energy penetration, wave energy power system, wave power generation}, + pages = {363--375}, +} + +@techreport{bull_technological_2013, + address = {Albuquerque, NM}, + title = {Technological {Cost}-{Reduction} {Pathways} for {Point} {Absorber} {Wave} {Energy} {Converters} in the {Marine} {Hydrokinetic} {Environment}.}, + url = {https://www.osti.gov/servlets/purl/1092993/}, + abstract = {This report considers and prioritizes the potential technical cost‐reduction pathways for offshore point absorber wave energy converters designed for ocean resources. This report focuses on cost‐reduction pathways related to the device technology rather than environmental monitoring or permitting opportunities. Three sources of information were used to understand current cost drivers and develop a prioritized list of potential cost‐reduction pathways: a literature review of technical work related to offshore wave activated body point absorbers, a reference device that was developed through the DOE Reference Model project, and a webinar with each of four industry device developers. Data from these information sources were aggregated and prioritized with respect to the potential impact on the lifetime levelized cost of energy, the potential for progress, the potential for success, and the confidence in success. Results indicated the four most promising cost‐reduction pathways include advanced controls, optimized structural design, improved power conversion, and optimized device profile.}, + language = {en}, + number = {SAND2013-7204, 1092993, 470210}, + urldate = {2021-10-20}, + institution = {Sandia National Lab}, + author = {Bull, Diana and Ochs, Margaret and Laird, Daniel and Boren, Blake and Jepsen, Richard}, + month = sep, + year = {2013}, + doi = {10.2172/1092993}, +} + +@techreport{ochs_technological_2013, + title = {Technological {Cost}-{Reduction} {Pathways} for {Point} {Absorber} {Wave} {Energy} {Converters} in the {Marine} {Hydrokinetic} {Environment}.}, + url = {https://www.osti.gov/servlets/purl/1092993/}, + number = {SAND2013-7204, 1092993, 470210}, + urldate = {2021-10-20}, + author = {Ochs, Margaret and Bull, Diana and Laird, Daniel and Jepsen, Richard and Boren, Blake}, + month = sep, + year = {2013}, + doi = {10.2172/1092993}, + pages = {SAND2013--7204, 1092993, 470210}, +} + +@article{coe_initial_2020, + title = {Initial conceptual demonstration of control co-design for {WEC} optimization}, + volume = {6}, + issn = {2198-6452}, + url = {https://doi.org/10.1007/s40722-020-00181-9}, + doi = {10.1007/s40722-020-00181-9}, + abstract = {While some engineering fields have benefited from systematic design optimization studies, wave energy converters have yet to successfully incorporate such analyses into practical engineering workflows. The current iterative approach to wave energy converter design leads to sub-optimal solutions. This short paper presents an open-source MATLAB toolbox for performing design optimization studies on wave energy converters where power take-off behavior and realistic constraints can be easily included. This tool incorporates an adaptable control co-design approach, in that a constrained optimal controller is used to simulate device dynamics and populate an arbitrary objective function of the user’s choosing. A brief explanation of the tool’s structure and underlying theory is presented. To demonstrate the capabilities of the tool, verify its functionality, and begin to explore some basic wave energy converter design relationships, three conceptual case studies are presented. In particular, the importance of considering (and constraining) the magnitudes of device motion and forces in design optimization is shown.}, + language = {en}, + number = {4}, + urldate = {2021-10-20}, + journal = {Journal of Ocean Engineering and Marine Energy}, + author = {Coe, Ryan G. and Bacelli, Giorgio and Olson, Sterling and Neary, Vincent S. and Topper, Mathew B. R.}, + month = nov, + year = {2020}, + pages = {441--449}, +} + +@misc{garcia-sanz_control_2018, + address = {Washington, DC}, + title = {Control {Co}-{Design} for {Wind}/{Tidal}/{Wave} {Energy} {Systems}}, + url = {https://arpa-e.energy.gov/sites/default/files/2.%20Garcia-Sanz_ARPA-E_Presentation.pdf}, + urldate = {2021-10-20}, + author = {Garcia-Sanz, Mario}, + month = jul, + year = {2018}, +} + +@article{garcia-sanz_control_2019, + title = {Control {Co}-{Design}: {An} engineering game changer}, + volume = {1}, + issn = {2578-0727}, + shorttitle = {Control {Co}-{Design}}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/adc2.18}, + doi = {10.1002/adc2.18}, + abstract = {Over the last few decades, control engineers have focused on developing innovative control theories and algorithms to regulate systems. These control efforts are usually at the last stage of a sequential strategy that allows engineering departments to work independently and consecutively toward the design of new products and systems. Control algorithms are usually developed at the end of that sequential process, once the mechanical, electrical, and other subsystems are completely defined. This paper discusses a different approach, named Control Co-Design (CCD). Following a concurrent engineering strategy that considers multidisciplinary subsystem interactions from the beginning of the design process, CCD applies control concepts to design the entire system and reach optimal solutions that are not achievable otherwise. This approach is a game changer for the control engineer, who will be not only the designer of advanced control algorithms but also the natural leader of the design of new products and systems. This paper describes some historic engineering breakthroughs achieved by applying CCD and explores some relevant application areas. It also presents three complementary CCD methodologies that include control-inspired paradigms, formal mathematical co-optimization techniques, and co-simulation campaigns to enhance engineering creativity and achieve radically new optimal designs.}, + language = {en}, + number = {1}, + urldate = {2021-10-20}, + journal = {Advanced Control for Applications}, + author = {Garcia-Sanz, Mario}, + year = {2019}, + keywords = {concurrent engineering, control, control co-design, design, systems engineering}, + pages = {e18}, +} + +@techreport{bull_systems_2017, + address = {Albuquerque, New Mexico}, + title = {Systems {Engineering} {Applied} to the {Development} of a {Wave} {Energy} {Farm}.}, + url = {https://www.osti.gov/biblio/1365534}, + number = {SAND2017-4507}, + institution = {Sandia National Lab}, + author = {Bull, Diana L. and Costello, Ronan Patrick and Babarit, Aurelien and Nielsen, Kim and Ferreira, Claudio Bittencourt and Kennedy, Ben and Malins, Robert Joseph and Dykes, Kathryn and Roberts, Jesse and Weber, Jochem}, + month = apr, + year = {2017}, +} + +@techreport{kilcher_marine_2021, + title = {Marine {Energy} in the {United} {States}: {An} {Overview} of {Opportunities}}, + shorttitle = {Marine {Energy} in the {United} {States}}, + url = {https://www.osti.gov/servlets/purl/1766861/}, + number = {NREL/TP-5700-78773, 1766861, MainId:32690}, + urldate = {2021-10-19}, + author = {Kilcher, Levi and Fogarty, Michelle and Lawson, Michael}, + month = feb, + year = {2021}, + doi = {10.2172/1766861}, + pages = {NREL/TP--5700--78773, 1766861, MainId:32690}, +} + +@techreport{noauthor_net_2021, + title = {Net {Zero} by 2050}, + url = {https://www.iea.org/reports/net-zero-by-2050}, + abstract = {Net Zero by 2050 - Analysis and key findings. A report by the International Energy Agency.}, + language = {en-GB}, + urldate = {2021-10-19}, + institution = {IEA}, + month = may, + year = {2021}, +} + +@misc{noauthor_climate_2019, + title = {Climate change impacts}, + url = {https://www.noaa.gov/education/resource-collections/climate/climate-change-impacts}, + urldate = {2021-10-19}, + journal = {NOAA}, + month = feb, + year = {2019}, +} + +@techreport{ipcc_summary_2021, + title = {Summary for {Policymakers}}, + url = {https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_SPM.pdf}, + urldate = {2021-10-19}, + institution = {Cambridge University Press}, + author = {{IPCC}}, + month = aug, + year = {2021}, +} + +@article{agte_mdo_2010, + title = {{MDO}: assessment and direction for advancement—an opinion of one international group}, + volume = {40}, + issn = {1615-147X, 1615-1488}, + shorttitle = {{MDO}}, + url = {http://link.springer.com/10.1007/s00158-009-0381-5}, + doi = {10.1007/s00158-009-0381-5}, + language = {en}, + number = {1-6}, + urldate = {2021-08-28}, + journal = {Structural and Multidisciplinary Optimization}, + author = {Agte, Jeremy and de Weck, Olivier and Sobieszczanski-Sobieski, Jaroslaw and Arendsen, Paul and Morris, Alan and Spieck, Martin}, + month = jan, + year = {2010}, + pages = {17--33}, +} + +@article{agte_mdo_2010-1, + title = {{MDO}: assessment and direction for advancement—an opinion of one international group}, + volume = {40}, + issn = {1615-147X, 1615-1488}, + shorttitle = {{MDO}}, + url = {http://link.springer.com/10.1007/s00158-009-0381-5}, + doi = {10.1007/s00158-009-0381-5}, + language = {en}, + number = {1-6}, + urldate = {2021-08-28}, + journal = {Structural and Multidisciplinary Optimization}, + author = {Agte, Jeremy and de Weck, Olivier and Sobieszczanski-Sobieski, Jaroslaw and Arendsen, Paul and Morris, Alan and Spieck, Martin}, + month = jan, + year = {2010}, + pages = {17--33}, +} + +@incollection{cooley_municipal_2012, + address = {Oxford ; New York}, + edition = {1st edition}, + title = {Municipal {Water} {Use}}, + isbn = {978-0-19-985944-3}, + language = {English}, + booktitle = {A {Twenty}-{First} {Century} {U}.{S}. {Water} {Policy}}, + publisher = {Oxford University Press}, + author = {Cooley, Heather}, + month = jul, + year = {2012}, +} + +@misc{walton_water_2016, + title = {Water {Systems} {Need} {Investment} and {Affordability}}, + url = {https://www.circleofblue.org/2016/united-states/water-systems-need-investment-affordability/}, + abstract = {Utilities are pulled by opposing economic and infrastructure pressures.}, + language = {en-US}, + urldate = {2021-05-28}, + journal = {Circle of Blue}, + author = {Walton, Brett}, + month = mar, + year = {2016}, +} + +@incollection{fischer_citizens_2000, + address = {Durham, NC}, + title = {Citizens as {Local} {Experts}}, + isbn = {978-0-8223-2622-9}, + language = {English}, + booktitle = {Citizens, {Experts}, and the {Environment}: {The} {Politics} of {Local} {Knowledge}}, + publisher = {Duke University Press Books}, + author = {Fischer, Frank}, + month = dec, + year = {2000}, +} + +@article{hohn_flints_2016, + chapter = {Magazine}, + title = {Flint’s {Water} {Crisis} and the ‘{Troublemaker}’ {Scientist}}, + issn = {0362-4331}, + url = {https://www.nytimes.com/2016/08/21/magazine/flints-water-crisis-and-the-troublemaker-scientist.html}, + abstract = {Marc Edwards took up the cause of water activists in Michigan a year ago — and earned their trust. Now he’s fighting to keep it.}, + language = {en-US}, + urldate = {2021-05-28}, + journal = {The New York Times}, + author = {Hohn, Donovan}, + month = aug, + year = {2016}, + keywords = {Edwards, Marc (1964- ), Flint (Mich), Hazardous and Toxic Substances, Hohn, Donovan, Lead, Ruffalo, Mark, Virginia Polytechnic Institute and State University, Water, Water Pollution}, +} + +@article{bosman_ep_2016, + chapter = {U.S.}, + title = {E.{P}.{A}. {Waited} {Too} {Long} to {Warn} of {Flint} {Water} {Danger}, {Report} {Says}}, + issn = {0362-4331}, + url = {https://www.nytimes.com/2016/10/21/us/epa-waited-too-long-to-warn-of-flint-water-danger-report-says.html}, + abstract = {The findings of the agency’s internal inspector general suggests the federal government should shoulder some of the blame for the city water supply’s continued lead contamination.}, + language = {en-US}, + urldate = {2021-05-28}, + journal = {The New York Times}, + author = {Bosman, Julie}, + month = oct, + year = {2016}, + keywords = {Bosman, Julie, Environmental Protection Agency, Flint (Mich), Lead, Water, Water Pollution}, +} + +@article{edwards_flint_2016, + title = {The {Flint} {Water} {Crisis}: {Overturning} the {Research} {Paradigm} to {Advance} {Science} and {Defend} {Public} {Welfare}}, + doi = {http://dx.doi.org/10.1021/acs.est.6b03573}, + number = {50}, + journal = {Environmental Science and Technology}, + author = {Edwards, Marc A. and Pruden, Amy}, + month = aug, + year = {2016}, + pages = {8935--8936}, +} + +@techreport{davis_flint_2016, + address = {Michigan}, + title = {Flint {Water} {Advisory} {Task} {Force} {Final} {Report}}, + institution = {Office of Governor Rick Snyder}, + author = {Davis, Matthew M. and Kolb, Chris and Reynolds, Lawrence and Rothstein, Eric and Sikkema, Ken}, + month = mar, + year = {2016}, + pages = {116}, +} + +@article{sorkin_contempt_2016, + title = {The {Contempt} {That} {Poisoned} {Flint}’s {Water}}, + url = {https://www.newyorker.com/news/amy-davidson/the-contempt-that-poisoned-flints-water}, + abstract = {When Michigan officials systematically ignored tests and dismissed concerns, it was the city’s citizens who suffered.}, + language = {en-US}, + urldate = {2021-05-28}, + journal = {The New Yorker}, + author = {Sorkin, Amy Davidson}, + month = jan, + year = {2016}, +} + +@incollection{vanderwarker_water_2012, + address = {Oxford ; New York}, + edition = {1st edition}, + title = {Water and {Environmental} {Justice}}, + isbn = {978-0-19-985944-3}, + abstract = {It is zero hour for a new US water policy! At a time when many countries are adopting new national approaches to water management, the United States still has no cohesive federal policy, and water-related authorities are dispersed across more than 30 agencies. Here, at last, is a vision forwhat we as a nation need to do to manage our most vital resource. In this book, leading thinkers at world-class water research institution the Pacific Institute present clear and readable analysis and recommendations for a new federal water policy to confront our national and global challenges at acritical time.What exactly is at stake? In the 21st century, pressures on water resources in the United States are growing and conflicts among water users are worsening. Communities continue to struggle to meet water quality standards and to ensure that safe drinking water is available for all. And new challengesare arising as climate change and extreme events worsen, new water quality threats materialize, and financial constraints grow. Yet the United States has not stepped up with adequate leadership to address these problems. The inability of national policymakers to safeguard our water makes the United States increasingly vulnerable to serious disruptions of something most of us take for granted: affordable, reliable, and safe water. This book provides an independent assessment of water issues and water management inthe United States, addressing emerging and persistent water challenges from the perspectives of science, public policy, environmental justice, economics, and law. With fascinating case studies and first-person accounts of what helps and hinders good water management, this is a clear-eyed look atwhat we need for a 21st century U.S. water policy.}, + language = {English}, + booktitle = {A {Twenty}-{First} {Century} {U}.{S}. {Water} {Policy}}, + publisher = {Oxford University Press}, + author = {Vanderwarker, Amy}, + month = jul, + year = {2012}, +} + +@article{goodnough_when_2016, + chapter = {U.S.}, + title = {When the {Water} {Turned} {Brown}}, + issn = {0362-4331}, + url = {https://www.nytimes.com/2016/01/24/us/when-the-water-turned-brown.html}, + abstract = {As every major decision was made over more than a year, officials at all levels of government acted in ways that contributed to the public health emergency in Flint, Mich.}, + language = {en-US}, + urldate = {2021-05-28}, + journal = {The New York Times}, + author = {Goodnough, Abby and Davey, Monica and Smith, Mitch}, + month = jan, + year = {2016}, + keywords = {Davey, Monica, Flint (Mich), Goodnough, Abby, Lead, Michigan, Smith, Mitch, Water, Water Pollution}, +} + +@article{schmidt_bush_2008, + title = {The {Bush} {Doctrine} and the {Iraq} {War}: {Neoconservatives} {Versus} {Realists}}, + volume = {17}, + issn = {0963-6412}, + shorttitle = {The {Bush} {Doctrine} and the {Iraq} {War}}, + url = {https://doi.org/10.1080/09636410802098990}, + doi = {10.1080/09636410802098990}, + abstract = {The aim of this article is to contribute to our understanding of both the debate over the war in Iraq and its implications for the future of U.S. foreign policy by examining the relationship between neoconservatism and realism. The article begins by establishing the connection between the tenets of neoconservatism and the arguments for war against Iraq. The primary focus is on the neoconservative Bush Doctrine that served as the primary justification for the Iraq War. Next, we turn to the arguments that realists put forth in their attempt to steer America away from the road to war. The realists, however, proved to be unsuccessful in their attempt to prevent war and in the final section we address the central question of the article; why did realism fail in the debate over Iraq?}, + number = {2}, + urldate = {2021-05-27}, + journal = {Security Studies}, + author = {Schmidt, Brian C. and Williams, Michael C.}, + month = may, + year = {2008}, + pages = {191--220}, +} + +@article{kaufmann_threat_2004, + title = {Threat {Inflation} and the {Failure} of the {Marketplace} of {Ideas}: {The} {Selling} of the {Iraq} {War}}, + volume = {29}, + issn = {0162-2889}, + url = {https://doi.org/10.1162/0162288041762940}, + doi = {10.1162/0162288041762940}, + number = {1}, + urldate = {2021-05-27}, + journal = {International Security}, + author = {Kaufmann, Chaim}, + month = jul, + year = {2004}, + pages = {5--48}, +} + +@article{nelkin_political_1975, + title = {The {Political} {Impact} of {Technical} {Expertise}}, + volume = {5}, + issn = {0306-3127}, + url = {https://doi.org/10.1177/030631277500500103}, + doi = {10.1177/030631277500500103}, + language = {en}, + number = {1}, + urldate = {2021-05-27}, + journal = {Social Studies of Science}, + author = {Nelkin, Dorothy}, + month = feb, + year = {1975}, + pages = {35--54}, +} + +@book{ricks_fiasco_2006, + address = {New York}, + title = {Fiasco: {The} {American} {Military} {Adventure} in {Iraq}, 2003 to 2005}, + isbn = {978-0-14-303891-7}, + shorttitle = {Fiasco}, + abstract = {Coming from The Penguin Press in February 2009, Thomas E. Ricks's The GambleThomas E. Ricks 's \#1 New York Times bestseller, Fiasco, transformed the political dialogue on the war in Iraq. Now Ricks has picked up where Fiasco left off-Iraq, late 2005. With more newsbreaking information, including hundreds of hours of interviews with top U.S. officials who were on the ground during the surge and beyond, The Gamble is the natural companion piece to Fiasco, and the two are sure to become the definitive examinations of what ultimately went wrong in Iraq.}, + language = {English}, + publisher = {Penguin Books}, + author = {Ricks, Thomas E.}, + year = {2006}, +} + +@inproceedings{grandi_evaluation_2013, + address = {Ljubljana, Slovenia}, + title = {Evaluation of current ripple amplitude in three-phase {PWM} voltage source inverters}, + isbn = {978-1-4673-4913-0 978-1-4673-4911-6}, + url = {http://ieeexplore.ieee.org/document/6601146/}, + doi = {10.1109/CPE.2013.6601146}, + abstract = {Determination of current ripple in three-phase PWM voltage source inverters (VSI) is important for both design and control purposes, since this is the most popular conversion topology for energy conversion systems. In this paper the complete analysis of the peak-to-peak current ripple distribution over a fundamental period is given for three-phase VSIs. In particular, peak-to-peak current ripple amplitude is analytically determined as a function of the modulation index. Minimum, maximum, and average values are also emphasized. Although the reference is made to continuous symmetric PWM, being the most simple and effective solution to minimize the current ripple, the analysis could be easily extended to either discontinuous or unsymmetrical modulation, both carrier-based and space vector PWM. The analytical developments for all the different subcases are verified by numerical simulations.}, + language = {en}, + urldate = {2021-05-17}, + booktitle = {2013 {International} {Conference}-{Workshop} {Compatibility} {And} {Power} {Electronics}}, + publisher = {IEEE}, + author = {Grandi, G. and Loncarski, J.}, + month = jun, + year = {2013}, + pages = {156--161}, +} + +@misc{yngve_solbakken_space_2017, + title = {Space {Vector} {PWM} {Intro}}, + url = {https://www.switchcraft.org/learning/2017/3/15/space-vector-pwm-intro}, + abstract = {Get rich, smart and famous by understanding the dark arts of space vector pulse width modulation! A must for everyone aspiring to become a star in the drives community!}, + language = {en-US}, + urldate = {2021-05-16}, + journal = {Switchcraft}, + author = {{Yngve Solbakken}}, + month = may, + year = {2017}, +} + +@misc{mathworks_permanent_nodate, + title = {Permanent magnet synchronous machine}, + url = {https://www.mathworks.com/help/physmod/sps/powersys/ref/permanentmagnetsynchronousmachine.html}, + urldate = {2021-05-16}, + journal = {Mathworks Help Center Documentation}, + author = {{Mathworks}}, +} + +@book{hanselman_brushless_2006, + address = {Lebanon, Ohio}, + edition = {2}, + title = {Brushless {Permanent} {Magnet} {Motor} {Design}}, + isbn = {1-881855-15-5}, + url = {https://blog.avislab.com/uploads/2014/05/BrushlessPermanentMagnetMotorDesignVersion2.pdf}, + abstract = {Written for electrical, electronics, and mechanical engineers responsible for designing and specifying motors, the book provides details of brushless DC and synchronous motors, as well as both radial and axial motor...}, + language = {en}, + urldate = {2021-05-14}, + publisher = {Magna Physics Publishing}, + author = {Hanselman, Duane C.}, + year = {2006}, +} + +@article{decoret_fourrier_2004, + title = {Fourrier transform of an impulsion train}, + language = {en}, + author = {Decoret, Xavier}, + month = jul, + year = {2004}, + pages = {3}, +} + +@misc{ka-raceing_ev_ka-raceing_2021, + title = {{KA}-{RaceIng} {Rollout} 2021 powered by {BASF}}, + url = {https://www.youtube.com/watch?v=xPRnP5qF-JQ}, + language = {German}, + collaborator = {{KA-RaceIng e.V.}}, + month = may, + year = {2021}, +} + +@misc{noauthor_vehicles_nodate, + title = {Vehicles – {ELEFANT} {RACING}}, + url = {https://elefantracing.de/vehicles}, + urldate = {2021-05-14}, +} + +@article{haugland_new_2019, + title = {A {New} {Motor}}, + url = {https://issuu.com/revolventnu/docs/spring_magazine_2019}, + number = {1}, + journal = {Revolve}, + author = {Haugland, Kristoffer}, + month = may, + year = {2019}, + pages = {20--21}, +} + +@misc{noauthor_mythen_nodate, + title = {Mythen}, + url = {https://electric.amzracing.ch/en/team/2019}, + urldate = {2021-05-14}, + journal = {AMZ Racing}, +} + +@misc{noauthor_amz_nodate, + title = {{AMZ} {Racing}}, + url = {https://electric.amzracing.ch/en/team/2019}, + urldate = {2021-05-14}, +} + +@incollection{woodson_review_1968, + address = {New York, NY}, + title = {Review of {Electromagnetic} {Theory}}, + volume = {1}, + url = {https://ocw.mit.edu/resources/res-6-003-electromechanical-dynamics-spring-2009/front-end-matter/app_b_emd.pdf}, + booktitle = {Electromechanical {Dynamics}}, + publisher = {John Wiley and Sons, Inc.}, + author = {Woodson, Herbert H. and Melcher, James R.}, + year = {1968}, + pages = {B19--B24}, +} + +@incollection{kassakian_introduction_2010, + series = {Addison-{Wesley} series in electrical engineering}, + title = {Introduction to {Rectifier} {Circuits}}, + isbn = {978-81-317-3320-2}, + booktitle = {Principles of {Power} {Electronics}}, + publisher = {Pearson Education}, + author = {Kassakian, John G. and Schlecht, Martin F. and Verghese, George C.}, + year = {2010}, + pages = {52}, +} + +@article{formula_student_germany_team_2019, + title = {Team {Profiles} {Electric}}, + url = {https://www.formulastudent.de/fileadmin/user_upload/all/2019/PR_Media/FSG2019%20magazine%20v20190724_LQ.pdf}, + journal = {Formula Student Germany}, + author = {{Formula Student Germany}}, + month = jul, + year = {2019}, + pages = {112--126}, +} + +@phdthesis{owen_benefits_2018, + address = {Cambridge, MA}, + type = {Thesis}, + title = {The benefits of {4WD} drive for a high-performance {FSAE} electric racecar}, + copyright = {MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.}, + url = {https://dspace.mit.edu/handle/1721.1/119907}, + abstract = {This thesis explores the performance of Rear-Wheel Drive (RWD) and Four-Wheel Drive (4WD) FSAE Electric racecars with regards to acceleration and regenerative braking. The benefits of a 4WD architecture are presented along with the tools for further optimization and understanding. The goal is to provide real, actionable information to teams deciding to pursue 4WD vehicles and quantify the results of difficult engineering trade-offs. Analytical bicycle models are used to discuss the effect of the Center of Gravity location on vehicle performance, and Acceleration-Velocity Phase Space (AVPS) is introduced as a useful tool for optimization. Lap-time Simulation is used to determine the regenerative braking energy available for recovery during a race for RWD and 4WD vehicles.}, + language = {eng}, + urldate = {2021-05-14}, + school = {Massachusetts Institute of Technology}, + author = {Owen, Elliot Douglas}, + year = {2018}, +} + +@article{wrobel_characterizing_2016, + title = {Characterizing the in situ {Thermal} {Behavior} of {Selected} {Electrical} {Machine} {Insulation} and {Impregnation} {Materials}}, + volume = {52}, + doi = {10.1109/TIA.2016.2589219}, + number = {6}, + journal = {IEEE Transactions on Industry Applications}, + author = {Wrobel, Rafal and Williamson, Samuel J. and Booker, Julian D. and Mellor, Phil H.}, + year = {2016}, + pages = {4678--4687}, +} + +@misc{sylvestre_120kw_nodate, + title = {{120kW} {Quad} {Inverter} for {All}-{Wheel} {Drive} {Electric} {Racecar}}, + url = {https://wisconsinracing.org/wp-content/uploads/2020/10/WR_Quad_Inverter.pdf}, + publisher = {Wisconsin Formula SAE Racing}, + author = {Sylvestre, Jason and Sixel, Will and Shozda, Alex}, +} + +@inproceedings{swaminathan_effect_2017, + title = {Effect of {Practical} {Losses} on {Optimal} {Design} of {Batch} {RO} {Systems}}, + booktitle = {Proceedings of {IDA} {World} {Congress} on {Desalination} and {Water} {Reuse}}, + publisher = {International Desalination Association}, + author = {Swaminathan, Jaichander and Stover, Richard L. and Tow, Emily W. and Warsinger, David M. and Lienhard, John H.}, + month = oct, + year = {2017}, +} diff --git a/ifacconf_latex/root.tex b/ifacconf_latex/root.tex new file mode 100644 index 0000000..3896539 --- /dev/null +++ b/ifacconf_latex/root.tex @@ -0,0 +1,361 @@ +%=============================================================================== +% $Id: ifacconf.tex 19 2011-10-27 09:32:13Z jpuente $ +% Template for IFAC meeting papers +% Copyright (c) 2007-2008 International Federation of Automatic Control +%=============================================================================== +\documentclass{ifacconf} + +\usepackage{graphicx} % include this line if your document contains figures +\usepackage{natbib} % required for bibliography +\usepackage{hyperref} +\usepackage{amsmath,amssymb} +\usepackage{mathtools} % for matrix left-alignment + +% real and imaginary symbols +\renewcommand{\Re}{\operatorname{\mathbb{R}e}} +\renewcommand{\Im}{\operatorname{\mathbb{I}m}} +%=============================================================================== +\begin{document} +\begin{frontmatter} + +\title{Force-Limited Control of Wave Energy Converters using a Describing Function Linearization\thanksref{footnoteinfo}} +% Title, preferably not more than 10 words. + +\thanks[footnoteinfo]{This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE–2139899.} + +\author[First]{Rebecca McCabe} +\author[Second]{Maha N. Haji} +\address*{Sibley School of Mechanical and Aerospace Engineering, Cornell University, + Ithaca, NY 14853 USA } + \address[First]{e-mail: rgm222@cornell.edu} + \address[Second]{e-mail: maha@cornell.edu} + +\begin{abstract} % Abstract of not more than 250 words. +Actuator saturation is a common nonlinearity in physical systems. In wave energy conversion, force saturation can be a convenient way to limit the size and cost of the generator and the mechanical loading on the drivetrain with minimal impact on energy generation. However, such nonlinear dynamics typically demand numerical time-domain simulation rather than analytical frequency-domain analysis, which increases computational cost and diminishes designer intuition. This paper proposes the use of describing functions to accurately linearize the force saturation dynamics and stay in the frequency domain. It explores the impact of the force limit on electrical power production of a generic single degree of freedom wave energy converter under energy-maximizing impedance control. Analytical expressions are obtained and the Smith chart is used as a visualization tool. The expressions are nondimensionalized to quantify the effect of the maximum force value on devices with different hydrodynamics and powertrain dynamics. Systems with predominately real-valued mechanical impedances are less sensitive to force limits than their more reactive counterparts. Sensitivity results are discussed in the context of sizing drivetrain components such as the generator, while the results can also apply to explore the impact of controller bandwidth and parameter error. The describing function method is over 200 times faster than a time-domain simulation, +%and X times faster than a spectral-domain simulation +showing promise as a technique to enable future studies such as large-scale design optimization and control co-design. +\end{abstract} + +\begin{keyword} +Constrained control, control of renewable energy resources, systems with saturation, nonlinear and optimal marine system control, sensors and actuators. +\end{keyword} + +\end{frontmatter} +%=============================================================================== + +\section{Introduction} +\subsection{Motivation} +Ocean wave energy converters are an immature yet promising source of renewable energy to decarbonize coastal electricity grids and small offshore systems. Due to waves' high-force, low-speed nature, sizing the device to collect maximum energy can lead to large structural and powertrain forces that ultimately reduce the system's economic viability. Wave Energy Converters (WECs) benefit from controllers that maximize power while obeying force constraints, although the resulting nonlinearity muddies intuition and increases computational cost. This paper examines the tradeoff of maximum force with power production using describing functions, a technique which is intuitive, analytical, and linear. This enables computational efficiency, the opportunity to apply linear system analysis tools, and the ability to couple with other models to perform multidisciplinary design optimization or control co-design in the future. The results equally apply to other types of impedance mismatch such as controller bandwidth limitations and parameter errors. + +\subsection{Literature Review} +Existing work on powertrain constraints in wave energy conversion is predominately in numerical constrained optimal control, typically using either model predictive control or spectral/pseudo-spectral methods. \cite{strofer_control_2023} implement a force constraint in the pseudo-spectral toolbox WecOptTool and optimizes the controller gains and drivetrain impedance. \cite{pena-sanchez_control_2022} utilize a pseudo-spectral method with simultaneous force and position constraints to perform economic optimization of the generator sizing. \cite{sichani_constrained_2014} sweep the value of a force constraint numerically and shows that the optimal damping gets higher as the force constraint lowers, while the optimal stiffness changes only slightly. \cite{tom_pseudo-spectral_2017} use a pseudo-spectral method with pitch amplitude and torque constraints, while also including a force term in the objective. \cite{faedo_optimal_2017} review model predictive control for WECs and notes constraints related to position, velocity, force, rate of change of force, and power flow direction (passivity). + +A minority of work tackles the problem analytically. \cite{zou_optimal_2017} use the Pontryagin maximum principle to show that a bang-singular arc-bang controller is optimal, revealing that saturating the unsaturated optimal solution can still be optimal in certain cases, while \cite{abdulkadir_optimal_2024} have extended the result to arrays. Both of these papers yield analytical piecewise expressions for the optimal control force, but finding the full state trajectory including the power still requires numerical simulation. %(as far as I could see? double check this) - +\cite{bacelli_geometric_2013} present a geometric tool to analyze simultaneous force and position constraints. The technique uses a spectral method (Galerkin's method) but needs to approximate constraints with their 2-norm, effectively constraining the root-mean-square of the signal rather than the peak. \cite{merigaud_geometrical_2023} likewise introduce a geometric tool, this one only accounting for motion amplitude constraints and focusing more on the hydrodynamics than the powertrain. The tool is visually and mathematically similar to a Smith chart. To the authors' knowledge, no one in the wave energy space has used describing functions to address constraints, although \cite{flower_describing-function_1980} utilize describing functions to model a WEC with friction-like nonlinear powertrain damping. Outside of the wave energy field, \cite{fukui_impedance_2021} have applied describing functions to model velocity saturation and torque saturation on a two-motor impedance-controlled system for a robotics application, and experimentally validate the results. + +%- Babarit 2023 PTO capping: effect of 3 different force caps and 3 different power caps on the energy spectrum, with energy calculated from real sea data in 4 different ways. The focus is not on the energy but on the accuracy of the energy prediction in different calculation methods. \cite{de_la_torre-castro_combined_2023} +% - Many people doing MPC with constraints +% - Tedeschi 2011 power saturation with simulink \cite{tedeschi_effect_2011} +% - Dan Herber 2014 \cite{herber_wave_2014} + +% STILL NEED TO CHECK +% - Giorgio's paper that implements constraints for a real WEC (+thesis?) +% - Ringwood follow on paper for pneumatic valve + +\subsection{Paper Contribution and Outline} +Wave energy converters are designed to resonate with incoming waves, and maximum power transfer requires impedance matching of the powertrain, controller, and hydrodynamic body. However, perfect impedance matching may not be possible in some conditions due to plant uncertainties, controller bandwidth, and actuator limitations. In this sense, force saturation can be seen as an impedance mismatch. Therefore, before analyzing the nonlinear dynamics of saturation, it is first informative to examine the properties of an impedance-mismatched linear system. This is outlined and visualized in section~\ref{sec:linear}, starting for a general system and then moving to the specific dynamics of an oscillating-body wave energy converter with an electric generator. In section~\ref{sec:nonlinear}, the describing function is introduced to handle the saturation nonlinearity, providing an intuitive linear approximation. Sensitivity results are provided in section~\ref{sec:sensitivities}, focusing on implications in powertrain sizing. + +\section{Peak Limiting in the Linear Case}\label{sec:linear} +\subsection{General Impedance-Matched System} +The analysis starts with a generic linear system modeled as a Thévenin equivalent circuit with AC voltage source $V_{th}$ and complex source impedance $Z_{th}$, shown in Fig.~\ref{fig:circuit}. +\begin{figure} +\begin{center} +\includegraphics[width=6cm]{ifacconf_latex/figs/IFAC CAMS Circuit drawing.pdf} % The printed column width is 8.4 cm. +\caption{Thévenin equivalent circuit for linear system} +\label{fig:circuit} +\end{center} +\end{figure} +The load impedance $Z_L$ is to be selected, with the conflicting goals of maximizing average power transfer $\overline{P}_L$ and minimizing the peak amplitude of load current $|I_L|$ or voltage $|V_L|$. Maximum power transfer occurs when there is impedance matching, meaning $Z_L = Z_{th}^*$ where $*$ indicates the complex conjugate. The load average power, peak voltage, and peak current at this matched point, denoted $\overline{P}_L^m, |V_L^m|,$ and $|I_L^m|$ respectively, are found as +\begin{equation}\label{eq:matched-values} + \overline{P}_L^m = \frac{|V_{th}|^2}{8 \Re(Z_{th})}, + |V_L^m| = \frac{|V_{th}| |Z_{th}|} {2 \Re(Z_{th})}, + |I_L^m| = \frac{|V_{th}|}{2 \Re(Z_{th})} +\end{equation} + +To consider all possibilities of the unmatched case, we set $Z_L = z Z_{th}^*$ for arbitrary complex number $z$. The space of $z$ can be visualized using a Smith chart, where $\Re(z)$ is on a curved horizontal axis and $\Im(z)$ is on a curved vertical axis. The axes are curved such that the chart can be simultaneously read as a standard polar plot of the complex reflection coefficient $\Gamma$, which is a transformation of $z$ defined as $\Gamma = \frac{z-1}{z+1}$. The impedance-matched case of $z=1$, $\Gamma = 0$ is found at the center of the plot, the minimum voltage at $z=0$, $\Gamma = -1$ on the left, and the minimum current at $z \rightarrow \infty$, $\Gamma = 1$ on the right. + +In the unmatched case, the average power, peak voltage, and peak current can be found using standard circuit techniques and expressed as fractions of their matched counterparts. The power ratio is: +\begin{equation}\label{eq:ratio-power} + \frac{\overline{P}_L}{\overline{P}_L^m} = 1 - |\Gamma|^2 +\end{equation} +\begin{figure}[bp!] + \centering + \includegraphics[width=\linewidth]{ifacconf_latex/figs/power-smith.png} + \caption{Smith chart representing the average power at the load for any $z=\frac{Z_L}{Z_{th}^*}$, using the expression (\ref{eq:ratio-power}). The real part of $z$ is plotted on the arcs labeled horizontally, while the imaginary part is plotted on the arcs labeled radially along the outside of the chart. The reflection coefficient $\Gamma$ is also represented as a polar plot centered at $z=1$.} + \label{fig:power-smith} +\end{figure} +\begin{figure*}[tb!] + \centering + \includegraphics[width=18.2cm]{ifacconf_latex/figs/IFAC CAMS paretos (2).pdf} + \caption{Smith charts representing the (a) peak voltage and (b) peak current at the load for any $z=\frac{Z_L}{Z_{th}}$, paired with (c) the pareto tradeoff between voltage, current, and power. The parameter $\alpha$ is swept, representing the relative reactance of the Thévenin impedance $Z_{th}$. Shaded regions indicate that the voltage (green) or current (pink) ratios exceed one. Dashed lines indicate the optimal contours.} + \label{fig:ratio-smith} +\end{figure*} +This relationship is visualized on the Smith chart in Fig.~\ref{fig:power-smith}. As the impedance ratio $z$ gets further away from the impedance-matched condition $z=1$ at the center of the circle, the power lowers quadratically. + +The corresponding voltage and current ratios are: +\begin{equation}\label{eq:ratios} +\begin{aligned} + \frac{|V_L|}{|V_L^m|} &= \sqrt{\frac{|\Gamma|^2 + 2 \Re(\Gamma) + 1}{\alpha^2 |\Gamma|^2 + 2 \alpha \Im(\Gamma) + 1} } \\ + \frac{|I_L|}{|I_L^m|} &= \sqrt{\frac{|\Gamma|^2 - 2 \Re(\Gamma) + 1}{\alpha^2 |\Gamma|^2 + 2 \alpha \Im(\Gamma) + 1} }\\ +\end{aligned} +\end{equation} + +The voltage and current relationships in (\ref{eq:ratios}) depend not only on $\Gamma$ but also on the phase of $Z_{th}$ via the parameter $\alpha = \frac{\Im(Z_{th})}{\Re(Z_{th})}$. These relationships are visualized on the Smith charts in Fig.~\ref{fig:ratio-smith}. + +Only positive $\alpha$ (inductive $Z_{th}$) are shown for brevity. The contours for negative $\alpha$ (capacitive $Z_{th}$) can be found by reflecting the graphs over the horizontal axis ($\Im(\Gamma) = 0)$ due to symmerty. On the Smith charts, points where the voltage and current ratios exceed 1 are shaded. These points are undesirable because they absorb less power than the baseline $z=1$, $\Gamma=0$ matched case while having higher peaks. The optimal contours (highest voltage and current ratios, $\frac{|V_L|}{|V_L^m|}$ and $\frac{|I_L|}{|I_L^m|}$, for a given power ratio $\frac{\overline{P}_L}{\overline{P}_L^m}$) are traced out with dashed lines. This optimal tradeoff $(\cdot)^\textrm{opt}$ can be found analytically by setting the partial derivative of $\frac{|V_L|}{|V_L^m|}$ and $\frac{|I_L|}{|I_L^m|}$ with respect to $\angle\, \Gamma$ equal to zero, where $\angle\, \Gamma= \tan^{-1} \frac{\Im(\Gamma)}{\Re(\Gamma)}$. This results in +\begin{equation}\label{eq:optimal-vi} +\begin{aligned} + %\frac{|V_L|}{|V_L^m|}^\textrm{opt} &= 2 \tan^{-1}{ \frac{\alpha^2 |\Gamma|^2 - \sqrt{(\alpha^2 + 1)(\alpha^2 |\Gamma|^4 + 1)} + 1}{\alpha (1 - |\Gamma|)^2}} \\ +\hspace{-8pt} \frac{|V_L|}{|V_L^m|}^\textrm{opt} \hspace{-13pt}= \frac{|I_L|}{|I_L^m|}^\textrm{opt} \hspace{-13pt}&= 2 \tan^{-1}{ \frac{\alpha^2 |\Gamma|^2 - \sqrt{(\alpha^2 + 1)(\alpha^2 |\Gamma|^4 + 1)} + 1}{\alpha (1 + |\Gamma|)^2}} +\end{aligned} +\end{equation} + +These optimal contours are aggregated in Fig.~\ref{fig:pareto} to show the tradeoff between power and voltage/current. Interestingly, as $|\alpha|$ grows (i.e., as $Z_{th}$ becomes less resistive and more reactive), there is less of a power penalty for a given voltage or current reduction. In other words, the power in the pure resistive $Z_{th}$ case is the most sensitive to voltage and current limits. If the goal is to obey a current limit $|I_L| \leq I_{max}$ without regard for the voltage, then the optimal solution from Fig.~\ref{fig:pareto} is expressed as: +\begin{equation} + \frac{\alpha^2 |\Gamma|^2 - \sqrt{(\alpha^2 + 1)(\alpha^2 |\Gamma|^4 + 1)} + 1}{\alpha (1 + |\Gamma|)^2} \leq \tan \frac{\Re(Z_{th}) I_{max}}{|V_{th}|} +\end{equation} +%Furthermore, the curves for the optimal voltage and current ratios align almost exactly. The sign difference on $|\Gamma|$ in the denominator has minimal effect at $|\Gamma|\rightarrow 0$, and also has minimal effect at $|\Gamma|\rightarrow 1$ because the numerator approaches zero. +\begin{figure} + \centering + \includegraphics[width=\linewidth]{ifacconf_latex/figs/pareto2.png} + \caption{Pareto front for optimal voltage and current ratios.} + \label{fig:pareto} +\end{figure} +Note that some of the optimal contours require a $z$ with nonzero imaginary part, i.e. a $Z_L$ that is more or less reactive than the impedance-matched case, rather than merely scaled up or down. Here it is worth discussing the difference between ``constrained optimal control" and ``optimal constrained control." The former refers to the unconstrained optimal controller that has been scaled or saturated until it meets the constraint, while the latter refers to the controller that is optimal for the constrained problem, which may be distinct. Scaling or saturating the control signal computed with the unconstrained optimal impedance (z = 1) yields a signal with a fundamental identical to one computed with a proportionally scaled linear controller impedance, effectively enforcing z to be a real number. This is distinct from the complex $z$ in the optimal profiles of (\ref{eq:optimal-vi}) and Fig.~\ref{fig:pareto}, which would be considered optimal constrained control. + +Furthermore, because the optimal voltage reduction path requires decreasing the impedance and the optimal current reduction path requires increasing the impedance, it is not possible to follow both paths simultaneously. For sufficiently high values of $|\alpha|$, it is possible to reduce both current and voltage simultaneously (i.e. avoid the shaded region of both Smith charts in Fig.~\ref{fig:ratio-smith} (a) and (b)), although for $\alpha=0$ a decrease in voltage is always associated with an increase in current and vice versa. This tradeoff is explored further in section (c) of Fig.~\ref{fig:ratio-smith}, a pareto front showing the nondominated combinations of the voltage, current, and power ratios. + +These plots reveal the effect of an impedance mismatch on power, current, and voltage, and can be used to choose an appropriate load impedance based on the relative importance of power generation and peak limiting. The extent to which a given impedance mismatch decreases the current, voltage, and power is strongly dependent on the Thévenin impedance phase parameter $\alpha$, although we note that the baseline signal amplitudes in the matched case also depend implicitly on $\alpha$ through (\ref{eq:matched-values}). +% Considering a weighted linear objective function $J$ + +% \begin{equation} +% J = a~ \frac{\overline{P}_L}{\overline{P}_L^m} - b~ \frac{|V_L|}{|V_L^m|} - (1 - a - b)~ \frac{|I_L|}{|I_L^m|} +% \end{equation} +% for $0 \leq a, b \leq 1$, we can substitute (\ref{eq:ratios}) and differentiate to derive the $\Gamma$ which maximizes $J$: + +% \begin{equation} +% \Gamma^\textrm{opt} = f(a, b, \alpha) +% \end{equation} +% This tradeoff is shown + +% Note that substituting $a=1, b=0$ recovers the optimal current condition and $a=1, b=1$ the optimal voltage condition from (\ref{eq:optimal-vi}). + +\subsection{Wave Energy Converters} +Applying the preceding analysis to a Wave Energy Converter (WEC) requires developing a Thévenin equivalent circuit for the WEC dynamics. We assume that the WEC consists of a floating body coupled to a power take-off (PTO) consisting of a drivetrain and a linear or rotational electric generator of the synchronous surface permanent magnet variety, although it is straightforward to substitute a hydraulic or other impedance provided the system remains linear. The generator is non-ideal, so the objective is electrical power, informed by the substantial differences when optimizing for mechanical versus electrical power which \cite{coe_useful_2023} summarize. The WEC dynamics in the frequency domain are: +\begin{equation}\label{eq:wec-dynamics} +\begin{aligned} + &((m+A)s^2 + B_h s + K_h) X + F_{PTO} = F_e &&\textrm{Body}\\ + &G \tau_{PTO} = F_{PTO},~G s X = \Omega &&\textrm{Gear ratio}\\ + &\tau_{PTO} = (B_d + \frac{K_d}{s}) \Omega + \tau_{gen} &&\textrm{PTO}\\ + &\tau_{gen} = K_t I,~V = I(R + s L) - K_t \Omega &&\textrm{Generator}\\ + &V = (B_c + \frac{K_c}{s}) I &&\textrm{Controller}\\ + &P_{elec} = \frac{1}{2} \Re(I^* V) &&\textrm{Power} +\end{aligned} +\end{equation} +where $s=j\omega$ is the Laplace variable, $m$ is the mass, $A$ is the added mass, $B_h$ is the hydrodynamic damping, $K_h$ is the hydrostatic stiffness, $X$ is the WEC position, $F_{PTO}$ is the power take-off force, $F_e$ is the wave excitation force, $G$ is the gear ratio in a linear PTO or the inverse of the equivalent gear radius in a rotary PTO, $K_d$ and $B_d$ are the drivetrain mechanical stiffness and damping, $\tau_{gen}$ and $\Omega$ are the generator torque and rotational speed, $K_t$ is the generator torque constant, $I$ and $V$ are the generator q-axis current and voltage, $R$ and $L$ are the generator winding resistance and inductance, $K_c$ and $B_c$ are the controller stiffness and damping, and $P_{elec}$ is the average electrical power. While typically the controller is between $\tau_{gen}$ and $\Omega$, here the controller is assumed to act between voltage and current. This will result in different controller gains but provides equivalent dynamics and will make the definition of the relevant Thévenin equivalent more convenient. A block diagram of these dynamics is shown in Fig.~\ref{fig:block-diagram-dynamics}. +\begin{figure} + \centering + \includegraphics[width=\linewidth]{ifacconf_latex/figs/IFAC CAMS Dynamics Diagram - Electrical Control.pdf} + \caption{Block diagram of dynamics.} + \label{fig:block-diagram-dynamics} +\end{figure} +The hydrodynamic coefficients $A$ and $B_h$ are frequency dependent, but this dependence is omitted for notational convenience. + +There are many ways to form a Thévenin equivalent circuit from these dynamics, depending on the desired line between the source and load impedance. Because we want to quantify electrical power rather than mechanical power, it makes sense to choose the controller as the load, $Z_L = Z_c = B_c + \frac{K_c}{s}$. This makes the Thévenin equivalent voltage correspond to generator q-axis voltage, $V_L = V$, and the Thévenin equivalent current correspond to generator q-axis current, $I_L = I$. With this choice, the Thévenin equivalent circuit parameters given by \cite{strofer_control_2023} are: +\begin{equation}\label{eq:thevenin} +\begin{aligned} + Z_{th} &= Z_w + \frac{K_t^2 G^2}{Z_m} \\ + |V_{th}| &= \frac{K_t G F_e}{|Z_m|} +\end{aligned} +\end{equation} +where we have defined the winding impedance $Z_w = R + s L$ and the mechanical impedance $Z_m = B_h + G^2B_d + (m+A)s + \frac{K_h + G^2 K_d}{s}$. + +From $Z_{th}$, we can derive $\alpha$ which relates to its phase and enables the practical interpretation of Fig.~\ref{fig:ratio-smith}: +\begin{equation}\label{eq:alpha} + \alpha = \frac{\Im(Z_{th})}{\Re(Z_{th})} = \frac{1+\Re(\frac{1}{\mathcal{Z}})}{\mathcal{L} + \Im(\frac{1}{\mathcal{Z}})} +\end{equation} +where $\mathcal{Z}$ and $\mathcal{L}$ represent the nondimensionalized mechanical impedance and inductance: +\begin{equation} + \mathcal{Z} = \frac{RZ_m}{K_t^2G^2}, \quad + \mathcal{L} = \frac{\omega L}{ R } +\end{equation} +noting that $\mathcal{L}$ is real while $\mathcal{Z}$ is complex. In most systems, $\mathcal{L} \approx 0$ because the wave period in the ocean is very slow compared to the electrical time constant of the winding. We previously saw that $|\alpha|$ greatly affects the sensitivity of power generation to a current or voltage limit. Now it is apparent that $\alpha$ depends on the phase or relative reactance of the mechanical impedance, and that mechanical impedances closer to pure damping result in higher $\alpha$ and are thus less sensitive to limits. + +In the matched case, the efficiency $\eta$ from mechanical to electrical power is simply: +\begin{equation}\label{eq:effic} + \eta = \frac{\overline{P}_L^m}{\overline{P}_{mech}^m} = \frac{\frac{|V_{th}|^2}{8 \Re(Z_{th})}}{\frac{|F_{e}|^2}{8 \Re(Z_{m})}} = \frac{1}{1 + \Re(\mathcal{Z})} +\end{equation} +Ultimately, the electrical power of a given WEC with optimal impedance-matched control can be evaluated dimensionally using (\ref{eq:matched-values}) and (\ref{eq:thevenin}), or nondimensionally using (\ref{eq:effic}). Then, for situations with one of several sources of impedance mismatch (either intentional with the intent to obey a given current or voltage limit, or unintentional due to parameter uncertainty or controller bandwidth limitations in broadband waves), the effect of a given reflection coefficient $\Gamma$ is found by plugging $\alpha$ from (\ref{eq:alpha}) into (\ref{eq:ratios}), or graphically via Fig.~\ref{fig:ratio-smith}. + +In WECs, a generator force limit of $|F_{gen}| \leq F_{max}$ is achieved with a q-axis current limit of $|I| \leq I_{max} = \frac{F_{max}}{K_t G}$. A limit on the q-axis voltage $V$ would have little practical utility directly. A limit on the phase voltage $V_s$ is needed to accurately represent the maximum voltage of a vector drive, and a limit on the position $X$ is required to represent actuator stroke length or powertrain kinematic constraints. The transfer function for $X$ is found from (\ref{eq:wec-dynamics}) as: +\begin{equation}\label{eq:X} + \frac{X}{F_e} = \frac{1}{Z_m - \frac{K_t^2 G^2 z Z_{th}^* s}{1 - z Z_{th}^* Z_w}} +\end{equation} +Meanwhile, the phase voltage is: +\begin{equation}\label{eq:Vs} + V_s^2 = V^2 + (L p \Omega I)^2 +\end{equation} +where $p$ is the number of machine poles. The phase voltage limit determines the high-speed portion of the generator's torque speed curve and can be evaluated by substituting (\ref{eq:ratios}) and (\ref{eq:X}) into (\ref{eq:Vs}) using $\Omega=GsX$. Smith plots similar to Fig.~\ref{fig:ratio-smith} could be made to visualize the effect of a position or phase voltage limit, although additional parameters besides $\alpha$ would need to be swept to visualize the full parameter space. Because the force (current) limit is already well-captured by the standard parameterization outlined earlier, and because force limits are often of primary interest to designers, the remainder of this paper focuses on just current limits. With this procedure, $\Gamma$ can be selected to enforce the current ratio $\frac{|I_L|}{|I_L^m|}$ to equal $\frac{I_{max}}{|I_L^m|}$, thus enforcing the limit. + +% as a function of $\zeta_u$ and $\omega_u^*$, and derive $\zeta_u$ and $\omega_u^*$ as a function of hydro params and drivetrain params + +\section{Saturation Nonlinearities}\label{sec:nonlinear} + +The previous section considered the effect of a \textit{linear} impedance mismatch. In other words, instead of $Z_L = Z_{th}^*$, the controller used a linear mismatched impedance $Z_L = z Z_{th}^*$. With this controller, the peak amplitude of the current waveform, which equals the fundamental amplitude since it is sinusoidal, equals the current limit $I_{max}$, with current ratio $\frac{I_{max}}{|I_L^m|}$. However, a nonlinear controller that produces a non-sinusoidal current waveform could spend more time at the current limit, which increases the fundamental amplitude and should produce more power. The basic idea is shown in Fig.~\ref{fig:sat-sin}. In the extreme case of a square wave current signal, the fundamental amplitude is a factor of $\frac{4}{\pi}\approx 1.27 $ higher than the current limit, so the current ratio would be $\frac{4}{\pi}\frac{I_{max}}{|I_L^m|}$. The resulting increase in the power contained in the fundamental can be found from Fig.~\ref{fig:pareto} by moving on the x-axis a factor of $\frac{4}{\pi}$ higher than a given starting point. The following section quantifies this effect for the cases where the current waveform is somewhere between a sin wave and a square wave using describing functions. + +\subsection{Describing Functions} +\begin{figure} + \centering + \includegraphics[width=8.4cm]{ifacconf_latex/figs/sin-saturation-3.png} + \caption{Plot of a saturated sinusoid with appropriate amplitdues labeled.} + \label{fig:sat-sin} +\end{figure} +We consider a saturation control law of the form +\begin{equation} + I_{L,sat}(t) = I_{max}\textrm{sat}(I_{L,temp}(t)/I_{max}) +\end{equation} +where $\textrm{sat}$ is the saturation function, $I_{L,temp}(t)$ is the time domain output of a standard linear impedance controller $I_{L,temp} = \frac{V_{L,sat}}{Z_C}$, stored temporarily in the controller's memory and never physically realized. Even though the relationship between $I_{L,temp}$ and $V_{L,sat}$ is linear, the temporary current $I_{L,temp}$ is not equal to $ I_L$ the current from a system with a linear controller, because $V_{L,sat} \neq V_L$. + +The waveform $I_{L,sat}(t)$ will be close to a saturated sinusoid, although not exact due to nonlinearities. Specifically, $I_{L,sat}(t)$ will inevitably contain harmonics due to saturation, shown as the orange arrow exiting the saturation block in Fig.~\ref{fig:block-diagram-nonlinear} (b). Those harmonics act as forces on the WEC and, due to the low pass nature of the effective mass-spring-damper dynamics, are substantially reduced but not eliminated in the velocity signal. The harmonics in velocity create harmonics in the voltage and thus harmonics in the hypothetical current before saturation $I_{L,temp}(t)$. Thus, $I_{L,sat}$ will have some small additional harmonics in addition to those of a saturated sinusoid, and here we neglect them due to the plant's low pass behavior. Sections (c) and (d) of Fig.~\ref{fig:block-diagram-nonlinear} both show this assumption as a green arrow exiting the controller block. + +Section (c) is the standard describing function method, which uses the fundamental of the saturated current signal, and (d) is the higher order describing function from \cite{nuij_higher-order_2006}, which uses higher harmonics of the saturated current signal. +\begin{figure*} + \centering + \includegraphics[width=18.2cm]{ifacconf_latex/figs/IFAC CAMS describing function block diagram.pdf} + \caption{Block diagram illustration of describing functions used to linearize a wave energy saturation nonlinearity. Mechanical power is shown to keep the diagram simple, but the same concept applies to electrical power.} + \label{fig:block-diagram-nonlinear} +\end{figure*} +The derivations immediately to follow preserve the higher current harmonics to enable higher order describing functions. %, while section \ref{sec:neglect-harmonics} uses standard describing functions for simplicity. + Assuming a sinusoidal temporary current signal, we can decompose the saturated sinusoid current signal into the sum of the fundamental and higher harmonics: +\begin{equation} + I_{L,sat}(t) \approx \sum_n |I_{L,sat,n}| \sin(n \omega t + \psi) +\end{equation} where $\psi$ is the same phase as $I_{L,temp}(t)$ had. The amplitude of the $n$th current harmonic $|I_{L,sat,n}|$ is defined equal to $f_{sat,n} |I_{L,temp}|$, where $f_{sat,n}$ is a saturation factor compared to the temporary unsaturated current amplitude $|I_{L,temp}|$. +\begin{equation}\label{f-sat-i-defn} + f_{sat,n} = \frac{|I_{L,sat,n}|}{|I_{L,temp}|} = \frac{|I_{L,sat,n}||Z_C|}{|V_{L,sat}|} +\end{equation} +To find $f_{sat,n}$, we can apply the describing function technique, leveraging Fourier analysis of a saturated sin wave to get an equivalent linear transfer function for the nonlinear saturation block, shown in (\ref{eq:f-sat-desc-fcn}), where $\theta = n \sin^{-1}\frac{I_{max}}{|I_{L,temp}|} $. +\begin{figure*}[htbp] +\begin{equation}\label{eq:f-sat-desc-fcn} + f_{sat,n} = +\begin{cases} +1 & \quad |I_{L,temp}| \leq I_{max} ~\And~ n = 1\\ +0 & \quad |I_{L,temp}| \leq I_{max} ~\And~ n \neq 1 \\ +\frac{2}{\pi} \left(\frac{I_{max}}{|I_{L,temp}|}\sqrt{1 - \left(\frac{I_{max}}{|I_{L,temp}|}\right)^2} + \theta \right) & \quad |I_{L,temp}| > I_{max} ~\And~ n = 1 \\ +0 & \quad |I_{L,temp}| > I_{max} ~\And~ n = 2,4,6,... \\ +\frac{4}{\pi} \frac{1}{n (n^2 - 1)} \left( n \sqrt{1 - (\frac{I_{max}}{|I_{L,temp}|})^2}\sin(\theta) - \frac{I_{max}}{|I_{L,temp}|}\cos(\theta) \right) & \quad |I_{L,temp}| > I_{max} ~\And~ n = 3,5,7,... +\end{cases} +\end{equation} +\end{figure*} +This equation is depicted graphically in Fig.~\ref{fig:desc-fcn} for the first 7 harmonics. As the amount of saturation increases, the fundamental amplitude decreases, and the higher harmonics become more prominent. The limit for large $\frac{|I_{L,temp}|}{I_{max}}$ is a square wave. + +\begin{figure}[htbp!] + \centering + \includegraphics[width=8.4cm]{ifacconf_latex/figs/fsat3.png} + \caption{Harmonic ratios $\frac{f_{sat,n}}{f_{sat,1}}$ as a function of the saturation amplitude ratio $\frac{|I_{L,temp}|}{I_{L,max}}$, for n = 1, 3, 5, and 7. All even harmonics are zero, and higher frequency harmonics have smaller amplitudes, which aligns with expectations.} + \label{fig:desc-fcn} +\end{figure} + +Consequently, at each harmonic frequency $n$, the saturation block can be approximated by an equivalent gain multiplier $f_{sat,n}$, such that the equivalent load impedance is $Z_L = Z_C / f_{sat,n}$ rather than $Z_L = Z_C$ as in the linear unsaturated case. This makes the nondimensional impedance for the $n$th harmonic $z_n = Z_C / (f_{sat,n} Z_{th}^*)$. %This multiplier must be calculated to enforce $f_{sat,n}$ to the desired level. The gain multiplier $m_n$ does not equal the current saturation factor $f_{sat,n}$ because $V_{L,sat} \neq V_L$. +Now we have a quasi-linear system, where the response is the sum of linear responses at different frequencies: +\begin{equation} + \overline{P}_L = \Sigma_{n} P_{L,n}(z_n) +\end{equation} + +% Because the plant is linear, each voltage harmonic will be a linear transformation of the current harmonics. This means that the current created by the saturated controller can be approximated by a sum of scaled-down responses to unsaturated controllers: +% \begin{equation}\label{m-sat-intro} +% \begin{aligned} +% \frac{|I_{L,sat,n}|}{|X_{sat,i}|} &\approx m_{sat,i} \frac{|F_{p,i}|}{|X_i|} = m_{sat,i} \sqrt{ (B_p i \omega)^2 + K_p^2} \\ +% I_{L,sat}(t) &\approx \sum_i m_{sat,i} \sqrt{ (B_p i \omega)^2 + K_p^2} ~|X_{sat,i}| \sin(i \omega t + \psi) \\ +% &\approx \sum_i m_{sat,i} (B_p \dot{x}_{sat,i} + K_p x_{sat,i} ) +% \end{aligned} +% \end{equation} +% Applied to the full system dynamic response: +% \begin{equation} +% \sum_i \left[ m \ddot{x}_{sat,i} + (B_h+m_{sat,i}B_p) \dot{x}_{sat,i} + (K_h + m_{sat,i}K_p) x_{sat,i} \right] \approx F_h \sin(\omega t) +% \end{equation} + +%\subsection{Neglecting Higher Harmonics}\label{sec:neglect-harmonics} +Optionally, a reasonable approximation is to only consider $f_{sat,1}$ the fundamental current harmonic, as in Fig.~\ref{fig:block-diagram-nonlinear} (c). Because the plant is essentially a second order low pass filter, the higher harmonics are attenuated and contain little energy. %In this section, we make this additional approximation and use $f_{sat}$ to refer to and $f_{sat,1}$. + +% The new dynamics are fully linear: +% \begin{equation} +% m \ddot{x}_{sat} + (B_h+m_{sat}B_p) \dot{x}_{sat} + (K_h + m_{sat}K_p) x_{sat} \approx F_h \sin(\omega t) +% \end{equation} + +% The gain multiplier $m_{sat}$ must be calculated from $f_{sat}$ such that the resulting saturated powertrain force is a factor $f_{sat}$ times the unsaturated powertrain force. From \eqref{f-sat-i-defn} and \eqref{m-sat-intro}, we have: +% \begin{equation} \label{eq:force-sat} +% m_{sat} = f_{sat} \frac{|X|} {|X_{sat}|} +% \end{equation} + +%Design takeaway: force saturation will have the least impact on energy generation when the excitation frequency equals the uncontrolled natural frequency (pure hydrodynamic response) $\omega_{n,u}$. For typical hydrodynamic coefficients, excitation frequencies higher than $\omega_{n,u}$ abruptly result in less energy, and excitation frequencies lower than $\omega_{n,u}$ more gradually result in less energy. This suggests that for force-limited systems, it may make sense to design $\omega_{n,u}$ to be higher than it would be in an unsaturated system, to avoid the steep dropoff in energy at the ocean excitation frequencies. This is very promising because $\omega_{n,u} = \sqrt{\frac{K_h}{m}}$, and lowering the mass would achieve the desired increase in $\omega_{n,u}$ while also decreasing structural costs. + +%\subsubsection{Including higher harmonics} +%Todo. Use the expression for $f_{sat,n}$ for i=3,5,7... in \eqref{f-sat-desc-fcn} to approximate the energy in the higher harmonics. + +\subsection{Limitations} +The main limitation of the describing function is that it only applies to regular waves. The saturated sinusoid shape of the force waveform relies on a sinusoidal voltage wave. Real waves come from a broadband spectrum and are irregular. It remains to be tested how accurate the results are for irregular waves. Even for regular waves, describing functions still are approximations that rely on the low pass filter behavior of the WEC. For WECs that are broadband, such as small WECs, this assumption may be poor. Future work includes a full error analysis of the describing functions compared to a fully nonlinear simulation. + +\section{Sensitivities}\label{sec:sensitivities} +Section \ref{sec:linear} and \ref{sec:nonlinear} will now be combined to yield overall sensitivity results. In a realistic WEC, perfect impedance matching may be possible in small waves, but above a certain threshold the generator's maximum force will be reached and a linear impedance mismatch or a nonlinear saturation strategy can be employed to extract as much energy as possible while respecting the constraint. + +For simplicity, we consider the $\alpha=0$ case in Fig.~\ref{fig:sensitivity}, corresponding to $Z_{th}$ purely real (resistive) and $Z_m$ purely imaginary (reactive). In a matched controller, power varies quadratically with the excitation force $F_e$ from (\ref{eq:matched-values}) and (\ref{eq:thevenin}). For a linear impedance mismatch, \eqref{eq:optimal-vi} indicates that the current ratio equals $1 - \Gamma$. Plugging in \eqref{eq:ratio-power} and \eqref{eq:matched-values} yields: +\begin{equation} + \overline{P}_L = \left( 1 - \left(1 - \frac{2 \Re(Z_{th}) I_{max}}{|V_{th}|}\right)^2 \right) \frac{|V_{th}|^2}{8 \Re(Z_{th})} +\end{equation} +Simplifying and setting all constants to enforce a normalized power of $1$ at $F_e=1$ (red marker in This is shown in Fig.~\ref{fig:sensitivity}) yields that the power scales linearly with $F_e$. Meanwhile, a nonlinear saturation strategy can provide a factor of up to $4/\pi$ larger fundamental, which means that it can achieve perfect impedance matching up until $F_e=\frac{4}{\pi}$ (blue marker in Fig.~\ref{fig:sensitivity}.) while also having a larger linear slope in the regions where it cannot achieve perfect matching. The describing function can quantify the power for larger $F_e$. This analysis allows designers to carefully select their largest wave for which impedance matching is possible, which will likely be much lower than the largest operational wave, because impedance mismatch can provide value at these points. +\begin{figure}[htbp!]\ + \centering + \includegraphics[width=8.4cm]{ifacconf_latex/figs/sensitivity-plot.png} + \caption{Comparison of the power versus excitation force for three controller types. The matched controller does not limit the generator force, while the other two do.} + \label{fig:sensitivity} +\end{figure} +%The generator is characterized by its maximum current, operating voltage, maximum displacement, resistance, and inductance. The current, voltage, and inductance dictate the generator's torque speed curve, typically considered its primary performance characteristic. The curve +%is pictured in Fig.~\ref{fig:ts-curve} and consists of a thermally-limited constant torque at low speeds (current-limited region) and a decreasing torque at high speeds when the back EMF voltage approaches that of the drive (voltage-limited region). The maximum displacement is an important machine sizing characteristic for linear generators, and can become relevant for rotational powertrains with buoy kinematic constraints. Finally, the resistance also affects the efficiency of the machine through (\ref{eq:effic}). A generator's size, and therefore cost, scales with its maximum torque $\tau_{max}$ and rotational speed $\omega_{max}$ for rotary generators, and maximum force $F_{max}$, velocity $\dot{x}_{max}$, and displacement $x_{max}$ for linear generators. Therefore, it is useful to express the power production as a function of these constraints. + +%\subsection{Dimensional Generator Sizing Implications} +%For comparison, we use cost values equal to that of a previous case study \cite{pena-sanchez_control_2022} that uses the pseudo-spectral method, a fully nonlinear numerical solver. + +% \begin{equation} +% CoS = 1.48 \cdot 10^3 \$/m +% CoF = 0.1656 \$/N +% C_{PTO} = 2.5 n_{gen} ( (L_{trans} + S_{max}) CoS + F_{trans} CoF) + C_{elec} +% \bar{LCOE} = C_{PTO} / EP +% \end{equation} + +\section{Conclusion} +This work presented an analytical framework for handling WEC generator force (current) constraints. First, the linear theory was reviewed, and key relationships for an impedance-mismatched Thévenin-equivalent circuit were visualized using Smith charts and Pareto fronts. Then, the specific dynamics for wave energy were introduced, and the implications of the nondimensional mechanical impedance and inductance on the Thévenin phase parameter $\alpha$ were highlighted. Next, describing function theory was introduced, with a description of where the nonlinearity is and how the low pass nature of the plant justifies neglecting higher harmonics. Finally, the two sections were combined together to demonstrate sensitivity to force limit under different control assumptions. + +A variety of extensions provide avenues for future work. The framework articulated here for force (current) constraints could easily be extended to other constraints, for example position, velocity, or phase voltage, by multiplying the ratios in (\ref{eq:ratios}) by the appropriate transfer function. Because these describing functions rely on a saturated-sin shape, they are not well-suited for examining two simultaneous constraints due to the overlapping nonlinearities, although the error remains to be quantified. The effect of irregular waves and frequency-dependent dynamics can likewise be investigated. In the context of WEC techno-economic optimization, the sensitivities should be coupled with a full generator model to inform the best design tradeoffs of power performance and machine size given realistic cost models. + +The analytical nature of this work provides intuition and computational speed for early-stage design or large-scale coupled optimization as needed. It does not take the place of numerical optimization such as the pseudo-spectral method, which can capture constraints fully nonlinearly, but still provides a relevant contribution to the field. For example, these analytical approximations could be used as the initial guess in a numerical optimization scheme to accelerate convergence. Finally, the general results related to impedance mismatch and signal limits can apply to many other domains of engineering that use impedance matching, such as circuits and robotics. + +The code for this work is available open-source at \url{https://github.com/symbiotic-engineering/IFAC_CAMS_2024/}. + +%\begin{ack} +%Place acknowledgments here. +%\end{ack} + +\bibliography{ifacconf_latex/references} + +% \appendix +% \section{Ratios in terms of $z$} % Each appendix must have a short title. +% Here, (\ref{eq:ratios}) is rewritten in terms of the impedance ratio $z$: +% \begin{equation}\label{eq:ratios-z} +% \begin{aligned} +% \frac{\overline{P}_L}{\overline{P}_L^m} &= \frac{4 \Re(z)}{|z|^2 + 2 \Re(z) + 1} \\ +% \frac{|V_L|}{|V_L^m|} &= \frac{2 |z|}{\sqrt{(1+\alpha^2)(|z|^2+1) + 2(1-\alpha^2)\Re(z) + 4 \alpha \Im(z) }} \\ +% \frac{|I_L|}{|I_L^m|} &= \frac{2}{\sqrt{(1+\alpha^2)(|z|^2+1) + 2(1-\alpha^2)\Re(z) + 4 \alpha \Im(z) }} +% \end{aligned} +% \end{equation} + +\end{document} diff --git a/saveallfigs.m b/saveallfigs.m new file mode 100644 index 0000000..442f417 --- /dev/null +++ b/saveallfigs.m @@ -0,0 +1,25 @@ +% saves all currently open figures as png to figs folder +function [] = saveallfigs(overwrite) + + if nargin == 0 + overwrite = false; + end + + FolderName = 'figs'; % Your destination folder + FigList = findobj(allchild(0), 'flat', 'Type', 'figure'); + for iFig = 1:length(FigList) + FigHandle = FigList(iFig); + if ~strcmp(FigHandle.Tag, 'EmbeddedFigure_Internal') % ignore live script inline plots + FigName = [num2str(get(FigHandle, 'Number')) '.png']; + set(0, 'CurrentFigure', FigHandle); + pathName = fullfile(FolderName, FigName); + if ~overwrite + while exist(pathName,'file') == 2 % don't overwrite existing figs + pathName = [pathName(1:end-4) '-(1).png']; + end + end + saveas(FigHandle,pathName); + end + end + +end \ No newline at end of file diff --git a/sensitivity_plot.m b/sensitivity_plot.m new file mode 100644 index 0000000..5a8fa21 --- /dev/null +++ b/sensitivity_plot.m @@ -0,0 +1,26 @@ +clear; close all +Hs = linspace(0,3); + +e1 = 1; +e2 = 1; +e3 = 4/pi; + +P_matched = e2 * Hs.^2; + +P_linear_mismatch = (1 - (1 - e1./Hs).^2) .* P_matched; +P_linear_mismatch(Hs < 1) = P_matched(Hs < 1); + +P_nonlinear_mismatch = (1 - (1 - e3./Hs).^2) .* P_matched; +P_nonlinear_mismatch(Hs < 4/pi) = P_matched(Hs < 4/pi); + +figure +plot(Hs,P_matched,'g-',Hs,P_linear_mismatch,'r--',Hs,P_nonlinear_mismatch,':b') +hold on +plot(1,1,'rd',4/pi,(4/pi)^2,'bd') +xlabel('Normalized Wave Excitation Force $F_e$','interpreter','latex') +ylabel('Normalized Average Power $\bar{P}_L$','interpreter','latex') +legend('Match: $\bar{P}_L = F_e^2$', ... + 'Linear Mismatch: $\bar{P}_L = 2 F_e - 1$', ... + 'Nonlinear Saturation: $\bar{P}_L = \frac{4}{\pi}(2 F_e - \frac{4}{\pi})$','interpreter','latex') +improvePlot +grid on