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study_PTOsizing.m
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study_PTOsizing.m
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% study_PTOsizing.m script m-file
% AUTHORS:
% Jeremy Simmons (email: [email protected])
% University of Minnesota
% Department of Mechanical Engineering
%
% CREATION DATE:
% December 31, 2021
%
% PURPOSE:
% The purpose of this script is to perform a design study of PTO
% architectures for wave-powered reverse osmosis operating in a known
% distibution of sea conditions. The script is set up to
% perform the same study for four different PTO architectures.
%
% The models used in the design study are simple, static models with that
% include two-way coupling with the time-averaged simulation results of a
% WEC; the coupling is set up such that the reaction force from the PTO is
% a function of the average WEC speed (or power absortion) and the average
% WEC speed (or power absorption) is function of the reaction torque from
% the PTO.
%
% In the design study, the WEC-driven pump displacement and RO module
% membrane area are varied across a grid of values. For each set
% of these design variables, an optimization is performed to select the
% nominal operating pressure of the system (either the RO feed pressure or
% the pressure at the outlet of the WEC_driven pump depending on the PTO
% architecture) and the switching duty (if applicable). This routine is
% performed for each sea state.
%
% The optimization of the operating pressure and switching duty is a
% nonlinear, constrained optimization which seeks to maximize the permeate
% production subject to the following constraints:
% 1) the electrical power production meets or exceeds the electrical demand
% 2) the operating pressure at the RO module is within a prescribe range
% If the design does not meet these constraints, the value of zero is
% recorded as the permeate production rate for that design.
%
% Once the results are obtained for the specified grid of design
% parameters, design parameters are selected for each sea state to give
% optimal combinations based on four possible configurations:
% A) the WEC-driven pump and RO module size are fixed across all sea
% conditions
% B) the WEC-driven pump is variable across all sea states while the active
% RO module size is fixed
% C) the active RO module size is variable across all sea states while the
% WEC-driven pump displacement is fixed.
% D) Both the WEC-driven pump and active RO module size are variable across
% all sea states
% The design combinations are organized based on the largest allowable
% value for the two design parameters; the design parameters are selected
% for each sea state from the set of designs that have design parameters
% values are less than or equal to the maximum allowable value, when
% variable by sea state. Otherwise, when the design parameter is fixed
% across the sea states, the set includes only designs that have the same
% value of the fixed design parameter. The design with greatest permeate
% production is selected from the set of available designs in each sea
% state.
%
%
% FILE DEPENDENCIES:
% PTOsizing_multiSS.m
% zero2nan.m
% parameters_timeAvePTO.m
% loadColors.m
% data_coulombPTO_dampingStudy_24-Aug-2022_1_slim.mat
%
% UPDATES
% 12/31/2021 - created.
% 06/15/2023 - add optional ERU (ERUconfig=0 -> w/o ERU; ERUconfig=1 ->
% w/ ERU). Values between 0 and 1 effectively set an efficiency of the ERU.
%
% Copyright (C) 2022 Jeremy W. Simmons II
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <https://www.gnu.org/licenses/>.
%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear
clc
%% %%%%%%%%%%%% SIMULATION/DESIGN PARAMETERS %%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialize parameter structure and get misc. base parameters
par = parameters_timeAvePTO();
% bounds on pressures in system
bounds.p_f_bnds = [4e6 8e6]; % [Pa/Pa] Bounds for feed pressure
bounds.p_w_bnds = [4e6 30e6]; % [Pa/Pa] Bounds for pressure at WEC driven pump
bounds.D_bnds = [0.1 1]; % [-] bounds for valve switching duty
% WEC: load time averaged results for WEC performance
filename_WECpowerCurve = 'data_coulombPTO_dampingStudy_20220927_slim.mat';
load(filename_WECpowerCurve)
par.T_c_data = T_c_data; % [Nm] Torque applied to WEC by PTO
par.PP_w_data = PP_w_data; % [W] Power transmitted by WEC to PTO
par.weight = weight;
par.Hs = Hs;
par.Tp = Tp;
clearvars T_c_data PP_w_data weight Hs Tp
%% %%%%%%%%%%%% Study Variables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% WEC-driven pump displacment
nD_w = 11; % Size of array for displacment
% D_w = linspace(0.05,2,nD_w);
D_wArray = logspace(log10(0.01),log10(.75),nD_w); % [m^3/s] displacement
% membrane area in Ro module
S_roArray = [1500 3000 4500 6000 9000 ];% [m^2] membrane area
nS_ro = length(S_roArray); % Size of array for permeate coefficient
% Specify PTO configurations
PTOarray = [1 1 3 3 4 1 1 3 3 4];
design_case = [1 2 1 2 1 3 4 3 4 3];
ERUconfig = (1)*ones(size(iiPTO)); % 0-w/o ERU; 1-w/ ERU
nPTO = length(iiPTO);
% Specify the set of sea-states to design for
SSset = [1:114];
par.SSset = SSset;
%% %%%%%%%%%%%% COLLECT DATA %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for iPTO = 1:nPTO
for iS_ro = 1:nS_ro
data(iPTO,iS_ro) = PTOsizing_multiSS(D_wArray,S_roArray(iS_ro), ...
bounds,PTOarray(iPTO),design_case(iPTO), ...
ERUconfig(iPTO),par);
end
end
%% %%%%%%%%%%%% SAVE DATA %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
filename = ['data_PTOsizing_',char(datetime("now",'Format','yyyyMMdd'))];
files = ls;
nfiles = size(files,1);
k = 1;
for j = 1:nfiles
if contains(files(j,:),filename)
k = k+1;
filenameTag = ['_',num2str(k)];
else
filenameTag = [];
end
end
save([filename,filenameTag],'-v7.3')
return
%% %%%%%%%%%%%% PLOTTING %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Cost Model
%% Plot results for each architecture on same plot
lines = [{'-'},{'-.'},{'--'},{':'},{':'}];
marker = [{'x'},{'s'},{'^'},{'*'}];
loadColors;
C = [black; maroon; blue; green];
figure
hold on
for iPTO = 1:nPTO
for iS_ro = 1:nS_ro
p(iPTO,iS_ro) = plot(1e3*data(iPTO,iS_ro).D_w(:),...
1e3*data(iPTO,iS_ro).q_permTotal(:),...
'Color', C(iPTO,:),'lineStyle',cell2mat(lines(iS_ro)),'lineWidth',1.5);
p(iPTO,iS_ro).Annotation.LegendInformation.IconDisplayStyle = 'off';
end
end
xLim = xlim;
yLim = ylim;
for iPTO = 1:nPTO
scatter(-999,-999,50,C(iPTO,:),'filled','s')
end
for iS_ro = 1:nS_ro
plot([-999 -998],[-999 -999],...
'k','lineStyle',cell2mat(lines(iS_ro)),'lineWidth',1.5);
end
xlim(xLim)
ylim(yLim)
legend('PTO 1','PTO 2','PTO 3','PTO 4',...
['S_{ro}=',num2str(S_roArray(1)),'m^2'],...
['S_{ro}=',num2str(S_roArray(2)),'m^2'],...
['S_{ro}=',num2str(S_roArray(3)),'m^2'])
xlabel('Displacement (L/rad)')
ylabel('Permeate Production (L/s)')
title('Design Performance')
%% Plotting Results
% Cost normalized by the cost per RO size
cost = @(D_w,S_ro,q_perm,lam_1,lam_2) ...
(D_w + lam_1*S_ro + lam_2)./zero2nan(q_perm);
lines = [{'-'},{'-.'},{'--'},{':'}];
marker = [{'x'},{'s'},{'^'},{'*'}];
loadColors;
C = [black; maroon; blue; green];
figure
hold on
for iPTO = 1:nPTO
for iS_ro = 1:nS_ro
p(iPTO,iS_ro) = plot(1e3*data(iPTO,iS_ro).D_w(:),...
cost(data(iPTO,iS_ro).D_w(:),S_roArray(iS_ro),24*3600*data(iPTO,iS_ro).q_permTotal(:),0.001,0.5),...
'Color', C(iPTO,:),'lineStyle',cell2mat(lines(iS_ro)),'lineWidth',1.5);
p(iPTO,iS_ro).Annotation.LegendInformation.IconDisplayStyle = 'off';
end
end
xLim = xlim;
yLim = ylim;
for iPTO = 1:nPTO
scatter(-999,-999,50,C(iPTO,:),'filled','s')
end
for iS_ro = 1:nS_ro
plot([-999 -998],[-999 -999],...
'k','lineStyle',cell2mat(lines(iS_ro)),'lineWidth',1.5);
end
xlim(xLim)
ylim(yLim)
legend('PTO 1','PTO 2','PTO 3','PTO 4',...
['S_{ro}=',num2str(S_roArray(1)),'m^2'],...
['S_{ro}=',num2str(S_roArray(2)),'m^2'],...
['S_{ro}=',num2str(S_roArray(3)),'m^2'])
xlabel('Displacement (L/rad)')
ylabel('Permeate Production (L/s)')
title('Design Performance')
%% mark minimum cost design
[~,iS_ro] = min(min(cost(1e3*D_w,S_ro,24*3600*q_permTotal,0.1,0.5)));
[~,iD_w] = min(cost(1e3*D_w(:,iS_ro),S_ro(:,iS_ro),24*3600*q_permTotal(:,iS_ro),0.1,0.5));
scatter(1e6*S_roArray(iS_ro),1e3*D_wArray(iD_w),50,'r*')