From 0635f54d011618e84a01af6df7043dcae174d2c9 Mon Sep 17 00:00:00 2001 From: chrord Date: Mon, 26 Mar 2018 00:21:57 +0200 Subject: [PATCH] codes --- Codes/Main/main.m | 225 +++++++++++++++++++ Codes/Main/startup.m | 8 + Codes/src/Bonferroni/DRO_CVaR_ICC.m | 103 +++++++++ Codes/src/Data_generation/AV_AEMO.mat | Bin 0 -> 2631980 bytes Codes/src/Data_generation/CC_matrices.m | 69 ++++++ Codes/src/Data_generation/PTDF_calc.m | 40 ++++ Codes/src/Data_generation/RTS_Data.m | 165 ++++++++++++++ Codes/src/Data_generation/RTS_Data2.m | 212 +++++++++++++++++ Codes/src/Real_time_dispatch/RT_solve_R.m | 51 +++++ Codes/src/Zymler/DRO_JCVaR_All.m | 83 +++++++ Codes/src/Zymler/DRO_JCVaR_All_solve_alpha.m | 66 ++++++ Codes/src/Zymler/DRO_JCVaR_All_solve_xY.m | 98 ++++++++ 12 files changed, 1120 insertions(+) create mode 100644 Codes/Main/main.m create mode 100644 Codes/Main/startup.m create mode 100644 Codes/src/Bonferroni/DRO_CVaR_ICC.m create mode 100644 Codes/src/Data_generation/AV_AEMO.mat create mode 100644 Codes/src/Data_generation/CC_matrices.m create mode 100644 Codes/src/Data_generation/PTDF_calc.m create mode 100644 Codes/src/Data_generation/RTS_Data.m create mode 100644 Codes/src/Data_generation/RTS_Data2.m create mode 100644 Codes/src/Real_time_dispatch/RT_solve_R.m create mode 100644 Codes/src/Zymler/DRO_JCVaR_All.m create mode 100644 Codes/src/Zymler/DRO_JCVaR_All_solve_alpha.m create mode 100644 Codes/src/Zymler/DRO_JCVaR_All_solve_xY.m diff --git a/Codes/Main/main.m b/Codes/Main/main.m new file mode 100644 index 0000000..d941fc7 --- /dev/null +++ b/Codes/Main/main.m @@ -0,0 +1,225 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Energy and Reserves Dispatch with\\ Distributionally Robust Joint Chance Constraints +% Christos ORDOUDIS, Viet Anh NGUYEN, Daniel KUHN, Pierre PINSON +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% This is the main script +% + +clear all; close all; clc; + +% call startup to add the necessary path +startup; + +tic + +%% + +% Data input + +RTS_Data2; + +% DRO input + +% Definition of dual norm used in the Wasserstein metric, value of \epsilon +% and the parameters for the algorithm in the Zymler approximation + +DRO_param.dual_norm = 'inf'; % dual norm +DRO_param.eps_joint_cvar = 0.05; % \epsilon +DRO_param.CVaR_max_iter = 40; % MaxIter +DRO_param.tolerance = 1e-1; % \eta +DRO_param.alpha_max = 1000; % \overline{\delta} +DRO_param.alpha_min = 1e-4; % \undeline{\delta} +DRO_param.penalty = 1e6; % BigM + +% Values of rho, the finite positive-valued vector P is defined + +% Vector for Bonferroni approximation + +rho_vectorC = [0 linspace(0.0001, 0.0025, 24)]; + +% Vector for Zymler approximation + +rho_vectorJC = [0 0.0001 linspace(0.001, 0.01, 23)]; + +% Number of individual runs (number of coupled datasets in the numerical +% study) + +IR_max = 100; +IR_sim = 100; + +% Number of out of sample data for each individual run (N') for testing +% dataset + +OOS_max = 200; +OOS_sim = 100; + +% Number of maximum sample size (N) + +N_max = 1000; + +% Number of sample data in training dataset (N) + +N = 100; + +% Total number of data + +Nscen = IR_max * (N_max + OOS_max); + +% Generation of data + +rng(4,'twister') + +% Number of wind farms + +wf=[1:6]; + +% Loading the historical data for wind farms + +wff=AV_AEMO2(:,wf); + +% Cutting off very extreme values + +cut_off_eps = 1e-2; +wff(wff(1-cut_off_eps)) = 1 - cut_off_eps; + +% Logit-normal transformation (Eq. (1) in ref. [31]) + +yy=log(wff./(1-wff)); + +% Calculation of mean and variance, note that we increase the mean to have +% higher wind penetration in our test-case + +mu = mean(yy)+1.5; +sigma_m=cov(yy); +sigma_m=sigma_m./(std(yy)'*std(yy)); + +% Inverse of logit-normal transformation (Eq. (2) in ref. [31]) + +R = chol(sigma_m); +y = repmat(mu,Nscen,1) + randn(Nscen,size(WindDATA,1))*R; +Wind = (1+exp(-y)).^(-1); + +% Checking correlation, mean and true mean of data + +corrcoef(Wind); +mean(Wind); +true_mean_Wind = (1+exp(-mu)).^(-1); + +% Reshaping the data structure + +nWind = Wind'; +nWind = reshape(nWind,size(WindDATA,1), N_max+OOS_max, IR_max); + +% Initializing the matrices to gather final results + +Joint_CVaR_Obj_IR = zeros(IR_sim, OOS_sim, length(rho_vectorC)); +CVaR_Obj_IR = zeros(IR_sim, OOS_sim, length(rho_vectorJC)); +ICC_TC = NaN(IR_sim,length(rho_vectorC)); +JCC_TC = NaN(IR_sim,length(rho_vectorJC)); + +% Loop for each individual run for 100 coupled datasets + +for j = 1:IR_sim + display('out of sample iteration:'); + j + + % For each coupled dataset, we pick N and N' samples + WPf_max = nWind(:,1:N_max,j)'; + WPr_max = nWind(:,N_max+1:N_max+OOS_max,j)'; + WPf = WPf_max(1:N,:); + WPr = WPr_max(1:OOS_sim,:); + + % Build the corresponding data related to wind power production + all = [1:N]; + system_info.Wscen = WPf(all,:)'; + system_info.mu = mean(system_info.Wscen,2); + system_info.xi = system_info.Wscen - repmat(system_info.mu, 1, size(system_info.Wscen,2)); + + % Calculation of A,B,C,b matrices for joint chance constraints + CC_jcc = CC_matrices(system_info, DRO_param); + jcc = CC_jcc.jcc; + + % Loop for each value of \rho in P vector + for i = 1:length(rho_vectorC) + + % optimize for each value of rho for Bonferroni approximation + + DRO_param.rho = rho_vectorC(i); + + DRO_ICC_CVaR = DRO_CVaR_ICC(system_info, DRO_param, jcc); + ICC_p_DA{j, i} = DRO_ICC_CVaR.p; + ICC_ru{j, i} = DRO_ICC_CVaR.ru; + ICC_rd{j, i} = DRO_ICC_CVaR.rd; + ICC_obj{j, i} = DRO_ICC_CVaR.Obj; + ICC_flag{j, i} = DRO_ICC_CVaR.Flag; + CVaR_Y{j,i} = DRO_ICC_CVaR.Y * system_info.xi; + CVaR_Qy{j,i} = DRO_ICC_CVaR.q; + CVaR_QY{j,i} = DRO_ICC_CVaR.qY * system_info.xi; + CVaR_Fy{j,i} = DRO_ICC_CVaR.fy; + CVaR_FY{j,i} = DRO_ICC_CVaR.fY * system_info.xi; + + % optimize for each value of rho for Zymler approximation + + DRO_param.rho = rho_vectorJC(i); + + DRO_JCC_CVaR = DRO_JCVaR_All(system_info, DRO_param, jcc); + JCC_p_DA{j, i} = DRO_JCC_CVaR.p; + JCC_ru{j, i} = DRO_JCC_CVaR.ru; + JCC_rd{j, i} = DRO_JCC_CVaR.rd; + JCC_obj{j, i} = DRO_JCC_CVaR.Obj; + JCC_flag{j, i} = DRO_JCC_CVaR.Flag; + Joint_CVaR_Y{j,i} = DRO_JCC_CVaR.Y * system_info.xi; + Joint_CVaR_Qy{j,i} = DRO_JCC_CVaR.q; + Joint_CVaR_QY{j,i} = DRO_JCC_CVaR.qY * system_info.xi; + Joint_CVaR_Fy{j,i} = DRO_JCC_CVaR.fy; + Joint_CVaR_FY{j,i} = DRO_JCC_CVaR.fY * system_info.xi; + + % Loop for each out-of-sample realization + for k = 1:OOS_sim + system_info.Wreal = WPr(k,:)'; + system_info.DWreal = system_info.Wreal - system_info.mu; + + % Solve real-time optimal power flow for the solution of Bonferroni + % approximation + RT_solution_CVaR = RT_solve_R(system_info,DRO_ICC_CVaR.p,DRO_ICC_CVaR.ru,DRO_ICC_CVaR.rd); + CVaR_Obj_IR(j,k,i) = RT_solution_CVaR.Obj_RT; + CVaR_lshed{j,k,i} = RT_solution_CVaR.lshed_RT; + CVaR_flow{j,k,i} = DRO_ICC_CVaR.fy + DRO_ICC_CVaR.fY * system_info.DWreal; + CVaR_p{j,k,i} = DRO_ICC_CVaR.Y * system_info.DWreal; + CVaR_q{j,k,i} = DRO_ICC_CVaR.q + DRO_ICC_CVaR.qY * system_info.DWreal; + CVaR_flag(j,k,i) = RT_solution_CVaR.Flag; + + + % Solve real-time optimal power flow for the solution of Zymler + % approximation + RT_solution_Joint_CVaR = RT_solve_R(system_info,DRO_JCC_CVaR.p,DRO_JCC_CVaR.ru,DRO_JCC_CVaR.rd); + Joint_CVaR_Obj_IR(j,k,i) = RT_solution_Joint_CVaR.Obj_RT; + Joint_CVaR_lshed{j,k,i} = RT_solution_Joint_CVaR.lshed_RT; + Joint_CVaR_flow{j,k,i} = DRO_JCC_CVaR.fy + DRO_JCC_CVaR.fY * system_info.DWreal; + Joint_CVaR_p{j,k,i} = DRO_JCC_CVaR.Y * system_info.DWreal; + Joint_CVaR_q{j,k,i} = DRO_JCC_CVaR.q + DRO_JCC_CVaR.qY * system_info.DWreal; + Joint_CVaR_flag(j,k,i) = RT_solution_Joint_CVaR.Flag; + + + end + + % Calculation of expected cost + + if DRO_ICC_CVaR.Flag == 0 + ICC_TC(j,i) = system_info.Cr1'*DRO_ICC_CVaR.ru + system_info.Cr2'*DRO_ICC_CVaR.rd + mean(CVaR_Obj_IR(j,:,i)); + else + ICC_TC(j,i) = NaN; + end + + if DRO_JCC_CVaR.Flag == 0 + JCC_TC(j,i) = system_info.Cr1'*DRO_JCC_CVaR.ru + system_info.Cr2'*DRO_JCC_CVaR.rd + mean(Joint_CVaR_Obj_IR(j,:,i)); + else + JCC_TC(j,i) = NaN; + end + + end +end + +Time = toc diff --git a/Codes/Main/startup.m b/Codes/Main/startup.m new file mode 100644 index 0000000..a10931d --- /dev/null +++ b/Codes/Main/startup.m @@ -0,0 +1,8 @@ +% This script adds the folder src into the path of matlab +% Notice that the src folder has to be in the same level as the Experiment1 +path1 = pwd; +path2 = strsplit(path1,filesep); +path3 = strjoin(path2(1:end-1),filesep); +path_src = strcat(path3,filesep,'src'); +path(genpath(path_src),path); +clear path1 path2 path3 path_src \ No newline at end of file diff --git a/Codes/src/Bonferroni/DRO_CVaR_ICC.m b/Codes/src/Bonferroni/DRO_CVaR_ICC.m new file mode 100644 index 0000000..ec35549 --- /dev/null +++ b/Codes/src/Bonferroni/DRO_CVaR_ICC.m @@ -0,0 +1,103 @@ +function[sol] = DRO_CVaR_ICC(si,DRO_param,jcc) + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % Energy and Reserves Dispatch with\\ Distributionally Robust Joint Chance Constraints + % Christos ORDOUDIS, Viet Anh NGUYEN, Daniel KUHN, Pierre PINSON + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + % This script implements the Bonferroni approximation + + yalmip('clear') + + % Getting the number of thermals power plants, wind farms, scenarions, + % transmission lines and nodes + Nunits = size(si.Pmax,1); + Nwind = size(si.Wmax,1); + Nscen = size(si.Wscen,2); + + + % Definition of variables + p = sdpvar(Nunits, 1); % Day-ahead power production from thermal power plants + ru = sdpvar(Nunits, 1); % Upward reserve dispatch from thermal power plants + rd = sdpvar(Nunits, 1); % Downward reserve dispatch from thermal power plants + Y = sdpvar(Nunits, Nwind, 'full'); % Linear decision rule for real-time power production + + + s_obj = sdpvar(1, Nscen); % sigma variable for obj + lambda_obj = sdpvar(1, 1); % lambda variable for obj + + + % create x by stacking up p, ru and rd + x = [p; ru; rd]; + + % Constraints set + CS = []; + + % Day-ahead constraints + CS = [CS, si.Pmin <= p - rd, p + ru <= si.Pmax, 0 <= ru <= si.ResCap, 0 <= rd <= si.ResCap]; + CS = [CS, sum(p) + sum(si.Wmax.*si.mu) - sum(si.D) == 0]; + CS = [CS, sum(Y, 1) == -si.Wmax']; + + % Run a for-loop to add the constraints related to the individual cvar + % The set of code below is generic, it can be copied and paste for any + % structure joint chance constraint of interest + + % find the number of Individual chance constraints we have + nICC = 0; + for j=1:size(jcc, 1) + nICC = nICC + size(jcc{j, 1}, 1); + end + + for j=1:size(jcc, 1) + A_C{j,1} = jcc{j,1}; + B_C{j,1} = jcc{j,2}; + C_C{j,1} = jcc{j,3}; + b_C{j,1} = jcc{j,4}; + end + A = cell2mat(A_C); + B = cell2mat(B_C); + C = cell2mat(C_C); + b = cell2mat(b_C); + + for j=1:size(jcc, 1) + eps_C(j) = jcc{j,5}/size(jcc{j, 1}, 1); + end + + eps = [repmat(eps_C(1),size(jcc{1, 1}, 1),1);repmat(eps_C(2),size(jcc{2, 1}, 1),1);repmat(eps_C(3),size(jcc{3, 1}, 1),1)]; + + % create variables + s = sdpvar(nICC, Nscen, 'full'); + lambda = sdpvar(nICC, 1); + tau = sdpvar(nICC, 1); + + for j = 1:nICC + CS = [CS, DRO_param.rho*lambda(j) + sum(s(j, :))/Nscen <= 0]; + CS = [CS, tau(j) <= s(j,:)]; + CS = [CS, (1 - 1/eps(j))*repmat(tau(j), 1, Nscen) + 1/eps(j)*( repmat(A(j,:)*x - b(j), 1, Nscen) + (B(j,:)*Y+C(j,:))*si.xi ) <= s(j,:) ]; + CS = [CS, norm(1/eps(j)*(B(j,:)*Y + C(j,:)), DRO_param.dual_norm) <= lambda(j)]; + end + + % Build the objective function + Obj = si.Cr1'*ru + si.Cr2'*rd + si.C'*p + DRO_param.rho*lambda_obj + 1/Nscen * sum(s_obj); + CS = [CS, si.C'*Y*si.xi <= s_obj]; + CS = [CS, norm( Y' * si.C, DRO_param.dual_norm) <= lambda_obj]; + + % Settings + optim_options = sdpsettings('solver', 'gurobi','gurobi.TimeLimit',1000,'gurobi.NumericFocus',3,'verbose',0); + + % Solve + sol = optimize(CS, Obj, optim_options); + + sol.p = value(p); + sol.Y = value(Y); + sol.ru = value(ru); + sol.rd = value(rd); + sol.Y = value(Y); + sol.fy = si.Qg*value(p) + si.Qw*si.DiagWmax * si.mu - si.Qd*si.D; + sol.fY = si.Qg*value(Y) + si.Qw*si.DiagWmax; + sol.q = si.PG * value(p); + sol.qY = si.PG * value(Y); + sol.Obj = value(Obj); + sol.Flag = sol.problem; + +end \ No newline at end of file diff --git a/Codes/src/Data_generation/AV_AEMO.mat b/Codes/src/Data_generation/AV_AEMO.mat new file mode 100644 index 0000000000000000000000000000000000000000..c76b8e82712d98b91f8edb419953edbe9d49e248 GIT binary patch literal 2631980 zcma&sLw7C=kS*X7>%_Kg+qP}nwr$(C?c~I^ZN9P5-@R+~y!WK)7u4X{B`c^RBPc|` zO2=VImLVq_#>Vqjz^_&?^){{~1>7XH7zgo5IaM^29?6ice@R+~^51tn3END?8e zl1CmfQDKo#N>U1=C?ug$g~{JULQ#{+97@bK&)qE^`{A}3Qc9)wm+sZim)hr6t-06U 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zyeCO~UuvRlbTEee_!veAc&3Lgov= 1 - eps + % For the j-th joint chance constraint: + % A = jcc{j, 1} + % B = jcc{j, 2} + % C = jcc{j, 3} + % b = jcc{j, 4} + % eps = jcc{j, 5} + + % Initialize the value for alpha + nJCC = size(jcc, 1); + maxK = 0; + for j = 1:nJCC + if size(jcc{j, 1}, 1) > maxK + maxK = size(jcc{j, 1}, 1); + end + end + + % initialize alpha to values of 1 + + input.alpha = (DRO_param.alpha_min + DRO_param.alpha_max)/2*ones(nJCC, maxK); + + + iter = 1; + + while iter <= DRO_param.CVaR_max_iter + + % First, fix alpha, solve for x and Y + sol_xY = DRO_JCVaR_All_solve_xY(si,DRO_param, input, jcc); + p_sol(:,iter) = sol_xY.p; + ru_sol(:,iter) = sol_xY.ru; + rd_sol(:,iter) = sol_xY.rd; + viol_sol(:,iter) = sol_xY.viol; + obj(iter) = sol_xY.Obj; + + if iter > 1 && (obj(iter) - obj(iter-1))/obj(iter) > 1e-1 + display('Error: Objective value has to be decreasing\n'); + break + end + + if iter > 1 && norm((obj(iter) - obj(iter-1))/obj(iter), 2) < DRO_param.tolerance + break + end + + % Update x and Y + input.p = sol_xY.p; + input.ru = sol_xY.ru; + input.rd = sol_xY.rd; + input.Y = sol_xY.Y; + + % solve the alpha subproblem + sol_alpha = DRO_JCVaR_All_solve_alpha(si,DRO_param, input, jcc); + + % update alpha + input.alpha = sol_alpha.alpha; + + iter = iter + 1; + end + + % Resolve the last time + DRO_sol_JCVaR = DRO_JCVaR_All_solve_xY(si,DRO_param, input, jcc); + + if norm(DRO_sol_JCVaR.viol, 2) < DRO_param.tolerance + DRO_sol_JCVaR.message = 'Problem is feasible'; + DRO_sol_JCVaR.Flag = 0; + else + DRO_sol_JCVaR.message = 'Problem is infeasible'; + DRO_sol_JCVaR.Flag = 12; + end +end + diff --git a/Codes/src/Zymler/DRO_JCVaR_All_solve_alpha.m b/Codes/src/Zymler/DRO_JCVaR_All_solve_alpha.m new file mode 100644 index 0000000..962d39a --- /dev/null +++ b/Codes/src/Zymler/DRO_JCVaR_All_solve_alpha.m @@ -0,0 +1,66 @@ +function[sol] = DRO_JCVaR_All_solve_alpha(si,DRO_param, input, jcc) +% In this subproblem, the values of x and Y are fixed +% Solve for alpha + + p = input.p; + Y = input.Y; + ru = input.ru; + rd = input.rd; + + x = [p; ru; rd]; + nJCC = size(jcc, 1); + maxK = 0; + for j = 1:nJCC + if size(jcc{j, 1}, 1) > maxK + maxK = size(jcc{j, 1}, 1); + end + end + + yalmip('clear') + + % Getting the number of thermals power plants, wind farms, scenarions, + % transmission lines and nodes + Nscen = size(si.Wscen,2); + + % Definition of variables + alpha = sdpvar(nJCC, maxK, 'full'); + + s = sdpvar(nJCC, Nscen, 'full'); + lambda = sdpvar(nJCC, 1); + tau = sdpvar(nJCC, 1); + + % Constraints set + CS = []; + CS = [DRO_param.alpha_min <= alpha <= DRO_param.alpha_max]; + + % Run a for-loop to add the constraints related to the joint cvar + % The set of code below is generic, it can be copied and paste for any + % structure jcc of interest + for j = 1:nJCC + A = jcc{j, 1}; + B = jcc{j, 2}; + C = jcc{j, 3}; + b = jcc{j, 4}; + eps = jcc{j, 5}; + % find the number of individual chance constraint belonging to this + K = size(A, 1); + CS = [CS, tau(j) <= s(j,:)]; + for k = 1:K + CS = [CS, (1 - 1/eps)*repmat(tau(j), 1, Nscen) + alpha(j,k)/eps*( repmat(A(k,:)*x - b(k), 1, Nscen) + (B(k,:)*Y+C(k,:))*si.xi ) <= s(j,:) ]; + CS = [CS, norm(alpha(j,k)/eps*(B(k,:)*Y + C(k,:)), DRO_param.dual_norm) <= lambda(j)]; + end + end + + % Optimization options + optim_options = sdpsettings('solver', 'gurobi','gurobi.TimeLimit',1000,'gurobi.NumericFocus',3,'verbose',0); %, 'verbose', 0 + + % Build the objective function + Obj = sum(DRO_param.rho*lambda) + (1/Nscen * sum(s(:))); + + % Solve + diag = optimize(CS, Obj, optim_options); + + sol.alpha = value(alpha); + sol.Flag = diag.problem; + +end \ No newline at end of file diff --git a/Codes/src/Zymler/DRO_JCVaR_All_solve_xY.m b/Codes/src/Zymler/DRO_JCVaR_All_solve_xY.m new file mode 100644 index 0000000..7740cf9 --- /dev/null +++ b/Codes/src/Zymler/DRO_JCVaR_All_solve_xY.m @@ -0,0 +1,98 @@ +function[sol] = DRO_JCVaR_All_solve_xY(si, DRO_param, input, jcc) +% In this subproblem, the values of alpha are fixed +% Solve for x and Y +% x contains 3 variables: p, r_u, r_d + + alpha = input.alpha; + + + yalmip('clear') + + % Getting the number of thermals power plants, wind farms, scenarions, + % transmission lines and nodes + Nunits = size(si.Pmax,1); + Nwind = size(si.Wmax,1); + Nscen = size(si.Wscen,2); + + % Definition of variables + p = sdpvar(Nunits, 1); % Day-ahead power production from thermal power plants + ru = sdpvar(Nunits, 1); % Day-ahead power production from thermal power plants + rd = sdpvar(Nunits, 1); % Day-ahead power production from thermal power plants + %y = sdpvar(Nunits, 1); % Linear decision rule for real-time power production + Y = sdpvar(Nunits, Nwind, 'full'); % Linear decision rule for real-time power production + + + + s_obj = sdpvar(1, Nscen); % sigma variable for obj + lambda_obj = sdpvar(1, 1); % lambda variable for obj + + + + + % create x by stacking up p, ru and rd + x = [p; ru; rd]; + + % Constraints set + CS = []; + + % Day-ahead constraints + CS = [CS, si.Pmin <= p - rd, p + ru <= si.Pmax, 0 <= ru <= si.ResCap, 0 <= rd <= si.ResCap]; + CS = [CS, sum(p) + sum(si.Wmax.*si.mu) - sum(si.D) == 0]; + CS = [CS, sum(Y, 1) == -si.Wmax']; + + % Run a for-loop to add the constraints related to the joint cvar + % The set of code below is generic, it can be copied and paste for any + % structure jcc of interest + + % find the number of Joint chance constraints we have + nJCC = size(jcc, 1); + % create variables + s = sdpvar(nJCC, Nscen, 'full'); + lambda = sdpvar(nJCC, 1); + tau = sdpvar(nJCC, 1); + viol = sdpvar(nJCC, 1); + + CS = [CS, viol >= 0]; + for j = 1:nJCC + A = jcc{j, 1}; + B = jcc{j, 2}; + C = jcc{j, 3}; + b = jcc{j, 4}; + eps = jcc{j, 5}; + + % find the number of individual chance constraint belonging to this + K = size(A, 1); + + CS = [CS, DRO_param.rho*lambda(j) + sum(s(j, :))/Nscen <= viol(j)]; + CS = [CS, tau(j) <= s(j,:)]; + for k = 1:K + CS = [CS, (1 - 1/eps)*repmat(tau(j), 1, Nscen) + alpha(j,k)/eps*( repmat(A(k,:)*x - b(k), 1, Nscen) + (B(k,:)*Y+C(k,:))*si.xi ) <= s(j,:) ]; + CS = [CS, norm(alpha(j,k)/eps*(B(k,:)*Y + C(k,:)), DRO_param.dual_norm) <= lambda(j)]; + end + end + + % Build the objective function + Obj = si.Cr1'*ru + si.Cr2'*rd + si.C'*p + DRO_param.rho*lambda_obj + 1/Nscen * sum(s_obj) + DRO_param.penalty*sum(si.C)*sum(viol); + CS = [CS, si.C'*Y*si.xi <= s_obj]; + CS = [CS, norm( Y' * si.C, DRO_param.dual_norm) <= lambda_obj]; + + % Settings + optim_options = sdpsettings('solver', 'gurobi','gurobi.TimeLimit',1000,'gurobi.NumericFocus',3,'verbose',0); + + % Solve + sol = optimize(CS, Obj, optim_options); + + sol.p = value(p); + sol.Y = value(Y); + sol.ru = value(ru); + sol.rd = value(rd); + sol.viol = value(viol); + sol.Y = value(Y); + sol.fy = si.Qg*value(p) + si.Qw*si.DiagWmax * si.mu - si.Qd*si.D; + sol.fY = si.Qg*value(Y) + si.Qw*si.DiagWmax; + sol.q = si.PG * value(p); + sol.qY = si.PG * value(Y); + sol.Obj = value(Obj); + sol.Flag = sol.problem; + +end \ No newline at end of file

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