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🔥 内容介绍

以可再生能源制氢为特征的能源系统将是今后能源互联网建设的重要方向之一.该文针对风-光-氢多主体能源系统的合作运行展开研究.首先,考虑主体间的电能交易建立各主体的优化运行模型,然后基于纳什谈判理论建立风-光-氢多主体合作运行模型,接着将其等效为联盟效益最大化和电能交易支付谈判两个子问题.为保护各主体隐私,运用交替方向乘子法提出上述两个子问题的分布式求解方法.最后通过算例验证所提合作运行模型以及分布式算法的有效性.仿真结果表明通过风-光-氢多主体的合作运行,可以较大幅度提高各主体的运行效益以及合作联盟的整体效益.此外,风光发电上网电价的降低,将促进风-光-氢多主体展开合作,以提升各自运行效益.

⛳️ 运行结果

📣 部分代码

function out = yalmiptest(prefered_solver,auto)%YALMIPTEST Runs a number of test problems.%% YALMIPTEST is recommended when a new solver or a new version% of YALMIP installed.%% EXAMPLES% YALMIPTEST % Without argument, default solver used% YALMIPTEST('solver tag') % Test with specified solver% YALMIPTEST(options) % Test with specific options structure from%% See also SDPSETTINGS​if ~exist('sedumi2pen.m')disp('Add /yalmip/extras etc to your path first...')disp('Read the <a href="https://yalmip.github.io/tutorial/installation/">Installation notes</a>.')returnend​if ~exist('callsedumi.m')disp('Still missing paths...Just do an addpath(genpath(''yalmiprootdirectory''));')disp('Read the <a href="https://yalmip.github.io/tutorial/installation/">Installation notes</a>.')returnend​% SDPT3 has a function called constraint.m which causes issuesdetected = which('constraint.m');if isa(detected,'cell')if length(detected)>0if isempty(strfind(detected{1},'extras\@constraint'))clcdisp('You seem to have some other toolbox with a function called constraint.m');disp('Delete that toolbox, or delete the function/class, or change path so that YALMIP is on top.');disp(detected{1})endreturnendend​detected = which('yalmip.m','-all');% Will not work in Octave as Octave only reports first item found?if isa(detected,'cell')if length(detected)>1clcdisp('You seem to have multiple installations of YALMIP in your path.')disp('Please correct this...');disp(detected)returnendend​% Pagination really doesn't work well with solversmore off​if exist('OCTAVE_VERSION', 'builtin')OctaveRunning = 1;elseOctaveRunning = 0;end​donttest = 0;if (nargin==1) && isa(prefered_solver,'char') && strcmp(prefered_solver,'test')donttest = 0;prefered_solver = '';elsedonttest = 1;end​if nargin==0prefered_solver = '';elseif ~(isa(prefered_solver,'struct') | isa(prefered_solver,'char'))error('Argument should be a solver tag, or a sdpsettings structure');endif isa(prefered_solver,'char')donttest = 1;endend​if ~(exist('callsedumi')==2)clcdisp('The directory yalmip/solvers is not in your path.')disp('These must be in path:')disp(' yalmip/');disp(' yalmip/extras');disp(' yalmip/operators');disp(' yalmip/modules');disp(' yalmip/solvers');disp('See <a href="https://yalmip.github.io/tutorial/installation/">installation guide</a>')returnend​foundstring = {'not found','found','internal'};teststring = {'-failed','+passed'};if ~donttestheader = {'Solver','Version','Status','Unit test'};elseheader = {'Solver','Version','Status'};end​[solvers,found] = getavailablesolvers(0);j = 1;status = ones(length(solvers),1);s = {solvers.tag};for i = 1:length(solvers)if solvers(i).showsame = find(strcmpi(solvers(i).tag,s));% Find all instances of same solver different versionsfor k = setdiff(same,i)% No reason to show for all versionssolvers(k).show = 0;enddata{j,1} = upper(solvers(i).tag);found_versions = same(find(found(same)));if ~isempty(found_versions)idx = min(found_versions);version = solvers(idx).version;if ~any(strcmpi(version,{'geometric','standard'}))data{j,2} = [solvers(idx).version ' ' solvers(idx).subversion];endelseidx = i;endstatus(j) = found(idx)+1+solvers(idx).builtin;data{j,3} = foundstring{found(idx)+1+solvers(idx).builtin};j = j+1;endend​if isa(prefered_solver,'char')ops = sdpsettings('Solver',prefered_solver);elseops = prefered_solver;endops.saveyalmipmodel = 1;​if ~((nargin==2) & (ops.verbose==0))[sortedName,loc] = sort({data{:,1}});loc = [loc(find(status(loc)==3)) loc(find(status(loc)==2)) loc(find(status(loc)==1))];dataSorted = reshape({data{loc,:}},[],3);yalmiptable({'Searching for installed solvers'},header,dataSorted);disp(' ')endif nargin<2disp('Press any key to continue test')pauseend​i=1;test{i}.fcn = 'test_core';test{i}.desc = 'Core functionalities';i = i+1;​test{i}.fcn = 'test_linear_programming';test{i}.desc = 'Linear programming (LP)';i = i+1;​test{i}.fcn = 'test_quadratic_programming';test{i}.desc = 'Quadratic programming (QP)';i = i+1;​test{i}.fcn = 'test_socp_programming';test{i}.desc = 'Second-order cone programming (SOCP)';i = i+1;​test{i}.fcn = 'test_semidefinite_programming';test{i}.desc = 'Semidefinite programming (SDP)';i = i+1;​test{i}.fcn = 'test_geometric_programming';test{i}.desc = 'Geometric programming (GP)';i = i+1;​test{i}.fcn = 'test_nonlinear_programming';test{i}.desc = 'Nonlinear programming (NLP)';i = i+1;​test{i}.fcn = 'test_nonlinear_semidefinite_programming';test{i}.desc = 'Nonlinear SDP (NLSDP)';i = i+1;​test{i}.fcn = 'test_exponential_cone_programming';test{i}.desc = 'Exponential cone programming (ECP)';i = i+1;​test{i}.fcn = 'test_milinear_programming';test{i}.desc = 'Mixed-integer LP (MIQP)';i = i+1;​test{i}.fcn = 'test_miquadratic_programming';test{i}.desc = 'Mixed-integer QP (MIQP)';i = i+1;​test{i}.fcn = 'test_misocp_programming';test{i}.desc = 'Mixed-integer SOCP (MISOCP)';i = i+1;​test{i}.fcn = 'test_nonconvex_quadratic_programming';test{i}.desc = 'Global nonconvex quadratic programming';i = i+1;​test{i}.fcn = 'test_nonconvex_global_programming';test{i}.desc = 'Global nonconvex programming';i = i+1;​pass_strings = {'Error','Passed','Solver not available'};​% Run test-problemsfor i = 1:length(test)tryif ops.verbosedisp(' ');disp(['Testing function ' test{i}.fcn]);disp(' ');end% First make call to figure out solverinfo = eval([test{i}.fcn '(ops)']);if ~OctaveRunningsols{i} = addLink(upper(cleanversion(info.yalmipmodel.solver.tag)));elsesols{i} = cleanversion(info.yalmipmodel.solver.tag);endpass(i) = info.problem == 0;if pass(i)results{i}='Success';elseresults{i}='Failed';endcatchpass(i) = 0;results{i} = 'Failed';sols{i} = '';endend​clear data;header = {'Test','Status', 'Solver'};for i = 1:length(pass)data{i,1} = test{i}.desc;data{i,2} = results{i};data{i,3} = sols{i};endif ops.verbosedisp(' ');endformats{1}.data.just = 'right';formats{2}.data.just = 'right';formats{3}.data.just = 'right';​formats{1}.header.just = 'right';formats{2}.header.just = 'right';formats{3}.header.just = 'right';​clcyalmiptable([],header,data,formats)​% Test if any LMI solver is installed.x = sdpvar(2);[p,aux1,aux2,m] = export(x>=0,[],[],[],[],0);if ~isempty(m)only_lmilab = strcmpi(m.solver.tag,'lmilab');only_fmincon = strcmpi(m.solver.tag,'fmincon-standard');elseonly_lmilab = 0;only_fmincon = 0;endif isempty(m)disp('You do not have any LMI solver installed')disp(' If you intend to solve LMIs you must install a solver.')elseif only_lmilabdisp('You do not have any good LMI solver installed')disp(' (only found <a href="https://yalmip.github.io/solver/lmilab/">LMILAB which should be avoided in YALMIP</a>).')disp('If you intend to solve LMIs, please install a better solver.')elseif only_fmincondisp('You do not have any LMI solver installed')disp(' (YALMIP will use a nonlinear solver which cannot be expected to work)')disp(' If you intend to solve LMIs you must install a solver.')endendx = binvar(1);[p,aux1,aux2,m] = export(x>=0,x,[],[],[],0);if isempty(m)disp('You do not have any LP/MILP solver installed')disp(' If you intend to solve LPs/MILPs, you have to install one.')elseonly_bnb = strcmpi(m.solver.tag,'bnb');if only_bnbdisp('You do not have any MILP solver installed')disp(' (only found internal <a href="https://yalmip.github.io/solver/bnb/">BNB</a>).')disp(' If you intend to solve MILP, please install a better solver.')endendx = binvar(1);[p,aux1,aux2,m] = export(x>=0,x^2,[],[],[],0);if isempty(m)disp('You do not have any QP/SOCP/MIQP/MISOCP solver installed')disp(' If you intend to solve QP/SOCP/MIQP/MISOCP you must install solver.')elseonly_bnb = strcmpi(m.solver.tag,'bnb');if only_bnbdisp('You do not have any MIQP/MISOCP solver installed (only found internal <a href="https://yalmip.github.io/solver/bnb/">BNB</a>)')disp(' If you intend to solve MIQP/MISOCP, please install a better solver.')endenddisp('See <a href="https://yalmip.github.io/allsolvers">guide on interfaced solvers</a>')​​​function sol = test_core(ops)​% Fakesol.yalmipmodel.solver.tag = '';sol.problem = 0;tryx = sdpvar(2,2);x = sdpvar(2,2,'symmetric');x = sdpvar(2,2,'full');x = sdpvar(2,2,'toeplitz');x = sdpvar(2,2,'hankel');x = sdpvar(2,2,'skew');if ~ishermitian(sdpvar(2,2,'hermitian','complex'))error('bug')endif ~issymmetric(sdpvar(2,2,'symmetric','complex'))error('bug')endif ~isreal(real(sdpvar(2,2,'symmetric','complex')))error('bug')endif isreal(sqrt(-1)*real(sdpvar(2,2,'symmetric','complex')))error('bug')endx = sdpvar(2,1,'','co');if ~isreal(x'*x)error('bug')endx = sdpvar(2,2,'','co');if ~isreal(diag(x'*x))error('bug')endx = sdpvar(1,1);y = sdpvar(2,2);x*eye(2);eye(2)*x;y*3;3*y;x = sdpvar(2,3);y = sdpvar(2,3);assign(x,randn(2,3));z = replace(x,x(1,1:2),[8 9]);z = x+y;z = x-y;z = x+1;z = x-1;z = x+ones(2,3);z = x-ones(2,3);z = ones(2,3)-x;z = ones(2,3)-x;z = eye(2)*x;z = x*eye(3);z = diag(x);z = trace(x(1:2,1:2));z = diff(x);z = fliplr(x);z = flipud(x);z = kron(x,eye(3));z = kron(eye(3),x);z = rot90(x);z = sum(x);z = diff(x);z = x';z = x.';z = tril(x);z = triu(x);z = [x y];z = [x;y];sdpvar x ydiag([x y])*[x^-1;y^-1];assert(isequal([x x;x x]*x-[x x;x x].*x,zeros(2)))assert(isequal(trace([x x;x x]*[x y;y x])-(x*x+x*y+y*x+x*x),0))% Regression ??yalmip('clear')sdpvar x(1+x+x^4)*(1-x^2);% Regression complex multiplcationA = randn(10,5)+sqrt(-1)*randn(10,5);b = randn(10,1)+sqrt(-1)*randn(10,1);x = sdpvar(5,1);res = A*x-b;assert(nnz(clean([res res]'*[res res]-res'*res,1e-8))==0)assert(isreal(clean(res'*res,1e-8)))assert(isreal(x*x'))catchsol.problem = 9;sol.info = 'Problems';end​function sol = test_semidefinite_programming(ops)t = sdpvar(1,1);Y = sdpvar(2,2);F = [Y<=t*eye(2), Y>=[1 0.2;0.2 1]];sol = optimize(F,t,ops);​function sol = test_linear_programming(ops)N = 5;A = [2 -1;1 0];B = [1;0];C = [0.5 0.5];[H,S] = create_CHS(A,B,C,N);x = [2;0];t = sdpvar(2*N,1);U = sdpvar(N,1);Y = H*x+S*U;F = (U<=1)+(U>=-1);F = F+(Y(N)>=-1);F = F+(Y(N)<=1);F = F+([Y;U]<=t)+([Y;U]>=-t);sol = optimize(F,sum(t),ops);​function sol = test_socp_programming(ops)x = sdpvar(2,1);a = [0;1];b = [1;1];F = norm(x-a)<=1;F = F+[norm(x-b) <= 1];sol = optimize(F,sum(x),ops);​function sol = test_misdp_programming(ops)x = intvar(4,1);e = magic(4)*x-1;sdpvar tobj = t;sol = optimize([t e';e eye(4)]>=0,obj,ops);​function sol = test_misocp_programming(ops)x = intvar(4,1);obj = norm(magic(4)*x-1,2);sol = optimize([-5 <= x <= 5],obj,ops);​function sol = test_miquadratic_programming(ops)x = intvar(4,1);obj = norm(magic(4)*x-1,2)^2;sol = optimize([-5 <= x <= 5],obj,ops);​function sol = test_milinear_programming(ops)x = intvar(4,1);obj = norm(magic(4)*x-1,1);sol = optimize([-5 <= x <= 5],obj,ops);​function sol = test_quadratic_programming(ops)x = sdpvar(10,1);sol = optimize([sum(x)==2, -1 <= x <= 1],x'*x,ops);​function sol = test_nonconvex_quadratic_programming(ops)x = sdpvar(10,1);ops.forceglobal = 1;sol = optimize([sum(x)==2, -1 <= x <= 1],-x'*x,ops);​function sol = test_nonconvex_global_programming(ops)x = sdpvar(3,1);ops.forceglobal = 1;sol = optimize([sum(x.^3)==2, -1 <= x <= 1],-x'*x,ops);​function sol = test_nonlinear_semidefinite_programming(ops)A = [-1 2;-3 -4];P = sdpvar(2,2);alpha = sdpvar(1,1);F = (P>=eye(2))+(A'*P+P*A <= -2*alpha*P)+(alpha >= 0);sol = optimize([F,P(:) <= 100],-alpha,ops);​function sol = test_geometric_programming(ops)t1 = sdpvar(1,1);t2 = sdpvar(1,1);t3 = sdpvar(1,1);t = [t1 t2 t3];obj = (40*t1^-1*t2^-0.5*t3^-1)+(20*t1*t3)+(40*t1*t2*t3);F = ((1/3)*t1^-2*t2^-2+(4/3)*t2^0.5*t3^-1 <= 1);F = [F, t>=0];sol = optimize(F,obj,ops);​function sol = test_nonlinear_programming(ops)sdpvar x ysol = optimize(x^2 + x^4 + exp(x) <= 1, x^2+y^2,ops);​function sol = test_exponential_cone_programming(ops)sdpvar x y zsol = optimize([expcone([x;2;z]),x==1],z,ops);​function html = addLink(x)​if length(x)>0html = ['<a href="https://yalmip.github.io/solver/' lower(x) '">' upper(x) '</a>'];elsehtml = '';end​function x = cleanversion(x)​s = strfind(x,'-');if ~isempty(s)x=x(1:s-1);end​

🔗 参考文献

[1]马腾飞,裴玮,肖浩,等.基于纳什谈判理论的风-光-氢多主体能源系统合作运行方法[J].中国电机工程学报, 2021, 41(1):15.DOI:10.13334/j.0258-8013.pcsee.200956.

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