fm_opfsdr.m

基于PSAT 软件的多目标最优潮流计算用于中小型电力系统的分析和管理

  mu_Iijcmax= mu(idx+nL);     idx = idx + Line.n;
  mu_Ijimax = mu(idx+nL);     idx = idx + Line.n;
  mu_Ijicmax= mu(idx+nL);     idx = idx + Line.n;
  if Rsrv.n
    mu_Prmin  = mu(idx+nR);   idx = idx + Rsrv.n;
    mu_Prmax  = mu(idx+nR);   idx = idx + Rsrv.n;
    mu_sumPrd = mu(idx+1);
  end

  % Computations for the System:  f(thetac,Vc,Qgc,Ps,Pd,lc) = 0
  % =====================================================

  V_snap = DAE.V;     ang_snap = DAE.a;
  DAE.V  = Vc;        DAE.a    = angc;
  DAE.Gl = zeros(n2,1);
  DAE.Gk = zeros(n2,1);

  if OPF.line, Line.Y = Y_cont; Line.con = line_cont; end
  fm_lf(1);

  glambda(SW,1+lc,kg);
  glambda(PV,1+lc,kg);
  glambda(PQ,1+lc);

  Glcall(SW);
  Gkcall(SW);
  Glcall(PV);
  Gkcall(PV);
  Glcall(PQ);

  % generator reactive powers
  DAE.gq = DAE.gq - sparse(busG,1,Qgc,Bus.n,1);

  % Demand & Supply
  DAE.gp = DAE.gp + sparse(Demand.bus,1,(1+lc)*Pd,Bus.n,1);
  DAE.gq = DAE.gq + sparse(Demand.bus,1,(1+lc)*Pd.*qonp,Bus.n,1);
  DAE.Gl = DAE.Gl + sparse(Demand.bus,1,Pd,2*Bus.n,1);
  DAE.Gl = DAE.Gl + sparse(Demand.bus+Bus.n,1,Pd.*qonp,2*Bus.n,1);
  g_Pdc = sparse(Demand.bus,nD,1+lc,2*Bus.n,Demand.n);
  g_Pdc = sparse(Demand.bus+Bus.n,nD,(1+lc)*qonp,2*Bus.n,Demand.n);
  DAE.gp = DAE.gp - sparse(Supply.bus,1,(1+lc+kg*ksu).*Ps,Bus.n,1);
  g_Psc = sparse(Supply.bus,nS,-(1+lc+kg*ksu),2*Bus.n,Supply.n);
  DAE.Gl = DAE.Gl - sparse(Supply.bus,1,Ps,2*Bus.n,1);
  DAE.Gk = DAE.Gk - sparse(Supply.bus,1,ksu.*Ps,2*Bus.n,1);

  gc1p = DAE.gp; gc2p = DAE.glfp;
  gc1q = DAE.gq; gc2q = DAE.glfq;
  fm_lf(2);
  Jlfvc = [DAE.J11, DAE.J12; DAE.J21, DAE.J22];
  [Iijc, Jijc, Hijc, Ijic, Jjic, Hjic] = fm_flows(OPF.flow,mu_Iijcmax, mu_Ijicmax);

  % Computations for the System:  f(theta,V,Qg,Ps,Pd) = 0
  % =====================================================

  DAE.V = V_snap;
  DAE.a = ang_snap;

  if OPF.line, Line.Y = Y_orig; Line.con = line_orig; end
  fm_lf(1);
  gcall(PQ);
  glambda(SW,1,0);
  glambda(PV,1,0);

  % Demand & Supply
  DAE.gp = DAE.gp + sparse(Demand.bus,1,Pd,Bus.n,1);
  DAE.gq = DAE.gq + sparse(Demand.bus,1,Pd.*qonp,Bus.n,1);
  DAE.gp = DAE.gp - sparse(Supply.bus,1,Ps,Bus.n,1);
  DAE.gq = DAE.gq - sparse(busG,1,Qg,Bus.n,1);

  fm_lf(2);
  Jlfv = [DAE.J11, DAE.J12; DAE.J21, DAE.J22];
  [Iij, Jij, Hij, Iji, Jji, Hji] = fm_flows(OPF.flow,mu_Iijmax, mu_Ijimax);

  % Gradient of [s] variables
  % =====================================================

  gs = s.*mu - ms;

  % Gradient of [mu] variables
  % =====================================================

  gmu = [Psmin-Ps;Ps-Psmax;Pdmin-Pd;Pd-Pdmax;Qgmin-Qg;Qg-Qgmax; ...
         Vmin-DAE.V;DAE.V-Vmax;Qgmin-Qgc;Qgc-Qgmax;Vcmin-Vc;Vc-Vcmax; ...
         lcmin-lc;lc-lcmax;Iij-Iijmax;Iijc-Iijcmax;Iji-Iijmax; ...
         Ijic-Iijcmax];
  if Rsrv.n
    gmu(Supply.n+supR) = gmu(Supply.n+supR) + Pr;
    gmu = [gmu; Prmin-Pr;Pr-Prmax;sum(Pr)-sum(Pd)];
  end
  gmu = gmu + s;

  % Gradient of [y] = [theta; DAE.V; Qg; Ps; Pd] variables
  % =====================================================

  if Rsrv.n,
    Jg = [Jlfv,g_Qg,g_Ps,g_Pd,Jz1; ...
          Jz2,g_Psc,g_Pdc,Jlfvc,DAE.Gk,g_Qgc,DAE.Gl,g_Pr];
  else,
    Jg = [Jlfv,g_Qg,g_Ps,g_Pd,Jz1; ...
          Jz2,g_Psc,g_Pdc,Jlfvc,DAE.Gk,g_Qgc,DAE.Gl];
  end

  dF_dy = Jg'*ro;

  dG_dy(n_d) = -w;                      % max loading factor
  dG_dy(n2+n_gen+1:n2+n_gen+Supply.n) = (1-w)*(Csb + 2*Csc.*Ps + 2*KTBS.*Ps);
  dG_dy(n2+n_gen+Supply.n+1:n2+n_a) =  -(1-w)*(Cdb + 2*Cdc.*Pd + 2*KTBD.*Pd ...
                                               + qonp.*(Ddb + 2*qonp.*Ddc.*Pd));
  dG_dy(n2+nS) = (1-w)*(Dsb + 2*Dsc.*Qg(nS));

  dH_dtV = Jij'*mu_Iijmax + Jji'*mu_Ijimax + [mu_t; mu_Vmax - mu_Vmin];
  dH_dtVc = Jijc'*mu_Iijcmax + Jjic'*mu_Ijicmax + [mu_t; mu_Vcmax - mu_Vcmin];
  if Rsrv.n,
    dH_dy = [dH_dtV; mu_Qgmax-mu_Qgmin; mu_Psmax-mu_Psmin; ... 
             mu_Pdmax-mu_Pdmin-mu_sumPrd; ...
             dH_dtVc; 0; mu_Qgcmax - mu_Qgcmin; mu_lcmax - mu_lcmin; ...
             mu_Psmax+mu_Prmax-mu_Prmin+mu_sumPrd];
  else
    dH_dy = [dH_dtV; mu_Qgmax-mu_Qgmin; mu_Psmax-mu_Psmin; mu_Pdmax-mu_Pdmin; ...
             dH_dtVc; 0; mu_Qgcmax - mu_Qgcmin; mu_lcmax - mu_lcmin];
  end

  gy = dG_dy - dF_dy + dH_dy;

  Jh(n_b+1:n_b+Line.n,1:n2) = Jij;
  Jh(n_b+1+Line.n:n_b+2*Line.n,1+n2+n_a:n4+n_a) = Jijc;
  Jh(n_b+1+2*Line.n:n_b+3*Line.n,1:n2) = Jji;
  Jh(n_b+1+3*Line.n:n_b+4*Line.n,1+n2+n_a:n4+n_a) = Jjic;

  % Hessian Matrix [D2xLms]
  % --------------------------------------------------------------------

  H3  = sparse(n_a,n_y);
  Hx = -ro(n2+Supply.bus);
  Sidx = 1:Supply.n;
  H3(n_gen+Sidx,n_d) = Hx;
  H3(n_gen+Sidx,n4+1+n_a) = Hx.*ksu;
  H5(n_gen+1,n2+n_gen+Sidx) = Hx';
  H41(end,n2+n_gen+Sidx) = Hx'.*ksu';
  Didx = 1:Demand.n;
  Hx = ro(n2+Demand.bus) + qonp.*ro(n3+Demand.bus);
  H3(n_gen+Supply.n+Didx,n_d) = Hx;
  H5(n_gen+1,n2+n_gen+Supply.n+Didx) = Hx';
  H3 = H3 - sparse(n_gen+nS,n2+n_gen+nS,(1-w)*(2*Csc+2*KTBS),n_a,n_y);
  H3 = H3 - sparse(nS,n2+nS,(1-w)*2*Dsc,n_a,n_y);
  H3 = H3 + sparse(n_gen+Supply.n+nD,n_gen+Supply.n+n2+nD, ...
		   (1-w)*(2*Cdc+2*KTBD+2*Ddc.*qonp.*qonp),n_a,n_y);

  V_snap = DAE.V;     ang_snap = DAE.a;
  DAE.V  = Vc;        DAE.a    = angc;
  if OPF.line, Line.Y = Y_cont; end
  Hess_c = -fm_hessian(ro(n2+1:n4))+Hijc+Hjic;
  DAE.V = V_snap;     DAE.a = ang_snap;
  if OPF.line, Line.Y = Y_orig; end
  Hess = -fm_hessian(ro(1:n2))+Hij+Hji;
  D2xLms = [Hess, H31; -H3; -H41, [Hess_c, Hcolk; Hrowk], H42; -H5];

  switch OPF.method
   case 1 % Newton Directions

    % reduced system
    H_m = sparse(1:n_s,1:n_s,mu./s,n_s,n_s);
    H_s = sparse(1:n_s,1:n_s,1./s,n_s,n_s);
    Jh(:,SW.bus+n2+n_a) = 0;
    Jh(:,SW.bus) = 0;
    gy = gy+(Jh.')*(H_m*gmu-H_s*gs);
    Jd = [D2xLms+(Jh.')*(H_m*Jh),-Jg.';-Jg,Z3];
    % reference angle for the actual system
    Jd(SW.bus,:) = 0;
    Jd(:,SW.bus) = 0;
    Jd(SW.bus,SW.bus) = speye(SW.n);
    gy(SW.bus) = 0;
    % reference angle for the critical system
    Jd(:,SW.bus+n2+n_a) = 0;
    Jd(SW.bus+n2+n_a,:) = 0;
    Jd(SW.bus+n2+n_a,SW.bus+n2+n_a) = speye(SW.n);
    gy(SW.bus+n2+n_a) = 0;
    % variable increments
    Dx = -Jd\[gy; -DAE.gp; -DAE.gq; -gc1p; -gc1q];
    Ds = -(gmu+Jh*Dx([1:n_y]));
    Dm = -H_s*gs-H_m*Ds;

   case 2 % Mehrotra's Predictor-Corrector

    % -------------------
    % Predictor step
    % -------------------
    % reduced system
    H_m  = sparse(1:n_s,1:n_s,mu./s,n_s,n_s);
    Jh(:,SW.bus+n2+n_a) = 0;
    Jh(:,SW.bus) = 0;
    gx = gy+(Jh.')*(H_m*gmu-mu);
    Jd = [D2xLms+(Jh.')*(H_m*Jh),-Jg.';-Jg,Z3];
    % reference angle for the actual system
    Jd(SW.bus,:) = 0;
    Jd(:,SW.bus) = 0;
    Jd(SW.bus,SW.bus) = speye(SW.n);
    gx(SW.bus) = 0;
    % reference angle for the critical system
    Jd(:,SW.bus+n2+n_a) = 0;
    Jd(SW.bus+n2+n_a,:) = 0;
    Jd(SW.bus+n2+n_a,SW.bus+n2+n_a) = speye(SW.n);
    gx(SW.bus+n2+n_a) = 0;
    % LU factorization
    [L,U,P] = lu(Jd);
    % variable increments
    Dx = -U\(L\(P*[gx; -DAE.gp; -DAE.gq; -gc1p; -gc1q]));
    Ds = -(gmu+Jh*Dx([1:n_y]));
    Dm = -mu-H_m*Ds;
    % centering correction
    a1 = find(Ds < 0);
    a2 = find(Dm < 0);
    if isempty(a1), ratio1 = 1; else, ratio1 = -s(a1)./Ds(a1);   end
    if isempty(a2), ratio2 = 1; else, ratio2 = -mu(a2)./Dm(a2); end
    alpha_P = min(1,gamma*min(ratio1));
    alpha_D = min(1,gamma*min(ratio2));
    c_gap_af = [s + alpha_P*Ds]'*[mu + alpha_D*Dm];
    c_gap = s'*mu;
    ms = min((c_gap_af/c_gap)^2,0.2)*c_gap_af/n_s;
    gs = mu+(Ds.*Dm-ms)./s;

    % -------------------
    % Corrector Step
    % -------------------
    % new increment for variable y
    gx = gy+(Jh.')*(H_m*gmu-gs);
    gx(SW.bus) = 0;
    gx(SW.bus+n2+n_a) = 0;
    % variable increments
    Dx = -U\(L\(P*[gx; -DAE.gp; -DAE.gq; -gc1p; -gc1q]));
    Ds = -(gmu+Jh*Dx([1:n_y]));
    Dm = -gs-H_m*Ds;
  end

  % =======================================================================
  % Variable Increments
  % =======================================================================

  Dtheta = Dx(nB);           idx = Bus.n;        % curr. sys.
  DV     = Dx(idx+nB);       idx = idx + Bus.n;
  DQg    = Dx(idx+nG);       idx = idx + n_gen;
  DPs    = Dx(idx+nS);       idx = idx + Supply.n;
  DPd    = Dx(idx+nD);       idx = idx + Demand.n;

  Dthetac = Dx(idx+nB);      idx = idx + Bus.n;  % crit. sys.
  DVc     = Dx(idx+nB);      idx = idx + Bus.n;
  Dkg     = Dx(1+idx);       idx = idx + 1;
  DQgc    = Dx(idx+nG);      idx = idx + n_gen;
  Dlc     = Dx(1+idx);       idx = idx + 1;
  if Rsrv.n, DPr = Dx(idx+nR);    idx = idx + Rsrv.n;    end

  Dro     = Dx(1+idx:end);                       % Lag. mult.

  % =======================================================================
  % Updating the Variables
  % =======================================================================

  % Step Lenght Parameters [alpha_P & alpha_D]
  %________________________________________________________________________

  a1 = find(Ds  < 0);
  a2 = find(Dm < 0);
  if isempty(a1), ratio1 = 1; else, ratio1 = (-s(a1)./Ds(a1));   end
  if isempty(a2), ratio2 = 1; else, ratio2 = (-mu(a2)./Dm(a2)); end
  alpha_P = min(1,gamma*min(ratio1));
  alpha_D = min(1,gamma*min(ratio2));

  % New primal variables
  %________________________________________________________________________

  DAE.a = DAE.a + alpha_P * Dtheta;
  DAE.V = DAE.V + alpha_P * DV;
  Ps = Ps + alpha_P * DPs;
  Pd = Pd + alpha_P * DPd;
  Qg = Qg + alpha_P * DQg;
  if Rsrv.n, Pr = Pr + alpha_P * DPr; end

  angc = angc + alpha_P * Dthetac;
  Vc   = Vc   + alpha_P * DVc;
  kg   = kg   + alpha_P * Dkg;
  Qgc  = Qgc  + alpha_P * DQgc;
  lc   = lc   + alpha_P * Dlc;
  s    = s    + alpha_P * Ds;

  % New dual variables
  %________________________________________________________________________

  ro = ro + alpha_D*Dro;
  mu = mu + alpha_D*Dm;

  % Objective Function
  %________________________________________________________________________

  s(find(s == 0)) = epsilon_mu;
  Fixd_c = sum(Csa) - sum(Cda) + sum(Dsa) - sum(Dda);
  Prop_c = Csb'*Ps  - Cdb'*Pd + Dsb'*Qg(nS) - Ddb'*(qonp.*Pd);
  TieBreaking = (sum(KTBS.*Ps.*Ps) - sum(KTBD.*Pd.*Pd));
  Quad_c = Csc'*(Ps.*Ps) - Cdc'*(Pd.*Pd) - Ddc'*(qonp.*qonp.*Pd.*Pd);
  Quad_q = Dsc'*(Qg(nS).*Qg(nS));
  if Rsrv.n, Reserve = Cr'*Pr; else, Reserve = 0; end
  G_obj = (1-w)*(Fixd_c + Prop_c + Quad_c + Quad_q + TieBreaking + Reserve) - ...
          ms*sum(log(s)) - w*lc;

  % =======================================================================
  % Reducing the Barrier Parameter
  % =======================================================================

  sigma = max(0.99*sigma, 0.1);     % Centering Parameter
  c_gap = s'*mu;                    % Complementarity Gap
  ms = min(abs(sigma*c_gap/n_s),1); % Evaluation of the Barrier Parameter

  % =======================================================================
  % Testing for Convergence
  % =======================================================================

  test1  = ms <= epsilon_mu;
  norma2 = norm(Dx,inf);
  test2  = norma2 <= epsilon_2;
  norma3 = norm([DAE.gp; DAE.gq; gc1p; gc1q],inf);
  test3  = norma3 <= epsilon_1;
  norma4 = abs(G_obj-G_obj_k_1)/(1+abs(G_obj));
  test4  = norma4 <= epsilon_2;
  if test1 & test2 & test3 & test4, break, end

  % Displaying Convergence Tests
  %________________________________________________________________________

  iteration = iteration + 1;
  if OPF.show
    fm_disp(['Iter. =',fvar(iteration,5),'  mu =', fvar(ms,8), ...
             '  |dy| =', fvar(norma2,8), '  |f(y)| =', ...
             fvar(norma3,8),'  |dG(y)| =' fvar(norma4,8)])
  end
  fm_status('opf','update',[iteration, ms, norma2, norma3, norma4], ...
            iteration)

  if iteration > iter_max, break, end
end

% Some settings ...
%____________________________________________________________________________

warning('on');
Demand = pset(Demand,Pd);
Supply = pset(Supply,Ps);

if Rsrv.n, Rsrv.con(:,10) = Pr; end
Iij  = sqrt(Iij);
Iji  = sqrt(Iji);
Iijc = sqrt(Iijc);
Ijic = sqrt(Ijic);
Iijmax  = sqrt(Iijmax);
Iijcmax = sqrt(Iijcmax);
MVA = Settings.mva;
Pay = ro(1:Bus.n).*DAE.glfp*MVA;
ISOPay = sum(Pay);

% Nodal Congestion Prices (NCPs)
%____________________________________________________________________________

Jlfv(SW.bus,:) = [];
Jlfv(:,SW.bus) = [];
dH_dtV(SW.bus,:) = [];
NCP = -Jlfv'\dH_dtV;
OPF.NCP = [NCP(1:SW.bus-1);0;NCP(SW.bus:end)];

OPF.obj = G_obj;
OPF.ms = ms;
OPF.dy = norma2;
OPF.dF = norma3;
OPF.dG = norma4;
OPF.iter = iteration;
OPF.gpc = gc2p;
OPF.gqc = gc2q;

SNB.init = 0;
LIB.init = 0;
CPF.init = 0;
OPF.init = 2;

% set Pg, Qg, Pl and Ql
Bus.Pl = OPF.basepl*Snapshot(1).Pl + sparse(Demand.bus,1,Pd,Bus.n,1);
Bus.Ql = OPF.basepl*Snapshot(1).Ql + sparse(Demand.bus,1,Pd.*qonp,Bus.n,1);
Bus.Pg = OPF.basepg*Snapshot(1).Pg + sparse(Supply.bus,1,Ps,Bus.n,1);
Bus.Qg = OPF.basepg*Snapshot(1).Qg + sparse(busG,1,Qg,Bus.n,1);

% Display Results
% --------------------------------------------------

TPQ = totp(PQ);

if (Settings.showlf | OPF.show) & clpsat.showopf

  OPF.report = cell(1,1);
  OPF.report{1,1} = ['Weighting Factor = ',fvar(w,8)];
  OPF.report{2,1} = ['Lambda = ',fvar(lc,8)];
  OPF.report{3,1} = ['Kg = ',fvar(kg,8)];
  OPF.report{4,1} = ['Total Losses = ',fvar(sum(DAE.glfp),8),' [p.u.]'];
  OPF.report{5,1} = ['Bid Losses = ',fvar(sum(DAE.glfp)-Snapshot(1).Ploss,8),' [p.u.]'];

  if ~noDem
    OPF.report{6,1} = ['Total demand = ', ...
                        fvar(sum(Pd),8),' [p.u.]'];
  end
  OPF.report{6+(~noDem),1} = ['TTL = ',fvar(sum(Pd)+TPQ,8),' [p.u.]'];

  fm_disp
  fm_disp('----------------------------------------------------------------')

  Settings.lftime = toc;

  if Fig.stat, fm_stat; end

  if iteration > iter_max
    fm_disp('IPM-OPF: Method did not Converge',2)
  elseif Fig.main
    if ~get(Fig.main,'UserData')
      fm_disp('IPM-OPF: Interrupted',2)
    else
      fm_disp(['IPM-OPF completed in ',num2str(toc),' s'],1)
    end
  else
    fm_disp(['IPM-OPF completed in ',num2str(toc),' s'],1)
    if Settings.showlf == 1
      fm_stat(OPF.report);
    else
      if Settings.beep
        beep
      end
    end
  end
  fm_status('opf','close')
else
  if iteration > iter_max
    fm_disp('IPM-OPF: Method did not Converge',2)
  elseif Fig.main
    if ~get(Fig.main,'UserData')
      fm_disp(['IPM-OPF: Interrupted'],2)
    else
      fm_disp(['IPM-OPF completed in ',num2str(toc),' s'],1)
    end
  else
    fm_disp(['IPM-OPF completed in ',num2str(toc),' s'],1)
  end
end

if iteration > iter_max,
  OPF.conv = 0;
else,
  OPF.conv = 1;
end
if Rsrv.n,
  OPF.guess = [s; mu; DAE.a; DAE.V; Qg; Ps; Pd; ...
               angc; Vc; kg; Qgc; lc; Pr; ro];
else
  OPF.guess = [s; mu; DAE.a; DAE.V; Qg; Ps; Pd; ...
               angc; Vc; kg; Qgc; lc; ro];
end
OPF.atc = (1+lc)*(sum(Pd)+TPQ)*MVA;
OPF.Vc = Vc;
OPF.ac = angc;

if noDem, Demand = restore(Demand); end

PQ = resetvlim(PQ);
if ~OPF.basepl
  PQ = pqreset(PQ,'all');
end
if ~OPF.basepg
  SW = swreset(SW,'all');
  PV = pvreset(PV,'all');
end