fm_opfsdr.m

电力系统的psat

  % 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(busS,n2+busS,(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
    if Settings.octave
      H_m = diag(mu./s);
      H_s = diag(1./s);
    else
      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);
    end
    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;
    if Settings.octave
      Jd(SW.bus,SW.bus) = eye(SW.n);
    else
      Jd(SW.bus,SW.bus) = speye(SW.n);
   end
    gy(SW.bus) = 0;
    % reference angle for the critical system
    Jd(:,SW.bus+n2+n_a) = 0;
    Jd(SW.bus+n2+n_a,:) = 0;
    if Settings.octave
      Jd(SW.bus+n2+n_a,SW.bus+n2+n_a) = eye(SW.n);
    else
      Jd(SW.bus+n2+n_a,SW.bus+n2+n_a) = speye(SW.n);
    end
    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
    if Settings.octave
      H_m  = diag(mu./s);
    else
      H_m  = sparse(1:n_s,1:n_s,mu./s,n_s,n_s);
    end
    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;
    if Settings.octave
      Jd(SW.bus,SW.bus) = eye(SW.n);
    else
      Jd(SW.bus,SW.bus) = speye(SW.n);
    end
    gx(SW.bus) = 0;
    % reference angle for the critical system
    Jd(:,SW.bus+n2+n_a) = 0;
    Jd(SW.bus+n2+n_a,:) = 0;
    if Settings.octave
      Jd(SW.bus+n2+n_a,SW.bus+n2+n_a) = eye(SW.n);
    else
      Jd(SW.bus+n2+n_a,SW.bus+n2+n_a) = speye(SW.n);
    end
    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(busS) - 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(busS).*Qg(busS));
  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 ...
%____________________________________________________________________________

Demand.con(:,7) = Pd;
Supply.con(:,6) = 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
for i = 1:Demand.n,
  k = Demand.bus(i);
  Bus.Pl(k) = Snapshot(1).Pl(k)+Pd(i);
  Bus.Ql(k) = Snapshot(1).Ql(k)+Pd(i)*qonp(i);
end

for i = 1:Supply.n
  k = Supply.bus(i);
  Bus.Pg(k) = Snapshot(1).Pg(k)+Ps(i);
end

for i = 1:n_gen
  Bus.Qg(nG(i)) = Qg(i);
end

% Display Results
%____________________________________________________________________________

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)+sum(PQ.con(:,4)),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)+sum(PQ.con(:,4)))*MVA;
OPF.Vc = Vc;
OPF.ac = angc;

if noDem,
  Demand.con = [];
  Demand.n = 0;
  Demand.bus = [];
end

if ~OPF.basepl
  Bus.Pl = buspl;
  Bus.Ql = busql;
  PQ.con(:,[4 5]) = pqcon;
end
if ~OPF.basepg
  Snapshot(1).Ploss = ploss;
  Bus.Pg = buspg;
  Bus.Qg = busqg;
  PV.con(:,4) = pvcon;
end