DLPF.m

 function [Xp_dlpf, Xq_dlpf, Pbus, BranchFlow, busAgl, busVol]=DLPF(mpc)
% This code realizes Decoupled Linearized Power Flow (DLPF),this code is from the publication of "Yang J, Zhang N, Kang C, et al. A State-Independent Linear Power Flow Model with Accurate Estimation of Voltage Magnitude[J]. IEEE Transactions on Power Systems, 2016, PP(99):1-1."

% Define matpower constants
define_constants;
% Load case
[baseMVA, bus, gen, branch] = deal(mpc.baseMVA, mpc.bus, mpc.gen, mpc.branch);
[ref, pv, pq] = bustypes(bus, gen);

% Matrices
Ybus = makeYbus(mpc);
Gbus = real(Ybus);
Bbus = imag(Ybus);
GP = Gbus;
BD = diag(sum(Bbus));             %shunt elements
BP = -Bbus + BD;
BQ = -Bbus;
GQ = -Gbus;                       %GQ approxiately equals -Gbus
Sbus = makeSbus(baseMVA, bus, gen);
Pbus = real(Sbus);
Qbus = imag(Sbus);

%
Xp_dlpf = [BP GP];
Xq_dlpf = [GQ BQ];

% Matrices in equation (11)
%      | Pm1 |   | B11  G12 |   | delta   |   
%      |     | = |          | * |         | 
%      | Qm1 |   | G21  B22 |   | voltage | 
B11 = BP([pv;pq],[pv;pq]);  
G12 = GP([pv;pq],pq);
G21 = GQ(pq,[pv;pq]);
B22 = BQ(pq,pq);
Pm1 = Pbus([pv;pq]) - GP([pv;pq],ref)*bus(ref,VM) - GP([pv;pq],pv)*bus(pv,VM);
Qm1 = Qbus(pq) - BQ(pq,ref)*bus(ref,VM) - BQ(pq,pv)*bus(pv,VM);

% Matrices in equation (17)
t1 =G12/B22;
t2 =G21/B11;
B11m = B11 - t1*G21;
B22m = B22 - t2*G12;
Pm2 = Pm1 - t1*Qm1;
Qm2 = Qm1 - t2*Pm1;

% Calculate voltage magnitude
n = size(bus,1);
busVol = zeros(n,1);
busVol(ref) = bus(ref,VM);
busVol(pv) = bus(pv,VM);
busVol(pq) = B22m\Qm2;
% Calculate voltage phase angle
busAgl = ones(n,1)*bus(ref,VA);
busAgl([pv;pq]) = busAgl([pv;pq]) + B11m\Pm2/pi*180;
% Calculate line lossless MW flow
branch(:,TAP) = 1;
BranchFlow = (busVol(branch(:,F_BUS))./branch(:,TAP)-busVol(branch(:,T_BUS))).*branch(:,BR_R)./(branch(:,BR_X).^2+branch(:,BR_R).^2)*baseMVA ...
    +(busAgl(branch(:,F_BUS))-busAgl(branch(:,T_BUS))).*branch(:,BR_X)./(branch(:,BR_X).^2+branch(:,BR_R).^2)/180*pi./branch(:,TAP)*baseMVA;