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Gurobi_IEEE33_NLP.m
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Gurobi_IEEE33_NLP.m
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%SB=100MVA,UB=12.66kV,IEEE-33 Bus,Distflow SOC-ACOPF
%%GUROBI9.0求解非线性问题
clear
clc
tic
%网络数据，标幺值
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Qload=[0.00028,0.0003,0.00034,0.00038,0.0004,0.00044,0.00046,0.00048,0.00052,0.00056,0.00058,0.0006,0.00056,0.00052,0.00048,0.00042,0.0004,0.00044,0.00048,0.00056,0.00052,0.00044,0.00036,0.00032;0.0001866666667,0.0002,0.0002266666667,0.0002533333333,0.0002666666667,0.0002933333333,0.0003066666667,0.00032,0.0003466666667,0.0003733333333,0.0003866666667,0.0004,0.0003733333333,0.0003466666667,0.00032,0.00028,0.0002666666667,0.0002933333333,0.00032,0.0003733333333,0.0003466666667,0.0002933333333,0.00024,0.0002133333333;0.0003733333333,0.0004,0.0004533333333,0.0005066666667,0.0005333333333,0.0005866666667,0.0006133333333,0.00064,0.0006933333333,0.0007466666667,0.0007733333333,0.0008,0.0007466666667,0.0006933333333,0.00064,0.00056,0.0005333333333,0.0005866666667,0.00064,0.0007466666667,0.0006933333333,0.0005866666667,0.00048,0.0004266666667;0.00014,0.00015,0.00017,0.00019,0.0002,0.00022,0.00023,0.00024,0.00026,0.00028,0.00029,0.0003,0.00028,0.00026,0.00024,0.00021,0.0002,0.00022,0.00024,0.00028,0.00026,0.00022,0.00018,0.00016;9.333333333e-05,0.0001,0.0001133333333,0.0001266666667,0.0001333333333,0.0001466666667,0.0001533333333,0.00016,0.0001733333333,0.0001866666667,0.0001933333333,0.0002,0.0001866666667,0.0001733333333,0.00016,0.00014,0.0001333333333,0.0001466666667,0.00016,0.0001866666667,0.0001733333333,0.0001466666667,0.00012,0.0001066666667;0.0004666666667,0.0005,0.0005666666667,0.0006333333333,0.0006666666667,0.0007333333333,0.0007666666667,0.0008,0.0008666666667,0.0009333333333,0.0009666666667,0.001,0.0009333333333,0.0008666666667,0.0008,0.0007,0.0006666666667,0.0007333333333,0.0008,0.0009333333333,0.0008666666667,0.0007333333333,0.0006,0.0005333333333;0.0004666666667,0.0005,0.0005666666667,0.0006333333333,0.0006666666667,0.0007333333333,0.0007666666667,0.0008,0.0008666666667,0.0009333333333,0.0009666666667,0.001,0.0009333333333,0.0008666666667,0.0008,0.0007,0.0006666666667,0.0007333333333,0.0008,0.0009333333333,0.0008666666667,0.0007333333333,0.0006,0.0005333333333;9.333333333e-05,0.0001,0.0001133333333,0.0001266666667,0.0001333333333,0.0001466666667,0.0001533333333,0.00016,0.0001733333333,0.0001866666667,0.0001933333333,0.0002,0.0001866666667,0.0001733333333,0.00016,0.00014,0.0001333333333,0.0001466666667,0.00016,0.0001866666667,0.0001733333333,0.0001466666667,0.00012,0.0001066666667;9.333333333e-05,0.0001,0.0001133333333,0.0001266666667,0.0001333333333,0.0001466666667,0.0001533333333,0.00016,0.0001733333333,0.0001866666667,0.0001933333333,0.0002,0.0001866666667,0.0001733333333,0.00016,0.00014,0.0001333333333,0.0001466666667,0.00016,0.0001866666667,0.0001733333333,0.0001466666667,0.00012,0.0001066666667;0.00014,0.00015,0.00017,0.00019,0.0002,0.00022,0.00023,0.00024,0.00026,0.00028,0.00029,0.0003,0.00028,0.00026,0.00024,0.00021,0.0002,0.00022,0.00024,0.00028,0.00026,0.00022,0.00018,0.00016;0.0001633333333,0.000175,0.0001983333333,0.0002216666667,0.0002333333333,0.0002566666667,0.0002683333333,0.00028,0.0003033333333,0.0003266666667,0.0003383333333,0.00035,0.0003266666667,0.0003033333333,0.00028,0.000245,0.0002333333333,0.0002566666667,0.00028,0.0003266666667,0.0003033333333,0.0002566666667,0.00021,0.0001866666667;0.0001633333333,0.000175,0.0001983333333,0.0002216666667,0.0002333333333,0.0002566666667,0.0002683333333,0.00028,0.0003033333333,0.0003266666667,0.0003383333333,0.00035,0.0003266666667,0.0003033333333,0.00028,0.000245,0.0002333333333,0.0002566666667,0.00028,0.0003266666667,0.0003033333333,0.0002566666667,0.00021,0.0001866666667;0.0003733333333,0.0004,0.0004533333333,0.0005066666667,0.0005333333333,0.0005866666667,0.0006133333333,0.00064,0.0006933333333,0.0007466666667,0.0007733333333,0.0008,0.0007466666667,0.0006933333333,0.00064,0.00056,0.0005333333333,0.0005866666667,0.00064,0.0007466666667,0.0006933333333,0.0005866666667,0.00048,0.0004266666667;4.666666667e-05,5.e-05,5.666666667e-05,6.333333333e-05,6.666666667e-05,7.333333333e-05,7.666666667e-05,8.e-05,8.666666667e-05,9.333333333e-05,9.666666667e-05,0.0001,9.333333333e-05,8.666666667e-05,8.e-05,7.e-05,6.666666667e-05,7.333333333e-05,8.e-05,9.333333333e-05,8.666666667e-05,7.333333333e-05,6.e-05,5.333333333e-05;9.333333333e-05,0.0001,0.0001133333333,0.0001266666667,0.0001333333333,0.0001466666667,0.0001533333333,0.00016,0.0001733333333,0.0001866666667,0.0001933333333,0.0002,0.0001866666667,0.0001733333333,0.00016,0.00014,0.0001333333333,0.0001466666667,0.00016,0.0001866666667,0.0001733333333,0.0001466666667,0.00012,0.0001066666667;9.333333333e-05,0.0001,0.0001133333333,0.0001266666667,0.0001333333333,0.0001466666667,0.0001533333333,0.00016,0.0001733333333,0.0001866666667,0.0001933333333,0.0002,0.0001866666667,0.0001733333333,0.00016,0.00014,0.0001333333333,0.0001466666667,0.00016,0.0001866666667,0.0001733333333,0.0001466666667,0.00012,0.0001066666667;0.0001866666667,0.0002,0.0002266666667,0.0002533333333,0.0002666666667,0.0002933333333,0.0003066666667,0.00032,0.0003466666667,0.0003733333333,0.0003866666667,0.0004,0.0003733333333,0.0003466666667,0.00032,0.00028,0.0002666666667,0.0002933333333,0.00032,0.0003733333333,0.0003466666667,0.0002933333333,0.00024,0.0002133333333;0.0001866666667,0.0002,0.0002266666667,0.0002533333333,0.0002666666667,0.0002933333333,0.0003066666667,0.00032,0.0003466666667,0.0003733333333,0.0003866666667,0.0004,0.0003733333333,0.0003466666667,0.00032,0.00028,0.0002666666667,0.0002933333333,0.00032,0.0003733333333,0.0003466666667,0.0002933333333,0.00024,0.0002133333333;0.0001866666667,0.0002,0.0002266666667,0.0002533333333,0.0002666666667,0.0002933333333,0.0003066666667,0.00032,0.0003466666667,0.0003733333333,0.0003866666667,0.0004,0.0003733333333,0.0003466666667,0.00032,0.00028,0.0002666666667,0.0002933333333,0.00032,0.0003733333333,0.0003466666667,0.0002933333333,0.00024,0.0002133333333;0.0001866666667,0.0002,0.0002266666667,0.0002533333333,0.0002666666667,0.0002933333333,0.0003066666667,0.00032,0.0003466666667,0.0003733333333,0.0003866666667,0.0004,0.0003733333333,0.0003466666667,0.00032,0.00028,0.0002666666667,0.0002933333333,0.00032,0.0003733333333,0.0003466666667,0.0002933333333,0.00024,0.0002133333333;0.0001866666667,0.0002,0.0002266666667,0.0002533333333,0.0002666666667,0.0002933333333,0.0003066666667,0.00032,0.0003466666667,0.0003733333333,0.0003866666667,0.0004,0.0003733333333,0.0003466666667,0.00032,0.00028,0.0002666666667,0.0002933333333,0.00032,0.0003733333333,0.0003466666667,0.0002933333333,0.00024,0.0002133333333;0.0002333333333,0.00025,0.0002833333333,0.0003166666667,0.0003333333333,0.0003666666667,0.0003833333333,0.0004,0.0004333333333,0.0004666666667,0.0004833333333,0.0005,0.0004666666667,0.0004333333333,0.0004,0.00035,0.0003333333333,0.0003666666667,0.0004,0.0004666666667,0.0004333333333,0.0003666666667,0.0003,0.0002666666667;0.0009333333333,0.001,0.001133333333,0.001266666667,0.001333333333,0.001466666667,0.001533333333,0.0016,0.001733333333,0.001866666667,0.001933333333,0.002,0.001866666667,0.001733333333,0.0016,0.0014,0.001333333333,0.001466666667,0.0016,0.001866666667,0.001733333333,0.001466666667,0.0012,0.001066666667;0.0009333333333,0.001,0.001133333333,0.001266666667,0.001333333333,0.001466666667,0.001533333333,0.0016,0.001733333333,0.001866666667,0.001933333333,0.002,0.001866666667,0.001733333333,0.0016,0.0014,0.001333333333,0.001466666667,0.0016,0.001866666667,0.001733333333,0.001466666667,0.0012,0.001066666667;0.0001166666667,0.000125,0.0001416666667,0.0001583333333,0.0001666666667,0.0001833333333,0.0001916666667,0.0002,0.0002166666667,0.0002333333333,0.0002416666667,0.00025,0.0002333333333,0.0002166666667,0.0002,0.000175,0.0001666666667,0.0001833333333,0.0002,0.0002333333333,0.0002166666667,0.0001833333333,0.00015,0.0001333333333;0.0001166666667,0.000125,0.0001416666667,0.0001583333333,0.0001666666667,0.0001833333333,0.0001916666667,0.0002,0.0002166666667,0.0002333333333,0.0002416666667,0.00025,0.0002333333333,0.0002166666667,0.0002,0.000175,0.0001666666667,0.0001833333333,0.0002,0.0002333333333,0.0002166666667,0.0001833333333,0.00015,0.0001333333333;9.333333333e-05,0.0001,0.0001133333333,0.0001266666667,0.0001333333333,0.0001466666667,0.0001533333333,0.00016,0.0001733333333,0.0001866666667,0.0001933333333,0.0002,0.0001866666667,0.0001733333333,0.00016,0.00014,0.0001333333333,0.0001466666667,0.00016,0.0001866666667,0.0001733333333,0.0001466666667,0.00012,0.0001066666667;0.0003266666667,0.00035,0.0003966666667,0.0004433333333,0.0004666666667,0.0005133333333,0.0005366666667,0.00056,0.0006066666667,0.0006533333333,0.0006766666667,0.0007,0.0006533333333,0.0006066666667,0.00056,0.00049,0.0004666666667,0.0005133333333,0.00056,0.0006533333333,0.0006066666667,0.0005133333333,0.00042,0.0003733333333;0.0028,0.003,0.0034,0.0038,0.004,0.0044,0.0046,0.0048,0.0052,0.0056,0.0058,0.006,0.0056,0.0052,0.0048,0.0042,0.004,0.0044,0.0048,0.0056,0.0052,0.0044,0.0036,0.0032;0.0003266666667,0.00035,0.0003966666667,0.0004433333333,0.0004666666667,0.0005133333333,0.0005366666667,0.00056,0.0006066666667,0.0006533333333,0.0006766666667,0.0007,0.0006533333333,0.0006066666667,0.00056,0.00049,0.0004666666667,0.0005133333333,0.00056,0.0006533333333,0.0006066666667,0.0005133333333,0.00042,0.0003733333333;0.0004666666667,0.0005,0.0005666666667,0.0006333333333,0.0006666666667,0.0007333333333,0.0007666666667,0.0008,0.0008666666667,0.0009333333333,0.0009666666667,0.001,0.0009333333333,0.0008666666667,0.0008,0.0007,0.0006666666667,0.0007333333333,0.0008,0.0009333333333,0.0008666666667,0.0007333333333,0.0006,0.0005333333333;0.0001866666667,0.0002,0.0002266666667,0.0002533333333,0.0002666666667,0.0002933333333,0.0003066666667,0.00032,0.0003466666667,0.0003733333333,0.0003866666667,0.0004,0.0003733333333,0.0003466666667,0.00032,0.00028,0.0002666666667,0.0002933333333,0.00032,0.0003733333333,0.0003466666667,0.0002933333333,0.00024,0.0002133333333;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];%节点无功(何立夫数据）;
Line=[33.0000000000000 + 0.00000000000000i,1.00000000000000 + 0.00000000000000i,0.0922000000000000 + 0.0470000000000000i;1.00000000000000 + 0.00000000000000i,2.00000000000000 + 0.00000000000000i,0.493000000000000 + 0.251100000000000i;2.00000000000000 + 0.00000000000000i,3.00000000000000 + 0.00000000000000i,0.366000000000000 + 0.186400000000000i;3.00000000000000 + 0.00000000000000i,4.00000000000000 + 0.00000000000000i,0.381100000000000 + 0.194100000000000i;4.00000000000000 + 0.00000000000000i,5.00000000000000 + 0.00000000000000i,0.819000000000000 + 0.707000000000000i;5.00000000000000 + 0.00000000000000i,6.00000000000000 + 0.00000000000000i,0.187200000000000 + 0.618800000000000i;6.00000000000000 + 0.00000000000000i,7.00000000000000 + 0.00000000000000i,0.711400000000000 + 0.235100000000000i;7.00000000000000 + 0.00000000000000i,8.00000000000000 + 0.00000000000000i,1.03000000000000 + 0.740000000000000i;8.00000000000000 + 0.00000000000000i,9.00000000000000 + 0.00000000000000i,1.04400000000000 + 0.740000000000000i;9.00000000000000 + 0.00000000000000i,10.0000000000000 + 0.00000000000000i,0.196600000000000 + 0.0650000000000000i;10.0000000000000 + 0.00000000000000i,11.0000000000000 + 0.00000000000000i,0.374400000000000 + 0.123800000000000i;11.0000000000000 + 0.00000000000000i,12.0000000000000 + 0.00000000000000i,1.46800000000000 + 1.15500000000000i;12.0000000000000 + 0.00000000000000i,13.0000000000000 + 0.00000000000000i,0.541600000000000 + 0.712900000000000i;13.0000000000000 + 0.00000000000000i,14.0000000000000 + 0.00000000000000i,0.591000000000000 + 0.526000000000000i;14.0000000000000 + 0.00000000000000i,15.0000000000000 + 0.00000000000000i,0.746300000000000 + 0.545000000000000i;15.0000000000000 + 0.00000000000000i,16.0000000000000 + 0.00000000000000i,1.28900000000000 + 1.72100000000000i;16.0000000000000 + 0.00000000000000i,17.0000000000000 + 0.00000000000000i,0.372000000000000 + 0.574000000000000i;1.00000000000000 + 0.00000000000000i,18.0000000000000 + 0.00000000000000i,0.164000000000000 + 0.156500000000000i;18.0000000000000 + 0.00000000000000i,19.0000000000000 + 0.00000000000000i,1.50420000000000 + 1.35540000000000i;19.0000000000000 + 0.00000000000000i,20.0000000000000 + 0.00000000000000i,0.409500000000000 + 0.478400000000000i;20.0000000000000 + 0.00000000000000i,21.0000000000000 + 0.00000000000000i,0.708900000000000 + 0.937300000000000i;2.00000000000000 + 0.00000000000000i,22.0000000000000 + 0.00000000000000i,0.451200000000000 + 0.308300000000000i;22.0000000000000 + 0.00000000000000i,23.0000000000000 + 0.00000000000000i,0.898000000000000 + 0.709100000000000i;23.0000000000000 + 0.00000000000000i,24.0000000000000 + 0.00000000000000i,0.896000000000000 + 0.701100000000000i;5.00000000000000 + 0.00000000000000i,25.0000000000000 + 0.00000000000000i,0.203000000000000 + 0.103400000000000i;25.0000000000000 + 0.00000000000000i,26.0000000000000 + 0.00000000000000i,0.284200000000000 + 0.144700000000000i;26.0000000000000 + 0.00000000000000i,27.0000000000000 + 0.00000000000000i,1.05900000000000 + 0.933700000000000i;27.0000000000000 + 0.00000000000000i,28.0000000000000 + 0.00000000000000i,0.804200000000000 + 0.700600000000000i;28.0000000000000 + 0.00000000000000i,29.0000000000000 + 0.00000000000000i,0.507500000000000 + 0.258500000000000i;29.0000000000000 + 0.00000000000000i,30.0000000000000 + 0.00000000000000i,0.974400000000000 + 0.963000000000000i;30.0000000000000 + 0.00000000000000i,31.0000000000000 + 0.00000000000000i,0.310500000000000 + 0.361900000000000i;31.0000000000000 + 0.00000000000000i,32.0000000000000 + 0.00000000000000i,0.341000000000000 + 0.536200000000000i];
Line(:,3)=Line(:,3)*100/(12.66^2);
r=real(Line(:,3));
x=imag(Line(:,3));
father=zeros(33,32);son=zeros(33,32);
for i=1:32
father(i,i)=1;
end
for i=[1:16,18:20,22:23,25:31]
son(i,i+1)=1;
end
son(1,18)=1;son(2,22)=1;son(5,25)=1;son(33,1)=1;
Umax=[1.07*1.07*ones(32,24);1.05*1.05*ones(1,24)];
Umin=[0.93*0.93*ones(32,24);1.05*1.05*ones(1,24)];
Pgmax=[zeros(32,24);ones(1,24)];
Qgmax=[zeros(32,24);ones(1,24)];
%定义变量
P=sdpvar(32,24);%线路有功
Q=sdpvar(32,24);%线路无功
U=sdpvar(33,24);%电压的平方
I=sdpvar(32,24);%电流的平方
Pg=sdpvar(33,24);%发电机有功
Qg=sdpvar(33,24);%发电机无功
Pin=-father*P+father*(I.*(r*ones(1,24)))+son*P;%节点注入有功
Qin=-father*Q+father*(I.*(x*ones(1,24)))+son*Q;%节点注入无功
Ploss_total=sum(sum(I.*(r*ones(1,24))));%目标函数，网损最小
%约束条件
C1=[U>=Umin,U<=Umax,Pg>=-Pgmax,Pg<=Pgmax,Qg>=-Qgmax,Qg<=Qgmax];%电压边界
C1=[C1,I>=0,I<=0.11,P>=-0.11,P<=0.11,Q>=-0.11,Q<=0.11];%电流和功率边界
C2=[Pin+Pload-Pg==0];%有功KCL约束
C3=[Qin+Qload-Qg==0];%无功KCL约束
C4=[U(Line(:,2),:)==U(Line(:,1),:)-2*(r*ones(1,24)).*P-2*(x*ones(1,24)).*Q+((r.^2+x.^2)*ones(1,24)).*I];%电压降落约束
C=[C1,C2,C3,C4];
toc%建模时间
ops=sdpsettings('solver','gurobi');
[model,recoverymodel,diagnostic,internalmodel] = export(C,Ploss_total,ops);%得到除去P^2+Q^2=UI的约束
params.Nonconvex=2;%启动gurobi非线性求解器
params.FeasibilityTol=1e-9;%由于gurobi采取的是双层模型，因此可行性步长应尽可能小
params.IntFeasTol=1e-9;%由于gurobi对非线性模型采用的是外嵌分支定界算法，相当于求解MIP问题，因此整数可行性要足够精确
L=length(model.obj);%决策变量数
%下面定义P^2+Q^2=UI的约束,模型为sum(Qval*x(Qrow)*x(Qcol))+q*x=rhs
for t=1:24
for j=1:32
model.quadcon(32*t-32+j).Qrow=[32*t-32+j,32*t-32+j+32*24,33*t-33+Line(j,1)+32*24*2];%P,Q,Uj
model.quadcon(32*t-32+j).Qcol=[32*t-32+j,32*t-32+j+32*24,32*t-32+j+32*24*2+33*24];%P,Q,I
model.quadcon(32*t-32+j).Qval=[1,1,-1];%P^2+Q^2-UI
model.quadcon(32*t-32+j).q=sparse(L,1);
model.quadcon(32*t-32+j).rhs=0;
model.quadcon(32*t-32+j).sense='=';%严格等号
end
end
result=gurobi(model,params);
assign(recover(recoverymodel.used_variables),result.x(1:L));%对决策变量赋值
toc%求解时间
Ploss_total=100*double(result.objval)