201 lines
10 KiB
Matlab
201 lines
10 KiB
Matlab
function [HSB,dhx,dgx,dgxT,N1,H1,diagE,diagF,GIJ,BIJ,L1,U1,LZ,UW]=formHSB(nodeNum,balNode,balNum,opfGoal,lineNum,transNum,lineI,lineJ,...
|
||
transI,transJ,T,transG,transB,pgNode,pvNode,G,B,e,f,pgNum,pvNum,pgvNum,xNum,capNum,capI,a,m,r,l,u,z,w,y,H1,N1,diagE,diagF)
|
||
%程序功能：预计算过程，形成修正方程系数矩阵
|
||
%编写时间：2010年11月
|
||
|
||
%% 形成等式约束雅可比矩阵
|
||
ef1=e(transI).*e(transJ)+f(transI).*f(transJ);
|
||
ef2=e(transI).*f(transJ)-e(transJ).*f(transI);
|
||
ef3=e(transI).*e(transI)+f(transI).*f(transI);
|
||
ef1G=ef1.*transG;
|
||
ef1B=ef1.*transB;
|
||
ef2G=ef2.*transG;
|
||
ef2B=ef2.*transB;
|
||
dhPTi=-ef1G+ef2B+2*ef3.*transG.*T;
|
||
dhPTj=-ef1G-ef2B;
|
||
dhPT=sparse(1:transNum,transI,dhPTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhPTj,transNum,nodeNum);%有功平衡方程P对变压器变比求偏导
|
||
dhQTi=ef1B+ef2G-2*ef3.*transB.*T;
|
||
dhQTj=ef1B-ef2G;
|
||
dhQT=sparse(1:transNum,transI,dhQTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhQTj,transNum,nodeNum);%无功平衡方程Q对变压器变比求偏导
|
||
dhP=sparse(1:pgNum,pgNode,ones(pgNum,1),pgNum,m);
|
||
dhQ1=sparse(1:pvNum,pvNode,ones(pvNum,1),pvNum,nodeNum);
|
||
dhQ=[sparse(pvNum,nodeNum) dhQ1];
|
||
dhcapK1=sparse(1:capNum,capI,(e(capI).^2+f(capI).^2),capNum,nodeNum); %功率平衡方程对电容电抗器组数求偏导
|
||
dhcapK=[sparse(capNum,nodeNum) dhcapK1];
|
||
%功率方程雅可比矩阵
|
||
deG=diagE*G;
|
||
dfB=diagF*B;
|
||
deB=diagE*B;
|
||
dfG=diagF*G;
|
||
dH1=sparse(1:nodeNum,1:nodeNum,H1,nodeNum,nodeNum);
|
||
dN1=sparse(1:nodeNum,1:nodeNum,N1,nodeNum,nodeNum);
|
||
Hij=-dH1-deG-dfB;
|
||
Nij=-dN1+deB-dfG;
|
||
Jij=dN1-dfG+deB;
|
||
Lij=-dH1+dfB+deG;
|
||
%合并形成功率方程雅可比矩阵
|
||
dhJacb=[Hij Nij;Jij Lij]';
|
||
%合并形成等式约束雅可比矩阵h(x)
|
||
dhx=[dhPT dhQT;dhP;dhQ;dhcapK;dhJacb];
|
||
%% 形成不等式约束雅可比矩阵▽g(x)
|
||
dgT1=sparse(1:transNum,1:transNum,ones(transNum,1),transNum,r-lineNum);
|
||
dglT=(e(transI).^2+f(transI).^2-e(transI).*e(transJ)-f(transI).*f(transJ)).*transG+(e(transI).*f(transJ)-e(transJ).*f(transI)).*transB;
|
||
dgT2=sparse(1:transNum,lineNum-transNum+1:lineNum,dglT,transNum,lineNum);
|
||
dgT=[dgT1 dgT2]; %所有不等式对变比求导的模块
|
||
dgP=sparse(1:pgNum,transNum+1:transNum+pgNum,ones(pgNum,1),pgNum,r); %所有不等式约束对PG求导的模块
|
||
dgQ=sparse(1:pvNum,transNum+pgNum+1:transNum+pgvNum,ones(pvNum,1),pvNum,r); %所有不等式约束对QR求导的模块
|
||
dgcapK=sparse(1:capNum,transNum+pgvNum+1:transNum+pgvNum+capNum,ones(capNum,1),capNum,r);%所有不等式约束对capK求导的模块
|
||
dgve=2*diagE;
|
||
dgvf=2*diagF;
|
||
sizeG=size(G);
|
||
GIJ=G(sub2ind(sizeG,lineI,lineJ));
|
||
BIJ=B(sub2ind(sizeG,lineI,lineJ));
|
||
dgleI=(2*e(lineI)-e(lineJ)).*GIJ+f(lineJ).*BIJ;
|
||
dgleJ=-e(lineI).*GIJ-f(lineI).*BIJ;
|
||
dglfI=(2*f(lineI)-f(lineJ)).*GIJ-e(lineJ).*BIJ;
|
||
dglfJ=-f(lineI).*GIJ+e(lineI).*BIJ;
|
||
dgle=sparse(lineI,(1:lineNum),dgleI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dgleJ,nodeNum,lineNum);
|
||
dglf=sparse(lineI,(1:lineNum),dglfI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dglfJ,nodeNum,lineNum);
|
||
dg0=sparse(m,transNum+pgvNum+capNum);
|
||
dgvl=[dgve dgle;dgvf dglf];
|
||
dgef=[dg0 dgvl]; %所有不等式约束对电压实部、虚部求偏导的模块
|
||
dgx=[dgT;dgP;dgQ;dgcapK;dgef]; %不等式约束雅克比矩阵
|
||
%% 形成对角阵
|
||
Z=sparse(1:r,1:r,z,r,r);
|
||
W=sparse(1:r,1:r,w,r,r);
|
||
L1=sparse(1:r,1:r,1./l,r,r);
|
||
U1=sparse(1:r,1:r,1./u,r,r);
|
||
LZ=L1*Z;
|
||
UW=U1*W;
|
||
%% 形成海森伯矩阵
|
||
%目标函数的海森伯矩阵▽2f(x)
|
||
if(opfGoal==2)
|
||
HSdfx=sparse(xNum,xNum);
|
||
else if(opfGoal==1)
|
||
HSdfx=sparse(transNum+1:transNum+pgNum,transNum+1:transNum+pgNum,2*a(pgNode),xNum,xNum);%仅目标函数对PG求偏导处的对角元为非零元素，其他都为0
|
||
else if(opfGoal==3)
|
||
d2ftei=-2*transG.*(e(transI)-e(transJ));
|
||
d2ftej=-d2ftei;
|
||
d2ftfi=-2*transG.*(f(transI)-f(transJ));
|
||
d2ftfj=-d2ftfi;
|
||
d2fte=sparse(1:transNum,transI,d2ftei,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftej,transNum,nodeNum);
|
||
d2ftf=sparse(1:transNum,transI,d2ftfi,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftfj,transNum,nodeNum);
|
||
d2fT0=sparse(transNum,transNum+pgvNum+capNum);
|
||
d2fT=[d2fT0 d2fte d2ftf];
|
||
d2fPGQR=sparse(pgvNum,xNum);
|
||
d2fcapK=sparse(capNum,xNum);
|
||
d2fee=2*(G-sparse(1:nodeNum,1:nodeNum,sum(G,2),nodeNum,nodeNum));
|
||
d2fff=d2fee;
|
||
zero_nodeNum=sparse(nodeNum,nodeNum);
|
||
d2f_ef_ef=[d2fee zero_nodeNum;zero_nodeNum d2fff];
|
||
d2efT=[d2fte d2ftf]';
|
||
d2f_ef=[d2efT sparse(2*nodeNum,pgvNum+capNum) d2f_ef_ef];
|
||
HSdfx=[d2fT;d2fPGQR;d2fcapK;d2f_ef];
|
||
else if(opfGoal==4)
|
||
d2ftei=2*transB.*(e(transI)-e(transJ));
|
||
d2ftej=-d2ftei;
|
||
d2ftfi=2*transB.*(f(transI)-f(transJ));
|
||
d2ftfj=-d2ftfi;
|
||
d2fte=sparse(1:transNum,transI,d2ftei,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftej,transNum,nodeNum);
|
||
d2ftf=sparse(1:transNum,transI,d2ftfi,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftfj,transNum,nodeNum);
|
||
d2fT0=sparse(transNum,transNum+pgvNum+capNum);
|
||
d2fT=[d2fT0 d2fte d2ftf];
|
||
d2fPGQR=sparse(pgvNum,xNum);
|
||
d2fcapK=sparse(capNum,xNum);
|
||
d2fee=-2*(B-sparse(1:nodeNum,1:nodeNum,sum(B,2),nodeNum,nodeNum));
|
||
d2fff=d2fee;
|
||
zero_nodeNum=sparse(nodeNum,nodeNum);
|
||
d2f_ef_ef=[d2fee zero_nodeNum;zero_nodeNum d2fff];
|
||
d2efT=[d2fte d2ftf]';
|
||
d2f_ef=[d2efT sparse(2*nodeNum,pgvNum+capNum) d2f_ef_ef];
|
||
HSdfx=[d2fT;d2fPGQR;d2fcapK;d2f_ef];
|
||
end
|
||
end
|
||
end
|
||
end
|
||
%等式约束海森伯矩阵与拉格朗日乘子y的乘积▽2h(x)*y
|
||
y1=y(1:nodeNum,1);
|
||
y2=y(nodeNum+1:2*nodeNum,1);
|
||
dhT2=2*ef3.*(transG.*y1(transI)-transB.*y2(transI)); %功率方程对变压器变比求二次偏导所得的列向量
|
||
HSdhT=sparse(1:transNum,1:transNum,dhT2,transNum+pgvNum+capNum,transNum+pgvNum+capNum);
|
||
eiG=e(transI).*transG;
|
||
ejG=e(transJ).*transG;
|
||
eiB=e(transI).*transB;
|
||
ejB=e(transJ).*transB;
|
||
fiG=f(transI).*transG;
|
||
fjG=f(transJ).*transG;
|
||
fiB=f(transI).*transB;
|
||
fjB=f(transJ).*transB;
|
||
ejG_fjB=ejG-fjB;
|
||
ejGfjB=ejG+fjB;
|
||
fjGejB=fjG+ejB;
|
||
ejB_fjG=ejB-fjG;
|
||
eiGfiB=eiG+fiB;
|
||
eiG_fiB=eiG-fiB;
|
||
eiB_fiG=eiB-fiG;
|
||
fiGeiB=fiG+eiB;
|
||
dP2_ei_t=(4*eiG.*T-ejG_fjB).*y1(transI)-ejGfjB.*y1(transJ);
|
||
dP2_ej_t=-eiGfiB.*y1(transI)-eiG_fiB.*y1(transJ);
|
||
dQ2_ei_t=(-4*eiB.*T+fjGejB).*y2(transI)+ejB_fjG.*y2(transJ);
|
||
dQ2_ej_t=eiB_fiG.*y2(transI)+fiGeiB.*y2(transJ);
|
||
HSdh_et=sparse(1:transNum,transI,dP2_ei_t+dQ2_ei_t,transNum,nodeNum)+sparse(1:transNum,transJ,dP2_ej_t+dQ2_ej_t,transNum,nodeNum);%功率方程先对变比求偏导，再对电压实部求偏导模块
|
||
dP2_fi_t=(4*fiG.*T-fjGejB).*y1(transI)+ejB_fjG.*y1(transJ);
|
||
dP2_fj_t=eiB_fiG.*y1(transI)-fiGeiB.*y1(transJ);
|
||
dQ2_fi_t=(-4*fiB.*T-ejG_fjB).*y2(transI)+ejGfjB.*y2(transJ);
|
||
dQ2_fj_t=eiGfiB.*y2(transI)-eiG_fiB.*y2(transJ);
|
||
HSdh_ft=sparse(1:transNum,transI,dP2_fi_t+dQ2_fi_t,transNum,nodeNum)+sparse(1:transNum,transJ,dP2_fj_t+dQ2_fj_t,transNum,nodeNum);%功率方程先对变比求偏导，再对电压虚部求偏导模块
|
||
HSdh_eft=[HSdh_et HSdh_ft];
|
||
HSdh_tef=HSdh_eft';
|
||
HSdhPQ=sparse(pgvNum,2*nodeNum); %功率方程先对PG、QR求偏导，再对其他变量求偏导的部分
|
||
d2hcap_e=sparse(1:capNum,capI,2*e(capI).*y2(capI),capNum,nodeNum); %功率方程先对capK求偏导，再对e求偏导的部分
|
||
d2hcap_f=sparse(1:capNum,capI,2*f(capI).*y2(capI),capNum,nodeNum); %功率方程先对capK求偏导，再对f求偏导的部分
|
||
HSdhcap_ef=[d2hcap_e d2hcap_f];
|
||
d2htPQ_ef=[HSdh_eft;HSdhPQ;HSdhcap_ef];
|
||
HSdhtPQ=[HSdhT d2htPQ_ef];
|
||
HSdhx1=sparse(m,pgvNum);
|
||
%潮流方程海森矩阵
|
||
diagy1=sparse(1:nodeNum,1:nodeNum,y1,nodeNum,nodeNum);
|
||
diagy2=sparse(1:nodeNum,1:nodeNum,y2,nodeNum,nodeNum);
|
||
HSdhey=-diagy1*G+diagy2*B+(-G*diagy1+B*diagy2);
|
||
HSdhefy=diagy1*B+diagy2*G-(B*diagy1+G*diagy2);
|
||
HSdhx2=[HSdhey HSdhefy;HSdhefy' HSdhey];
|
||
HSdhx=[HSdhtPQ;HSdh_tef HSdhx1 HSdhcap_ef' HSdhx2];
|
||
%形成不等式约束二阶偏导的矩阵▽2g(x)*(z+w)
|
||
ZWcl=z(transNum+pgvNum+capNum+nodeNum+1:end)+w(transNum+pgvNum+capNum+nodeNum+1:end);
|
||
ZWv=z(transNum+pgvNum+capNum+1:transNum+pgvNum+capNum+nodeNum)+w(transNum+pgvNum+capNum+1:transNum+pgvNum+capNum+nodeNum);
|
||
dgeiT=((2*e(transI)-e(transJ)).*transG+f(transJ).*transB).*ZWcl(lineNum-transNum+1:end);
|
||
dgejT=(-e(transI).*transG-f(transI).*transB).*ZWcl(lineNum-transNum+1:end);
|
||
dgeT=sparse(1:transNum,transI,dgeiT,transNum,nodeNum)+sparse(1:transNum,transJ,dgejT,transNum,nodeNum);%不等式约束先对变比求偏导，再对e求偏导的模块
|
||
dgfiT=((2*f(transI)-f(transJ)).*transG-e(transJ).*transB).*ZWcl(lineNum-transNum+1:end);
|
||
dgfjT=(-f(transI).*transG+e(transI).*transB).*ZWcl(lineNum-transNum+1:end);
|
||
dgfT=sparse(1:transNum,transI,dgfiT,transNum,nodeNum)+sparse(1:transNum,transJ,dgfjT,transNum,nodeNum);%不等式约束先对变比求偏导，再对f求偏导的模块
|
||
HSdgefT=[dgeT dgfT];
|
||
HSdgT=[sparse(transNum,transNum+pgvNum+capNum) HSdgefT];
|
||
HSdgee=sparse(lineI,lineI,2*GIJ.*ZWcl,nodeNum,nodeNum)-sparse(lineI,lineJ,GIJ.*ZWcl,nodeNum,nodeNum)...
|
||
-sparse(lineJ,lineI,GIJ.*ZWcl,nodeNum,nodeNum)+sparse(1:nodeNum,1:nodeNum,2*ZWv,nodeNum,nodeNum);
|
||
HSdgff=HSdgee;
|
||
HSdgef=sparse(lineI,lineJ,BIJ.*ZWcl,nodeNum,nodeNum)-sparse(lineJ,lineI,BIJ.*ZWcl,nodeNum,nodeNum);
|
||
HSdgfe=HSdgef';
|
||
HSdgx1=[HSdgee HSdgef;HSdgfe HSdgff]; %所有不等式约束对e、f求二次偏导模块
|
||
HSdgxtPQ_0=sparse(pgvNum+capNum,xNum);
|
||
HSdgef_0=[HSdgefT' sparse(2*nodeNum,pgvNum+capNum)];
|
||
HSdgx=[HSdgT;HSdgxtPQ_0;HSdgef_0 HSdgx1]; %合成不等式约束海森矩阵
|
||
%求和形成H(.)矩阵.
|
||
dgxT=dgx'; %求dgx的转置
|
||
MULdgx=dgx*(UW-LZ)*dgxT;
|
||
H=HSdhx+HSdgx-HSdfx+MULdgx; %求和形成H(.)矩阵.
|
||
%% 根据以上所求的各个矩阵合成海森伯矩阵
|
||
HSB0=sparse(m,m);
|
||
HSB=[H dhx;dhx' HSB0];
|
||
balN=transNum+pgvNum+capNum+nodeNum+balNode;
|
||
HSB(balN,:)=0; %保持平衡节点电压虚部不变，始终为0，即将海森矩阵中平衡节点虚部所对应的行列元素置0，对角元素置1
|
||
HSB(:,balN)=0;
|
||
HSB_balN=sub2ind(size(HSB),balN,balN);
|
||
HSB(HSB_balN)=ones(balNum,1);
|
||
balN1=transNum+pgvNum+capNum+balNode;
|
||
HSB(balN1,:)=0; %保持平衡节点电压实部不变，始终为0，即将海森矩阵中平衡节点实部所对应的行列元素置0，对角元素置1
|
||
HSB(:,balN1)=0;
|
||
HSB_balN1=sub2ind(size(HSB),balN1,balN1);
|
||
HSB(HSB_balN1)=ones(balNum,1);
|
||
HSB=sparse(HSB);
|