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);