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jacobian.m
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jacobian.m
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function [Jacob,PQ,U,Uangle]=jacobian(Busnum,Balance,PVi,PVu,U,Uangle,Y,Angle,P0,Q0,r,c)
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%**************************************************************************
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% 程序功能 : 子函数——形成雅可比矩阵Jacobian
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% 编 者:
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% 编制时间:2010.12
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%**************************************************************************
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%% 分别求雅克比矩阵的子阵H,L,N,J及有功无功分量P,Q
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AngleIJ = Uangle(r) - Uangle(c)- Angle';
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U(PVi) = PVu;
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temp1= -sparse(1:Busnum,1:Busnum,U,Busnum,Busnum)*Y*sparse(1:Busnum,1:Busnum,U,Busnum,Busnum); % 计算雅克比矩阵可利用的中间变量
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temp2 = sum(temp1.*sparse(r,c,sin(AngleIJ)),2);
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temp3 = sum(temp1.*sparse(r,c,cos(AngleIJ)),2);
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temp4=sparse(1:Busnum,1:Busnum,temp2,Busnum,Busnum);
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temp5=sparse(1:Busnum,1:Busnum,temp3,Busnum,Busnum);
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H = temp1.*sparse(r,c,sin(AngleIJ))-temp4;
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L = temp1.*sparse(r,c,sin(AngleIJ))+temp4;
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N = temp1.*sparse(r,c,cos(AngleIJ))+temp5;
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J = -temp1.*sparse(r,c,cos(AngleIJ))+temp5;
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Q = Q0+temp2'; %求有功分量P
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P = P0+temp3'; %求无功分量Q
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%% 处理平衡节点和pv节点
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H(:,Balance) = 0;
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H(Balance,:) = 0;
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H(Balance,Balance) = 100; % 平衡节点对应的对角元素置一个有限数
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L(:,PVi) = 0;
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L(PVi,:) = 0;
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L = L+sparse(PVi,PVi,ones(1,length(PVi)),Busnum,Busnum); % PV节点对应的对角元素置为1
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J(:,Balance) = 0;
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J(PVi,:) = 0;
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N(:,PVi) = 0;
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N(Balance,:) = 0;
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Q(PVi) = 0; % 将pv节点的无功不平衡分量置零
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P(Balance) = 0; % 平衡节点的有功功率不平衡分量置零
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%% 合成PQ和雅可比矩阵
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PQ = cat(2,P,Q); % 形成功率不平衡分量列向量
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Jacob = cat(1,cat(2,H,N),cat(2,J,L)); % 形成Jacobian矩阵
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end
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