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牛顿-拉夫逊法进行潮流计算%本程序的功能是用牛顿-拉夫逊法进行潮流计算
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% n=input('请输入节点数:n=');
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% nl=input('请输入支路数:nl=');
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% ph=input('请输入平衡母线节点号:ph=');
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% jd=input('请输入误差精度jd=');
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% B=input('请输入由支路参数形成的矩阵:B=');
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% A=input('请输入各节点参数形成的矩阵:A=');
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n=4
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nl=4
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ph=4
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jd=0.00001
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B=[1 2 0.10+0.40i 0.01528i 1 ;
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1 3 0+0.3i 0 1/1.1 ;
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1 4 0.12+0.50i 0.01920i 1 ;
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2 4 0.08+0.40i 0.01413i 1 ;]
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A=[-0.30-0.18i 1.0 0 2; %1号PQ节点
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-0.55-0.13i 1.0 0 2; %2号PQ节点
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0.5 1.1 1.1 3; %3号PV节点
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0 1.05 0 1;] %4号平衡节点
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Y=zeros(n);e=zeros(1,n);f=zeros(1,n);V=zeros(1,n);
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for i=1:nl
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p=B(i,1);q=B(i,2);
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Y(p,q)=Y(p,q)-1./(B(i,3)*B(i,5));
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Y(q,p)=Y(p,q);
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Y(q,q)=Y(q,q)+1./(B(i,3)*B(i,5)^2)+B(i,4);
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Y(p,p)=Y(p,p)+1./B(i,3)+B(i,4);
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end %形成节点导纳矩阵
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disp('节点导纳矩阵Y为:');
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disp(Y);
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G=real(Y);B=imag(Y); %Y=G+jB
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for i=1:n
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e(i)=real(A(i,2));
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f(i)=imag(A(i,2)); %V=e+jf
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V(i)=A(i,3);
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end
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for i=1:n
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S(i)=A(i,1)
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end
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P=real(S);Q=imag(S);
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Ci=0;a=1;NO=2*n;N=NO-1;%开始求雅克比矩阵,M为迭代次数
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while a~=0
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a=0;
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for i=1:n
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if i~=ph
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C(i)=0;
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D(i)=0;
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for j=1:n
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C(i)=C(i)+G(i,j)*e(j)-B(i,j)*f(j);
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D(i)=D(i)+G(i,j)*f(j)+B(i,j)*e(j);
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end
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P1=C(i)*e(i)+f(i)*D(i);
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Q1=f(i)*C(i)-D(i)*e(i); %求Pi,Qi
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V2=e(i)^2+f(i)^2;
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if A(i,4)~=3 %若节点不是PV节点
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DP=P(i)-P1;
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DQ=Q(i)-Q1;
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for j=1:n
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if j~=ph&j~=i %节点不为平衡节点时非对角线元素
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X1=-G(i,j)*e(i)-B(i,j)*f(i);
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X2=B(i,j)*e(i)-G(i,j)*f(i);
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X3=X2;
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X4=-X1;
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p=2*i-1;q=2*j-1;J(p,q)=X1;J(p,N)=DP;m=p+1;
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J(m,q)=X3;J(m,N)=DQ;q=q+1;J(p,q)=X2;J(m,q)=X4;
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elseif j==i&j~=ph %节点不为平衡节点时对角线元素
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X1=-C(i)-G(i,i)*e(i)-B(i,i)*f(i);
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X2=-D(i)+B(i,i)*e(i)-G(i,i)*f(i);
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X3=D(i)+B(i,i)*e(i)-G(i,i)*f(i);
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X4=-C(i)+G(i,i)*e(i)+B(i,i)*f(i);
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p=2*i-1;q=2*j-1;J(p,q)=X1;J(p,N)=DP;m=p+1;
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J(m,q)=X3;J(m,N)=DQ;q=q+1;J(p,q)=X2;J(m,q)=X4;
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end
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end
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else %若节点是PV节点
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DP=P(i)-P1;
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DV=V(i)^2-V2;
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for j=1:n
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if j~=ph&j~=i
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X1=-G(i,j)*e(i)-B(i,j)*f(i);
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X2=B(i,j)*e(i)-G(i,j)*f(i);
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X5=0;
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X6=0;
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p=2*i-1;q=2*j-1;J(p,q)=X1;J(p,N)=DP;m=p+1;
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J(m,q)=X5;J(m,N)=DV;q=q+1;J(p,q)=X2;J(m,q)=X6;
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elseif j==i&j~=ph
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X1=-C(i)-G(i,i)*e(i)-B(i,i)*f(i);
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X2=-D(i)+B(i,i)*e(i)-G(i,i)*f(i);
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X5=-2*e(i);
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X6=-2*f(i);
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p=2*i-1;q=2*j-1;J(p,q)=X1;J(p,N)=DP;m=p+1;
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J(m,q)=X5;J(m,N)=DV;q=q+1;J(p,q)=X2;J(m,q)=X6;
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end
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end
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end
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end
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end
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disp('雅克比矩阵J:');
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disp(J);
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DJ=-J(:,[1:NO-2]);%修正方程系数矩阵DJ=-J
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DW=J([1:NO-2],N); %修正方程常数项矩阵DW
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DY=DJ\DW;
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disp('第M次修正方程的解DY:');
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disp(DY);
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for i=1:NO-2
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DET=abs(DW(i));
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if DET>=jd
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a=a+1;
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end
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end
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Ci=Ci+1;
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for i=1:n-1
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e(i)=e(i)+DY(2*i-1);
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f(i)=f(i)+DY(2*i);
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end
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E=e+f*j;
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disp('节点电压的第C(i)次近似值:');
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disp(E);
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disp('迭代次数:');
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disp(Ci-1);
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for k=1:n
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V(k)=sqrt(e(k)^2+f(k)^2);
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O(k)=atan(f(k)./e(k))*180./pi;
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end %收敛后节点电压用极坐标表示的结果
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E=e+f*j;
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disp('各节点的实际电压标么值E为(节点号从小到大排列):');disp(E);
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disp('各节点的电压大小V为(节点号从小到大排列):');disp(V);
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disp('各节点的电压相角O(单位:度)为(节点号从小到大排列):');disp(O);
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for p=1:n
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C(p)=0;
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for q=1:n
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C(p)=C(p)+conj(Y(p,q))*conj(E(q));
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end
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S(p)=E(p)*C(p);
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end
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end
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disp('各节点的功率S为(节点号从小到大排列):');
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disp(S);
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disp('平衡节点功率为:');
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disp(S(ph));
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disp('各条支路的首端功率Si为:');
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for i=1:nl
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p=B(i,1);q=B(i,2);
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Si(p,q)=E(p)*(conj(E(p))*conj(B(i,4))+(conj(E(p)./B(i,5))-conj(E(q)))*conj(1./(B(i,3)*B(i,5))));
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disp(Si(p,q)); %计算支路首端功率Si
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end
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disp('各条支路的末端功率Sj为:')
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for i=1:nl
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p=B(i,1);q=B(i,2);
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Sj(q,p)=E(q)*(conj(E(q))*conj(B(i,4))+(conj(E(q)./B(i,5))-conj(E(p)))*conj(1./(B(i,3)*B(i,5))));
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disp(Sj(q,p));
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end %计算支路末端功率Sj
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disp('各条支路的功率损耗为:');
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for i=1:nl
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p=B(i,1);q=B(i,2);
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DS(i)=Si(p,q)+Sj(p,q);
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disp(DS(i));
v3g;r$q8M0U,]5l\]
end
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