Beijing Jiaotong University
电力系统潮流计算
仿真报告
姓名：TYP 班级：电气0906 学号：09291183 指导老师：吴俊勇 完成日期：2012.6.24
一、实验内容
电力系统潮流计算是研究电力系统稳态运行情况的一种基本电气计算。它的任务是根据给定的运行条件和网路结构确定整个系统的运行状态，如各母线上的电压（幅值及相角）、网络中的功率分布以及功率损耗等。电力系统潮流计算的结果是电力系统稳定计算和故障分析的基础。
对于简单系统，可以将其分为开式网络和闭式网络手工计算。对于复杂电力系统，根据定解条件，应用牛顿—拉夫逊法进行计算，在手工计算中，由于涉及大量变量、微分方程、矩阵计算，求解很烦琐，而且容易出错，计算不同系统时需要重新计算。故而我们可以借助计算机来进行潮流计算，方便快捷且准确率高。
二、计算机潮流计算方法
我们常用牛顿—拉夫逊法来进行潮流计算。
牛顿—拉夫逊法(简称牛顿法)在数学上是求解非线性代数方程式的有效方法，其要点是把非线性方程式的求解过程变成反复地对相应的线性方程式进行求解的过程，即通常所称的逐次线性化过程。
1、基本原理
从几何意义上，牛顿—拉夫逊法实质上就是切线法，是一种逐步线性化的方法。
2、牛顿—拉夫逊法潮流求解过程
以下讨论的是用直角坐标形式的牛顿—拉夫逊法潮流的求解过程。当采用直角坐标时，潮流问题的待求量为各节点电压的实部和虚部两个分量，由于平衡节点的电压向量是给定的，因此待求量共2(n-1)需要2(n-1)个方程式。事实上，除了平衡节点的功率方程式在迭代过程中没有约束作用以外，其余每个节点都可以列出两个方程式。
求解过程大致可以分为以下步骤： (1)形成节点导纳矩阵； (2)将各节点电压设初值 ；
(3)将节点初值代入相关求式，求出修正方程式的常数项向量； (4)将节点电压初值代入求式，求出雅可比矩阵元素； (5)求解修正方程，求修正向量； (6)求取节点电压的新值；
(7)检查是否收敛，如不收敛，则以各节点电压的新值作为初值自第3步重新开始进行狭义次迭代，否则转入下一步；
(8)计算支路功率分布，PV节点无功功率和平衡节点功率。
其用程序仿真的过程可以由以下流程图来简单表示出来：
三、Matlab程序
1、原代码
%潮流计算
fprintf('开始潮流计算\\n');
fprintf('请输入待求网络的相应参数\\n'); %参数输入部分
n=input('网络中的节点数:n='); L=input('网络中的支路数:L='); ss=input('平衡节点ss='); pr=input('误差精度:pr='); X1=input('支路参数:X1='); X2=input('节点参数:X2=');
X=input('节点号和对地参数:X='); fprintf('参数输入部分结束\\n\\n'); Y=zeros(n); %置迭代次数 mm=1;
%创建节点导纳矩阵 for i=1:L
if X1(i,6)==0 %不含变压器的支路 p=X1(i,1); q=X1(i,2);
Y(p,q)=Y(p,q)-1/X1(i,3); Y(q,p)=Y(p,q);
Y(p,p)=Y(p,p)+1/X1(i,3)+0.5*X1(i,4); Y(q,q)=Y(q,q)+1/X1(i,3)+0.5*X1(i,4); else %含有变压器的支路 p=X1(i,1); q=X1(i,2);
Y(p,q)=Y(p,q)-1/(X1(i,3)*X1(i,5)); Y(q,p)=Y(p,q);
Y(p,p)=Y(p,p)+1/X1(i,3);
Y(q,q)=Y(q,q)+1/(X1(i,5)^2*X1(i,3)); end end Y;
OrgS=zeros(2*n-2,1);
DetaS=zeros(2*n-2,1); %将OrgS、DetaS初始化 %创建OrgS，用于存储初始功率参数
h=0; j=0;
for i=1:n %对PQ节点的处理 if i~=ss&&X2(i,6)==2 h=h+1; for j=1:n
OrgS(2*h-1,1)=OrgS(2*h-1,1)+real(X2(i,3))*(real(Y(i,j))*real(X2(j,3))-imag(Y(i,j))*imag(X2(j,3)))+imag(X2(i,3))*(real(Y(i,j))*imag(X2(j,3))+imag(Y(i,j))*real(X2(j,3)));
OrgS(2*h,1)=OrgS(2*h,1)+imag(X2(i,3))*(real(Y(i,j))*real(X2(j,3))-imag(Y(i,j))*imag(X2(j,3)))-real(X2(i,3))*(real(Y(i,j))*imag(X2(j,3))+imag(Y(i,j))*real(X2(j,3))); end end end
for i=1:n %对PV节点的处理，注意这时不可再将h初始化为0 if i~=ss&&X2(i,6)==0 h=h+1; for j=1:n
OrgS(2*h-1,1)=OrgS(2*h-1,1)+real(X2(i,3))*(real(Y(i,j))*real(X2(j,3))-imag(Y(i,j))*imag(X2(j,3)))+imag(X2(i,3))*(real(Y(i,j))*imag(X2(j,3))+imag(Y(i,j))*real(X2(j,3)));
OrgS(2*h,1)=OrgS(2*h,1)+imag(X2(i,3))*(real(Y(i,j))*real(X2(j,3))-imag(Y(i,j))*imag(X2(j,3)))-real(X2(i,3))*(real(Y(i,j))*imag(X2(j,3))+imag(Y(i,j))*real(X2(j,3))); end end end OrgS;
%创建PVU 用于存储PV节点的初始电压 PVU=zeros(n-h-1,1); t=0;
for i=1:n
if X2(i,6)==0 t=t+1;
PVU(t,1)=X2(i,3); end end PVU;
%创建DetaS，用于存储有功功率、无功功率和电压幅值的不平衡量
h=0;
for i=1:n %对PQ节点的处理 if i~=ss&&X2(i,6)==2 h=h+1;
DetaS(2*h-1,1)=real(X2(i,2))-OrgS(2*h-1,1); DetaS(2*h,1)=imag(X2(i,2))-OrgS(2*h,1); end end t=0;
for i=1:n %对PV节点的处理，注意这时不可再将h初始化为0 if i~=ss&&X2(i,6)==0 h=h+1; t=t+1;
DetaS(2*h-1,1)=real(X2(i,2))-OrgS(2*h-1,1);
DetaS(2*h,1)=real(PVU(t,1))^2+imag(PVU(t,1))^2-real(X2(i,3))^2-imag(X2(i,3))^2; end end DetaS;
%创建I，用于存储节点电流参数 i=zeros(n-1,1); h=0;
for i=1:n if i~=ss h=h+1;
I(h,1)=(OrgS(2*h-1,1)-OrgS(2*h,1)*sqrt(-1))/conj(X2(i,3)); end end I;
%创建Jacbi(雅可比矩阵) Jacbi=zeros(2*n-2); h=0; k=0;
for i=1:n %对PQ节点的处理 if X2(i,6)==2 h=h+1; for j=1:n if j~=ss k=k+1;
if i==j %对角元素的处理
Jacbi(2*h-1,2*k-1)=-imag(Y(i,j))*real(X2(i,3))+real(Y(i,j))*imag(X2(i,3))+imag(I(h,1));
Jacbi(2*h-1,2*k)=real(Y(i,j))*real(X2(i,3))+imag(Y(i,j))*imag(X2(i,3))+real(I(h,1));
Jacbi(2*h,2*k-1)=-Jacbi(2*h-1,2*k)+2*real(I(h,1));
Jacbi(2*h,2*k)=Jacbi(2*h-1,2*k-1)-2*imag(I(h,1)); else %非对角元素的处理
Jacbi(2*h-1,2*k-1)=-imag(Y(i,j))*real(X2(i,3))+real(Y(i,j))*imag(X2(i,3));
Jacbi(2*h-1,2*k)=real(Y(i,j))*real(X2(i,3))+imag(Y(i,j))*imag(X2(i,3));
Jacbi(2*h,2*k-1)=-Jacbi(2*h-1,2*k); Jacbi(2*h,2*k)=Jacbi(2*h-1,2*k-1); end
if k==(n-1) %将用于内循环的指针置于初始值，以确保雅可比矩阵换行
k=0; end end end end end k=0;
for i=1:n %对PV节点的处理 if X2(i,6)==0 h=h+1; for j=1:n if j~=ss k=k+1;
if i==j %对角元素的处理
Jacbi(2*h-1,2*k-1)=-imag(Y(i,j))*real(X2(i,3))+real(Y(i,j))*imag(X2(i,3))+imag(I(h,1));
Jacbi(2*h-1,2*k)=real(Y(i,j))*real(X2(i,3))+imag(Y(i,j))*imag(X2(i,3))+real(I(h,1));
Jacbi(2*h,2*k-1)=2*imag(X2(i,3)); Jacbi(2*h,2*k)=2*real(X2(i,3)); else %非对角元素的处理
Jacbi(2*h-1,2*k-1)=-imag(Y(i,j))*real(X2(i,3))+real(Y(i,j))*imag(X2(i,3));
Jacbi(2*h-1,2*k)=real(Y(i,j))*real(X2(i,3))+imag(Y(i,j))*imag(X2(i,3));
Jacbi(2*h,2*k-1)=0; Jacbi(2*h,2*k)=0; end
if k==(n-1) %将用于内循环的指针置于初始值，以确保雅可比矩阵换行
k=0; end end end end end Jacbi;
%求解修正方程，获取节点电压的不平衡量 DetaU=zeros(2*n-2,1); DetaU=inv(Jacbi)*DetaS; DetaU;
%修正节点电压 j=0;
for i=1:n %对PQ节点处理 if X2(i,6)==2 j=j+1;
X2(i,3)=X2(i,3)+DetaU(2*j,1)+DetaU(2*j-1,1)*sqrt(-1); end end
for i=1:n %对PV节点的处理 if X2(i,6)==0 j=j+1;
X2(i,3)=X2(i,3)+DetaU(2*j,1)+DetaU(2*j-1,1)*sqrt(-1); end end X2;
%开始循环
**********************************************************************
while abs(max(DetaU))>pr
OrgS=zeros(2*n-2,1); %!!!初始功率参数在迭代过程中是不累加的，所以在这里必须将其初始化为零矩阵 h=0; j=0;
for i=1:n
if i~=ss&&X2(i,6)==2
h=h+1; for j=1:n
OrgS(2*h-1,1)=OrgS(2*h-1,1)+real(X2(i,3))*(real(Y(i,j))*real(X2(j,3))-imag(Y(i,j))*imag(X2(j,3)))+imag(X2(i,3))*(real(Y(i,j))*imag(X2(j,3))+imag(Y(i,j))*real(X2(j,3)));
OrgS(2*h,1)=OrgS(2*h,1)+imag(X2(i,3))*(real(Y(i,j))*real(X2(j,3))-imag(Y(i,j))*imag(X2(j,3)))-real(X2(i,3))*(real(Y(i,j))*imag(X2(j,3))+imag(Y(i,j))*real(X2(j,3))); end end end
for i=1:n
if i~=ss&&X2(i,6)==0 h=h+1; for j=1:n
OrgS(2*h-1,1)=OrgS(2*h-1,1)+real(X2(i,3))*(real(Y(i,j))*real(X2(j,3))-imag(Y(i,j))*imag(X2(j,3)))+imag(X2(i,3))*(real(Y(i,j))*imag(X2(j,3))+imag(Y(i,j))*real(X2(j,3)));
OrgS(2*h,1)=OrgS(2*h,1)+imag(X2(i,3))*(real(Y(i,j))*real(X2(j,3))-imag(Y(i,j))*imag(X2(j,3)))-real(X2(i,3))*(real(Y(i,j))*imag(X2(j,3))+imag(Y(i,j))*real(X2(j,3))); end end end OrgS;
%创建DetaS h=0;
for i=1:n
if i~=ss&&X2(i,6)==2 h=h+1;
DetaS(2*h-1,1)=real(X2(i,2))-OrgS(2*h-1,1); DetaS(2*h,1)=imag(X2(i,2))-OrgS(2*h,1); end end t=0;
for i=1:n
if i~=ss&&X2(i,6)==0 h=h+1; t=t+1;
DetaS(2*h-1,1)=real(X2(i,2))-OrgS(2*h-1,1);
DetaS(2*h,1)=real(PVU(t,1))^2+imag(PVU(t,1))^2-real(X2(i,3))^2-imag(X2(i,3))^2; end end DetaS; %创建I
i=zeros(n-1,1); h=0;
for i=1:n if i~=ss h=h+1;
I(h,1)=(OrgS(2*h-1,1)-OrgS(2*h,1)*sqrt(-1))/conj(X2(i,3)); end end I;
%创建Jacbi
Jacbi=zeros(2*n-2); h=0; k=0;
for i=1:n
if X2(i,6)==2 h=h+1; for j=1:n if j~=ss k=k+1; if i==j
Jacbi(2*h-1,2*k-1)=-imag(Y(i,j))*real(X2(i,3))+real(Y(i,j))*imag(X2(i,3))+imag(I(h,1));
Jacbi(2*h-1,2*k)=real(Y(i,j))*real(X2(i,3))+imag(Y(i,j))*imag(X2(i,3))+real(I(h,1));
Jacbi(2*h,2*k-1)=-Jacbi(2*h-1,2*k)+2*real(I(h,1));
Jacbi(2*h,2*k)=Jacbi(2*h-1,2*k-1)-2*imag(I(h,1)); else
Jacbi(2*h-1,2*k-1)=-imag(Y(i,j))*real(X2(i,3))+real(Y(i,j))*imag(X2(i,3));
Jacbi(2*h-1,2*k)=real(Y(i,j))*real(X2(i,3))+imag(Y(i,j))*imag(X2(i,3));
Jacbi(2*h,2*k-1)=-Jacbi(2*h-1,2*k);
Jacbi(2*h,2*k)=Jacbi(2*h-1,2*k-1); end
if k==(n-1) k=0; end end end end end k=0;
for i=1:n
if X2(i,6)==0 h=h+1; for j=1:n if j~=ss k=k+1; if i==j
Jacbi(2*h-1,2*k-1)=-imag(Y(i,j))*real(X2(i,3))+real(Y(i,j))*imag(X2(i,3))+imag(I(h,1));
Jacbi(2*h-1,2*k)=real(Y(i,j))*real(X2(i,3))+imag(Y(i,j))*imag(X2(i,3))+real(I(h,1));
Jacbi(2*h,2*k-1)=2*imag(X2(i,3)); Jacbi(2*h,2*k)=2*real(X2(i,3)); else
Jacbi(2*h-1,2*k-1)=-imag(Y(i,j))*real(X2(i,3))+real(Y(i,j))*imag(X2(i,3));
Jacbi(2*h-1,2*k)=real(Y(i,j))*real(X2(i,3))+imag(Y(i,j))*imag(X2(i,3));
Jacbi(2*h,2*k-1)=0; Jacbi(2*h,2*k)=0; end
if k==(n-1) k=0; end end end end end Jacbi
DetaU=zeros(2*n-2,1);
DetaU=inv(Jacbi)*DetaS; DetaU
%修正节点电压 j=0;
for i=1:n
if X2(i,6)==2 j=j+1;
X2(i,3)=X2(i,3)+DetaU(2*j,1)+DetaU(2*j-1,1)*sqrt(-1); end end
for i=1:n
if X2(i,6)==0 j=j+1;
X2(i,3)=X2(i,3)+DetaU(2*j,1)+DetaU(2*j-1,1)*sqrt(-1); end end X2
mm=mm+1; %迭代次数加1 end mm
2、数据输入
开始潮流计算
请输入待求网络的相应参数 网络中的节点数:n=22 网络中的支路数:L=40 平衡节点ss=1
误差精度:pr=0.0001
支路参数:X1=[1,7,0.0+0.015i,0.0+0.0i,1,1.05; 2,9.,0.0+0.0217i,0.0+0.0i,1,1.075; 3,2.,0.0+0.0124i,0.0+0.0i,1,1.1; 4,19,0.0+0.0i,0.0+0.0i,1,1.025; 5,18,0.0+0.0375i,0.0+0.0i,1,1.05; 6,17,0.0+0.0337i,0.0+0.0i,1,1; 7,8,0.0106+0.074i,0.0+0.0i,1,1; 7,9,0.0147+0.104i,0.0+0.0i,1,1; 8,9,0.0034+0.0131i,0.0+0.0i,1,1; 8,22,0.0537+0.19i,0.0+0.0i,1,1;
8,22,0.0+0.1653i,0.0+0.0i,1,0; 9,10,0.0+0.002i,0.0+0.0i,1,1; 9,22,0.0559+0.218i,0.0+0.0i,1,1; 9,22,0.0+0.1954i,0.0+0.0i,1,0; 10,11,0.0+0.018i,0.0+0.0i,1,1; 11,11,0.0-1.3675i,0.0+0.0i,1,0; 11,12,0.0033+0.0343i,0.0+0.0i,1,1; 11,12,0.0+1.8797i,0.0+0.0i,1,0; 12,12,0.0-1.3675i,0.0+0.0i,1,0; 12,12,0.0-1.3675i,0.0+0.0i,1,0; 12,13,0.00245+0.0255i,0.0+0.0i,1,1; 12,13,0.0+1.395i,0.0+0.0i,1,0; 12,15,0.0+0.018i,0.0+0.0i,1,1; 13,17,0.0+0.01i,0.0+0.0i,1,1; 14,15,0.0-0.002i,0.0+0.0i,1,1; 14,19,0.0034+0.02i,0.0+0.0i,1,1; 16,16,0.0+0.5018i,0.0+0.0i,1,0; 16,17,0.0+0.001i,0.0+0.0i,1,0.975; 16,18,0.0033+0.0333i,0.0+0.0i,1,1; 16,19,0.0578+0.218i,0.0+0.0i,1,1; 16,19,0.0+0.1887i,0.0+0.0i,1,0; 16,20,0.0165+0.0662i,0.0+0.0i,1,1; 16,20,0.0+0.2353i,0.0+0.0i,1,0; 16,21,0.0374+0.178i,0.0+0.0i,1,1; 16,21,0.0+0.1i,0.0+0.0i,1,0; 19,21,0.0114+0.037i,0.0+0.0i,1,1; 20,22,0.0214+0.0859i,0.0+0.0i,1,1; 20,22,0.0+0.3008i,0.0+0.0i,1,0; 21,22,0.015+0.0607i,0.0+0.0i,1,1; 21,22,0.0+0.2198i,0.0+0.0i,1,0]
节点参数:X2=[0, 0.0+0.0i ,1.0,0.0,0,1; 0,6.0+3.2i,1.0,0.0,0,2; 0,3.1+0.0i,1.0,1.0,0,0; 0,1.6+0.7i,1.0,0.0,0,2; 0,4.3+3.34i,1.0,0.0,0,2; 0,-0.01+0.0i,1.0,0.0,0,0; 0,0.0+0.0i,1.0,0.0,0,2; 0,-2.87-1.44i,1.0,0.0,0,2; 0,-3.176-2.21i,1.0,0.0,0,2; 0,0.183+0.0i,1.0,0.0,0,2; 0,0.0+0.0i,1.0,0.0,0,2; 0,0.0+0.0i,1.0,0.0,0,2; 0,0.0+0.0i,1.0,0.0,0,2;
0,0.0+0.0i,1.0,0.0,0, 2; 0,0.0+0.0i,1.0,0.0,0, 2; 0,-5-2.9i,1.0,0.0,0, 2; 0,0.0+0.0i,1.0,0.0,0, 2; 0,-4.3-2.6i,1.0,0.0,0, 2; 0,-0.8-0.662i,1.0,0.0,0, 2; 0,-0.719-0.474i,1.0,0.0,0, 2; 0,-0.7-0.5i,1.0,0.0,0, 2; 0,-2.265-1.69i,1.0,0.0,0, 2]
节点号和对地参数:
X=[1,0;2,0;3,0;4,0;5,0;6,0;7,0;8,0;9,0;10,0;11,0;12,0;13,0;14,0;15,0;16,0;17,0;18,0;19,0;20,0;21,0;22,0] 参数输入部分结束
四、仿真结果
由于结果太长，粘入后一部分。
DetaU =
1.0e+152 *
0.0000 -0.0000 0.8278 1.2904 -0.6757 -0.5324 0.0138 0.0600 -0.3561 0.7466 -0.0086 -0.5668 -0.0710 0.7725
-0.1085 -4.6600 -8.8086 0.7060 -1.1456 0.3951 -0.0042 0.0181 -0.4711 -0.5285 4.4101 1.0732 5.4030 1.8329 0.1459 1.2651 0.0512 1.2975 -0.1952 0.0423 -0.5872 0.4488 0.1269 0.6914 -0.1404 0.4546 0.1120 0.04 X2 =
1.0e+152 *
Columns 1 through 3
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Jacbi =
1.0e+155 *
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五、实验心得
经过这次潮流计算编程的相关学习，我对于利用Matlab计算电力系统潮流的方法和思想都有了一定的了解，同时也知道了Matlab编程的基本思想。在使用Matlab仿真的过程中我遇到了不少问题，比如矩阵输入的疏忽使得行列不对等就让我重新检查了好几遍源程序和输入。还有在参数设定的时候前后没有统一也造成了很大的麻烦。由此可见，不管做什么都要认真细致，不可忽略细节。还有可能因为误差不同而造成的结果差异较大而不断进行改进和检查，反复研
究，在进步的同时也加深对Matlab软件的了解，使用的也会更为顺手。
总体说来，感觉收获很大，不仅加深了对电力系统潮流计算步骤的理解，也使对Matlab工具的应用更加熟练，相信以后的学习过程中这次的经历也会带来很大的帮助，加深了学习的乐趣和自己学习的热情。
“路漫漫其修远兮，吾将上下而求索”!这次大作业的Matlab仿真并不是学习的结束，而是新的开始！认真对待每一份作业，并且花时间去琢磨和钻研，总会有收获的。
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