电力系统潮流计算仿真报告

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1、 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，

2、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

3、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

4、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nn);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,

5、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); endendY;OrgS=zeros(2*n-2,

6、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

7、)+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 endendfor 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,

8、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 endendOrgS;%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)=

9、0 t=t+1; PVU(t,1)=X2(i,3); endendPVU;%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); endendt=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(

10、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; endendDetaS;%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); endendI;%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)

11、=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*

12、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

13、endk=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

14、*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 endendJacbi;%求解修正方程，获取节点电压的不平衡量Det

15、aU=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); endendfor 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); endendX2;%开始循环*while abs(max(DetaU)prOrgS=zeros(2

16、*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(

17、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 endendfor 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

18、(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 endendOrgS;%创建DetaSh=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

19、,2)-OrgS(2*h,1); endendt=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; endendDetaS;%创建Ii=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);

20、 endendI;%创建JacbiJacbi=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

21、*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=

22、0; end end end endendk=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*

23、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 endendJacbiDetaU=zeros(2*n-2,1);DetaU=inv(Jacbi)*DetaS;DetaU%修正节点电压j=0;f

24、or 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); endendfor 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); endendX2mm=mm+1; %迭代次数加1endmm2、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

25、.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+0.064i,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

26、,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

27、.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

28、.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+0.164i,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+0.060

29、7i,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,

30、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,-0.864-0.662i,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

31、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

32、.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 0.0489X2 = 1.0e+152 * Columns 1 through 3 0 0 0.0000 0 0.0000 + 0.0000i -0.0000 + 0.0000i 0 0.0000 -0.6061 - 2.4840i 0 0.0000 + 0.0000i 1.232

33、4 + 0.8115i 0 0.0000 + 0.0000i 2.1905 + 0.4803i 0 -0.0000 0.0700 + 0.1603i 0 0 0.2226 + 0.0678i 0 -0.0000 - 0.0000i 0.4741 + 0.1168i 0 -0.0000 - 0.0000i -0.7678 + 0.3106i 0 0.0000 0.7060 - 0.1106i 0 0 -3.7987 + 3.0737i 0 0 1.4448 - 5.2542i 0 0 2.1504 + 0.6668i 0 0 -0.7980 - 0.1097i 0 0 -1.6845 - 1.2

34、253i 0 -0.0000 - 0.0000i 1.0346 + 4.5579i 0 0 1.7606 + 5.3485i 0 -0.0000 - 0.0000i 0.3183 + 0.0898i 0 -0.0000 - 0.0000i 0.4975 + 0.0130i 0 -0.0000 - 0.0000i 0.0975 - 0.2849i 0 -0.0000 - 0.0000i 0.1583 - 0.8069i 0 -0.0000 - 0.0000i 0.5199 - 0.1895i Columns 4 through 6 0 0 0.0000 0 0 0.0000 0.0000 0 0

35、 0 0 0.0000 0 0 0.0000 0 0 0 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 Jacbi = 1.0e+155 * Columns 1 through 6 -0.0843 0.1860 0.0000 0.0000 0 0 0.1860 0.0843 -0.0000 0

36、.0000 0 0 0 0 0 0 0.0192 -0.0225 0 0 0 0 0.0029 0.0193 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0354 0.0143 0 0 0 0 -0.0143 0.0354 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

37、0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0078 0.0002 0 0 0 0 -0.0002 -0.0078 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0489 -0.2003 -0.1723 -0.4288 0 0 0 0 -0.0050 -0.0012 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 7

38、through 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0068 0.0292 0 0 0 0 0.0548 0.1236 0 0 0 0 0 0 0 0 0.0179 -0.0053 0 0 0 0 0.0054 0.0223 0 0 0 0 -0.0065 0.0006 0 0 0 0 -0.0006 -0.0065 0 0 0 0 0.0068 0.0040 0 0 0 0 -0.0040 0.0068 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0522 0.1587 0 0 0 0 -0.1587 -0.0522 0 0 -0.0085 0.0024 0 0 0