电力系统分析大作业.doc

题目：编写程序计算图1所示算例系统的潮流及三相短路电流。潮流计算：方法不限，计算系统的节点电压和相角。短路电流：4号母线发生金属性三相短路时（zf=0），分别按照精确算法和近似算法计算短路电流、系统中各节点电压以及网络中各支路的电流分布，并对两种情况下的计算结果进行比较。近似算法是指：形成节点导纳矩阵时，所有节点的负荷都略去不计，短路前网络处于空载状态，短路前各节点电压均为1.0。计算步骤：(1) 进行系统正常运行状态的潮流计算，求得(2) 形成不含发电机和负荷的节点导纳矩阵YN；(3) 将发电机表示为电流源()和导纳()的并联组合；节点负荷用恒阻抗的接地支路表示；形成包括所有发电机支路和负荷支路的节点导纳矩阵Y，即在YN中的发电机节点和负荷节点的自导纳上分别增加发电机导纳和负荷导纳（）；(4) 利用，计算节点阻抗矩阵，从而得到阻抗矩阵中的第f列；(5) 利用公式(6-7)或(6-10)计算短路电流；(6) 利用公式(6-8)或(6-11)计算系统中各节点电压；(7) 利用公式(6-9)计算变压器支路的电流；对输电线路利用型等值电路计算支路电流。图1 3机9节点系统表1 9节点系统支路参数支路R（p.u.）X（p.u.）B/2(TK) （p.u.）1400.05761.02700.06251.03900.05861.0450.010.0850.088460.0170.0920.079570.0320.1610.153690.0390.170.179780.00850.0720.0745890.01190.10080.1045表2 9节点系统发电机参数发电机编号节点类型PG（p.u.）VG（p.u.）（p.u.）（p.u.）1平衡1.040.31.1372PV1.631.0250.31.2113PV0.851.0250.31.043表3 9节点系统负荷参数节点编号节点类型Pi（p.u.）Qi（p.u.）4PQ005PQ1.250.56PQ0.90.37PQ008PQ10.359PQ00表4 短路前9节点潮流计算结果（供参考）节点编号电压幅值(p.u.)电压相角(rad)节点有功(p.u.)节点无功(p.u.)11.040.00.71640.270521.0259.281.630.066531.0254.660.85-0.108641.0258-2.2170050.9956-3.989-1.25-0.561.0127-3.687-0.90-0.371.02583.7200081.01590.728-1.0-0.3591.03241.96700程序代码：format longA=1 4 0 0.0576 0; 2 7 0 0.0625 0; 3 9 0 0.0586 0; 4 5 0.01 0.085 0.088; 4 6 0.017 0.092 0.079; 5 7 0.032 0.161 0.153; 6 9 0.039 0.17 0.179; 7 8 0.0085 0.072 0.0745; 8 9 0.0119 0.1008 0.1045; y=zeros(9,9);for k=1:9 m=A(k,1); n=A(k,2); y(m,m)=y(m,m)+1/(A(k,3)+1i*A(k,4)+1i*A(k,5); y(n,n)=y(n,n)+1/(A(k,3)+1i*A(k,4)+1i*A(k,5); y(m,n)=y(m,n)-1/(A(k,3)+1i*A(k,4); y(n,m)=y(n,m)-1/(A(k,3)+1i*A(k,4);end U=1.04,1.025,1.025,1,1,1,1,1,1;a=0,0,0,0,0,0,0,0,0;P=1,1.63,0.85,0,-1.25,-0.9,0,-1,0;Q=0,0,0,0,-0.5,-0.3,0,-0.35,0;dP=0,0,0,0,0,0,0,0,0;dQ=0,0,0,0,0,0,0,0,0;G=real(y);B=imag(y);Pt=zeros(1,9);Qt=zeros(1,9);H=zeros(8,8);N=zeros(8,6);M=zeros(6,8);L=zeros(6,6);Ai=zeros(1,9);Bi=zeros(1,9);JJ=zeros(14,14);I=zeros(1,9); k=0;precision=1;while precision0.0000001 for m=2:9 for n=1:9 pt(n)=U(m)*U(n)*(G(m,n)*cos(a(m)-a(n)+B(m,n)*sin(a(m)-a(n); end dP(m)=P(m)-sum(pt); end for m=4:9 for n=1:9 qt(n)=U(m)*U(n)*(G(m,n)*sin(a(m)-a(n)-B(m,n)*cos(a(m)-a(n); end dQ(m)=Q(m)-sum(qt); end for m=1:8 for n=1:8 if m=n else H(m,n)=-U(m+1)*U(n+1)*(G(m+1,n+1)*sin(a(m+1)-a(n+1)-B(m+1,n+1)*cos(a(m+1)-a(n+1); end end end for m=1:8 for n=1:6 if m=n+2 else N(m,n)=-U(m+1)*U(n+3)*(G(m+1,n+3)*cos(a(m+1)-a(n+3)+B(m+1,n+3)*sin(a(m+1)-a(n+3); end end end for m=1:6 for n=1:8 if m+2=n else M(m,n)=U(m+3)*U(n+1)*(G(m+3,n+1)*cos(a(m+3)-a(n+1)+B(m+3,n+1)*sin(a(m+3)-a(n+1); end end end for m=1:6 for n=1:6 if m=n else L(m,n)=-U(m+3)*U(n+3)*(G(m+3,n+3)*sin(a(m+3)-a(n+3)-B(m+3,n+3)*cos(a(m+3)-a(n+3); end end end %雅克比i不等于j for m=1:8 for n=1:9 Ai(n)=U(n)*(G(m+1,n)*sin(a(m+1)-a(n)-B(m+1,n)*cos(a(m+1)-a(n); end H(m,m)=U(m+1)*U(m+1)*B(m+1,m+1)+U(m+1)*sum(Ai); end for m=1:6 for n=1:9 Bi(n)=U(n)*(G(m+1,n)*cos(a(m+1)-a(n)+B(m+1,n)*sin(a(m+1)-a(n); end N(m+2,m)=-U(m+1)*U(m+1)*G(m+1,m+1)-U(m+1)*sum(Bi); end for m=1:6 for n=1:9 Bi(n)=U(n)*(G(m+3,n)*cos(a(m+3)-a(n)+B(m+3,n)*sin(a(m+3)-a(n); end M(m,m+2)=U(m+3)*U(m+3)*G(m+3,m+3)-U(m+3)*sum(Bi); end for m=1:6 for n=1:9 Ai(n)=U(n)*(G(m+3,n)*sin(a(m+3)-a(n)-B(m+3,n)*cos(a(m+3)-a(n); end L(m,m)=U(m+3)*U(m+3)*B(m+3,m+3)-U(m+3)*sum(Ai); end %雅克比i等于j,Ai(n)=U(n)*(G(m,n)*sin(a(m)-a(n)-B(m,n)*cos(a(m)-a(n) %Bi(n)=U(n)*(G(m,n)*cos(a(m)-a(n)+B(m,n)*sin(a(m)-a(n); for m=1:8 for n=1:8 JJ(m,n)=H(m,n); end end for m=1:8 for n=1:6 JJ(m,n+8)=N(m,n); end end for m=1:6 for n=1:8 JJ(m+8,n)=M(m,n); end end for m=1:6 for n=1:6 JJ(m+8,n+8)=L(m,n); end end %雅克比矩阵JJ形成 for m=1:8 PQ(m)=dP(m+1); end for m=9:14 PQ(m)=dQ(m-5); end dUa=-inv(JJ)*PQ; precision=max(abs(dUa); for m=1:8 a(m+1)=a(m+1)+dUa(m); end for m=9:14 U(m-5)=U(m-5)+dUa(m); endk=k+1;end u=U.*cos(a)+i*U.*sin(a);i=y*u.;I=conj(i);pq=u.*I.;P=real(pq);Q=imag(pq); format longXE=1 0.3 1.137; 2 0.3 1.211; 3 0.3 1.043; 4 0 0; 5 0 0; 6 0 0; 7 0 0; 8 0 0; 9 0 0;disp(HEQIBO大作业)disp(迭代次数)kdisp(节点导纳矩阵)ydisp(电压幅值)Udisp(电压相角)a=a*360/(2*pi)disp(节点有功)Pdisp(节点无功)Q disp(输出修正后的发电机节点和负荷节点的自导纳)for m=1:9if abs(P(m)0.000001 & abs(Q(m)0.000001 if P(m)0 y(m,m)=y(m,m)-1i*(1/XE(m,2); else y(m,m)=y(m,m)-conj(pq(m)/U(m)/U(m); end disp(m); disp( 点自导纳=); disp(y(m,m);endend z=inv(y);line=z(:,4);If=u(4)/z(4,4);for m=1:9 uu(m)=u(m)-line(m)*If;endIf1=1/z(4,4);for m=1:9 uu1(m)=1-line(m)/z(4,4);endwuchai0=(abs(If)-abs(If1)/abs(If);wuchai1=(angle(If)-angle(If1)/angle(If); for m=1:9wuchau0(m)=(abs(uu(m)-abs(uu1(m)/abs(uu(m);endfor m=1:9wuchau1(m)=(angle(uu(m)-angle(uu1(m)/angle(uu(m);endfor m=1:9 hang=A(m,:); Y=zeros(2,2); if hang(1)3 & hang (2)3 Y(1,1)=Y(1,1)+1/(A(m,3)+1i*A(m,4)+1i*A(m,5); Y(1,2)=Y(1,2)-1/(A(m,3)+1i*A(m,4); Y(2,1)=Y(2,1)-1/(A(m,3)+1i*A(m,4); Y(2,2)=Y(2,2)+1/(A(m,3)+1i*A(m,4)+1i*A(m,5); ii(m,1)=Y(1,1)*uu(hang(1)+Y(1,2)*uu(hang(2); ii(m,2)=Y(2,1)*uu(hang(1)+Y(2,2)*uu(hang(2); else Y(1,1)=Y(1,1)+1/(A(m,3)+1i*A(m,4); Y(1,2)=Y(1,2)-1/(A(m,3)+1i*A(m,4); Y(2,1)=Y(2,1)-1/(A(m,3)+1i*A(m,4); Y(2,2)=Y(2,2)+1/(A(m,3)+1i*A(m,4); ii(m,1)=(uu(hang(2)-uu(hang(1)*Y(1,2); ii(m,2)=(uu(hang(1)-uu(hang(2)*Y(2,1); endend a=zeros(9,6);for m=1:9 a(m,1)=A(m,1); a(m,2)=A(m,2); a(m,3)=real(ii(m,1); a(m,4)=imag(ii(m,1); a(m,5)=real(ii(m,2); a(m,6)=imag(ii(m,2);end b=zeros(9,6);for m=1:9 b(m,1)=A(m,1); b(m,2)=A(m,2); b(m,3)=abs(ii(m,1); b(m,4)=angle(ii(m,1)*360/(2*pi); b(m,5)=abs(ii(m,2); b(m,6)=angle(ii(m,2)*360/(2*pi);end for n=1:3 for m=1:5 s=a(m,:); a(m,:)=a(m+1,:); a(m+1,:)=s; m=m+1; end n=n+1;end for n=1:3 for m=1:5 s=a(m+3,:); a(m+3,:)=a(m+4,:); a(m+4,:)=s; m=m+1; end n=n+1;end for n=1:3 for m=1:5 s=b(m,:); b(m,:)=b(m+1,:); b(m+1,:)=s; m=m+1; end n=n+1;end for n=1:3 for m=1:5 s=b(m+3,:); b(m+3,:)=b(m+4,:); b(m+4,:)=s; m=m+1; end n=n+1;end disp(输出节点阻抗矩阵的第4列)linedisp(精确计算短路电流If的模值和角度)disp( 模值)abs(If)disp( 相角)angle(If)*360/(2*pi)disp(精确计算短路时各节点电压模值)sb=abs(uu);sb.disp(近似计算短路电流If的模值和角度)disp( 模值)abs(If1)disp( 相角)angle(If1)*360/(2*pi)disp(近似计算短路时各节点电压模值)sb=abs(uu1);sb.disp(电流幅值误差)wuchai0disp(电流相角误差)wuchai1disp(电压模值误差)sb2=wuchau0(m);sb.disp(电压相角误差)sb2=wuchau0(m);sb.disp(短路时各支路电流)disp( i j Iij实部 Iij虚部 Iji实部 Iji虚部)adisp( i j Iij模值 Iij相角（角度制） Iji模值 Iji相角（角度制）)b程序输出：迭代次数k = 6节点导纳矩阵y = Columns 1 through 2 0 -17.361111111111111i 0 0 0 -16.000000000000000i 0 0 0 +17.361111111111111i 0 0 0 0 0 0 0 +16.000000000000000i 0 0 0 0 Columns 3 through 4 0 0 +17.361111111111111i 0 0 0 -17.064846416382252i 0 0 3.307378962025307 -39.308888726118973i 0 -1.365187713310580 +11.604095563139930i 0 -1.942191248714727 +10.510682051867931i 0 0 0 0 0 +17.064846416382252i 0 Columns 5 through 6 0 0 0 0 0 0 -1.365187713310580 +11.604095563139930i -1.942191248714727 +10.510682051867931i 2.552792092601728 -17.338230096448523i 0 0 3.224200387138842 -15.840927014229456i -1.187604379291148 + 5.975134533308591i 0 0 0 0 -1.282009138424115 + 5.588244962361526i Columns 7 through 8 0 0 0 +16.000000000000000i 0 0 0 0 0 -1.187604379291148 + 5.975134533308591i 0 0 0 2.804726852537284 -35.445613130217033i -1.617122473246136 +13.697978596908444i -1.617122473246136 +13.697978596908444i 2.772209954136233 -23.303249023271615i 0 -1.155087480890097 + 9.784270426363174i Column 9 0 0 0 +17.064846416382252i 0 0 -1.282009138424115 + 5.588244962361526i 0 -1.155087480890097 + 9.784270426363174i 2.437096619314212 -32.153861805106949i电压幅值U = Columns 1 through 5 1.040000000000000 1.025000000000000 1.025000000000000 1.025788393258783 0.995630858099912 Columns 6 through 9 1.012654324716820 1.025769372724423 1.015882583914507 1.032352949992867电压相角a = Columns 1 through 5 0 9.280005410115612 4.664751395991118 -2.216787825522439 -3.988805317089334 Columns 6 through 9 -3.687396083579451 3.719701083228682 0.727536074732491 1.966716137662446节点有功P = Columns 1 through 5 0.716410223294816 1.630000000497858 0.850000000702516 -0.000000025697624 -1.250000002366959 Columns 6 through 9 -0.899999977519977 -0.000000019551833 -0.999999996198353 0.000000011109476节点无功Q = Columns 1 through 5 0.270459228171328 0.066536597663860 -0.108597108021278 0.000000011922588 -0.500000006230195 Columns 6 through 9 -0.300000004111775 0.000000009225475 -0.350000009089799 0.000000025044123输出修正后的发电机节点和负荷节点的自导纳 1 点自导纳= 0 -20.694444444444443i 2 点自导纳= 0 -19.333333333333332i 3 点自导纳= 0 -20.398179749715585i 5 点自导纳= 3.813786954304306 -17.842628046459438i 6 点自导纳= 4.101847755710743 -16.133476148403645i 8 点自导纳= 3.741185838313620 -23.642390592830793i输出节点阻抗矩阵的第4列line = 0.042326231465589 + 0.123442631204099i 0.029922918148477 + 0.068062588575066i 0.028728951359995 + 0.069354564261722i 0.050452867906982 + 0.147143616395286i 0.053428213981267 + 0.118084130280524i 0.051072395055106 + 0.120394292476911i 0.036156859429409 + 0.082242294528204i 0.038155250415874 + 0.080071332122179i 0.034340673192314 + 0.082901822480845i精确计算短路电流If的模值和角度 模值ans = 6.594462305579217 相角ans = -73.290879319913785精确计算短路时各节点电压模值ans = 0.183133872715700 0.571246049912469 0.545627263197906 0.000000000000000 0.152668951455946 0.156064320359132 0.457245615301596 0.449470067165668 0.453126816334169近似计算短路电流If的模值和角度 模值ans = 6.428677053587584 相角ans = -71.074091494391354近似计算短路时各节点电压模值ans = 0.161073825503356 0.525238565694205 0.519215284403616 0.000000000000000 0.187790714933885 0.172008879771889 0.427231780272993 0.438373685547942 0.425780890866260电流幅值误差wuchai0 = 0.025140071215719电流相角误差wuchai1 = 0.030246435110243电压模值误差ans = 0.161073825503356 0.525238565694205 0.519215284403616 0.000000000000000 0.187790714933885 0.172008879771889 0.427231780272993 0.438373685547942 0.425780890866260电压相角误差ans = 0.161073825503356 0.525238565694205 0.519215284403616 0.000000000000000 0.187790714933885 0.172008879771889 0.427231780272993 0.438373685547942 0.425780890866260短路时各支路电流 i j Iij实部 Iij虚部 Iji实部 Iji虚部a = Columns 1 through 5 4.000000000000000 5.000000000000000 -0.713621236630144 1.634838873421884 0.709722007988762 4.000000000000000 6.000000000000000 -0.604473035474057 1.554737730940463 0.602167738224884 5.000000000000000 7.000000000000000 -0.916299804525820 1.639799633459405 0.888255924637366 6.000000000000000 9.000000000000000 -0.745258404908797 1.561866748776531 0.723004162852629 7.000000000000000 8.000000000000000 0.491817558836839 0.121114167179097 -0.509776367826706 8.000000000000000 9.000000000000000 0.051012693255221 0.105594528938633 -0.071622007626573 1.000000000000000 4.000000000000000 0.577899315383659 -3.126445987274670 -0.577899315383659 2.000000000000000 7.000000000000000 1.380073501911230 -1.429684038904686 -1.380073501911230 3.000000000000000 9.000000000000000 0.651382143638526 -1.468678344995518 -0.651382143638526 Column 6 -1.621982291960454 -1.542626089825346 -1.550798216295114 -1.455122379797101 -0.056050536396400