matlab节点导纳矩阵示例.doc

Y =

3.7500 -11.2500i -2.5000 + 7.5000i 0 -1.2500 + 3.7500i 0
-2.5000 + 7.5000i 10.8340 -32.5000i -1.6670 + 5.0000i -1.6670 + 5.0000i -5.0000 +15.0000i
0 -1.6670 + 5.0000i 12.9170 -38.7500i -10.0000 +30.0000i -1.2500 + 3.7500i
-1.2500 + 3.7500i -1.6670 + 5.0000i -10.0000 +30.0000i 12.9170 -38.7500i 0
0 -5.0000 +15.0000i -1.2500 + 3.7500i 0 6.2500 -18.7500i

JJ =

11.2500 3.7500 -7.5000 -2.5000 0 0 -3.7500 -1.2500
-3.7500 11.2500 2.5000 -7.5000 0 0 1.2500 -3.7500
-7.5000 -2.5000 33.4000 10.5340 -5.0000 -1.6670 -5.0000 -1.6670
2.5000 -7.5000 -11.1340 31.6000 1.6670 -5.0000 1.6670 -5.0000
0 0 -5.0000 -1.6670 38.9750 12.8420 -30.0000 -10.0000
0 0 1.6670 -5.0000 -12.9920 38.5250 10.0000 -30.0000
-3.7500 -1.2500 -5.0000 -1.6670 -30.0000 -10.0000 38.7500 12.9170
1.2500 -3.7500 1.6670 -5.0000 10.0000 -30.0000 -12.9170 38.7500

JJ =

11.5406 3.1996 -7.7223 -3.1029 0 0 -3.8183 -1.3384
-4.4412 11.3818 3.1029 -7.7223 0 0 1.3384 -3.8183
-8.0396 -2.1511 35.0648 12.0317 -5.3599 -1.5576 -5.3622 -1.5238
2.1511 -8.0396 -11.5380 35.6400 1.5576 -5.3599 1.5238 -5.3622
0 0 -5.2222 -1.9705 40.0793 12.8630 -30.9519 -10.1136
0 0 1.9705 -5.2222 -13.7724 39.8246 10.1136 -30.9519
-3.8576 -1.2203 -5.2038 -1.9989 -30.8297 -10.4802 39.8912 12.8685
1.2203 -3.8576 1.9989 -5.2038 10.4802 30.8297 -13.6994 39.8104

JJ =

11.3861 3.1619 -7.6217 -3.0453 0 0 -3.7644 -1.3171
-4.3623 11.1866 3.0453 -7.6217 0 0 1.3171 -3.7644
-7.9246 -2.1368 34.7163 11.8401 -5.2904 -1.5440 -5.2913 -1.5116
2.1368 -7.9246 -11.4391 35.1173 1.5440 -5.2904 1.5116 -5.2913
0 0 -5.1585 -1.9397 39.5849 12.6953 -30.5425 -9.9876
0 0 1.9397 -5.1585 -13.5953 39.2852 9.9876 -30.5425
-3.8018 -1.2050 -5.1397 -1.9661 -30.4266 -10.3354 39.3681 12.7062
1.2050 -3.8018 1.9661 -5.1397 10.3354 -30.4266 -13.5065 39.2683

JJ =

11.3850 3.1617 -7.6210 -3.0448 0 0 -3.7640 -1.3169
-4.3617 11.1850 3.0448 -7.6210 0 0 1.3169 -3.7640
-7.9237 -2.1368 34.7136 11.8386 -5.2899 -1.5439 -5.2907 -1.5115
2.1368 -7.9237 -11.4386 35.1136 1.5439 -5.2899 1.5115 -5.2907
0 0 -5.1580 -1.9394 39.5811 12.6940 -30.5394 -9.9867
0 0 1.9394 -5.1580 -13.5940 39.2811 9.9867 -30.5394
-3.8013 -1.2049 -5.1392 -1.9659 -30.4235 -10.3343 39.3641 12.7050
1.2049 -3.8013 1.9659 -5.1392 10.3343 -30.4235 -13.5050 39.2641

S5 =

1.2982 + 0.2445i

S =

0 -0.5370 - 0.0977i 0 -0.0630 - 0.0023i 0
0.5489 + 0.1333i 0 0.2469 + 0.0815i 0.2793 + 0.0806i -0.8751 - 0.0954i
0 -0.2431 - 0.0701i 0 0.1891 - 0.0121i -0.3960 - 0.0677i
0.0633 + 0.0033i -0.2746 - 0.0664i -0.1887 + 0.0132i 0 0
0 0.8895 + 0.1387i 0.4087 + 0.1058i 0 0

>>

clc
G(1,1)=3.750;B(1,1)=-11.250;G(1,2)=-2.500;B(1,2)=7.500;
G(1,3)=0;B(1,3)=0;G(1,4)=-1.250;B(1,4)=3.750;
G(1,5)=0;B(1,5)=0;
G(2,1)=-2.500;B(2,1)=7.500;G(2,2)=10.834;B(2,2)=-32.500;G(2,3)=-1.667;B(2,3)=5.000;
G(2,4)=-1.667;B(2,4)=5.000;G(2,5)=-5.000;B(2,5)=15.000;
G(3,1)=0;B(3,1)=0;G(3,2)=-1.667;B(3,2)=5.000;G(3,3)=12.917;B(3,3)=-38.75;
G(3,4)=-10.000;B(3,4)=30.000;G(3,5)=-1.250;B(3,5)=3.750;
G(4,1)=-1.250;B(4,1)=3.750;G(4,2)=-1.667;B(4,2)=5.000;G(4,3)=-10.000;B(4,3)=30.000;
G(4,4)=12.917;B(4,4)=-38.750;G(4,5)=0;B(4,5)=0;
G(5,1)=0;B(5,1)=0;G(5,2)=-5.000;B(5,2)=15.000;G(5,3)=-1.250;B(5,3)=3.750;
G(5,4)=0;B(5,4)=0;G(5,5)=6.25;B(5,5)=-18.750;
Y=G+j*B
delt(1)=0; delt(2)=0; delt(3)=0; delt(4)=0;
u(1)=1.0; u(2)=1.0; u(3)=1.0; u(4)=1.0;
ps(1)=-0.60;qs(1)=-0.10;ps(2)=0.20;qs(2)=0.20;
ps(3)=-0.45;qs(3)=-0.15; ps(4)=-0.40;qs(4)=-0.05;
k=1;precision=1;
N1=4;
while precision>0.00001
delt(5)=0;u(5)=1.06;
for m=1:N1
for n=1:N1+1
pt(n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
qt(n)=u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
end
pi(m)=sum(pt);qi(m)=sum(qt);
dp(m)=ps(m)-pi(m);
dq(m)=qs(m)-qi(m);
end
for m=1:N1
for n=1:N1
if m==n
H(m,m)=-qi(m)-u(m)^2*B(m,m); N(m,m)=pi(m)+u(m)^2*G(m,m);
J(m,m)=pi(m)-u(m)^2*G(m,m); L(m,m)=qi(m)-u(m)^2*B(m,m);
JJ(2*m-1,2*m-1)=Hm,m); JJ(2*m-1,2*m)=N(m,m);
JJ(2*m,2*m-1)=J(m,m); JJ(2*m,2*m)=L(m,m);
else
H(m,n)=u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
J(m,n)=-u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
N(m,n)=-J(m,n);L(m,n)=H(m,n);
JJ(2m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=N(m,n);
JJ(2*m,2*n-1)=J(m,n); JJ(2*m,2*n)=L(m,n);
end
end
end
JJ
for m=1:N1
PP(2*m-1)=dp(m);
PP(2*m)=dq(m);
end
uu=inv(JJ)*PP';precision=max(abs(uu));
for n=1:N1
delt(n)=delt(n)+uu(2*n-1);
u(n)=u(n)+uu(2*n)*u(n);
end
k=k+1;
end
for n=1:N1+1
U(n)=u(n)*(cos(delt(n))+j*sin(delt(n)));
end
for m=1:N1+1
I(m)=Y(5,m)*U(m);
end
S5=U(5)*sum(conj(I))
for m=1:N1+1
for n=1:N1+1
S(m,n)=U(m)*(conj(U(m))-conj(U(n)))*conj(-Y(m,n));%
end
end
end
S %