📄 output.txt
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欢迎使用潮流精灵2007!
求节点导纳矩阵：
z41=0.040000+j(0.090000) ==> y41=1/Z41=1/(0.040000+j(0.090000))=4.123711+j(-9.278350)
z12=0.050000+j(0.120000) ==> y12=1/Z12=1/(0.050000+j(0.120000))=2.958580+j(-7.100592)
z23=0.030000+j(0.080000) ==> y23=1/Z23=1/(0.030000+j(0.080000))=4.109589+j(-10.958904)
导纳矩阵中的各元素:Y11=......Y12=......Ynn=......
形成导纳矩阵YB:
YB=
7.082291+j(-16.378941) -2.958580+j(7.100592) 0.000000+j(0.000000) -4.123711+j(9.278350)
-2.958580+j(7.100592) 7.068169+j(-18.059496) -4.109589+j(10.958904) 0.000000+j(0.000000)
0.000000+j(0.000000) -4.109589+j(10.958904) 4.109589+j(-10.958904) 0.000000+j(0.000000)
-4.123711+j(9.278350) 0.000000+j(0.000000) 0.000000+j(0.000000) 4.123711+j(-9.278350)
------------------------------------------------------------------------------------------------------------
第0次迭代：K=0
1、计算各PQ、PV节点功率的不平衡量，及PV节点电压的不平衡量:
取：
U1(0)=e1(0)+f1(0)=1.000000+j0.000000
U2(0)=e2(0)+f2(0)=1.000000+j0.000000
U3(0)=e3(0)+f3(0)=0.950000+j0.000000
节点4是平衡节点,保持U4=e4+f4=1.000000+j0.000000为定值。
a/计算各PQ、PV节点功率：
Pi(0)=求和... Qi(0)=求和... Ui(0)=ei(0)^2+fi(0)^2
下面的符号别忘了带角标!
P1=+1.000000*(7.082291*1.000000--16.378941*0.000000)+0.000000*(7.082291*0.000000+-16.378941*1.000000)
+1.000000*(-2.958580*1.000000-7.100592*0.000000)+0.000000*(-2.958580*0.000000+7.100592*1.000000)
+1.000000*(0.000000*0.950000-0.000000*0.000000)+0.000000*(0.000000*0.000000+0.000000*0.950000)
+1.000000*(-4.123711*1.000000-9.278350*0.000000)+0.000000*(-4.123711*0.000000+9.278350*1.000000)
=0.000000
Q1=+0.000000*(7.082291*1.000000--16.378941*0.000000)-1.000000*(7.082291*0.000000+-16.378941*1.000000)
+0.000000*(-2.958580*1.000000-7.100592*0.000000)-1.000000*(-2.958580*0.000000+7.100592*1.000000)
+0.000000*(0.000000*0.950000-0.000000*0.000000)-1.000000*(0.000000*0.000000+0.000000*0.950000)
+0.000000*(-4.123711*1.000000-9.278350*0.000000)-1.000000*(-4.123711*0.000000+9.278350*1.000000)
=-0.000001
P2=+1.000000*(-2.958580*1.000000-7.100592*0.000000)+0.000000*(-2.958580*0.000000+7.100592*1.000000)
+1.000000*(7.068169*1.000000--18.059496*0.000000)+0.000000*(7.068169*0.000000+-18.059496*1.000000)
+1.000000*(-4.109589*0.950000-10.958904*0.000000)+0.000000*(-4.109589*0.000000+10.958904*0.950000)
+1.000000*(0.000000*1.000000-0.000000*0.000000)+0.000000*(0.000000*0.000000+0.000000*1.000000)
=0.205480
Q2=+0.000000*(-2.958580*1.000000-7.100592*0.000000)-1.000000*(-2.958580*0.000000+7.100592*1.000000)
+0.000000*(7.068169*1.000000--18.059496*0.000000)-1.000000*(7.068169*0.000000+-18.059496*1.000000)
+0.000000*(-4.109589*0.950000-10.958904*0.000000)-1.000000*(-4.109589*0.000000+10.958904*0.950000)
+0.000000*(0.000000*1.000000-0.000000*0.000000)-1.000000*(0.000000*0.000000+0.000000*1.000000)
=0.547945
P3=+0.950000*(0.000000*1.000000-0.000000*0.000000)+0.000000*(0.000000*0.000000+0.000000*1.000000)
+0.950000*(-4.109589*1.000000-10.958904*0.000000)+0.000000*(-4.109589*0.000000+10.958904*1.000000)
+0.950000*(4.109589*0.950000--10.958904*0.000000)+0.000000*(4.109589*0.000000+-10.958904*0.950000)
+0.950000*(0.000000*1.000000-0.000000*0.000000)+0.000000*(0.000000*0.000000+0.000000*1.000000)
=-0.195205
U3^2=(0.950000)^2+(0.000000)^2=0.902500
于是：DPi=Pi-Pi(0);DQi=Qi-Qi(0);DUi^2=Ui^2-(ei(0)^2+fi(0)^2)
DP1=P1-P1(0)=-0.600000-(0.000000)=-0.600000
DQ1=Q1-Q1(0)=-0.250000-(-0.000001)=-0.249999
DP2=P2-P2(0)=-0.300000-(0.205480)=-0.505480
DQ2=Q2-Q2(0)=-0.100000-(0.547945)=-0.647945
DP3=P3-P3(0)=0.400000-(-0.195205)=0.595205
D(U3)^2=(U3)^2-(e3(0)^2+f3(0)^2)=0.902500-((0.950000)^2+(0.000000)^2)=0.000000
2、计算雅可比矩阵中各元素:
I1=(P1-jQ1)/U1*=(0.000000-j-0.000001)/(1.000000-j0.000000)=0.000000+j0.000001=a11+jb11
I2=(P2-jQ2)/U2*=(0.205480-j0.547945)/(1.000000-j0.000000)=0.205480+j-0.547945=a22+jb22
Q3=+0.000000*(0.000000*1.000000-0.000000*0.000000)-0.950000*(0.000000*0.000000+0.000000*1.000000)
+0.000000*(-4.109589*1.000000-10.958904*0.000000)-0.950000*(-4.109589*0.000000+10.958904*1.000000)
+0.000000*(4.109589*0.950000--10.958904*0.000000)-0.950000*(4.109589*0.000000+-10.958904*0.950000)
+0.000000*(0.000000*1.000000-0.000000*0.000000)-0.950000*(0.000000*0.000000+0.000000*1.000000)
=-0.520548
I3=(P3-jQ3)/U3*=(-0.195205-j-0.520548)/(0.950000-j0.000000)=-0.205479+j0.547946=a33+jb33
雅可比矩阵的各个元素分别为：
H11=偏P1/偏f1=-B11*e1+G11*f1+b11=-(-16.378941)*1.000000+7.082291*0.000000+0.000001=16.378941
N11=偏P1/偏e1=G11*e1+B11*f1+a11=7.082291*1.000000+-16.378941*0.000000+0.000000=7.082291
J11=偏Q1/偏f1=-G11*e1-B11*f1+a11=-(7.082291)*1.000000-(-16.378941)*0.000000+0.000000=-7.082291
L11=偏Q1/偏e1=-B11*e1+G11*f1-b11=-(-16.378941)*1.000000+7.082291*0.000000-(0.000001)=16.378941
H12=偏P1/偏f2=-B12*e1+G12*f1=-(7.100592)*1.000000+-2.958580*0.000000=-7.100592
N12=偏P1/偏e2=G12*e1+B12*f1=-2.958580*1.000000+7.100592*0.000000=-2.958580
J12=偏Q1/偏f2=-G12*e1-B12*f1=-(-2.958580)*1.000000-(7.100592)*0.000000=2.958580
L12=偏Q1/偏e2=-B12*e1+G12*f1=-(7.100592)*1.000000+-2.958580*0.000000=-7.100592
H13=偏P1/偏f3=-B13*e1+G13*f1=-(0.000000)*1.000000+0.000000*0.000000=0.000000
N13=偏P1/偏e3=G13*e1+B13*f1=0.000000*1.000000+0.000000*0.000000=0.000000
J13=偏Q1/偏f3=-G13*e1-B13*f1=-(0.000000)*1.000000-(0.000000)*0.000000=0.000000
L13=偏Q1/偏e3=-B13*e1+G13*f1=-(0.000000)*1.000000+0.000000*0.000000=0.000000
H21=偏P2/偏f1=-B21*e2+G21*f2=-(7.100592)*1.000000+-2.958580*0.000000=-7.100592
N21=偏P2/偏e1=G21*e2+B21*f2=-2.958580*1.000000+7.100592*0.000000=-2.958580
J21=偏Q2/偏f1=-G21*e2-B21*f2=-(-2.958580)*1.000000-(7.100592)*0.000000=2.958580
L21=偏Q2/偏e1=-B21*e2+G21*f2=-(7.100592)*1.000000+-2.958580*0.000000=-7.100592
H22=偏P2/偏f2=-B22*e2+G22*f2+b22=-(-18.059496)*1.000000+7.068169*0.000000+-0.547945=17.511551
N22=偏P2/偏e2=G22*e2+B22*f2+a22=7.068169*1.000000+-18.059496*0.000000+0.205480=7.273649
J22=偏Q2/偏f2=-G22*e2-B22*f2+a22=-(7.068169)*1.000000-(-18.059496)*0.000000+0.205480=-6.862689
L22=偏Q2/偏e2=-B22*e2+G22*f2-b22=-(-18.059496)*1.000000+7.068169*0.000000-(-0.547945)=18.607441
H23=偏P2/偏f3=-B23*e2+G23*f2=-(10.958904)*1.000000+-4.109589*0.000000=-10.958904
N23=偏P2/偏e3=G23*e2+B23*f2=-4.109589*1.000000+10.958904*0.000000=-4.109589
J23=偏Q2/偏f3=-G23*e2-B23*f2=-(-4.109589)*1.000000-(10.958904)*0.000000=4.109589
L23=偏Q2/偏e3=-B23*e2+G23*f2=-(10.958904)*1.000000+-4.109589*0.000000=-10.958904
H31=偏P3/偏f1=B31*e3+G31*f3=-(0.000000)*0.950000+0.000000*0.000000=0.000000
N31=偏P3/偏e1=31*e3+B31*f3=0.000000*0.950000+0.000000*0.000000=0.000000
R31=偏U3^2/偏f1=0
S31=偏U3^2/偏e1=0
H32=偏P3/偏f2=B32*e3+G32*f3=-(10.958904)*0.950000+-4.109589*0.000000=-10.410959
N32=偏P3/偏e2=32*e3+B32*f3=-4.109589*0.950000+10.958904*0.000000=-3.904109
R32=偏U3^2/偏f2=0
S32=偏U3^2/偏e2=0
H33=偏P3/偏f3=-B33*e3+G33*f3+b33=-(-10.958904)*0.950000+4.109589*0.000000+0.547946=10.958905
N33=偏P3/偏e3=G33*e3+B33*f3+a33=4.109589*0.950000+-10.958904*0.000000+-0.205479=3.698630
R33=偏U3^2/偏f3=*f3=2*0.000000=0.000000
S33=偏U3^2/偏e3=*e3=2*0.950000=1.900000
3、所以可以得到K=0时的雅可比矩阵:
J(0)=
16.378941 7.082291 -7.100592 -2.958580 0.000000 0.000000
-7.082291 16.378941 2.958580 -7.100592 0.000000 0.000000
-7.100592 -2.958580 17.511551 7.273649 -10.958904 -4.109589
2.958580 -7.100592 -6.862689 18.607441 4.109589 -10.958904
0.000000 0.000000 -10.410959 -3.904109 10.958905 3.698630
0.000000 0.000000 0.000000 0.000000 0.000000 1.900000
至此，可以建立修正方程组如下：....
解得：
df1=-0.029441
de1=-0.051634
df2=-0.010387
de2=-0.058860
df3=0.023476
de3=0.000000
因为：ei(1)=ei(0)+dei(0); fi(1)=fi(0)+dfi(0)
所以：
e1(1)=e1(0)+de1(0)=1.000000+-0.051634=0.948366
f1(1)=f1(0)+df1(0)=0.000000+-0.029441=-0.029441
e2(1)=e2(0)+de2(0)=1.000000+-0.058860=0.941140
f2(1)=f2(0)+df2(0)=0.000000+-0.010387=-0.010387
e3(1)=e3(0)+de3(0)=0.950000+0.000000=0.950000
f3(1)=f3(0)+df3(0)=0.000000+0.023476=0.023476
------------------------------------------------------------------------------------------------------------
第1次迭代：K=1
1、计算各PQ、PV节点功率的不平衡量，及PV节点电压的不平衡量:
取：
U1(1)=e1(1)+f1(1)=0.948366+j-0.029441
U2(1)=e2(1)+f2(1)=0.941140+j-0.010387
U3(1)=e3(1)+f3(1)=0.950000+j0.023476
节点4是平衡节点,保持U4=e4+f4=1.000000+j0.000000为定值。
a/计算各PQ、PV节点功率：
Pi(1)=求和... Qi(1)=求和... Ui(1)=ei(1)^2+fi(1)^2
下面的符号别忘了带角标!
P1=+0.948366*(7.082291*0.948366--16.378941*-0.029441)+-0.029441*(7.082291*-0.029441+-16.378941*0.948366)
+0.948366*(-2.958580*0.941140-7.100592*-0.010387)+-0.029441*(-2.958580*-0.010387+7.100592*0.941140)
+0.948366*(0.000000*0.950000-0.000000*0.023476)+-0.029441*(0.000000*0.023476+0.000000*0.950000)
+0.948366*(-4.123711*1.000000-9.278350*0.000000)+-0.029441*(-4.123711*0.000000+9.278350*1.000000)
=-0.576380
Q1=+-0.029441*(7.082291*0.948366--16.378941*-0.029441)-0.948366*(7.082291*-0.029441+-16.378941*0.948366)
+-0.029441*(-2.958580*0.941140-7.100592*-0.010387)-0.948366*(-2.958580*-0.010387+7.100592*0.941140)
+-0.029441*(0.000000*0.950000-0.000000*0.023476)-0.948366*(0.000000*0.023476+0.000000*0.950000)
+-0.029441*(-4.123711*1.000000-9.278350*0.000000)-0.948366*(-4.123711*0.000000+9.278350*1.000000)
=-0.219427
P2=+0.941140*(-2.958580*0.948366-7.100592*-0.029441)+-0.010387*(-2.958580*-0.029441+7.100592*0.948366)
+0.941140*(7.068169*0.941140--18.059496*-0.010387)+-0.010387*(7.068169*-0.010387+-18.059496*0.941140)
+0.941140*(-4.109589*0.950000-10.958904*0.023476)+-0.010387*(-4.109589*0.023476+10.958904*0.950000)
+0.941140*(0.000000*1.000000-0.000000*0.000000)+-0.010387*(0.000000*0.000000+0.000000*1.000000)
=-0.276997
Q2=+-0.010387*(-2.958580*0.948366-7.100592*-0.029441)-0.941140*(-2.958580*-0.029441+7.100592*0.948366)
+-0.010387*(7.068169*0.941140--18.059496*-0.010387)-0.941140*(7.068169*-0.010387+-18.059496*0.941140)
+-0.010387*(-4.109589*0.950000-10.958904*0.023476)-0.941140*(-4.109589*0.023476+10.958904*0.950000)
+-0.010387*(0.000000*1.000000-0.000000*0.000000)-0.941140*(0.000000*0.000000+0.000000*1.000000)
=-0.058702
P3=+0.950000*(0.000000*0.948366-0.000000*-0.029441)+0.023476*(0.000000*-0.029441+0.000000*0.948366)
+0.950000*(-4.109589*0.941140-10.958904*-0.010387)+0.023476*(-4.109589*-0.010387+10.958904*0.941140)
+0.950000*(4.109589*0.950000--10.958904*0.023476)+0.023476*(4.109589*0.023476+-10.958904*0.950000)
+0.950000*(0.000000*1.000000-0.000000*0.000000)+0.023476*(0.000000*0.000000+0.000000*1.000000)
=0.388124
U3^2=(0.950000)^2+(0.023476)^2=0.903051
于是：DPi=Pi-Pi(1);DQi=Qi-Qi(1);DUi^2=Ui^2-(ei(1)^2+fi(1)^2)
DP1=P1-P1(1)=-0.600000-(-0.576380)=-0.023620
DQ1=Q1-Q1(1)=-0.250000-(-0.219427)=-0.030573
DP2=P2-P2(1)=-0.300000-(-0.276997)=-0.023003
DQ2=Q2-Q2(1)=-0.100000-(-0.058702)=-0.041298
DP3=P3-P3(1)=0.400000-(0.388124)=0.011876
D(U3)^2=(U3)^2-(e3(1)^2+f3(1)^2)=0.902500-((0.950000)^2+(0.023476)^2)=0.000000
2、计算雅可比矩阵中各元素:
I1=(P1-jQ1)/U1*=(-0.576380-j-0.219427)/(0.948366-j-0.029441)=-0.600000+j0.250000=a11+jb11
I2=(P2-jQ2)/U2*=(-0.276997-j-0.058702)/(0.941140-j-0.010387)=-0.293597+j0.065613=a22+jb22
Q3=+0.023476*(0.000000*0.948366-0.000000*-0.029441)-0.950000*(0.000000*-0.029441+0.000000*0.948366)
+0.023476*(-4.109589*0.941140-10.958904*-0.010387)-0.950000*(-4.109589*-0.010387+10.958904*0.941140)
+0.023476*(4.109589*0.950000--10.958904*0.023476)-0.950000*(4.109589*0.023476+-10.958904*0.950000)
+0.023476*(0.000000*1.000000-0.000000*0.000000)-0.950000*(0.000000*0.000000+0.000000*1.000000)
=-0.030396
I3=(P3-jQ3)/U3*=(0.388124-j-0.030396)/(0.950000-j0.023476)=0.407512+j0.042066=a33+jb33
雅可比矩阵的各个元素分别为：
H11=偏P1/偏f1=-B11*e1+G11*f1+b11=-(-16.378941)*0.948366+7.082291*-0.029441+0.250000=15.574717
N11=偏P1/偏e1=G11*e1+B11*f1+a11=7.082291*0.948366+-16.378941*-0.029441+-0.600000=6.598806
J11=偏Q1/偏f1=-G11*e1-B11*f1+a11=-(7.082291)*0.948366-(-16.378941)*-0.029441+-0.600000=-7.798806
L11=偏Q1/偏e1=-B11*e1+G11*f1-b11=-(-16.378941)*0.948366+7.082291*-0.029441-(0.250000)=15.074717
H12=偏P1/偏f2=-B12*e1+G12*f1=-(7.100592)*0.948366+-2.958580*-0.029441=-6.646854
N12=偏P1/偏e2=G12*e1+B12*f1=-2.958580*0.948366+7.100592*-0.029441=-3.014861
J12=偏Q1/偏f2=-G12*e1-B12*f1=-(-2.958580)*0.948366-(7.100592)*-0.029441=3.014861
L12=偏Q1/偏e2=-B12*e1+G12*f1=-(7.100592)*0.948366+-2.958580*-0.029441=-6.646854
H13=偏P1/偏f3=-B13*e1+G13*f1=-(0.000000)*0.948366+0.000000*-0.029441=0.000000
N13=偏P1/偏e3=G13*e1+B13*f1=0.000000*0.948366+0.000000*-0.029441=0.000000
J13=偏Q1/偏f3=-G13*e1-B13*f1=-(0.000000)*0.948366-(0.000000)*-0.029441=0.000000
L13=偏Q1/偏e3=-B13*e1+G13*f1=-(0.000000)*0.948366+0.000000*-0.029441=0.000000
H21=偏P2/偏f1=-B21*e2+G21*f2=-(7.100592)*0.941140+-2.958580*-0.010387=-6.651920
N21=偏P2/偏e1=G21*e2+B21*f2=-2.958580*0.941140+7.100592*-0.010387=-2.858190
J21=偏Q2/偏f1=-G21*e2-B21*f2=-(-2.958580)*0.941140-(7.100592)*-0.010387=2.858190
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