📄 output.txt
字号:
L21=偏Q2/偏e1=-B21*e2+G21*f2=-(7.100592)*0.941140+-2.958580*-0.010387=-6.651920
H22=偏P2/偏f2=-B22*e2+G22*f2+b22=-(-18.059496)*0.941140+7.068169*-0.010387+0.065613=16.988708
N22=偏P2/偏e2=G22*e2+B22*f2+a22=7.068169*0.941140+-18.059496*-0.010387+-0.293597=6.546119
J22=偏Q2/偏f2=-G22*e2-B22*f2+a22=-(7.068169)*0.941140-(-18.059496)*-0.010387+-0.293597=-7.133313
L22=偏Q2/偏e2=-B22*e2+G22*f2-b22=-(-18.059496)*0.941140+7.068169*-0.010387-(0.065613)=16.857483
H23=偏P2/偏f3=-B23*e2+G23*f2=-(10.958904)*0.941140+-4.109589*-0.010387=-10.271176
N23=偏P2/偏e3=G23*e2+B23*f2=-4.109589*0.941140+10.958904*-0.010387=-3.981526
J23=偏Q2/偏f3=-G23*e2-B23*f2=-(-4.109589)*0.941140-(10.958904)*-0.010387=3.981526
L23=偏Q2/偏e3=-B23*e2+G23*f2=-(10.958904)*0.941140+-4.109589*-0.010387=-10.271176
H31=偏P3/偏f1=B31*e3+G31*f3=-(0.000000)*0.950000+0.000000*0.023476=0.000000
N31=偏P3/偏e1=31*e3+B31*f3=0.000000*0.950000+0.000000*0.023476=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*0.023476=-10.507436
N32=偏P3/偏e2=32*e3+B32*f3=-4.109589*0.950000+10.958904*0.023476=-3.646837
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*0.023476+0.042066=10.549501
N33=偏P3/偏e3=G33*e3+B33*f3+a33=4.109589*0.950000+-10.958904*0.023476+0.407512=4.054349
R33=偏U3^2/偏f3=*f3=2*0.023476=0.046952
S33=偏U3^2/偏e3=*e3=2*0.950000=1.900000
3、所以可以得到K=1时的雅可比矩阵:
J(1)=
15.574717 6.598806 -6.646854 -3.014861 0.000000 0.000000
-7.798806 15.074717 3.014861 -6.646854 0.000000 0.000000
-6.651920 -2.858190 16.988708 6.546119 -10.271176 -3.981526
2.858190 -6.651920 -7.133313 16.857483 3.981526 -10.271176
0.000000 0.000000 -10.507436 -3.646837 10.549501 4.054349
0.000000 0.000000 0.000000 0.000000 0.046952 1.900000
至此，可以建立修正方程组如下：....
解得：
df1=-0.002060
de1=-0.004378
df2=-0.003565
de2=-0.004529
df3=-0.003917
de3=-0.000193
因为：ei(2)=ei(1)+dei(1); fi(2)=fi(1)+dfi(1)
所以：
e1(2)=e1(1)+de1(1)=0.948366+-0.004378=0.943988
f1(2)=f1(1)+df1(1)=-0.029441+-0.002060=-0.031500
e2(2)=e2(1)+de2(1)=0.941140+-0.004529=0.936611
f2(2)=f2(1)+df2(1)=-0.010387+-0.003565=-0.013952
e3(2)=e3(1)+de3(1)=0.950000+-0.000193=0.949807
f3(2)=f3(1)+df3(1)=0.023476+-0.003917=0.019560
------------------------------------------------------------------------------------------------------------
第2次迭代：K=2
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(2)=e1(2)+f1(2)=0.943988+j-0.031500
U2(2)=e2(2)+f2(2)=0.936611+j-0.013952
U3(2)=e3(2)+f3(2)=0.949807+j0.019560
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(2)=求和... Qi(2)=求和... Ui(2)=ei(2)^2+fi(2)^2
下面的符号别忘了带角标!
P1=+0.943988*(7.082291*0.943988--16.378941*-0.031500)+-0.031500*(7.082291*-0.031500+-16.378941*0.943988)
+0.943988*(-2.958580*0.936611-7.100592*-0.013952)+-0.031500*(-2.958580*-0.013952+7.100592*0.936611)
+0.943988*(0.000000*0.949807-0.000000*0.019560)+-0.031500*(0.000000*0.019560+0.000000*0.949807)
+0.943988*(-4.123711*1.000000-9.278350*0.000000)+-0.031500*(-4.123711*0.000000+9.278350*1.000000)
=-0.599959
Q1=+-0.031500*(7.082291*0.943988--16.378941*-0.031500)-0.943988*(7.082291*-0.031500+-16.378941*0.943988)
+-0.031500*(-2.958580*0.936611-7.100592*-0.013952)-0.943988*(-2.958580*-0.013952+7.100592*0.936611)
+-0.031500*(0.000000*0.949807-0.000000*0.019560)-0.943988*(0.000000*0.019560+0.000000*0.949807)
+-0.031500*(-4.123711*1.000000-9.278350*0.000000)-0.943988*(-4.123711*0.000000+9.278350*1.000000)
=-0.249791
P2=+0.936611*(-2.958580*0.943988-7.100592*-0.031500)+-0.013952*(-2.958580*-0.031500+7.100592*0.943988)
+0.936611*(7.068169*0.936611--18.059496*-0.013952)+-0.013952*(7.068169*-0.013952+-18.059496*0.936611)
+0.936611*(-4.109589*0.949807-10.958904*0.019560)+-0.013952*(-4.109589*0.019560+10.958904*0.949807)
+0.936611*(0.000000*1.000000-0.000000*0.000000)+-0.013952*(0.000000*0.000000+0.000000*1.000000)
=-0.300049
Q2=+-0.013952*(-2.958580*0.943988-7.100592*-0.031500)-0.936611*(-2.958580*-0.031500+7.100592*0.943988)
+-0.013952*(7.068169*0.936611--18.059496*-0.013952)-0.936611*(7.068169*-0.013952+-18.059496*0.936611)
+-0.013952*(-4.109589*0.949807-10.958904*0.019560)-0.936611*(-4.109589*0.019560+10.958904*0.949807)
+-0.013952*(0.000000*1.000000-0.000000*0.000000)-0.936611*(0.000000*0.000000+0.000000*1.000000)
=-0.099703
P3=+0.949807*(0.000000*0.943988-0.000000*-0.031500)+0.019560*(0.000000*-0.031500+0.000000*0.943988)
+0.949807*(-4.109589*0.936611-10.958904*-0.013952)+0.019560*(-4.109589*-0.013952+10.958904*0.936611)
+0.949807*(4.109589*0.949807--10.958904*0.019560)+0.019560*(4.109589*0.019560+-10.958904*0.949807)
+0.949807*(0.000000*1.000000-0.000000*0.000000)+0.019560*(0.000000*0.000000+0.000000*1.000000)
=0.400189
U3^2=(0.949807)^2+(0.019560)^2=0.902515
于是：DPi=Pi-Pi(2);DQi=Qi-Qi(2);DUi^2=Ui^2-(ei(2)^2+fi(2)^2)
DP1=P1-P1(2)=-0.600000-(-0.599959)=-0.000041
DQ1=Q1-Q1(2)=-0.250000-(-0.249791)=-0.000209
DP2=P2-P2(2)=-0.300000-(-0.300049)=0.000048
DQ2=Q2-Q2(2)=-0.100000-(-0.099703)=-0.000297
DP3=P3-P3(2)=0.400000-(0.400189)=-0.000189
D(U3)^2=(U3)^2-(e3(2)^2+f3(2)^2)=0.902500-((0.949807)^2+(0.019560)^2)=0.000000
2、计算雅可比矩阵中各元素:
I1=(P1-jQ1)/U1*=(-0.599959-j-0.249791)/(0.943988-j-0.031500)=-0.626031+j0.285503=a11+jb11
I2=(P2-jQ2)/U2*=(-0.300049-j-0.099703)/(0.936611-j-0.013952)=-0.318699+j0.111198=a22+jb22
Q3=+0.019560*(0.000000*0.943988-0.000000*-0.031500)-0.949807*(0.000000*-0.031500+0.000000*0.943988)
+0.019560*(-4.109589*0.936611-10.958904*-0.013952)-0.949807*(-4.109589*-0.013952+10.958904*0.936611)
+0.019560*(4.109589*0.949807--10.958904*0.019560)-0.949807*(4.109589*0.019560+-10.958904*0.949807)
+0.019560*(0.000000*1.000000-0.000000*0.000000)-0.949807*(0.000000*0.000000+0.000000*1.000000)
=0.014795
I3=(P3-jQ3)/U3*=(0.400189-j0.014795)/(0.949807-j0.019560)=0.421479+j-0.006897=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)*0.943988+7.082291*-0.031500+0.285503=15.523926
N11=偏P1/偏e1=G11*e1+B11*f1+a11=7.082291*0.943988+-16.378941*-0.031500+-0.626031=6.575509
J11=偏Q1/偏f1=-G11*e1-B11*f1+a11=-(7.082291)*0.943988-(-16.378941)*-0.031500+-0.626031=-7.827572
L11=偏Q1/偏e1=-B11*e1+G11*f1-b11=-(-16.378941)*0.943988+7.082291*-0.031500-(0.285503)=14.952919
H12=偏P1/偏f2=-B12*e1+G12*f1=-(7.100592)*0.943988+-2.958580*-0.031500=-6.609674
N12=偏P1/偏e2=G12*e1+B12*f1=-2.958580*0.943988+7.100592*-0.031500=-3.016535
J12=偏Q1/偏f2=-G12*e1-B12*f1=-(-2.958580)*0.943988-(7.100592)*-0.031500=3.016535
L12=偏Q1/偏e2=-B12*e1+G12*f1=-(7.100592)*0.943988+-2.958580*-0.031500=-6.609674
H13=偏P1/偏f3=-B13*e1+G13*f1=-(0.000000)*0.943988+0.000000*-0.031500=0.000000
N13=偏P1/偏e3=G13*e1+B13*f1=0.000000*0.943988+0.000000*-0.031500=0.000000
J13=偏Q1/偏f3=-G13*e1-B13*f1=-(0.000000)*0.943988-(0.000000)*-0.031500=0.000000
L13=偏Q1/偏e3=-B13*e1+G13*f1=-(0.000000)*0.943988+0.000000*-0.031500=0.000000
H21=偏P2/偏f1=-B21*e2+G21*f2=-(7.100592)*0.936611+-2.958580*-0.013952=-6.609211
N21=偏P2/偏e1=G21*e2+B21*f2=-2.958580*0.936611+7.100592*-0.013952=-2.870104
J21=偏Q2/偏f1=-G21*e2-B21*f2=-(-2.958580)*0.936611-(7.100592)*-0.013952=2.870104
L21=偏Q2/偏e1=-B21*e2+G21*f2=-(7.100592)*0.936611+-2.958580*-0.013952=-6.609211
H22=偏P2/偏f2=-B22*e2+G22*f2+b22=-(-18.059496)*0.936611+7.068169*-0.013952+0.111198=16.927298
N22=偏P2/偏e2=G22*e2+B22*f2+a22=7.068169*0.936611+-18.059496*-0.013952+-0.318699=6.553385
J22=偏Q2/偏f2=-G22*e2-B22*f2+a22=-(7.068169)*0.936611-(-18.059496)*-0.013952+-0.318699=-7.190784
L22=偏Q2/偏e2=-B22*e2+G22*f2-b22=-(-18.059496)*0.936611+7.068169*-0.013952-(0.111198)=16.704901
H23=偏P2/偏f3=-B23*e2+G23*f2=-(10.958904)*0.936611+-4.109589*-0.013952=-10.206888
N23=偏P2/偏e3=G23*e2+B23*f2=-4.109589*0.936611+10.958904*-0.013952=-4.001981
J23=偏Q2/偏f3=-G23*e2-B23*f2=-(-4.109589)*0.936611-(10.958904)*-0.013952=4.001981
L23=偏Q2/偏e3=-B23*e2+G23*f2=-(10.958904)*0.936611+-4.109589*-0.013952=-10.206888
H31=偏P3/偏f1=B31*e3+G31*f3=-(0.000000)*0.949807+0.000000*0.019560=0.000000
N31=偏P3/偏e1=31*e3+B31*f3=0.000000*0.949807+0.000000*0.019560=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)*0.949807+-4.109589*0.019560=-10.489223
N32=偏P3/偏e2=32*e3+B32*f3=-4.109589*0.949807+10.958904*0.019560=-3.688964
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)*0.949807+4.109589*0.019560+-0.006897=10.482326
N33=偏P3/偏e3=G33*e3+B33*f3+a33=4.109589*0.949807+-10.958904*0.019560+0.421479=4.110443
R33=偏U3^2/偏f3=*f3=2*0.019560=0.039119
S33=偏U3^2/偏e3=*e3=2*0.949807=1.899613
3、所以可以得到K=2时的雅可比矩阵:
J(2)=
15.523926 6.575509 -6.609674 -3.016535 0.000000 0.000000
-7.827572 14.952919 3.016535 -6.609674 0.000000 0.000000
-6.609211 -2.870104 16.927298 6.553385 -10.206888 -4.001981
2.870104 -6.609211 -7.190784 16.704901 4.001981 -10.206888
0.000000 0.000000 -10.489223 -3.688964 10.482326 4.110443
0.000000 0.000000 0.000000 0.000000 0.039119 1.899613
至此，可以建立修正方程组如下：....
解得：
df1=-0.000009
de1=-0.000026
df2=-0.000027
de2=-0.000030
df3=-0.000053
de3=-0.000007
因为：ei(3)=ei(2)+dei(2); fi(3)=fi(2)+dfi(2)
所以：
e1(3)=e1(2)+de1(2)=0.943988+-0.000026=0.943961
f1(3)=f1(2)+df1(2)=-0.031500+-0.000009=-0.031509
e2(3)=e2(2)+de2(2)=0.936611+-0.000030=0.936581
f2(3)=f2(2)+df2(2)=-0.013952+-0.000027=-0.013979
e3(3)=e3(2)+de3(2)=0.949807+-0.000007=0.949800
f3(3)=f3(2)+df3(2)=0.019560+-0.000053=0.019507
------------------------------------------------------------------------------------------------------------
各节点电压为:
U1=e1+jf1=0.943961+j(-0.031509)
U2=e2+jf2=0.936581+j(-0.013979)
U3=e3+jf3=0.949800+j(0.019507)
U4=e4+jf4=1.000000+j(0.000000)
------------------------------------------------------------------------------------------------------------
平衡节点功率为:
S~4=......
=(1.000000+j0.000000)[(-4.123711-j(9.278350))(0.943961-j(-0.031509))(0.000000-j(0.000000))(0.936581-j(-0.013979))(0.000000-j(0.000000))(0.949800-j(0.019507))(4.123711-j(-9.278350))(1.000000-j(0.000000))]
=0.523441+j(0.390012)
------------------------------------------------------------------------------------------------------------
线路上功率及损耗为：
s~41=U4[U*4y*40+(U*4-U*1)y*41]
=(1.000000+j(0.000000)){(1.000000-j(0.000000))(0.000000-j(0.000000))+[(1.000000-j(0.000000))-(0.943961-j(0.000000))](4.123711-j(-9.278350))}
=0.523441+j(0.390012)
s~14=U1[U*1y*10+(U*1-U*4)y*14]
=(0.943961+j(-0.031509)){(0.943961-j(-0.031509))(0.000000-j(0.000000))+[(0.943961-j(-0.031509))-(1.000000-j(-0.031509))](4.123711-j(-9.278350))}
=-0.506397+j(-0.351663)
dS41=S41+S14=(0.523441+j0.390012)+(-0.506397+j-0.351663)=0.017044+j0.038349
s~12=U1[U*1y*10+(U*1-U*2)y*12]
=(0.943961+j(-0.031509)){(0.943961-j(-0.031509))(0.000000-j(0.000000))+[(0.943961-j(-0.031509))-(0.936581-j(-0.031509))](2.958580-j(-7.100592))}
=-0.093603+j(0.101664)
s~21=U2[U*2y*20+(U*2-U*1)y*21]
=(0.936581+j(-0.013979)){(0.936581-j(-0.013979))(0.000000-j(0.000000))+[(0.936581-j(-0.013979))-(0.943961-j(-0.013979))](2.958580-j(-7.100592))}
=0.094674+j(-0.099095)
dS12=S12+S21=(-0.093603+j0.101664)+(0.094674+j-0.099095)=0.001070+j0.002569
s~23=U2[U*2y*20+(U*2-U*3)y*23]
=(0.936581+j(-0.013979)){(0.936581-j(-0.013979))(0.000000-j(0.000000))+[(0.936581-j(-0.013979))-(0.949800-j(-0.013979))](4.109589-j(-10.958904))}
=-0.394674+j(-0.000905)
s~32=U3[U*3y*30+(U*3-U*2)y*32]
=(0.949800+j(0.019507)){(0.949800-j(0.019507))(0.000000-j(0.000000))+[(0.949800-j(0.019507))-(0.936581-j(0.019507))](4.109589-j(-10.958904))}
=0.400000+j(0.015108)
dS23=S23+S32=(-0.394674+j-0.000905)+(0.400000+j0.015108)=0.005326+j0.014203
------------------------------------------------------------------------------------------------------------
有两种方法可以求出网络总损耗，任选其一:
法一：DDS~=求和dS＝0.023441+j0.055121
法二:
Q3=+0.019507*(0.000000*0.943961-0.000000*-0.031509)-0.949800*(0.000000*-0.031509+0.000000*0.943961)
+0.019507*(-4.109589*0.936581-10.958904*-0.013979)-0.949800*(-4.109589*-0.013979+10.958904*0.936581)
+0.019507*(4.109589*0.949800--10.958904*0.019507)-0.949800*(4.109589*0.019507+-10.958904*0.949800)
+0.019507*(0.000000*1.000000-0.000000*0.000000)-0.949800*(0.000000*0.000000+0.000000*1.000000)
=0.015109
DDS~=+(-0.600000+j-0.250000)+(-0.300000+j-0.100000)+(0.400000+j0.015109)+(0.523441+j0.390012)
=0.023441+0.055121
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