HW2
Problem 1
a.It’s obvious that the loss in the earth capacitance is △Q=BU2, which means
earth capacitance is proportional to reactive loss. Earth capacitance of the line is
5÷100=0.05 p.u. and 15÷100=0.15 p.u. at the bus 2.
1 1
0.05 -
0.02 0.06 0.02 0.06
1 1
- 0.05 0.15
0.02 0.06 0.02 0.06
i
i i
Ybus
i i
i i
+
+ +
=
+ +
+
æ ö
ç ÷
ç ÷
ç ÷
ç
ø
+
÷
è
Using matlab to simplify the matrix:
Y =
5.0000 -14.9500i -5.0000 +15.0000i
-5.0000+15.0000i 5.0000 -14.8000i
The power flow equations are:
2
2 2 21 21 2
2
2 2 21 21 2
=-1-1.05 ( 5cos 15sin ) 5 0
=-0.5-1.05 ( 5sin 15cos ) 14.8 0
P V V
Q V V
q q
q q
D ´ - + - =
D ´ - - - =
b.
2 2
2 21 21 21 2 2 21 21
2 2 21 21 2 2 21 21
2 21
( ) ( )
,
-1.05 (5cos 14.8sin )-10 , -1.05 ( 5sin 14.8cos )
( ) ( ) -1.05 (5sin +14.8cos ) 29.6 ,-1.05 (5cos 14.8sin )
,
P P
V V V
J
Q Q V V
V
q q q q q
q q q q
q
¶ D ¶ D
é ù
ê ú
¶ ¶ ´ - ´ - -
é ù
ê ú
= =
ê ú
¶ D ¶ D ´ - ´ -
ê ú
ë û
ê ú
¶ ¶
ë û
Using matlab to calculate:
Assume
(0) (0)
2 21
1, 0V
q
= = °
. Use matlab to calculate.
V2 converges to
22
1.0113 -0.051 radV
q
Ð Ð=
