§ 9-4 Complex power
A sinusoidal voltage:
????
? VV
A sinusoidal current:
iII ???
?
jQPj VIVIVIVI i ????????? ????? ? s i nco s
We define the complex power
iIVIVS ?? ? ?????
???_
?c o sVIP ? --active(average) power
?s i nVIQ ?
--reactive power
VIS ?
222 QPS ??
(功率三角形 )
S
Q
P
?
)s i n (s i n iVIVIQ ??? ? ???
l o a di n d u c t i v eQi 00 ???? ??? ?
l o a dc a p a c i t i v eQi 00 ???? ??? ?
c u r r e n ta c t i v eI ???c o s
c u r r e n tr e a c t i v eI ???s i n
?V
?I
?cosI ?sinI
?
The complex power delivered to several interconnected loads
is the sum of the complex power delivered to each of the
individual loads no matter how the loads are interconnected.
)()()( 2211_2_1__ NNN jQPjQPjQPSSSS ??????????? ??
NPPPP ???? ?21 NQQQQan d ???? ?21
)SSSS( N???? ?21
?
??
?
?377156,
A
B
C D
?
?
?
?0120
A?11 02? A?12 03?
??? ?15040
A,?1 169 844 ?
P174-6(a) Which of the element A,B,C,D must be source?
(b) How much average is each of the sources supplying?
5.2 2 51.821 1 021 2 0 jS A ?????????
4.513.611 1 021 5 040 jS B ????????????
3.6 4 91.4 2 71 1 69 8 4.437.71 5 6 jS C ????????????
3 7 21.2 8 41 2 0337.71 5 6 jS D ????????????
1Z
1
?I
?I
?
?
?
V
C
2
?I
We raise PF
.),(95.0
).(8.0co s
,1000,
0200
1
11
Cf i n dl a g g i n gPFIf
l a g g i n g
WPloadZ
VV
?
?
???
??
?
?
?
VASWP 12 5 08.0/10 0 010 0 0 11 ????
???? 9.368.0c o s 11 ??
V a rSQ 7509.36s i n1250s i n 111 ??? ??
VAjjQPS 7 5 01 0 0 0111_ ????
???? 2.1895.0c o s ??at VAjS 3 2 91 0 0 02.18
95.0
1 0 0 0_ ???? ?
V a rjSSS C 4211___ ???? AIVIS C 1 0 7.22 0 0/4 2 122 ????
FVICICV ??? 5.332 0 03 1 4 1 0 7.21 22 ??????
?V
?I
1
?I
2
?I
1?
?
11 cos?I
???? t a nc o st a nc o s 111112 III ??
VV
VI
V
IC
?
???
?
)t a n( t a nc o s 1112 ???
2
1 I
CV ??
95.08.0 ??PFIf
F
V
PC ?
?
?? 5.33
2 0 03 1 4
)2.18t a n9.36( t a n1 0 0 0)t a n( t a n
22
11 ?
?
??????
2
11 )t a n( t a n
V
P
?
?? ??
)t a n( t a nc o s 111 ??? ?? I