§ 9-3 Apparent power and power factor
We assume
)c o s ()c o s ( ????? ???? tIitV mm
The phase angle by which the voltage leads the current is ??? ??
?? c o sc o s21 VIPorIVP mm ??
p o w e ra p p a r e n tVAVIS ????? )(
The ratio of the real or average
power to the apparent power is
called the power factor(PF),SPVIPPF ??
In the sinusoidal case,?c o s?PF
For a purely resistive load,PF=1.,0??
For a purely reactive load,PF=0.,90 ?? ??
?
?
?
????
???
l o a dc a p a c i t i v e
l o a di n d u c t i v e
?
?
?
?
60
60 5.0c o s5.0 ??? ?PFIf
The term leading or lagging referring to the phase of the
current with respect to the voltage.
Leading PF---capacitive load,Lagging PF--inductive load.
Example:
sI
?
?
??
?
?
VV s ?060
12 j?
51 j?
AjjjI s ?? 1.53121.535 6043 605112 60 ????????????
VAS s 7201260 ???
WP s 4 3 21.53co s1260 ??? ?
WP lo a d 4 3 2112212 22 ?????
6.01.53c o sc o s ??? ??PF
A generator produce an output voltage of 200V at 60
Hz,PF=1,P=1000W,I1=5A,If PF=0.5,I2=10A,When
R=0.2,P1=5W;P2=20W.(PF>0.85)