0195136047.pdf

3.1 SINUSOIDAL STEADY-STATE PHASOR ANALYSIS 121

Solution

−

+

V

(a)

Inductive

load

Capacitor added (in parallel)

for power factor correction (improvement)

C

Source

SL =

P

P = PS = PR = 100 kW

QL = 75 kVAR = P tan φL

(b)

QC = −42.13

kVAR

QS = 32.87

kVAR

1002 + 752 = 125 kVA

cos φL

cos−^1 0.95 = 18.19° = φS

cos

−^1 0.8 = 36.87

° = φL

=

Figure E3.1.9(a)Circuit.

(b)Power triangles.

The circuit and the power triangles are shown in Figure E3.1.9. The real powerP=PS=PR

delivered by the source and absorbed by the load is not changed when the capacitor (considered

ideal) is connected in parallel with the load. After the capacitor is connected, noting thatQCis

negative,QS=QL+QC=100 tan(18.19)=32.87 kVAR,

SS=

P

cosφS

=

100

0. 95

= 105 .3kVa

(Note that the power factor correction reduces the current supplied by the generator signifi-

cantly.) So

QC=QS−QL= 32. 87 − 75 =− 43 .13 kVAR

Thus the capacitor is delivering 43.13 kVAR to the system (or absorbing negative kVAR). Then

Vrms^2

XC

=

1002

XC

=− 43. 13 × 103 or XC=− 0. 232 =−

1

ωC

or

C=

1

2 π× 60 × 0. 232

= 0 .0114 F or 11 .4mF

Fourier Series

The phasor method of circuit analysis can be extended (by using the principle of superposition)
to find the response in linear systems due to nonsinusoidal, periodic source functions. A periodic
function (t) with periodTcan be expressed inFourier series,

f(t)=

∑∞

n= 0

ancosnωt+

∑∞

n= 1

bnsinnωt (3.1.45)