0195136047.pdf

10.2 SINGLE- AND THREE-PHASE SYSTEMS 459

(a) The line current of the motor, before the addition of the capacitor bank, is

IM=

S 3 φ

√

3 VL

=

25 , 000

√

3 × 220

= 65 .6A

After the addition, the new value of line current is

Icorr=

PM

√

3 VLPFcorr

=

17 , 680

√

3 × 220 × 0. 9

= 51 .55A

(b) The corrected new value of reactive power is

Qcorr=PMtan(cos−^10. 9 )= 17 .68 tan 25.8°= 8 .56 kVAR

The kVA (kVAR ) rating of the capacitor bank needed to improve the power factor from

0.707 to 0.9 lagging is then found as

Qcap=Qcorr−QM= 8. 56 − 17. 68 =− 9 .12 kVAR

The power triangle is shown in Figure E10.2.1.

SM = 25 kVA
Scorr = 19.64
kVA

25.8°

45 °

PM = 17.68 kW

QM = 17.68 kVAR

Qcorr = 8.56 kVAR

Qcap = 9.12 kVA R

Figure E10.2.1Power triangle

(c) Per-phase capacitive kVAR= 9. 12 / 3 = 3 .04 kVAR. With wye connection,

VLN^2

XC

=

(

220 /

√

3

) 2

XC

= 3. 04 × 103

or

XC=

(

220 /

√

3

) 2

3. 04 × 103

= 5. 31 

Hence,

C=

1

2 π× 60 × 5. 31

= 500 μF

(d) With delta connection,

VL^2

XC

=

2202

XC

= 3. 04 × 103

or