Question

Q1. AC Power Calculation 1. For the following voltage and current phasors, calculate the complex power, apparent power, real power, and reactive power. Specify whether the pf is leading or lagging. (a) V = 120/ 30 V rms, 1 = 6.2/ - 25 A rms (b)V= 220/30 mms, 1 = 0.50/60 Arms (c) V = 250/- 10 Vrms, I = 6.21 - 25 Arms (d)V= 110/30°Vrms, 1 = 0.40/-70'Arms (e) P = 100kW, pf = 0.88 lagging

Answer 1

This problem belongs to the complex power calculation and is entirely based on one concept i.e.

Complex power S = V_rms*(I_rms)^*

where (I_rms)^* denotes the conjugate of RMS value of current through the terminals of the element across which the complex power is to be calculated.

Complex power S can be denoted in cartesian form as

S = P+jQ

here P= real power in watts

Q= reactive power in VAR

Also, S= |S|<φ_v-φ_i

|S| is the apparent power and

<φ​​​​​​​_v-φ_i is the power factor angle

if <φ​​​​​​​_v-φ_i is positive, the power factor is said to be lagging.

if <φ​​​​​​​_v-φ_i is negative, the power factor is said to be leading.

cos(<φ​​​​​​​_v-φ_i) gives the power factor.

Given below is the solution of all the five parts-
a) V - 120 L30 V some I = 6-2 2-25° Anims I* - 6.2 25. A sms S = Venus (I sme)* = (120230) (6.2225) VA = 74455" VA = (426.74 + ; 609.44 ) VA " Complexe power = (426-74 + j 609.44) VA Apparent power = 151 = 744 VA Real power = 426.74 W Reactive power = + 609.44 VAR 20,- 0; = 55° > ... power factor is lagging praca ( 55°) = 0.57 logging

b) v=220 230 V arms I = 0.5%60A sms I* = 0.5L-60* A sms se Voms (Iym;)* VA = (220L30') (0:52-60°) VA = 110 L-30' VA = (9526.-;55) VA ... Complex power = (.95.26 - ; 55) VA i = 110L-30° VA Apparent power = 15)= 110 VA Real power = 95.26 W Reactive power? - 55 NAR Lov - Oi = - 30 į ... power factor is leading pf = cod (+30) = 0; 866 leading

c) V = 250 L-10 V grims I = 62 L-25 A sms I' = 6.2 L 25° A sms S. (Vorms) C I sms)* VAD = (2 502-10) (6.2L25) VA = 1550 Lt5 INA = (1497-18 + j 401:16) VAI ... Complex power = (1497:18 + ; 401. 16) VA . v 1 = 1550 L15VA. 1 Apparent power = 151= 1550 VA Real power = 1497-18 W Reactive power = 401 16 VAR 20-0i = 150.00 ... power factor is lagging pf = cop (15) = (0.965 logging

d) v = 10 230° V sams I = 0.40 (-70* A rums I* = 0.40 470* A soms S - (Vorms) (Inms)* = (11030') (0.40 L70) VA VEZ = 44 2100 VARJ E ( 1-64 64 3 33 ) + . | Here Lor0i = 100 ? in this condition is not possib L 90' - 90 Low-oi .. such voltage and current phasor relationship cannat occur across any element. ... it is imalid condition.

e) P: 100W pf = 0.88 lagging 151 (0.38) = 100*10° 151 = 113.636 KVA cano = 0.88 ::0 = + +9(0.88) = 28:35 i sin 0 = 0.47 id = is1 sino = 53.408 KVAR :. Complen power=s=p+; & = (100 +j 53.408) KvA wer = SI = 113.636 KVA Real power = soolew Reactive power = 53.408 KVAR pf in logging
Hope this answer would help!