Question

A 23-V, 50 Hz, 1-ph supply is feeding the following loads which are connected across it. 

(i) A motor load of 4 kW, 0.8 lagging p.f. 

(ii) A rectifier of 3 kW at 0.6 leading p.f. 

(ii) A lighter-load of 10 kVA at unity p.f. 

(iv) A pure capacitive load of 8 kVA 

Determine : Total kW, Total kVAR, Total kVA

Answer 1

S. No.	Item	kW	P.f	kVA	kVAR	I	Is	Ir
1	Motor	4	0.8 lag	5	3 − ve, Lag	21.74	17.4	13.04 Lag (−)
2	Rectifier	3	0.6 Lead	5	4 + ve, Lead	21.74	13.04	17.4 Lead (+)
3	Light-Load	10	1.0	10	zero	43.48	43.48	zero
4	Capacitive Load	Zero	0.0 Lead	8	8 + ve Lead	34.8	zero	34.8 Lead (+)
	Total	17	-	Phasor  Addition  required	+ 9 + ve Lead	Phasor  Addition  required	73.92	39.16 Lead (+)

Performing the calculations as per the tabular entries above, following answers are obtained 

Total kW = 17 Total kVAR = + 9, leading

Total kVA = √(17² + 9²) = 19.2354

Overall circuit p.f = KW/KVA = 17/19.2354 = 0.884 leading

Overall Current = 19235.4/230 = 83.63 amp