Power triangle

A 220V, 50Hz single-phase power supply feeds the following loads in parallel

- a motor of 55 kVA with a lagging power factor of 0.7;

P = 55*0.7
=38.5kW

I = 55000/220
=250A

- a pure resistive heating load of 10 kW;
I = 10000/220
= 45.45A


- a furnace load of 15 kW with a lagging power factor of 0.6.
P = 15kW
S = 15000/0.6
= 25kVA
I = 15000/(220*0.6)
= 113.6A



Determine:

(a)the total active power and reactive power taken from the power supply;

P = 38.5 + 10 +15

= 63.5kW

Q = Kw*tan
1 = 0.7cos = 1.02tan
= 38.5*1.02
= 39.27kVAR

2 = 0.6cos = 1.33tan
= 15*1.33
= 19.95kVAR

= 59.22kVAR


(b)the overall power factor;

tan = kW/kVAR
= 63.5/59.22
= 1.07tan

= 0.68cos


(c) the total current demand.

I = P/V*cos
= 63500/(220*0.68)

= 424.46A


P = 63.5kW
PF = 0.68cos
Q = 59.22kVAR
I = 424.46A