Question

Phase voltage and current of a star-connected inductive load is 150 V and 25 A. Power factor of load is 0.707 (lag). Assuming that the system is 3-wire and power is measured using two watt meters, find the readings of watt meters.

Answer 1

V_ph = 150V; V_L = 150√3V; I_phI_L = 25A

Total power = √3V_L I_Lcosφ 

= √3 x 150 x √3 x 25 x 0.707 = 7954W 

∴ W₁  + W₂ + = 7954W ... (i) 

cosφ =  0.707; φ = cos-1(0.707) = 45°; tan 45°  = 1 

Now, for a lagging power factor, 

tanφ(W₁ - W₂)/(W₁ + W₂) or 1

= √3(W₁ - W₂)/7954

∴ (W₁ - W₂)  = 4592 W ... (ii) 

From (i) and (ii) above, we get, W₁ = 6273W; W₂ = 1681W.