Question

A 240V three phase power system supplies two loads in parallel: Load 1: measured line current 30A, power factor 0.85 lagging, and Load 2: measured power 10kW, reactive power -7.5kVar A. Determine the power factor of load 2. B. Determine the total real power (in kW), reactive power (in kVAR), apparent power (in kVA), power factor and line current (in A) of the two loads.

Answer 1

Load (1) I_C = 30 A cos Phi = 0.85 lag Phi_1 = cos^- 1 (0.85) Phi_1 = 31.78 I_C rightarrow I_L angle - Phi_1 I_C rightarrow 30 angle - 31.78 A complex power S_1 = squareroot 3 VI_C S_1 = squareroot 3 times 240 times (30 angle - 31.78) S_1 = squareroot 3 times 240 times 30 angle 31.78 S_1 = 12470.7 angle 31.78 VA S_1 = 10601 + j 6568 VA \r\n for load (2) P = 10 k w Q = -7.5 k VAR Phi_2 = tan^- 1 (- 7.5 times 10^3/10 times 10^3) Phi_2 = -36.86 PF rightarrow cos Phi_2 rightarrow cos (-36.86) rightarrow 0.8 leading S_2 = P + j Q S_2 = 10 times 10^3 - j 7.5 times 10^3 VA (b) total complex power ST = S_1 + S_2 = 10601 + j 6568 + 10000 - j 7500 S_T = 20601 - j 932 S_T = 20622 angle - 2.6 degree VA S_T = P_T - j Q_T P_T = 20.601 k w Q_T = 0.932 k VAR S_T = 20.622 K V A p f = cos (- 2.6 degree) p f = 0.998 lead S_T = squareroot 3 V_C I_S 20622 angle - 2.6 = squareroot 3 times 240 times I_S