determine phase - voltage and powera balanced

Question

Determine phase - voltage and power:

A balanced star connected load is supplied from a symmetrical 3-phase 440 Volt system. The current in each of the phase is 40 Amp and lags 30^o behind the phase voltage. Determine

1.      phase voltage,

2.      power,

3.      reactive power drawn by a the load, and

4.      phase impedance.

Solution

For three phase star connected load voltage applied V_L = 440 Volt

(a)                  V _ph    = 440/ √3 = 254.03 Volt

Power current = I ph = 40 ∠ - 30^o Amp = I _L

 (b)       Power P_3φ =3 V_L I _L cos φ   = 3 × 440 × 40 cos 30^o

                                                            = 26400 Watt = 26.4 kW

(c)        Reactive power drawn by the load:

Q_3φ = √3 VL I L sin φ

= √3 × 440 × 40 sin 30^o

= 15242.047 V_ar = 15.24 kVA_r

 (e)       Phase impedance Z _ph = V _ph I _ph

               =254.03 ∠ 0^o / 40 ∠- 30^o = 6.35 ∠ 30^o Ω