determine impedance in each branch - delta

Question

Determine Impedance in each branch - delta connection:

A delta connected balanced 3-phase load is supplied from a 3-phase 400 V supply. The line current is 30 Amp and the power taken by the load is 10 kW. Determine

1.      impedance in each branch,

2.      the phase current,

3.      power factor, and

4.      Power consumed if the same load is connected in star.

Solution

Delta Connection Load

Line current I_L = 30 Amp

Phase current I _ph = 30/√ 3 = 17.32 Amp

(a) Phase impedance Z _ph = V _ph / I _ph  =   400 V/17.32 Amp

                                                                          = 23.095 Ω

(b) Phase current I_ph = 30 Amp (already calculated)

(c) Total 3-phase power = 10 kW

     But 3-phase power =  √3 VL  I _L cos φ

∴          cos φ=   P/ √3 V_L  I _L       = 10 × 1000 /√3 × 400 × 30

                                                       = 0.4811

(d) The same power shall be consumed if load is delta connected i.e. 10 kW.