Question

In a balanced Y-Y three-phase circuit 120 10 Van    V rms. The load impedance per phase is 20 15 ZZ j L Y    . Determine the load voltages and line currents. Consider a positive sequence for the three-phase circuit.

Answer 1

Given Information:

Balanced Y-Y three phase circuit

Phase Voltage = Van = 120 < 10° V

Load Impedance = Zy = 20 +j15 Ω = 25 < 36.86° Ω

Required Information:

Load Voltages = Vab, Vbc, Vca = ?

Line currents = Ia, Ib, Ic = ?

Answer:

Vab = 208 < 40°

Vbc = 208 < -80°

Vca = 208 < 160°

Ia = 4.8 < -26.86°

Ib = 4.8 < -146.86°

Ic = 4.8 < 93.14°

Explanation:

Since it is balanced 3 phase system, all phases have equal magnitude and 120° phase shift

Van = 120 < 10° V

Vbn = 120 < -110° V

Vcn = 120 < 130° V

In a Y connected system, the phase voltage and line voltage are related as

Vab = $\sqrt{3}$(Van) <+30°

Vab = $\sqrt{3}$*120<10°+30°

Vab = 208 < 40°

Vbc = 208 < -80°

Vca = 208 < 160°

In a Y connected circuit, Iphase = Iline

Ia = Van/Zy

Ia = 120 < 10°/25 < 36.86°

Ia = 4.8 < -26.86°

Ib = 4.8 < -146.86°

Ic = 4.8 < 93.14°