Question 3: (PEO - May 2016)
A balanced Y-connected three-phase load consisting of an impedance of
17/62⁰ Ω in each phase is connected to a balanced three-phase, 50 Hz source as shown in the circuit of Figure 2 below through a distribution line having an impedance, ZL, of 0.1+j0.3 Ω, between the source and the load. The voltage at the load is 600 V, line-to-line.
a) Find the line current from the source, and the voltage at the source.
b) Find the total active and reactive power of the Y-connected load.
c) A three-phase induction motor is connected in parallel with the Y-connected load. The motor output is 23 hp at an efficiency of 83% and a power factor of 0.85 lagging. Determine the new line current with the motor connected, and the voltage at the source. Also, find the average and reactive power drawn by the induction motor. Assume the impedance in the wires connecting the Y-connected load and the induction motor is negligible.
d) If we wish to correct the power factor at the loads to unity, how many VARs of a three-phase capacitor bank are needed (assuming no losses in the capacitor bank)? If the capacitor bank is connected in Y, what is the required phase impedance?
e) What is the new line current with the capacitor bank of (d) connected?
f) Draw a phasor diagram showing the line currents without power factor correction and with the power factor corrected to unity.