Question

A 3-phase, Y-connected 4-wire system with grounded neutral carrying 60 A at 60 Hz per phase when balanced has 3rd harmonic current. The harmonic current is measured at 3 A/phase.

a. For this system to remain without voltage distortion, what must be the current that the neutral carries to ground? (Easy answer.)

b. The 3rd harmonic frequency is 180 Hz. If there is reactance XL = 2 Ω/phase in the line, what is the per phase capacitance (mF) of a series-connected power factor correction capacitor (measured line-neutral) in the line for there to be resonance at the harmonic frequency? [Answer: 0.442 mF,. Resonance in power factor correction capacitors is a problem in a circuit with harmonic distortion, because at resonance the only resistance in the line is the (small) resistance of the wires, causing too much current and the capacitors can overheat and burn up.]

Answer 1

(a) If the system has to be undistorted in terms of voltage then the current from neutral to ground should be the value of harmonic current of the system, only because of the harmonics there is a distortion in the voltage. If the harmonic currents flow through the grounded neutral it discharges into ground and will not have any effect on the system.

Given that

harmonic current per phase (Ih) = 3A

Neutral current (In) = 3*3A = 9A

(Since the neutral carries the sum of the currents of all the phases)

Therefore, the current through the neutral to avoid the voltage distortion is 9A.

(b)

The solution to the problem (b) is shown in the above image. I hope you are satisfieed with my work.