Discussion in 'Homework Help' started by zamansabbir, Oct 26, 2008.

1. ### zamansabbir Thread Starter Member

May 27, 2008
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Hi,
I am facing an interesting problem.This problem is not about my homework but I got this from a book written on Electrical machines(by B.L.Theraja) .In his book he told that power factor of a three phase induction motor become less than 0.5 when running on light load.But I am thinking about is there any mathematical proof to get the problem solved?I am thinking but could not get hold on it....What I get oppose the problem.I tried to make a relation between voltage and current........I want help

2. ### steveb Senior Member

Jul 3, 2008
2,431
469
I think the basic approach would be to make an equivalent stator circuit. You can find this approach in most motor theory books. Typically a wye-connection is assumed and each of the three phases is represented with an equivalent single phase circuit. The stator side appears to be a resistance (from the stator windings) plus a stator inductance equal to the 3-phase mutual inductance plus the stator leakage inductance. Then a resistive component is added to represent the mechanical power dissipation. This is a frequency dependent resistance that can be related to the motor details (induction motor in this case).

I think if you pick up a text book and apply their equivalent circuit, you can derive the relations you want. Intuitively, the claim makes sense. With a light mechanical load, the circuit appears mostly inductive which will have a low power factor. It also makes sense from the point of view of power conservation. If you have high AC current and voltage, but don't dissipate a lot energy, then power factor must be low.

The following book is very good on the subject.

P.C. Krause, O. Wasynczuk and S.D. Sudhoff, “Analysis of Electric Machinery and Drive Systems”, 2nd edition, IEEE Series on Power Engineering, Mohamed E. El-Hawary, Series Editor, Wiley Inter-science, ISBN 0-471-14326-X, 2002

Last edited: Oct 26, 2008

Nov 21, 2006
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