# Dispersion Coefficient of Induction Motor

The power factor and dispersion coefficient of an induction motor have a relationship. The smaller the dispersion coefficient, the better the power factor. Power factor is an important factor in designing an induction motor. The power factor depends upon two factors:

i) Magnetizing current(Im) :

A large value of the magnetizing current indicates a poor power factor. Magnetizing current is indirectly proportional to the power factor. As the magnetizing current is large, the power factor is poor.

ii) Ideal short circuit current (Isc):

It is defined as the current drawn by the motor at a standstill, neglecting its resistance. A large value of ideal short circuit current will be drawn for a small value of leakage reactance, giving a good power factor.

The dispersion coefficient is defined as the ratio of the magnetizing current to the ideal short circuit current.
Thus dispersion coefficient,

σ = Im/Isci
= Im/(Es /Xs )      Isci = Es /Xs
=Im.Xs /Es

For small values of Im and Xs, the dispersion coefficient is small, and the power factor is good. Thus, for a small value of the dispersion coefficient, the power factor is good, whereas for a large value of the dispersion coefficient, the power factor is poor.

The dispersion coefficient increased with an increase in the number of poles. The induction motor of a large number of poles has a higher dispersion coefficient, and thus, the power factor of the induction motor is poor.