# Dispersion Coefficient of Induction Motor

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

i) Magnetizing current :

A large value of the magnetizing current indicates 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 standstill neglecting its resistance. A large value of ideal short circuit current will be drawn for small value of leakage reactance giving good power factor.

Dispersion coefficient defined as the ratio of magnetizing current to 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 dispersion coefficient is small and power factor is good. Thus for a small value of dispersion coefficient power factor is good, whereas for large value of dispersion coefficient power factor is poor.

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