Winding Inductances Calculation of Surface-Mounted Brushless Machines

1. Winding Inductances Calculation of Surface-mounted Brushless Machines

1. Air Gap Inductance

Technique One

A polar coordinate based 2-d model is employed in [1] to predict the air gap component of winding inductances. The air gap components of the self and mutual inductances can be obtained:

        [pic 1]        

        [pic 2]        

where

        [pic 3]        

        [pic 4]        

where Kdpv is the winding factor, Ksov is the slot opening factor and Fv(r) is a function dependent on the radius and harmonic order. Ksov and Fv(r) can be derived as:

        [pic 5]        

        [pic 6]         

Technique Two

The air gap inductance can be calculated through the use of the winding functions to accumulate the flux-linkage in the winding [2, 3]. It is done by exciting each coil in turn, and adding the flux-linkage of every coil including the excited one which result in the total inductance being composed of a set of n self-inductances and n(n-1) mutual inductances, where n is the number of coils in the winding. Then the total air gap self flux-linkage of the phase winding can be obtained:

        [pic 7]        

where Ncoils is the total number of coils in the phase winding. The total air gap mutual inductance between two phases is calculated in the same manner, except that the summation over m is taken for the coils of one phase while the summation over n is taken for the coils of the other phase.

1. Slot Leakage Inductance

All teeth-wound nonoverlapping winding

A 2-d analysis was employed in [4] to develop an analytical model for the slot leakage inductance calculation of double layer nonoverlapping winding permanent magnet (PM) machines. The slot component of the self and mutual inductances can be derived as:

        [pic 8]        

        [pic 9]        

where the permeance coefficients are obtained:

        [pic 10]        

        [pic 11]        

Alternate teeth-wound nonoverlapping winding

The analysis in [4] was extended in [5] to include a number of winding layers up to 4 and any phase, pole and slot combination. Following the principles described in [5], the slot leakage inductance of permanent-magnet machines with a single layer nonoverlapping winding can be obtained:

        [pic 12]        

        [pic 13]