Estimation of coefficients of multivariable power series approximating magnetic nonlinearity of AC machines

Tadeusz J Sobczyk,Adam Warzecha

doi:10.2478/aee-2015-0030

Abstract

Abstract Energy based approach was used in the study to formulate a set of functions approximating the magnetic flux linkages versus independent currents. The simplest power series that approximates field co-energy and linked fluxes for a two winding core of an induction machine are described by a set of common unknown coefficients. The authors tested three algorithms for the coefficient estimation using Weighted Least-Squared Method for two different positions of the coils. The comparison of the approximation accuracy was accomplished in the specified area of the currents. All proposed algorithms of the coefficient estimation have been found to be effective. The algorithm based solely on the magnetic field co-energy values is significantly simpler than the method based on the magnetic flux linkages estimation concept. The algorithm based on the field co-energy and linked fluxes seems to be the most suitable for determining simultaneously the coefficients of power series approximating linked fluxes and field co-energy.

Highlights

Determining winding inductances of electrical machines with nonlinear cores is very important for their circuital models [1, 2]
Magnetic field computation techniques are employed to obtain the physical quantities which are necessary in calculations procedures [7]
The simplified method based on the distribution of magnetic field density in an air gap of an electric machine was mentioned in [10]

Summary

Introduction

Determining winding inductances of electrical machines with nonlinear cores is very important for their circuital models [1, 2]. The co-energy and flux linkages are multivariable functions of independent currents of machine windings and all of them can be approximated by mutually related Taylor series. All others terms in that series appear when magnetic nonlinearity is considered They are written as the quadratic forms of currents but using the current dependant matrices. The matrix A4 (i,φ ), in the first term representing magnetic nonlinearity in the co-energy function, is of the dimension N H N It can be written as a product of a matrix with constant elements and a specially arranged vector of the currents:. The proposed algorithm is described based on an example of a machine with two windings, when the co-energy and flux linkages are approximated taking into account the first nonlinear term only. It means that field computations have to be performed N times

Estimation method

Testing calculations

Findings

Conclusions