Accounting for Magnetic Saturation Effects in Complex Multi-harmonic Model of Induction Machine

Tomasz Garbiec,Mariusz Jagiela

doi:10.3390/en13184670

Abstract

Computations of quasi-dynamic electromagnetic field of induction machines using the complex magnetic vector potential require the use of the so-called effective magnetization curves, i.e., such in which the magnetic permeability is proportional to the amplitudes of magnetic flux density B or magnetic field strength H, not their instantaneous values. There are several definitions of that parameter mentioned in the literature provided for the case when B or H are monoharmonic. In this paper, seven different methods of determining the effective magnetization curves are compared in relation to the use of a field-circuit multi-harmonic model of an induction machine. The accuracy of each method was assessed by computing the performance characteristics of a solid-rotor induction machine. One new definition of the effective permeability was also introduced, being a function of multiple variables dependent on amplitudes of all the harmonics considered. The analyses demonstrated that the best practical approach, even for the multi-harmonic case, is to express the effective magnetic permeability as the ratio of the amplitudes of the fundamental harmonics of the magnetic flux density and the magnetic field strength, and assuming the sinusoidal variation of the latter.

Highlights

Numerical models based on the use of the finite element method have become an indispensable tool in the design of electrical machines
The multi-harmonic model in this case is understood as the De-Gersem type model formulated using the magnetic vector potential, where permeance slot harmonics of the magnetic field distribution in the air gap are extracted via Fourier transform of an air-gap magnetic field
Analyzing the conclusions drawn in the mentioned works, it is not possible to clearly state which method of defining the effective magnetic permeability will be most appropriate when using the multi-harmonic model with a strong coupling, as proposed by Garbiec et al Some of them assume the sinusoidal variation of the magnetic flux density in calculating the effective magnetic permeability [12,13,14,15], while others assume that it should be determined assuming sinusoidal variation of the magnetic field strength, or that it is insignificant for the accuracy of the calculations [10,11,14]

Summary

Introduction

Numerical models based on the use of the finite element method have become an indispensable tool in the design of electrical machines. Analyzing the conclusions drawn in the mentioned works, it is not possible to clearly state which method of defining the effective magnetic permeability will be most appropriate when using the multi-harmonic model with a strong coupling, as proposed by Garbiec et al Some of them assume the sinusoidal variation of the magnetic flux density in calculating the effective magnetic permeability (which facilitates the calculations using the magnetic vector potential) [12,13,14,15], while others assume that it should be determined assuming sinusoidal variation of the magnetic field strength, or that it is insignificant for the accuracy of the calculations [10,11,14] The latter approach was adopted in the authors’ previous work, and satisfactory results were achieved [9]. The results of calculations were compared with those obtained with the time-domain model and with the results of measurements performed on the physical model under one of the previous works where the efficient computational method for fast determination of the performance characteristics of solid-rotor induction machines was presented [17]

Effective Magnetic Permeability

Analyzed Machine

Results

Physical Validation

Conclusions