An approach to compute saturated induction motors in steady state

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

“…Definition of the effective magnetic permeability, as used in the previous works of the authors [9,14,16,17], is the reference point for the considerations presented herein:…”

“…The application of the above-mentioned approach essentially involves the problem of modeling the nonlinearity of the magnetic materials. Taking this into account in the monoharmonic field models based on the use of the complex magnetic vector potential method is not a new task and it has been described to date in several works, including [10][11][12][13][14][15][16]. They propose several different methods of defining the so-called effective magnetic permeability based, among others, on the development of nonlinear waveforms in the Fourier series [14,16], averaging the magnetic reluctivity [10,15,16] or equivalence of energy stored in ferromagnetic components [10][11][12][13].…”

“…Taking this into account in the monoharmonic field models based on the use of the complex magnetic vector potential method is not a new task and it has been described to date in several works, including [10][11][12][13][14][15][16]. They propose several different methods of defining the so-called effective magnetic permeability based, among others, on the development of nonlinear waveforms in the Fourier series [14,16], averaging the magnetic reluctivity [10,15,16] or equivalence of energy stored in ferromagnetic components [10][11][12][13]. However, 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 available formulas use averaging of magnetic reluctivity in terms of mean or RMS value. Also, the Fourier series truncated to the fundamental component and assuming sinusoidal variation of the magnetic flux density or magnetic field strength is used [14][15][16]. The seventh method considered in this paper is a new approach proposed by the authors that relies upon formulating the so-called multidimensional effective magnetic permeability.…”

Time‐harmonic field‐circuit model for brushless doubly fed induction machine

“…Five formulations taken from the literature are as follows. The ones based on the fundamental component of Fourier series expansion of magnetic flux density or magnetic field intensity are as follows: [19] $$${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}1}\left({H}_{\mathrm{e}\mathrm{f}\mathrm{f}}\right)=\frac{2}{\pi }\underset{0{}}{\overset{\pi }{\int }}{\mu }_{\mathrm{D}\mathrm{C}}\left({H}_{\mathrm{e}\mathrm{f}\mathrm{f}}\,\mathrm{sin}\,\alpha \right){\mathrm{sin}}^{2}\,\alpha d\alpha $$$ and $$${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}2}\left({B}_{\mathrm{e}\mathrm{f}\mathrm{f}}\right)={\left(\frac{2}{\pi }\underset{0{}}{\overset{\pi }{\int }}\frac{{\mathrm{sin}}^{2}\,\alpha }{{\mu }_{DC}\left({B}_{\mathrm{e}\mathrm{f}\mathrm{f}}\,\mathrm{sin}\,\alpha \right)}d\alpha \right)}^{-1}$$$ …”