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Chaotic dynamic behavior of switched reluctance motor taking into account of magnetic saturation effects

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Abstract

The aim of this paper is to present a mathematical model of 6/2 SRM that takes into account magnetic saturation effects which is unavoidable in a SRM for some values of phase current and rotor position and to study its global dynamics according to the control frequency in open loop. A mathematical model of the SRM characterizing its overall dynamical behavior is presented. Using a semi-analytical approach, flux-linkage and static torque are fast computed to determine the incremental inductance and voltage per unit speed. These parameters are integrated in the dynamical model in order to take into account geometric design and magnetic saturation of the SRM. The obtained precise model and close to the Finite Element Analysis, is thereafter used to study the chaotic behavior of the SRM using standard nonlinear analysis techniques. The bifurcation diagrams, phase portrait, Poincare maps and time series analysis of the 6/2 SRM was given. As a result, the global dynamics of the SRM (periodicity, sub-harmonic and chaotic behavior) is clearly reported. The 6/2 SRM presents a chaotic behavior for an operating frequency beyond 275 Hz. This work can be useful for machine engineers since the dynamic instability can be the cause of vibration and noise in the machine. The results obtained could then be useful and help avoid such noisy operation of the machine for industrial applications.

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Abbreviations

\(I_{\max }\) :

Maximum value of phase current (A)

\(E\) :

DC phase voltage (V)

\(R\) :

Phase resistance (\(\Omega\))

J Z :

Current density (A/m2)

A Z :

Magnetic potential in z direction (A)

μ:

Magnetic permeability (Wb/(A.m))

L :

Axial length of the machine (m)

S :

Represents the surface of a notch (m2)

S k :

Surface of the element k of the mesh (m2)

A k :

Magnetic potential on the element k (A).

\(\psi\) :

Magnetic flux (Wb)

\(W_{em}^{^{\prime}}\) :

Magnetic co-energy (H.A2)

\(\theta\) :

Electrical rotor position (rad)

\(I\) :

Phase current (A

\(T_{e}\) :

Electromagnetic torque (N.m)

\(N_{dr}\) :

Number of tooth on the rotor of SRM

\(U\) :

Phase voltage (V)

\(\Omega\) :

Angular speed of SRM (rad/s)

T L :

Load torque (N.m)

f V :

Viscous friction coefficient (N.m.s)

J :

Moment of inertia (kg.m2)

\(\Psi_{I}\) :

Incremental inductance (H)

\(\Psi_{\theta }\) :

Voltage per speed unit (V)

A 0, A n, B n :

Fourier coefficients

A c :

Matrix of the coefficient of interpolation

\(\omega\) :

Electrical angular speed (rad/s)

\(f\) :

Frequency (Hz)

\(T\) :

Period of phase voltage (s

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  1. Department of Physics, Faculty of Science, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon

    Golam Guidkaya, Eric Duckler Kenmoe Fankem & Joseph Yves Effa

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  1. Golam Guidkaya
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  2. Eric Duckler Kenmoe Fankem
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  3. Joseph Yves Effa
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Correspondence to Joseph Yves Effa.

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Guidkaya, G., Kenmoe Fankem, E.D. & Effa, J.Y. Chaotic dynamic behavior of switched reluctance motor taking into account of magnetic saturation effects. Int J Syst Assur Eng Manag 13, 1556–1571 (2022). https://doi.org/10.1007/s13198-021-01460-w

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