Hopf Bifurcation and Chaos in Synchronous Reluctance Motor Drives

Abstract

This paper first presents the occurrence of Hopf bifurcation and chaos in a practical synchronous reluctance motor drive system. Based on the derived nonlinear system equation, the bifurcation analysis shows that the system loses stability via Hopf bifurcation when the-axis component of its three-phase motor voltages loses its control. Moreover, the corresponding Lyapunov exponent calculation further proves the existence of chaos. Finally, computer simulations and experimental results are used to support the theoretical analysis.

Oscillatory Stability and Eigenvalue Sensitivity Analysis of A DFIG Wind Turbine System

“…A small positive perturbation in H g makes λ 3,4 shift toward the imaginary axis. However, as λ 3,4 are not the key modes for the oscillatory stability of the studied system, the increase in H g will not deteriorate the system stability. For λ 5,6 , the most critical parameters are R s , R r , L ls , and L lr .…”

“…The increase in R s and decrease in L ls and L lr make λ 1,2 move toward left in the s-plane. For λ 3,4 , the most sensitive parameter is H g . A small positive perturbation in H g makes λ 3,4 shift toward the imaginary axis.…”

“…Therefore, practical analysis of DFIG stability will have to involve the bifurcation phenomena. In recent years, some researchers studied stability of industrial motor drives with a wealth of nonlinear dynamics according to the bifurcation and chaos theories [1]- [4]. However, earlier studies mainly deal with dc and simple ac motor drives.…”

Controller Design for Synchronous Reluctance Motor Drive Systems with Direct Torque Control

“…Recently, many researchers have created new research topics for synchronous reluctance motor drives. For example, Gao and Chau present the occurrence of Hopf bifurcation and chaos in practical synchronous reluctance motor drive systems [25]. Bianchi, Bolognani, Bon, and Pre propose a torque harmonic compensation method for a synchronous reluctance motor [26].…”

Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control

“…A bifurcation diagram shows the long term qualitative changes (equilibria or periodic orbits) of a system as a function of a bifurcation parameters of the system. The complete dynamics of the system with the variation of the parameters can be studied with the help of bifurcation diagram [27][28][29]. Nonlinear dynamical system undergoes abrupt qualitative changes when crossing bifurcation points [30].…”