Lyapunov Exponent and Spectral Analysis for Chaos Detection in the Wounded Rotor Induction Motor with an Internal Fault

ABSTRACT

The conventional method for finding the location of turn-to-turn stator fault on the stator winding of the induction motor is spectral analysis. Using the harmonics method, the current spectrum can show the location of the fault. In this paper, it is shown that the chaos phenomenon could occur when fault arises on the motor. The spectrum of chaotic system has a wide range of harmonics. Consequently, spectral analysis is confused in this state. For this reason, first inductances of an induction machine with a turn-to-turn fault in stator winding are determined by the winding function theory. Using the nonlinear control theory, a first-order Poincare's map of the induction machine is computed and a new extended Poincare's map is drawn for the induction machines. In addition, the characteristic multipliers and the largest Poincare's exponents are calculated with this map. The new map is capable of modeling electrical machines in nonlinear and unbalanced cases for stability, bifurcation, and chaos analysis. The characteristic multiplier and Poincare's exponents of the extended map show the condition of a system. Chaos phenomena are observable in the condition of machines with a fault. In such cases, spectral analysis shows that the machine's current spectrum is varied in each period by a continuous spectrum of chaotic systems; consequently, identification of the location of an internal fault is not easily possible with conventional methods such as the Fourier spectrum or harmonics identification on a machine's terminal current. The experimental results supported the chaotic manner of the faulty induction motor.

KEYWORDS:

• Chaos
• Induction motor
• Internal fault
• Lyapunov exponents
• Nonlinear analysis
• Poincare's map

Additional information

Notes on contributors

S. M. Shariatmadar

S M Shariatmadar was born in Qom, Iran, in August 1973. He received the BSc degree from Tehran University, Tehran, Iran, in 1996, the MSc degree from the South Tehran Branch, Azad University, in 2003 and the PhD degree in electrical engineering at the Science and Research Branch, Islamic Azad University Tehran, Iran in 2011. His current research interests include modeling, analysis, and control of electrical machines, power electronic drives, and nonlinear phenomena in power electronics systems.