International Journal of Science and Research (IJSR), India Online ISSN: 2319-7064 Volume 2 Issue 1, January 2013 www.ijsr.net Non Linear Modeling of Split Phase Type Single Phase Induction Motor Sujay Sarkar 1 , Subhro Paul 2 , Pradip Kumar Saha 3 , Gautam Kumar Panda 4 1 Student (P.G) Jalpaiguri Government Engineering College sujay.sarkar1234@gmail.com 2 Student (P.G) Jalpaiguri Government Engineering College subhroee@hotmail.com 3 HOD Electrical Department Jalpaiguri Government Engineering College p_ksaha@rediffmail.com 4 Professor Electrical Department Jalpaiguri Government Engineering College g_panda@rediffmail.com Abstract: Single-phase induction machines are found in various appliances such as refrigerators, washing machines, driers, air conditioners and fans. This paper presents a mathematical model and simulation results of dynamic characteristics of the split phase induction motor for different values of the inductor and moment of inertia at no-load conditions. Based on the state vector analysis of the system, the d–q axis model of the split phase induction motor is deduced. It reveals the periodicity and chaos for various system parameters. Accordingly, a chaotic-speed fan is derived varying the motors’ internal parameters or the operations. Keywords: split phase induction motor, bifurcation, chaos, non-linear, periodicity 1. Introduction In home appliances, single-phase induction motors are commonly used.The split phase induction motor has two windings, the main winding and the auxiliary winding. These windings are displaced in space by 90 electrical. The auxiliary winding has higher current ratio between resistance and reactance, by designing it at a higher current density. It is assumed that the system has magnetic linearity and negligible slotting of the stator and rotor. Also the parameters here are considered, for simplicity, to be lumped rather than distributed. Chaos is a phenomenon that occurs in nature, from as large as the universe to as tiny as a particle. Chaos can be defined as the qualitative study of the unstable periodic long term behaviour in a deterministic system that exhibits sensitive dependence on initial condition. A chaos theory is a field of study in mathematics, with applications in several disciplines including physics, engineering, economics, biology, and philosophy. 2. D-Q axis modeling of the motor The D-Q model a single phase induction machine can be considered to be an unsymmetrical two phase induction machine. To build a Motor model, we need mainly The Stator and Rotor Voltage equations. Let us take the following motor (a) (b) Figure 1: (a) Motor Model (b) Phasor diagram The voltage equation can be written as qs m qs qs b p v r i λ ω = + 398