Comparative Study Of Inter-Turn Short Circuit Fault In Stator And Rotor Windings On A Small and Medium Power Wound Rotor Induction Machine T. D. Razafimahefa 1 N. Heraud 1 E. J. R. Sambatra 2 and O. Wailly 1 Abstract— An accurate model and reliable detection system of an induction motor is a very important tool for diagnostic and fault detection. This paper deals with modelling of an inter-turn short circuit in stator and rotor windings of an induction machine and the fault detection at start-up. Winding function approach is chosen for the fault modeling and time-frequency analysis is proposed for the detection of fault. The detection method is based on detection of sidebands at certain frequencies using Wigner-Ville Distribution. Keywords-induction machine; start-up; short circuit; winding function; time-frequency analysis I. INTRODUCTION The diagnostic and fault detection in the induction ma- chine have become a major preoccupation of industrial and researchers because these machines are the hearts of all industrial processes. In this paper we present a comparative study of short circuit fault between turns in the stator and rotor windings on a Small and Medium Power Wound Rotor Induction Machine at start-up. Inter-turn short circuit fault is an evolving fault. So, it is important to be able to detect it at start-up, in order to limit the damage that this kind of fault could cause to the machine. A model of this machine using the Winding Function Approach (WFA) was chosen. This approach was chosen because it uses the geometric parameters and the configurations of the windings of the machine [1]. A study in permanent regime is done by using external measurable variables of the machine subjected to the fault and healthy states. In order to carry out a depth comparative study of the two types of the fault, we propose a study at start-up performing by time-frequency analysis of stator and rotor currents. For this analysis we use the Wigner-Ville Distribution (WVD), which is known for its effectiveness on the analysis of non-stationary signals. The WVD is a time-frequency representation of the signal. he has significant advantages over other methods using time- frequency analysis [2]. Applied to a Small Power Wound Rotor Induction Machine (SPWRIM) whose the detection of short-circuit fault is not easy because this latter has very low 1 Tsivalalaina David Razafimahefa is with Labora- tory SPE-UMR CNRS 6134,University of Corse, France david.razafimahefa@gmail.com 1 Nicolas Heraud is with Laboratory SPE-UMR CNRS 6134,University of Corse, France heraud@univ-corse.fr 1 Olivier Wailly is with Laboratory SPE-UMR CNRS 6134,University of Corse, France olivier.wailly@yahoo.fr 2 Eric Jean Roy Sambatra is with the Institut Suprieur de Technologie D’Antsiranana, Madagascar ericsambatra@gmail.com impact on the inertia. A SPWRIM makes it very vulnerable to any external perturbation and also due to its intrinsic parameters, it behaves like a high-pass filter. Using these techniques also allows us to have the information in the three phases that will make most effective the detection [3]. II. DEVELOPED WFA MODEL FOR FAULTY SPWRIM A. Equation system The differential equations system (1) and (2), governing the SPWRIM can be written in vector-matrix form as: [ V ]=[R][I ]+[I ].ω . d [L] d θ +[L] d [I ] dt (1) [ V ] is the stator and rotor voltages vector, [I ] the stator and rotor currents vector, [R] the stator and rotor resistances matrix, [L] the stator and rotor inductances matrix and ω the shaft rotational speed of the machine. The equation of motion is expressed as: J d [ω ] dt f v ω = T e − T l (2) with ω = d[θ ] dt & T e = 1 2 [T ] t d[L] dθ [I ] J is the total inertia of the rotor, f v the viscous frictional torque, T e the electromagnetic torque, T l the load torque and θ the angular position. B. Winding fault modeling It is apparent that the successful simulation of an induction machine depends on the calculation of self and mutual inductances of the stator and the rotor coils. Therefore we chose the Winding Function Approach (WFA) for the calculation of their inductances. This is an effective method to study electrical machines because it uses the geometry of the machine [1]. This method assumes no symmetry in the placement of any motor coil in slots. The mutual inductance L BA between two windings A and B is given by the equation below (assume that permeance of iron is infinite)[4][5]: L BA = μ 0 rl g  2π 0 n B (θ S )N A (θ S )d θ S (3) The equation (3) is for two winding situated on the stator or on the rotor, with g the length of the airgap, θ S the angular position along the stator, l the length of stack, and r a radius 2015 23rd Mediterranean Conference on Control and Automation (MED) June 16-19, 2015. Torremolinos, Spain 978-1-4799-9936-1/15/$31.00 ©2015 IEEE 184