International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 21 (2017) pp. 11323-11329 © Research India Publications. http://www.ripublication.com 11323 Using the Least Squares Methods for Detecting Short Circuit Faults in Electrical Systems Abderrezak Metatla Department of Mechanical engineering, August 20, 1955, Skikda University, Algeria, Bp 26 route El Hadaiek, Skikda Algeria Orcid Id: 0000-0002-2061-7863 Samia Benzahioul Department of Technology, August 20, 1955, Skikda University, Algeria, Bp 26 route El Hadaiek, Skikda Algeria Orcid Id: 0000-0001-8076-3355 Ridha Kelaiaia Department of Mechanical engineering, August 20, 1955, Skikda University, Algeria, Bp26 route El Hadaiek, Skikda Algeria Orcid Id: 0000-0003-3626-0288 Abstract This paper presents the technique for estimating parameters based on the method of least squares with and without forgetting factor is presented in this work. This technique is applied to power systems with or without faults. An evaluation in numerical simulation of a coil with iron core with or without fault short-circuit of turns, allows discuss the quality of the estimation of physical parameters of the coil. Keywords: fault, parameters estimation, electrical systems, least square, detection. INTRODUCTION Systems identification is a large area which includes different approaches. This difference is due, firstly, to the family of models: model knowledge or behavior, parametric or non- parametric models, deterministic or stochastic models and secondly, to operating contexts: online or offline, open or closed loop, with or without control of the input signals. The aim of this work is to apply some approaches of parametric identification on line of dynamic processes, in particular, the method of least squares with or without forgetting factor [1] for the electrical systems. The iron core coil is the basic structure of all the electrical machines. Therefore, it is important to test our approach on this system. We show that the identification methods used to build functioning and dysfunction models useful for applications in the field of detection and diagnosis of faults. This paper is organized as follows: In Section2, we present a mathematical presentation of the coil. In Section3, we present a least squares method to identify the parameters of the proposed model. In Section4, we present a least squares with factor forget to improve the speed of convergence of the proposed algorithm. In Section5, we present a model with fault, where we take into account of the failure of short circuit turns. In Section6, we conclude the paper by summarizing the main contribution and at the same time we provide some remarks. . MODEL OF THE COIL The coil iron core contains two magnetic and electric circuits when the coil is crossed by an electric current, it creates losses in the two circuits: in the magnetic circuit by hysteresis and in the electric circuit by eddy current. When these losses are negligible the coil is represented by two resistors and an inductor, the schemes of the coil can be illustrated in (figure 1) [2]. Figure 1: The iron core coil The use and simplification of mesh and Kirchhoff laws gives the following model: () () . .() . () di t du t a bi t c ut dt dt    (1) Such as, p p r l r r a * ) (   , r b  and p r l c  r p r l um m i i1 i2