Electric Power Systems Research 104 (2013) 87–92 Contents lists available at ScienceDirect Electric Power Systems Research jou rn al hom e page: www.elsevier.com/locate/epsr Prediction of flashover voltage of insulators using least squares support vector machine with particle swarm optimisation Sid Ahmed Bessedik a,∗ , Hocine Hadi b a Electrical Engineering DPT, Univ. Ammar Telidji Laghouat, P.O. Box 37G, Laghouat 03000, Algeria b Electrical Engineering Laboratory of Oran (LGEO), Univ. of Sciences and Technology of Oran, Mohamed Boudiaf USTO, BP1505 El Mnouar Oran, Algeria a r t i c l e i n f o Article history: Received 4 November 2012 Received in revised form 18 June 2013 Accepted 21 June 2013 Available online 21 July 2013 Keywords: High voltage insulators Polluted insulators Critical flashover voltage Least squares support vector machine (LS-SVM) Particle swarm optimisation (PSO) a b s t r a c t This paper describes the application of least squares support vector machine combined with particle swarm optimisation (LS-SVM-PSO) model to estimate the critical Flashover Voltage (FOV) on polluted insulators. The characteristics of the insulator: the diameter, the height, the creepage distance, the form factor and the equivalent salt deposit density were used as input variables for the LS-SVM-PSO model, and critical flashover voltage was estimated. In order to train the LS-SVM and to test its performance, the data sets are derived from experimental results obtained from the literature and a mathematical model. First, the LS-SVM regression model, with Radial Basis Function (RBF) kernel, is established. Then a global optimiser, PSO is employed to optimise the hyper-parameters needed in LS-SVM regression. Afterward, a LS-SVM-PSO model is designed to establish a nonlinear model between the above mentioned characteristics and the critical flashover voltage. Satisfactory and more accurate results are obtained by using LS-SVM-PSO to estimate the critical flashover voltage for the considered conditions compared with the previous works. © 2013 Elsevier B.V. All rights reserved. 1. Introduction The reliability of the power system mainly depends on the environmental and weather conditions which cause flashover on polluted insulators leading to system outages. A major problem of insulation systems is the accumulation of airborne pollutants due to natural, industrial or even mixed pollution, during the dry weather period and their subsequent wetting, mainly by high humidity. At the coastal areas the high voltage insulators are affected by salt particles that settle on the insulators surfaces. These particles are not dangerous in its dry condition but with high environmental humidity or drizzle rain conditions the salt can absorb the water and form a thin film with high conductivity. This layer gives an ideal path for the leakage current to pass through between the high voltage side and the ground side. The conductivity of this layer depends on the type of salts which this layer consists of [1,2]. High failure rate of polluted insulator due to the flashover has been found near the coastal areas [3]. This problem was the motivation for the installation of a test station performs laboratory tests on artificially polluted insulators. Several researches concerning the insulators performance under pollution conditions have been conducted, in which ∗ Corresponding author. Tel.: +213 553038614; fax: +213 41425509. E-mail address: ahmed 7b@yahoo.fr (S.A. Bessedik). mathematical or physical models have been used [4–7]. Experi- ments have been conducted [8–10]. And simulation programmes have been developed [11,12]. A variety of prediction models have been proposed in the liter- ature. Artificial Neural Networks (ANNs) models are developed for the qualitative control of the insulators by determining important parameters (such as leakage current or the critical flashover volt- age) [13–16], an Adaptive Neuro-Fuzzy Inference System (ANFIS) [17], and Fuzzy Logic (FL) model [18] have been applied in order to estimate the critical flashover voltage on polluted insulators. Recently, SVM has been used as a popular algorithm developed from the machine learning community [19]. Due to its advan- tages and remarkable generalisation performance (i.e. error rates on test sets) over other methods, SVM has attracted attention and gained extensive applications. As simplification of traditional SVM, Suykens and Vandewalle have proposed the use of the least squares support vector machines LS-SVM [20], LS-SVM encom- passes similar advantages as SVM, but its additional advantage is that it requires solving a set of only linear equations (linear programming), which is much easier and computationally more simple. The SVMs and LS-SVMs are called uniformly as SVMs for the convenient narration. The parameters in regularisation item and kernel function are called hyper-parameters in SVMs, which plays an important role to the algorithm performance. Iterative gradient- based algorithms rely on smoothed approximations of a function. So, it does not ensure that the search direction points exactly to an optimum of the generalisation performance measure which is often 0378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2013.06.013