Research Article Control of Chaos in a Single Machine Infinite Bus Power System Using the Discrete Sliding Mode Control Technique Mohamed Zribi , 1 Muthana T. Alrifai , 1 and Nejib Smaoui 2 1 Department of Electrical Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait 2 Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait Correspondence should be addressed to Mohamed Zribi; mohamed.zribi10@gmail.com Received 30 November 2017; Accepted 27 March 2018; Published 6 June 2018 Academic Editor: Victor S. Kozyakin Copyright © 2018 Mohamed Zribi et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Under certain conditions, power systems may exhibit chaotic behaviors which are harmful and undesirable. In this paper, the discrete time sliding mode control technique is used to control a chaotic power system. Te objective of the control is to eliminate the chaotic oscillations and to bring order to the power system. Two discrete time sliding mode control (DSMC) schemes are proposed for a fourth order discrete time chaotic power system. Te frst DSMC control scheme is based on the well-known exponential reaching law. Te second DSMC control scheme is based on the recently developed double power reaching law. It is shown that the states of the controlled system converge to their desired values. Simulation results are presented for diferent values of the gains of the controllers as well as for diferent initial conditions. Tese results indicate that both control schemes work well. However, the simulation results show that the second control scheme gave better results since it was able to greatly reduce the chattering problem. 1. Introduction Chaos in power systems was observed by [1, 2] over a range of loading conditions. Chaotic oscillations in power systems are harmful and undesirable. Te increasing demand for electric power forces the power system to operate nearly close to its stability boundary. In this operating environment, a sudden disturbance can lead to a chaotic behavior [3–6]. Chaos is related to many power system instability phenomena such as voltage collapse which occurs when the power system is heavily loaded. Voltage collapse is characterized by a slow change in the operating point of the system caused by an increase in loads which results in a gradual decrease in voltage magnitudes until a sharp accelerated drop in voltage occurs. Voltage collapse can result in catastrophic blackouts [7–12]. Terefore, it is imperative to properly control the power system so that chaos is suppressed and chaotic oscillations are eliminated. Chaos suppression in power systems has received the attention of many researchers. In recent years, many control methods were applied to suppress chaos and stabilize the voltage of the power systems [13–19]. Adaptive control was proposed in [13]. Fuzzy and neural control methods were discussed in [14–16]. Linear and nonlinear state feedback con- trollers are developed in [18] for the control of the bifurcation phenomenon in a power system A passivity-based adaptive controller was used in [19] to suppress chaotic oscillations in a power system. Due to its simple implementation, good transient re- sponse, and robustness to parameters uncertainties and to disturbances, the sliding mode control technique has been applied to many nonlinear systems such as sof landing control, trajectory tracking, motor control, and power system control [20–25]. Power system chaos suppression using the sliding mode technique was proposed in the literature [26– 28]. In [26], an approach that combines time scale separation design and sliding mode control was proposed. High order sliding mode controller was reported in [27]; the controller design was based on backstepping method. As a result of the extensive use of computers in the imple- mentation of controllers, discrete time sliding mode control has generated a sizable amount or research interest. Tere is subtle diference between continuous time sliding mode control and discrete time sliding mode control. For the DSMC, the control signal is determined once in every sampling interval and it is held constant during the sampling Hindawi Discrete Dynamics in Nature and Society Volume 2018, Article ID 5758324, 14 pages https://doi.org/10.1155/2018/5758324