A fuzzy queueing based model for controlling power demand of electric vehicle charging Ulas Baran Baloglu Yakup Demir Munzur University Firat University Department of Computer Engineering Department of Electrical and Electronics Engineering Tunceli, Turkey Elazig, Turkey e-mail: ulasbaloglu@gmail.com e-mail: ydemir@firat.edu.tr Abstract—The rapid penetration of electric vehicles may lead problem of charging and discharging [6]. In another study, the to peak problems in a traditional grid so that some of the smart problem was tried to be solved only by using a genetic grid research is focused on charging strategies for electric scheduler structure [7]. The Joint Searching (JS) scheduling vehicles. The charging problem is suitable for using a queue algorithm is used with time-of-use pricing to maximize the structure, and fuzzy queueing can be implemented for this profit of the charging stations [8]. The main problem of these purpose. This paper presents a fuzzy queueing based model, studies is the high computational cost so that it was difficult to which can also control the power demand of electric vehicle obtain a practical and feasible solution. Stochastic models are charging. A charging model should guarantee that all charging computationally faster, and they are more influential in requirements can be satisfied before vehicles leaving the making decisions based on predictions [3]. In a previous charging stations. Simulation results exhibit that the proposed model decreases average waiting time of vehicles and also the study, Munoz and Ruspini also used fuzzy queueing in EV proposed model utilize charging stations better than a charging [9]. The proposed study differs than this previous traditional queueing model. study by applying the fuzzy queueing method in a different way. Keywords—Electric Vehicles; Fuzzy Queueing; Smart Grid In this study, we prefer to use fuzzy queueing in the proposed solution. Fuzzy queueing is a robust method, which I. INTRODUCTION used to model queueing systems with a fixed number of The penetration of electric vehicles (EVs) is rapidly servers, fuzzy arrival, and service rates [9]. Fuzzy queueing is increasing because of technological developments and low a method with multiple parallel servers, which have finite or carbon emission policies. Manufacturers are releasing new and infinite system capacity and the arrivals to this system is competitive models every year, and EVs are already seen as a managed by a possibility distribution [10]. The fuzzy part of the solution for global warming. Nevertheless, with this queueing has been previously analyzed and described in technological shift, some new problems arise. The electricity various studies [11] - [13]. Since fuzzy queueing model in EV infrastructure we use today is not robust for a scenario in charging process is more promising and realistic than the which a large number of vehicles want to be charged traditional queueing model, it would be useful to do research simultaneously. Due to their charging requirements, the on it [14]. integration of a vast number of EVs will be significant for the This paper describes how to model the uncertainty in power demand of electric grids. That's why some of the smart electric vehicle charging by using a fuzzy queueing based grid research is focused on charging strategies for electric model. Unlike the previous studies in the literature, in this vehicles. study not only uncertainty is modeled but also load control is The problem related to scheduling or controlling EV carried out, so that power demand of the grid is controlled charging may reduce the peak loads and the operational costs during EV charging process. Another contribution is the of a grid so that this issue have been studied by various application of a fuzzy queueing in a different way to the researchers [1], [2]. Some of them used stochastic models to vehicle charging process. It has been shown in the simulations model and investigated a fleet of EVs. Clayton copula, that the proposed method produces better results than a Gaussian copula, and non-parametric copula were used to traditional queueing method, and the proposed method utilizes model the load profile [3], [4]. Other studies in the literature charging stations better. investigated optimization methods and dynamic programming The rest of this paper is organized as follows. In Section II [5]. An improved particle swarm optimization and the genetic we explain preliminaries that are used to construct the algorithm was also combined to solve the optimization Copyright © 2017 held by the authors 53 proposed charging model and problem definition is given. In B. Fuzzy Queueing Based Model Section III efficiency of the proposed model is evaluated. We In this study, we use the fuzzy queueing model for EV finally conclude the paper in Section IV. charging. In this model  denotes arrival rate of EVs to a charging station with Poisson distribution. The fuzzy service II. THE PROPOSED MODEL time of charging station is denoted by . The proposed fuzzy There are many uncertainties in the charging process of queueing model aims to have the least load on the grid while electric vehicles when real world situations are considered. An appropriately serving EVs. The  rate is state independent optimization should be done by considering various because arrival rate does not depend on how many vehicles uncertainties, such as the number of simultaneous EVs to be are already waiting in a charging station. connected to the grid or how fast the charge should be completed. In modeling the uncertain real-world problems, the In the system there are total C charging stations, the total fuzzy queues play a significant role. load is T and the maximum allowed load per charging station is M. If the system reaches the maximum allowed load, new EV charging problem is suitable for using a queue arrivals have to wait. In the proposed queue model service rate structure. Queue structure is concerned with modeling systems and arrival rate of customers are fuzzy decision variables. where some customers wait for a service. Fuzzy queues are Thus, service rate and arrival rate are described by linguistic used to represent the situations, which are difficult for terms, such as low, moderate or high instead of probability traditional queueing methods. The EV charging process can be functions. more suitably described by linguistic terms, such as urgent, fast or slow rather than probability distributions. When there are N EVs in the system, then the rate of departure from charging stations is, A. Fuzzy Set Theory Uncertainty can be modeled with various approaches, and d = N for 0  N < C (2) one way of doing this is using the fuzzy set theory, which formulates uncertainty by incorporating the linguistic variables. Fuzzy sets have elements with degrees of membership. A triangular fuzzy number can represent a triple d = C for C  N and T  M. (3) with the following membership function: Little's Law explains the average number of customers, their effective arrival rate and service time. According to Little’s Law, expected number of EVs in the system EN is (1) defined as follows. (4) In this membership function of the fuzzy set A; L, M and H values denote low, moderate and high charging desires Let Ak denotes the number of EVs at the kth charging respectively, and L