=Paper=
{{Paper
|id=Vol-1853/p10
|storemode=property
|title=A fuzzy queueing based model for controlling power
demand of electric vehicle charging

|pdfUrl=https://ceur-ws.org/Vol-1853/p10.pdf
|volume=Vol-1853
|authors=Ulas Baran Baloglu,Yakup Demir
|dblpUrl=https://dblp.org/rec/conf/system/BalogluD17
}}
==A fuzzy queueing based model for controlling power
demand of electric vehicle charging
==
<pdf width="1500px">https://ceur-ws.org/Vol-1853/p10.pdf</pdf>
<pre>
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<M<H. This function is represented in                       station forming a queue.
Fig. 1. The triangular fuzzy number is denoted by (L, M, H)
triple, and it becomes a non-fuzzy number when all values
equal to each other.                                                                                                                        (5)


                                                                                  EN and EW values are calculated by using the Markov
                                                                               process.


                                                                                                                                            (6)


                                                                                   where A is a fuzzy set,  denotes time taken to start
                                                                               charging, and LV denotes the number of leaving EVs. LV is
                                                                               calculated as

                                                                                                                                            (7)
       Figure 1. Membership function of the triangular fuzzy set.




                                                                          54
                                                                            Simulations have been conducted to evaluate the fuzzy
                                                                        queueing based charging model. Two different types of
                                                                        charging stations were used in these simulations. The
                                                                        properties of these charging stations according to SAE
                                                                        standards are given in Table I [15]. AC Level 2 charging
                                                                        stations are used to utilize fast charging.
                                                                            In the simulation environment, there are total 20 charging
                                                                        stations formed by 15 AC Level 1 charging stations and 5 AC
                                                                        Level 2 charging stations. The total number of electric
                                                                        vehicles is 200, charging utilization is 100, and inter-arrival
               Figure 2. Entities of the problem space.                 time is taken as 0. Service time depends on the state of charge
                                                                        of electric vehicle batteries, and service rate is determined by
   Finally, expected waiting time in the queue is denoted as            the SAE charging properties.
EW and expected occupation time for a charging station is
denoted as E[S]. These values are calculated as follows,                    In the first simulation environment, the proposed model is
                                                                        compared with the traditional queueing model according to the
                                                                        average waiting time. Average waiting time of each EV is
                                                            (8)         calculated by dividing total waiting time by the total number
                                                                        of vehicles. As it is seen in Fig. 3, it can be seen that the
                                                                        proposed model achieved a lower average waiting time than
                                                                        the traditional model. As the number of EVs increased, the
                                                             (9)        performance gap also increased. This result indicates that
                                                                        proposed model can better organize the vehicle charging
                                                                        process. Finally, a sudden increase has been observed in the
C. Problem Definition                                                   average waiting time for both models when the number of
                                                                        EVs is greater than 140. The reason is due to the resource
    EV charging problem can be defined as finding a balance             limitations, which brings a difficulty to the both models in
between the grid load and total waiting time of EVs in the              making an optimization.
queue of stations. Grid load shouldn’t be increased too much
to cause peaks, and total waiting time of an EV shouldn’t                   In the second simulation environment, the number of EVs
affect the daily routines of EV owners. As a result of a limited        served by each charging station is analyzed for both models.
number of charging stations and limited allocated power                 There are again 200 EVs and 20 charging stations in the
resource, the problem can be formulated as finding the best             simulation environment. In Fig. 4, it is observed that the
resource allocation to organize the charging process.                   proposed model utilizes charging stations in a better way than
                                                                        the traditional queueing model. In this simulation, a more
    As illustrated in Fig. 2 there are three entities in this           homogeneous workload for charging stations also indicates
problem: EVs, stations and the utility. Charging stations aim           that the available resources are used in a more efficient way,
to serve the largest number of EVs while EVs aim to satisfy             which is also among one of the goals of this study.
their charging demands. As the total number of charging
stations is limited, only a portion of EVs being charged
simultaneously in the charging stations. A model should                               TABLE I.      SAE CHARGING PROPERTIES
guarantee that all charging requirements can be satisfied                Type             Voltage (V)
                                                                                                           Peak            Average Charging
before EVs leaving the charging stations. Finally, the priority                                            Current (A)     Time (Hour)
of the utility is preventing peak occurrences in the grid.               AC Level 1       120              16              7-17
                                                                         AC Level 2       240              31              3-7
                  III.   SIMULATION RESULTS
    In the simulation environment, charging stations have the
first come first served (FSCF) principle, and jockeying is not
allowed for the EVs as stations can be geographically away
from each other. Charging stations work simultaneously, and
priority is assigned to EVs according to their charging
demands. There are two assumptions for the simulation
environment, which simplify the construction of the
simulation environment and do not affect the outcome of this
study.
       EV batteries are assumed to be charged at the same
        rate.
       All EV batteries are assumed to have the same
        capacity.
                                                                                      Figure 3. Comparison of average waiting time.

                                                                   55
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