WIRELESS COMMUNICATIONS AND MOBILE COMPUTINGWirel. Commun. Mob. Comput. 2015; 15:1049–1065
Published online 11 August 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.2508
SPECIAL ISSUE PAPER
Multi-priority queuing for electric vehicles charging atpublic supply stations with price variationDhaou Said1,2*, Soumaya Cherkaoui1 and Lyes Khoukhi2
1 Department of Electrical and Computer Engineering, Université de Sherbrooke, Sherbrooke, Canada2 ICD/ERA, CNRS UMR-STMR 6279, University of Technology of Troyes, France
Dhaou Said, Department of Electrical and Computer Engineering, Université de Sherbrooke, Sherbrooke, Canada.E-mail: [email protected]
1. INTRODUCTION
Electric vehicles (EVs) are increasingly becoming popularas a result of many factors among which the concern ofmany road users with greenhouse emissions and the recentadvances in EVs engineering that made them more per-forming. The popularity of EVs is expected to grow evenmore in the next years as we see municipalities adoptingthe technology for their public transportation fleets andwith charging stations made available at many public park-ing areas. A large adoption of EVs poses, however, manychallenges from the point of view of electricity demandmanagement. In fact, EVs charging operations will beone of the most challenging issues for demand responsesystems in the smart grid [1]. This is because the load intro-duced by the charging of one vehicle in a neighborhoodmay be equivalent to the one of an entire new household inthe area [2].
The vehicle-to-grid (V2G) interface within the smartgrid has to offer the capability to manage the charging loadof EVs wisely both according to demand and by provid-
ing smart functionalities to improve EV charging processexperience for users [3,4]. One of the most challengingissues in EVs charging management is how to satisfy EVsdemand adequately, to meet users’ expectations, in all gridsituations while ensuring grid stability. EV charging pro-cess has to be managed in a way to ensure grid operationefficiency, especially at peak load times, while loweringcharging times for EVs to maintain users’ satisfaction.
Charging time is an important factor to consider from theusers’ point of view, because charging an EV takes consid-erably longer than a regular vehicle, that is, tens of minutesat least [1]. The charging time is composed of two param-eters: the waiting time and the service time, which in turndepends on the EV state of charge (SoC) needed. Givena SoC, the service time will only depend on the type ofelectric vehicle supply equipment (EVSE) (charging sta-tions) used. The waiting time is thus a factor that has tobe reduced in each EV public supply station (EVPSS), andtherefore, scheduling the charging of EVs at available sta-tions in a way to minimize their waiting time is a key toachieving users’ satisfaction.
Multi-priority queuing EV charging with price variation D. Said, S. Cherkaoui and L. Khoukhi
In this work, we consider the problem of EVs charg-ing time optimization in EVPSS using queuing modeltechniques. In particular, we propose an optimized charg-ing process for electric vehicles at EVPSS when the loaddemand is expected to be high. For this, we consider amodel where EVs communicate to the smart grid their indi-vidual EV charging demand information before the plug-inphase, that is, while the EVs are on the roadside, to allowthe grid to manage adequately their charging process.
Our contributions in this paper are threefold. (i) Wepresent two analytical formulations of the EV chargingproblem. The first one is based on a multi-service queuingmodel. This model takes into account a number of con-straints including the number of EVPSS with their chargingcapacity, the arrival process of vehicles with their initialSoC, and the vehicles required charge level at the end ofthe process. The second mode is an extension of the firstone. It is based on cut-off priority queuing and consid-ers a realistic mobility model with an EV priority leveladded to the constraints considered in the first model. (ii)We also propose two algorithms: the first, called best avail-able EVPSS (BA-EVPSS), is used for assigning vehiclesto EVPSS based on the defined constraints and supposesprior EV/smart grid communication when EVs are on road;the second algorithm, called advanced BA-EVPSS, takesinto account a realistic mobility scenario with a time-of-usepricing (TOUP) variation. This algorithm can be used bythe smart grid not only to satisfy EVs demand but also tofurther grid stability. (iii) Finally, we demonstrate that theproposed algorithms can effectively manage EVs chargingdemand within the defined constraints while consideringrealistic EV charging characteristics.
The remainder of the paper is organized as follows.In Section 2, we present the related work. We formu-late a multi-server queuing model of EVs charging pro-cess in Section 3. EVs charging time and EVs waitingtime when considering a queuing model for multi-EVPSSare analyzed in Section 4. In Section 5, we present ourmulti-server priority queuing model. The cut-off disciplinedescription of EVs queues is formulated in Section 6, andfairness and complexity analysis are presented in Section 7.The performance evaluation of EVs charging at EVPSS interms of charging time is presented in Section 8. Finally,Section 9 concludes the paper.
2. RELATED WORK
Existing related works can be classified into two classes:(i) stochastic modeling for EV charging processes and (ii)V2G protocols and standardization for EV/EVSE commu-nication. In the first class of works, the authors in [2]describe a tool based on a stochastic model for distribu-tion grid planning, which provides a characterization ofpossible grid operation conditions, voltage profiles, branchloading, grid peak power, and energy losses. Lojowska etal. present in [3] a Monte Carlo simulation approach for thederivation of the system load due to EVs based on a model
representing real vehicle commuting patterns. In these twoworks, EVs charging time optimization according to con-straints associated with each EV is not addressed. In [4],an EV charging station is represented using mathemati-cal models to derive the parameters needed for chargingstations planning. Nevertheless, parameters such as EVspriority or maximum charging time for each individualEVs are not taken into account in the scheduling process.
In the second class of works, authors in [5,6] and [22]made a good summary of current standard protocols andrelated architectures for EV and grid interaction. In [7],the basic principles of standard V2G communication inter-faces currently under specification in the ISO/IEC arepresented, with a focus on control communication butwithout a regard to administrative data, especially for V2Gintegration because EVs are still on the road. In [8], Rutheet al. present a generic V2G information model allowingmutual charge scheduling negotiations between EVs andgrid operators. The work discusses a system model withtheoretical concerns without treating a specific chargingmode (slow, rapid, or fast) as in realistic situations. More-over, the work does not consider the case where EVs needto communicate with the grid to know the most suitableEVPSS in terms of waiting time and cost.
In this work, we present optimization models of EVscharging process in terms of charging time minimizationwhile taking into account constraints including a ran-dom arrival of vehicles with a random initial value ofEVs SoC and maximum SoC. Furthermore, realistic EVSEcharacteristics were used.
3. M/M/s MODEL OF ONE EVPUBLIC SUPPLY STATION
In this section, we present a basic queuing theory that willbe used to represent our EV charging model with somedefined constraints related to realistic situations of EVscharging process.
Figure 1 shows the system considered to represent EVscharging process. The input data are the EVs in need ofcharging, and the output data are the EVs with the requiredSoC. Each EVPSS is considered a multi-server queue withS identical servers, each operating with an exponential ser-vice rate �. The EVs arrival process is assumed to bePoisson with arrival rate �.
Figure 1. Schematic view of our EV charging model for oneEVPSS.
D. Said, S. Cherkaoui and L. Khoukhi Multi-priority queuing EV charging with price variation
Figure 2. The state transition diagram.
In general, every EV that arrives can immediately enterservice if there is an available plug-in socket in the EVPSS.If all servers are occupied, then the EV has to wait untila plug-in socket becomes available. The scheduling disci-pline adopted is first-come-first-serve. The number of EVsis assumed to be high.
In principle, any practical queuing process tends toderive its major results with Markov chains [9–12] byincorporating information in the state description. In thiswork, each state of the chain corresponds to the numberof EVs in the queue, and state transitions occur when newEVs arrive or an EV reaches its required SoC and departs.
We use the birth-death process as a stochastic model todescribe the evolution of our system. The state transitiondiagram is represented in Figure 2. The model has twocases. The first case is where the number of plugged-in EVsis k � s; the overall completion rate is then k�. The sec-ond case is where the number of plugged-in EVs is k � s;the entire plug-in sockets are occupied, and the completionrate is s�.Definition: a stochastic process with state space� D f1, 2, 3, : : :g is said to be a Markov chain [10,13,14] if
P .XnC1 D j jXn D i , Xn�1 D xn�1, : : : , X0 D x0/
D P .XnC1 D j jXn D i /(1)
where Xn is a random variable that represents the value ofthe chain at step n.
The transition probabilities function with time homoge-nous is defined as
p.m, mC n/ D pij.0, n/ � p.n/ij , 8m (2)
and the transition matrix is defined as
P D Œ pij� (3)
Considering the equations and the state transition diagramgiven earlier, the correspondent transition matrix is
PD
2666666666666664
�� � 0 0
� �.�C�/ � 0 0
0 2� �.�C 2�/ � 0 0
0 0 3� �.�C 3�/ � 0 0
�
� � � � � .... � .... �
�
� � � � s� �.�C s�/ �
� � � � � .... � .... �
3777777777777775
(4)
The stationary condition related to our Markov chainmodel is given by the following:
� � P D 0 (5)
where � D Œ�0,�1, : : : ,�N � is the vector of stationarydistribution. N is the state number.
To solve this Markov chain model, we have to solvebalance equations in each state, and we use the total prob-ability to solve the initial condition �0.State 0: the leaving rate due to arrivals is �0�. The enteringrate to state 0 due to departures from state 1 is �1�.
�1 D�
��0 (6)
State 1: the leaving rate of state 1 is .�C�/�1. The enteringrate to state 1 due to arrivals from state 0 is �0�, and theentering rate due to departures from state 2 is 2��2 wherethe number two (2) means that they are two EVs in EVPSSsimultaneously.
.�C �/�1 D ��0 C 2��2 (7)
Using (6) and (7), we obtain the following:
�2 D1
2
��
�
�2
�0 (8)
The balance equation for state 2 is expressed as follows:
.�C 2�/�2 D ��1 C 3��3 (9)
Using Equation (5) and (6), we obtain the following:
�3 D1
3 � 2
��
�
�3
�0 (10)
The general recursive form of the stationary distribution(state k) is as follows:
Multi-priority queuing EV charging with price variation D. Said, S. Cherkaoui and L. Khoukhi
The total probability condition is as follows:
s�1XkD0
1
kŠ
��
�
�k
�0 C
NXkDs
�1
sŠ
�k�s 1
sŠ
��
�
�k
�0 D 1 (12)
where N is the number of states en S is the number of plug-in in EVPSS.
The �0 expression can be easy derived by simplifyingEquation (12) as follows:
�0 D
s�1XkD0
1
kŠ
��
�
�k
C
NXkDs
�1
sŠ
�k�s 1
sŠ
��
�
�k!�1
(13)Thus, the behavior of the Markov chain is completelycharacterized once its transition matrix P, the transitiondiagram, and the initial condition �0 are given.
The mean queue length is given in [10] by
E.Lq/ D
NXkDS
.k � S/ � �k (14)
and the mean waiting time in the queue is givenby [9,10]
In this section, we suppose that our EV charging sys-tem is composed by m EVPSS, where each one isformed by a number Si.i D 1 : : :m/ of plug-in sockets.Figure 3 illustrates our multi-EVPSS model as a parallelM/M/s queues.
Same to the last part, our model is completely character-ized by given the transition matrix. We use a form of blockmatrix notation to highlight the transition matrix of ourmulti-EVPSS model PEVPSS and to allow a good saving ofcomputation effort. Each Pi represents the transition matrixof M/M/si given by Figure 3.
D. Said, S. Cherkaoui and L. Khoukhi Multi-priority queuing EV charging with price variation
Figure 4. Schematic view of information exchange between thesmart grid and EVs when considering the BA-EVPSS algorithm.
PEVPSS D
2666666666664
P1 0 0 0 : : :
0 P2 0 0 : : :
0 0 P3 0 0..
�
�
�
0 0 0 0 0.. 0 0 0 Pm
3777777777775
(16)
Alike Equation (5), we have
�EVPSS � PEVPSS D 0 (17)
where �EVPSS D��1
EVPSS,�2EVPSS, : : : ,�m
EVPSS
�denotes
the vector of stationary distribution of multi-queue modeland �kD1:::m
EVPSS is the stationary distribution vector of eachone queue model.
The proposed model assumes that an EV that needs tocharge its battery can communicate its position and itsactual SoC to the smart grid to know the nearer availableEVPSS. By running BA-EVPSS algorithm, the smart gridcan find out the available EVPSS in terms of the small-est waiting time in each EVPSS. This algorithm takes intoaccount the initial SoC and the initial position of each EVand updates EVPSS state after any EV satisfaction.
Figure 4 shows the exchange of information between thegrid and each EV while the EVs are on the road. Initially,each vehicle sends its profile, that is, position and SoC, tothe smart grid. On the basis of these input data, the smartgrid executes the BA-EVPSS algorithm and sends to theEVs the information about the best available EVPSS.
5. MULTI-SERVER PRIORITYQUEUES
The proposed EV charging model process can be enhancedusing a multi-server priority queue concept. In this section,we adopt the multi-EVPSS model presented in Sections 3and 4, and we improve it by including a priority strat-egy that includes a TOUP model while taking mobility ofvehicles. The proposed enhancements will enable energycost (i.e., price cost) monitoring over time and adjust theEV charging according to the EV charging need and costconstraints.
We focused on large variations of the charging time thathas a major impact on the effectiveness and cost of thecharging process at EV public stations. Our objective is
Multi-priority queuing EV charging with price variation D. Said, S. Cherkaoui and L. Khoukhi
Figure 5. Markov chain illustration of the case of two priority classes .H, L/ in multi-servers for one EVPSS.
to improve EVs satisfaction in terms of charging serviceby achieving waiting time reduction and charging costminimization.
The proposed model is based on using three importantparameters: (i) individual EV position, (ii) charging pri-ority, and (iii) the EV price constraints information; allof which are communicated to the smart grid before theplug-in phase, that is, while the EVs are on the roadside.
In the following paragraphs, we present the three modelsproposed in this work.
5.1. Priority queuing strategy
A priority-based system having separate buffers to accom-modate high-priority (HP) and low-priority (LP) incomingEVs was adopted as presented in Figure 5. Indeed, a sim-
D. Said, S. Cherkaoui and L. Khoukhi Multi-priority queuing EV charging with price variation
Figure 7. Schematic view of our cut-off priority EV charging model for one EVPSS.
ple case of two priority classes, high .H/ and low .L/,is considered, with respectively an arrival rate �H and�L and an exponentially distributed sizes the rates �H
and �L.Figure 5 illustrates a Markov chain of the charging
system model, which states the number of HP and LPjobs; hence, this chain grows infinitely in two dimen-sions. Indeed, we observe that HP jobs simply see anM/M/s queue, and thus, their mean delay is well-known.LP jobs, however, have access to either an M/M/k .k DS : : : 1/ or no server at all, depending on the number ofHP jobs. As a result, the LP class will lead to a largewaiting delay.
In order to take into account priority, we will refine ourstrategy description in Section 6 taking into account twotypes of interaction, namely smart grid EV and smart gridEVPSS.
5.2. TOUP price model use
The price variation model is very important in such casestudy. In fact, in many research works, various time-differentiated pricing models have been proposed [15,16],such as real-time pricing, day-ahead pricing, TOUP,critical-peak pricing, and inclining block rates.
Research findings [17] indicate that compared withother pricing models, TOUP provides more incen-tives for customers to shift load to the less expen-sive (hence loaded) hours. Thereby, we use the TOUPmodel throughout this study to give incentives for arriv-ing EVs to go to the EVPSS with low price, whichwill improve the EVs load balancing to reduce EVPSSbusy state.
Table I. The estimated periods for all EVs to join any EVPSS.
EV1 EV2 � � � EVJ � � � EVN
EVPSS1 T 11 T 2
1 � � � T J1 � � � T N
1
EVPSS2 T 12 T 2
2 � � � T J2 � � � T N
2
� � � � � � � � � � � � � � � � � � � � �
EVPSSi T 1i T 2
i � � � T Ji � � � T N
i
� � � � � � � � � � � � � � � � � � � � �
EVPSSm T 1m T 2
m � � � T Jm � � � T N
m
5.3. Mobility model
Without losing generality, we consider a scenario as illus-trated in Figure 6, where a number of roads (e.g., 4)allow accessing part of a town as illustrated by the cir-cle. We consider that N EVs can get through these roadsto m EVPSSs located in this part of the city, which cov-ers a certain area (e.g., 4 km� 4 km). All vehicles aretraveling with a speed that cannot exceed a certain value(e.g., 50 km/h). We assume EVs, the smart grid, andEVPSSs can communicate with each other while EVs areon the road and that EVs communicate their position,SoC, and priority level to smart grid when they are onthe roadside.
We suppose that the time needed by any EV enter-ing the town to reach any EVPSS can be calculated.This calculation is today possible with most navigationtools that can easily calculate time to destination givena current position and traffic conditions. This time dura-tion for vehicle J to reach EVPSS i is noted TJD1:::N
iD1:::m ,where N is number of EVs and m is the numberof EVPSSs.
This time information, which is presented as in Table I,will be used by smart grid as a parameter to decide whichEVPSS can best serve a particular EV.
6. CUT-OFF DISCIPLINE FORM/M/s QUEUE
Using the three parameters (priority, price, and mobil-ity) modeled as described in Section 5, the proposedmulti-server priority queues model is a Markov chain witha cut-off discipline priority queues. Figures 7–9 describethe proposed charging model for one EVPSS.
Indeed, when arriving, EVs are placed in differentqueues of EVPSS, each of which has a different servicepriority; the queues discipline is preemptive. In this work,LP EVs receive service only when no HP EVs are waiting,
Figure 8. Cut-off priority threshold for any EVPSS.
Multi-priority queuing EV charging with price variation D. Said, S. Cherkaoui and L. Khoukhi
Figure 9. The state transition diagram for one EVPSS.
Table II. Notation for our cut-off priority queuing model.
Notation Description
NH The EV number in the HP queueNL The EV number in the LP queue�H The arrival rate into the HP queue�L The arrival rate into the LP queue
� D �H D �L Processing or service rate for an EV�
1�
is the mean service time /
n The number of busy plug-in sockets in EVPSSS The number of plug-in sockets in EVPSSS0 The cut-off level for admission of LP EVs in charging service�c
n The steady-state probabilities with cut-off considerationE.WH/ The mean waiting time for an EV in the HP queueE.LqH/ The mean HP queue lengthE.WL/ The mean waiting time for an EV in the LP queueE.LqL/ The mean LP queue length
but an LP EV that is receiving service is not interruptedif an HP EV arrives and all servers are busy. As a result,our model presents two EV categories and a first-in-first-out discipline for each category. The Table II gives us thenotation for our cut-off priority queuing model.
Let us consider the two priorities levels (HP and LP)and a total of S plug-in sockets (servers) in the EVPSS(Figure 7). We define a cut-off level of S0 for admission ofLP EVs according to the following discipline:
- For the LP EVs: (i) Serve an arriving LP EV if andonly if fewer than S0 plug-in sockets are occupied;otherwise, place it in the queue. (ii) Serve an LPEV from the queue whenever one of S0 busy plug-insockets becomes free.
- For the HP EV: An HP EV enters charging serviceimmediately unless all plug-in sockets are busy, inwhich case it can be queued.
Under this discipline, we preempt the HP charging servicerelative to the LP one in order to serve arriving HP EVs.Thus, an arriving LP EV is kept waiting if the num-ber of busy plug-in sockets when it arrives is above aspecified cut-off level S0 (Figures 8 and 9). The unoc-
cupied plug-in sockets are kept free for subsequent HPEVs arrivals.
We define the workload parameters as follows:
� D �L C �H ,�H D �L D �,
�L D �L=�, �H D �H=� and � D �H C �L
In the EVSS, let n be the number of busy plug-in sockets.If n < S0, no EVs of either priority wait, and all arriv-
ing EVs for both priorities (HP and LP) are admitted toimmediate charging service.
If S0 � n < S, only HP EVs are admitted, and arrivingLP EVs are placed in the queue. Waiting EVs are servedfrom the queue, in first-in-first-out order, whenever thenumber of busy plug-in sockets gets reduced to S0 � 1 bythe completion of service for a previous EV. We use threeparameters to describe our cut-off priority model; n, NH
and NL, which are defined in Table I. Figure 9 describes theproposed cut-off discipline.
Multi-priority queuing EV charging with price variation D. Said, S. Cherkaoui and L. Khoukhi
Figure 10. The multi-server cut-off priority queues model.
The mean length of the LP queue is given by
E.LqL/ D �LE.WL/ (33)
Equations (18)–(33) detail the model illustrated inFigures 7–9, which are presented for one EVPSS. For ourmulti-server cut-off priority model presented in Figure 10,we adopt the same idea used in the Section 4 to allow agood saving of computation effort. We use a form of blockmatrix notation to highlight the waiting time and the cut-off threshold vectors for all EVPSS in our multi-EVPSSmodel, which are given by the following:
Vect_WL D ŒE.WL/iD1:::m� (34)
Vect_WH D ŒE.WH/iD1:::m� (35)
Vect_CutOff DhS0
iD1:::m
i(36)
By the waiting time vectors given by Equations (34)and (35), our model manages the charging process for allEVs. Indeed, for each EV requesting the charging service,the smart grid selects the EVPSS that has the reducedaverage waiting time. The smart grid also controls thecongestion of each EVPSS with the dynamic update ofthe cut-off threshold given by Equation (36) to promoteor not more HP EVs in one EVPSS compared with theother. Indeed, after receiving the first message from an EVrequesting the charging service, the smart grid calculatesthe waiting time for each EVPSS and selects the best onefor the EV according to its mobility scenario and its prior-ity level and its price threshold fixed by each EVSS in thebeginning. After any EV response, the smart grid operatesa dynamic cut-off priority threshold parameter updatefor all EVPSSs to balance the number of EV betweenall EVPSS and to decrease the EVPSS congestion. Thisaction improves the regulation and grid stabilization.
We adopt for our cut-off priority model the followingalgorithm, which takes account of the EV priority level
D. Said, S. Cherkaoui and L. Khoukhi Multi-priority queuing EV charging with price variation
and the price politics doted in each charging period. Addi-tionally, the algorithm takes into consideration the mobilitymodel presented in Section 5, by using the initial SoC andinitial position of each EV, and updates EVPSS state (HPqueue length, LP queue length, cut-off vector) after eachEV satisfaction.
7. FAIRNESS AND COMPLEXITYANALYSIS
In our EV charging system, we aim at a fair schedul-ing of EVs based on the arrival of requests for serviceto the smart grid and on the priority of the requestingEVs. The fair scheduling of EVs charging in EVPSSis performed according to the priority disciplines. Thefirst-come-first-serve method is adopted, where the EVsarriving with the same priority are treated in the orderof arrival.
From the description of our two algorithms, the BA-EVPSS and advanced BA-EVPSS, we can see that thecomplexity is in the order of O.n/.
Figure 11 illustrates a schematic view of informa-tion flow patterns between the smart grid and EVs byconsidering the advanced BA-EVPSS algorithm. Indeed,added to the position and SoC of EV, we supposethat each EV communicates the priority level and priceconstraints information to the smart grid before theplug-in phase.
8. PERFORMANCE EVALUATION
In this section, simulation results and discussions arepresented to highlight the performance of our two EVcharging algorithms. We used MATLAB to perform thesimulations.
The EVs arrival (to the city) flow variation is modeledby Poisson distribution. We assume that all EVPSS areequipped by a level 3 plug-in, which is the most rapid EVcharger. After the end of the overall charging time duration,all vehicles should be satisfied. The parameters for our EVscharging process are generated as follows:
Multi-priority queuing EV charging with price variation D. Said, S. Cherkaoui and L. Khoukhi
Figure 11. Schematic view of information flow patternsbetween the smart grid and EVs and EVPSS by considering the
advanced BA-EVPSS algorithm.
The EV number is 1000. The initial EV SoC is a uniform distribution between
1% and 90%.
The 1% of EV SoC is a sufficient value to arrive to anearest EVPSS.
The EVPSS number is 20. The number or socket plug-in in each EVPSS is a
random value between 1 and 10. The EV SoC maximal is 7 kW. The charging rate in each EVPSS is 20 kW/h, and the
maximal time for EV to be full charged is 20 min. � D �H D �L D 1=3; arrival intensity. � D �H D �L D 1=50; service intensity.
For mobility modeling, we considered a scenario of fourroads that allow access to part of a town having an areaof 4 km� 4 km where the EVPSSs are placed randomly.All vehicles are traveling with speeds that cannot exceed50 km/h.
0 1000 2000 3000 4000 5000 60000
10
20
30
40
50
60
Time (s)
EV
s
Figure 13. Average queuing length variation.
0 100 200 300 400 500 600 700 800 900 10000
10
20
30
40
50
60
70
80
90
EVs number
Initi
al E
VSoC
(%
)
Figure 12. Initial EV state of charge (one simulation for 1000 EVs).
D. Said, S. Cherkaoui and L. Khoukhi Multi-priority queuing EV charging with price variation
0 1000 2000 3000 4000 5000 6000 70000
100
200
300
400
500
600
700
800
900
1000Arrivals and departures flow
Average time (s)
EV
s
EV arrival time
EV departure time
Figure 14. Arrivals/departures flow (simulation for 1000 EVs).
Two sets of simulations were performed. First, we ransimulations without considering vehicles priority, and sec-ond, we performed simulations considering two prioritylevels for EVs.
For the first set of simulations, Figure 12 shows anexample scenario of the initial average EV SoC of a simu-lation, which takes a random value between 1% and 90%.Depending on the initial SoC value and the EV position,the smart grid selects the suitable EVPSS. We assume thatan EV always consumes the energy with its maximumpower limit until its performance threshold is satisfied. Thesimulations were run 50 times, and the average values foreach EV were taken.
Figure 13 shows the average queue length variationduring the whole charging process operations for 1000
vehicles. The maximum average EVs number in the queueis under 60 EVs. It is clear that our charging process canalso be seen as a form of scheduling algorithm used by thesmart grid to manage grid power.
Figure 14 shows the average arrival time for each EVcorresponding to the blue continuous curve comparedwith its departure time highlighted by the red dash. Weobserve that the departure time is sensitive to the num-ber of arriving EVs, which are characterized by randompower demand. This power demand is proportional tothe load time. For each EV, the departure time dependson the charging time of all EVs that joined the sameEVPSS before it. This is why the departure time becomesincreasingly large.
Figure 15 shows an example scenario of the wait-ing time of EVs depending on the number of availableplug-in socket in EVPSS. We observe that the averagewaiting time is sensitive to the number of plug-in sock-ets in each EVPSS. In addition to its non-complex timeoperation, it is clear that our BA-EVPSS algorithm fol-lows inversely the number of plug-in sockets variation inorder to lessen the individual waiting time for each EV.The BA-EVPSS algorithm picks up the first EVPSS thathas the smallest average waiting time and communicatesits information to the EV. In the scenario that is illustratedin Figure 15, we observe that the smart grid chooses thethird EVPSS that has 10 plug-in sockets to respond to theEV demand.
In what follows, we study the charging time of theproposed BA-EVPSS algorithm compared with that of R-EVPSS. In R-EVPSS algorithm, an EVPSS is selectedaccording to its queue length; the arriving EV is directedto the EVPSS that has the smallest EV number in its queuewithout taking into account the cumulative EV chargingtime needed by all EVs in each queue.
0
2000
4000
EVPSS number
Tim
e (s
)
0 2 4 6 8 10 12 14 16 18 200
5
10
Plu
g-in
soc
ket
Waiting time In each EVPSS
number of plug-in socket in each EVPSS
Figure 15. Waiting time in each EVPSS versus plug-in socket number for one example simulation.
Multi-priority queuing EV charging with price variation D. Said, S. Cherkaoui and L. Khoukhi
100 200 300 400 500 600 700 800 900 1000
7
8
9
10
11
12
13
EV number
Ave
rage
tim
e (m
in)
BA-EVPSS waiting time
R-EVPSS waiting time
Figure 16. Average waiting time comparison between BA-EVPSS and R-EVPSS algorithms.
Figure 17. The time to plug-in diagram for any EV.
0
10
20
EV number
EV
PS
S
100 20 30 40 50 60 70 80 90 1001
1.5
2
Prio
rity
leve
l
Station availablePriority for each EVPSS
Figure 18. Selected EVPSS for each arrival EV.
Figure 16 compares our algorithm (represented by theblue dash curve) and the R-EVPSS algorithm (highlightedby red curve). We observe that the average waiting timegiven by R-EVPSS algorithm is higher than the corre-sponding average waiting time given by BA-EVPSS.
Our BA-EVPSS is effective in managing EVs chargingprocess according to the constraints of the requested SoCand price when EVs have the same priority. However, thepriority of each EV is an important parameter to consider,
200
400
600
800
EV number
Ave
rage
tim
e (s
)
10 20 30 40 50 60 70 80 90 100
1
Average time to plug-in(SMART Case)Average time to plug-in (STUPID case)
Figure 19. The time to plug-in under SMART and STUPID casesfor 100 arrival EVs.
Figure 20. The time to plug-in under SMART and STUPID casesfor arrival EVs(500 EVs).
and the charging service may need to be preempted for oneEV and not for another.
To resolve those BA-EVPSS algorithm limits, we evalu-ate the performance of our advanced BA-EVPSS algorithmthat uses a multi-sever queuing model and a cut-off prioritystrategy using the TOUP model. We study the efficiency ofour advanced BA-EVPSS algorithm by the SMART casealgorithm, compared with the STUPID case in terms ofwaiting time for each EV arriving to an EVPSS. The vari-ation of the electricity price in each EVPSS is also takeninto account in our model.
In the STUPID case, an EVPSS is selected by an LP EVaccording to its path and queue length and price level; infact, the arriving EV is directed to the nearest EPVSS thathas the smallest EV number in its queue with the cheapestpower price. For an HP EV, an EVPSS is chosen accordingto its path and queue length only. For any EV level priority(HP and LP), the STUPID algorithm is running not onlywithout taking into account the cumulative EV chargingtime needed by all EVs in each HP and LP queue but alsowithout taking into consideration the dynamic update ofthe cut-off parameter.
D. Said, S. Cherkaoui and L. Khoukhi Multi-priority queuing EV charging with price variation
Table III. Time to plug-in comparison between STUPID and SMART cases.
STUPID case SMART case Saving rates (%)
First range [1 100] EVs 800 730 8.75Second range [101 300] EVs 955 725 24.08Third range [301 500] EVs 1000 710 29
As presented in Figure 17, we define the time to plug-in for any EV as the sum of the waiting time in the EVPSqueue, the time to join the EVPSS, and the grid responsetime. We assume that the time taken between the EVrequest and the time of the grid response should not exceed0.2 s for any EV. We also assume that the cut-off parameterupdate for any EVPSS is carried out after any EV responseand will take 0.1 s.
Figure 18 shows an example scenario of the selectedEVPSS for each arriving EV. The outcome of the advancedBA-EVPSS algorithm corresponds to the blue dash curve,the green points highlights the priority level designed bythe value one (1) for low .L/ and two (2) for high .H/,which are fixed for each EV before the plug-in phase (i.e.,while the EVs are on the roadside).
We observe that for each EVs demand, the smart gridselects, using our advanced BA-EVPSS algorithm, the bestEVPSS according to the constraints of price, priority level,EV position, and EV SoC.
In what follows, we study the charging time of theadvanced BA-EVPSS algorithm corresponding to theSMART case compared with the STUPID case.
Figure 19 shows the average time to plug-in simulatedfor 100 EVs using the advanced BA-EVPSS algorithmdescribed by SMART case compared with the STUPIDcase. We observe that in the SMART case, the EV rela-tively takes less time to plug-in than in the STUPID case,especially when the number of EVs is relatively high. Thisconfirms that with the use of the advanced BA-EVPSSalgorithm, the grid manages the EVs charging process inan efficient manner in terms of time to plug-in and satisfiesEVs according to their profile description communicatedwhile on the road.
We observe the same results compared with Figure 19when considering 500 EVs as shown in Figure 20.
Table III presents the observation results obtained fromFIG.19 and 20, which illustrate the performance compari-son between the SMART case where we use the advancedBA-EVPSS algorithm to manage the charging process andthe STUPID case, in terms of time to plug-in variation.As shown in Table III, it is clear that the advanced BA-EVPSS algorithm reduces the waiting time for the chargingprocess of 1000 EVs with a saving rate of more than 8%, 24%, and 29 %, respectively, for the three ranges ofEVs; [1 100], [101 300], and [301 500]. Moreover, the sav-ing time to plug-in reduction is growing up from 8.75% to29% when the EV number reaches 500. This result provesthe effectiveness of our advanced BA-EVPSS mainly for ahigh EV number.
9. CONCLUSIONS
In this paper, we focused on the EV charging problem
where EVs need to communicate with the grid to know
the best EVPSS in terms of waiting time and cost before
the plug-in phase (i.e., while the EVs are on the road-
side). To this effect, efficient charging algorithms for EVs
at public station based on multi-queuing models were
formulated, developed, and tested through simulations con-
sidering realistic EVs and EVPSS constraints. The first
algorithm is BA-EVPSS where two principal objectives are
taken into account: (i) satisfying single EV charging power
demands and (ii) optimizing the charging time for each EV.
The second algorithm is the advanced BA-EVPSS algo-
rithm. Advanced BA-EVPSS is based on a queuing model
with a cut-off priority scheme and a price variation strategy.
Advanced BA-EVPSS is proposed for two main purposes:
(i) to manage the EVs charging process to satisfy all EVs
demands in terms of time to plug-in and price and (ii)
to control the congestion of each EVPSS by the dynamic
update of the cut-off threshold. We evaluated the perfor-
mances of the proposed algorithms by simulations con-
sidering realistic EVs characteristics and public stations
charging models (socket level 3). The results showed that
the proposed charging algorithms manage EVs demand in
an efficient way according to individual EV parameters
communicated to the smart grid before the beginning of the
charging process. Moreover, simulation results have shown
that our charging algorithms can be seen as a scheduling
form of EVs, and can also improve the grid stability as
both the waiting time for EVs charging and congestion
of EVPSS system were reduced. With the advanced algo-
rithm, the smart grid can flatten the consumption curve in
each EVPSS so as to achieve EVs charging cost optimiza-
tion, in addition to improving grid stability by the update
of the cut-off vector after each EV satisfaction.
The implementation of the proposed charging algo-
rithms involves low computation complexity. In future
work, we will introduce additional constraints (e.g., multi-
ple priority levels for EVs) in the proposed algorithms. We
also plan to take advantage in a future extended load man-
agement technique of possible EV discharging processes in
peak periods where the power price and demand are higher.
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AUTHORS’ BIOGRAPHIES
Dhaou Said was born in Achaba,Eljem, Mahdia, Tunisia. He receivedhis engineering diploma and master’sof research degree in electric engineer-ing and communication systems fromNational School of Engineers of Tunis.He is currently a PhD student in elec-trical and computer engineering at theUniversity of Sherbrooke, Canada. His
research topics include VANET communication and elec-tric vehicle to smart grid interactions techniques.
D. Said, S. Cherkaoui and L. Khoukhi Multi-priority queuing EV charging with price variation
Soumaya Cherkaoui is a fullprofessor at the Department of Elec-trical and Computer Engineering ofUniversité de Sherbrooke, Canada,which she joined in 1999. Since 2005,she has been an adjunct full profes-sor at Lulea University, Sweden, andhas been the Director of Interlab,a research laboratory that conducts
research funded by both government and industry. Beforejoining U. Sherbrooke as a faculty member, Pr. Cherkaouiworked for industry as a project leader on projects thattargeted the aerospace industry. Pr. Cherkaoui was aninvited visiting professor at the University of Toronto,Monash University, Bell Laboratories, the University ofCalifornia at Berkeley, and the University of Montreal. Pr.Cherkaoui has over 100 publications in reputable journals,conferences, and workshops in the area of communicationnetworks. She has participated as a general chair, editor,member of technical committee, session chair, or program
committee member of many conferences or referencedjournals. She is a professional engineer of Quebec, Canada,and an IEEE and IEEE Communications Society member.
Lyes Khoukhi received his PhDdegree in electrical and computerengineering from the University ofSherbrooke, Canada, in 2006. In 2008,he was researcher with the Departmentof Computer Science and OperationsResearch, University of Montreal,Canada. Since 2009, he is an assis-tant professor with the University of
Technology of Troyes, France. He has more than 50 publi-cations in reputable journals, conferences, and workshopsin the area of QoS management in mobile and wireless net-works. His research interests include mobile and wirelessnetworks, QoS and multimedia, resources management,and communication protocols.
