Towards an Optimal Assignment and Scheduling for ...

Towards an Optimal Assignment and Scheduling for Charging Electric Vehicles Azizbek Ruzmetov 1 , Ahmed Nait-Sidi-Moh 2,* , Mohamed Bakhouya 3 , Jaafar Gaber 1 1

2

University of Technology of Belfort-Montbéliard, Belfort, France {azizbek.ru zmetov; gaber}@utbm.fr

University of Picard ie Jules Verne-LTI-INSSET, Saint Quentin, France ahmed.nait-sid i-moh@u-p icardie.fr * Corresponding author 3

Aalto University, FIN-00076 Aalto, Finland [email protected]

Abstract–In recent years, very great research effort have been made to further develop the power engine of electric vehicles and batteries. However, little attention has been paid so far to the fact that charging process for electric vehicles is completely different from refueling process of vehicles that are powered by conventional power engines. One of the major obstacles for the large deployment of electric vehicles is the uncertainty of drivers to get a suitable and vacant place at a charging station. In this paper, an integrated platform is introduced with the main objective to increase the synergy between different system entities, such as energy providers, charging stations and electric vehicles. The platform architecture is based on communications technologies, Web services and geo-positioning techniques. An optimization approach for optimal scheduling and assignment of electric vehicles to charging stations is proposed. Preliminary results are presented to illustrate this approach and show the usefulness of this integrated solution. Keywords: Electric vehicles, Web services, Communication technologies, Smart grid, Modeling and evaluation,Optimization.

I. INT RODUCTION Depending on electric power and the extent of the conservation of energy, three main types of technologies have been developed: Fully electric vehicles (FEV), hybrid electric vehicles (HEV), and plug-in hybrid electric vehicles (PHEV). FEV are primarily suited for short journeys with limited ranges. However, the charging process takes several hours and batteries have to be efficiently used since the propulsion of these vehicles depend on their energy storage capacity. H EV technologies have been developed to overcome the limitations of FEV in order to extend range capability. If the battery reaches its minimu m state-of-charge, another source or an engine could be activated to propel and recharge batteries. HEV has an advantage over FEV since recharging the battery at a recharging point is not required. PHEV was introduced and has large battery pack that can be charged either by an onboard engine, regenerative breaking of motor or external electric supply [4]. For examp le, Opel has developed an energy management system to regulate the interaction between the electric motor, gasoline engine, generator and battery.

Recently, the smart grid technology and concepts are changing the way the world views energy. Such technology platform delivers sustainable, economic and secure electricity supplies by integrating energy producers and consumers. This allo ws updating the electricity utilit ies around the world and redesigning their power networks. In other words, this is largely in response to growth in user demand, regulatory changes, and the restructuring of generation capacity to include distributed supply from renewable sources such as wind and solar energy. Consequently, there is a co mpelling need to incorporate far mo re pervasive co mmunicat ions systems. The resulting “smart grid” is a synthesis of energy and its management, informat ion and commun ication technologies and infrastructures. The smart grid is a key technology for building charging infrastructures for EV charg ing needs. It provides visibility and control needed to mitigate the load impacts and protect components of the distribution network fro m being overloaded by EVs. Smart grid ensures also that electricity generating capacity is used most efficiently. With a s mart grid, utilities can manage when and how EV charg ing occurs while still adhering to customer preferences. In the near future, EVs will p lay a significant role in the road traffic. Ho wever, original characteristics of EVs are limited cruising range, long charging times, and the ability to regain energy during deceleration. This requires novel routing algorith ms, since the task is now to determine the most economical route rather than just the shortest one. This paper addresses one of the most major issues, related to the uncertainty of the drivers to get a suitable and vacant place at a charging station. In particular, we introduce a framework to allo w the collaboration and commun ication between EVs and the infrastructure. The remainder of this paper is structured as follows. Section II presents an overview of the related work. In Sect ion III, the integrated framework architecture and optimization model of charging process are presented with preliminary results. Conclusion and future work are presented in Section IV.

II.

RELAT ED WORK

It is a well-known fact that EVs offer many benefits over traditional internal co mbustion engine (ICE) vehicles such as lower operating costs and considerable potential to run on locally produced renewable energy. Recently several new concepts have been proposed on how to use grid-connected EVs for grid services, also known as vehicle-to-grid (V2G) and energy management [4, 5, 6, 7, 8, 15]. These concepts usually involve both discharging and charging of EVs to help the grid to level out peaks in overall consumption. In [11], a mu lti-agent system has been used to model and control the charging and discharging of PHEVs. Furthermore, authors compared the reducing imbalance costs by reactive scheduling and proactive scheduling. Simu lations show that reactive scheduling is able to reduce imbalance costs by 14%, wh ile proactive scheduling yields the highest imbalance cost reduction of 44%. The authors examine in [12] the problem of optimizing the charge pattern of a PHEV. The optimizat ion goal is to simu ltaneously min imize the total cost of fuel and electricity, and the total battery health degradation over a 24 h naturalistic drive cycle. The first objective is calculated using stochastic optimization fo r power management, whereas the second objective is evaluated through an electrochemistry-based model of anode-side resistive film format ion in lithiu m-ion batteries. In [13], a genetic optimization algorith m is applied to optimize the charging behavior of a PHEV connected to the grid with respect to maximizing energy trading profits in a vehicle-to-grid (V2G) context and min imizing battery aging costs at the same time. The study proposes a method to use the vehicle batteries in an optimized way under the consideration of battery aging costs and variable electricity prices.

deliverance and exchange of information and linear programming for optimal scheduling, guidance and prediction of electrical charging process es. Furthermo re, in the selection process of charging stations , priority is given to stations that are situated in suitable position and on the straightway of driver’s final destination (with sufficient energy in the EV battery to reach the destination) and to stations that have some capabilit ies (nearby supermarket, restaurant, etc.). III.

PROPOSED APPROACH

A. Platform architecture Fig. 1 presents the architecture of the proposed framework. It could integrate all core services such as: 

Identificat ion of drivers and charging of EVs



Billing of energy consumption and services



Finding and reserving charging stations



Gu idance of EVs to charging stations



Managing load of charging station groups



Collecting vehicle data for analy zing purposes



Operating and maintain ing charging infrastructures



Offline operations to ensure reliable charg ing in the event of connectivity failure of the public network.

EVs interactive user interface and the mobile s mart phone portal (e.g. iPhone and Android Apps) offers drivers with informat ion about charging station locations, charging process, and billing details. Furthermore, it p rovides battery state-of-charge and travel distance on displayed on an embedded map.

In [14], a charging/discharging process has been formulated as a global scheduling optimization problem, in which powers of charging are considered to minimize the total cost of all EVs. The authors in [7, 8] focused on developing effective charging algorith ms for fast charging and increasing cycle of battery life . In the same context, some approaches for effective planning charging times are proposed in [9, 10]. All these algorith ms and approaches help (and serve) to organ ize and build the efficient tools and reliable applications for modern charging infrastructures. For driver journeys, finding not only most nearest charging point but free and most relevant (with additional capabilit ies) is one of the most important problems for the drivers. This requires finding the path with the minimu m d istance to travel, time fro m an orig in (EV location) to a destination (free charging point). Finding such paths is based on algorithms such as Dijkstra and Bellman [1, 2, 3]. As the traffic condition changes regularly and increasing nu mber of requests, finding adequate charging stations for drivers is required. In this paper, an optimization approach for optimal scheduling and assignment of EVs to charging stations is introduced. In part icular, a framework is proposed and combine we co mbine information and co mmun ication technologies, Web services, geo-positioning techniques for

Figure 1. Charging process architecture

As illustrated in Fig. 1, EVs and charging stations are the main entit ies of the system. Each charging station is composed of many charging places that are connected to a central controller. Information about charging stations are saved in the central controller. For example, free/occupied charging points, charging power of charging points, energy pricing, the location of charging stations, etc.. EV drivers connect to the central controller by their own mob ile devices (mobile phones,

PDA), the embedded application sends requests and receives responses from the central controller. We recall that each charging station is composed of several charging places (called also charging points . All informat ion regarding a charging station are collected frequently and stored in the central controller. Furthermore, the central controller regularly updates information about charging processes, e.g. how many EVs are under charging process. In other word, the solution we propose allows to optimally handle requests received from drivers such as finding the nearest charging station and reserving a charging place. On the other hand, the system allows assisting drivers to choose adequate and optimal solutions for EVs charg ing . The interaction and communicat ion between system co mponents are based on the following principles: real-time positioning using geo-positioning techniques (GPS and EGNOS), bidirectional commun ication between EVs and infrastructure (V2G2V) via wireless technologies (GPRS or 3G), as illustrated in Fig. 2.

B. Optimal assignment of EVs to charging stations This subsection presents the optimal scheduling of EVs to charging stations. The study is based on the linear programming optimization. The problem fo rmulat ion is started by a global knowledge of the process context such as informat ion about the status of charging stations, informat ion about EVs such as battery level with possible distances to carry out using the remaining power, GPS coordinates, distance between a EV and nearest charging stations, etc.. All these information can be obtained through exchanges between EVs, the infrastructure (or central controller), and charging stations as shown in Fig.1.

Figure 2. Communications V2G and G2V

The general charging process includes four main steps: 

warning drivers about battery status

 

sending request to the infrastructure (or central controller) searching, by the central controller, a charging station with free charging points according to stored informat ion in the central controller database



sending an adequate and optimal solution to drivers.

In fact, after receiving warning information about battery level and distance to be travelled with remaining energy, the embedded application sends a request to the central controller, which in turn processes the request and informs the driver about the suitable charging station. The scheduling and charging process is based on the algorith m described in Fig. 3 (with CS - Charging station, CP - Charging Po int, DB Database, Full Ch - Fu ll Charging.

Figure 3. The block diagram of general algorithm of charging process.

This study consists in selecting the best choice of assignment of EVs to charging stations with minimu m costs and waiting times (to avoid overloading stations). Therefore, we assume the follo wing:  There are limited resources (a finite number of charging points available at each charging station). 

There is an explicit economic function (or objective function) to optimize. Th is function is supposed to be linear.



The problem is subject to some constraints which are expressed by linear equations (no exponents or cross products).



The resources are homogeneous (everything is in one unit of measure).



The decision variab les are b inary (we either make an assignment of an EV to a charging station or not).

The assignment of EVs to charging stations will be carried out according to the following matrix (see Table I). Let consider N EVs and M charging stations (N and M are supposed to be non-negative integers with N >>M ). A SSIGNMENT COEFFICIENTS OF EVS TO CHARGING STATION .

TABLE I.

EV1 EV2 EV3 ... EVN

S1 c(1,1) c(2,1) c(3,1) ... c(N,1)

S2 c(1,2) c(2,2) c(3,2) ... c(N,2)

S3 c(1,3) c(2,3) c(3,3) ... c(N,3)

... ... ... ... ... ...

SM c(1,M) c(2,M) c(3,M) .... c(N,M)

For i = 1, ..., N,

In the following, we define all parameters of the system that are required for the problem formu lation. For i (1≤i≤N), j (1≤j≤M) and t  IN (set of non-negative integers),

x(i,j,t)

Set of EVs (EV1 , EV2 ,..., EVN), Set of charging stations (S 1 , S2 , ..., S M ), Assignment coefficient of EVi to a station Sj , Distance separating EVi and Sj at time t, Power level of the battery, Distance to be carried out with the remaining power Bi (t), State of S j at time t, Status of road traffic along the shortest path between EVi and Sj at time t, Binary variables where :

1, if EVi is assigned to S j at t xi, j, t    0, otherwise

(2)

Mathematically, the assignment optimization prob lem can be formulated as follows: N

M

Minimize Z t    c(i, j, t ) x(i, j, t ) i 1 j 1

Subject to: For i = 1, ..., N , and a given time t,

For j = 1, ..., M , and a g iven time t, N

 x(i, j, t )  n i 1

(5)

j

c(i, j, t )  f (d (i, j, t ), Bi (t ), dis i (t ), Sta j (t ), Tr(i, j, t )) (6) Assuming that the coefficient c(i,j,t) is expressed according to the system parameters, one should verify the feasibility constraints and received informat ion based on the process architecture of Fig.1. A coefficient c(i,j,t) can be considered as an assignment score of a EVi to a station S j at time t. For i = 1, ..., N, j  {1, ..., M}, and a given time t ,

d (i, j, t )  dis i (t ) (1)

More details about these coefficients are given hereafter.

Staj (t) Tr(i,j,t)

This means that a given EVi should be assigned to only one charging station at time t.

For i = 1, ..., N, j = 1, ..., M, and a g iven time t ,

An electric vehicle EVi is assigned to a charging station S j0 when the associated coefficient c(i,j,t) takes the min imu m value c* (i, j0 ,t).

N M c(i,j,t) d(i,j,t) Bi (t) disi(t)

(4)

j 1

This means that a given charging station S j may receive until n j EVs at a given time t. This constraint is flexible and the number of assigned EVs to a given charg ing station S j may change according to the status of S j .

For 1≤i≤N and 1≤j≤M, each assignment coefficient c(i,j) in the matrix, can be optimally calculated according to informat ion exchanged with the central controller). Considering the dynamic behavior of the studied system, each coefficient c(i,j) depends on the time, we write also c(i,j,t) as the assignment coefficient at the time t.

c*( i, j0 ,t) = min 1≤j≤M { c(i,j,t)}

M

 x(i, j, t )  1

(3)

(7)

Furthermore, we denote the distance between a vehicle EVi and a charging station Sj (candidate for receiving EVi ) that should be smaller than the distance to be carried out with the remain ing power in the battery Bi . C. Resolution and discussions The Microsoft Excel solver was used for solving this assignment optimization problem. It is more useful and can be handled without having strong mathemat ics background. We illustrate our approach with a numerical example. At this stage of our research, we allocate a nu merical value to each assignment coefficient c(i,j,t) representing the assignment value of a EVi to a station Sj at a given time t. The values expressed by the equation (6) are chosen according to the system status and the collected information fro m both EVs and charging stations. The fo llo wing nu merical values were used : 

N = 12 Electric Vehicle: EV1 , ..., EV12 ,



M = 5 Charg ing Stations: S 1 , ..., S 5 ,



The optimal assignment is calcu lated for t = t 0 . For t ≠ t0 , the system status may be changed, and then the values of the assignment coefficient c(i,j,t) change too. This will affect the assignment of EVs to charging stations. This issue will be considered in our future work.

The obtained optimal solution corresponding to the optimal values of assignment coefficients c(i,j,t 0) is given by the gray part of the table II.

TABLE II.

VALUES OF ASSIGNMENT COEFFICIENTS FOR t = t0.

t = t0 EV1 EV2 EV3 EV4 EV5 EV6 EV7 EV8 EV9 EV10 EV11 EV12  EVs

S1

S2

S3

S4

S5

29

10

29

33

41

38

24

30

16

25

11

40

33

24

19

12

16

19

14

38

41

23

37

12

27

28

47

13

28

37

35

26

10

40

21

22

10

28

17

31

32

15

39

19

26

16 19

33 44

29 35

35 14

44 24

40

39

18

10

45

≤3

≤2

≤5

≤1

≤2

REFERENCES

The follwoing Table summarizes the obtained optimal results. TABLE III. Charging station

OP TIMAL ASSIGNMENT AND SCHEDULING .

S1

S2

S3

3 2 5  of authorize d EVs 3 2 4  of assigned EVs EV3 11 EV1 10 EV4 Assigne d EVS & EV10 36 EV6 Optimal value of EV11 19 EV8 10 EV7 c(i,j,t0 ) EV12

S4 1 1

In our future work, this study will be extended by further developing the proposed model and integrating more co mp lex and concrete situations of the EVs and smart grids. The explicit exp ression of the assignment coefficients c(i,j,t), as given in the equation (6), will be developed. Charging and discharging times of the EVs will be integrated into the formal model. We will also study the impact of charging accelerat ion on the scheduling and assignment and charging process of EVs. Simulat ions will be also conducted to show the efficiency of the proposed scheduling algorith m

S5 2 2

19 EV2 25 13 EV5 12 10 EV9 26 18

These results show that all problem constraints are satisfied: 

All EVs are assigned and each one is assigned to exactly one charging station.



The number of authorized EVs at each charg ing station is not exceeded.



Each assignment is carried out with the min imu m value of c(i,j,t).



The global assignment score of all EVs is optimized.

IV. CONCLUSION AND FUTURE WORK This paper proposes an integrated platform for increasing the synergy between electric vehicles and charging stations. The interaction and co mmunicat ion between the EVs and the platform is ensured by the use of strengths of informat ion and communicat ion technologies, Web services and geopositioning techniques . Based on information provided by the platform main ly, the status of charging stations and the status of the EVs as well as their positions and the remaining power in their batteries, we study the scheduling and assignment of EVs to charging stations as an optimization problem. We first formulate the problem by a linear program, in which the assignment of all EVs should verify certain constraints such as the status of charging stations and the characteristics of EVs. The obtained results showed that the proposed scheduling algorith m provides the optimal solution.

[1]

E.W. Dijkstra, "A note on two problems in connect ion with graphs", Numer. Math., 1, pp. 269–271, 1959.

[2]

E. Bellman, "On a routing problem", Q. Appl. Math., 16, pp. 87–90, 1958.

[3]

S. Dreyfus, "An appraisal of some shortest path algorithms", Oper. Res., 17, pp. 395–412, 1969.

[4]

"Electrifying the Automobile–Variations, Strategy for the Electro-era, Magazine ADAC", 19 pages, April 2011.

[5]

F.Pan, R.Bent, A.Berscheid, "Online dynamic scheduling for charging PHEVs in V2G", Power Engineering Society General Meeting 2012.

[6]

F. Pan, R. Bent, A. Berscheid, and D. Izraelevitz, "Locating phev exchange stations in v2g. Smart Grid Communications (SmartGridComm)", First IEEE International Conference on, Gaithersberg, MD, 2010.

[7]

Herman L.N. Wiegman, "A Review of Battery Charging Algorithms and Methods", University of Wisconsin – Madison, Nov 28, 1999.

[8]

Abd El-Shafy A. Nafeh, "An effective and safe charging algorithm for lead-acid batteries in PV systems", International Journal of Energy Research. Volume 35, Issue 8, pages 733–740, 25 June 2011.

[9]

Olle Sundstrӧmand Carl Bindeing, "Planning electric-drive vehicle charging under constrained grid conditions", International Conference on Power System T echnology, IEEE 2010.

[10] Hye-Jin Kim, Junghoon Lee, Gyung-Leen Park, Min-Jae Kang, and Mikyung Kang, "An Efficient Scheduling Scheme on Charging Stations for Smart Transportation", Springer, 2010. [11] Stijn Vandael, Nelis Boucke, Tom Holvoet, Klaas De Craemer and Geert Deconinck, "Decentralized coordination of plug-in hybrid vehicles for imbalance reduction in a Smart Grid", AAMAS, 2011. [12] Saeid Bashash, Scott J. Moura, Joel C. Forman, Hosam K. Fathy, "Plugin hybrid electric vehicle charge pattern optimization for energy cost and battery longevity", Journal: Journal of Power Sources - Journal of Power Sources , vol. 196, no. 1, pp. 541-549, 2011. [13] Benedikt Lunz, Hannes Walz, Dirk Uwe Sauer , "Optimizing vehicle-togrid charging strategies using genetic algorithms under the consideration of battery aging", IEEE Conference of Vehicle Power and Propulsion VPPC , pp. 1-7, 2011. [14] Yifeng He, Bala Venkatesh, Ling Guan, "Optimal Scheduling for Charging and Discharging of Electric Vehicles", IEEE transactions on smart grid, vol. 3, no. 3, September 2012. [15] W. Ait-Cheik-Bihi, M. Bakhouya, J. Gaber, R. Outbib, E. Coatanea, X. Z. Gao, K. Zenger, Towards an Integrated Service-oriented Energy Management Platform for Plugin Hybrid Electric Vehicles, 2012 IFAC Workshop on Multivehicle Systems, Espoo, Finland, 2012.