smart charging strategy - university of hong kong
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Energy Conversion and Management 78 (2014) 508–517
Contents lists available at ScienceDirect
Energy Conversion and Management
journal homepage: www.elsevier .com/locate /enconman
A scenario of vehicle-to-grid implementation and its double-layeroptimal charging strategy for minimizing load variance withinregional smart grids
0196-8904/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.enconman.2013.11.007
⇑ Corresponding author. Tel.: +86 755 88018525; fax: +86 755 88018536.E-mail addresses: [email protected] (L. Jian), [email protected]
(X. Zhu), [email protected] (Z. Shao), [email protected] (S. Niu),[email protected] (C.C. Chan).
Linni Jian a,⇑, Xinyu Zhu a, Ziyun Shao b, Shuangxia Niu c, C.C. Chan d
a Department of Electrical and Electronic Engineering, South University of Science and Technology of China, Shenzhen 518055, Chinab School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, Chinac Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kongd Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam, Hong Kong
a r t i c l e i n f o a b s t r a c t
Article history:Received 17 June 2013Accepted 3 November 2013
Keywords:Electric vehicleCharging strategyVehicle-to-gridSmart gridLoad varianceRegional grid
As an emerging new electrical load, plug-in electric vehicles (PEVs)’ impact on the power grid has drawnincreasing attention worldwide. An optimal scenario is that by digging the potential of PEVs as a move-able energy storage device, they may not harm the power grid by, for example, triggering extreme surgesin demand at rush hours, conversely, the large-scale penetration of PEVs could benefit the grid throughflattening the power load curve, hence, increase the stability, security and operating economy of the grid.This has become a hot issue which is known as vehicle-to-grid (V2G) technology within the framework ofsmart grid. In this paper, a scenario of V2G implementation within regional smart grids is discussed.Then, the problem is mathematically formulated. It is essentially an optimization problem, and the objec-tive is to minimize the overall load variance. With the increase of the scale of PEVs and charging postsinvolved, the computational complexity will become tremendously high. Therefore, a double-layer opti-mal charging (DLOC) strategy is proposed to solve this problem. The comparative study demonstratesthat the proposed DLOC algorithm can effectively solve the problem of tremendously high computationalcomplexity arising from the large-scaled PEVs and charging posts involved.
� 2013 Elsevier Ltd. All rights reserved.
1. Introduction
Plug-in electric vehicles (PEVs) which are also known as grid-enabled EVs, can be generally categorized into battery EVs (BEVs),plug-in hybrid EVs (PHEVs), and extended-range EVs (EREVs) [1].BEVs are usually equipped with large capacity batteries, whichcan be charged by connecting into power grid via onboard chargingcircuit or specialized ac–dc charging device. BEVs are wholly pro-pelled by electric power through the electromechanical conversionof traction motors. On the contrary, in PHEVs and EREVs, both theinternal combustion engine (ICE) and the electric motor are com-bined together. From the EV development point of view, EREVsmore originate from BEVs for solving the ‘‘range anxiety problem’’of BEVs [2], and PHEVs are likely derived from traditional hybridEVs (HEVs). The key difference lies in that PHEVs are equippedwith larger capacity battery packs, and their batteries can becharged by plugging into power grid. Thus, PHEVs are able to beoperated with the charge–depletion mode, just like the BEVs, as
well as the charge–sustained mode, which is similar to traditionalHEVs [3].
With serious concerns on global warming and energy crisis,plenty of motivations for developing and commercializing PEVshave come out, such as reducing the greenhouse gases emissionand the dependence on fossil fuel, increasing the energy efficiencyand the utilization of renewable energy, and so on. At the sametime, the impact of PEVs as an emerging new electrical load onthe power grid has drawn more and more attention worldwide.The possible challenge for power grid lies in that the penetrationof large number of PEVs may trigger extreme surges in demandat rush hours, and therefore, harm the stability and security ofthe existing power grid. Nevertheless, there are potential opportu-nities for power grids as well. It is predicted that if PEVs arecharged at off-peak hours, the existing U.S. power grid can supportthe conversion of 84% of light duty vehicles to PEVs in U.S. withoutsignificantly adding investment [4]. An optimal scenario is to digthe potential of PEVs as moveable energy storage devices, whichmeans PEVs withdraw power from grid at off-peak hours and thenfeedback energy deposited in the onboard batteries to grid at peakhours. This concept is also termed as vehicle-to-grid (V2G) tech-nology [5,6]. It has been demonstrated that the V2G option canaid to flatten the power load curves [7–10], reduce power losses,
L. Jian et al. / Energy Conversion and Management 78 (2014) 508–517 509
improve voltage profile [11–13], and integrate renewable energysources [14,15]. Consequently, the implementation of V2G is be-lieved to be able to improve the efficiency and reliability of thepower grid, as well as reduce its overall operating cost and carbonemission.
The key to the implementation of V2G is how to effectively inte-grate information into energy conversion, transmission and distri-bution. V2G should be carried out within the framework of smartgrid [16–18], so that the status information of power grid can beperceived. In addition, the demand information of PEV ownersshould also be taken into account, so that the function of PEVs astransportation means can be guaranteed. The problem formulationand mathematically modeling concerning all this crucial informa-tion can lead to the optimal charging strategies for PEVs, whichaim at maximizing the benefits of V2G. Recently, several studieson the economic issues related to the V2G implementation [19–21] have been made. The basic idea is to encourage EV owners tomanage their energy consumption and regulate their charging pro-file by using financial incentives, such as floating electricity pricingor subsidy mechanism. Nevertheless, in our opinion, these aremuch more complicated problems which involve quite difficult as-pects, such as, the regulation of electricity production, the utiliza-tion of intermittent renewable energy, the deployment of energystorage systems, and so on. In some region, for example, in China,the design and application of floating electricity pricing is a rathercrucial issue even concerned with upper-level economic reformand government policy making.
The purpose of this paper is to discuss a possible scenario ofV2G implementation within regional smart grid. The related math-ematical formulation is also analyzed. It is essentially an optimiza-tion problem, and the objective is to minimize the overall loadvariance. With the increase of the scale of PEVs and charging postsinvolved, the computational complexity will become tremendouslyhigh. Therefore, a double-layer optimal charging (DLOC) strategy isproposed to solve this problem.
2. A scenario of V2G implementation within regional smart grid
V2G is a rather sophisticated concept. It involves new techniquepatterns, innovative business models and even novel industrialrules. Although consensus has not been reached on how to defineV2G to date, it can still be explicitly understood in the view of itsessential missions that are expected can be achieved in the future:(1) PEVs are either being connected to grid or running on the way;(2) When PEVs are plugged into grid, they exchange electric energywith grid and try to bring positive effects to grids by functioning asenergy storage devices; (3) The energy exchange between PEVs andpower grid should guarantee that PEVs have sufficient electricpower for running on the way at least before they are connectedto grid next time. The key task of V2G is to plan optimal charging/discharging (usually use ‘charging’ for short) schedules for PEVsto fulfill the missions mentioned above. For this, the informationcommunications among PEVs, power grid, charging posts areindispensable. Fig. 1 illustrates the information flow and the energyflow concerning V2G in regional smart grid. The central control cen-ter takes charge of acquiring and processing the key signals, andbased on that, generating optimal charging instructions to guidethe energy exchanging between PEVs and power grid bridged bythe charging posts. In what follows, a possible scenario for imple-menting V2G within regional smart grid will be elaborated.
2.1. Recording the charging posts involved
The central control center (CCC) should be aware which charg-ing posts (CPs) are available for the V2G operation, and what their
key charging-planning-related parameters are. All the CPs, no mat-ter whether they are public or private, should be reported to theCCC, and consequently, the CCC builds data tuples on its serverto record every CP involved:
CP ¼ CPID;CPLoc; PmaxCP ; Flag
� �ð1Þ
where the entities are: CPID is the identity number of the CP, CPLoc
the location of the CP; PmaxCP the allowed maximum charging power
of the CP and Flag is the to indicate whether the CP is availablefor public use, Flag = 0 means this is a public CP, while, Flag = 1represents this is a private CP.
2.2. Registering the plug-in electric vehicles involved
The CCC should also understand the necessary information onPEVs involved. Vehicle owners who are willing to associate theirPEVs with V2G in the regional smart grid should register theirvehicles in advance by, for example, submitting the registrationform online to the CCC as illustrated in Fig. 2. Then, CCC will allota unique identity number for each PEV that are successfully regis-tered. Consequently, CCC builds data tuples on its server to recordevery PEV involved:
EV ¼ EVID; EVMod;BATTyp;BATCap; Socupper; Soclower
� �ð2Þ
where the entities represent: EVID is the identity number of the PEV,EVMod the model of the PEV, BATTyp the type of the battery equipped,BATCap the capacity of the battery equipped, Socupper the allowedupper limit for the Soc value of battery and Soclower is the allowedlower limit for the Soc value of battery.
The battery state-of-charge (Soc) is an equivalent quantity of afuel gauge for battery packs. It indicates the amount of electric en-ergy left in a battery compared with the energy it has when it isfully charged [22,23]. In order to extend the lifetime of batteries,upper limit and lower limit for the Soc value should be set to avoidover charging and deep discharging, which both can harm thephysical constitution of batteries.
2.3. Proposing request for joining V2G Operation
Normally, the CCC plans the charging schedule for every 24 h(one-day cycle), such as from 06:00 am to 05:59 am (next day).Thus, each vehicle owner who intends to join V2G operation forthe coming one-day cycle should propose request to the CCC beforethe deadline (06:00 am), and tell when and where their PEVs willbe connected to grid. This can be conducted by logging into theonline application system as shown in Fig. 3.
For our mathematical modeling which will be presented in Sec-tion 3 and 4, some key information should be reported to the CCC:(1) The estimated latest moment that this PEV can be connectedinto grid; (2) The estimated earliest moment that this PEV willbe detached from grid; (3) Which charging post this PEV will beconnected to; (4) The estimated battery Soc value when this PEVconnected into grid; (5) The required battery Soc value when thisPEV detached from grid. For point 3), if the vehicle owner plansto connect his/her PEV into his/her private charging post, he/shereports the ID No. of the charging post directly. Otherwise, he/she reports the location or area where the PEV will stop, and re-quest the CCC to allocate a public charging post for the PEV. Forpoint 4), the battery Soc value when the PEV connected into gridis affected by many factors, such as the energy efficiency of thePEV, the initial Soc when the last charging is completed, the travelway of the PEV before being connected in, the on board passengersand loads, and so on. We believe that with better understanding onthe people’s lifestyle and the social eco-environment in the regionconsidered, an ‘Estimator’ program can be developed to help the
Fig. 1. A scheme of V2G within regional smart grid.
Fig. 2. Interface of online PEV registration system.
Fig. 3. Interface of online application system for joining V2G operation.
510 L. Jian et al. / Energy Conversion and Management 78 (2014) 508–517
vehicle owner exactly estimate the battery Soc when his/her PEVconnected into grid.
Fig. 4. Interface of charging post allocation plan (an example).
2.4. Request confirmation and data preparation
After the vehicle owner submits his/her request, the CCC at-tempts to include the proposed PEV into the V2G operation by
allocating an available charging post for it. On the server of theCCC, there is a database to record the mappings between the loca-tion where PEV stops and all the charging posts installed nearby.The charging posts are available on first-proposed first-served.The allocation may be failed for two reasons: (1) There is not anycharging post located within the area where the PEV will stop;(2) The charging posts nearby have all been allocated to other PEVs.The CCC feedbacks its allocation results to the vehicle owners andasks for their confirmation by the interface as shown in Fig. 4. If theplan is confirmed, this case will be included into the V2Goperation.
Next, the CCC conduct data preparation for mathematical for-mulation according to the confirmed allocation plans. Firstly, itgenerates a set of the active charging posts as:
SACP ¼ A1CP;A
2CP;A
3CP; � � � ;A
NCP
h ið3Þ
where AnCP , n ¼ 1;2;3; � � � ;N, represents the n-th active charging post
that is assigned to offer charging services in the next 24-h, and N isthe number of the active charging posts.
Secondly, the CCP builds up a 2D data tuple for each chargingpost An
CP as given by (4).
L. Jian et al. / Energy Conversion and Management 78 (2014) 508–517 511
AnCP ¼
Cs�1ACP�n ; Ce�1
ACP�n ; EVID�1ACP�n ; BATCap�1
ACP�n ; Socupper�1ACP�n ; Soclower�1
ACP�n ; Socs�1ACP�n ; Soce�1
ACP�n
Cs�2ACP�n ; Ce�2
ACP�n ; EVID�2ACP�n ; BATCap�2
ACP�n ; Socupper�2ACP�n ; Soclower�2
ACP�n ; Socs�2ACP�n ; Soce�2
ACP�n
..
. ... ..
. ... ..
. ... ..
. ...
Cs�kACP�n ; Ce�k
ACP�n ; EVID�kACP�n ; BATCap�k
ACP�n ; Socupper�kACP�n ; Soclower�k
ACP�n ; Socs�kACP�n ; Soce�k
ACP�n
..
. ... ..
. ... ..
. ... ..
. ...
Cs�KðnÞACP�n ; Ce�KðnÞ
ACP�n ; EVID�KðnÞACP�n ; BATCap�KðnÞ
ACP�n ; Socupper�KðnÞACP�n ; Soclower�KðnÞ
ACP�n ; Socs�KðnÞACP�n ; Soce�KðnÞ
ACP�n
2666666666664
3777777777775ð4Þ
In practice, the one-day cycle is evenly divided into T time-slots,and the length of each time-slot is given by Dt. For example, wecan assume Dt = 15 min, and there are totally 96 time-slots in the24 h period. Therefore, the quantities in (4) are: Cs�k
ACP�n is the k-thcharging service offered by An
CP will start at the beginning of theCs�k
ACP�n-th time-slot, Ce�kACP�n is the k-th charging service offered by
AnCP will finish at the ending of the Ce�k
ACP�n-th time-slot, EVID�kACP�n is
the ID No. of the PEV connected to AnCP during the k-th charging ser-
vice offered by AnCP , BATCap�k
ACP�n the battery capacity of the PEV con-nected to An
CP during the k-th charging service offered by AnCP ,
Socupper�kACP�n the allowed battery Soc upper limit of the PEV connected
to AnCP during the k-th charging service offered by An
CP , Soclower�kACP�n the
allowed battery Soc lower limit of the PEV connected to AnCP during
the k-th charging service offered by AnCP , Socs�k
ACP�n the estimated bat-tery Soc value of PEV when the k-th charging service offered by An
CP
starts, Soce�kACP�n the required battery Soc value of PEV when the k-th
charging service offered by AnCP ends and K(n) is the Charging post
AnCP is assigned to offer K(n) times charging service in the coming
one-day cycle.Up till now, the CCC gets enough information on the PEVs, the
charging posts, and the vehicle owners’ desires. Some other keypoints should be gotten known before the CCC can carry out opti-mal charging planning for every charging service, and this will beelaborated in the following sections. We must make it clear thatthe scenario of V2G implementation herein presented is comeout by focusing on the essential functions V2G operation, it doesnot concern any considerations on economic incentives, businessmodels or government policy makings.
3. Problem formulation
The optimal charging planning is to determine the chargingpower at each time slot for every charging post when it is offeringcharging services for PEVs. For each charging post, its chargingpower in the same time slot is kept unchanged. The objective isto minimize the overall load variance of the regional grid duringthe coming one-day cycle. Hence, the problem can be formulatedas:
minXT
t¼1
1T
PtCon � PAvg þ
XN
n¼1
PtACP�n
!224
35 ð5Þ
Subject to:
PtCon þ
XN
n¼1
PtACP�n 6 Pt
max; t 2 ½1; T� ð6Þ
PAvg ¼XT
t¼1
PtCon þ
XN
n¼1
PtACP�n
!,T ð7Þ
� PmaxACP�n 6 Pt
ACP�n 6 PmaxACP�n; t 2 [
k¼KðnÞk¼1 Cs�k
ACP�n;Ce�kACP�n
h i;
n 2 ½1;N� ð8Þ
PtACP�n ¼ 0; t 2 ½1; T� � [k¼KðnÞ
k¼1 ½Cs�kACP�n;C
e�kACP�n�; n 2 ½1;N� ð9Þ
XCe�kACP�n
t¼Cs�kACP�n
½Dt � PtACP�n� ¼ Soce�k
ACP�n � Socs�kACP�n
� �� BATCap�k
ACP�n; k 2 ½1;KðnÞ�;
n 2 ½1;N� ð10Þ
Soclower�kACP�n 6 Sock
ACP�nðjÞ 6 Socupper�kACP�n ; j 2 ½Cs�k
ACP�n;Ce�kACP�n�;
k 2 ½1;KðnÞ�; n 2 ½1;N� ð11Þ
SockACP�nðjÞ ¼ Socs�k
ACP�n þXj
t¼Cs�kACP�n
Dt � PtACP�n=BATCap�k
ACP�n
h ið12Þ
where PtACP�n is the charging power of An
CP in the t-th time slot, PtCon
the estimated conventional power in the t-th time slot, PAvg the esti-mated average power of the regional grid during the coming one-day cycle, Pt
max the maximum total power that can be supplied bythe regional grid in the t-th time slot, Pmax
ACP�n the allowed maximumworking power of An
CP , SockACP�nðjÞ the battery Soc value at the end of
the j-th time slot when AnCP offers its k-th charging service.
In the above mathematical modeling, the 24-h-ahead conven-tional power load (power load of the regional grid excluding PEVloads) forecasting [24–26] is involved. It is believed that with thedevelopment of smart grid, the load forecasting can be achievedwith high accuracy. It can be observed from the above formulationthat the number of variables increase linearly with the number ofcharging posts involved, and the number of restraints are related toboth the number of charging posts and the number of charging ser-vices they plan to offer, which is decided by the number of PEVs in-volved. This means, with the large scale of penetration of PEVs andcharging posts, the computational complexity will become tre-mendously high.
4. Double-layer optimal charging strategy
In order to solve the problem of tremendously high computa-tional complexity arising from large-scaled PEVs and chargingposts involved, a double-layer optimal charging (DLOC) strategyis proposed. The basic idea is to categorize all the charging postsin the regional grid under the administration of several chargingstations. In the first layer optimization, the CCC plans the optimaloperating power schedule for each charging station as a wholeaiming to minimize the overall load variance. Then in the secondlayer optimization, the station control server plans the chargingpower for each charging post under its governance, aiming to meetthe instructions ordered by CCC which has been generated in thefirst layer optimization. Fig. 5 illustrates both the energy flowand the information flow in the proposed DLOC strategy.
The charging posts located in the same area, or connected to thesame node transformer can be classified into the same chargingstation, such as those installed on the same streets, in the sameparking lot, or in the same residential community.
4.1. First layer optimization
After the induction of charging stations, the data tuple given by(1) should be updated to:
CP ¼ CPID;CPLoc; PmaxCP ;CSID; Flag
� �ð13Þ
where the newly added entity CSID denotes the identity number ofcharging station to which this charging post is associated. Then, theset given by (3) evolves into:
SCS�hACP ¼ A1�h
CP ;A2�hCP ;A3�h
CP ; � � � ;ANðhÞ�hCP
h ið14Þ
Fig. 5. Energy flow and information flow in proposed DLOC strategy.
Fig. 6. A charging process.
512 L. Jian et al. / Energy Conversion and Management 78 (2014) 508–517
where SCS�hACP is the set of the active charging posts in the h-th charg-
ing station, h 2 ½1;H�, and H is the number of the active chargingstation in the V2G operation for the coming one-day cycle. An�h
CP de-notes the n-th active charging post in the h-th charging station,n 2 ½1;NðhÞ�, N(h) is the number of the active charging post in theh-th charging station. An�h
CP is also a 2D data tuple with the samestructure as illustrated in (4), but the entities are updated into:
Cs�k�hACP�n: the k-th charging service offered by An�h
CP will start at thebeginning of the Cs�k�h
ACP�n -th time-slot;Ce�k�h
ACP�n: the k-th charging service offered by An�hCP will finish at
the ending of the Ce�k�hACP�n-th time-slot;
EVID�k�hACP�n : the ID No. of the PEV connected to An�h
CP during the k-thcharging service offered by An�h
CP ;BATCap�k�h
ACP�n : the battery capacity of the PEV connected to An�hCP
during the k-th charging service offered by An�hCP ;
Socupper�k�hACP�n : the allowed battery Soc upper limit of the PEV con-
nected to An�hCP during the k-th charging service offered by An�h
CP ;Soclower�k�h
ACP�n : the allowed battery Soc lower limit of the PEV con-nected to An�h
CP during the k-th charging service offered by An�hCP ;
Socs�k�hACP�n: the estimated battery Soc value of PEV when the k-th
charging service offered by An�hCP starts;
Soce�k�hACP�n: the required battery Soc value of PEV when the k-th
charging service offered by An�hCP ends.
In the first layer optimization, the target variables become theoperating power of charging stations at every time slot. Thus, theobjective function given in (5) can be changed to:
minXT
t¼1
1T
PtCon � PAvg þ
XH
h¼1
PtCS�h
!224
35 ð15Þ
where PtCS�h is the operating power of the h-th charging station at
the t-th time slot. The restraints (6) and (7) can be changed to:
PtCon þ
XH
h¼1
PtCS�h 6 Pt
max; t 2 ½1; T� ð16Þ
PAvg ¼XT
t¼1
PtCon þ
XH
h¼1
PtCS�h
!,T ð17Þ
Moreover, restraints (8) and (9) can be rewritten as:
�XNðhÞn¼1
nhnðtÞP
max�hACP�n
� �6 Pt
CS�h 6XNðhÞn¼1
nhnðtÞP
max�hACP�n
� �ð18Þ
nhnðtÞ ¼
0; if : t 2 ½1; T� � [k¼KðnÞk¼1 Cs�k
ACP�n;Ce�kACP�n
h i1; if : t 2 [k¼KðnÞ
k¼1 Cs�kACP�n;C
e�kACP�n
h i8><>: ð19Þ
where Pmax�hACP�n is the allowed maximum working power of the charg-
ing post An�hCP .
The restraints (10)–(12) are set to guarantee the demandedcharging quantities of each charging service, and to make sure thatthe batteries are neither over charged nor deeply discharged. Con-sidering the k-th charging service that going to be offered by thecharging post An�h
CP , the charging process can be illustrated by thechange of battery Soc versus time as shown in Fig. 6. As long asthe battery Soc value is located in the shadow area, the restraints(10)–(12) can be satisfied.
Denoted by Wk�hACP�nðtÞ the accumulated charging quantity from
the first time slot to the t-th time slot offered by the charging postAn�h
CP in its k-th charging service, it can be known from Fig. 6 thatthe lower boundary and upper boundary of Wk�h
ACP�nðtÞ are givenby (20)–(23).
9=;
Table 1Specifications of cases simulated.
Number of plug-inEVs
Number of chargingposts
Number of chargingstations
Number of charging/dischargingservices
Computing time consumed (s)
Model 1 Model 2
Case 1 100 100 10 336 1.38 0.64 (Layer 1) + 0.38 (Layer 2) = 1.02Case 2 500 500 22 1738 12.72 1.51 (Layer 1) + 1.17 (Layer 2) = 2.68Case 3 1000 1000 31 3433 32.60 2.32 (Layer 1) + 2.06 (Layer 2) = 4.38Case 4 2000 2000 44 6919 81.67 3.67 (Layer 1) + 3.60 (Layer 2) = 7.27
Fig. 7. Power load and connected PEVs. (a) Case 1. (b) Case 3. (c) Case 4. (d) Case 5.
L. Jian et al. / Energy Conversion and Management 78 (2014) 508–517 513
Wk�hACP�nðtÞ
���lower¼
0; if : t<Cs�k�hACP�n
Sock�hACP�nðtÞ
���lower�Socs�k�h
ACP�n
� �BATCap�k�h
ACP�n ; if : Cs�k�hACP�n 6 t6Ce�k�h
ACP�n
Soce�k�hACP�n�Socs�k�h
ACP�n
� �BATCap�k�h
ACP�n ; if : t>Ce�k�hACP�n
8>>><>>>:
ð20Þ
Wk�hACP�nðtÞ
���upper¼
0; if : t<Cs�k�hACP�n
Sock�hACP�nðtÞ
���upper�Socs�k�h
ACP�n
� �BATCap�k�h
ACP�n ; if : Cs�k�hACP�n 6 t6Ce�k�h
ACP�n
Soce�k�hACP�n�Socs�k�h
ACP�n
� �BATCap�k�h
ACP�n ; if : t>Ce�k�hACP�n
8>>>><>>>>:
ð21Þ
where
Sock�hACP�nðtÞ
���lower¼max Soclower�k�h
ACP�n ; Socs�k�hACP�n�
Pmax�hACP�n t�Cs�k�h
ACP�nþ1� �
Dt
BATCap�k�hACP�n
24
35; Soce�k�h
ACP�nþPmax�h
ACP�n t�Ce�k�hACP�n
� �Dt
BATCap�k�hACP�n
24
35
8<:
9=;
ð22Þ
Sock�hACP�nðtÞ
���upper¼min Socupper�k�h
ACP�n ; Socs�k�hACP�nþ
Pmax�hACP�n t�Cs�k�h
ACP�n þ1� �
Dt
BATCap�k�hACP�n
24
35; Soce�k�h
ACP�n �Pmax�h
ACP�n t�Ce�k�hACP�n
� �Dt
BATCap�k�hACP�n
24
35
8<:
ð23Þ
Thus, the accumulated charging quantity from the first time slot tothe t-th time slot offered by the h-th charging station as a whole hasthe lower boundary and the upper boundary, given by:
WhðtÞ���
lower¼XNðhÞn¼1
XKðnÞk¼1
Wk�hACP�nðtÞ
���lower
ð24Þ
WhðtÞ���
upper¼XNðhÞn¼1
XKðnÞk¼1
Wk�hACP�nðtÞ
���upper
ð25Þ
Fig. 8. Optimal charging schedules in Case 1. (a) Charging station #1. (b) Charging station #2. (c) Charging station #3. (d) Charging station #4. (e) Charging station #5. (f)Charging station #6. (g) Charging station #7. (h) Charging station #8. (i) Charging station #9. (j) Charging station #10.
514 L. Jian et al. / Energy Conversion and Management 78 (2014) 508–517
Hence, the following restraint can be derived:
WhðtÞ���
lower6
Xm
t¼1
ðDt � PtCS�hÞ 6WhðtÞ
���upper
; m 2 ½1; T� ð26Þ
Finally, the first layer optimization problem is obtained. Its objec-tive function is given by (15), and the restraint conditions are givenby (16)–(26).
4.2. Second layer optimization
In the second layer optimization, the station control serverplans the charging power for each charging post under its gover-nance, aiming to meet the instructions ordered by CCC which has
been generated in the first layer optimization. The problem canbe formulated as:
minXT
t¼1
1T
XNðhÞn¼1
Pt�hACP�n � Pt
CS�h
!224
35; h 2 ½1;H� ð27Þ
Subject to:
� Pmax�hACP�n 6 Pt�h
ACP�n 6 Pmax�hACP�n ; t 2 [
k¼KðnÞk¼1 Cs�k�h
ACP�n;Ce�k�hACP�n
h i;
n 2 ½1;NðhÞ� ð28Þ
Pt�hACP�n ¼ 0; t 2 ½1; T� � [k¼KðnÞ
k¼1 Cs�k�hACP�n;C
e�k�hACP�n
h i; n 2 ½1;NðhÞ� ð29Þ
Fig. 9. Optimal charging services provided by charging post #8 in Case 1. (a) Model 1. (b) Model 2.
Fig. 10. Optimal charging services provided by charging post #69 in Case 1. (a) Model 1. (b) Model 2.
L. Jian et al. / Energy Conversion and Management 78 (2014) 508–517 515
XCe�k�hACP�n
t¼Cs�k�hACP�n
½Dt �Pt�hACP�n� ¼ Soce�k�h
ACP�n� Socs�k�hACP�n
� ��BATCap�k�h
ACP�n ; k2 ½1;KðnÞ�;
n2 ½1;NðhÞ� ð30Þ
Soclower�k�hACP�n 6 Sock�h
ACP�nðjÞ 6 Socupper�k�hACP�n ; j 2 Cs�k�h
ACP�n;Ce�k�hACP�n
h i;
k 2 ½1;KðnÞ�; n 2 ½1;NðhÞ� ð31Þ
Sock�hACP�nðjÞ ¼ Socs�k�h
ACP�n þXj
t¼Cs�k�hACP�n
Dt � Pt�hACP�n=BATCap�k�h
ACP�n
h ið32Þ
1 For interpretation of color in Fig. 7, the reader is referred to the web version othis article.
The proposed DLOC strategy can effectively reduce the computa-tional complexity. For the first layer, the number of variables de-pends on the number of charging stations, which is dramaticallyshrunk compared to the number of all charging posts in the regionalgrid. For the second layer, the optimization program can be exe-cuted at the same time for all the charging stations. The resultsand performance will be presented in the following section.
5. Results and discussions
Several cases are studied to assess the performance of the pro-posed V2G and the DLOC strategy. A set of programs are designedto randomly generate the data needed for simulation studies. Theone-day cycle starts at 06:00 am and ends at 05:59 am (nextday). The time slot Dt ¼ 15 min, and there are totally 96 time-slotsin the 24 h period. Some practical situations are taken into accountwhen designing the random data generation programs, for exam-ple, the conventional load is likely to reach peak values at noonand in the evening, the PEVs are likely to be connected to grid atnight and at noon, and so forth. Limited by the length of the article,the details on data generation are not included herein.
Totally six cases with different problem scales are simulated.Table 1 lists the specifications of these cases. For each case, twomodels are employed. One is the single-layer model (Model 1)introduced in Section 3, and the other is the double-layer model(Model 2) proposed in Section 4. Fig. 7 gives1 the performances ofV2G operation in several selected cases. It can be observed thatthe overall load curves (blue curve) are successfully flattened withthe help of the PEV loads (red cure). Moreover, it can also be found
f
Fig. 11. Comparison of computing time consumed.
516 L. Jian et al. / Energy Conversion and Management 78 (2014) 508–517
that the peak value of the total load is slightly lower than that of theconventional load, attributed to the energy feedback of the PEVs.This demonstrates that power grid is able to contain newly addedPEV loads to some extend without boosting its capacity, if the V2Goperation can be effectively carried out.
The obtained PEV load curves by using two modeling methodsare the same. This implies that the proposed DLOC strategy agreesvery well with the design objectives. Nevertheless, this does notmean that Model 2 is exactly equivalent to Model 1. Fig. 8 givesthe optimal charging schedules of the 10 charging stations in Case1, in which, the red curves are the results of the first layer optimi-zation of Model 2, and the blue curves are obtained by summing upthe charging schedules of all the charging posts in the same charg-ing station calculated in Model 1. It can be found that there are tinydifferences between the results obtained by using these twomodels.
Moreover, Figs. 9 and 10 gives the optimal charging schedulesof two selected charging post in Case 1 obtained by using twomodels, the charging post Nos. 8 and 69. Both charging postsare assigned to offer five charging services (I–IV) in the coming24-h. The upper part of each plot gives the resulted optimalcharging power provided by the corresponding charging post.With these regulated charging profiles, the electricity charging de-mand of the PEV connected can be guaranteed, moreover, theminimized overall load variance can be achieved. The lower partof each plot illustrates the battery Soc curve of the PEV connectedto the corresponding charging post by engaging the optimalcharging pattern. Subtle distinctions can also be observed in theresults of the two models.
The two models are solved on the same workstation (CPU3.20 GHz, RAM 6 GB), and the computing time consumed are listedin Table 1. For Model 2, the time consumed in the first layer opti-mization plus the longest time consume in the second layer opti-mization is given for comparing with that consumed bycalculating the Model 1. Fig. 11 visually illustrates the comparisonbetween the two models. It is worth noting that, for Case 6, theModel 1 is failed to be solved due to the running out of the RAM.Both Table 1 and Fig. 11 demonstrate that the proposed DLOCstrategy can dramatically reduce the computational complexity.
6. Conclusions
In this paper, a possible scenario of V2G implementation withinregional smart grid is discussed. The key information on the powergrid, the charging posts, the PEVs and the vehicle owners’ demandsshould be perceived by the central control center, so that it cangenerate optimal charging schedules to fulfill the demands of each
charging services, and to minimize the overall load variance in theregional grid. Next, the problem concerning V2G operation ismathematically formulated. With the increase of the scale of PEVsand charging posts involved, the computational complexity willbecome tremendously high. Therefore, a double-layer optimalcharging (DLOC) strategy is proposed to solve this problem. Casestudies demonstrated that the V2G operation can help flatten theoverall power load curves and it enables power grid to containnewly added PEV loads to some extend without boosting its capac-ity. Comparative study shows that the proposed DLOC strategy candramatically reduce the computational complexity. The outstand-ing performance on reducing overall load variance of regionalpower grid implies that tremendous economic and social interestscan be derived from V2G implementation, which demonstrates thereasonability and necessity of developing V2G. In future work, a lotmore practical issues, such as financial incentives, will be takeninto account, and could be estimated and testified by using theDLOC strategy presented in this paper.
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