Medium-term planning of vehicle-to-grid aggregators for ...scientiairanica.sharif.edu/article_20612_2d46e91860b5464a08d1116… · aggregator and the vehicle owners on division of

Scientia Iranica D (2020) 27(3), 1413{1423

Sharif University of TechnologyScientia Iranica

Transactions D: Computer Science & Engineering and Electrical Engineeringhttp://scientiairanica.sharif.edu

Medium-term planning of vehicle-to-grid aggregatorsfor providing frequency regulation service

M.H. Sarparandeha;�, M. Kazemib, and M. Ehsana

a. Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran.b. Faculty of Electrical Engineering, University of Shahreza, Shahreza, Iran..

Received 7 May 2017; received in revised form 9 December 2017; accepted 26 June 2018

KEYWORDSElectric vehicles;Frequency regulation;Pricing;Vehicle-to-Grid(V2G);Aggregator.

Abstract. Utilization of electric vehicle battery to provide frequency regulation servicein electricity markets is a technically feasible and economically attractive idea. The role ofaggregators as a middleman between electric vehicle owners and the frequency regulationmarket has been discussed in the literature. However, the economic interaction betweenthe aggregator and the vehicle owners on division of interests is still a missing point. In thispaper, a new pricing model for aggregators of electric vehicles is proposed such that notonly its pro�t is maximized, but also the vehicle owners have su�cient incentives to takepart in the o�ered vehicle-to-grid program. In the proposed model, the aggregator takesinto account the depreciation cost of electric vehicle batteries and the cost of net energytransaction between the electric vehicles and the grid and, then, considers these items insettling accounts with vehicle owners. The proposed model has been implemented on PJMfrequency regulation market, and the results are discussed in the paper.© 2020 Sharif University of Technology. All rights reserved.

1. Introduction

The application of Electric Vehicles (EVs) in trans-portation systems is a growing trend as they improvefuel consumption e�ciency and reduce green-house gasemissions [1]. On the other hand, the decline of batterycost would decrease EVs cost. For example, based ona comparison of 2017 and 2015, it was predicted thatbattery cost would drop by 25% [2]. It was also esti-mated that EVs would cost less than 22,000$ by 2040[3]. In this way, a remarkable share for EVs in futureautomobile markets is predictable as stated in [4].

Along with the increasing number of EVs, the ideaof utilizing EV batteries as distributed energy storage

*. Corresponding author.E-mail address: [email protected]. (M.H.Sarparandeh)

doi: 10.24200/sci.2018.20612

resources in electricity markets will be practicable.This service, which is known as vehicle-to-grid (V2G),has been de�ned as the power that can be fed to thegrid by EVs through appropriate connections when theEVs are parked [5].

V2G can be applied to various electricity marketssuch as peak power, spinning reserves, and frequencyregulation markets. Some cost-bene�t studies haveevaluated the pro�tability of V2G for each marketand have demonstrated that one of the most prof-itable markets for V2G is the frequency regulationmarket [5,6]. Frequency regulation service is theuse of fast response resources such as synchronizedgenerators that have Automatic Generation Control(AGC) capability to keep the moment by momentbalancing between generation and load. Regulationfacilitates maintaining frequency under the proposedmarket arrangements and managing the di�erencesbetween actual and scheduled power ows betweenbalancing areas. The units that wish to participate

1414 M.H. Sarparandeh et al./Scientia Iranica, Transactions D: Computer Science & ... 27 (2020) 1413{1423

in the regulation market must submit their bid to thesystem operator. Then, the system operator broadcastsAGC signal to the selected units in real time.

EV batteries are a suitable source for frequencyregulation service due to their fast response in com-parison with conventional thermal units [7]. However,the number of EVs is too huge for the power systemoperator to communicate with all of them directly.Furthermore, the minimum bid size requirements ofcurrent electricity markets are obstacles to direct par-ticipation. Hence, several papers in the literaturehave proposed a structure in which aggregators submitenergy or regulation bids to markets on behalf of a eetof EVs [8,9]. In this structure, the aggregators contractwith interested EV owners and utilize their batterycapacities according to some pre-speci�ed conditions.

Although the technical and economic aspects ofV2G for providing frequency regulation service havebeen investigated in several pieces of research, properpricing of this service is still a missing point in theliterature. In other words, it is not clari�ed that howand how much the EV owners are paid by aggregatorsfor sharing their batteries' capabilities. In [10], thepro�t from the participation of EVs in energy, reserve,and regulation markets was calculated; however, theshare of the aggregator and EV owners from this pro�twas not determined. In [11], EVs optimize chargingand regulation decisions, and the aggregator only sumsthe optimal decisions for each EV and submits bidsto the Independent System Operator (ISO). It seemsas if the aggregator is a nonpro�t organization in [11],and its pro�t is not taken into account. In [12], thebidding strategy of an aggregator that participated inthe day-ahead electrical energy market was addressed,ignoring the bene�ts of EV owners. A similar approachcan be found in [13], where the pro�t of the aggrega-tor was maximized through the optimal simultaneousbidding of V2G energy and ancillary services, whilethe bene�ts of EV owners were not modeled, and thecompetition between di�erent competing aggregatorswas ignored. In contrast, the problem considered in[14] assumes a hypothetical problem that a companyowning a eet of EVs schedules its EV eet so asto optimize its battery charging, V2G revenue, andvehicles' duty/service. The problem was modeled as amulti-criteria decision-making problem and solved byanalytic hierarchy process. However, the aggregator isassumed to be an exogenous player in [14], whose deci-sions are neglected. In [15], the aggregator maximizedits pro�t from participation in the frequency regulationmarket while minimizing the charging costs of EVs. In[15], the EV owners were not paid for V2G service;thus, there was not enough incentive for EV owners toparticipate in V2G.

In this paper, the aggregator pays the EV ownersfor V2G service according to the number of hours that

they provide frequency regulation, taking into accountEV batteries depreciation and the net electrical energyexchanged between the EV batteries and the grid. Theprice determination of V2G service is a necessary stepto evaluate whether there are su�cient incentives forboth the EV owner and the aggregator to participatein such a cooperation. Hence, we have tried to modelthe pricing scheme of an aggregator for V2G service bymaximizing the aggregator's pro�t and considering theeconomic behavior of EV owners.

The rest of the article is organized as follows.The pricing model with which the aggregator and theowners of EVs deal to cooperate on providing frequencyregulation service via V2G is proposed in Section 2.Section 3 is devoted to a case study in which the V2Gpricing model is utilized for frequency regulation as anancillary service in PJM electricity market, and theresults are presented in the same section. Finally, someremarks and directions for future work are discussed inSection 4.

2. Pricing framework modeling

This paper proposes medium-term planning for an EVaggregator to maximize its pro�t. The aggregator usesavailable battery capacities of its contracted EVs toparticipate in the frequency regulation market. In thisway, the aggregator adjusts its strategy to participatein the regulation market and to interact with EVowners. The main decision variable of the aggregatorin this process is its o�ered price to EV owners. In thissection, the interactions between aggregators and theother participants are modeled, and a pricing schemefor V2G is proposed.

2.1. Model of interaction with EVsThe aggregator o�ers the price to EV owners inexchange for their V2G service. This price{hereinafterreferred to as V2G price{will a�ect the number of EVswho are willing to sign on. If the V2G price is verylow, then no EV owner will agree on the contract. Thehigher is the price o�ered, more EV owners are willingto contract with the aggregator.

This procedure is similar to that of retailers'medium-term planning in which the o�ered price ofretailer de�nes the number of its clients. Di�erentmethods have been proposed in the literature to ad-dress this problem from the retailer's perspective. In[16{18], the relation between the number of contractedcustomers and the o�ered retail price is introducedby Price-Quota-Curve (PQC). In this paper, in linewith [16{18], a \V2G supply function" is proposed tomodel the relationship between V2G price o�ered bythe aggregator and the number of EVs who accept theV2G program.

The V2G supply function provides the number of

M.H. Sarparandeh et al./Scientia Iranica, Transactions D: Computer Science & ... 27 (2020) 1413{1423 1415

Figure 1. Vehicle-to-Grid (V2G) supply function.

Figure 2. Share of parked Electric Vehicles (EVs) independence on day types [20].

EV owners that are willing to share their EV batteriesin exchange for the o�ered V2G price. Figure 1 showsa piecewise linear PQC. The precise derivation of thisfunction is an econometric problem, which is beyondthe scope of this paper. Thus, the function has beenconsidered as an input to our model and has beenestimated by a hypothetical curve for the case study.However, the curve meets two important properties:it is increasing and its derivative is increasing, too.The latter can be explained by \diminishing marginalproduct": the property whereby the marginal productof an input declines as the quantity of the inputincreases [19]. Those EVs that are attracted to V2Gcontract earlier can provide V2G service more hoursof the day in comparison to busy EVs that may joinsubsequently.

Contracted EVs are not always parked and readyfor V2G service. The share of available EVs can beestimated by statistical studies for di�erent hours ofthe day and di�erent day types, i.e., weekdays andweekends. In [20], the share of parked EVs wasdesignated for di�erent day types. Figure 2 displaysthe share of parked EVs for di�erent hours and daytypes for a typical area.

In addition, it should be noted that not all parkedEVs are available for V2G service. Only those EVs areavailable (a) that are parked in a place with necessaryinfrastructure (at least an outlet), (b) whose ownersactually plugged-in the EV, and (c) whose batteries'

State-of-Charge (SoC) is proper enough to be used bythe aggregator for the regulation service. In order tomodel the e�ect of the above-mentioned conditions, an\availability ratio" is used here. The availability ratiois de�ned as the ratio of available EVs ready for V2G tothe number of parked EVs. In practice, the aggregatorcan determine the availability ratio of EVs based on itsdatabase record.

In order to guarantee the active participation andmutual bene�t of aggregator and EVs, the quality ofthe interaction between the involved parties should beconsidered properly. For this purpose, three di�erenttypes of payment are considered in this paper. Inthe �rst payment category, the aggregator pays theEV owners for every hour that the EVs are availablefor this service. In the second payment, at the endof each settlement period (e.g. a month), the netelectrical energy received by each EV from the gridor injected to the grid by the EV will be metered andaccounted in transactions between the aggregator andthe EV owners. In the last one, the aggregator pays\battery depreciation cost" to the EV owners, which isa payment term in their invoice to compensate for theirbattery depreciation. These payments are discussed inthe following sub-sections in detail.

2.2. Model of interaction with regulationmarket

The aggregator bids to the frequency regulation marketfor every hour according to the number of estimatedavailable EVs. Nevertheless, the aggregator estimateshave an error that is simulated in our model by astandard error. Hence, the number of real availableEVs has been sampled for every hour randomly bya normal probability distribution function with theestimated number of available EVs as expected valueand 5% of EVs as standard deviation. If the electricpower of EVs' batteries is not su�cient to accomplishthe frequency regulation service, the aggregator willoperate a back-up battery bank.

The assumed regulation market structure of thispaper is similar to the frequency regulation marketof PJM. It is worth mentioning that the ancillaryservices that are used to balance the generation andconsumption of electricity in real time (with littledi�erence in di�erent electricity markets, academicand technical literature) include frequency response,frequency regulation, spinning reserve, non-spinningreserve, and supplemental reserve. In PJM, frequencyresponse is not a stand-alone ancillary service product.All resources that provide spinning reserve must besynchronized with the grid and must be frequencyresponsive. Spinning, non-spinning, and supplementalreserves are reserve capabilities that can be convertedfully into energy or load, which can be removed fromthe system within 10 minutes of the request from


the PJM dispatcher. Frequency regulation, which isour goal market, refers to the control action that isperformed to correct for load changes that may causethe power system to operate above or below 60 Hz.The response time of this service is 2 seconds, and itsduration is 5 minutes.

The mechanism for procuring frequency regula-tion service in PJM regulation market is describedin [21]. Regulation service providers must submit theiro�ers to PJM market. Then, PJM utilizes these o�erstogether with energy o�ers and resource schedules todetermine the lowest cost alternative for these servicesthrough an optimization process. In this process, theRegulation Market Clearing Price (RMCP) for eachhour of the operating day is determined [21].

Regulation resources will receive the followingregulation signals in PJM [22]:

� Assigned regulation (AReg): This is the regulationquantity (MW), which is announced to the partic-ipants whose o�ers are accepted in the regulationmarket. This signal is static during each hour, yetis sent on a 10-second scan rate;

� Regulation control signal (RegA): This signal issent by PJM to frequency regulation resources inreal time to modify their generation/consumptionaccording to the signal value and their contract.This signal will be transmitted on a 2-second scanrate;

� Fast or dynamic regulation (RegD): As a specialfeature of PJM market, this signal, which has afunction similar to RegA, is transmitted by PJMto frequency regulation resources. However, it ispreferred to be utilized for energy storage devices,since this signal is short-term balanced around zero.

To clarify the di�erences between RegA andRegD, it is worth mentioning that there are di�erenttypes of regulation resources such as conventionalpower plants (e.g., combined cycle, hydroelectric, etc.),the energy storage resources (e.g., batteries, ywheels,EVs, etc.), and also dispatchable loads. Energy storagesystems are more precise in tracking regulation signalthan other regulation resources; however, they su�erfrom limited energy capacity. RegD signal has a meanvalue of zero that prevents energy storage resourcesfrom excess charge/discharge. RegA is a function ofslow �lter of Area Control Error (ACE) and can remainfull raise or lower for extended periods, whereas RegDis a function of fast �lter of ACE. Figure 3 representsthe formation of these signals clearly [22].

It is worth mentioning that the implementationof the concept of V2G in practice requires bidirectionalcommunication infrastructure between the aggregatorand the EVs-through which the aggregator receives thestatus of EVs and transmits the regulation signal to

Figure 3. Formation of traditional regulation signal andfast (dynamic) regulation signal [22].

EVs. Thus, V2G can be realized after the widespreadinstallation of smart meters and the development ofsmart grid. The pricing framework proposed in thispaper presumes such infrastructure to be available.

2.3. Model of EV's battery degradationThe e�ects of frequent charge/discharge cycles due toV2G on the lifetime of commercial Lithium-ion cellswere discussed in [23{25]. The battery life is usuallyexpressed as the number of cycles resulting in itscapacity drop to a predetermined level (e.g., 80% ofits initial capacity). It is shown that the achievablecycle count is a function of Depth-of-Discharge (DoD).Figure 4 illustrates the battery lifetime in cycles versusDoD [26]. As is shown in Figure 4, battery cyclelife is related to the DoD. In other words, shallowcycling has much less impact on battery lifetime thandeep cycling. Since frequency regulation causes shallowtype of cycling, the battery degradation is not muchworrying. Nevertheless, the lack of compensation for itmay be frustrating for EV owners.

The curve depicted in Figure 4 has been estimatedby Eq. (1) based on the approach of Rosenkranz [27]and the Fraunhofer ISE's model, as stated in [25]and [26]:

NCycles = 1331� (DoDV 2G)�1:8248; (1)

where NCycles is the expected battery lifetime in terms

Figure 4. Estimated battery lifetime in cycles as afunction of Depth-of-Discharge (DoD) [26].


of cycles, and DoDV 2G is the DoD of EV batteryfor providing regulation service. By assuming a �xedcycling pattern, DoDV 2G can be determined throughthe following equation.

DoDV 2G = Pch � Tch=Ebat; (2)

where Pch is the charge/discharge power in kW, Tch isthe charge/discharge duration in hour, and Ebat is thecapacity of battery in kWh.

Due to the unknown cycling pattern in trackingregulation signal, expressing battery lifespan in termsof its energy throughput would be more practical. Theenergy throughput is a parameter that speci�es thetransacted energy of a battery in both charge and dis-charge modes over its whole lifetime. This parametercan be calculated by the following equation [24]:

EET = NCycles �DoDV 2G � Ebat: (3)

In the above equation, EET is the lifetime energythroughput of the battery in kWh. In this way, the\battery depreciation cost" can be obtained throughEq. (4):

Cdep = Ebat � �bat � ET =EET ; (4)

where Cdep is the battery depreciation cost during acertain period in $, �bat is the battery price in $/kWh,and ET is the total transferred energy during the sameperiod in kWh.

2.4. Proposed pricing modelThe proposed pricing scheme for V2G service can bedescribed by an optimization problem that maximizesthe aggregator's pro�t and considers the behavior ofthe EV owners through V2G supply function. Theobjective function is described in Eq. (5):

max�V 2G

T =�Tt=1�fr(t)�Nest(t)� PEV � �Tt=1

Nreal(t)� �V 2G � Enet � �r � Cdep;EV� Cdep;bb; (5)

where T is the pro�t of aggregator during the sim-ulation time span in $. The main decision variableof this optimization problem is �V 2G, which is o�eredby the aggregator to EV owners in exchange for usingtheir battery for regulation service. The objective has4 terms. The �rst one �T(t=1)�fr(t) � Nest(t) � PEVmodels the revenue gained from participating in theregulation market in which �fr(t) is the frequencyregulation price of the electricity market in hour tin $/kWh, PEV is the rated charge/discharge powerof EV batteries in kW, and Nest(t) is the estimatednumber of EVs in hour t who are ready to provideregulation service, which is obtained by V2G supplyfunction. The second term, i.e., �Tt=1Nreal(t) � �V 2G,

models the payment of the aggregator to EV owners forparticipation in V2G program. In this term, �V 2G isV2G price that the aggregator o�ers to pay EV ownersin $/h, and Nreal(t) is the real number of EVs in hourt who are ready to provide regulation service, which issimulated in our model by adding a standard error toNest(t). The third term in Eq. (5) models the paymentto EV owners for the net energy delivered by themto the grid, where �r is the retail electricity price in$/kWh, and Enet is the sum of net energy transferredto/from grid by EV batteries over simulation timespan in kWh. Finally, Cdep;EV and Cdep;bb are batterydepreciation cost in $ for whole EV batteries and back-up battery bank, respectively, which are calculated byEq. (4).

The capacity o�ered to the regulation market isNest(t) � PEV based on the explanations of Eq. (5).However, a ratio of this capacity is utilized by theregulation market in each 2-second time step, whichis determined by the RegD signal (see Section 2.2). Inthis way, the transacted power in the regulation marketcan be evaluated using Eq. (6).

PReg(�) = RegD(�)�Nest(t)� PEV ; (6)

where PReg(�) is the power that must be deliveredto/absorbed from the grid by the aggregator in timestep � in kW, RegD(�) is the value of the frequencyregulation signal sent by the power system operatorto the aggregator in time step � , which is �1 <RegD(�) < 1. In the proposed model, PReg(�) canbe provided by the EV batteries as the �rst optionor the backup battery bank as the second option.The shares of EV batteries and the backup battery inproviding regulation power are determined by PEV f (�)and Pbbb(�) through Eqs. (7) and (8), respectively.

PEV f (�) =8><>:Nreal(t)�PEV if PReg(�)>Nreal(t)�PEV�Nreal(t)�PEV if PReg(�)>�Nreal(t)�PEVPReg(�) otherwise (7)

Pbb(�) =

8>>>>>>>>>><>>>>>>>>>>:

minfPReg(�)� PEV f (�); Pbb;rgif PReg(�) > PEV f (�)

0 if PReg(�) = PEV f (�)

maxfPReg(�)� PEV f (�);�Pbb;rgif PReg(�) < PEV f (�)

(8)

In the above equations, PEV f (�) and Pbb(�) arethe powers of EV eet and back-up battery bankin time step � in kW, respectively, and Pbb;r is therated power of back-up battery bank in kW. The


batteries deliver electricity to the grid when PEV f (�)and Pbb(�) are positive, and charge when these powersare negative.

The performance of the aggregator in providingfrequency regulation service will be poor if it fails tofollow PReg(�) completely due to the shortage of EV eet and back-up battery bank constraints. Di�erentmarkets adopt di�erent methods for calculating theperformance of frequency regulation service providers.However, the performance depends on the di�erencebetween the regulation service actually provided andthe regulation supposed to be provided. This quantitycan be calculated by Eq. (9):

Pdi� (�) =

8>>>>>><>>>>>>:P �bb(�)� Pbb;r if P �bb(�) > Pbb;r

�P �bb(�)� Pbb;r if P �bb(�) < �Pbb;r0 otherwise

(9)

where P �bb(�) is the power of back-up battery bankin time step � , provided that the capacity of back-upbattery bank is unlimited. P �bb(�) will be obtained byEq. (8), if Pbb;r is in�nite.

The SoC of the back-up battery bank will bechanged after any charge/discharge. Its value in anytime step is dependent on its previous value as de-scribed in Eq. (10) for a 2-second frequency regulationtime step:

SoCbb(�) =8><>:SoCbb(� � 1)� Pbb(�)Ebb��dis�1800 if Pbb(�) � 0

SoCbb(� � 1)� Pbb(�)��chEbb�1800 if Pbb(�) < 0 (10)

where SoCbb(�) is the state of charge of back-up batterybank in time step � , Ebb is the capacity of back-upbattery bank in kWh, and �ch and �dis are chargingand discharging e�ciency of the battery, respectively.For a 2-second frequency regulation time step, an hourconsists of 1800 time steps.

A similar equation can be considered for EVbatteries by substituting the power and capacity of theEV battery into the parameters of the back-up batterybank. If the resultant SoC from Eq. (10) is outside therange of zero to one, the following modi�cation mustbe performed:

If SoCbb(�) > 1,8>>>>>><>>>>>>:Pmdi� (�) = Pdi� (�) + Ebb(SoCbb(�)� 1)� 1800

Pmbb (�) = Pbb(�) + Ebb(SoCbb(�)� 1)� 1800

SoCmbb (�) = 1

(11)

If SoCbb(�) < 0,8>>>>>><>>>>>>:Pmdi� (�) = Pdiff (�)� Ebb � SoCbb(�)� 1800

Pmbb (�) = Pbb(�)� Ebb � SoCbb(�)� 1800

SoCmbb (�) = 0

(12)

In the above equations, variables with superscript of mare modi�ed variables.

We have considered the average ratio of Pdiff (�)to PReg(�) during simulation time span as the perfor-mance criteria, and the cases with poor performanceare eliminated from solutions.

As the last equation, the total transferred energyof back-up battery bank during the time span ofsimulation can be obtained through Eq. (13) as follows:

ET;bb = �T�=1jPbb(�)j=1800; (13)

where ET;bb is the total transferred energy of back-upbattery bank during T . A similar equation can beconsidered for EV batteries by replacing Pbb(�) withPEV f (�)=Nreal(t).

The planning horizon is set to be one year, and theaggregator can update the V2G price annually. Sincethe time steps in frequency regulation service are tothe extent of few seconds, the simulation time spanis reduced to one month, i.e., a �nancial settlementperiod between the aggregator and the EV owners,as the representative of twelve months of the year soas to decrease the solution time. In addition, thepro�t of the aggregator is a complicated function of theV2G price with many conditional functions. Hence,the problem has been optimized by an evolutionaryoptimization method. The genetic algorithm, which isused in this paper, is one of the evolutionary algorithmsthat is most commonly applied to solve combinatorialoptimization problems.

Figure 5 displays the owchart of our pricingframework. As can be seen in Figure 5, the aggregator�rst sets a V2G price to be o�ered to the EV owners.Then, the number of EVs that are eager to participatein frequency regulation service and also the numberof available EVs for every hour of the day can beestimated. During the simulation time span, the AGCsignal is transmitted from the power system operatorto the aggregator, while the aggregator utilizes thebatteries of available EVs to ful�ll its obligationstowards the power market. In case of lack of capacityto provide frequency regulation service, the back-upbattery bank will be operated.

At the end of each simulation time span, thefollowing required parameters are obtained: totaltransferred energy of EV batteries and the backupbattery bank, the number of hours of availability for


Figure 5. Flowchart of the proposed pricing framework.

each EV during simulation time span, and net energytransaction between the EVs and the grid. Then, thecosts, revenues, and �nally the pro�t of aggregator foreach V2G price are calculated. Genetic algorithm con-siders the current generation of V2G prices as decisionvariables and the corresponding pro�t of the aggregatoras �tness values to generate the next generation of V2Gprices so that the pro�t of aggregator can be improved.This iterative algorithm continues until the terminationcriteria are satis�ed.

3. Case study and results

This study applied the pricing framework proposed inthe previous section to the frequency regulation marketof The PJM-one of the world's largest competitive

wholesale electricity markets. First, the input data ofthe case study are introduced; then, the results arepresented.

3.1. Input data and optimization parametersThe pricing model described in Section 2 and depictedby Figure 5 is implemented on PJM electricity market.In our case study, the V2G price o�ered by theaggregator to EV owners is determined so that theaggregator pro�t is maximized in a time span of onemonth. RMCP and RegD signal have been derivedfrom real historical data of PJM for a one monthperiod. Utilization of real historical data is a properway to consider the uncertainty and random nature ofchanging RMCP, volatile RegD signal, and uncertainnumber of available EVs in each hour. A one-monthperiod includes 31�24 hours, and each has di�erentparameters and conditions. In the case of RegDsignal that has a variant quantity in every two-secondperiod, using its real historical data in a one-monthperiod will consider the signal's stochastic nature, too.Therefore, the real historical data have been appliedto model the random changes and the uncertaintyof these parameters as an alternative for probabilitydistribution functions used in stochastic methods.

The RMCP of PJM electricity market on 1 Jan-uary 2013 is depicted in Figure 6 [28]. The RMCP isthe sum of the regulation market capability clearingprice and the regulation market performance clearingprice [29]. The price at which the aggregator settlesthe net electrical energy ow between an EV and thegrid, i.e., �r, is set to 12 cents per kWh. This valueis chosen in a way that is close to the average retailelectricity prices for residential customers across PJMregion. RegD signal in January 2013 is obtained fromPJM website whose changes for a one-hour period areplotted in Figure 7 [30].

As discussed in Section 2, \V2G supply function"has been considered by a hypothetical curve illustratedin Figure 1. In addition, data of [20] are used tode�ne the share of parked EVs for di�erent types ofthe day (please see Figure 2), and the availability

Figure 6. PJM regulation market clearing price (1January 2013) [28].


Figure 7. RegD signal in (PJM) (1 January 2013, 02:00 {03:00 AM) [30].

Figure 8. Availability share of Electric Vehicles (EVs)that have a contract with the aggregator.

ratio is assumed to be 0.75. By assuming the above-mentioned data, the available EVs are presented inFigure 8.

Assuming that the EVs are of plug-in type andthat they are connected to the grid through householdsockets, it is reasonable to consider the size of 3 kW forrating power electronics converter-which is an interfacebetween the EV battery and the grid. The capacityof EV batteries is supposed to be similar and equalto 20 kWh, although as will be seen later, frequencyregulation service following RegD signal does not a�ectthe SoC of EV batteries signi�cantly. Therefore, thecapacity of EV batteries does not have a remarkableimpact on our model. Both charging e�ciency (�ch)and discharging e�ciency (�dis) of EV batteries areconsidered to be 0.95 as in [31], resulting in round-trip e�ciency of approximately 0.9. The capacity ofthe back-up battery bank is considered to be �xed andequal to 1000 kWh, and the converter rated power isequal to 200 kW. The initial SoC for back-up batterybank and all EVs is assumed to be 50%.

As is stated in [23], DoDV 2G is considered to be3% in some papers, resulting in 106 cycles. It is arational approximation for our case, because, duringJanuary 2013, we could not �nd a period longer than10 minutes in which regulation signal (RegD) hadsimilar signs for all 2-second time steps. Therefore,for an EV battery with 20 kWh capacity and 3 kW

charge/discharge power, a maximum of 2.5% DoD isfeasible according to Eq. (2).

The battery price of Lithium-ion batteries isdeclining and has fallen from 500{550 $/kWh in 2014to less than 400 $/kWh in 2017 and, based on someassertions, even to a surprising value of 200 $/kWh [32].A battery price of 350 $/kWh has been concluded as aresult of various declared prices for our case study.

The pricing model has been optimized by NSGA-II algorithm in MATLAB 7.12.0. NSGA-II is acontrolled elitist genetic algorithm. Since it is elitist,it prefers solutions with a better �tness value. As itis controlled, it also favors the solutions that increasethe diversity of the population. Diversity of populationhelps the algorithm converge to the optimal solution.The population size of each generation in NSGA-IIalgorithm is set to 20 individuals. In order to ensureappropriate performance of the aggregator in providingfrequency regulation, the cases where the average ratioof Pdiff (�) to PReg(�) during simulation time span ismore than 1% are eliminated from solutions. The algo-rithm termination criteria include the combination ofthe maximum number of generations, time constraints,and lack of signi�cant improvement in �tness values.

3.2. ResultsBy using the mentioned data of the previous subsec-tion, the proposed algorithm of Figure 5 is applicable.The optimum level of V2G price is 3.81 cents perhour. This price will attract 702 EV owners to reachan agreement with the aggregator to provide V2Gservice for frequency regulation market. The economicresults for various V2G price scenarios are shown inTable 1. The value of the objective function is declaredin this table term by term. As can be seen in thistable, for V2G prices higher than 7 cents per hour,the aggregator will lose due to high payments to EVowners; meanwhile, the EV owners do not have enoughmotivation to participate in V2G service for prices lessthan 1 cent per hour.

Based on Eqs. (7) and (8), when the capacity ofEV batteries is lower than the requested power by thefrequency regulation market, the capacity of backupbattery is used. Figures 9 and 10 display the transactedpower between the EV eet and the grid and thatbetween back-up battery bank and the grid for a periodof one hour, respectively.

The results of analyzing the charge/discharge pat-tern of the back-up battery bank during our monthlyperiod show that this battery bank has been rarelyutilized, because the prediction error of the availableEVs is assumed to be low. Because of this fact, theSoC of the back-up battery bank will not approach itsboundary limits. For more clari�cation, the power andthe SoC of the backup battery are presented for thewhole January in Figures 11 and 12, respectively.


Table 1. Economic results of various Vehicle-to-Grid (V2G) price scenarios in a 1-month period.

V2G Price(cent/hour)

No. ofEVs

Revenue ofaggregator

($)

Back-upbatteries

degradationcost ($)

EV eetbatteries

degradationcost ($)

Payment fornet transacted

power ($)

Payment forV2G to EVowners ($)

Pro�t ofaggregator

($)

2 250 13521 3 975 1810 3488 7246

3 500 27043 6 1949 3613 10481 10994

3.81 702 37995 8 2738 5082 18635 11532

4 750 40564 9 2923 5436 20950 11247

5 1000 54086 12 3897 7228 34822 8127

6 2000 108170 17 7795 14466 83684 2209

7 3500 189300 20 13637 25328 170290 {19947

8 5000 270430 19 19488 36221 279120 {64424

Figure 9. Electric Vehicle (EV) eet batteries powerduring January 1, 02:00 to 03:00 AM.

Figure 10. Back-up batteries power during January 1,02:00 to 03:00 AM.

From the aggregator's point of view, the monthlypro�t is 11,532$, which means more than 135,000$pro�t in a year. Moreover, an EV owner whose vehicleis available 60% of the day on average for V2G servicewill receive more than 200$ per year. If the cost ofrequired communication and control infrastructure forV2G implementation is considered to be about 1000$

Figure 11. Back-up battery bank power during January.

Figure 12. Back-up battery bank state of charge duringJanuary.

per vehicle, the payback period to recoup the fundsexpended for required infrastructure will be 5 years.Based on what we have proposed, the aggregator trans-fers this fund to EV owners. Because, in this case, theEVs with maximum availability time at home have themotivation to participate in V2G service. However, theaggregator may pay this initial cost, and the EV ownerspay it by installments through their income from V2G.


4. Conclusion

Implementation of Vehicle-to-Grid (V2G) concept re-quires active participation of EV owners. In this paper,a novel pricing model was proposed to determine theprice that an aggregator should pay EV owners in orderto encourage them to take part in providing frequencyregulation service, while the pro�t of the aggregator ismaximized. The proposed pricing model was appliedto PJM frequency regulation market, considering fastregulation (RegD) signal. The results indicated thatthe depth of discharge for both EV batteries and theback-up batteries was insigni�cant enough to ensurenumerous life cycles for the batteries. In addition, theSoC of the back-up battery bank would not approachthe fully charged/discharged mode. Moreover, thefast regulation signal used in our case had a meanvalue of zero, which has a negligible impact on SoCof EV batteries. Therefore, EV owners would not beconcerned about driving with empty battery in thehours ahead.

The paper comes to the following �ndings:

� A model was presented for the interaction betweenthe aggregators and EV owners that considered theinterests of both parties and motivated them toparticipate in V2G;

� A pricing scheme was introduced to maximize thepro�t of aggregators;

� If the V2G supply function was obtained precisely,the exact pro�t of EV owners and aggregatorscould be determined so as to evaluate the economicattractiveness of V2G.

In the future works, the capacity of back-up batterybank can be considered as a variable to be optimizedas the second objective in addition to V2G price. Inaddition, the economic risk of the aggregator can beconsidered as an independent objective. Furthermore,the aggregator planning problem can be dealt with asa multi-criteria decision-making problem.

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Biographies

Mohammad Hossein Sarparandeh received BScand MSc degrees in Electrical Engineering from SharifUniversity of Technology, Tehran, Iran in 2008 and2010, respectively. He is currently pursuing the PhDdegree at the Department of Electrical Engineering,Sharif University of Technology, Tehran, Iran. Hisresearch interests include operation & planning ofpower systems, microgrids, and power markets.

Mostafa Kazemi received the BSc, MSc, and PhDdegrees in Electrical Engineering from Sharif Univer-sity of Technology, Tehran, Iran in 2010, 2012, and2016, respectively. He is currently with the Depart-ment of Electrical Engineering, University of Shahreza,Shahreza, Iran. His research interests include eco-nomics and planning of restructured power systems.

Mehdi Ehsan received the BSc and MSc degreesin Electrical Engineering from Technical College ofTehran University, Tehran, Iran in 1963 and the PhDand DIC degrees from Imperial College University ofLondon, London, U.K. in 1976. He currently is a FullProfessor at the Department of Electrical Engineer-ing, Sharif University of Technology, Tehran and TheCenter of Excellence in Power System Managementand Control. His research interests are restructuring,planning & control of power systems as well as powersystem dynamics.

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