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IET Generation, Transmission & Distribution

Research Article

Day-ahead electric vehicle aggregator biddingstrategy using stochastic programming in anuncertain reserve market

ISSN 1751-8687Received on 27th November 2018Revised 24th March 2019Accepted on 11th April 2019doi: 10.1049/iet-gtd.2018.6951www.ietdl.org

Bing Han1,2, Shaofeng Lu1 , Fei Xue1, Lin Jiang2

1Department of Electrical and Electronic Engineering, Xi'an Jiaotong-Liverpool University, Suzhou 215123, People's Republic of China2Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool L69 3GJ, UK

E-mail: [email protected]

Abstract: Electric vehicle (EV) as dynamic energy storage systems could provide ancillary services to the grids. The aggregatorcould coordinate the charging/discharging of EV fleets to attend the electricity market to get profits. However, the aggregatorprofits are threatened by the uncertainty of the electricity market. In this study, an EV aggregator bidding strategy in the day-ahead market (DAM) is proposed, both reserve capacity and reserve deployment are considered. The novelty of this study isthat: (i) The uncertainty of the reserve developments is addressed in terms of both time and amount. (ii) Scenario-basedstochastic programming method is used to maximise the average aggregator profits based on one-year data. The proposedmethod, jointly considers the reserve capacity in the DAM and the reserve deployment requirements in the real-time market(RTM). (iii) The risk of the deployed reserve shortage is addressed by introducing a penalty factor in the model. (iv) An owner-aggregator contract is designed, which is used to mitigate the economic inconsistency issue between the EV owners and theaggregator. Results verify the performance of the proposed strategy, that is the average aggregator profits are guaranteed bymaximising reserve deployment payments and mitigating the penalties in RTM and thus the reserve deployment requirementsuncertainty is well managed.

NomenclatureIndices

n number of EVs from 1 to Nt time from 1 to Mm any time between 1 and Mω number of scenarios from 1 to Ωq number of days from 1 to Q

Parameters

M total time intervalsN total number of electric vehicles (EVs)Ω total number of scenariosQ number of days for Monte Carlo simulationVω number of days for scenario ωπt′ hourly probability of reserve deployment at time tπω probability of reserve deployment for scenario ωΔT duration of each time intervalPn EV maximum charging/discharging power of EV n

(kW)En battery capacity of EV n (kWh)SOC, SOC lower/upper battery state of charge (SOC) boundariesDd battery degradation parameter ($/kWh)SOCn

a SOC of EV n at arrival time

SOCd SOC at departure time of all EVsSOCt, n minimum SOC of EV n at time ttna, tnd arrival/departure time of EV nαu, αd penalty for reserve up/down deployment shortage ($/

kWh)K charging cost discount parameterH rebate to each EV owner for attending aggregator

scheduling in reserve market ($)r t

u, r td deployed up/down reserve prices at time t ($/kWh)

rt+, rt

− charging/discharging real-time prices at time t ($/kWh)

gtu, gt

d reserve up/down capacity prices at time t ($/kWh)

λt, ωu , λt, ω

d amount of the reserve up/down capacity is required todeploy at time t of scenario ω

xt, qu reserve up deployment requirement at time t of day q

xt, ωu , xt, ω

d reserve up/down deployment requirements at time tof scenario ω

Variables

pn, t+, e, pn, t

−, e charging/discharging operations of EV n at time tunder self-scheduling strategy (kW)

pn, t+, DA, pn, t

−, DA day-ahead (DA) base load plan for EV n charging/discharging operations at time t (kW)

pn, tu, DA, pn, t

d, DA DA plan of reserve up/down capacities of EV n attime t (kW)

pn, t, ωu , pn, t, ω

d deployed up/down reserve of EV n at time t inscenario ω (kW)

Δpn, t, ω+ ,

Δpn, t, ω−

charging/discharging power deviations of EV n attime t in scenario ω (kW)

st, ωu , st, ω

d reserve up/down deployment shortage at t ofscenario ω (kW)

1 IntroductionWith the deterioration of situations arising from global warmingand energy crisis, governments have proposed plans to increase thepenetration level of plug-in electric vehicles (PEVs) [1], e.g. anational plan ‘ten cities and thousand units’ has been proposed bythe Chinese government to promote the penetration level of PEVswith the aim of five million PEVs adoptions in 2020 in China [2].As an alternative transportation tool, electric vehicle (EV) has theadvantage of zero exhaust gas emissions and minimal noise.However, the development of EV is facing many technologicallimitations at present, such as high initial cost, greenhouse gasemission during manufacturing and disposal [3]. In addition, themass charging behaviours of EVs could cause serious problems inpower grid's operation, such as unbalanced load conditions,harmonic distortions, transformer overloading and voltagefluctuations [4]. Thus, the exponential growth of EV will become acrucial issue of power grid's operation in the future.

IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2019

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On the other hand, it is estimated that most of the time (95%)EVs are parked [5]. In this case, from the power grids operationviewpoint, the EV battery can be regarded as a Battery EnergyStorage Systems (BESSs), rather than a traditional energyconsuming load. EV battery is suitable for providing regulationservice due to its fast ramp speed characteristics compared withconventional thermal generators. Vehicle-to-Grids technologyenables the integration of EVs in power grids and it makes EVspossible to provide ancillary services to the power grids [6].However, there are three main issues for EVs to provide ancillaryservices to the grids. Firstly, the primary role of EV is to work as atransportation tool and the EV travelling behaviour is randomness.It makes EV cannot make the response to the grids all the time.The second issue is that a single EV cannot meet the currentelectricity market regulations that the minimum bidding size in themegawatt range [7]. The third issue is that ancillary servicesrequire battery charge and discharge frequently, which leads to adegradation problem for the EV. In this circumstance, theaggregator is required to work as a mediate agent between EVs andthe power grids to participate in energy and ancillary markets [8].

1.1 Literature review

The EVs charging and discharging scheduling problem inelectricity markets has been studied in several papers, and it couldbe mainly categorised from stakeholders’ viewpoints into threeparts [9]. In [10–12], the EVs charging/discharging are scheduledfrom the power grids viewpoint to reduce the total operating cost orensure the power grids stability by reducing power fluctuationlevel. The power grids constraints such as total load limits, voltagedrop and phase balances are involved in these models. Thecooperative EVs charging with power grids and transportationnetworks have been widely investigated [13]. Sun et al. [14]proposed a stochastic security constrained unit commitment modelcoupled with a traffic model, which jointly consider the EVscharging impact to power grids and the traffic network. In [15], anEV charging station planning scheme is proposed by couplingtransportation network and distribution network. A spatial-temporal model is built in [16] to investigate the optimisationproblem of generators, EVs and wind power in transmission anddistribution systems.

Another viewpoint is for aggregator profits maximisation. It hasbeen shown that the EV aggregator could get higher profits fromproviding ancillary services or attending different demand responseprogrammes compared with charging EVs during low electricityprice hours [17, 18]. The EVs charging/discharging can bescheduled from EV owners viewpoint, such as charging feeminimisation including battery degradation cost [19]. Mohammadiet al. [20] proposed a distributed EVs charging algorithm tominimise the charging cost. This paper focuses on the aggregatorprofits maximisation in the electricity market.

The aggregator profits maximisation problem in the electricitymarket is threatened by uncertainties. The information gap betweenthe predicted and the actual prices are considered in [21] and theuncertainty of real-time (RT) price is addressed by using robustoptimisation method [22]. Besides the deviation of electricityprices, some literature focused on the cooperation between theaggregator or BESS with renewable energy sources and theuncertainty of renewable is represented by scenarios in the model[23]. In addition, EVs owners’ driving behaviours are naturallyrandom. The stochastic programming method was utilised toconsider the uncertainty of EVs driving characteristics [24, 25].Furthermore, the uncertainty from the electricity market includesancillary services such as reserve deployment requirements.

To address the uncertainty of ancillary services, the robustoptimisation method is used in [26] to deal with the uncertainamount of reserve deployment requirements. It is claimed that theprobability density function of the amount of reserve deploymentrequirements is hard to build due to the characteristic of regulationand reserve markets. A probability-based model is applied in [27]to assess the aggregator's capability in providing ancillary servicesto power grids. Two types of probabilities (i.e. the probability ofthe day-ahead (DA) bidding is accepted in DA market (DAM) and

the probability of the reserve is required to deploy in RT market(RTM)) are utilised in the model to represent the marketenvironment by taking battery degradation into consideration. Ascenario-based model is built in [28] to deal with the uncertaintyprices, and the probability of each price scenario is calculatedbased on Monte Carlo simulation. Nevertheless, the common issuein the probability-model based and the scenario-based model is thatthe relationship between the proposed reserve in DAM with thedeployed reserve in RTM is not presented and also differentamount of reserve deployment requirements is not taken intoaccount. The impact of the uncertainty of reserve deploymentrequirements are addressed by using stochastic programming in[29, 30] and additionally considered uncertainty of EV owners’behaviours and market prices. The risk of the deviation betweenthe DA bidding and the RT operation is considered in [31] and it isassumed that the aggregator will be penalised if there is anydifference between the RT-based load with the DA bidding-basedload plan.

To summarise, several papers discussed the EVs charging/discharging scheduling problem from three stakeholders’viewpoints to minimise the network cost and loss (power gridsviewpoint), maximise profits by providing ancillary services inelectricity market (EV aggregator viewpoint) and minimisecharging fee including discharging income and battery degradationcost (EV owners viewpoint). To specify, some researchersinvestigated the aggregator profits maximisation in the electricitymarket by considering the uncertainty of prices, EV owners’driving behaviours, renewable energy sources and reservedeployment requirements. However, there are four issues in theEVs scheduling problem are ignored in the existing researches:

• First, fewer papers considered the uncertainty of reservedeployment requirements in terms of time and amount aspects.In [26], a robust optimisation method is used to take theuncertainty of the reserve deployment times in one day intoaccount. However, it only considered the worst scenario whichmakes the results too conservative and the uncertainty of theamount is not considered.

• Secondly, fewer papers investigated the relationship between theDA bidding with different reserve deployment requirements inRTM. That is, the impact of the reserve deployment in RTM tothe DA bidding is neglected. Authors in [29, 30] discussed theEV bidding strategy in DAM and reserve market usingstochastic programming method, however, the relationshipbetween the DAM and reserve market is not considered.

• Then, the risk of reserve deployment shortage due to theuncertain RTM is not appropriately evaluated in mostreferences. Moreover, the impact of the reserve deployment onEVs charging/discharging is less discussed, such as in [26, 29,31].

• Finally, most existing studies simplicity focused on the EVscharging/discharging from a single stakeholder's viewpoint butneglect the economic relationship between differentstakeholders, such as in [27, 32]. The aggregator profits aremaximised while the EV owners economic benefits aresacrificed (charging fee increase). The economic inconsistencyissue between the aggregator and EV owners is not fullyaddressed, which make the aggregator scheduling resultsunrealistic since the EV owners are unwilling to attend theaggregator schedule.

1.2 Main contributions

In this paper, a stochastic DA aggregator bidding strategy in powergrids reserve market is proposed while taking the reservedeployment requirements uncertainty into account. The maincontributions of this paper are summarised as follows:

• In order to address the uncertain reserve market in terms of bothamount and time of reserve deployment requirements, stochasticprogramming method is used in this work.

• The relationship between the proposed reserve capacity in DAMand the deployed reserve in RTM is formulated and the impact

2 IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2019

of reserve deployment shortage is considered by introducing apenalty factor in the model.

• To mitigate the economic inconsistency issue between ownersand the aggregator, a newly proposed owner-aggregator contractis designed in this paper, i.e. the EV owners’ economic benefitsare guaranteed meanwhile the aggregator profits are maximised.

1.3 Paper organisation

The remaining part of this paper is organised as follows: Section 2presents a scenario-based reserve deployment model. Section 3builds the EVs scheduling model from owners and aggregatorviewpoints, respectively. Section 4 presents scheduling results anddiscussions. Section 5 draws the conclusions.

2 Electricity markets2.1 Reserve market participation

The primary role of the aggregator in attending electricity marketsis to satisfy EV owners’ driving requirements, after that, it couldprovide ancillary services to power grids to maximise profits [27].

Fig. 1 illustrates the framework of aggregator participation inthe reserve market. According to the electricity markets operationmechanism, the aggregator needs to submit a reserve up/downcapacities and base load plans to power grids in DAM. If the planis accepted, the aggregator receives income for stand-by reservecapacity. In RT operation of power grids, when the generationcannot meet the demand, the reserve up capacity proposed by theaggregator could be required to deploy to offset such imbalances. Ifthe demand is less than the generation, then the reserve downcapacity will be deployed, that is to increase aggregator chargingpower (or decrease discharging power) and thus accommodate theimbalances. The aggregator operates in RTM should deployenough reserve according to power grid requirements in RTM. Theaggregator can receive additional payments as a rebate for reservedeployment [27].

This paper is based on the reserve market model proposed in[24, 33] and previous work [34]. In additionally considering theimpact of uncertain reserve deployment requirements in RTM onthe DA aggregator bidding. Moreover, the risk of the aggregatornot being able to deploy enough reserve (shortage) is considered inthe model. Thus, a reserve deployment shortage penalty factor isintroduced in the model, which means the aggregator will receive apenalty according to the difference between the deployed reserveand the power grid requirements. For the primary role of theaggregator, not only the EV owners driving requirements should bemet but also the economic benefits (charging and batterydegradation cost) of each owner should be guaranteed [9].

To mitigate the economic inconsistency issue between EVowners and the aggregator, an owner-aggregator contract isimplemented after DAM and RTM. The aggregator receives adiscounted charging/discharging cost to each EV owner and alsooffers additional battery degradation compensation to each owner.

Moreover, the aggregator provides a rebate to each EV owner forattending reserve market.

2.2 Uncertainty of reserve deployment requirements

Reserve service is essential to ensure the security and reliability ofthe grids [35] by requiring deployed reserve. That is, theaggregator should change the EVs operation temporally based onpower grids reserve deployment requirements. In this case, the EVscharging and discharging scheduling problem is complicated by theuncertain reserve deployment requirements.

The uncertainty of reserve deployment requirements in twenty-four hours can be represented by a series of scenarios and theprobability of each scenario. Binary numbers are used to representwhether the reserve is required to deploy or not. It is assumed thatonly reserve up is deployed in the model, and different reservedeployment requirements scenarios can be generated based on theMonte Carol simulation method.

Fig. 2 illustrates the procedure to generate the reservedeployment requirements data for Q days. At each time a randomnumber i is generated between 0 and 1 and compared with thehourly reserve deployment probability πt′ [29]. If the hourlyprobability is equal to or greater than the random number, thereserve up capacity is deployed (xt, q

u = 1). Otherwise, the reserve isnot deployed (xt, q

u = 0). After that, all scenarios in Q days can berepresented by [x1, ω

u , . . . , xM, ωu ], ∀ω ∈ Ω. Finally, the probability

of each scenario can be calculated based on

πω = VωQ ∀ω (1)

and the probability πω with the reserve deployment requirements ofeach scenario will be involved in the stochastic programming ofthe DA aggregator bidding model.

3 EVs scheduling strategyThis section describes the EVs scheduling strategy from EV ownerand aggregator viewpoints, respectively.

3.1 EV owners’ scheduling (self-scheduling) strategy

3.1.1 Charging fee minimisation: The objective function of theself-scheduling strategy is formulated as follows:

Min J1 + J2 (2a)

J1 = ∑t = 1

M

∑n = 1

N(rt

+pn, t+, e − rt

−pn, t−, e)ΔT , (2b)

J2 = ∑t = 1

M

∑n = 1

NDd(pn, t

+, e + pn, t−, e)ΔT . (2c)

Fig. 1 Framework of the aggregator participation in reserve market


3

where J1 is the charging cost/discharging income and J2 is thecorresponding battery degradation cost.

3.1.2 Self-scheduling constraints: Power limits: When EVs arenot connected to the grid, EVs charging/discharging power limitsare represented in the following constraints:

pn, t+, e =

0 1 ≤ t < tna

[0, Pn] tna ≤ t < tnd

0 tnd ≤ t ≤ M

∀n, t, (3)

pn, t−, e =

0 1 ≤ t < tna

[0, Pn] tna ≤ t < tnd

0 tnd ≤ t ≤ M

∀n, t, (4)

where the EVs charging/discharging operations are restrictedbetween 0 to Pn when EVs are connected to the grid. When EVsare off the grid, EVs cannot be scheduled and thus the charging/discharging powers are both set to 0.

State of charge (SOC) limits: Constraints (5) and (6) are used toguarantee EV battery will not be overcharged or discharged at eachtime

SOCna +

∑t = 1m (pn, t

+, e − pn, t−, e)ΔT

En≤ SOC ∀n, m (5)

SOCna +

∑t = 1m (pn, t

+, e − pn, t−, e)ΔT

En≥ SOC ∀n, m (6)

To meet EV owners’ next day driving requirements, constraint (7)is used to make sure EVs are charged to desired values at departuretime

SOCna +

∑t = 1M (pn, t

+, e − pn, t−, e)ΔT

En≥ SOCd ∀n . (7)

The battery degradation parameter Dd is calculated based on thebattery capital cost, cycle time and depth-of-discharge (DoD),which has been discussed in [36]

Dd = CcapLcEsDoD (8)

where Ccap, Lc and Es are the initial investigation cost of the battery($), battery lifetime in cycles and battery capacity (kWh).

3.2 Stochastic DA aggregator bidding strategy

This section shows the stochastic DA aggregator bidding strategybased on different scenarios.

3.2.1 Expected aggregator profits maximisation: The objectivefunction of the aggregator is to maximise the expected profits inenergy and reserve markets by taking all scenarios into account

Max DRC − DCDDAM

+ ∑ω = 1

Ωπω(RRD, ω − RPE, ω − RDE, ω)

RTM

+KJ1* − (DBD − J2*) − NHcontract

,(9a)

where the aggregator profits come from three aspects: DAM, RTMand the owner-aggregator contract.

In DAM, DRC (9b) represents the DA reserve capacity planincome. It represents the available stand-by reserve, which couldbe deployed in RTM

DRC = ∑t = 1

M

∑n = 1

N(gt

upn, tu, DA + gt

dpn, td, DA)ΔT . (9b)

DCD in (9c) represents the charging cost and discharging income ofthe DA base load plan. The aggregator will submit the EVscharging/discharging plan in DAM to power grids for DA baseload bidding. DBD in (9d) is the battery degradation cost due tocharging/discharging

DCD = ∑t = 1

M

∑n = 1

N(rt

+pn, t+, DA − rt

−pn, t−, DA)ΔT , (9c)

DBD = Dd ∑t = 1

M

∑n = 1

N(pn, t

+, DA + pn, t−, DA)ΔT . (9d)

In RTM, RRD, ω in (9e) represents the reserve deployment profits:the aggregator receives additional payments by deploying reservebased on power grids’ requirements. RPE, ω in (9f) represents thepenalty for reserve deployment shortage

RRD, ω = ∑t = 1

M

∑n = 1

N(r t

upn, t, ωu + r t

dpn, t, ωd )ΔT , (9e)

RPE, ω = ∑t = 1

M(αust, ω

u + αdst, ωd )ΔT . (9f)

The last term RDE, ω (9g) represents the cost of charging/dischargingdeviations in RT operation due to the uncertain reserve deploymentrequirements. It is assumed that the aggregator could adjust theproposed DA base load plan in RT operation only after the reserveis deployed

RDE, ω = ∑t = 1

M

∑n = 1

N(rt

+Δpn, t, ω+ − rt

−Δpn, t, ω− )ΔT . (9g)

In owner-aggregator contract, J1* and J2* represent the optimalcharging/discharging cost and battery degradation cost from self-scheduling, respectively. KJ1* stands for the discounted charging/discharging fee received from EV owners. Moreover, theaggregator provides additional battery degradation payments to EVowners (DBD − J2*).

3.2.2 Aggregator scheduling constraints: The maximum rangeof EVs charging/discharging operations at each time is defined inthe following constraints :

Fig. 2 Flowchart of reserve deployment requirements scenariosgeneration approach based on Monte Carlo simulation


pn, t+, DA =

0 1 ≤ t < ta, n

[0, Pn] ta, n ≤ t < td, n

0 td, n ≤ t ≤ M∀n, t, (10)

pn, t−, DA =

0 1 ≤ t < ta, n

[0, Pn] ta, n ≤ t < td, n

0 td, n ≤ t ≤ M∀n, t, (11)

Power limits: The relationship between EVs charging/dischargingoperations with reserve up/down capacities are described in thefollowing constraints:

pn, t+, DA − pn, t

−, DA − pn, tu, DA ≥ − Pn ∀t, n, (12)

pn, t+, DA − pn, t

−, DA + pn, td, DA ≤ Pn ∀t, n, (13)

and these equations suggest that the EVs charging/dischargingpower with corresponding reserve up/down capacities should notbe greater than the maximum charging power or the maximumdischarging power for each EV n at each time t.

Reserve limits: Constraints (14) and (15) are used to make surethe summation of the deployed reserve and the charging/discharging deviations are less than its reserve capacity when thereserve is deployed for each scenario

0 ≤ pn, t, ωu + Δpn, t, ω

− ≤ xt, ωu pn, t

u, DA ∀t, n, ω, (14)

0 ≤ pn, t, ωd + Δpn, t, ω

+ ≤ xt, ωd pn, t

d, DA ∀t, n, ω . (15)

Constraints (16)–(18) suggest that the DA reserve up/downcapacities of each EV, the deployed reserve and the powerdeviation at each time should not be <0

pn, tu, DA ≥ 0, pn, t

d, DA ≥ 0 ∀n, t, (16)

pn, t, ωu ≥ 0, pn, t, ω

d ≥ 0, ∀n, t, ω, (17)

Δpn, t, ω+ ≥ 0, Δpn, t, ω

− ≥ 0 ∀n, t, ω . (18)

SOC limits: The relationship between EV battery SOC limits withEVs the DA charging/discharging power, DA reserve capacities,RT deployed reserve and the RT charging/discharging deviationsare formulated in the following constraints:

SOCna +

∑t = 1m − 1 (pn, t

+, DA − pn, t−, DA − pn, t, ω

u )ΔTEn

+∑t = 1

m − 1 (pn, t, ωd + Δpn, t, ω

+ − Δpn, t, ω− )ΔT

En

+ (pn, m+, DA − pn, m

−, DA + pn, md, DA)ΔT

En≤ SOC ∀n, m, ω,

(19)

SOCna +

∑t = 1m − 1 (pn, t

+, DA − pn, t−, DA − pn, t, ω

u )ΔTEn

+∑t = 1

m − 1 (pn, t, ωd + Δpn, t, ω

+ − Δpn, t, ω− )ΔT

En

+ (pn, m+, DA − pn, m

−, DA − pn, mu, DA)ΔT

En≥ SOCn, m, ∀n, m, ω .

(20)

Moreover, to guarantee that EVs are charged at the desired value atdeparture time, the minimum SOC of EV n at each time iscalculated based on:

SOCn, m = max SOC, SOCd − P(M − m)ΔTEn

∀m, n . (21)

Deviation balance: The relationship between the deployed reserve,charging/discharging deviations, reserve shortages and the powergrids reserve deployment requirements at time t scenario ω areshown in as follows:

st, ωu + ∑

n = 1

Npn, t, ω

u = Δpn, t, ω− + λt

uxt, ωu ∑

n = 1

Npn, t

u, DA, ∀t, ω, (22)

st, ωd + ∑

n = 1

Npn, t, ω

d = Δpn, t, ω+ + λt

dxt, ωd ∑

n = 1

Npn, t

d, DA, ∀t, ω, (23)

The reserve down deployment is not considered in this model, thusvalue of reserve down deployment amount and the reserve downdeployment requirements are both set to zero, that isλt

d = xt, ωd = 0, ∀t, ω.

The reserve deployment shortage variable at each time andscenario is defined as follows:

st, ωu ≥ 0, st, ω

d ≥ 0 ∀t, ω . (24)

3.3 Deterministic DA aggregator bidding strategy

The objective function of DA bidding strategy under deterministicreserve deployment requirements is shown in

∑ω = 1

Ωπω(DRC, ω − DCD, ω − DBD, ω + RRD, ω − RPE, ω

−RDE, ω) + KJ1* + J2* − NH,(25)

subjects to: (10)–(24). Since this section shows the deterministicstrategy, the DA bidding plan is unique for each scenario. In thiscase the variables in pn, t

+, DA, pn, t−, DA, pn, t

u, DA and pn, td, DA in stochastic

strategy are substituted by pn, t, ω+, DA, pn, t, ω

−, DA, pn, t, ωu, DA and pn, t, ω

d, DA in thedeterministic strategy.

3.4 No-deployment-considered bidding strategy

The objective function of the no-deployment-considered strategy isthe same with the stochastic strategy, that is with objective function(9a)–(9g) subjects to constraints (10)–(24). Since no-reserve-deployment is considered in this strategy, the variables represent areserve deployment in the model are set to zeros, that ispn, t, ω

u = pn, t, ωd = 0, ∀n, t, ω. Algorithm 1 (Fig. 3) shows the

calculation process of the aggregator average profits under the no-reserve-deployment-considered strategy.

4 Scheduling results and discussionsThe proposed self-scheduling strategy and the aggregator biddingstrategies are formulated as linear programming problems andthese problems are solved by the CPLEX [37].

4.1 Parameters and settings

One hundred EVs in a residential community are considered in themodel from 13 pm to 13 pm next day with one hour each interval(N = 100, M = 24, ΔT = 1 h). The hourly charging RT price and thehourly reserve capacities prices are available in [27], and theaggregator could receive an additional reward at the time forinjecting energy back to the grids [19]. Reserve shortage penaltyvalues are set as αu = αd = 0.13 $/kWh. Three types of EVscharacteristics and proportion are summarised in Table 1. It isassumed that all EVs have the same battery degradation parameter,Dd = 0.083 $/kWh [19].

The EV owners driving patterns are assumed to follow theGaussian distribution, i.e. arrival time, departure time and thebattery SOC at arrival time follow the Gaussian distribution.Table 2 illustrates the EVs driving information parameters.


5

4.2 Scenario-based reserve deployment requirements

A summary of reserve deployment requirements times in one dayamong 365 days is shown in Fig. 4. It suggests that within 365days, there are 70 days that no reserve is required. There are 128and 112 days that require reserve once and twice in one day,respectively. There are 35 days that reserve is required three timesand 16 days for four times. In the end, there are only 2 days thatreserve is required five and six times in one day, respectively.

According to the statistical information, the probability of eachscenario πω is illustrated in Fig. 5 In total, there 125 scenarios in365 days, i.e. Ω = 125. Scenario 1 represents that no reserve isrequired, which has the highest probability π1 = 0.19.

4.3 Self-scheduling strategy

In this section, the EV owners’ scheduling strategy results arepresented. In Fig. 6, EVs have less charging power at the beginning(13 pm–17 pm) due to the reason that most EVs are off the grid,i.e. most EVs are not available during these times. For the availableEVs, they operate in charging mode because the charging price isrelatively lower. For operating in charging mode during thesetimes, it could make EVs prepare enough energy to discharge in thefollowing peak hours and thus get revenue. After that, during peakhours (16 pm–21 pm), EVs operate in discharging mode to injectenergy back to the grid to receive revenue. However, the maximumdischarging power appears at 19 pm, with 687.80 kW which islower than the peak charging power (732.20 kW) at 2 am. There

are two reasons, the first reason is that there are still some EVs notarriving at the community at 19 pm, and the second reason is thatsome EVs battery SOC are too low to operate in discharging mode.During the time from 23 pm to 7 am, most EVs operate in chargingstatus because these periods are in off-peak time. Finally, after 7am, only a few EVs operate in discharging mode, because thebattery SOC is enough to satisfy owner driving requirements.Before departure, the RT price starts to rise, which is higher thanmidnight, and it leads to some EVs to operate in discharging mode.

The average battery SOC of the available EVs is also presentedin Fig. 6. It can be seen from the figure that at each time, the SOCis strictly bounded between 0.1 and 1 which guarantees that EVswill not be overcharged or discharged. Moreover, in the morning ofthe next day (around 7 am), the average SOC reaches 0.95 whichguarantees EV owners the next days’ driving requirements.

Fig. 3 Algorithm 1: Average profits under No-Deployment-ConsideredBidding Strategy

Table 1 EV typesEV type Charging rate, kW Capacity, kWh Proportion, %BYD e6 8 64 40Tesla model S 10 100 30Nissan Leaf 6.6 30 30

Table 2 EV information model dataMean Variance Min Max

initial SOC 0.3 0.1 0.1 1arrival time 18:00 2 h 13:00 13:00 next daydeparture time 07:00 2 h 13:00 13:00 next day

Fig. 4 Summary of number of times reserve deployment requirements inone day among 365 days

Fig. 5 Probability of each scenario

Fig. 6 Charging/discharging of EVs results and the average EVs batterySOC under self-scheduling strategy


4.4 Aggregator profits under deterministic strategy

The scheduling results of the aggregator profits under deterministicreserve deployment requirements are presented in Fig. 7. Theresults show that the minimum profit of the aggregator within 365days is $21.72, under the condition that no reserve is required intwenty-four hours. The reason is that for no-reserve-deployment,the aggregator cannot get additional payments from RTM, eventhough there is no charging/discharging deviation or deployedreserve shortage penalties in RT operation.

For reserve deployment with 20, 40, 60, 80 and 100%, it can beseen from the figure that the highest profits could reach $450.39which is significantly greater than the scenario without reservedeployed ($21.72). The reason is that the aggregator could receiveadditional reserve deployment payments from RTM. Moreover, theaggregator will not receive any penalties for reserve deploymentshortage due to the reason that the reserve deploymentrequirements are deterministic, and they are already taken intoaccount in the aggregator DA bidding plan.

4.5 Aggregator profits under stochastic strategy

Fig. 8 presents the DA base load plan with different amount ofreserve deployment requirements in 24 h. It suggests that EVs aremainly working in discharging mode during peak hours (17 pm–21pm) and charging mode during off-peak hours (23 pm–3 am). Forthe different amount of reserve deployment requirements, it hasless impact on DA base load plan. The DA base load plan is similarto the charging/discharging plan under self-scheduling strategy inFig. 6, except that the maximum discharging power of thestochastic programming method ($324.44) is less than the self-scheduling (687.80 kW). It is due to the reason that, in order to

deploy reserve capacity during peak hours, the proposed (DA plan)discharging power during this time is reduced.

The DA reserve up capacity plan is shown in Fig. 9. It can beseen that the higher reserve deployment amount, the less reserve upcapacity will be proposed in the DA plan. The reason is that theaggregator will propose less reserve capacity in order to reduce therisk of reserve deployment shortage in RTM.

Fig. 10 illustrates the aggregator profits in 365 days underdifferent amount of reserve deployment requirements. In DAscheduling, the DA bidding plan is made based on 125 scenarios.In this case, once the DA bid plan is determined, it is suitable forall scenarios in RT operation. The results in Fig. 10 show that thehighest profit the aggregator could get is $443.02 which is slightlyless than the deterministic strategy ($450.39). In addition, thelowest profit is $−15.37 which is much less than the deterministicstrategy ($21.72).

4.6 Aggregator profits under no-reserve-deploymentconsidered strategy

In order to make a comparison with the deterministic andstochastic strategies, the scheduling results of aggregator profitswithout considering reserve deployment in DA scheduling arepresented in Fig. 11. It can be seen from the figure that, the highestaggregator profits could get is $21.72 which is much less than thestochastic ($443.02) and deterministic strategies ($450.39). Thelowest profit is $−357.66 which is much lower than thedeterministic and stochastic strategies. The reason is that theaggregator will not deploy reserve in RTM and thus lead to penalty.Therefore the profit is much lower than the deterministic andstochastic strategies.

Fig. 7 Aggregator profits with different reserve deployed amount underdeterministic DA bidding strategy

Fig. 8 DA base load plan with different amount of reserve deploymentrequirements under stochastic programming strategy

Fig. 9 DA reserve up capacity plan with different amount of reservedeployment under stochastic programming method

Fig. 10 Aggregator profits with different reserve deployed amount understochastic DA bidding strategy


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4.7 Effectiveness of the stochastic strategy

According to the results in previous sections, the aggregator couldget the highest profits under the deterministic strategy. However,this is not practical in the real world, since the aggregator cannotestimate the reserve deployment requirements twenty-four hoursahead accurately. It is more practical to apply the stochasticstrategy. In this case, this section makes a comparison between thestochastic strategy and the deterministic strategy.

Fig. 12 illustrates the average aggregator profits in 365 daysunder different amount of reserve deployment requirements.

For 10% requirement, the aggregator profit of stochasticstrategy is $71.53 and deterministic strategy is $84.47. Theaggregator gets the highest profits with a 50% requirement with$80.08 and 93.46 for two strategies, respectively. For the no-reserve-deployment-considered strategy, the higher amount reserveis required to deploy, the lower profits aggregator will receive.Since there is no-reserve-deployment in this strategy, theaggregator will receive a penalty based on the amount of reservedeployment requirements.

4.8 Discussions

This section discusses the main findings of this paper. By making acomparison between Figs. 7 and 10 under deterministic and thestochastic strategies, both strategies achieve the lowest profitswhen no reserve is required to deploy in one day. The maindifference between the two strategies is that when no reserve isrequired the profits under the stochastic strategy is much less thanthe deterministic ($−15.37 and 21.72), respectively. It is found thatthe stochastic strategy aims to optimise the average profits based

on one-year data, with a sacrifice on profits under the no-reserve-required scenario.

Referring to Fig. 12, the one-year average profits under thestochastic strategy is 14.31–16.77% less than the deterministicstrategy, due to the uncertainty of the reserve deployments in RTM.On the other hand, with the reserve deployment amount range from30 to 100%, the aggregator profits under stochastic strategyslightly reduced. The reason is that the aggregator could obtainmore income with the reserve deployment amount increase, but isfaced with the risk of not being able to provide reserve alsoincreases which leads to the aggregator receive more penalty.

5 ConclusionsIn this paper, a DA aggregator bidding strategy in uncertain reservemarket is proposed. The uncertainty of reserve market is addressedin terms of amount and time of reserve deployment requirementsbased on stochastic programming method. The risk of theaggregator not being able to deploy enough reserve is consideredby introducing a penalty factor in the model. Moreover, an owner-aggregator contract is designed in this paper to mitigate theeconomic inconsistency issue between EV owners (charging feeminimisation) and the aggregator (profits maximisation).

The scheduling results verify the proposed stochasticprogramming strategy effectively managed the uncertainty of thereserve deployment requirements that the average aggregatorprofits are 14.31–16.77% less than the optimal average profitsunder the deterministic strategy based on one-year data.

The future work will focus on the EV aggregators indistribution systems in different locations. That is, to build a spatialand temporal model of EV aggregators scheduling strategy in adistribution system.

6 AcknowledgmentThis project was supported and sponsored in part by the 2016NSFC Young Scientist Programme Project no. 61603306 and inpart by the Research Development Fund RDF-14-01-15 at Xi'anJiaotong-Liverpool University.

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