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Optimal Energy Trading for Building Microgridwith Electric Vehicles and Renewable Energy

ResourcesDuong Tung Nguyen and Long Bao Le

Abstract—In this paper, we study an optimal power biddingand scheduling problem for a microgrid (MG), which consistsof distributed generators (DGs), battery storage units, a largegarage with many charging stations for electric vehicles (EVs),MG local load, and renewable energy sources (RESs). We proposeto utilize EVs as a dynamic energy storage facility to accom-modate the variability of RESs in a realistic economic modelfor the electricity market. The power scheduling and biddingproblem is formulated as a two-stage stochastic programmingproblem considering the uncertainties of RESs and electricityprice. Specifically, a multi-objective function is introduced tobalance the tradeoff between maximizing the MG revenue andminimizing the MG operating cost. Importantly, appropriatepenalty metrics capturing involuntary load shedding, renewableenergy curtailment, and bid deviation are integrated into theobjective function. Numerical results confirm the effectiveness ofthe proposed optimization framework in enhancing the operationefficiency of the MG, reducing curtailment of renewable energyresources compared to the conventional scheme and flexibility ofthe proposed framework in balancing different design objectives.

Index Terms—Renewable energy, electric vehicle, battery.

NOMENCLATUREΔT Duration of time slot (h)ηcj , η

dj Charging and discharging efficiency of EV j

ηck, ηdk Charging and discharging efficiency of battery k

ψt Penalty cost parameter of bid deviation ($/kWh)ρs Probability of scenario sbs,cj,t , b

s,dj,t Binary variable, “1” if charging/discharging EV j

bs,ck,t Binary variable, “1” if charging battery kbs,dk,t Binary variable,, “1” if discharging battery kCi(.) Production cost of DG i ($)CDi,t Shutdown offer cost of DG i at time t ($)CUi,t Startup offer cost of DG i at time t ($)DRi, URi Ramping-down/up rate limit of DG i (kW)DTi, UTi Minimum down/up time of DG i (h)E

capj Capacity of battery of EV j (kWh)

Ecapk Capacity of battery k (kWh)

es,DAt Day-ahead price at time t in scenario s ($/kWh)es,RTt Real-time price at time t in scenario s ($/kWh)Ii,t Commitment status of DG i, “1” if ON {0, 1}Lst Total system load at time t in scenario s (kW)

LSst Realized involuntary load curtailment (kW)

LSmaxt Maximum involuntary load curtailment (kW)

NG,NV Number of DGs and number of EVsNH,NS Number of time slots and number of scenariosNK Number of battery storage unitsNW,NP Number of wind/solar power generating unitsPmaxi Maximum power generation of DG i (kW)

The authors are with INRS-EMT, University of Quebec, Montreal, Quebec,Canada. Emails: {duong.nguyen,long.le}@emt.inrs.ca.

Pmini Minimum power generation of DG i (kW)Pt Day-ahead hourly bid (kW)P st Actual power delivery at time t in scenario s (kW)P

g,maxt Maximum power exchange between the MG and

the grid (kW)P si,t Power generation of DG i (kW)P

s,cj,t , P

s,dj,t Charging/discharging power of EV j (kW)

Pc,maxj Maximum charging power of EV j (kW)P

d,maxj Maximum discharging power of EV j (kW)P

s,ck,t , P

s,dk,t Charging/discharging power of battery k (kW)

Pc,maxk Maximum charging power of battery k (kW)P

d,maxk Maximum discharging power of battery k (kW)P sp,t Available output power of solar unit p (kW)P

s,pvsp,t Amount of power curtailment of solar unit p (kW)P

s,wsw,t Amount of power curtailment of wind unit w (kW)P sw,t Available output power of wind unit w (kW)SDi,t Shutdown cost of DG i at time t ($)SOCd

j Desired SOC when EV j departsSOCmax

j Maximum SOC of battery of EV j

SOCminj Minimum SOC of battery of EV j

SOCmaxk Maximum SOC of battery k

SOCmink Minimum SOC in battery k

SOCsj,t SOC of battery of EV j at time t in scenario s

SOCsk,t SOC of battery k at time t in scenario s

SUi,t Startup cost of DG i at time t ($)t, s, i, j, k Time slot/scenario/DG/EV/battery indextaj , t

dj Arrival time and departure time of EV j

URi Ramping-up rate limit of DG i (kW)V LLt Value of lost load ($/kWh)V Wt , V PV

t Cost of wind and solar energy curtailment ($/kWh)w, p Wind/solar unit indexyi,t “1” if DG i is started up at time slot t {0, 1}zi,t “1” if DG i is shutdown at time slot t {0, 1}

I. INTRODUCTION

More active participation of the demand side into thepower energy management and trading activities and efficientintegration of electric vehicles (EVs) and renewable energyresources (RESs) into the power system are important ob-jectives in designing the future smartgrid. In fact, renewableenergy generating units have various advantages over thetraditional ones since they are the green sources of powerwith almost-zero operating and emissions costs. However, itis a challenging task to integrate RESs into the grid mainlydue to their stochastic and intermittent nature. In general, thevolatility and intermittency of RESs can be mitigated if wecan store and utilize renewable energy effectively. Varioussolutions for renewable energy storage have been proposed

978-1-4799-3653-3/14/$31.00 ©2014 IEEE

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in the literature such as using pumped-storage hydro units [1],battery storage units [2], or compressed air energy storage[3] to compensate for the variability of renewable energygeneration.Electric vehicle (EV) is another vital component in the

future smart grid. Due to the economical and environmentaladvantages of EVs over normal cars, it is projected that EVswill make a revolution in the transportation sector. The impactof a large EV penetration on a residential distribution grid wasinvestigated in [4]. Reference [5] studied a joint optimizationproblem of EVs and household appliances considering userthermal comfort requirement. In [6] the authors proposed anoptimization framework to maximize the profit for a fleet ofEVs in a multi-settlement electricity market with the supportof energy storage units. However, RESs were not consideredin this work, and the proposed problem is deterministic.The flexibility in the EV charging process over time can beexploited to accommodate the uncertainties of RESs. Ref-erences [7], [8] evaluated the impacts of EV charging onthe scheduling and operation of power systems with RESsand thermal generators. Different from these works where theauthors aimed to minimize operation cost of large-scale powersystems from the grid operator viewpoint, we plan to studythe benefits of coordinating EVs with RESs in a MG settingwhere our objective is to maximize the MG revenue in theelectricity market while simultaneously minimizing the MGoperation cost.The main contributions of this paper can be summarized

as follows. We propose a comprehensive model to determinean optimal bidding and scheduling strategy for a MG. Themodel is formulated as a two-stage stochastic programmingproblem considering the uncertainties of RESs and electricityprices. The formulation captures a realistic multi-settlementelectricity market model [6]. Penalty costs for involuntaryload shedding, renewable energy curtailment, and bid deviationare all taken into account. Numerical results are presentedto demonstrate the performance of the proposed optimizationframework. Specifically, we compare a smart EV chargingscheme with an uncontrolled EV charging strategy. We showthat a smart EV charging scheme can result in significantprofit improvement for the MG in terms of increasing the MGrevenue and reducing the MG operation cost. Furthermore, thesmart EV charging strategy could help reduce the amount ofrenewable energy curtailment which is necessary to mitigatethe bid deviation charges.The rest of the paper is organized as follows. The system

model and solution approach are described in Section II.Detailed problem formulation is presented in Section III.Numerical results are presented in section IV followed byconclusion in Section V.

II. SYSTEM MODELA. System ModelWe consider a MG which is operated in the grid-connected

mode where the MG consists of the following components:RESs, DGs (e.g. microturbines, fuel cells), battery storageunits, a few buildings with their associated loads, and a largegarage with many charging stations for EVs. The MG loadsmodel the aggregated load from buildings and the EV chargingload. The optimization horizon is one day with a discretetime slotted model where each time slot is one hour. The

MG is assumed to participate in the two-settlement electricitymarket where the MG has to submit its hourly bids to theday-ahead market several hours before the real-time powerdelivery [1]. The bid can be offer bid for exporting powerto the market or demand bid for importing power from themarket. Any mismatch between the real-time power deliveryand the day-ahead schedule is penalized, and it is compensatedby exchanging power in the real-time balancing market. Itis reasonable to assume the MG is a price-taker due to itssmall size [1]. A grid operator is responsible for calculatingthe clearing electricity price which is used to determine theMG revenue and the MG operation cost. Note that both day-ahead price and real-time price are unknown to the MG whenit submits its bids to the market [1], [9].The uncertainties of RESs and the electricity price render

finding an optimal bidding strategy for the MG a difficulttask. To avoid a high penalty charge on bid deviation, itis sometimes preferable to curtail output power from RESsto keep the actual power delivery as close as possible tothe day-ahead schedule. However, curtailments of renewableenergy generation is undesirable. Therefore, we impose an-other penalty cost to limit the amount of renewable energycurtailment. Furthermore, due to the high operating cost ofDGs, they are only operated when the electricity price is highor when the imported power reaches the power limit.Since the battery storage units are expensive, we are in-

terested in other sources for storing renewable energy. In thiswork, the flexibility in EV charging and discharging processesis exploited to support the operation of RESs. Normally, EVsare charged immediately at the power rating when they arriveat the parking garage. We refer to this as the uncontrolledcharging scheme. However, by adjusting the charging schedulefor EVs smartly considering both the variation in electricityprices and the renewable energy generation, we can not onlyincrease the economic benefits for the MG we can but alsoreduce the amount of renewable energy curtailment. In partic-ular, EVs can be charged more when the electricity price islow and/or when the renewable energy is surplus. Also, whenthe electricity price is high and/or when the local sources lackof power to support the local demand, EVs can be dischargedpower or to provide energy to the local demand.

B. Solution ApproachWe consider the uncertainties of RESs, day-ahead electricity

price and real-time electricity price in this paper. We usethe approach in [10] to model wind speed where the actualwind speed is the sum of its forecast value and the forecasterror. The wind forecast error is then modeled by an ARMAmodel [10]. Wind power is calculated from the wind speedby using wind turbine power curve [2]. Solar power is alsomodeled by the approach that we used in our previous workwhere the solar power is a function of solar irradiance [10].A normal distribution is used to model solar irradiance. Forsimplicity, the day-ahead and real-time prices are also assumedto follow normal distributions taking into account that theuncertainty in forecasting the real-time price is higher thanthe uncertainty in forecasting the day-ahead price [11]. MonteCarlo simulation method is used to generate a large numberof scenarios that capture these uncertain parameters. Scenarioreduction techniques [12], [13] can be employed to reducethe the computational burden. The underlying optimization

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problem is formulated as a two-stage stochastic programming.The first-stage decisions are made before any uncertain pa-rameters are unveiled considering the potential realization ofuncertainties while the second-stage decisions are made afterthe uncertainties are disclosed, and they depend on the firststage decisions [1], [13].

III. PROBLEM FORMULATION

The underlying two-stage stochastic optimization problem ispresented in this section. The first-stage decisions include theday-ahead hourly bids and the commitment statues for DGs.The second-stage decisions 1 include the dispatch of DGs,the curtailment of involuntary load and renewable energy,the battery/EV charging decisions, and the real-time powerdelivery between the MG and the grid. we describe theobjective function and all constraints in the following.

A. Objective Function

We propose to minimize the following objective function

minNG∑i=1

NH∑t=1

(SUi,t + SDi,t) +NS∑s=1

ρs

NG∑i=1

NH∑t=1

C(P si,t)

+NS∑s=1

ρs

NH∑t=1

ΔT{Pte

s,DAt + (P s

t − Pt)es,RTt + ψt|P

st − Pt|

+V Wt .

NW∑w=1

Ps,wsw,t + V PV

t .

NP∑p=1

Ps,pvsp,t + V LL

t LSst

}

(1)

where the Pt is the hourly bid submitted to the day-aheadmarket, and P s

t − P t is the power exchange in the real-timebalancing market. The convention here is that if power isimported from the main grid, it will take a positive value,and vice versa.This objective function indeed captures the start-up, shut-

down, and operating costs of DGs, the cost of power exchangein the market, the penalty costs for bid deviation, renewableenergy curtailment, and involuntary load curtailment. Note thata negative value of Pte

s,DAt + (P s

t −Pt)es,RTt implies that the

MG makes revenue by selling power to the main grid. Thecost function for small DGs can be expressed as [2]

Ci(Psi,t) = ai + biP

si,t, ∀ i, t, s. (2)

B. Power Exchange with Main Grid

The hourly bid and the actual power delivery is limited bythe line capacity between the MG and the main grid, i.e.,

−P g,maxt ≤ Pt ≤ P

g,maxt ;−P g,max

t ≤ P st ≤ P

g,maxt , ∀ i, t. (3)

1All the second-stage decision variables are denoted with a superscript s.

C. Constraints for DGsThe constraints for DGs are given as follows [8], [10]:

Pmini Ii,t ≤ P s

i,t ≤ Pmaxi Ii,t (4)

P si,t − P

si,t−1 ≤ URi(1− yi,t) + Pmin

i yi,t (5)P si,t−1 − P

si,t ≤ DRi(1− zi,t) + Pmin

i zi,t (6)t+UTi−1∑

l=t

Ii,t ≥ UTiyi,t;

t+DTk−1∑l=t

Ii,t ≥ DTiyi,t (7)

SUk,t ≥ CUk,t(Ik,t − Ik,t−1); SUk,t ≥ 0 (8)SDk,t ≥ CDk,t(Ik,t−1 − Ik,t); SDk,t ≥ 0 (9)yi,t − zi,t = Ii,t − Ii,t−1; yi,t + zi,t ≤ 1 (10)

∀i, t, s.Here, the constraints for the operation of DGs include

generation constraints (4), ramping up/down constraints (5)-(6), minimum up/down time (7), start-up cost and shut downcost constraints (8)-(9). The relationship between the start-upindicator (yk,t) and shutdown indicator (zk,t) is shown in (9).A DG cannot be started up and shut down simultaneously.

D. Battery ConstraintsThe following constraints represent the charging/discharging

limits for battery k (11), state of charge (SOC) limits (12),charging/discharging state constraints where battery k is notallowed to be charged and discharged simultaneously (13). Thedynamic battery state is given in (14).

0 ≤ Ps,ck,t ≤ b

s,ck,tP

c,maxk ; 0 ≤ P

s,dk,t ≤ b

s,dk,tP

d,maxk (11)

SOCmink ≤ SOCs

k,t ≤ SOCmaxk ; SOCs

k,NH = SOCsk,1 (12)

bs,ck,t + b

s,dk,t = 1; b

s,ck,t, b

s,dk,t ∈ {0, 1} (13)

SOCsk,t+1 = SOCs

k,t +ΔT (ηckP

ck,t

Ek

−P dk,t

ηdkEk

) (14)

∀k, t, s.

E. EV ConstraintsSimilar to constraints for battery storage units, the con-

straints for EV battery operation are written as follows:

0 ≤ Ps,cj,t ≤ b

s,cj,tP

c,maxj ; 0 ≤ P

s,dj,t ≤ b

s,dj,tP

j,maxk (15)

SOCminj ≤ SOCs

j,t ≤ SOCmaxj ; SOCs

j,NH = SOCdj (16)

bs,cj,t + b

s,dj,t = 1; b

s,cj,t , b

s,dj,t ∈ {0, 1} (17)

SOCsj,t+1 = SOCs

j,t +ΔT (ηcjP

cj,t

Ej

−P dj,t

ηdjEj

) (18)

∀j, s, t ∈ [taj , tdj ]. If an EV comes to the garage more than

once during the optimization horizon, each time we will assigna different ID j for the EV.

F. Renewable Energy CurtailmentThe amount of renewable energy curtailment is limited by

the maximum available renewable energy generation, i.e.,

0 ≤ Ps,wst ≤ P s

w,t; 0 ≤ Ps,pvst ≤ P s

p,t, ∀ w, p, t, s. (19)

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G. Involuntary Load CurtailmentThe involuntary load curtailment has to be less than the

maximum allowable curtailment and the actual demand, i.e.,

0 ≤ LSst ≤ LSmax

t , : 0 ≤ LSst ≤ Ls

t , ∀ t, s. (20)

H. Power Balance ConstraintThe sum of total local generation (i.e., DGs and RESs),

the actual power delivery, the amount of involuntary loadcurtailment , and the discharging power from battery unitsand EVs must be equal to the sum of the MG local load andthe charging power from battery units and EVs, i.e., ∀ s, t.NG∑i=1

P si,t +

NW∑w=1

(P sw,t − P

s,wsw,t ) +

NP∑p=1

(P sp,t − P

s,pvsp,t ) + P s

t

+LSst +

NK∑k=1

(P s,dk,t − P

s,ck,t ) +

NV∑k=1

(P s,dj,t − P

s,cj,t ) = Ls

t (21)

In summary, we have formulated the power scheduling andbidding problem as a mixed integer linear program (MILP) 2which can be solved easily by CPLEX [15].

0 2 4 6 8 10 12 14 16 18 20 22 240

200

400

600

800

1000

1200

1400

1600

Time (h)

Powe

r (kW)

LoadWindSolar

(a) Base load, forecasted wind power, forecasted solar power

0 2 4 6 8 10 12 14 16 18 20 22 240.02

0.03

0.04

0.05

0.06

0.07

0.08

Time (h)

Price

($/kW

h)

Day−aheadReal−time

(b) Electricity price

Fig. 1. Base load and forecasts of wind/solar power, and electricity prices

IV. NUMERICAL RESULTSWe consider a MG which consists of one fuel cell unit,

one wind turbine, one solar panel, one battery storage unit,a large garage with 100 EVs, and the aggregated load frombuildings in the MG. Data for the fuel cell unit, wind turbine,and PV source is retrieved from [2]. We take the historicaldata for wind speed [16], solar irradiance [17], and electricityprices [9] as their forecast values. Wind speed forecast error ismodeled by an ARMA time series [10]. Solar irradiance, day-ahead price, and real-time price are assumed to follow normaldistributions with the standard deviations are set to 10%, 10%,and 20% of the corresponding mean values. To representuncertainties, we generate 3000 different scenarios, which is

2The objective function (1) can be transformed to an equivalent linearfunction with some auxiliary variables t deal with the absolute term [14].

further reduced to 20 scenarios by using GAMS/SCENRED[18]. Wind power is calculated from the wind speed and thewind turbine power curve, and the solar power is calculatedfrom the solar irradiance. Data for base load is taken from[13] with an appropriate scaling coefficient. Base load and theforecasts for wind power, solar power, and electricity pricesare shown in Figs. 1(a)-1(b).

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08360

370

380

390

400

410

420

VRES($/kWh)

Obj. (

$) ψ = 0.05 $/kWh, optimalψ = 0.05 $/kWh, uncontrolledψ = 0.10 $/kWh, optimalψ = 0.10 $/kWh, uncontrolled

(a) Cost

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

50

100

150

200

250

300

350

400

450

500

VRES ($/kWh)

Curta

ilmen

t (kWh

)

ψ = 0.05 $/kWh, optimalψ = 0.05 $/kWh, uncontrolled ψ = 0.10 $/kWh, optimalψ = 0.10 $/kWh, uncontrolled

(b) Renewable energy curtailment

Fig. 2. Comparison between smart EV charging scheme and uncontrolled EVcharging scheme (varying V RES )

Penalty charges for involuntary load curtailment, renewableenergy curtailment (V W

t = V PVt = V RES , ∀t), and bid devi-

ation (ψt = ψ, ∀t) are $1000/MWh, $20/MWh , $80/MWh,respectively. There is one battery unit with the capacity of300kWh in the MG. The maximum and minimum SOCs are0.9 and 0.2, respectively. The maximum charging/dischargingpower is 100kW. The charging/discharging efficiency for bat-tery units and EVs are set to 0.9. The maximum involuntaryload curtailment is equal to 50kW. The capacity of the linebetween the MG and the main grid is set to 3000kW.We assume all EVs are Nissan Leaf with the battery capacity

of 24kW [5]. We also assume the garage is equipped with allLevel II charging stations with the charging/discharging powerratings of 7.2kW, and each EV takes only one trip during theoptimization horizon. The maximum and minimum SOC ofeach EV is set to 0.9 and 0.2, respectively. The initial SOCsof EVs are assumed to be uniformly distributed in the rangeof [0.2, 0.9] [5]. The arrival time and departure time of EVsare modeled by normal distributions with the means of 8 A.Mand 5 P.M, respectively, and both the standard deviations areset to 2 hours. The desired SOCs of EVs when they leave thegarage are set to SOCmax.Figs. 2(a), 2(b) illustrate the advantages of the proposed EV

charging scheme over the uncontrolled one. In the uncontrolledEV charging scheme, each EV is charged immediately at therated power when it arrives at the garage, and the chargingprocess stops when the EV reaches its desired SOC. As wecan observe, smart EV charging offers a lower cost (optimalvalue for objective function) as well as a smaller amount ofrenewable energy curtailment compared to the uncontrolledEV charging scheme. In addition, the MG cost increasesand the amount of renewable energy curtailment decreases as

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V RES increases, and they get saturated as V RES is sufficientlylarge.Figs. 3(a), 3(b) compare the performances due to the two

schemes by varying the bid deviation penalty parameter (ψ)for two cases, namely with and without a battery unit inthe MG. We can observe that the total cost as well as thetotal amount of renewable energy curtailment increase as ψincreases. It is because as ψ increases, we have to maintain astricter requirement where the real-time power delivery mustbe very close to the day-ahead schedule. Also, it is evident thatthe smart EV charging scheme results in a lower cost and lessrenewable energy curtailment than that due to the uncontrolledscheme.

0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2340

360

380

400

420

440

460

480

ψ ($/kWh)

Obj. (

$)

No battery, optimalNo battery, uncontrolledWith battery, optimalWith battery, uncontrolled

(a) Cost

0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

200

400

600

800

1000

1200

ψ ($/kWh)

Curta

ilmen

t (kWh

)

No battery, optimalNo battery, uncontrolledWith battery, optimalWith battery, uncontrolled

(b) Renewable energy curtailment

Fig. 3. Comparison 2 between smart EV charging scheme and uncontrolledEV charging scheme (varying ψ)

We define LSF (Load Scaling Factor) [10] as a coefficientthat we use to scale the base load curve in Fig. 1(a). Theoptimal hourly bids that MG submitted to the day-aheadmarket with different values of LSF is presented in Fig. 4.The impacts of ψ and battery capacity on the optimal solutionare presented in Fig. 5. As we can see, the MG operationcost reduces as the battery capacity increases or the penaltyparameter for bid deviation (ψ) decreases.

0 2 4 6 8 10 12 14 16 18 20 22 24−1500

−1000

−500

0

500

1000

1500

2000

Time (h)

Powe

r (kW)

LSF = 0.5LSF = 1.0LSF = 1.5LSF = 2.0

Fig. 4. Optimal day-ahead bid

V. CONCLUSIONAn optimal day-ahead power bidding and scheduling prob-

lem for a MG with EVs and RESs is considered in this

paper. We formulate this problem as a two-stage programming

0 100 200 300 400 500 600 700 800 900 1000340

350

360

370

380

390

400

Battery Capacity (kWh)

Obj. (

$)

ψ = 0.04 $/kWhψ = 0.08 $/kWhψ = 0.12 $/kWhψ = 0.16 $/kWh

Fig. 5. Impact of ψ and battery capacity on the optimal solution

problem considering uncertainties of RESs and electricityprices. The EVs in the parking garage are utilized as a dynamicenergy storage facility to compensate for the variability ofRESs. Simulation results show that by smartly coordinatingthe EV charging with renewable energy generation, we canincrease significantly the profit of the MG in the deregulatedelectricity market, reduce the MG operating cost as well asthe amount of renewable energy curtailment.

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