smart microgrids: optimal joint scheduling for electric vehicles and home appliances

IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 1, JANUARY 2014 239

Smart Microgrids: Optimal Joint Scheduling forElectric Vehicles and Home Appliances

Mosaddek Hossain Kamal Tushar, Chadi Assi, Senior Member, IEEE, Martin Maier, Senior Member, IEEE, andMohammad Faisal Uddin

Abstract—The integration of renewable energy sources and elec-trical vehicles (EVs) into microgrids is becoming a popular greenapproach. To reduce greenhouse gas emissions, several incentivesare given to use renewable energy sources and EVs. By using EVsas electricity storage and renewable energy sources as distributedgenerators (DGs), microgrids become more reliable, stable, andcost-effective. In this paper, we propose an optimal centralizedscheduling method to jointly control the electricity consumption ofhome appliances and plug-in EVs as well as to discharge the latterones when they have excess energy, thereby increasing the relia-bility and stability of microgrids and giving lower electricity pricesto customers.Wemathematically formulate the schedulingmethodas a mixed integer linear programming (MILP) problem and solveit to optimality. We compare the optimal solution to that obtainedfrom a scheduling framework, where EVs do not have dischargecapabilities, decentralized charge control using game theory andto a solution obtained from a naive scheduling framework.

Index Terms—Optimization, scheduling, smart microgrids,V2G.

I. INTRODUCTION

R ECENT studies have shown that a substantial amount ofpower losses in the existing power grid is due to long dis-

tance transmission and distribution [1]. Failures on the transmis-sion and distribution lines of the power grid cause almost 90% ofthe power outages. It is hence clear that the old hierarchical, cen-trally controlled grid is not suitable for future needs [2]. Currentelectricity generators, the largest emitters of greenhouse gases,are heavily dependent on fossil fuel. Electric power generatorsproduce nearly 41% of the world greenhouse gases [3]. Anothersignificant greenhouse gas emitter is the transportation system,which produces 23% of the world greenhouse gases, followedby residential houses, which produce 6% of the total greenhousegases [3].The evolution of smart microgrids and electric vehicles (EVs)

holds promise to address the above problems. A smart micro-grid is a modern and small-scale version of the future powergrid [4]. Similar to the conventional power grid, smart micro-grids generate, distribute, and regulate the flow of electricity to

Manuscript received January 05, 2013; revised May 02, 2013, July 20, 2013,and September 25, 2013; accepted November 02, 2013. Date of current versionDecember 24, 2013. This work has been partially supported by Concordia Uni-versity and partially by NSERC Strategic grant. Paper no. TSG-00860-2012.M. H. K. Tushar, C. Assi, and M. F. Uddin are with Concordia University,

Montreal, QC H3G 2W1, Canada.M. Maier is with Institut National de la Recherche Scientifique (INRS), Mon-

treal, QC H5A 1K6, Canada.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TSG.2013.2290894

consumers. In case of shortage of power generation, they auto-matically switch to use the energy stored in backup batteries orimport electricity from neighbouring microgrids or the powergrid. Electric power can be stored or exported to other micro-grids or the power grid in case of excess power generation.The overall load profile of the power grid, as well as of the

microgrid, may change due to the introduction of EVs. Charginga large population of EVs has a significant impact on the powergrid [5]. On the other hand, the introduction of EVs in the micro-grid opens up opportunities to store and regulate power gener-ated from highly intermittent energy generators. Usually, a mi-crogrid operator needs a large and costly backup battery bank tostore electric power to mitigate the demand. EVs can be used asa cheap replacement of the backup battery bank. US departmentof transportation data indicates that including overnight hours avehicle spends nearly 75% parked at home [6]. In the US, it ispredicted that by 2020 25% and by 2040 two thirds of light-dutyvehicles ought to be EVs. Further, it is expected that current re-search outcomes on high power lithium-ion micro battery tech-nology will accelerate the replacement of internal combustioncars by the EVs [7]. The integration of a large population ofEVs has a significant impact on the power grid. Specifically, inV2G (vehicle-to-grid) operation, one million EVs with 16 kWhbattery capacity can supply 2000 MW to the grid for a time pe-riod of up to two hours while discharging at a rate of 2 kWh.EVs may play a dual role in microgrids; they act as loads to themicrogrid when plugged in for charging and as storage for elec-tricity in the stationary state. Alongwith charging infrastructure,investment required to develop intelligent IT infrastructure forsmart charging of EVs and reliable services to home [6].Currently, most of the home appliances consume electricity

in a continuous fashion with tight scheduling [8]. Some ofthem consume electricity continuously while others operate ina distributed fashion with flexible scheduling. An intelligentscheduling strategy can optimally determine the schedule of EVcharging and discharging and the schedule of home applianceelectricity consumption. The resultant scheduling pattern issuch that the load profile of the electricity system follow therenewable energy generation pattern. This reduces the amountof imported electricity from the neighboring grid as well asthe capital and operational costs of the microgrid. Further, theoptimal scheduling improves the service availability, stability,and reliability of the microgrid operations.Several opportunities and limitations concerning the integra-

tion of EVs with the power grid and renewable energy sourceswere identified and used to formulate control methods forcharging EVs [9]. The authors discuss two such methods: i) aglobal control method for charging EVs based on global load

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240 IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 1, JANUARY 2014

information that is communicated by means of load signaling,and ii) local control methods for charging EVs based on localload conditions of the microgrid. Preliminary results show thatan energy control strategy based on load information offersbenefits, especially by avoiding the need for supplementarygenerated capacity, which originates from additional peakloads. The design goal of both strategies is to charge EVs byshifting the charging from peak hours to off-peak hours inorder to flatten the electricity demand of the grid. The authorsassume that residential loads are not flexible (i.e., deferrable) toconsume electricity from the grid. Further, the paper does notconsider EVs for electricity storage.A dispatch model based on a cost-benefit analysis of micro-

grids for selling electricity from a residential area to office build-ings was presented in [10]. Simulation results show that incor-porating EVs into the microgrids not only minimizes the storageand operational costs, but also results in cost savings for theowners of EVs. In [10], the microgrid charges EV batteries athome at a low electricity price after office hours and dispatch theenergy to office buildings at a higher price during the day. Theelectricity price paid at home for charging EVs is considered thebattery degradation cost. In their work, the authors assumed thatEVs do not feed power back into the grid.The authors of [11] demonstrated a decentralized EV charging

scheme using the Nash certainty equivalence principle. Theirapproachmaybeviewed as a valleyfilling approach.The schemeshifts the charging of EVs from peak hours to off-peak hours bycontrolling the peak and off-peak electricity prices. The multi-player game theory in theNash equilibriumconditiondeterminesthe peak and off-peak hour electricity price. In theirwork, the au-thors claimed that centralized control for charging a largenumberof EVs is computationally intractable and impractical.Another decentralized EV charging protocol was proposed in

[12]. The main objective of this work is to shift vehicle chargingfrom peak hours to off-peak hours by imposing a penalty onthe electricity price. The proposed protocol considers differentprices for different hours of the day andminimizes the peak hourload by imposing penalties on vehicles intended to be chargedin peak hours.The stochastic nature of EVs and renewable energy sources

was considered for EV charging in [13] and [14]. They modelthe charging system by means of a continuous time Markovchain. Two performance matrices, called vehicle chargingblocking probability and average reward, are considered toevaluate their charging policies. They classify EVs with respectto their different charging capacity and prioritize them accord-ingly [14]. The motivation of the paper is to devise an optimalcharging strategy to server the maximum number of EVs.Unlike previous work, we investigate a microgrid that is con-

nected to the power grid and has a fixed number of renewableenergy sources (e.g., wind turbine, photovoltaic panels, etc.) fora small residential community. The microgrid consumers havehome appliances and EVs. We propose a centralized joint op-timal electricity consumption scheduling method for appliancesand EVs with the objective to minimize the amount of importedelectricity from the grid. We use EVs as distributed storage tostore electricity. EVs are mobile and connected to the micro-grid in a random fashion. In case of shortage of power, the mi-crogrid uses the electricity stored in EVs (with discharge capa-

Fig. 1. Microgrid architecture.

bility) and in cases, when the stored electric energy is not suf-ficient, uses electricity from the grid, whereas most of the pre-vious works consider microgrids with renewable energy sourceseither is a charge station for EVs or trade energy from residen-tial microgrids to commercial microgrids. Others use the con-ventional power grid and have developed schemes to flatten thepower generation. In the proposed model, we consider an inde-pendent residential microgrid which can be operated in islandedmode or in grid connected mode. We formulate the schedulingproblem as an integer linear programming problem (MILP) tojointly control electricity consumption of home appliances aswell as the charging and discharging of EVs, and present numer-ical benchmark comparisons with a naive scheme and decentral-ized EV charging control framework. Our scheduling methodresults in the optimal use of electricity generated from renew-able energy sources andminimizes the amount of imported elec-tricity from the grid. Consequently, it reduces the electricityprice for the microgrid customers. Further, the optimal sched-uling method enables EVs to store electricity during peak gen-eration hours, which may be used later during high demand. Indoing so, our approach helps increase the service availabilityand stability of the microgrid.The remainder of the paper is organized as follows. In

Section II, the system model is described and the MILPproblem formulation is presented. In Section III, the naivescheduling technique is discussed. Section IV describes thedecentralized charging control strategy using non-cooperativegame. In Section V, numerical results for both naive and op-timal scheduling algorithms are presented. Finally, we concludein Section VI.

II. SYSTEM MODEL

We consider the microgrid shown in Fig. 1 with multiplerenewable distributed generators (DGs), a central controller, aset of home appliances , and a set of EVs

. For renewable energy sources, home appliancesand EVswe adopt the notations of Table I. The central controllerof the microgrid is responsible for scheduling and controllingthe flow of electricity from DGs to the customers’ appliances.A smart meter or aggregator of each customer’s home sends in-formation (operational time slot, consumption rate, maximumand minimum capacity, etc.) of each appliance to the central

TUSHAR et al.: SMART MICROGRIDS: OPTIMAL JOINT SCHEDULING FOR ELECTRIC VEHICLES AND HOME APPLIANCES 241

TABLE INOTATIONS

controller. In the following subsections, we discuss each com-ponent of the system model. Finally, in Section II-E we presentthe objective function and constraints of the model.

A. Renewable Energy

We consider a microgrid with renewable energy sources(wind turbine, photovoltaic cell, etc.). The total electricity gen-erated in an hour is given by

(1)

Note that renewable energy sources are stochastic in nature [15].Several stochastic models exist to predict the short-term and/orlong-term power generation. In this paper, a Markov chain statetransition probability is used to predict the next 24 hours of elec-tricity generation, as described next. Also, the proposed systemmodel is capable to integrate any renewable, non-renewable, orweather predicted energy source model. The only requirementis that the model would be able to forecast power generation ineach time interval for next (i.e., ) hours.1) Wind Turbine: Wind is a highly unstable phenomenon

that cannot be fully described by any probability distributionscience wind speed at every hour is correlated with the speedat previous hours. A Markov chain represents the system tran-sition from one state to another over time. The order of theMarkov chain gives the number of time steps influencing thepresent state of the system [16]. A first order Markov chain isused for the simulation of wind speed prediction. A second orhigher-order Markov chain model can improve the wind speedprediction. Our Markov chain model for wind speed predictionuses the historical time series data for a given geographic area[17]. Suppose is the historical wind speedtime series data representing the hourly wind speed in meter persecond (m/s) for a long duration (3 or more years). Let de-note the states of wind speed for the time series wind speed data. Then, the first order Markov transition probability matrix

can be determined as follows:

(2)

where and is the total number of tran-sitions from wind speed to wind speed for the next hour inthe wind speed time series data . Synthetic wind speed datacan be generated by taking the cumulative probability distribu-tion of the first order Markov state transition probability matrixof (2):

(3)

For generating sequences of wind speed time series data, aninitial state is selected randomly. Then a random number ischosen between 0 and 1 using a uniform random number gen-erator. The value of the random number is compared with thevalues in row of the cumulative probability distribution of thefirst order or second order Markov state transition probabilitymatrix. If the value of the random number is greater than theprevious state and less than or equal to the following state, thefollowing state is selected. Next, the speed state is converted towind speed by using the following equation

(4)

where and are the wind speed boundary of the state, andis a uniformly distributed random number over . In doingso, wind speed time series of any length can be generated. Thevalidity of this prediction model is described in more detail in[16].


From the historical (observed) or synthetic wind speed timeseries data, Markov first order state transition matrix can be con-structed. More precisely, from the current wind speed using (3)and (4) the next wind speed can be predicted. Let the predictedwind speed for hour be . The electricity generated froma wind turbine in hour is then given by:

(5)

where , , and represent the air density in , swaparea of the turbine and Betz limit (maximum value of 0.59).Practical wind turbines have a cut-in and cutoff wind speed ap-proximately from 2 m/s to 5 m/s and from 15 m/s to 25 m/s,respectively. At cutoff wind speed or beyond, a wind turbinegenerates a constant amount of electric power at its maximumcapacity, whereas below the cut-in wind speed the wind turbinedoes not produce any power.

2) Solar Power: Markov models for solar radiation usinghistorical data have been successfully used in climatology. Inthis paper, a solar radiation model with impact of cloud inten-sity on solar radiation is considered [18]. Solar radiation statescan be expressed by the following Markov first order transitionprobability matrices (6) and (7).

(6)

(7)

where is the total number of radiation states. For example,state refers to the case when the sun is fully coveredby clouds and solar cells do not produce any power. For, represents the maximum intensity of solar radiation (in

). In this case (full sunlight, clear sky), solar cells producemaximum power. In (6) and (7), matrices and denote thetransition probability matrix among solar radiation states andintensity of the solar radiation , respectively. Note that

in matrix denotes the transition probability form solarradiation state to in .Under the assumption that the cloud size is exponentially

distributed with mean , the solar radiation state is . As-suming that transitions among solar radiation states are sequen-tial and circular, the transition matrix for solar radiation can beexpressed as a continuous time Markov chain [18]

(8)

where denotes the variation rate between solar radiations[13]. The instantaneous power of the solar panel, , is di-rectly related to the current solar radiation . Thus, the elec-

tricity generated by the photovoltaic (PV) panel can be calcu-lated as follows [19]

(9)

where the value of is the corresponding efficiency which de-pends on the single PV cell area, ambient temperature, internalimpedance, global irradiation, and other parameters at time

. is a critical radiation point in beyondwhich an increase of radiation results in a smaller increase inefficiency. is the number of photovoltaic cells in the PVpanel. We assume, a 0.01 PV cell with efficiency(unit-less), and at 25 .

B. Home Appliances

Let be the set of customers and be the set of homeappliances (e.g., washer, dryer, refrigerator) for each customer

. Each appliance is scheduled to consume electricity orremain idle in each time interval (e.g., an hour) during the day.Residential customers may have different types of appliancesnamely, first, Type A (hard load), where certain appliances mayhave strict scheduling requirement, for example, a refrigeratorshould remain operational at all times, second, Type B (softload), where many appliances may require constant amount ofelectricity consumption in a continuous fashion with flexiblescheduling for a limited amount of time (e.g., washing machine)and lastly, Type C (soft load), where some appliances may needa fixed amount of electricity with irregular scheduling (e.g.,EV). Let be the electricity consumption of a home appli-ance in time interval . Then, the total electric energy(kWh) consumed by appliance during a day is given by

(10)

where . In case of a hard load (Type A), for each hour, is equal to 1 if . For a soft load (Type C), if anappliance consumes unit of energy (kWh) during a day thenfor each hour if . In this case, when ,appliance consumes units of electricity, otherwise it re-mains idle. Suppose that the microgrid has home appliances,

, then the total electric energyconsumed by appliance (Type C) per daymust satisfy its target amount of electricity , which can beexpressed as follows:

(11)

Type B appliances consume electricity in a continuousfashion. Thus, in any time slot, if a type B equipment isscheduled to consume electricity, it will continue to consumeelectricity until the total consumption is equal to the targetsuch that

(12)


where denotes the number of time slots neededby appliance to reach its target energy consumption and

is a binary variable, which denotes the start time of typeB appliance . If , appliance starts consuming elec-tricity in time slot . As type B appliances consume electricitycontinuously, the following constraint must be satisfied

(13)

C. Electric Vehicle

We assume that the arrival of EVs to the microgrid follows aPoisson process with an arbitrary randomly distributed energylevel. The EV stays at home (microgrid) for a random amountof time period and then departs for driving. At home, an EVcharges its battery to a target energy level for the followingdriving schedule. EV is a special type of soft load, which canbe scheduled in a flexible way i.e., charging, discharging, or re-maining idle during its residence in the microgrid. If the arrivaltime of EV is and departure time is , the energy level atarrival is and the target energy level is . The en-ergy consumption from the microgrid between arrival anddeparture by EV is given by

(14)

where denote the strategies of (defined in I). Iffor and 0 otherwise, then the above (14) can berewritten as

(15)

For both safety and longevity of EVs’ batteries, each EVmustnot discharge below the minimum discharge level. Therefore,

(16)

where is defined as

(17)

Note that for the proposed model when we consider only EVswithout discharge capabilities, we simply ignore the state. In this case, can either take 0 or 1.Each EV may charge, discharge, or remain idle throughout

the duration of its residence in the microgrid. Therefore, the netenergy consumption by EVs can be computed as

(18)

The microgrid central controller must ensure that each EVhas the target energy level when it departs for driving. Thus, thefollowing relation must hold

(19)

However, an EV should not charge beyond its battery capacityand discharge below , as given by

(20)

D. Pricing Model

We define the cost function (in hour ) as the unitprice of the electricity consumption from renewableenergy sources, discharging of Evs as well as importedpower from the external grid or microgrids, whereby

. Here, (e.g.,0.10 $/kWh) represents a constant for local energy use and(e.g., ) is a function, which increases withthe increase of import from the external grid or microgrids;(e.g., 0.15 $/kWh) is a constant which represents the unit

selling price of electricity due to EVs battery discharge;is plus the compensation due to the EV’s battery discharge.We assume . For each hour, let the electricityprice for the microgrid be . Then, we have

(21)Let and

. Therefore, the daily total electricity cost is given by

(22)

The microgrid central controller adjusts the electricity unit pricefor the whole community by the amount of imported electricity

in each hour. The controller does not charge the price tocommunity if the total electricity demand is equal to or lower

than that of produced. Consequently, the daily totalupdated electricity price for the microgrid community is givenby

(23)

The cost of adjustment, , is as follows

if,

(24)

where the import electricity is obtained as

(25)

The adjustment in (24) can be calculated from the followinginequalities:

(26)

(27)

(28)

where , is an large integer number and is a in-dicating binary variable. In case of import, otherwisewe set .


E. Problem Formulation

To achieve best (i.e., minimum) daily price for customers,while predicting the hourly renewable energy generationand fixed activation matrix for appliances and EVs ,we can write the objective function of the problem as follows:

Objective:

(29)

which requires to determine the values of the variablesand . Therefore, the optimization problem (29) can besolved by determining the optimal schedule of the appli-ances and changing states of EVs during their residence inthe microgrid. Formally,

(30)

is equivalent to

(31)

subject to:For type A & C

(32)For type B

(33)

(34)

For EV:

(35)

(36)

and (26)–(28).The formulated mathematical model contains continuous

( and ) and discrete decision variables, and henceforms an MILP (Mixed Integer Linear Programming) model).By solving the above MILP problem, we can obtain the optimalschedule for different working states of home appliances andEVs, respectively. The minimization of imported electricitymodel (31) shifts soft loads to consume electricity from lowpower generation time slots to high power generation timeslots. EVs charge their batteries in high power generation timeslots and discharge, when the amount of power generated by

the microgrid is low. The formulated MILP problem for jointscheduling of home appliances and EVs is solved using theIBM CPLEX MILP solver.

III. NAIVE SCHEDULING SCHEME

In our naive scheduling scheme, the microgrid central con-troller schedules home appliances and EVs for electricity con-sumption without prior knowledge of the amount of generatedelectricity and operational time slots of the home appliances andEVs. Thus, as soon as a home appliance and/or an EV is ready,the central controller of the microgrid schedules the applianceand/or EV to consume electricity regardless of the amount ofelectricity generated by the microgrid. Therefore, the amountof imported electricity from the external grid or microgrids inan hour can be expressed as:

(37)

where and

if

if .

(38)The total amount of imported electrical energy is given by

(39)

where

ifotherwise.

(40)

IV. DECENTRALIZED EV CHARGING CONTROL USINGNON-COOPERATIVE GAME

A decentralized EV charging control strategy allows each EVto determine its own charging pattern. The decentralized modelis composed of a utility responsible for collecting all optimalcharging strategies proposed by all EVs and broadcasting theaggregated EV demand along with predicted base demand. Theproblem is formulated as a non-cooperative game where eachEV is a player and utility of the microgrid is the controller ofthe game. Each EV reacts with an optimal charging strategy forminimizing its own electricity costs by receiving the base andaggregated EV demand. The game continues until there are nochanges in the charging strategy or total energy costs of any ofthe EVs. The game is a non-cooperative selfish game becauseeach EV decides its “happiness” (charging scheme) by knowingall other EVs’ charging strategies [11], [20]. For an individualEV , we adopt the notation in Table I. Here, base load is calcu-lated by summing up the amount of the electricity requested byeach individual home. Each appliance is scheduled to consumeelectricity as soon as an appliance is ready. Therefore, the baseload in each hour is given by:

(41)


For each time slot between arrival and departure ,EV ’s charging control can be defined as follows:

(42)

with an initial energy level of . Each EV must becharged to a target energy level at the time of departure .Moreover, the energy level of EV must not violate the upperand lower bound while residing in the microgrid. Therefore, thefollowing conditions must hold:

(43)

and

(44)

where represents the charge control strategy at time slotand denotes the maximum charging and discharging rate ofEV . Value can be chosen from any finite number of in-teger values between that represent the strategies of EV. To compare with the proposed optimal charging strategy, the

same strategies (1:charging, 0:remain idle and 1:discharging)are chosen. Therefore, we can define the set of feasible chargingstrategies for a predefined target as

(45)Let

(46)

be the set of charging strategies of EVs and

(47)

the set of charging strategies for EVs without EV . Each EVminimizes its own operating cost by determining a chargingstrategy with respect to the charging strategy adopted by otherEVs. More specifically, the cost function of EV can be ex-pressed as follows:

(48)where the tracking cost is a non negative constant and

(49)

The price is given by

(50)

Here, is defined as

(51)where represent the amount of elec-tricity used by the microgrid customers from renewable energysources, discharged EV battery, and imported electricity from

the grid, respectively. The parameter values of the price func-tion used for simulation a set to ,

and . Here, is the amountof electricity imported from the grid. Here, , are constantand is convex [20], therefore, is a convex function. Optimalcharging strategy for an EV is obtained via negotiation betweenelectricity cost and cost incurred deviating from the strategy.The decentralized charge control strategy thus forms a non-co-operative dynamic game. Each EV resides at home shares baseload information and also tracks the average charging strategyof the whole EV population. A set of charging controls is atNash-equilibrium if, for all EVs , is the chargingstrategy that minimizes the operation cost (48) with respect to

[11], [20]. The negotiation of charging strategies for a daycan be determined by the following procedure [11], [20]:S1) The utility broadcasts the predicted base load

to all EV agents.S2) Each EV agent proposes a charging control strategy

to minimizes its operating cost (48) with respect tothe common aggregated EV demand broadcast by theutility.

S3) The utility collects all proposed charging control strate-gies , and updates the aggregated EV demand. TheEVs’ aggregated demand is broadcast to all EVs.

S4) Repeat step and until the proposed optimalcharging strategy of each EV no longer changes.

Higher values of tracking cost put more emphasis on min-imizing the deviation from the average strategy, and on theother hand lower values put more emphasis on the electricityprice. The authors of these algorithms chose , whichconverge the homogeneous system to the Nash-equilibrium bysmoothing the valley filling curve [11], [20]. For heterogeneoussystem the game converges to -Nash equilibrium. For eachEV agent the minimization of (48) with the constraints from(43) to (44) and base load , becomes the mixed integerquadratic problem(MIQP). We solve the problem by using theIBM CPLEX MIQP solver.

V. NUMERICAL RESULTS

In this section, we evaluate our proposed algorithms (EVswith and without discharge capabilities) and compare the resultswith our optimal results with those obtained from naive sched-uling and decentralized EV charging control schemes. In ourproposed model, we consider a wind turbine with radius 10 m,air density 1.28 , cut-in wind speed 2 m/s, cut-off windspeed 25 m/s, ) and photovoltaic energy sourceswith maximum radiation: 1000 , photovoltaic panel area50 , and with a maximum production capacity of 1.5 MWh(from (5)) and 0.5 MWh (from (9)), respectively. The amountof electricity from the renewable energy sources is predictedfor each hour of a day by using the renewable energy modelsdescribed in Section II. To generate synthetic time series wetook observed wind speed time series during one day from theNDCD (National Climate Data Center) of NOAA (NationalOceanic and Atmospheric Administration, USA). We assume asmall community with 200 residential subscribers for the sim-ulation. In the simulation, we select 1400 appliances randomlydistributed over these 200 household customers. Note that eachcustomer owns 6 to 8 appliances. Such appliances include hardand soft loads. Hard loads with daily and hourly consumption


Fig. 2. Amount of electric energy imported from the external grid/microgrid.

include: a 4.0 kWh (2.0 kWh per hour) electric oven, a 0.8 kWh(0.8 kWh per hour) microwave, five (0.1 kWh per hour each)2.0 kWh light bulb, a 0.36 kWh (0.12 kWh per hour) flat screenTV, a 3.6 kWh (0.150 kWh per hour) refrigerator, a 6 kWh(1.0 kWh per hour) heating system, and a 0.25 kWh (0.05 kWhper hour) laptop. Soft loads (Type B) with daily and hourlyconsumption include: a 1.6 kWh (0.8 kWh per hour) washingmachine, a 2.4 kWh (1.2 kWh per hour) dishwasher, a 6 kWh(2.0 kWh per hour) dryer, and a 0.027 kWh (0.009 kWh perhour) battery charger. For the simulation, we vary the numberof EVs from 10 to 600, where each EV applies 3 kWh perhour charging and discharging rate with 24 kWh capacity and3 kWh (13.5%) minimum discharge energy level. The arrivaland departure of each EV in a time slot follows a Poissonprocess, and the initial and targetenergy level ( is in between 70% to 100% of )are selected randomly, with the restriction that the time span ofeach EV is sufficient to charge its battery to the target energylevel. We have also considered certain real life EVs patternwhere most of the EVs are unavailable during morning toafternoon. In this case we took the EVs arrival and departurepattern extracted from the investigation of NHTS [21]. Wehave executed the simulation with 40 iterations. Fig. 2 depictsthe amount of imported electricity vs. number of EVs foroptimal (EV with and without discharge capabilities) and naivescheduling. The amount of imported electricity is always highin naive scheduling in comparison to the optimal schedulingschemes. The reason of this improvement in optimal schedulingschemes over naive scheduling is that optimal scheduling isable to predict future loads and power generation whereas thenaive approach schedules appliances and EVs without anyprior knowledge. We also observe that the optimal schedulingwith EVs having discharge capabilities performs substantiallybetter than EVs without discharge capabilities. Note that bothschemes can predict future loads and the amount of generatedelectricity but the storage and discharge capabilities EVs leadsto a significantly improve performance.Fig. 3 shows the performance improvement of the proposed

optimal scheduling compared to naive scheduling solution. Inthe case of optimal (EV with discharge) vs. naive scheduling,the performance of the optimal solution is much better and the

Fig. 3. Performance improvement.

performance gain increases as the number of EVs increases.Specifically for 10 EVs the performance improvement is nearly8.5%, while for 400 EVs the performance improvement is 175.37%. As the number of EVs increases, the storage capabilityof the system increases as well and the optimal scheduling (EVwith discharge) shows a clearly superior performance over thenaive approach. The optimal (with discharge) scheduling alsooutperforms optimal scheduling (w/o discharge), as shown inFig. 3. Optimal (w/o discharge) scheduling performs better thanthe naive scheduling scheme. In this case, for 10 and 590 EVsthe performance improvement is 4.30% and 84.34%, respec-tively. Fig. 3 also shows that after reaching a certain numberof EVs (470) the performance improvement(optimal schedulingwith EVs discharge) decreases as the number of EVs increases.This is because the overall load of the microgrid increases anda small amount of electricity is available to store.Next, we compare the hourly imported electricity during a

day for optimal and naive scheduling schemes. In most cases,both optimal schedulingmodels require less imported electricitythan the naive scheduling. However, in some cases (e.g., hour24 in Fig. 4) the imported electricity using the naive scheme isless than that of optimal scheduling (without EV discharge ca-pability). This is due to the fact that the optimal scheduling algo-rithm intelligently shifts the soft load in order to consume elec-tricity during high power generation hours. In contrast, naivescheduling schedules a load in a time slot if it is ready at thattime and still has not yet achieved its target consumption. As aresult, the total amount of imported electricity is much highercompared to the optimal scheduling schemes.Fig. 5 depicts the imported electricity with respect to hourly

load and hourly renewable (here, solar cell) energy generationduring a day. Fig. 5 illustrated how the optimal scheduling withor without EV discharge capabilities shifts some loads from lowpower generation regions to high power generation regions inorder to minimize the amount of imported electricity. Further-more, Fig. 5 depicts that the naive scheme does not shift anyload from peak hours to off-peak hours, this is because naivescheme does not have any prior knowledge about the amountof future power generation and future loads. In this case, naivescheduling imports the same amount of electricity as demanded


Fig. 4. The hourly amount of electricity imported during a day.

to fulfil the actual demand of an hour (i.e., in Fig. 5: from 8 P.M.to 6 A.M.). In all other cases, the amount of imported electricityin the naive algorithm is the difference between the amount ofelectricity demanded and the amount of electricity generated ineach hour (i.e., daytime). Now, if we compare the imported elec-tricity between the optimally scheduling EVs with discharge ca-pability and optimal scheduling without EVs discharge capa-bility, in most cases, the optimal scheduling with EV dischargecapability imports less electricity than optimally scheduling EVwithout discharge capability. In few cases (i.e., 7:00 and 19:00in Fig. 5), however, this not true because the optimal solutionwith EV discharge capability schedules appliances such thatthe imported electricity is minimized. Fig. 6 shows the EVscontribution (amount of discharged electricity) to the micro-grid in each hour during a day with respect to hourly load andhourly electricity generation. We observed that optimal sched-uling with EV discharge capability discharges EVs batteries ifthe demand in an hour is higher than the amount of electricitygenerated in that hour. In most cases, the number of EVs dis-charging their batteries increases while the amount of load in-creases. In Fig. 6, the time period from 12 to 16 hours showsthat some EVs discharge their batteries while the amount of ac-tual load is lower than the amount of electricity generation. Theoptimal scheduling shifts some of the loads from the low powergeneration hours (with higher load) to high power generationhours with lower load (shown in Fig. 7) to minimize the amountof imported electricity. Fig. 7 shows the amount of generatedelectricity, actual load, and effective load (distributed by bothoptimal scheduling) in each hour of a day. Both optimal sched-uling (EVs with or w/o discharge capability) schedule loadswith respect to the amount of electricity generated from the re-newable energy sources in an hour. The resultant load regulationshifts loads from high periods to low periods in order to followthe renewable energy generation curve. In our solution, the re-sults presented in Figs. 6 and 7 clearly show that the optimalscheduling with EV discharge capability shifts both load and thealready generated electricity from one time slot to another timeslot and thereby minimizes the amount of imported electricity.On the other hand, optimally scheduling EV without dischargecapability, only shifts loads from one time slot to another timeslot. As a result, both optimal scheduling strategiesminimize the

Fig. 5. Hourly electricity imported with Naive, EVs with and EVs w/odischarge Scheduling (generation-vs-demand), using only photovoltaic energysource.

Fig. 6. EVs’ contribution (stored electricity) to microgrid.

amount of imported electricity by effectively scheduling homeappliances and EVs to consume less power. In case of optimalscheduling without EV discharge capability, the amount of im-ported electricity is higher than the amount of imported elec-tricity achieved by the optimal scheduling scheme with EV dis-charge capability as we observed from Fig. 7 from 17 to 22hours. During these hours, the optimal scheduling with EV dis-charge capability, EVs discharge to mitigate the extra load, asshown in Fig. 6. Thus, the optimal schedulingwith EV dischargecapability outperforms the optimal scheduling without EV dis-charge capability.Next we compare our proposed optimal (EV with dis-

charging) strategy with the decentralized Ev charging controlstrategy of Section IV. We consider both renewable and non-re-newable energy sources. In our comparison, for every cases,the decentralized EV charging control strategy imports moreenergy than the optimal EV with discharging policy. Figs. 8 and9 show the amount of hourly imported electricity of the decen-tralized EV charging control strategy and the proposed optimalwith EV discharging during a day. In most cases, the amountof electricity imported by the optimal EV with discharge is lessthan that of the decentralized EV charging control scheme. In


Fig. 7. Optimal load Scheduling for EVs with and w/o discharge capability.

some cases such as, hour 21, 03, 05, 08 in Fig. 8 and 20, 22, 24,01–06 in Fig. 9, the decentralized algorithm import less elec-tricity than the optimal EV discharge, but the total import arehigher in decentralized EV charging scheme. This is becausethe objective of the decentralized EV charging control schemeis to valley filling by shifting load from low generation periodsto high generation periods. On the other hand, optimal withEV discharge scheduling scheme minimizes the total importin a day by jointly determining the optimal scheduling of EVsand home appliances to consume electricity. Therefore, ourproposed optimal EV with discharging imports less electricitycompared to the decentralized EV charging control algorithm ina day. This is also true because the decentralized algorithm onlyi) regulates EV load while the proposed algorithm regulates allsoft load including EVs and ii) for non-homogeneous systemsthe decentralized EV charging control method produces -Nashequilibrium. Fig. 10 shows the comparison of the hourly re-quested load, load regulated by the decentralized EV chargingcontrol and the proposed optimal EV with discharging. Bothoptimal and decentralized schemes schedule loads with respectto the amount of electricity generated from the non-renewableenergy sources in each hour. The resultant load regulation shiftsloads from peak hours to off-peak hours in order to followthe energy generation curve. Both algorithms fill the valley byshifting load from peak hours to off-peak hours. In Figs. 8, 9,and 10, our simulations started at 1:00 P.M. and ended next dayat 1:00 P.M. Here, the load is shifted from the evening highdemand period to the midnight low demand period.Next, Figs. 11 and 12 show the comparison between the de-

centralized EV charging scheme and our proposed optimal EVwith discharging scheme. In both cases, our proposed sched-uling strategy imports less energy than the decentralized EVcharging strategy. Fig. 11 shows the comparison between theamount of electric energy imported by the decentralized EVcharging control strategy and our proposed optimal EV withdischarging policy, while using a non-renewable energy sourcewith a capacity of 300 kW in each hour. Also, Fig. 12 representsthe comparison of both schemes with respect to the amount ofimported energy. For both cases, we vary the number of EVsto determine the effect of EV population on the imported en-ergy. The amount of imported electric energy reduces for the

Fig. 8. Hourly load vs. import electricity of decentralized charging and optimalEV with discharge. Electricity from renewable sources.

Fig. 9. Hourly load vs. import electricity of decentralized charging and optimalEV with discharging. Power Generator: non-renewable.

Fig. 10. Load regulated (valley-filling) by decentralized and optimal EV withdischarging schemes. Power generator: non-renewable (750 kW).

increasing number of EVs (Fig. 12). This is due to valley fillingcharacteristics of both of the algorithms. Further, increasing thenumber of EVs increases the amount of imported energy. This


Fig. 11. Decentralized EV charging control vs. optimal EV with discharging:effect on the energy import by varying the number of EV. Power generator:non-renewable.

Fig. 12. Decentralized EV charging control vs. optimal EV with discharging:effect on the energy import by varying the number of EV. Power generator:non-renewable. Power generator: renewable.

is because after a certain number of EVs, the total effective de-mand increases for both algorithms (Figs. 11 and 12). The rate ofincrement of imported energy for optimal EV with dischargingis less compared to the decentralized EV charging control. Thisis because the optimal schedule with EV discharging jointlyschedules home appliances and EVs optimally, while the decen-tralized EV charging control only schedules EVs for chargingand discharging.

VI. CONCLUSIONS

In this paper, we have proposed joint centralized optimalscheduling schemes for home appliances and EVs in a grid-con-nected microgrid powered by renewable energy sources. Themicrogrid uses EVs as electricity storage to improve the ef-ficiency and reliability of the system. We have observed thatthe optimal scheduling schemes clearly outperform the naivescheduling scheme by better managing the electricity con-sumption and shifting soft loads from high demand (and/or lowpower generation) periods to low demand (and/or high powergeneration) periods. For instance, our simulation results show

that the performance increase of optimal scheduling EV with orwithout discharge capability is almost 175% for 400 EVs and85% for 590 EVs, respectively, compared to naive scheduling.Also, the optimal algorithm with EV discharge outperforms thedecentralized EV charging control method using a non-cooper-ative game. The running time of the proposed joint schedulingalgorithm is small for a residential community. For 500 homes(3500 home appliances) with 1000 EVs, it took from less thana second to 138 seconds for each iteration in a computer (Intelcore i5 processor with 4 GBmemory). In real-time implementa-tion, upon receiving the requests from the hard load appliances,microgrid allocates energy with no delay. In case of soft load(type B and C), microgrid determines the schedule of electricityallocation and allocates power according the schedule. Fora very large community, we believe that the algorithm mayhave some scalability issues in real-time implementations. Theproposed algorithm has two very significant properties: i) loadregulation and ii) energy or power regulation. The proposedjoint charging schedule optimally regulates power and load,which yields a minimum electricity import needed by themicrogrid. This will save energy production costs of the powergrid and ensure optimal use of locally generated renewableenergy of the microgrid. The proposed joint centralized sched-uling schemes do not depend on several interactions betweenend systems and the central controller, which is essential fordecentralized EV charging control methods to determine theoptimal schedule. The interactions may not produce an optimalEV charging schedule due to inconsistencies in the flow ofinformation. The proposed joint scheduling policies are capableto accommodate any energy source model. The optimal jointscheduling is sensitive to the variation of load, load character-istics and stochastic nature of renewable energy generation. Wehave shown that our proposed model always produces optimalresults for a microgrid with renewable, non-renewable, or bothenergy sources. For future work, the model may be modified tocompensate for errors in real-time prediction of load and powergeneration.

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Mosaddek Hossain Kamal Tushar received hisB.Sc. degree in applied physics and electronics andhis M.Sc. degree in computer science from DhakaUniversity, Bangladesh. He also received his M.S.in information technology (MIT) from University ofNew South Wales, Sydney, Australia, in 2006. Cur-rently, he is persuing his Ph.D. degree in electricaland computer engineering at Concordia University,Montreal, QC, Canada. Before beginning his Ph.D.studies he was a faculty member of the Departmentof Computer Science & Engineering at University of

Dhaka, Bangladesh, from 1997 to 2011.

Chadi Assi (SM’07) received his B.Eng. degreefrom the Lebanese University, Beirut, Lebanon, in1997 and his Ph.D. degree from the City Universityof New York (CUNY) in April 2003. He is currentlya full professor with the Concordia Institute for Infor-mation Systems Engineering, Concordia University,Montreal, QC, Canada. Before joining ConcordiaUniversity in August 2003 as an Assistant Professor,he was a Visiting Researcher with Nokia ResearchCenter, Boston, MA, USA, where he worked onquality of service in passive optical access networks.

His research interests are in the areas of networks and network design andoptimization. He received the prestigious Mina Rees Dissertation Award fromCUNY in August 2002 for his research on wavelength-division multiplexingoptical networks. He is on the Editorial Board of IEEE CommunicationsSurveys & Tutorials, IEEE TRANSACTIONS ON COMMUNICATIONS, and IEEETRANSACTIONS ON VEHICULAR TECHNOLOGIES. His current research interestsare in the areas of network design and optimization, network modeling andnetwork reliability.

Martin Maier (SM’07) was educated at the Tech-nical University of Berlin, Germany, and receivedM.Sc. and Ph.D. degrees (both with distinction)in 1998 and 2003, respectively. He is a full Pro-fessor with the Institut National de la RechercheScientifique (INRS), Montreal, QC, Canada. Inthe summer of 2003, he was a postdoc fellow atthe Massachusetts Institute of Technology (MIT),Cambridge, MA, USA. He was a Visiting Professorat Stanford University, Stanford, CA, USA, October2006 through March 2007. Dr. Maier is a co-recip-

ient of the 2009 IEEE Communications Society Best Tutorial Paper Awardand Best Paper Award presented at The International Society of Optical En-gineers (SPIE) Photonics East 2000-Terabit Optical Networking Conference.He is the founder and creative director of the Optical Zeitgeist Laboratory(www.zeitgeistlab.ca). His research activities aim at rethinking the role of op-tical networks and exploring novel applications of optical networking conceptsand technologies across multidisciplinary domains, with a particular focus oncommunications, energy, and transport for emerging smart grid applicationsand bimodal fiber-wireless (FiWi) broadband access networks. He is the authorof the book Optical Switching Networks (Cambridge University Press, 2008),which was translated into Japanese in 2009, and the lead author of the bookFiWi Access Networks (Cambridge University Press, 2012). He served on theTechnical Program Committees of IEEE INFOCOM, IEEE GLOBECOM, andIEEE ICC, and is an Editorial Board member of the IEEE CommunicationsSurveys and Tutorials as well as Elsevier Computer Communications.

Mohammad Faisal Uddin received his B.Sc degreefrom Islamic University of Technology (IUT),Dhaka, Bangladesh, in 2002 and his M.A.Sc. degreefrom Concordia University, Montreal, QC, Canadain 2006, both in electrical engineering. He receivedhis Ph.D. in electrical and computer engineeringfrom Concordia University in 2012. His researchinterests are in the area of optimization theory andits applications in communications networks.

smart microgrids: optimal joint scheduling for electric vehicles and home appliances

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