ieee transactions on smart grid, vol. 5, no. 3, may 2014 …cv.znu.ac.ir/afsharchim/dai/a...

IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 3, MAY 2014 1439

A Game-Theoretic Approach to Energy Trading inthe Smart Grid

Yunpeng Wang, Student Member, IEEE, Walid Saad, Member, IEEE, Zhu Han, Fellow, IEEE,H. Vincent Poor, Fellow, IEEE, and Tamer Başar, Life Fellow, IEEE

Abstract—Electric storage units constitute a key element in theemerging smart grid system. In this paper, the interactions andenergy trading decisions of a number of geographically distributedstorage units are studied using a novel framework based on gametheory. In particular, a noncooperative game is formulated be-tween storage units, such as plug-in hybrid electric vehicles, oran array of batteries that are trading their stored energy. Here,each storage unit’s owner can decide on the maximum amountof energy to sell in a local market so as to maximize a utility thatreflects the tradeoff between the revenues from energy tradingand the accompanying costs. Then in this energy exchange marketbetween the storage units and the smart grid elements, the price atwhich energy is traded is determined via an auction mechanism.The game is shown to admit at least one Nash equilibrium and anovel algorithm that is guaranteed to reach such an equilibriumpoint is proposed. Simulation results show that the proposedapproach yields significant performance improvements, in termsof the average utility per storage unit, reaching up to 130.2%compared to a conventional greedy approach.

Index Terms—Double auctions, electric storage unit, energymanagement, noncooperative games.

I. INTRODUCTION

M ODERNIZING the electric power grid and realizing thevision of a “smart grid” is contingent upon the deploy-

ment of novel smart grid elements such as renewable energysources and energy storage units [1]. In this respect, electricstorage units are inherently devices that can store energy, orextra electricity available at participating customers. Deploy-ment of storage units in future smart grid systems faces manychallenges at different levels such as studying the impact of in-tegrating storage units on the grid’s operation, determining therequired grid infrastructure (communication and control nodes)

Manuscript received April 25, 2013; revised May 21, 2013; acceptedSeptember 17, 2013. Date of current version April 17, 2014. This researchwas supported by Centerpoint LLC, by the National Science Foundationunder Grants CNS-1406947, CNS-1265268, CNS-1253731, CNS-1117560,ECCS-1028782, and CNS-0953377, and by the Air Force Office of ScientificResearch under MURI Grants FA9550-09-1-0643 and FA9550-10-1-0573.A preliminary version of this work was presented in [35]. Paper no.TSG-00322-2013.Y. Wang and W. Saad are with the Electrical and Computer Engineering

Department, University of Miami, Coral Gables, FL 33146 USA (e-mail:[email protected]; [email protected]).Z. Han is with the Electrical and Computer Engineering Department, Univer-

sity of Houston, Houston, TX, 77004 USA (e-mail: [email protected]).H. V. Poor is with the Electrical Engineering Department, Princeton Univer-

sity, Princeton, NJ, 08544 USA (e-mail: [email protected]).T. Başar is with the Coordinated Science Laboratory, University of Illinois at

Urbana-Champaign, IL, 61801 USA (e-mail: [email protected]).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.2013.2284664

to enable smart energy exchange, and developing new powermanagement strategies [2]–[6]. The potential economic impactof deploying energy storage units was explored in [7], whichalso studied the feasible level of energy storage in the distri-bution system. The possibility of having groups of controllableloads and sources of energy in power systems was investigatedin [8] which deployed a distribution network of solar panelsor wind turbines. In [9], distributed resources are allocated bythe provision of two-way energy flow and a unified, operationalvalue proposition of energy storage is presented. Other relatedproblems have assessed the advantages of deploying and main-taining storage units such as [10]–[18].One main challenge pertaining to introducing energy storage

units within the smart grid is the analysis of the energy tradingdecision making processes involving complex interactionsbetween the storage units (and their owners) and the varioussmart grid elements. A game theoretic approach to the con-trol of individual sources/loads was adopted in [19], whichenhanced the reliability and robustness of a power systemwithout using central control. In [20], a new technique based oncooperative game theory was proposed to allow wind turbinesto aggregate their generated energy and optimize their profits.Reactive power compensation was studied in [21] using gametheory with the objective of optimizing wind farm generation.A strategic game model was developed in [22] to analyze anoligopoly within an energy market with various grid-levelconstraints. Transmission expansion planning and generationexpansion planning were studied through a dominant strategyusing three game-theoretic levels in [23]. Using an IEEE30-bus test system, a comprehensive approach to evaluatingelectricity markets was presented in [24] to study the impactof various constraints on the market equilibrium. Developing adistributed energy storage system for transferring photovoltaicpower to electric vehicles as well as introducing efficient powermanagement schemes between storage units and the smart gridhave been studied in [5] and [10], respectively. However, littlework seems to have been conducted, from the storage units’point of view, on the energy exchange markets that arise dueto the competition among a number of storage units, each ofwhich could belong to a different customer and can interact atdifferent levels. Due to the promising outlook of introducingenergy storage units into the smart grid, devising new schemesto model and analyze the competition accompanying suchenergy exchange markets is both challenging and desirable.Themain contribution of this paper is to develop a new frame-

work that enables a number of storage units belonging to dif-ferent customers to individually and strategically choose theamount of stored energy that they wish to sell to customers inneed of energy (e.g., other nodes or substations on the grid).Compared to related works on smart grid markets [10], [13],[20], [24], [25], our paper has several new contributions: 1) we

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1440 IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 3, MAY 2014

design a novel double-auction market model that allows the in-corporation of power markets with multiple buyers and multiplesellers; 2) in contrast to the classical single shot, static auctionmodels which assume that sellers have a constant amount tosell, we have developed here a novel framework that combines adouble auction with a noncooperative game allowing the sellersto strategically decide on the amounts they put up for sale de-pending on the current market state, thus, yielding a dynamicpricing mechanism; 3) we develop new results on the existenceof a Nash equilibrium for games that exhibit a discontinuity inthe utility function due to the presence of an underlying auc-tionmodel, unlike the classical models that often assume contin-uous utilities; and 4) we propose a new learning algorithm thatis guaranteed to reach an equilibrium for a game with two levelsof interactions: a market based on auction theory and a nonco-operative game. We are particularly interested in overcomingtwo key challenges: a) introducing a new approach using whichthe storage units can intelligently decide on the energy amountto sell while taking into account the effect of these decisions onboth their utilities and the energy trading price in the market;and b) developing and analyzing a mechanism to characterizethe trading price of the energy trading market that involves thestorage units and the potential energy buyers in the grid. To thisend, we model the competition between a number of storageunits that are seeking to sell their surplus energy as a nonco-operative game in which the strategy of each unit is to select aself-profitable amount of energy surplus to sell so as to optimizea utility function that captures the tradeoff between the econom-ical benefits of trading energy and the related costs (e.g., batterylife reduction, storage unit efficiency, or other practical aspects).Then, a double auction mechanism is proposed to determine thetrading price that potentially governs the market resulting fromthe interactions between the storage units and energy buyers.This mechanism is shown to be strategy-proof such that eachbuyer or seller has an incentive to be truthful in its reserva-tion bids or prices. For the studied game, we show the existenceof at least one Nash equilibrium and we propose a novel algo-rithm to find a Nash equilibrium of the game. Subsequently, wealso show the convergence of the proposed algorithm. Exten-sive simulations are run to evaluate and assess the performanceof the proposed game-theoretic approach.The remainder of the paper is organized as follows: Section II

presents the studied system model trading. In Section III, weformulate the game and develop the underlying auction mech-anism. In Section IV, we introduce the concept of the bestresponse and describe our proposed algorithm. Simulationresults are presented in Section V, while conclusions are drawnin Section VI.

II. SYSTEM MODEL

Consider a smart grid system having a number of nodes thatare in need of energy. These nodes could represent substationsand/or distributed energy sources that are servicing an areaor group of consumers (e.g., loads, pumped-storage in hydroplants, etc.). Here, we consider that a certain number, , of thesmart grid elements is unable to meet their demand due to fac-tors such as intermittent generation and varying consumptionlevels at the grid’s loads. In this respect, such grid elementsmust find alternative sources of energy by acquiring this energyfrom other elements that have excess energy stored in energystorage units. Thus, we consider that a number, , of storageunits are deployed in the grid. In particular, all these unitsbelong to customers that have excess energy that they wish

to sell. We let and denote, respectively, the sets of allsellers and all buyers. In what follows, we use seller to

imply any storage unit and buyer to imply any smart gridelement . Our model generally involves several types ofelectricity sellers and buyers.Each buyer has a maximum unit price or reservation

bid at which it is willing to participate in an energy tradewith a seller. Since we focus on the storage units’ perspectiveof the market, we assume that the buyers wish to buy a fixedamount of energy . This models a scenario in which, over acertain given time period, is imposed on the buyers from thepractical energy requirements of the users and customers. Wecan also view as an average value of the amount of additionalenergy demand that buyer foresees for a certain period of time.For the storage units, i.e., the sellers, each unit can choosean amount of energy to sell such that:

(1)

with being the maximum total energy that seller wants tosell in the market, being the maximum storage unit ca-pacity, and being the energy that each storage unit wants tokeep and is not interested in selling. For each seller , we definea reservation price per unit energy sold, under which sellerwill not trade energy.Given these buying and selling profiles of the various grid ele-

ments, an energy exchange market is set up in which the buyersseek to acquire energy so as to meet their demand while thesellers, i.e., the storage units and their owners, seek to collectrevenues from selling their extra energy surplus. Here, allsellers and buyers will interact so as to determine variousenergy trading properties that include the quantities exchangedand the price at which energy is traded. Unlike conventionalmarkets in which the sellers control only the reservation prices,in our model, the storage units can also strategically choose themaximum quantity of energy that they want to put up forsale in the market. The choice of a proper is directly depen-dent on an inherent tradeoff between the potential profits thatthe sellers foresee and the accompanying costs that relate to thephysical characteristics of the storage devices. Indeed, such atradeoff is a byproduct of the fact that frequently charging ordischarging of storage devices is costly as it can lead to a reduc-tion in the storage device’s lifespan as well as to other practicalcosts [6], [25], [26]. Hence, given the buyers’ set of bids andenergy requirements, the maximum energy amount that anyseller decides to trade strongly affects both the gains/revenuesand cost of every storage unit in as well as the trading price.Fig. 1 provides an illustrative example of the model considered.To analyze such an energy exchange market, we next propose anew framework that builds on the powerful analytical tools ofgame theory and auction theory.

III. A GAME-THEORETIC APPROACH TO ENERGY TRADING

In this section, we first formulate a noncooperative game be-tween the sellers, and then study the proposed energy tradingmechanism using a double auction, also discussing its variousproperties. The main notation is listed in Table I.

A. Noncooperative Game Model

The complex interactions and decision making pro-cesses of the storage units are analyzed using the analyt-ical tools of noncooperative game theory [27]. In partic-ular, we formulate a noncooperative game in normal form,

, which is characterized by three

WANG et al.: A GAME-THEORETIC APPROACH TO ENERGY TRADING IN THE SMART GRID 1441

Fig. 1. An illustrative example of the model studied.

TABLE ISUMMARY OF NOTATION

main elements: a) a set of sellers or players, b) the actionor strategy of each player which maps to an amount ofenergy, , that will be sold, and c) a utilityfunction of each seller which reflects the gains andcosts from trading and selling energy. Before defining theutility functions, we note that, in the game , the reservationprice is not included as part of seller ’s strategy space. Thisimplies that the sellers must reveal their correct reservationprices when participating in the game. This consideration ismotivated by the fact that, when we determine the market’strading price, as explained in the next section, we will developa truthful and strategy-proof double auction mechanism thatguarantees that no buyer or seller can benefit by cheating orchanging its true reservation price or bid.Given a certain strategy choice by any storage unit ,

the utility function can be characterized by

(2)

where is the vector of all strategy selections,is the vector of actions se-

lected by the opponents of storage unit , is the price atwhich energy is traded between seller and buyer , is thequantity of energy exchanged from seller to buyer , andis a function that reflects the cost of selling energy. As previ-ously mentioned, these costs depend on numerous factors suchas the physical type of the storage unit or the amount of timethe unit is put into charging or discharging modes. Moreover,we note that must be an increasing function of the amount,

, sold in total by storage unit . Here, the utility in(2) is also a function of the amount of energy that every buyer

must buy and of the buyers’ reservation bids. However,for notational convenience, we have not explicitly written thisdependence.The goal of each storage unit is to choose a strategy

in order to maximize its utility as given in (2). For characterizinga desirable outcome for the studied game , one must derive asuitable solution for all optimization problems that the sellersneed to solve. We can first see that, in (2), every vector of strate-gies selected by the sellers will yield different trading prices

. These prices are also functions of the reservation pricesof the sellers, the quantity bought, and the reservation bids ofthe buyers or grid elements. Thus, prior to finding a solution forthe energy exchange game, we will first introduce a scheme forcharacterizing the trading price.

B. Double Auction Mechanism For Market Analysis

The formulated game is useful to study the sellers’ inter-actions. However, in order to find the prices at which energyis traded, we must define suitable mechanisms using the richtools of double auctions [28] and [29]. Inherently, a double auc-tion is a suitable representation for a trading market that in-volves multiple sellers and multiple buyers. For the proposedgame , applying a double auction is needed so as to derivethe trading prices, the quantities of energy traded, as well as thenumber of involved sellers and buyers, given the chosen strategyvector (maximum quantities offered for sale), the reservationprices , the quantities to be bought, and the bids

.When dealing with a double auction, the buyers and sellers

have to decide on whether to be truthful about their reservationbids and prices, given: i) the potential utility that they will obtainas captured by the first term of (2), and ii) the buyers’ potentialsavings with being the quantity boughtby from . Here, our emphasis is on having a double auctionmechanism that yields, for any , a solution that is truthful andstrategy-proof. A truthful auction is a scheme in which no seller

can benefit by cheating about its reservation price suchas by misreporting it, and no buyer will gain by under-bidding or over-bidding. A strategy-proof solution is of interestas it guarantees truthful reporting by all buyers and sellers.With this in mind, for the proposed system, we develop a

double auction scheme that follows from [28] and [29]. In thisscheme, the first step is to sort the sellers in increasing order oftheir reservation prices such that, without loss of generality, wehave

(3)

The next step is to arrange the buyers in decreasing order of theirreservation bids, as follows:

(4)

We note that the orderings in (3) and (4) assume that whenevertwo buyers or sellers have equal reservation prices or bids, onecan group them into a single, virtual buyer or seller.Following this sorting process, the supply curve (sellers’ priceas a function of the energy amount , ) and the de-

mand curve (buyers’ bids as a function of the amount of re-quired energy , for all can be generated. These twocurves will intersect at a point that corresponds to a given sellerand a certain buyer with . This intersection point

is easily computed using known numerical and graphical tech-niques [28]. Once we determine the seller and buyer at the


Fig. 2. An illustrative example of solving a double auction.

supply and demand intersection point, double auction theory im-plies that and buyers will practically participatein the market and the energy trading process. Here, as shown in[29], we must exclude seller and buyer from the marketso as to guarantee that the total supply and demand will matchwhile ensuring a strategy proof and truthful auction mechanism.However, if one does not need to maintain truthfulness, the pro-posed approach can easily be modified so as to allow sellerand buyer to also trade energy.Therefore, in order to match the supply and demand, all

sellers whose indices are such that and all buyers suchthat will be part of the double auction trade. To deter-mine the trading price, once the intersection is identified, onecan select any suitable point within the interval [28].For our energy market, given a seller’s strategy vector , weassume that all sellers and buyers will exchangeenergy at a price such that

(5)

Here, the price depends on since, for every maximum energyto sell vector , the intersection point of demand and supply mayoccur at different and .This solution of the double auction is illustrated in Fig. 2,

which shows the supply (solid line) and demand (dashed line)curves. The intersection of these two curves can be used to deter-mine the trading price and quantities. Once the trading price andquantities are determined from the double auction, the next stepis to define a proper utility function and introduce the strategicoperation for the proposed game.Once the trading price is found, we need to find the amount

of energy that is traded between the sellers and thebuyers. First, given the unified trading price in (5), thesellers will be indifferent between buyers. This implies that, atthe double auction solution, each seller’s utility in (2) dependsonly on the quantity sold but not on the identity of the buyer whobought this amount. Hence, assuming that the cost functionis quadratic, by using the proposed double auction, (2) becomes

(6)

with being the total quantity of energy sold by andbeing a penalty factor that weighs the costs reaped by storageunit when discharging/selling energy. Here, wemust stress thatour analysis can accommodate any type of cost function .

Once the auction is concluded, different approaches can beapplied to find the quantity of energy traded between each of the

participating sellers and participating buyers [28].For our work, we will apply the technique of [29] in which theentire volume traded is divided in a way to maintain the truthful-ness of the auction. Using this approach, the total amountthat is sold by any storage unit , for a given strategy vector is

if

if(7)

where and represents the fraction of theoversupply that is allotted to seller . Themechanism in (7) implies that whenever the total demand at theauction’s outcome exceeds the supply, then every seller wouldsell all of the energy that it introduced into the market. How-ever, when the total supply exceeds the total demand, then allsellers get an equal share of the oversupply’s burden. Here,

. Nonetheless, if, for a seller ,

we have , then, sellerdoes not sell any energy as per the second case in (7). The

remaining “oversupply”of this seller is subsequently divided equally between the other

sellers and the result is added to their share. This scheme will be repeated as long as each seller sells a non-negative quantity. Here, for the “oversupply” case, the total en-ergy put into the market by the participating sellers, , is

greater than or equal to that requested by the buyers, ,but the real energy obtained by seller is the expected energy,and thus mathematically, . For the “over-demand”case, the amount of energy requested by the buyers exceeds theamount put into the market by the sellers, that is, .An analogous process can be carried out to find the amountbought by the grid’s elements or buyers. Using (7), as shownin [28] and [29], we will have the following:Lemma 1: In the proposed game , by using (7), no seller or

buyer benefits by cheating about its reservation priceor reservation bid . The double auction is thus

strategy-proof or truthful.

IV. PROPOSED SOLUTION AND ALGORITHM

Any storage unit can use the proposed double auctionin order to estimate its utility, as per (6), for every given thestrategy choices of its opposing players. Each seller seeksto maximize its utility by selecting the proper strategy. In order to solve a noncooperative game in normal form

such as , one popular solution is that of a Nash equilibrium[27]. A Nash equilibrium is a state of the game such that noplayer can increase its utility by unilaterally deviating from thisequilibrium state. Formally, the Nash equilibrium is defined asfollows [27]:Definition 1: Consider the proposed noncooperative game in

normal form , with given by(6) given the underlying double auction. A vector of strategiesis said to be at a Nash equilibrium (NE), if and only if, it

satisfies the following set of inequalities:

(8)

Next, we first prove the existence of an NE for the proposedgame and, then, we propose an algorithm that could find an NEfor our model. Before going through our analysis, we first point


out that, in general, the existence of an NE is not guaranteedfor any noncooperative game. In particular, when the strategyspaces are compact such as in our proposed game, the existence of an NE is contingent upon having a utilityfunction in (6) that is continuous in [27]. However, in ourgame, the double auction process introduces a discontinuity inthe utilities in (6) due to the dependence on the trading price.Showing the existence of an NE for a discontinuous utility func-tion is known to be more challenging than the classical case inwhich the utility is a continuous function [27]. Nonetheless, forthe proposed game, we can obtain the following existence result:Theorem 1: For the noncooperative game

, there exists at least onepure-strategy Nash equilibrium.

Proof: Assume , is anon-empty, convex and compact set. As shown in [30], if, is 1) graph-continuous, 2) upper semi-con-

tinuous in , and 3) quasi-concave in , then the gamepossesses a pure-strategy Nash

equilibrium.A function is said to be graph continuous if there exists a

function such that iscontinuous in . In particular, as shown in [30], a piecewisecontinuous function is graph continuous if the strategy space iscompact. Due to the discontinuity of our utility function asvaries, we define

(9)

at a jump point. Thus, we can assume that in a given range ,

(10)

and when is a small value, the slope becomes infinite, whichimplies that the function is a piecewise continuous function on.Mathematically, is upper semi-continuous at

if there exists a neighborhood such that

(11)

Similarly, for a jump point of utility function, we definesuch that ,

(12)

Clearly, the utility function is upper semi-continuous becauserational players seek a higher profit around the jump point. Here,we only need to prove that the utility function is quasi-concave.In a given range of constant price, by simplifying (6) and (7),

we have

if ,

if ,

(13)

Before proceeding further with the proof, we need to state thefollowing lemma from [31]:

Lemma 2: Suppose is quasilinear andis quasi-concave. Then is quasi-

concave.This result has been extended to concave functions with strict

conditions in [31]. Now,

(14)

where and belong to the action set of seller . Thus,is both quasi-concave and quasi-convex, and hence it is

a quasi-linear function. Subsequently we can obtain the partialderivative with respect to from (13), as follows:

(15)

Thus, is a concave function (which is quasi-concave).Following Lemma 2, we substitute (14) into (15),

(16)

Thus, is a quasi-concave function of .Intuitively, the partial derivative of on is positive be-

fore the local maximum of and negative after it. The partialderivative of on is 1 or a nonnegative number depending onthe auction except at the inflection point when . Aroundthis inflection point, firstly increases then might de-crease as varies in a price-holding graph-continuous range.Therefore, is a quasi-concave function in , and the game

possesses a pure-strategy Nashequilibrium as it satisfies all required conditions.At any NE of the proposed game, no storage unit can improve

its utility by unilaterally changing the maximum quantity of en-ergy that it wishes to sell, given the equilibrium strategies of theother storage units. Having established existence, we must de-velop a scheme that allows the game to reach an NE. To doso, we must first define the notion of a best response:Definition 2: The best response of any storage unit

to the vector of strategies is a set of strategies forseller such that

(17)

Hence, for any storage unit , when the other storageunits’ strategies are chosen as given by , any best responsestrategy in is at least as good as any other strategy in. Using the concept of a best response, we can subsequently

define a novel algorithm that can be used by the storage unitsand buyers so as to exchange energy. In particular, we proposethe following iterative algorithm that is guaranteed to convergeto a Nash equilibrium of the game:Theorem 2: There exists a searching inertia weight ,

, such that, the iterative algorithm

(18)

converges to an NE.


Proof: In the proposed model, the classical best responsedynamics may not converge due to the underlying auctionmechanism. Depending on the different amounts betweensellers and buyers, the price is a piecewise continuous function.From (6) and (17), we have

(19)

When selling amounts are less than buying, the best responseof each seller is a constant. When selling amounts are greaterthan buying, and, we only use best response for iterations, wehave

(20)

whereTo sum all sellers,

(21)

The second term on right hand side is not 0 and this might leada price change. In other words, in iteration ,

,

.(22)

It is possible that, in iteration , the best response changesthe total amount in (21) and this can lead to a pricechanging loop.However, from (6) and (17), our proposed algorithm in (17)

has

(23)Similarly, to sum over all sellers,

(24)

In particular, when , we have (24). Thus, there must exista weight , such that

.(25)

Remark 1: We note that the above result is generated for thecase in which the sellers are able to sustain the over-supply. Similar results can easily be generated for the case inwhich the oversupply cannot be split among all sellers; how-ever, this case is omitted due to space limitations.Remark 2: With a given price range, the utility in (6) can

be viewed as a concave function. More precisely, there exists aweight, such that no player could arbitrarily approach its cur-rent best response, which might change the price and pull someparticipating players out of the auction.In a given price range,

(26)

An increasing/decreasing monotonic function would approachits upper/lower boundaries. It is not difficult to obtain the upperboundary from concavity as follows:

(27)

For the lower boundary,

(28)

In particular, because is Lipschitz continuous when theweight holds the price in a range,

(29)

Thus, we have

(30)

Remark 3: The upper and lower boundaries ofare also bounded by (22).

Due to the above-mentioned price and boundary analysis, wecan conclude that after some number ofiterations , where is a small value. Substituting in (18), weobtain (at the final iteration)

(31)

which is the best response of . Consequently, our algorithmconverges to an NE.


Fig. 3. Average action per seller (storage unit) resulting from the proposedgame approach; buyers, sellers.

Determining the precise computational complexity for theproposed approach is challenging due to the fact that the tradingprice varies during the iterative process, which subsequentlyleads to a varying number of participating sellers. However, wecan obtain some insights on the computational complexity byassuming a constant trading price in (19). The computa-tional complexity for comparing the amount sold by sellers withthe energy requested by the buyers in (19) is , whereseller and buyer determine the trading price (see Fig. 2). Inthis respect, if we assume that the trading price does not change,then the amount of computation required to calculatein (19) is since this value is independent of the marketsize. The computational complexity needed for calculating

in (19)is . This represents the individual seller’s computa-tional complexity for the proposed sequential algorithm. As wehave participating sellers, if the trading price is a con-stant, the total computational complexity of the proposed se-

quential algorithm is . For the parallel

algorithm, the proposed approach would require a lower com-putational complexity, , but then it will lead to moreiterations than in the sequential case as seen from Fig. 3.The sellers and buyers in the proposed noncooperative game

can interact using a novel algorithm composed of two phases:a strategic dynamics phase and an actual market and energytrading stage. Our strategic dynamics stage begins with everyseller choosing an initial strategy .While this initial strategycan be chosen arbitrarily by each seller, the most intuitive choiceis that each seller starts by trying to sell all of its available sur-plus of stored energy. Therefore, we let .Subsequently, an iterative process begins in which the sellerscan take turns in choosing their maximum amounts of energy tosell (i.e., strategies). To this end, at any iteration , any storageunit , during its turn to act, will choose a strategy that ap-proaches its best response strategy, as given by (17) and (18).This iterative algorithm is executed until guaranteed conver-gence to an NE. In particular, the proposed algorithm has beenshown to always converge to a Nash equilibrium in Theorem 2.

TABLE IIPROPOSED ENERGY TRADING SOLUTION

A summary of the proposed algorithm is given in Table II. Here,we note that, although in Table II we present a sequential imple-mentation of the algorithm, the players may also utilize a par-allel approach. In a sequential implementation, the players actsequentially, in an arbitrary order such that each player is able toobserve (or is notified by the auctioneer of) the actions taken bythe previous players. In contrast, in a parallel approach, at an it-eration , all players respond, using (18), to the actions observedby the other players at iteration . Once an NE of the gameis reached, the last phase of the algorithm is the practical marketoperation. During this final phase, given the equilibrium strate-gies, all sellers and buyers submit their bids and then engage inan actual double auction in which each storage unit discharges(sells) the desired energy amount and is rewarded accordingly.One possible approach to determine is to gradually lower

its value from 1 until a suitable value guarantees reaching anNE.This weight essentially ensures that the price, which introducesthe discontinuity, is bounded within a certain range after a cer-tain number of iterations. Determining this weight depends onthe various buyers/sellers’ parameters. The control center of theutility company needs to dynamically determine a weight andchange it if needed using time-dependent information observedfrom the participating users. At the beginning, the control centercould start with an initial weight (either arbitrarily or chosenbased on historical data), and set a periodic schedule to dynami-cally adjust the weight. The control center can gradually and pe-riodically optimize the current weight to meet the observed net-work environment. One possible strategy is to follow a classicalbisection method [31]. The application of this method helps thecontrol center adjust the speed of convergence. At each step,the center divides the weight interval into two. A subinterval isselected depending on whether an NE could be effectively ob-tained or not. The center would use a previous subinterval as anew interval in the next step and this process is continued untilthe interval is sufficiently small and convergence is guaranteed.Nonetheless, we have to stress that we have proven that there


exists a weight such that the proposed algo-rithm is guaranteed to converge to an NE, and thus, in practice,the control center will eventually reach this weight, as the rangewithin which the weight varies is finite.For practical implementation, the utility company’s control

center acts as an auctioneer [28] that guides the energy marketand monitors the interactions of the storage units. This auc-tioneer utilizes a storage-to-grid communication network suchas in [6] or [32] (and references therein) to communicate withall grid elements and storage units. Thus, the auctioneer playsmainly two roles: a) sorting out the sellers and the buyers oncebids are received, as per (3) and (4), and b) gathering their strate-gies whenever they must act during the dynamics phase. At agiven iteration during Phase I of the proposed approach, anyseller must compute its utility in (2) so as to update its strategy.The strategy update can be based either on the current state (forthe sequential algorithm) or on the state of the grid in the pre-vious iteration (for the parallel implementation). For enablingthis strategy update, the auctioneer and the storage units interactover the communication infrastructure using either an open ora private method. In the open method, when interacting witha certain seller, the auctioneer conveys the current opponentsstrategy vector , the reservation bids, and the type of auc-tion being implemented. Once this information is obtained, theseller can calculate its best strategy using classical optimizationtechniques [31] and pursue the proposed auction procedure.The disadvantage of the open method is that the auctioneer

must disclose the current strategies and reservation prices/bidsto the sellers. In many cases, it is of interest to keep this infor-mation private. Hence, alternatively, when an auctioneer com-municates with a certain seller , this seller will submit a re-stricted set of potential strategies for the current itera-tion. Then, the control center feeds back the trading prices andamount of energy that seller will potentially obtain at the cur-rent time, for each of the submitted strategies. Using this data,each seller builds, using function smoothing methods such asin [33], an estimate of its utility under the current strategies,and, subsequently, find the optimal strategy response for this it-eration using optimization methods. For this private implemen-tation, the sellers do not require any knowledge of the type ofauction being used nor of the strategies and reservation prices oftheir opponents (or the bids of the buyers). In addition, the con-trol center does not require any knowledge of the utility func-tions that are being used by the players. The only informationthat would circulate, as dictated by the method, would be thetrading price and the energy sold for any potential strategysubmitted by any seller to the auctioneer during its turn.We finally note that, in the presence of an elaborate commu-

nication infrastructure, the sellers and the buyers can interactdirectly without the need for a control center. In this case, eachseller can, individually, decide on the amount of energy it wantsto sell at each iteration of the proposed approach, while directlynotifying the other players of its choice. The rest of the opera-tion would still follow the iterative process discussed earlier.

V. SIMULATION RESULTS AND ANALYSIS

For simulating the proposed system, we consider a geograph-ical region in which a number of storage units have a surplus ofstored energy that they wish to sell to existing customers (e.g.,loads, substations, etc.) in a smart grid. Each unit has a surplusbetween 75 MWh and 220 MWh that can be sold. The reserva-tion prices of the sellers are chosen randomly from a range of

dollars per MWh while reservation bids of the buyers

Fig. 4. The ending double auction market performance based on sequentialiterations with storage units and buyers.

are chosen randomly from a range of dollars per MWh.The demand of each buyer is chosen randomly from within arange of MWh. Unless stated otherwise, the cost perenergy sold is set to . All statistical resultsare averaged over all possible random values for the differentparameters (prices, bids, demand, etc.) using a large number ofindependent simulation runs.In Fig. 3, we show, for a smart grid with buyers and

sellers, the average action per seller (storage unit) re-sulting from the proposed game approach at the equilibriumusing both sequential and parallel approaches. The sequentialalgorithm’s performance is compared with that of the parallelalgorithm in which the sellers, simultaneously, attempt to sellenergy depending on their previous actions. Here, in particular,we choose the same weight for both the sequential andthe parallel algorithms. InFig. 3,we can see that, for the proposedalgorithm, the trading action per storage unit converges to dif-ferent values with increasing iterative steps. Fig. 3 shows thattwo players out of six decide not to participate in themarket. Thedashed line relates to those sellers who do not participate in themarketdue to the fact thatwould the tradingpricewould then leadto a negative utility.However, these sellerswould still have someenergy in hand and they can offer it for sale at a later time instantin which the trading price in another auction or area might givethemanopportunity toobtainpositiveutility.Thus, although theydo not trade at the current market price, they will maintain theiravailable energy and eventually participate in a future market. Inparticular, we use the “dashed line” to indicate a baseline actionvalue of 1 to represent those sellers that do not participate in themarket, but rather prefer to wait for future trading opportunities.Wecanalso observe that, for the sequential algorithm (solid line),the action of player 1 increases a little at the beginning. This isdue to the fact that, the playerwhoplaysfirst in one iteration has ahigheropportunity to sell energy thanothers. Ingeneral, as seen inFig. 3, because of the competition over the resources, the actionsare essentially decreasing, which means that at the equilibrium,not all players will sell their maximum available energy.Given the same setting as in Fig. 3, Fig. 4 shows the price re-

sulting from the double auction phase for the case of the sequen-tial algorithm. In this figure, the intersection point demonstratesthat seller 5 and buyer 2 determine the trading price. The total


Fig. 5. Performance assessment in terms of average utility per seller as thenumber of storage units varies for buyers.

amount sold by participating sellers (seller 1 to 4) is equal to thedemand of participating buyers (buyer 1 and 2). If the solid anddashed lines intersect at a point of the 3rd buyer (the 3rd rangeof the dashed line), seller 5 and buyer 3 lower the trading price.Although all four participating sellers might sell more than be-fore, the associated reduction in the trading price will lead tolower revenues.Fig. 5 presents, for a smart grid with buyers, the

average achieved utility per seller resulting from the proposedgame as the number of storage units varies. Here, we set

for the sequential algorithm and for the par-allel algorithm. For comparison purposes, we develop a con-ventional, baseline greedy algorithm using which, iteratively,each seller tries to sell the maximum amount that it could sell[while accounting for the changes of the utility in (6)] whilefirst choosing the highest-bid buyers. The greedy process con-tinues until no additional energy trade is possible. In this greedyscheme, the trading price is selected as the middle point betweenthe concerned buyer’s reservation bid and the concerned seller’sreservation price. In Fig. 5, we can see that the average utility perstorage unit is decreasing with . The reason behind this mainlyinvolves two issues. First, the increase in sellers can lead to in-creased competition and, thus, a decrease in the overall tradingprice. Second, the number of sellers that will actuallyparticipate in the final energy exchange market reaches a certainmaximum that no longer increases with due to the fixed de-mand (i.e., the number of buyers). This figure demonstrates that,for all , the proposed noncooperative game approach yields asignificant performance improvement, in terms of the averageutility achieved per storage unit. In particular, this advantage ofthe proposed approach reaches up to 130.2% (the maximum at

) relative to a conventional greedy approach.Fig. 6 shows, for buyers, the average number of it-

erations needed before convergence of the different algorithmsas the number of storage units increases. In this figure, wecan see that the average number of iterations of the proposed se-quential algorithm is similar to that of the classical best responsealgorithm (whenever this algorithm converges, recall from The-orem 2 that a best response dynamics may not converge). As ex-pected, Fig. 6 shows that the parallel algorithm requires a muchhigher number of iterations. In particular, the average numberof iterations resulting from the sequential algorithm varies from

Fig. 6. Average number of iterations per seller as the number of storage unitsvaries for buyers.

Fig. 7. Average number of action per seller resulting from the proposed gameapproach as the number of storage units varies for buyers.

7.7 at to 8.2 at , in contrast, for the parallel case,it varies from 25.8 at to 32.5 at . This result indi-cates that the proposed algorithm, particularly with a sequentialimplementation, has a reasonably fast convergence speed.Fig. 7 shows for buyers, the average action per seller

for both the sequential and the parallel algorithms as the numberof storage units grows. We can see that the average action perplayer resulting from both the sequential and the parallel algo-rithms is greater than that of the greedy strategy. Thus, usingthe proposed algorithm provides the sellers with more incen-tives to trade larger amounts in the markets. This is in fact fur-ther reflected in the enhanced utility achieved by the proposedapproach, as seen in Fig. 5. Finally, Fig. 7 also shows that the se-quential and the parallel algorithms converge to nearly the sameactions at the equilibrium.Fig. 8 shows, for different buyers and sellers, the average

utility per seller as the penalty factor varies. From (6), we cansee that the utility would decrease with increasing and this iscorroborated in Fig. 8. In particular, when is equal to 1, theutility of each player is dramatically influenced by the penaltypart in (6). The first revenue term in (6) the sellers obtained in theauction remains the same as the second penalty term increases,even though the total utility is positive.


Fig. 8. Performance assessment in terms of the penalty factor resulting fromthe proposed game approach for different numbers of buyers and sellers.

Fig. 9. Performance assessment in terms of average utility per seller as thenumber of buyers varies, for sellers.

Fig. 9 shows the average utility from the different proposedapproaches as the number of buyers varies, for sellers.Each iteration consists of a series of choices by the sellers, usingthe same initial information. In Fig. 9, we can also see that, asthe number of buyers, , increases the average utility per sellerincreases due to the availability of additional buyers that arewilling to participate in the market. In fact, Fig. 9 shows that, asincreases, the sellers have larger utilities due to the availability

of more buyers. In particular, our proposed algorithm yields aperformance improvement ranging between 72.3% (for

) to 234.4% (for ) relative to the greedyscheme. Further inspection of Fig. 9 reveals that any change inthe numbers of buyers does not impact the increasing averageutility rate of our algorithm,while the greedy algorithm reaches amaximumwhen the number of buyers is similar to that of sellers.Fig. 10 shows, for a smart grid with buyers and

sellers, the state of charge represented by the battery amount perplayer resulting from a time-dependent game as time evolves.Here, we show the results for the proposed sequential algorithmwith a weight . For our simulations, we assume thatthe period corresponds to 1 hour as is typical in a residentialcommunity [34]. In Fig. 10, we can see that, for the proposed

Fig. 10. Performance assessment in terms of the amount per player as thenumber of runs varies for initial buyers and sellers.

Fig. 11. Performance assessment in terms of the amount stored by Player 2compared with underlying battery limitations as the number of runs varies.

game, four sellers would sell their energy into the market duringthe first time instant. Then, after the first run, all players recon-sider their roles and still participate in the market, especially forthose that did not sell/buy enough in the previous time slots.The iteration would then lead to a new trading price and thisprocess continues, as previous users are still in the market andno new players join this group. In Fig. 10, we can see that allplayers have an opportunity to act as sellers or buyers everyhour. Player 1, for example, acts as a buyer during the first hour.After the second hour, this player changes from a buyer to aseller, and then acts as a buyer at the fifth hour. Player 4 sellsa small amount in the first three hours and becomes a seller atthe fourth and sixth time instants. During the second and thirdhours, Player 2 does not sell a large amount despite the fact thatit had acted as a buyer and fully charged at the first time in-stant. After 4 hours have elapsed, Player 2 sells 12.8 MWh. Thisplayer tends to sell the energy because it reaches its battery limi-tation and has an incentive to become a seller after the first hour.In Fig. 11, we show how the amount of energy in Player 2’s

battery changes within this player’s minimum and maximumbattery capacity. In this figure, we can see that Player 2 reaches


its maximum battery capacity two times. Correspondingly, thisplayer acts as a seller twice at the second and fourth hour. Incontrast to Players 3 and 4, Player 2 frequently uses its storageunit so as to obtain potential utility through time-dependentlybuying/selling energy. In essence, Fig. 11 shows how the pro-posed game can be used to handle the battery limitations of theusers as well as their time-dependent behavior.

VI. CONCLUSIONS

In this paper, we have introduced a novel approach forstudying the complex interactions between a number of storageunits seeking to sell part of their stored energy surplus to smartgrid elements. We have formulated a noncooperative gamebetween the storage units in which each unit strategicallychooses the maximum amount of energy surplus that it iswilling to sell so as to optimize a utility function that capturesthe benefits from energy selling as well as the associated costs.To determine the trading price that governs the energy trademarket between storage units and smart grid elements, we haveproposed an approach based on double auctions, which leadsto a strategy-proof outcome. We have shown the existence ofa Nash equilibrium and studied its properties. Further, to solvethe underlying game, we have proposed a novel algorithmusing which the storage units can reach a Nash equilibrium forour model. Simulation results have shown that the proposedapproach enables the storage units to act strategically while im-proving their average utilities. For future work, it is of interestto extend the model to a dynamic game model in which allplayers could time-dependently observe each others’ strategiesas well as the grid’s state and dynamically determine theirunderlying actions. In this respect, the work done in this paperserves as a basis for developing such a more elaborate dynamicgame model in which players can make long-term decisionswith regard to their energy trading processes.

REFERENCES[1] H. Farhangi, “The path of the smart grid,” IEEE Power Energy Mag.,

vol. 8, no. 1, pp. 18–28, Jan. 2010.[2] S. J. Kazempour, M. P. Moghaddam, M. Haghifam, and G. Yousefi,

“Electric energy storage systems in a market-based economy: Com-parison of emerging and traditional technologies,” Elsevier RenewableEnergy, vol. 34, no. 12, pp. 2630–2639, Jun. 2009.

[3] I. Hadjipaschalis, A. Poullikkas, and V. Efthimiou, “Overview of cur-rent and future energy storage technologies for electric power appli-cations,” Elsevier Renewable Sustain. Energy Rev., vol. 13, no. 6, pp.1513–1522, Aug. 2009.

[4] H. Akhavan-Hejazi and H. Mohsenian-Rad, “A stochastic program-ming framework for optimal storage bidding in energy and reservemar-kets,” in Proc. IEEE PES Conf. Innov. Smart Grid Technol. (ISGT’13),Washington, DC, USA, Feb. 2013.

[5] J. R. Aguero, P. Chongfuangprinya, S. Shao, L. Xu, F. Jahanbakhsh,and H. L. Willis, “Integration of plug-in electric vehicles and dis-tributed energy resources on power distribution systems,” in Proc.Elect. Veh. Conf. (IEVC), Gaithersburg, MD, USA, Mar. 2012.

[6] E. Hossain, Z. Han, and H. V. Poor, Smart Grid Communications andNetworking. Cambridge, U.K.: Cambridge Univ. Press, 2012.

[7] J. Lassila, J. Haakana, V. Tikka, and J. Partanen, “Methodology to an-alyze the economic effects of electric cars as energy storages,” IEEETrans. Smart Grid, vol. 3, no. 1, pp. 506–516, Mar. 2012.

[8] N. Hatziargyriou, H. Asano, R. Iravani, and C. Marnay, “An overviewof ongoing research, development, and demonstration projects,” IEEEPower Energy Mag., vol. 8, pp. 78–94, 2007.

[9] A. Thatte and L. Xie, “Towards a unified operational value index ofenergy storage in smart grid environment,” IEEE Trans. Smart Grid,vol. 3, no. 3, pp. 1418–1426, Sep. 2012.

[10] N. Rotering andM. Ilic, “Optimal charge control of plug-in hybrid elec-tric vehicles in deregulated electricity markets,” IEEE Trans. PowerSyst., vol. 26, no. 3, pp. 1021–1029, Aug. 2011.

[11] D. Lindley, “Smart grids: The energy storage problem,” Nature, vol.463, no. 7277, pp. 18–18, Jan. 2010.

[12] D. Rastler, “Electricity energy storage technology options: A whitepaper primer on applications, costs and benefits,” in Elect. Power Res.Inst., 2010.

[13] N. Lu, J. H. Chow, and A. A. Desrochers, “Pumped-storage hydro-turbine bidding strategies in a competitive electricity market,” IEEETrans. Power Syst., vol. 19, no. 2, pp. 834–841, May 2004.

[14] J. Garcia-Gonzalez, R. R. de la Muela, L. M. Santos, and A. M.González, “Stochastic joint optimization of wind generation andpumped-storage units in an electricity market,” IEEE Trans. PowerSyst., vol. 23, no. 2, pp. 460–468, May 2008.

[15] R. Sioshansi, P. Denholm, T. Jenkin, and J. Weiss, “Estimating thevalue of electricity storage in pjm: Arbitrage and somewelfare effects,”Elsevier Energy Econ., vol. 31, no. 2, pp. 269–277, Aug. 2009.

[16] G. Caralis, D. Papantonis, and A. Zervos, “The role of pumped storagesystems towards the large scale wind integration in the greek powersupply system,” Elsevier Renewable Sustain. Energy Rev., vol. 16, no.5, pp. 2558–2565, Jun. 2012.

[17] F. Díaz-González, A. Sumper, O. Gomis-Bellmunt, and V. Robles,“A review of energy storage technologies for wind power applica-tions,” Elsevier Renewable Sustain. Energy Rev., vol. 16, no. 4, pp.2154–2171, May 2012.

[18] C. Garnier, J. Currie, and T.Muneer, “Integrated collector storage solarwater heater: Temperature stratification,” Elsevier Appl. Energy, vol.86, no. 9, pp. 1465–1469, Sep. 2009.

[19] W. W. Weaver and P. T. Krein, “Game-theoretic control of small-scale power systems,” IEEE Trans. Power Del., vol. 24, no. 3, pp.1560–1567, 2009.

[20] E. Baeyens, E. Y. Bitar, P. P. Khargonekar, and K. Poolla, “Wind en-ergy aggregation: A coalitional game approach,” in Proc. 50th IEEEConf. Decision Control (CDC), Orlando, FL, USA, Dec. 2011.

[21] X. Z. Xu and Q. Chen, “Research on reactive power compensation al-gorithm based on game theory in wind farm,” Key Eng. Mater., vol.439, pp. 989–993, 2010.

[22] B. F. Hobbs, C. B. Metzler, and J.-S. Pang, “Strategic gaming analysisfor electric power systems: An MPEC approach,” IEEE Trans. PowerSyst., vol. 15, no. 2, pp. 638–645, 2000.

[23] S. K. Ng, C. Lee, and J. Zhong, “A game-theoretic approach to studystrategic interaction between transmission and generation expansionplanning,” in Proc. 38th North Amer. Power Symp., 2006, pp. 115–12.

[24] E. Bompard,W. Lu, and R. Napoli, “Network constraint impacts on thecompetitive electricity markets under supply-side strategic bidding,”IEEE Trans. Power Syst., vol. 21, no. 1, pp. 160–170, Feb. 2006.

[25] T. H. Bradley and A. A. Frank, “Design, demonstrations and sustain-ability impact assessments for plug-in hybrid electric vehicles,” Else-vier Renewable Sustain. Energy Rev., vol. 13, pp. 115–128, Jan. 2009.

[26] A. Simpson, “Cost-benefit analysis of plug-in hybrid electric vehicletechnology,” in Proc. 22nd Int. Battery, Hybrid, Fuel Cell Elect. Veh.Symp., Yokohama, Japan, Oct. 2006.

[27] T. Başar and G. J. Olsder, “Dynamic noncooperative game theory,” inSIAM Series Classics Appl. Math., Philadelphia, PA, USA, 1999.

[28] D. Friedman, D. P. Friedman, and J. Rust, The Double Auction Market:Institutions, Theories, and Evidence. Boulder, CO, USA: WestviewPress, 1993.

[29] P. Huang, A. Scheller-Wolf, and K. Sycara, “Design of a multi-unitdouble auction e-market,” Comput. Intell., vol. 18, no. 4, pp. 596–617,Feb. 2002.

[30] P. Dasgupta and E. Maskin, “The existence of equilibrium in discon-tinuous economic games, I: Theory,” JSTOR Rev. Econ. Studies, vol.53, no. 1, pp. 1–26, Jan. 1986.

[31] S. Boyd and L. Vandenberghe, Convex Optimization. New York:Cambridge Univ. Press, 2004.

[32] B. Jansen, C. Binding, O. Sundstrom, andD.Gantenbein, “Architectureand communication of an electric vehicle virtual power plant,” in Proc.Int. Conf. Smart Grid Commun., Gaithersburg, MD, USA, Oct. 2010.

[33] A. W. Bowman and A. Azzalini, Applied Smoothing Techniques forData Analysis: The Kernel Approach with S-Plus Illustrations: TheKernel Approach with S-Plus Illustrations. New York: Oxford Univ.Press, 1997.

[34] S. Shao, T. Zhang, M. Pipattanasomporn, and S. Rahman, “Impact oftou rates on distribution load shapes in a smart grid with phev penetra-tion,” in IEEE PES Transm. Distrib. Conf. Expo., Apr. 2010, pp. 1–6.

[35] W. Saad, Z. Han, H. V. Poor, and T. Başar, “A noncooperative game fordouble auction-based energy trading between PHEVs and distributiongrids,” in Proc. IEEE Int. Conf. Smart Grid Commun. (Smart-Grid-Comm), Brussels, Belgium, Oct. 2011.


YunpengWang (S’12) received his B.S. degree fromNorth China Electric Power University, Beijing, in2009 and the M.S. degree from Stevens Institute ofTechnology, Hoboken, NJ, USA, in 2012, both inelectrical engineering. He is now pursuing his Ph.D.degree in the Electrical & Computer EngineeringDepartment, University of Miami, Coral Gables, FL,USA. His primary research interests revolve aroundthe smart grid, particularly control and design ofmicrogrids, with emphasis on game theory appliedto power systems.

Walid Saad (S’07–M’10) received his B.E. degreein computer and communications engineering fromLebanese University in 2004, his M.E. in Com-puter and Communications Engineering from theAmerican University of Beirut (AUB), Lebanon,in 2007, and his Ph.D degree from the Universityof Oslo, Norway, in 2010. Currently, he is anAssistant Professor at the Electrical and ComputerEngineering Department at the University of Miami,Coral Gables, FL, USA. Prior to joining UM, he hasheld several research positions at institutions such as

Princeton University and the University of Illinois at Urbana-Champaign.His research interests include wireless and small cell networks, game theory,

network science, cognitive radio, wireless security, and smart grids. He hasco-authored one book and over 85 international conference and journal pub-lications in these areas. He was the author/co-author of the papers that receivedthe Best Paper Award at the 7th International Symposium on Modeling and Op-timization in Mobile, Ad Hoc and Wireless Networks (WiOpt), in June 2009, atthe 5th International Conference on InternetMonitoring and Protection (ICIMP)in May 2010, and at IEEE WCNC in 2012. Dr. Saad is a recipient of the NSFCAREER Award in 2013.

Zhu Han (S’01–M’04–SM’09–F’14) received theB.S. degree in electronic engineering from TsinghuaUniversity, Chiina, in 1997, and the M.S. and Ph.D.degrees in electrical engineering from the Universityof Maryland, College Park, MD, USA, in 1999 and2003, respectively.From 2000 to 2002, he was an R&D Engineer of

JDSU, Germantown, MD, USA. From 2003 to 2006,he was a Research Associate at the University ofMaryland. From 2006 to 2008, he was an assistantprofessor in Boise State University, ID, USA.

Currently, he is an Assistant Professor in Electrical and Computer EngineeringDepartment at the University of Houston, TX, USA. His research interests in-clude wireless resource allocation and management, wireless communicationsand networking, game theory, wireless multimedia, security, and smart gridcommunication.Dr. Han is an Associate Editor of IEEE TRANSACTIONS ON WIRELESS

COMMUNICATIONS since 2010. Dr. Han is the winner of IEEE Fred W. EllersickPrize 2011. Dr. Han is an NSF CAREER award recipient 2010. Dr. Hanis the coauthor for several papers that won the best paper awards in IEEEconferences.

H. Vincent Poor (S’72–M’77–SM’82–F’87) re-ceived the Ph.D. degree in EECS from PrincetonUniversity, Princeton, NJ, USA, in 1977. From 1977until 1990, he was on the faculty of the Universityof Illinois at Urbana-Champaign. Since 1990 hehas been on the faculty at Princeton, where he isthe Michael Henry Strater University Professor ofElectrical Engineering and Dean of the School ofEngineering and Applied Science. Dr. Poor’s re-search interests are in the areas of stochastic analysis,statistical signal processing, and information theory,

and their applications in wireless networks and related fields such as socialnetworks and smart grid. Among his publications in these areas are the recentbooks Smart Grid Communications and Networking (Cambridge UniversityPress, 2012) and Principles of Cognitive Radio (Cambridge University Press,2013).Dr. Poor is a member of the National Academy of Engineering and the Na-

tional Academy of Sciences, a Fellow of the American Academy of Arts andSciences, an International Fellow of the Royal Academy of Engineering (U.K.),and a Corresponding Fellow of the Royal Society of Edinburgh. He is also aFellow of the Institute of Mathematical Statistics, the Acoustical Society ofAmerica, and other organizations. In 1990, he served as President of the IEEEInformation Theory Society, and in 2004-07 he served as the Editor-in-Chiefof the IEEE TRANSACTIONS ON INFORMATION THEORY. He received a Guggen-heim Fellowship in 2002 and the IEEE Education Medal in 2005. Recent recog-nition of his work includes the 2010 IET Ambrose Fleming Medal, the 2011IEEE Eric E. Sumner Award, the 2011 Society Award of the IEEE Signal Pro-cessing Society, and honorary doctorates from Aalborg University, the HongKong University of Science and Technology and the University of Edinburgh.

Tamer Başar (S’71–M’73–SM’79–F’83–LF’13)received the B.S.E.E. from Robert College, Istanbul,and M.S., M.Phil, and Ph.D. from Yale University,New Haven, CT, USA. He is with the Universityof Illinois at Urbana-Champaign (UIUC), IL, USA,where he holds the positions of Swanlund EndowedChair; Center for Advanced Study Professor ofElectrical and Computer Engineering; Research Pro-fessor at the Coordinated Science Laboratory; andResearch Professor at the Information Trust Insti-tute. He is a member of the U.S. National Academy

of Engineering, and Fellow of IEEE, IFAC and SIAM, and has served aspresident of IEEE CSS, ISDG, and AACC. He has received several awards andrecognitions over the years, including the highest awards of IEEE CSS, IFAC,AACC, and ISDG, and a number of international honorary doctorates andprofessorships. He has over 600 publications in systems, control, communica-tions, and dynamic games, including books on non-cooperative dynamic gametheory, robust control, network security, wireless and communication networks,and stochastic networked control. He is the Editor-in-Chief of Automatica andeditor of several book series. His current research interests include stochasticteams, games, and networks; security; and cyber-physical systems.

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