A Survey of Algorithms for Distributed Charging Control of Electric Vehicles in Smart Grid
Nanduni I. Nimalsiri, Chathurika P. Mediwaththe, Elizabeth L. Ratnam, Marnie Shaw, David B. Smith, Saman K. Halgamuge
TThis article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 1
A Survey of Algorithms for Distributed ChargingControl of Electric Vehicles in Smart Grid
Nanduni I. Nimalsiri , Chathurika P. Mediwaththe ,
Member, IEEE , Elizabeth L. Ratnam ,
Member, IEEE ,Marnie Shaw, David B. Smith ,
Member, IEEE , and Saman K. Halgamuge,
Fellow, IEEE
Abstract — Electric vehicles (EVs) are an eco-friendly alterna-tive to vehicles with internal combustion engines. Despite theirenvironmental benefits, the massive electricity demand imposedby the anticipated proliferation of EVs could jeopardize thesecure and economic operation of the power grid. Hence, properstrategies for charging coordination will be indispensable tothe future power grid. Coordinated EV charging schemes canbe implemented as centralized, decentralized, and hierarchicalsystems, with the last two, referred to as distributed chargingcontrol systems. This paper reviews the recent literature ofdistributed charging control schemes, where the computationsare distributed across multiple EVs and/or aggregators. First,we categorize optimization problems for EV charging in termsof operational aspects and cost aspects. Then under each cate-gory, we provide a comprehensive discussion on algorithms fordistributed EV charge scheduling, considering the perspectivesof the grid operator, the aggregator, and the EV user. We alsodiscuss how certain algorithms proposed in the literature copewith various uncertainties inherent to distributed EV chargingcontrol problems. Finally, we outline several research directionsthat require further attention.
Index Terms — Decentralized control, distributed optimization,electric vehicles, hierarchical control.
I. I
NTRODUCTION I NCREASED societal awareness of environmental issuesassociated with vehicular emissions has spurred the devel-opment of cleaner solutions for transportation. In this respect,electrified vehicles are emerging as the defining trend of trans-portation [1]. Recently, a dramatic increase in the adoptionof EVs has additionally been attributed to decreasing batterycosts and cheaper electricity prices compared to escalatingfuel prices [2]. Despite the numerous benefits of EVs, largepopulations of grid-connected vehicles will potentially creategrid congestion problems leading to costly network expansion.For example, charging a single EV will potentially double the
Manuscript received December 12, 2018; revised June 3, 2019 and August 2,2019; accepted September 6, 2019. The Associate Editor for this article wasA. Malikopoulos. (Corresponding author: Nanduni I. Nimalsiri.)
N. I. Nimalsiri and D. B. Smith are with the Research School of Elec-trical, Energy and Materials Engineering, The Australian National Uni-versity, Canberra, ACT 2601, Australia, and also with Data61, CSIRO,Eveleigh, NSW 2015, Australia (e-mail: [email protected];[email protected]).C. P. Mediwaththe, E. L. Ratnam, and M. Shaw are with theResearch School of Electrical, Energy and Materials Engineering,The Australian National University, Canberra, ACT 2601, Australia(e-mail: [email protected]; [email protected];[email protected]).S. K. Halgamuge is with the Department of Mechanical Engineering,The University of Melbourne, Melbourne, VIC 3010, Australia, and alsowith the Research School of Electrical, Energy and Materials Engineering,The Australian National University, Canberra, ACT 2601, Australia (e-mail:[email protected]).Digital Object Identifier 10.1109/TITS.2019.2943620 energy consumption of an average household [3]. In caseswhere millions of EVs simultaneously charging across thegrid, new peak load events will arise and/or existing peak loadevents will be compounded.By contrast, coordinated EV charging using intelligent con-trol strategies supported by Information and CommunicationTechnology (otherwise known as smart charging ) potentiallyoffers opportunities to improve grid utilization and limit net-work expansion. Researchers have been developing numeroussmart charging algorithms, many of which require the acqui-sition and processing of large amounts of information at acentral point. In cases where the large computational overhead,or requirements for supporting communication infrastruc-ture are considered impractical, alternatives to centralizedapproaches, such as distributed algorithms have been consid-ered. In particular, distributed algorithms are highly scalableboth from computation and communication points of view.As opposed to centralized control schemes where all therelevant parameters are collected and a central calculation isperformed by a single entity, distributed control schemes areperformed by several entities that obtain certain relevant para-meters via communication. Specifically, a distributed chargecontrol scheme assigns the processing load over several agents,so that each agent only needs to solve its own small-scaleproblem, and as such, each agent bears the control of thecharge schedules to a certain extent. Distributed chargingschemes, in particular, can be realized as decentralized and hierarchical schemes, where decentralized schemes share thecomputational load across EVs and hierarchical schemes sharethe computational load across both EVs and aggregators(intermediaries between the power grid and the EV users).In this paper, we review a specific class of EV chargingschemes, namely distributed EV charging schemes . The keycontributions of this paper are summarized as follows: distrib-uted EV charging has not seen a focused survey, and to thebest of our knowledge, this paper is the first (1) to presentan explicit review of distributed charging control algorithms;(2) to elucidate the distinction between different permutationsof distributed charging control architectures, based on themethod of sharing computation and the structure of commu-nication; (3) to provide a comprehensive classification of EVcharging optimization problems (OPs) to better understandthe existing distributed EV charging schemes studied underoperational and cost aspects of grid operators, EV users, andaggregators; and (4) to assess several distributed EV chargingschemes with respect to managing uncertainties related to thepower grid, the electricity market, and the behaviour of EVusers. his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
There have been several surveys related to EVs and theirinfluences [4]–[6]. A number of surveys related to EV chargingschemes are presented in [7]–[10]. By contrast, we review aspecific category of EV charging schemes referred to as dis-tributed EV charging schemes. Specifically, the authors in [7]describe centralized and decentralized schemes, without men-tion of hierarchical schemes that have been widely explored inthe recent literature. The authors in [8] propose a more generalclassification of charging schemes as uncontrolled, indirectlycontrolled, smart, and bidirectional. In [9], charging schemesare first classified as unidirectional or bidirectional and then ascentralized or decentralized, and whether mobility aspects areconsidered or not. Complementary to [8] and [9], we reviewdistributed charging schemes based on two significant classi-fications that consider: (1) the distributed control architecturemodel; and (2) the objective function of the OP, and thus wepresent a concise and comprehensive overview of distributedcharging schemes. Further, we consider several other uncertainaspects of EV charging other than EV mobility. The authorsin [10] present a classification based on grid, aggregator,and customer oriented charging. By contrast, we first classifycharging schemes based on the operational and cost aspects ofthe OP, and then further classify with regard to the objectivesof grid-operator, aggregator, and EV user.This paper is organized as follows. In Section II, we providebackground to EV charging. In Section III, we identify severalproperties of EV charge control schemes. In Section IV, con-trol architectures for coordinated EV charging are introduced.Section V reviews a number of distributed EV charging controlschemes and related uncertainties. In Section VI, we highlightseveral future research directions, followed by the conclusionin Section VII. II. B
ACKGROUND
An EV uses electrical energy as the principle means ofpropulsion. Fig. 1 illustrates the bidirectional power flowbetween EVs and the smart grid, where electrical energy gen-erated by power plants and renewable energy sources (RESs)recharges the EV battery (grid-to-vehicle: G2V) and the elec-trical energy delivered back to the grid discharges the EVbattery (vehicle-to-grid: V2G). An aggregator often acts asa proxy between EVs and the power grid as well as theelectricity market in managing smart interactions, so that thegrid-operator need not directly deal with a large numberof EVs. In reality, an aggregator could be a utility com-pany, an EV charging facility, a fleet operator of a parkinglot or a communication device at a transformer [11]. Theinformation exchange between smart entities is through twoway digital communication enabled by ubiquitous wirelessnetworks and broadband power lines. The power networksand communication networks together build up a complexnetwork. Therefore, proper control strategies supported bywell established communication, measurement, and controlinfrastructures are crucial for the successful rollout of EVs.In an EV battery, the state of charge (SoC) is the percentageof remaining energy capacity. The relationship between theexternal charging power and the rate of change of SoC ofthe battery can be approximated using a battery model [12].
Fig. 1. Interactions between EVs and the smart grid.
Due to the conversion losses during charging, only a part ofthe total amount of energy drawn from the grid is effectivelydispatched for charging an EV [13].Demand-side management (DSM) of EVs refers to reducingthe peak load by shifting EV charging to time periods withless congestion [14]. Given the duration that EVs are typicallyidle (e.g., overnight at a residence and during work hours atan office), EVs are considered an ideal prospect for DSM.As such, the three key dimensions that need to be consideredfor DSM of EVs are: (1) space (where to charge); (2) time(when to charge); and (3) speed (at what rate to charge).An EV owner might charge the battery overnight, e.g., startwhen arriving home and finish the next morning when depart-ing for work. During the day time, an EV owner might chargethe battery at the kerbside or in a parking lot. EVs can alsobe charged in EV charging stations (EVCSs) at times whenimmediate charging becomes inevitable during a trip. Com-pared to charging at home, EVCS operators may offer lowerprices because they generally purchase large volumes of powerfrom the wholesale power market at cheap rates. In addition,the deployment of fast charging stations, especially in denselypopulated areas where the majority of users have no accessto over-night charging is also becoming increasingly popular.Importantly, fast charging solutions reduce long charging timesand potential range anxiety of drivers. Furthermore, wirelesspower transfer for EVs using magnetic resonance is alsogaining widespread interest [15].EVs outfitted with bidirectional power converters (chargersand inverters) can act as electrical loads (during charging) aswell as electrical sources (during discharging). Because EVsremain mostly stationary over the course of a day, opportuni-ties to partake in ancillary services through V2G operationsare possible. Nonetheless, V2G operation exhibits severaldrawbacks, including premature degradation of batteries andincreased operational energy losses.III. P
ROPERTIES OF
EV C
HARGING C ONTROL S CHEMES
Here we introduce some important properties relating to EVcharging control schemes.
A. One-Time, Open-Loop Versus Recursive Closed-LoopControl
One-time, open-loop control strategies ( offline strategies )are calculated once, based on the predicted operation ofthe system, and thus assume perfect knowledge in advanceof EV scheduling. For instance, EV charging schemes such his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
NIMALSIRI et al. : SURVEY OF ALGORITHMS FOR DISTRIBUTED CHARGING CONTROL OF EVs IN SMART GRID 3
Fig. 2. Charging at (a) variable rates and (b-c) discrete rates. as [13], [16], [17] are formulated such that all the EVsare available for negotiating their charge schedules at thebeginning of the time horizon. However, in a more realisticsetting, neither the EV arrival times nor the status of thedistribution power network is known a priori. By contrast,recursive closed-loop control strategies ( online strategies ) arecalculated multiple times, based on feedback measurements,hence capable of handling numerous uncertainties, includingthe mobility of EVs. For instance, EV charging schemes suchas [18]–[20] solve the control problem progressively in theorder that information becomes available (See Section V-Cfor more details).
B. Charging at Variable Versus Discrete Rates
In the literature, EV charge rate is often considereda variable that can take an infinite number of valuesbetween zero and the maximum charge rate, as depictedin Fig. 2(a) [21]–[24]. In practice, residential charging ismostly done at discrete rates (Fig. 2(b-c)), because discreterate chargers with simple on-off controllers are much cheaperthan variable rate chargers that require sophisticated equipmentto modulate the power. Further, the efficiency of a chargerpotentially decreases if charging is not conducted at its fullcapacity [25]. Nevertheless, variable rate charging (VRC) canbe better exploited for DSM, compared to charging at a fixedrate.For an OP with VRC, it is required to find the charge ratesfor each time instant at which the EVs are grid-connected.In the cases of discrete rate charging (DRC) , the maxi-mum output power of the charging equipment or the maxi-mum charging power of the battery restricts the charge rate.In particular, DRC can be implemented in an uninterrupted(constant) [26] or interrupted (binary) [27] manner as shownin Figs. 2(b-c). The decision variables for the former DRC arethe times at which each EV starts charging. The additionaldecision variables for the later DRC, where EVs are chargedat discrete time slots that are separated by idle slots, are tocharge at a predefined rate or to not charge at all. With sucha charging approach, the battery gets to cool down duringthe idle slots, which in turn improves the battery life [28]. Foreffective operation, the number of on-off switchings should notbe too high, as frequent switching will also deteriorate somebatteries [29], and in cases of wide-spread implementation,frequent switching reduces the quality of power delivered togrid-connected customers [30], [31]. To balance the flexibilityof VRC against the practicality of DRC, researchers haverecently considered charging schemes with a finite set ofcharge rates between zero and a maximum value [32].
C. Homogeneous Versus Heterogeneous EV Specifications
Certain EV charge scheduling algorithms such as the onepresented in [16] perform well for a homogeneous or identicalEV population. However, a practical algorithm should per-form with heterogeneous charging specifications from the EVpopulation. In particular, heterogeneity in the charge duration,charge rate, along with heterogeneity in user preferences suchas charging location are needed for practical demonstrations.
D. Pricing Strategies A flat rate refers to a pricing scheme with a fixed fee foreach energy unit regardless of the time at which energy isconsumed. In contrast, a time-varying pricing regime providesan incentive to coordinate EV charging. For example, a time-of-use (TOU) rate, where electricity is billed at a differentrate during peak, shoulder and off-peak periods, providesan incentive to shift EV charging from the peak pricingperiod. In this way, grid congestion co-incident with the peakpricing period is alleviated. However, new charging peaks(or rebound peaks) potentially form when many EVs chargesimultaneously during the off-peak pricing period. To mitigatethe rebound peaks, a resurgence of interest in real-time pricing (RTP) strategies that reflect contemporaneous power systemconditions has occurred. RTP represents either the actualenergy cost for a utility generating electricity or purchasingelectricity at a wholesale level, or the cost imposed by a utilityfor load control. RTP rates are generally increasing functionsof the instantaneous demand, hence users can influence thereal-time electricity rate by adjusting their energy consump-tion [33]. In addition, customized pricing strategies are alsoproposed in certain EV charging control schemes [34], [35].IV. EV C HARGING C ONTROL A RCHITECTURES
In this section, we describe EV charging control architec-tures illustrated in Fig. 3. We consider charging decisionsfor a group of EVs that are made by a central entity or byindividual EVs, with the former called centralized control,and the later called decentralized control.
Hierarchical controlfeatures aggregators and EVs arranged like a tree structure.An aggregator may either directly or indirectly control a groupof EVs. A direct aggregator decides the charge schedule foreach EV in the group. By contrast, an indirect aggregator broadcasts information signals to the EVs to coordinate theircharge profiles. As such, an indirect aggregator is not requiredto be computationally powerful since the computation load isshared by the other entities.
A. Centralized Control Architecture
Fig. 3(a) depicts a centralized architecture, where the chargeschedule of each EV is decided by a direct aggregator, whocollects the charge requirements of all the EVs, then solves anOP to determine the rate at which each EV will charge, andcommunicates the optimization-based charge schedule back tothe EV owners. Consequently, each EV owner relinquishessome autonomy over their charge schedule. Nevertheless, cen-tralized schemes have the advantage that they often produce his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Fig. 3. Centralized EV charging control architecture and variations of distributed (decentralized, hierarchical) EV charging control architectures. optimal solutions as complete information of the entire systemis available to the aggregator. Further, centralized schemescan readily consider various global system states and couplingconstraints. However, such benefits must be weighed againstthe EV owner concerns with the privacy of information relayedto the communication network. Moreover, a single point offailure at the aggregator (e.g., failure to solve the OP) couldpotentially collapse the entire system, creating the need for abackup system.A key challenge for centralized approaches is scalability,especially when the size of the OP increases in the lengthof the planning time horizon and the number of connectedEVs. Therefore, a centralized approach is potentially compu-tationally intractable with respect to the implementation time.Additional complexities arise when the number of controlvariables and constraints of each EV increases. Furthermore,centralized approaches require EV users to communicateto the central controller complete information of chargingrequirements and technical specifications of EVs. This maypotentially lead to practical obstacles such as communicationbottlenecks, bandwidth limitations, and costly expansion ofthe supporting infrastructure to handle the explosive increaseof data from rapid EV uptake. Consequently, centralizedapproaches may lose their efficiency and become impracticalwhen large numbers of EVs grid-connect.
B. Decentralized Control Architecture
Decentralized systems are different from the centralizedsystems in that each EV acts as an independent decision-makerwho solves its own problem that is small in size. As such,decentralized solutions do not always correlate with optimalcharging regimes, especially in cases where there is a lack ofcomplete information at the individual EV tier. Nevertheless,there is considerable interest in decentralized solutions, sincethey are highly scalable (in terms of computational complex-ity) and practical with respect to field implementation.Depending on the structure of the communication network,Figs. 3(b-c) depict two decentralized control architectures.The decentralized Type 1 (T1) is a center free design whereEVs locally compute and adjust their schedules by commu-nicating with the other EVs, until a global equilibrium is achieved. Such an architecture enforces EVs to continuouslycommunicate their scheduling information with the other EVs,resulting in a large communication overhead, especially whenthe number of EVs is very high. The decentralized ( T2 )architecture reduces the communication overhead by intro-ducing an indirect aggregator who gathers certain informa-tion and broadcasts control (coordination) signals to all theEVs. As such, the requirement for large scale communicationinfrastructure is reduced. Importantly, decentralized chargingschemes are more resilient to network failures, especially whencontrollers are designed to operate in the event of a centralizedcommunication failure. C. Hierarchical Control Architecture
In the recent literature, we observe a particular interestin hierarchical control system design that is not fully cen-tralized, nor fully decentralized. Unlike centralized systems,hierarchical systems delegate control and computational loadto multiple direct or indirect aggregators via a tree-like com-munication topology. By doing so, the need for network-widecommunication is also reduced. Each aggregator coordinatesa group of EVs while influencing the decisions of the otheraggregators. A group may include EVs in a single location,e.g., situated in a parking lot or located in an apartmentblock. Each hierarchical architecture, depicted in Figs. 3(d-h),balances the benefits of centralized and decentralized archi-tectures in a distinctive manner. First four structures (depictedin Figs. 3(d-g)) feature three tiers: a central aggregator onthe top tier, sub-aggregators in the middle tier, and EVs atthe lower tier. A hierarchical ( T1 ) architecture features acentral aggregator that calculates a collective charging planfor all the sub-aggregators, where sub-aggregators decide eachEV-specific schedule. In the hierarchical ( T2 ) architecture,the central aggregator issues control signals to each sub-aggregator, transferring the computational overhead to mul-tiple sub-aggregators that determine the charge schedules ofEVs in their groups. In the hierarchical (T3) architecture,a central aggregator calculates a collective charging plan forall sub-aggregators, whereby each sub-aggregator indirectlycontrols a group of EVs by broadcasting signals, transferringthe computational overhead of calculating charge schedules his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. NIMALSIRI et al. : SURVEY OF ALGORITHMS FOR DISTRIBUTED CHARGING CONTROL OF EVs IN SMART GRID 5 to the EVs. The hierarchical ( T4 ) is a communication struc-ture where all the aggregators (central aggregator and sub-aggregators) and EVs coordinate via indirect control signals.It is worth mentioning that the hierarchical (T3) and (T4)control architectures preserve decentralized behavior of EVs.The hierarchical structures depicted in Figs. 3(d-g) are stillvulnerable to single points of failure. For example, if thecentral aggregator collapses, all the sub-aggregators and EVswill be left uncontrolled. To mitigate against such an occur-rence, the hierarchical ( T5 ) architecture that is composed of acommunication network across the aggregators (as depictedin Fig. 3(h)) is proposed. In cases where a link betweentwo aggregators collapses, an alternative communication pathconnecting the aggregators would improve system resilience.However, if one of the aggregators collapses, EVs connectedto that particular aggregator will remain uncontrolled.V. D ISTRIBUTED
EV C
HARGING C ONTROL A LGORITHMS
A distributed algorithmic approach divides a centralizedOP into a set of subproblems of a much smaller scale,that is solved by several EVs and/or aggregators. As such,decentralized and hierarchical control architectures naturallyalign with distributed computational systems. In this section,we review numerous decentralized and hierarchical chargingcontrol schemes that have been proposed in the literature.Much of the early literature formulates the EV chargingcontrol problem as a constrained OP , with charge rates andcharge durations defined as the decision variables, and withvarious constraints introduced to incorporate requirements ofthe grid operator, aggregators, and EV users. The realizationof a distributed algorithm for a centralized OP is notablychallenging, especially in certain non-convex OPs where theobjective function and constraints are coupled to the individualcharge rates of EVs, to network capacity or to electricityprices. Despite non convexity and NP-hardness, certain OPshave been solved to attain optimality or near optimalityusing a variety of techniques, e.g., relaxation [36], cuts [37],preprocessing [38], heuristics [19], randomization [39].In Fig. 4, and in what follows, we organize EV chargingcontrol OPs into two categories based on (A)
Operationaspects and (B)
Cost aspects , and discuss numerous distributedalgorithmic approaches that have been proposed to solve them.
A. Operation Aspects1) Grid Operator’s Perspective:a) Load regulation:
Among all possible ways of regulat-ing the EV load, numerous studies are focused on flatteningthe aggregate load (EV and non-EV load) curve. By flatteningload curve peaks, the risk of overloading transformers andother electrical infrastructure is reduced. Further, a flattenedload curve eliminates the requirement to ramp up and down thegenerators, enabling a steady-state operation with maximumefficiency. Scheduling EVs to fill the overnight load valley,where the non-EV load is at its lowest, is widely addressed inthe literature. Although the influence of a single EV is minor,the aggregate influence of a fleet of EVs can be substantial interms of load flattening.
Fig. 4. The classification of EV charging control problems and the respectivedistributed EV charging control schemes from the literature.
Consider a power system where N number of EVs scheduletheir charge profiles over T time slots, each of length (cid:2) t .Let s arri , s depi , b i , p mini , p maxi and η i be the SoC at arrival,the expected SoC at departure, the battery capacity, the mini-mum charging power, the maximum charging power, and thecharging efficiency of the i th EV. Let D ( t ) be the non-EV loadprofile, which is known a priori. The charge rates denoted by p i ( t ) are the decision variables. The most intuitive approachfor load flattening (or valley filling) is minimizing variance ofthe aggregate load profile [41] and the corresponding OP ismin p i ( t ) T (cid:2) t = ( D ( t ) + N (cid:2) i = p i ( t )) (1a)subject to, T (cid:2) t = η i p i ( t )(cid:2) t = ( s depi − s arri ) b i , (1b) p mini ≤ p i ( t ) ≤ p maxi , (1c)where the energy demand and the range of acceptable chargerates of the EV are defined by constraints (1b) and (1c)respectively. One potential approach to fill the load valley isto influence EV users through electricity prices [21]. As such,an aggregator may broadcast control signals, for example,price-like signals that vary in proportion to the aggregatedemand. Accordingly, each EV user will selfishly seek tominimize charging costs by scheduling the EV to charge ata time that fills the load valley.Game theory is a promising tool that can be used tocoordinate EV charging by way of optimizing individualEV charge preferences. In [16], a non-cooperative game is his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. established to coordinate a large population of EVs who areweakly coupled via a common electricity price. The proposedgame is based on a decentralized (T2) architecture, wherethe utility (indirect aggregator) broadcasts the aggregate EVdemand after collecting the charge strategies of all the EVs.In response, EVs update their charge strategies and report themto the utility. The process iterates until the penalty imposed forthe deviations of individual charge strategies from the averagecharge strategy vanishes. Specifically, the load curve valleyis filled at the Nash Equilibrium (NE) of the game – a statewhere none of the EVs benefit by unilaterally deviating fromtheir chosen charge strategies [21]. More formally, f i ( p ∗ i ; p ∗− i ) ≥ f i ( p i ; p ∗− i ) ; ∀ p i ∈ P i , ∀ i ∈ { , .., N } (2)where f is the payoff function, p i is the charge sched-ule vector of EV i , p − i is the vector containing thecharge schedules of all the EVs other than EV i ( p − i =[ p , .., p i − , p i + , .., p N ] ), P i is the set of all feasible chargeschedule vectors of EV i , and p ∗ are the EV charge schedulevectors at the NE [21]. Due to nature of the specific penaliza-tion strategy in [16], the proposed algorithm is proved to beoptimal only for an infinite, homogeneous EV population.In contrast, Gan et al. [21] present an optimal decentralized(T2) charging (ODC) algorithm that converges to optimalityfor both homogeneous and heterogeneous EV fleets. In theproposed algorithm, the utility (indirect aggregator) progres-sively guides EVs by altering a control signal (e.g., electricityprice) in response to the last received EV charge profiles.At each iteration, upon receiving the control signal from theutility, EVs individually update their charge profiles in orderto minimize the sum of the electricity cost and the penaltyfor deviating from the charge schedule calculated in theprevious iteration. Importantly, the ODC algorithm performswell even with asynchronous consumption, e.g., where EVs donot necessarily update their charge profiles in each iterationor update their charge profiles using outdated control signals.Therefore, the proposed charging scheme is quite robust tocommunication delays and failures. In [42], a variant of theODC algorithm is developed to solve a discrete OP that isfocused on charging EVs at discrete charge rates. In eachiteration, a communication device at the transformer (indirectaggregator) broadcasts the normalized demand using the EVcharge profiles from the previous iteration. Accordingly, eachEV computes a probability distribution over its potentialcharge profiles and samples from the distribution to updateits charge profile.Based on the decentralized (T2) architecture, Li et al. [41]presents an online algorithm to regulate EV loads through anindirect aggregator who publishes a charging reference usingthe real-time aggregate EV load, after which EVs make binarydecisions to charge or not, by comparing their SoC with thereference signal. It is shown that such an algorithm solvesa generalized maximum weight OP. Importantly, the proposedalgorithm is an on-line algorithm, which does not rely on fore-casts, and as such, it is not affected by forecast errors. Usingdynamic programming (DP) and game theory, an algorithm forvalley filling and peak load shaving is developed in [43]. Theproblem of scheduling a single EV is solved using a forward induction DP algorithm. Since including multiple EVs in theDP algorithm increases the quantity of states at each time step,a non-cooperative game is formulated to coordinate multipleEVs in a decentralized (T2) manner.A possible drawback of the mentioned charging schemesin [16], [21], [41]–[43] is the iterative nature of the respectiveroutines, and the subsequent time they potentially take toreach the global equilibrium. Alternatively, the authors in [26]propose a non-iterative approach of scheduling a single EV at atime in a sequential manner in accordance with a decentralized(T2) model. The algorithm aims to minimize both the varianceand the maximum peak of the aggregate load. A weightfactor is carefully chosen to adjust the priorities between thetwo objectives. Once connected to the grid, an EV receivesfrom the grid operator (indirect aggregator), the aggregateload profile for the scheduling horizon, i.e., non-EV loadplus the power required to charge EVs already scheduled.Based on that information, EV solves a local OP to find itscharge schedule and reports the updated load profile to thegrid operator, who then submits it to the next EV. Such ascheduling approach is greedy in the sense that it determinesthe charge schedule of an EV only once, which occurs atthe time when the EV grid-connects. Although the extensivebidirectional communication at each time step is eliminated,a possible disadvantage is the waiting period encountered byEVs that connect simultaneously. To overcome that issue,the authors modify the algorithm to update the total loadprofile by combining the charge schedules of all the EVs thatconnect simultaneously. Still, there exists the risk of formingadverse second peaks if a large number of EVs grid-connect atthe exact same time. The study in [44] also utilizes a sequentialscheduling approach to design a decentralized (T2) chargingscheme that aims to minimize the mean square error betweenthe real-time aggregate load and a reference operating pointestimated offline using data related to non-EV load and EVmobility. Network-aware charging refers to the consideration ofdistribution network constraints (e.g., overload control con-straints, nodal voltage constraints) in EV charge scheduling.With network-aware charging, the operational envelopes ofexisting power systems are considered to limit costly net-work expansion. In what follows, we discuss load regulationschemes focused on network-aware EV charging. b) Load regulation with overload control:
Sustainedoverloading of a transformer can overheat the transformerwindings, which results in its premature failure. Incorporatinga distribution overload constraint as follows N (cid:2) i = p i ( t ) + D ( t ) ≤ C ; ∀ t ∈ { , .., T } , (3)where C is the rated capacity of the transformer/feeder, is away to minimize congestion by limiting the maximum powerthat a transformer can carry at any time. By considering theoptimal valley filling theory of ODC [21] and the distributionnetwork topology across EVs, Ghavami et al. [3] develop twodecentralized (T2) algorithms based on the gradient projectionmethod (GPM), to minimize the load variance subject to the his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. NIMALSIRI et al. : SURVEY OF ALGORITHMS FOR DISTRIBUTED CHARGING CONTROL OF EVs IN SMART GRID 7 overload constraint (3). In the first algorithm, the primal prob-lem of (1) is augmented with a cost function that associates tothe overload constraint of the feeder and the GPM is applied.A limitation that exists in that algorithm is requiring thestep size of the GPM to be smaller than a certain systemdependent threshold. The second algorithm is an applicationof the primal-dual method to circumvent the nonseparabilityof the problem and interestingly, the second approach does notrequire a specific upper bound on the step size. While bothoverload control methods are observed to be quite effectivein controlling feeder overload, the first algorithm seems toattain faster convergence whereas the second algorithm seemsto perform better in terms of overload control.By extending the algorithms in [21] and [45], the ref-erence [23] proposes three decentralized (T2) algorithms tominimize the total load variance subject to network capacityconstraint (3). Since the charge rates of EVs are coupled byboth the electricity cost and the transformer capacity, twocontrol signals are introduced to flatten the load profile andto manage the overload constraint. The first two algorithmsminimize load variance using the ODC algorithm and enforcecapacity constraint using the alternating direction method ofmultipliers (ADMM) – a powerful tool for solving large scaleOPs by breaking the problem into smaller and manageablesubproblems which are easier to solve. Those two algorithmsdiffer in the time scale at which the two subroutines execute.The third algorithm employs ADMM for both subroutines.These different algorithms result in different message passingstructures and exhibit different trade-offs between the feasibil-ity and the optimality of the solutions. A sparsity promotingEV charging scheme in [46] also employs the ADMM methodto generate a set of sub-problems with decoupled feeder over-load constraints, which are solved by EVs independently usingthe dual-gradient method. However, none of the algorithmsin [23], [46] are online, hence they do not capture real-timedynamics of the system.In the decentralized (T2) charging scheme proposed in [47],the transformer overload constraints are handled by incorpo-rating the transformer load levels in the price-signals publishedby the aggregator. In [48], a decentralized (T2) ant-basedswarm algorithm is proposed, where EVs are treated as antsof a dynamic reunion. Each ant (EV) decides a valley fillingcharge schedule according to the pheromones released by theother ants, which are updated whenever the total load surpassesthe maximum power capacity of the transformer. Althoughthe convergence of the proposed algorithm is guaranteed,the time to converge is uncertain, and as such, the approach ispotentially impractical for real-time implementations. Inspiredby the water filling principle in information theory, the authorsin [49] propose a decentralized (T2) algorithm for flatteningthe load profile. For each single EV, a constant water level isdefined and it is adjusted through an iterative bisection methoduntil the charge rates obtained by subtracting the non-EV loadprofile from the water level satisfy the energy demand ofthe EV. The water filling process is performed by EVs, oneat a time, in coordination with the indirect-aggregator. Theoverload constraints of transformers are handled by reducingthe energy demands of EVs according to a specific ratio, and as such, the congestion is prevented at the expense of nottotally satisfying the EV demands. In order to ensure a fairdispatch of power, EVs are served in a circular order, andconsequently certain EVs may encounter a considerably longwaiting period. In [50], the algorithm in [49] is extended toa decentralized (T2) charging control scheme with discreterates, using the idea of pulse width modulation. Later in [51],the algorithm in [49] is utilized to approximately solve theproblem of valley filling and peak load shaving, by defining atime point before and after which EVs discharge and chargerespectively.The study in [52] presents a decentralized (T2) algorithm toavoid persistent bus congestion while ensuring a proportionallyfair share of the distribution network capacity among the EVs.It is assumed that the congestion level of every branch canbe measured and communicated to the downstream EVs inreal-time with a reasonably low delay. To avoid bus conges-tion, EVs are charged at the maximum rate when the networkis lightly loaded, and at a relatively low rate when the networkis highly loaded. Hence, the intuition of the algorithm is toquickly control the charge rates in real-time such that thebottleneck lines and transformers are appropriately utilized.At times when the grid is overly congested, some EVs maynot be fully charged by their deadlines, in favor of protectingthe power system assets, thus the algorithm provides a besteffort service. Since charge rates of EVs that belong to thesame transformer are coupled, the dual decomposition methodis used to obtain a set of distributively solvable subproblems,each of which is solved by an individual EV. Further, chargerates of EVs are adjusted based on the congestion price signalsissued by the measurement nodes installed on the way tothe substation. In a later work [53], the authors extend thealgorithm to a dynamic setting where household loads and thenumber of EVs being charged change over time. The mainlimitation of charging schemes in [52], [53] is the heavy com-munication overhead, where each EV receives a message every20ms. Moreover, the algorithms rely heavily on fast scalemeasurements and low latency broadband communications,hence a robust communication and measurement infrastructureis crucial. c) Load regulation with voltage control:
Another impor-tant consideration of a network-aware charging control schemeis the maintenance of a proper voltage level at every node ofthe grid. It can be enforced using an approximated power flowmodel [54], [55]. The authors in [55], [56] introduce an algo-rithm called shrunken-primal-dual subgradient, to minimizeload variance while regulating nodal voltage magnitudes. Thealgorithm features a two-tier projection where primal and dualvariables are shrunken and expanded. The system operator(indirect aggregator) guides EVs through several iterationsby broadcasting the dual variable associated with the nodalvoltages and the Lagrangian gradient calculated from therecent charge profiles of EVs. Unlike an ordinary primal-dualsubgradient method which suffers from regularization errors,the proposed algorithm converges to optimality without regu-larizing the Lagrangian. However, such an algorithm requiresan accurate network model and knowledge of injections andextractions of real and reactive power at every point in the his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. network, which in practice will always be imprecise, andtherefore real-time control methods to make up for these errorswill be necessary. d) Load regulation with voltage and overload control:
By utilizing a linearized power flow model, the authors in [54]formulate an OP to regulate the charging load of EVs whileminimizing the operational cost. Specifically, a network-awarecharging scheme that respects both voltage and feeder trans-former limits is developed. Since the transformer capacity andnodal voltages couple power flow across buses, a decoupledand decentralized (T2) algorithm is formulated using theADMM and Frank-Wolfe methods. Besides provable conver-gence, the algorithm protects the privacy of users by onlysharing the sum of EV charge profiles with the controlcenter (indirect aggregator) through a communication protocolarranged over a tree graph rooted at the control center. As such,EVs which constitute the tree nodes add their charge profilesto the aggregate charge profiles from the downstream nodesand forward to the parent nodes. Upon receiving the sumof charge schedules, the control center broadcasts the costgradient vector, based on which the EVs reschedule.The authors in [39] present a random access chargingalgorithm to protect the distribution grid from bus congestionand voltage drop. The OP is formulated to maximize thenumber of EVs that can be charged under the given systemcapacity. The underlying system architecture is a decentralized(T2) model, where EVs take charging decisions based on theinformation of load capacities and voltage drops of systembuses published by the control center (indirect aggregator).At every time slot, a set of EVs suspend charging processto provide opportunities to the waiting EVs, thereby ensuresfairness within the implementation. It is worth mentioning thatthe respective algorithm involves no forecasts, and no convexoptimizations – and as such, implementation appears to besimpler than other considered approaches. e) Maximize operational efficiency:
Another importantoperational aspect from the grid operator’s standpoint is bal-ancing the electricity generation and the demand for enhancedoperational efficiency. To this end, the authors in [57] presenta decentralized (T2) and token based IT infrastructure, whichprovides energy as a service via generation and consumptionof tokens of energy. It is comprised of a heuristic algorithm tomaximize the average utilization of generation, while ensuringthat the total amount of power consumed by EVs is lessthan the amount of power allocated for charging the EVs.The practical implementation of such a system requires aperfect and seamless communication infrastructure for thenegotiation of token exchange between the producers andthe consumers of energy. In [58], a game theoretic approachfollowing a decentralized (T2) architecture is proposed tobalance the planned electricity generation in real-time. It is atwo-stage algorithm where EVs and energy storage systemsaim to flatten the load profile by adjusting the residentialload to follow a day ahead energy plan. In the first stage,EV users play a non-cooperative game with mixed strategiesto determine the day ahead anticipated demands that minimizethe electricity costs, based on which the aggregator determinesa plan to generate or purchase electricity for the next day. In the second stage, EV owners play a real-time game toadjust their consumption patterns so as to stay close to thepredicted demands. The implementation of such a schemerequires specific equipment to be installed at the houses, andhence incurs a high capital investment for the EV customers.
2) Aggregator’s Perspective:Manage ancillary services:
If proper incentives areoffered, EV users are likely to actively participate in a mul-titude of ancillary services: frequency regulation [59]–[62],voltage control [63], spinning reserve [64], [65], active andreactive power compensation [66], [67] etc. To manage thevariability of renewable power generation, contribution from alarge number of EVs is required. In a market environment, EVsseeking to contribute to ancillary services could be managedby a third party aggregator.Frequency regulation is a short time scale ancillary servicewhich aims to establish an instantaneous balance between thegeneration and the demand. As such, energy stored in EV bat-teries can be used to fine-tune the frequency and voltage of thegrid by charging them when generation exceeds demand anddischarging them when demand exceeds generation. A numberof charging schemes are proposed to suppress the primaryfrequency fluctuations of the power grid [68]–[70].Liu et al. [70] present a decentralized (T2), V2G controlscheme, where the aggregator estimates the regulation capa-bility of the EV fleet. Whenever the frequency deviation is outof the predefined dead band, EVs with sufficient SoC dischargepower using an adaptive frequency droop control method.A potential drawback of such a method is that it requires a pri-ori analysis of the specification of droop parameters. On thecontrary, the authors in [71] propose a decentralized (T2)regulation algorithm that follows a plug-and-play concept,without requiring such parameterization. It has an indirectaggregator generating a set of virtual price signals to reflectthe deviation of the aggregate EV charge/discharge profilesfrom the day ahead energy schedule derived from [72]. Basedon these signals, EVs compute their schedules to optimize thevirtual cost/income from charging and discharging.The authors in [73] propose a backup battery bank deployedby an aggregator to maintain a stable regulation capacity. Theinteractions between aggregator and EVs in a V2G marketare modelled as a decentralized (T2) game, where the payoffof an EV is interpreted as the payment that an EV receivesfor participating in the frequency regulation service. Basedon the command signal issued by the grid, specifying a powerlevel for regulation, the aggregator computes all possible Nashequilibria, selects one randomly, and then EVs simply followit. However, the authors have not incorporated the EVs’ owncharging requirements into the game model.The authors in [34] develop a V2G scheme for providingdistributed spinning reserve to customers with different reli-ability levels. When a shortage of generation capacity or apower outage happens, customers with lower subscription ofreliability are cut off, and distributed spinning reserve fromEVs is used to provide power to those customers with highersubscription of reliability. The proposed decentralized (T2)scheme consists of two levels of games that are coordinated bythe electricity retail market (indirect aggregator). At the lower his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
NIMALSIRI et al. : SURVEY OF ALGORITHMS FOR DISTRIBUTED CHARGING CONTROL OF EVs IN SMART GRID 9 level is a non-cooperative game that coordinates the chargeschedules based on a specific V2G strategy. At the upperlevel, an evolutionary game is implemented to evolve the EVs’V2G strategies. For each evolving step of the evolutionarygame, the lower level non-cooperative game finds a new NE.Hence, both levels reach equilibrium when the evolutionaryequilibrium is reached. Although a reliability-differentiatedpricing scheme appears very beneficial for realizing DSM,in practice, it is hard to differentiate the delivery of electricityin terms of reliability due to the intrinsic limitations of currentpower systems [74]. As a result, the research direction outlinedin [34] has not received sufficient attention in the recentliterature.Active and reactive power compensation contributes tovoltage regulation, power loss reduction and power factorcorrection [67]. The authors in [66] present a hierarchical (T1)V2G scheme for the active power compensation of EVCSsthat intend to provide active power with minimum incrementalcosts of EVs. The aggregators (EVCS controllers) coordinateusing a task-swap mechanism, such that, for each activecurrent, a single aggregator receives the current measurementinformation of sudden active load change, according to whicha command signal specifying the appropriate active powerto be compensated is distributed to their EVs. In contrast,the authors in [67] present an algorithm for reactive powercompensation of EVs. The objective function of the aggregatoris interpreted as the total insufficiency of reactive powerreservoir, which is to be minimized. The objective functionof an EV is defined as the sum of parking cost, charging cost,and penalty cost (for unscheduled EVs), which is also to beminimized. The resultant multi objective OP is solved usingthe normalized normal constraint method to obtain a set ofwell-distributed pareto optimal solutions. Then a decentral-ized (T2) algorithm based on Lagrangian decomposition isproposed to make the optimization scalable as the number ofEVs grows.
3) EV User’s Perspective:a) Provision of ancillary services:
There is considerableliterature on approaches to involve EVs in ancillary serviceswithout an intermediary, e.g., a third party aggregator. Forexample, the authors in [75] present a decentralized (T1)algorithm where consensus filtering is utilized to acquireconsistent and accurate frequency signals by all the EVs.However, consensus mechanisms often require a large num-ber of iterations before reaching the stopping criterion, andhence take a significantly longer computing time. In contrast,the decentralized (T2) algorithms proposed in [64], [68], [69]facilitate EVs to contribute to frequency regulation and spin-ning reserve according to the frequency deviation at the plug-interminal, which is a signal of supply and demand imbalancein the power grid. The decentralized (T2) scheme proposedin [17] is comprised of two algorithms for load shifting andfrequency regulation, with the later based on a frequencydroop control method. Since the two control algorithms arefunctionally separated by time scale (load shifting on a longtime scale and frequency regulation on a short time scale), theyare combined to balance both objectives. The study in [76]proposes an iterative, decentralized (T2) algorithm for voltage control, where an indirect aggregator broadcasts the voltageon all pilot nodes based on the charge profiles of EVs inthe previous iteration. Accordingly, EVs updates their chargeprofiles to limit their impact on the voltage plan. b) Minimize the charging power losses:
From the EVuser’s standpoint, another objective to consider is the min-imization of power losses caused by the internal resistanceof a battery during charging. The authors in [77] propose adecentralized (T1) scheme to minimize the power losses duringcharging, while satisfying the system constraints. The OPis characterized by a Lagrangian variable called incrementalcost, and the charge rates are determined by exchanging theinformation of incremental cost and available global powercapacity, using a consensus algorithm. A limitation of [77] isthe required initialization procedure during each EV chargecycle. Later, the authors in [78] extended the work to aninitialization-free charge control scheme where EVs start fromany charge power allocation. c) Maximize the EV user convenience:
EV users oftenwish to attain a high level of user convenience in their chargingoperations. A form of an objective function for maximizinguser convenience ismax p i ( t ) N (cid:2) i = T (cid:2) t = w i ( t ) p i ( t ), (4)where w i is a weight factor. The authors in [27] devise aDRC scheme to select the optimal EV subset that maxi-mizes the weighted sum (4), with a weight factor chosento characterize the charging duration and the final SoC ofEVs. The resultant combinatorial, non-convex OP is solvedusing the ADMM method. In the proposed hierarchical (T4)system, the sub-aggregators report the average EV energydemand of their respective groups to the central aggregator,who then completes the update of the dual variable andbroadcasts to the EVs to decide whether they should charge ornot based on a threshold discriminator. In contrast, Malhotra et al. [24] present a DRC scheme with a hierarchical (T5)control architecture to maximize the cumulative user conve-nience characterized by the remaining SoC, remaining time tocharge, and charge rate, while also sharing the limited amountof power available from the grid (global power constraint).Here, sub-aggregators at the substations exchange EV userconvenience values through a consensus algorithm and locallyevaluate the specific threshold control signals to define the setof EVs allowed to charge within the global power constraint.Additionally, the local power constraints of substations areensured by truncating the ordered set of EV user conveniencevalues of each substation. Although the algorithm is shownoptimal for the homogeneous case, it exhibits a very smalloptimality gap for the heterogeneous case.In contrast to maximizing the weighted sum as in (4),another form of an objective function focused on enhancing theEV user convenience is maximizing the charge rates of EVs,such that the desired final SoC is achieved within the shortesttime. The authors in [79] propose a local control method whereEVs are able to act independently without relying on externalcontrol signals to operate. Specifically, each individual EV his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
10 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS maximizes the charge rate while maintaining the service cableloading and the voltage of the customer point of connectionwithin acceptable limits. An additional charge rate constraint isimposed to avoid large variations of the charge rate over con-secutive time steps, for the purpose of prolonging the batteryservice time. However, when compared to the correspondingcentralized control method, the proposed local control methodis not as capable of maintaining network parameters withinthe specified limits, and thus requires larger safety margins. d) Charging fairness:
Classical heuristic charge schedul-ing algorithms ensure various types of fairness criteria, suchas the first come first serve, earliest deadline first, shortest jobfirst, lottery policy [26]. Except for the first come first serve,the other policies require centralized data collection of EVsto decide their ordering, hence can undermine the efficiencyof the algorithm. Depending on the objective function chosen,the solution may provide different notions of fairness: equalaccess fairness, proportional fairness, max-min fairness, etc.Inspired by the bandwidth sharing approach that is usedin communication networks, the authors in [80] develop apacketized, decentralized (T2) charge control approach, wheresharing power among EVs is considered analogous to theproblem of sharing a constrained channel in communicationsystems. All the EVs are assigned with a similar automatonin order to ensure fair and equal access to the feeder capacity.EVs are then charged over multiple short time intervals usingcharge packets that are approved after checking whether theirload could be accommodated into the distribution system. Thealgorithm does not require EVs to report their charge schedulesback, and thus provides benefits over many other schemes byreducing communication overhead significantly.Several charging schemes have been proposed to ensureproportional fairness based on certain priority criteria (e.g.,current SoC, remaining time to charge). The authors in [81]formulate a decentralized (T1) charge control scheme to max-imize the weighted sum of SoC of EVs for the next time step,using Karush-Kuhn-Tucker (KKT) conditions of optimalityand consensus algorithms. Interestingly, by ensuring fairnessin the SoC distribution, EVs attain a reasonable SoC evenin the event of an early departure. Inspired by the conceptof congestion pricing in Internet traffic control, the authorsin [82] propose a charging scheme, where fairness is ensuredbased on the amount that the EVs wish to pay, defined interms of a parameter called willingness-to-pay (WTP). Theobjective function of an EV user is chosen to maximize thedifference of its utility (a non-decreasing logarithmic functionof the EV demand and the WTP value) and the energy cost.An interesting observation made is that as EVs with large WTPvalues finish charging, the price turns cheaper for EVs withsmaller WTP value.Additive increase multiplicative decrease (AIMD) is analgorithm that is suitable for large scale systems where usersjoin and leave frequently. AIMD also exhibits the notion offairness by sharing the available resources fairly among all thesystem entities. Using the AIMD algorithm, the authors in [83]develop a set of decentralized (T2) charge control schemes tomaximize the limited amount of power that can be obtainedfrom the grid. During the additive phase of the algorithm, EVs increase their charge rates by additive factors until theaggregate power demand of EVs reaches the available powercapacity, which is known as a capacity event. Upon detecting acapacity event, the multiplicative decrease phase activates andEVs reduce their charge rates by multiplicative factors deter-mined in a probabilistic manner. Specifically, three scenariosof interest are considered, namely a domestic, a workplace, andan EVCS, with utility functions of equal power sharing, fairpower sharing, and minimum time power-sharing respectively.Parameters of the domestic charging scenario are fine-tunedto assign the same priority to each EV (equal fairness),whereas the parameters of the workplace charging scenarioare fine-tuned to allocate higher charge rates for EVs who arein need of more energy (proportional fairness). Compared tothe algorithms which require extensive communication amongsystem entities, AIMD is proven to be highly efficient as itcan be implemented by EVs without any communication atall, except that of the notification of the capacity event. e) Minimize battery degradation:
In certain distributedcharge-discharge schemes, as in [34], [51], [84], the minimumand maximum SoC are specified to protect the battery fromearly degradation. In several other schemes such as [18],[34], [55], [71], [85], [86], the cost of battery degradation isincluded in the objective function of the OP.
B. Cost Aspects
Here we review cost aspects and associated objective func-tions for distributed algorithmic approaches from the perspec-tive of the (1) grid operator, (2) EV user, and (3) aggregator.
1) Grid Operator’s Perspective:a) Minimize the cost of power operations:
Cost of powergeneration is an important concern of the grid operator. Shao et al. [37] present a bidirectional power control framework tominimize fuel costs and startup-shutdown costs of generators.A hierarchical (T3) framework is developed to model thecooperative power dispatch among the system operator (SO)on the top level, aggregators in the middle level and EVs atthe bottom level. Since the grid side formulation (upstream)and the EVs side formulation (downstream) can be connectedvia the aggregator net power, the system architecture fitsBenders decomposition – a technique that is useful whenthe number of constraints of an OP is considerably high.The SO solves the master problem for determining the netpower of each aggregator that contributes to a minimal overallgeneration cost, while also considering a series of constraintssuch as grid reserve, power balance, transmission capacity,and minimum/maximum aggregator net power. The resultantpower shares of the aggregators and the charge/dischargepowers determined by the EVs are then fine-tuned for severaliterations using approximate benders cuts.In addition to minimizing the generation cost, the algorithmin [17] aims to charge EVs with minimal carbon dioxideemissions, while reducing the dependency of conventionalregulation plants. Here, the grid controller (indirect aggregator)publishes a cheap power trajectory, upon which EVs executea decentralized (T2) algorithm that consists of two parts: gainand SoC deficiency. The former becomes significant when thedue time is short and the power is cheap. The latter ensures that his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
NIMALSIRI et al. : SURVEY OF ALGORITHMS FOR DISTRIBUTED CHARGING CONTROL OF EVs IN SMART GRID 11
EVs with lower SoC receive higher charge rates. In contrast,the OP in [87] is formulated as a multi-objective OP aimedto minimize both the generator costs and the EV chargingcosts. In the proposed hierarchical (T2) system, the SO (centralaggregator) optimizes the system dispatch using the mostrecent charge schedules of EVs and alters the price signal,so that the sub-aggregators reschedule. The negotiation processhappens until neither SO nor sub-aggregators change decisionsbetween two successive iterations. At this point, the systemachieves a socially optimal equilibrium. In the hierarchical(T1) charge-discharge control scheme in [85], the upper-levelaims to minimize the total cost of system operation by jointlydispatching generators and aggregators, and accordingly thelower-level computes the charge-discharge strategies for eachEV following the dispatch instructions from the upper-level. b) Maximize the grid operator revenue:
Stackelberggame (SG) is a type of a non-cooperative game that dealswith multi-level decision making processes of a group offollowers in response to the decision of a leader [22]. Foran energy trading game between the grid operator and EVgroups (EVGs), Tushar et al. [22] model a hierarchical (T2)SG to decide the strategic electricity price that optimizes boththe EV charging cost and the revenue of the grid operatorfrom selling energy. Given the amount of energy requestedby EVGs, the grid operator (leader) chooses an electricityprice to maximize the revenue. Accordingly, EVGs (followers)choose the amount of energy that they wish to purchase inorder to optimize a utility that captures a trade-off between thebenefit from charging and the associated cost. Since the totalamount of energy offered to the set of EVGs is constrainedin the study, EVGs seek a variational equilibrium, which is atype of a generalized-NE (GNE) that is more socially stable.For a given GNE demands of EVGs, the grid chooses anenergy price that maximizes the revenue of the grid. Thegame eventually converges to a socially optimal Stackelbergequilibrium, where EVGs achieve their equilibrium strategiesfor the optimal energy price determined by the grid operator.In [88], a decentralized (T2) charge/discharge control frame-work is proposed to optimize the revenue of a set of microgridsand the charging cost of EVs. Specifically, a dynamic pricingpolicy is proposed to decide the electricity price based on thereal-time supply-demand curve of each microgrid. In response,the charging decisions are made by EVs using a multi-attributedecision process.
2) EV User’s Perspective:Minimize the EV charging costs:
EV users are oftenconsidered as price anticipators who are willing to adjust theircharge profiles according to their impact on the electricityprice. A form of an objective function for minimizing thecharging cost of a group of EVs ismin p i ( t ) T (cid:2) t = N (cid:2) i = c ( t ) p i ( t ), (5)where c ( t ) represents the electricity price, which with respectto RTP is a function of the instantaneous total demand. Theintuition from equation (5) is that the action taken by auser affects the performance of the other users through c ( t ) . In a decentralized charging setup, each EV user wishes toselfishly choose an action which minimizes its individualcharging cost. As such, EV charging can be interpreted as anon-cooperative game among the EV users. If every EV userof the game picks their cost-minimizing strategy, there will bea stable state, known as the NE, where no user can decreasethe cost unilaterally (2). Given the vector of charge schedulesof all the other EVs other than EV i ( p − i ), and assuming that p − i is fixed, the best response strategy of EV i can be definedby min p i f i ( p i ; p − i ), (6)where f i is the payoff function and p i = (cid:3) Tt = p i ( t ) . In thedecentralized (T1) energy scheduling game described in [33],each user computes the best response strategy by solving (6)and announces that to the other users to update their bestresponses accordingly. The update process takes place until nonew schedule is announced by any user. When users simplyfollow what is best for them, the total energy cost monoton-ically decreases in each iteration until the game convergesto the NE. Besides provable convergence, such an algorithmis strategy proof, which means no user benefits from beinguntruthful when broadcasting the charge schedule. Similarly,in [47], a decentralized (T2), non-cooperative and dynamicgame is proposed to coordinate EVs through price-signals thatare broadcasted by an indirect aggregator.For the problem of minimizing the overall energy cost ofa set of EVs controlled by a set of aggregators, the authorsin [13] devise a non-cooperative game that follows a hierar-chical (T5) control architecture. For each potential subgameamong the aggregators, the optimal charge profiles that resultin the NE are calculated using the best response strategies(6). The significance of their study is incorporating two userbehavioral models called expected utility theory and prospecttheory to evaluate the ideal and non-ideal actions of the aggre-gators respectively. In contrast, the authors in [86] propose anon-cooperative game implemented as a decentralized (T2)system, in which the NE is calculated by considering thedistribution of driving patterns and the relationship betweenthe EV demand and its influence on the electricity spot prices.In [89], a strictly convex N-person game in the form of adecentralized (T2) system is developed using a probabilisticmodel of the EV charging patterns. In more detail, a datacenter notifies to the EVs, the mean and variance of thehistorical EV loads, based on which the EV users calculatethe most cost-effective time to start charging their EVs forthat particular day. The game continues for the next day withupdated information from the previous day, and as such, eachday is an iteration of the game seeking the NE state. Mostimportantly, smart chargers tend to learn a better strategy in aprogressive manner. However, all the above-mentioned gametheoretic approaches require a lot of computational overheaddue to the iterative routine. In contrast, Cao et al. [90] proposea heuristic algorithm to minimize the charging costs in aregulated market operated under TOU pricing. Specifically,the authors consider a much realistic scenario, where themaximum EV charging power is different at various SoC his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
12 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS levels. In addition to minimizing the charging costs (day-ahead), the authors in [91] consider minimizing the thermaloverloading of transformers. The combined OP is transferredto a partial Lagrangian problem which is separable betweenfleet operators who coordinate with the Distribution SystemOperator (DSO) in a decentralized (T2) manner. The authorsin [92] propose a hierarchical (T2) control scheme to minimizethe EV charging costs while abiding by substation supplyconstraints. To avoid peak load at the substation transformer,a capacity based tariff scheme is proposed to surcharge loadexcursions exceeding a penalty load threshold.None of the charging schemes mentioned above considerdischarging of EVs. Interestingly, Nguyen and Song proposea decentralized (T2) algorithm to coordinate charge and dis-charge of multiple EVs in a building’s garage. Here, EVsintend to charge and discharge in a way that the total paymentto the building is minimized. Since each EV wants to scheduleits energy profile in order to pay less, a non-cooperative gameis played to select their best strategies (6) independently.In contrast, the authors in [93] propose a decentralized (T1)charge control system that constitutes a retail market layer ofEVs and a set of aggregators who are requested to providecertain amounts of energy from EVs. In response to the pricesannounced by the aggregators, EVs play a multi-stage game tominimize the charge-discharge costs. The NE of the game issought using a consensus-based algorithm, where EVs estimatethe average charge available in their immediate neighborhoodsand decide the amount of energy to trade.
3) Aggregator’s Perspective:a) Maximize the aggregator profit:
In the real world,an aggregator is a profit-seeking entity with a large customerbase. Oftentimes, aggregators purchase energy at wholesaleprices through long term bilateral contracts or by participat-ing in the day ahead electricity market based on forecastedelectricity prices [94]. The OP for maximizing profits earnedfrom selling the purchased electricity ismax p i ( t ) J (cid:2) j = N j (cid:2) i = T (cid:2) t = ( c ret ( t ) − c pur ( t ) ) p i ( t ), (7)where i , N j , c ret , and c pur denote EV i , number of EVs ofaggregator j , electricity retail price, and purchase price respec-tively. For charging EVs in multiple local communities withmultifamily dwellings, Qi et al. [36] propose a hierarchical(T2) scheme where a primary distribution transformer (centralaggregator) serves multiple parking decks (sub-aggregators)that purchase electricity from the utility at TOU rates and sellit to the customers at retail prices. In addition to maximizingthe revenue of the sub-aggregators, the unfulfilled chargingdemands are penalized to minimize the loss of customergoodwill. The transformer capacity constraints are enforced byapplying Lagrangian relaxation and including them as penaltyterms in the original objective function. The resultant OP issolved using the distributed subgradient method with respectto each parking deck. In detail, the sub-aggregators constantlyreport their projected power consumption profiles to the centralaggregator, who then updates the Lagrangian multipliers andbroadcasts to the charging decks back. Interestingly, only the aggregate charging demand of each parking deck is required tobe publicized, hence the algorithm does not disclose individualEV charging information to the central aggregator.Xu et al. [20] present a hierarchical (T1) charging con-trol framework to maximize the profit of the aggregator byminimizing the energy purchase costs under TOU tariffs.A three-step procedure is carried out wherein the first stepeach aggregator reports to the DSO the aggregate powerboundaries based on customer charging requirements and localtransformer capacity limit. In the second step, the DSO decidesthe optimal power share of each aggregator. Then in the finalstep, each aggregator allocates charge rates to the EVs in theirgroups, using a heuristic method which chooses to dispatchpower in the order of the desired SOC and the remainingparking duration of EVs. Most importantly, heuristic powerallocation algorithms are often fast to compute, lending them-selves to real-time operation solutions for large populationsof EVs. In [95], a decentralized (T2) charging scheme isproposed, where EVs respond to the distribution locationalmarginal prices that are published by the aggregators, whoaim to receive incentives for preventing congestion inducedby the EV loads.Setting an appropriate electricity price quote, especially atEVCSs has several trade-offs. A very high rate may turn awaythe customers and reduce the revenue of EVCS, whereas a verylow rate may overwhelm the EVCS without earning a properrevenue. Consequently, this leads to a price competition amongEVCSs under different ownership. The authors in [96] proposea decentralized (T2) framework that consists of a hierarchicalgame. At the upper level, a non-cooperative game models thecompetition between EVCSs who aim to maximize the profitsby buying power at a lower price and selling them at a higherprice. Based on those prices obtained from the non-cooperativegame, multiple evolutionary games take place at the lowerlevel to evolve EVs’ strategies in choosing EVCSs.EVCSs are also capable of producing their own electricityby installing renewable power generators (RPGs) and therebyearn revenue from selling electricity to both the grid andthe EVs. The authors in [97] propose a decentralized (T2),supermodular, non-cooperative game to coordinate multipleEVCSs that carefully select electricity prices to maximize theirrevenues. If the amount of electricity generated by the RPGsis insufficient to satisfy the demand of customers, then theEVCS buys electricity from the grid at retail price. If theEVCS has excess electricity, it is sold to the grid at wholesaleprice. In the proposed game, a unique NE among EVCSs isachieved by playing the best response strategies. Given thatthe infrastructure cost incurred is not extremely high, adoptingRPGs at EVCSs is considered very beneficial. b) Minimize the costs of power supply: In certainschemes proposed in the literature, minimizing the costs ofsupplying power is considered as an objective from the aggre-gator perspective. For example, the authors in [86] developa decentralized (T2) algorithm to minimize the operationalcost of a utility (aggregator) and the charging cost plusbattery degradation cost of the EVs, using the ADMM method.The problem is initially formulated as a joint OP with atrade-off parameter between the dual objective functions. It is his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
NIMALSIRI et al. : SURVEY OF ALGORITHMS FOR DISTRIBUTED CHARGING CONTROL OF EVs IN SMART GRID 13 then converted to a standard exchange OP with EVs andthe aggregator considered as agents with coupled objectivefunctions. At each time step, the aggregator solves its local OPand propagates incentive signals, upon which EVs scheduletheir charging jobs. In [98], a decentralized charging schemeis proposed to minimize the utility’s cost related to activepower. Specifically, a reduction of the EV charging cost isoffered by the utility as an added incentive for the EV owners.By leveraging a time-dependent extension of the well knownoptimal power flow (OPF) problem, the authors first formulatea joint OPF-EV charging control problem, which is then solvedusing a valley filling bisection algorithm that is performedby EVs in a decentralized (T2) manner. However, the pro-posed algorithm employs time-invariant prices, therefore it isnot applicable for a time-varying electricity market. In [19],a hierarchical (T3) scheme is proposed to minimize the costsfor electricity supply. It comprises a set of fleet agents (FAs),each of whom manages a number of contracted EVs throughthree main steps. In the first step, the local EV constraints areaggregated towards the FA, and in the second step, a collectivecharging plan for the EV fleet is determined using dynamicprogramming. In the final step, the FA propagates a controlsignal, based on which EVs locally determine their chargeschedules using a heuristic function. It is interesting to notethat the proposed scheme ensures a constant execution time interms of vertical scalability (independent of the EV fleet size).
C. Uncertain Aspects of EV Charging Control Optimization
Deterministic OPs assume that the data for a problem isknown accurately in advance. However, for many practicalproblems like EV charging, certain information (e.g., powerdemand, power generation, plug-in and plug-out times of EVs,electricity prices) cannot be known with certainty. Althoughthere is a rich literature on distributed EV charging control,not all of them have considered such uncertain aspects. In areal-world implementation, algorithms that do not adapt tothese uncertain aspects are unlikely to be successful. In thissection, we review how certain distributed charging schemeshave managed uncertainties that are depicted in Fig. 5.Many of the charge scheduling algorithms proposed in theliterature do not consider the mobility aspects of EVs, instead,they treat EVs as static loads with fixed spatio-temporalparameters (e.g., [27], [73], [82], [94]). In contrast, a mobility-aware
EV charge scheduling scheme adapts to various tempo-ral variations, such as random arrivals; unplanned departures;and spatial variations that include charging locations, avail-ability of charging slots at EVCSs, EVs’ locations at differentpoints in time along with their varying power requirementsacross different locations, etc. In more detail, an EV mayplug-in at any random time of the day, and may plug-outbefore the designated deadline. Having these uncertaintiespresent, it is not possible to follow the original charge scheduleuntil the end of the scheduled time horizon. In order todeal with the random behaviors of EVs, many of the pro-posed distributed charge scheduling schemes repeat their staticalgorithm at the beginning of every time slot with updatedinformation [19], [21]. For instance, in the hierarchical (T3)
Fig. 5. Uncertain aspects of EV charging control problems. charging scheme [19], the adaptability to a dynamic environ-ment is achieved through continuous repetition of the threesteps of the algorithm at each time step. In contrast, the authorsin [56] propose an event driven approach, which triggers thesystem to recompute charge sequences when one or more EVsplug-in or one or more of connected EVs plug-out before theirdesignated deadlines. The authors in [99] model a stochasticgame that embeds a Markov decision process, defined in termsof a state transition matrix that takes into consideration therandomness of EV arrivals, departures, and charging demand.Another type of an optimization method that is often usedto tackle EV mobility issue is moving (receding) horizonoptimization [18], [20]. This approach first finds charge sched-ules of EVs for a finite time horizon which begins at thecurrent time and ends at some future time (e.g., latest departuretime among all the EVs). The charge rates that are foundfor the current time step are executed in real, while the restare discarded. When the next time step arrives, the controltime horizon is shifted forward by one time step, and theoptimization is repeated with updated information. Other thanthe aforementioned techniques, probability distributions canalso be employed to tackle the uncertainties of EV chargingwith respect to the EV arrival and departure times.An EV user may need to charge the battery at any locationduring its journey. Given the EV’s route information, averagespeed, charging specification and location of the chargingstations, the authors in [100] model a mobility-aware frame-work where a set of aggregators (charging service providers),each of which controls a set of charging stations, collaborateamong themselves to schedule EVs that are subscribed toeach aggregator in any of the charging stations of its ownor others. It is interesting to note that the proposed frameworkis a dynamic version of the hierarchical (T5) architecture sinceEVs are allowed to move between aggregators.The non-EV demand of a community often follows a trend,hence most papers consider non-EV load as deterministicand predictable ahead of time using methods like regression,time-series methods, machine learning, etc. The algorithmsin [18], [92] use a similar day approach, where the loadsfrom recent days with identical EV user behaviors and weatherconditions are averaged out. Using forecasted non-EV loadapproximations eliminates the requirement of real-time com-munication and synchronization among system entities. Nev-ertheless, forecasted information is vulnerable to errors. Thus,it is likely that there is a discrepancy between the forecastedload and the actual power consumption. A technique thatcan possibly be applied to cope with demand uncertainty isrecomputing the charge schedules at each new time step, withreal-time non-EV load data. Alternatively, the decentralized his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
14 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS (T2) charging scheme in [48] performs a charging adjustmentmechanism to shift the charging time periods of EVs withrespect to the deviation of the real-time non-EV load profilefrom the forecasted one.An online charge control scheme proposed in [101] controlsEV charging in each time slot entirely based on the currentinformation, without relying on any prediction of future infor-mation. Therefore, the algorithm is robust under any EV andnon-EV demand profile. It employs an event-driven discretetime model, where an event is defined by an EV arrival,an EV departure, or a change in the non-EV load profile.At any time, the scheduler computes charge sequences usingthe information that is available so far (charge profiles ofEVs already scheduled and the past and current non-EV load)and keeps the schedules unchanged until the occurrence ofthe next event. As opposed to the traditional time slottedmodels where lengths of time slots are fixed, the time intervalsof the proposed algorithm are defined by the occurrence ofevents, such that neither the non-EV load nor the numberof EVs changes in the middle of a time interval. By doingso, the algorithm is more capable of capturing the systemdynamics, which is not achievable through traditional timeslotted models unless the time slots are set infinitely small.The daily and seasonal variability of renewable energygeneration contribute to energy uncertainty. The impact ofenergy uncertainty is particularly high if the system has a largenumber of small scale distributed generators, such as wind andsolar. In the decentralized (T2) algorithm proposed in [17],EV charge rates are regulated to mitigate the uncertainties ofelectric power generation from a wind farm. The decentralized(T2) algorithm presented in [45] schedules deferrable (EV)loads to compensate for the random fluctuations in renew-able generation and uncertain predictions about future powerdemands, which are modeled as causal filters with randomdeviations around their expectation. The real-time versionof the particular algorithm shifts EV loads to periods withhigh renewable generation using information that is currentlyavailable and the updated predictions. The hierarchical (T2)SG formulated in [22] is later extended to a discrete timefeedback SG in order to accommodate the time-varying natureof the amount of energy available from the grid. Further,in [83], the AIMD algorithm is exploited to assign chargerates to the EVs in almost real-time while accommodating thetime varying nature of both the available power capacity andthe number of EVs being charged. Another technique that ispossible – although not commonly applied in the distributedEV charging context – is the Monte Carlo simulation methodwhere the energy uncertainties can be modeled as differentprobability distributions.Network uncertainty is generally related to the time-varyingthermal loading sensitivities of grid components. For exam-ple, transformers and distribution feeders are sensitive totemperature and their capacities may be lower than con-tinuous rated values on a hot day [3]. Grid components(e.g., transmission and distribution assets) may sometimesmalfunction beyond a certain temperature threshold, hencetheir thermal capacities are required to be considered whenmodeling network-aware charging schemes. The thermal constraints of distribution feeders are captured in [3]. Forcharging control of EVs served by a single temperature-constrained substation transformer, the authors in [102] presenta decentralized (T2), incentive-based and price-coordinateddemand scheduling scheme that determines EV charge sched-ules using a dual-ascent algorithm, embedded in a predictivecontrol scheme to introduce robustness against disturbances.In an electricity market, price fluctuations are often a con-sequence of power demand fluctuations, thus price uncertaintycorrelates to the demand uncertainty. For example, with RTPrates, users are charged less during the valley periods and moreduring the peak periods. However, if users cooperate to achievea flat load curve, then everyone will be charged by a nearlyequal, and fair electricity rate, which in turn will mitigate theprice uncertainty. As such, coordination of EV charging createsan opportunity for the community to save money together.Table I summarizes several important features of distrib-uted EV charging schemes reviewed in this paper.
Online algorithms compute the EV charge schedules progressively,without perfect knowledge of inputs available from the start(Section III-A). The
VRC characteristic allows for chargingat variable rates (Section III-B).
Pricing scheme indicatesthe type of pricing (flat rates, day-ahead, RTP, TOU orcustomized) used in the charging scheme, if any (Section III-D).
Mobility aware charging considers the uncertainty ofEV behaviour (e.g., arrival/departure times) (Section V-C),while network aware charging considers the distribution net-work constraints (Section V-A1).
Iterative algorithms involverepeated computation of the charge profiles, until meeting aspecific stopping criterion. Further, it is indicated whether anyforecast data is used for the computation and whether V2Goperations are supported by the charging scheme.VI. R
ESEARCH D IRECTIONS
In our survey of distributed charging schemes, we havepresented Table I, which provides a number of useful insights.With respect to the algorithmic techniques involved, manyof the distributed charging schemes require iterative calcu-lation of the charge schedules. The computation time ofsuch algorithms is highly affected by the time taken byan EV/aggregator to find the charge schedule/s in a singleiteration, and the number of iterations is dependent on thenumber of participating EVs/aggregators. As such, algorithmsemploying less complex optimization methods to recomputethe charge schedules are more practical for a large EV popu-lation. Further, many of the distributed charging schemes aredriven by control signals that rely on a perfect communicationmedium. Preferable algorithms for real-world applicationsare resilient to network latency and other potential networkfailures, and do not require large investments for extensivebidirectional communications. Moreover, most of the revieweddistributed algorithms commonly utilize forecast data, withprecise forecasting techniques deemed critical for real-worldimplementation.It is evident that the problem of load regulation (loadflattening) is well investigated in many distributed charg-ing schemes related to operation aspects, however veryfew of them incorporate both network-awareness and his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
NIMALSIRI et al. : SURVEY OF ALGORITHMS FOR DISTRIBUTED CHARGING CONTROL OF EVs IN SMART GRID 15
TABLE IC
HARACTERISTICS OF
EV C
HARGING C ONTROL S CHEMES his article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
16 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS mobility-awareness. In the literature for distributed EV charg-ing, algorithms for minimizing network energy losses arenot investigated satisfactorily. It is also noticeable that manypapers on distributed V2G frameworks consider only oneoperational objective, either regulating load or regulating fre-quency, but not both. Hence, extensions to existing distrib-uted V2G frameworks to achieve more than one operationalobjective will potentially have significant impact. Moreover,distributed EV charging schemes that consider OPs withmultiple operational objectives are limited to the perspectiveof a single entity (e.g., they do not consider overload controland voltage control while maximizing EV user convenience).With respect to the cost aspects of EV charging control, it canbe realized that distributed charging control schemes focusedon enhancing the system-wide social welfare through costoptimization of multiple parties (EV users, grid operators,aggregators) are very limited.Distributed charging schemes that consider combinationsof multiple objectives with respect to both the operationaland cost aspects (e.g., maximizing user convenience andminimizing charging costs) are yet to be explored further.Another potential topic of interest is to study OPs wheredifferent individuals of the same entity have distinct objectivefunctions, e.g., distributed coordination of several aggregatorswhere certain aggregators aim to minimize the charging costson behalf of their EV customers and the other aggregatorsaim to maximize their profit from selling energy to the EVcustomers. In addition, future research can focus on developingdistributed EV charging algorithms to accommodate variousuncertain aspects discussed in Section V-C.Many of the existing distributed EV charge control schemesexploit simpler and linear battery models. However, thosebattery models are not accurate in practice, since the realinternal power of the battery is a nonlinear function of theexternal power, due to internal power losses. Hence, distributedEV charge control schemes involving realistic and accuratebattery models [12] are required. Moreover, the considerationof transient process of the batteries and variations in chargingefficiencies is needed to improve future practical applications.The traditional electric grid transports electricity overlong distances and through complex electricity transporta-tion routes. Alternatively, EVs can obtain electricity fromother EVs through vehicle-to-vehicle (V2V) power exchange.For example, in parking lots or EVCSs, EVs with V2Gcapability can exchange or trade electricity in a localizedpeer-to-peer (P2P) manner [106]. Formulation of decentral-ized algorithmic approaches for supporting demand responsethrough P2P transaction systems is another research directionof growing interest. In addition, blockchain-based, decentral-ized charge-discharge schemes (e.g., [107]) are preferable formanaging secured and distributed energy transactions in a V2Gand V2V market without reliance on a third party aggregator.VII. C
ONCLUSION
A distributed control paradigm, in contrast to a central-ized approach, addresses numerous challenges (e.g., com-putational and communication challenges) in coordinating alarge population of EVs. In this paper, we have presented a comprehensive survey of distributed EV charge controlalgorithms that are compatible with decentralized and hier-archical control architectures. First, we have classified OPsfor EV charging control with respect to operational aspectsand cost aspects. Under each category, we have reviewedthe state-of-the-art distributed charge control schemes fromthe perspectives of the grid operator, the EV user, and theaggregator.From the perspective of the grid operator, we have reviewednumerous distributed algorithms for load regulation, conges-tion management, improved efficiency, maximized revenue andminimized power generation and supply costs. With respectto the EV user, we have reviewed distributed algorithms forimproved user convenience, provision of ancillary services,minimized charging losses, lower EV charging costs, and therelative fairness of different charging approaches. In consid-ering the aggregator perspective, distributed charge controlschemes with respect to managing ancillary services, maxi-mizing the revenue, and minimizing the power supply costsare also reviewed. A crucial aspect of any EV charge controlsystem is uncertainty. Thus, we have reviewed numerousalgorithms that have been proposed to tackle various uncertainaspects of EV charging. Finally we have identified severalresearch directions with respect to distributed EV chargingcontrol. R
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Nanduni I. Nimalsiri received the B.Sc.Eng. degree(Hons.) in computer science and engineering fromthe University of Moratuwa, Moratuwa, Sri Lanka.She is currently pursuing the Ph.D. degree in engi-neering and computer science, majoring in engineer-ing, with the Research School of Engineering, TheAustralian National University (ANU), Canberra,ACT, Australia. She is also a Research Studentwith Data61, CSIRO. Her current research interestsinclude distributed control and optimization of EVcharging in smart grid.
Chathurika P. Mediwaththe received the B.Sc.degree (Hons.) in electrical and electronic engineer-ing from the University of Peradeniya, Sri Lanka,and the Ph.D. degree in electrical engineering fromthe University of New South Wales, Sydney, NSW,Australia, in 2017. She is currently a ResearchFellow with the Research School of Electrical,Energy and Materials Engineering (RSEEME) andthe Battery Storage and Grid Integration Program,The Australian National University, Australia. Herresearch interests include electricity demand-sidemanagement, renewable energy integration into distribution power networks,game theory and optimization for resource allocation in distributed networks,and machine learning.
Elizabeth L. Ratnam received the B.Eng. degree(Hons.) and the Ph.D. degree from The Universityof Newcastle, Australia, all in electrical engineering,in 2006 and 2016, respectively. She subsequentlyheld post-doctoral research positions with the Centerfor Energy Research, University of California atSan Diego, and with the California Institute forEnergy and Environment, University of Californiaat Berkeley. From 2001 to 2012, she held variouspositions at Ausgrid, a utility that operates one of thelargest electricity distribution networks in Australia.She currently holds a Future Engineering Research Leader (FERL) Fellowshipfrom The Australian National University (ANU). She joined the ResearchSchool of Engineering, ANU, as a Research Fellow and a Lecturer in 2018.Her research interests include applications of optimization and control theoryto power distribution networks.
Marnie Shaw received the B.Sc. (Hons.) and Ph.D.degrees from the School of Physics, The Universityof Melbourne, Melbourne, VIC, Australia, in 1999and 2003, respectively. She was the Head of DataAnalysis at Descartes Therapeutics Inc., Boston, anInstructor at Harvard University, and a Scientistat the University of Heidelberg, Germany. She iscurrently a Research Leader of the Battery Storageand Grid Integration Program with the AustralianNational University and the Convenor of the EnergyEfficiency Research Cluster at the ANU EnergyChange Institute. Her research interests lie in applying data analytics andmachine learning to a range of data-rich problems, including the integrationof renewable energy into the electricity grid.
David B. Smith received the B.E. degree in electri-cal engineering from the University of New SouthWales, Sydney, NSW, Australia, in 1997, and theM.E. (research) and Ph.D. degrees in telecommu-nications engineering from the University of Tech-nology, Sydney, in 2001 and 2004, respectively.Since 2004, he has been with National Informationand Communications Technology Australia (NICTA;incorporated into Data61 of CSIRO in 2016) andThe Australian National University (ANU), Can-berra, ACT, Australia. He is currently a PrincipalResearch Scientist with Data61, CSIRO, and an Adjunct Fellow with ANU.He has a variety of industry experience in electrical and telecommunicationsengineering. He has published over 150 technical refereed articles. His currentresearch interests include wireless body area networks, game theory fordistributed signal processing, disaster tolerant networks, 5G networks, theIoT, distributed optimization for smart grid, electric vehicles, and privacyfor networks. He has made various contributions to the IEEE standardizationactivity in personal area networks. He was a recipient of four conference BestPaper Awards. He is an Area Editor of
IET Smart Grid and has served on thetechnical program committees for several leading international conferences inthe fields of communications and networks.