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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

arXiv:1911.06500v1eess.SY

TL;DR

The expected proliferation of EVs may threaten secure and economical grid operation through increased electricity demand, creating a need for coordinated charging control. This paper surveys distributed EV charging algorithms across operational and cost objectives, stakeholder perspectives, architectures, and uncertainties. It concludes that distributed charging research spans diverse grid, aggregator, and user objectives, while realistic battery models and uncertainty handling remain important directions.

  • Problem

    Large EV populations can create grid congestion and peak-load problems, motivating charging coordination strategies that address uncertain real-world conditions.

  • Method

    The paper surveys distributed EV charging algorithms, classifies optimization problems by operational and cost aspects, and analyzes decentralized and hierarchical schemes across three stakeholder perspectives.

  • Results

    The review covers distributed algorithms for grid regulation, congestion, efficiency, revenue, user costs and convenience, ancillary services, fairness, and uncertainty management.

  • Takeaways & Limitations

    Distributed charging control provides a structured way to study EV scheduling across grid operators, aggregators, and users while accounting for uncertainty.

Abstract

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Electric vehicles (EVs) are an eco-friendly alternative to vehicles with internal combustion engines. Despite their environmental benefits, the massive electricity demand imposed by the anticipated proliferation of EVs could jeopardize the secure and economic operation of the power grid. Hence, proper strategies for charging coordination will be indispensable to the future power grid. Coordinated EV charging schemes can be implemented as centralized, decentralized, and hierarchical systems, with the last two, referred to as distributed charging control systems. This paper reviews the recent literature of distributed charging control schemes, where the computations are distributed across multiple EVs and/or aggregators. First, we categorize optimization problems for EV charging in terms of operational aspects and cost aspects. Then under each category, we provide a comprehensive discussion on algorithms for distributed EV charge scheduling, considering the perspectives of the grid operator, the aggregator, and the EV user. We also discuss how certain algorithms proposed in the literature cope with various uncertainties inherent to distributed EV charging control problems. Finally, we outline several research directions that require further attention.

I. INTRODUCTION

The anticipated growth of EVs could create major grid congestion and peak-load problems, motivating coordinated smart charging. This survey focuses on distributed charging schemes and classifies their algorithms, architectures, objectives, and treatment of uncertainty.

  • Millions of simultaneously charging EVs could create new peak-load events or compound existing ones.
  • Smart charging can improve grid utilization and limit network expansion, while distributed algorithms reduce centralized computation and communication burdens.
  • Distributed control divides processing across several entities, allowing each agent to solve a smaller problem while retaining partial control over charge schedules.
  • The survey reviews distributed charging algorithms, distinguishes decentralized and hierarchical architectures, classifies optimization problems, and assesses uncertainty management.
  • The review considers charging objectives from the perspectives of grid operators, aggregators, and EV users.
  • EV charging control involves bidirectional G2V and V2G power flows, while aggregators mediate interactions between EVs, the grid, and electricity markets.

III. PROPERTIES OF EV CHARGING CONTROL SCHEMES

EV charging control schemes differ in whether they operate once or recursively, and in whether charging rates are continuously variable or discrete. These choices affect responsiveness, equipment requirements, and scheduling variables.

  • A. One-Time, Open-Loop Versus Recursive Closed-Loop Control: One-time open-loop strategies calculate schedules once from predicted system operation and assume advance knowledge of EV scheduling.
  • A. One-Time, Open-Loop Versus Recursive Closed-Loop Control: Recursive closed-loop strategies repeatedly use feedback measurements, enabling them to handle uncertainties such as EV mobility.
  • B. Variable-Rate Versus Discrete-Rate Charging: Residential charging commonly uses discrete rates because simple on-off chargers cost less than equipment needed to modulate variable power.
  • B. Variable-Rate Versus Discrete-Rate Charging: Variable-rate charging selects charge rates at each grid-connected time instant, whereas discrete-rate charging restricts rates through charger or battery maximum output.
  • B. Variable-Rate Versus Discrete-Rate Charging: Uninterrupted discrete-rate charging chooses EV start times, while interrupted binary charging adds decisions about when charging is active.

C. Homogeneous Versus Heterogeneous EV Specifications

Practical EV charging control must account for heterogeneous vehicle specifications and user preferences. Centralized architectures can exploit complete information but face privacy, failure, scalability, and infrastructure challenges.

  • C. Homogeneous Versus Heterogeneous EV Specifications: Algorithms designed for homogeneous EV populations may not perform practically without heterogeneous charge durations, charge rates, and user preferences.
  • A. Centralized Control Architecture: Hierarchical control arranges aggregators and EVs in a tree, allowing direct or indirect aggregator coordination.
  • A. Centralized Control Architecture: A centralized aggregator collects all EV requirements, solves an optimization problem, and communicates optimized charge schedules to EV owners.
  • A. Centralized Control Architecture: Centralized schemes can produce optimal solutions with complete system information but require EV owners to relinquish some scheduling autonomy.
  • A. Centralized Control Architecture: Centralized control may expose charging information, create a single point of failure, and become impractical as planning horizons and connected-EV populations grow.

B. Decentralized Control Architecture

Decentralized architectures distribute computation among EVs or aggregators, trading centralized information and optimality for scalability and resilience. Their communication structures determine overhead, coordination, and failure behavior.

  • B. Decentralized Control Architecture: Decentralized systems assign each EV a small individual problem, but incomplete information can prevent globally optimal charging regimes.
  • B. Decentralized Control Architecture: Type 1 is center-free: EVs repeatedly exchange scheduling information and adjust local schedules until reaching global equilibrium.
  • B. Decentralized Control Architecture: Type 1 communication overhead can become large as the EV population grows because EVs continuously communicate with one another.
  • B. Decentralized Control Architecture: Type 2 introduces an indirect aggregator that gathers information and broadcasts coordination signals, reducing large-scale communication requirements.
  • B. Decentralized Control Architecture: Hierarchical systems distribute computation across aggregators and EVs, reduce network-wide communication, and preserve decentralized EV behavior in some architectures.
  • B. Decentralized Control Architecture: Hierarchical designs can remain vulnerable to single points of failure, although inter-aggregator paths can improve resilience to communication-link failures.

A. Operation Aspects

Operation-focused distributed charging schemes address grid loading, congestion, voltage, and generation-demand balance through decentralized and related architectures.

  • Load regulation: Load flattening fills overnight valleys and reduces peak-related infrastructure stress and generator ramping.The aggregate influence of an EV fleet can substantially affect load profiles.
  • Load regulation: Iterative decentralized schemes use price-like signals, aggregate demand, or game-theoretic updates to coordinate EV charge profiles.Some approaches converge to optimality for homogeneous and heterogeneous fleets, while others use non-cooperative games or dynamic programming.
  • Load regulation: Non-iterative sequential scheduling can reduce aggregate-load variance and peak demand, avoiding the potentially long convergence of iterative routines.The sequential approach schedules one EV at a time under a decentralized model.
  • Network-aware charging: Network-aware schemes incorporate transformer, feeder, branch, and voltage constraints to limit congestion and costly network expansion.Methods include gradient projection, primal-dual optimization, dual decomposition, and shrunken-primal-dual subgradient algorithms.
  • Network-aware charging: Overload-control methods are effective, with primal gradient projection converging faster and primal-dual control performing better on overload control.The gradient-projection method requires a system-dependent upper bound on step size; the primal-dual method does not.
  • Operational efficiency: Other operational objectives include maximizing generation utilization and balancing planned generation with demand through token-based and game-theoretic decentralized schemes.The token-based approach requires seamless communication for producer-consumer negotiation.

2) Aggregator’s Perspective:

From the aggregator’s perspective, distributed EV control can support ancillary services, including frequency regulation, spinning reserve, and active or reactive power compensation.

  • Provision of ancillary services: EV batteries can provide frequency regulation by charging during generation surplus and discharging during generation shortfall.Distributed schemes address frequency fluctuations using frequency signals, droop control, or game-based coordination.
  • Provision of ancillary services: V2G control can estimate fleet regulation capability and activate discharge from EVs with sufficient SoC when frequency leaves a predefined dead band.Adaptive frequency droop control is used, but droop parameters require prior specification analysis.
  • Provision of ancillary services: Distributed spinning reserve can prioritize customers with higher reliability subscriptions during generation shortages or outages.The scheme uses two coordinated game levels for EV V2G strategies and charge schedules.
  • Provision of ancillary services: Active and reactive power compensation can support voltage regulation, reduce power losses, and correct power factor.A hierarchical V2G scheme coordinates aggregators through task swapping for active-power compensation.

3) EV User’s Perspective:

EV-user-oriented distributed charging schemes target fair access, lower charging losses, user convenience, battery protection, and autonomous operation within system constraints.

  • Minimize charging power losses: Consensus-based decentralized control can minimize charging losses while satisfying system constraints through incremental-cost and capacity information exchange.An initialization-free extension allows EVs to start from any charge-power allocation.
  • Maximize EV user convenience: User-convenience objectives include maximizing weighted SoC outcomes or charging rates to reach a desired final SoC quickly.Hierarchical ADMM selects an EV subset using weights tied to charging duration and final SoC.
  • Maximize EV user convenience: Local control lets each EV maximize its charge rate while maintaining service-cable loading, connection-point voltage, and charge-rate variation limits.Compared with centralized control, the local method is less capable of maintaining network parameters within specified limits.
  • Charging fairness: Fairness schemes use priority criteria, consensus, packetized access, or AIMD to distribute limited feeder or grid capacity among EVs.AIMD increases charge rates until a capacity event, then applies probabilistic multiplicative decreases across domestic, workplace, and EVCS settings.
  • Minimize battery degradation: Battery degradation is addressed by specifying SoC bounds or including degradation cost in distributed charge-discharge objectives.The surveyed schemes use both explicit protection constraints and objective-function penalties.

B. Cost Aspects

The survey organizes cost-oriented distributed charging objectives by stakeholder: grid operator, EV user, and aggregator.

  • Cost aspects are reviewed from the perspectives of the grid operator, EV user, and aggregator.

1) Grid Operator’s Perspective:

From the grid operator’s perspective, distributed EV charging schemes address operational costs, emissions, regulation needs, and revenue through hierarchical coordination, incentives, and strategic pricing.

  • Minimize the cost of power operations: Hierarchical control can coordinate system operators, aggregators, and EVs to minimize generator fuel and startup-shutdown costs.The reviewed framework uses a bidirectional power-control structure with the system operator at the top, aggregators in the middle, and EVs at the bottom.
  • Minimize the cost of power operations: Some schemes jointly reduce generation costs, carbon dioxide emissions, and dependence on conventional regulation plants through decentralized EV scheduling.A grid controller publishes a cheap power trajectory, while EVs use gain and state-of-charge deficiency terms to determine charging behavior.
  • Minimize the cost of power operations: Hierarchical negotiation can jointly minimize generator and EV charging costs by iteratively changing system dispatch and price signals.The system operator uses recent EV schedules, modifies the price signal, and continues negotiation until decisions stabilize.
  • Maximize the grid operator revenue: A hierarchical Stackelberg game sets electricity prices to balance EV charging costs with grid-operator revenue from energy sales.EV groups act as followers responding to the grid operator’s strategic pricing decision.

2) EV User’s Perspective:

From the EV user’s perspective, distributed charging is modeled around individual or group cost minimization, often using non-cooperative games and best-response updates under network and operational constraints.

  • Minimize the EV charging costs: EV users may minimize charging costs by adjusting their charge profiles in response to electricity prices tied to instantaneous total demand.Under real-time pricing, each user’s action affects other users through the price function.
  • Minimize the EV charging costs: In decentralized charging, each EV chooses an individually cost-minimizing action, producing a Nash equilibrium where no user can reduce cost unilaterally.The game uses other EVs’ schedules as given when defining each EV’s best-response strategy.
  • Minimize the EV charging costs: Best-response scheduling repeatedly exchanges users’ preferred schedules until no new schedule is announced, while total energy cost decreases monotonically.The reviewed algorithm is described as convergent and strategy proof, so users do not benefit from untruthful schedule broadcasts.
  • Minimize the EV charging costs: A hierarchical aggregator game can compute equilibrium charge profiles while incorporating expected utility theory and prospect theory as behavioral models.The formulation targets the overall energy cost of EVs controlled by multiple aggregators.
  • Minimize the EV charging costs: Other distributed formulations jointly minimize charging costs and transformer thermal overload while satisfying substation supply constraints.One approach uses a separable partial Lagrangian coordinated between fleet operators and the distribution system operator.
  • Minimize the EV charging costs: Some decentralized schemes coordinate both charging and discharging by having EVs independently select payment-minimizing energy profiles.The resulting interaction is modeled as a non-cooperative game among EVs in a building garage.

3) Aggregator’s Perspective:

From the aggregator’s perspective, distributed charging schemes optimize profit or supply costs while coordinating customer demand, transformer limits, incentives, and competition among charging-service providers.

  • Maximize the aggregator profit: Aggregators can maximize profit by minimizing energy purchase costs under time-of-use tariffs and coordinating aggregate power with the distribution system operator.The reviewed three-step procedure reports aggregate power boundaries, assigns optimal power shares, and then lets aggregators allocate charging.
  • Maximize the aggregator profit: A hierarchical transformer-and-parking-deck structure lets sub-aggregators buy at time-of-use rates, sell at retail prices, and penalize unfulfilled demand.The central aggregator is a primary distribution transformer serving multiple parking decks.
  • Maximize the aggregator profit: Publishing each parking deck’s aggregate demand avoids disclosing individual EV charging information to the central aggregator.The scheme therefore coordinates using aggregate rather than vehicle-level charging information.
  • Maximize the aggregator profit: Charging-service providers face a pricing trade-off: high rates may reduce customers, whereas low rates may overload the station without adequate revenue.This trade-off motivates decentralized hierarchical games for price competition among EV charging stations.
  • Maximize the aggregator profit: EV charging stations with renewable generators can use a decentralized supermodular game to select electricity prices and maximize revenue from grid and EV sales.When renewable generation is insufficient, the station purchases electricity to meet customer demand.
  • Minimize the costs of power supply: ADMM-based decentralized optimization can jointly account for utility operating costs, EV charging costs, and battery degradation costs.The formulation is converted into an exchange problem with EVs and the aggregator as agents with coupled objectives.

C. Uncertain Aspects of EV Charging Control Optimization

Distributed EV charging must address uncertain demand, mobility, prices, network capacity, renewable generation, and non-EV loads. The reviewed literature uses online, event-driven, predictive, incentive-based, and adaptive methods to respond to these conditions.

  • Uncertainty types: Deterministic optimization assumes accurate advance knowledge, whereas EV charging involves uncertain demand, generation, plug-in times, plug-out times, and electricity prices.The paper reviews how distributed schemes address these uncertainties because algorithms that ignore them may be unsuitable for real-world implementation.
  • Mobility uncertainty: Mobility-aware scheduling adapts to random arrivals, unplanned departures, charging locations, station-slot availability, and changing EV locations.Many surveyed algorithms instead model EVs as static loads with fixed spatio-temporal parameters.
  • Mobility uncertainty: Continuous recomputation, event-driven updates, and stochastic-game models provide different responses to changing EV connection states.Events can include EV plug-ins and early plug-outs before designated deadlines.
  • Mobility uncertainty: Mobility-aware coordination can let aggregators collaborate to schedule traveling EVs across charging stations controlled by different providers.The framework uses route, speed, charging, and station-location information to coordinate service across aggregators.
  • Non-EV demand uncertainty: Forecasted non-EV loads can be derived from similar days with comparable EV behavior and weather, reducing the need for real-time communication and synchronization.The surveyed approaches treat community non-EV demand as trend-based and predictable in advance.
  • Non-EV demand uncertainty: Some schemes shift EV charging periods according to deviations between real-time non-EV load and its forecast.This provides a charging adjustment mechanism for forecast error.
  • Online control: An event-driven online controller uses only current information and is therefore described as robust under any EV and non-EV demand profile.It recomputes charge sequences when EV arrivals, departures, or non-EV load changes occur.
  • Renewable-generation uncertainty: Renewable-generation uncertainty can be addressed by regulating EV charge rates to mitigate wind-generation variability.The reviewed literature also schedules deferrable EV loads in response to energy uncertainty.

VI. RESEARCH DIRECTIONS

The survey identifies practical and methodological gaps in distributed EV charging, spanning scalability, communication, forecasting, objective coverage, uncertainty, and battery realism. It therefore points toward more robust, multi-objective, and physically accurate charging-control algorithms.

  • Scalability and communication: Less complex optimization methods are more practical for large EV populations because iterative computation grows with participating EVs or aggregators.Many schemes recompute schedules iteratively, with total computation time depending on per-iteration scheduling effort and iteration count.
  • Scalability and communication: Real-world algorithms should tolerate network latency and failures without requiring extensive bidirectional communication infrastructure.Many reviewed schemes rely on perfect communication, creating a practical boundary for deployment.
  • Uncertainty: Precise forecasting is critical because most reviewed distributed algorithms rely on forecast data.Forecasting quality is identified as a practical requirement for real-world implementation.
  • Objective coverage: Distributed charging research should combine network-awareness and mobility-awareness, while addressing energy losses and multiple operational objectives.The survey notes limited treatment of network- and mobility-aware control, network-energy-loss minimization, and joint objectives such as load and frequency regulation.
  • Objective coverage: Future work should examine combined operational and cost objectives, including distinct objectives among individuals within the same entity.Examples include jointly maximizing user convenience and minimizing charging costs, or coordinating aggregators with different goals.
  • Battery modeling: More realistic battery models should capture nonlinear internal power losses, transient processes, and charging-efficiency variations.The survey characterizes simpler linear models as inaccurate in practice and calls for accurate models in distributed control.

VII. CONCLUSION

The paper surveys distributed EV charge-control algorithms for decentralized and hierarchical architectures. It classifies operational and cost objectives, reviews schemes from grid-operator, EV-user, and aggregator perspectives, addresses uncertainty, and identifies research directions.

  • Scope and classification: The survey covers distributed EV charge-control algorithms compatible with decentralized and hierarchical architectures.It presents a comprehensive review of this specific class of charging schemes.
  • Scope and classification: It classifies EV charging optimization problems by operational and cost aspects and reviews schemes from three stakeholder perspectives.The perspectives are the grid operator, EV user, and aggregator.
  • Findings and directions: The reviewed objectives include grid regulation and costs, user convenience and charging costs, aggregator services and revenue, and uncertainty handling.The survey also identifies several research directions for distributed EV charging control.
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