In this paper, an electric vehicle (EV) charging competition, among EV aggregators that perform coordinated EV charging, is explored while taking into consideration potential non-ideal actions of the aggregators. In the coordinated EV charging strategy presented in this paper, each aggregator determines EV charging start time and charging energy profiles to minimize overall EV charging energy cost by including consideration of the actions of the neighboring aggregators. The competitive interactions of the aggregators are modeled by developing a two-stage non-cooperative game among the aggregators. The game is then studied under prospect theory to examine the impacts of non-ideal actions of the aggregators in selecting EV charging start times according to subjectively evaluating their opponents' actions. It is shown that the non-cooperative interactions among the aggregators lead to a subgame perfect @math -Nash equilibrium when the game is played with either ideal, or non-ideal, actions of the aggregators. A case study presented demonstrates that the benefits of the coordinated EV charging strategy, in terms of energy cost savings and peak-to-average ratio reductions, are significantly resilient to non-ideal actions of the aggregators.
Game theory is also used in the context of distributed optimal operation in EV charging systems @cite_30 @cite_22 @cite_0 @cite_29 . Based on game theory, @cite_22 explores optimal price competition among EV charging stations with renewable energy generation to attract EVs. Using a non-cooperative game-theoretic approach, @cite_0 investigates an optimal demand response method for effective scheduling of plug-in hybrid EV charging. By investigating a non-cooperative game among self-interested EV owners, an optimal valley filling pricing mechanism to coordinate EV charging is proposed in @cite_1 . Using a non-cooperative game among EVs at a parking lot, @cite_18 studies an effective way of obtaining EV charging strategies at a unique Nash equilibrium under the constrained distribution transformer capacity. The non-cooperative Stackelberg game-theoretic approach in @cite_26 investigates the optimal bi-level grid-to-vehicle coordination between the power grid and plug-in EV groups with limited energy supply. Most of the game-theoretic demand-side management literature optimizes important aspects of various energy markets conforming to conventional game theory that fundamentally assumes rational choices by users.
@cite_30 @cite_18 @cite_26 @cite_22 @cite_29 @cite_1 @cite_0
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In this paper, the problem of optimally charging or discharging customer-owned storage units in a smart grid is studied. In particular, a noncooperative game is formulated between customers equipped with distributed storage units who seek to decide on their optimal charging strategy so as to optimize a utility that reflects both the monetary benefit from the charging discharging operation and the associated penalty from power regulation. In contrast to the traditional game-theoretic models that are often based on rational and objective decisions, we introduce the behavioral framework of prospect theory (PT) so as to explicitly incorporate how the customers estimate their utilities with respect to their real-world considerations of gains and losses. The existence of the mixed-strategy Nash equilibrium is shown for the PT case and the properties of the game are analyzed under both PT and classical game theory. Simulation results show how the individual customer perceptions on their utilities can significantly impact the overall charging and discharging operations. This paper develops a strategy to coordinate the charging of autonomous plug-in electric vehicles (PEVs) using concepts from non-cooperative games. The foundation of the paper is a model that assumes PEVs are cost-minimizing and weakly coupled via a common electricity price. At a Nash equilibrium, each PEV reacts optimally with respect to a commonly observed charging trajectory that is the average of all PEV strategies. This average is given by the solution of a fixed point problem in the limit of infinite population size. The ideal solution minimizes electricity generation costs by scheduling PEV demand to fill the overnight non-PEV demand “valley”. The paper's central theoretical result is a proof of the existence of a unique Nash equilibrium that almost satisfies that ideal. This result is accompanied by a decentralized computational algorithm and a proof that the algorithm converges to the Nash equilibrium in the infinite system limit. Several numerical examples are used to illustrate the performance of the solution strategy for finite populations. The examples demonstrate that convergence to the Nash equilibrium occurs very quickly over a broad range of parameters, and suggest this method could be useful in situations where frequent communication with PEVs is not possible. The method is useful in applications where fully centralized control is not possible, but where optimal or near-optimal charging patterns are essential to system operation. Efficient and reliable demand side management techniques for community charging of plug-in hybrid electrical vehicles (PHEVs) and plug-in electrical vehicles (PEVs) are needed, as large numbers of these vehicles are being introduced to the power grid. To avoid overloads and maximize customer preferences in terms of time and cost of charging, a constrained nonlinear optimization problem can be formulated. In this paper, we have developed a novel cooperative distributed algorithm for charging control of PHEVs PEVs that solves the constrained nonlinear optimization problem using Karush-Kuhn-Tucker (KKT) conditions and consensus networks in a distributed fashion. In our design, the global optimal power allocation under all local and global constraints is reached through peer-to-peer coordination of charging stations. Therefore, the need for a central control unit is eliminated. In this way, single-node congestion is avoided when the size of the problem is increased and the system gains robustness against single-link node failures. Furthermore, via Monte Carlo simulations, we have demonstrated that the proposed distributed method is scalable with the number of charging points and returns solutions, which are comparable to centralized optimization algorithms with a maximum of 2 sub-optimality. Thus, the main advantages of our approach are eliminating the need for a central energy management coordination unit, gaining robustness against single-link node failures, and being scalable in terms of single-node computations. Constrained charging control of large populations of Plug-in Electric Vehicles (PEVs) is addressed using mean field game theory. We consider PEVs as heterogeneous agents, with different charging constraints (plug-in times and deadlines). The agents minimize their own charging cost, but are weakly coupled by the common electricity price. We propose an iterative algorithm that, in the case of an infinite population, converges to the Nash equilibrium associated with a related decentralized optimization problem. In this way we approximate the centralized optimal solution, which in the unconstrained case fills the overnight power demand valley, via a decentralized procedure. The benefits of the proposed formulation in terms of convergence behavior and overall charging cost are illustrated through numerical simulations.