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.
Empirical evidence from social studies has illustrated that the axiom of rationality of game theory can be violated when users face risk and uncertainty in decision-making @cite_44 . In @cite_28 , discrepancies between rational choice and alternative user behavioral models in an energy market are reviewed. Prospect theory has attracted great attention in various research communities to understand impacts of deviations from rationality @cite_13 @cite_8 @cite_31 . A comprehensive discussion on the potential of prospect theory to understand how decision-making under risk and uncertainty can affect various smart grid applications is given in @cite_40 . In @cite_16 , optimal energy exchange among geographically-distributed consumer-owned energy storage devices is compared under classical game theory and prospect theory. In @cite_9 , the effects of subjective consumer behavior on an energy storage charging-discharging system are investigated using a utility framing method derived from prospect theory. In contrast to previous work, this paper presents precepts of prospect theory to realize potential non-ideal behavior of EV aggregators in a non-cooperative game-theoretic EV charging system.
@cite_8 @cite_28 @cite_9 @cite_44 @cite_40 @cite_31 @cite_16 @cite_13
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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. In this paper, the interactions and energy exchange decisions of a number of geographically distributed storage units are studied under decision-making involving end-users. In particular, a noncooperative game is formulated between customer-owned storage units where each storage unit's owner can decide on whether to charge or discharge energy with a given probability so as to maximize a utility that reflects the tradeoff between the monetary transactions from charging discharging and the penalty from power regulation. Unlike existing game-theoretic works which assume that players make their decisions rationally and objectively, we use the new framework of prospect theory (PT) to explicitly incorporate the users' subjective perceptions of their expected utilities. For the two-player game, we show the existence of a proper mixed Nash equilibrium for both the standard game-theoretic case and the case with PT considerations. Simulation results show that incorporating user behavior via PT reveals several important insights into load management as well as economics of energy storage usage. For instance, the results show that deviations from conventional game theory, as predicted by PT, can lead to undesirable grid loads and revenues thus requiring the power company to revisit its pricing schemes and the customers to reassess their energy storage usage choices. Game theoretic models have found widespread use in the analysis and design of radio resource management algorithms for a wide variety of systems such as cellular, ad hoc and sensor networks. The fundamental principle behind such models and much of game theory has been the reliance on expected utility theory (EUT). In this paper, we consider a simple wireless random access game where instead of following the precepts of EUT, the players follow the precepts of Prospect Theory (PT), a theory developed by Kahneman and Tversky to explain real-life decision making that often deviates from the behavior expected under EUT. Specifically, we consider a game where selfish players adjust their transmission probabilities over a collision channel according to rewards received for successful transmission while incurring energy and delay costs. We compare and contrast the Nash equilibria achieved under both EUT and PT and highlight the differences in them. In this paper, the problem of energy trading between smart grid prosumers, who can simultaneously consume and produce energy, and a grid power company is studied. The problem is formulated as a single-leader, multiple-follower Stackelberg game between the power company and multiple prosumers. In this game, the power company acts as a leader who determines the pricing strategy that maximizes its profits, while the prosumers act as followers who react by choosing the amount of energy to buy or sell so as to optimize their current and future profits. The proposed game accounts for each prosumer’s subjective decision when faced with the uncertainty of profits, induced by the random future price. In particular, the framing effect, from the framework of prospect theory (PT), is used to account for each prosumer’s valuation of its gains and losses with respect to an individual utility reference point. The reference point changes between prosumers and stems from their past experience and future aspirations of profits. The followers’ noncooperative game is shown to admit a unique pure-strategy Nash equilibrium (NE) under classical game theory which is obtained using a fully distributed algorithm. The results are extended to account for the case of PT using algorithmic solutions that can achieve an NE under certain conditions. Simulation results show that the total grid load varies significantly with the prosumers’ reference point and their loss-aversion level. In addition, it is shown that the power company’s profits considerably decrease when it fails to account for the prosumers’ subjective perceptions under PT.