Abstract
This study uses a game-theoretic analysis of bid-based electricity supply market equilibrium. Electricity supply markets are modeled as strategic interactions of bidders that supply electric power to the market and the bidders’ pure strategies are the cost function parameters of power generation. We demonstrate that the resultant bidding game is a convex game and has a unique pure-strategy Nash equilibrium (PNE) when the bid-cost functions are parameterized by marginal costs of power generation. The PNE of the power-supply bidding game is reformulated in terms of a variational inequality and as a fixed-point of a recursive mapping. We propose two distributed learning algorithms and their variations with convergence analysis to compute a PNE. Three types of measures are proposed and analyzed for quantification of inefficiency due to falsified bidding actions corresponding to the marginal cost function parameters of supply-market participative generators. A numerical case study with a 26-bus power network is presented to illustrate and demonstrate our results.
Highlights
The smart grid infrastructure, including smart sensors and meters, and communication technology has led to many fundamental problems of power systems research, such as optimal power flow, unit commitment, and economic dispatch being revisited
Game theory has been a tool for formal analysis of economic behavior and a conceptual abstraction framework incorporated with advanced mathematical tools for studying strategic interactions of rational decision-makers
1) DISTRIBUTED PROJECTED GRADIENT DESCENT ALGORITHM To find a pure-strategy Nash equilibrium (PNE) of the game defined in Section II-B, we propose a method of distributed learning that has the following form of a recursive formula: xi(k+1) =
Summary
The smart grid infrastructure, including smart sensors and meters, and communication technology has led to many fundamental problems of power systems research, such as optimal power flow, unit commitment, and economic dispatch being revisited. Motivated by the application of supply function equilibria (SFE) in the wholesale market for the supply side, we consider a retail electricity market model to match the power demand and a supply-bidding game in which private parameters of power-generation cost functions are strategically reported to the market operator. The market operator determines the electricity price through economic dispatch based on the reported parameterized supply functions and the bidders corresponding to power-generation units are price-takers. We assume that the optimal economic dispatch profiles in (5) are strictly feasible for the inequalities (4) This is not just for mathematical convenience, but for two-sided options of each generation unit to report true or false parameter values of supply function so that the computed economic dispatch profiles with reported parameter values are feasible
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