Decentralized Nash equilibrium learning by strategic generators for economic dispatch

This paper studies an electricity market consisting of an independent system operator (ISO) and a group of generators. The goal is to solve the economic dispatch (ED) problem, i.e., make the generators collectively meet a given amount of power demand while minimizing the aggregate generation cost. The ISO by itself cannot solve the ED problem as the generators are strategic and do not share their cost functions. Instead, each generator submits to the ISO the price per unit of electricity at which it is willing to provide power to the ISO, which constitutes its bid. Based on the bids, the ISO decides how much production to allocate to each generator. The resulting Bertrand competition model defines the game among the generators where the actions are the bids and the payoffs are the profits. We provide a provably correct, decentralized strategy, termed NE SEEKING ALGORITHM, that takes the generators' bids to a neighborhood of the efficient Nash equilibrium and show that the optimal production of the generators converges to the optimizer of the ED problem. During the play, each generator only knows the amount of power the ISO requests it to produce and is not aware of the number of players, their actions, or their payoffs. Our algorithm can be understood as “learning via repeated play”, where generators are “myopically selfish”, changing their bid at each iteration with the sole aim of maximizing their payoff.