Decentralized Nash equilibrium seeking by strategic generators for DC optimal power flow

This paper studies an electricity market consisting of an independent system operator (ISO) and a group of generators. The goal is to solve the DC optimal power flow (DC-OPF) problem: have the generators collectively meet the power demand while minimizing the aggregate generation cost and respecting line flow limits. The ISO by itself cannot solve the DC-OPF problem as the generators are strategic and do not share their cost functions. Instead, each generator submits to the ISO a bid, consisting of the price per unit of electricity at which it is willing to provide power. Based on the bids, the ISO decides how much production to allocate to each generator to minimize the total payment while meeting the load and satisfying the line limits. We provide a provably correct, decentralized iterative scheme, termed BID ADJUSTMENT ALGORITHM for the resulting Bertrand competition game. The algorithm takes the generators bids to any desired neighborhood of the efficient Nash equilibrium at a linear convergence rate. As a consequence, the optimal production of the generators converges to the optimizer of the DC-OPF problem. 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.