Efficient and Robust Equilibrium Strategies of Utilities in Day-Ahead Market with Load and Renewable Uncertainty

In this project, we understand the equilibrium strategies of utilities in electricity market and the impact of load and renewable uncertainty.

In the first work, we study the equilibrium strategies. We consider the scenario where N utilities strategically bid for electricity in the day-ahead market and balance the mismatch between the committed supply and actual demand in the real-time market. Each utility aims at minimizing its per-unit electricity cost by optimizing the bidding strategy, in face of uncertainty in demand and local renewable generation. The per-unit electricity cost of a utility is determined by both the day-ahead clearing price and the real-time spot price affected by the market-level supply-demand mismatch. We model the interactions among utilities as a non-cooperative game and study the equilibrium strategies. We show that all utilities bidding according to (net load) prediction is a unique pure strategy Nash Equilibrium with two salient properties. First, it incurs no loss of efficiency; hence, the competition among utilities does not increase the social cost. Second, it is robust and (0, N-1)-immune. Irrational fault behaviors of any subset of the utilities only help reduce the costs of other rational utilities. We prove the results hold for correlated prediction errors and a general class of real-time spot pricing models, which capture the relationship between the spot price, the day-ahead clearing price, and the market-level mismatch. Simulations based on real-world traces corroborate our theoretical results.

Our study highlights a set of sufficient conditions, according to which the market operator can design real-time pricing schemes, so that the interactions among utilities admit a unique and efficient pure strategy Nash Equilibrium and it is robust to irrational fault behaviors.

In the second work, we study the impact of renewable generation at the equilibrium, where all utilities bid according to their predictions. In particular, we study how the uncertainty from distributed renewable generation in the utility or an active district (microgrid) affects the average buying cost of utilities and the cost-saving of the active district. Our analysis shows that the renewable uncertainty in an active district can (i) increase the average buying cost of the utility serving the active district, termed as local impact, and (ii) somewhat surprisingly, reduce the average buying cost of other utilities participating in the same electricity market, termed as global impact. Moreover, the local impact will lead to an increase in the electricity retail price of active district, resulting in a cost-saving less than the case without renewable uncertainty. These observations reveal an inherent economic incentive for utilities to improve their load forecasting accuracy, in order to avoid economy loss and even extract economic benefit in the electricity market. We verify our theoretical results by extensive experiments using real-world traces. Our experimental results show that a 9% increase in load forecasting error (modeled by the standard deviation of the mismatch between real-time actual demand and day-ahead purchased supply) will increase the average buying cost of the utility by 10%.


  • T. Zhao, H. Yi, M. Chen, C. Wu, and Y. Xu, “Efficient and Robust Equilibrium Strategies of Utilities in Day-ahead Market with Load Uncertainty”, arXiv:1909.05578, 2019. [PDF]

  • H. Yi, M. Hajiesmaili, Y. Zhang, M. Chen, and X. Lin, “Impact of Uncertainty of Distributed Renewable Generation on Deregulated Electricity Supply Chain”, accepted for publication in IEEE Transactions on Smart Grid. [PDF]