Strategic Commitment to a Production Schedule with Uncertain Supply and Demand: Renewable Energy in Day-Ahead Electricity Markets

We consider a day-ahead electricity market that consists of multiple competing renewable firms (e.g., wind generators) and conventional firms (e.g., coal-fired power plants) in a discrete-time setting. The market is run in every period, and all firms submit their price-contingent production schedules in every day-ahead market. Following the clearance of a day-ahead market, in the next period, each (renewable) firm chooses its production quantity (after observing its available supply). If a firm produces less than its cleared day-ahead commitment, the firm pays an undersupply penalty in proportion to its underproduction. We explicitly characterize firms' equilibrium strategies by introducing and analyzing a supply function competition model. The purpose of an undersupply penalty is to improve reliability by motivating each firm to commit to quantities it can produce in the following day. We prove that in equilibrium, imposing or increasing a market-based undersupply penalty rate in a period can result in a strictly larger renewable energy commitment at all prices in the associated day-ahead market, and can lead to lower equilibrium reliability in all periods with probability 1. We also show in an extension that firms with diversified technologies result in lower equilibrium reliability than single-technology firms in all periods with probability 1.