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

Motivated by the increase in variable renewable energy (such as wind and solar) generation, we study a day-ahead electricity market that consists of finitely many competing firms, each facing supply uncertainty. Each firm commits to a price-contingent production schedule in the day-ahead market, and chooses its actual production quantity after the day-ahead market is cleared and the firm’s available supply is realized. If a firm produces less than its cleared production commitment, the firm pays an undersupply penalty in proportion to its underproduction. We investigate two cases regarding overproduction: each firm either receives a credit or pays a penalty in proportion to its overproduction. Using differential equations theory, we explicitly characterize the firms’ committed production schedules and actual production strategies in equilibrium with and without subsidies. The purpose of an undersupply penalty is to improve system reliability by motivating each firm to commit to a production schedule it can deliver in the production stage. We prove that imposing or increasing a market-based undersupply penalty rate can result in a strictly larger production commitment at all prices for each firm in equilibrium, thereby resulting in a strictly lower equilibrium system reliability and day-ahead price with probability 1. We also show that linking penalties (and credit) to the price in a common electricity market results in maximum degradation of the system reliability (due to a higher undersupply penalty rate).