Strategic equilibrium bidding for electricity suppliers in a day-ahead market using inverse optimization

We consider the problem of devising optimal bidding strategies for electricity suppliers in a day-ahead market where each supplier bids a linear non-decreasing function of its generating capacity for each of the 24 hours. The market operator schedules suppliers based on their bids to meet demand during each hour and determines hourly market clearing prices. Each supplier strives to submit bids that maximize her individual profit, conditional upon other suppliers bids. This process achieves a Nash equilibrium when no supplier is motivated to modify her bid. Solving the profit maximization problem requires information of rivals' bids which are typically not available. We develop an inverse optimization approach for estimating rivals' cost functions given historical market clearing prices and production levels, and use these functions to compute the Nash equilibrium bids. We propose sufficient conditions for the existence and uniqueness of the Nash equilibrium, and provide out-of-sample performance guarantees for the estimated cost parameters. Numerical experiments show that our approach achieves higher profit than the one proposed in [16], which relies instead on the assumption that other suppliers' bids are normally distributed.