Robust supply function bidding in electricity markets with renewables

We study a two-stage electricity market with renewables. Each energy producer in the market has a portfolio of both renewable and conventional energy generators. In the day-ahead (DA) market, each producer submits a parameterized supply function (i.e., the amounts of energy to produce at various prices) to the independent system operator (ISO), who determines the DA market clearing price and the amounts of DA committed energy by each producer. In the real-time market, each producer tries to fulfill its DA committed energy with (zero-cost) renewables. If the renewable energy is insufficient, the producer uses conventional energy generation and incurs a cost; otherwise, it sells the surplus of renewable energy to the ISO at a predetermined feed-in tariff. We study the robust supply function equilibrium (SFE) in this market, where each producer has incomplete information about the other producers' marginal costs and the distribution of its random renewable energy, and performs worst-case optimization against these unknown variables. We fully characterize the unique robust SFE, and study the impact of the feed-in tariff on the equilibrium outcome.