Optimizing Bidding Curves for Renewable Energy in Two-Settlement Electricity Markets

Coordination of day-ahead and real-time electricity markets is imperative for cost-effective electricity supply and also to provide efficient incentives for the energy transition. Although stochastic market designs feature the least-cost coordination, they are incompatible with current deterministic markets. This paper proposes a new approach for compatible coordination in two-settlement markets based on benchmark bidding curves for variable renewable energy. These curves are optimized based on a bilevel optimization problem, anticipating per-scenario responses of deterministic market-clearing problems and ultimately minimizing the expected cost across day-ahead and real-time markets. Although the general bilevel model is challenging to solve, we theoretically prove that a single-segment bidding curve with a zero bidding price is sufficient to achieve system optimality if the marginal cost of variable renewable energy is zero, thus addressing the computational challenge. In practice, variable renewable energy producers can be allowed to bid multi-segment curves with non-zero prices. We test the bilevel framework for both single- and multiple-segment bidding curves under the assumption of fixed bidding prices. We leverage duality theory and McCormick envelopes to derive the linear programming approximation of the bilevel problem, which scales to practical systems such as a 1576-bus NYISO system. We benchmark the proposed coordination and find absolute dominance over the baseline solution, which assumes that renewables agnostically bid their expected forecasts. We also demonstrate that our proposed scheme provides a good approximation of the least-cost, yet unattainable in practice, stochastic market outcome.