Marginal Pricing in Adaptive Robust Unit Commitment Under Load and Capacity Uncertainty

The increase of renewables in the grid and the volatility of the load create uncertainties in the day-ahead prices of electricity markets. Adaptive robust optimization (ARO) and stochastic optimization have been used to make commitment and dispatch decisions that adapt to the load and capacity uncertainty. While these approaches have been successfully applied in the Reliability Unit Commitment (RUC) stage, they have not been adopted in the Day-Ahead Market (DAM). One significant step towards their use in the DAM is the establishment of marginal prices, uplifts and payments in ARO formulations in unit commitment. So far, most pricing methods cater to deterministic problems without pricing the load and capacity uncertainty. In addition, since the DAM is not set up using robust optimization, there are out-of-market corrections in the RUC. These corrections introduce ad hoc uplift payments and volatility that reflect the gap between the DAM and the Real-Time Market. In this work, we provide locational marginal prices (LMPs) for generation and uncertainty in the ARO setting and discuss uplifts and recovery mechanisms. Our method prices the uncertainty in the DAM stage, so it could reduce ad hoc pricing corrections and uplifts after the RUC stage. In addition, the LMPs we derive can deter self-scheduling in some cases, addressing some of the major disadvantages of pricing in deterministic formulations.