Distributionally Robust Operating Reserve Demand Curves

Abstract

Operating Reserve Demand Curves (ORDCs) are used to determine prices and dispatch levels for operating reserves. They are intended to represent the expected cost of lost load given a specific amount of operating reserve in the system and are constructed using a reserve error probability distribution, which is typically constructed from historical data and is often assumed as Gaussian. This paper is the first to propose a Distributionally Robust (DR) ORDC using a robust representation of the reserve error distribution. We use an ambi-guity set in the form of a Wasserstein ball around the empirical distribution, which reduces to the empirical distribution when the ball radius is set to zero. Using published ORDC data from ERCOT, numerical results illustrate how the DR ORDC is a more accurate representation of the historical reserve error data when the Wasserstein ball radius is chosen to be zero and how the Wasserstein ball radius can be raised (lowered) to make the DR ORDC more (less) conservative. We find that the DR ORDC conservatively approximates the tails of the reserve error distribution by raising prices at high operating reserve levels.