Energy and reserve scheduling under correlated nodal demand uncertainty: An adjustable robust optimization approach

Abstract

This paper presents a nonparametric approach based on adjustable robust optimization to consider correlated nodal demand uncertainty in a joint energy and reserve scheduling model with security constraints. In this model, up- and down-spinning reserves provided by generators are endogenously defined as a result of the optimization problem. Adjustable robust optimization is used to characterize the worst-case load variation under a given user-defined uncertainty set. This paper differs from recent previous work in two respects: (i) nonparametric correlations between nodal demands are accounted for in the uncertainty set, and (ii) based on the binary expansion linearization approach, a mixed-integer linear model is provided for the optimization related to the worst-case demand. The resulting problem is formulated as a trilevel program and solved by means of Benders decomposition. Empirical results suggest that the incorporation of nodal correlations can be effectively captured by the robust scheduling model.