A multistage distributionally robust optimization approach for generation dispatch with demand response under endogenous and exogenous uncertainties

Abstract

AbstractDecision‐dependent (endogenous) uncertainties (DDUs), as a new type of uncertainties revealed recently, couple dispatch decisions with uncertainty parameters and thus render power system dispatch more challenging. However, most previous works handled various DDUs via stochastic programming (SP) or robust optimization (RO) in a two‐stage framework, which undoubtedly introduces the drawbacks of SP and RO, and cannot meet the nonanticipativity requirements in power scheduling. In this paper, a multistage distributionally robust optimization (DRO) method for generation dispatch with demand response (DR) is proposed considering the DDUs of deferrable loads and the decision‐independent (exogenous) uncertainties (DIUs) of wind power and regular loads. By analyzing the structure of decision‐dependency parameters, a novel data‐driven decision‐dependent ambiguity set is proposed, which provides a generic framework for formulating DDUs and DIUs simultaneously. Then a multistage DRO model with nested max‐min structure is developed to integrate the merits of DRO and nonanticipativity into generation dispatch. The proposed model is solved by tailored reformulation method and improved stochastic dual dynamic integer programming (SDDiP). Case studies illustrate the effectiveness of the proposed approach by comparing with the multistage SP, RO, and decision‐independent DRO methods.