A Multistage Distributionally Robust Optimization Approach for
Generation Dispatch with Demand Response under Endogenous and Exogenous
Uncertainties
Abstract
Decision-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, we propose a multistage distributionally robust optimization
(DRO) method for generation dispatch with demand response (DR)
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.