Data-Driven Distributionally Robust Optimization for Power System Operations

Abstract

Decisions are often made in an uncertain environment. For example, in power system operations, decision makers need to schedule generators without the accurate outcome of various uncertain parameters, e.g., electricity load and renewable energy. If we have access to the (joint) probability distribution of these uncertain parameters, we can apply the stochastic programming approaches to schedule the generators. However, in practice, we can hardly have access to such (true) probability distribution. Under such circumstances, stochastic programming approaches may produce over-optimistic solutions and lead to an unreliable power system. In this dissertation, we propose data-driven optimization methods to model uncertainty directly based on the historical data. More specifically, we statistically infer key characteristics of the (ambiguous) probability distribution (e.g., support, mean, mean absolute deviation, unimodality, etc.) based on the historical data and construct an ambiguity set consisting of all probability distributions that match the inferred characteristics. Then, we make distributionally robust decisions that hedge against the worst-case distributions within the ambiguity set. We study new data-driven distributionally robust optimization models as well as their solution approaches and applications on power system operations, including optimal power flow, unit commitment, and transmission expansion planning. The specific contributions of this dissertation include (i) a distributionally robust optimization approach for unit commitment and reserve procurement and an algorithm based on generalized linear decision rule; (ii) a Wasserstein-moment ambiguity set for the distributionally robust chance-constrained optimal power flow problem and a tractable convex conservative approximation based on worst-case conditional value-at-risk; (iii) a general framework for distributionally robust optimization models to incorporate shape information of probability distributions into ambiguity sets; (iv) an adaptive two-stage robust transmission expansion planning model and an algorithm based on prioritization decision rule.