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Wasserstein Distributionally Robust Chance-Constrained Optimization for Energy and Reserve Dispatch: An Exact and Physically-Bounded Formulation

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Abstract

In the context of transition towards sustainable, cost-efficient and reliable energy systems, the improvement of current energy and reserve dispatch models is crucial to properly cope with the uncertainty of weather-dependent renewable power generation. In contrast to traditional approaches, distributionally robust optimization offers a risk-aware framework that provides performance guarantees when the distribution of uncertain parameters is not perfectly known. In this paper, we develop a distributionally robust chance-constrained optimization with a Wasserstein ambiguity set for energy and reserve dispatch, and provide an exact reformulation. While preserving the exactness, we then improve the model by enforcing physical bounds on the uncertainty space, resulting in a bilinear program. We solve the resulting bilinear model with an iterative algorithm which is computationally efficient and has convergence guarantee. A thorough out-of-sample analysis is performed to compare the proposed model against a scenario-based stochastic program. We also compare the performance of the proposed exact reformulation against an existing approximate technique in the literature, built upon a conditional-value-at-risk measure. We eventually show that the proposed physically-bounded exact reformulation outperforms the other methods by achieving a cost-optimal yet reliable trade-off between reserve procurement and load curtailment.