Distributionally robust optimal power flow based on multi-transport hyperrectangle ambiguity set

Abstract

The Wasserstein distributionally robust optimization has become the preferred method for addressing the uncertainties in optimal power flow problems caused by renewable energy sources. However, when the system involves high-dimensional random variables, such as multiple solar or wind farms, the curse of dimensionality associated with this method leads to a slow convergence rate of Wasserstein ambiguity sets. Therefore, it is essential to explore novel ambiguity sets which can effectively address the dimensionality problem. This paper proposes a distributionally robust optimal power flow model based on a multi-transport hyperrectangle ambiguity set to tackle the uncertainties in wind power. First, this paper presents the multi-transport hyperrectangle, which resolves the curse of dimensionality issue associated with Wasserstein ambiguity sets. Furthermore, the wind power curtailment cost in the objective function is reformulated into a tractable form using duality theory, enabling commercial solvers to provide efficient solutions. Finally, tests conducted on the modified IEEE 14-bus and IEEE 118-bus systems demonstrate that the proposed ambiguity set maintains a stable convergence rate under high-dimensional random variables without rapid deterioration as the sample size increases. Moreover, the model achieves significant cost reductions while ensuring system stability.