A Unified Joint Optimization Algorithm Considering Higher-Order Uncertainty in Distribution Networks

Abstract

To mitigate the conservativeness caused by the uncertainty of renewable energy sources (RESs) outputs and find an accurate and efficient solution for the operation in distribution networks, a unified joint optimization algorithm considering higher-order uncertainty is proposed. The higher-order uncertainty, i.e., the probability distribution (PD) of the uncertainty is better described by adopting Wasserstein-Moment (WM) metric ambiguity set in the distributionally robust chance constraint (DRCC) for active/reactive power from and reverse to the substation. Then, a unified joint optimization model combining the stochastic programming (SP) that utilizes scenario-based data and the DRCC that addresses higher-order uncertainty is established to better accommodate uncertainty. A tractable and efficient solution algorithm is proposed by using conditional value-at-risk (CVaR) approximation approach, spectral clustering approach, and a proposition that certain branches on the loop must be connected during the process of joint optimization while not affecting the optimal solution. Numerical simulations are conducted on the modified IEEE 33-bus and an actual 151-bus distribution networks to verify the feasibility and effectiveness of the proposed algorithm.

Keywords: Distribution Networks, renewable energy source (RES), higher-order uncertainty, joint optimization, stochastic programming (SP), distributionally robust chance constraint (DRCC)