An Adaptive Distributionally Robust Model for Three-Phase Distribution Network Reconfiguration

Distributed generator (DG) volatility has a great impact on system operation, which should be considered beforehand due to the slow time scale of distribution network reconfiguration (DNR). However, it is difficult to derive accurate probability distributions (PDs) for DG outputs and loads analytically. To remove the assumptions on accurate PD knowledge, a deep neural network is first devised to learn the reference joint PD from historical data in an adaptive way. The reference PD along with the forecast errors are enveloped by a distributional ambiguity set using Kullback-Leibler divergence. Then a distributionally robust model for three-phase unbalanced DNR is proposed to obtain the optimal configuration under the worst-case PD of DG outputs and loads within the ambiguity set. The result inherits the advantages of stochastic optimization and robust optimization. Finally, a modified column-and-constraint generation method with efficient scenario decomposition is investigated to solve this model. Numerical tests are carried out using an IEEE unbalanced benchmark and a practical-scale system in Shandong, China. Comparison with the deterministic, stochastic and robust DNR methods validates the effectiveness of the proposed method.