A data-driven multi-stage stochastic robust optimization model for dynamic optimal power flow problem

The uncertainty caused by the distributed generations(DG) with inconspicuous patterns has been an essential subject in the optimization scheduling for the distribution network. We propose a novel data-driven approach to deal with the dynamic optimal power flow(DOPF) problem which contains uncertain variables with their un-known probability distribution. The data-driven model is made to learn the joint probability distribution of the uncertain variables and use robust optimization(RO) to solve the multi-stage stochastic linear DOPF by averaging the worst case from each uncertainty set. In contrast to the motivation for traditional RO to find solutions that perform well on the worst-case realization, our proposed approach adds robustness to the historical data as a tool to avoid overfitting as the number of data points tends to infinity. The application verification for the AC OPF problem is presented for the IEEE-33 system. The simulation verifies the feasibility and robustness of the pro-posed approach and its results are compared with those of other data-driven stochastic optimization methods. We prove that the proposed approach can effectively solve the overvoltage problem caused by the high permeability of photovoltaic generation and achieve a better out-of-sample performance guarantee, and also has obvious economic advantages over other data-driven methods.