Traditionally before solving the optimal power flow considering uncertainty (OPF-U) problem, the predicted value of uncertainty parameters, such as wind power, e.g., is derived from data using a statistics approach or machine learning. Based on the predicted uncertainty parameters, the solution to the OPF-U problem can be obtained by the prescriptive analytics technique, such as robust optimization (RO). However, it is unclarified how the prediction error in predictive analytics affects solving the OPF-U problem in prescriptive analytics. We propose an adjustable framework method combining machine learning and RO for the OPF-U problem. The k-nearest neighbor is applied to obtain k samples around the predicted value from sufficient historical data. And the optimization results from a minimum volume ellipsoid set containing the k samples are applied to construct KMV set. Then a robust fluctuation region with an adjustable budget level is gained from the KMV set by a two-term exponential formula, which can be embedded into a two-stage RO model. Computational experiments under test cases of different uncertainty scales show the robustness and adjustability of the proposed fluctuation region are better than the state-of-the-art box and ellipsoidal sets. The solution of the proposed two-stage RO model is more economical than the state-of-the-art RO model. The out-of-sample simulation also demonstrates the proposed adjustable Predictive&Prescriptive method can reduce the computational burden as the scale of the system increases when predictive and prescriptive analytics are separated.
Keywords: Machine learning; Optimal power flow; Two-stage robust optimization; Uncertain fluctuation region.
© 2023 The Authors. Published by Elsevier Ltd.