Robust Kernel Density Estimation Based Data-Driven Optimal Scheduling for Power Systems Considering Data Errors and Uncertainties of Renewable Energy

This paper proposes a data-driven robust scheduling method for power systems incorporating variable energy. Robust kernel density estimation (RKDE) is combined with distributionally robust optimization (DRO) to address the uncertainties of renewable energy and possible outliers during data collection and transmission. RKDE is employed to infer the potential probability distribution. In this process, the outliers will be assigned a very small weight so that they hardly affect the probability density curve. Subsequently, the distribution derived from RKDE serves as the center of a distributional ambiguity set, with distances between distributions measured using the Wasserstein metric. Since RKDE converges to the true distribution quickly with the expansion of sample data, the proposed approach is less conservative than the empirical distribution-based DRO (EDRO). Moreover, compared with general KDE, RKDE has a unique advantage in suppressing the influence of outliers and improving the accuracy of distribution estimation. To demonstrate the superiority of the proposed approach, we present tests on Case-118 and Case-1888rte systems from MATPOWER 6.0. Numerical results indicate that the proposed approach exhibits lower conservatism and superior outlier suppression capability when compared to EDRO and KDE-based DRO (KDRO).