Data quality aware chance-constrained DC-OPF: a variational Bayesian Gaussian mixture approach

The contamination of outliers severely damages the data quality, resulting in the inaccurate data-driven optimisation model. This study proposes a data quality aware chance-constrained model for the direct current optimal power flow (DC-OPF) problem under uncertainties. Under the framework of Bayesian statistics, the variational Bayesian Gaussian mixture model (VBGMM) is employed to extract the probabilistic information from the available historical data, i.e. realisations of random variables. VBGMM can identify the outliers by capturing their probability characteristics, in which way improving the data quality. Notably, VBGMM automatically determines the number of components, which is a remarkable difference from the conventional Gaussian mixture model. In addition, based on the affine policy, a method integrating VBGMM with chance-constrained programming is proposed to make VBGMM scalable. The proposed method is firstly tested on a 6-bus system for an illustrative purpose, and then on a 118-bus system for validating the potential practical application. Comparative studies verify the effectiveness of the proposed method.