Hybrid Score-Driven Multivariate Probabilistic Forecasting of Correlated PV Generation Using Deep Mixture Density Network

With massive integration of photovoltaic (PV) generation in power systems, multivariate probabilistic forecasting (MPF) is essential for analysis and decision-making of power systems, which provides comprehensive information about uncertainty of future PV generation. Traditional MPF methods separate probabilistic forecasting and dependency structure estimation, limiting their ability to generate multivariate distributions in an analytical form. This paper innovatively proposes a hybrid score-driven MPF method to directly generate semi-parametric joint predictive density of correlated PV generation using deep mixture density network. Firstly, an integrated framework of MPF based on multivariate Gaussian mixture models is established to unify the training of probabilistic forecasting and the optimization of conditional correlation modeling. Then, a novel hybrid score-based network loss function with the closed-form expression is meticulously devised for the robust training of MPF. In addition, graph structure learning is incorporated to adaptively capture spatial dependency among correlated PV generation. To address overwhelming parameters of joint distributions, a parameter-reduced structure of covariance matrices using incomplete Cholesky decomposition is formulated, which enhances the tractability of MPF in high-dimensional settings. Comprehensive case studies on three realistic PV power datasets are conducted to validate the superior performance of the proposed method for day-ahead multivariate probabilistic forecasting.