Probabilistic Load Flow Calculation for Distribution Networks Based on Advanced Source-Load Modeling and Time-Varying D-Vine Copula

With the large-scale integration of distributed photovoltaic generation (PV) into modern distribution networks, the inherent stochasticity and volatility of renewable energy outputs have imposed non-negligible impacts on the secure and economic operation of power systems. Conventional probabilistic power flow (PPF) methods are limited in accurately modeling source–load uncertainty and, more importantly, in capturing complex nonlinear and time-varying dependence among multiple renewable energy sources. To address these issues, this paper proposes a novel PPF calculation framework based on advanced source-load modeling and time-varying D-vine Copula. Firstly, an enhanced finite mixture Beta model and a Gaussian cluster mixture model are developed to characterize the uncertainty of PV output and load demand, respectively. Secondly, a time-varying D-vine Copula model based on the generalized autoregressive score framework is constructed. And a two-stage regularized profile likelihood estimation method is proposed to estimate correlation parameters, capturing the dynamic nonlinear dependence among multiple PV generators. Finally, the de-randomized Sobol sequence-based Quasi-Monte Carlo method is adopted to perform stochastic power flow calculation. Simulation results on a real-world 129-bus distribution system in East China verify the accuracy and effectiveness of the proposed method.