Probabilistic optimal power flow (POPF) plays a crucial role in ensuring the economic and secure operation of power systems with multiple fluctuating loads and renewable energy power generations. However, the practical application of POPF faces challenges because of the lack of accurate input scenarios and the heavy computational burden. With the increasing power system uncertainties and frequent changes in topologies, the existing POPF analysis methods struggle to achieve both high precision and efficient training. To address these issues, firstly, this work decomposes the POPF into three stages: 1) the generation of source-load random scenarios; 2) the non-linear mapping derived from the Karush-Kuhn-Tucker conditions; and 3) the non-linear mapping derived from the power flow equations. Secondly, this work proposes two Bayesian deep neural networks to separately solve each stage of the POPF. Multi-collinearity reduction conditional variational autoencoder can generate source-load random scenarios while consistency condition guided Bayesian deep neural network can predict POPF calculation results. The work further conducts numerical simulations on four IEEE benchmark power systems with multiple renewable energy sources, using uncertainty data collected from the Belgian wind power generation, photovoltaic power generation and load dataset. The simulation results demonstrate that: 1) the precision in generating source-load random scenarios has been enhanced, leading to a reduction of up to 128% in the distribution statistical quantities of the accuracy measures; and 2) the mean absolute error of active power injections, and voltage angles as well as the mean absolute percentage error of the voltage amplitudes in the benchmark systems are reduced by at least 0.7% compared to deterministic neural networks.
Keywords
Bayesian deep neural networks
Multi-collinearity reduction
Probabilistic optimal power flow
Multiple source renewable energy
