Maximum entropy based probabilistic load flow for assessing input uncertainties and line outages in wind-integrated power systems

Abstract

The swift expansion of distributed generation, particularly from photovoltaics and wind turbines, poses a formidable challenge to conventional probabilistic load flow (PLF) methods. This paper addresses the urgent need for a robust and efficient PLF approach by investigating a maximum entropy (ME) based probabilistic density function (PDF) approximation, utilizing advanced cumulant arithmetic from linearized power flow formulation. The ME-PLF method notably enhances the accuracy of output PDFs under extensive uncertainties, such as load demand fluctuations and disturbances in network branches. Unlike the Gram–Charlier expansion (GCE) reconstruction method, ME-PLF effectively eliminates the issue of erroneously obtaining negative values in the tail regions of the PDFs. Additionally, the fundamental cumulant method (CM) is refined to better model dependencies between wind power generators (WPGs) and loads. The simulations are conducted using the MATLAB programming software. Results from practical test systems have been validated against those obtained using the Monte Carlo simulation method. The suggested method has been proven to be highly effective due to its preciseness and reduced computational effort. © 2025 Elsevier B.V.