Probabilistic Power Flow in Renewable-Rich Power Systems: A Comprehensive Review of Mathematical and AI-Based Methods

This paper presents a comprehensive and systematic review of probabilistic power flow (PPF) methods applied to power systems with high penetration of renewable energy sources (RES). The study covers developments from the 1970s to recent advances (2017–2025), including mathematical, approximation-based, and artificial intelligence (AI) approaches. A structured classification of methods is provided, along with a comparative analysis based on standardized performance metrics such as computation time, mean absolute percentage error (MAPE), root mean square error (RMSE), and Wasserstein distance. The results indicate that while Monte Carlo simulation remains a robust reference method, several AI-based approaches report substantial reductions in online computation time within their own benchmark settings. However, these reported speed increases are strongly dependent on hardware configuration, software implementation, benchmark system, and whether training costs are included. Finally, key research gaps are identified, particularly in scalability, topology-aware modeling, and unbalanced systems, and future research directions are outlined.