Power Flow Methods for Efficient Analysis of Modern Distribution Networks—Review

Power Flow (PF) analysis is a fundamental tool in distribution systems since it determines the steady-state operating point for specified input conditions. Modern distribution networks face high distributed energy resource (DER) penetration and variable operating conditions, requiring repeated PF evaluations in time-series and scenario-based studies. Their unbalanced operation and high R/X ratios can challenge conventional PF solvers, thereby requiring accurate, robust, and scalable methods. Prior studies have examined nonlinear distribution PF solvers and uncertainty-based formulations, but the review literature remains limited to specific categories and lacks a unified discussion of linearized models, numerical robustness, and acceleration techniques. Therefore, this paper presents a state-of-the-art review of PF methods for modern distribution networks, covering 205 studies published between 2000 and 2026. It summarizes conventional nonlinear PF formulations, reviews linearized models with their assumptions and applicability, and surveys numerical robustness strategies for improved convergence. The methods are compared according to their applicability to radial, weakly meshed, and unbalanced networks, while practical selection criteria are provided based on accuracy, convergence reliability, and computational requirements. Probabilistic, interval, and fuzzy approaches are also reviewed under renewable and load uncertainty. Finally, acceleration strategies for repeated PF evaluation are discussed, emphasizing sparse numerical implementations, topology-based schemes, and physics-informed surrogate models.