Iterative Linear Programming-Based Angle-Relaxed Branch Flow Model and Its Application to Volt-Var Control

This paper addresses the challenge of optimizing distribution networks under the increasing integration of distributed energy resources and the inherent nonconvexity of AC power flow equations. Traditional methods relying on conic-relaxed formulations often fail to accurately capture critical voltage and power flow dynamics, particularly when the optimization objective does not directly minimize current magnitudes. To overcome these limitations, we propose an iterative linear formulation for the angle-relaxed branch flow model (BFM-ar), termed BFM-it. This approach iteratively linearizes the branch flow equations and updates key parameters—such as losses and voltage estimates—so that each iteration solves a linear program that progressively converges to the true nonlinear AC power flow solution. Both mathematical analysis and numerical experiments confirm that the BFM-it achieves convergence with errors on the order of machine precision, while demonstrating superior performance in volt-var control compared to conventional methods. The proposed method not only enhances modeling accuracy but also offers a computationally efficient framework for real-time distribution network optimization.