Phase Transitions for Optimality Gaps in Optimal Power Flows A Study on the French Transmission Network

2018/07/14 by Terrence W. K. Mak, Mak, Terrence W. K., Lyndon Shi +3 · 1 citation
Engineering · #Electric Power System Optimization #FOS: Mathematics #Optimal Power Flow Distribution #Optimization and Control (math.OC) #Power System Optimization and Stability

paper · pdf · doi:10.48550/arxiv.1807.05460

openalex publication_date 2018/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates phase transitions on the optimality gaps in Optimal Power Flow (OPF) problem on real-world power transmission systems operated in France. The experimental results study optimal power flow solutions for more than 6000 scenarios on the networks with various load profiles, voltage feasibility regions, and generation capabilities. The results show that bifurcations between primal solutions and the QC, SOCP, and SDP relaxation techniques frequently occur when approaching congestion points. Moreover, the results demonstrate the existence of multiple bifurcations for certain scenarios when load demands are increased uniformly. Preliminary analysis on these bifurcations were performed.

Citations

• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming

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