On the Tightness of Convex Optimal Power Flow Model Based on Power Loss Relaxation

TL;DR

This paper evaluates and improves the tightness of convex relaxations in optimal power flow models, demonstrating that a penalty-based approach effectively reduces relaxation gaps, especially in large-scale networks with low loads.

Contribution

It introduces a unified evaluation framework and a heuristic penalty algorithm to enhance the tightness of convex ACOPF models, addressing relaxation gaps in power system optimization.

Findings

Relaxation gaps are significant in large-scale networks with low loads.

The proposed TRA effectively reduces the relaxation gap.

Evaluation framework benchmarks tightness reinforcement approaches.

Abstract

Optimal power flow (OPF) is the fundamental mathematical model in power system operations. Improving the solution quality of OPF provide huge economic and engineering benefits. The convex reformulation of the original nonconvex alternating current OPF (ACOPF) model gives an efficient way to find the global optimal solution of ACOPF but suffers from the relaxation gaps. The existence of relaxation gaps hinders the practical application of convex OPF due to the AC-infeasibility problem. We evaluate and improve the tightness of the convex ACOPF model in this paper. Various power networks and nodal loads are considered in the evaluation. A unified evaluation framework is implemented in Julia programming language. This evaluation shows the sensitivity of the relaxation gap and helps to benchmark the proposed tightness reinforcement approach (TRA). The proposed TRA is based on the penalty function method which penalizes the power loss relaxation in the objective function of the convex ACOPF model. A heuristic penalty algorithm is proposed to find the proper penalty parameter of the TRA. Numerical results show relaxation gaps exist in test cases especially for large-scale power networks under low nodal power loads. TRA is effective to reduce the relaxation gap of the convex ACOPF model.