On the Robustness and Scalability of Semidefinite Relaxation for Optimal Power Flow Problems

TL;DR

This paper demonstrates that semidefinite relaxation methods can reliably solve large-scale optimal power flow problems with thousands of buses within practical timeframes, addressing previous concerns about scalability and robustness.

Contribution

The study provides empirical evidence that SDP relaxations are scalable and robust for large power systems, with detailed comparisons of solver performance and solution quality.

Findings

Large problem instances with ~10,000 buses solved within minutes.

Test case with 25,000 buses solved within half an hour.

Largest case with 82,000 buses solved within eight hours.

Abstract

Semidefinite relaxation techniques have shown great promise for nonconvex optimal power flow problems. However, a number of independent numerical experiments have led to concerns about scalability and robustness of existing SDP solvers. To address these concerns, we investigate some numerical aspects of the problem and compare different state-of-the-art solvers. Our results demonstrate that semidefinite relaxations of large problem instances with on the order of 10,000 buses can be solved reliably and to reasonable accuracy within minutes. Furthermore, the semidefinite relaxation of a test case with 25,000 buses can be solved reliably within half an hour; the largest test case with 82,000 buses is solved within eight hours. We also compare the lower bound obtained via semidefinite relaxation to locally optimal solutions obtained with nonlinear optimization methods and calculate the optimality gap.