Tight-and-cheap conic relaxation for the optimal reactive power dispatch problem

TL;DR

This paper introduces a tight conic relaxation method for the complex ORPD problem, enabling near-global solutions with small optimality gaps and demonstrating effectiveness on large power system test cases.

Contribution

It proposes a novel convex conic relaxation for the ORPD problem that improves solution quality and computational efficiency over existing methods.

Findings

Achieves near-global optimal solutions with small gaps

Effective on large-scale test cases with up to 3375 buses

Outperforms nonconvex relaxations in solution quality

Abstract

The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The ORPD problem is modelled as a mixed-integer nonlinear optimization problem and its complexity is increased compared to the ACOPF problem, which is highly nonconvex and generally hard to solve. Recently, convex relaxations of the ACOPF problem have attracted a significant interest since they can lead to global optimality. We propose a tight conic relaxation of the ORPD problem and show that a round-off technique applied with this relaxation leads to near-global optimal solutions with very small guaranteed optimality gaps, unlike with the nonconvex continuous relaxation. We report computational results on selected MATPOWER test cases with up to 3375 buses.