Tightening QC Relaxations of AC Optimal Power Flow Problems via Complex Per Unit Normalization

TL;DR

This paper introduces two novel improvements to QC relaxations for AC optimal power flow problems, utilizing complex per unit normalization and polar representations to achieve tighter convex envelopes and enhanced solution accuracy.

Contribution

The paper proposes a new complex per unit normalization technique and polar representation to tighten QC relaxations of AC OPF problems, improving their accuracy.

Findings

Tighter convex envelopes achieved with the proposed methods.

Empirical results show improved relaxation accuracy over state-of-the-art.

Guidelines for selecting the complex base power angle based on test cases.

Abstract

Optimal power flow (OPF) is a key problem in power system operations. OPF problems that use the nonlinear AC power flow equations to accurately model the network physics have inherent challenges associated with non-convexity. To address these challenges, recent research has applied various convex relaxation approaches to OPF problems. The QC relaxation is a promising approach that convexifies the trigonometric and product terms in the OPF problem by enclosing these terms in convex envelopes. The accuracy of the QC relaxation strongly depends on the tightness of these envelopes. This paper presents two improvements to these envelopes. The first improvement leverages a polar representation of the branch admittances in addition to the rectangular representation used previously. The second improvement is based on a coordinate transformation via a complex per unit base power normalization that rotates the power flow equations. The trigonometric envelopes resulting from this rotation can be tighter than the corresponding envelopes in previous QC relaxation formulations. Using an empirical analysis with a variety of test cases, this paper suggests an appropriate value for the angle of the complex base power. Comparing the results with a state-of-the-art QC formulation reveals the advantages of the proposed improvements.