Convex Relaxation of AC Optimal Power Flow with Flexible Transmission Line Impedances

TL;DR

This paper introduces a convex relaxation approach for AC optimal power flow problems that incorporate flexible transmission line impedances, enhancing solution tractability and optimality.

Contribution

It develops a novel convexification method by modeling flexible lines as equivalent transformer pairs, reformulating the problem into a semi-definite program.

Findings

Improved solution tractability for AC optimal power flow with flexible lines

Enhanced optimality through convex relaxation techniques

Validated on IEEE 118-bus system with positive results

Abstract

Flexible transmission line impedances on one hand are a promising control resource for facilitating grid flexibility, but on the other hand add much complexity to the concerned optimization problems. This paper develops a convexification method for the AC optimal power flow with flexible line impedances. First, it is discovered that a flexible-impedance line is equivalent to a constant-impedance line linking a pair of transformers with correlated and continuously adjustable tap ratios. Then, with this circuit equivalent, the original optimization problem is reformulated into a semi-definite program under the existing convex relaxation framework, which improves the solution tractability and optimality in an easy-to-implement manner. The proposed method is verified by numerical tests on the IEEE 118-bus system.