Pitfalls of Zero Voltage Values in Optimal Power Flow Problems

TL;DR

This paper examines the problematic assumptions of zero voltage values in optimal power flow models, revealing issues with feasibility and relaxation gaps, and proposing valid equalities to address these challenges.

Contribution

It highlights the limitations of zero voltage assumptions in power flow formulations and introduces new valid equalities to improve relaxation accuracy.

Findings

Zero voltage assumptions can lead to infeasible solutions.

A nonzero relaxation gap exists in the power-voltage formulation.

Valid equalities can eliminate the relaxation gap in the branch flow model.

Abstract

The existence of strictly positive lower bounds on voltage magnitude is taken for granted in optimal power flow problems. Nevertheless, it is not possible to rely on such bounds for a variety of real-world network optimization problems. This paper discusses a few issues related to 0 V assumptions made during the process of deriving optimization formulations in the current-voltage, power-voltage and power-lifted-voltage variable spaces. The differences between the assumptions are illustrated for a 2-bus 2-wire test case, where the feasible sets are visualized. A nonzero relaxation gap is observed for the canonical multiconductor nonlinear power-voltage formulation. A zero gap can be obtained for the branch flow model semi-definite relaxation, using newly proposed valid equalities.