Pitfalls of Zero Voltage Values in Optimal Power Flow Problems

Frederik Geth

Published 2022-11-08Version 1

The existence of strictly positive lower bounds on voltage magnitude is taken for granted in optimal power flow problems. Nevertheless, it 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 a 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.