Representing ZIP loads in convex relaxations of optimal power flow problems

Abstract

The ZIP load models consist of constant-impedance, constant-current, and constant-power loads, which is crucial to access the network performance. Generally, including the constant-impedance and constant-power load model in the optimal power flow (OPF) problem is typically straightforward in convex formulations. However, further inclusion of an exact constant-current load model results in non-convex terms and is computationally challenging. Hence, this paper proposes a new approach for extending convex relaxations of OPF problems to include representations of ZIP load models. Exploiting knowledge of the reference bus’ phase angle, this approach uses geometric relationships to relax the voltage magnitude expressions in order to model the constant-current components, thus enabling convex representations of ZIP load models. The proposed approach is applied to semidefinite, second-order cone and quadratic convex programming relaxations of the OPF problem and demonstrated using several test cases.