Semidefinite Relaxation Represented ZIP loads in Optimal Power Flow

Abstract

Load modeling is one of the most significant fields in optimal power flow (OPF) problems. However, recent research especially in semidefinite relaxation based OPF has paid much more attention on efficiency, stability and accuracy on convex relaxation reformulation other than load modeling. In this paper, we propose a relatively tightness semidefinite programming (SDP) extension implemented with geometry relations to formulate static ZIP load model, also named as the polynomial load model, which is modeled as constant impedance, constant current and constant power loads, depending on the relation of node voltage magnitude. Such enhanced convex relaxation represented ZIP loads is tighter than that of the former literature reported, since the relaxed polynomial model performs well in detailed load behavior of voltage magnitude dependent. Available SDP formulations on OPF proposed recently can be straightforwardly implemented with the proposed convexity load models. The proposed ZIP load model is tested with up to 118 buses IEEE benchmark on the usage of standard semidefinite programming solvers. The results show that the proposed SDP relaxation represented ZIP load model is on the emergence of both computationally affordable consumption and the accuracy of represented load behavior in reality, since dropping the extra rank relaxation than a previously introduced model.