Economic dispatch with heavy loading and maximum loading identification using convex relaxation of AC OPF

The objective of this paper is to explore two engineering applications of convex relaxation of AC OPF: (i) to conduct economic dispatch at heavy loading conditions; and (ii) to identify the system's loading limit. The conventional AC OPF formulation solved by interior point method has difficulty to converge when the system is reaching its loading limit due to the singularity of the Jacobian matrix. Existing methods to identify loading limits include continuous power flow (CPF) method. For CPF, the direction of power transfer has to be identified first. Then, a PV nose is obtained and the maximum loading level is at the nose point. Using convex relaxation of alternating current optimal power flow (AC OPF), we will not encounter singularity issues. In this paper, we will formulate a semi-definite programming (SDP) relaxation of AC OPF-based optimization problems to conduct economic dispatch and loading limit identification. Advantages of SDP OPF over MATPOWER are demonstrated. Further, loading limits identified by SDP OPF are compared with those found using the CPF method of MATPOWER. Our research indicates that two methods will lead to the same solutions for the tested systems.