A Convex Relaxation of Optimal Power Flow with Synchronous Generator Capability Curves

A method for incorporating synchronous generator capability curves (GCC) into the constraints of the optimal power flow (OPF) problem is proposed. The steady-state equivalent circuit of the synchronous machine in qd variables is added as a branch in the branch flow model (BFM) of the nonlinear power system equations. Semi-definite programming is used to formulate a computationally efficient, convex relaxation of the BFM-based OPF with the GCC constraints. This enables the inclusion of nonlinear GCC equations, which vary with terminal voltage magnitude and include the impact of rotor saliency and stator resistance, in the OPF. Numerical verification and case studies are provided.