In this paper, optimal power flow (OPF) is analyzed and determined with transient stability constraints. PEBS (potential energy boundary surface) method is applied to assess the transient stability. The related transient stability constraints represented by a dot product are introduced in the OPF model. Though OPF with transient stability constraints is a semi-infinite programming problem, it can be transformed to a standard programming problem by transcription techniques. Improved Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is adopted to simplify the complicated derivation of Hessian matrix. It splits the Hessian matrix into computable and approximated parts with the approximated part being updated iteratively. With superlinear convergence property, the computation burden is reduced. The proposed algorithm has been fully validated on the New England 39-bus test system.
- Hessian matrices
- Load flow
- Power system transient stability