Eigenvalue-optimisation-based optimal power flow with small-signal stability constraints

• Published in: IET generation, transmission & distribution transmission & distribution, 2013-05, Vol.7 (5), p.440-450
• Main Authors: Li, Peijie, Wei, Hua, Li, Bin, Yang, Yude
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; damping controllers; Disturbances. Regulation. Protection; eigenvalues and eigenfunctions; eigenvalue‐optimisation‐based NLSDP model; eigenvalue‐optimisation‐based optimal power flow; Electrical engineering. Electrical power engineering; Electrical power engineering; Exact sciences and technology; interior point method; large‐interconnected power system; load flow; Lyapunov theorem; Mathematical models; Miscellaneous; nonlinear programming; nonlinear semidefinite programming model; Nonlinearity; nonLipschitz property; Operation. Load control. Reliability; positive definite constraints; Power flow; Power networks and lines; power system interconnection; power system stability; Programming; Robustness; small‐signal stability constrained‐optimal power flow model; Spectra; SSSC‐OPF model; Stability; stability margin; system state matrix
• ISSN: 1751-8687; 1751-8695; 1751-8695
• DOI: 10.1049/iet-gtd.2012.0171

The occasional oscillation in large interconnected power system can cause the small-signal stability problem. As a complement to the damping controllers, the small-signal stability constrained-optimal power flow (SSSC-OPF) model has been used to obtain the required stability margin. Applying the approximate technique to SSSC-OPF may not only increase the value of the objective function, but also suffer the oscillation of the iterations during the solving process. In this study, an eigenvalue-optimisation-based non-linear semi-definite programming (NLSDP) model and algorithm is proposed for the small-signal stability constraints. It is a significant challenge to model the SSSC-OPF directly because of the implicit and non-Lipschitz property for the spectral abscissa of the system state matrix. Based on the Lyapunov theorem, the positive definite constraints can express the small-signal stability accurately and equivalently, so that SSSC-OPF can be modelled as NLSDP. Afterward, the NLSDP model is transformed into a non-linear programming problem by formulating the positive definite constraints into non-linear ones, which can be solved by the interior point method finally. Numerical simulations for two systems confirm the validity of the model and the robustness of the algorithm.