Open AccessEigenvalue‐optimisation‐based optimal power flow with small‐signal stability constraints
Author(s) -
Li Peijie,
Wei Hua,
Li Bin,
Yang Yude
Publication year - 2013
Publication title -
iet generation, transmission and distribution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.92
H-Index - 110
eISSN - 1751-8695
pISSN - 1751-8687
DOI - 10.1049/iet-gtd.2012.0171
Subject(s) - robustness (evolution) , control theory (sociology) , electric power system , eigenvalues and eigenvectors , lipschitz continuity , mathematics , mathematical optimization , stability (learning theory) , lyapunov function , linear programming , computer science , power (physics) , nonlinear system , mathematical analysis , biochemistry , chemistry , gene , physics , control (management) , quantum mechanics , artificial intelligence , machine learning
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.