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

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.