Small-signal Stability Constrained Optimal Power Flow Based on NLSDP

For the implicit and non-Lipschitz property of spectral abscissa of system state matrix,it is a big challenge to model the small-signal stability constraints of optimal power flow(OPF) directly.Based on the eigenvalue optimization,this paper presented a nonlinear semi-definite programming(NLSDP) model to handle the small-signal stability constraints.According to the Lyapunov theorem,positive definite constraints were introduced to describe the small-signal stability,yielding an accurate equivalent expression.By formulating the positive definite constraints into nonlinear ones,the NLSDP model was transformed into a nonlinear programming,which could be solved by the interior point method.Numerical simulations on WSCC-9 and IEEE-14 systems confirmed the validity of the model and high robustness of the algorithm.It offers a new idea for considering small-signal stability constraints.