小干扰稳定约束最优潮流的非线性半定规划方法

Small-signal Stability Constrained Optimal Power Flow Based on NLSDP

基于特征值优化理论,提出含小干扰稳定约束最优潮流的非线性半定规划模型和算法,以期解决由于系统状态矩阵谱横坐标函数的隐式和非李普希茨特性引起的建模难问题。在模型中,根据李雅谱诺夫定理,引入正定约束精确表达小干扰稳定。算法设计上,将模型中的正定约束转为非线性约束,使建立的非线性半定规划转换为非线性模型,利用现代内点法进行求解。WSCC-9节点及IEEE-14节点两个系统的计算验证了模型的有效性和算法的高度可靠性,为这一领域的发展提供了新的思路。

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.