随机激励下基于微分包含理论的电力系统低频振荡分析

Small-signal Stability Analysis of Power System Under Stochastic Excitation Through Differential Inclusion Theory

可再生能源大规模、高密度的接入显著改变了电力系统静/动态特性,对系统建模、仿真、分析和控制带来了挑战。该文针对含不确定性的电力系统稳定性分析问题,引入微分包含理论,建立一种随机激励下电力系统低频振荡分析模型。针对含不确定性的电力系统稳定性问题,采用线性多胞体(polytopic linear differential inclusion,PLDI)微分方法,将包含不确定性的随机激励表征为有限个元素的凸包。基于凸包李雅谱诺夫(Lyapunov)函数法推导多胞体系统稳定判据,并给出强阻尼系统约束条件;进而,基于Hankel范数逼近法,给出一种适用于大规模柔性互联系统的低频振荡分析方法。以简单两机系统、10机39节点系统验证所提出方法及稳定判据。仿真结果表明,该文所提方法能准确地刻画随机激励下的电力系统本质。

The large-scale, high-density integration of renewable generations significantly influence on the static\dynamic characteristics of power system, and bring challenges to system modeling, simulation, analysis and control.Aiming at solving stability analysis issue containing uncertainty, differential inclusion theory was introduced to establish a small-signal stability model in this paper. Based on the polytopic linear differential inclusion theory(PLDI), a power system under stochastic disturbances was described as variety elements of convex hull. Convex hull Lyapunov function(CHLF) was used to derive the stability criterion and construct strongly damping constraints for PLDI system.Subsequently, Hankel normal approximation was introduced to obtain the model reduction, and an optimization technique was built for stability analysis. The validity of the proposed method and criterion was tested under both simple two-machine system and New England system. The simulation results show that the proposed method can accurately reflect the intrinsic character of power system with stochastic disturbance.