正规形理论在电力系统稳定性研究中的应用(一)--从非线性系统到线性系统的映射

电力系统稳定性问题的求解，迄今主要有两种方法：逐步积分的数值解法和利用李雅普诺夫直接法理论的求解法。逐步积分法因为求解时间长，难于满足在线使用的速度要求，并且无法提供稳定裕度的信息；直接法由于求解的精度问题，仍在不断的改进之中。该系列文章介绍正规形理论在电力系统稳定性问题中的应用尝试，以扩大对稳定性问题研究的思路。使用正规形理论研究非线性微分方程的性质，只需要对方程进行适当的线性和非线性变换，将非线性的微分方程组转化为线性微分方程组，非线性系统在某个平衡点上的稳定和不稳定流形相应变换为线性系统的稳定与不稳定于空间，而电力系统在主导不稳定平衡点处的稳定流形是稳定域边界的主要部分；不稳定流形可以预测电力系统故障后的失稳模式，因此应用正规形理论可以研究电力系统稳定性问题。

Application of normal form in study of power system stability Part 1 :Mapping from nonlinear system to linear system

There are mainl y two kinds of method to solve the stability issue of electric power sys-tem thus far,one is step by step integral method,the other is directive method based on Liyapunov theory.Since the step by step method needs much time to solve stability problem,it can not satisfy the rapidity desired by online application,and it can not offer the information of stability either,such as stability margin.The directive method is under continuous improvement for the issue of precision.In order to widen the thoughtway of power system stability study,the application of normal form theory in it is introduced here.To apply the normal form theory to the study of nonlinear differential equation s,it is needed to carry out proper linear and nonlinear transformation for trans-forming the nonlinear differential equation set to a linear equation set.The stable and unstable manifolds on an unstable equilibrium point of nonlinear system are transformed synchronously to the stable and unstable subspaces of linear system.The stable manifolds of a controlling equilibrium point in an electric power system are the main parts of the stability boundary and the unstable manifolds of this point may offer information of unstable modes for a post-fault power system.Therefore,stability issue of electric power system can be studied by applying normal form theory.The research found for the doctoral program of higher education(RFDP-98069814).