多时间尺度电力系统的模型降阶及稳定性分析 (一)基本理论

ORDER REDUCTION AND STABILITY ANALYSIS FOR MULTI-TIME SCALE POWER SYSTEMS Part One Fundamental Theory

在双时间尺度系统中 ,慢流形的存在性及其基本特征的研究为系统时间尺度分解及系统降阶提供了理论基础。但对于多时间尺度的电力系统模型降阶问题而言 ,还必须研究快流形的存在性及其基本特征 ,以给出固定系统慢动态的降阶条件。文中研究了慢流形的基本理论及略去快动态的条件 ,提出了系统快流形这一不变流形的存在性定理 ,并在系统初值落在快流形的条件下 ,实现系统的精确降阶。文中所得到的结果不仅为电力系统降阶奠定了理论基础 ,而且可以对电力系统的短期失稳与中。

In a two-time scale power system, the theoretical foundation for time-scale differentiation and model reduction can be established through the study on existence and fundamental characteristics of slow manifolds. But for a multi-time scale power system, existence and fundamental characteristics of fast manifolds must also be studied in order to obtain the model reduction condition of fixing slow dynamics. The basic theory of slow manifolds and the conditions for omitting fast dynamics are studied. A theorem on existence of fast manifolds is established, and it is proved that accurate model reduction can be realized if the initial point of the system falls into the fast manifolds. Conclusions of this paper not only lay the theoretical foundation of model reduction of power systems, but also can be used to explain short-term, mid-term and long-term instability of power systems.