用时间序列的李雅普诺夫指数计算预报电力系统中的某些失稳现象

PREDICTING SOME COLLAPSES IN POWER SYSTEMS BY COMPUTING WINDOWED LYAPUNOV EXPONENTS OF TIME SERIES

电力系统存在非线性失稳现象 ,分叉现象 (特别是不稳定极限集导致的分叉现象 )是导致非线性失稳的原因之一。该文提出了直接利用对实际系统采样得到的时间序列窗口上Lyapunov指数的计算 ,来预报与不稳定极限集分叉有关或类似的失稳现象。因为用方程法研究分叉时 ,所采用的方程、初值和参数等对实际系统存在一定的误差 ,而分叉现象又对方程、初值和参数极为敏感。

Simulation has proved that there are nonlinear instabilities in power systems. Bifurcation can cause some nonlinear instabilities, especially non stable limit set bifurcation, in which the time behavior usually undergoes a period of positive largest Lyapunov exponent, before the system suddenly goes unstable. This paper suggests that predicting some instabilities by directly computing the windowed largest Lyapunov exponent of the time series that sampled from the actual system. The aim is to remedy the defects that are in predicting instabilities by system equations, as bifurcation is sensitive to the forms, initial conditions, parameters of the equations, while there must be inevitable errors between the actual systems and their models (equations) which are established from the sampled data.