关于电力传输系统次谐分岔的椭圆函数计算.pdf

Computation of Elliptic Functions for Subharmonic Bifurcation in a Power Transmission System 1 Xingwu Chen, Weinian Zhang Department of Mathematics, Sichuan University Chengdu, Sichuan P. R. China 610064 matzwn@ Abstract In order to control oscillation with large deviation, a nonlinear nonautonomous power transmission system is discussed. In this paper we show the techniques in computation of elliptic functions, which are employed in determining subharmonic bifurcation of the system. Keywords: Power transmission system, nonlinear oscillation, subharmonic bifurcation, elliptic functions 1. Introduction Power transmission systems oscillate periodically when they run normally. However, sometimes they perform irregularly (see [1, 2, 3]), oscillating persistently with no definite amplitude and no definite frequency, or oscillating suddenly, randomly and chaotically. Disintegration could be caused in some serious cases. As reported in [4], in 1966 when US Northwest System and Southwest System were connected together a strange oscillation, which the operator had never observed, occurred six times a minute and it finally resulted in disintegration. Similar phenomena also occurred in China [2]. Since such morbid oscillations are very harmful to security of power transmission systems, recently great efforts are made to research complicated oscillations of power transmission systems both in theory and in practice. The people want to understand the mechanism deeply, find mor