次同步谐振中的非线性振荡分析

Analysis of non-linear oscillation in sub-synchronous resonance

为了缓解次同步谐振对发电机轴系造成的损坏,利用中心流形理论和分岐理论研究了出现在次同步谐振中的非线性振荡。研究表明,这种振荡是发生在非双曲平衡点邻域内的一种非线性奇异现象。在虚轴左侧附近,轨道不稳的非线性振荡使原来渐近稳定的系统跃变为增幅振荡,导致次同步谐振;在虚轴右侧附近,轨道稳定的非线性振荡使原来增幅振荡的系统跃变为小模等幅振荡,大大缓解次同步谐振。数值仿真结果验证了此观点的正确性。

Abstract： In order to ease the breakage of generator shafting caused by sub - synchronous resonance, the non - lin- ear oscillation in sub - synchronous resonance is studied through center manifold theory and bifurcation theory. The study shows that the oscillation is an odd non - linear phenomenon that takes place near the non - hyperbolic equi- librium. Near the left side of false shaft, the non - linear oscillation with unstable orbit changes the gradually stable oscillation of system jump into the increasing one ; near the right side, the non - linear oscillation with stable orbit changes the increasing oscillation into the continuous one, sub -synchronous resonance being eased greatly. The numerical simulation verifies that the view mentioned in this paper is correct.