基于轨迹模式空间解耦及模式能量序列的振荡分析 (一)理论基础

Oscillation Analysis Based on Trajectory Modes Decoupled in Space and Mode-energy-sequence Part One Theoretical Basis

针对电力系统振荡行为的分析,揭示互补群群际能量观点与特征频率正弦幅值观点的异同,严格证明两者在哈密顿单机无穷大系统中的一致性。但非线性因素则可能在线性化分析中引入大误差,而时变因素及饱和等本质非线性因素还可能使平衡点特征根方法完全失效。为了克服这些困难,从实际受扰轨迹的互补群群际能量的观点出发,描述了复杂受扰系统的振荡特性。多机系统轨迹可以通过互补群惯量中心-相对运动(CCCOI-RM)变换,严格映射为一系列时变单机映象轨迹,并通过各映象系统的振荡能量反映原多机系统的振荡行为,包括多频率的时变非线性振荡。

This paper reveals the similarities and differences between the view of the complementary-cluster inter-group energy and the sinusoidal amplitude of characteristic frequency in power system oscillation behavior analysis.It is strictly proved that they are consistent in the Hamilton one-machine infinite-bus(H-OMIB)system.However,the nonlinear factors may cause large errors to the linear analysis.Besides,the time-varying factors and inherently nonlinear factors such as saturation may make the equilibrium point eigenvalue method completely invalid.In order to overcome these difficulties,this paper describes the oscillation characteristic of the complex disturbed system from the view of complementary-cluster inter-group energy.For the multi-machine system,the trajectories can be mapped into a series of time-varying image system trajectory through complementary-clusters center-of-inertial relative-motion(CCCOI-RM)transform.Then,the oscillation behavior of the original multi-machine system is reflected by the oscillation energy of the image systems including the time-varying nonlinear oscillation with multi-frequency.