Complex phenomena such as prolongedly undamped ultra-low frequency oscillation (ULFO) and eigenmode re-excitation are observed in the simulations of hydroelectric power systems. Emphases are put on nonlinearities and mode interactions, which cannot be analyzed by traditional eigen-analysis methods. In order to investigate the mechanism of the evolvement of the nonlinear dynamic process in ULFO, this paper proposes a method to analyze the mode interactions quantificationally. First, a disturbed trajectory is decoupled into a set of time-varying components. Second, transfer matrices of eigenmodes are extracted along the trajectory. Third, consecutive sequences of eigenvalues and trajectories of components are formed by a proposed technique. Based on the decoupled components and transfer matrices, the mechanisms of mode interactions and inheritance relationships between eigenmodes are analyzed. The causes and developments of the above complex phenomena are revealed by the proposed method in a test two-machine system. Meanwhile, the accuracy of the eigenmode matching technique is verified in the New England system.

中文翻译：

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基于轨迹特征值的超低频振荡模式相互作用分析

在水力发电系统的仿真中，观察到了复杂的现象，例如长时间无阻尼的超低频振荡（ULFO）和本征模式再励磁。重点放在非线性和模式相互作用上，这是传统的本征分析方法无法分析的。为了研究ULFO中非线性动力学过程演化的机理，提出了一种定量分析模态相互作用的方法。首先，将受干扰的轨迹解耦为一组随时间变化的分量。其次，沿着轨迹提取本征模的传递矩阵。第三，通过提出的技术形成特征值和分量轨迹的连续序列。根据解耦的分量和传递矩阵，分析了本征模式之间的模式相互作用和继承关系的机理。在试验两机系统中，通过提出的方法揭示了上述复杂现象的原因和发展。同时，在新英格兰系统中验证了本征模匹配技术的准确性。