This work is devoted to the analysis of a mathematical model of hydropower unit, consisting of synchronous generator, hydraulic turbine, and speed governor. It is motivated by the accident happened on the Sayano-Shushenskaya hydropower plant in 2009. In the analysis we follow the line of classical mathematical control theory approach developed in the works of famous scientists J.C. Maxwell, I.A. Vishnegradsky, A.A. Andronov, and F. Tricomi for the study of centrifugal turbine governor and electrical machines limit-load problem. It is shown that the occurrence of vibrations in the Sayano-Shushenskaya hydropower plant can be caused by nonlinear dynamics of the closed-form model.

这项工作致力于分析由同步发电机，水轮机和调速器组成的水力发电机组的数学模型。它是由2009年Sayano-Shushenskaya水电站发生的事故引起的。在分析中，我们遵循著名科学家JC Maxwell，IA Vishnegradsky，AA Andronov和F. Tricomi的工作开发的经典数学控制理论方法。用于研究离心式涡轮调速器和电机的极限负荷问题。结果表明，萨亚诺-舒申斯克水电站的振动是由闭合形式模型的非线性动力学引起的。