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中文摘要：
为了深入揭示水轮发电机组系统稳定的规律性，建立了含尾水管道和调压井，并考虑弹性水击效应的水力发电机组系统的非线性数学模型。该模型物理意义清晰，便于分析，适用于大波动情况。在此基础上，以PID参数为分析参数，运用Hoff分岔存在性直接代数判据对系统的稳定性进行了理论分析；通过计算Lyapunov指数对系统的稳定性及分岔特性进行了进一步分析；并对系统的响应特性进行了仿真分析。理论分析及数值模拟分析表明：非线性动力学理论可以很好的为水力发电机组系统稳定性提供参数选择依据，并为水力发电机组出现的低频振荡提供了理论解释。
英文摘要：
A nonlinear mathematical model is presented for hydro-turbine governing system with long tailrace and surge tank based on theoretical analysis and consideration of the effect of elastic water column to study the nonlinear dynamical behaviors of the system. This has clear physical meanings and is easy to use and applicable to analysis of system dynamical characteristics with large fluctuation amplitudes. It uses a direct algebra criterion from the existence of Hoff bifurcation to examine the system＇s bifurcation behaviors, taking adjustment coefficients as bifurcation parameters. Numerical simulations are presented to describe the features of a specific system, including the Lyapunov exponents for demonstration of steady bifurcation. The results show that this criterion can be used to choose the system＇s parameters and the present study provides a feasible explanation for low-frequency oscillations in hydropower system.
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