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针对水轮机调节系统中可能存在的Hopf振荡等复杂动力学现象,首先给出了非线性系统Hopf分岔存在性、分岔方向及稳定性判定定理,并具体针对水轮机调节系统刚性和弹性水击下对应的四维和六维系统,推导出各自相应的Hopf和双Hopf分岔存在性判定条件及相关特征量的计算公式;随后通过仿真从系统的稳定域、Jacobi特征根、平衡点、状态变量时域响应、系统振荡周期、相空间极限环等多个角度证明了水轮机刚性和弹性系统中分岔现象的存在,仿真结果与理论分析一致.研究发现,根据稳定域和分岔方向合理地选取PID控制参数对保证系统的安全稳定运行极其重要.“,”To study the complex dynamic phenomena such as Hopf bifurcation that existed in the hydroturbine governing system, the Hopf bifurcation existence, direction and stability judging theorem of nonlinear system was firstly presented,and then the existence judging conditions and computational formulas of the correlated characteristic variables of the Hopf and double-Hopf bifurcation were derived by employing the four- and six-dimension systems of the rigid or elastic water hammer for the hydroturbine governing system. Then the existence of the bifurcation in the system is confirmed from the system stability range, Jacobi eignvalue, equilibrium point, time-domain response of state variables, system oscillation period, limit cycle of phase space perspective by simulation. The simulation results are in good accordance with theoretical analysis. The research results also show that it was of great importance to select appropriate PID parameters based on the stability rank and bifurcation direction to ensure the system safe and stable operation.