变顶高尾水洞水电站水轮机调节系统的Hopf分岔及其动态仿真

基于刚性水击、非线性水轮机、三阶发电机、PID调速器等模型,建立了变顶高尾水洞水电站的水轮机调节系统的非线性模型,运用Hopf分岔理论分析了动力系统的分岔现象,以PID调节参数作为动力系统的分岔参数分析了接力器时间常数、尾水洞坡度和甩负荷对系统稳定域的影响,并采用RKF方法对系统进行了负荷变化的动态仿真。结果表明,系统的Hopf分岔为亚临界,接力器时间常数增大时系统稳定域减小,尾水洞坡度应取较小值,机组甩负荷时系统稳定域增大;在稳定域内系统是渐进稳定的,所建立的模型可用于大波动和小波动的动态仿真。

Hopf Bifurcation and Dynamic Simulation of Hydraulic Turbine Governing System of Hydropower Station with Sloping Ceiling Tailrace Tunnel

The nonlinear model of hydraulic turbine governing system with sloping ceiling tailrace tunnel was established based on the models of rigid water hammer, nonlinear water turbine, three-order generator, and PID governing system. The bifurcation phenomenon of the dynamic system was analyzed by means of the Hopf bifurcation theory. The influences of the engager relay time constant, the sloping value of sloping ceiling tailrace tunnel and the load rejection on the stability domain of the system were analyzed by regarding PID parameters as the bifurcation parameters. Finally, the dynamic simulation of load variation was carried out by the RKF algorithm. The results indicate that the Hopf bifurcation of the system is subcritical, the stability domain of the system decreases while the engager relay time constant increases, the sloping value of sloping tailrace tunnel should be smaller and the stability domain of the system increases when the load decreases. Moreover, the system is gradually stable in the stable domain and the established model can be used for the dynamic simulation of large or small fluctuations.