基于Hopf分岔的变顶高尾水洞水电站水轮机调节系统稳定性研究  

Stability analysis of hydro-turbine governing system of hydropower station with inclined ceiling tailrace based on Hopf bifurcation

作　　者：郭文成[1] 杨建东[1] 王明疆[1,2] 

机构地区：[1]武汉大学水资源与水电工程科学国家重点实验室,湖北武汉430072 [2]中国电建集团西北勘测设计研究院有限公司,陕西西安710065

出　　处：《水利学报》2016年第2期189-199,共11页Journal of Hydraulic Engineering

基　　金：国家自然科学基金项目(51379158);国家留学基金委公派留学基金(201506270057)

摘　　要：运用Hopf分岔理论对变顶高尾水洞水电站水轮机调节系统的稳定性进行研究。首先建立水轮机调节系统非线性数学模型,其中改进的引水系统动力方程可更准确描述变顶高尾水洞明满流分界面运动特性,据此模型进行非线性动力系统Hopf分岔的存在性、分岔方向等的分析,推导得到系统发生Hopf分岔的代数判据;然后利用代数判据绘制了系统的稳定域,并分析了系统在不同状态参数下的稳定特性;最后利用稳定域分析了变顶高尾水洞在机组负荷调整下的稳定性工作原理。结果表明:变顶高尾水洞水电站水轮机调节系统的Hopf分岔是超临界的;明满流引起的水流惯性变化在机组减负荷时对系统的稳定性有利、增负荷时对系统的稳定性不利,明流段水位波动的作用对于系统的稳定性在增、减负荷下都是有利的。Based on the Hopf bifurcation theory, the stability analysis of hydro-turbine governing system of hydropover station with inclined ceiling tailrace is studied. Firstly, the nonlinear mathematical model is established . This model contains the momentum equation of pipeline system which can accurately describe the motion characteristics of the interface of free surface pressurized flow in inclined ceiling tailrace. According to the nonlinear mathematical model, the existence and direction of Hopf bifurcation of nonlinear dynamic system are analyzed. Furthermore, the algebraic criterion of the occurrence of Hopf bifurcation is derived. Then t^e stability domain of hydro-turbine governing system is drawn by the algebraic criterion, and the characteristics of stability under different state parameters are investigated. Finally, the stability working principle of inclined ceiling tailrace in the condition of load adjustment is studied based on stability do- main. The results indicate that the Hopf bifurcation of hydro-turbine governing system of hydropower station with in,：lined ceiling tailrace is supercritical. The variation of water inertia caused by free surface pressurized flo is favorable for the stability under load reduction, but it is unfavorable under load increase. However, the water-level fluctuation of free surface flow is always favorable for the stability under load reduction and load increase.

关 键 词：变顶高尾水洞 水轮机调节 非线性系统 稳定性 HOPF分岔 

分 类 号：TV732[水利工程—水利水电工程]