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首页> 外文期刊>Energy Conversion & Management >Nonlinear modeling and stability analysis of hydro-turbine governing system with sloping ceiling tailrace tunnel under load disturbance
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Nonlinear modeling and stability analysis of hydro-turbine governing system with sloping ceiling tailrace tunnel under load disturbance

机译：荷载作用下斜顶尾水隧洞水轮机调节系统的非线性建模与稳定性分析

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In order to overcome the problem of nonlinear dynamics of hydro-turbine governing system with sloping ceiling tailrace tunnel, which is caused by the interface movement of the free surface-pressurized flow in the tailrace tunnel, and the difficulty of analyzing the stability of system, this paper uses the Hopf bifurcation theory to study the stability of hydro-turbine governing system of hydropower station with sloping ceiling tailrace tunnel. Firstly, a novel and rational nonlinear mathematical model of the hydroturbine governing system is proposed. This model contains the dynamic equation of pipeline system which can accurately describe the motion characteristics of the interface of free surface-pressurized flow in sloping ceiling tailrace tunnel. According to the nonlinear mathematical model, the existence and direction of Hopf bifurcation of the nonlinear dynamic system are analyzed. Furthermore, the algebraic criterion of the occurrence of Hopf bifurcation is derived. Then the stability domain and bifurcation diagram of hydro-turbine governing system are drawn by the algebraic criterion, and the characteristics of stability under different state parameters are investigated. Finally, the influence of step load value, ceiling slope angle and section form of tailrace tunnel and water depth at the interface in tailrace tunnel on stability are analyzed based on stable domain. The results indicate that: The Hopf bifurcation of hydro-turbine governing system with sloping ceiling tailrace tunnel is supercritical. The phase space trajectories of characteristic variables stabilize at the equilibrium points and stable limit cycles when the system state parameter point locates in the stable domain and unstable domain, respectively. Under negative disturbance and positive disturbance, the effect laws of step load value, tailrace tunnel slope angle and water depth in tailrace tunnel are inverse. Tailrace tunnel section form has significant influence on the stability under negative disturbance, while it has little influence on the stability under positive disturbance. (C) 2015 Elsevier Ltd. All rights reserved.
机译：为了克服斜尾天花板水轮机调节系统非线性动力学的问题，该问题是由尾水通道中自由面增压流的界面运动引起的，并且难以分析系统的稳定性，本文利用霍夫夫分叉理论研究了斜顶尾水隧洞水电站水轮机调节系统的稳定性。首先，提出了一种新颖合理的水轮机调节系统非线性数学模型。该模型包含管道系统的动力学方程，该方程可以准确地描述倾斜的天花板尾水隧洞中自由表面加压流界面的运动特性。根据非线性数学模型，分析了非线性动力系统Hopf分支的存在性和方向。此外，推导了出现霍普夫分支的代数准则。然后根据代数准则绘制了水轮机调节系统的稳定域和分叉图，并研究了不同状态参数下的稳定特性。最后，基于稳定域，分析了尾水隧洞的阶跃荷载值，顶坡角和尾水隧洞的断面形状以及尾水隧洞界面处的水深对稳定性的影响。研究结果表明：斜顶式尾水隧洞的水轮机调节系统霍普夫分岔是超临界的。当系统状态参数点分别位于稳定域和不稳定域时，特征变量的相空间轨迹稳定在平衡点和稳定极限环上。在负扰动和正扰动下，阶跃荷载值，尾矿隧洞倾斜角和尾矿隧洞水深的影响规律相反。尾部隧道断面形状对负扰动下的稳定性影响很大，而对正扰动下的稳定性影响很小。 （C）2015 Elsevier Ltd.保留所有权利。

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