变顶高尾水洞水轮机调节系统哈密顿模型

Hamiltonian model of a hydro-turbine governing system with inclined ceiling tailrace

为了研究变顶高尾水洞水轮机调节系统瞬态能量变化特征、揭示变顶高尾水洞水轮机调节系统稳定机理,对引水系统动力学方程进行改进,使其更准确描述变顶高尾水洞明满流运动特性。利用广义哈密顿系统在描述能量流变化的优势,构造了变顶高尾水洞水轮机调节系统哈密顿函数,将传统水轮机调节系统仿射非线性方程转化为哈密顿系统形式。首先,从理论上验证了在广义哈密顿理论框架下,变顶高尾水洞水轮机调节系统能量流的变化与实际物理系统的一致性;其次,通过数值模拟表明,所选择的哈密顿函数可以有效地描述变顶高尾水洞水轮机调节系统在瞬态过程中能量变化特征;最后,探究了在无负荷扰动、阶跃负荷扰动和随机负荷扰动情况下,变顶高水轮机调节系统的能量变化规律。

To better study the transient energy change and stabilization mechanism of the hydro-turbine governing system with inclined ceiling tailrace,considering the nonlinear model of the hydro-turbine governing system with inclined ceiling tailrace,the momentum equation of pipeline system is developed in order to accurately describe the dynamic characteristic of the interface of free surface pressurized flow in tailrace.To make full use of strengths of generalized Hamiltonian system in describing energy flow,the Hamilton function of the hydro-turbine with inclined ceiling tailrace is constructed and the traditional affine nonlinear equations for the hydro-turbine governing system with inclined ceiling tailrace are converted into Hamiltonian system.Firstly,the energy flow of the hydro-turbine governing system with inclined ceiling tailrace in the framework of generalized Hamiltonian theory is proved theoretically to be consistent with the real system.Moreover,the simulation results indicate that the constructed Hamiltonian function can effectively describe the energy change of the hydro-turbine governing system with inclined ceiling tailrace in transient process.The regularity of the energy change for the hydro-turbine governing system with inclined ceiling tailrace is deeply studied under no-load,step load and random load,respectively.