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| Hamiltonian model of nonlinear hydraulic turbine with elastic water column |
| Zeng Yun1, Zhang Lixiang1, Xu Tianmao2, Guo Yakun3 |
| (1.Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming, Yunnan 650051, China； 2.Computing Center, Kunming University of Science and Technology, Kunming, Yunnan 650051, China； 3.School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE, UK) |
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Abstract To bring the hydraulic turbine and hydraulic system into the theory frame of the generalized Hamiltonian and study the dynamic mechanism of its operation and control, the model of its Hamiltonian system was studied. The hydraulic dynamics with elastic water column in increment described by transfer function were improved into first order differential equations in relative value, and it connects with the differential equation of the guide vane opening to compose the affine nonlinear system of extended hydraulic turbine. By constructing the Hamiltonian function of hydraulic turbine, the affine nonlinear model of hydraulic turbine was converted to Hamiltonian system by adopting orthogonal decomposition realization, and it was realized into Hamiltonian dissipative forms by decomposing the structure matrix and designing the dissipative feedback. The variation of dissipative structure, feedback equivalence and energy flow in built Hamiltonian model were studied, the energy flow of Hamiltonian were consistent with actual system in description of generalized energy. Simulation indicates that the Hamiltonian function contains detailed main information of energy change of hydraulic turbine in transient, and is feasible.
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Received: 20 December 2009
Published: 30 November 2010
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