(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)
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.
[1]程代展,席在荣,卢强,等.广义Hamilton控制系统的几何结构及其应用[J].中国科学:E辑,2000,30(4):341-355.Cheng Daizhan,Xi Zairong,Lu Qiang,et al.Geometrical structure and application of generalized controlled Hamiltonian systems[J].Science in China:Series E,2000,30(4):341-355.(in Chinese)[2]Van der Schaft A.L2-gain and passivity techniques in nonlinear control[M].Berlin:Springer,1996.[3]王冰,季海波,陈欢,等.基于Hamilton能量理论的水轮发电机水门与励磁非线性L2控制[J].电机与控制学报,2006,10(1):9-13.Wang Bing,Ji Haibo,Chen Huan,et al.Nonlinear L2 design for the water-gate and excitation control of hydroturbine generator based on Hamiltonian energy theory[J].Electric Machines and Control,2006,10(1):9-13.(in Chinese)[4]曾云,王煜,张成立.非线性水轮发电机组哈密顿系统研究[J].中国电机工程学报,2008,28(29):88-92.Zeng Yun,Wang Yu,Zhang Chengli.Study for Hamiltonian system of nonlinear hydraulic turbine generating unit[J].Proceedings of the CSEE,2008,28(29):88-92.(in Chinese)[5]孙元章,焦晓红,申铁龙.电力系统非线性鲁棒控制[M].北京:清华大学出版社,2007.[6]王玉振.广义Hamilton控制系统理论--实现、控制与应用[M].北京:科学出版社,2007.[7]袁寿其,刘厚林.泵类流体机械研究进展与展望[J].排灌机械,2007,25(6):46-51.Yuan Shouqi,Liu Houlin.Research progress and prospect on fluid machinery-pumps[J].Drainage and Irrigation Machinery,2007,25(6):46-51.(in Chinese).[8]沈祖诒.水轮机调节系统分析[M].北京:水利水电出版社,1991.[9]Oldenburger R,Donelson J.Dynamic response of a hydroelectric plant[J].Power Apparatus and Systems-Part Ⅲ:Transactions of the American Institute of Electrical Engineers,1962,81(3):403-418.[10]Vournas C D.Second order hydraulic turbine models for multimachine stability studies[J].IEEE Trans Energy Conversion,1990,5(2):239-244.[11]IEEE Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies.Hydraulic turbine and turbine control models for system dynamic studies[J].IEEE Trans Power System,1992,7(2):167-179.[12]De Jaeger E,Janssens N,Malfliet B,et al.Hydro turbine model for system dynamic studies[J].IEEE Trans Power System,1994,9(4):1709-1715.[13]Kundur P.Power System Stability and Control[M].New York:McGraw-Hill,1994.[14]Lu Qiang,Sun Chunxiao,Sun Yuangzhang.Nonlinear governor control for hydroturbine generator sets[C]//IEEE TENCON '93 Proceedings of Computer,Communication,Control and Power Engineering.Beijing:[s.n.],1993.[15]Quiroga O D.Modelling and nonlinear control of voltage frequency of hydroelectric power plant[D].Ph-Tesis:Instituto de Organización y Control de Sistemas Indus-triales,Universidad Politécnica de Cataluňa,2000.[16]Wang Yuzhen,Cheng Daizhan,Hu Xiaoming.Problems on time-varying port-controlled Hamiltonian systems:geometric structure and dissipative realization[J].Automatica,2005,41(5):717-723.
