Abstract: A nonlinear model was established for a hydroturbine speed governing system with complex penstocks to study nonlinear behaviors of the system. A response curve with critical points of Hopf Bifurcation was obtained through a theoretical analysis. It was shown that the system is stable on one side of the curve but unstable on the other side. The stability of the system was analyzed on both sides of the Hopf bifurcation curve by means of numerical simulations. These simulations not only justified the theoretical analysis but also determined a proper range of PID parameters for a stable governor. The nonlinear dynamic behaviors of the governing system were clarified by using bifurcation diagram, Poincare map, power spectrum diagram, time domain diagram, phase orbits diagram and a spectrum diagram. These analysis methods and results will be useful for allowing a hydropower station in safe operations.
[1] 沈祖诒.水轮机调节系统分析[M].北京:水利电力出版社,1996.[2]Liu Yijian, Fang Yanjun. BGNN neural network based on improved e.coli foraging optimization algorithm used in the nonlinear modeling of hydraulic turbine[J]. Lecture Notes in Computer Science, 2009,5551(1):624-634.[3]陈帝伊,杨朋超,马孝义,等.水轮机调节系统的混沌现象分析及控制[J].中国电机工程学报,2010,30(4):63-70.Chen Diyi,Yang Pengchao,Ma Xiaoyi,et al.Chaos of hydroturbine governing system and its control[J].Proceedings of the CSEE,2010,30(4):63-70.(in Chinese)[4]Khodabakhshian A,Hooshmand R.A new PID controller design for automatic generation control of hydro power systems[J].International Journal of Electrical Power & Energy Systems, 2010,32(5):375-382.[5] Mohamad Hasmaini, Mokhlis Hazlie, Bakar Ab Halim Abu, et al. A review on islanding operation and control for distribution network connected with small hydro power plant[J]. Renewable and Sustainable Energy Reviews, 2011,15(8):3952-3962.[6] 张兰金,王正伟,常近时.混流式水泵水轮机全特性曲线S形区流动特性[J].农业机械学报, 2011,42(4):39-43.Zhang Lanjin,Wang Zhengwei,Chang Jinshi.Flow of pumpturbine on Sshaped region of complete characteristics[J].Transactions of the Chinese Society for Agricultural Machinery,2011,42(4):39-43.(in Chinese)[7] 黄志伟,周建中,张勇传.水轮发电机组转子不对中-碰摩耦合故障动力学分析[J].中国电机工程学报,2010,30(8):88-93.Huang Zhiwei,Zhou Jianzhong,Zhang Yongchuan.Dynamic analysis on hydraulic generator rotors with coupling faults of misalignment and rubimpact[J].Proceedings of the CSEE,2010,30(8):88-93.(in Chinese)[8]Zeng Yun,Guo Yakun,Zhang Lixiang,et al.Torque model of hydro turbine with inner energy loss characteristics[J].Science China Technological Sciences,2010,53(10):2826-2832.[9]Pennacchi Paolo,Chatterton Steven,Vania Andrea. Modeling of the dynamic response of a francis turbine[J].Mechanical Systems and Signal Processing,2012,29:107-119.[10] Date Abhijit,Akbarzadeh Aliakbar.Design and cost analysis of low head simple reaction hydroturbine for remote area power supply [J].Renewable Energy,2009,34(2):409-415.[11]Li Chaoshun,Zhou Jianzhong.Parameters identification of hydraulic turbine governing system using improved gravitational search algorithm[J].Energy Conversion and Management, 2011,52(1):374-381.[12]Li Wei, Vanfretti Luigi, Chompoobutrgool Yuwa. Development and implementation of hydro turbine and governor models in a free and open source software package[J]. Simulation Modelling Practice and Theory, 2012,24:84-102.[13]曾云, 张立翔, 徐天茂, 等. 弹性水击下非线性水轮机的哈密顿模型[J].排灌机械工程学报,2010,28(6):515-520.Zeng Yun,Zhang Lixiang,Xu Tianmao,et al.Hamiltonian model of nonlinear hydraulic turbine with elastic water column[J].Journal of Drainage and Irrigation Machinery Engineering,2010,28(6):515-520.(in Chinese)[14]凌代俭.水轮机调节系统分岔与混沌特性的研究[D].南京:河海大学水利水电工程学院,2007.[15]李继彬,冯贝叶.稳定性、分支与混沌[M].昆明:云南科技出版社,1995.