Please wait a minute...
Chin. Phys. B, 2018, Vol. 27(12): 128202    DOI: 10.1088/1674-1056/27/12/128202
INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY Prev   Next  

Nonlinear fast-slow dynamics of a coupled fractional order hydropower generation system

Xiang Gao(高翔)1,2, Diyi Chen(陈帝伊)1,2,3, Hao Zhang(张浩)1,2, Beibei Xu(许贝贝)1,2, Xiangyu Wang(王翔宇)3
1 Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A & F University, Yangling 712100, China;
2 Institute of Water Resources and Hydropower Research, Northwest A & F University, Yangling 712100, China;
3 Australasian Joint Research Centre for Building Information Modelling, School of Built Environment, Curtin University, WA 6102, Australia
Abstract  

Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system (HGS) are analyzed. A mathematical model of hydro-turbine governing system (HTGS) with rigid water hammer and hydro-turbine generator unit (HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient e is variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast-slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values.

Keywords:  fast-slow dynamics      fractional order      nonlinear dynamics      hydropower generation system  
Received:  18 May 2018      Revised:  09 October 2018      Accepted manuscript online: 
PACS:  82.40.Bj (Oscillations, chaos, and bifurcations)  
  88.60.K- (Hydroturbines)  
  88.40.fc (Modeling and analysis)  
Fund: 

Project supported by the National Natural Science Foundation of China for Outstanding Youth (Grant No. 51622906), the National Natural Science Foundation of China (Grant No. 51479173), the Fundamental Research Funds for the Central Universities (Grant No. 201304030577), the Scientific Research Funds of Northwest A & F University (Grant No. 2013BSJJ095), and the Science Fund for Excellent Young Scholars from Northwest A & F University and Shaanxi Nova Program, China (Grant No. 2016KJXX-55).

Corresponding Authors:  Diyi Chen     E-mail:  diyichen@nwsuaf.edu.cn

Cite this article: 

Xiang Gao(高翔), Diyi Chen(陈帝伊), Hao Zhang(张浩), Beibei Xu(许贝贝), Xiangyu Wang(王翔宇) Nonlinear fast-slow dynamics of a coupled fractional order hydropower generation system 2018 Chin. Phys. B 27 128202

[1] Sarasúa J I, Pérez-Díaz J I, Wilhelmi J R and Á J 2015 Energy Conv. Manag. 106 151
[2] Zeng Y, Zhang L X, Guo Y K, Qian J and Zhang C L 2014 Nonlinear Dyn. 76 1921
[3] Zeng Y, Zhang L X, Guo Y K and Qian J 2015 Int. J. Control Autom 13 867
[4] Joseph A, Desingu K, Semwal R R, Chelliah T R and Khare D 2017 IEEE T. Energy Conver. 33 430
[5] Mesnage H, Alamir M, Perrissin-Fabert N and Alloin Q 2017 Eur. J. Ccontrol 34 24
[6] Moradi H, Alasty A and Vossoughi G 2013 Energy Conv. Manag. 68 105
[7] Pico H V, Mccalley J D, Angel A, Leon R and Castrillon N J 2012 IEEE T. Power Syst. 27 1906
[8] Michelsen F A, Wilhelmsen O Zhao L and Åsen K I 2013 Energy Conv. Manag. 67 160
[9] Poirier M, Gagnon M, Tahan A, Coutu A and Chamberland-Lauzon J 2017 Mech. Syst. Signal Pr. 82 193
[10] Alexopoulos A and Weinberg G V 2014 Phys. Lett. A 378 2478
[11] Li W, Zhang M T and Zhao J F 2017 Chin. Phys. B 26 090501
[12] Bardeji S G, Figueiredo I N and Sousa E 2017 Appl. Num. Math. 114 188
[13] Izsák F and Szekeres B J 2017 Appl. Math. Lett. 71 38
[14] Jothiprakash V, Arunkumar R 2013 Water Resour. Manag. 27 1963
[15] Layek G C and Pati N C 2017 Phys. Lett. A 381 3568
[16] Kumar S, Kumar D and Singh J 2016 Adv. Nonlinear Anal. 5 383
[17] Andrew L Y T, Li X F, Chu Y D and Zhang H 2015 Chin. Phys. B 24 100520
[18] Pahnehkolaei S M A, Alfi A and Machado J A T 2017 Commun. Nonlinear Sci. Num. Simul. 47 328
[19] Sakaguchi H and Okita T 2016 Phys. Rev. E 93 022212
[20] Ma J H and Ren W B 2016 Int. J. Bifur. Chaos 26 1650181
[21] Li H H, Chen D Y, Zhang H, Wang F F and Ba D D 2016 Mech. Syst. Signal Proc. 80 414
[22] Xu B B, Chen D Y, Tolo S, Patelli E and Jiang Y L 2018 Int. J. Elec. Power 95 156
[23] Si G Q, Diao L J, Zhu J W, Lei Y H and Zhang Y B 2017 Chin. Phys. B 26 060503
[24] Li H H, Chen D Y, Xu B B, Tolo S and Patelli E 2017 Nonlinear Dyn. 90 535
[25] Mandić P D, T B Š Lazarević M P and Bošković M 2017 ISA T. 67 76
[26] Pay S S 2016 Chin. Phys. B 25 040204
[27] Xu B B, Chen D Y, Zhang H and Zhou R 2015 Nonlinear Dyn. 81 1263
[28] Xu B B, Chen D Y, Behrens P, Ye W, Guo P C and Luo X Q 2018 Energy Conv. Manag. 174 208
[1] Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application
Yong-Bing Hu(胡永兵), Xiao-Min Yang(杨晓敏), Da-Wei Ding(丁大为), and Zong-Li Yang(杨宗立). Chin. Phys. B, 2022, 31(11): 110501.
[2] Analysis and implementation of new fractional-order multi-scroll hidden attractors
Li Cui(崔力), Wen-Hui Luo(雒文辉), and Qing-Li Ou(欧青立). Chin. Phys. B, 2021, 30(2): 020501.
[3] Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control
Karthikeyan Rajagopal, Anitha Karthikeyan, and Balamurali Ramakrishnan. Chin. Phys. B, 2021, 30(12): 120512.
[4] Leader-following consensus of discrete-time fractional-order multi-agent systems
Erfan Shahamatkhah, Mohammad Tabatabaei. Chin. Phys. B, 2018, 27(1): 010701.
[5] Using wavelet multi-resolution nature to accelerate the identification of fractional order system
Yuan-Lu Li(李远禄), Xiao Meng(孟霄), Ya-Qing Ding(丁亚庆). Chin. Phys. B, 2017, 26(5): 050201.
[6] Prompt efficiency of energy harvesting by magnetic coupling of an improved bi-stable system
Hai-Tao Li(李海涛), Wei-Yang Qin(秦卫阳). Chin. Phys. B, 2016, 25(11): 110503.
[7] Controllability of fractional-order Chua's circuit
Zhang Hao (张浩), Chen Di-Yi (陈帝伊), Zhou Kun (周坤), Wang Yi-Chen (王一琛). Chin. Phys. B, 2015, 24(3): 030203.
[8] A novel adaptive-impulsive synchronization of fractional-order chaotic systems
Leung Y. T. Andrew, Li Xian-Feng, Chu Yan-Dong, Zhang Hui. Chin. Phys. B, 2015, 24(10): 100502.
[9] Function projective lag synchronization of fractional-order chaotic systems
Wang Sha (王莎), Yu Yong-Guang (于永光), Wang Hu (王虎), Ahmed Rahmani. Chin. Phys. B, 2014, 23(4): 040502.
[10] Nonlinear dissipative dynamics of a two-component atomic condensate coupling with a continuum
Zhong Hong-Hua (钟宏华), Xie Qiong-Tao (谢琼涛), Xu Jun (徐军), Hai Wen-Hua (海文华), Li Chao-Hong (李朝红). Chin. Phys. B, 2014, 23(2): 020314.
[11] Generalized projective synchronization of the fractional-order chaotic system using adaptive fuzzy sliding mode control
Wang Li-Ming (王立明), Tang Yong-Guang (唐永光), Chai Yong-Quan (柴永泉), Wu Feng (吴峰). Chin. Phys. B, 2014, 23(10): 100501.
[12] The propagation of shape changing soliton in a nonuniform nonlocal media
L. Kavitha, C. Lavanya, S. Dhamayanthi, N. Akila, D. Gopi. Chin. Phys. B, 2013, 22(8): 084209.
[13] Propagation of electromagnetic soliton in anisotropic biquadratic ferromagnetic medium
L. Kavitha, M. Saravanan, D. Gopi. Chin. Phys. B, 2013, 22(3): 030512.
[14] A fractional order hyperchaotic system derived from Liu system and its circuit realization
Han Qiang (韩强), Liu Chong-Xin (刘崇新), Sun Lei (孙蕾), Zhu Da-Rui (朱大锐). Chin. Phys. B, 2013, 22(2): 020502.
[15] The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium
Ahmed E. Abouelregal, Ashraf M. Zenkour. Chin. Phys. B, 2013, 22(10): 108102.
No Suggested Reading articles found!