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