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Journal of Control Science and Engineering
Volume 2017 (2017), Article ID 2796090, 14 pages
https://doi.org/10.1155/2017/2796090
Research Article

Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

1School of Information Engineering, Gansu Forestry Technological College, Tianshui, Gansu 741020, China
2School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China
3School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China
4School of Applied Mathematics, Xinjiang University of Finance & Economics, Wulumuqi, Xinjiang 830000, China

Correspondence should be addressed to Jiangang Zhang; moc.621@6775177gjgnahz

Received 11 February 2017; Revised 3 July 2017; Accepted 26 July 2017; Published 12 September 2017

Academic Editor: Yongji Wang

Copyright © 2017 Hongwei Luo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Z. Shen, Analysis of Hydro-Turbine Governing System, Publishing House of Water Conservancy & Power, Beijing, China, 1991.
  2. H. Huang and Z. Yan, “Present situation and future prospect of hydropower in China,” Renewable and Sustainable Energy Reviews, vol. 13, no. 6-7, pp. 1652–1656, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. B. Lehner, G. Czisch, and S. Vassolo, “The impact of global change on the hydropower potential of Europe: a model-based analysis,” Energy Policy, vol. 33, no. 7, pp. 839–855, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. S. R. Shakya and R. M. Shrestha, “Transport sector electrification in a hydropower resource rich developing country: energy security, environmental and climate change co-benefits,” Energy for Sustainable Development, vol. 15, no. 2, pp. 147–159, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. C. Jiang, Y. Ma, and C. Wang, “PID controller parameters optimization of hydro-turbine governing systems using deterministic-chaotic-mutation evolutionary programming (DCMEP),” Energy Conversion and Management, vol. 47, no. 9-10, pp. 1222–1230, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. X. Liu and C. Liu, “Eigenanalysis of oscillatory instability of a hydropower plant including water conduit dynamics,” IEEE Transactions on Power Systems, vol. 22, no. 2, pp. 675–681, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. P. Pennacchi, S. Chatterton, and A. Vania, “Modeling of the dynamic response of a Francis turbine,” Mechanical Systems and Signal Processing, vol. 29, pp. 107–119, 2012. View at Publisher · View at Google Scholar
  8. J. Li and Q. Chen, “Nonlinear dynamical analysis of hydraulic turbine governing systems with nonelastic water hammer effect,” Journal of Applied Mathematics, vol. 2014, Article ID 412578, 11 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. C. K. Sanathanan, “Accurate low order model for hydraulic turbine-penstock,” IEEE Transactions on Energy Conversion, vol. 2, no. 2, pp. 196–200, 1987. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Chen, C. Ding, X. Ma, P. Yuan, and D. Ba, “Nonlinear dynamical analysis of hydro-turbine governing system with a surge tank,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 37, no. 14-15, pp. 7611–7623, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. Y. Zeng, Y. Guo, L. Zhang, T. Xu, and H. Dong, “Nonlinear hydro turbine model having a surge tank,” Mathematical and Computer Modelling of Dynamical Systems, vol. 19, no. 1, pp. 12–28, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. C. S. Li, J. Z. Zhou, J. Xiao, and H. Xiao, “Hydraulic turbine governing system identification using T-S fuzzy model optimized by chaotic gravitational search algorithm,” Engineering Applications of Artificial Intelligence, vol. 26, no. 9, pp. 2073–2082, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. D. J. Ling and Y. Tao, “An analysis of the Hopf bifurcation in a hydroturbine governing system with saturation,” IEEE Transactions on Energy Conversion, vol. 21, no. 2, pp. 512–515, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. Galias and M. J. Ogorzalek, “Bifurcation phenomena in second-order digital filter with saturation-type adder overflow characteristic,” IEEE Transactions on Circuits and Systems, vol. 37, no. 8, pp. 1068–1070, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  15. I. Dobson, F. Alvarado, and C. DeMarco, “Sensitivity of Hopf bifurcations to power system parameters,” in Proceedings of the 1992 31st IEEE Conference on Decision and Control, pp. 2928–2933, Tucson, Ariz, USA, December 1992. View at Publisher · View at Google Scholar
  16. A. Nayfeh, A. Harb, and C.-M. Chin, “Bifurcations in a power system model,” in Proceedings of the International Symposium on Circuits and Systems (ISCAS '95), vol. 1, pp. 283–286, Seattle, DC, USA, May 1995. View at Publisher · View at Google Scholar
  17. G. J. Silva, A. Datta, and S. P. Bhattacharyya, “PI stabilization of first-order systems with time delay,” in PID Controllers for Time-Delay Systems, vol. 37, pp. 2025–2031, Birkhäuser Boston, Boston, Mass, USA, 2005. View at Publisher · View at Google Scholar · View at Scopus
  18. H. Shu and Y. Pi, “PID neural networks for time-delay systems,” Computers and Chemical Engineering, vol. 24, no. 2-7, pp. 859–862, 2000. View at Publisher · View at Google Scholar · View at Scopus
  19. B. Strah, O. Kuljaca, and Z. Vukic, “Speed and active power control of hydro turbine unit,” IEEE Transactions on Energy Conversion, vol. 20, no. 2, pp. 424–434, 2005. View at Publisher · View at Google Scholar · View at Scopus
  20. C. S. Li and J. Z. Zhou, “Parameters identification of hydraulic turbine governing system using improved gravitational search algorithm,” Energy Conversion and Management, vol. 52, no. 1, pp. 374–381, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Khodabakhshian and R. Hooshmand, “A new PID controller design for automatic generation control of hydro power systems,” International Journal of Electrical Power and Energy Systems, vol. 32, no. 5, pp. 375–382, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. M. Liu, L. Yang, D. Gan, D. Wang, F. Gao, and Y. Chen, “The stability of AGC systems with commensurate delays,” European Transactions on Electrical Power, vol. 17, no. 6, pp. 615–627, 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. C.-K. Zhang, L. Jiang, Q. H. Wu, Y. He, and M. Wu, “Delay-dependent robust load frequency control for time delay power systems,” IEEE Transactions on Power Systems, vol. 28, no. 3, pp. 2192–2201, 2013. View at Publisher · View at Google Scholar · View at Scopus
  24. D. Chen, C. Ding, Y. Do, X. Ma, H. Zhao, and Y. Wang, “Nonlinear dynamic analysis for a Francis hydro-turbine governing system and its control,” Journal of the Franklin Institute, vol. 351, no. 9, pp. 4596–4618, 2014. View at Publisher · View at Google Scholar · View at Scopus
  25. B. Xu, D. Chen, H. Zhang, F. Wang, X. Zhang, and Y. Wu, “Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag,” Communications in Nonlinear Science and Numerical Simulation, vol. 47, pp. 35–47, 2017. View at Publisher · View at Google Scholar · View at Scopus
  26. F. Wang, D. Chen, B. Xu, and H. Zhang, “Nonlinear dynamics of a novel fractional-order Francis hydro-turbine governing system with time delay,” Chaos, Solitons and Fractals, vol. 91, pp. 329–338, 2016. View at Publisher · View at Google Scholar · View at Scopus
  27. Y. Zhang, J. Cao, and W. Xu, “Stability and Hopf bifurcation of a Goodwin model with four different delays,” Neurocomputing, vol. 165, pp. 144–151, 2015. View at Publisher · View at Google Scholar · View at Scopus
  28. H. Zhang, D. Y. Chen, B. B. Xu, and F. F. Wang, “Nonlinear modeling and dynamic analysis of hydro-turbine governing system in the process of load rejection transient,” Energy Conversion and Management, vol. 90, pp. 128–137, 2015. View at Publisher · View at Google Scholar · View at Scopus
  29. W. Ning, C. Jie, and W. Jicheng, “Neuron intelligent control for hydraulic turbine generators,” in Proceedings of the 1994 IEEE International Conference on Industrial Technology (ICIT '94), pp. 288–292, Guangzhou, China, December 1994. View at Publisher · View at Google Scholar
  30. W. Group, “Hydraulic turbine and turbine control models for system dynamic studies,” IEEE Transactions on Power Systems, vol. 7, no. 1, pp. 167–179, 1992. View at Publisher · View at Google Scholar · View at Scopus
  31. S. Čelikovský and G. Chen, “On the generalized Lorenz canonical form,” Chaos, Solitons & Fractals, vol. 26, no. 5, pp. 1271–1276, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  32. R. Shaw, “Strange attractors, chaotic behavior, and information flow,” A Journal of Physical Sciences, vol. 36, no. 1, pp. 80–112, 2014. View at Publisher · View at Google Scholar · View at Scopus
  33. J. K. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1977. View at MathSciNet
  34. B. D. Hassard, N. D. Kazarinoff, and Y.-H. Wan, Theory and Applications of Hopf Bifurcation, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, 1981. View at MathSciNet