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The slow-fast dynamical behaviors of a hydro-turbine governing system under periodic excitations

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Abstract

This paper studies the dynamic evolution behaviors of the hydro-turbine governing system by using Adams–Bashforth–Moulton algorithm. Based on the non-autonomous dynamic model of the hydro-turbine governing system, the effects of the frequency and intensity of periodic excitation on the dynamic characteristics of the hydro-turbine governing system are analyzed in detail. Due to the different scales between the natural frequency and the excitation frequency, the fast-slow effect is obviously found on the behavior of the system under different motion modes. Furthermore, the influence rules of the fast-slow effect for the dynamic behavior of the hydro-turbine governing system are given. The results of the study can contribute to the optimization analysis and control of the hydro-turbine governing system in practical process.

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References

  1. Xu, B.B., Chen, D.Y., Zhang, H., Zhou, R.: Dynamic analysis and modeling of a novel fractional-order hydro-turbine-generator unit. Nonlinear Dyn. 79, 2066–2070 (2015)

    Google Scholar 

  2. Guo, W.C., Yang, J.D., Wang, M.J., Lai, X.: Nonlinear modeling and stability analysis of hydro-turbine governing system with sloping ceiling tailrace tunnel under load disturbance. Energy Convers. Manag. 106, 127–138 (2015)

    Article  Google Scholar 

  3. Jiang, C.W., Ma, Y.C., Wang, C.M.: PID controller parameters optimization of hydro-turbine governing systems using deterministic-chaotic-mutation evolutionary programming (DCMEP). Energy Convers. Manag. 47, 1222–1230 (2015)

    Article  Google Scholar 

  4. Guo, W.C., Yang, J.D., Chen, J.P., Wang, M.J.: Nonlinear modeling and dynamic control of hydro-turbine governing system with upstream surge tank and sloping ceiling tailrace tunnel. Nonlinear Dyn. 84, 1383–1397 (2016)

    Article  MathSciNet  Google Scholar 

  5. Chen, D.Y., Ding, C., Do, Y.H., Ma, X.Y., Zhao, H., Wang, Y.C.: Nonlinear dynamic analysis for a Francis hydro-turbine governing system and its control. J. Frankl. Inst.-Eng. Appl. Math. 351, 4596–4618 (2014)

    Article  Google Scholar 

  6. Nanda, J., Sreedhar, M., Dasgypta, A.: A new technique in hydro thermal interconnected automatic generation control system by using minority charge carrier inspired algorithm. Int. J. Electr. Power Energy Syst. 68, 259–268 (2015)

    Article  Google Scholar 

  7. Beran, V., Sedlacek, M., Marsik, F.: A new bladeless hydraulic turbine. Appl. Energy 72, 243–263 (2013)

    Google Scholar 

  8. Vieira, F., Ramos, H.M.: Optimization of operational planning for wind/hydro hybrid water supply systems. Renew. Energy 34, 928–936 (2009)

    Article  Google Scholar 

  9. Padhy, M.K., Saini, R.P.: A review on silt erosion in hydro turbines. Renew. Sustain. Energy Rev. 12, 1974–1987 (2008)

    Article  Google Scholar 

  10. Wu, R.Q., Chen, J.Z.: Hydraulic Transients of Hydropower Station. China Water Power Press, Beijing (1997). (in Chinese)

    Google Scholar 

  11. Wang, W., Zeng, D.L., Liu, J.Z., Niu, Y.G., Cui, C.: Feasibility analysis of changing turbine load in power plants using continuous condenser pressure adjustment. Energy 64, 533–540 (2014)

    Article  Google Scholar 

  12. Zhang, R., Wang, Y., Zhang, Z.D., Bi, Q.S.: Nonlinear behaviors as well as the bifurcation mechanism in switched dynamical systems. Nonlinear Dyn. 79, 465–471 (2015)

    Article  Google Scholar 

  13. Karimi, M., Mohamad, H., Mokhlis, H., Bakar, A.H.A.: Under-frequency load shedding scheme for islanded distribution network connected with mini-hydro. Int. J. Electr. Power Energy Syst. 42, 127–138 (2012)

    Article  Google Scholar 

  14. Zeng, Y., Zhang, L.X., Guo, Y.K., Qian, J., Zhang, C.L.: The generalized Hamiltonian model for the shafting transient analysis of the hydro turbine generating sets. Nonlinear Dyn. (2014). doi:10.1007/s11071-014-1257-9

    MATH  Google Scholar 

  15. Nagode, K., Skrjanc, I.: Modelling and internal fuzzy model power control of a Francis water turbine. Energies 7, 874–889 (2014)

    Article  Google Scholar 

  16. Guo, W.C., Yang, J.D., Yang, W.J., Chen, J.P., Teng, Y.: Regulation quality for frequency response of turbine regulating system of isolated hydroelectric power plant with surge tank. Int. J. Electr. Power Energy Syst. 73, 528–538 (2015)

    Article  Google Scholar 

  17. Chen, D.Y., Ding, C., Ma, X.Y., Yuan, P., Ba, D.D.: Nonlinear dynamical analysis of hydro-turbine governing system with a surge tank. Appl. Math. Model. 37, 7611–7623 (2013)

    Article  MathSciNet  Google Scholar 

  18. Pico, H.V., McCalley, J.D., Angel, A., Leon, R., Castrillon, N.J.: Analysis of very low frequency oscillations in hydro-dominant power systems using multi-unit modeling. IEEE Trans. Power Syst. 27, 1906–1915 (2012)

    Article  Google Scholar 

  19. Zhang, H., Chen, D.Y., Xu, B.B., Wang, F.F.: Nonlinear modeling and dynamic analysis of hydro-turbine governing system in the process of load rejection transient. Energy Convers. Manag. 90, 128–137 (2015)

    Article  Google Scholar 

  20. Khodabakhshian, A., Hooshmand, R.: A new PID controller design for automatic generation control of hydro power systems. Int. J. Electr. Power Energy Syst. 32, 375–382 (2010)

    Article  Google Scholar 

  21. Yang, J.D., Wang, M.J., Wang, C., Guo, W.C.: Linear modeling and regulation quality analysis for hydro-turbine governing system with an open tailrace channel. Energies 8, 11702–11717 (2015)

    Article  Google Scholar 

  22. Minakov, A.V., Platonov, D.V., Dekterev, A.A., Sentyabov, A.V., Zakharov, A.V.: The numerical simulation of low frequency pressure pulsations in the high-head Francis turbine. Comput. Fluids 111, 197–205 (2015)

    Article  Google Scholar 

  23. Wang, S.J., Xu, C., Yuan, P., Wang, Y.Y.: Hydrodynamic optimization of channelling device for hydro turbine based on lattice Boltzmann method. Comput. Math. Appl. 61, 3722–3729 (2011)

    Article  Google Scholar 

  24. Borkowski, D., Wegiel, T.: Small hydropower plant with integrated turbine-generators working at variable speed. IEEE Trans. Energy Convers. 28, 452–459 (2013)

    Article  Google Scholar 

  25. Chaudry, M.H.: Applied Hydraulic Transients. Van Nostrand, New York (2014)

    Book  Google Scholar 

  26. Kishor, N.: Zero-order TS fuzzy model to predict hydro turbine speed in closed loop operation. Appl. Soft. Comput. 8, 1074–1084 (2008)

    Article  Google Scholar 

  27. Guo, W.C., Yang, J.D., Chen, J.P., Yang, W.J., Teng, Y., Zeng, W.: Time response of the frequency of hydroelectric generator unit with surge tank under isolated operation based on turbine regulating modes. Electr. Power Compon. Syst. 43, 2341–2355 (2015)

    Article  Google Scholar 

  28. IEEE Working Group: Hydraulic turbine and turbine control model for system dynamic studies. IEEE Trans. Power Syst. 7, 167–179 (1992)

    Google Scholar 

  29. Ling, D.J., Shen, Z.Y.: The nonlinear model of hydraulic turbine governing systems and its PID control and Hopf bifurcation. Proc. CSEE 25, 97–102 (2005). (in Chinese)

    Google Scholar 

  30. Wang, M.J., Yang, J.D., Wang, H.: Analysis of stability of tailrace open channel in small fluctuation governing system. J. Hydroelectr. Eng. 34, 161–168 (2015)

    Google Scholar 

  31. Xu, B.B., Chen, D.Y., Zhang, H., Wang, F.F.: The modeling of the fractional-order shafting system for a water jet mixed-flow pump during the startup process. Commun. Nonlinear Sci. Numer. 29, 12–24 (2015)

    Article  Google Scholar 

  32. Nagornov, R., Osipoy, G., Komarov, M., Pikoysky, A., Shilnikov, A.: Mixed-mode synchronization between two inhibitory neurons with post-inhibitory rebound. Commun. Nonlinear Sci. Numer. 36, 175–191 (2016)

    Article  MathSciNet  Google Scholar 

  33. Zulke, A.A., Varela, H.: The effect of temperature on the coupled slow and fast dynamics of an electrochemical oscillator. Rep. Sci (2016). doi:10.1038/srep24553

  34. Sakaguchi, H., Okita, T.: Cooperative dynamics in coupled systems of fast and slow phase oscillators. Phys. Rev. E (2016). doi:10.1103/PhysRevE.93.022212

    Google Scholar 

  35. De Maesschalck, P., Kutafina, E., Popovic, N.: Sector-delayed-Hopf-type mixed-mode oscillations in a prototypical three-time-scale model. Appl. Math. Comput. 273, 337–352 (2016)

    MathSciNet  Google Scholar 

  36. Xu, Y., Pei, P., Guo, R.: Stochastic averaging for slow-fast dynamical system with fractional Brownian motion. Discrete Contin. Dyn. Syst. Ser. B 20, 2257–2267 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  37. Han, X.J., Bi, Q.S., Ji, P., Kurths, J.: Fast-slow analysis for parametrically and externally excited systems with two slow rationally related excitation frequencies. Rev. E, Phys (2015). doi:10.1103/PhysRevE.92.012911

    Google Scholar 

Download references

Acknowledgements

This work was supported by the scientific research foundation of National Natural Science Foundation–Outstanding Youth Foundation (51622906), National Science Foundation (51479173), Fundamental Research Funds for the Central Universities (201304030577), Scientific research funds of Northwest A&F University (2013BSJJ095), the scientific research foundation on water engineering of Shaanxi Province (2013slkj-12), the Science Fund for Excellent Young Scholars from Northwest A&F University and Shaanxi Nova program (2016KJXX-55).

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Authors and Affiliations

  1. Institute of Water Resources and Hydropower Research, Northwest A&F University, Yangling, 712100, Shaanxi, People’s Republic of China

    Hao Zhang, Diyi Chen & Beibei Xu

  2. Australasian Joint Research Centre for Building Information Modelling, School of Built Environment, Curtin University, Bentley, WA, 6102, Australia

    Diyi Chen, Changzhi Wu & Xiangyu Wang

  3. Department of Housing and Interior Design, Kyung Hee University, Seoul, Korea

    Xiangyu Wang

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  1. Hao Zhang
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  2. Diyi Chen
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  3. Beibei Xu
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  4. Changzhi Wu
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Correspondence to Diyi Chen.

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Zhang, H., Chen, D., Xu, B. et al. The slow-fast dynamical behaviors of a hydro-turbine governing system under periodic excitations. Nonlinear Dyn 87, 2519–2528 (2017). https://doi.org/10.1007/s11071-016-3208-0

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