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Dynamic analysis of multi-unit hydropower systems in transient process

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Abstract

This paper addresses a mathematical model and dynamic analysis of multi-unit hydropower systems in transient process. In this work, the first unit is assumed to be subject to a sudden load decrease, while the second unit runs with load. An approach to the description of the six stochastic dynamic transfer coefficients of the hydro-turbine is proposed for the second unit. Moreover, a novel dynamic model for the multi-unit hydropower system, able to take into account the eventual occurrence of water hammer in the penstock and the nonlinearity of the generator, is introduced. Also, a numerical application is analyzed in order to investigate the effectiveness of the approach proposed and the dynamic characteristics of the system under study. Finally, a comparative analysis is proposed in order to validate the proposed system. The methods and results implemented in this work provide theoretical tools to guarantee the stable operation of hydropower stations.

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References

  1. Pico, H.V., McCalley, J.D., Angel, A., et al.: Analysis of very low frequency oscillations in hydro-dominant power systems using multi-unit modeling. IEEE Trans. Power Syst. 27, 1906–1915 (2012). doi:10.1109/TPWRS.2012.2187805

    Article  Google Scholar 

  2. Wei, S.P.: Simulation of Hydraulic Turbine Regulating System. Huazhong University of Science & Technology Press, Wuhan (2011). (in Chinese). ISBN: 9787560971483

  3. Guo, W.C., Yang, J.D., Wang, M.J.: 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). doi:10.1016/j.enconman.2015.09.026

    Article  Google Scholar 

  4. Pennacchi, P., Chatterton, S., Vania, A.: Modeling of the dynamic response of a Francis turbine. Mech. Syst. Signal Process. 29, 107–119 (2012). doi:10.1016/j.ymssp.2011.05.012

    Article  Google Scholar 

  5. Pennacchi, P., Borghesani, P., Chatterton, S.: A cyclostationary multi-domain analysis of fluid instability in Kaplan turbines. Mech. Syst. Signal Process. 60–61, 375–390 (2015). doi:10.1016/j.ymssp.2014.08.026

    Article  Google Scholar 

  6. 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. 76, 1921–1933 (2014). doi:10.1007/s11071-014-1257-9

    Article  MATH  Google Scholar 

  7. Jain, S.V., Swarnkar, A., Motwani, K.H., et al.: Effects of impeller diameter and rotational speed on performance of pump running in turbine mode. Energy Convers. Manag. 89, 808–824 (2015). doi:10.1016/j.enconman.2014.10.036

    Article  Google Scholar 

  8. Kranjcic, D., Stumberger, G.: Differential evolution-based identification of the nonlinear kaplan turbine model. IEEE Trans. Energy Convers. 29, 178–187 (2014). doi:10.1109/TEC.2013.2292927

    Article  Google Scholar 

  9. De Jaeger, E., Janssens, N., Malfliet, B., et al.: Hydro turbine model for system dynamic studies. IEEE Trans. Power Syst. 9, 1709–1715 (1994). doi:10.1109/59.331421

    Article  Google Scholar 

  10. Li, Y.L., Xu, D.L.: Chaotification of quasi-zero-stiffness system with time delay control. Nonlinear Dyn. 86, 353–368 (2016). doi:10.1007/s11071-016-2893-z

    Article  MathSciNet  Google Scholar 

  11. Guido, A.R., Adiletta, G.: Dynamics of a rigid unbalanced rotor with nonlinear elastic restoring forces: part I theoretical analysis. Nonlinear Dyn. 19, 359–385 (1999). doi:10.1023/A:1008336006400

    Article  MATH  Google Scholar 

  12. Chang, J.S.: Transients of Hydraulic Machine Installations. Higher Education Press, Beijing (2005). [in Chinese]. ISBN: 7040176475

  13. IEEE Working Group: Hydraulic-turbine and turbine control-models for system dynamic studies. IEEE Trans. Power Syst. 7, 167–79 (1992)

  14. Chen, D.Y., Ding, C., Ma, X.Y., et al.: Nonlinear dynamical analysis of hydro-turbine governing system with a surge tank. Appl. Math. Model. 37, 7611–7623 (2013). doi:10.1016/j.apm.2013.01.047

    Article  MathSciNet  Google Scholar 

  15. Zeng, Y., Zhang, L.X., Guo, Y.K., et al.: Hamiltonian stabilization additional L-2 adaptive control and its application to hydro turbine generating sets. Int. J. Control Autom. Syst. 13, 867–876 (2015). doi:10.1007/s12555-013-0460-7

    Article  Google Scholar 

  16. Chen, L.P., He, Y.G., Chai, Y., Wu, R.C.: New results on stability and stabilization of a class of nonlinear fractional-order systems. Nonlinear Dyn. 75, 633–641 (2014). doi:10.1007/s11071-013-1091-5

    Article  MathSciNet  MATH  Google Scholar 

  17. Shen, Z.Y.: The Analysis of Hydraulic Turbine System (1st edn). Water Resources and Electric Power Press, Beijing (1991). (in Chinese). ISBN: 9787120014407

  18. 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. 81, 1263–1274 (2015). doi:10.1007/s11071-015-2066-5

    Article  Google Scholar 

  19. Shen, Z.Y.: Hydraulic Turbine Regulation. China Water & Power Press, Beijing (1998). (in Chinese). ISBN: 9787801244123

  20. Kishor, N., Singh, S.P., Raghuvanshi, A.S.: Dynamic simulations of hydro turbine and its state estimation based LQ control. Energy Convers. Manag. 47, 3119–3137 (2006). doi:10.1016/j.enconman.2006.03.020

    Article  Google Scholar 

  21. Kishor, N., Saini, R.P., Singh, S.P.: A review on hydropower plant models and control. Renew. Sustain. Energy Rev. 11, 776–796 (2007). doi:10.1016/j.rser.2005.06.003

    Article  Google Scholar 

  22. Chen, D.Y., Ding, C., Do, Y.H., et al.: Nonlinear dynamic analysis for a Francis hydro-turbine governing system and its control. J. Franklin Inst. I(351), 4596–4618 (2014). doi:10.1016/j.jfranklin.2014.07.002

    Article  Google Scholar 

  23. Teran, L.A., Roa, C.V., Munoz-Cubillos, J., et al.: Failure analysis of a run-of-the-river hydroelectric power plant. Eng. Fail. Anal. 68, 87–100 (2016). doi:10.1016/j.engfailanal.2016.05.035

    Article  Google Scholar 

  24. Pavesi, G., Cavazzini, G., Ardizzon, G.: Numerical analysis of the transient behaviour of a variable speed pump-turbine during a pumping power reduction scenario. Energies 9, (2016). doi:10.3390/en9070534

  25. 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). doi:10.1007/s11071-015-2577-0

    Article  MathSciNet  Google Scholar 

  26. Trivedi, C., Cervantes, M.J., Gandhi, B.K., Dahlhaug, Q.G.: Transient pressure measurements on a high head model Francis turbine during emergency shutdown, total load rejection, and runaway. J. Fluids Eng. 136, (2014). doi:10.1115/1.4027794

  27. Trivedi, C., Cervantes, M.J., Gandhi, B.K.: Investigation of a High Head Francis Turbine at Runaway Operating Conditions. Energies 9, (2016). doi:10.3390/en9030149

  28. Nuantong, W., Taechajedcadarungsri, S.: Optimal design of VLH axial hydro-turbine using regression analysis and multi-objective function (GA) optimization methods. J. Appl. Fluid. Mech. 9, 2291–2298 (2016)

    Article  Google Scholar 

  29. Shiva, C.K., Mukherjee, V.: Automatic generation control of hydropower systems using a novel quasi-oppositional harmony search algorithm. Electr. Power Compon. Syst. 44, 1478–1491 (2016). doi:10.1080/15325008.2016.1147103

    Article  Google Scholar 

  30. Qian, J., Zeng, Y., Guo, Y.K., Zhang, L.X.: Reconstruction of the complete characteristics of the hydro turbine based on inner energy loss. Nonlinear Dyn. 86, 963–974 (2016). doi:10.1007/s11071-016-2937-4

    Article  Google Scholar 

  31. Ardizzon, G., Cavazzini, G., Pavesi, G.: A new generation of small hydro and pumped-hydro power plants: advances and future challenges. Renew. Sustain. Energy Rev. 31, 746–761 (2014)

    Article  Google Scholar 

  32. Zhang, H., Chen, D.Y., Xu, B.B., et al.: Nonlinear modeling and dynamic analysis of hydro-turbine governing system in the process of load rejection transient. Energy Convers. Manag. 90, 128–137 (2015). doi:10.1016/j.enconman.2014.11.020

  33. Carapellucci, R., Giordano, L., Pierguidi, F.: Techno-economic evaluation of small-hydro power plants: modelling and characterisation of the Abruzzo region in Italy. Renew. Energy 75, 395–406 (2015). doi:10.1016/j.renene.2014.10.008

    Article  Google Scholar 

  34. Florides, G., Kalogirou, S.: Ground heat exchangers—a review of systems, models and applications. Renew. Energy 32, 2461–2478 (2007). doi:10.1016/j.renene.2006.12.014

    Article  Google Scholar 

  35. Bank, R.E., Coughran, W.C., Fichtner, W., et al.: Transient simulation of silicon devices and circuits. IEEE Trans. Comput. Aided Des. Integr. Circuit Syst. 4, 436–451 (2006). doi:10.1109/TCAD.1985.1270142

    Article  Google Scholar 

  36. Shampine, L.F.: Numerical Solution of Ordinary Differential Equations. Chapman & Hall, New York (1994)

    MATH  Google Scholar 

  37. Ling, D.J., Tao, Y.: An analysis of the Hopf bifurcation in a hydroturbine governing system with saturation. IEEE Trans. Energy Convers. 21, 512–515 (2006). doi:10.1109/TEC.2005.860407

    Article  Google Scholar 

  38. Ba, D.D., Yuan, P., Chen, D.Y., et al.: Modeling and analysis of nonlinear hydro-turbine governing system with complex penstocks. J. Drain. Irrigation Mach. Eng. 30, 428–435 (2012). doi:10.3969/j.issn.1674-8530.2012.04.011. (in Chinese)

    Google Scholar 

Download references

Acknowledgements

This work was supported by the scientific research foundation of National Natural Science Foundation of China—Outstanding Youth Foundation (51622906), National Natural Science Foundation of China (51479173), Fundamental Research Funds for the Central Universities (201304030577), Scientific research funds of Northwest A&F University (2013BSJJ095), 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

    Huanhuan Li, Diyi Chen & Beibei Xu

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

    Diyi Chen

  3. Institute for Risk and Uncertainty, University of Liverpool, Peach Street, Chadwick Building, Liverpool, L69 7ZF, UK

    Silvia Tolo & Edoardo Patelli

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  1. Huanhuan Li
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Correspondence to Diyi Chen.

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Li, H., Chen, D., Xu, B. et al. Dynamic analysis of multi-unit hydropower systems in transient process. Nonlinear Dyn 90, 535–548 (2017). https://doi.org/10.1007/s11071-017-3679-7

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