Influence of the Francis Turbine location under vortex rope excitation on the Hydraulic System Stability

  • Alligne, S. ;
  • Nicolet, C. ;
  • Allenbach, P. ;
  • Kawkabani, B. ;
  • Simond, J.J. ;
  • Avellan, F.
  • Accepted : 2009.05.27
  • Published : 2009.12.01


Hydroelectric power plants are known for their ability to cover variations of the consumption in electrical power networks. In order to follow this changing demand, hydraulic machines are subject to off-design operation. In that case, the swirling flow leaving the runner of a Francis turbine may act under given conditions as an excitation source for the whole hydraulic system. In high load operating conditions, vortex rope behaves as an internal energy source which leads to the self excitation of the system. The aim of this paper is to identify the influence of the full load excitation source location with respect to the eigenmodes shapes on the system stability. For this, a new eigenanalysis tool, based on eigenvalues and eigenvectors computation of the nonlinear set of differential equations in SIMSEN, has been developed. First the modal analysis method and linearization of the set of the nonlinear differential equations are fully described. Then, nonlinear hydro-acoustic models of hydraulic components based on electrical equivalent schemes are presented and linearized. Finally, a hydro-acoustic SIMSEN model of a simple hydraulic power plant, is used to apply the modal analysis and to show the influence of the turbine location on system stability. Through this case study, it brings out that modeling of the pipe viscoelastic damping is decisive to find out stability limits and unstable eigenfrequencies.


Instability;Vortex rope;Eigenvalues;Viscoelastic damping;Francis Turbine


  1. Jacob,T., 1994, “Similitude in stability of operation tests for Francis turbine,” Hydropower & Dams, Vol. 1.
  2. Jacob, T., Prenat, J.E. and Maria, D., 1988, “Comportement dynamique d'une turbine Francis a forte charge comparaison modele prototype”, La houille blanche, Vol. 3, pp. 293-300.
  3. Jacob, T., Prenat, J.E., Vullioud, G. and Araguas, B.L., 1992, “Surging of 140MW Francis Turbine at high load, analysis and solution,” IAHR Symposium on Hydraulic Machinery and systems, Sao Paolo.
  4. Koutnik, J. and Pulpitel, L., 1996, “Modelling of the Francis Turbine full load surge,” IAHR Symposium on Hydraulic Machinery and systems, Lausanne.
  5. Brennen, C. and Acosta, A.J., 1973, “Theoretical, quasi static analysis of cavitation compliance in turbopumps,” Journal Spacecraft, Vol. 10, pp. 175-180.
  6. Brennen, C. and Acosta, A.J., 1976, “The dynamic transfer function for a cavitating inducer,” Journal of fluids engineering ASME, Vol. 98, pp. 182-191.
  7. Tsujimoto, Y., Kamijo, K. and Yoshida, Y., 1993, “Theoretical analysis of rotating cavitation in inducers,” Journal of fluids engineering ASME, Vol. 115, pp. 135-141.
  8. Duttweiller, M. and Brennen, C., 2002, “Surge instability on a cavitating propeller,” Journal of fluids Mechanics, Vol. 458, pp. 133-152.
  9. Brennen, C. and Watanabe, S., 2003, “Dynamics of a cavitating propeller in a water tunnel,” Journal of fluids engineering, Vol. 125, pp. 283-292.
  10. Koutnik, J., Nicolet, C., Schohl, G.A. and Avellan, F., 2006, “Overload surge event in a pumped storage power plant,” IAHR Symposium on Hydraulic Machinery and systems, Yokohama.
  11. Chen, C., Nicolet, C., Yonezawa, K., Farhat, M., Avellan, F. and Tsujimoto, Y., 2007, “One dimensional analysis of full load draft tube surge,” ASME fluids engineering, San Diego.
  12. Nicolet, C., Greiveldinger, B., Herou, J.J., Kawkabani, B., Allenbach, P., Simond, J.J and Avellan, F., 2007, “High order modeling of Hydraulic Power Plant in Islanded Power Network,” IEEE Transactions of powersystem, Vol 22.
  13. Kundur, P., 1994, “Power system stability and control,” EPRI.
  14. Nicolet, C., 2007, “Hydroacoustic modelling and numerical simulation of unsteady operation of hydroelectric systems,” Ph. D. Thesis No3751, Laboratory for Hydraulic Machines, Swiss Federal Institute University, Lausanne.
  15. Wylie, B. and Streeter, V., 1993, “Fluid transients in systems,” E.C Prentice Hall, New Jersey.
  16. Xianlin, L. and Chu, L., 2007, “Eigenanalysis of Oscillatory Instability of a Hydropower Plant Including Water Conduit Dynamics,” IEEE Transactions on Power Systems, Vol 22(2), pp. 675-681
  17. Haban, V., Koutnik, J. and Pochyly, F., 2002, “1D mathematical model of high frequency pressure oscillations induced by RSI including an influence of fluid second viscosity,” IAHR Symposium on Hydraulic Machinery and systems, Lausanne.

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