Engineering with Computers

, Volume 20, Issue 1, pp 45–53 | Cite as

The design of robust multi-loop-cascaded hydro governors

Original Article


In the present paper, a new multi-loop-cascaded governor is proposed for hydro turbine controls. A turbine model is obtained that covers the effects of the water hammer, travelling waves, inelastic water penstocks and head loss due to the friction. Plant parameter uncertainties are taken into account to investigate stability robustness. The polynomial H robust control design method is used to design the multi-loop-cascaded governor. Water and load disturbance, and permanent oscillations in the power systems such as inter-area modes are included in the robust design procedure. Robust performance is achieved by using parameterised dynamic weighting functions of the design theory. The designed governor ensures that the overall system remains asymptotically stable for all norm-bounded uncertainties. Simulation results show that the system performance specifications and stability margins are improved significantly even in the presence of parameter uncertainties.


Multi-loop-cascaded control  Robust governor  Speed control 



Polynomial notation is employed and the polynomials are assumed to be functions of the complex s variable. X* denotes complex conjugate of the X.


S: complex frequency \( s = j\omega ,{\text{ j}} = {\sqrt {{\text{ - 1}}} } \) and ω is the frequency.


R+: Set of all positive real numbers


R: Set of all real numbers


R(.): Set of all real rational functions


R[.]: Set of finite polynomials with real coefficients


Rmxm(.): Set of all real (mxm) matrices


Rmxm[.]: Set of polynomial (mxm) matrices.


  1. 1.
    IEEE Working Group (1992) Hydraulic turbine and turbine control models for system dynamic studies. IEEE Trans PAS 7:167–179.Google Scholar
  2. 2.
    Eker İ, Tumay M (2002) Robust multivariable-cascade governors for hydroturbine controls. Elect Eng 84:229–237CrossRefGoogle Scholar
  3. 3.
    Mansoor SP, Jones DI, Bradley DA, Aris FC, Jones GR (2000) Reproducing oscillatory behaviour of a hydroelectric power station by computer simulation. Control Eng Practice 8:1261–1272CrossRefGoogle Scholar
  4. 4.
    Saleh RAF, Bolton HR (2001) Comparison of an adaptive stabilizer and a fuzzy logic stabilizer for superconducting generator governor control. Elect Power Sys Res 57:65–71CrossRefGoogle Scholar
  5. 5.
    Hannett LN, Fardanesh B (1994) Field test to validate hydro turbine-governor model structure and parameters. IEEE Trans PAS 9:1744–1751CrossRefGoogle Scholar
  6. 6.
    Bourles H, Colledani F, Houry MP (1997) Robust continuous speed governor control for small-signal and transient stability. IEEE Trans PAS 12:129–135.CrossRefGoogle Scholar
  7. 7.
    Eker İ, Aydın İŞ (2001) Governors for hydroturbines: New control schemes and robust designs. In: Proceedings of the 36th Universities Power Engineering Conference (UPEC’2001), Swansea, UK, 12–14 September 2001Google Scholar
  8. 8.
    Grimble MJ (1994) Robust industrial control. Prentice-Hall, Hemel Hempstead, UKGoogle Scholar
  9. 9.
    Forrai A, Tanoi T, Hashimoto S, Funato H, Kamiyama K (2001) Robust controller design with hard constraints on the control signal. Elect Eng 83:179–186CrossRefGoogle Scholar
  10. 10.
    Eker İ, Aydın İŞ (2001) Robust cascade design of governors. In: Proceedings of the 36th Universities Power Engineering Conference (UPEC’2001), Swansea, UK, 12–14 September, 2001Google Scholar
  11. 11.
    Sket IS, Limebeer DJN, Macdonald DC (1993) Turbine generator laboratory model tests to damp torsional oscillations with supplementary signals. IEEE Trans EC 8:85–91Google Scholar
  12. 12.
    IEEE Tutorial Course Text (1980) Power system stabilization via excitation control. 81 EHO 175–0 PWRGoogle Scholar
  13. 13.
    Eker İ, Aydın İŞ (2001) Design of multi-loop multivariable cascade hydro governors. In: Proceedings of the 36th Universities Power Engineering Conference, Swansea, UK, 12–14 September, 2001Google Scholar
  14. 14.
    Eilts LE, Schleif FR (1997) Governing features and performance of the first 600 MW hydrogenerating unit at Grand Coulee. IEEE Trans PAS 96:457–466.Google Scholar
  15. 15.
    Herron J, Wozniak L (1991) A state-space pressure and speed sensing governor for hydro generators. IEEE Trans EC 6:414–418CrossRefGoogle Scholar
  16. 16.
    Menelaou MC, Macdonald DC (1982) Supplementary signals to improve transient stability, on-line application to a micro-generator. IEEE Trans PAS 101:3543–3550.Google Scholar
  17. 17.
    Eker İ, Aydın İŞ (2001) Design and performance requirements for improved governor control. In: Proceedings of the 4th International Energy Congress (ITEC 2001), Çeşme, İzmir, Turkey, 8–12 July 2001Google Scholar
  18. 18.
    Choi HH (2002) Variable structure output feedback control design for a class of uncertain dynamic systems. Automatica 38:335–341CrossRefMATHGoogle Scholar
  19. 19.
    Eker İ, Aydın İŞ (2001) Multi-cascade robust governor design for hydroturbines. In: Proceedings of the 36th Universities Power Engineering Conference (UPEC’2001), Swansea, UK, 12–14 September, 2001Google Scholar
  20. 20.
    Swidenbank E, Brown MD, Flynn D (1999) Self-tuning turbine generator control for power plant. Mechatronics 9:513–537CrossRefGoogle Scholar
  21. 21.
    Eker İ, Aydın İŞ (2001) Adaptive mutli-loop governors. In: Proceedings of the 36th Universities Power Engineering Conference (UPEC’2001), Swansea, UK, 12–14 September 2001Google Scholar
  22. 22.
    Lansberry JE, Wozniak L (1994) Adaptive hydro generator governor tuning with a genetic algorithm. IEEE Trans EC 9:179–185CrossRefGoogle Scholar
  23. 23.
    Zames G (1981) Feedback and optimal sensitivity: model reference transformation, multiplicative seminorms, and approximate inverses. IEEE Trans AC 26:301–320MATHGoogle Scholar
  24. 24.
    Eker İ, Johnson MA (1996) New aspects of cascade and multi-loop process control. Trans Chemie Part-A: Chem Eng Res Design 74:38–54Google Scholar
  25. 25.
    Khundur P (1994) Power system stability and control. McGraw-Hill, LondonGoogle Scholar
  26. 26.
    Eker İ (2002) Hydro-turbine models for robust governor designs in hydro-power generation. In: The 2nd International Conference on Responsive Manufacturing, Gaziantep, Turkey, 26–28 June 2002Google Scholar
  27. 27.
    EEE Committee Report (1972) Dynamic models for steam and hydro turbines in power system studie. IEEE Trans PAS:128–139Google Scholar
  28. 28.
    Yu YN (1983) Electric power system dynamics. Academic Press, New YorkGoogle Scholar
  29. 29.
    Kwakernaak H (1993) Robust control and H-optimisation. Automatica 29:255–273CrossRefMathSciNetMATHGoogle Scholar
  30. 30.
    Orelind G, Wozniak L, Medanic L, Whittemore T (1989) Optimal PID gain schedule for hydro generators: design and application. IEEE Trans EC-4:300–307Google Scholar

Copyright information

© Springer-Verlag London Limited 2004

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringUniversity of GaziantepGaziantepTurkey

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