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Modeling and Control of a Wind Turbine

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Bond Graphs for Modelling, Control and Fault Diagnosis of Engineering Systems

Abstract

In this chapter, the model of a wind turbine considering the blades, gearbox, and a doubly fed generator is presented. The aerodynamic model for the blades considers the structural forces applied in the blade, in order to calculate the output torque. This output torque is used as the input of the next stage, and is transmitted by the main shaft and bearing to the gearbox. For the gearbox part, the model used here is based on a planetary gear. The use of the gearbox stage in the model is because most of the installed wind turbines have kept this configuration. The variable-speed wind turbine with doubly fed generator configuration is considered. This configuration has some important advantages, e.g., the losses in the power electronics converter (using for their control) are reduced, as compared to a direct-driver synchronous generator configuration, the stress of the mechanical structure is reduced, and the possibility of controlling the reactive power. The complete system behavior is effectively analyzed through simulations. In order to do this, real data provided in the open literature for a 750 kW wind turbine are considered in the model; with its control system taken into account. Moreover, the control of the electrical energy is the fundamental part of a wind turbine. In this context, as mentioned before, the doubly fed induction generator (DFIG) offers an economical benefit to different variable-speed wind turbines configurations. The stator is directly connected to the power network, while the rotor is connected through slip rings to a power electronic converter. The main advantage of this configuration is the fact that the power electronic converter has to handle only a fraction (30 %) of the total power. Therefore, the losses in the power electronic converter can be reduced. The doubly fed induction generator model used in this chapter is based on the Park reference framework. This allows obtaining the inverse model in a simplified manner. Two power electronics converters, machine side converter (MSC) and network side converter (NSC), respectively, are used to build a DC-link between them, thus allowing the power transfer. With the MSC, it is possible to control the torque or speed in the DFIG and the power factor at the stator terminals, while with the NSC functions the DC-link voltage is kept constant. Then, the control laws for the MSC and NSC are presented in this chapter. The control laws applied to the doubly fed induction generator are derived from the inverse model, using the bicausality concepts. The inverse bond graph is used in order to obtain the mathematical expression to control the torque and the active power delivered by the generator. The robustness of the proposed control applied to the wind turbine model is verified for constant and variable wind speed operation conditions.

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Abbreviations

DFIG:

Doubly fed induction generator

MSC:

Machine side converter

NSC:

Network side converter

DC:

Direct current

Cp:

Power coefficient

BEM:

Blade element momentum

DFIM:

Doubly fed induction motor

References

  1. Agarwal, S., Chalal, L., Dauphin-Tanguy, G., & Guillaud, X. (2012). Bond graph model of wind turbine blade. IFAC Proceedings Volumes, 45(2), 409–414.

    Google Scholar 

  2. Borutzy, W. (2011). Bond graph modelling of engineering systems: Theory, applications and software support, Chapter 2. New York: Springer Science Business Media, LLC.

    Google Scholar 

  3. Brown, F. (2001). Engineering system dynamics. New York: Marcel Dekker. ISBN 0-8247-0616-1.

    Google Scholar 

  4. Buhl, M. L. Jr. (2004). A new empirical relationship between thrust coefficient and induction factor for the turbulent windmill state. NREL/TP-500-36834. Golden, CO: National Renewable Energy Laboratory.

    Google Scholar 

  5. Burton, T., Sharpe, D., Jenkins, N., & Bossanyi, E. (2001). Wind energy handbook (p. 11). New York: Wiley.

    Book  Google Scholar 

  6. Coudert, N., Dauphin-Tanguy, G., & Rault, A. (1993). Mechatronic design of an automatic gear box using bond graphs. In IEEE International Conference on Systems, Man and Cybernetics, ‘Systems Engineering in the Service of Humans’ (pp. 216–221).

    Google Scholar 

  7. Dauphin-Tanguy, G. (2000). Les bond graphs. Paris: Hermès Science Editor.

    Google Scholar 

  8. Deur, J., Ivanović, V., Assadian, F., Kuang, M., Tseng, E. H., & Hrovat, D. (2012). Bond graph modeling of automotive transmissions and drivelines. Proceedings of the 7th Vienna International Conference on Mathematical Modelling (MATHMOD), Vienna, Austria.

    Google Scholar 

  9. Etienne-Vidal, P., Pietrzak-David, M., & Bonnet, F. (2008). Mixed control strategy of a doubly fed induction machine. Electrical Engineering (Archiv fur Elektrotechnik), 90(5), 337–346.

    Article  Google Scholar 

  10. Gallo, C., Kasuba, R., Pintz, A., & Spring, J. (1986). Design and dynamic simulation of a fixed pitch 56 kw wind turbine drive train with a continuously variable transmission. U.S. Department of Energy Conservation and Renewable Energy Wind/Ocean Technology Division, NASA CR-179543.

    Google Scholar 

  11. Gawthrop, P. J. (1995). Bicausal bond graph. Proceedings of the International Conference on Bond Graph Modeling and Simulation (ICBGM’95) (Vol. 27, pp. 83–88).

    Google Scholar 

  12. Gonzáñez-Contreras, M., Rullán-Lara, J. L., Vela-Valdés, L. G., & Claudio, S. A. (2007). Modeling, simulation and fault diagnosis of the three-phase inverter using bond graph. In IEEE International Symposium on Industrial Electronics (pp. 130–135).

    Google Scholar 

  13. Guo, Y., Keller, J., & Parker, R. G. (2012). Dynamic analysis of wind turbine planetary gears using an extended harmonic balance approach. International Conference on Noise and Vibration Engineering, Leuven, Belgium, September 17–19, 2012.

    Google Scholar 

  14. Hadi, S. (1999). Power system analysis (pp. 26–28). New York: McGraw-Hill Editions.

    Google Scholar 

  15. Hansen, A. D., Sorensen, P., Iov, F., & Blaabjerg, F. (2005). Centralized power control of wind farm with doubly fed induction generators. Renewable Energy, 31(7), 935–951.

    Article  Google Scholar 

  16. Hansen, M. O. L., Sorensen, J. N., Voutsinas, S., Sorensen, N., & Madsen, H. A. (2006). State of the art in wind turbine aerodynamics and aeroelasticity. Progress in Aerospace Sciences, 42, 285–330.

    Article  Google Scholar 

  17. Józef, W., Jerzy, K., & Zawiśla, S. (2006). Gears and graphs. Journal of Theoretical and Applied Mechanics, 44(1), 139–162.

    Google Scholar 

  18. Karnopp, D. (1991). State functions and bond graph dynamic models for rotary, multi-winding electrical machines. Journal of the Franklin Institute, 328(1), 45–54.

    Article  MathSciNet  Google Scholar 

  19. Karnopp, D., Margolis, D., & Rosenberg, R. (1990). System dynamics: A unified approach. New York: Wiley.

    Google Scholar 

  20. Kubiak, P. (1996). Analyse symbolique des systèmes physiques modélises par bond graph en comportant des éléments multiports. Thèse Université des Sciences et Technologies de Lille, USTL. Lille France.

    Google Scholar 

  21. Luo, Y., & Tan, D. (2011). Dynamics modeling of planetary gear set considering meshing stiffness based on bond graph. Procedia Engineering, 24, 850–855.

    Article  Google Scholar 

  22. Lydia, M., Immanuel Selvakumar, A., Suresh Kumar, S., & Edwin Prem Kumar, G. (2013). Advanced algorithms for wind turbine power curve modeling. IEEE Transaction on Sustainable Energy, 4(3), 827–835.

    Article  Google Scholar 

  23. Mezghanni, D., Andoulsi, R., Mami, A., & Dauphin-Tanguy, G. (2007). Bond graph modeling of a photovoltaic system feeding an induction motor-pump. Simulation Modeling Practice and Theory, 15(10), 1224–1238.

    Article  Google Scholar 

  24. Mikati, M., Santos, M., & Armenta, C. (2013). Electric grid dependence on the configuration of a small-scale wind and solar power hybrid system. Renewable Energy, 57, 587–593.

    Article  Google Scholar 

  25. Miller, A., Chang, B., Issa, R., & Chen, G. (2013). Review of computer-aided numerical simulation in wind energy. Renewable and Sustainable Energy Reviews, 25, 122–134.

    Article  Google Scholar 

  26. Morel, L., Godfroid, H., Mirzaian, A., & Kauffmann, J. (1998). Double-fed induction machine: Converter optimization and field oriented control without position sensor. IEE Proceedings—Electric Power Applications, 145(4), 360–368.

    Article  Google Scholar 

  27. Moriarty, P. J., & Hansen, A. C. (2005). AeroDyn theory manual. National Renewable Energy Laboratory NREL/TP-500-36881.

    Google Scholar 

  28. Mukerjee, A., Karmakar, R., & Samantaray, A. K. (1999). Modeling of basic induction motors and source loading in rotor-motor systems with regenerative force field. Simulation Practice Theory, 7, 563–576.

    Article  Google Scholar 

  29. Mukherjee, A., Karmakar, R., & Samantaray, A. K. (2000). Modelling and simulation of engineering systems through bond graph. New Delhi: Narosa Publishing House.

    Google Scholar 

  30. Ngwomo, R. F., & Scarvarda, S. (1999). Dimensioning problems in system design using bicausal bond graph. Simulation Practice and Theory, 577–587.

    Google Scholar 

  31. Ngwompo, R. F., Scavarda, S., & Thomasset, D. (1996). Inversion of linear time-invariant SISO systems modelled by bond graph. Journal of the Franklin Institute, 333(B)(2), 157–174.

    Article  MathSciNet  MATH  Google Scholar 

  32. Ontiveros, L. J., Mercado, P. E., & Suvire, G. O. (2010). A new model of the doubly-feed induction generator wind turbine. IEEE/PES Transmission and Distribution Conference and Exposition: Latin America.

    Google Scholar 

  33. Patel Mukund, R. (2000). Wind and solar power systems. Boca Raton, FL: CRC Press LLC.

    Google Scholar 

  34. Patiño, C., Tapia, R., Medina, A., & Fuerte, C. (2014). Wind turbine inverse control: A bond graph approach. IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC2014) (pp. 1–6). doi:10.1109/ROPEC.2014.7036354.

  35. Peresada, S., Tilli, A., & Tonielli, A. (2004). Power control of a doubly fed induction machine via output feedback. Control Engineering Practice, 12(1), 41–57.

    Article  Google Scholar 

  36. Ragheb, A., & Ragheb, M. (2010). Wind turbine gearbox technologies. Proceedings of the 1st International Nuclear and Renewable Energy Conference (INREC10), Amman, Jordan, March 21–24, 2010.

    Google Scholar 

  37. Rosenberg, R. C., & Adry, A. N. (1979). Solvability of bond graph structures with loops. IEEE Transactions on Circuits and Systems, CAS-26(2), 130–137.

    Article  MathSciNet  Google Scholar 

  38. S. Junco. (1999). Real- and complex-power bond graph modeling of the induction motor. Proceedings of the International Conference on Bond Graph Modeling and Simulation (ICBGM’99), San Francisco (Vol. 31, pp. 323–328).

    Google Scholar 

  39. Sahm, D. (1979). A two-axis, bond graph model of the dynamics of synchronous electrical machines. Journal of the Franklin Institute, 308(3), 205–218.

    Article  Google Scholar 

  40. Samantaray, A. K., Dasgupta, S. S., & Bhattacharyya, R. (2010). Sommerfeld effect in rotationally symmetric planar dynamical systems. International Journal of Engineering Science, 48(1), 21–36.

    Article  Google Scholar 

  41. Samantaray, A. K., Dasgupta, S. S., & Bhattacharyya, R. (2010). Bond graph modeling of an internally damped non-ideal flexible spinning shaft. Journal of Dynamic Systems, Measurement, and Control, 132(6), 502--509.

    Google Scholar 

  42. Sanchez, R., Dauphin-Tanguy, G., Guillaud, X., & Colas, F. (2010). Bond graph based control of a three-phase inverter with LC filter connection to passive and active loads. Simulation Modelling Practice and Theory, 18, 1185–1198.

    Article  Google Scholar 

  43. Sanchez, R., Guillaud, X., & Dauphin-Tanguy, G. (2012). Hybrid electrical power system modeling and management. Simulation Modelling Practice and Theory, 25, 190–205.

    Article  Google Scholar 

  44. Sanchez, R., & Medina, A. (2014). Wind turbine model simulation: A bond graph approach. Simulation Modelling Practice and Theory, 41, 28–45.

    Article  Google Scholar 

  45. Tapia, R., & Medina, A. (2015). Doubly-fed wind turbine generator control: A bond graph approach. Simulation Modelling Practice and Theory, 53, 149–166.

    Article  Google Scholar 

  46. Tore, B., & Reza, K. (2011). Wind turbine modeling using the bond graph. IEEE International Symposium on Computer-Aided Control System Design (CACSD) (pp. 1208–1213).

    Google Scholar 

  47. Xu, L., & Wei, C. (1995). Torque and reactive power control of a doubly fed induction machine by position sensorless scheme. IEEE Transactions on Industry Application, 31(3), 636–642.

    Article  Google Scholar 

  48. Younsy, R., El-Batanony, I., Tritsch, J. B., Naji, H., & Landjerit, B. (2001). Dynamic study of a wind turbine blade with horizontal axis. European Journal of Mechanics, A. Solids, 20, 241–252.

    Article  MATH  Google Scholar 

  49. Zaimeddine, R., & Undeland, T. (2010). DTC control schemes for induction motor fed by three-level NPC-VSI using space vector modulation. International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM 2010), Pisa, Italy, June 14–16, 2010.

    Google Scholar 

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Authors and Affiliations

  1. División de Estudios de Posgrado, Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, 58000, Mexico

    R. Tapia Sánchez & A. Medina Rios

Authors
  1. R. Tapia Sánchez
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  2. A. Medina Rios
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Correspondence to R. Tapia Sánchez .

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Editors and Affiliations

  1. Department of Computer Science, Bonn-Rhein-Sieg University of Applied Sciences, Sankt Augustin, Germany

    Wolfgang Borutzky

Appendix

Appendix

Table 15.6 Wind turbine data
Full size table

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Sánchez, R.T., Rios, A.M. (2017). Modeling and Control of a Wind Turbine. In: Borutzky, W. (eds) Bond Graphs for Modelling, Control and Fault Diagnosis of Engineering Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-47434-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-47434-2_15

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