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Full- and Reduced-Order State-Space Modeling of Wind Turbine Systems with Permanent Magnet Synchronous Generator

Author

Listed:
  • Christoph M. Hackl

    (Department of Electrical Engineering and Information Technology, Munich University of Applied Sciences, Lothstraße 64, 80335 München, Germany
    These authors contributed equally to this work.)

  • Pol Jané-Soneira

    (Institute of Control Systems (IRS), Karlsruhe Institute of Technology (KIT), Kaiserstraße 12, 76131 Karlsruhe, Germany
    These authors contributed equally to this work.)

  • Martin Pfeifer

    (Institute of Control Systems (IRS), Karlsruhe Institute of Technology (KIT), Kaiserstraße 12, 76131 Karlsruhe, Germany
    These authors contributed equally to this work.)

  • Korbinian Schechner

    (Research Group “Control of Renewable Energy Systems”, Munich School of Engineering, Technical University of Munich, Lichtenbergstraße 4a, 85748 Garching, Germany
    These authors contributed equally to this work.)

  • Sören Hohmann

    (Institute of Control Systems (IRS), Karlsruhe Institute of Technology (KIT), Kaiserstraße 12, 76131 Karlsruhe, Germany)

Abstract

Full-order state-space models represent the starting point for the development of advanced control methods for wind turbine systems (WTSs). Regarding existing control-oriented WTS models, two research gaps must be noted: (i) There exists no full-order WTS model in form of one overall ordinary differential equation that considers all dynamical effects which significantly influence the electrical power output; (ii) all existing reduced-order WTS models are subject to rather arbitrary simplifications and are not validated against a full-order model. Therefore, in this paper, two full-order nonlinear state-space models (of 11th and 9th-order in the ( a , b , c )- and ( d , q )-reference frame, resp.) for variable-speed variable-pitch permanent magnet synchronous generator WTSs are derived. The full-order models cover all relevant dynamical effects with significant impact on the system’s power output, including the switching behavior of the power electronic devices. Based on the full-order models, by a step-by-step model reduction procedure, two reduced-order WTS models are deduced: A non-switching (averaging) 7th-order WTS model and a non-switching 3rd-order WTS model. Comparative simulation results reveal that all models capture the dominant system dynamics properly. The full-order models allow for a detailed analysis covering the high frequency oscillations in the instantaneous power output due to the switching in the power converters. The reduced-order models provide a time-averaged instantaneous power output (which still correctly reflects the energy produced by the WTS) and come with a drastically reduced complexity making those models appropriate for large-scale power grid controller design.

Suggested Citation

  • Christoph M. Hackl & Pol Jané-Soneira & Martin Pfeifer & Korbinian Schechner & Sören Hohmann, 2018. "Full- and Reduced-Order State-Space Modeling of Wind Turbine Systems with Permanent Magnet Synchronous Generator," Energies, MDPI, vol. 11(7), pages 1-33, July.
    • Handle: RePEc:gam:jeners:v:11:y:2018:i:7:p:1809-:d:157274
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    References listed on IDEAS

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    1. Sánchez, J.A. & Veganzones, C. & Martínez, S. & Blázquez, F. & Herrero, N. & Wilhelmi, J.R., 2008. "Dynamic model of wind energy conversion systems with variable speed synchronous generator and full-size power converter for large-scale power system stability studies," Renewable Energy, Elsevier, vol. 33(6), pages 1186-1198.
    2. Bououden, S. & Chadli, M. & Filali, S. & El Hajjaji, A., 2012. "Fuzzy model based multivariable predictive control of a variable speed wind turbine: LMI approach," Renewable Energy, Elsevier, vol. 37(1), pages 434-439.
    3. Mohamed Zribi & Muthana Alrifai & Mohamed Rayan, 2017. "Sliding Mode Control of a Variable- Speed Wind Energy Conversion System Using a Squirrel Cage Induction Generator," Energies, MDPI, vol. 10(5), pages 1-21, May.
    4. Ting-Chia Ou & Kai-Hung Lu & Chiou-Jye Huang, 2017. "Improvement of Transient Stability in a Hybrid Power Multi-System Using a Designed NIDC (Novel Intelligent Damping Controller)," Energies, MDPI, vol. 10(4), pages 1-16, April.
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    Cited by:

    1. Ralf Stetter, 2020. "Approaches for Modelling the Physical Behavior of Technical Systems on the Example of Wind Turbines," Energies, MDPI, vol. 13(8), pages 1-27, April.

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