Full- and Reduced-Order State-Space Modeling of Wind Turbine Systems with Permanent Magnet Synchronous Generator
Department of Electrical Engineering and Information Technology, Munich University of Applied Sciences, Lothstraße 64, 80335 München, Germany
Institute of Control Systems (IRS), Karlsruhe Institute of Technology (KIT), Kaiserstraße 12, 76131 Karlsruhe, Germany
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.
Authors to whom correspondence should be addressed.
Received: 21 June 2018 / Revised: 5 July 2018 / Accepted: 6 July 2018 / Published: 10 July 2018
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 (
)- and (
)-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.
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Hackl, C.M.; Jané-Soneira, P.; Pfeifer, M.; Schechner, K.; Hohmann, S. Full- and Reduced-Order State-Space Modeling of Wind Turbine Systems with Permanent Magnet Synchronous Generator. Energies 2018, 11, 1809.
Hackl CM, Jané-Soneira P, Pfeifer M, Schechner K, Hohmann S. Full- and Reduced-Order State-Space Modeling of Wind Turbine Systems with Permanent Magnet Synchronous Generator. Energies. 2018; 11(7):1809.
Hackl, Christoph M.; Jané-Soneira, Pol; Pfeifer, Martin; Schechner, Korbinian; Hohmann, Sören. 2018. "Full- and Reduced-Order State-Space Modeling of Wind Turbine Systems with Permanent Magnet Synchronous Generator." Energies 11, no. 7: 1809.
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