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

Christoph M. Hackl, Pol Jané-Soneira, Martin Pfeifer, Korbinian Schechner and Sören Hohmann
Additional contact information
Christoph M. Hackl: Department of Electrical Engineering and Information Technology, Munich University of Applied Sciences, Lothstraße 64, 80335 München, Germany
Pol Jané-Soneira: Institute of Control Systems (IRS), Karlsruhe Institute of Technology (KIT), Kaiserstraße 12, 76131 Karlsruhe, Germany
Martin Pfeifer: Institute of Control Systems (IRS), Karlsruhe Institute of Technology (KIT), Kaiserstraße 12, 76131 Karlsruhe, Germany
Korbinian Schechner: Research Group “Control of Renewable Energy Systems”, Munich School of Engineering, Technical University of Munich, Lichtenbergstraße 4a, 85748 Garching, Germany
Sören Hohmann: Institute of Control Systems (IRS), Karlsruhe Institute of Technology (KIT), Kaiserstraße 12, 76131 Karlsruhe, Germany

Energies, 2018, vol. 11, issue 7, 1-33

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.

Keywords: wind turbine system; wind energy conversion system; dynamic modeling; control design model; control system; operation management; switching behavior; nonlinear dynamics; model reduction; comparative simulation (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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