Model-based control of wind turbines for active power control: A unified sector-nonlinearity approach based on Takagi-Sugeno modeling

Florian Pöschke; Horst Schulte

doi:10.1515/auto-2021-0047

Published by De Gruyter (O) October 1, 2021

Model-based control of wind turbines for active power control

A unified sector-nonlinearity approach based on Takagi-Sugeno modeling

Modellbasierter Reglerentwurf zur aktiven Leistungsregelung von Windturbinen

Ein generalisierter Ansatz basierend auf Sektornichtlinearitäten mittels Takagi-Sugeno Formulierung

Florian Pöschke

Florian Pöschke is a research associate in the Control Engineering Group at the Department of Engineering I (Energy and Information), University of Applied Sciences Berlin (HTW). His research topics are: Modeling and Control of Nonlinear Dynamical Systems using Polytopic State-space Models (Takagi-Sugeno fuzzy systems, quasi-LPV systems); Model-based Control of Wind turbines, Wind farms and Electrical power systems.
and Horst Schulte

Horst Schulte is the head of the Control Engineering Group at the Department of Engineering I (Energy and Information), University of Applied Sciences Berlin (HTW). His research topics are Computational Intelligence in Automatic Control; Modeling, Stability Analysis and Control of Nonlinear Dynamic Systems; Robust and Fault-tolerant Control; Applications in Wind Energy, PV Systems, Electric Power Systems, and Electromobility.

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https://doi.org/10.1515/auto-2021-0047

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Abstract

This paper addresses the model-based control design of wind turbines using the sector-nonlinearity approach. Building on the Takagi-Sugeno framework, this approach introduces an exact representation of the underlying nonlinear dynamics into the control design. The unified wind turbine control design followed in this study addresses both established (power optimization in the partial load and power limitation in the full-load region) and further requirements for wind turbine systems. An important control objective for wind turbines is the ability to support grid operators with frequency control. To achieve this, an active power control scheme is inherited in the design model such that changes in the power generation can be balanced and the grid frequency may be controlled. First, the derivation of models designed to achieve the multiple control objectives is presented in detail. After that, a unified synthesis procedure based on linear matrix inequalities is discussed and applied. Finally, the quality of the design process is evaluated through simulation studies for representative scenarios.

Zusammenfassung

Dieser Beitrag befasst sich mit dem modellbasierten Regelungsentwurf für Windturbinen mithilfe des Ansatzes der Sektornichtlinearitäten. Basierend auf einer Takagi-Sugeno Formulierung erlaubt diese Methode eine exakte Beschreibung der unterliegenden nichtlinearen Modellierung in den Regelungsentwurf einzubringen. Das Regelungskonzept umfasst dabei die üblichen Entwurfsziele, d. h. Leistungsoptimierung im Teillast- sowie Leistungsbegrenzung im Volllastbereich als auch weiterführende Anforderungen zur Frequenzregelung des elektrischen Netzes. Diese stellt eine wichtige Eigenschaft zur Einbettung von Windenergieanlagen in das Energiesystem dar. Um diese Funktionalität zu realisieren, wird die aktive Leistungsregelung im Entwurfsmodell berücksichtigt. Damit ist, mit dem Ziel die Netzfrequenz zu stabilisieren, die Möglichkeit zur Leistungsanpassung bei Laständerungen im elektrischen Netz gegeben. In diesem Beitrag wird im Detail auf die Erstellung von geeigneten Entwurfsmodellen unter Berücksichtigung der gestellten Anforderungen eingegangen. Anschließend wird der generalisierte Entwurf, basierend auf linearen Matrix Ungleichungen, diskutiert und auf das Regelungsproblem angewandt. Den Abschluss bildet die Evaluierung des Reglers mithilfe von Simulationsstudien in repräsentativen Szenarien.

Keywords: Takagi-Sugeno fuzzy systems; LMI-based design; control of renewable energy resources

Schlagwörter: Takagi-Sugeno Fuzzy Systeme; Lineare Matrix Ungleichungen; Regelung erneuerbarer Erzeuger

Funding source: H2020 European Research Council

Award Identifier / Grant number: 883985

Funding statement: This research is part of the project EU-Project POSYTYF (POwering SYstem flexibiliTY in the Future through RES), https://posytyf-h2020.eu. The POSYTYF project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 883985.

About the authors

M. Eng. Florian Pöschke

Florian Pöschke is a research associate in the Control Engineering Group at the Department of Engineering I (Energy and Information), University of Applied Sciences Berlin (HTW). His research topics are: Modeling and Control of Nonlinear Dynamical Systems using Polytopic State-space Models (Takagi-Sugeno fuzzy systems, quasi-LPV systems); Model-based Control of Wind turbines, Wind farms and Electrical power systems.

Prof. Dr.-Ing. Horst Schulte

Horst Schulte is the head of the Control Engineering Group at the Department of Engineering I (Energy and Information), University of Applied Sciences Berlin (HTW). His research topics are Computational Intelligence in Automatic Control; Modeling, Stability Analysis and Control of Nonlinear Dynamic Systems; Robust and Fault-tolerant Control; Applications in Wind Energy, PV Systems, Electric Power Systems, and Electromobility.

Appendix A Model parameters

Table 1

Rated values of 5MW NREL Wind Turbine [16].

Symbol	Value	Unit
λ rated	7.0895
ω r , rated	12.1 · π / 30 = 1.2671	rad s
ω g , rated	12.1 · n g · π / 30 = 122.9096	rad s
T g , rated	4.30935 · 10 4	Nm
P r , rated	5.296610 · 10 6	W
v rated	11.26	m/s

Table 2

Parameters of 5MW NREL Wind Turbine adapted to control-oriented models [8].

Symbol	Value	Unit
ρ	1.225	kg / m 3
τ β	0.1	s
τ v	4	s
d T	70000	Ns / m
J g	534.1	kg m 2
J r	38759.227 · 10 3	kg m 2
k T	1981900	N / m
m blade	17740	kg
m nacelle	240000	kg
m rotor	110000	kg
m tower	347640	kg
m T	436865	kg
n g	97
R	63	m

Analytical function of c Q –λ curve

c Q λ , β = c ˜ Q λ , β 1 + sgn c ˜ Q λ , β 2 .

The coefficients c i were published in [8] and determined by fitting the c i parameters of the tailored function (18) to the values of c Q obtained from FAST/AeroDyn simulations of the 5 MW turbine. The following values were obtained:

c 1 = 0.005 c 2 = 1.53 c 3 = 0.5 c 4 = 0.18 c 5 = 121 c 6 = 27.9 c 7 = 198 c 8 = 2.36 c 9 = 5.74 c 10 = 11.35 c 11 = 16.1 c 12 = 201 .

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Received: 2021-02-21

Accepted: 2021-08-24

Published Online: 2021-10-01

Published in Print: 2021-10-26