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Gain Scheduled H Control of Wind Turbines for the Entire Operating Range

  • Fernando A. Inthamoussou
  • Fernando D. BianchiEmail author
  • Hernán De Battista
  • Ricardo J. Mantz
Chapter
Part of the Advances in Industrial Control book series (AIC)

Abstract

Two different operating modes can be clearly identified in wind turbine control systems. In low wind speeds, the main control objective is the energy capture maximization, whereas in high wind speeds it is desired to regulate turbine power and speed at their rated values. The fulfillment of these different control objectives implies the transition through low controllability operating conditions that impose severe constraints on the achievable performance. The control task is usually tackled using two separate controllers, one for each operating mode, and a switching logic. Although satisfactory control solutions have been developed for low and high wind speeds, controller design needs refinement in order to improve performance in the transition zone. This chapter overviews a control scheme covering the entire operating range with focus on the transition zone. H and advanced anti-windup techniques are exploited to design a high performance control solution for both operating modes with optimum performance in the transition zone.

Keywords

Anti-windup Gain-scheduling control H optimal control Robust control Wind turbines control 

Nomenclature

β

Pitch angle

\(\beta_{r}\)

Pitch angle command

\(\beta_{o}\)

Optimum pitch angle

\(\Theta\)

Torsion angle

λ

Tip-speed-ratio

λo

Optimum tip-speed-ratio

ρ

Air density

τ

Time constant of the pitch actuator

\(\Omega_{g}\)

Generator speed

\(\Omega_{N}\)

Rated rotational speed

\(\Omega_{r}\)

Rotor speed

\(B_{r}\)

Intrinsic rotor damping

\(B_{s}\)

Drive-train damping

\(C_{P}\)

Power coefficient

\(C_{{P_{\hbox{max} } }}\)

Maximum power coefficient

\(J_{g}\)

Generator inertia

\(J_{t}\)

Rotor inertia

\(K_{s}\)

Drive-train stiffness

\(k_{\beta }\)

Torque-pitch gain

\(k_{gs}\)

Gain-scheduling gain

\(k_{V}\)

Torque-wind speed gain

\(N_{g}\)

Gear-box ratio

\(P_{r}\)

Rotor power

\(P_{N}\)

Rated power

\(R\)

Rotor radius

\(T_{g}\)

Generator torque

\(T_{N}\)

Rated torque

\(T_{r}\)

Aerodynamic torque

\(T_{sh}\)

Shaft torque

\(V\)

Wind speed

\(V_{N}\)

Rated wind speed

\({\parallel }G(s){\parallel }_{\infty }\)

Denotes the \(\infty\)-norm of the stable system with transfer function \(G(s)\)

\(\bar{x}\)

Denotes steady-state value of x

\(\hat{x}\)

Denotes variation with respect to the steady-state value of x

\(\dot{x}\)

Denotes \({\text{d}}x/{\text{d}}t\)

Notes

Acknowledgments

The research of F.A. Inthamoussou, H. De Battista, and R.J. Mantz was supported by Universidad Nacional de La Plata (project 11/I164 2012/15), CONICET (PIP 00361 2012/14), CICpba and ANPCyT (PICT 2012-0037 2013/16) of Argentina. The research of F.D. Bianchi was supported by the European Regional Development Funds (ERDF, FEDER Programa Competitivitat de Catalunya 2007–2013).

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Fernando A. Inthamoussou
    • 1
  • Fernando D. Bianchi
    • 2
    Email author
  • Hernán De Battista
    • 1
  • Ricardo J. Mantz
    • 3
  1. 1.CONICET and Instituto LEICI, Facultad de IngenieríaUniversidad Nacional de La PlataLa PlataArgentina
  2. 2.Catalonia Institute for Energy ResearchIRECSant Adrià de BesòsSpain
  3. 3.CIC and Instituto LEICI, Facultad de IngenieríaUniversidad Nacional de La PlataLa PlataArgentina

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