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Analysis and emulation of pitch control forces in wind turbines

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Abstract

In this paper, a hardware in the loop (HIL) scheme using a polynomial approximation for the calculation of aerodynamic forces associated with wind turbine blades is presented. The proposed approach allows the real-time calculation of forces acting on a blade for use as input data for a force emulating system. The blade element momentum (BEM) theory was used to calculate the axial and tangential forces, but an iterative algorithm needs to be executed for each time of the system’s operation. In order to allow a real-time calculation, the BEM algorithm can be executed for a range of rotor angular speeds, wind velocities, and pitch angles covering the conditions under which the wind turbine will operate. The resulting power, torque, and forces are then approximated by polynomials and implemented in an HIL test facility. A comparison between the results obtained from the BEM algorithm and polynomials demonstrates the accuracy of the proposed approach. An experimental setup comprised of the software used for the force and pitch angle calculation and the hardware used for the force emulation and pitch angle control is presented. Experimental results obtained with the system running in real-time demonstrate the ability to apply effective moments without the need for an extensive test structure.

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Abbreviations

α :

Angle of attack [rad]

\(\alpha_{\text{o}}\) :

Optimal angle of attack [rad]

β :

Pitch angle [rad]

β ref :

Reference pitch angle [rad]

β 0 :

Optimal twist angle [rad]

κ :

Resultant aerodynamic force angle [rad]

λ :

Specific velocity [1]

λ r :

Local specific velocity [1]

\(\mu\) :

Radius ratio [1]

\(\mu_{{\rm r}}\) :

Bearing friction coefficient [1]

ρ :

Air density [kg/m3]

\(\rho_{\text{b}}\) :

Blade specific mass [kg/m3]

\(\sigma_{\text{p}}\) :

Prandtl correction coefficient [1]

ʋ :

Cinematic viscosity [m2/s]

ϕ :

Total angle [rad]

ω :

Rotor angular velocity [rad/s]

ω max :

Optimal angular velocity [rad/s]

\(a\) :

Axial interference factor [1]

\(a_{ {\min} }\) :

Minimal axial interference factor [1]

\(a^{\prime }\) :

Rotational interference factor [1]

\(a_{\text{G}}\) :

Glauert’s axial interference factor [1]

A r :

Actuator area ration [m2]

B :

Number of blades [1]

C :

Chord distance [m]

\(C_{\text{D}}\) :

Drag coefficient [1]

\(C_{\text{L}}\) :

Lift coefficient [1]

\(C_{\text{Lo}}\) :

Optimal lift coefficient [1]

\(C_{\text{M}}\) :

Moment coefficient [1]

\(C_{\text{p}}\) :

Power coefficient [1]

\(C_{Tr}\) :

Glauert’s coefficient [1]

\({{\rm d}}F_{\text{a}}\) :

Infinitesimal axial force [N]

\({{\rm d}}F_{\text{D}}\) :

Infinitesimal drag force [N]

\({{\rm d}}F_{{\rm L}}\) :

Infinitesimal lift force [N]

\({{\rm d}}F_{{\rm aMT}}\) :

Infinitesimal axial force from Moment Theory [N]

\({{\rm d}}F_{{\rm CA,B}}\) :

Infinitesimal centrifugal force at points A or B [N]

\({{\rm d}}F_{{\rm CIA,B}}\) :

Infinitesimal tangential centrifugal force at points A or B [N]

\({{\rm d}}F_{{\rm t}}\) :

Infinitesimal tangential force [N]

\({{\rm d}}F_{{\rm R}}\) :

Infinitesimal resultant force [N]

\({{\rm d}}T_{{\rm ae}}\) :

Infinitesimal aerodynamic momentum [Nm]

\(D_{{\rm mB}}\) :

Bearing average diameter [m]

F a :

Axial force [N]

\(F_{{\rm fE}}\) :

Actuator emulation system friction force [N]

F aB :

Bearing axial force [N]

F C ref :

Hydraulic compensated reference force [N]

F C eff :

Hydraulic effective force [N]

F H ref :

Hydraulic reference force [N]

F rB :

Bearing radial force [N]

F ref :

Reference force [N]

F t :

Tangential force [N]

\(I\) :

Blade polar inertia [kg m2]

I max,min :

Maximum or minimum moment of inertia [m4]

I p :

Centrifugal moment of inertia [m4]

L :

Length of lever [m]

m :

Blade mass [kg]

mg :

Weight force [N]

p A :

Pressure in the chamber A [Pa]

p B :

Pressure in the chamber B [Pa]

p S :

Hydraulic supply pressure [Pa]

p T :

Hydraulic reservoir pressure [Pa]

P T :

Turbine power [W]

r :

Local blade radius [m]

r GZ :

Distance between mass center and the longitudinal axis [m]

R :

Turbine radius [m]

R 0 :

Minimum effective turbine radius [m]

Re :

Reynolds number [1]

T a :

Axial moment [Nm]

T ae :

Aerodynamic moment [Nm]

T L :

Load moment [Nm]

T C :

Centrifugal moment [Nm]

T fB :

Bearing friction moment [Nm]

\(T_{{\rm H}}\) :

Hydraulic moment [Nm]

\(T_{{\rm I}}\) :

Blade inertia moment [Nm]

T k :

Bearing resultant moment [Nm]

\(T_{{\rm L}}\) :

Load torque [Nm]

T t :

Tangential moment [Nm]

\(T_{{\rm tB}}\) :

Bearing tangential moment [Nm]

T g :

Weight force moment [Nm]

T gi :

Instant weight force moment [Nm]

v :

Wind velocity [m/s]

v r :

Relative wind velocity [m/s]

y AZ :

Distance between attack edge and gravity center [m/s]

y ZC :

Distance between turbine rotational axis and blade gravity center [m]

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Acknowledgements

This work was carried out with the support of CAPES (Coordination for the Improvement of Higher Education Personnel), Reivax SA Control and Automation, and CNPq (National Council for Scientific and Technological Development).

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Authors and Affiliations

  1. Department of Mechanical Engineering, LASHIP, Federal University of Santa Catarina, Trindade, Florianópolis, SC, 88040-900, Brazil

    Marcos P. Nostrani, Facundo Enrique Gonzalez & Victor Juliano De Negri

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  1. Marcos P. Nostrani
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  2. Facundo Enrique Gonzalez
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  3. Victor Juliano De Negri
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Correspondence to Victor Juliano De Negri.

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Technical Editor: Celso Kazuyuki Morooka.

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Nostrani, M.P., Gonzalez, F.E. & De Negri, V.J. Analysis and emulation of pitch control forces in wind turbines. J Braz. Soc. Mech. Sci. Eng. 42, 262 (2020). https://doi.org/10.1007/s40430-020-02350-1

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