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Simplified NREL5MW turbine for Simulink

The turbine included in the toolbox is based on the 5MW virtual turbine described in [Jonkman et. al.], with modifications as described in [grunnet et. al.]

This page gives a detailed description of the turbine model including all parameters.

The NREL 5MW simulation model used in SimWindFarm is a simplified aeroelastic model based on lookup tables for the aerodynamics (C_P/C_T), a simple 3rd order drive train model, a 1st order generator model, 1st order pitch actuator, and a 2nd order tower dynamics.

The turbines are controlled using the control strategy from [Jonkman et. al.], which includes a simplified start up procedure and pitch control for full load operation.

Figure 1 illustrates the structure of the NREL 5MW, with inputs being the wind speed at the nacelle, the average wind speed over the rotor area (effective wind speed), and the power reference supplied by the farm controller. The outputs available to the farm controller are produced power, measured generator speed, nacelle wind speed, and blade pitch angle.

Turbine simulation structure

With the variables given by the below table

Variable Description unit
Omega rotor speed tfrac{rad}{s}
omega generator speed tfrac{rad}{s}
beta pitch angle degrees
M_{shaft} main shaft torque Nm
M_{gen} generator torque Nm
F_{tow} tower thrust N
P_{dem} power demand W
P_{ref} generator power reference W
beta_{ref} pitch angle reference degrees
V_{nac} nacelle wind speed tfrac{m}{s}
V_{rot} average wind speed over the rotor tfrac{m}{s}
V_E effective wind speed tfrac{m}{s}
V_{meas} measured wind speed tfrac{m}{s}
beta_{meas} measured pitch angle degrees
P_{meas} measured produced power W
omega_{meas} measured generator speed tfrac{rad}{s}

Aerodynamics

The aerodynamics of the turbine can be described using two static relationships,

 begin{aligned} M_{shaft}&=tfrac{1}{2} v_{rot}^3 rho A C_P(lambda,beta) Omega^{-1} F_{tow}&=tfrac{1}{2} v_{rot}^2 rho A C_T(lambda,beta) end{aligned}

where C_P and C_T are two look-up tables derived from the geometry of the blades with inputs tip speed ration (lambda=tfrac{ROmega}{v_{rot}}) and pitch angle. The parameters are air density ,rho, and rotor disc area, A.

Drive Train

The 3rd order drive train model is based on two rotating shafts connected through a gearbox with torsion spring constant K_{shaft}, viscous friction B_{shaft}, and gear ration N.

 begin{aligned} dot{Omega}&=tfrac{1}{I_{rot}}left(M_{shaft}-phi K_{shaft}-dot{phi}B_{shaft}right)  dot{omega}&=tfrac{1}{I_{gen}}left(-M_{gen}+tfrac{1}{N}(phi K_{shaft}+dot{phi}B_{shaft})right) dot{phi}&=Omega-tfrac{1}{N}omega end{aligned}

where phi is the shaft torsion angle and I_{gen}/I_{rot} are the inertias of the generator and rotor respectively.

Generator

In the baseline NREL 5MW turbine there is no generator model, but a simple 1st order model is included in this benchmark, with input P_{ref} and time constant tau_{gen}.

 dot{M}_{gen}=tfrac{1}{tau_{gen}}left(tfrac{P_{ref}}{omega}-M_{gen}right)

Notice that the baseline turbine assumes a torque reference, but a power reference is used here instead.

Tower

The tower deflection, z, is modeled as a spring-damper system with spring constant K_{tow} and damping B_{tow}.

 ddot{z}=tfrac{1}{m_{tow}}left(F_{tow}-K_{tow}z-B_{tow}dot{z}right)

Pitch Servo

The pitch actuator does not use the NREL model which is a spring-damper system and not used in their FAST simulation. Instead a second order system with a time constant of tau_beta and input delay lambda from input u_beta to pitch rate dot{beta} is used.

The actuator is controlled by a proportional regulator with constant K_{beta} resulting in a pitch servo.

begin{aligned} ddot{beta}&=tfrac{1}{tau_{beta}}(u_{beta}^{lambda}-dot{beta}) u_beta&=K_betaleft(beta_{ref}-beta_{meas}right) end{aligned}

Rotor Control

The control strategy for the NREL5MW is divided into two regions; 1) partial load and 2) full load.

In region 1) the control is a simple lookup-table with generator speed as input and generator power reference as output. The blade pitch is kept constant at 0, see the figure below.

Turbine Pitch Control Regions

In region 2) the generator power reference is kept constant at the rated power while the rotor speed is controlled using the blade pitch angle, by a gain scheduled PI controller.

The gain scheduled PI controller is shown in the equation below, and the gains are based on linearisation of the power production sensitivity to blade pitch angle.

  begin{aligned} label{eq:gainsched}    beta_{ref}&=K_P(beta)omega_{err}+K_I(beta)int_0^tomega_{err}     K_{P/I}(beta)&=K_{P/I,0}frac{beta_2}{beta_2+beta}  end{aligned}

where omega_{err}=omega_{rated}-omega, and K_{P/I} are the proportional and integral gains, K_{P/I,0} is the base gain at beta=0^circ and beta_2 is the pitch angle where the pitch sensitivity is doubled.

The controller presented in [Jonkman et. al.] always operates at full power rating and in order to be able to de-rated the turbine the control strategy has been altered slightly by letting the dynamic power rating change the transition point between region 1 and region 2.

Turbulence
Davidson, P.A.
Oxford University Press, 2004
[BibTeX]

@book{Davidson:2004,
  author = {P. A. Davidson},
  title = {Turbulence},
  publisher = {Oxford University Press},
  year = {2004}
}

Analytical Modelling of Wind Speed Deficit in Large Offshore Wind Farms
Frandsen, S., Barthelmie, R., Pryor, S., Rathmann, O., Larsen, S and Højstrup, J
Wind Energy, 2006, Vol. 9, pp. 39-53
[BibTeX]

@article{Frandsen:2006,
  author = {Sten Frandsen and Rebecca Barthelmie and Sara Pryor and Ole Rathmann and Søren Larsen and Jørgen Højstrup},
  title = {Analytical Modelling of Wind Speed Deficit in Large Offshore Wind Farms},
  journal = {Wind Energy},
  year = {2006},
  volume = {9},
  pages = {39--53}
}

Aeolus Toolbox for Dynamic Wind Farm Model, Simulation and Control
Grunnet, J.D., Soltani, M., Knudsen, T., Kragelund, M. and Bak, T.
In Proc. of the 2010 European Wind Energy Conference, 2010
[BibTeX]

@conference{grunnet:2010,
  author = {Jacob Deleuran Grunnet and Mohsen Soltani and Torben Knudsen and Martin Kragelund and Thomas Bak},
  title = {Aeolus Toolbox for Dynamic Wind Farm Model, Simulation and Control},
  booktitle = {Proc. of the 2010 European Wind Energy Conference},
  year = {2010}
}

A note on wind generator interaction
Jensen, N.
Risø National Laboratory, 1983
[BibTeX]

@techreport{Jensen:1983,
  author = {N. Jensen},
  title = {A note on wind generator interaction},
  institution = {Risø National Laboratory},
  year = {1983}
}

Definition of a 5-MW Reference Wind Turbine for Offshore System Development
Jonkman, J., Butterfield, S., Musial, W. and Scott, G.
National Renewable Energy Laboratory, 2009
[BibTeX]

@techreport{NREL5MW,
  author = {J. Jonkman and S. Butterfield and W. Musial and G. Scott},
  title = {Definition of a 5-MW Reference Wind Turbine for Offshore System Development},
  institution = {National Renewable Energy Laboratory},
  url = {http://www.nrel.gov/wind/pdfs/38060.pdf},
  year = {2009}
}

Lateral coherence in isotropic turbulence and in the natural wind
Kristensen, L. and Jensen, N.O.
Boundary-Layer Meteorology, November, 1979, Vol. 17, pp. 353-373
[BibTeX] [DOI]

@article{kristensen:1979,
  author = {Kristensen, L. and Jensen, N.~O.},
  title = {Lateral coherence in isotropic turbulence and in the natural wind},
  journal = {Boundary-Layer Meteorology},
  year = {1979},
  volume = {17},
  pages = {353-373},
  doi = {http://dx.doi.org/10.1007/BF00117924}
}

Wake Meandering: A Pragmatic Approach
Larsen, G.C., Madsen, H.A., Thomsen, K. and Larsen, T.J.
Wind Energy, 2008, Vol. 11, pp. 377-395
[BibTeX]

@article{Larsen:2008b,
  author = {Gunner C. Larsen and Helge Aa. Madsen and Kenneeth Thomsen and Torben J. Larsen},
  title = {Wake Meandering: A Pragmatic Approach},
  journal = {Wind Energy},
  year = {2008},
  volume = {11},
  pages = {377--395}
}

Modeling and Simulation of Offshore Wind Farms for Farm Level Control
Soltani, M., Knudsen, T. and Bak, T.
In European Offshore Wind Conference and Exhibition (EOW) 2009, 2009
[BibTeX]

@inproceedings{mohsen:2009c,
  author = {Mohsen Soltani and Torben Knudsen and Thomas Bak},
  title = {Modeling and Simulation of Offshore Wind Farms for Farm Level Control},
  booktitle = {European Offshore Wind Conference and Exhibition (EOW) 2009},
  year = {2009}
}

Three-Dimensional Wind Simulation
Veers, P.S.
Sandia National Laboratories, 1988 (SAND88-0152 UC-261)
[BibTeX]

@techreport{Veers:1988,
  author = {Paul S. Veers},
  title = {Three-Dimensional Wind Simulation},
  institution = {Sandia National Laboratories},
  year = {1988},
  number = {SAND88-0152 UC-261}
}

Wind Models for Simulation of Power Fluctuations from Wind Farms
Sørensen, P., Hansen, A., AndrĂ©, P., Rosas, C.
Journal of Wind Engineering and Industrial Aerodynamics, 2002
[BibTeX]

@Article{Soerensen02,
  author = 	 {Poul Sørensen and Anca D. Hansen and Pedro AndrĂ© and Carvalho Rosas},
  title = 	 {Wind Models for Simulation of Power Fluctuations from Wind Farms},
  journal = 	 {Journal of Wind Engineering and Industrial Aerodynamics},
  year = 	 2002,
  volume = 	 90,
  pages = 	 {1381-1402}
}