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Definition of a 5-MW Reference Wind Turbine for Offshore System Development
J. Jonkman, S. Butterfield, W. Musial, and G. Scott
Technical Report NREL/TP-500-38060 February 2009
Definition of a 5-MW Reference Wind Turbine for Offshore System Development
J. Jonkman, S. Butterfield, W. Musial, and G. Scott
Prepared under Task No. WER5.3301
Technical Report NREL/TP-500-38060 February 2009
NOTICE
This report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.
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Acronyms and Abbreviations
ADAMS® = Automatic Dynamic Analysis of Mechanical Systems
A2AD = ADAMS-to-AeroDyn
BEM = blade-element / momentum
CM = center of mass
DLL = dynamic link library
DOE = U.S. Department of Energy
DOF = degree of freedom
DOWEC = Dutch Offshore Wind Energy Converter project
DU = Delft University
ECN = Energy Research Center of the Netherlands
equiripple = equalized-ripple
FAST = Fatigue, Aerodynamics, Structures, and Turbulence
GE = General Electric
IEA = International Energy Agency
MSL = mean sea level
NACA = National Advisory Committee for Aeronautics
NREL = National Renewable Energy Laboratory
NWTC = National Wind Technology Center
OCS = offshore continental shelf
OC3 = Offshore Code Comparison Collaborative
PI = proportional-integral
PID = proportional-integral-derivative
RECOFF = Recommendations for Design of Offshore Wind Turbines project
WindPACT \equiv Wind Partnerships for Advanced Component Technology project
w.r.t. = with respect to
Nomenclature
Ad = discrete-time state matrix
B_{d} = discrete-time input matrix
C_{d} = discrete-time output state matrix
C_{\varphi} = effective damping in the equation of motion for the rotor-speed error
D_{d} = discrete-time input transmission matrix
fc = corner frequency
GK = gain-correction factor
IDrivetrain = drivetrain inertia cast to the low-speed shaft
I_{G e n} = generator inertia relative to the high-speed shaft
IRotor = rotor inertia
K_{D} = blade-pitch controller derivative gain
K_{I} = blade-pitch controller integral gain
K_{P} = blade-pitch controller proportional gain
K_{\varphi} = effective stiffness in the equation of motion for the rotor-speed error
M_{\varphi} = effective inertia (mass) in the equation of motion for the rotor-speed error
n = discrete-time-step counter
NGear = high-speed to low-speed gearbox ratio
P = mechanical power
P_{\theta} = rated mechanical power
∂P∂θ = sensitivity of the aerodynamic power to the rotor-collective blade-pitch angle
t = simulation time
TAero = aerodynamic torque in the low-speed shaft
TGen = generator torque in the high-speed shaft
T_{s} = discrete-time step
\boldsymbol{u} = unfiltered generator speed
x = for the control-measurement filter, the filter state
x,y,z = set of orthogonal axes making up a reference-frame coordinate system
y = for the control-measurement filter, the filtered generator speed
α = low-pass filter coefficient
Δθ = small perturbation of the blade-pitch angles about their operating point
ΔΩ = small perturbation of the low-speed shaft rotational speed about the rated speed
∆Ω = low-speed shaft rotational acceleration
\zeta_{\varphi} = damping ratio of the response associated with the equation of motion for the rotor-speed error
\theta = full-span rotor-collective blade-pitch angle
\theta_{K} = rotor-collective blade-pitch angle at which the pitch sensitivity has doubled from its value at the rated operating point
\pi = the ratio of a circle’s circumference to its diameter
\varphi = the integral of \dot{\varphi} with respect to time
\dot{\varphi} = small perturbation of the low-speed shaft rotational speed about the rated speed
\ddot{\varphi} = low-speed shaft rotational acceleration
\boldsymbol{\mathcal{Q}} = low-speed shaft rotational speed
\varOmega_{O} = rated low-speed shaft rotational speed
\omega_{\varphi n} = natural frequency of the response associated with the equation of motion for the rotor-speed error
Executive Summary
To support concept studies aimed at assessing offshore wind technology, we developed the specifications of a representative utility-scale multimegawatt turbine now known as the “NREL offshore 5-MW baseline wind turbine.” This wind turbine is a conventional three-bladed upwind variable-speed variable blade-pitch-to-feather-controlled turbine. To create the model, we obtained some broad design information from the published documents of turbine manufacturers, with a heavy emphasis on the REpower 5M machine. Because detailed data was unavailable, however, we also used the publicly available properties from the conceptual models in the WindPACT, RECOFF, and DOWEC projects. We then created a composite from these data, extracting the best available and most representative specifications. This report documents the specifications of the NREL offshore 5-MW baseline wind turbine—including the aerodynamic, structural, and control-system properties—and the rationale behind its development. The model has been, and will likely continue to be, used as a reference by research teams throughout the world to standardize baseline offshore wind turbine specifications and to quantify the benefits of advanced land- and sea-based wind energy technologies.
Table of Contents
1 Introduction .
2 Blade Structural Properties .
3 Blade Aerodynamic Properties ...
4 Hub and Nacelle Properties ....... 12
5 Drivetrain Properties ....... . 14
6 Tower Properties ... ... 15
7 Baseline Control System Properties ....... . 17 7.1 Baseline Control-Measurement Filter .. ...17 7.2 Baseline Generator-Torque Controller . ..19 7.3 Baseline Blade-Pitch Controller . ..20 7.4 Baseline Blade-Pitch Actuator . ..26 7.5 Summary of Baseline Control System Properties. ..26
8 FAST with AeroDyn and ADAMS with AeroDyn Models...... .. 28
9 Full-System Natural Frequencies and Steady-State Behavior ......... ..... 30
10 Conclusions . 33
References ... 34
Appendix A FAST Input Files . 38
A.1 Primary Input File .... 38
A.2 Blade Input File – NRELOffshrBsline5MW_Blade.dat . .40
A.3 Tower Input File – NRELOffshrBsline5MW_Tower_Onshore.dat .... .41
A.4 ADAMS Input File – NRELOffshrBsline5MW_ADAMSSpecific.dat . ..42
A.5 Linearization Input File – NRELOffshrBsline5MW_Linear.dat .. .43
Appendix B AeroDyn Input Files ... 44
B.1 Primary Input File – NRELOffshrBsline5MW_AeroDyn.ipt . 44
B.2 Airfoil-Data Input File – Cylinder1.dat .. .44
B.3 Airfoil-Data Input File – Cylinder2.dat .. .44
B.4 Airfoil-Data Input File – DU40_A17.dat . .45
B.5 Airfoil-Data Input File – DU35_A17.dat . .47
B.6 Airfoil-Data Input File – DU30_A17.dat .. .48
B.7 Airfoil-Data Input File – DU25_A17.dat . .50
B.8 Airfoil-Data Input File – DU21_A17.dat ..... ...52
B.9 Airfoil-Data Input File – NACA64_A17.dat . .54
Appendix C Source Code for the Control System DLL . 57
List of Tables
Table 1-1. Gross Properties Chosen for the NREL 5-MW Baseline Wind Turbine. 2
Table 2-1. Distributed Blade Structural Properties . 5
Table 2-2. Undistributed Blade Structural Properties ........... 6
Table 3-1. Distributed Blade Aerodynamic Properties . 7
Table 4-1. Nacelle and Hub Properties . . 13
Table 5-1. Drivetrain Properties .. . 14
Table 6-1. Distributed Tower Properties .. 15
Table 6-2. Undistributed Tower Properties . 16
Table 7-1. Sensitivity of Aerodynamic Power to Blade Pitch in Region 3 23
Table 7-2. Baseline Control System Properties . ... 27
Table 9-1. Full-System Natural Frequencies in Hertz .. .. 30
List of Figures
Figure 3-1. Corrected coefficients of the DU40 airfoil . 9
Figure 3-2. Corrected coefficients of the DU35 airfoil . 9
Figure 3-3. Corrected coefficients of the DU30 airfoil . . 10
Figure 3-4. Corrected coefficients of the DU25 airfoil .. ..... 10
Figure 3-5. Corrected coefficients of the DU21 airfoil . . 11
Figure 3-6. Corrected coefficients of the NACA64 airfoil . 11
Figure 7-1. Bode plot of generator speed low-pass filter frequency response ......... ..... 18
Figure 7-2. Torque-versus-speed response of the variable-speed controller ...... ...... 20
Figure 7-3. Best-fit line of pitch sensitivity in Region 3 . . 24
Figure 7-4. Baseline blade-pitch control system gain-scheduling law ..... . 25
Figure 7-5. Flowchart of the baseline control system .... . 27
Figure 9-1. Steady-state responses as a function of wind speed . .. 32
1 Introduction
The U.S. Department of Energy’s (DOE’s) National Renewable Energy Laboratory (NREL), through the National Wind Technology Center (NWTC), has sponsored conceptual studies aimed at assessing offshore wind technology suitable in the shallow and deep waters off the U.S. offshore continental shelf (OCS) and other offshore sites worldwide. To obtain useful information from such studies, use of realistic and standardized input data is required. This report documents the turbine specifications of what is now called the “NREL offshore 5-MW baseline wind turbine” and the rationale behind its development. Our objective was to establish the detailed specifications of a large wind turbine that is representative of typical utility-scale land- and sea-based multimegawatt turbines, and suitable for deployment in deep waters.
Before establishing the detailed specifications, however, we had to choose the basic size and power rating of the machine. Because of the large portion of system costs in the support structure of an offshore wind system, we understood from the outset that if a deepwater wind system is to be cost-effective, each individual wind turbine must be rated at 5~\mathrm{MW} or higher [23]. Ratings considered for the baseline ranged from 5 MW to 20\ \mathrm{MW} . We decided that the baseline should be 5 MW because it has precedence:
Feasible floater configurations for offshore wind turbines scoped out by Musial, Butterfield, and Boone [23] were based on the assumption of a 5-MW unit. Unpublished DOE offshore cost studies were based on a rotor diameter of 128\mathrm{~m~} , which is a size representative of a 5- to 6-MW wind turbine. The land-based Wind Partnerships for Advanced Component Technology (WindPACT) series of studies, considered wind turbine systems rated up to 5 MW [19,24,29]. The Recommendations for Design of Offshore Wind Turbines project (known as RECOFF) based its conceptual design calculations on a wind turbine with a 5-MW rating [32]. The Dutch Offshore Wind Energy Converter (DOWEC) project based its conceptual design calculations on a wind turbine with a 6-MW rating [8,14,17].
• At the time of this writing, the largest wind turbine prototypes in the world—the Multibrid M5000 [5,21,22] and the REpower 5M [18,26,27]—each had a 5-MW rating.
We gathered the publicly available information on the Multibrid M5000 and REpower 5M prototype wind turbines. And because detailed information on these machines was unavailable, we also used the publicly available properties from the conceptual models used in the WindPACT, RECOFF, and DOWEC projects. These models contained much greater detail than was available about the prototypes. We then created a composite from these models, extracting the best available and most representative specifications.
The Multibrid M5000 machine has a significantly higher tip speed than typical onshore wind turbines and a lower tower-top mass than would be expected from scaling laws previously developed in one of the WindPACT studies [29]. In contrast, the REpower 5M machine has properties that are more “expected” and “conventional.” For this reason, we decided to use the specifications of the REpower 5M machine as the target specifications for our baseline model.
The wind turbine used in the DOWEC project had a slightly higher rating than the rating of the REpower 5M machine, but many of the other basic properties of the DOWEC turbine matched the REpower 5M machine very well. In fact, the DOWEC turbine matched many of the properties of the REpower 5M machine better than the turbine properties derived for the WindPACT and RECOFF studies.3 As a result of these similarities, we made the heaviest use of data from the DOWEC study in our development of the NREL offshore 5-MW baseline wind turbine.
The REpower 5M machine has a rotor radius of about 63\textrm{m} . Wanting the same radius and the lowest reasonable hub height possible to minimize the overturning moment acting on an offshore substructure, we decided that the hub height for the baseline wind turbine should be 90\;\mathrm{m} . This would give a 15{\cdot}\mathrm{m} air gap between the blade tips at their lowest point when the wind turbine is undeflected and an estimated extreme 50-year individual wave height of 30\,\textrm{m} (i.e., 15{\cdot}\mathrm{m} amplitude). The additional gross properties we chose for the NREL 5-MW baseline wind turbine, most of which are identical to those of the REpower 5M, are given in Table 1-1. The (x,y,z) coordinates of the overall center of mass (CM) location of the wind turbine are indicated in a tower-base coordinate system, which originates along the tower centerline at ground or mean sea level (MSL). The x\cdot -axis of this coordinate system is directed nominally downwind, the yaxis is directed transverse to the nominal wind direction, and the z -axis is directed vertically from the tower base to the yaw bearing.
Table 1-1. Gross Properties Chosen for the NREL 5-MW Baseline Wind Turbine
<html>| Rating | 5MW |
| Rotor Orientation,Configuration | Upwind,3 Blades |
| Control | VariableSpeed,CollectivePitch |
| Drivetrain | High Speed, Multiple-Stage Gearbox |
| Rotor,HubDiameter | 126 m, 3 m |
| Hub Height | 90 m |
| Cut-In, Rated, Cut-Out Wind Speed | |
| Cut-ln,RatedRotorSpeed | 3 m/s, 11.4 m/s,25 m/s |
| Rated Tip Speed | 6.9 rpm, 12.1 rpm |
| 80 m/s | |
| Overhang,Shaft Tilt,Precone | 5 m, 5°, 2.5° |
| Rotor Mass | 110,000 kg |
| NacelleMass | 240,000 kg |
| TowerMass CoordinateLocationofOverallCM | 347,460 kg (-0.2 m, 0.0 m, 64.0 m) |
The actual REpower 5M wind turbine uses blades with built-in prebend as a means of increasing tower clearance without a large rotor overhang. Because many of the available simulation tools and design codes cannot support blades with built-in prebend, we chose a 2.5^{\circ} -upwind precone in the baseline wind turbine to represent the smaller amount of precone and larger amount of prebend that are built into the actual REpower 5M machine.
The rotor diameter indicated in Table 1-1 ignores the effect of blade precone, which reduces the actual diameter and swept area. The exact rotor diameter in the turbine specifications (assuming that the blades are undeflected) is actually (126~\mathrm{m})\times c o s(2.5^{\circ})=125.88~\mathrm{m} and the actual swept area is (\pi/4)\times(125.88~\mathrm{m})^{2}=12{,}445.3~\mathrm{m}^{2} .
We present other information about this model as follows:
The blade structural properties in Section 2 The blade aerodynamic properties in Section 3
• The hub and nacelle properties in Section 4
• The drivetrain properties in Section 5
• The tower properties in Section 6
• The baseline control system properties in Section 7 The aero-servo-elastic FAST (Fatigue, Aerodynamics, Structures, and Turbulence) [11] with AeroDyn [16,20] and MSC.ADAMS® (Automatic Dynamic Analysis of Mechanical Systems) with A2AD (ADAMS-to-AeroDyn) [ 6,15] and AeroDyn models of the wind turbine in Section 8
• The basic responses of the land-based version of the wind turbine, including its fullsystem natural frequencies and steady-state behavior in Section 9.
Although we summarize much of this information5 for conciseness and clarity, Section 7 contains a high level of detail about the development of the wind turbine’s baseline control system. These details are provided because they are fundamental to the development of more advanced control systems.
The NREL offshore 5-MW baseline wind turbine has been used to establish the reference specifications for a number of research projects supported by the U.S. DOE’s Wind & Hydropower Technologies Program [1,2,7,12,28,33,34]. In addition, the integrated European
Union UpWind research program6 and the International Energy Agency (IEA) Wind Annex XXIII Subtask 2^{7} Offshore Code Comparison Collaboration (OC3) [13,25] have adopted the NREL offshore 5-MW baseline wind turbine as their reference model. The model has been, and will likely continue to be, used as a reference by research teams throughout the world to standardize baseline offshore wind turbine specifications and to quantify the benefits of advanced land- and sea-based wind energy technologies.
2 Blade Structural Properties
The NREL offshore 5-MW baseline wind turbine has three blades. We based the distributed blade structural properties of each blade on the structural properties of the 62.6-m-long LM Glasfiber blade used in the DOWEC study (using the data given in Appendix A of Ref. [17]). Because the blades in the DOWEC study were 1.1\textrm{m} longer than the 61.5-m-long LM Glasfiber blades [18] used on the actual REpower 5M machine, we truncated the 62.6{\-}\mathrm{m} blades at 61.5{\-\mathrm{m}} span to obtain the structural properties of the NREL 5-MW baseline blades (we found the structural properties at the blade tip by interpolating between the 61.2{\cdot}{\cdot}\mathrm{m} and 61.7{-}\mathrm{m} stations given in Appendix A of Ref. [17]). Table 2-1 lists the resulting properties.
The entries in the first column of Table 2-1, labeled “Radius,” are the spanwise locations along the blade-pitch axis relative to the rotor center (apex). “BlFract” is the fractional distance along the blade-pitch axis from the root (0.0) to the tip (1.0). We located the blade root 1.5\;\mathrm{m} along the pitch axis from the rotor center, equivalent to half the hub diameter listed in Table 1-1.
“AeroCent” is the name of a FAST input parameter. The FAST code assumes that the bladepitch axis passes through each airfoil section at 25\% chord. By definition, then, the quantity (\mathrm{AeroCent}-0.25) is the fractional distance to the aerodynamic center from the blade-pitch axis along the chordline, positive toward the trailing edge. Thus, at the root (i.e., BlFract =0.0 ), AeroCent =0.25 means that the aerodynamic center lies on the blade-pitch axis [because \left(0.25-\right. 0.25)=0.0] , and at the tip (i.e., BlFract =1.0 ), AeroCent =0.125 means that the aerodynamic center lies 0.125 chordlengths toward the leading edge from the blade-pitch axis [because (0.125
Table 2-1. Distributed Blade Structural Properties
<html>| Radius | BIFract | AeroCent | StrcTwst BMassDen | FlpStff | EdgStff | GJStff | EAStff | Alpha | Flplner | Edglner | PrecrvRefPreswpRef | FlpcgOf | EdgcgOf | FlpEAOf EdgEAOf | |||
| (m) | (-) | (-) | () (kg/m) | (N·m²) (N·m²) | (N·m²) | (N) | (-) (kg·m) | (kg·m) | (m) | (m) | (m) | (m) | (m) (m) | ||||
| 1.50 | 0.00000 | 0.25000 | 13.308 | 678.935 | 18110.00E+6 | 18113.60E+6 | 5564.40E+6 | 9729.48E+6 | 0.0 | 972.86 | 973.04 | 0.0 | 0.0 | 0.0 | 0.00017 | 0.0 | 0.0 |
| 1.70 | 0.00325 | 0.25000 | 13.308 | 678.935 | 18110.00E+6 | 18113.60E+6 | 5564.40E+6 | 9729.48E+6 | 0.0 | 972.86 | 973.04 | 0.0 | 0:0 | 0.0 | 0.00017 | 0.0 | 0.0 |
| 2.70 | 0.01951 | 0.24951 | 13.308 | 773.363 | 19424.90E+6 | 19558.60E+6 | 5431.59E+6 | 10789.50E+6 | 0.0 | 1091.52 | 1066.38 | 0.0 | 0:0 | 0.0 | -0.02309 | 0.0 | 0.0 |
| 3.70 | 0.03577 | 0.24510 | 13.308 | 740.550 | 17455.90E+6 | 19497.80E+6 | 4993.98E+6 | 10067.23E+6 | 0.0 | 60996 | 1047.36 | 0.0 | 0.0 | 0.0 | 0.00344 | 0.0 | 0.0 |
| 4.70 | 0.05203 | 0.23284 | 13.308 | 740.042 | 15287.40E+6 | 19788.80E+6 | 4666.59E+6 | 9867.78E+6 | 0.0 | 873.81 | 1099.75 | 0.0 | 0.0 | 0.0 | 0.04345 | 0.0 | 0.0 |
| 5.70 | 0.06829 | 0.22059 | 13.308 | 592.496 | 10782.40E+6 | 14858.50E+6 | 3474.71E+6 | 7607.86E+6 | 0.0 648.55 | 873.02 | 0.0 | 0.0 | 0.0 | 0.05893 | 0.0 | 0.0 | |
| 6.70 | 0.08455 | 0.20833 | 13.308 | 450.275 | 7229.72E+6 | 10220.60E+6 | 2323.54E+6 | 5491.26E+6 | 0.0 | 456.76 | 641.49 | 0.0 | 0.0 | 0.0 | 0.06494 | 0.0 | 0.0 |
| 7.70 | 0.10081 | 0.19608 | 13.308 | 424.054 | 6309.54E+6 | 9144.70E+6 | 1907.87E+6 | 4971.30E+6 | 0.0 | 400.53 | 593.73 | 0:0 | 0.0 | 0.0 | 0.07718 | 0.0 | 0.0 |
| 8.70 | 0.11707 | 0.18382 | 13.308 | 400.638 | 5528.36E+6 | 8063.16E+6 | 1570.36E+6 | 4493.95E+6 | 0.0 | 351.61 | 547.18 | 0.0 | 0.0 | 0.0 | 0.08394 | 0.0 | 0.0 |
| 9.70 | 0.13335 | 0.17156 | 13.308 | 382.062 | 4980.06E+6 | 6884.44E+6 | 1158.26E+6 | 4034.80E+6 | 0.0 | 316.12 | 490.84 | 0.0 | 0.0 | 0.0 | 0.10174 | 0.0 | 0.0 |
| 10.70 | 0.14959 | 0.15931 | 13.308 | 399.655 | 4936.84E+6 | 7009.18E+6 | 1002.12E+6 | 4037.29E+6 | 0.0 | 303.60 | 503.86 | 0:0 | 0.0 | 0.0 | 0.10758 | 0.0 | 0.0 |
| 11.70 | 0.16585 | 0.14706 | 13.308 | 426.321 | 4691.66E+6 | 7167.68E+6 | 855.90E+6 | 4169.72E+6 | 0.0 289.24 | 544.70 | 0:0 | 0.0 | 0.0 | 0.15829 | 0.0 | 0.0 | |
| 12.70 | 0.18211 | 0.13481 | 13.181 | 416.820 | 3949.46E+6 | 7271.66E+6 | 672.27E+6 | 4082.35E+6 | 0.0 246.57 | 569.90 | 0.0 | 0.0 | 0.0 | 0.22235 | 0.0 | 0.0 | |
| 13.70 | 0.19837 | 0.12500 | 12.848 | 406.186 | 3386.52E+6 | 7081.70E+6 | 547.49E+6 | 4085.97E+6 | 0.0 215.91 | 601.28 | 0:0 | 0.0 | 0.0 | 0.30756 | 0:0 | 0:0 | |
| 14.70 | 0.21465 | 0.12500 | 12.192 | 381.420 | 2933.74E+6 | 6244.53E+6 | 448.84E+6 | 3668.34E+6 | 0.0 187.11 | 546.56 | 0.0 | 0.0 | 0.0 | 0.30386 | 0.0 | 0.0 | |
| 15.70 | 0.23089 | 0.12500 | 11.561 | 352.822 | 2568.96E+6 | 5048.96E+6 | 335.92E+6 | 3147.76E+6 | 0.0 160.84 | 468.71 | 0.0 | 0.0 | 0.0 | 0.26519 | 0.0 | 0.0 | |
| 16.70 | 0.24715 | 0.12500 | 11.072 | 349.477 | 2388.65E+6 | 4948.49E+6 | 311.35E+6 | 3011.58E+6 | 0.0 148.56 | 453.76 | 00 | 0:0 | 0.0 | 0.25941 | 0.0 | 0.0 | |
| 17.70 | 0.26341 | 0.12500 | 10.792 | 346.538 | 2271.99E+6 | 4808.02E+6 | 291.94E+6 | 2882.62E+6 | 0.0 | 140.30 | 436.22 | 0.0 | 0.0 | 0.0 | 0.25007 | 0.0 | 0.0 |
| 19.70 | 0.29595 | 0.12500 | 10.232 | 339.333 | 2050.05E+6 | 4501.40E+6 | 261.00E+6 | 2613.97E+6 | 0.0 | 124.61 | 398.18 | 0.0 | 0.0 | 0.0 | 0.23155 | 0.0 | 0.0 |
| 21.70 | 0.32846 | 0.12500 | 9.672 | 330.004 | 1828.25E+6 | 4244.07E+6 | 228.82E+6 | 2357.48E+6 | 0.0 | 109.42 | 362.08 | 0.0 | 0.0 | 0.0 | 0.20382 | 0.0 | 0.0 |
| 23.70 | 0.36098 | 0.12500 | 9.110 | 321.990 | 1588.71E+6 | 3995.28E+6 | 200.75E+6 | 2146.86E+6 | 0.0 | 94.36 | 335.01 | 0.0 | 0.0 | 0.0 | 0.19934 | 0.0 | 0.0 |
| 25.70 | 0.39350 | 0.12500 | 8.534 | 313.820 | 1361.93E+6 | 3750.76E+6 | 174.38E+6 | 1944.09E+6 | 0.0 | 80.24 | 308.57 | 0.0 | 0.0 | 0.0 | 0.19323 | 0.0 | 0.0 |
| 27.70 29.70 31.70 33.70 35.70 37.70 39.70 41.70 43.70 45.70 47.70 49.70 51.70 53.70 55.70 56.70 57.70 58.70 59.20 59.70 60.20 60.70 61.20 61.70 62.20 62.70 63.00 | 0.42602 0.45855 0.49106 0.52358 0.55610 0.58862 0.62115 0.65366 0.68618 0.71870 0.75122 0.78376 0.81626 0.84878 0.88130 0.89756 0.91382 0.93008 0.93821 0.94636 0.95447 0.96260 0.97073 0.97886 0.98699 0.99512 1.00000 | 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 0.12500 | 7.932 0.12500 7.321 6.711 6.122 5.546 4.971 4.401 3.834 3.332 2.890 2.503 2.116 1.730 1.342 0.954 0.760 0.574 0.404 0.319 0.253 0.216 0.178 0.140 0.101 0.062 0.023 0.000 | 294.734 287.120 263.343 253.207 241.666 220.638 200.293 179.404 165.094 154.411 138.935 129.555 107.264 98.776 90.248 83.001 72.906 68.772 66.264 59.340 55.914 52.484 49.114 45.818 41.669 11.453 10.319 | 1102.38E+6 875.80E+6 681.30E+6 534.72E+6 408.90E+6 314.54E+6 238.63E+6 175.88E+6 126.01E+6 107.26E+6 90.88E+6 76.31E+6 61.05E+6 49.48E+6 39.36E+6 34.67E+6 30.41E+6 26.52E+6 23.84E+6 19.63E+6 16.00E+6 12.83E+6 10.08E+6 7.55E+6 4.60E+6 0.25E+6 0.17E+6 | 3447.14E+6 3139.07E+6 2734.24E+6 2554.87E+6 2334.03E+6 1828.73E+6 1584.10E+6 1323.36E+6 1183.68E+6 1020.16E+6 797.81E+6 709.61E+6 518.19E+6 454.87E+6 395.12E+6 353.72E+6 304.73E+6 281.42E+6 261.71E+6 158.81E+6 137.88E+6 118.79E+6 101.63E+6 85.07E+6 64.26E+6 6.61E+6 5.01E+6 | 144.47E+6 119.98E+6 81.19E+6 69.09E+6 57.45E+6 45.92E+6 35.98E+6 27.44E+6 20.90E+6 18.54E+6 16.28E+6 14.53E+6 9.07E+6 8.06E+6 7.08E+6 6.09E+6 5.75E+6 5.33E+6 4.94E+6 4.24E+6 3.66E+6 3.13E+6 2.64E+6 2.17E+6 1.58E+6 0.25E+6 0.19E+6 | 1632.70E+6 1432.40E+6 1168.76E+6 1047.43E+6 922.95E+6 760.82E+6 648.03E+6 539.70E+6 531.15E+6 460.01E+6 375.75E+6 328.89E+6 244.04E+6 211.60E+6 181.52E+6 160.25E+6 109.23E+6 100.08E+6 92.24E+6 63.23E+6 53.32E+6 44.53E+6 36.90E+6 29.92E+6 21.31E+6 4.85E+6 3.53E+6 | 0.0 62.67 0.0 49.42 0.0 37.34 0.0 29.14 0.0 22.16 0.0 17.33 0.0 13.30 0.0 9.96 0.0 7.30 0.0 6.22 0.0 5.19 0.0 4.36 0.0 3.36 0.0 2.75 0.0 2.21 0.0 1.93 0.0 1.69 0.0 1.49 0.0 1.34 0.0 1.10 0.0 680 0.0 0.71 0.0 0.56 0.0 0.42 0.0 0.25 0.0 0.04 0.0 0.02 | 263.87 237.06 196.41 180.34 162.43 134.83 116.30 97.98 98.93 85.78 69.96 61.41 45.44 39.57 34.09 30.12 20.15 18.53 17.11 11.55 9.77 8.19 6.82 5.57 4.01 0.94 0.68 | 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 | 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0:0 0.0 0.0 00 0:0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0:0 0.0 0.0 00 0.0 0.0 0.0 | 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 | 0.14994 0.15421 0.13252 0.13313 0.14035 0.13950 0.15134 0.17418 0.24922 0.26022 0.22554 0.22795 0.20600 0.21662 0.22784 0.23124 0.14826 0.15346 0.15382 0.09470 0.09018 0.08561 0.08035 0.07096 0.05424 0.05387 0.05181 | 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0:0 0.0 | 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 00 0.0 0.0 00 0.0 0.0 0.0 |
-\,0.25)=-0.125].
The flapwise and edgewise section stiffness and inertia values, “FlpStff,” “EdgStff,” “FlpIner,” and “EdgIner” in Table 2-1, are given about the principal structural axes of each cross section as oriented by the structural-twist angle, “StrcTwst.” The values of the structural twist were assumed to be identical to the aerodynamic twist discussed in Section 3.
“GJStff” represents the values of the blade torsion stiffness. Because the DOWEC blade data did not contain extensional stiffness information, we estimated the blade extensional stiffness values—“EAStff” in Table 2-1—to be 10^{7} times the average mass moment of inertia at each blade station. This came from a rule of thumb derived from the data available in the WindPACT rotor design study [19], but the exact values are not important because of the low rotational speed of the rotor.
The edgewise CM offset values, “EdgcgOf,” are the distances in meters along the chordline from the blade-pitch axis to the CM of the blade section, positive toward the trailing edge. We neglected the insignificant values of the flapwise CM offsets, “FlpcgOf,” and flapwise and edgewise elastic offsets, “FlpEAOf” and “EdgEAOf,” given in Appendix A of Ref. [17]. Instead, we assumed that they were zero as shown in Table 2-1.
The distributed blade section mass per unit length values, “BMassDen,” given in Table 2-1 are the values documented in Appendix A of Ref. [17]. We increased these by 4.536\% in the model to scale the overall (integrated) blade mass to 17{,}740\ \mathrm{kg} , which was the nominal mass of the blades in the REpower 5M prototype. In our baseline specifications, the nominal second mass moment of inertia, nominal first mass moment of inertia, and the nominal radial CM location of each blade are 11{,}776{,}047{\mathrm{~kg}}{\cdot}{\mathrm{m}}^{2} , 363,231~\mathrm{kg}\cdot\mathrm{m} , and 20.475\mathrm{~m~} with respect to (w.r.t.) the blade root, respectively.
We specified a structural-damping ratio of 0.477465\% critical in all modes of the isolated blade, which corresponds to the 3\% logarithmic decrement used in the DOWEC study from page 20 of Ref. [14].
Table 2-2 summarizes the undistributed blade structural properties discussed in this section.
Table 2-2. Undistributed Blade Structural Properties
<html>| nuodon. 61.5 m | |
| Length (w.r.t. Root Along Preconed Axis) MassScalingFactor | 4.536 % |
| Overall(Integrated)Mass | |
| 17,740kg | |
| SecondMassMomentofInertia(w.r.t.Root) | 11,776,047 kg·m |
| FirstMassMomentofInertia(w.r.t.Root) CM Location (w.r.t. Root along gPreconedAxis) | 363,231kg·m |
| 20.475m | |
| Structural-DampingRatio(AllModes) | 0.477465 % |
3 Blade Aerodynamic Properties
Similar to the blade structural properties, we based the blade aerodynamic properties of the NREL 5-MW baseline wind turbine on the DOWEC blades (using the data described in Table 1 on page 13 of Ref. [14] and in Appendix A of Ref. [17]). We set the FAST with AeroDyn and ADAMS with AeroDyn models to use 17 blade elements for integration of the aerodynamic and structural forces. To better capture the large structural gradients at the blade root and the large aerodynamic gradients at the blade tip, the 3 inboard and 3 outboard elements are two-thirds the size of the 11 equally spaced midspan elements. Table 3-1 gives the aerodynamic properties at the blade nodes, which are located at the center of the blade elements.
The blade node locations, labeled as “RNodes” in Table 3-1, are directed along the blade-pitch axis from the rotor center (apex) to the blade cross sections. The element lengths, “DRNodes,” sum to the total blade length of 61.5\,\mathrm{~m~} indicated in Table 2-2. The aerodynamic twist, “AeroTwst,” as given in Table 3-1, are offset by -0.09182^{\circ} from the values provided in Appendix A of Ref. [17] to ensure that the zero-twist reference location is at the blade tip. Integrating the chord distribution along the blade span reveals that the rotor solidity is roughly 5.16\% .
As indicated in Table 3-1, we incorporated eight unique airfoil-data tables for the NREL offshore 5-MW baseline wind turbine. The two innermost airfoil tables represent cylinders with drag coefficients of 0.50 (Cylinder1.dat) and 0.35 (Cylinder2.dat) and no lift. We created the remaining six airfoil tables by making corrections for three-dimensional behavior to the twodimensional airfoil-data coefficients of the six airfoils used in the DOWEC study (as detailed in
Table 3-1. Distributed Blade Aerodynamic Properties
<html>| Node (- | RNodes (m) | AeroTwst (°%) | DRNodes (m) | Chord (m) | AirfoilTable (-) |
| 1 | 2.8667 | 13.308 | 2.7333 | 3.542 | Cylinder1.dat |
| 2 | 5.6000 | 13.308 | 2.7333 | 3.854 | Cylinder1.dat |
| 3 | 8.3333 | 13.308 | 2.7333 | 4.167 | Cylinder2.dat |
| 4 | 11.7500 | 13.308 | 4.1000 | 4.557 | DU40_A17.dat |
| 5 | 15.8500 | 11.480 | 4.1000 | 4.652 | DU35 A17.dat |
| 6 | 19.9500 | 10.162 | 4.1000 | 4.458 | DU35 A17.dat |
| 7 | 24.0500 | 9.011 | 4.1000 | 4.249 | DU30 A17.dat |
| 8 | 28.1500 | 7.795 | 4.1000 | 4.007 | DU25 A17.dat |
| 9 | 32.2500 | 6.544 | 4.1000 | 3.748 | DU25 A17.dat |
| 10 | 36.3500 | 5.361 | 4.1000 | 3.502 | DU21 A17.dat |
| 11 | 40.4500 | 4.188 | 4.1000 | 3.256 | DU21 A17.dat |
| 12 | 44.5500 | 3.125 | 4.1000 | 3.010 | NACA64 A17.dat |
| 13 | 48.6500 | 2.319 | 4.1000 | 2.764 | NACA64 A17.dat |
| 14 | 52.7500 | 1.526 | 4.1000 | 2.518 | NACA64 A17.dat |
| 15 | 56.1667 | 0.863 | 2.7333 | 2.313 | NACA64 A17.dat |
| 16 | 58.9000 | 0.370 | 2.7333 | 2.086 | NACA64 A17.dat |
| 17 | 61.6333 | 0.106 | 2.7333 | 1.419 | NACA64 A17.dat |
Appendix A of Ref. [14]).8 In these airfoil tables, “DU” refers to Delft University and “NACA” refers to the National Advisory Committee for Aeronautics. We used AirfoilPrep v2.0 [9 ] to “tailor” these airfoil data. We first corrected the lift and drag coefficients for rotational stall delay using the Selig and Eggars method for 0^{\circ} to 90^{\circ} angles of attack. We then corrected the drag coefficients using the Viterna method for 0^{\circ} to 90^{\circ} angles of attack assuming an aspect ratio of 17. Finally, we estimated the Beddoes-Leishman dynamic-stall hysteresis parameters. We made no corrections to the DOWEC-supplied pitching-moment coefficients. The resulting threedimensionally corrected airfoil-data coefficients are illustrated graphically in Figure 3-1 through Figure 3-6. The numerical values are documented in the AeroDyn airfoil-data input files that make up Appendix B.
Figure 3-1. Corrected coefficients of the DU40 airfoil
Angle of Attack, °
Figure 3-2. Corrected coefficients of the DU35 airfoil
Figure 3-3. Corrected coefficients of the DU30 airfoil
Angle of Attack, °
Figure 3-4. Corrected coefficients of the DU25 airfoil
Figure 3-5. Corrected coefficients of the DU21 airfoil
Angle of Attack, °
Figure 3-6. Corrected coefficients of the NACA64 airfoil
Angle of Attack, °
4 Hub and Nacelle Properties
As indicated in Table 1-1, we located the hub of the NREL 5-MW baseline wind turbine 5\textrm{m} upwind of the tower centerline at an elevation of 90\textrm{m} above the ground when the system is undeflected. We also specified the same vertical distance from the tower top to the hub height used by the DOWEC study—that is, 2.4~\mathrm{m} (as specified in Table 6 on page 26 of Ref. [14]). Consequently, the elevation of the yaw bearing above ground or MSL is 87.6\;\mathrm{m} . With a shaft tilt of 5^{\circ} , this made the distance directed along the shaft from the hub center to the yaw axis 5.01910 m and the vertical distance along the yaw axis from the tower top to the shaft 1.96256\mathrm{~m~} . The distance directed along the shaft from the hub center to the main bearing was taken to be 1.912\;\mathrm{m} (from Table 6 on page 26 of Ref. [14]).
We specified the hub mass to be 56,780~\mathrm{kg} like in the REpower 5M, and we located its CM at the hub center. The hub inertia about the shaft, taken to be 115{,}926\ \mathrm{kg}\mathrm{.m}^{2} , was found by assuming that the hub casting is a thin spherical shell with a radius of 1.75\textrm{m} (this is 0.25\mathrm{~m~} longer than the actual hub radius because the nacelle height of the DOWEC turbine was 3.5\textrm{m} , based on the data in Table 6 on page 26 of Ref. [14]).
We specified the nacelle mass to be 240{,}000\ \mathrm{kg} like in the REpower 5M and we located its CM 1.9\;\mathrm{m} downwind of the yaw axis like in the DOWEC turbine (from Table 7 on page 27 of Ref. [14]) and 1.75\textrm{m} above the yaw bearing, which was half the height of the DOWEC turbine’s nacelle (from Table 6 on page 26 of Ref. [14]). The nacelle inertia about the yaw axis was taken to be 2,607,890~\mathrm{kg}\mathrm{.m}^{2} . We chose this to be equivalent to the DOWEC turbine’s nacelle inertia about its nacelle CM, but translated to the yaw axis using the parallel-axis theorem with the nacelle mass and downwind distance to the nacelle CM.
We took the nacelle-yaw actuator to have a natural frequency of 3\,\mathrm{\:Hz} , which is roughly equivalent to the highest full-system natural frequency in the FAST model (see Section 9), and a damping ratio of 2\% critical. This resulted in an equivalent nacelle-yaw-actuator linear-spring constant of 9,028,320,000\;\;\mathrm{N}{\cdot}\mathrm{m}/\mathrm{rad} and an equivalent nacelle-yaw-actuator linear-damping constant of 19,160,000\;\mathrm{N{\cdotm}/(r a d/s)} . The nominal nacelle-yaw rate was chosen to be the same as that for the DOWEC 6-MW turbine, or 0.3^{\circ}/\mathbf{s} (from page 27 of Ref. [14]).
Table 4-1 summarizes the nacelle and hub properties discussed in this section.
Table 4-1. Nacelle and Hub Properties
<html>| ElevationofYawBearingaboveGround | 87.6 m |
| Vertical Distance along Yaw Axis from Yaw Bearing to Shaft | 1.96256 m |
| Distance along Shaft from Hub Center to Yaw Axis | 5.01910 m |
| Distance alongShaftfromHubCentertoMainBearing | 1.912 m |
| Hub Mass | 56,780 kg |
| Hub Inertia about Low-Speed Shaft | 115,926 kg·m² |
| NacelleMass | 240,000kg |
| NacelleInertiaaboutYawAxis | 2,607,890 kg·m2 |
| Nacelle CM Location Downwind of Yaw Axis | 1.9 m |
| NacelleCMLocationaboveYawBearing | 1.75 m |
| EquivalentNacelle-Yaw-ActuatorLinear-SpringConstant | 9,028,320,000 N·m/rad |
| EquivalentNacelle-Yaw-Actuator Linear-DampingConstant | 19,160,000 N·m/(rad/s) |
| Nominal Nacelle-Yaw Rate | 0.3 %s |
5 Drivetrain Properties
We specified the NREL 5-MW baseline wind turbine to have the same rated rotor speed (12.1 rpm), rated generator speed (1173.7\,\mathrm{rpm}) , and gearbox ratio (97:1) as the REpower 5M machine. The gearbox was assumed be a typical multiple-stage gearbox but with no frictional losses—a requirement of the preprocessor functionality in FAST for creating ADAMS models [11]. The electrical efficiency of the generator was taken to be 94.4\% . This was chosen to be roughly the same as the total mechanical-to-electrical conversion loss used by the DOWEC turbine at rated power—that is, the DOWEC turbine had about 0.35\ \mathrm{MW} of power loss at about 6.25\ \mathrm{MW} of aerodynamic power (from Figure 15, page 24 of Ref. [14]). The generator inertia about the highspeed shaft was taken to be 534.116\;\;\mathrm{kg}\cdot\mathrm{m}^{2} , which is the same equivalent low-speed shaft generator inertia used in the DOWEC study (i.e., 5,025,500\;\mathrm{kg}\mathrm{.m}^{2} from page 36 of Ref. [14]).
The driveshaft was taken to have the same natural frequency as the RECOFF turbine model and a structural-damping ratio—associated with the free-free mode of a drivetrain composed of a rigid generator and rigid rotor—of 5\% critical. This resulted in an equivalent driveshaft linearspring constant of 867{,}637{,}000\;\mathrm{N{\cdot}m/r a d} and a linear-damping constant of 6{,}215{,}000\;\mathrm{N}\mathbf{\cdot}\mathrm{m}/(\mathrm{rad}/\mathrm{s}) .
The high-speed shaft brake was assumed to have the same ratio of maximum brake torque to maximum generator torque and the same time lag as used in the DOWEC study (from page 29 of Ref. [14]). This resulted in a fully deployed high-speed shaft brake torque of 28,116.2\;\mathrm{N}\mathrm{{\cdot}m} and a time lag of 0.6\;\mathrm{s} . This time lag is the amount of time it takes for the brake to fully engage once deployed. The FAST and ADAMS models employ a simple linear ramp from nothing to full braking over the 0.6-s period.
Table 5-1 summarizes the drivetrain properties discussed in this section.
<html>| Table5-1.DrivetrainProperties | |
| RatedRotorSpeed | 12.1 rpm |
| RatedGeneratorSpeed | 1173.7 rpm |
| GearboxRatio | 97 :1 |
| ElectricalGeneratorEfficiency | 94.4 % |
| Generator Inertia about High-Speed Shaft | 534.116 kg·m² |
| EquivalentDrive-ShaftTorsional-Spring Constant | 867,637,000 N·m/rad |
| EquivalentDrive-Shaft Torsional-Damping Constant | 6,215,000 N·m/(rad/s) |
| Fully-DeployedHigh-SpeedShaftBrakeTorque | 28,116.2 2N·m |
| High-SpeedShaftBrakeTimeConstant | 0.6 s |
6 Tower Properties
The properties of the tower for the NREL offshore 5-MW baseline wind turbine will depend on the type support structure used to carry the rotor-nacelle assembly. The type of support structure will, in turn, depend on the installation site, whose properties vary significantly through differences in water depth, soil type, and wind and wave severity. Offshore support-structure types include fixed-bottom monopiles, gravity bases, and space-frames—such as tripods, quadpods, and lattice frames (e.g., “jackets”)—and floating structures. This section documents the tower properties for the equivalent land-based version of the NREL 5-MW baseline wind turbine. These properties provide a basis with which to design towers for site-specific offshore support structures. For example, different types of offshore support structures for the NREL 5- MW baseline wind turbine have been designed for—and investigated in—separate phases of the OC3 project [13,25].
We based the distributed properties of the land-based tower for the NREL 5-MW baseline wind turbine on the base diameter (6\;\mathrm{m}) and thickness (0.027\;\mathrm{m}) , top diameter (3.87\;\mathrm{m}) and thickness (0.019\;\mathrm{m}) , and effective mechanical steel properties of the tower used in the DOWEC study (as given in Table 9 on page 31 of Ref. [14]). The Young’s modulus was taken to be 210\;\mathrm{GPa} , the shear modulus was taken to be 80.8\ \mathrm{GPa} , and the effective density of the steel was taken to be 8{,}500\;\mathrm{kg}/\mathrm{m}^{3} . The density of 8{,}500\;\mathrm{kg}/\mathrm{m}^{3} was meant to be an increase above steel’s typical value of 7{,}850~\mathrm{kg}/\mathrm{m}^{3} to account for paint, bolts, welds, and flanges that are not accounted for in the tower thickness data. The radius and thickness of the tower were assumed to be linearly tapered from the tower base to tower top. Because the REpower 5M machine had a larger tower-top mass than the DOWEC wind turbine, we scaled up the thickness of the tower relative to the values given earlier in this paragraph to strengthen the tower. We chose an increase of 30\% to ensure that the first fore-aft and side-to-side tower frequencies were placed between the one- and three-per-rev frequencies throughout the operational range of the wind turbine in a Campbell diagram. Table 6-1 gives the resulting distributed tower properties.
The entries in the first column, “Elevation,” are the vertical locations along the tower centerline relative to the tower base. “HtFract” is the fractional height along the tower centerline from the tower base (0.0) to the tower top (1.0). The rest of columns are similar to those described for the distributed blade properties presented in Table 2-1.
The resulting overall (integrated) tower mass is 347{,}460\;\mathrm{kg} and is centered at 38.234\;\mathrm{m} along the tower centerline above the ground. This result follows directly from the overall tower height of 87.6\;\mathrm{m} .
Table 6-1. Distributed Tower Properties
<html>| Elevation HtFract | TMassDen | TwFAStif | TwSSStif | TwGJStif | TwEAStif | TwFAlner | TwSSIner | TwFAcgOf | TwSScgOf | |
| (kg/m) | (N·m²) | (N·m²) | (N·m²) | (N) (kg·m) | (kg.m) | (m) | (m) | |||
| (m) 0.00 | (-) 0.0 | 5590.87 | 614.34E+9 | 614.34E+9 | 472.75E+9 | 138.13E+9 | 24866.3 | 24866.3 | 0.0 | 0.0 |
| 8.76 | 0.1 | 5232.43 | 534.82E+9 | 534.82E+9 | 411.56E+9 | 129.27E+9 | 21647.5 | 21647.5 | 0.0 | 0.0 |
| 17.52 | 0.2 | 4885.76 | 463.27E+9 | 463.27E+9 | 356.50E+9 | 120.71E+9 | 18751.3 | 18751.3 | 0.0 | 0.0 |
| 26.28 | 0.3 | 4550.87 | 399.13E+9 | 399.13E+9 | 307.14E+9 | 112.43E+9 | 16155.3 | 16155.3 | 0.0 | 0.0 |
| 35.04 | 0.4 | 4227.75 | 341.88E+9 | 341.88E+9 | 263.09E+9 | 104.45E+9 | 13838.1 | 13838.1 | 0.0 | 0.0 |
| 43.80 | 0.5 | 3916.41 | 291.01E+9 | 291.01E+9 | 223.94E+9 | 96.76E+9 | 11779.0 | 11779.0 | 0.0 | 0.0 |
| 52.56 | 0.6 | 3616.83 | 246.03E+9 | 246.03E+9 | 189.32E+9 | 89.36E+9 | 9958.2 | 9958.2 | 0.0 | 0.0 |
| 61.32 | 0.7 | 3329.03 | 206.46E+9 | 206.46E+9 | 158.87E+9 | 82.25E+9 | 8356.6 | 8356.6 | 0.0 | 0.0 |
| 70.08 | 0.8 | 3053.01 | 171.85E+9 | 171.85E+9 | 132.24E+9 | 75.43E+9 | 6955.9 | 6955.9 | 0.0 | 0.0 |
| 78.84 | 0.9 | 2788.75 | 141.78E+9 | 141.78E+9 | 109.10E+9 | 68.90E+9 | 5738.6 | 5738.6 | 0.0 | 0.0 |
| 87.60 | 1.0 | 2536.27 | 115.82E+9 | 115.82E+9 | 89.13E+9 | 62.66E+9 | 4688.0 | 4688.0 | 0.0 | 0.0 |
We specified a structural-damping ratio of 1\% critical in all modes of the isolated tower (without the rotor-nacelle assembly mass present), which corresponds to the values used in the DOWEC study (from page 21 of Ref. [14]).
Table 6-2 summarizes the undistributed tower properties discussed in this section.
Table 6-2. Undistributed Tower Properties
<html>| HeightaboveGround | 87.6 m |
| Overall (lntegrated) Mass | 347,460 kg |
| CM Location (w.r.t. Ground along Tower Centerline) | 38.234 m |
| Structural-Damping gRatio(AllModes) | 1 % |
7 Baseline Control System Properties
For the NREL 5-MW baseline wind turbine, we chose a conventional variable-speed, variable blade-pitch-to-feather configuration. In such wind turbines, the conventional approach for controlling power-production operation relies on the design of two basic control systems: a generator-torque controller and a full-span rotor-collective blade-pitch controller. The two control systems are designed to work independently, for the most part, in the below-rated and above-rated wind-speed range, respectively. The goal of the generator-torque controller is to maximize power capture below the rated operation point. The goal of the blade-pitch controller is to regulate generator speed above the rated operation point.
We based the baseline control system for the NREL 5-MW wind turbine on this conventional design approach. We did not establish additional control actions for nonpower-production operations, such as control actions for normal start-up sequences, normal shutdown sequences, and safety and protection functions. Nor did we develop control actions to regulate the nacelleyaw angle. (The nacelle-yaw control system is generally neglected within aero-servo-elastic simulation because its response is slow enough that it does not generally contribute to large extreme loads or fatigue damage.)
We describe the development of our baseline control system next, including the controlmeasurement filter (Section 7.1), the generator-torque controller (Section 7.2), the blade-pitch controller (Section 7.3), and the blade-pitch actuator (Section 7.4). Section 7.5 shows how these systems are put together in the overall integrated control system.
7.1 Baseline Control-Measurement Filter
As is typical in utility-scale multimegawatt wind turbines, both the generator-torque and bladepitch controllers use the generator speed measurement as the sole feedback input. To mitigate high-frequency excitation of the control systems, we filtered the generator speed measurement for both the torque and pitch controllers using a recursive, single-pole low-pass filter with exponential smoothing [30]. The discrete-time recursion (difference) equation for this filter is
y\Bigl[n\Bigr]\!=\!\bigl(I\!-\!\alpha\bigr)u\bigl[n\bigr]\!+\!\alpha y\bigl[n-I\bigr]\!\,,
with
\alpha=e^{-2\pi T_{s}f_{c}}\,,
where y is the filtered generator speed (output measurement), \boldsymbol{u} is the unfiltered generator speed (input), \alpha is the low-pass filter coefficient, n is the discrete-time-step counter, T_{s} is the discrete time step, and f_{c} is the corner frequency.
By defining the filter state,
x\big[n\big]=y\big[n-I\big]\,,
x\big[n+l\big]=y\big[n\big],
one can derive a discrete-time state-space representation of this filter:
\begin{array}{c}{{x\big[n+l\big]=A_{d}x\big[n\big]+B_{d}u\big[n\big]}}\\ {{y\big[n\big]=C_{d}x\big[n\big]+D_{d}u\big[n\big]}}\end{array}
where A_{d}=\alpha is the discrete-time state matrix, B_{d}={\cal I}\!-\!\alpha is the discrete-time input matrix, C_{d}=\alpha is the discrete-time output state matrix, and D_{d}=l\!-\!\alpha is the discrete-time input transmission matrix.
The state-space representation of Eq. (7-4) is useful for converting the filter into other forms, such as transfer-function form or frequency-response form [31].
We set the corner frequency (the -3 dB point in Figure 7-1) of the low-pass filter to be roughly one-quarter of the blade’s first edgewise natural frequency (see Section 9) or 0.25~\mathrm{Hz} . For a discrete time step of 0.0125\ \mathrm{s} , the frequency response of the resulting filter is shown in the Bode plot of Figure 7-1.
We chose the recursive, single-pole filter for its simplicity in implementation and effectiveness in the time domain. The drawbacks to this filter are its gentle roll-off in the stop band (-6 dB/octave) and the magnitude and nonlinearity of its phase lag in the pass band [30]. We considered other linear low-pass filters, such as Butterworth, Chebyshev, Elliptic, and Bessel filters because of their inherent advantages relative to the chosen filter. Like the chosen filter, a Butterworth filter has a frequency response that is flat in the pass band, but the Butterworth filter offers steeper roll-off in the stop band. Chebyshev filters offer even steeper roll-off in the stop band at the expense of equalized-ripple (equiripple) in the pass band (Type 1) or stop band (Type 2), respectively. Elliptic filters offer the steepest roll-off of any linear filter, but have equiripple in both the pass and stop bands. Bessel filters offer the flattest group delay (linear phase lag) in the pass band. We designed and tested examples of each of these other low-pass filter types, considering state-space representations of up to fourth order (four states). None were found to give superior performance in the overall system response, however, so they did not warrant the added complexity of implementation.
Figure 7-1. Bode plot of generator speed low-pass filter frequency response
7.2 Baseline Generator-Torque Controller
The generator torque is computed as a tabulated function of the filtered generator speed, incorporating five control regions: 1,\,1\,\%,\,2,\,2\% , and 3. Region 1 is a control region before cut-in wind speed, where the generator torque is zero and no power is extracted from the wind; instead, the wind is used to accelerate the rotor for start-up. Region 2 is a control region for optimizing power capture. Here, the generator torque is proportional to the square of the filtered generator speed to maintain a constant (optimal) tip-speed ratio. In Region 3, the generator power is held constant so that the generator torque is inversely proportional to the filtered generator speed. Region 1\% , a start-up region, is a linear transition between Regions 1 and 2. This region is used to place a lower limit on the generator speed to limit the wind turbine’s operational speed range. Region 2\% is a linear transition between Regions 2 and 3 with a torque slope corresponding to the slope of an induction machine. Region 2\% is typically needed (as is the case for my 5-MW turbine) to limit tip speed (and hence noise emissions) at rated power.
We found the peak of the power coefficient as a function of the tip-speed ratio and blade-pitch surface by running FAST with AeroDyn simulations at a number of given rotor speeds and a number of given rotor-collective blade-pitch angles at a fixed wind speed of 8~\mathrm{m/s} . From these simulations, we found that the peak power coefficient of 0.482 occurred at a tip-speed ratio of 7.55 and a rotor-collective blade-pitch angle of 0.0^{\circ} . With the 97:1 gearbox ratio, this resulted in an optimal constant of proportionality of 0.0255764\;\mathrm{N{\cdot}m/r p m}^{2} in the Region 2 control law. With the rated generator speed of 1173.7\ \mathrm{{rpm}} , rated electric power of 5\,\mathrm{\textrm{MW}} , and a generator efficiency of 94.4\% , the rated mechanical power is 5.296610\:\mathrm{MW} and the rated generator torque is 43{,}093{.}55\ \mathrm{N}\mathrm{{\cdot}m} . We defined Region 1\% to span the range of generator speeds between 670 rpm and 30\% above this value (or 871\;\;\mathrm{rpm}) . The minimum generator speed of 670 rpm corresponds to the minimum rotor speed of 6.9~\mathrm{rpm} used by the actual REpower 5M machine [26]. We took the transitional generator speed between Regions 2\% and 3 to be 99\% of the rated generator speed, or 1,\!161.963\mathrm{~rpm} . The generator-slip percentage in Region 2\% was taken to be 10\% , in accordance with the value used in the DOWEC study (see page 24 of Ref. [14]). Figure 7-2 shows the resulting generator-torque versus generator speed response curve.
Figure 7-2. Torque-versus-speed response of the variable-speed controller
Because of the high intrinsic structural damping of the drivetrain, we did not need to incorporate a control loop for damping drivetrain torsional vibration in our baseline generator-torque controller.
We did, however, place a conditional statement on the generator-torque controller so that the torque would be computed as if it were in Region 3—regardless of the generator speed— whenever the previous blade-pitch-angle command was 1^{\mathbf{o}} or greater. This results in improved output power quality (fewer dips below rated) at the expense of short-term overloading of the generator and the gearbox. To avoid this excessive overloading, we saturated the torque to a maximum of 10\% above rated, or 47{,}402.91\ \mathrm{N}\mathrm{{\cdot}m} . We also imposed a torque rate limit of 15,000 \mathbf{N}\mathbf{\bullet}\mathbf{m}/\mathbf{s} . In Region 3, the blade-pitch control system takes over.
7.3 Baseline Blade-Pitch Controller
In Region 3, the full-span rotor-collective blade-pitch-angle commands are computed using gainscheduled proportional-integral (PI) control on the speed error between the filtered generator speed and the rated generator speed (1173.7 rpm).
We designed the blade-pitch control system using a simple single-degree-of-freedom (singleDOF) model of the wind turbine. Because the goal of the blade-pitch control system is to regulate the generator speed, this DOF is the angular rotation of the shaft. To compute the required control gains, it is beneficial to examine the equation of motion of this single-DOF system. From a simple free-body diagram of the drivetrain, the equation of motion is
T_{\mathit{A e r o}}-N_{\mathit{G e a r}}T_{\mathit{G e n}}=\left(I_{\mathit{R o t o r}}+N_{\mathit{G e a r}}^{2}I_{\mathit{G e n}}\right)\frac{d}{d t}\big(\varOmega_{o}+Δ\varOmega\big)=I_{\mathit{D r i v e t r a i n}}Δ\dot{\varOmega}\,,
where T_{A e r o} is the low-speed shaft aerodynamic torque, T_{G e n} is the high-speed shaft generator torque, N_{G e a r} is the high-speed to low-speed gearbox ratio, I_{D r i v e t r a i n} is the drivetrain inertia cast to the low-speed shaft, I_{R o t o r} is the rotor inertia, I_{G e n} is the generator inertia relative to the highspeed shaft, \varOmega_{o} is the rated low-speed shaft rotational speed, \varDelta{\varOmega} is the small perturbation of low-speed shaft rotational speed about the rated speed, Δ\dot{\varOmega} is the low-speed shaft rotational acceleration, and t is the simulation time.
Because the generator-torque controller maintains constant generator power in Region 3, the generator torque in Region 3 is inversely proportional to the generator speed (see Figure 7-2), or
T_{G e n}\left(N_{G e a r}\Omega\right)\!=\!\frac{P_{o}}{N_{G e a r}\varOmega},
where P_{0} is the rated mechanical power and \Omega is the low-speed shaft rotational speed.
Similarly, assuming negligible variation of aerodynamic torque with rotor speed, the aerodynamic torque in Region 3 is
T_{_{A e r o}}\left(\theta\right)\!=\!\frac{P\big(\theta,\varOmega_{o}\big)}{\varOmega_{o}},
where P is the mechanical power and \theta is the full-span rotor-collective blade-pitch angle.
Using a first-order Taylor series expansion of Eqs. (7-6) and (7-7), one can see that
T_{G e n}\approx\frac{P_{o}}{N_{G e a r}\Omega_{o}}-\frac{P_{0}}{N_{G e a r}\Omega_{0}^{2}}\varDelta\Omega
T_{_{A e r o}}\approx\frac{P_{_{0}}}{\Omega_{\!\scriptscriptstyle0}}\!+\!\frac{1}{\Omega_{\!\scriptscriptstyle0}}\!\left(\frac{\partial{P}}{\partial\theta}\right)\!\varDelta\theta\,,
where \varDelta\theta is a small perturbation of the blade-pitch angles about their operating point. With proportional-integral-derivative (PID) control, this is related to the rotor-speed perturbations by
\varDelta\theta=K_{P}N_{\mathit{G e a r}}\varDelta\varOmega+K_{I}\intop_{\theta}^{t}N_{\mathit{G e a r}}\varDelta\varOmega d t+K_{D}N_{\mathit{G e a r}}\varDelta\dot{\varOmega}\,,
where K_{P},\,K_{I}, and K_{D} are the blade-pitch controller proportional, integral, and derivative gains, respectively.
By setting \dot{\varphi}=\varDelta\varOmega , combining the above expressions, and simplifying, the equation of motion for the rotor-speed error becomes
\underbrace{\bigg[I_{D r i v e r a i n}+\frac{1}{\Omega_{\!0}}\bigg(-\frac{\partial{P}}{\partial{\theta}}\bigg)N_{G e a r}K_{D}\bigg]}_{M_{\!\varphi}}\ddot{\varphi}+\underbrace{\Bigg[\frac{1}{\Omega_{\!o}}\bigg(-\frac{\partial{P}}{\partial{\theta}}\bigg)N_{G e a r}K_{P}-\frac{P_{0}}{\Omega_{\!0}^{2}}\Bigg]}_{C_{\varphi}}\dot{\varphi}+\underbrace{\Bigg[\frac{1}{\Omega_{\!0}}\bigg(-\frac{\partial{P}}{\partial{\theta}}\bigg)N_{G e a r}K_{I}\Bigg]}_{K_\varphi}\varphi=0\cdot
One can see that the idealized PID-controlled rotor-speed error will respond as a second-order system with the natural frequency, \omega_{\varphi n} , and damping ratio, \zeta_{\varphi}, , equal to
\omega_{\varphi n}=\sqrt{\frac{K_{\varphi}}{M_{\varphi}}}
and
\zeta_{\varphi}=\frac{C_{\varphi}}{2\sqrt{K_{\varphi}M_{\varphi}}}\!=\!\frac{C_{\varphi}}{2M_{\varphi}\omega_{\varphi n}}\,.
In an active pitch-to-feather wind turbine, the sensitivity of aerodynamic power to the rotorcollective blade-pitch angle, \partial P/\partial\theta , is negative in Region 3. With positive control gains, then, the derivative term acts to increase the effective inertia of the drivetrain, the proportional term adds damping, and the integral term adds restoring. Also, because the generator torque drops with increasing speed error (to maintain constant power) in Region 3, one can see that the generator-torque controller introduces a negative damping in the speed error response (indicated by the -P_{o}/\varOmega_{o}^{2} term in Eq. (7-11)). This negative damping must be compensated by the proportional term in the blade-pitch controller.
In the design of the blade-pitch controller, Ref. [10] recommends neglecting the derivative gain, ignoring the negative damping from the generator-torque controller, and aiming for the response characteristics given by \omega_{\varphi n}=0.6~\mathrm{rad/s} and \zeta_{\varphi}=0.6 to 0.7. This specification leads to direct expressions for choosing appropriate PI gains once the sensitivity of aerodynamic power to rotor-collective blade pitch, \partial P/\partial\theta , is known:
K_{P}=\frac{2I_{D r i v e t r a i n}\varOmega_{0}\zeta_{\varphi}\omega_{\varphi_{n}}}{N_{G e a r}\left(-\frac{{\partial}{P}}{{\partial}{\theta}}\right)}
K_{I}=\frac{I_{D r i v e t r a i n}\varOmega_{0}\omega_{\varphi n}^{2}}{N_{G e a r}\left(-\frac{\partial P}{\partial\theta}\right)}\,.
The blade-pitch sensitivity, \partial P/\partial\theta , is an aerodynamic property of the rotor that depends on the wind speed, rotor speed, and blade-pitch angle. We calculated it for the NREL offshore 5-MW baseline wind turbine by performing a linearization analysis in FAST with AeroDyn at a number of given, steady, and uniform wind speeds; at the rated rotor speed ( \varOmega_{\!_{0}}=12.1\;\mathrm{{rpm})} ; and at the corresponding blade-pitch angles that produce the rated mechanical power (P_{0}=5.296610\;\mathrm{MW}) . The linearization analysis involves perturbing the rotor-collective blade-pitch angle at each operating point and measuring the resulting variation in aerodynamic power. Within FAST, the partial derivative is computed using the central-difference-perturbation numerical technique. We created a slightly customized copy of FAST with AeroDyn so that the linearization procedure would invoke the frozen-wake assumption, in which the induced wake velocities are held constant while the blade-pitch angle is perturbed. This gives a more accurate linearization for heavily loaded rotors (i.e., for operating points in Region 3 closest to rated). Table 7-1 presents the results.
Table 7-1. Sensitivity of Aerodynamic Power to Blade Pitch in Region 3
<html>| Wind Speed (m/s) | Rotor Speed (rpm) | PitchAngle (%) | partial P /partial theta(watt/rad) |
| 11.4-Rated | 12.1 | 0.00 | -28.24E+6 |
| 12.0 | 12.1 | 3.83 | -43.73E+6 |
| 13.0 | 12.1 | 6.60 | -51.66E+6 |
| 14.0 | 12.1 | 8.70 | -58.44E+6 |
| 15.0 | 12.1 | 10.45 | -64.44E+6 |
| 16.0 | 12.1 | 12.06 | -70.46E+6 |
| 17.0 | 12.1 | 13.54 | -76.53E+6 |
| 18.0 | 12.1 | 14.92 | -83.94E+6 |
| 19.0 | 12.1 | 16.23 | -90.67E+6 |
| 20.0 | 12.1 | 17.47 | -94.71E+6 |
| 21.0 | 12.1 | 18.70 | -99.04E+6 |
| 22.0 | 12.1 | 19.94 | -105.90E+6 |
| 23.0 | 12.1 | 21.18 | -114.30E+6 |
| 24.0 | 12.1 | 22.35 | -120.20E+6 |
| 25.0 | 12.1 | 23.47 | -125.30E+6 |
As Table 7-1 shows, the sensitivity of aerodynamic power to rotor-collective blade pitch varies considerably over Region 3, so constant PI gains are not adequate for effective speed control. The pitch sensitivity, though, varies nearly linearly with blade-pitch angle:
\frac{\partial P}{\partial\theta}\!=\!\left[\frac{\frac{\partial P}{\partial\theta}\big(\theta\!=\!0\big)}{\theta_{K}}\right]\!\theta\!+\!\left[\frac{\partial P}{\partial\theta}\big(\theta\!=\!0\big)\right]
\frac{1}{\frac{\partial P}{\partial\theta}}\!=\!\frac{1}{\frac{\partial P}{\partial\theta}\!\left(\theta\!=\!\theta\right)\!\left(1\!+\!\frac{\theta}{\theta_{\!\scriptscriptstyle K}}\right)},
where \frac{\partial P}{\partial\theta}\!\left(\theta=\!0\right) is the pitch sensitivity at rated and \theta_{K} is the blade-pitch angle at which the pitch sensitivity has doubled from its value at the rated operating point; that is,
\frac{\partial P}{\partial\theta}\big(\theta=\theta_{\kappa}\big)=2\frac{\partial P}{\partial\theta}\big(\theta\!=\!0\big).
On the right-hand side of Eq. (7-16a), the first and second terms in square brackets represent the slope and intercept of the best-fit line, respectively. We computed this regression for the NREL 5-MW baseline wind turbine and present the results in Figure 7-3.
Figure 7-3. Best-fit line of pitch sensitivity in Region 3
The linear relation between pitch sensitivity and blade-pitch angle presents a simple technique for implementing gain scheduling based on blade-pitch angle; that is,
K_{P}\left(\theta\right)=\frac{2I_{D r i v e t r a i n}\varOmega_{\rho}\zeta_{\varphi}\omega_{\varphi n}}{N_{G e a r}\left[-\frac{\partial P}{\partial\theta}\big(\theta=0\big)\right]}G K\left(\theta\right)
K_{I}\left(\theta\right)\!=\!\frac{I_{D r i v e t r a i n}\varOmega_{\theta}\omega_{\varphi n}^{2}}{N_{G e a r}\left[-\frac{\hat{\partial}P}{\hat{\partial}\theta}(\theta=\theta)\right]}{G K}(\theta),
where G K(\theta) is the dimensionless gain-correction factor (from Ref. [10]), which is dependent on the blade-pitch angle:
G K\left(\theta\right)=\frac{I}{I+\frac{\theta}{\theta_{K}}}.
In our implementation of the gain-scheduled PI blade-pitch controller, we used the blade-pitch angle from the previous controller time step to calculate the gain-correction factor at the next time step.
Using the properties for the baseline wind turbine and the recommended response characteristics from Ref. [10], the resulting gains are \underline{{K_{P}}}(\theta=0^{\circ})=0.01882681\ \mathrm{s},\ K_{I}(\theta=0^{\circ})=0.008068634, and K_{D}\,=\,0.0\,\stackrel{\cdot}{\mathbf{s}}^{2} . Figure 7-4 presents the gains at other blade-pitch angles, along with the gaincorrection factor. We used the upper limit of the recommended damping ratio range, \zeta_{\varphi}=0.7 , to compensate for neglecting negative damping from the generator-torque controller in the determination of K_{P} .
Unfortunately, the simple gain-scheduling law derived in this section for the proportional and integral gains cannot retain consistent response characteristics (i.e., constant values of \omega_{\varphi n} and \zeta_{\varphi}) across all of Region 3 when applied to the derivative gain. We, nevertheless, considered adding a derivative term by selecting and testing a range of gains, but none were found to give better performance in the overall system response. Instead, the baseline control system uses the gains derived previously in this section (without the derivative term).
Figure 7-4. Baseline blade-pitch control system gain-scheduling law
Rotor-Collective Blade-Pitch Angle, º
We set the blade-pitch rate limit to 8^{\circ}/\mathrm{s} in absolute value. This is speculated to be the bladepitch rate limit of conventional 5-MW machines based on General Electric (GE) Wind’s longblade test program. We also set the minimum and maximum blade-pitch settings to 0^{\circ} and 90^{\circ} , respectively. The lower limit is the set blade pitch for maximizing power in Region 2, as described in Section 7.2. The upper limit is very close to the fully feathered blade pitch for neutral torque. We saturated the integral term in the PI controller between these limits to ensure a fast response in the transitions between Regions 2 and 3.
7.4 Baseline Blade-Pitch Actuator
Because of limitations in the FAST code, the FAST model does not include any blade-pitch actuator dynamic effects. Blade-pitch actuator dynamics are, however, needed in ADAMS. To enable successful comparisons between the FAST and ADAMS response predictions, then, we found it beneficial to reduce the effect of the blade-pitch actuator response in ADAMS. Consequently, we designed the blade-pitch actuator in the ADAMS model with a very high natural frequency of 30\;\mathrm{Hz} , which is higher than the highest full-system natural frequency in the FAST model (see Section 9), and a damping ratio of 2\% critical. This resulted in an equivalent blade-pitch actuator linear-spring constant of 971,350,000 N•m/rad and an equivalent blade-pitch actuator linear-damping constant of 206,000\;\mathrm{N{\cdot}m/(r a d/s)} .
7.5 Summary of Baseline Control System Properties
We implemented the NREL offshore 5-MW wind turbine’s baseline control system as an external dynamic link library (DLL) in the style of Garrad Hassan’s BLADED wind turbine software package [3]. Appendix C contains the source code for this DLL, and Figure 7-5 presents a flowchart of the overall integrated control system calculations. Table 7-2 summarizes the baseline generator-torque and blade-pitch control properties we discussed earlier in this section.
Figure 7-5. Flowchart of the baseline control system
Table 7-2. Baseline Control System Properties
<html>| Corner Frequency of Generator-Speed Low-Pass Filter | 0.25 Hz |
| PeakPowerCoefficient | 0.482 |
| Tip-Speed Ratio atPeakPower Coefficient | 7.55 |
| Rotor-CollectiveBlade-PitchAngleatPeakPowerCoefficient | 0.0° |
| Generator-Torque Constant in Region 2 | |
| RatedMechanicalPower | 0.0255764 N·m/rpm2 |
| Rated Generator Torque | 5.296610MW |
| Transitional GeneratorSpeedbetweenRegions1and112 | 43,093.55 N·m |
| Transitional GeneratorSpeedbetweenRegions1%2 and 2 | 670 rpm |
| TransitionalGeneratorSpeedbetweenRegions2%2and3 | 871 rpm |
| 1,161.963 rpm | |
| Generator SlipPercentage in Region 21%2 | 10 % |
| MinimumBladePitchforEnsuringRegion3Torque | 1° |
| MaximumGeneratorTorque | 47,402.91 N·m |
| Maximum Generator TorqueRate | 15,000 N·m/s |
| Proportional Gain atMinimumBlade-PitchSetting | 0.01882681 S |
| Integral Gain at Minimum Blade-Pitch Setting | 0.008068634 |
| Blade-Pitch Angle at which the Rotor Power Has Doubled | 6.302336° |
| Minimum Blade-Pitch Setting | 。0 |
| MaximumBlade-PitchSetting | 。06 |
| MaximumAbsoluteBladePitchRate | 8 %s |
| Equivalent Blade-Pitch-Actuator Linear-Spring Constant | 971,350,000N·m/rad |
| Equivalent Blade-Pitch-Actuator Linear-Damping Constant | 206,000 N·m/rad/s |
8 FAST with AeroDyn and ADAMS with AeroDyn Models
Using the turbine properties described previously in this report, we put together models of the NREL offshore 5-MW baseline wind turbine within FAST [11] with AeroDyn [16,20]. The input files for these models are given in Appendix A and Appendix B, for version (v) 6.10a-jmj of FAST and v12.58 of AeroDyn, respectively. We then generated the higher fidelity ADAMS with AeroDyn models through the preprocessor functionality built into the FAST code.
The input files in Appendix A are for the FAST model of the equivalent land-based version of the NREL 5-MW baseline wind turbine. The input files for other versions of the model, such as those for different support structures, require only a few minor changes. These include changes to input parameters “PtfmModel” and “PtfmFile,” which identify the type and properties of the support platform, and modifications to the prescribed mode shapes in the tower input file, “TwrFile.”
Although most of the input-parameter specifications in Appendix A and Appendix B are selfexplanatory, the specifications of the prescribed mode shapes needed by FAST to characterize the flexibility of the blades and tower deserve a special explanation. The required mode shapes depend on the member’s boundary conditions. For the blade modes, we used v2.22 of the Modes program [4] to derive the equivalent polynomial representations of the blade mode shapes needed by FAST. The Modes program calculates the mode shapes of rotating blades, assuming that a blade mode shape is unaffected by its coupling with other system modes of motion. This is a common assumption in wind turbine analysis. For the tower modes, however, there is a great deal of coupling with the rotor motions, and in offshore floating systems, there is coupling with the platform motions as well. To take the former factor into account, we used the linearization functionality of the full-system ADAMS model to obtain the tower modes for the land-based version of the NREL 5-MW baseline wind turbine. In other words, we built an ADAMS model of the wind turbine, enabled all system DOFs, and linearized the model. Then we passed a best-fit polynomial through the resulting tower mode shapes to get the equivalent polynomial representations of the tower mode shapes needed by FAST.
Not including platform motions, the FAST model of the land-based version of the NREL 5-MW baseline wind turbine incorporates 16 DOFs as follows:
• Two flapwise and one edgewise bending-mode DOFs for each of the three blades One variable-generator speed DOF and one driveshaft torsional DOF • One nacelle-yaw-actuator DOF • Two fore-aft and two side-to-side bending-mode DOFs in the tower.
Not including platform motion, the higher fidelity ADAMS model of the land-based version of the wind turbine incorporates 438 DOFs as follows:
One hundred and two DOFs in each of the three blades, including flapwise and edgewise shear and bending, torsion, and extension DOFs
• One blade-pitch actuator DOF in each of the three blades
• One variable-generator speed DOF and one driveshaft torsional DOF • One nacelle-yaw actuator DOF One hundred and twenty-six DOFs in the tower, including fore-aft and side-to-side shear and bending, torsion, and extension DOFs.
The support platform motions in, for example, the floating-platform versions of the NREL 5- MW baseline wind turbine add six DOFs per model.
We use a constant time step of 0.0125 s in FAST’s fixed-step-size time-integration scheme and a maximum step size of 0.0125 s in ADAMS’ variable-step-size time integrator. We have AeroDyn perform aerodynamic calculations every other structural time step (i.e., 0.025 s) to ensure that there are at least 200-azimuth-step computations per revolution at 12~\mathrm{rpm} . Data are output at 20~\mathrm{Hz} or every fourth structural time step. We made these time steps as large as possible to ensure numerical stability and suitable output resolution across a range of operating conditions.
9 Full-System Natural Frequencies and Steady-State Behavior
To provide a cursory overview of the overall system behavior of the equivalent land-based version of the NREL 5-MW baseline wind turbine, we calculated the full-system natural frequencies and the steady-state response of the system as a function of wind speed.
We obtained the full-system natural frequencies with both the FAST model and the ADAMS model. In FAST, we calculated the natural frequencies by performing an eigenanalysis on the first-order state matrix created from a linearization analysis. In ADAMS, we obtained the frequencies by invoking a “LINEAR/EIGENSOL” command, which linearizes the complete ADAMS model and computes eigendata. To avoid the rigid-body drivetrain mode, the analyses considered the wind turbine in a stationary condition with the high-speed shaft brake engaged. The blades were pitched to their minimum set point (0^{\circ}) , but aerodynamic damping was ignored. Table 9-1 lists results for the first 13 full-system natural frequencies.
Table 9-1. Full-System Natural Frequencies in Hertz
<html>| Mode | Description | FAST | ADAMS |
| 1 | 1stTowerFore-Aft | 0.3240 | 0.3195 |
| 2 | 1stTowerSide-to-Side | 0.3120 | 0.3164 |
| 3 | 1stDrivetrainTorsion | 0.6205 | 0.6094 |
| 4 | 1stBladeAsymmetricFlapwiseYaw | 0.6664 | 0.6296 |
| 5 | 1stBladeAsymmetricFlapwisePitch | 0.6675 | 0.6686 |
| 6 | 1stBladeCollectiveFlap | 0.6993 | 0.7019 |
| 7 | 1stBladeAsymmetricEdgewisePitch | 1.0793 | 1.0740 |
| 8 | 1stBladeAsymmetricEdgewiseYaw | 1.0898 | 1.0877 |
| 9 | 2ndBladeAsymmetricFlapwiseYaw | 1.9337 | 1.6507 |
| 10 | 2ndBladeAsymmetricFlapwisePitch | 1.9223 | 1.8558 |
| 11 | 2ndBladeCollectiveFlap | 2.0205 | 1.9601 |
| 12 | 2nd Tower Fore-Aft | 2.9003 | 2.8590 |
| 13 | 2nd TowerSide-to-Side | 2.9361 | 2.9408 |
The agreement between FAST and ADAMS is quite good. The biggest differences exist in the predictions of the blades’ second asymmetric flapwise yaw and pitch modes. By “yaw” and “pitch” we mean that these blade asymmetric modes couple with the nacelle-yaw and nacellepitching motions, respectively. Because of the offsets of the blade section CM from the pitch axis, higher-order modes, and tower-torsion DOFs—which are available in ADAMS, but not in FAST—ADAMS predicts lower natural frequencies in these modes than FAST does.
Bir and Jonkman have published [2] a much more exhaustive eigenanalysis for the NREL 5-MW baseline wind turbine. The referenced publication documents the natural frequencies and damping ratios of the land- and floating-platform versions of the 5-MW turbine across a range of operating conditions.
We obtained the steady-state response of the land-based 5-MW baseline wind turbine by running a series of FAST with AeroDyn simulations at a number of given, steady, and uniform wind speeds. The simulations lengths were long enough to ensure that all transient behavior had died out; we then recorded the steady-state output values. We ran the simulations using the bladeelement / momentum (BEM) wake option of AeroDyn and with all available and relevant landbased DOFs enabled. Figure 9-1 shows the results for several output parameters, which are defined as follows:
“GenSpeed” represents the rotational speed of the generator (high-speed shaft).
• “RotPwr” and “GenPwr” represent the mechanical power within the rotor and the electrical output of the generator, respectively.
· “RotThrust” represents the rotor thrust.
• “RotTorq” represents the mechanical torque in the low-speed shaft. “RotSpeed” represents the rotational speed of the rotor (low-speed shaft).
• “BlPitch1” represents the pitch angle of Blade 1.
? “GenTq” represents the electrical torque of the generator.
. “TSR” represents the tip-speed ratio.
• “OoPDefl1” and “IPDefl1” represent the out-of-plane and in-plane tip deflections of Blade 1 relative to the undeflected blade-pitch axis. “TTDspFA” and “TTDspSS” represent the fore-aft and side-to-side deflection of the tower top relative to the centerline of the undeflected tower.
As planned, the generator and rotor speeds increase linearly with wind speed in Region 2 to maintain constant tip-speed ratio and optimal wind-power conversion efficiency. Similarly, the generator and rotor powers and generator and rotor torques increase dramatically with wind speed in Region 2, increasing cubically and quadratically, respectively. Above rated, the generator and rotor powers are held constant by regulating to a fixed speed with active bladepitch control. The out-of-plane tip deflection of the reference blade (Blade 1) reaches a maximum at the rated operating point before dropping again. This response characteristic is the result of the peak in rotor thrust at rated. This peak is typical of variable generator speed variable blade-pitch-to-feather wind turbines because of the transition that occurs in the control system at rated between the active generator-torque and the active blade-pitch control regions. This peak in response is also visible, though less pronounced, in the in-plane tip deflection of the reference blade and the tower-top fore-aft displacement.
Start-up transient behavior is an artifact of computational analysis. To mitigate this behavior, we suggest using the steady-state values of the rotor speed and blade-pitch angles found in Figure 9-1 as initial conditions in simulations.
Figure 9-1. Steady-state responses as a function of wind speed
10 Conclusions
To support concept studies aimed at assessing offshore wind technology, we developed the specifications of a representative utility-scale multimegawatt turbine now known as the “NREL offshore 5-MW baseline wind turbine.” This wind turbine is a conventional three-bladed upwind variable-speed variable blade-pitch-to-feather-controlled turbine. To create the model, we obtained some broad design information from the published documents of turbine manufacturers, with a heavy emphasis on the REpower 5M machine. Because detailed data was unavailable, however, we also used the publicly available properties from the conceptual models in the WindPACT, RECOFF, and DOWEC projects. We then created a composite from these data, extracting the best available and most representative specifications. This report documented the specifications of the NREL offshore 5-MW baseline wind turbine—including the aerodynamic, structural, and control-system properties—and the rationale behind its development. The model has been, and will likely continue to be, used as a reference by research teams throughout the world to standardize baseline offshore wind turbine specifications and to quantify the benefits of advanced land- and sea-based wind energy technologies.
References
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Appendix A FAST Input Files
A.1 Primary Input File
<html>| FAST INPUT FILE | |
| NREL 5.0 Mw Baseline Wind Turbine for Use in Offshore Analysis. Properties from Dutch Offshore Wind Energy Converter (DowEC） 6Mw Pre-Design (10046_009.pdf） and REpower 5M 5Mw(5m_uk.pdf);C | |
| SIMULATION CONTROL- False Echo 3 | -Echo input data to"echo.out"(flag) |
| ADAMSPrep 1 3 | -ADAMS preprocessor mode {1: Run FAST,2: use FAST as a preprocessor to create an ADAMS model，3: do |
| AnalMode | |
| NumB1 | |
| 630.0 | -Number of blades (-) |
| TMax DT | -Total run time (s) |
| 0.0125 | -Integration time step (s) |
| TURBINE CONTROL-- | |
| θ YCMode | -Yaw control mode {0:none，1:user-defined from routine UserYawCont，2:user-defined from Simulink} |
| TYCOn | -Time to enable active yaw control (s）[unused when YcMode=0] |
| 9999.9 PCMode | -Pitch control mode {0:none,1:user-defined from routine Pitchcntrl,2: user-defined from Simulink |
| 1 TPCOn | |
| 0.0 VSContrl | -Time to enable active pitch control（s）[unused when PCMode=0] |
| 2 VS_RtGnSp | |
| 9999.9 | Rated generator speed for simple variable-speed generator control(HSS side）(rpm）[used only when |
| 9999.9 VS_RtTq | Rated generator torque/constant generator torque inRegion 3 for simplevariable-speed generator co |
| 9999.9 VS_Rgn2K | |
| 9999.9 VS_S1Pc | |
| 2 GenModel | |
| True GenTiStr | |
| True GenTiStp | -Method to stop the generator {T:timed using TimGenof，F:when generator power = 0} (flag) |
| 9999.9 SpdGenOn | |
| 0.0 TimGenOn TimGenOf | -Time to turn on the generator for a startup_(s)[used only when GenTiStr=True] |
| 9999.9 1 HSSBrMode | -Time to turn off the generator (s）[used only when GenTiStp=True] |
| 9999.9 THSSBrDp | -HSS brake model {1:simple,2:user-defined from routine UserHSSBr} (switch) |
| 9999.9 | Time to initiate deployment of the HSS brake(s) |
| TiDynBrk -Time to initiate deployment of the dynamic generator brake [CURRENTLY IGNORED](s) | |
| 9999.9 | TTpBrDp(1) -Time to initiate deployment of tip brake 1(s) |
| 9999.9 | TTpBrDp(2) -Time to initiate deployment of tip brake 2 (s) |
| 9999.9 | TTpBrDp(3) -Time to initiate deployment of tip brake 3(s）[unused for 2 blades] |
| 9999.9 | |
| 9999.9 | TBDepISp(2) - Deployment-initiation speed for the tip brake on blade 2 (rpm) |
| 9999.9 | TBDepISp(3) - Deployment-initiation speed for the tip brake on blade 3 (rpm） [unused for 2 blades] TYawManS |
| 9999.9 | -Time to start override yaw maneuver and end standard yaw control (s) YawManRat |
| 0.3 | ） (） - |
| 0.0 NacYawF 9999.9 | -Final yaw angle for override yaw maneuvers(degrees) |
| 9999.9 | TPitManS(1)-Time to start override pitch maneuver for blade 1 and end standard pitch control(s) |
| 9999.9 | |
| 8.0 | TPitManS(3)-Time to start override pitch maneuver for blade 3 and end standard pitch control (s）[unused for 2 |
| 8.0 | PitManRat(1)-Pitch rate (in absolute value） at which override pitch maneuver for blade 1 heads toward final pitc |
| 8.0 | PitManRat(2)-Pitch rate(in absolute value）at whichoverride pitch maneuver for blade 2 heads toward final pitc |
| 0.0 | PitManRat(3)- Pitch rate (in absolute value） at which override pitch maneuver for blade 3 heads toward final pitc |
| 0.0 | BlPitch(1）-Blade 1 initial pitch (degrees) BlPitch(2）-Blade 2 initial pitch (degrees) |
| 0.0 | BlPitch(3）-Blade 3 initial pitch (degrees）[unused for 2 blades] |
| 0.0 | |
| 0.0 | |
| 0.0 | BlPitchF(3) - Blade 3 final pitch for override pitch maneuvers (degrees）[unused for 2 blades] |
| ENVIRONMENTALCONDITIONS-- | |
| 9.80665 True | Gravity -Gravitational acceleration(m/s^2) |
| FEATURE FLAGS -- | |
| FlapDOF1 FlapDOF2 EdgeDOF | - First flapwise blade mode DoF (flag) |
| True | Second flapwise blade mode DoF (flag) |
| True | First edgewise blade mode DoF (flag) |
| False TeetDOF | -Rotor-teeter DoF （flag）[unused for 3 blades] |
| -Drivetrain rotational-flexibility DoF (flag) | |
| True DrTrDOF | -Generator DoF (flag) |
| True GenDOF | |
| True YawDOF | -Yaw DOF (flag) |
| True TwFADOF1 | First fore-aft tower bending-mode DoF (flag) |
| True TwFADOF2 | Second fore-aft tower bending-mode DoF (flag) |
| True TwSSDOF1 | -First side-to-side tower bending-mode DoF (flag) |
| True | -Second side-to-side tower bending-mode DoF (flag) |
| TwSSDOF2 True | -Compute aerodynamic forces (flag) |
| CompAero False | |
| CompNoise | -Compute aerodynamic noise (flag) |
| OoPDefl | INITIAL CONDITIONS --- |
| 0.0 IPDefl | -Initial out-of-plane blade-tip displacement (meters) |
| 0.0 TeetDefl | -Initial in-plane blade-tip deflection (meters) |
| 0.0 Azimuth | -Initial or fixed teeter angle (degrees）[unused for 3 blades] |
| 0.0 | -Initial azimuth angle for blade 1 (degrees) |
| 12.1 RotSpeed | -Initial or fixed rotor speed (rpm) |
| 0.0 NacYaw | Initial or fixed nacelle-yaw angle (degrees) Initialside-to-side tower-top displacement（meters) |
| 0.0 TTDspFA 0.0 TTDspSS | -Initial fore-aft tower-top displacement (meters) |
| TURBINE CONFIGURATION- | TipRad | -The distance from the rotor apex to the blade tip(meters) |
| 63.0 1.5 1 | HubRad PSpnE1N | - The distance from the rotor apex to the blade root (meters) -Number of the innermost blade element which is still part of the pitchable portion of the blade for |
| 0.0 0.0 | UndSling HubCM | - Undersling length [distance from teeter pin to the rotor apex](meters）[unused for 3 blades] |
| OverHang | -Distance from rotor apex to hub mass [positive downwind] (meters) | |
| -5.01910 | ||
| 1.9 0.0 | NacCMxn | -Downwind distance from the tower-top to the nacelle CM (meters) |
| 1.75 | NacCMyn | Lateraldistance fromthe tower-top tothe nacelle CM(meters) |
| NacCMzn | ||
| 87.6 | -Vertical distance from the tower-top to the nacelle CM(meters) | |
| 1.96256 | TowerHt | -Height of tower above ground level [onshore] or MSL [offshore](meters) |
| 0.0 | Twr2Shft | -Vertical distance from the tower-top to the rotor shaft (meters) |
| -5.0 | TwrRBHt | -Tower rigid base height (meters) |
| 0.0 | ShftTilt | -Rotor shaft tilt angle (degrees) |
| -2.5 | Delta3 | -Delta-3 angle for teetering rotors(degrees）[unused for 3 blades] |
| -2.5 | PreCone(1) | -Blade 1 cone angle (degrees) |
| PreCone(2) | Blade 2 cone angle (degrees) | |
| -2.5 | PreCone(3) | - Blade 3 cone angle (degrees）[unused for 2 blades] |
| 0.0 | AzimB1Up | - Azimuth value to use for I/0 when blade 1 points up (degrees) |
| 0.0 | YawBrMass | MASS AND INERTIA - |
| 240.00E3 | NacMass | -Yaw bearing mass (kg) |
| 56.78E3 | HubMasS | - Nacelle mass (kg) |
| 0.0 | -Hub mass (kg) | |
| 0.0 | TipMass(1) | -Tip-brake mass,blade 1 (kg) |
| 0.0 | TipMass(2) | -Tip-brake mass,blade 2 (kg) |
| 2607.89E3 | TipMass(3) | -Tip-brake mass,blade 3(kg）[unused for 2 blades] |
| 534.116 | NacYIner | -Nacelle inertia about yaw axis (kg m^2) - Generator inertia about HSS (kg m^2) |
| 115.926E3 | GenIner HubIner | ）[ ] ] - |
| DRIVETRAIN | ||
| 100.0 | GBoxEff | Gearbox efficiency (%) |
| 94.4 | GenEff | Generatorefficiency[ignored by the Theveninanduser-defined generator models](%) |
| 97.0 | GBRatio | Gearbox ratio （-) |
| False | GBRevers | Gearbox reversal{T:if rotor and generator rotate in opposite directions}(flag) |
| 28.1162E3 HSSBrTqF | -Fully deployed HSS-brake torque (N-m) | |
| 0.6 | HSSBrDT | Time for HSS-brake to reach full deployment once initiated(sec）[used only when HSSBrMode=1] |
| DynBrkFi | File containing a mech-gen-torque vs HSS-speed curve for a dynamic brake [CURRENTLY IGNORED](quote | |
| 867.637E6 | DTTorSpr | -Drivetrain torsional spring (N-m/rad) |
| 6.215E6 | DTTorDmp | -Drivetrain torsional damper (N-m/(rad/s)) |
| SIMPLE INDUCTION GENERATOR -- | ||
| 9999.9 | SIG_S1Pc | -Rated generator slip percentage (%）[used only when VsContrl=0 and GenModel=1] |
| 9999.9 | SIG_SySp | -Synchronous（zero-torque）generator speed（rpm）[used only when VSContrl=0 and GenModel=1] |
| 9999.9 | SIG_RtTq | -Rated torque (N-m）[used only when VSContrl=0 and GenModel=1] -Pull-out ratio（Tpullout/Trated）（-）[used only when VSContrl=0 and GenModel=1] |
| 9999.9 | SIG_PORt | THEVENIN-EQUIVALENT INDUCTION GENERATOR--- |
| Line frequency [50 or 60](Hz）[used only when VSContrl=0 and GenModel=2] | ||
| 9999.9 | TEC_Freq TEC_NPol | |
| 8666 | TEC_SRes | -Stator resistance (ohms）[used only when VsContrl=0 and GenModel=2] |
| 9999.9 | TEC_RReS | -Rotor resistance (ohms）[used only when vsContrl=0 and GenModel=2] |
| 9999.9 9999.9 | TEC_VLL | Line-to-line RMS voltage (volts）[used only when VSContrl=0 and GenModel=2] |
| 9999.9 | TEC_SLR | -Stator leakage reactance (ohms）[used only when VsContrl=0 and GenModel=2] |
| 9999.9 | TEC_RLR | -Rotor leakage reactance (ohms）[used only when VSContrl=0 and GenModel=2] |
| 9999.9 | TEC_MR | - Magnetizing reactance (ohms）[used only when vsContrl=0 and GenModel=2] |
| θ | PLATFORM -Platform model {0:none,1:onshore，2:fixed bottom offshore,3:floating offshore}(switch) | |
| PtfmModel | - Name of file containing platform properties (quoted string）[unused when PtfmModel=0] | |
| PtfmFile | TOWER - | |
| 20 | TwrNodes | Number of tower nodes used for analysis (-) |
| "NRELOffshrBsline5Mw_Tower_Onshore.dat" | TwrFile - Name of file containing tower properties (quoted string) NACELLE -YAW - | |
| 9028.32E6 | -Nacelle-yaw spring constant (N-m/rad) | |
| 19.16E6 | YawSpr | -Nacelle-yaw damping constant (N-m/(rad/s)) |
| 0.0 | YawDamp | - Neutral yaw position--yaw spring force is zero at this yaw (degrees) |
| YawNeut | FURLING | |
| -Read in additional model properties for furling turbine (flag) | ||
| False | Furling | - Name of file containing furling properties (quoted string） [unused when Furling=False] |
| FurlFile | ROTOR-TEETER -- | |
| Rotor-teeter spring/damper model {0:none,1:standard,2:user-defined from routine UserTeet}(swi | ||
| θ | TeetMod | Rotor-teeter damper position (degrees）[used only for 2 blades and when TeetMod=1] |
| 0.0 | TeetDmpP | - Rotor-teeter damping constant (N-m/(rad/s)）[used only for 2 blades and when TeetMod=1] |
| 0.0 | TeetDmp | |
| 0.0 | TeetCDmp | Rotor-teeter rate-independent Coulomb-damping moment (N-m）[used only for 2 blades and when TeetMod |
| 0.0 | TeetSStP | |
| 0.0 | - Rotor-teeter hard-stop position (degrees）[used only for 2 blades and when TeetMod=1] | |
| 0.0 | TeetHStP | - Rotor-teeter soft-stop linear-spring constant (N-m/rad) [used only for 2 blades and when TeetMod=1] |
| 0.0 | TeetSSSp | |
| TeetHSSp | -Rotor-teeter hard-stop linear-spring constant (N-m/rad） [used only for 2 blades and when TeetMod=1] TIP-BRAKE - | |
| 0.0 | -Tip-brake drag constant during normal operation,Cd*Area(m^2) | |
| 0.0 | TBDrConN | |
| 0.0 | TBDrConD | -Tip-brake drag constant during_ fully-deployed operation, Cd*Area (m^2) |
| TpBrDT | -Time for tip-brake to reach full deployment once released (sec) | |
| -Name of file containing properties for blade 3(quotedstring) | ||
| BLADE- | ||
| "NRELOffshrBsline5MW_Blade.dat" | ||
| "NRELOffshrBsline5MW_Blade.dat" "NRELOffshrBsline5MW_Blade.dat" | AERODYN | BldFile(3) |
| "NRELOffshrBsline5Mw_AeroDyn.ipt" | -NOISE | ADFile | -Name of file containing AeroDyn input parameters (quoted strin | |
| NoiseFile | -Name of file containing aerodynamic noise input parameters (quoted string）[used only when CompNois -ADAMS- | |||
| "NRELOffshrBsline5Mw_ADAMSSpecific.dat" | ADAMSFile -LINEARIZATIONCONTROL-- | -Name of file containing ADAMS-specific input parameters (quote | ||
| "NRELOffshrBsline5MW_Linear.dat" | OUTPUT- | LinFile | - Name of file containing FAST linearization parameters (quoted | |
| True SumPrint | -Print summary data to".fsm"(flag) | |||
| True | TabDelim | -Generate a tab-delimited tabular output file.(flag) | ||
| "ES10.3E2" | OutFmt | -Format used for tabular output except time.Resulting field should be 10 characters.(quoted strin | ||
| 30.0 | ||||
| 4 | TStart | -Time to begin tabular output (s) | ||
| DecFact | -Decimation factor for tabular output{1:output every time step}（-) | |||
| 1.0 | SttsTime | - Amount of time between screen status messages (sec) | ||
| -3.09528 | NcIMUxn | -Downwind distance from the tower-top to the nacelle IMu (meters) | ||
| 0.0 | NcIMUyn | -Lateraldistance from the tower-top to the nacelle IMu (meters) | ||
| 2.23336 | NcIMUzn | -Verticaldistance fromthe tower-top to the nacelle IMu(meters) | ||
| 1.912 | ShftGagL | -Distance from rotor apex[3 blades]orteeter pin[2 blades]toshaft straingages[positiveforup | ||
| 1 | NTwGages | |||
| 10 | TwrGagNd | - List of tower nodes that have strain gages [1 to TwrNodes]（-） [unused if NTwGages=0] | ||
| 1 | NB1Gages | -Number of blade nodes that have strain gages for output [0 to 9]（-) | ||
| 9 | BldGagNd | - List of blade nodes that have strain gages [1 to BldNodes]（-）[unused if NBlGages=0] | ||
| OutList | -The next line(s) contains a list of output parameters.See OutList.txt for a listing of available | |||
| "WindVxi | ，WindVyi | ，WindVzi" | -Longitudinal，lateral,and vertical wind speeds | |
| "WaveElev" | -Waveelevationat the platform referencepoint | |||
| "Wave1Vxi，Wave1Vyi，Wave1Vzi" | -Longitudinal，lateral,and vertical wave particle velocities a | |||
| "Wave1Axi ，Wave1Ayi ，Wave1Azi" | -Longitudinal，lateral,and vertical wave particle acceleration | |||
| "GenPwr | ，GenTq" | - Electrical generator power and torque | ||
| "HSSBrTq" | -High-speed shaft brake torque | |||
| "BldPitch1，BldPitch2，BldPitch3" | -Pitch angles for blades 1，2，and 3 | |||
| "Azimuth" | -Blade 1 azimuth angle | |||
| "RotSpeed ，GenSpeed" | - Low-speed shaft and high-speed shaft speeds | |||
| "NacYaw | ，NacYawErr" | - Nacelle yaw angle and nacelle yaw error estimate | ||
| "OoPDefl1，IPDefl1 ，TwstDefl1" | - Blade 1 out-of-plane and in-plane deflections and tip twist | |||
| "OoPDefl2，IPDefl2，TwstDefl2" | -Blade 2 out-of-plane and in-plane deflections and tip twist | |||
| "OoPDefl3，IPDef13 ，TwstDefl3" | -Blade 3 out-of-plane andin-plane deflections and tiptwist | |||
| "TwrClrnc1,TwrClrnc2，TwrClrnc3" | -Tip-to-tower clearance estimate for blades 1,2,and 3 | |||
| "NcIMUTAxS， NcIMUTAys, NcIMUTAzs" | -Nacelle IMU translational accelerations (absolute） in the nonr | |||
| -Tower fore-aft andside-to-sidedisplacements and toptwist | ||||
| "PtfmSurge, PtfmSway，PtfmHeave" | -Platform translational surge, sway, and heave displacements | |||
| "PtfmRoll，PtfmPitch，PtfmYaw" | -Platform rotational roll,pitch and yaw displacements | |||
| "PtfmTAxt，PtfmTAyt，PtfmTAzt" | -Platform translation accelerations (absolute）in the tower-bas | |||
| "RootFxc1，RootFyc1，RootFzc1" | - Out-of-plane shear,in-plane shear, and axial forces at the ro | |||
| "RootMxc1，RootMyc1，RootMzc1" | -In-plane bending,out-of-plane bending,and pitching moments a | |||
| "RootFxc2，RootFyc2，RootFzc2" | - Out-of-plane shear,in-plane shear,and axial forces at the ro | |||
| "RootMxc2，RootMyc2，RootMzc2" | -In-plane bending, out-of-plane bending, and pitching moments a | |||
| "RootFxc3，RootFyc3，RootFzc3" | -Out-of-plane shear,in-plane shear,and axial forces at the ro | |||
| "RootMxc3，RootMyc3，RootMzc3" | -In-plane bending,out-of-plane bending,and pitching moments a | |||
| "Spn1MLxb1， Spn1MLyb1，Spn1MLzb1" | - Blade 1 local edgewise bending, flapwise bending, and pitching | |||
| "Spn1MLxb2，Spn1MLyb2，Spn1MLzb2" | -Blade 2 local edgewise bending,flapwise bending,and pitching | |||
| "Spn1MLxb3，Spn1MLyb3，Spn1MLzb3" | - Blade 3 local edgewise bending,flapwise bending,and pitching | |||
| "RotThrust，LSSGagFya，LSSGagFza" | -Rotor thrust and low-speed shaft 0- and 90-rotating shear forc | |||
| "RotTorq ,LSSGagMya, LSSGagMza" | -Rotor torque and low-speed shaft 0- and 90-rotating bending mo | |||
| "YawBrFxp，YawBrFyp，YawBrFzp" | -Fore-aft shear，side-to-side shear,and vertical forces at the -Side-to-side bending,fore-aft bending，and yaw moments at the | |||
| "YawBrMxp，YawBrMyp，YawBrMzp" | ||||
| "TwrBsFxt，TwrBsFyt，TwrBsFzt" | -Fore-aft shear，side-to-side shear, and vertical forces at the | |||
| "TwrBsMxt，TwrBsMyt，TwrBsMzt" | -Side-to-side bending,fore-aft bending， and yaw moments at the | |||
| "TwHt1MLxt，TwHt1MLyt， TwHt1MLzt" | -Local side-to-side bending，fore-aft bending,and yaw moments | |||
| "FairiTen , Fair1Ang , Anch1Ten ，AnchiAng" | -Line 1 fairlead and anchor effective tensions and vertical ang | |||
| "Fair2Ten，Fair2Ang，Anch2Ten，Anch2Ang" | -Line 2 fairlead and anchor effective tensions and vertical ang | |||
| - Line 3 fairlead and anchor effective tensions and vertical ang | ||||
| "Fair3Ten，Fair3Ang，Anch3Ten ，Anch3Ang" | ||||
| "Fair4Ten ，Fair4Ang ，Anch4Ten ，Anch4Ang" | - Line 4 fairlead and anchor effective tensions and vertical ang | |||
| "Fair5Ten，Fair5Ang，Anch5Ten，Anch5Ang" | - Line 5 fairlead and anchor effective tensions and vertical ang | |||
| "Fair6Ten ，Fair6Ang，Anch6Ten，Anch6Ang" | - Line 6 fairlead and anchor effective tensions and vertical ang | |||
| "Fair7Ten，Fair7Ang ，Anch7Ten ，Anch7Ang" | -Line 7 fairlead and anchor effective tensions and vertical ang | |||
| "Fair8Ten ，Fair8Ang ，Anch8Ten ，Anch8Ang" | -Line 8 fairlead and anchor effective tensions and vertical ang | |||
| "TipSpdRat，RotCp ，RotCt ，RotCq" -Rotor tip speed ratio and power，thrust，and torque coefficien END of FAST input file (the word "END" must appear in the first 3 columns of this last line). | ||||
A.2 Blade Input File – NRELOffshrBsline5MW_Blade.dat
<html>| FAST INDIVIDUAL BLADE FILE | ||
| NREL5.0 Mw offshorebaseline blade input properties. | ||
| BLADE | PARAMETERS | |
| 49 NBlInpSt | Numberofblade input stations （-） | |
| False CalcBMode Calculate | blade modeshapesinternally{T:ignore emodeshapes | from below,F:use mode shapes from |
| 0.477465 BldF1Dmp(1) Blade | eflap mode #1structural damping in percent of critical (%) | |
| 0.477465 BldF1Dmp(2) Blade flap | mode #2 structural damping in percent of critical | (%) |
| 0.477465 BldEdDmp（1）- Blade edge | mode #1structural damping in | percent of critical (%) |
| BLADE EADJUSTMENT FACTORS | ||
| 1.0 1.0 1.04536 AdjB1Ms | FlStTunr(1) - Blade flapwise modal stiffness tuner, 1st mode (-) - Blade flapwise modal stiffness tuner，2nd mode (-) -Factor to adjust blade mass density （-) | ||||||||
| FlStTunr(2) 1.0 AdjFlSt | |||||||||
| 1.0 AdjEdSt | -Factor to adjust blade flap stiffness （-) - Factor to adjust blade edge stiffness (-) | ||||||||
| DISTRIBUTED BLADE PROPERTIES | |||||||||
| BlFract | AeroCent StrcTwst | BMassDen | FlpStff | EdgStff | GJStff EAStff | Alpha | FlpIner | EdgIner | PrecrvRef Pre |
| （-） | (-) (deg) | (kg/m) | (Nm~2) | (Nm~2) | (Nm~2) (N) | (-) | (kg m) | (kg m) (m) | (m) |
| 00000'0 | 0.25000 13.308 | 678.935 | 18110.00E6 | 18113.60E6 | 5564.40E6 9729.48E6 | 0.0 | 972.86 | 973.04 0.0 | 0.0 |
| 0.00325 | 0.25000 13.308 | 678.935 | 18110.00E6 | 18113.60E6 | 5564.40E6 9729.48E6 | 0.0 | 972.86 | 973.04 0.0 | 0.0 |
| 0.01951 | 0.24951 | 13.308 773.363 | 19424.90E6 | 19558.60E6 | 5431.59E6 | 10789.50E6 0.0 | 1091.52 | 1066.38 | 0.0 0.0 |
| 0.03577 | 0.24510 | 13.308 740.550 | 17455.90E6 | 19497.80E6 | 4993.98E6 | 10067.23E6 0.0 | 966.09 | 1047.36 0.0 | 0.0 |
| 0.05203 | 0.23284 13.308 | 740.042 | 15287.40E6 | 19788.80E6 | 4666.59E6 | 9867.78E6 0.0 | 873.81 | 1099.75 0.0 | 0.0 |
| 0.06829 | 0.22059 13.308 | 592.496 | 10782.40E6 | 14858.50E6 | 3474.71E6 7607.86E6 | 0.0 | 648.55 | 873.02 0.0 | 0.0 |
| 0.08455 | 0.20833 13.308 | 450.275 | 7229.72E6 | 10220.60E6 | 2323.54E6 5491.26E6 | 0.0 | 456.76 | 641.49 0.0 | 0.0 |
| 0.10081 | 0.19608 13.308 | 424.054 | 6309.54E6 | 9144.70E6 | 1907.87E6 | 4971.30E6 0.0 | 400.53 | 593.73 0.0 | 0.0 |
| 0.11707 | 0.18382 13.308 | 400.638 | 5528.36E6 | 8063.16E6 | 1570.36E6 | 4493.95E6 0.0 | 351.61 | 547.18 0.0 | 0.0 |
| 0.13335 | 0.17156 13.308 | 382.062 | 4980.06E6 | 6884.44E6 | 1158.26E6 | 4034.80E6 0.0 | 316.12 | 490.84 0.0 | 0.0 |
| 0.14959 | 0.15931 13.308 | 399.655 | 4936.84E6 | 7009.18E6 | 1002.12E6 | 4037.29E6 0.0 | 303.60 | 503.86 0.0 | 0.0 |
| 0.16585 | 0.14706 13.308 | 426.321 | 4691.66E6 | 7167.68E6 | 855.90E6 | 4169.72E6 0.0 | 289.24 | 544.70 0.0 | 0.0 |
| 0.18211 | 0.13481 13.181 | 416.820 | 3949.46E6 | 7271.66E6 | 672.27E6 | 4082.35E6 0.0 | 246.57 | 569.90 0.0 | 0.0 |
| 0.19837 | 0.12500 12.848 | 406.186 | 3386.52E6 | 7081.70E6 | 547.49E6 | 4085.97E6 0.0 | 215.91 | 601.28 0.0 | 0.0 |
| 0.21465 | 0.12500 12.192 | 381.420 | 2933.74E6 | 6244.53E6 | 448.84E6 | 3668.34E6 0.0 | 187.11 | 546.56 0.0 | 0.0 |
| 0.23089 | 0.12500 11.561 | 352.822 | 2568.96E6 | 5048.96E6 | 335.92E6 | 3147.76E6 0.0 | 160.84 | 468.71 0.0 | 0.0 |
| 0.24715 | 0.12500 11.072 | 349.477 | 2388.65E6 | 4948.49E6 | 311.35E6 | 3011.58E6 0.0 | 148.56 | 453.76 0.0 | 0.0 |
| 0.26341 | 0.12500 10.792 | 346.538 | 2271.99E6 | 4808.02E6 | 291.94E6 | 2882.62E6 0.0 | 140.30 | 436.22 0.0 | 0.0 |
| 0.29595 | 0.12500 10.232 | 339.333 | 2050.05E6 | 4501.40E6 | 261.00E6 | 2613.97E6 0.0 | 124.61 | 398.18 0.0 | 0.0 |
| 0.32846 | 0.12500 | 9.672 330.004 | 1828.25E6 | 4244.07E6 | 228.82E6 | 2357.48E6 0.0 | 109.42 | 362.08 0.0 | 0.0 |
| 0.36098 | 0.12500 | 9.110 321.990 | 1588.71E6 | 3995.28E6 | 200.75E6 | 2146.86E6 0.0 | 94.36 | 335.01 0.0 | 0.0 |
| 0.39350 | 0.12500 | 8.534 313.820 | 1361.93E6 | 3750.76E6 | 174.38E6 | 1944.09E6 0.0 | 80.24 | 308.57 0.0 | 0.0 |
| 0.42602 | 0.12500 | 7.932 294.734 | 1102.38E6 | 3447.14E6 | 144.47E6 | 1632.70E6 0.0 | 62.67 | 263.87 0.0 | 0.0 |
| 0.45855 | 0.12500 | 7.321 287.120 | 875.80E6 | 3139.07E6 | 119.98E6 | 1432.40E6 0.0 | 49.42 | 237.06 0.0 | 0.0 |
| 0.49106 | 0.12500 | 6.711 263.343 | 681.30E6 | 2734.24E6 | 81.19E6 | 1168.76E6 0.0 | 37.34 | 196.41 0.0 | 0.0 |
| 0.52358 | 0.12500 | 6.122 253.207 | 534.72E6 | 2554.87E6 | 69.09E6 | 1047.43E6 0.0 | 29.14 | 180.34 0.0 | 0.0 |
| 0.55610 | 0.12500 | 5.546 241.666 | 408.90E6 | 2334.03E6 | 57.45E6 | 922.95E6 0.0 | 22.16 | 162.43 0.0 | 0.0 |
| 0.58862 | 0.12500 | 4.971 220.638 | 314.54E6 | 1828.73E6 | 45.92E6 | 760.82E6 0.0 | 17.33 | 134.83 0.0 | 0.0 |
| 0.62115 | 0.12500 | 4.401 200.293 | 238.63E6 | 1584.10E6 | 35.98E6 | 648.03E6 0.0 | 13.30 | 116.30 0.0 | 0.0 |
| 0.65366 | 0.12500 | 3.834 179.404 | 175.88E6 | 1323.36E6 | 27.44E6 | 539.70E6 0.0 | 9.96 | 97.98 0.0 | 0.0 |
| 0.68618 | 0.12500 | 3.332 165.094 | 126.01E6 | 1183.68E6 | 20.90E6 | 531.15E6 0.0 | 7.30 | 98.93 0.0 | 0.0 |
| 0.71870 | 0.12500 | 2.890 154.411 | 107.26E6 | 1020.16E6 | 18.54E6 | 460.01E6 0.0 | 6.22 | 85.78 0.0 | 0.0 |
| 0.75122 | 0.12500 | 2.503 138.935 | 90.88E6 | 797.81E6 | 16.28E6 | 375.75E6 0.0 | 5.19 | 69.96 0.0 | 0.0 |
| 0.78376 | 0.12500 | 2.116 129.555 | 76.31E6 | 709.61E6 | 14.53E6 9.07E6 | 328.89E6 0.0 | 4.36 | 61.41 0.0 45.44 0.0 | 0.0 |
| 0.81626 | 0.12500 | 1.730 107.264 | 61.05E6 | 518.19E6 | 8.06E6 | 244.04E6 0.0 | 3.36 2.75 | 39.57 0.0 | 0.0 |
| 0.84878 | 0.12500 1.342 | 98.776 | 49.48E6 | 454.87E6 395.12E6 | 7.08E6 | 211.60E6 0.0 | 2.21 | 34.09 0.0 | 0.0 0.0 |
| 0.88130 | 0.12500 0.954 | 90.248 | 39.36E6 34.67E6 30.41E6 26.52E6 23.84E6 19.63E6 16.00E6 12.83E6 10.08E6 7.55E6 4.60E6 0.25E6 0.17E6 ，coeff of x^3 ，coeff ofx^4 ，coeff of x^5 ，coeff of x^6 ，coeff of x^3 | 353.72E6 304.73E6 281.42E6 261.71E6 158.81E6 137.88E6 118.79E6 101.63E6 85.07E6 64.26E6 6.61E6 5.01E6 | 6.09E6 5.75E6 5.33E6 4.94E6 4.24E6 3.66E6 3.13E6 2.64E6 2.17E6 1.58E6 0.25E6 0.19E6 | 181.52E6 0.0 160.25E6 0.0 109.23E6 0.0 100.08E6 0.0 92.24E6 0.0 63.23E6 0.0 53.32E6 0.0 44.53E6 0.0 36.90E6 0.0 29.92E6 0.0 21.31E6 0.0 4.85E6 0.0 3.53E6 0.0 | 1.93 1.69 1.49 1.34 1.10 0.89 0.71 0.56 0.42 0.25 0.04 0.02 | 30.12 0.0 20.15 0.0 18.53 0.0 17.11 0.0 11.55 0.0 9.77 0.0 8.19 0.0 6.82 0.0 5.57 0.0 4.01 0.0 0.94 0.0 0.68 0.0 | 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 |
| 0.89756 0.91382 0.93008 0.93821 0.94636 0.95447 0.96260 0.97073 0.97886 0.98699 0.99512 1.00000 0.0622 1.7254 -3.2452 4.7131 -2.2555 -0.5809 1.2067 | 0.12500 0.12500 0.574 0.12500 0.404 0.12500 0.319 0.12500 0.253 0.12500 0.216 0.12500 0.178 0.12500 0.140 0.12500 0.101 0.12500 0.062 0.12500 0.023 0.12500 0.000 BldFl1sh(2)- Flap mode 1，coeff of x^2 BldF11Sh(3) BldF11Sh(4) BldF11Sh(5) BldFl1Sh(6)- BldF12Sh(2) - Flap mode 2, coeff of x^2 BldF12Sh(3) | 0.760 83.001 72.906 68.772 66.264 59.340 55.914 52.484 49.114 45.818 41.669 11.453 10.319 BLADE MODE SHAPES | |||||||
| 0.0622 | BldFl1Sh(2)- Flap mode 1，coeff of x^2 | |||
| 1.7254 | BldF11Sh(3) | coeff of x^3 | ||
| -3.2452 | BldF11Sh(4) | coeff of x^4 | ||
| 4.7131 | BldF11Sh(5) | coeff of x^5 | ||
| -2.2555 | BldF11Sh(6) | -Flapmode2， | coeff of x^6 | |
| -0.5809 | BldF12Sh(2) | coeffofx^2 | ||
| 1.2067 | BldF12Sh(3) | coeff of x^3 | ||
| -15.5349 | BldF12Sh(4) | coeff of x^4 | ||
| 29.7347 | BldF12Sh(5) | coeff of x^5 | ||
| -13.8255 | BldF12Sh(6) | Edge mode 1, | coeff of x^6 | |
| 0.3627 | BldEdgSh(2) | coeff of x^2 | ||
| 2.5337 | BldEdgSh(3) | coeff of x^3 | ||
| -3.5772 | BldEdgSh(4) | coeff of x^4 | ||
| 2.3760 | BldEdgSh(5) | coeff of x^5 | ||
| -0.6952 | BldEdgSh(6) | coeff of x^6 |
A.3 Tower Input File – NRELOffshrBsline5MW_Tower_Onshore.dat
| 1.0 1.0 1.0 TOWERADJUSTMUNTFACTORS-- | TwrFADmp(1）-Tower 1st fore-aft mode structural damping ratio(%) TwrFADmp(2) - Tower 2nd fore-aft mode structural damping ratio (%) FAStTunr(1）-Tower fore-aft modal stiffness tuner,1st mode（-) FAStTunr(2)-Tower fore-aft modal stiffness tuner，2nd mode （-) SSStTunr(1）-Tower side-to-side stiffness tuner，1st mode （-) SSStTunr(2)- Tower side-to-side stiffness tuner，2nd mode (-) -Factor to adjust tower mass density （-) TwFAIner TwSSIner TwFAcgOf TwSScgof (kg m) (kg m) (m) (m) 138.127E9 24866.3 24866.3 0.0 0.0 21647.5 21647.5 0.0 0.0 120.707E9 18751.3 18751.3 0.0 0.0 112.433E9 16155.3 16155.3 0.0 0.0 104.450E9 13838.1 13838.1 0.0 0.0 96.758E9 11779.0 11779.0 0.0 0.0 89.357E9 9958.2 9958.2 0.0 0.0 82.247E9 8356.6 8356.6 0.0 0.0 75.427E9 6955.9 6955.9 0.0 0.0 68.899E9 5738.6 5738.6 0.0 0.0 62.661E9 4688.0 4688.0 0.0 0.0 | |
| 1.0 1.0 1.0 1.0 1.0 1.0 AdjTwMa 1.0 AdjFASt 1.0 AdjSSSt HtFract TMassDen （-） (kg/m) (Nm^2) 0.0 5590.87 614.343E9 0.1 5232.43 534.821E9 0.2 4885.76 463.267E9 0.3 4550.87 399.131E9 0.4 4227.75 341.883E9 0.5 3916.41 291.011E9 0.6 3616.83 246.027E9 0.7 3329.03 206.457E9 0.8 3053.01 171.851E9 0.9 2788.75 141.776E9 1.0 2536.27 115.820E9 TOWER 0.7004 2.1963 TwFAM1Sh(3) -5.6202 TwFAM1Sh(4) 6.2275 TwFAM1Sh(5) -2.5040 TwFAM1Sh(6）- -70.5319 -63.7623 TwFAM2Sh(3) - 289.7369 TwFAM2Sh(4) - -176.5134 TwFAM2Sh(5）- 22.0706 TwFAM2Sh(6）- 1.3850 -1.7684 TwSSM1Sh(3)- 3.0871 TwSSM1Sh(4) -2.2395 TwSSM1Sh(5) - 0.5357 TwSSM1Sh(6)- -121.2097 184.4151 TwSSM2Sh(3）- -224.9037 TwSSM2Sh(4)- 298.5360 TwSSM2Sh(5） -135.8377 TwSSM2Sh(6) | -Factor to adjust tower fore-aft stiffness （-) -Factor to adjust tower side-to-side stiffness （-) DISTRIBUTED TOWER PROPERTIES TwFAStif TwSSStif TwGJStif TwEAStif (Nm~2) (Nm~2) (N) 614.343E9 472.751E9 534.821E9 411.558E9 129.272E9 463.267E9 356.495E9 399.131E9 307.141E9 341.883E9 263.087E9 291.011E9 223.940E9 246.027E9 189.323E9 206.457E9 158.874E9 171.851E9 132.244E9 141.776E9 109.100E9 115.820E9 89.126E9 FORE-AFT MODE SHAPES TwFAM1Sh(2）- Mode 1，coefficient of x^2 term ，coefficient of x^3 term ，coefficient of x^4 term ，coefficient of x^5 term ，coefficient of x^6 term TwFAM2Sh(2) - Mode 2，coefficient of x^2 term ，coefficient of x^3 term ，coefficient of x^4 term ，coefficient of x^5 term ，coefficient of x^6 term TOWER SIDE-TO-SIDE MODE SHAPES -- TwSSM1Sh(2）-Mode 1，coefficient of x^2 term ，coefficient of x^3 term ，coefficient of x^4 term ，coefficient of x^5 term ，coefficient of x^6 term TwSSM2Sh(2）- Mode 2，coefficient of x^2 term ，coefficient of x^3 term ，coefficient of x^4 term ，coefficient of x^5 term coefficientofx^6term |
A.4 ADAMS Input File – NRELOffshrBsline5MW_ADAMSSpecific.dat
<html>| FAST 2 ADAMS PREPROCESSOR,ADAMS-SPECIFIC DATA FILE NREL 5.0 Mw offshore baseline ADAMS-specific input properties. | ||
| FEATUREFLAGS | ||
| True | SaveGrphcs -Save GRAPHICS output (flag) | |
| False | MakeLINacf | -Make an ADAMS/LINEAR control/ command file(flag) |
| DAMPING PARAMETERS | ||
| 0.01 0.01 | CRatioTGJ | -Ratio of damping to stiffness for the tower torsion deflection |
| 0.01 | CRatioTEA | -Ratio of damping to stiffness for the tower extensional deflection |
| 0.01 | CRatioBGJ | -Ratio of damping to stiffness for the blade torsion deflections （-） |
| CRatioBEA | -Ratio of damping to stiffness for the blade extensional deflections （-) | |
| 971.350E6 | BLADEPITCHACTUATORPARAMETERS-- | |
| 0.206E6 | BPActrSpr | - Blade pitch actuator spring stiffness constant (N-m/rad) |
| BPActrDmp GRAPHICSPARAMETERS- | -Blade pitch actuator damping constant (N-m/(rad/s)) | |
| 20 | NSides | -Number of sides used in GRAPHICS CYLINDER and FRUSTUM statements （-) |
| 3.000 | TwrBaseRad | - Tower base radius used for linearly tapered tower GRAPHICS CYLINDERs (m) |
| 1.935 | TwrTopRad | |
| 7.0 | NacLength | -Length of nacelle used for the nacelle GRAPHICS (m) |
| 1.75 | NacRadBot | -Bottom (opposite rotor） radius of nacelle FRUSTUM used for the nacelle GRAPHICS (m) |
| 1.75 | NacRadTop -Top | (rotor end) radius of nacelle FRUSTUM used for the nacelle GRAPHICS (m) |
| 1.0 | GBoxLength | -Length，width，and height of the gearbox BOx for gearbox GRAPHICS(m) |
| 2.39 1.195 | GenLength | -Length of the generator CYLINDER used for generator GRAPHICS (m) |
| 4.78 | HSSLength | |
| 0.75 | LSSLength GenRad | -Length of the low-Speed shaft CYLINDER used for LSS GRAPHICS (m) |
| 0.2 | HSSRad | -Radius of the generator CYLINDER used for generator GRAPHICS (m) |
| 0.4 | LSSRad | -Radius of the high-Speed shaft CYLINDER used for HSS GRAPHICS (m) |
| 0.875 | HubCylRad | Radius of the low -Speed shaft CYLINDER used for LSS GRAPHICS (m) |
| 0.18 | ThkOvrChrd | -Radius of hub CYLINDER uSed for hub GRAPHICS (m) |
| 0.0 | BoomRad | -Ratio of blade thickness to blade chord used for blade element BOX GRAPHICS （-) Radius of the tail boom CYLINDER used for tail boom GRAPHICS (m) |
| FASTLINEARIZATION CONTROLFILE | |
| NREL5.0Mwoffshorebaselinelinearizationinputproperties. PERIODICSTEADYSTATESOLUTION True CalcStdy | |
| 3 TrimCase 0.0001 DispTol | Calculate periodic steady state condition{False:linearize about initialconditions}(flag) Convergence tolerance forthe 2-norm of displacements inthe periodic steady state calculation(rad |
| 0.0010 VelTol NAzimStep | Convergencetoleranceforthe2-normofvelocities inthe periodic steady state calculation(rad MODELLINEARIZATION |
| 36 1 Mdl0rder NInputs | Order of output linearized model {1:1st order A，B，Bd，C，D，Dd; 2:2nd order M，C，K，F，Fd,Vel INPUTSANDDISTURBANCES of inputwinddisturbances[1 toNDisturbs]{1:horizontalhub-height windspeed，2:horizon |
| θ | (none）or1to4+NumBl]（-) toNInputs]{1:nacelleyawangle,2:nacelleyawrate,3:generatorto Number of wind disturbances[0(none）or 1to 7]（-) |
| NDisturbs Disturbnc | Number of control inputs [0 CntrlInpt List ofcontrolinputs[1 -List |
Appendix B AeroDyn Input Files
B.1 Primary Input File – NRELOffshrBsline5MW_AeroDyn.ipt
<html>| NREL 5.0 Mw offshore baseline aerodynamic input properties; Compatible with AeroDyn v12.58. | |||||
| SI | SysUnits | ( bu）[i uo I q ] pu du o s su o w | |||
| BEDDOES | StallMod | ||||
| USE_CM | UseCm | - Use aerodynamic pitching moment model? [USE_CM or No_CM] (unquoted string) | |||
| EQUIL | InfModel | -Inflow model [DYNIN or EQUIL](unquoted string) | |||
| WAKE | IndModel | - Induction-factor model [NoNE or WAKE or SWIRL](unquoted string) | |||
| 0.005 | AToler | -Induction-factor tolerance (convergence criteria）（-) | |||
| PRANDt1 | TLModel | - Tip-losS model (EQUIL only） [PRANDtl，GTECH,or NONE](unquoted string) | |||
| PRANDt1 | HLModel | -Hub-losS model (EQUIL only）[PRANdtl or NONE](unquoted string) | |||
| "WindData\90m_12mps" | WindFile - Name of file containing wind data (quoted string) | ||||
| 90.0 | HH | -Wind reference(hub）height [TowerHt+Twr2Shft+OverHang*SIN(ShftTilt)](m) | |||
| 0.0 | TwrShad | -Tower-shadow velocity deficit (-) | |||
| 9999.9 | ShadHWid | - Tower-shadow half width (m) | |||
| 9999.9 | T_Shad_Refpt-Tower-shadow reference point (m) | ||||
| 1.225 | AirDens | -Air density (kg/m^3) | |||
| 1.464E-5 KinVisc | -Kinematic air viscosity [CURRENTLY IGNORED](m^2/sec) | ||||
| 0.02479 | DTAero | -Time interval for aerodynamic calculations (sec) | |||
| 8 | NumFoil | - Number of airfoil files (-) | |||
| "AeroData\Cylinder1.dat" "AeroData\Cylinder2.dat" | FoilNm - Names of the airfoil files [NumFoil lines](quoted strings) | ||||
| "AeroData\DU40_A17.dat" | |||||
| "AeroData\DU35_A17.dat" | |||||
| "AeroData\DU30_A17.dat" | |||||
| "AeroData\DU25_A17.dat" | |||||
| "AeroData\DU21_A17.dat" | |||||
| "AeroData\NACA64_A17.dat" | |||||
| 17 | BldNodes | Chord NFoil | Number of blade nodes used for analysis (-) | ||
| RNodes | AeroTwst | DRNodes | 3.542 | PrnElm | |
| 2.8667 | 13.308 | 2.7333 | 1 | NOPRINT | |
| 5.6000 | 13.308 | 2.7333 3.854 | 1 | NOPRINT | |
| 8.3333 | 13.308 | 2.7333 4.167 | 2 | NOPRINT | |
| 11.7500 | 13.308 | 4.1000 4.557 | 3 | NOPRINT | |
| 15.8500 | 11.480 | 4.1000 4.652 | 4 | NOPRINT | |
| 19.9500 | 10.162 | 4.1000 4.458 | 4 | NOPRINT | |
| 24.0500 | 9.011 | 4.1000 4.249 | 5 | NOPRINT | |
| 28.1500 | 7.795 | 4.1000 4.007 | 6 6 | NOPRINT | |
| 32.2500 | 6.544 | 4.1000 3.748 4.1000 | 7 | NOPRINT | |
| 36.3500 | 5.361 | 3.502 4.1000 3.256 | 7 | NOPRINT | |
| 40.4500 | 4.188 | 4.1000 3.010 | 8 | NOPRINT | |
| 44.5500 | 3.125 2.319 | 4.1000 2.764 | 8 | NOPRINT | |
| 48.6500 | 1.526 | 4.1000 2.518 | 8 | NOPRINT NOPRINT | |
| 52.7500 | 0.863 | 2.7333 2.313 | 8 | NOPRINT | |
| 56.1667 | 0.370 | 2.7333 2.086 | 8 | ||
| 58.9000 | 0.106 | 2.7333 | 1.419 8 | NOPRINT | |
| 61.6333 | NOPRINT | ||||
B.2 Airfoil-Data Input File – Cylinder1.dat
<html>| RoundrootsectionwithaCdof0.50 | |
| MadebyJasonJonkman | |
| 1 | Numberofairfoiltablesinthisfile |
| 0.0 TableIDparameter | |
| 0.0 Stall angle (deg) | |
| 0.0 | Nolongerused,enter zero |
| 0.0 | No longer used,enter zero |
| 0.0 | Nolongerused，enterzero |
| 0.0 0.0 | Zero Cn angle of attack(deg) |
| 0.0 Cn | Cn slope for zero lift (dimensionless) |
| 0.0 | extrapolatedtovalueatpositivestallangleofattack |
| 0.0 | Cnatstallvaluefornegativeangleofattack |
| 0.50 Minimum CD value | Angle of attack for minimum CD(deg) |
| -180.00 0.000 0.5000 | |
| 0.00 0.000 0.5000 | 0.000 |
| 180.00 0.000 | 0.000 |
| 0.5000 0.000 | |
B.3 Airfoil-Data Input File – Cylinder2.dat
0.0 Table ID parameter 0.0 Stall angle (deg) 0.0 No longer used, enter zero 0.0 No longer used, enter zero 0.0 No longer used, enter zero 0.0 Zero Cn angle of attack (deg) 0.0 Cn slope for zero lift (dimensionless) 0.0 Cn extrapolated to value at positive stall angle of attack 0.0 Cn at stall value for negative angle of attack 0.0 Angle of attack for minimum CD (deg) 0.35 Minimum CD value -180.00 0.000 0.3500 0.000 0.00 0.000 0.3500 0.000 180.00 0.000 0.3500 0.000
B.4 Airfoil-Data Input File – DU40_A17.dat
DU40 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of DOW
Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 1 Number of airfoil tables in this file 0.0 Table ID parameter 9.00 Stall angle (deg) 0.0 No longer used, enter zero 0.0 No longer used, enter zero 0.0 No longer used, enter zero -1.3430 Zero Cn angle of attack (deg) 7.4888 Cn slope for zero lift (dimensionless) 1.3519 Cn extrapolated to value at positive stall angle of attack -0.3226 Cn at stall value for negative angle of attack 0.00 Angle of attack for minimum CD (deg) 0.0113 Minimum CD value
-180.00 0.000 0.0602 0.0000
-175.00 0.218 0.0699 0.0934
-170.00 0.397 0.1107 0.1697
-160.00 0.642 0.3045 0.2813
-155.00 0.715 0.4179 0.3208
-150.00 0.757 0.5355 0.3516
-145.00 0.772 0.6535 0.3752
-140.00 0.762 0.7685 0.3926
-135.00 0.731 0.8777 0.4048
-130.00 0.680 0.9788 0.4126
-125.00 0.613 1.0700 0.4166
-120.00 0.532 1.1499 0.4176
-115.00 0.439 1.2174 0.4158
-110.00 0.337 1.2716 0.4117
-105.00 0.228 1.3118 0.4057
-100.00 0.114 1.3378 0.3979
-95.00 -0.002 1.3492 0.3887 -90.00 -0.120 1.3460 0.3781 -85.00 -0.236 1.3283 0.3663 -80.00 -0.349 1.2964 0.3534 -75.00 -0.456 1.2507 0.3394
-70.00 -0.557 1.1918 0.3244 -65.00 -0.647 1.1204 0.3084 -60.00 -0.727 1.0376 0.2914 -55.00 -0.792 0.9446 0.2733 -50.00 -0.842 0.8429 0.2543
-45.00 -0.874 0.7345 0.2342 -40.00 -0.886 0.6215 0.2129 -35.00 -0.875 0.5067 0.1906 -30.00 -0.839 0.3932 0.1670 -25.00 -0.777 0.2849 0.1422 -24.00 -0.761 0.2642 0.1371 -23.00 -0.744 0.2440 0.1320 -22.00 -0.725 0.2242 0.1268 -21.00 -0.706 0.2049 0.1215 -20.00 -0.685 0.1861 0.1162
-19.00 -0.662 0.1687 0.1097 -18.00 -0.635 0.1533 0.1012 -17.00 -0.605 0.1398 0.0907 -16.00 -0.571 0.1281 0.0784
-15.00 -0.534 0.1183 0.0646
-14.00 -0.494 0.1101 0.0494 -13.00 -0.452 0.1036 0.0330
-12.00 -0.407 0.0986 0.0156 -11.00 -0.360 0.0951 -0.0026 -10.00 -0.311 0.0931 -0.0213 -8.00 -0.208 0.0930 -0.0600 -6.00 -0.111 0.0689 -0.0500 -5.50 -0.090 0.0614 -0.0516 -5.00 -0.072 0.0547 -0.0532 -4.50 -0.065 0.0480 -0.0538
| -4.00 -3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 10.50 11.00 11.50 12.00 12.50 13.00 13.50 14.50 15.00 15.50 16.00 16.50 17.00 17.50 18.00 19.00 19.50 20.50 21.00 22.00 23.00 24.00 25.00 26.00 28.00 30.00 32.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 75.00 80.00 85.00 90.00 95.00 100.00 105.00 110.00 115.00 120.00 125.00 130.00 135.00 140.00 145.00 150.00 155.00 160.00 170.00 175.00 | -0.054 -0.017 0.003 0.014 0.009 0.004 0.036 0.073 0.137 0.213 0.292 0.369 0.444 0.514 0.580 0.645 0.710 0.776 0.841 0.904 0.967 1.027 1.084 1.140 1.193 1.242 1.287 1.333 1.368 1.400 1.425 1.449 1.473 1.494 1.513 1.538 1.587 1.614 1.631 1.649 1.666 1.681 1.699 1.719 1.751 1.767 1.798 1.810 1.830 1.847 1.861 1.872 1.881 1.894 1.904 1.915 1.929 1.903 1.820 1.690 1.522 1.323 1.106 0.880 0.658 0.449 0.267 0.124 0.002 -0.118 -0.235 -0.348 -0.453 -0.549 -0.633 -0.702 -0.754 -0.787 -0.797 -0.782 -0.739 -0.664 -0.410 -0.226 | 0.0411 0.0349 0.0299 0.0255 0.0198 0.0164 0.0147 0.0137 0.0113 0.0114 0.0118 0.0122 0.0124 0.0124 0.0123 0.0120 0.0119 0.0122 0.0125 0.0129 0.0135 0.0144 0.0158 0.0174 0.0198 0.0231 0.0275 0.0323 0.0393 0.0475 0.0580 0.0691 0.0816 0.0973 0.1129 0.1288 0.1650 0.1845 0.2052 0.2250 0.2467 0.2684 0.2900 0.3121 0.3554 0.3783 0.4212 0.4415 0.4830 0.5257 0.5694 0.6141 0.6593 0.7513 0.8441 0.9364 1.0722 1.2873 1.4796 1.6401 1.7609 1.8360 1.8614 1.8347 1.7567 1.6334 1.4847 1.3879 1.3912 1.3795 1.3528 1.3114 1.2557 1.1864 1.1041 1.0102 0.9060 0.7935 0.6750 0.5532 0.4318 0.3147 0.1144 0.0702 | -0.0544 -0.0554 -0.0558 -0.0555 -0.0534 -0.0442 -0.0469 -0.0522 -0.0573 -0.0644 -0.0718 -0.0783 -0.0835 -0.0866 -0.0887 -0.0900 -0.0914 -0.0933 -0.0947 -0.0957 -0.0967 -0.0973 -0.0972 -0.0972 -0.0968 -0.0958 -0.0948 -0.0942 -0.0926 -0.0908 -0.0890 -0.0877 -0.0870 -0.0870 -0.0876 -0.0886 -0.0917 -0.0939 -0.0966 -0.0996 -0.1031 -0.1069 -0.1110 -0.1157 -0.1242 -0.1291 -0.1384 -0.1416 -0.1479 -0.1542 -0.1603 -0.1664 -0.1724 -0.1841 -0.1954 -0.2063 -0.2220 -0.2468 -0.2701 -0.2921 -0.3127 -0.3321 -0.3502 -0.3672 -0.3830 -0.3977 -0.4112 -0.4234 -0.4343 -0.4437 -0.4514 -0.4573 -0.4610 -0.4623 -0.4606 -0.4554 -0.4462 -0.4323 -0.4127 -0.3863 -0.3521 -0.3085 -0.1858 -0.1022 |
B.5 Airfoil-Data Input File – DU35_A17.dat
DU35 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of DOW
Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 1 Number of airfoil tables in this file 0.0 Table ID parameter 11.50 Stall angle (deg) 0.0 No longer used, enter zero 0.0 No longer used, enter zero 0.0 No longer used, enter zero -1.8330 Zero Cn angle of attack (deg) 7.1838 Cn slope for zero lift (dimensionless) 1.6717 Cn extrapolated to value at positive stall angle of attack -0.3075 Cn at stall value for negative angle of attack 0.00 Angle of attack for minimum CD (deg) 0.0094 Minimum CD value
-180.00 0.000 0.0407 0.0000
-175.00 0.223 0.0507 0.0937
-170.00 0.405 0.1055 0.1702
-160.00 0.658 0.2982 0.2819
-155.00 0.733 0.4121 0.3213
-150.00 0.778 0.5308 0.3520
-145.00 0.795 0.6503 0.3754
-140.00 0.787 0.7672 0.3926
-135.00 0.757 0.8785 0.4046
-130.00 0.708 0.9819 0.4121
-125.00 0.641 1.0756 0.4160
-120.00 0.560 1.1580 0.4167
-115.00 0.467 1.2280 0.4146
-110.00 0.365 1.2847 0.4104
-105.00 0.255 1.3274 0.4041
-100.00 0.139 1.3557 0.3961 -95.00 0.021 1.3692 0.3867 -90.00 -0.098 1.3680 0.3759 -85.00 -0.216 1.3521 0.3639 -80.00 -0.331 1.3218 0.3508 -75.00 -0.441 1.2773 0.3367 -70.00 -0.544 1.2193 0.3216 -65.00 -0.638 1.1486 0.3054 -60.00 -0.720 1.0660 0.2884 -55.00 -0.788 0.9728 0.2703 -50.00 -0.840 0.8705 0.2512 -45.00 -0.875 0.7611 0.2311 -40.00 -0.889 0.6466 0.2099 -35.00 -0.880 0.5299 0.1876 -30.00 -0.846 0.4141 0.1641 -25.00 -0.784 0.3030 0.1396 -24.00 -0.768 0.2817 0.1345 -23.00 -0.751 0.2608 0.1294 -22.00 -0.733 0.2404 0.1243 -21.00 -0.714 0.2205 0.1191 -20.00 -0.693 0.2011 0.1139 -19.00 -0.671 0.1822 0.1086 -18.00 -0.648 0.1640 0.1032 -17.00 -0.624 0.1465 0.0975 -16.00 -0.601 0.1300 0.0898 -15.00 -0.579 0.1145 0.0799 -14.00 -0.559 0.1000 0.0682 -13.00 -0.539 0.0867 0.0547 -12.00 -0.519 0.0744 0.0397 -11.00 -0.499 0.0633 0.0234 -10.00 -0.480 0.0534 0.0060 -5.54 -0.385 0.0245 -0.0800 -5.04 -0.359 0.0225 -0.0800 -4.54 -0.360 0.0196 -0.0800 -4.04 -0.355 0.0174 -0.0800 -3.54 -0.307 0.0162 -0.0800 -3.04 -0.246 0.0144 -0.0800 -3.00 -0.240 0.0240 -0.0623 -2.50 -0.163 0.0188 -0.0674 -2.00 -0.091 0.0160 -0.0712 -1.50 -0.019 0.0137 -0.0746 -1.00 0.052 0.0118 -0.0778 -0.50 0.121 0.0104 -0.0806 0.00 0.196 0.0094 -0.0831 0.50 0.265 0.0096 -0.0863 1.00 0.335 0.0098 -0.0895 1.50 0.404 0.0099 -0.0924 2.00 0.472 0.0100 -0.0949 2.50 0.540 0.0102 -0.0973
| 3.00 | 0.608 | 0.0103 | -0.0996 |
| 3.50 | 0.674 | 0.0104 | -0.1016 |
| 4.00 | 0.742 | 0.0105 | -0.1037 |
| 4.50 | 0.809 | 0.0107 | -0.1057 |
| 5.00 | 0.875 | 0.0108 | -0.1076 |
| 5.50 | 0.941 | 0.0109 | -0.1094 |
| 6.00 | 1.007 | 0.0110 | -0.1109 |
| 6.50 | 1.071 | 0.0113 | -0.1118 |
| 7.00 | 1.134 | 0.0115 | -0.1127 |
| 7.50 | 1.198 | 0.0117 | -0.1138 |
| 8.00 | 1.260 | 0.0120 | -0.1144 |
| 8.50 | 1.318 | 0.0126 | -0.1137 |
| 9.00 | 1.368 | 0.0133 | -0.1112 |
| 9.50 | 1.422 | 0.0143 | |
| 10.00 | 1.475 | 0.0156 | -0.1100 |
| 10.50 | 1.523 | 0.0174 | -0.1086 |
| 11.00 | 0.0194 | -0.1064 | |
| 11.50 | 1.570 1.609 | -0.1044 | |
| 12.00 | 0.0227 | -0.1013 | |
| 12.50 | 1.642 | 0.0269 | -0.0980 |
| 13.00 | 1.675 | 0.0319 | -0.0953 |
| 13.50 | 1.700 | 0.0398 | -0.0925 |
| 14.00 | 1.717 | 0.0488 | -0.0896 |
| 14.50 | 1.712 | 0.0614 | -0.0864 |
| 15.50 | 1.703 | 0.0786 | -0.0840 |
| 16.00 | 1.671 1.649 | 0.1173 | -0.0830 |
| 16.50 | 0.1377 0.1600 | -0.0848 | |
| 17.00 | 1.621 | -0.0880 | |
| 17.50 | 1.598 | 0.1814 | -0.0926 |
| 18.00 | 1.571 | 0.2042 | -0.0984 |
| 19.00 | 1.549 | 0.2316 | -0.1052 |
| 19.50 | 1.544 | 0.2719 | -0.1158 |
| 20.00 | 1.549 | 0.2906 | -0.1213 |
| 21.00 | 1.565 | 0.3085 | -0.1248 |
| 22.00 | 1.565 | 0.3447 | -0.1317 |
| 23.00 | 1.563 | 0.3820 | -0.1385 |
| 24.00 | 1.558 | 0.4203 | -0.1452 |
| 25.00 | 1.552 | 0.4593 | -0.1518 |
| 26.00 | 1.546 | 0.4988 | -0.1583 |
| 28.00 | 1.539 | 0.5387 | -0.1647 |
| 30.00 | 1.527 | 0.6187 | -0.1770 |
| 32.00 | 1.522 | 0.6978 | -0.1886 |
| 35.00 | 1.529 | 0.7747 | -0.1994 |
| 40.00 | 1.544 | 0.8869 | -0.2148 |
| 45.00 | 1.529 | 1.0671 | -0.2392 |
| 50.00 | 1.471 | 1.2319 | -0.2622 |
| 55.00 | 1.376 | 1.3747 | -0.2839 |
| 60.00 | 1.249 | 1.4899 | -0.3043 |
| 65.00 | 1.097 | 1.5728 | -0.3236 |
| 70.00 | 0.928 | 1.6202 | -0.3417 |
| 75.00 | 0.750 | 1.6302 | -0.3586 |
| 80.00 | 0.570 | 1.6031 | -0.3745 |
| 85.00 | 0.396 | 1.5423 | -0.3892 |
| 90.00 | 0.237 | 1.4598 | -0.4028 |
| 95.00 | 0.101 -0.022 | 1.4041 1.4053 | -0.4151 |
| 100.00 | -0.143 | -0.4261 | |
| 105.00 | 1.3914 | -0.4357 | |
| 110.00 | -0.261 | 1.3625 | -0.4437 |
| 115.00 | -0.374 | 1.3188 | -0.4498 |
| 120.00 | -0.480 | 1.2608 | -0.4538 |
| 125.00 | -0.575 | 1.1891 | -0.4553 |
| -0.659 | 1.1046 | -0.4540 | |
| 130.00 | -0.727 | 1.0086 | -0.4492 |
| 135.00 | -0.778 | 0.9025 | -0.4405 |
| 140.00 | -0.809 | 0.7883 | -0.4270 |
| 145.00 | -0.818 | 0.6684 | -0.4078 |
| 150.00 | -0.3821 | ||
| -0.800 | 0.5457 | -0.3484 | |
| 155.00 | -0.754 | 0.4236 | |
| 160.00 | -0.677 | 0.3066 | -0.3054 |
| 170.00 | -0.417 | 0.1085 | -0.1842 |
| 175.00 180.00 | -0.229 0.000 | 0.0510 0.0407 | -0.1013 0.0000 |
B.6 Airfoil-Data Input File – DU30_A17.dat
<html>| DU30airfoilwithanaspectratioof17. Original-180 to180degCl，Cd，and Cm versus A0Adata taken fromAppendixA of DoW | |
| ClandCdvalues correctedforrotationalstalldelay andCdvalues correctedusing gtheViternan methodforθto90degAoAby | |
| 1 Numberofairfoiltablesinthisfile | |
| 0.0 TableIDp parameter | |
| 9.00 Stalla angle (deg) | |
| 0.0 No longer used， 0.0 No used, | enterzero |
| longer 0.0 No longer used， | enterzero enterzero |
7.00 1.197 0.0107 -0.1287
7.50 1.256 0.0112 -0.1289
8.00 1.305 0.0125 -0.1270
9.00 1.390 0.0155 -0.1207
9.50 1.424 0.0171 -0.1158
10.00 1.458 0.0192 -0.1116
10.50 1.488 0.0219 -0.1073
11.00 1.512 0.0255 -0.1029
11.50 1.533 0.0307 -0.0983
12.00 1.549 0.0370 -0.0949
12.50 1.558 0.0452 -0.0921
13.00 1.470 0.0630 -0.0899
13.50 1.398 0.0784 -0.0885
14.00 1.354 0.0931 -0.0885
14.50 1.336 0.1081 -0.0902
15.00 1.333 0.1239 -0.0928
15.50 1.326 0.1415 -0.0963
16.00 1.329 0.1592 -0.1006
16.50 1.326 0.1743 -0.1042
17.00 1.321 0.1903 -0.1084
17.50 1.331 0.2044 -0.1125
18.00 1.333 0.2186 -0.1169
18.50 1.340 0.2324 -0.1215
19.00 1.362 0.2455 -0.1263
19.50 1.382 0.2584 -0.1313
20.00 1.398 0.2689 -0.1352
20.50 1.426 0.2814 -0.1406
21.00 1.437 0.2943 -0.1462
22.00 1.418 0.3246 -0.1516
23.00 1.397 0.3557 -0.1570
24.00 1.376 0.3875 -0.1623
25.00 1.354 0.4198 -0.1676
26.00 1.332 0.4524 -0.1728
28.00 1.293 0.5183 -0.1832
30.00 1.265 0.5843 -0.1935
32.00 1.253 0.6492 -0.2039
35.00 1.264 0.7438 -0.2193
40.00 1.258 0.8970 -0.2440
45.00 1.217 1.0402 -0.2672
50.00 1.146 1.1686 -0.2891
55.00 1.049 1.2779 -0.3097
60.00 0.932 1.3647 -0.3290
65.00 0.799 1.4267 -0.3471
70.00 0.657 1.4621 -0.3641
75.00 0.509 1.4708 -0.3799
80.00 0.362 1.4544 -0.3946
85.00 0.221 1.4196 -0.4081
90.00 0.092 1.3938 -0.4204
95.00 -0.030 1.3943 -0.4313
100.00 -0.150 1.3798 -0.4408
105.00 -0.267 1.3504 -0.4486
110.00 -0.379 1.3063 -0.4546
115.00 -0.483 1.2481 -0.4584
120.00 -0.578 1.1763 -0.4597
125.00 -0.660 1.0919 -0.4582
130.00 -0.727 0.9962 -0.4532
135.00 -0.777 0.8906 -0.4441
140.00 -0.807 0.7771 -0.4303
145.00 -0.815 0.6581 -0.4109
150.00 -0.797 0.5364 -0.3848
155.00 -0.750 0.4157 -0.3508
160.00 -0.673 0.3000 -0.3074
170.00 -0.547 0.1051 -0.2786
175.00 -0.274 0.0388 -0.1380
180.00 0.000 0.0267 0.0000
B.7 Airfoil-Data Input File – DU25_A17.dat
DU25 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of DOW
Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 1 Number of airfoil tables in this file 0.0 Table ID parameter 8.50 Stall angle (deg) 0.0 No longer used, enter zero 0.0 No longer used, enter zero 0.0 No longer used, enter zero -4.2422 Zero Cn angle of attack (deg) 6.4462 Cn slope for zero lift (dimensionless) 1.4336 Cn extrapolated to value at positive stall angle of attack -0.6873 Cn at stall value for negative angle of attack 0.00 Angle of attack for minimum CD (deg) 0.0065 Minimum CD value
| -180.00 -175.00 -170.00 -160.00 -155.00 -150.00 -145.00 -140.00 -135.00 -130.00 -125.00 -120.00 -115.00 -110.00 -105.00 -100.00 -95.00 -90.00 -85.00 -80.00 -75.00 -70.00 -65.00 -60.00 -55.00 -50.00 -45.00 -40.00 -35.00 -30.00 -25.00 -24.00 -23.00 -22.00 -0.792 -21.00 -0.801 -20.00 -0.815 0.2237 0.0739 -19.00 -0.833 0.1990 0.0618 -18.00 -0.854 0.1743 0.0488 -17.00 -0.879 0.1498 0.0351 -16.00 -0.905 0.1256 0.0208 -15.00 -0.932 0.1020 0.0060 -14.00 -0.959 0.0789 -0.0091 -13.00 -0.985 0.0567 -0.0243 -13.00 -0.985 0.0567 -0.0243 -12.01 -0.953 0.0271 -0.0349 -11.00 -0.900 0.0303 -0.0361 -9.98 -0.827 0.0287 -0.0464 -8.98 -0.753 0.0271 -0.0534 -8.47 -0.691 0.0264 -0.0650 -7.45 -0.555 0.0114 -0.0782 -6.42 -0.413 0.0094 -0.0904 -5.40 -0.271 0.0086 -0.1006 -5.00 -0.220 0.0073 -0.1107 -4.50 -0.152 0.0071 -0.1135 -4.00 -0.084 0.0070 -0.1162 -3.50 -0.018 0.0069 -0.1186 -3.00 0.049 0.0068 -0.1209 -2.50 0.115 0.0068 -0.1231 -2.00 0.181 0.0068 -0.1252 -1.50 0.247 0.0067 -0.1272 -1.00 0.312 0.0067 -0.1293 -0.50 0.377 0.0067 -0.1311 0.00 0.444 0.0065 -0.1330 0.50 0.508 0.0065 -0.1347 1.00 0.573 0.0066 -0.1364 1.50 0.636 0.0067 -0.1380 2.00 0.701 0.0068 -0.1396 2.50 0.765 0.0069 -0.1411 3.00 0.827 0.0070 -0.1424 3.50 0.890 0.0071 -0.1437 4.00 0.952 0.0073 -0.1448 4.50 1.013 0.0076 -0.1456 5.00 1.062 0.0079 -0.1445 6.00 1.161 0.0099 -0.1419 6.50 1.208 0.0117 -0.1403 7.00 1.254 0.0132 -0.1382 7.50 1.301 0.0143 -0.1362 8.00 1.336 0.0153 -0.1320 8.50 1.369 0.0165 -0.1276 9.00 1.400 0.0181 -0.1234 9.50 1.428 0.0211 -0.1193 10.00 1.442 0.0262 -0.1152 10.50 1.427 0.0336 -0.1115 11.00 1.374 0.0420 -0.1081 | 0.000 0.368 0.735 0.695 0.777 0.828 0.850 0.846 0.818 0.771 0.705 0.624 0.530 1.2545 0.426 1.3168 0.314 1.3650 0.195 1.3984 0.073 1.4169 -0.050 1.4201 -0.173 1.4081 -0.294 1.3811 -0.409 1.3394 0.3017 -0.518 1.2833 0.2866 -0.617 1.2138 0.2707 -0.706 1.1315 0.2539 -0.780 1.0378 0.2364 -0.839 0.9341 0.2181 -0.879 0.8221 0.1991 -0.898 0.7042 0.1792 -0.893 0.5829 0.1587 -0.862 0.4616 0.1374 -0.803 0.3441 0.1154 -0.792 0.3209 0.1101 -0.789 0.2972 0.1031 0.2730 0.0947 0.2485 0.0849 | 0.0202 0.0000 0.0324 0.1845 0.0943 0.3701 0.2848 0.2679 0.4001 0.3046 0.5215 0.3329 0.6447 0.3540 0.7660 0.3693 0.8823 0.3794 0.9911 0.3854 1.0905 0.3878 1.1787 0.3872 0.3841 0.3788 0.3716 0.3629 0.3529 0.3416 0.3292 0.3159 |
| 11.50 | 1.316 | 0.0515 | -0.1052 |
| 12.00 | 1.277 | 0.0601 | -0.1026 |
| 12.50 | 1.250 | 0.0693 | -0.1000 |
| 13.00 | 1.246 | 0.0785 | -0.0980 |
| 13.50 | 1.247 | 0.0888 | -0.0969 |
| 14.00 | 1.256 | 0.1000 | -0.0968 |
| 14.50 | 1.260 | 0.1108 | -0.0973 |
| 15.00 | 1.271 | 0.1219 | -0.0981 |
| 15.50 | 1.281 | 0.1325 | -0.0992 |
| 16.00 | 1.289 | 0.1433 | -0.1006 |
| 16.50 | 1.294 | 0.1541 | -0.1023 |
| 17.00 | 1.304 | 0.1649 | -0.1042 |
| 17.50 | 1.309 | 0.1754 | -0.1064 |
| 18.00 | 1.315 | 0.1845 | -0.1082 |
| 18.50 | 1.320 | 0.1953 | -0.1110 |
| 19.00 | 1.330 | 0.2061 | -0.1143 |
| 19.50 | 1.343 | 0.2170 | -0.1179 |
| 20.00 | 1.354 | 0.2280 | -0.1219 |
| 20.50 | 1.359 | 0.2390 | -0.1261 |
| 21.00 | 1.360 | 0.2536 | -0.1303 |
| 22.00 | 1.325 | 0.2814 | -0.1375 |
| 23.00 | 1.288 | 0.3098 | -0.1446 |
| 24.00 | 1.251 | 0.3386 | -0.1515 |
| 25.00 | 1.215 | 0.3678 | -0.1584 |
| 26.00 | 1.181 | 0.3972 | -0.1651 |
| 28.00 | 1.120 | 0.4563 | -0.1781 |
| 30.00 | 1.076 | 0.5149 | -0.1904 |
| 32.00 | 1.056 | 0.5720 | -0.2017 |
| 35.00 | 1.066 | 0.6548 | -0.2173 |
| 40.00 | 1.064 | 0.7901 | -0.2418 |
| 45.00 | 1.035 | 0.9190 | -0.2650 |
| 50.00 | 0.980 | 1.0378 | -0.2867 |
| 55.00 | 0.904 | 1.1434 | -0.3072 |
| 60.00 | 0.810 | 1.2333 | -0.3265 |
| 65.00 | 0.702 | 1.3055 | -0.3446 |
| 70.00 | 0.582 | 1.3587 | -0.3616 |
| 75.00 | 0.456 | 1.3922 | -0.3775 |
| 80.00 | 0.326 | 1.4063 | -0.3921 |
| 85.00 | 0.197 | 1.4042 | -0.4057 |
| 90.00 | 0.072 | 1.3985 | -0.4180 |
| 95.00 | -0.050 | 1.3973 | -0.4289 |
| 100.00 | -0.170 | 1.3810 | -0.4385 |
| 105.00 | -0.287 | 1.3498 | -0.4464 |
| 110.00 | -0.399 | 1.3041 | -0.4524 |
| 115.00 | -0.502 | 1.2442 | -0.4563 |
| 120.00 | -0.596 | 1.1709 | -0.4577 |
| 125.00 | -0.677 | 1.0852 | -0.4563 |
| 130.00 | -0.743 | 0.9883 | -0.4514 |
| 135.00 | -0.792 | 0.8818 | -0.4425 |
| 140.00 | -0.821 | 0.7676 | -0.4288 |
| 145.00 | -0.826 | 0.6481 | -0.4095 |
| 150.00 | -0.806 | 0.5264 | -0.3836 |
| 155.00 | 0.4060 | -0.3497 | |
| 160.00 | -0.758 | -0.3065 | |
| 170.00 | -0.679 -0.735 | 0.2912 0.0995 | -0.3706 |
| 175.00 | -0.368 | -0.1846 | |
| 180.00 | 0.000 | 0.0356 0.0202 | 0.0000 |
B.8 Airfoil-Data Input File – DU21_A17.dat
DU21 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of DOW
Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 1 Number of airfoil tables in this file 0.0 Table ID parameter 8.00 Stall angle (deg) 0.0 No longer used, enter zero 0.0 No longer used, enter zero 0.0 No longer used, enter zero -5.0609 Zero Cn angle of attack (deg) 6.2047 Cn slope for zero lift (dimensionless) 1.4144 Cn extrapolated to value at positive stall angle of attack -0.5324 Cn at stall value for negative angle of attack -1.50 Angle of attack for minimum CD (deg) 0.0057 Minimum CD value
-180.00 0.000 0.0185 0.0000
-175.00 0.394 0.0332 0.1978
-170.00 0.788 0.0945 0.3963
-160.00 0.670 0.2809 0.2738
-155.00 0.749 0.3932 0.3118
-150.00 0.797 0.5112 0.3413
-145.00 0.818 0.6309 0.3636
-140.00 0.813 0.7485 0.3799
| -135.00 -130.00 -125.00 -120.00 -115.00 -110.00 -105.00 -100.00 -95.00 -90.00 -85.00 -80.00 -75.00 -70.00 -65.00 -60.00 -55.00 -50.00 -45.00 -40.00 -35.00 -30.00 -25.00 -24.00 -23.00 -22.00 -21.00 -20.00 -19.00 -18.00 -17.00 -16.00 -15.00 -14.50 -12.01 -11.00 -9.98 -8.12 -7.62 -7.11 -6.60 -6.50 -6.00 -5.50 -5.00 -4.50 -4.00 -3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 10.00 10.50 11.00 11.50 12.00 12.50 13.00 13.50 14.00 14.50 | 0.786 0.739 0.675 0.596 0.505 0.403 0.294 0.179 0.060 -0.060 -0.179 -0.295 -0.407 -0.512 -0.608 -0.693 -0.764 -0.820 -0.857 -0.875 -0.869 -0.838 -0.791 -0.794 -0.805 -0.821 -0.843 -0.869 -0.899 -0.931 -0.964 -0.999 -1.033 -1.050 -0.953 -0.900 -0.827 -0.536 -0.467 -0.393 -0.323 -0.311 -0.245 -0.178 -0.113 -0.048 0.016 0.080 0.145 0.208 0.270 0.333 0.396 0.458 0.521 0.583 0.645 0.706 0.768 0.828 0.888 0.948 0.996 1.046 0.0079 1.095 0.0090 5.50 1.145 0.0103 6.00 1.192 0.0113 6.50 1.239 0.0122 7.00 1.283 7.50 1.324 8.00 1.358 8.50 1.385 9.00 1.403 9.50 1.401 1.358 1.313 1.287 1.274 1.272 1.273 1.273 1.273 1.272 1.273 | 0.8612 0.9665 1.0625 1.1476 1.2206 1.2805 1.3265 1.3582 1.3752 1.3774 1.3648 1.3376 1.2962 1.2409 1.1725 1.0919 1.0002 0.8990 0.7900 0.6754 0.5579 0.4405 0.3256 0.3013 0.2762 0.2506 0.2246 0.1983 0.1720 0.1457 0.1197 0.0940 0.0689 0.0567 0.0271 0.0303 0.0287 0.0124 0.0109 0.0092 0.0083 0.0089 0.0082 0.0074 0.0069 0.0065 0.0063 0.0061 0.0058 0.0057 0.0057 0.0057 0.0057 0.0057 0.0057 0.0057 0.0058 0.0058 0.0059 0.0061 0.0063 0.0066 0.0071 | 0.3911 0.3980 0.4012 0.4014 0.3990 0.3943 0.3878 0.3796 0.3700 0.3591 0.3471 0.3340 0.3199 0.3049 0.2890 0.2722 0.2545 0.2359 0.2163 0.1958 0.1744 0.1520 0.1262 0.1170 0.1059 0.0931 0.0788 0.0631 0.0464 0.0286 0.0102 -0.0088 -0.0281 -0.0378 -0.0349 -0.0361 -0.0464 -0.0821 -0.0924 -0.1015 -0.1073 -0.1083 -0.1112 -0.1146 -0.1172 -0.1194 -0.1213 -0.1232 -0.1252 -0.1268 -0.1282 -0.1297 -0.1310 -0.1324 -0.1337 -0.1350 -0.1363 -0.1374 -0.1385 -0.1395 -0.1403 -0.1406 -0.1398 -0.1390 -0.1378 -0.1369 -0.1353 -0.1338 0.0131 -0.1317 0.0139 -0.1291 0.0147 -0.1249 0.0158 -0.1213 0.0181 -0.1177 0.0211 -0.1142 0.0255 -0.1103 0.0301 -0.1066 0.0347 -0.1032 0.0401 -0.1002 0.0468 -0.0971 0.0545 -0.0940 0.0633 -0.0909 0.0722 -0.0883 0.0806 -0.0865 0.0900 -0.0854 |
15.00 1.275 0.0987 -0.0849
15.50 1.281 0.1075 -0.0847
16.00 1.284 0.1170 -0.0850
16.50 1.296 0.1270 -0.0858
17.00 1.306 0.1368 -0.0869
17.50 1.308 0.1464 -0.0883
18.00 1.308 0.1562 -0.0901
18.50 1.308 0.1664 -0.0922
19.00 1.308 0.1770 -0.0949
19.50 1.307 0.1878 -0.0980
20.00 1.311 0.1987 -0.1017
20.50 1.325 0.2100 -0.1059
21.00 1.324 0.2214 -0.1105
22.00 1.277 0.2499 -0.1172
23.00 1.229 0.2786 -0.1239
24.00 1.182 0.3077 -0.1305
25.00 1.136 0.3371 -0.1370
26.00 1.093 0.3664 -0.1433
28.00 1.017 0.4246 -0.1556
30.00 0.962 0.4813 -0.1671
32.00 0.937 0.5356 -0.1778
35.00 0.947 0.6127 -0.1923
40.00 0.950 0.7396 -0.2154
45.00 0.928 0.8623 -0.2374
50.00 0.884 0.9781 -0.2583
55.00 0.821 1.0846 -0.2782
60.00 0.740 1.1796 -0.2971
65.00 0.646 1.2617 -0.3149
70.00 0.540 1.3297 -0.3318
75.00 0.425 1.3827 -0.3476
80.00 0.304 1.4202 -0.3625
85.00 0.179 1.4423 -0.3763
90.00 0.053 1.4512 -0.3890
95.00 -0.073 1.4480 -0.4004
100.00 -0.198 1.4294 -0.4105
105.00 -0.319 1.3954 -0.4191
110.00 -0.434 1.3464 -0.4260
115.00 -0.541 1.2829 -0.4308
120.00 -0.637 1.2057 -0.4333
125.00 -0.720 1.1157 -0.4330
130.00 -0.787 1.0144 -0.4294
135.00 -0.836 0.9033 -0.4219
140.00 -0.864 0.7845 -0.4098
145.00 -0.869 0.6605 -0.3922
150.00 -0.847 0.5346 -0.3682
155.00 -0.795 0.4103 -0.3364
160.00 -0.711 0.2922 -0.2954
170.00 -0.788 0.0969 -0.3966
175.00 -0.394 0.0334 -0.1978
180.00 0.000 0.0185 0.0000
B.9 Airfoil-Data Input File – NACA64_A17.dat
NACA64 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of D
Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 1 Number of airfoil tables in this file 0.0 Table ID parameter 9.00 Stall angle (deg) 0.0 No longer used, enter zero 0.0 No longer used, enter zero 0.0 No longer used, enter zero -4.4320 Zero Cn angle of attack (deg) 6.0031 Cn slope for zero lift (dimensionless) 1.4073 Cn extrapolated to value at positive stall angle of attack -0.7945 Cn at stall value for negative angle of attack -1.00 Angle of attack for minimum CD (deg) 0.0052 Minimum CD value
-180.00 0.000 0.0198 0.0000
-175.00 0.374 0.0341 0.1880
-170.00 0.749 0.0955 0.3770
-160.00 0.659 0.2807 0.2747
-155.00 0.736 0.3919 0.3130
-150.00 0.783 0.5086 0.3428
-145.00 0.803 0.6267 0.3654
-140.00 0.798 0.7427 0.3820
-135.00 0.771 0.8537 0.3935
-130.00 0.724 0.9574 0.4007
-125.00 0.660 1.0519 0.4042
-120.00 0.581 1.1355 0.4047
-115.00 0.491 1.2070 0.4025
-110.00 0.390 1.2656 0.3981
-105.00 0.282 1.3104 0.3918
| -100.00 -95.00 -90.00 -85.00 -80.00 -75.00 -70.00 -65.00 -60.00 -55.00 -50.00 -45.00 -40.00 -35.00 -30.00 -25.00 -24.00 -23.00 -22.00 -21.00 -20.00 -19.00 -18.00 -17.00 -16.00 -15.00 -14.00 -13.50 -13.00 -12.00 -11.00 -10.00 -9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 8.50 9.00 9.50 10.00 10.50 11.00 11.50 12.00 12.50 13.00 13.50 14.00 14.50 15.00 15.50 16.00 16.50 17.00 17.50 18.00 18.50 19.00 19.50 20.00 21.00 22.00 23.00 24.00 25.00 26.00 28.00 30.00 32.00 35.00 | 0.169 0.052 -0.067 -0.184 -0.299 -0.409 -0.512 -0.606 -0.689 -0.759 -0.814 -0.850 -0.866 -0.860 -0.829 -0.853 -0.870 -0.890 -0.911 -0.934 -0.958 -0.982 -1.005 -1.082 -1.113 -1.105 -1.078 -1.053 -1.015 -0.904 -0.807 -0.711 -0.595 -0.478 -0.375 -0.264 -0.151 -0.017 0.088 0.213 0.328 0.442 0.556 0.670 0.784 0.898 1.011 1.103 1.181 1.257 1.293 1.326 1.356 1.382 1.400 1.415 1.425 1.434 1.443 1.451 1.453 1.448 1.444 1.445 1.447 1.448 1.444 1.438 1.439 1.448 1.452 1.448 1.438 1.428 1.401 1.359 1.300 1.220 1.168 1.116 1.015 0.926 0.855 0.800 | 1.3410 0.3838 1.3572 0.3743 1.3587 0.3636 1.3456 0.3517 1.3181 0.3388 1.2765 0.3248 1.2212 0.3099 1.1532 0.2940 1.0731 0.2772 0.9822 0.2595 0.8820 0.2409 0.7742 0.2212 0.6610 0.2006 0.5451 0.1789 0.4295 0.1563 0.3071 0.1156 0.2814 0.1040 0.2556 0.0916 0.2297 0.0785 0.2040 0.0649 0.1785 0.0508 0.1534 0.0364 0.1288 0.0218 0.1037 0.0129 0.0786 -0.0028 0.0535 -0.0251 0.0283 -0.0419 0.0158 -0.0521 0.0151 -0.0610 0.0134 -0.0707 0.0121 -0.0722 0.0111 -0.0734 0.0099 -0.0772 0.0091 -0.0807 0.0086 -0.0825 0.0082 -0.0832 0.0079 -0.0841 0.0072 -0.0869 0.0064 -0.0912 0.0054 -0.0946 0.0052 -0.0971 0.0052 -0.1014 0.0052 -0.1076 0.0053 -0.1126 0.0053 -0.1157 0.0054 -0.1199 0.0058 -0.1240 0.0091 -0.1234 0.0113 -0.1184 0.0124 -0.1163 0.0130 -0.1163 0.0136 -0.1160 0.0143 -0.1154 0.0150 -0.1149 0.0267 -0.1145 0.0383 -0.1143 0.0498 -0.1147 0.0613 -0.1158 0.0727 -0.1165 0.0841 -0.1153 0.0954 -0.1131 0.1065 -0.1112 0.1176 -0.1101 0.1287 -0.1103 0.1398 -0.1109 0.1509 -0.1114 0.1619 -0.1111 0.1728 -0.1097 0.1837 -0.1079 0.1947 -0.1080 0.2057 -0.1090 0.2165 -0.1086 0.2272 -0.1077 0.2379 -0.1099 0.2590 -0.1169 0.2799 -0.1190 0.3004 -0.1235 0.3204 -0.1393 0.3377 -0.1440 0.3554 -0.1486 0.3916 -0.1577 0.4294 -0.1668 0.4690 -0.1759 0.5324 -0.1897 |
| 0.804 0.793 | 0.6452 0.7573 | -0.2126 -0.2344 | |
| 45.00 50.00 | 0.763 | 0.8664 | -0.2553 |
| 40.00 55.00 | 0.717 | 0.9708 | -0.2751 |
| 60.00 | 0.656 | 1.0693 | -0.2939 |
| 65.00 | 0.582 | 1.1606 | -0.3117 |
| 70.00 | 1.2438 | -0.3285 | |
| 0.495 | |||
| 75.00 | 0.398 | 1.3178 | -0.3444 |
| 80.00 | 0.291 | 1.3809 | -0.3593 |
| 85.00 | 0.176 | 1.4304 | -0.3731 -0.3858 |
| 90.00 95.00 | 0.053 -0.074 | 1.4565 1.4533 | -0.3973 |
| 100.00 | -0.199 | 1.4345 | -0.4075 |
| 105.00 | -0.321 | 1.4004 | -0.4162 |
| 110.00 | -0.436 | 1.3512 | -0.4231 |
| 115.00 | -0.543 | 1.2874 | -0.4280 |
| 120.00 | -0.640 | 1.2099 | -0.4306 |
| 125.00 | -0.723 | 1.1196 | -0.4304 |
| 130.00 | -0.790 | 1.0179 | -0.4270 |
| 135.00 | -0.840 | 0.9064 | -0.4196 |
| 140.00 | -0.868 | 0.7871 | -0.4077 |
| 145.00 | -0.872 -0.850 | 0.6627 | -0.3903 |
| 150.00 | -0.798 | 0.5363 0.4116 | -0.3665 -0.3349 |
| 155.00 160.00 | -0.714 | 0.2931 | -0.2942 |
| 170.00 | -0.749 | 0.0971 | -0.3771 |
| 175.00 | -0.374 | 0.0334 | -0.1879 |
| 180.00 | 0.000 | 0.0198 | 0.0000 |
Appendix C Source Code for the Control System DLL
!=== SUBROUTINE DISCON ( avrSWAP, aviFAIL, accINFILE, avcOUTNAME, avcMSG ) !DEC$ ATTRIBUTES DLLEXPORT, ALIAS:'DISCON' :: DISCON
! This Bladed-style DLL controller is used to implement a variable-speed ! generator-torque controller and PI collective blade pitch controller for ! the NREL Offshore 5MW baseline wind turbine. This routine was written by ! J. Jonkman of NREL/NWTC for use in the IEA Annex XXIII OC3 studies.
IMPLICIT
NONE
! Passed Variables:
REAL(4), INTENT(INOUT) :: avrSWAP (*)
INTEGER(4), INTENT( OUT)
INTEGER(1), INTENT(IN ) INTEGER(1), INTENT( OUT) INTEGER(1), INTENT(IN )
:: accINFILE ({}^{*}) :: avcMSG ({}^{*}) :: avcOUTNAME ({}^{*})
! The swap array, used to pass data to, and r ! A flag used to indicate the success of this ! The address of the first record of an array ! The address of the first record of an array ! The address of the first record of an array
! Local Variables:
REAL(4)
REAL(4)
REAL(4)
REAL(4), PARAMETER
REAL(4)
REAL(4), SAVE
REAL(4)
REAL(4)
REAL(4)
REAL(4), SAVE
REAL(4), SAVE
REAL(4), SAVE
REAL(4), SAVE
REAL(4), SAVE
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), SAVE
REAL(4)
REAL(4)
REAL(4)
REAL(4)
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4)
REAL(4)
REAL(4)
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), PARAMETER
REAL(4), SAVE
REAL(4), SAVE
REAL(4), PARAMETER
REAL(4), SAVE
REAL(4), SAVE
INTEGER(4)
INTEGER(4)
:: Alpha
:: BlPitch (3)
:: ElapTime
:: CornerFreq 1.570796
:: GenSpeed
:: GenSpeedF
:: GenTrq
:: GK
:: HorWindV
:: IntSpdErr
:: LastGenTrq
:: LastTime
:: LastTimePC
:: LastTimeVS
:: OnePlusEps =\ 1.\theta\ + EPSILON(OnePlusEps)
:: PC_DT = 0.00125
:: PC_KI = 0.008068634
:: PC_KK = 0.1099965
:: PC_KP = 0.01882681
:: PC_MaxPit = 1.570796
:: PC_MaxRat = 0.1396263
:: PC_MinPit = 0.0
:: PC_RefSpd = 122.9096
:: PitCom (3)
:: PitComI
:: PitComP
:: PitComT
:: PitRate (3)
:: R2D = 57.295780
:: RPS2RPM = 9.5492966
:: SpdErr
:: Time
:: TrqRate
:: VS_CtInSp = 70.16224
:: VS_DT = 0.00125
:: VS_MaxRat = 15000.0
:: VS_MaxTq = 47402.91
:: VS_Rgn2K = 2.332287
:: VS_Rgn2Sp = 91.21091
:: VS_Rgn3MP = 0.01745329
:: VS_RtGnSp = 121.6805
:: VS_RtPwr = 5296610.0
:: VS_Slope15
:: VS_Slope25
:: VS_SlPc 10.0
:: VS_SySp
:: VS_TrGnSp
:: I
:: iStatus
:: K
:: NumBl
! Current coefficient in the recursive, singl ! Current values of the blade pitch angles, r ! Elapsed time since the last call to the con ! Corner frequency (-3dB point) in the recurs ! Current HSS (generator) speed, rad/s. ! Filtered HSS (generator) speed, rad/s. ! Electrical generator torque, N-m. ! Current value of the gain correction factor ! Horizontal hub-heigh wind speed, m/s. ! Current integral of speed error w.r.t. time ! Commanded electrical generator torque the l ! Last time this DLL was called, sec. ! Last time the pitch controller was called, ! Last time the torque controller was called, ! The number slighty greater than unity in si ! Communication interval for pitch controlle ! Integral gain for pitch controller at rated ! Pitch angle were the the derivative of the ! Proportional gain for pitch controller at r ! Maximum pitch setting in pitch controller, ! Maximum pitch rate (in absolute value) in ! Minimum pitch setting in pitch controller, ! Desired (reference) HSS speed for pitch con ! Commanded pitch of each blade the last time ! Integral term of command pitch, rad. ! Proportional term of command pitch, rad. ! Total command pitch based on the sum of the ! Pitch rates of each blade based on the curr ! Factor to convert radians to degrees. ! Factor to convert radians per second to rev ! Current speed error, rad/s. ! Current simulation time, sec. ! Torque rate based on the current and last t ! Transitional generator speed (HSS side) bet ! Communication interval for torque controlle ! Maximum torque rate (in absolute value) in ! Maximum generator torque in Region 3 (HSS s ! Generator torque constant in Region 2 (HSS ! Transitional generator speed (HSS side) bet ! Minimum pitch angle at which the torque is ! Rated generator speed (HSS side), rad/s. -- ! Rated generator generator power in Region 3 ! Torque/speed slope of region 1 1/2 cut-in t ! Torque/speed slope of region 2 1/2 inductio ! Rated generator slip percentage in Region 2 ! Synchronous speed of region ^{2\ 1/2} induction ! Transitional generator speed (HSS side) bet
INTEGER(4), PARAMETER :: UnDb = 85 ! I/O unit for the debugging information INTEGER(1) :: iInFile ( 256) ! CHARACTER string cInFile stored as a 1-byt INTEGER(1) :: iMessage ( 256) ! CHARACTER string cMessage stored as a 1-byt INTEGER(1), SAVE :: iOutName (1024) ! CHARACTER string cOutName stored as a 1-byt LOGICAL(1), PARAMETER :: PC_DbgOut = .FALSE. ! Flag to indicate whether to output debuggin CHARACTER( 256) :: cInFile ! CHARACTER string giving the name of the par CHARACTER( 256) :: cMessage ! CHARACTER string giving a message that will CHARACTER(1024), SAVE :: cOutName ! CHARACTER string giving the simulation run CHARACTER( 1), PARAMETER :: Tab = CHAR( 9 ) ! The tab character. CHARACTER( 25), PARAMETER :: FmtDat = "(F8.3,99('"//Tab//"',ES10.3E2,:))" ! The format of the debugging data
! Set EQUIVALENCE relationships between INTEGER(1) byte arrays and CHARACTER strings:
EQUIVALENCE (iInFile , cInFile ) EQUIVALENCE (iMessage, cMessage) EQUIVALENCE (iOutName, cOutName)
! Load variables from calling program (See Appendix A of Bladed User's Guide):
iStatus = NINT( avrSWAP( 1) ) NumBl = NINT( avrSWAP(61) ) BlPitch (1) = avrSWAP( 4) BlPitch \mathbf{\Psi}(2)\mathbf{\Psi}=\mathbf{\Psi} avrSWAP(33) BlPitch (3) = avrSWAP(34) GenSpeed = avrSWAP(20) HorWindV = avrSWAP(27) Time = avrSWAP( 2)
! Initialize aviFAIL to 0:
aviFAIL =6
! Read any External Controller Parameters specified in the User Interface ! and initialize variables:
DO \texttt{T}=\texttt{1} ,MIN( 256, NINT( avrSWAP(50) ) ) iInFile (I) = accINFILE (I) ! Sets cInfile by EQUIVALENCE
ENDDO
DO \ I~=~1,\mathsf{M I N} ( 1024, NINT( avrSWAP(51) ) ) iOutName(I) = avcOUTNAME(I) ! Sets cOutName by EQUIVALENCE
ENDDO
! Inform users that we are using this user-defined routine:
aviFAIL \mathit{\Theta}=\;1
cMessage = 'Running with torque and pitch control of the NREL offshore '// & '5MW baseline wind turbine from DISCON.dll as written by J. '// & 'Jonkman of NREL/NWTC for use in the IEA Annex XXIII OC3 ' // & 'studies.'
! Determine some torque control parameters not specified directly:
VS_SySp = VS_RtGnSp/( 1.\theta{\mathrm{~+~}}\theta.\theta1^{*}\forall5\_51\mathsf{P c} )
VS_Slope15 = ( VS_Rgn2K*VS_Rgn2Sp*VS_Rgn2Sp )/( VS_Rgn2Sp - VS_CtInSp )
VS_Slope25 = ( VS_RtPwr/VS_RtGnSp )/( VS_RtGnSp - VS_SySp
IF ( VS_Rgn2K ==0.\theta ) THEN ! .TRUE. if the Region 2 torque is flat, and thus, the denominator in the ELSE condition is VS_TrGnSp = VS_SySp
ELSE ! .TRUE. if the Region 2 torque is quadratic with speed VS_TrGnSp = ( VS_Slope25 - SQRT( VS_Slope25*( VS_Slope25 - 4.0*VS_Rgn2K*VS_SySp ) ) )/( 2.0*VS_Rgn2K )
! Check validity of input parameters:
IF ( CornerFreq <=0.9 ) THEN aviFAIL \mathrm{~\ensuremath~{~\vert~\mathbf~{~\mu~}~}~}=\mathrm{~\ensuremath~{~\mathbf~{~-~}~}~}1
cMessage = 'CornerFreq must be greater than zero.' ENDIF IF ( VS_DT <=\ \Theta\,.\,\Theta ) THEN aviFAIL \begin{array}{r l}{\mathbf{\Sigma}=}&{{}-\mathbf{1}}\end{array} cMessage =\cdot\mathsf{v s}\_\mathsf{D T} must be greater than zero.' ENDIF IF ( VS_CtInSp < 0.0 ) THEN aviFAIL \begin{array}{r l}{\mathbf{\Sigma}=}&{{}-\mathbf{1}}\end{array} cMessage = 'VS_CtInSp must not be negative.' ENDIF IF ( VS_Rgn2Sp \zeta= VS_CtInSp ) THEN aviFAIL \begin{array}{r l}{\mathbf{\Sigma}=}&{{}-\mathbf{1}}\end{array} cMessage = 'VS_Rgn2Sp must be greater than VS_CtInSp.' ENDIF IF ( VS_TrGnSp \boldsymbol{<} VS_Rgn2Sp ) THEN aviFAIL \begin{array}{r l}{\mathbf{\Sigma}=}&{{}-\mathbf{1}}\end{array} cMessage = 'VS_TrGnSp must not be less than VS_Rgn2Sp.' ENDIF IF ( VS_SlPc <=\ \Theta\,.\,\Theta ) THEN aviFAIL \begin{array}{r l}{\mathbf{\Sigma}=}&{{}-\mathbf{1}}\end{array} cMessage \begin{array}{r l}{\mathsf{\Pi}=}&{{}^{\prime}\mathsf{V S}\_{\mathsf{S}}\mathsf{1}\mathsf{P c}}\end{array} must be greater than zero.' ENDIF IF ( VS_MaxRat <=\ \Theta\,.\,\Theta ) THEN aviFAIL \begin{array}{r l r}{-1}&{{}}&{-1}\end{array} cMessage = 'VS_MaxRat must be greater than zero.' ENDIF IF ( VS_RtPwr < 0.0 ) THEN aviFAIL \begin{array}{r l}{\mathbf{\Sigma}=}&{{}-\mathbf{1}}\end{array} cMessage = 'VS_RtPwr must not be negative.' ENDIF IF ( VS_Rgn2K < 0.0 ) THEN aviFAIL = -1 cMessage = 'VS_Rgn2K must not be negative.' ENDIF IF ( VS_Rgn2K*VS_RtGnSp*VS_RtGnSp \textgreater VS_RtPwr/VS_RtGnSp ) THEN aviFAIL cMessage = 'VS_Rgn2K*VS_RtGnSp^2 must not be greater than VS_RtPwr/VS_RtGnSp.' ENDIF IF ( VS_MaxTq < VS_RtPwr/VS_RtGnSp ) THEN aviFAIL \begin{array}{r l}{\mathbf{\Sigma}=}&{{}-\mathbf{1}}\end{array} cMessage = 'VS_RtPwr/VS_RtGnSp must not be greater than VS_MaxTq.' ENDIF IF ( PC_DT <=0.\theta ) THEN aviFAIL \begin{array}{r l}{\mathbf{\chi}=}&{{}-1}\end{array} cMessage \begin{array}{r l}{=}&{{}^{\cdot}\mathsf{P C}\_\mathsf{D T}}\end{array} must be greater than zero.' ENDIF IF ( PC_KI <=0.\theta ) THEN aviFAIL \begin{array}{r l}{\mathbf{\chi}=}&{{}-1}\end{array} cMessage \begin{array}{r l}{=}&{{}^{\cdot}\mathsf{P C}_{-}\mathsf{K I}}\end{array} must be greater than zero.' ENDIF IF ( PC_KK <=0.\theta ) THEN aviFAIL \begin{array}{r l}{\mathbf{\chi}=}&{{}-1}\end{array} cMessage =\because P C\_K K must be greater than zero.' ENDIF IF ( PC_RefSpd <=0.\theta ) THEN aviFAIL \begin{array}{r l}{=}&{{}-1}\end{array} cMessage = 'PC_RefSpd must be greater than zero.' ENDIF IF ( PC_MaxRat <=0.\theta ) THEN aviFAIL \begin{array}{r l}{=}&{{}-1}\end{array} cMessage = 'PC_MaxRat must be greater than zero.' ENDIF IF ( PC_MinPit >= PC_MaxPit ) THEN aviFAIL \begin{array}{r l}{=}&{{}-1}\end{array} cMessage \begin{array}{r l}{=}&{{}\cdot\mathsf{P C}_{\mathrm{s}}}\end{array} _MinPit must be less than PC_MaxPit.' ENDIF
header:
IF ( PC_DbgOut ) THEN
OPEN ( UnDb, FILE=TRIM( cOutName )//'.dbg', STATUS ,= 'REPLACE' )
WRITE (UnDb,'(/////)')
WRITE (UnDb,'(A)') 'Time '//Tab//'ElapTime'//Tab//'HorWindV'//Tab//'GenSpeed'//Tab//'GenSpeedF'//Tab//'RelSpdErr'//Tab 'SpdErr '//Tab//'IntSpdErr'//Tab//'GK '//Tab//'PitComP'//Tab//'PitComI'//Tab//'PitComT'//Tab// 'PitRate1'//Tab//'PitCom1'
WRITE (UnDb,'(A)') '(sec)'//Tab//'(sec) '//Tab//'(m/sec) '//Tab//'(rpm) '//Tab//'(rpm) '//Tab//'(%) '//Tab '(rad/s)'//Tab//'(rad) '//Tab//'(-)'//Tab//'(deg) '//Tab//'(deg) '//Tab//'(deg) '//Tab// '(deg/s) '//Tab//'(deg)
ENDIF
! Initialize the SAVEd variables:
! NOTE: LastGenTrq, though SAVEd, is initialized in the torque controller ! below for simplicity, not here.
GenSpeedF = GenSpeed ! This will ensure that generator speed filter will use the initial value of PitCom = BlPitch ! This will ensure that the variable speed controller picks the correct contr GK =\ 1.\theta/\left(\ \ 1.\theta\ +\ \mathsf{P i t C o m}(1)/\mathsf{P C}\_\mathsf{K K}\ \ \right) ) ! This will ensure that the pitch angle is unchanged if the initial SpdErr is IntSpdErr = PitCom(1)/( GK*PC_KI ) ! This will ensure that the pitch angle is unchanged if the initial SpdErr is LastTime = Time ! This will ensure that generator speed filter will use the initial value of LastTimePC = Time - PC_DT ! This will ensure that the pitch controller is called on the first pass LastTimeVS = Time - VS_DT ! This will ensure that the torque controller is called on the first pass
ENDIF
! Main control calculations:
IF ( ( iStatus b=~\theta ) .AND. ( aviFAIL b=~\theta ) ) THEN ! Only compute control calculations if no error has occured and we are
! Abort if the user has not requested a pitch angle actuator (See Appendix A
! of Bladed User's Guide):
IF ( NINT(avrSWAP(10)) /=\theta ) THEN ! .TRUE. if a pitch angle actuator hasn't been requested aviFAIL \begin{array}{r l}{\mathbf{\Sigma}=}&{{}-\mathbf{1}}\end{array} cMessage = 'Pitch angle actuator not requested.'
ENDIF
! Set unused outputs to zero (See Appendix A of Bladed User's Guide):
avrSWAP(36) =6.6 ! Shaft brake status: 0=off avrSWAP(41) =6.6 ! Demanded yaw actuator torque avrSWAP(46) =0.01 ! Demanded pitch rate (Collective pitch) avrSWAP(48) =0.01 Demanded nacelle yaw rate avrSWAP(65) =6.6 ! Number of variables returned for logging avrSWAP(72) =0.01 ! Generator startup resistance avrSWAP(79) =0.01 Request for loads: 0=none avrSWAP(80) =6.6 ! Variable slip current status avrSWAP(81) =\theta.\theta! ! Variable slip current demand
! Compute the elapsed time since the last call to the controller:
ElapTime = Time - LastTimeVS
! Only perform the control calculations if the elapsed time is greater than ! or equal to the communication interval of the torque controller: ! NOTE: Time is scaled by OnePlusEps to ensure that the contoller is called ! at every time step when \mathsf{V S\_D T}\ =\ \mathsf{D T} , even in the presence of ! numerical precision errors.
IF ( ( Time*OnePlusEps - LastTimeVS ) >=\mathsf{V S}\_\mathsf{D T} ) THEN ! Compute the generator torque, which depends on which region we are in:
IF ( ( GenSpeedF >= VS_RtGnSp ) .OR. ( PitCom(1) >= VS_Rgn3MP ) ) THEN ! We are in region 3 - power is constant GenTrq = VS_RtPwr/GenSpeedF
ELSEIF ( GenSpeedF \zeta\!= VS_CtInSp ) THEN ! We are in region 1 - torque is zero GenTrq =6.6
ELSEIF ( GenSpeedF \varsigma VS_Rgn2Sp ) THEN ! We are in region 1 1/2 - linear ramp in to GenTrq = VS_Slope15*( GenSpeedF - VS_CtInSp )
ELSEIF ( GenSpeedF < VS_TrGnSp ) THEN ! We are in region 2 - optimal torque is pro GenTrq = VS_Rgn2K*GenSpeedF*GenSpeedF
ELSE ! We are in region 2 1/2 - simple induction GenTrq = VS_Slope25*( GenSpeedF - VS_SySp )
ENDIF
! Saturate the commanded torque using the maximum torque limit:
GenTrq = MIN( GenTrq , VS_MaxTq ) ! Saturate the command using the maximum torque limit ! Saturate the commanded torque using the torque rate limit:
IF ( iStatus ==6 ) LastGenTrq = GenTrq ! Initialize the value of LastGenTrq on the first pass only TrqRate = ( GenTrq - LastGenTrq )/ElapTime ! Torque rate (unsaturated) TrqRate = MIN( MAX( TrqRate, -VS_MaxRat ), VS_MaxRat ) ! Saturate the torque rate using its maximum absolute value GenTrq = LastGenTrq ^+ TrqRate*ElapTime ! Saturate the command using the torque rate limit
! Reset the values of LastTimeVS and LastGenTrq to the current values:
LastTimeVS = Time LastGenTrq = GenTrq
ENDIF
! Set the generator contactor status, avrSWAP(35), to main (high speed)
! variable-speed generator, the torque override to yes, and command the
! generator torque (See Appendix A of Bladed User's Guide):
avrSWAP(35) =~1,\theta ! Generator contactor status: 1=main (high speed) variable-speed generator
avrSWAP(56) =6.8 ! Torque override: 0=yes
avrSWAP(47) = LastGenTrq ! Demanded generator torque
! Pitch control:
! Compute the elapsed time since the last call to the controller:
ElapTime = Time - LastTimePC
! Only perform the control calculations if the elapsed time is greater than ! or equal to the communication interval of the pitch controller: ! NOTE: Time is scaled by OnePlusEps to ensure that the contoller is called ! at every time step when {\mathsf{P C}}\_{\mathsf{D T}}\ =\ {\mathsf{D T}} , even in the presence of ! numerical precision errors.
IF ( ( Time*OnePlusEps - LastTimePC ) >={\mathsf{P C}}\_{\mathsf{D T}} ) THEN ! Compute the gain scheduling correction factor based on the previously ! commanded pitch angle for blade 1:
6\mathsf{K}~=~1.6/ ( 1.0 + PitCom(1)/PC_KK )
! Compute the current speed error and its integral w.r.t. time; saturate the integral term using the pitch angle limits:
SpdErr = GenSpeedF - PC_RefSpd
IntSpdErr = IntSpdErr ^+ SpdErr*ElapTime
IntSpdErr = MIN( MAX( IntSpdErr, PC_MinPit/( GK*PC_KI ) ), &
PC_MaxPit/( GK*PC_KI )
! Compute the pitch commands associated with the proportional and integral gains:
PitComP \mathsf{\Omega}=\mathsf{\ G K}^{*}\mathsf{P C}\mathsf{\Pi}_{-}\mathsf{K P}^{*} SpdErr ! Proportional term PitComI \texttt{=}\mathsf{G K}^{*}\mathsf{P C}\_\mathsf{K I}^{*} IntSpdErr ! Integral term (saturated)
! Superimpose the individual commands to get the total pitch command; ! saturate the overall command using the pitch angle limits:
PitComT = PitComP ^+ PitComI ! Overall command (unsaturated) PitComT = MIN( MAX( PitComT, PC_MinPit ), PC_MaxPit ) ! Saturate the overall command using the pitch angle ! Saturate the overall commanded pitch using the pitch rate limit: ! NOTE: Since the current pitch angle may be different for each blade ! (depending on the type of actuator implemented in the structural ! dynamics model), this pitch rate limit calculation and the ! resulting overall pitch angle command may be different for each ! blade.
DO \smash{\mathrm{~K~}=\,1} ,NumBl ! Loop through all blades
ENDDO ! K - all blades ! Reset the value of LastTimePC to the current value:
LastTimePC = Time
! Output debugging information if requested:
IF ( PC_DbgOut ) WRITE (UnDb,FmtDat) Time, ElapTime, HorWindV, GenSpeed*RPS2RPM, GenSpeedF*RPS2RPM, & 100.0*SpdErr/PC_RefSpd, SpdErr, IntSpdErr, GK, PitComP*R2D, PitComI \approx\mathsf{R}2\mathsf{D} , & PitComT*R2D, PitRate(1) \ast\mathtt{R}_{2\mathsf{D}} , PitCom(1) \ast\mathtt{R}_{2\mathsf{D}}
ENDIF
! Set the pitch override to yes and command the pitch demanded from the last ! call to the controller (See Appendix A of Bladed User's Guide):
avrSWAP(55) =6.6 ! Pitch override: 0=yes
avrSWAP(42) = PitCom(1) ! Use the command angles of all blades if using individual pitch
avrSWAP(43) = PitCom(2) ! "
avrSWAP(44) = PitCom(3) ! "
avrSWAP(45) = PitCom(1) ! Use the command angle of blade 1 if using collective pitch ! Reset the value of LastTime to the current value:
LastTime = Time
ENDIF
! Convert CHARACTER string to byte array for the return message:
DO \texttt{T}=\texttt{1} ,MIN( 256, NINT( avrSWAP(49) ) ) avcMSG(I) = iMessage(I) ! Same as cMessage by EQUIVALENCE
ENDDO
<html>| FormApproved REPORTDOCUMENTATIONPAGE OMB No.0704-0188 | |||||||||
| Thepublicreportingburdenfor thiscollectionof informationisestimated toaverage1hourperresponse,including thetimeforreviewinginstructions,searching existingdatasources, collectionofinformation,includingsuggestionsforreducingtheburden，toDepartmentofDefense，ExecutiveServicesandCommunicationsDirectorate(0704-0188).Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currentlyvalidOMBcontrolnumber. | |||||||||
| PLEASEDONOTRETURNYOURFORMTOTHEABOVEORGANIZATION. 1.REPORT DATE (DD-MM-YYYY) February2009 | 2.REPORTTYPE technical report | 3.DATES COVERED(From-To) | |||||||
| 4.TITLE AND SUBTITLE Development | Definition of a 5-MW ReferenceWind Turbine for OffshoreSystem | 5a.CONTRACT NUMBER DE-AC36-08-GO28308 | |||||||
| 5b.GRANTNUMBER 5c.PROGRAMELEMENTNUMBER | |||||||||
| 6.AUTHOR(S) J. Jonkman, S. Butterfield, W. Musial, and G. Scott | 5d.PROJECTNUMBER NREL/TP-500-38060 5e.TASKNUMBER | ||||||||
| WER5.3301 5f.WORKUNITNUMBER | |||||||||
| 7.PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES) National Renewable Energy Laboratory 1617 ColeBlvd. Golden,CO80401-3393 | 8.PERFORMINGORGANIZATION REPORTNUMBER NREL/TP-500-38060 | ||||||||
| 9.SPONSORING/MONITORINGAGENCYNAME(S)ANDADDRESS(ES) | 10.SPONSOR/MONITOR'SACRONYM(S) NREL | ||||||||
| 12.DISTRIBUTIONAVAILABILITYSTATEMENT National TechnicalInformationService U.S.Departmentof Commerce | 11.SPONSORING/MONITORING AGENCYREPORTNUMBER | ||||||||
| 5285 Port Royal Road Springfield,VA 22161 13.SUPPLEMENTARYNOTES | |||||||||
| 14.ABSTRACT(Maximum200Words) This report describes a three-bladed, upwind, variable-speed, variable blade-pitch-to-feather-controlled | |||||||||
| technology. | |||||||||
| 15.SUBJECTTERMS offshore wind energy development; wind turbine design model; wind turbine specifications | |||||||||
| 16. SECURITY CLASSIFICATION OF: | |||||||||
| a. REPORT Unclassified | b.ABSTRACT Unclassified | c.THIS PAGE Unclassified | 17. LIMITATION OFABSTRACT UL | 18.NUMBER 19a.NAMEOFRESPONSIBLEPERSON OFPAGES 19b.TELEPHONE NUMBER (Include area code) | |||||
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