Engee documentation

Wind Turbine

A turbine that converts kinetic wind energy into rotational motion.

blockType: Engee1DMechanical.Turbomachinery.WindTurbine

wind turbine

Path in the library:

/Physical Modeling/1D Mechanical/Engines & Motors/Wind Turbine

Description

Block Wind Turbine It is a wind turbine that converts wind motion into mechanical rotational energy. Wind turbines use wind energy to produce electricity. The development of wind turbines is aimed at improving the efficiency, reliability and economy of individual turbines, while the development of a wind farm involves the strategic placement of several turbines to optimize energy harvesting. This block can be used to model individual wind turbines and entire wind farms. It is possible to analyze turbine performance, energy generation, and interactions in a wind farm, as well as the impact of various geometries, configurations, control algorithms, and turbine placement plans on wind farm performance and energy generation.

The incoming wind speed and the angle of the blades are set as input data, and additionally, the thrust acting on the turbine can be output. The effects of thrust and inertia can be taken into account. Parameterize the unit using tabular power and thrust coefficients or lift and drag coefficients of the airfoil.

Parameterization by power and thrust coefficients

If for the parameter Parameterization the value is set Tabulated data for power and thrust coefficients, the block calculates the coefficients of wind energy utilization and thrust using tabular data in such a way that



where

  • — the reference angle of the blade installation;

  • — reference speed coefficient;

  • and — parameter values Power coefficient table, Cp(β,λ) and Thrust coefficient table, Ct(β,λ) accordingly;

  • — smoothed speed coefficient.

The block uses the following equation as the basis for determining the speed coefficient

where

  • — parameter value Turbine radius;

  • — the difference in angular velocities between the shaft and the housing;

  • — the speed of the air flow falling on the rotor. This value is a scalar of the input port V.

The block uses the following equation to describe a smoothed version of the velocity coefficient equation

where — parameter value Wind velocity threshold.

The unit uses the following equations as the basis for calculating power and thrust



where

  • — parameter value Air density;

  • — the area of the circle swept by the turbine blades.

To establish a relationship between the parameters of the unit and the nominal mechanical power of the wind turbine, it is necessary to determine the power of the wind turbine at peak power factor and nominal wind speed. The rated power corresponds to the unit parameters calculated by the formula

where

  • — the peak value of the wind energy utilization factor; this is the maximum value of the parameter Power coefficient table, Cp(β,λ);

  • — swept surface area of the rotor;

  • — nominal wind speed. Nominal wind speeds are usually from 10 before 15 m/s. At this wind speed, the designs of wind turbine controllers can change their operating strategy to maintain their rated power.

The unit uses numerically smoothed equations for thrust, power, and torque such that







where — parameter value Rotational velocity threshold. When , the unit smoothly reduces the power to zero.

The block assumes that . The generated power is zero when the rotor rotation speed is zero and the non-zero value is it affects the starting torque. The starting moment is related to so that

Your model may be sensitive to this behavior of the starting torque if you are simulating rotor braking in high winds.

Parameterization by lift and drag coefficients of an aerodynamic profile

If for the parameter Parameterization the value is set Tabulated data for airfoil lift and drag coefficients, it is possible to parameterize the coefficients of lift and drag, as well as the geometry of the aerodynamic profile for a given blade element. The default values correspond to the reference wind turbine NREL 5-MW [3]. The unit treats the propeller as a solid disk. The law of conservation of momentum is applied to the air passing through the disk when the block calculates the induced velocity. . The unit uses the induced velocity to determine the magnitude and direction of the total flow velocity in a vector of radial points along the blade, which are then used to determine lift and drag based on interpolation tables of lift and drag coefficients. These values are specific to this parameterization.:

  • — thrust calculated according to the impulse theory;

  • — axial flow velocity created by the movement of the blades of the wind turbine;

  • — radial velocity at the location of the blade;

  • — axial velocity at the location of the blade;

  • — thrust calculated according to the theory of the blade element;

  • — the torque calculated according to the theory of the blade element;

  • — number of propeller blades;

  • — the dimensionless position of the comet, set by the first element of the parameter Nondimensional radial location vector, r;

  • — the rotation speed of the wind turbine;

  • — the radius of the wind turbine blade;

  • — element-wise coefficients of lifting force and drag , respectively;

  • — the angle of flow at a given point along the blade;

  • — axial induction coefficient;

  • — tangential coefficient of induction;

  • — smoothed speed coefficient in each element of the blade.

The block uses momentum theory to determine the smoothed thrust equation in such a way that

where the block uses the Glauert correction in the turbulent wake mode when So that

The smoothed axial induction coefficient is

The block interpolates values from the parameter Nondimensional radial location vector, r to find . The block then interpolates the lift and drag coefficients to find and based on tabular values of the angle of attack and coefficients of lift and drag. The unit uses the theory of the blade element to calculate thrust and torque in such a way that



where



The unit performs this integration for each discrete element of the blade. The block samples according to the value in the parameter Number of blade elements and calculates the tangential coefficient of induction in each element of the blade as

Assumptions and limitations

The unit generates torque and power only at positive angular velocities.

Ports

Input

# V — incoming wind speed, m/s
scalar

Details

The input port associated with the speed of the incoming wind, measured in m/s.

Data types

Float64
Complex numbers support

I don’t

# β — blade installation angle, degrees
scalar

Details

The input port associated with the angle of installation of the turbine blades, measured in degrees.

Data types

Float64
Complex numbers support

I don’t

Conserving

# R — turbine shaft
rotational mechanics

Details

A non-directional port connected to the shaft of a wind generator.

Program usage name

rod_flange

Output

# T — thrust, N
scalar

Details

The output port associated with the axial force that the wind applies to the turbine blades, measured in N.

Dependencies

To use this port, check the box Output thrust.

Data types

Float64
Complex numbers support

I don’t

Parameters

Wind Turbine

# Parameterization — a variant of wind turbine parameterization
Tabulated data for power and thrust coefficients | Tabulated data for airfoil lift and drag coefficients

Details

The choice of the method of parameterization of the wind turbine: according to the coefficients of thrust and power, or according to the coefficients of lift and drag of the aerodynamic profile.

Values

Tabulated data for power and thrust coefficients | Tabulated data for airfoil lift and drag coefficients
Default value

Tabulated data for power and thrust coefficients
Program usage name

parameterization
Evaluatable

No

# Turbine radius — blade end radius
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The distance from the center of the turbine hub to the ends of the blades.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

80.0 m
Program usage name

rotor_radius
Evaluatable

Yes

# Pitch angle vector, β — the reference angle of the blade installation
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

The reference angle of the blade installation. The length of this vector determines the number of rows in the parameters Power coefficient table, Cp(β,λ) and Thrust coefficient table, Ct(β,λ).

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for power and thrust coefficients.

Units

rad | deg | rev | mrad | arcsec | arcmin | gon
Default value

[0.0, 3.0, 5.0, 10.0, 20.0, 90.0] deg
Program usage name

pitch_angle_vector
Evaluatable

Yes

# Tip speed ratio vector, λ — reference speed coefficient

Details

Reference speed coefficient . — the ratio of the speed of the end of the blade to the speed of the incoming flow. The length of this vector determines the number of columns in the parameters Power coefficient table, Cp(β,λ) and Thrust coefficient table, Ct(β,λ). The block supports negative values . The values must be strictly monotonically increasing.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for power and thrust coefficients.

Default value

[0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 15.0]
Program usage name

lambda_vector
Evaluatable

Yes

# Power coefficient table, Cp(β,λ) — table of wind energy usage coefficients

Details

Wind energy utilization coefficients for a given installation angle and speed coefficient. Each row corresponds to an element of the vector in the parameter Pitch angle vector, β, and each column corresponds to an element of the vector in the parameter Tip speed ratio vector, λ. The block assumes that .

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for power and thrust coefficients.

Default value

[0.001 0.0161 0.1446 0.3865 0.5009 0.4404 0.2545 0.0002 -0.1384; 0.0016 0.0173 0.1079 0.2676 0.3779 0.4111 0.3838 0.3176 0.2753; 0.0027 0.0197 0.1151 0.2606 0.3469 0.3558 0.3069 0.2222 0.1718; 0.0054 0.0283 0.1315 0.2364 0.2589 0.2022 0.0929 -0.0455 -0.1204; 0.0109 0.0536 0.132 0.1256 0.012 -0.1752 -0.4017 -0.6435 -0.7655; -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01]
Program usage name

C_P_matrix
Evaluatable

Yes

# Thrust coefficient table, Ct(β,λ) — table of thrust coefficients

Details

Thrust coefficients for a given installation angle and speed coefficient. Each row corresponds to an element of the vector in the parameter Pitch angle vector, β, and each column corresponds to an element of the vector in the parameter Tip speed ratio vector, λ.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for power and thrust coefficients and check the box Output thrust.

Default value

[0.0 0.2451 0.674 0.9616 1.0 0.9882 0.843 0.0002 -0.1341; 0.0016 0.2541 0.5942 0.8582 0.9561 0.9754 0.9599 0.9092 0.8669; 0.0027 0.2705 0.6113 0.8503 0.9339 0.9407 0.8993 0.8016 0.7239; 0.0054 0.3215 0.6475 0.8205 0.8482 0.7727 0.5565 -0.045 -0.1171; 0.2035 0.4335 0.6485 0.6348 0.2129 -0.1684 -0.3701 -0.5712 -0.6681; -0.05 -0.05 -0.05 -0.05 -0.05 -0.05 -0.05 -0.05 -0.05]
Program usage name

C_T_matrix
Evaluatable

Yes

# Number of blades — number of blades

Details

The number of blades of the wind turbine.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for airfoil lift and drag coefficients.

Default value

3
Program usage name

blade_count
Evaluatable

Yes

# Nondimensional radial location vector, r — radial position

Details

The radial position for a given set of blade sizes. Meaning 1 equivalent to the radius of the blade. The first element of this vector defines — komel.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for airfoil lift and drag coefficients.

Default value

[0.1, 0.17, 0.23, 0.36, 0.5, 0.63, 1.0]
Program usage name

r_vector
Evaluatable

Yes

# Blade twist vector, θ_tw(r) — turning the blade elements
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

The corners turning the blade for a given radial position. The elements of this vector are correlated one-to-one with the elements of the vector in the parameter Nondimensional radial location vector, r.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for airfoil lift and drag coefficients.

Units

rad | deg | rev | mrad | arcsec | arcmin | gon
Default value

[13.31, 13.31, 11.48, 9.01, 6.54, 4.19, 0.11] deg
Program usage name

twist_vector
Evaluatable

Yes

# Normalized chord length vector, c(r)/R — length of the chord of the blade element

Details

The length of the chord, normalized to the radius, for a given radial position along the blade. The elements of this vector are correlated one-to-one with the elements of the vector in the parameter Nondimensional radial location vector, r and columns in the parameters Airfoil lift coefficient table, Cl(α,r) and Airfoil drag coefficient table, Cd(α,r).

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for airfoil lift and drag coefficients.

Default value

[0.068, 0.074, 0.076, 0.069, 0.061, 0.053, 0.023]
Program usage name

normalized_chord_vector
Evaluatable

Yes

# Airfoil angle of attack vector, α — Angle of attack
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

Range of angles of attack. The elements of this vector are correlated one-to-one with the rows in the parameters Airfoil lift coefficient table, Cl(α,r) and Airfoil drag coefficient table, Cd(α,r).

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for airfoil lift and drag coefficients.

Units

rad | deg | rev | mrad | arcsec | arcmin | gon
Default value

[-180.0, -170.0, -160.0, -150.0, -140.0, -130.0, -120.0, -110.0, -100.0, -90.0, -80.0, -70.0, -60.0, -50.0, -40.0, -30.0, -20.0, -10.0, 0.0, 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0, 100.0, 110.0, 120.0, 130.0, 140.0, 150.0, 160.0, 170.0, 180.0] deg
Program usage name

alpha_vector
Evaluatable

Yes

# Airfoil lift coefficient table, Cl(α,r) — lifting force coefficients of the aerodynamic profile

Details

Coefficients of the lifting force of the profile for a given angle of attack and radial position along the blade. The rows of this matrix correspond one to one to the parameter Airfoil angle of attack vector, α. The columns of this matrix correspond one to one to the parameter Nondimensional radial location vector, r.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for airfoil lift and drag coefficients.

Default value

[0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.397 0.547 0.547 0.735 0.788 0.749; 0.0 0.642 0.685 0.685 0.695 0.67 0.659; 0.0 0.757 0.816 0.816 0.828 0.797 0.783; 0.0 0.762 0.832 0.832 0.846 0.813 0.798; 0.0 0.68 0.756 0.756 0.771 0.739 0.724; 0.0 0.532 0.609 0.609 0.624 0.596 0.581; 0.0 0.337 0.411 0.411 0.426 0.403 0.39; 0.0 0.114 0.182 0.182 0.195 0.179 0.169; 0.0 -0.12 -0.061 -0.061 -0.05 -0.06 -0.067; 0.0 -0.349 -0.302 -0.302 -0.294 -0.295 -0.299; 0.0 -0.557 -0.523 -0.523 -0.518 -0.512 -0.512; 0.0 -0.727 -0.708 -0.708 -0.706 -0.693 -0.689; 0.0 -0.842 -0.838 -0.838 -0.839 -0.82 -0.814; 0.0 -0.886 -0.895 -0.895 -0.898 -0.875 -0.866; 0.0 -0.839 -0.858 -0.858 -0.862 -0.838 -0.829; 0.0 -0.685 -1.013 -1.013 -0.815 -0.869 -0.958; 0.0 -0.311 -0.8496 -0.8496 -0.8284 -0.8284 -0.711; 0.0 0.137 0.288 0.288 0.444 0.521 0.442; 0.0 1.368 1.458 1.458 1.442 1.358 1.382; 0.0 1.7825 1.398 1.398 1.354 1.311 1.428; 0.0 1.904 1.265 1.265 1.076 0.962 0.926; 0.0 1.903 1.258 1.258 1.064 0.95 0.804; 0.0 1.69 1.146 1.146 0.98 0.884 0.763; 0.0 1.323 0.932 0.932 0.81 0.74 0.656; 0.0 0.88 0.657 0.657 0.582 0.54 0.495; 0.0 0.449 0.362 0.362 0.326 0.304 0.291; 0.0 0.124 0.092 0.092 0.072 0.053 0.053; 0.0 -0.118 -0.15 -0.15 -0.17 -0.198 -0.199; 0.0 -0.348 -0.379 -0.379 -0.399 -0.434 -0.436; 0.0 -0.549 -0.578 -0.578 -0.596 -0.637 -0.64; 0.0 -0.702 -0.727 -0.727 -0.743 -0.787 -0.79; 0.0 -0.787 -0.807 -0.807 -0.821 -0.864 -0.868; 0.0 -0.782 -0.797 -0.797 -0.806 -0.847 -0.85; 0.0 -0.664 -0.673 -0.673 -0.679 -0.711 -0.714; 0.0 -0.41 -0.547 -0.547 -0.735 -0.788 -0.749; 0.0 0.0 0.0 0.0 0.0 0.0 0.0]
Program usage name

C_L_matrix
Evaluatable

Yes

# Airfoil drag coefficient table, Cd(α,r) — drag coefficients of the aerodynamic profile

Details

Drag coefficients of the airfoil for a given angle of attack and radial position along the blade. The rows of this matrix correspond one to one to the parameter Airfoil angle of attack vector, α. The columns of this matrix correspond one to one to the parameter Nondimensional radial location vector, r.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for airfoil lift and drag coefficients.

Default value

[0.35 0.0602 0.0267 0.0267 0.0202 0.0185 0.0198; 0.35 0.1107 0.0968 0.0968 0.0943 0.0945 0.0955; 0.35 0.3045 0.2876 0.2876 0.2848 0.2809 0.2807; 0.35 0.5355 0.5232 0.5232 0.5215 0.5112 0.5086; 0.35 0.7685 0.7656 0.7656 0.766 0.7485 0.7427; 0.35 0.9788 0.9882 0.9882 0.9911 0.9665 0.9574; 0.35 1.1499 1.173 1.173 1.1787 1.1476 1.1355; 0.35 1.2716 1.3084 1.3084 1.3168 1.2805 1.2656; 0.35 1.3378 1.3875 1.3875 1.3984 1.3582 1.341; 0.35 1.346 1.407 1.407 1.4201 1.3774 1.3587; 0.35 1.2964 1.3664 1.3664 1.3811 1.3376 1.3181; 0.35 1.1918 1.2676 1.2676 1.2833 1.2409 1.2212; 0.35 1.0376 1.1156 1.1156 1.1315 1.0919 1.0731; 0.35 0.8429 0.9187 0.9187 0.9341 0.899 0.882; 0.35 0.6215 0.6904 0.6904 0.7042 0.6754 0.661; 0.35 0.3932 0.4503 0.4503 0.4616 0.4405 0.4295; 0.35 0.1861 0.2388 0.2388 0.2237 0.1983 0.1785; 0.35 0.0931 0.0718 0.0718 0.0287 0.0287 0.0111; 0.35 0.0113 0.0087 0.0087 0.0065 0.0057 0.0052; 0.35 0.0393 0.0192 0.0192 0.0262 0.0255 0.015; 0.35 0.3998 0.2689 0.2689 0.228 0.1987 0.2379; 0.35 0.8441 0.5843 0.5843 0.5149 0.4813 0.4294; 0.35 1.2873 0.897 0.897 0.7901 0.7396 0.6452; 0.35 1.6401 1.1686 1.1686 1.0378 0.9781 0.8664; 0.35 1.836 1.3647 1.3647 1.2333 1.1796 1.0693; 0.35 1.8347 1.4621 1.4621 1.3587 1.3297 1.2438; 0.35 1.6334 1.4544 1.4544 1.4063 1.4202 1.3809; 0.35 1.3879 1.3938 1.3938 1.3985 1.4512 1.4565; 0.35 1.3795 1.3798 1.3798 1.381 1.4294 1.4345; 0.35 1.3114 1.3063 1.3063 1.3041 1.3464 1.3512; 0.35 1.1864 1.1763 1.1763 1.1709 1.2057 1.2099; 0.35 1.0102 0.9962 0.9962 0.9883 1.0144 1.0179; 0.35 0.7935 0.7771 0.7771 0.7676 0.7845 0.7871; 0.35 0.5532 0.5364 0.5364 0.5264 0.5346 0.5363; 0.35 0.3147 0.3 0.3 0.2912 0.2922 0.2931; 0.35 0.1144 0.1051 0.1051 0.0995 0.0969 0.0971; 0.35 0.0602 0.0267 0.0267 0.0202 0.0185 0.0198]
Program usage name

C_D_matrix
Evaluatable

Yes

# Number of blade elements — number of blade elements

Details

The number of blade elements per blade.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Tabulated data for airfoil lift and drag coefficients.

Default value

20
Program usage name

blade_element_count
Evaluatable

Yes

Environment and Dynamics

# Output thrust — turbine engine thrust simulation option

Details

By checking this box, you can simulate the thrust forces acting on the turbine. Checking this box activates the T port.

Default value

false (switched off)
Program usage name

enable_thrust_output
Evaluatable

No

# Model inertia — inertia modeling option

Details

Setting this flag allows you to simulate inertia caused by the movement of the rotor. The block applies inertia at the R port.

Default value

false (switched off)
Program usage name

enable_inertia
Evaluatable

No

# Air density — air density
kg/m^3 | g/m^3 | g/cm^3 | g/mm^3 | lbm/ft^3 | lbm/gal | lbm/in^3

Details

Constant air density.

Units

kg/m^3 | g/m^3 | g/cm^3 | g/mm^3 | lbm/ft^3 | lbm/gal | lbm/in^3
Default value

1.225 kg/m^3
Program usage name

rho_air
Evaluatable

Yes

# Rotor inertia — inertia of the wind turbine rotor
kg*m^2 | g*m^2 | kg*cm^2 | g*cm^2 | lbm*in^2 | lbm*ft^2 | slug*in^2 | slug*ft^2

Details

Inertia of the wind turbine rotor.

Dependencies

To use this option, check the box Model inertia.

Units

kg*m^2 | g*m^2 | kg*cm^2 | g*cm^2 | lbm*in^2 | lbm*ft^2 | slug*in^2 | slug*ft^2
Default value

3.5e7 kg*m^2
Program usage name

I_rotor
Evaluatable

Yes

# Initial rotor rotational velocity — initial angular velocity of the rotor
rad/s | deg/s | rad/min | deg/min | rpm | rps

Details

The initial rotation speed in the port is R.

Dependencies

To use this option, check the box Model inertia.

Units

rad/s | deg/s | rad/min | deg/min | rpm | rps
Default value

0.0 rad/s
Program usage name

w_start
Evaluatable

Yes

Advanced

# Wind velocity threshold — threshold value for smoothing wind speed
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

The wind speed at which the block applies smoothing.

Units

m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn
Default value

0.01 m/s
Program usage name

v_threshold
Evaluatable

Yes

# Rotational velocity threshold — threshold value for smoothing angular velocity
rad/s | deg/s | rad/min | deg/min | rpm | rps

Details

The rotation speed at which the block applies smoothing. This parameter smooths out the torque and power when the rotation speed approaches 0 or crosses it. As the value of this parameter increases, the block applies more smoothing over wider speed ranges.

Units

rad/s | deg/s | rad/min | deg/min | rpm | rps
Default value

0.01 rad/s
Program usage name

w_threshold
Evaluatable

Yes

Literature

  1. Buhl Jr., Marshall L. «New Empirical Relationship between Thrust Coefficient and Induction Factor for the Turbulent Windmill State». National Renewable Energy Lab (NREL), Golden, CO (United States), No. NREL/TP-500-36834 (2005).

  2. Jain, Palash, Jayant Sirohi, and Christopher Cameron. «Design, Analysis, and Testing of a Passively Deployable Autorotative Decelerator». Journal of Aircraft 59, no. 1 (January 2022): 272–277. https://doi.org/10.2514/1.C036509.

  3. Jonkman, Jason. «Definition of a 5-MW Reference Wind Turbine for Offshore System Development». National Renewable Energy Lab (NREL), Golden, CO (United States), No. NREL/TP-500-38060 (2009).

  4. Manwell, J. F., J. G. McGowan, and A. L. Rogers. Wind Energy Explained: Theory, Design and Application. 1st ed. Wiley. 2009. https://doi.org/10.1002/9781119994367.