# Wind Turbine (Mechanical)

Turbine that converts wind kinetic energy into mechanical power

Since R2023a

• Libraries:
Simscape / Electrical / Electromechanical

## Description

The Wind Turbine (Mechanical) block represents a wind turbine that converts the kinetic energy of the wind into mechanical power. The power of the turbine depends on the nondimensional power coefficient Cp. You can tabulate this coefficient with blade pitch angle and tip speed ratio by specifying the Power coefficient table, Cp(β,TSR) parameter.

The values at the physical signal ports V and β represent the wind speed and the collective blade pitch. Port R models the mechanical rotational conserving port associated with the shaft.

### Equations

The block calculates the coefficients of power by using a table lookup such that

where:

• βRef is the reference pitch angle.

• λRef is the reference tip speed ratio.

• CP,Ref is the Power coefficient table parameter.

• λSmooth is the smoothed tip speed ratio.

The block uses this equation as the basis for the instantaneous tip speed ratio

`$\lambda =\frac{R\omega }{V},$`

where:

• R is the Turbine radius parameter.

• ɷ is the differential angular velocity between the shaft and the case.

• V is the incident air velocity on the rotor. This value is the physical signal input port V.

The block uses this equation to describe the smoothed version of the instantaneous tip speed ratio equation

`${\lambda }_{Smooth}=\frac{R\omega V}{\left({V}^{2}+{V}_{Thr}^{2}\right)},$`

where VThr is the Wind speed threshold parameter. The block uses this equation as a basis for the power

`$Power=\frac{1}{2}{C}_{p}\rho A{V}^{3}=Torque\cdot \omega ,$`

where:

• ρ is the Air density parameter.

• A is the area of the circle swept by the turbine blades, and A = πr2.

To relate the block parameters to the wind turbine mechanical power rating, determine the wind turbine power at the peak power coefficient and the rated wind speed. The rated power corresponds to the block parameters using the equation

`$Powe{r}_{rated}=\frac{1}{2}{C}_{P,\mathrm{max}}\rho A{V}_{rated}^{3},$`

where:

• CP,max is the peak power coefficient. This is the maximum value in the Power coefficient table, Cp(β,TSR) parameter.

• Vrated is the rated wind speed. Rated wind speeds are typically 10 to 15 m/s. The designs of wind turbine controller can alter strategy at this wind speed to maintain the rated power.

• A is the rotor swept area, where A = πr2.

The block uses numerically smoothed equations for the power, such that

`$Powe{r}_{Smooth}=\frac{{C}_{P}\rho A{\left({V}^{2}+{V}_{thr}^{2}\right)}^{3/2}}{2}.$`

### Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Use nominal values to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources. One of these sources is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

## Assumptions and Limitations

The block generates power only for positive angular velocities.

## Ports

### Inputs

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Physical signal input associated with the incident wind velocity, in m/s.

Physical signal input associated with the pitch angle of the turbine blades, in deg.

### Conserving

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Mechanical rotational conserving port associated with the wind turbine shaft.

## Parameters

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### Main

Distance from the turbine hub center to the blade tips.

Reference collective blade pitch angle. The length of this vector defines the number of rows in the Power coefficient table, Cp(β,TSR) parameter.

Reference tip speed ratio (TSR). TSR is the ratio of the blade tip speed to wind speed. The length of this vector defines the number of columns in the Power coefficient table, Cp(β,TSR) parameter. The block supports negative TSR values. The values must be strictly monotonically increasing.

Power coefficients for a given pitch angle and tip speed ratio. Each row corresponds to an element in the Pitch angle vector, β parameter, and each column corresponds to an element in the Tip speed ratio vector, TSR parameter. The default parameter value is ```[0.0010, 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, 0.1320, 0.1256, 0.0120, -0.1752, -0.4017, -0.6435, -0.7655; -0.01 * ones(1, 9)]```.

Threshold velocity smoothing location. This parameter smooths the torque, thrust, and power when the rotational speed approaches or crosses 0. The block applies more smoothing over greater velocity ranges as you increase the value of this parameter.

Threshold velocity smoothing location. This parameter smooths the torque, thrust, and power when the rotational speed approaches or crosses 0. The block applies more smoothing over greater velocity ranges as you increase the value of this parameter.

Constant density of air.

### Mechanical

Whether to model the rotor inertia of the mechanical translational port R.

Inertia of the rotor attached to mechanical translational port R.

#### Dependencies

To enable this parameter, select the Include inertia parameter.

Damping of the rotor.

## Version History

Introduced in R2023a