# Wind Turbine (Mechanical)

**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

$${C}_{p}=tablelookup\left({\beta}_{Ref},{\lambda}_{Ref},{C}_{p,Ref},\beta ,{\lambda}_{smooth},\text{interpolation=linear,extrapolation=nearest}\right),$$

where:

*β*is the reference pitch angle._{Ref}*λ*is the reference tip speed ratio._{Ref}*C*is the_{P,Ref}**Power coefficient table**parameter.*λ*is the smoothed tip speed ratio._{Smooth}

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 *V _{Thr}* 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 = πr*.^{2}

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:

*C*is the peak power coefficient. This is the maximum value in the_{P,max}**Power coefficient table, Cp(β,TSR)**parameter.*V*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._{rated}*A*is the rotor swept area, where*A = πr*.^{2}

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.

## Examples

## Assumptions and Limitations

The block generates power only for positive angular velocities.

## Ports

### Inputs

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2023a**