# Rotor

The rotor part is composed of the Hub, the blades and the pitch actuators..

## 1 Parameters

The number of blades of the rotor (typically 2 or 3 - max value is 30)

• Default value: 3
• Unit:
• Range: 0 — 30

#### Cone angle

The angle between the rotor's plane of rotation and the direction of the blades. A positive angle cones the blades "forward", towards the wind direction.

• Default value: 2.5
• Unit: $°$
• Range: -80 — 80

#### Pitch actuator mode

The requested pitch angles determined by the pitch controller can be applied to the blade structure in several ways.

Options:

PID controller:

Will apply a torque at the root of the blades about the pitch axis. The magnitude of this torque is determined by the pitch actuator gains.

Python script:

Use a Python script, see Python script controller

No structural pitch (default):

Causes the blade structure to remain in its initial pitch orientation. However, the aerodynamic loads on the blades are affected by the pitch angle.
This option does not have an effect if stiff blades are used.

#### Pitch rotational inertia

The rotational inertia (i.e angular mass) of the blade about the pitch axis. This value is relevant when tuning the pitch actuator gains.

• Default value: 28600
• Unit: $\text{kg}\cdot\text{m}^2$
• Range: 0 — 1e+08

#### Reference actuator torque

The reference torque that the actuator will apply at the root of the blade when pitching. This value is multiplied by the output of the PID.

• Default value: 5e+06
• Unit: $\text{N}\cdot\text{m}$
• Range: 0 — 1e+08

#### Proportional gain

The factor that the pitch error will be multiplied by when computing the pitch actuator torque.

• Default value: 1
• Unit: ${1} \over {\text{rad}}$
• Range: -1e+07 — 1e+08

#### Integral gain

The factor that the integral of the pitch error will be multiplied by when computing the pitch actuator torque.

• Default value: 2
• Unit: ${1} \over {\text{rad}\cdot\text{s}}$
• Range: -1e+07 — 1e+08

#### Derivative gain

The factor that the time derivative of the pitch error will be multiplied by when computing the pitch actuator torque.

• Default value: 0.25
• Unit: ${\text{s}} \over {\text{rad}}$
• Range: -1e+07 — 1e+08

#### Reduction factor for structural data

This number of structural stations (location along the blade with given structural properties) are averaged into one station (i.e. a value of 2 will half the number of structural stations ).

• Default value: 1
• Unit:
• Range: 1 — 200

#### Structural scale factor

This factor scales the blade stiffness up or down

• Default value: 1
• Unit:
• Range: 0.001 — 10000

#### Torsional inertia factor

The torsional inertia of each finite element of the blade will be multiplied by this value.

• Default value: 1
• Unit:
• Range: 1e-99 — 1e+99

#### Target Cp

The target efficiency (Cp) of the rotor as a percentage of the incoming power. The maximum calue is Betz' limit: 16/27 = 59.3% Typically in the area 40-55% for a well designed blade. This value is only used for calculating rotor info, and not used in any simulation.

• Default value: 49
• Unit: $\text{%}$
• Range: 1 — 59.3

#### Target rated rpm

The target rated rpm of the rotor. Typically in the area 10 - 14 rpm for a utility scale wind turbine (2-10 MW). This value is used for calculating rotor info, and not used in any simulation. It is also used to calculate gear box ratio if the 'Ratio scheme' is 'From generator'. It is useful when using Ashes to make a new WT design or change an existing one. Thus, a typical use case is the initial stage of a project when there are several alternatives to use for WT rating. A representative WT can then quickly be designed to be used in preliminary design of sub structr

• Default value: 12
• Unit: $\text{rpm}$
• Range: 1 — 10000

#### Target cut-in rpm

The target cut-in rpm is the minimum operational rpm. Cut-in rpm is where the the WT starts producing power and corresponds to the cut-in wind speed. This parameter is called 'target' as it is only used to calculate rotor info about the corresponding intervals for 1P and nP frequencies (and periods) and is not used for any simulation.

If it is set greater than the Target rated rpm parameter, then it autimatically is reduced to be equal.

This parameter is not shown if the number of blades is zero.

This parameter does not necessarily correspond to the actual generator cut-in rpm. However, the user can (and it is generally recommended to) manually set this parameter to the actual cut-in rpm of the generator.

The default value is the cut-in rpm of the NREL 5MW ref. WT.

• Default value: 6.9
• Unit: $\text{rpm}$
• Range: 0 — 10000

## 2 Information Pane

The rotor Information pane contains general information about the characteristics of the rotor.

### 2.1 Required/ rated characteristics

This information is very relevant when it comes to designing a new rotor, as it gives an indication of the characteristics of the Generator and the Gearbox for the turbine to match certain requirements. This is typically useful when modifying the characteristics of the rotor, to make sure that they match the characteristics of the Generator and the Gearbox.

#### 2.1.1 Example 1

For the NREL 5 MW rotor, the rated RPM is 12.1 RPM. If a rated RPM of 10 was required, changing the value of Target rated RPM in the Advanced parameters of the rotor would modify the Information pane and show the gearbox ratio or the rated Generator RPM necessary to achieve the new RPM of the rotor.

#### 2.1.2 Example 2

In this example we try to define an 8 MW wind turbine with blades upscaled from the NREL 5 MW blades. These new blades are 79.84 m long. If I use these 8 MW blades instead of the default NREL 5 MW blades, in order to design the whole turbine accordingly, the workflow is:
2. Go to the Generator part and modify the rated power to 8 MW
3. Check the Rotor characteristics and establish the optimal TSR (in this case 8) and optimal Cp (in this case 49%)
4. Insert the optimal Cp in the Target Cp parameter
5. Based on the Cp, the rated power and the swept area of the rotor, Ashes will establish the required rated wind speed (for example 11.08 m.s-1)
6. Based on this wind speed, the optimal TSR and the rotor radius (in this case, accounting for the hub radius and the cone and tilt angle, Ashes gives a radius of 81.26 m), establish the rated RPM (in this case 10.41)
7. Enter the rated RPM in the Target rated RPM parameter
8. The information pane will tell you which values can be input to the Generator rated RPM (in this case 1010) or to the Gearbox ratio (in this case 112.7) so that their characteristics match those of the rotor
9. Modify the characteristics of the Generator or the Gearbox
Note that you still have to modify the dimensions of the turbine (for example the tower length or the nacelle mass) to match the specifications of the new rotor.

#### 2.1.3 Suggested time step

The Suggested maximum timestep is calculated so that at rated RPM, the rotor does not rotate more than 2 degrees during one time step. It is thus given by
$$t_s = \text{floor}\left(\frac{2}{\omega_R}\right) = \text{floor}\left(\frac{2\cdot60}{RPM_g/G\cdot360}\right)$$

where
• $$\omega_R$$
is the rated speed in degrees per second
• $$RPM_g$$
is the rated generator speed, in rotations per minute
• $$G$$
is the gearbox ratio
For example, for the NREL 5-MW wind turbine, which has a rated generator speed of 1173.7 RPM and a gearbox ratio of 97, the suggested time step is 0.027 sec.

### 2.2 Wind speed table

The Information pane of the rotor gives a table with characteristics of the rotor for different wind speeds. The different column of the table are explained below:

 Wind Wind speed for which the characteristics are given TSR Tip speed ratio corresponding to the rated RPM and the given wind speed Betz Maximum power extractable from the wind according to Betz law (i.e. assuming that the Cp of the rotor is equal to Bezt limit, 16/27) Req. eff Gives the efficiency required to produce the rated power and what percentage of the Bezt limit that corresponds to. Note that no value is given if an efficiency higher than the Betz limit is required. X% Gives the power produced at that wind speed assuming the target Cp (without pitching the blades)