# Stepwise wind

The Stepwise wind can be selected in the Atmosphere part, and can be either defined by parameters within Ashes or by an external file.

## 1 Parameter based

The parameters to define a stepwise wind are explained in the User Manual, in the Stepwise wind section. The parameters necessary to define the magnitude of the wind speed at hub height
$$V_{hub}$$
of a stepwise wind are
• the start speed
$$V_0$$

• the end speed
$$V_e$$
• start-up duration
$$T_0$$

• number of steps
$$N$$
• step duration
$$T_{s}$$
The role of these parameters is illustrated in the following figure:

The magnitude of the wind speed is then given by the following equation:

$$V_{hub}=\left\{\begin{array}{lll} V_0&\text{for}&t{<}T_0\\ V_0+i\cdot\frac{V_e-V_0}{N}&\text{for}&T_0+(i-1)T_s\leq t {<} T_0+iT_s\text{ and }i=[1,2...N]\\ V_e&\text{for}&t\geq T_e\end{array}\right.$$

The same equation applies for the Wind angle
$$\alpha$$
,  replacing the start speed
$$V_0$$
and the end speed
$$V_e$$
with the start angle
$$\alpha_0$$
and the end angle
$$\alpha_e$$
, respectively:
$$\alpha=\left\{\begin{array}{lll} \alpha_0&\text{for}&t{<}T_0\\ \alpha_0+i\cdot\frac{\alpha_e-\alpha_0}{N}&\text{for}&T_0+(i-1)T_s\leq t {<} T_0+iT_s\text{ and }i=[1,2...N]\\ \alpha_e&\text{for}&t\geq T_e\end{array}\right.$$

Note: the is no interpolation at all performed for stepwise winds, any quantity (wind speed or wind angle) will change within one stime step. Linearly interpolated wind can be defined with the Linear wind part.

## 2 Input file based

When importing a stepwise wind from file, the format consists of three columns. Details of how to define an input file for stepwise wind can be found in the User Manual under the Stepwise wind file section. The figure below illustrates such a file:

$$\begin{array}{lll} \text{# Time}&\text{Wind speed}&\text{Wind angle}\\ 0&V_1&\alpha_1\\ T_2&V_2&\alpha_2\\ \vdots&\vdots&\vdots\\ T_N&V_N&\alpha_N\\ \end{array}$$

Note: the first temporal coordinate must be equal to 0.

The wind speed at hub height
$$V_{hub}$$
applied during the simulation is then defined as

$$V_{hub}=\left\{\begin{array}{lll} V_1&\text{for}&t{<}T_2\\ V_i&\text{for}&T_i\leq t {<}T_{i+1}\text{ and }i=[2,3...N]\\ V_N&\text{for}&t\geq T_N\\ \end{array}\right.$$

Similarly, the Wind angle
$$\alpha$$
is defined as

$$\alpha=\left\{\begin{array}{lll} \alpha_1&\text{for}&t{<}T_2\\ \alpha_i&\text{for}&T_i\leq t {<}T_{i+1}\text{ and }i=[2,3...N]\\ \alpha_N&\text{for}&t\geq T_N\\ \end{array}\right.$$

Note: there is no interpolation at all performed for stepwise winds, any quantity (wind speed or wind angle) will change within one time step. Linearly interpolated wind can be defined with the Linear wind part.