Linear approach

The linear approach is scaling the original profile ( $P_{original}^t$ ) of the current time step ( $t$ ) to the mean value for the selected period ( $P_{mean}^{f(t)}$ ). It is linearly interpolated using the scaling factor ( $S^{f(t)}$ ). Therefore, the scaling factor and average value have to be assigned to the current time step. This is illustrated by $f(t)$ . For Example if a monthly period is considered the average value array has 12 entries. So one of these 12 entries has to be assigned to the current time step. All time steps in january are referred to the first entry, all time steps in february to the second entry, and so on.

$P_{new}^t = P_{original}^t \cdot S^{f(t)} + P_{mean}^{f(t)} \cdot \left(1 - S^{f(t)}\right)$

The scaling factor ( $S^{k}$ ) can either be provided by the user or calculated based on the simultaneity factor ( $SF$ ). Therefore the maximum of the original values ( $P_{original}$ ) for all time steps in the current period ( $k$ , $A$ ) and the average value have to be determined.

$S^{k} = \frac{SF \cdot \max(P_{original}^i \forall i \in A) - \overline{P_{original}^i \forall i \in A}}{\max(P_{original}^i \forall i \in A) - \overline{P_{original}^i \forall i \in A}}$

As periods can be selected a daily (1), a weekly (2), a monthly (3) or a yearly (4) one. An example code is shown below: