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:

../../examples/example_linear.py

"""
example python scripts for the linear 'simple' scaling to an average value
"""
from tssm import DAILY, MONTHLY, WEEKLY, YEARLY
from tssm import TimeSeriesScalingModule as tssm


def main() -> None:
    """
    main function to show linear scaling examples
    """
    # initialize class with a number of buildings of 202 with a simultaneity factor of 0.786
    scaling_module = tssm(202, 0.786)
    # read profile from data.csv file and use the Electricity column
    scaling_module.data.read_profile_from_csv_with_date("./data.csv", "Electricity", "Date")
    # calculate linear scaled values with a daily simultaneity factor and average value
    daily_scaled_values = scaling_module.calculate_using_average_values(DAILY)
    # print results
    print(f"daily_scaled_values: {daily_scaled_values}")
    # calculate linear scaled values with a weekly simultaneity factor and average value
    weekly_scaled_values = scaling_module.calculate_using_average_values(WEEKLY)
    # print results
    print(f"weekly_scaled_values: {weekly_scaled_values}")
    # calculate linear scaled values with a monthly simultaneity factor and average value
    monthly_scaled_values = scaling_module.calculate_using_average_values(MONTHLY)
    # print results
    print(f"monthly_scaled_values: {monthly_scaled_values}")
    # calculate linear scaled values with a yearly simultaneity factor and average value
    yearly_scaled_values = scaling_module.calculate_using_average_values(YEARLY)
    # print results
    print(f"yearly_scaled_values: {yearly_scaled_values}")
    # use a given scaling factor
    # calculate linear scaled values with a daily simultaneity factor and average value using a given scaling factor
    daily_scaled_values_given_scaling_factor = scaling_module.calculate_using_average_values(DAILY, scaling_factor=[0.861] * 365)
    # print results
    print(f"daily_scaled_values_given_scaling_factor: {daily_scaled_values_given_scaling_factor}")
    # calculate linear scaled values with a weekly simultaneity factor and average value using a given scaling factor
    weekly_scaled_values_given_scaling_factor = scaling_module.calculate_using_average_values(WEEKLY, scaling_factor=[0.861] * 53)
    # print results
    print(f"weekly_scaled_values_given_scaling_factor: {weekly_scaled_values_given_scaling_factor}")
    # calculate linear scaled values with a monthly simultaneity factor and average value using a given scaling factor
    monthly_scaled_values_given_scaling_factor = scaling_module.calculate_using_average_values(MONTHLY, scaling_factor=[0.861] * 12)
    # print results
    print(f"monthly_scaled_values_given_scaling_factor: {monthly_scaled_values_given_scaling_factor}")
    # calculate linear scaled values with a yearly simultaneity factor and average value using a given scaling factor
    yearly_scaled_values_given_scaling_factor = scaling_module.calculate_using_average_values(YEARLY, scaling_factor=[0.861])
    # print results
    print(f"yearly_scaled_values_given_scaling_factor: {yearly_scaled_values_given_scaling_factor}")
    # new init module to downscale the profile to the original one
    scaling_module_down = tssm(202, 0.786, one_2_many=False)
    # read profile from data.csv file and use the Electricity column
    scaling_module_down.data.read_profile_from_csv_with_date("./data.csv", "Electricity", "Date")
    # overwrite original profile to the up-scaled values
    scaling_module_down.data.original = daily_scaled_values
    # calculate linear scaled values with a daily simultaneity factor and average value
    daily_scaled_values_downscaled = scaling_module_down.calculate_using_average_values(DAILY)
    # compare sums to show that the profiles are equal
    print(f"Sum of original profile {scaling_module.data.original.sum():_.0f} and downscaled {daily_scaled_values_downscaled.sum():_.0f}")


if __name__ == "__main__":
    main()