Candidate Periods definition

The choice of representative periods is preceded by the choice of candidate periods to become representative.

We can note \(d\subset[0,T]\) these periods and group them into a set \(\mathcal{D}\).

\[\mathcal{D} = \text{ Set of candidate periods}\]

To each period \(d\) we can associate the load function normalized in absolute power:

\[\begin{split}\hat{f}_{|d}= \left\{\begin{array}{ccc} d & \longrightarrow & [0,1] \\ t & \mapsto & \frac{f(t)-f_{min}}{f_{max}-f_{min}} \end{array}\right. \text{ où } \left.\begin{array}{l} f_{min} = \underset{t\in[0,T]}{\text{min }} f(t) \\ f_{max} = \underset{t\in[0,T]}{\text{max }} f(t) \end{array}\right.\end{split}\]

Note

Potentially : \(\forall t \in d , \hat{f}_{|d}(t)>0 \text{ or } \forall t \in d , \hat{f}_{|d}(t)<1\)

We associatethe duration function:

\[\begin{split}\tilde{C}(\hat{f}_{|d}) = \left\{\begin{array}{ccc} \mathbb{R}_+ & \longrightarrow & [0,1] \\ x & \mapsto & \frac{\lambda(\{t\in d|f(t)\geq x\})}{\lambda(d)} \end{array}\right.\end{split}\]

Warning

Currently in periods, the set of candidate periods corresponds to a uniform split of the global period \([0,T]\). It means that RP_length must divide TemporalData length. A periods of 336 hours would have 7 candidate periods of 48 hours partitioning the 336 hours.

It could be possible to have overlapping candidate periods in future version.