*5.1. Scenarios of Loading*

Figure 5 shows the scenarios generated based on the historical loading data of the transformer and the scheduled demand for the following day based on the day-ahead dynamic price, as supplied by the aggregator. First, a set of 1000 scenarios are generated using Gaussian copula to represent the correlation among different time steps based on the data of previous one month. In order to simplify the calculation, this set of scenarios is reduced to 20 that closely represent the behavior of all the members of the set. Figure 5c shows that the set of reduced scenarios can capture the dynamics of all the time steps of the following day based on the day-ahead price. Thus, the set of reduced scenarios can address the uncertainties with the loading of the following day.

**Figure 5.** Transformer loading, (**a**) historical values of one month previous and based on scheduled loads for the following day, (**b**) generated scenarios based on Gaussian copula to represent the correlation and (**c**) reduced scenarios and the scheduled load.
