# A Novel Virtual Power Plant Uncertainty Modeling Framework Using Unscented Transform
## 5 Methodology  
In this paper, the UT is used to manage the uncertainties related to variable renewable energy production and intermittent power demands. The UT is applied to create a forecasting method for power generation and demand minute-by-minute, allowing both current and forecasted energy to be treated as random variables in a 1-day future.  
In order to verify the effectiveness of the model, the very simple and effective persistence method is used. Equation (9) defines the persistence forecast in which the index is assumed to remain constant, relative to the previous step. This technique tends to perform better on small time scales (e.g., minutes) than larger time scales (e.g., hourly and daily). Persistence assumes that conditions will remain constant, relative to the previous stage of the forecast.  
\[P(t+\Delta t)=kt(t)\ P_{o}(t+\Delta t) \tag{10}\]  
The UT method and the persistence of two days of input data are used. The methodology is applied to all VPP users, after which, the result with the errors is compared with the third day of reference data for the model. The third day is for comparison and analysis of the model between the two methodologies.  
To further illustrate the methodology, we randomly choose a load to present, and then all are similarly solved. The findings are presented in Table 1, below, with their proper comparisons. In Figure 8, the proposed methodology uses the UT. It applies to the minute historical data over the 2 days. The answer is a forecast that contains an interval range of UT+ and UT\(-\), which is the predictability gap where the demand will be inserted.  
Figure 6: Electricity demand (low voltage).  
Figure 7: Total Generation and Total Electricity Demand.  
The available historical data are data from loads and generations that were chosen arbitrarily, from an observational point of view. The three midweek days are considered for use in the simulation. All data are separated into independent days, day 1 has data from 1 to 1440, day 2 has data from 1441 to 2880 and day 3 has data from 2881 to 4320, in such a way that to simulate the chunk UT and persistence uses only 2 days, the first and second, respectively, which, after running their algorithms, will generate the third day as results that will be compared with the real data.  
After applying the UT methodology, the historical reference data of the three days are used to compare and verify the prediction error in the UT interval, as shown in Figure 9.  
Figure 10 shows the persistence of the third day using 2 days of historical data.  
After persistence is applied, the three-day historical data are compared and verified for the error, as shown in Figure 11.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**0.22 kV** & **UT** & **Persistence** \\ \hline Home 1 & 2.3\% & 7.3\% \\ Home 2 & 0.4\% & 4.5\% \\ Home 3 & 0.5\% & 7.5\% \\ Home 4 & 1.9\% & 4.1\% \\ Home 5 + EV & 0.23\% & 3.3\% \\ \hline PV 1 & 2.8\% & 3.5\% \\ PV 2 & 5.9\% & 11.3\% \\ PV 3 & 0.7\% & 8.8\% \\ Condominium & 0\% & 1.8\% \\ Shopping Mall & 0.6\% & 2.1\% \\ Electric Vehicle & 25.2\% & 39.3\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Daily Forecast Errors.  
Figure 8: UT applied in home 1 demand.  
Finally, Figure 12 shows the comparison of prediction errors in the UT and persistence.  
In Figure 12, one can visibly verify the low proportion of error of the UT method in relation to persistence. The errors presented in this specific case for house 1 connected to the 220 V system were 2.3% for the UT and 7.3% for persistence.  
Figure 11: Persistence applied on demand forecasting plus error.  
Figure 9: UT applied on demand house 1 plus error.