## 4 Results and Discussion
### Comparison Between the Training and Synthetic Data
#### 3.2.2 Case Study 2: Generation of Synthetic Power Consumption Data for a Pig Farm  
A similar comparison was performed for the pig farm dataset. Once again, the number of states varied between 10 and 26, and for each one, steps 2, 3.1, and 3.2 from the methodology were implemented. The results from the analysis are summarized in Figure 10. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Metric**} & **Synthetic Data** & **Synthetic Data** & **Synthetic Data** \\  & **with 12 States** & **for 18 States** & **for 24 States** \\ \hline \hline Average Frobenius distance of the & & 0.22 & 0.31 & 0.46 \\ hourly matrices (Favg h) & & 0.08 & 0.15 & 0.43 \\ Average Frobenius distance of the & & & \\ hour-change matrices (Favg h-ch) & & & \\ Average \(R^{2}\) of the hourly matrices & & & \\ Average \(R^{2}\) of the hour-change & & & \\ matrices (R\({}^{2}\).avg h-ch) & & & \\ Relative error of the variance & & & \\ (\(\sigma^{2}\).rel.diff) & & & \\ Relative error of the standard & & & \\ deviation (\(\sigma\).rel.diff) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between the metrics of the three generated datasets of the domestic consumer with 12, 18, and 24 states. Figure 8: Dependency of the average Frobenius distances, average \(R^{2}\)s, relative difference of the variance, and standard deviation for the investigated number of states of the synthetic data for a domestic house. It can be seen that the lowest average hourly Frobenius distances were achieved for 10, 11, and 12 states, though there was also a minimum at 17 states and 23 states. Similarly, the lowest average hour-change Frobenius distances were achieved at 10, 11, and 12 states, and local minimums can be observed at 17 and 24 states. The average hourly and hour-change \(R^{2}\) values also had the highest values at 10, 11, and 12 states, yet local maximums can be observed at 17, 23, and 24 states. Regarding the statistical measures, the relative difference of the variance had a minimum at 21 states, and local minimums at 14 and 23 states. Similarly, the relative difference of the standard deviation had a minimum at 15, 16, and 17 states and local minimums at 19, 22, and 24 states. However, it should be noted that the relative errors in all cases were below 5%. Figure 9: Seven days of sample data from the original time series for a house (**a**) and from the generated synthetic data with 12 states (**b**), 18 states (**c**), and 24 states (**d**). Once again, there is no ideal number of states for which all measures are optimal, and therefore, the following situations were further investigated (Table 3):  
* the generated data with 12 states, for which all measures except for the variance have near-optimal values;
* the generated data for 17 states, for which all measures except the variance have a local peak value;
* the generated data for 23 states, for which there are local peak values for the Frobenius distances, \(R^{2}\), and the variance. It can be seen that for the investigated agricultural consumer, the probabilistic metrics generally increased with the number of states, though the relative error of the variance decreased. Therefore, to better understand the difference between the selected scenarios, seven days of data were generated for each one of them to perform a visual comparison (Figure 11). It can be visually observed that in all cases, the generated data greatly resembled the original one; nevertheless, with the increase in the number of states, the scattering of the data was lower and better matched the original dataset. This allowed us to make the conclusion that when the evaluation metrics are similar, the scenario with higher number of states should be preferred. Figure 10: Dependency of the average Frobenius distances, average \(R^{2}\)s, relative differences of the variance, and standard deviation for the different number of states of the synthetic data of a pig farm.