# Colored Petri Net Modelling and Evaluation of Drone Inspection Methods for Distribution Networks
## 4 Results
### Determining a UAV Grouping Method  
As an example of model-based system design improvement, it is possible to check the results obtained for the task described in Section 4.1 by changing the monitoring scheme. In Table 4, the section of the object \(P\)3-_P_8 has the highest monitoring frequency which is almost three times higher. This is an obvious hint of an unbalanced system configuration. It can be explained by the short distances between checkpoints \(P\)3-_P_7 and \(P\)7-_P_8 (Table 3). Assume we do not want to change the number and the type of drones. We will expand section \(P\)3-_P_8 by adding segment \(P\)3-_P_4 or \(P\)2-_P_3 to balance the allocation of resources. For the first option, the responsibilities of the drones are shared as \(P\)0-_P_3, \(P\)4-_P_6 and \(P\)4-_P_8. The result of the simulation is shown in Table 5. The distribution of the monitoring frequencies has become more balanced, but the minimum frequency is still around 1.5. For the second option, the responsibilities of the drones are shared as \(P\)0-_P_2, \(P\)3-_P_6 and \(P\)2-_P_8. The result of the simulation is shown in Table 6. With this monitoring scheme, it is possible to increase the minimum frequency to 1.8. This is a typical example of how model-based systems design can be used for a what-if analysis. Other monitoring scheme options will not increase the frequency of monitoring due to the arrangement of short and long sections. Thus, the second option (_P_0-_P_2, \(P\)3-_P_6 and \(P\)2-_P_8) can be considered the most suitable when three drones are used. The number of UAVs directly affects the frequency of monitoring, and its optimal choice is another typical example of systems design. Let us assume that each section is monitored by one drone. Then the number of drones needed to monitor the whole object \begin{table}
\begin{tabular}{c c} \hline \hline
**Section** & **Monitoring Frequency in a Day** \\ \hline \(P\)0–_P_2 & 2.250252 \\ \(P\)3–_P_6 & 1.875104 \\ \(P\)2–_P_8 & 2.604552 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Monitoring frequency in a day for the configurations \(P\)0–_P_2, \(P\)3–_P_6 and \(P\)2–_P_8. \begin{table}
\begin{tabular}{c c} \hline \hline
**Section** & **Monitoring Frequency in a Day** \\ \hline \(P\)0–_P_3 & 1.484486 \\ \(P\)3–_P_6 & 1.888126 \\ \(P\)3–_P_8 & 5.388123 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Monitoring frequency in a day. \begin{table}
\begin{tabular}{c c} \hline \hline
**Section** & **Monitoring Frequency in a Day** \\ \hline \(P\)0–_P_3 & 1.504622 \\ \(P\)4–_P_6 & 2.769266 \\ \(P\)4–_P_8 & 2.682439 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Monitoring frequency in a day for the configurations \(P\)0–_P_3, \(P\)4–_P_6 and \(P\)4–_P_8. will be equal to the number of sections into which it will be divided. In our example application, the object is divided into eight sections. We can easily vary parameters as well as the number of drones in our model. The results are presented in Table 7 and in Figure 7. Figure 7 represents the dependence of monitoring frequency (number of flights per day) on the number of drones for the whole object. The table represents the number of flights per day on sections between take-off and landing points. Each number corresponds to monitoring by one drone. As a route, the shortest path is assumed, i.e., if the section includes an intersection point, the drone does not visit an additional branch. This is why the lowest frequency of monitoring by one drone in Figure 7 differs from the value in Table 7 corresponding to take-off at point 0 and landing at point 8. According to the simulation results (Figure 7), if one UAV monitors the entire object, the monitoring frequency will be 0.73 times per day. This frequency is the minimum for the characteristics of the drone specified before. The highest monitoring frequency will correspond to the lowest monitoring frequency of a section, assuming that the object is divided into eight sections. Simulation results for each of these sections are shown in Table 7 in the highlighted cells.