# On the Use of LoRa Technology for Logic Selectivity in MV Distribution Networks
## 7 Experimental Tests
### 50.S3 Poly-Phase Short Circuit (Threshold 600 A)  
According to Table 9, the maximum clearing time for the non-directional short-circuit fault 50.S3 is 120 ms. Consequently, considering a fault detection time \(T_{D}\) of 27 ms and a trip time \(T_{TRIP}\) of 60 ms, there is a maximum time interval \(T_{MBW}\) of 33 ms, after which the PR has to command the tripping of the CB if it has not received a Blind message. Therefore, in this case, the timer associated with the protection relay can be set to 33 ms to take advantage of all the useful time.  
The time \(T_{MBW}\) sets a constraint on the maximum \(T_{packet}\) of the LoRa package and, as stated above, the larger the \(T_{packet}\), the greater the allowed SF, which implies a better receiver sensitivity and a wider communication range.  
For the considered case, the \(T_{packet}\) associated with the Blind message, together with the processing time, must not exceed 33 ms. Since, as described in Section 5, \(T_{packet}\) depends on numerous parameters, for all the tests considered, only the parameters BW and SF were varied. The parameters that have no direct influence on the receiver sensitivity values and link budget were set to the typical values of the LoRa transmission. In particular, the authors chose the following configuration:  
* CR = 1,
* PL = 4 bytes,
* Total preamble of 12.25 symbols,
* header explicit,
* CRC enabled.  
According to these parameters, different combinations of BW and SF leads to the \(T_{packet}\) values shown in Table 10.  
All the \(T_{packet}\) values highlighted in green are lower than 33 ms, and the corresponding SF and BW configuration can be used for the 50.S3 fault. The unacceptable times, corresponding to the configurations to be discarded, are highlighted in red. It can be noticed that the pairs of SF and BW equal to (7;125), (8;250), and (9;500) result in a \(T_{packet}\) of 30.98 ms. Even if this time interval is lower than the allowable \(T_{MBW}\), these configurations leave a margin of only 2 ms to perform all other necessary processing (apart from eventual deviation of the actual \(T_{packet}\) from the nominal value); so, these pairs of SF and BW were discarded. The configurations that guarantee the correct functioning of the logic are those obtained with the pair (7;500), which returns a nominal \(T_{packet}\) of 7.74 ms, and the pairs (7;250)  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & \multicolumn{3}{c}{**SF**} \\ \hline
**BW** & **7** & **8** & **9** & **10** & **11** & **12** \\ \hline
125 & 30.98 & 51.71 & 103.42 & 209.85 & 413.70 & 827.39 \\ \hline
250 & 15.49 & 30.98 & 51.71 & 103.42 & 209.85 & 413.70 \\ \hline
500 & 7.74 & 15.49 & 30.98 & 51.71 & 103.42 & 209.85 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Values of \(T_{packet}\) in ms depending on BW and SF, with CR = 1, CRC disabled, and implicit header. The red color indicates values of the table that are not feasible. The green color indicates values of the table that are feasible.  
and (8;500) that give a nominal \(T_{packet}\) of 15.49 ms. The latter are those that give a receiver sensitivity of \(-120\) dBm and thus ensure the highest possible link budget for this type of fault. The configuration (7;500), instead, provides a higher receiver sensitivity, \(-117\) dBm, and, therefore, a reduced link budget. This means that the SF and BW pairs (7;250) and (8;500) allow for longer distance coverage.  
As a case study for performing the tests regarding the fault 50.S3, the values SF = 7 and BW = 250 were set. As an example, Figure 9 shows the time-frequency diagram obtained by acquiring one of the LoRa packets through the Tektronix real-time spectrum analyzer RSA 3408A.