# On the Use of LoRa Technology for Logic Selectivity in MV Distribution Networks
## 5 LoRa Technology for Logic Selectivity Implementation  
According to the constraints highlighted in Section 4, Blind messages have to reach the upstream protections before the expiration of the Maximum Blind Waiting time \(T_{MBW}\) to reliably implement the logic selectivity. The following relationship thus has to be verified:  
\[T_{packet}<T_{MBW}\Rightarrow T_{packet}<T_{FC}-T_{D}-T_{TRIP} \tag{12}\]  
\(T_{MBW}\) is determined by \(T_{FC}\), which is in turn imposed by the network operator and depends on the considered fault, and, in some cases, it may vary with the characteristics of the MV line. The \(T_{packet}\) depends on several parameters, but once the length of the preamble is fixed and the header, CR, and CRC are set, \(T_{packet}\) doubles if the SF is increased by one unit or if the bandwidth is halved. As an example, if a fault current greater than 600 A is considered, the fault has to be cleared in 500 ms; with a detection time of 27 ms and a trip time of 60 ms, a \(T_{MBW}\) equal to 413 ms is obtained. If the LoRa configurations presented in Table 5 are considered, it can be noticed that not all the combination of SF and BW are feasible. In Table 6, in fact, the \(T_{packet}\) values highlighted in red are not compliant with the allowed \(T_{MBW}\) and, so, the associated SF and BW combinations are not suitable for logic selectivity. \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 & 37.12 & 64 & 128 & 256 & 30.08 & 860.16 \\
250 & 18.56 & 32 & 64 & 128 & 215.04 & 430.08 \\
500 & 9.28 & 16 & 32 & 64 & 107.52 & 215.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values of \(T_{packet}\), in ms, versus BW and SF, with CR = 1. The red color indicates values of the table that are not feasible. The values of receiver sensitivity, shown in Table 7, also depend on the combination of SF and BW, according to Equation (8). The achievement of the condition in Equation (12) indirectly imposes a limit on the minimum receiver sensitivity and, consequently, on the maximum communication range that can be assured under these conditions. The minimum value of receiver sensitivity, equal to \(-132\) dBm, can be obtained (highlighted in bold in the table) with SF equal to \(10\) and BW of \(125\) kHz. Even lower values and, therefore, greater distances would be obtained with the SF and BW pairs that are not allowed and for which the condition in Equation (12) would not be fulfilled. These values are highlighted in red. In theory, however, it is possible to optimize the Lora packet to reduce the transmission time and further improve receiver sensitivity. As stated above, in LoRa technology, the header is, in fact, optional and can be eliminated to reduce transmission times. The CRC can also be disabled in order to reduce the \(T_{packet}\). Even though the elimination of the CRC eliminates the check on the integrity of the sent bits, this does not represent a particular problem in the implementation of logic selectivity, because if an invalid or corrupt message is received, in most cases, there is not enough time to request and wait for data retransmission. As an example, Table 8 shows the \(T_{packet}\) obtained in the same LoRa configurations as in Table 5, but with CRC disabled. In this case, only the configuration with BW equal to \(125\) kHz and SF equal to \(12\) results in a time greater than \(T_{MBW}\). It is also possible to choose the configuration with SF equal to \(11\) and a BW of \(125\) kHz and obtain a sensitivity of \(-134.5\) dB, thus assuring a wider coverage range.