# Method for Calculating of Lightning Impact Level on Overhead Transmission Line
## 3 Results
### Testing the Method on Real Power Lines  
A study of the method on real overhead lines is important, primarily for power suppliers. Moreover, it is necessary to quickly obtain knowledge of the most lightning-affected sections of power lines. In some cases, the method can also be beneficial to people selecting the optimal route (least amount of lightning strikes) for power transmission lines based on lightning density [15]. To test the method on real regional overhead lines, you need to prepare the initial data. These include the coordinates of overhead line towers, coordinates of lightning strikes, and the range of power line buffer. If everything is simple enough with the coordinates, the buffer size must be calculated. In this work, the OHTLs buffer is chosen within the LDN error limit. This error can be estimated from the maximum deviation span (MDS) parameter of each flash. Figure 2 shows a histogram of the MDS parameter distribution. Figure 1: The (**a**) row shows the location of power lines and lightning strikes on the ground. The plots in the (**b**) row show the total number of lightning strikes that affect each tower. The plots in the (**c**) row show the desired impact level on the power lines according to the proposed method. Understanding that the propagation of radio waves in the atmosphere is more complex than in the vacuum depends on many parameters, such as wavelength, source power and others, for simplicity, we take the speed of radio waves as the speed of light propagation through a vacuum. We transform the MDS parameter into the lightning strike radius \(R_{l}\):  
\[R_{l}=\frac{MDS\text{-}c}{2} \tag{9}\]  
where \(c\) is the speed of light in vacuum, equal to 299,792,458 m/s. Table 2 shows a summary of the transformed MDS parameter \(R_{l}\) from a dataset containing 41,656 lightning strikes to the study area. The mean and median values are almost equal and are about 1350 m. Recent Blitzor-tung LDN accuracy studies in Japan [16] showed similar results with a value of about 1400 m, so we will accept the lightning data set as valid. Therefore, for our calculations, we take the size of the overhead line buffer zone to be approximately equal to the range of the MDS parameter from Table 2: from 100 to 2300 m.  
We will construct a map of the average annual ground flash density according to the technique [5] and show selected power lines on it (Figure 3). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Min** & **1 st Qu** & **Median** & **Mean** & **3 rd Qu** & **Max** \\ \hline
125.5 & 1006.7 & 1347.9 & 1350.4 & 1707.9 & 2248.3 \\ \hline \end{tabular}
\end{table} 
Table 2: A summary of the \(R_{l}\) parameter in meters. Figure 2: The MDS parameter distribution. Over the 5-year period from 2016 to 2020, 44 and 175 lightning strikes entered the buffer zones (R = 2300 m) of \"North\" and \"South\" power lines, respectively. The main concentration of lightning is located in the first half and at the end of the \"North\" OHTL. In the \"South\" OHTL, the main concentration of lightning is located in the second half and the first quarter. The distribution of these flashes is shown in Figure 4.  
The intensity vectors of the average annual lightning impact \(e\), obtained for the buffer area in the range from 0.1 to 2.3 km of each of the power lines, can be displayed as a 3D surface. Such imaging is sufficient to identify the most frequently affected sections of power lines. Sections with the highest intensity correspond to areas with the highest lightning concentration. The vectors \(e\) for the \"North\" line and \"South\" line are shown in Figure 5.  
Figure 3: A map of the average annual ground flash density of the Murmansk region for 5 years (2016–2020). The map shows the “North” OHTL (from above, 110 kV, 269 towers, 75 km length) and the “South” OHTL (from below, 150 kV, 300 towers, 74.6 km length). Figure 4: The distribution of flashes near the transmission line and inside its buffer area. The “North” power line is shown on the left, and the “South” power line is shown on the right.