## 3 Geometry of Test Transmission Poles and Determination of Soil Parameters
### Transmission Pole TP1
\begin{array}{ll}K_{1}(\lambda)=\frac{\rho_{2}\alpha_{2}(\lambda)-\rho_{1}}{ \rho_{2}\alpha_{2}(\lambda)+\rho_{1}};&\alpha_{1}(\lambda)=1+\frac{2K_{1}e^{- 2\lambda t_{1}}}{1-K_{1}e^{-2\lambda t_{1}}}\\ K_{2}(\lambda)=\frac{\rho_{3}\alpha_{3}(\lambda)-\rho_{2}}{\rho_{3}\alpha_{3}( \lambda)+\rho_{2}};&\alpha_{2}(\lambda)=1+\frac{2K_{2}e^{-2\lambda t_{2}}}{1- K_{2}e^{-2\lambda t_{2}}}\\ K_{3}(\lambda)=\frac{\rho_{4}-\rho_{3}}{\rho_{4}+\rho_{3}};&\alpha_{3}(\lambda) =1+\frac{2K_{2}e^{-2\lambda t_{3}}}{1-K_{3}e^{-2\lambda t_{3}}}\end{array}  \tag{7}\]  
The determination of \(\rho\) from (4) is necessary for the evaluation of OF, and it can only be accomplished by numerical integration. As \(\lambda\) increases to infinity, the main function \(f(\lambda)\) converges toward zero, and the integration is finished when the value of the integrated function is successively 10 times smaller than \(10^{-6}\). The integrated function has an oscillatory character, so one value below \(10^{-6}\) is not enough. The integration step size used was \(10^{-2}\). The parameter limits for the three- and four-layer models are presented in Table 3.  
In Table 3, it can be seen that the resistivity limits of the first layer are set to the value of the measured resistivity shown in Table 2. It is important that the specific resistivity of the first layer matches the measured layer as much as possible. The others cannot be compared with the measurement directly because the measurement covers several layers at once. ABC is used for many engineering problems [43; 44; 45; 46; 47], and we used an implementation in which the number of finite elements is counted dynamically. Simpler static counting is not possible since a scout phase might not be employed for every iteration [46]. A total of 105,000 fitness evaluations were used as the stopping criteria, obtained based on more test runs and deemed sufficient enough to obtain the correct results. According to the rule from [73], the population size is 5 to 10 times the number of parameters, but it can also be larger. In the case of a three-layer soil model, the population number is 6 times 5 parameters, which is 30, and so, based on the dynamic fitness evaluation count, the maximum number of iterations is 3500. In the case of a four-layer soil model, the population number is \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Three-Layer Model**} & \multicolumn{2}{c}{**Four-Layer Model**} \\ \hline
**Parameter** & **Lower Limit** & **Upper Limit** & **Lower Limit** & **Upper Limit** \\ \hline Resistance of the first soil layer \(\rho_{1}\) (\(\Omega\)m) & 45.5 & 45.5 & 45.5 & 45.5 \\ \hline Thickness of the first soil layer \(h_{1}\) (m) & 0.1 & 50 & 0.1 & 33.5 \\ \hline Resistance of the second soil layer \(\rho_{2}\) (\(\Omega\)m) & 5 & 7000 & 5 & 7000 \\ \hline Thickness of the second soil layer \(h_{2}\) (m) & 0.1 & 50 & 0.1 & 33.3 \\ \hline Resistance of the third soil layer \(\rho_{3}\) (\(\Omega\)m) & 5 & 7000 & 5 & 7000 \\ \hline Thickness of the third soil layer \(h_{3}\) (m) & - & - & 0.1 & 33.5 \\ \hline Resistance of the fourth soil layer \(\rho_{4}\) (\(\Omega\)m) & - & - & 5 & 7000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter limits for the three- and four-layer soil models. 6 times 7 parameters, which is 42, and so, based on the dynamic fitness evaluation count, the maximum number of iterations is 2500. According to our experience using ABC, the internal parameter limit was set to 100. In Table 4, the calculation results are presented for the three- and four-layer soil models using 30 independent runs of ABC. The table contains the OF best value (B), worst value (W), mean value (M), and standard deviation (SD). The calculated parameters of the best solution are also presented. Based on Table 4, it can be seen that B for the four-layer model (3.1133) is marginally better than B for the three-layer model (3.1398), and that M for the three-layer model is lower (3.2261) than M for the four-layer model (3.2992).