## 2 Methodology
### Simulation Work of Voltage Uprating for 132 kV Transmission Tower  
The commercial ANSYS Maxwell software was used as the simulation platform to simulate the proposed voltage uprating of 132 kV transmission tower. The software has the ability to model the component based on its properties, such as permittivity \begin{table}
\begin{tabular}{c c c} \hline \hline  & **(a)** & \\ \hline
**Clearance Type** & **Minimum Clearance (m)** & **Result** \\ \hline Phase-to-earth & 2.40 & Fulfilled \\ Phase-to-phase & 4.79 & Fulfilled \\ Phase-to-ground & 16.39 & Fulfilled \\ \hline \hline  & **(b)** & \\ \hline
**Clearance Type** & **Minimum Clearance(m)** & **Result** \\ \hline  & \(15^{\circ}\) & \(57^{\circ}\) \\ Phase-to-earth & 2.07 & \(1.01\) & Fulfilled \\ Phase-to-phase & 4.79 & 4.46 & Fulfilled \\ Phase-to-ground & 16.42 & 17.25 & Fulfilled \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Minimum electrical clearance for **(a)** still air and **(b)** wind conditions. Figure 6: **(a)** The proposed model of voltage uprating for 132 kV transmission tower, **(b)** analysis of electrical clearances under still air, and **(c)** wind conditions. and conductivity of the materials. The proposed model of voltage uprating for 132 kV transmission line material properties is summarised in Table 8. In this study, the proposed models including a two-dimensional simplified steel crossarm, a proposed model of steel lattice body and a suspension string insulator. In this simulation, the total number of elements was 345,214, which was obtained by the adaptive meshing method. Figure 7 shows the meshing plot of the proposed voltage uprating simulation model based on finer mesh theory. In this study, it was found that the adaptive meshing method was three times repeatedly refined until the model was converged, which starts from step one passed with 204,336 elements, followed by step two passed with 265,572 elements, and then step three passed with 345,214 elements where the convergence percentage error was 1%. In this study, there were nine configurations considered, i.e., phase-to-earth at the different steel crossarms. The configurations were also considered under still air and wind conditions, respectively. The available minimum electrical clearances of L1 to L9 were defined to represent the nearest distance phase-to-earth, as shown in Figure 8. L1, L2, and L3 represent under still air conditions, while L4, L5, and L6 represent under normal wind conditions and L7, L8, and L9 represent under extreme wind conditions. However, the phase-to-earth of the top (L1, L4, L7) and mid-section (L2, L5, L8) crossarm electrical have similar distances, thus, simulations for both were conducted only once. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structure** & **Material** & \
\begin{tabular}{c} **Relative Permititivity** \\ **(\(\mathbf{\hat{c}}\)r)** \\ \end{tabular} &
\begin{tabular}{c} **Bulk Conductivity** \\ **(\(\mathbf{\sigma}\)), S/m** \\ \end{tabular} \\ \hline Crossarm & Steel & 1 & \(2\times 10^{6}\) \\ Tower body structure & Steel & 1 & \(2\times 10^{6}\) \\ Suspension string insulator & Glass & 5.5 & \(2\times 10^{-14}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Proposed model material properties. Figure 7: The 2D meshing plot of the proposed voltage uprating model. For still air and normal wind conditions, the BIL was modelled to simulate lightning impulse conditions. In contrast, a shielding failure was also considered to simulate the condition under such an event. Meanwhile, the extreme wind condition simulated also under BIL modelled by considering the power frequency withstand voltage. Three applied voltages were considered to represent the BIL, BIL + 10% and BIL +25%, injected at the steel lattice body structure (backflashover) and phase conductor (shielding failure) as indicated in Table 9.  
The two-dimensional design was chosen to evaluate the voltage profile distribution, focusing mainly on the phase-to-earth electrical clearance.