# Numerical Analysis of a Spiral Tube Damping Busbar to Suppress VFTO in 1000 kV GIS
## 5 The Improved Design of the Damping Busbar
Calculate the air gap length as a first step to calculate the magnetic flux density in order to calculate the power loss in the litz wire for the optimal design of the coil. Thus, the length of the air gap was calculated by using [PERSON]'s law, as shown below:  
\[l_{g}=\frac{N^{2}A_{c}\mu_{0}}{L}. \tag{8}\]  
Many different combinations of strand diameter and number of strands could be designed and manufactured for any given cost. Thus, the number of bundles and, finally, the litz coil diameter could be obtained using a critical condition (diameter of the litz wire no greater than the width of the spiral slot on the damping busbar surface). The previously described technique was used to calculate the litz coil design. Simulations were performed using MATLAB software by keeping the length of the coil, number of turns, and transient current parameters constant. The results are listed in Table 5.  
It is worth noting that the inductance value of both the damping busbar and the spiral litz coil was calculated at 2 MHz. An accurate choice of construction type of the litz design leads to a higher capability for greater current carrying capacities. The larger Type 2 and 3 litz designs have this essential feature for high-frequency power supply, inverter, and grounding applications. A Type 2 litz construction is distinguished by bundles of twisted wires together, while Type 3 features individually insulated bundles of Type 2 litz wire [39]. As a consequence, in this study we aimed to add a spiral litz coil located in the sweeping spiral on the surface of the damping busbar in order to improve its performance in VFTO mitigation. EMTP simulation was carried out to study the VFTO with and without installing the improved damping busbar. L\({}_{\text{coil}}=0.1\) mH is the equivalent inductance of the spiral litz coil and L\({}_{\text{busbar}}=0.33656\) mH is the equivalent inductance of the damping busbar. Thus, L\({}_{\text{eq. }}=0.43656\) mH is the equivalent inductance of the improved damping busbar. The simulation was set up based on L\({}_{\text{damp}}=0.43656\) mH, as presented in Figure 6. Thus, Figure 9(b) shows the higher damping effect of the improved damping busbar. In order to clarify the damping effect, Figure 9(d) illustrates the damping effect of the improved damping busbar for a singular switching operation at approximately the same moment (0.013 s.). In order to clarify the higher damping effect shown in Figure 9(b), further details about the damping effect of the improved design are discussed in the next section. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Inductance Value**} & \multicolumn{4}{c}{**Simulation Results for Litz Coil Design**} \\ \cline{2-5}  & **Number of** & **Number of** & **Strand Diameter** & **Construction Type** \\  & **Bundles** & **Strands** & **[mm]** & **Construction Type** \\ \hline
0.1 & 5 & 140 & 0.899 & \\
0.3 & 5 & 140 & 0.838 & \\
3.0 & 5 & 140 & 0.702 & type 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation results for the litz coil design.