# Numerical Analysis of a Spiral Tube Damping Busbar to Suppress VFTO in 1000 kV GIS
## 5 The Improved Design of the Damping Busbar  
A further enhancement of the suppression effect was investigated by designing a spiral litz coil connected in series with the busbar, which increases the total inductance value. In order to design the spiral coil, an algorithm based on air-gap calculation was developed. This algorithm designs a spiral coil for a specific inductance value, which was determined as an input value. Other parameters, such as VFTC characteristics and the number of turns of the damping busbar, were also inserted in the input data. Furthermore, litz wire was chosen for the improved design because it is mostly used for the frequency range 10 kHz to 2 MHz. The main advantage of this configuration is to minimize the power losses due to \"skin and proximity effect\", and it is desirable in high-frequency applications as well. [PERSON] and [PERSON] applied a simple method for a suitable [PERSON] wire design [35]. The flowchart of the procedure used to calculate the spiral coil design parameters is shown in Figure 9. By determining the inductance value and the number of turns, then magnetic flux density could be calculated. After that, the eddy power losses in the [PERSON] coil were calculated for the optimal design. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**VFTO Characteristics Parameters**} & \multicolumn{3}{c}{**Simulation Results**} \\ \cline{2-4}  & **L = 0 mH** & **L = 0.3** & **L = 3 mH** \\ \hline Rise time [ns] & 10 & 30 & 35 \\ Maximum amplitude of VFTO [p.u.] & 1.554 & 1.13 & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Influence of the equivalent inductance of the damping busbar on VFTO suppression. Figure 8: Influence of the inductance value on VFTO suppression at the load side of a 1000 kV GIS: at inductance values (**a**) L = 0 mH, (**b**) L = 0.3 mH, (**c**) L = 3 mH. However, we can divide the strand-level proximity effect into the internal proximity effect (the effect of other currents within the bundle) and the external proximity effect, but the total proximity effect may be considered a result of the total field at any given strand [36; 37; 38]:  
\[P_{eddy,stmnd}=\frac{\pi\omega^{2}\overline{\hat{B}^{2}}d_{s}{}^{4}nl}{128\rho_{c }}(1+\frac{\pi^{2}nd_{s}{}^{2}}{4K_{d}p^{2}}) \tag{6}\]  
where \(\omega\) is the angular frequency, \(l\) is the length of the bundle, \(\rho_{c}\) is the resistivity of copper, p is the pitch of the twisting, n is the number of strands in a bundle, \(d_{s}\) is the diameter of each strand, \(\overline{\hat{B}^{2}}\) is the peak magnetic flux density, and \(K_{a}\) is the strand packing factor. Thus, the AC resistance factor, \(F_{r}=R_{ac}/R_{dc}\), for a litz-wire winding for arbitrary waveforms and 2-D or 3-D field geometries can be expressed as follows:  
\[F_{r}=\frac{R_{ac}}{R_{dc}}=1+\frac{(\pi nN_{s})^{2}d_{s}{}^{6}}{192\delta^{4 }b^{2}}. \tag{7}\]  
The power loss in a stranded-wire winding is derived from \(P=F_{r}P_{r}=F_{r}\frac{l_{max}^{2}l}{nA_{s}}\), where \(A_{s}\) is the cross-sectional area of a strand. Consequently, by inserting the operating frequency, the AWG (American wire gauge) can be chosen (i.e., when frequency range is from 1.4 MHz to 2.8 MHz, then the  
Figure 9: The flowchart of the procedure to calculate the litz coil design. best choice is AWG = 48), which means that about 70% loss reduction is achieved. Eddy power losses were calculated, and the final design was determined according to the critical factor (diameter of litz wire no more than the width of the spiral slot on the damping busbar surface). The aim of calculating the air gap was to determine the magnetic flux density in order to calculate the power losses in the litz wire for the optimal design of the coil. Thus, for a typical design, we completed the following:  
1. Determine \(A_{c}\) of the core, which was an aluminum cylinder (busbar body) in our study. 2. Determine the number of turns which was commensurate with the design. 3. Determine the inductance value which achieves an effective design to avoid saturation. 4.