*3.2. Discussion*

As shown in Figure 7a, when the disconnector is opened, the VFTO for the whole process at the power supply side appears as a superposition of high-frequency transients and a sine wave. After SF6 gas discharges, the disconnector gap restores the insulation state; then, the current disappears, the high-frequency transient components gradually decay, and, finally, the voltage wave continues as a sinusoidal wave with the supply voltage.

In addition, the VFTO for the full process at the load side has an approximate step shape, which is a superposition of high-frequency transients and a stepped wave. Each step of the ladder wave corresponds to SF6 gas breakdown, the step magnitude is the breakdown voltage, and the narrow pulse at the ladder edge is the highest frequency of the VFTO, as shown in Figure 7c.

Moreover, the VFTC for the whole process is the superposition of high-frequency transients with zero current amplitude. When the critical breakdown voltage (BV) of the SF6 gas is equal to the transient recovery voltage of the gap, the SF6 gas collapses and the gap transfers from the insulation state into a conductive state; then, the circuit produces a high-frequency transient current, as shown in Figure 7e. Additionally, when the critical breakdown voltage of SF6 gas exceeds the transient recovery voltage of the gap, the current disappears during discharge of the SF6 gas.

The simulation results show that the maximum amplitude of the VFTO decreased from 1.554 to 1.13 p.u., which means that the damping busbar functioned as a VFTO suppressor. The damping effect of the new design is evident from the simulation results, and the mitigation effect was about 27%. Table 3 illustrates the transient characteristics of the VFTO waveform under opening operation before and after installing the damping busbar. A singular switching operation (opening) of the disconnector was simulated in EMTP-ATP (Alternative Transients Program) software.

**Figure 7.** *Cont*.

**Figure 7.** Very fast transient overvoltage (VFTO) and VFTC waveforms: VFTO at the source side (**a**) before installing the damping busbar and (**b**) after installing it; VFTO at the load side (**c**) before installing the damping busbar and (**d**) after installing it; VFTC (**e**) before installing the damping busbar and (**f**) after installing it.



#### **4. Inductance E**ff**ect on Suppressing VFTO**

When VFTO passes through the inductance, the wavefront is smoothed, its steepness is reduced, and the amplitude is decreased. The inductance *Li* increases the round-trip time of the travelling wave, which in turn leads to a reduction in the high-frequency components of the VFTO. The travelling wave leads to a higher voltage on the inductance of the small circuit, which causes the parallel resistance *Ri* to absorb the travelling wave energy, increase the consumption of active power, and reduce the amplitude of the VFTO.

The inductance value of the damping busbar is an important factor for an obvious VFTO suppression effect. The limitation on the steepness of the transients is a result of the inductance effect of the damping busbar. Figure 8 describes the influence of the inductance value on VFTO suppression at the load side during transient phenomena.

The more considerable value of the equivalent inductance of the damping busbar leads to an obvious suppression effect. Table 4 illustrates the transient characteristics of the VFTO waveform under an opening operation for different values of equivalent inductance of the damping busbar.

**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.

**Table 4.** Influence of the equivalent inductance of the damping busbar on VFTO suppression.


It can be observed that a higher damping effect was achieved by increasing the equivalent inductance of the damping busbar. Furthermore, increasing the inductance value can damp the VFT waveform's front. It is also helpful for absorbing the sharp spikes of the VFT since surge arresters do not act quickly enough to prevent steep-fronted switching transients. Therefore, installing an additional spiral coil with the damping busbar is highly valuable to attenuating the effects of VFTs. For this reason, a spiral coil of resistive litz wire was designed to be installed in the helical groove and connected in series with the damping busbar.

#### **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. Sullivan, C.R. and Zhang, R.Y applied a simple method for a suitable litz 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 litz coil were calculated for the optimal design. 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 [36–38]:

$$P\_{\rm eddy, standard} = \frac{\pi\omega^2 \overline{B^2} d\_s^4 nl}{128\rho\_c} (1 + \frac{\pi^2 n d\_s^2}{4K\_a p^2}) \tag{6}$$

where ω is the angular frequency, *l* is the length of the bundle, ρc is the resistivity of copper, p is the pitch of the twisting, n is the number of strands in a bundle, ds is the diameter of each strand, B ˆ 2 is the peak magnetic flux density, and Ka is the strand packing factor. Thus, the AC resistance factor, *Fr* = *Rac*/*Rdc*, for a litz-wire winding for arbitrary waveforms and 2-D or 3-D field geometries can be expressed as follows:

$$F\_I = \frac{R\_{\rm nc}}{R\_{\rm dc}} = 1 + \frac{\left(\pi n N\_s\right)^2 d\_s^{\rm 6}}{192 \delta^4 b^2}.\tag{7}$$

**Figure 9.** The flowchart of the procedure to calculate the litz coil design.

The power loss in a stranded-wire winding is derived from *P* = *FrPr* = *Fr <sup>I</sup>*2*rms*.*<sup>l</sup> nAs* , where *As* 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 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:


$$d\_{\mathcal{S}} = \frac{N^2 A\_{\mathcal{C}} \mu\_0}{L}. \tag{8}$$

Many di fferent 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.

**Table 5.** Simulation results for the litz coil design.


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. Lcoil = 0.1 mH is the equivalent inductance of the spiral litz coil and Lbusbar = 0.33656 mH is the equivalent inductance of the damping busbar. Thus, Leq. = 0.43656 mH is the equivalent inductance of the improved damping busbar. The simulation was set up based on Ldamp = 0.43656 mH, as presented in Figure 6. Thus, Figure 10b shows the higher damping e ffect of the improved damping busbar. In order to clarify the damping e ffect, Figure 10d illustrates the damping e ffect 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 e ffect shown in Figure 10b, further details about the damping e ffect of the improved design are discussed in the next section.

**Figure 10.** VFTO waveform at the load side: (**a**) before installing the damping busbar, (**b**) after installing the improved design of the damping busbar; VFTO at the load side for one breakdown at 0.013 s: (**c**) before installing the damping busbar, (**d**) after installing the improved design of the damping busbar.
