## 3 Design and Analysis
### Dielectric Appraisal of FGIL Apropos of the Stranded Conductor
#### 3.3.1 Breakdown Voltage of the Proposed Configuration Regarding Streamer Breakdown Theory  
Per the streamer breakdown theory, a streamer may result in a partial discharge such as a corona or a complete gap discharge, and the associated potential level is considered as the breakdown voltage [58; 69]. The minimum breakdown voltage in SF\({}_{6}\) insulated equipment can be evaluated by using Equation (4), where \(BV\) is the breakdown voltage in kV, \(P\) is the gas pressure in kPa, and \(d\) is the electrode gap in centimeters [58; 69]. However, the effect of electrode surface irregularity should also be considered, as it significantly degrades the minimum breakdown voltage. Considering the conductor's surface irregularity in the model developed above, Equation (5) can be used for the evaluation of the minimum breakdown voltage, where \(BV\) is the breakdown voltage in kV, \(C\) is the curvature factor, \(d\) is the electrode gap in centimeters, \(F\) is the field utilization factor, \(P\) is the gas pressure in kPa, and \(S\) is the electrode roughness factor [58]. Further, considering the case when the dielectric medium comprises sulfur hexafluoride and nitrogen gases at a ratio of 20:80, its breakdown strength will be lesser in comparison to pure SF\({}_{6}\) gas, and will depend upon the percentage of SF\({}_{6}\) in the mixture. Thus, Equation (6) can be used for the evaluation of possible degradation in the minimum breakdown voltage of the gas mixture [69]. Figure 13 shows the electrode gap comparison between the 132-kV conventional and proposed GIL scheme which is further used in the evaluation of the minimum breakdown voltage for the proposed scheme. Reduction in electrode gap resulted due to the reduction of conductor diameter from 89 mm to 44.5 mm, as the proposed scheme comprises a stranded aluminum conductor whereas the conventional scheme comprises a hollow aluminum conductor. However, the ampacity of both conductors was kept approximately the same. Further, the diameter of the ground electrode was also reduced from 226 to 127.2 mm, as it is based on the dimensional evaluations performed in Section 3.1 regarding the standard field utilization factor as well as the standard dimensional specifications for GILs. Figure 14 represents the breakdown voltage for 100% SF\({}_{6}\) content and the respective reduction in this breakdown voltage due to surface irregularity of the stranded conductor using Equations (4) and (5). Moreover, it also highlights the reduction in breakdown voltage due to the reduced SF\({}_{6}\) content in the SF\({}_{6}\) and N\({}_{2}\) gas mixture through Equation (6). Critical analysis of Figures 13 and 14 shows that the BV for the given dimensional and operational specifications of the proposed 132 kV pliable GIL was well above the normal operating voltage and the standard basis insulation level (BIL) value of 132 kV. Thus, per the evaluated dimensional specifications, the proposed FGIL scheme exhibits good dielectric withstand capability. \[BV\ =\ 1.321\cdot(Pd)^{0.915} \tag{4}\]  
\[BV\ =\ 0.8775\cdot F\cdot S\cdot C\cdot P\cdot d \tag{5}\]  
\[m\ =\ 38.03\cdot n^{0.21} \tag{6}\]3.2 Breakdown Field Strength of the Proposed Configuration Regarding Critical Field Intensity Theory  
In the critical field intensity method, the breakdown voltage of a dielectric gas is associated with critical field, electrode gap, FUF, electrode surface irregularity, and gas pressure [69]. According to this theory, the operational and design magnitudes of the electric field should be well below its critical value in order to avoid dielectric breakdown through avalanche [58]. Further, in accordance with GIL standards, the typical allowable design criterion regarding electric field strength is approximately 20 kV/mm, and might be higher such that the influenced region is not substantially enormous [24]. Thus, concerning the practical viability of the proposed 132-kV FGIL scheme, its electrostatic field appraisal regarding operational, design, and critical field values is essentially required.