*2.3. Assessment Methodology*

To correctly quantify the contribution of each particular metallic section at the holistic transient behavior of the substation, a parametric analysis was employed as follows: The first stage of the computational process will contain the initial GIS configuration (5 GIS bus sections, see Figure 1), taking into account phase-to-enclosure fault inside BUS4 enclosure, modeled through a galvanic connection between the phase conductor and the inner wall of the enclosure. The results obtained in this first analysis stage will represent the baseline for the investigation carried out in this paper.

With each future analysis step an additional bus section will be removed from the model until the single GIS bus section configuration is achieved (see Figures 5 and 6 for analysis of step 2 and step 4). Minimizing the number of elements contained by the model will reduce the computational e ffort bringing improvements of the required computational time. With each GIS bus section extracted from the computational domain, the number of elements contained by the model decrease by approximately 16% (considering that the complete configuration contained five sections and the grounding grid structure remained constant during the simulations).

**Figure 5.** CAD representation of analysis stage 2: GIS model with four bus sections' modules.

Through overlapped graphical representations and numerical comparisons of the TGPR waveform computed for di fferent GIS configurations, the transient response of the substation during voltage breakdown fault is assessed. This analysis will determine if the computed values of transient ground potential rise generated throughout the substation during phase-to-enclosure fault considering a single GIS bus section (the last stage of the investigation, see Figure 7) provide the worst-case scenario, within acceptable deviation range from the full GIS configuration model. As a result, a suitable modeling technique will be achieved and presented, and, therefore, the computational domain could be reduced for further analysis and investigations. Moreover, the transient response of the grounding grid in the presence of the metallic enclosure will be assessed and discussed. Due to the fact that there was no available 3D model representing the entire GIS metallic ensemble, quantifying the impact of the

enclosure on the grounding grid performance when very-high-frequency transients flowed throughout the system was an impossible task. The response of the grid was expected not to be uniform across the substation, although it is based on the approximative symmetrical geometric shape of the earthing system due to the presence of the metallic enclosure. It is well known that during the very fast transient regime the effective area of the grounding grid is significantly reduced and, therefore, the grounding grid subsystems responsible for the fault energy clearance will be identified.

**Figure 6.** CAD representation of analysis stage 4: GIS model with two bus sections' modules.

**Figure 7.** CAD representation of the final analysis stage: GIS model with a single bus section.

Figure 7 illustrates the CAD model considering the final analysis stage, single bus GIS configuration (containing only the faulted bus). The purple dots, highlighted in Figure 7, represent the established analysis locations across the substations, as follows: upper side of the BUS4 (faulted bus) enclosure, grounding lead that connects BUS4 enclosure with the earthing system, copper strip located on the GIS platform, copper strip located on the inner wall of the GIS building, and vertical rod.

Quantifying the total discharge current by the enclosure toward the grounding grid considering such complex electromagnetic interactions within several metallic structures requires a detailed analysis of the contribution of each particular bus section. The entire structure of the grounding grid was considered during the computational process. Hence, the impact of adding or subtracting particular GIS bus sections from the model was analyzed.

#### **3. Simulations and Results**

The simulation was performed using an I7-7700 CPU, 3.60 GHz, personal computer with 16.0 GB of RAM and required 4 h of computational time for an 800-μs simulation period for the analyzed five GIS buses' configuration.

In the following section, several simplifications of the computational domain are proposed, tested, and performed in order to try to reduce computation time. Moreover, reducing the number of elements contained by the model will simplify the mathematical formulation associated with the electromagnetic field problem under study. When GIS arrangements contain four, three, two, and single modules then the computational e ffort has been reduced accordingly.

It has to be mentioned that when large matrix systems describing the model are conceived by the electromagnetic algorithm implemented in XGSLab software package, a well-known problem, known as an ill-conditioned system, might arise due to the low-frequency breakdown numerical instability. An ill-conditioned problem defines a condition of a small change in the inputs (the right-hand side of the equations' system) that leads to a large change in the output without real correlation with the physical phenomenon. However, using an appropriate numerical solver and suitable mathematical techniques, an accurate solution can be provided even for matrix systems containing a large number of elements and unknowns [49]. When low frequencies were considered during the simulation process, an artificial phase shift of the transient electromagnetic wave was observed, caused by the numerical instabilities associated with the low-frequency breakdown [50]. In order to overcome the low-frequency breakdown challenge, frequencies between 0–1000 Hz were not considered during the computational process. Considering the very fast nature of the physical phenomenon, the output of the method was not a ffected by the low-frequency spectrum elimination.

Figure 8 shows characteristics of TGPR on the grounding lead associated with BUS4 under influence of faulted bus enclosure with the earthing system considering five, four, and one GIS bus section's(s') configuration. The analysis was performed on the grounding lead that connects the faulted bus enclosure with the earthing system for di fferent gas-insulated substation configurations.

**Figure 8.** Transient ground potential rise on the grounding lead associated with BUS4.

Considering additional GIS bus sections into the computational domain is equivalent to generating multiple parallelism conditions between each pair of metallic elements contained by the model (aluminum bar–aluminum bar, aluminum bar–copper strip) through which electromagnetic couplings are developed. While single GIS bus module configuration (only the faulted bus section) was analyzed, the transient response computed at the level of grounding lead was more severe (approximately double), due to the fact that the fault energy was not cleared throughout a complex metallic structure as in the case of four and five GIS bus sections' configuration. It can be noted that the computed voltage waveforms were characterized by similar harmonics when four and five GIS modules were considered during the computational domain.

When the analysis was performed on the upper side of BUS4 metallic enclosure, similar behavior to that of the TGPR was observed, as in the previous case: Gradually extracting additional GIS bus section from the model caused an amplifying e ffect on the oscillatory character of the voltage waveform combined with the reduction of the maximum amplitude (see also Figures 9 and 10). A steeper character 0.045 (time to peak) μs can be observed when a single bus is considered in comparison with 0.14 μs when four and five buses are considered, respectively. Similar harmonics and time-to-peak parameters describing the transient voltage waveforms computed during the computational process considering five and four GIS bus sections, respectively, could be observed (see Figure 7).

**Figure 9.** Transient ground potential rise on the upper side of metallic enclosure (BUS4).

Figure 10 illustrates the absolute maximum TGPR amplitude computed on the upper side of the metallic enclosure while considering di fferent GIS configurations during the computational process. Besides the parallelism conditions generated by multiple GIS sections contained in the computational domain, the proportions of equivalent inductance, capacitance, and resistance into the circuit were modified. From the harmonic point of view, the multiple parallel GIS modules behaved as a filter (see Figures 8, 9 and 11).

**Figure 10.** Comparison between TGPR computed considering five GIS configurations.

**Figure 11.** Transient ground potential rise across copper strip located on GIS platform, considering different GIS buses' configuration.

The amplification effect influencing the oscillatory character of the transient overvoltage waveform provided by gradually extracting bus sections from the model could be observed also across the copper strip ring located on GIS concrete platform surroundings (Figure 11). However, as the distance from the transient source increased, as well as from the aluminum bars' configuration, the impact of electromagnetic couplings developed between particular metallic enclosure elements did not affect in a similar manner the maximum TGPR values recorded as in previous locations.

Let us assume that the first significant frequency period can be determined within the first 0.2 μs (nonperiodic signal) in all the cases presented in Figure 11. The time-to-peak parameters related to TGPR waveforms computed while five, four, and one GIS bus section(s) were 0.0525 μs for first two cases and 0.0775 μs, respectively, however, with different polarities. The multiple reflections of the electromagnetic wave travelling within aluminum bars' configuration, considering multiple GIS bus sections contained by the model, generated relatively steeper voltage waveform in comparison with a single GIS bus configuration.

Figure 12 illustrates the transient overvoltage computed on the inner wall of the GIS building, analysis location, highlighted in Figure 5, considering different gas-insulated substation configurations.

**Figure 12.** TGPR on the copper strip located on the inner wall of GIS building.

Considering the five GIS bus sections' configuration, the maximum amplitude describing TGPR computed across copper strip located on the inner wall of GIS building was attenuated with 87%, if compared with the maximum amplitude computed throughout the substation, which was considered as a reference value (on the metallic enclosure of BUS4).

When the transient electromagnetic wave reached the grounding grid, conductors located outside GIS building, vertical rods, and copper conductor, the oscillatory character was fully damped, as depicted in Figure 13, regardless of the GIS configuration considered during the computational process. Similar maximum amplitudes of the transient ground potential rise were computed on the vertical rod in comparison with those obtained at the previous analysis location; hence, the efficiency of the grounding grid decreased when the distance from the transient source increased. Comparing the TGPR computed, taking into account different GIS configurations, the worst-case scenario was obtained when five GIS buses were included in the computational domain and similar transient response of the vertical rods was computed when single and four GIS buses' configurations were considered. However, in order to achieve an accurate assessment regarding the holistic behavior of the substation, the number of GIS sections in the model must be limited in the computational process.

**Figure 13.** TGPR, one particular vertical rod, comparison considering several GIS configurations.
