**5. Conclusions**

Several important objectives were accomplished during the current study, which contributes to a better understanding of the holistic transient behavior of the gas-insulated substation.

The numerical instabilities due to the low-frequency breakdown were overpassed by neglecting the first frequencies' decades from the spectrum, between 0–1000 Hz during the computational process. By means of fast Fourier transform, the numerical algorithm embedded in the XGSLab software package computed the harmonic components of the transient source waveform, and the solution of the associated mathematical problem was obtained in the frequency domain. Applying the inverse fast Fourier transform, the time domain solution was computed. Considering the very fast nature of the physical phenomenon, the harmonic components with characteristic frequencies below 1000 Hz did not affect the overall transient behavior of the system under study.

A novel electromagnetic field-based model was developed, representing a real gas-insulated substation configuration. Based on the TGPR assessment at various locations across the substations, the proper modeling technique was established.

The effective area of the grounding grid during the voltage breakdown fault was identified. Based on the numerical and graphical results, a pattern regarding the fault energy flowing throughout the substation was established, which will contribute to a better understanding of the holistic transient behavior of a typical GIS substation.

The electromagnetic couplings developed inside the GIS building between the metallic enclosure and certain components of the grounding grid affected the behavior of the latter near the GIS platform.

**Author Contributions:** Conceptualization M.A., L.C., and D.D.M.; methodology M.A. and L.C.; software R.A.; validation M.A. and L.C.; formal analysis D.D.M. and L.C.; investigation A.M. and L.C.; writing—original draft preparation M.A.; writing—A.M., L.C., and D.D.M; visualization D.D.M. and H.N.; supervision D.D.M. and H.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded the Technical University of Cluj-Napoca through its Ph.D. scholarship program. The APC was funded by European Union's Horizon 2020 research & innovation program under gran<sup>t</sup> agreemen<sup>t</sup> Nr. 815301 and Ministry of Education and Research, "International Campus" project, Grant number: CNFIS-FDI-2020-0340.

**Conflicts of Interest:** The authors declare no conflict of interest.
