**1. Introduction**

Typically, the gas-insulated substation (GIS) requires 10–25% of the area allocated to a conventional air-insulated substation due to its superior dielectric characteristics of the insulation material, sulphur hexafluoride (SF6), compared to air. SF6 gas is widely used in high-voltage energy applications also because of its high electric arc quenching capacity, which is chemically inert, nontoxic, and nonflammable [1]. Due to dielectric material strength reasons, local values of the electric field inside GIS enclosure, there are two types of GIS topology: three-phase system encapsulated in a single coaxial pipe for nominal voltages below 145 kV and each phase conductor individually encapsulated in a coaxial pipe for nominal voltages above 145 kV [2]. Besides the occurrence of the widely known and studied short circuit at power frequency fault, gas-insulated substations are

subjected to severe transient regimes generated by the switching events. As a result of the relatively low speed of the disconnector switch contacts' movement during switching events, 0.6 cm/s [3], there is dielectric breakdown phenomena occurrence followed by the appearance of electric arc in the contact cavity causing the generation of transient overvoltage characterized by very-high-frequency (Very Fast Transient Overvoltage, VFTO) [4].

The amplitude and waveform of the very fast transient overvoltage (VFTO) depends on the configuration of the GIS substation, the trapped charge stored by the GIS equipment [5], the resistance of the electric arc formed between contacts [6], the capacity at the transformer terminals [7], and the gas pressure [7]. Measurements and digital simulations' amplitudes of transient overvoltage were determined to be between 0.5 p.u. and 2.05 p.u. [8–10]. During switching events in GIS, the transient electromagnetic wave travels toward the metal enclosure through sulphur hexafluoride (SF6)-air bushings and the metallic flanges located between each particular metallic enclosure [11,12]. Moreover, when the difference of the potential between the inner wall of the enclosure and the phase conductor exceeds the breakdown voltage of the dielectric material an electric arc is initiated, generating a short circuit between both metallic structures. When the voltage increases over the breakdown voltage of the insulating arrangement, an arc discharge takes place [13]. This is characterized by a heavy flow of current through the gas between the electrodes and the high dissipation of energy in the form of heat. The breakdown voltage of pure SF6 gas (below 1 bar gas pressure) is around 240 kV when a 20-mm gap between experimental electrodes is considered [14].

When a short circuit between the phase conductor and the inner wall of the enclosure occurs, due to voltage breakdown phenomena, an important amount of energy is leaked toward the metallic enclosure. Usually, GIS module enclosure is connected from place to place through grounding leads to the earthing system of the substation, thereby generating dangerous levels of transient ground potential rise (TGPR). In order to accurately compute and assess the TGPR occurring in GIS, the three-dimensional configuration of the metallic shell as well as grounding grid conductors need to be considered.

There are several locally applied mitigation techniques (like ferrite rings, shunt resistors, etc.) proposed in the literature [15–17]. However, these cannot be generally adopted due to mechanical constraints and they usually require high additional financial efforts. Moreover, the international standards and guidelines provide recommendations regarding the VFTO suppression without a technical and mathematical background [1]. An accurate assessment of the holistic transient response of the substation can highlight the critical locations across the GIS and its vicinity. As a result, suitable mitigation techniques can be applied only where they are necessary.

There are two main approaches widely used when GIS analysis needs to be employed: circuit theory and electromagnetic field theory approaches. The former is the predominant method adopted and used in industry and literature for simulation and investigation of the transient regimes in GIS. The circuit theory approach is based on the representation of encapsulated ensemble by equivalent electrical circuits and distributed parameters: propagation speed, equivalent capacitance, equivalent inductance, and characteristic impedance providing solutions in the frequency and time domain [18–24]. The circuit formulation methodology is based on Kirchhoff's laws embedded in different software interfaces providing numerical solutions for an energy system operating at a known voltage level, based only on the transverse mode of propagation of the electromagnetic wave, TEM, meaning that the method neglects the electric and magnetic field in the direction of propagation. [25]. The method neglects the effects of propagation losses (skin effect, etc.), which result in a lower damping coefficient for very-high-frequency components associated with transient regimes. An important drawback of the method consists of the impossibility to consider the three-dimensional configuration of the GIS metallic enclosure, as well as of the grounding grid conductors during the computational process. Considering such complex metallic structures possessed by a gas-insulated substation configuration (e.g., enclosure, structure resistance, grounding grid conductors) located in a relatively small air volume, electromagnetic couplings will occur between different metallic subsystems, which cannot be quantified in the final solution provided by circuit theory approach.

On the other hand, the electromagnetic field theory approach can be applied toward GIS three-dimensional geometries regardless of the complexity of the model to be studied [25]. Full-wave numerical electromagnetic analysis (NEA) methods are defined as methodologies allowing the direct numerical solution of Maxwell's equations in both frequency and time domain [25]. These methods are becoming the most promising approaches to study complex transient phenomena that cannot be straightforwardly solved by means of circuit theory or transmission line approaches (e.g., by using electromagnetic transient program (EMTP)). Computational electromagnetics are getting increasing attention not only in the research fields but also in the industrial fields as well as in gas-insulated substation analysis. A method solving Maxwell's equation directly can be classified into a di fferential equation–(DE) and an integral equation–(IE) based method [25]. The most commonly used numerical approaches in solving Maxwell equations, applicable to gas-insulated substation analysis, are method of moments (MoM) finite element method (FEM), finite di fferences time domain approach (FDTD) and partial equivalent element circuit (PEEC) method, which will be further applied and discussed. In the vast majority of the case studies available in the literature, MoM, the IE-based method approach applied to gas-insulated substation analysis, is focused on safety assessment during steady state, unbalanced condition, and power frequency faults [26–28]. Although the mentioned studies provide a comprehensive safety assessment analysis, the proposed Computer-aided design based (CAD) models representing the GIS metallic enclosure and adjacent inner phase conductors are not properly validated.

Current studies present FEM numerical approach as a viable solution for dielectric design, regarding GIS insulation material, in order to ensure that the electric field and its gradient are within acceptable limits, below critical values imposed by the manufacturer [2]. Furthermore, studies containing partial discharge detection in dielectric media (dielectric strength analysis) alongside mechanical stress analysis and voltage breakdown between disconnecting switch (DS) contacts are available in public literature [29–33]. FEM software packages can handle geometries regardless of the required accuracy (DS contacts' chamber). However, the limitation of the method arises when large geometries need to be included in the computational domain. FDTD, similar to FEM, is based on the DE form of Maxwell equations, resulting in the necessity to consider the entire volume space containing the geometry under study as computational domain, which implies a high amount of digital resources [34–39]. By adopting suitable boundary conditions (perfect matching layer [36], perfect electrical conductor [36]), the area of interest can be extended, considering several simplifying assumptions. Nevertheless, the computational e ffort required by considering the entire GIS metallic enclosure during the analysis represents an important drawback of the FDTD approach. The PEEC method is based on an integral equation description of the geometry that is interpreted in terms of circuit elements: partial inductances and partial capacitances, a partial potential, which represents the intermediate elements between electromagnetic field approach and interpretation of Maxwell's equations in circuit domain [40]. According to [41,42], the PEEC method shows satisfactory accuracy in comparison with experimental results and with simulation results calculated by the MoM and the FDTD method considering several types of electrodes with di fferent diameters and positions with respect to the soil surface and lengths even when more complex structures are analyzed. Several PEEC numerical approaches applied to transient phenomena can be found in literature [43–47]. However, the extension of application toward gas-insulated substation transient analysis remains a challenging task due to high complexity of metallic structures involved in the computational domain.

The aim of the following study was to provide a clear understanding of the transient ground potential rise, across the metallic structures located inside GIS building, during switching operations considering di fferent gas-insulated substation configurations (one GIS configuration contains a certain number of GIS modules) in order to identify the suitable modeling technique achieving e fficient computational e fforts. Through the proposed analysis methods, a parametric analysis was employed in order to accurately quantify the transient response of the system when an additional GIS bus section is connected to the model, by adopting a PEEC approach. For numerical modeling and simulation, the XGSLab software (XGSLab 9.4.1.5 version, SINT Ingegneria, Bassano del Grappa, Italy) package was used [48].


The computational e ffort limitations arising when the DE-based methods are employed by presenting the PEEC approach application on GIS transient behavior analysis thus allowing to consider of the entire substation during the simulation process.

Up to now, due to the fact that there is no available digital model representing the three-dimensional GIS enclosure, the transient response of the grounding system in the presence of the metallic enclosure, connected in several locations to the grid, hence creating closed current loops a ffecting the fault energy flowing throughout the substation, could not be assessed.

#### *General Description of the System*

The investigated system is a 110-kV substation with three-phase GIS modules placed in a dedicated building. The substation has a double bus configuration containing four GIS modules, further noted from BUS1 to BUS4, and a bus coupler (BC) arranged in a horizontal layout. The two-bus system of the double bus configuration is placed vertically, one on the top of the other (see Figure 1).

**Figure 1.** General layout of the substation, initial configuration.

Inside the coaxial pipe, the phase conductors are located in a radial configuration, with respect to the geometric origin of the enclosure.

The grounding grid layout can be described as follows: A copper strip contour (40 × 5 mm) is located on the GIS platform surroundings to which each GIS module is connected through two copper grounding leads. On the inner wall of the GIS building an additional copper strip contour is installed at h = 0.3 m, which ensures the conduction paths toward the external grounding system. Three copper conductor contours are buried outside the GIS building at di fferent depths with respect to the soil surface and di fferent distances from the GIS building wall. Taking into account the very fast time distribution of the transient regime, the auxiliary equipment located near the GIS building (autotransformers, lightning protection systems, etc.) were not considered during the computational process. The geometrical characteristics and the implemented materials, adopted during the computational process, associated with the system components are presented in Table 1.


**Table 1.** Geometric characteristics of the model components.
