*2.2. Transformer*

In this work, a Delta-Star (Δ − Y) 22/0.4 kV transformer is modeled in the EMTP-RV environment, according to Cigre Guidelines [32]. The transformer comprises three basic building blocks as Figure 2 to present the 3-phase transformer model, see Figure 3. In high voltage studies, capacities on the MV side, LV side, and between MV and LV sides play a crucial role in obtaining more realistic results. The capacitor sizes are derived from the work in [33].

**Figure 2.** Basic building block for each phase of the transformer, EMTP-RV model.

**Figure 3.** ΔY-connection model of the transformer with measured capacitances.

## *2.3. Spark Gap*

A spark gap is the most commonly used device used to protect the transformers by limiting the overvoltage amplitude (chopping the voltage at a certain level). The spark gap is triggered when the overvoltage across its terminals exceeds the critical flashover voltage [34]. In most works, for the sake of simplicity, to model the behavior of the spark gap, a voltage-controlled switch is used [6,21], which cannot take into account the nature of different surge impulses. In this paper, to avoid such shortcomings and to simulate the behavior of the spark gap as close as the practical situation, the disruptive e ffect (DE) method (7) is used [35]. In this formulation, the flashover occurs when the integral part becomes greater than or equal to D. The integral function enables calculating the moment that the spark gap is ready to be triggered regardless of the waveform.

$$\int\_{t\_0}^{t} \left[ \left| \mathbf{v}\_{\mathcal{S}^{ap}}(t) \right| - \mathbf{v}\_0 \right]^{\mathbf{k}} dt \ge D \tag{7}$$

where k and D are an empirical constant and the disruptive e ffect constant (kV μs), respectively; v0 is the onset voltage of primary ionization (kV); and t0 is the time corresponding to this primary ionization.
