**5. Simulations and Results**

To verify and validate the effectiveness and accuracy of the proposed method for ASPAR, various simulation tests were carried out under different fault locations, line loadings, and various shunt reactor configurations, designs, compensation rates, and placements. The EMTP software was utilized with a 50 ms data window length (WL) and 1.92 kHz sampling frequency rate (32 samples per cycle for 60 Hz).

The reactors used in the simulations of this paper were grounded efficiently or to reduce the secondary arc current, and the three-phase shunt reactors were grounded through a reactance *Xn*. In the literature, two methods for calculating *Xn* have been proposed [34–36]. The method presented in [34,35] is independent of the transmission line length, but reduced the fault current less than the method presented in [36]. The reactance value calculated according to the method in [34,35] was always less than the [35] method. The following is the calculation of *Xn* based on these two methods.

$$F = \frac{1}{X\_{\text{sh}} \times B\_1} \tag{8}$$

$$X\_{\rm II} = \frac{X\_{\rm sl}}{3} \times \left(\frac{B\_1}{B\_0} - 1\right) (\Omega) \tag{9}$$

$$X\_{\rm nl} = \frac{B\_1 - B\_0}{3F \times B\_1 \left(B\_0 - (1 - F) \, B\_1\right)} \,\mathrm{(\Omega\text{)}}\tag{10}$$

where *B*0, *B*0, *F*, *Xsh*, and *Xn* are positive sequence line susceptance, zero sequence line susceptance, shunt compensation rate, the equivalent reactance of line shunt reactor, and equivalent reactance of neutral reactor, respectively. The reactances calculated in (9) and (10) corresponded to the placement of the reactor only on one side of the line. If the transmission line is compensated from both sides, the reactance value of each reactor on each side of the line was twice of the *Xsh* and *Xn* reactances calculated above. In other words, the reactive power consumption of the equivalent reactor was divided into two. Table 2 shows the number of shunt reactors for the placement of one or both sides of the line, three rates of compensation 0.5, 0.75, and 0.95, and three modes of effective grounding and grounding based on the methods in [34–36].


**Table 2.** Reactance values of the shunt reactors for the simulations.

Table 3 shows the performance of the proposed technique for di fferent power system conditions and types of shunt compensation. Fault clearing detection delay (FCDD) is defined as the time di fference between the secondary arc extinction detection and the secondary arc extinction moment obtained from the simulation. Simulations were performed for medium and high loading of the transmission line and various fault locations. By measuring the faulty phase voltage on both sides of the transmission line, the algorithm was tested for both substations adjacent to the line. As can be seen, regardless of the power system conditions and the type and rate of compensation, the proposed scheme can accurately and quickly detect fault clearance. The average FCDD for 324 tested cases was 32 ms.

Figure 5a shows the faulty phase voltage at Bus 2 for the single line to ground fault at 30% of the line. The *Xsh* and *Xn* of the inductively grounded shunt compensators at each side of the lines were 2380.60 and 461.42 Ω, respectively. Fundamental voltage magnitude fluctuations cause energy spreadation in low frequency components on the most signal processing methods. The HHT method adaptively distinguishes between fundamental voltage magnitude fluctuations and the presence of a low frequency component, therefore the spectrum extracted from the sub-synchronous components receives the least e ffect from the fundamental component. During the secondary arc, due to the reduction of the fault current, the length of the arc fluctuates more, and as a result, the voltage of the faulty phase fluctuates severely (Figure 5a). As demonstrated in Figure 5b, the proposed criterion is independent of the arc behavior and the *IN* value is zero during the secondary arc. This is due to the use of *IMF*1 and the excellent ability of HHT to decompose signal components with minimal spectrum leakage. Similar waveforms of field measurements, obtained from electrical systems reported in [37], showed similar voltage behavior, hence, it is important that the secondary arc extinction detection method is independent of the voltage behavior during the dead-time.

Due to the growth of renewable resource penetrations in the power system, the need for adaptive protection methods is increasing. Renewable resources are generally connected to the power system through power electronic interfaces, and one of their destructive e ffects is increasing the power system THD [38]. Many of the methods proposed in the literature are based on the increase of THD during the secondary arc and the sharp decrease after the fault clearance. In the presence of renewable resources, many of these methods lose their ability to function properly due to the lack of THD reduction after fault clearance [4–10]. The proposed method does not use the harmonics in voltage to calculate the criterion, and in addition, due to the high capability of the HHT method, the proposed method can have a correct and fast performance regardless of the high penetration of renewable resources in the power system and THD value.


**Table 3.** Fault clearing detection delay (FCDD, ms) for various power system and fault conditions and in the presence of the shunt reactor.

In Table 4, a group of recent papers have been selected for qualitative comparison with the presented method. As can be seen, the strengths of the proposed method include the following:


 **Figure 5.** Faulty phase voltage oscillation during the secondary arc. (**a**) Faulted phase voltage waveform (p.u.). (**b**) Proposed index, IN (p.u.).


**Table 4.** Comparison of the methods for detection of secondary arc extinction.

NM = Not mentioned.
