**4. Proposed Method**

Many high voltage transmission lines have shunt compensation, which is placed on either side of the transmission line or one side only. Reactors are usually grounded by inductance to reduce the flow of secondary arc current, and after the fault clearance, the shunt reactor and capacitor of the transmission line are parallel to each other. The energy trapped in the reactor and shunt capacitor of the transmission line oscillates until complete damping, and this energy oscillation between the transmission line and the parallel compensation creates a sub-synchronous component in the isolated phase voltage. In the literature, the created resonance after fault clearance has been used to diagnose secondary arc extinction [15,18,24–29]. There is no sub-frequency component during fault, however, after the secondary arc extinguishing in the frequency range of 0 to 60 Hz, a sub-synchronous component appears in the faulty phase voltage for compensated transmission lines. Therefore, in this paper, the energy in the bandwidth of 0 to 55 Hz of the faulty phase voltage was

used as a criterion for detecting secondary arc extinction. The frequency of these sub-synchronous components is practically between 30 Hz and 45 Hz for 60 Hz power systems [33].

Due to the limitations on the computational burden, a small data window should be used in protection system, and on the other hand, there is an edge effect in all signal processing methods, hence, both of these constraints should always be considered in choosing the length of the data window. The following index is proposed as a criterion for detecting secondary arc extinction:

$$IN(i) = \sum\_{f=0}^{55} \bar{\mathcal{U}}\_1 \Big( f, \frac{WL}{2} \Big) \tag{7}$$

where *IN* represents the sum of the energy of all sub-synchronous components in the faulty phase voltage. *U* is the last measured window of the faulty phase voltage with the length of WL. *U*1 is the first decomposed IMF of *U*. = *U*1 is the output of the Hilbert transformation of *U*1, where the central sample of the data window was used here to calculate IN for avoiding the edge effect. HHT can extract sub-synchronous components without being affected by the fundamental 60 Hz component.

Figure 2a shows the faulty phase voltage at Bus 1 for the single line to ground transient fault at 30% of the line. The reactance of the effectively grounded shunt compensator at Bus 2 was 1506.60 Ω. The fault occurred at 350 ms and after 150 ms, the faulty phase was completely isolated from both sides. From 350 to 500 ms, the transient fault had an extremely large current without any differences in its characteristics from the permanent fault. Transient fault at this stage is called the primary arc and its length is almost constant. From the moment of 0.5 s onward, the arc length increased slowly until the transient fault was cleared. The simulation was performed for 1.2 s. Figure 2b shows the spectrum extracted by HHT. The HHT method has a small leakage spectrum and the different components have little effect on each other. Figure 2c illustrates the proposed index for a 1920 Hz sampling frequency (32 samples per 60 Hz cycle) and WL = 50 ms, where the value is zero during the secondary arc and increases after the secondary arc is extinguished.

Figure 3 shows the first three extracted IMFs from the voltage waveform in Figure 2a. The voltage waveform was decomposed to 10 IMFs, but high-order IMFs had very little energy and are not shown here. In the EMD method, *IMF*1 always contains high-frequency contents of the input signal. As shown in Figure 3a,b, the sub-synchronous component only appeared in the *IMF*1 of the frequency spectrum. Thereby, *IMF*1 is the most suitable *IMF* to monitor the sub-synchronous component due to secondary arc extinction.

Figure 4 shows the flowchart of the proposed algorithm. The proposed method detects fault clearance for shunt compensated transmission lines, and recognition of permanent or transient faults was not within the scope of this paper, and the fault type was assumed to be a transient single line to ground (SLG) fault. After the single-pole operation of the CBs on both sides of the transmission line, the faulty phase was isolated. It was assumed that the distance protections on both sides of the transmission line quickly de-energized the faulty phase. Some papers have assumed that the fault was transient and waited for the secondary arc extinction. In this case, if the secondary arc is not detected after a certain time (about 1.5 to 3 s), it is concluded that the fault is not transient and the initial assumption is wrong, and the three-phase trip command is issued. In this case, the secondary arc extinction detection algorithm is used to detect the nature of the fault. The problem with this fault nature recognition is the delay of about 1.5 to 3 s, which means that the system has been in two phases for this period in the presence of a permanent fault for no reason, and this causes the power system to move more toward instability. In another category of papers, a separate method was proposed to identify the nature of the fault, which did this much faster than the first case. These methods usually use the presence of odd harmonics during the secondary arc or the presence of high frequency components during the primary arc at voltage. In any case, the detection of fault instant, fault location, and fault nature was not in the scope of this paper and the contribution of this paper is in the detection of secondary arc extinction.

**Figure 2.** The faulty phase voltage at Bus 1 for the single line to ground transient fault. (**a**) The faulty phase voltage *U* (p.u.). (**b**) The spectrum extracted by Hilbert-Huang Transform (HHT), and (**c**) the proposed index *IN*.

**Figure 3.** Intrinsic mode functions (IMFs) extracted from the voltage waveform in Figure 2a and their extracted spectrum using the HT (**a**) *IMF*1 (**b**) *IMF*1 spectrum (**c**) *IMF*2 (**d**) *IMF*2 spectrum (**e**) *IMF*3 (**d**) *IMF*3 spectrum.

**Figure 4.** Flowchart of the proposed algorithm.

The algorithm was delayed 50 ms, thus all samples in the data window were measured after faulty phase isolation, next, the algorithm began to calculate IN using the faulty phase voltage. In the simulations performed in this paper, IN, during the secondary arc, was in most cases zero

and sometimes takes very small values. However, after the secondary arc extinction, its value increases and must be greater than the threshold value of 0.01 p.u. for 5 ms to confirm fault clearance. The counting strategy is used in digital protection to improve the reliability of the relay operation or avoid relay maloperation. Checking a protection decision for several times improves the probability of successful operation.

Due to the presence of noise in real signals and to prevent protecting system mal-operation, IN was not compared with zero or smaller threshold value, however, the proposed criterion did not need any pre-calculation of the threshold value and the threshold value had a global feature. After each comparison of IN with the threshold level, the data window shifted forward and the new IN value was calculated. After secondary arc extinction and deionization of the arc path, the reclose command was issued for the local CB.

The main contributions of this paper include the following:

