**1. Introduction**

In recent years, the protection of transmission lines by reclosing switches has become a challenge of improving the reliability of power systems [1]. Approximately 80% of faults in overhead transmission lines are transient (arcing) and single-phase to earth. As a result, there is no need to permanently de-energize the transmission line and send the repair team to patrol for maintenance purposes, then, actually the fault will be cleared by temporary de-energizing of the transmission line and by reclosing the circuit breakers (CBs), the transmission line can restore to its normal operation. In the case of single-phase faults, isolating the faulty phase is enough and there is no need to three phases reclosing [2]. After fault, the arc current will has an extremely large value and its length is constant, and the fault at this stage is called the primary arc. After the faulty phase is isolated from both sides of the line, the arc is still fed through the healthy phases [3]; the fault at this stage is called the secondary arc. Due to the low current of the secondary arc, the ionized column of the arc becomes narrower and moves with the wind, and its length increases until the extinction of it. The time of the secondary arc that occurred is called the dead-time. Dead-time is much less than the reclose time setting in traditional methods, usually between 0.2–0.8 s, hence single-phase reclosure can be done much faster, which has the following benefits for the power system:


Lightning flashover is the prime cause of transient faults. When lightning strikes the tower body or guard wires, the lightning current passes through the tower body and enters the ground. If the grounding resistance is high, the voltage drop across the tower body will also be large, and eventually a flashover will occur between the tower body and the phase conductor. High tower height, high ground resistance, high pollution severity on insulators, and high average isokeraunic level along the transmission line are all factors that increase the likelihood of transient faults occurring in an overhead transmission line. Obviously, it is possible for lightning to strike the tower, but not cause a fault, but this will weaken the insulation properties of the insulators. In general, the high incidence of thunder storms increases the likelihood of transient faults. In ASPAR studies, modeling starts from the primary arc onward, and previous events have no e ffect on the results of these studies.

Adaptive single phase auto-reclosing methods must be able to quickly and accurately detect the moment of secondary arc extinction. In this regard, various algorithms have been proposed, a few important groups of them are discussed as follows.

Due to the quasi-square waveform of the arc voltage, the faulty phase voltage contains the odd harmonics of the fundamental component. After the fault clearance, the values of these harmonics decrease and will ideally reach zero. The approaches presented in [4–10] calculated the harmonic content of the faulty phase voltage or healthy phase currents using various signal processing techniques including time-time (TT) transform, discrete wavelet transform, wavelet packet, and total harmonic distortion (THD). Finally, the fault nature and the moment of extinction of the secondary arc were detected using the calculated criterion values and changings. In the presence of renewable resources, the value of THD is always greater than zero, and this disrupts the performance of such methods.

In [11], the third harmonic of the zero sequence voltage at the local substation was used as a criterion to detect secondary arc extinction. Using voltage measurements at both sides of the line was suggested in [12] by a communication-aided index for ASPAR based on predicted and measured voltage of the faulty phase. The approach proposed in [13] computes the secondary arc current based on measurements to decrease reclosing delay. The proposed real-time method requires signals measured on both sides of the transmission line, however, it can continue to work with local measurements.

In [14], based on local faulty phase voltage and the adaptive cumulative sum method, an increase in voltage amplitude due to fault clearing was recognized. The algorithm [15] utilized the least square method to predict present voltage magnitude value; at the arc extinction moment, the di fference between predicted and measured voltage magnitude increased and an adaptive threshold-less approach detected fault extinction. Ghaderi-Baayeh, in [16], introduced a new method for ASPAR based on the second derivative of the faulty phase local voltage angle to determine the secondary arc extinction time in transient fault cases. In [17], the absolute value of the first derivative of the faulted phase local voltage measurement was used to detect the secondary arc extinction. The proposed algorithm has fast performance and uses a low sampling frequency rate and adaptive threshold value. In [18], based on local voltage measurements, a combination of voltage and angle first derivation was utilized to identify fault type and arc extinction detection.

In [19], based on traveling wave theory and using local measured voltage for three types of mixed transmission systems, the occurrence of fault and its location are determined. In the case of fault in the overhead line section, reclosure permission was issued. In [20], for mixed transmission systems, based on wavelet transform and the di fference between the currents in the active part of the cable and

those in the shields, the overhead section fault was detected. Reclosure into a permanent fault caused damage to the generator shaft of nearby power plants. Since the reclose commands issued for each side of the line were not synchronous, one side of the line always reclosed faster. In [21], a method for selecting the side of the line that should lead reclosing was proposed. In [22], the fault nature, whether permanent or transient, was determined based on the locally measured voltage and using a featured classifier based on support vector machine.

Shunt reactors are widely used in high voltage transmission lines to improve power system stability and line voltage profile regulation [23]. The methods presented in [24–30] are effective for shunt compensation transmission lines. In these methods, the beat frequency generated after the quenching of the secondary arc was used to detect the quenching of the secondary arc. In [24], the local measured voltage frequency was analyzed using modal transformation and a simple zero crossing algorithm. The secondary arc extinction time was then specified for single- and double-phase-to-ground faults. In [25], mode currents of shunt reactors were calculated, then the presence and number of natural frequencies were used to distinguish the fault nature. In [26], the differences of faulty phase terminal voltage between the two fault states after arc extinction was utilized as a criterion to detect fault nature and clearance. In [27,28], the instantaneous power algorithm was utilized to compute faulty phase reactive and active power, respectively, using local voltage and current measurements. Increasing faulty phase reactive or active power after secondary arc extinction was used to detect arc extinction for shunt compensated transmission lines. In [29], based on the cascaded delayed signal cancellation technique and using the faulted phase local voltage of the shunt compensated line, the average distortion rate was calculated to identify the fault nature and clearance.

The majority of ASPARs presented so far only used the measured data on one side of the transmission line, but references [12,13,30] required measured data on both sides of the transmission line. In [30], the presence of phasor measurement units (PMUs) on both sides of the transmission line was necessary to identify the type of fault and its clearance time.

Long and high voltage transmission lines are very prone to transient faults. On the other hand, to prevent overvoltage, most of these lines are shunt compensated on either side or one side. After the secondary arc extinction, the trapped energy oscillation between the line capacitor and the reactor inductance creates a sub-synchronous component in the isolated phase voltage. In this study, by using the presence of sub-synchronous components in the faulty phase voltage spectrum, an index was proposed to detect fault clearance. During the fault, the voltage of the faulty phase does not contain any sub-synchronous components, however, after extinguishing of the secondary arc, due to the resonance between the shunt reactor and the line capacitor, a sub-synchronous component appears in the voltage. This change in frequency content from 0 to 60 Hz is introduced to detect secondary arc extinction. The Hilbert-Huang Transform (HHT) method is used in this algorithm, which can ideally monitor sub-synchronous components with very low spectrum leakage and high accuracy. Since the proposed method, unlike many previous methods, does not use the THD of measured signals, consequently, it is not sensitive to the presence of renewable resources and is a good option for protecting the grid in the high penetration of renewable resources. System simulation studies show that the proposed algorithm estimates the fault clearing instant accurately for auto-reclosing.

The rest of the paper is structured as follows. Section 2 describes the modeling of the understudy system and Section 3 provides an introduction to the Hilbert–Huang transform. Section 4 presents the new algorithm followed by the simulation results in Section 5 and conclusions.
