Formation and propagation characteristics of pseudo-wavefronts of optical polarization states signal inside OPGW under lightning strikes

Lightning strikes on Optical Fiber Composite Overhead Ground Wires (OPGW) result in a phenomenon where the current traveling wave along the OPGW’s outer stranding propagates faster than the optical signals inside the fiber. This leads to the emergence of pseudo-wavefronts ahead of the optical polarization state signal after lightning strikes OPGW, introducing errors in lightning point localization based on the optical polarization state. This paper investigates the formation and propagation characteristics of pseudo-wavefronts. The study employs theoretical analysis and simulation to examine the process of optical polarization state formation during OPGW lightning strikes. Additionally, it conducts comparative analyses between laboratory-simulated OPGW lightning strikes and field measurements obtained from OPGW lightning monitoring systems. The results affirm the existence of the proposed pseudo-wavefront phenomenon, which substantially impacts the precision of lightning point localization. Notably, the duration of pseudo-wavefront effects increases with greater distance from the lightning point and higher lightning current amplitudes. These findings raise questions regarding the suitability of traditional wavefront calibration methods based on the traveling wave approach. This research contributes valuable insights for the practical implementation of lightning point localization methodologies relying on OPGW self-sensing technology.


Introduction
Lightning strikes have long been a significant contributor to power transmission line tripping and failures.Consequently, as China advances in the construction of an intelligent power grid centered around ultra-high voltage (UHV) networks, it is imperative to enhance the level of lightning monitoring and protection for these networks.Among the recognized fault location methods in recent years, the traveling wave method has emerged as one of the most effective.However, it currently faces several challenges, including waveform distortion [1] , difficulty in positioning when the power grid structure is complex [2] , uncertain traveling wave speed [3] , and difficulties in detecting traveling wavefronts [4] .
OPGW serve a dual purpose as lightning conductors and communication channels due to their internal optical fibers.In recent years, research on lightning localization based on OPGW has raised attention [5] .This method leveraged the magneto-optic effect within optical fibers to locate lightning strikes by monitoring changes in optical polarization states induced by lightning currents.In contrast to the traveling wave method, OPGW's internal optical signals exhibited higher resistance to interference, maintained stable wave velocities, and remained relatively unaffected by wavefront distortion, thus enhancing reliability.
In the realm of traditional traveling wave methods, whether following single-end or double-end principles for localization, the precise identification and calibration of traveling wavefronts were crucial factors that directly influence the precision and accuracy of localization.Researchers have proposed a range of techniques for wavefront identification, including Kalman filtering, wavelet analysis, mathematical morphology, Hilbert-Huang Transform (HHT), Singular Value Decomposition (SVD), and wavelet modulus maxima [6] .OPGW optical polarization state-based lightning localization was equally applicable to both single-end and double-end methods.A laboratory-based study employed single-end measurements with a delayed optical fiber and an improved SVD algorithm for lightning fault localization in [7].The experiment validated the effectiveness and measurement accuracy of this method.However, single-end localization encountered challenges related to signal inundation, and a single delayed optical fiber might not eliminate measurement dead zones, making the double-end method a more practical choice.An analysis of field data from trials conducted in Jiaxing highlighted the potential limitations of traditional traveling wavefront calibration algorithms in the context of lightning localization.These limitations manifested in substantial localization errors, exhibiting a consistent pattern characterized by smaller errors near the line's central section and progressively larger errors toward the line's terminations.This observed pattern could be attributed to the differential propagation speeds between optical signals within the OPGW and the electrical currents propagating along the external stranding.The consequence of this propagation speed discrepancy was the modulation of optical signals by the faster-moving electrical currents, resulting in the formation of an offset ahead of the wavefront.This offset, referred to in this paper as pseudowavefront, presented a significant challenge to the conventional traveling wavefront calibration methods.Consequently, this research undertook an exhaustive exploration of the formation and propagation characteristics of the pseudo-wavefront to comprehensively address its impact on the accuracy of lightning localization.
This paper employs a multifaceted approach, incorporating theoretical simulations, laboratory experiments, and analysis of field data to elucidate and substantiate the existence and propagation behaviors of the pseudo-wavefront.The primary objective of this research is to provide invaluable insights aimed at enhancing the practical implementation of lightning strike point localization methods based on OPGW technology, thereby contributing to the advancement of the field.

The mechanism of pseudo-wavefront formation
The structure of an OPGW comprises two principal components: an outer layer consisting of stranding and an inner layer composed of optical fiber units.When a stable, polarized laser signal is meticulously applied to the internal optical fibers of the OPGW, it prompts the illustration of a schematic diagram depicting the transient current and the propagation of optical polarization state within the OPGW during a lightning strike, as presented in Figure 1.
During a lightning strike directed at the OPGW, a substantial transient current swiftly travels along the outer stranding, propagating vigorously towards both extremities of the line.This current engenders a magnetic field component aligned parallel to the direction of optical propagation within the OPGW, which precise rotation in the polarization state of the optical signal as it gracefully traverses the corresponding segment of optical fiber.The angular deviation θ elegantly mirrors the magnitude of the magnetic field engendered by the potent lightning current, which can be expressed as follows: where V is the dielectric constant of the medium, and L is the distance over which light propagates in the magneto-optical material.According to the equation for calculating the magnetic field intensity around a current-carrying straight conductor: where μ0 is the magnetic permeability of the medium; I is the current in the conductor; r is the distance to the center of the conductor.We combine Equations ( 1) and ( 2) and assume the incident polarized light intensity is Φ0, the transmitted light intensity is Φm, and α is the angle between the optical axes of the polarizer and analyzer.According to Malus's law, the amplitude of the current after modulation Im can be expressed as: where k is a coefficient.In Figure 1, the propagation velocity of transient currents, I1 and I2, generated by lightning strikes along the outer stranding of OPGW is denoted as the wavefront velocity Vi.The propagation velocity of polarized light Im within the optical fiber is represented as Vc, where Vc = C/n.
Where n signifies the refractive index of the optical fiber (n = 1.4685), and C denotes the speed of light in a vacuum (C = 3 × 10 8 m/s).Consequently, Vc is approximately 2.0429 × 10 8 m/s, whereas the wavefront velocity, Vi, of the traveling wave is approximately 2.9 ×10 8 m/s.As a result, I2 possesses a higher velocity than Im, leading to interference modulation on the leading part of the Im signal during its propagation which constitutes a significant source of error that cannot be disregarded in OPGW lightning localization.From Figures 2 and 3, it is evident that in the simulated lightning-induced optical polarization state signal waveforms, regardless of the magnitude of the lightning current or the distance from the strike point, there is a noticeable apparent displacement of the waveform.This result precisely indicates that the preceding displacement is a consequence of the difference in propagation speeds between the current wave and the speed of light.The fast propagation of the current wave reaches the monitoring point before the actual optical signal waveform leading edge arrives, thus causing interference and modulation of the optical signal.This is exactly the root of the apparent displacement.Although this segment of apparent displacement appears relatively small on the surface, it can become more significant under certain conditions, such as when the grounding method of the ground wire is not a tower-by-tower grounding or in the presence of exceptionally high lightning currents.In such cases, the impact on the localization of the waveform leading edge becomes more pronounced.Table 1 shows the maximum amplitudes of the pseudo-wavefront displacement at distances of 10 km, 15 km, and 20 km from the lightning strike point for various lightning current magnitudes.It illustrates a direct relationship between the maximum amplitude of the pseudo-wavefront and both the lightning current and the distance from the strike point.Specifically, when the lightning current reaches 150 kA, the apparent displacement has already entered a state of saturated oscillation.Based on simulation results, the following conclusions can be drawn: the farther the distance from the lightning strike point is, the longer the range and greater the amplitude of the apparent displacement is; additionally, larger lightning currents result in greater amplitudes of the apparent displacement.

Simulation of OPGW lightning-induced optical polarization state propagation characteristics
Research indicates that the primary factors causing interference to the distance measurement wavefront edge are the magnitude of the lightning current and the length of the distance from the lightning strike point.Therefore, in practical applications, especially for lengthy transmission lines, significant lightning currents, and lightning strikes on the far end of the line, the impact of the apparent displacement due to differences in the speeds of optical and electrical signals should not be overlooked during lightning strike location data processing.Neglecting this factor could lead to significant errors or even render the localization ineffective.

Analysis of lightning strike signals on OPGW based on field measurements
Two sets of monitoring systems were selected for the on-site measurements of OPGW lightninginduced optical polarization state signal waveforms on the Jiaxing transmission line, with one set shown in Figure 3.It can be observed that there are no apparent displacements in the waveform at the A end, and the waveform rises sharply.However, at the B end, as indicated by the dashed box in Figure 4(b), apparent displacements are present in the signal, and conventional filtering methods cannot effectively remove them as part of noise processing.To illustrate the extent of the impact caused by the presence of apparent displacements on localization results, this paper employs a combination of wavelet analysis commonly used in traveling wave ranging and the HHT for waveform calibration.Additionally, an optimization algorithm that takes into account the phenomenon of apparent displacements due to differences in optical and electrical signal speeds is used for localization.These methods are compared and validated against the results obtained from the lightning location system (LLS), as shown in Table 2.  2, it can be observed that using the typical waveform calibration method commonly employed in traveling wave ranging results in a positioning error of 6 to 7 tower spans.However, when considering the phenomenon of apparent displacements caused by differences in optical and electrical signal speeds and utilizing the optimized algorithm, the localization results align with those obtained from the lightning location system (LLS).
Through on-site measurements of lightning strikes on OPGW and the analysis of optical polarization state signal waveforms, as well as the analysis of localization results, it has been verified that the apparent displacement phenomenon mentioned in this paper indeed exists.Neglecting this phenomenon during the localization process could potentially introduce significant errors.Research indicates that the traditional traveling wave method for waveform calibration may not be entirely suitable for OPGW optical polarization state lightning strike localization, highlighting the need to account for the influence of differences in optical and electrical signal speeds.

Conclusions
(1) When lightning strikes OPGW, the current traveling wave velocity along the outer stranding surpasses the propagation speed of optical signals within the fiber.Before the optical polarization state signal reaches the measurement point at the end of the line, the traveling wave has already arrived.This process modulates the leading portion of the lightning-induced optical polarization state, resulting in the phenomenon known as a pseudo-wavefront.
(2) The amplitude of the pseudo-wavefront is directly correlated with both the magnitude of the lightning current and the distance from the lightning strike point.As the distance from the lightning strike point increases, the range and amplitude of the pseudo-wavefront's influence grow proportionally.Larger lightning currents result in greater pseudo-wavefront amplitudes.
(3) In practical applications, the presence of the pseudo-wavefront will introduce substantial errors in the localization results when lightning currents are substantial or when the lightning strike point is close to either end of the transmission line.This highlights that traditional traveling wavefront calibration algorithms may not be entirely suitable for OPGW optical polarization state method lightning localization, necessitating consideration of the impact of the difference in optical and electrical signal propagation speeds.

Figure 1 .
Figure 1.Schematic diagram of lightning strike OPGW.The angular deviation θ elegantly mirrors the magnitude of the magnetic field engendered by the potent lightning current, which can be expressed as follows: This paper employs ATP-EMTP to simulate lightning strikes on the OPGW, aiming to acquire current data at various distances along the OPGW during lightning strikes, serving as the foundation for calculating the Faraday effect integral of the lightning pulse signal.The simulation incorporates a negative double-exponential current wave model with parameters of 2.6/50 μs for the lightning current model.The overhead line utilizes the JMarti model of Line/Cable Constants (LCC), while the towers are represented by using a single-circuit cup-shaped multi-wave impedance model.The simulation operates at a voltage level of 220 kV, employing a double lightning wire model.Both OPGW and conventional ground wires are grounded at each tower.The distance between towers is consistently set at 450 m for all spans, with a total of 73 towers included in the model, resulting in an approximate total simulated line length of 32.4 km.The simulation positions the lightning strike at the top of tower 19, with distances from point A (L1 = 8.1 km) and point B (L2 = 24.3km) as illustrated in Figure1.Throughout the simulation, the distribution of transient currents along the OPGW during lightning strikes at various locations along the entire line is measured.For instance, at the moment of the lightning strike at tower 19, the transient current variation trend of continuous six towers on the OPGW in the direction of point B, referred to as I2, which depicted in Figure2.The simulation results reveal that transient current propagates along the OPGW and gradually attenuates.Despite adopting the tower-by-tower grounding, not all of the current dissipates near the lightning strike point.Instead, it continues to propagate backward.Although the amplitude diminishes, current is still present, even at the rearmost few towers at point B, where there is a transient current of approximately 12 A. As long as there is current, it will influence the magnetic field intensity inside the OPGW.The simulation provides temporal and spatial data on the distribution of transient currents during lightning strikes on the OPGW ground wire.By utilizing Equations (1) to (3), the Faraday rotation angle θ and the lightning optical polarization state signal Im can be computed.To simplify calculations, constant values of 1 are employed for the incident light intensity Φ0 and the coefficient k.Positions at distances of 10 km, 15 km, and 20 km from the lightning strike point within the L2 segment have been selected as examples to analyze and investigate their waveform propagation characteristics.The simulated experiments encompass 5 scenarios with lightning current magnitudes of 20 kA, 60 kA, 100 kA, 120 kA, and 150 kA.Figures 2 and 3 illustrate the optical pulse signal waveforms for lightning current magnitudes of 20 kA and 100 kA, respectively.

Figure 2 .
Figure 2. Polarization waveform of lightning light when lightning current is 20 kA.

Figure 3 .
Figure 3. Polarization waveform of lightning light when lightning current is 100 kA.

Figure 4 .
Figure 4.In the waveform of lightning signal example 1 in the field, the two figures on the left and right represent the signals measured at the A end and B end, respectively.

Table 1 .
The maximum pseudo-wavefront amplitudes for various lightning current magnitudes.

Table 2 .
Positioning results of various wave head calibration methods.