Lightning-Induced Transients on Buried Shielded Transmission Lines

This paper is primarily concerned with the analysis of induced transient current and voltage surges on buried shielded transmission lines due to earth-conduction effects of nearby lightning discharges. An analytical method is presented in this paper to model the conductive coupling mechanisms in the earth and to determine the amount of coupling between a lightning discharge to ground and an earth-return transmission line. The transmission line is assumed to be a long straight horizontal coaxial cable with an inner shield and an outer armor, terminated on both ends with typical communication-equipment load impedances. The general case is considered here, in which the outermost conductor is not necessarily in perfect contact with the conducting earth, but has a contact impedance with the earth, as in cables with an outer dielectric covering for corrosion or water protection. Average lightning-channel conditions and a representative buriedcable geometry are examined. The results are conveniently displayed via several graphs of the time histories of the resulting transient current and voltage surges.     

Etude des perturbations induites par une décharge orageuse sur un câble de télécommunication

Experimental results presented in this paper show the waveform and magnitude of the interference signals that occur on a telecommunication cable located nearby a lightning discharge. The measurements were performed at Saint-Privat-d’Allier (France). We then study the current induced in the outer shield of aerial cables of several lengths and in the common mode voltages which appear on the load impedances. We also give a few results obtained from a buried cable. We will compare experimental results and theoretical predictions that are based on the computation of the electric field radiated by the lightning current and on the coupling of the electric field with the wire structure. This last point is approached through the transmission line theory.     

Protection of Buried Cable from Direct Lightning Strike

This paper presents studies of protection schemes for buried cables. A formula is introduced that gives the maximum peak lightning current for various ground resistivities. Maximum and minimum arcing distances beneath the surface are calculated using the internal breakdown gradient of the soil. The susceptible region for a buried cable is shown to be related to the maximum arcing distance, while the number of buried shield wires required for adequate protection is determined by the minimum arcing distance. The effectiveness of the proposed protective schemes is demonstrated by electrogeometrical theory. Finally, the qualifications of the new schemes are discussed.     

The Capacitances and Surface Charge Distributions of a Shielded Unbalanced Pair (Short Papers)

The capacitance matrix of an unbalanced shielded pair cable is determined theoretically. The wires of the cable are asymmetrically located about the axis of the shield and have different radii; however, the axes of the wires are restricted to lie on a line passing through the axis of the shield. The elements of the capacitance matrix are determined as particular elements of the inverse of a truncated intinite matrix, which relates the Fourier coefficients of the surface charge densities on the inner conductors and the shield to the applied voltage excitations on the cable conductors. The capacitances and surface charge distributions are evaluated numerically for a shielded pair cable, which, due to inaccuracies in the cable manufacturing processes, has one wire with a smaller or larger radius than the other wire of the pair and/or has one wire closer to or farther from the axis of the shield than the other wire of the pair.     

光缆通信线路防雷设计与安装

根据雷电的形成过程和雷击大地时雷电流的分布规律，分析了光缆遭遇雷击的原因，提出了避开雷区、雷点，阻止光缆诱导雷电，引接雷电入地的光缆防雷设计思路，介绍了光缆的防雷设计与安装的方法。     

智慧小区直埋光缆的防雷设计

从光缆的结构入手,分析了直埋光缆遭受雷击的原因,并进行了直埋光缆防雷的安全距离测算,最后提出了智慧小区直埋光缆经济可行的防雷解决方案。工程实践证明该解决方案取得了一定的效果。     

Perturbations induites par une onde de foudre sur un réseau de câbles blindés aériens

In this work we study the coupling of a lightning wave with an overhead shielded cables network. The study is led directly in the time domain with hold in account of the loads nonlinear character, and the effect of a finite conductivity of the shield and soil. After discretization by the method so-called FDTD (Finite Difference Time Domain) of the lines equations excited by a lightning wave and the application in every node of the network of the Kirchhoff’s laws in current and voltage, we deduct a equations system linear or no, of which the resolution permits us to deduct the induced electric quantities in every node of the network. In this study we propose a concept for the coupling analysis of a lightning wave with a shielded cable without use of the least FFT; the shielded cables are treated in a single stage. In this work we also put in evidence the disadvantages of the coupling analysis in the frequency domain.     

Cable Shielding Effectiveness Testing

This paper discusses an improved method of measuring the effectiveness of cable shielding and describes the results of tests on single- and multi-branched cables. Effects of significant shielding parameters of cables are also reported. These are the the effect of number of shield braid layers, braid material, braid angle, optical coverage, cable length, and wire size. The test method permits measurement of long specimens using high currents with a uniform current distribution along the cable shield. Measurements were made in the frequency range 0.5 to 100 MHz. The method is offered as a standard technique for measuring the shielding effectiveness* of shielded cables.     

A Model for Currents and Voltages Induced Within Long Transmission Cables by an Electromagnetic Wave

A model is presented for determining the transient currents and voltages induced within a long coaxial cable by a uniform plane traveling wave whose variation with time may be specified. The cable may be located above or within a half-space lossy dielectric with the wave incident from the half-space lossless dielectric. This results in a model for either aerial or buried cables with the source of the wave located in the atmosphere. A method is also presented for generalizing the approach to more complex cables encountered in communication systems. A demonstration of the applicability of this model is presented by analyzing the response of a 0.375-in coaxial cable for both aerial and buried situations. An incident electromagnetic wave with a rectangular time domain waveform is used to demonstrate the transient response. This waveshape is adequate to clearly indicate the transient phenomena. It is found that voltage enhancement results in both aerial and buried cables when the incident wave approaches grazing incidence. This voltage enhancement can be significant especially for aerial cables. Cable shield current enhancement also results for an aerial but not for a buried cable.     

Transient plane wave coupling to bare and insulated cables buriedin a lossy half-space

The current induced on an infinite bare or insulated cable buried in a lossy earth medium due to a transient plane wave is presented. An exact solution is formulated in the frequency domain using a spatial transform under the thin-wire approximation. The widely used equivalent circuit transmission line model is derived from the exact solution. Results are presented for typical transmission structures under high frequency transient excitation and the exact solution is compared with the transmission line approximation. The transmission line approach provides good results for a wide range of cases. For accurate results in the high frequency situation it is necessary that the correct incident field expressions be used and that a complete representation of the earth's electrical properties (σ and ϵ) be retained     

Time-domain study of a shielding cable system with a nonlinear load

An impulse current of several kiloamperes was injected to the shield of a shielded cable, which was terminated by a varistor. The induced voltage on the inner conductor caused by this impulse current reaches an amplitude in excess of the varistor's threshold level. The clamped voltage across the varistor and the injected current have been studied for different termination conditions of the shielding cable. Furthermore, this paper also presents the use of a lumped circuit to simulate the transfer impedance of an “electrically short” shielded cable in the time domain. In combination with the varistor circuit model, the shielded cable with the nonlinear load, a varistor, was also simulated straightforwardly in the time domain. Good agreement was found between the measured voltage and current oscillograms and the calculated waveforms. It is thereby demonstrated the validity of the developed lumped circuit model for the transfer impedance of a shielded cable     

The Capacitances and Surface-Charge Distributions of a Shielded Balanced Pair

The capacitance matrix of a straight pair of uniform wires symmetrically placed in a shield is determined theoretically. Exact expressions for the elements of the capacitance matrix are determined as particular elements of the inverse of an infinite matrix which relates the Fourier coefficients of the surface-charge densities on the inner conductors and the shield to the applied voltage excitations on the cable conductors. If the wire diameter is small relative to the wire separation, and if the wire separation is small relative to the shield diameter, then accurate numerical approximations for the elements of the capacitance matrix are obtained to any degree of accuracy by suitably truncating the infinite matrix. Once the elements of the capacitance matrix are determined, then the distributions of the surface-charge densities on the peripheries of the inner conductors, and the shield are determined for any arbitrary excitation of the cable structure. In particular, the various capacitances associated with the cable structure, e.g., the direct, ground, and mutual capacitances, are determined from a comparison of the surface-charge densities resulting from a "balanced" excitation and a "longitudinal" excitation. The Fourier coefficients of the surface-charge densities are required to determine the propagation parameters and the associated propagation modes of the cable structure. The surface-charge distributions are evaluated numerically for a typical standard production cable using 22-gauge wires. The results of this paper will be extended by a perturbational method to include twisted wires in a shield; also, certain types of asymmetries in the cable geometry will be considered. Hence, the propagation constants and the associated propagation modes of unbalanced and/or twisted shielded pair cables can also be determined.     

Analyzing electromagnetic pulse coupling by combining TLT, MoM, andGTD/UTD

An important problem in electromagnetic compatibility (EMC) analysis is to determine the coupling of an electromagnetic field into a shielded cable. Using the transmission line theory (TLT), the disturbance voltage induced inside the cable is easily calculated from the current distribution on its shield. This current distribution depends on the incident electromagnetic field and is efficiently determined by the method of moments (MoM). Extending the MoM with the geometrical and uniform theory of diffraction (GTD/UTD) makes it possible to solve scattering problems that are too large and too complex for the plain MoM. The combination of the three approaches-TLT, MoM, and GTD/UTD-allows calculation of the disturbance voltage inside a shielded cable, which is part of a complex scattering structure. The fundamentals of each method and the way of putting them together are shown in this paper. The application of the proposed method is demonstrated by an example: the pulse coupling between a monopole antenna and a shielded cable is analyzed, taking into account a large conducting structure in the vicinity     

Current flow in coaxial braided cable shields

In the last few years, much effort has been made to describe the behavior of shielded cables. Many researchers have attempted to understand how an electromagnetic field couples into a braided coaxial cable. There are some important publications on this topic. Nevertheless, up to now, it has not been possible to predict analytically the coupling through a braid shield. An electromagnetic field outside a cable induces a disturbance current in the cable shield. The coupling from the current in the shield into the cable can be described by the transfer impedance. How the current flows in the cable shield is an important quantity in this coupling process. Therefore, to understand the coupling mechanism into a cable, it is necessary to understand the behavior of the current flow in such a braided shield. The paper discusses the current flow in a braided cable shield. The assumption often made in the literature, that a braided shield behaves like a homogeneous tube with apertures, is shown to be inaccurate. It is also shown that the standard braid of the shield used had the same properties as a braid made with insulated wires.     

Lightning induced disturbances in buried cables - part II: experiment and model validation

This paper presents experimental results obtained at the International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, Florida during the summers of 2002 and 2003. Currents induced by triggered and natural lightning events were measured at the terminations of a buried power cable, in the cable shield, and in the inner cable conductor. Measurements of the horizontal component of the magnetic field above the ground surface for both natural and triggered lightning are also presented. For distant natural lightning events, locations of ground strike points were determined using the U.S. National Lightning Detection Network (NLDN). Based on the theoretical developments presented in Part I of this paper , the field-to-buried cable coupling equations are solved in both the time domain and in the frequency domain. The obtained experimental results are then used to validate the numerical simulations provided by the relevant developed codes.     

Auswirkungen von Blitzschlägen auf 20-kV-Energiekabel

Recently appeared defects on high voltage cables have required an urgent evaluation of the impact of lightning strikes necessary. In some cases overvoltages between the copper wire screen of the cable and earth may appear which cause damages of the cablesheath. Field measurements with a classification of the voltage impulses at the copper wire screen have been made to evaluate the number of events. Additionally a numerical model was developed to study the effects of atmospheric discharges on underground cables with emphasis to the influence on the cablesheath. This numeric method was also applied to estimate the effectiveness of different protection arrangements. This contribution presents evaluation methods for overvoltages of cables and a model used firstly for calculating the stress caused by differential voltages and secondly to determinate the influence of protection measures.     

Couplage entre le champ électromagnétique rayonné par un coup de foudre et une ligne de télécommunication aérienne ou enterrée

This paper describes the determination of the current induced by a lightning discharge on a telecommunications cable using a transmission line theory. The electromagnetic field due to the return stroke is calculated by modeling the channel by a vertical antenna situated above a perfectly conducting ground. The electromagnetic coupling to a telecommunications line is then determined by introducing the finite conductivity of the ground into the transmission line model. Examples are given for various positions of the lightning discharge with respect to telecommunications cable. A comparison with results obtained during the last experiment at Saint-Privat-d’Allier is also presented. To get the response of a buried cable the authors first determine the propagation constant and the primary parameters of the line. The reference for the voltage is also analysed. The authors show that the choice of the origin at the infinity allows to take into account the energy propagating in the ground parallel to the cable.     

Triggered lightning testing of an airport runway lighting system

The interaction of rocket-triggered lightning with an airport runway lighting system has been studied. The lighting system included a buried counterpoise with attached vertical ground rods for protection of the series lighting cable from lightning. Experimental data for voltages and currents at various locations in the runway lighting system due to direct lightning strikes are presented along with the causative lightning current. The data include the first measurements of the responses of an underground bare conductor (counterpoise) to direct lightning strikes. These measurements can serve as ground truth for the testing of the validity of various counterpoise models.     

SPICE-like models for the analysis of the conducted and radiated immunity of shielded cables

The aim of this work is the development and validation of compact SPICE models suitable to analyze the conducted and radiated immunity of shielded cables. The reference structures are coaxial cables, and shielded cables with two parallel wires (i.e., twinax cable). The conducted and radiated immunity of the shielded cables are evaluated considering as source a known injected current on the cable shield, and the coupling with an external plane wave electromagnetic field, respectively. The circuit models are validated by comparing the results with those obtained by other approaches. The developed models are then used to quantify the main grounding practices of shielded cables.     

Peripheral Cable-Shield Termination: The System EMC Kernel

This paper presents experimental data that show an over-whelming dependence of system electromagnetic compatibility (EMC) on system cable effects, rather than leakage through cracks, seams, and other box (LRU and WRA) openings. A laboratory experiment compares cable-shield RF leakage from a pigtail-terminated cable with that of one that has been terminated peripherally. Theoretical justification for these empirical observations is presented. That a shielded conductor carrying an RF current i induces its own return current -i on the inside surface of the shield is proved. By confining this return current to the inside of the shield, external emissions are attenuated by the intrinsic shielding effectiveness (which can be quite a large number) of the shield.