Horizontal Conductor Research Articles

Contribution to studies on calculation of the magnetic field under power lines

AbstractThe paper presents in a tutorial manner a theoretical study of the calculation of magnetic fields in vicinity of overhead electric power lines. Exact and simplified methods of the determination of the magnetic field of a straight overhead conductor based on the Fourier transform technique and on the concept of complex ground return plane are presented. The decomposition of the magnetic fields in two components: magnetic field obtained in free space from the Biot‐Savart law and the magnetic field produced by earth current is discussed. It is shown that in practical cases the effects from earth currents can be neglected as compared with effects from line currents. A solution for modeling magnetic fields produced by sagging conductor, described by the catenary equation, is also proposed. The effect of the catenary on the magnetic field spatial distribution is investigated. The calculation results of magnetic field produced by sagging conductor and the magnetic field of a conventional model consisting of a horizontal conductor hanging on the effective height lying between the maximum and minimum heights of catenaries is compared and discussed. As an example the magnetic field of a real‐power catenary high voltage 2 × 220 kV power line is demonstrated. Copyright © 2006 John Wiley & Sons, Ltd.

Modeling of a buried conductor for an electromagnetic transient simulation

AbstractThe paper has proposed a distributed‐line model of a buried bare conductor with horizontal and vertical configuration by assuming an artificial insulator outside of the bare conductor so that the characteristic impedance and the propagation velocity of the buried conductor is evaluated as an insulated conductor (cable) by the cable constants/parameters of the EMTP. A shunt admittance is added to the conductor at every short distance to represent currents flowing into the earth from the original bare conductor. The admittance circuit and the parameters are evaluated either by experimental results or by published references of grounding electrodes. The model circuit has been applied to simulate transient currents and voltages on horizontal and vertical buried conductors, and the simulation results are compared with the measured results. It has been observed that the simulation results of the currents agree satisfactorily with the measured results, but the results of the voltages do not seem satisfactory. The reason for this has been discussed based on the measured results. © 2006 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Depth Estimates for Slingram Electromagnetic Anomalies from Dipping Sheet-like Bodies by the Normalized Full Gradient Method

The Normalized Full Gradient (NFG) method was proposed in the mid-1960s and was generally used for the downward continuation of the potential field data. The method eliminates the side oscillations which appeared on the continuation curves when passing through anomalous body depth. In this study, the NFG method was applied to Slingram electromagnetic anomalies to obtain the depth of the anomalous body. Some experiments were performed on the theoretical Slingram model anomalies in a free space environment using a perfectly conductive thin tabular conductor with an infinite depth extent. The theoretical Slingram responses were obtained for different depths, dip angles and coil separations, and it was observed from NFG fields of the theoretical anomalies that the NFG sections yield the depth information of top of the conductor at low harmonic numbers. The NFG sections consisted of two main local maxima located at both sides of the central negative Slingram anomalies. It is concluded that these two maxima also locate the maximum anomaly gradient points, which indicates the depth of the anomaly target directly. For both theoretical and field data, the depth of the maximum value on the NFG sections corresponds to the depth of the upper edge of the anomalous conductor. The NFG method was applied to the in-phase component and correct depth estimates were obtained even for the horizontal tabular conductor. Depth values could be estimated with a relatively small error percentage when the conductive model was near-vertical and/or the conductor depth was larger.

Numerical Analysis of Wave Propagation Characteristics on a Buried Horizontal Conductor by an FDTD Method

Fundamental characteristics of a 34-m long horizontal conductor buried at a depth of 1m have been studied with an FDTD method. An equivalent radius of a buried thin wire is shown to be 0.23 times the side of cells employed, which is the same as that of an aerial thin wire. The rate of current dissipating from each section of the buried conductor to the injected current is roughly equal to that of the section length to the total length although it is somewhat influenced by the direction of a current lead. As the conductivity of the ground is higher, the wavefronts of a voltage and a current become less steep. The high permittivity distorts wavefronts of a voltage and a current with their propagation. However, its influence appears only initially and the response at the injection point is little influenced by it. The transient grounding resistance at 5μs calculated by the FDTD method is 10 to 20% lower than the resistance calculated by Sunde’s formula.

Corona power loss, electric field, and current density profiles in bundled horizontal and vertical bipolar conductors

In this paper, computation of the corona current and, hence, the corona power loss associated with bipolar high-voltage direct current (HVDC) conductors is presented using the finite-element method (FEM) and the method of characteristics (MOC). The former method is used to solve Poisson's equation while the latter is used to satisfy the current continuity condition. The ground-plane current density and electric field profiles associated with the HVDC conductors are also calculated as a prerequisite for the computation of the corona current. The effectiveness of the present method is demonstrated using HVDC full-scale and laboratory-model transmission lines. Horizontal and vertical bipolar configurations are tested with 2 and 4 bundles. Comparison between previously measured and computed profiles and present calculations shows satisfactory agreement with previous measured and calculated values.

Interpretation of Thick Conductive Zones using Time-Domain EM Parasections

Conductivity-depth images of moving-loop time-domain EM data assist in distinguishing between near-surface and deep conductors. Use of differential conductivity provides improved resolution of conductors relative to the spiked conductivity of Smith et al. (1994). The conductance parameter is complementary to differential conductivity, in providing superior detection of conductors at depth under a conductive overburden. Field and model data from Frazers Plateau shows how differential conductivity-depth images assist in distinguishing between a wide surficial conductor and a deep basement conductor. Field and model data from the Ernest Henry mineral deposit show that the conductance parameter is superior in identifying the location of a weak, deep horizontal basement conductor (the primary mineralisation with conductance order 25 S) when it is under the conductive overburden characteristic of that environment (7 S).

Resonances in inhomogeneous dielectric bodies of revolution placed in the multilayered media?TM modes

In this paper, a rigorous method-of-moments (MoM) solution is given for the problem of determining the hybrid HEM-mode resonant frequencies and associated quality factors of inhomogeneous dielectric bodies of revolution (BORs). The body of interest may be placed in an arbitrarily stratified dielectric medium, including the case when it is bounded by one or two horizontal perfect electric conductor (PEC) plates. The general modal electric field integral equation is given, which is then specialized to sample geometry and solved numerically. A comparison of obtained data with results given by other authors is given. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 87–92, 1999.

EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

The equation of pattern formation induced by buoyancy or by surface-tension gradient in finite systems confined between horizontal poor heat conductors is introduced by Knobloch[1990] ∂u∂t=αu-μ∇2u-∇4u+k∇⋅(|∇u|2∇u+β∇2u∇u-γu∇u+δ∇|∇u|2)where u is the planform function, µ is the scaled Rayleigh number, K = 1 and α represents the effects of a heat transfer finite Biot number. The cofficients β, δ and γ do not vanish when the boundary conditions at top and bottom are not identical ( β≠0,δ≠0) or non-Boussinesq effects are taken into account ( γ≠0). In this paper, the Knobloch equation with α > 0 is considered, the global existence in L2-space and the finite existence time of solution in V2-space have been obtained respectively.

A discussion of `Faraday cage’ lightning protection and application to real building structures

Lightning protection has been practised for almost 250 years but we still lack an exact expression of the protective effect produced by the air termination. In this paper, protection primarily refers to the `Faraday cage’ (meshwork) type of external protection. The interior of a completely enclosed metal shell is free from the effects of any external changes of electric field – but apart from special constructions – a genuine Faraday cage hardly constitutes a practical solution to the lightning problem. In most cases, we practise this type of protection with an air termination network consisted of square meshes of horizontal conductors. The mesh size results from the `rule of thumb’ rather than from a thorough analysis. Protective mechanism of the Faraday cage (meshwork) scheme for a structure (roof) constructed of good conductor, poor conductor and good non-conductor are analysed and discussed in the paper. The protective schemes were analysed based on the `critical’ distance theory and the `ratio of chord’ theorem. Differences among these three types of protection mechanisms are considered. It appears, that the meshwork only seldom works as air termination but rather as a collector for the current flowing from another part of the roof. Some important still unsolved problems are also presented.

Resonances in inhomogeneous dielectric bodies of revolution placed in the multilayered media-HEM-modes

In this paper, a rigorous method-of-moments (MoM) solution is given for the problem of determining the hybrid HEM-mode resonant frequencies and associated quality factors of inhomogeneous dielectric bodies of revolution (BORs). The body of interest may be placed in an arbitrarily stratified dielectric medium, including the case when it is bounded by one or two horizontal perfect electric conductor (PEC) plates. The general modal electric field integral equation is given, which is then specialized to sample geometry and solved numerically. A comparison of obtained data with results given by other authors is given. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 87–92, 1999.

Audio frequency magneto-telluric survey of Norikura Volcano in central Japan

Norikura Volcano has not been active during the last 10,000 years in spite of the activity of the surrounding volcanic mountains. To study past volcanic activities, geological studies were carried out extensively. However, quite a few geophysical investigations were conducted to contribute to volcanology. Our objective is to detect the present subsurface structure of Norikura Volcano and to define volcanic stratifications. In the vicinity of Norikura Volcano, geothermal fields are still active. Subsurface volcanic rocks in this area have been exposed to geothermal activity and altered. To comprehend volcanic stratifications of Norikura and geothermal activity, we conducted audio frequency magneto-telluric (AMT) surveys around Norikura Volcano. AMT survey is useful in clearly defining the resistivity structure related to volcanic regions. The AMT data were acquired over a frequency range 10 Hz–10 kHz. Decomposition analysis was applied to the tensor impedance data. Subsequently, apparent resistivity and phase data were inverted using a two-dimensional magneto-telluric (MT) inversion and a model of Norikura was derived. The final model manifests that the surface resistors are in agreement with andesite lava or dacite lava. As for the deeper structure, a horizontal conductor is situated above resistive basements. The alteration of the conductor was weak, while basement rocks were strongly altered and/or heated through the thermal activity. The existence of these layers seems to indicate the degree of thermal activity of Norikura Volcano.

Resonances in inhomogeneous dielectric bodies of revolution placed in the multilayered media—TE modes

In this paper a simple method of moments (MoM) solution is given for the problem of determining TE resonant frequencies of inhomogeneous dielectric bodies with rotational symmetry. The body of interest may be placed in arbitrarily stratified dielectric medium, which also may be bounded by one or two horizontal perfect electric conductor (PEC) plates. The general electric field integral equation is given, which is then specialized to sample geometry and solved numerically. A comparison of obtained data with results given by other authors is included. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21: 1–4, 1999.

Resonances in inhomogeneous dielectric bodies of revolution placed in the multilayered media?TE modes

In this paper a simple method of moments (MoM) solution is given for the problem of determining TE resonant frequencies of inhomogeneous dielectric bodies with rotational symmetry. The body of interest may be placed in arbitrarily stratified dielectric medium, which also may be bounded by one or two horizontal perfect electric conductor (PEC) plates. The general electric field integral equation is given, which is then specialized to sample geometry and solved numerically. A comparison of obtained data with results given by other authors is included. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21: 1–4, 1999.

Asymmetry issues in power system restoration

This paper is one of a series presented on behalf of the Transmission Operation Subcommittee with the intent of focusing attention on EHV asymmetry issues during restoration. Many existing EHV lines have unsymmetrical (horizontal) conductor spacing without being transposed. These characteristics generate unacceptable negative sequence currents (NSC). Under light-load condition and during restoration, NSC has caused cascade tripping of a number of generators resulting in an area wide blackouts, has prevented synchronization of incoming generators, and has blocked remote cranking of thermal units. The paper describes a simple and approximate method for assessing the extent of NSC in EHV lines and then determining corrective measures. It recommends that when attempting to provide an offsite source to a thermal power plant the extent of NSC be determined and if unacceptable, either the operation be deferred to after the initial restoration phase, or the appropriate "underlying load" be determined for connection to the receiving end of the EHV lines.

A numerical study of mechanisms of accretion for rotating snow sleeves evolving on conductor rods

AbstractIt is the purpose of this paper to construct a mathematical/computational model for the accretion of snow on rotating snow sleeves attached to conductor rods, and to consider some of the limitations in the use of the assumption of perfect cylindrical‐sleeve growth, as currently employed to provide estimates of snow‐loading intensity.For purposes of illustration, three rotating snow accretion regimes are considered, in which the direction of the airflow is always taken as perpendicular to the axis of the conductor rod. Firstly, a horizontal conductor rod is free to rotate and is initially bare. Rotation of the system (conductor rod and accreted snow) is initiated by snow torque, due to eccentric snow loading on the windward side of the conductor, and is driven by aerodynamic torque generated by the windflow past the evolving, rotating, asymmetrical sleeve growth. Secondly, a vertical conductor rod is free to rotate and the bare rod is given an initial small angular velocity; the rotation of the accreting system is then driven by aerodynamic torque alone. Thirdly, a horizontal rod is fixed and is initially covered by an annulus of snow, supported by a thin layer of (unfrozen) water existing between the conductor and the snow sleeve. In this case, the rotation of the snow sleeve is due to the combined snow and aerodynamic torques and is now retarded by the viscous torque due to the rotating thin film of water.Asymptotic solutions obtained for small accretion time supplement numerical results derived from the computational models. Numerical results on these rotating non‐periodic snow accretion regimes are presented as a function of the wind speed, snow precipitation rate and diameter of the conductor rod.

Accurate quasi-TEM spectral domain analysis of single and multiple coupled microstrip lines of arbitrary metallization thickness

The quasi-TEM spectral domain approach (SDA) is extended to rigorously and efficiently analyze single and multiple coupled microstrip lines of arbitrary metallization thickness. The charge distributions on both the horizontal and vertical conductor surfaces are modeled by global basis functions. This results in a relatively small matrix for accurate determination of the line parameters of coupled thick microstrips. A convergence study is performed for the results of a pair of coupled lines with crucial structural parameters to explore the conditions for obtaining reliable solutions using the technique. Results for thick microstrips are validated through comparison with those from available measurements and another theoretical technique. The soundness of the technique is further demonstrated by looking into the trend of the results obtained by a simplified model in which the structural parameters are pushed, step by step, to the numerical extremities. Variations of circuit parameters of a four-line coupled microstrip structure due to the change of finite metallization thickness are presented and discussed. >

Snow accretion on horizontal rotating conductor rods

Snow accretion on horizontal rotating conductor rods

Development of aerial fibre optic cables for operation on 400 kV power lines

The paper reports on advances in the development and testing of self-supporting aerial fibre optic cable to be used on high-voltage grid networks. The environmental effects they must withstand are first discussed with emphasis on the influence of the electric field created by neighbouring conductors. Finite element analysis is used to determine the voltage on the cable under different conditions of vertical and horizontal position, conductor phasing and distance from the tower. Dry banding and the consequent arcing have been modelled, together with the influence of electrode shape on voltage stress at the fixing point. Reduction of the mechanical and electrical stress concentrations at the earth grip by the use of a stress-relieving trumpet is shown to give a dramatic improvement to the erosion resistance of the cable. Test procedures are described which are recommended as the basis for a qualification specification. The concept of suppressing discharges on the sheath surface by use of a partially conducting layer is investigated by finite element analysis. The practicability of realising such a system is also discussed. Finally, field experience on 132 and 400 kV lines in the UK is described.

Mutual coupling between horizontal earth return conductors using actual routing parameters

A formula for calculating mutual coupling between diversely routed, horizontal earth-return conductors that measure grounding system impedance is derived by using the complex ground plane concept used to approximate the Carson equation. Each potential conductor section is approximated with equal-length segments that parallel one of the current conductor sections. By repeating the parallel segmentation of each potential conductor section with each subsequent current conductor section and summing the segment mutuals, overall mutual couplings between diversely routed conductors is obtained. This process is useful for calculating mutual to the potential conductor and for comparing possible potential conductor routings so as to minimize the overall mutual coupling.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modeling of transmission line exposure to direct lightning strokes

A new model for assessing the exposure of free-standing structures and horizontal conductors above flat ground to direct lightning strokes is introduced. A recently developed criterion for positive leader inception modified to account for positive leaders initiated under the influence of a negative descending lightning stroke, is discussed. Subsequent propagation of the positive leader is analyzed to define the point of encounter of the two leaders which determines the attractive radius of a structure or the attractive lateral distance of a conductor. These parameters are investigated for a wide range of heights and return-stroke currents. A method for analyzing shielding failure and determining the critical shielding angle is also described. The predictions of the model are compared with field observations and previously developed models.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>