FDTD analysis of distribution line voltages induced by non-vertical lightning (original) (raw)
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FDTD analysis of distribution line voltages induced by inclined lightning channel
Electric Power Systems Research
This paper investigates lightning induced voltages on a distribution line, when the lightning channel is not vertical but angled to the line and the earth representation is based on the finite-difference time-domain (FDTD) method. The effect of the current flowing into the earth, after the lightning channel touches the earth, is also investigated. The induced voltages are quite dependent on the angle of the channel to the line as can be easily estimated. It is found that the lightning angle with the line causes significant increase of the voltage and the effect of the earth resistivity on the induced voltage has been made clear when considering the inclined channel. Since the induced voltage is, in theory, proportional to the frequency of the inducing current, i.e. inversely proportional to rise time Tf when the inducing and induced circuits are parallel. When the lightning channel is angled, the proportional relation is less clear than that in the vertical channel. This fact has to be taken into account when discussing the effect of Tf. The current flowing in the earth is also affected by the lightning inclination and the voltage drop along the earth surface due to the current becomes larger than that in the vertical lightning case.
IEEE Transactions on Electromagnetic Compatibility, 2000
In this paper, the lightning-generated electromagnetic fields over lossy ground produced by lightning strikes either to flat ground or to a tall tower are calculated using the 2-D finitedifference time-domain (FDTD) method. The resultant horizontal and vertical electric fields are used as forcing functions in the discretized Agrawal electromagnetic coupling equations for the calculation of induced voltages on overhead horizontal conductors without employing the Cooray-Rubinstein formula. Comparison of the results with those obtained using the 3-D FDTD method and with experimental data found in the literature is used to test the validity of the examined method. The approach employed here generally provides sufficient accuracy while allowing significant reduction in computation time and storage requirements as compared to the 3-D FDTD method. From the analysis carried out in this paper, induced voltages appear to be strongly dependent on ground conductivity, somewhat influenced by return-stroke speed, and essentially independent of return-stroke model [transmission-line (TL), modified transmission line with linear current decay with height (MTLL), or modified transmission line with exponential current decay with height (MTLE)]. Index Terms-Electromagnetic coupling model, finite-difference time-domain (FDTD) method, lightning electromagnetic pulse (LEMP), lightning-induced voltage.
IEEE Transactions on Electromagnetic Compatibility, 2015
In this paper, lightning-induced voltages on multiconductor lines with surge arresters and pole transformers have been computed using the 3-D finite-difference time-domain method. This method uses a subgrid model, in which spatial discretization is fine (cell side length is 0.5 m) in the vicinity of overhead wires and coarse (cell side length is 5 m) in the rest of the computational domain. In the simulations, four-conductor lines with surge arresters and pole transformers are considered. The 1-cm-radius overhead conductors are represented by placing a wire having an equivalent radius of about 0.12 m (0.23 × 0.5 m) in the center of an artificial rectangular prism having a cross-sectional area of 1 m × 1 m (2 cells × 2 cells) and the modified (relative to air) constitutive parameters: lower electric permittivity and higher magnetic permeability. The computed lightning-induced voltage waveforms agree reasonably well with the corresponding ones measured in the small-scale experiment of Piantini et al. (2007).
Lightning induced voltages on an distribution network over an inclined terrain
2011 International Symposium on Lightning Protection, 2011
This paper presents the induced voltages produced by a lightning that hits the top of a mountain over a line placed parallel to the inclined surface, compared with the result found when the line is placed over a flat terrain. The electromagnetic fields produced by the lightning channel are calculated by means of the Finite Difference Time Domain Method (FDTD) and the lightning induced voltages are calculated with the Agrawal approach. This work shows that exists important differences in the lightning induced voltages when we take into account the topography.
Lightning-induced voltages on overhead lines
IEEE Transactions on Electromagnetic Compatibility, 1993
The paper discusses a modeling procedure that permits calculation of lightning-induced voltages on overhead lines starting from the channel-base current. The procedure makes use of 1) a lightning return-stroke model proposed by the authors for the calculation of the lightning electromagnetic field; and 2) a coupling model already presented in the literature based on the transmission line theory for field-to-overhead line coupling calculations. Both models are discussed and tested with experimental results. The hypothesis of perfect conducting ground, generally adopted in studies on the subject, is discussed in order to better assess its validity limits. The procedure is applied for the analysis of the voltages induced on an overhead line by a nearby lightning return stroke with a striking point equidistant from the line terminations. The analysis shows that the vertical and horizontal components of the electric field are both to be taken into account in the coupling mechanism. The peak value and the maximum time derivative of the channel-base current are shown to affect both the peak value and the maximum front steepness of the induced voltages while, for the examined case, the returnstroke velocity affects practically only the front steepness of the induced voltages. A comparison with other models proposed for the same purpose is presented. Peak value and maximum front steepness of the induced voltages calculated using other lightning return-stroke models differ; these differences are of the same order of magnitude as those that would result from different sets of characteristic parameters of the lightning discharge. It is also shown that a different coupling model used in the power-lightning literature by several other authors may result in a less accurate estimation of the induced voltages.
Lightning-induced voltages at both ends of a 448-m power-distribution line
1992
Lightning-induced voltages due to return strokes in ground flashes beyond about 5 km are measured simultaneously at both ends of an unenergized 448-m power-distribution line. The measurements represent an extension of an earlier experiment on the same line in which voltages were obtained at only one end of the line. In addition to the induced voltage measurements, the causative lightning electric and magnetic fields are recorded. The voltage and field measurements are made as a function of the lightning direction and of the power-line termination. For both measured and idealized electric fields as inputs to a time-domain transmission-line coupling model, we calculate line voltages as a function of the incident angle of the lightning electromagnetic radiation and of the line termination. Measured and predicted voltages calculated from the coupling model with measured fields as inputs show, overall, good agreement in waveshape, but the predicted voltages are about a factor of three larger in amplitude. To the extent that the results can be compared, there is reasonable agreement with the earlier experiment on the same line. I. INTRODUCTION EMBERS of the Lightning Research Laboratory of the M University of Florida (UF), working in the Tampa Bay area of Florida during the summer of 1979, made the first simultaneous measurements of lightning return-stroke electric and magnetic fields and the power-line voltages induced by those fields [l]. Voltage measurements were made at one end of a 500-m unenergized overhead distribution line. The Tampa experiment provided evidence of the importance of the lightning horizontal electric field component [2].' Previously, the importance of the horizontal electric field was known theoretically (e.g., [3]), but was not shown experimentally for the case of lightning until 1980 [4]. Further, the vertical component of the electric field was generally viewed in the previous power literature as the only important inducing field (e.g., [5] and [6a]-[6dJ). Comparison of measured line voltages from Tampa with calculated voltages derived from measured vertical electric fields and calculated horizontal Manuscript
Jurnal Teknologi, 2013
This paper investigates the effect of design parameters on the induced voltages on a distribution power line. This investigation is based on perfect ground conductivity, single stroke lightning and lightning without branches. The design of the parameters includes, d, the striking distance of the lightning, h, the height of the conductor, and r, the diameter of the conductor, all of which are elements that produce the variations in the induced voltage on a distribution power line with respect to a vertical or an inclined lightning channel. Thus, the outcome of this investigation can act as a guide for utility companies or other power engineers in order to plan an appropriate protection scheme for a distribution power line.
IEEE Transactions on Power Delivery, 2010
In this paper, the effect of the tilt angle of return stroke channel and the stratified lossy ground on the lightning-induced voltages on the overhead lines are studied using the modified transmission-line model with linear current decay with height (MTLL). The results show that the lightning-induced voltages from oblique discharge channel are larger than those from the vertical discharge channel, and the peak values of the induced voltages will increase with increasing the tilt angle. When the ground is horizontally stratified, the peak of the induced voltages will increase with increasing the conductivity of the lower layer at different distances. When the upper ground conductivity increases, the voltage peak values will decrease if the overhead line is nearby the lightning strike point and increase if the overhead line is far from the lightning strike point. Moreover, the induced voltages are mainly affected by the conductivity of the lower layer soil when the conductivity of the upper layer ground is smaller than that of the lower layer ground at far distances. When the ground is vertically stratified, the induced voltages are mainly affected by the conductivity of the ground near the strike point when the overhead line and the strike point are located above the same medium; if the overhead line and the strike point are located above different mediums, both of the conductivities of the vertically stratified ground will influence the peak of the induced voltages and the conductivity of the ground which is far from the strike point has much more impact on induced voltages.
Electric Power Systems Research, 2020
This paper discusses the simulation of lightning-induced voltages on a three-phase compact distribution line considering either a first order finite-difference time-domain solution of telegrapher's equations or a version of Marti's transmission line model extended to include the influence of external electromagnetic fields, named EMD model. The validity of both models is first demonstrated by means of comparisons with lightning-induced voltages measured in rocket-triggered lightning experiments. It is then shown that the EMD model can be used in the simulation of lightning-induced voltages on compact distribution lines provided special attention is given to the model fitting in the modal domain, regardless if complex or real poles are used. Results obtained with the vector fitting technique are seen to be more reliable than those obtained using Bode's asymptotic method, which must be used with caution in the modeling of compact distribution lines. The obtained results are relevant because compact distribution lines contain both bare and covered conductors, which is likely to pose difficulties to the simulation of transients with transmission line models based on modal-domain theory.
One of the main issues that has to be faced when evaluating lightning-induced overvoltages on a realistic network configuration is to implement the algorithm that solves the field-to-line coupling problem into an electromagnetic simulator that is able to represent with a high level of detail all the power system components. On one hand, numerical stability conditions of the finite-difference time-domain schemes have been deeply investigated in the presence of boundary conditions known analytically; on the other hand, there is not so much literature on the situations in which such conditions are provided in a numerical way through an external electromagnetic simulator. The study reveals that the commonly used linear extrapolation of currents at the line extremities might rise to numerical instabilities. An efficient solution using the method of characteristics is presented and validated. Index Terms-Finite-difference time domain (FDTD), lightning electromagnetic pulse, lightning-induced effects and protection, numerical methods and modeling.