Calculation Of Lightning-induced Voltages Research Articles

A Thévenin-Type Version of the Extended Modal-Domain Model for Lightning-Induced Voltage Calculations

In this paper, a new procedure is proposed for determining the external current sources required for evaluating lightning-induced voltages on overhead lines with the extended-modal domain (EMD) model. Unlike the original model, in which the calculation of the inducing current sources depends on the fitting of the characteristic admittance of the line, in the proposed procedure this calculation is performed using the characteristic impedance of the line. This significantly simplifies the use of the EMD model because now all parameters can be readily obtained from the built-in fitting tool that is usually available in electromagnetic transient programs to derive the parameters of Marti’s transmission line model. The validity of the proposed procedure is demonstrated through examples that indicate its accuracy in the calculation of lightning-induced voltages on overhead distribution lines terminated with different types of loads, including transformers and surge arresters, and multiple grounding points.

Evaluation of the extended modal-domain model in the calculation of lightning-induced voltages on parallel and double-circuit distribution line configurations

This paper evaluates the applicability of the extended modal-domain (EMD) model in the calculation of lightning-induced voltages on parallel and double-circuit distribution lines. The influence of a real and constant transformation matrix and of the fitting technique required in the model on the induced-voltage waveforms is also investigated. It is shown that the EMD model presents good accuracy in most of the tested configurations. Also, in most cases the influence of the frequency selected for the calculation of the transformation matrix required in the EMD model is minimal. On the other hand, the requirement of using strictly real poles and residues and the use of the built-in fitting tool available in the Alternative Transients Program (ATP) have both a detrimental influence on the accuracy of the EMD model, at least in the investigated cases.

Time-Domain Procedures for Lightning-Induced Voltage Calculation in Electromagnetic Transient Simulators

In this paper, two time-domain procedures are proposed for the calculation of lightning-induced voltages using lossy transmission line models available in electromagnetic transient simulators. In both procedures, the influence of the incident electromagnetic field is represented in the form of current sources that are connected externally at the ends of the illuminated line. One of the procedures is formulated directly in the phase-domain and is compatible with the universal line model (ULM). The second procedure is formulated in the modal domain and is compatible with the transmission line model proposed by Marti. Both procedures are validated taking as reference a first order FDTD solution of telegrapher's equations considering the presence of external electromagnetic fields. It is shown that the proposed procedures can be efficiently and accurately used for the calculation of lightning-induced voltages on overhead lines.

A New Channel-Base Current Model for Lightning-Induced Voltage Calculations

We propose a new channel-base current model, which is particularly well suited for lightning-induced voltage calculations. We will show that this new proposal meets a significant number of characteristics required to these applications, and favorably compares to existing solutions.

Exact and Approximate Analytical Solutions for Lightning-Induced Voltage Calculations

In this paper, we thoroughly review all analytical solutions (both exact and approximate) presented to date in the literature for evaluation of voltages induced on a lossless horizontal conductor, placed over an infinite-conductivity ground, and excited by an external field produced by either a step function or a linearly rising current, moving unattenuated and undistorted along a vertical lightning channel. We also obtain the exact analytical solution for the step-function current case in the time domain via development in the s -domain. To date, there had been three attempts to obtain such solution, all of which yielding incorrect results.

Calculation of Lightning Induced Voltages on Overhead Lines Using an Analytical Fitting Representation of Electric Fields

The lightning electromagnetic field which illuminated the overhead line is the nonuniform field. When analyzing the lightning induced overvoltages on overhead lines by in frequency domain, to get an accurate response, the observation points of the horizontal electric field along the overhead line should be as many as possible. However, the expression of the horizontal electric field is formulated in the integral form and should be solved by the time-consuming numerical integration process at every observation point, which leads to a low calculation efficiency. This paper proposes an efficient method to avoid the numerical integration process at all the observation points and to enhance the calculation efficiency. In this method, the horizontal electric field at a few observation points along the line are calculated in the numerical way first, then the amplitudes and phases of the horizontal electric field along the line are fitted separately at every frequency with the fitting functions of the position $x$ along the line. The amplitudes are fitted by the Fourier series, and the phases are fitted by the polynomial functions. Based on the obtained analytical fitting representations, the transmission line response could be solved efficiently. The two different lightning electromagnetic pulse (LEMP) validation examples show the validity and general applicability of the proposed method.

Calculation of Lightning-Induced Voltages on Overhead Lines from Oblique Return Stroke Channel above Stratified Lossy Ground in Time Domain

Calculation of Lightning-Induced Voltages on Overhead Lines from Oblique Return Stroke Channel above Stratified Lossy Ground in Time Domain

Calculation of Lightning-Induced Voltages and Currents on the Transformers Courtyard of Tucuruí Hydroelectric Generation Plant Using the Finite-Difference Time-Domain Method

In this work, voltages and currents induced due to lightning occurrence on the transformers' courtyard of Tucurui hydroelectric generation plant are calculated by employing the Finite-Difference Time-Domain method. The transient functions are obtained for 500 kV-transmission lines at the output of the power plant. In order to the simulations become viable from the computational point of view, it was necessary to use parallel processing for dividing the analysis region into 24 subdomains (24 computer cores were used). The simulated problem in this work consists on an 1 kA-lightning stroke on phase A of the output transmission system of the Tucurui's plant. In this work, induced voltages between the phase A of the line and the following reference points were obtained: a) the courtyard grounding mesh for voltage transformers, b) ground grid in the first floor concrete, c) rock (basalt) surface at the base of the plant, d) the soil's layer and water surfaces. Transient voltages induced between the phases A, B and V of the transmission line are also analyzed. These data are important because the electrical system is based on voltage differences between phases. It is also noticed that, in this case, the maximum induced voltage between phases A and B is approximately 157.9 kV/kA. It is also performed a study regarding voltage supportability for line insulators on the structure.

A New Tool for Calculation of Lightning-Induced Voltages in Power Systems—Part I: Development of Circuit Model

In this paper, we present a new tool for lightning-induced voltage calculations. The tool, a circuit model which can be integrated into power systems simulators, is based on the theory developed by Andreotti (2001, 2009, 2013). In Part II, the accuracy, stability, and efficiency of the new tool are demonstrated via comparison with other solutions/codes found in the literature and with experimental data.

The Effect of an Ocean-Land Mixed Propagation Path on the Lightning Electromagnetic Fields and Their Induced Voltages on Overhead Lines

We use a full-wave approach based on the finite-element method solution to Maxwell's equations for the evaluation of the effect of an ocean-land mixed propagation path on the above-ground lightning electromagnetic fields and their induced voltages on overhead lines. Two cases of normal and oblique strikes are studied. For normal strike, it is shown that neither the vertical electric field nor the azimuthal magnetic field is affected by the considered mixed propagation path. For an oblique strike, however, the azimuthal magnetic field is slightly affected when the observation point is close to the ocean-land interface (i.e., 5 m or so), while the vertical electric field remains unchanged. For both normal and oblique strikes, at moderate and far distances from the channel base and when the observation point is located in the vicinity of the ocean-land interface, the radial electric field is markedly affected by this interface. For the calculation of lightning-induced voltages, two cases, namely, the ocean-side and the river-crossing transmission lines are studied. For the ocean-side transmission line, as the overhead line gets closer to the ocean, the induced voltages on the line midpoint decrease while increasing behavior is observed in the voltages induced on the line terminations. For the river-crossing transmission line, the lightning-induced voltages along the line experience a significant change in terms of their peak values and waveshapes. In some cases, the enhancement in induced voltages can be as high as a factor of 2 with respect to that obtained by assuming a homogeneous propagation path characterized by the electrical properties of the land.

A New Tool for Calculation of Lightning-Induced Voltages in Power Systems—Part II: Validation Study

In the companion paper (Part I), a new tool for lightning-induced voltage calculations, called CiLIV, has been presented. In this paper (Part II), predictions made with the new tool are compared to experimental data and to outputs of analytical procedures/numerical codes found in the literature.

Close electric fields and lightning-induced voltages predicted by a return-stroke model including corona and nonlinear channel resistance

In this paper, a return-stroke model based on nonuniform transmission line theory that includes nonlinear losses and corona is used for calculating close electric fields and lightning-induced voltages on an overhead line. A study is performed to identify the influence of return-stroke corona on close electric fields and line overvoltages considering different model assumptions. It is shown that the consideration of corona affects the attenuation and distortion of the return-stroke current. Close vertical electric fields predicted by the model present waveforms, peak values, and decay with distance that are in agreement with measured data. A simpler case in which the return-stroke speed is artificially set to a prescribed value by controlling the inductance and capacitance of the channel is shown to lead to results that are in agreement with the complete return-stroke model considering nonlinear losses and corona. Similar conclusions apply to popular engineering return-stroke models typically used in lightning-induced voltage calculations provided the return-stroke speed is suitably adjusted. It is also shown that lightning-induced voltages calculated with the considered model are in good agreement with experimental data.

A Comparison Between Analytical Solutions for Lightning-Induced Voltages Calculation

An exact closed form solution for the calculation of lightning-induced voltages on overhead lines has been recently proposed by A. Andreotti et al. (2012). Predictions of this exact formulation are compared here to those based on approximate analytical solutions proposed in the literature. DOI: http://dx.doi.org/10.5755/j01.eee.20.5.2967

Analytical investigation of parameters effect on lightning-induced overvoltages on overhead lines

The evaluation of induced overvoltages from indirect lightning has been for more years one of the most important problems in designing and coordinating the protection of overhead power lines. In this paper, we discuss a modeling procedure that permits calculation of lightning-induced voltages on overhead lines starting from the channel-base current. The calculation is based on two main points: the calculation of the electromagnetic field radiated by lightning in a given point and a coupling model already presented in the literature based on the transmission line theory for field-to-overhead line coupling calculations.

Three-Dimensional FDTD Calculation of Lightning-Induced Voltages on a Multiphase Distribution Line With the Lightning Arresters and an Overhead Shielding Wire

To suppress the lightning-induced voltages on a distribution line, lightning arresters and/or overhead shielding wire can be installed, and the effectiveness of these countermeasures are usually studied by simulations. Traditionally, field-to-transmission line coupling techniques based on the distributed-parameter circuit theory are used for the calculation of the lightning-induced voltages. Recently, the finite-difference time-domain (FDTD) method that directly and numerically solves Maxwell's equations was applied to the calculation of the lightning-induced voltages. Compared with the conventional methods, the FDTD-based calculation is advantageous in terms of the modeling of inhomogeneous ground parameters, 3-D structures, and grounding systems. But, in the previous works, the distribution line was simulated simply by a single-phase line. Moreover, the representation of lightning arresters in the FDTD method was not yet established. This paper proposes a technique to incorporate the lightning arresters in the FDTD-based lightning overvoltage calculations. In this technique, the voltage-current relationships of the lightning arresters are represented by piecewise linear curves, which can be obtained directly from the data sheets or measured results. For validation purpose, the lightning-induced voltages on a three-phase distribution line equipped with the lightning arresters and a multipoint-grounded overhead shielding wire are calculated by the proposed method, and the results are compared with those obtained by the conventional method and a very good agreement is found.

An Analytical Approach to Calculation of Lightning Induced Voltages on Overhead Lines in Case of Lossy Ground—Part II: Comparison With Other Models

In the companion paper (Part I), an analytical approach for calculating lightning-induced voltages for the case of lossy ground has been developed. In this paper (Part II), predictions of the new formulation are compared to those based on other approaches found in the literature.

An Analytical Approach to Calculation of Lightning Induced Voltages on Overhead Lines in Case of Lossy Ground—Part I: Model Development

Andreotti (2009, 2013) have presented analytical solutions for the evaluation of voltages induced on lossless, single-, and multi-conductor lines for the case of infinite-conductivity ground and both step and linearly rising currents moving without attenuation and at a constant speed along a vertical lightning channel. These solutions were derived in an exact way (i.e., no approximations were introduced in their derivation). In this paper (Part I), the previous work is extended to the case of lossy ground. In the companion paper (Part II), the results obtained using this new formulation are compared with those given by other formulas/solutions found in the literature.

Fast and efficient calculation of lightning-induced voltages in frequency-dependent transmission lines over lossy ground

This paper presents a fast and efficient algorithm for the calculation of electromagnetic fields radiated from lightning return-stroke channel as well as lightning-induced voltages in frequency-dependent transmission lines. The algorithm developed in this paper employs a mixed time-frequency macro-model that is based on tracing the poles and residues of the transfer function of the lightning-transmission-line system. Accurate and fast calculation of electromagnetic field data along the excited transmission line is critical to obtain the source terms (or forcing functions) in field-to-transmission-line coupling equations. Using the proposed method, we are able to obtain a closed form solution for the lumped sources required for the analysis of a two-conductor transmission line exposed to nonuniform electromagnetic fields. The algorithm provides high accuracy as well as significant speed gain for multiconductor transmission lines (MTL) as well. To demonstrate the application of the proposed method, we will compare our results with those obtained using other methods or measurements.

Analytical Formulations for Lightning-Induced Voltage Calculations

Recently, Andreotti (2009) have presented an analytical solution for the evaluation of voltages induced on an infinitely long, lossless, single-conductor located at a given height above an infinite-conductivity ground plane, and excited by an external field due to a step current wave moving without attenuation and at a constant speed along a vertical lightning channel. The solution presented, in contrast to previously published solutions, was derived in an exact way, i.e., no approximations were introduced in its derivation. In this paper, this exact approach is extended to more practical line configurations. Specifically, still for the case of an external field due to a step current and perfectly conducting ground, the cases of terminated single-conductor line and multiconductor line (including grounded conductors) will be studied. Further, single- and multiconductor lines (including grounded conductors) excited by an external field due to a linearly rising current will be examined.

Calculation of Lightning-Induced Voltages on Overhead Distribution Lines Including Insulation Breakdown

This paper investigates the influence of considering actual insulation volt-time curves both in the calculation of lightning-induced voltages and in the estimation of the number of flashovers an overhead wire may experience per year due to nearby lightning strokes. The flashover mechanism is modeled according with the integration method, which is used as a reference for comparisons with the simplified 1.5 CFO flashover criterion traditionally used in the estimation of the lightning performance of overhead distribution lines. Sensitivity analysis show the dependence of flashovers on the shape and front time of the assumed channel-base current. The obtained results suggest that the simplified 1.5 CFO flashover criterion is likely to underestimate the number of flashovers an overhead line may experience per year due to nearby lightning strokes. This result is confirmed by statistical analyses considering a Monte Carlo-based approach. It is also shown that more realistic flashover rate estimates can be obtained in the statistical analysis of lightning-induced voltages provided a reduced threshold level (1.2 CFO in the particular case evaluated in this paper) is considered instead of the 1.5 CFO level traditionally used in this type of study.