On the contribution of the electromagnetic field components in field-to-transmission line interaction

Based on the transmission line approximation, three different equivalent formulations have been proposed for evaluating the interaction between an external electromagnetic field and a transmission line. The difference among these 'coupling' formulations, which are summarized for the case of a lossless line, lies essentially in the representation of the source terms as a function of the external electromagnetic field components. In the paper we show that the contribution of a given electromagnetic field component is different depending on the particular adopted formulation. To show that, the three formulations are employed to calculate the voltages induced on an overhead line by a nearby lightning strike, and the contribution to the induced voltage of the various electromagnetic field components explicitly appearing in each formulation is emphasized. We conclude that it is misleading to speak about the contribution of a given electromagnetic field component to the total induced voltages without first specifying the coupling formulation one is using.

Lightning electromagnetic field coupling to overhead transmission line networks and to buried cables

Emanuel Petrache

Lightning-induced voltages in power and communication systems are nowadays one of the main causes of power quality and electromagnetic compatibility. In recent years, due to the increasing demand by customers for good quality in the power supply along with the widespread use of sensitive devices connected to distribution lines, the protection against lightning-induced disturbances became of primary importance. As a consequence, for a correct protection and insulation coordination, the accurate estimation of lightning-induced overvoltages is essential. In addition, sensitive electronic components used in power and communication systems may suffer logic upset or damage at significantly lower levels of induced electromagnetic interferences. As a result, the evaluation of lightning-induced disturbances in underground cables has recently gained more interest compared to the past. The major aim of the present thesis is the development of models and computer codes, allowing the computation of the voltages and currents induced by an external transient electromagnetic excitation, especially due to lightning discharge, along realistic -and hence complex- transmission line networks and in buried cables. After a brief introduction on lightning phenomenology, Chapter 2 presents an overview of lightning return stroke modeling and methods for the calculations of lightning-generated electromagnetic fields above and inside the ground. We show in this chapter, that the simplified expression recently proposed by Cooray for the calculation of electric field penetrating the ground yields very good approximations to the exact numerical solutions, for distances as close as 100 m. The main original contributions of this thesis are presented in Chapters 3 through 5. They consist of theoretical and experimental work as follows. In Chapter 3, based on the Agrawal et al. coupling model, extended to the case of a multiconductor line and interfaced with EMTP program, a new software tool called LIOV-EMTP96, developed in the framework of a collaboration with the University of Bologna, is described. This software tool is able to analyze the response of complex distribution systems to indirect lightning. We carried out several experimental campaigns to test and validate the LIOV-EMTP96 code. First of all, we used the NEMP simulator of the Swiss Federal Institute of Technology (SEMIRAMIS) to illuminate a reduced-scale model of a multiconductor line. Then, we used a more complex 27-line reduced-scale network illuminated by the VERIFY NEMP simulator belonging to the Swiss Defence Procurement Agency (Spiez). And, finally, we used experimental data obtained by means of artificially-initiated lightning in 2002 and 2003 on an experimental distribution line at the International Center for Lightning Research and Testing, Camp Blanding, Florida. Calculations performed with the developed program have been tested versus the obtained experimental results, and a very good agreement between the simulations and the measurements is found. It is concluded that LIOV-EMTP96 is adequate for the analysis of the response of complex distribution systems to indirect lightning and for their protection in view of optimal insulation coordination and power quality achievement. Chapter 4 presents efficient calculation methods to estimate lightning-induced disturbances in buried cables in both time- and frequency-domain. Concerning the parameters of the underground cable, different expressions for the ground impedance are analyzed and compared. We propose a logarithmic approximation for the ground impedance of a buried cable that is shown to be very accurate. In addition, unlike most of the considered approximations, the proposed expression has an asymptotic behavior at high frequencies. As a result, the corresponding transient ground resistance in time-domain has no singularity at t = 0, and therefore, does not require any special treatment in a direct time domain solution. The time-domain solution of electromagnetic field-to-buried cable coupling equations is also investigated using the point-centered FDTD (Finite Difference Time Domain) method. The coupling model includes the effect of ground admittance, which appears in terms of an additional convolution integral. An analytical expression for the ground transient resistance in the time-domain is also proposed which is shown to be accurate and non-singular. For the case of coaxial buried cables, the coupling with the inner conductor is also investigated using a frequency domain approach based on Green's functions. Chapter 4 provides, in addition, recommendations concerning the modeling and computation of lightning-induced disturbances on buried cable. Chapter 5 presents extensive experimental results obtained at the International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, Florida, in 2002 and 2003. We measured currents induced by triggered and natural lightning events at the ends of a shielded buried cable, both in the cable shield and in the inner conductor. The horizontal magnetic field was also measured. Additionally, a close natural lightning event has also been recorded during the 2003 summer campaign. For the natural lightning events recorded in 2002, the waveforms are correlated with the data obtained by the U.S. National Lightning Detection Network (NLDN). The obtained experimental data were used to test the theoretical models and the developed computer codes for the analysis of lightning-induced disturbances in buried cables. In general, reasonably good agreement was found between numerical simulations and experimentally-recorded waveforms. It was also found that the ground conductivity affects in a significant way lightning-induced currents in buried cables. Therefore, an accurate representation of the ground electrical parameters is a key issue in the determination of such disturbances.

EPFL2004

Guideline for Numerical Electromagnetic Analysis Method

Carlo Alberto Nucci, Mario Paolone, Marcos Rubinstein

The aim of this document is to provide an extended description and application guide of methods belonging to the so-called Numerical Electromagnetic Analysis (NEA) applied to the calculation of electromagnetic transients in power systems. As known, the accurate computation of electromagnetic transients is a fundamental requirement of several studies in the area of power systems. Lightning and switching studies are, for instance, typical subjects where the accuracy of transient’s computation has a direct influence to the proper sizing of components like insulators and breakers. Traditional approaches adopted since now were based on the combination of circuit and transmission lines theories. These approaches, analytically and numerically validated by numerous contributions to the literature, rely on specific assumptions that are inherently relaxed by NEA methods. Indeed, NEA methods mostly rely on the numerical solution of the full-wave Maxwell’s equations and, in this respect, the assessment of their accuracy, as well as the description of the various numerical methodologies, have motivated the preparation of this Technical Brochure. In this context, this guide will first discuss the general aspects and limitations associated to classical circuit and transmission lines theories. In particular, the guide will make reference to the modelling approaches used to represent the most typical power system components, like transmission lines, grounding systems, towers etc., within EMTP-like simulation tools (Electromagnetic Transient Program). A first comparison with the most typical NEA methods is presented in order to discuss the main differences and better support the contents of this guide. Then, the guide focuses on the analytical formulation of the most used NEA methods like, the Finite-Difference Time-Domain (FDTD), the Transmission Line Matrix ‘TLM’, the Finite-Element Method in Time Domain (FEMTD), the Method of Moment (MoM) and the Partial Element Equivalent Circuit (PEEC) method. A further remark refers to the comparative analysis of NEA vs EMTP-like simulation approaches. Such an assessment, addressed in this document in various sections, aims at stressing the advantages and drawbacks of both methods. Indeed, NEA methods, although characterized, in general, by better accuracies, result into non-negligible computation times that require the availability of specific computation environments. Such a characteristic is due to the inherent numerical complexity of NEA solvers that require the treatment of large amount of data that, additionally, have an influence on the results accuracy. To this end, the last part of the guide refers to the benchmarking of the various NEA methods by means of typical test cases. In this respect, the members of the Cigré WG C4.501 agreed to include a specific section of the brochure aimed at providing the NEA-computed electromagnetic transients with reference to the most typical test cases like: (i) lightning surge calculation in substations, (ii) influence of grounding on lightning surge calculation in substations, (iii) surge voltages on overhead lines, (iv) lightning-induced surges on distribution lines, (v) LEMP and induced surges calculation in overhead lines above a lossy ground and (vi) simulations of very fast transients (VTFs) in GIS. Additionally, as NEA methods represent power tools for the computation of parameters of power systems components, the guide has also provided benchmarking examples for the following assessments: (a.) surge characteristics of transmission towers, (b.) surge characteristics of grounding electrodes, vertical grounding rods, horizontal grounding electrode and complex grounding configurations, (c.) influence of grounding on surge propagation in overhead transmission lines, (d.) propagation characteristics of PLC signals along power coaxial cables, (e.) lightning surge characteristics of wind-turbine towers.

2013

Lightning-induced voltages on overhead lines

Michel Ianoz

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 return-stroke 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.