W. Janischewskyj

Current and electromagnetic field associated with lightning-return strokes to tall towers

An analysis of electric and magnetic fields radiated by lightning first and subsequent return strokes to tall towers is presented. The contributions of the various components of the fields, namely, static, induction, and radiation for the electric field, and induction and radiation for the magnetic field are illustrated and discussed. It is shown in particular that the presence of a tower tends, in general, to increase substantially the electric and magnetic field peaks and their derivatives. This increase is mainly caused by the presence of two oppositely propagating current wavefronts originating from the tower top and by the very high propagation velocity of current pulses within the tower, and depends essentially on the wavefront steepness of the channel-base current. Because of the last factor, the increase of the field magnitudes is found to be significantly higher for subsequent return strokes, which are characterized by much faster risetimes compared to first return strokes. The presented results are consistent with experimental observations of current in lightning strokes to the Toronto CN Tower and of the associated electric and magnetic fields measured 2 km away. These findings partially explain the fact that subsequent return strokes characterized by lower current peaks but higher front steepnesses and return stroke speeds may result in higher field peaks. The results obtained have important implications in electromagnetic (EM) compatibility. It is found that lightning strokes to tall metallic objects lead to increased EM field disturbances. Also, subsequent return strokes are to be considered an even more important source of EM interference than first return strokes. Indeed, EM fields from subsequent strokes are characterized by faster fronts and additionally, they may reach greater peaks than first strokes. Lastly, findings of this study emphasize the difficulty of extracting reliable lightning return stroke current information from remote EM field measurements using oversimplified formulae.

Analysis of Corona Losses on DC Transmission Lines: I - Unipolar Lines

Theoretical calculation of corona losses for practical unipolar dc transmission line configurations presents considerable difficulty because of the nonlinear nature of the equations describing the space-charge fields. The application of numerical methods to obtain solutions of practical interest is discussed. One of the difficulties in the analysis of space-charge fields is the determination of the actual charge distribution around the conductor in the corona. A numerical iterative method of computing this charge distribution is presented. The method is applicable to any general configuration for which the space-charge-free field can be calculated. The line- to-plane configuration is considered. A method of including the effect of conductor surface irregularities in the theoretical calculation of corona losses is outlined, and it is suggested that, by the same method, Popkovs formula may also be modified to make it applicable to lines with practical transmission-line conductors. Calculations by the method of analysis developed as well as by the modified Popkov equation are compared with experimental results.

Finite Element Solution for Electric Fields of Coronating DC Transmission Lines

Analytical computation of steady-state corona losses on HVDC transmission lines presupposes knowledge of two quantities: of the electric field vector and of the space charge. Both quantities could be sought in the entire interelectrode space, but it is mandatory to know them at least at electrode surfaces.

Analysis of Corona Losses on DC Transmission Lines Part II - Bipolar Lines

As in the case of unipolar corona, theoretical calculation of corona losses for bipolar dc transmission line configurations involves the analysis of the nonlinear ionized field in the interelectrode region. However, the complexity of the analysis is increased considerably because of the presence of ions of both polarities in the region.

Lightning surge response of ground electrodes

Experimental and analytical evidence shows that lighning surge currents ionize the air in the soil. This ionization process tends to increase the contact area of the electrode with surrounding material. The larger area results in lower resistance and less voltage stress per unit current. Most realistic models for non-linear changes in footing resistance are difficult to derive. Recently, a similarity approach to footing modeling was proposed [1]. We describe the approach and derive a new model for low-current response, based on electrode size and surface area. The simple model agrees well with formulas derived by Rudenberg [2] for a wide range of electrode shapes. When models for impulse footing impedance are used in the prediction of lightning outage rates, the currents computed for backflashovers on EHV transmission lines are often over 400 kA. These currents are well beyond the values estimated from observations of lightning radiated fields for negative flashes. In spite of that, lightning flashovers are observed on 500-kV lines. To resolve the discrepancy, in addition to the work on surge-reduced footing resistance, the surge response of a conducting ground plane was studied. Any ground electrode, even a perfectly conducting plane, will exhibit a transient surge impedance as the front of the lightning current spreads out. This impedance is fairly high (60 ¿) at the base of the tower but quickly falls off to low values. In effect, the ground plane near the tower looks like an extension of the tower, bent outward.

Far-field-current relationship based on the TL model for lightning return strokes to elevated strike objects

New general expressions relating lightning return stroke currents and far radiated electric and magnetic fields are proposed, taking into account the effect of an elevated strike object, whose presence is included as an extension to the transmission line (TL) model. Specific equations are derived for the case of tall and electrically short objects. The derived expressions show that, for tall structures (when the round-trip propagation time from top to bottom within the tower is greater than the current zero-to-peak risetime), the far field is enhanced through a factor with respect to an ideal return stroke initiated at ground level. The enhancement factor can be expressed in terms of the return stroke wavefront speed v, the speed of light in vacuum c, and the current reflection coefficient at the top of the elevated strike object. For typically negative values of this top reflection coefficient, lightning strikes to tall towers result in a significant enhancement of the far electromagnetic field. Expressions relating the far electromagnetic field and the return stroke current are also presented for electrically short towers and for very long return stroke current wavefronts. For the case of return strokes initiated at ground level (h=0), these expressions represent a generalization of the classical TL model, in which the reflections at the ground are now taken into account. We describe also simultaneous measurements of return stroke current and its associated electric and magnetic fields at two distances related with lightning strikes to the 553-m-high Toronto Canadian National (CN) Tower performed during 2000 and 2001. The derived expressions for tall strike objects are tested versus obtained sets of simultaneously measured currents and fields associated with lightning strikes to the CN Tower, and a reasonable agreement is found. Additionally, it is shown that the peak of the electromagnetic field radiated by a lightning strike to a 553-m-high structure is relatively insensitive to the value of the return stroke velocity, in contrast to the lightning strikes to ground.

Electrostatic Field of a System of Parallel Cylindrical Conductors

The paper presents an investigation of the electrostatic field of a system of infinitely long parallel cylindrical conductors. Existing analytical techniques can be used only to solve rigorously the field of simple geometries such as a single conductor over a ground plane or inside a grounded cylinder and an isolated two-conductor bundle. Until now only approximate analytical solutions have been obtained for the more practical multiconductor systems; in these, each conductor is represented by a line charge at its center.

Electromagnetic field radiation model for lightning strokes to tall structures

This paper describes the observation and analysis of electromagnetic field radiation from lightning strokes to tall structures. Electromagnetic field waveforms and current waveforms of lightning strokes to the CN Tower have been simultaneously measured since 1991. A new calculation model of electromagnetic field radiation is proposed. The proposed model consists of the lightning current propagation and distribution model and the electromagnetic field radiation model. Electromagnetic fields calculated by the proposed model, based on the observed lightning current at the CN Tower, agree well with the observed fields at 2 km north of the tower.

Calculation of the extreme loading condition of a power system for the assessment of voltage stability

The extreme loading condition (XLC) of a power system is defined by assuming a load increase (according to a predefined pattern for both active and reactive powers) until a maximum is reached for one of the loads. The XLC is significant for the assessment of voltage stability. Its calculation, as presented, is based on increasing the load admittances while first keeping the generator voltage phasors constant and then adjusting these phasors for satisfying operational requirements with respect to the generation powers. The secant method is used for the efficient and reliable determination of the maximal value of the loading parameter mu , while for the voltage adjustment a fast convergent Newton module is employed. The XLC can be calculated for both normal operation and contingencies. >

Simultaneous measurement of lightning parameters for strokes to the Toronto Canadian National Tower

Successful simultaneous measurements of significant parameters for lightning strikes to the Canadian National (CN) Tower in Toronto have been performed since the summer of 1991. Three 10-bit 10-ns computer-controlled double-channel digitizers, with long segmented memory, have simultaneously captured the current derivative at the CN Tower and the corresponding electric and magnetic fields 2.0 km north of the tower. Lightning flashes to the tower were videotaped from two mutually perpendicular directions for the purpose of constructing a three-dimensional image of the lightning path. Furthermore, the return stroke velocity, a parameter also needed for the analysis of lightning radiation models, has been measured by a computer-controlled photodiode system. In this paper all relevant parameters for a CN Tower lightning stroke, observed on August 17, 1991, are shown and analyzed.