358 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 50, NO. 2, MAY2008 Influence of Independent Towers and Transmission Lines on Lightning Return Stroke Current and Associated Fields Satoru Miyazaki, Member, IEEE, and Masaru Ishii, Fellow, IEEE Abstract—The influence of elevated objects, when they are hit by lightning, on the measured lightning currents and associated fields is studied. For the present study, an electromagnetic model of re- turn strokes with the help of NEC-4 is employed. Cases of strokes to ground, to independent towers, and to a transmission line are com- pared and the validity of comparison is discussed. The influence of the independent tower of 70 m in height, which simulates Berger’s tower, on the peaks of currents is negligible even for the fast-rising current, which corresponds to a subsequent return-stroke current. The shape of the lightning current at the top of a transmission line is less influenced than that at the top of an independent tower of the same height. Elevated objects significantly decrease the amplitude of vertical electric fields in a close range. If the ground conductivity is infinite, the peak amplitude of electromagnetic field at a distant range will be significantly increased by the presence of an elevated object. In actual cases of finitely conducting ground, however, the increase of the peak field is limited due to the propagation effect. Index Terms—Electromagnetic fields, lightning, moment meth- ods, power transmission time. I. INTRODUCTION P ARAMETERS of lightning return-stroke current, such as the peak amplitude or the rise time, are essential in planning lightning protection. They have been collected principally by direct measurements at elevated objects [1], [2]. On the other hand, the peak amplitude of current has been estimated from associated remote electromagnetic fields [3]. Directly measured currents at the top of an elevated object and associated fields are affected by the presence of the elevated object itself. In analyzing lightning faults of transmission lines, it is important to discuss the influence of not only towers but also of an earth wire on lightning currents and associated fields. Effect of towers and earth wires on lightning-induced overvoltages in medium- voltage distribution lines had been investigated [4]; however, effects of them on lightning currents and associated fields have not been investigated yet. Lightning return-stroke current and associated fields have been calculated using engineering models or electromagnetic models [5] of return strokes. In studies with engineering mod- els, current in an independent tower and in the lightning channel Manuscript received October 23, 2006; revised March 18, 2007 and August 4, 2007. The authors are with the Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan (e-mail: m-satoru@ieee.org; ishii@iis.u-tokyo. ac.jp). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEMC.2007.915285 is typically calculated by employing frequency-independent re- flection coefficients of the current wave at the ground and at the top of the independent tower [6]–[16]. The reflection coeffi- cients are given, implicitly assuming the grounding impedance of the independent tower, the characteristic impedance of the in- dependent tower, and the characteristic impedance of the light- ning channel. Actually, the reflection coefficients are frequency- dependent, and show dependence on the initial rise time of the measured lightning current [17]. This frequency depen- dence of reflection coefficients influences current distribution in elevated objects and lightning channel especially for light- ning currents having steep fronts. It is possible to employ frequency-dependent reflection coefficients in engineering mod- els, and a method for determining them from a measurement was proposed [18]. On the other hand, electromagnetic mod- els [19]–[22], which numerically solve Maxwell’s equations, incorporate the effect of the frequency-dependent reflection co- efficients automatically only by giving geometry and electrical parameters of the components of the system. There have been discussions on the influence of an inde- pendent tower on return-stroke currents and associated fields [10]–[15]. However, some of them [13]–[15] compare different models of lightning channels for the case of hitting an inde- pendent tower and the case of hitting the ground. This happens because an employed engineering model for return strokes hit- ting an independent tower does not produce a self-consistent solution, as an ideal current source is inserted in series be- tween the channel and the independent tower. An ideal cur- rent source has infinite impedance, and hence, it is inconsistent to assume partial reflection. To avoid this difficulty, Rachidi et al. [6] proposed a distributed-shunt-current-source represen- tation of lightning channels, and Baba and Rakov [7] proposed an engineering model that employs a lumped voltage source. Furthermore, the finite conductivity of actual ground dimin- ishes the initial narrow peak of a distant electromagnetic field waveform. Electromagnetic fields associated with a lightning return stroke to an elevated object have an initial spike that is produced by multiple reflections of the current wave within the elevated object. Therefore, the propagation effect for lightning return strokes to an elevated object is more significant than for return strokes to ground [23], [24]. This effect has to be taken into account in evaluation of influence of elevated objects on distant electromagnetic fields. In this paper, the influence of elevated objects, which include transmission lines, on the lightning return-stroke current and the associated fields in their wave fronts is studied using an 0018-9375/$25.00 © 2008 IEEE