Modeling Lightning Attachment to Tall Towers

Lightning return stroke resulting from the downward leader attachment to tall towers is modeled as a point current source in series with the lightning channel and tower. Assuming a quasi-transverse electromagnetic fleld structure, expressions for the current at the top of the tower, at the base of the tower and along the tower are presented. 1. INTRODUCTION Modeling the lightning strike to tall towers is an interesting problem, especially due to the fast expansion of the mobile telecommunication network and the resulting increase in the number of towers and associated lightning events to the towers. Measurements show that return stroke peak currents at the top and bottom of a tall tower are difierent. For instance, Gorin and Shkilev (1) reports median return stroke peak currents of 9kA at 533m level of the 540m tall Ostankino TV tower in Moscow, whereas they have measured 18kA at the bottom at 47m level. The increased value of the return stroke peak current at the bottom of the tower is due to the transient processes in the tower during the lightning return stroke. Also, it has been observed that the average value of the peak electric and magnetic flelds from the from tower lightning return strokes are 2 to 3 times larger than that would be expected for a return stroke of similar peak current striking level ground (2). Analysis of current waveforms at the top and bottom of the tower gives indications of current re∞ections at the tower bottom and tower top (3), which could be approximately explained by modeling the tower as a transmission line with re∞ection coe-cients at the tower ground interface and at the tower-lightning channel interface and the lightning as a current or voltage source at tower top. However, there are difierences among researchers on the nature of the source to be used at the tower top for modeling the lightning interaction (4{7). This issue is addressed in this paper and a new model for lightning interaction with the tower is proposed. 2. THE MODEL In normal negative ground ∞ashes, a stepped-leader, usually negatively charged, descends towards the ground from the thundercloud. When the leader approaches the ground, electric flelds at the tips of grounded objects are enhanced. When the fleld exceeds the break down value of the air an upward leader is initiated from the object towards the descending leader. When the upward and downward moving leaders meet, a lightning return stroke happens, associated with large currents and large fleld changes. The upward wave efiectively neutralizes the negative charge and the downward wave neutralizes the positive charge of the upward leader from the tower, charge on the tower, and charge from the grounding network. The upward current can be treated as due to positive charge ∞ow and the downward current can be treated as due to negative charge ∞ow, giving rise to current vectors in the same direction in the channel and the tower initially. According to the above picture, the undisturbed current source, representative of the return stroke initiation at the attachment point between the two oppositely charged leaders, is in SERIES with the lightning channel and can not be in parallel with remote ground as reference as suggested in (4). The series point current source is very similar to the source in the Transmission Line (TL) model of the return stroke to ground proposed by (8). In that model, a point current source at the base of the lightning channel launches a current wave upward and this current is assumed to be the same as the current that would be measured at the base of the channel. The current wave is assumed to be traveling without any attenuation and distortion as if in a lossless transmission line, and hence the name of the model, TL model. The actual geometry of the twoconductor TL or the associated fleld structure was not discussed until quite recently. Thottappillil etal., (9{11) showed that the exact fleld solution of the problem of a vanishingly thin perfectly conducting vertical wire above a perfectly conducting ground plane, excited by a point source at the junction of the wire and ground plane, is a spherical transverse electromagnetic fleld structure (spherical TEM) centered at the point source. This fleld structure is associated with an unattenuating current traveling at speed of light and the problem can be modeled as a TL with lightning channel as one conductor and the ground plane as the second conductor. In the TL model of return stroke, the speed is assumed