International Conference on Power Systems Transients – IPST 2003 in New Orleans, USA 1 s-Domain Analysis of Lightning Surge Response of a Transmission Tower with Phase Conductors Asim Kaygusuz 1 , M. Salih Mamis 1 , and Erhan Akin 2 (1) Dept. of Electrical and Electronics Engineering, Inonu University, 44069-Malatya, Turkey (e-mail: akaygusuz@inonu.edu.tr, smamis@inonu.edu.tr), (2) Dept. of Computer Engineering, Firat University, Elazig, Turkey (e-mail: eakin@firat.edu.tr ) Abstract – Lightning surges on a transmission tower with a shield wire and phase conductors are analyzed using an s- domain method. The voltages induced on the phase conduc- tors and surges at the position of the tower crossarms are computed to obtain the insulator voltages. Response of the system determined in the s-domain is transformed into the time domain using Fast Inverse Laplace Transform (FILT). It has been shown that lightning surge response of a transmis- sion tower can be determined easily using Coupling Coeffi- cient Matrix (CCM) defined in this paper. The solution pro- cedure is programmed with MATLAB. The results obtained using the proposed method are compared with those obtained using Electromagnetic Transients Program (EMTP). Keywords – Transmission Lines, Lightning Surge, s-Domain Analysis, Fast Inverse Laplace Transform, EMTP. I. INTRODUCTION Analysis of lightning surges is important for power sys- tems, since lightning strokes on transmission towers, shield wires and phase conductors may cause insulation flashover which may lead interruption of continuous power transmis- sion. When a lightning stroke occurs on a tower or on a shield wire near the tower, potential across the insulation strings becomes excessive and a fault between the phase conductor and a tower crossarm may occur. One end of the insulation chain follow the potential at tower crossarm and other follow the potential on the phase conductor, which is the sum of nominal system operating voltage and induced potential due to lightning. For calculation of the potential across the insulator strings, the surges both on the tower and induced voltages on the phase conductors need to be determined. There are many works that have been devoted to the analysis of lightning surges on transmission towers. Ex- perimental studies on this subject have usually been carried out in Japan [1-4] and measured results have become an important base for computer simulations. In the experimen- tal work done by Kawai surge response of transmission tower has been measured [1]. Later Ishii performed ex- periments on a full scale tower with phase conductors and ground wires [2, 3] and as a result of these experiments a multistory tower model has been proposed for multicon- ductor analysis in EMTP. Series of experiments later have been continued on a different tower configuration [4] to generalize the results obtained in previous works. On the other hand, in the area of numerical developments, Almeida and Correia De Barros [5] used finite element method for the EMTP simulation. Later Ishii and Baba [6] analyzed a large scale UHV transmission tower using mo- ment method by solving electric field equations directly, and in their study the effect of slant elements, horizontal elements and crossarm has been investigated. Using the same method, they also investigated lightning surge charac- teristics of a transmission line comprising a tower, a shield wire and phase conductors with the help of computer pro- gram NEC-2 [7]. Next, in one of the works tower body and crossarms are modeled in details using short lines sec- tions [8]. Recently, Mozumi et al. analyzed archorn volt- ages of a simulated 500 kV twin-circuit line [9]. In this paper, lightning surges on a transmission tower are analyzed using s-domain formulation by taking the ef- fect of the shield wire and phase conductors into account. Potential on the insulator strings is determined from the difference of the voltages at position of tower crossarms and induced voltages on the phase conductors. The study in this paper proceeds the work done to obtain the tower surge response using nonuniform single phase line model- ing [10-12]. In [13] the lightning surges on the tower with a ground wire has been computed but the effect of phase conductors has not been considered. This technique is ex- tended here to involve the effect of the phase conductors. The lightning surges are computed by means of CCM de- fined in the next section. For the frequency to time domain conversion Fast Inverse Laplace Transform (FILT) is used. Computed results show good agreement with the results obtained using EMTP. Main advantage of the s-domain analysis is that frequency dependent effects can be included directly into the analysis. Although variation in system to- pology as well as the inclusion of nonlinear effects such as the back-flashover events require major numeri- cal/theoretical efforts, for specific applications, the fre- quency domain approach can be used as a standard against which to compare time domain solutions. II. S-DOMAIN ANALYSIS OF THREE-PHASE LINES In this study, a three phase transmission system with a shield wire shown in Fig. 1 is considered. Current and volt- age relations on a multiphase transmission line in the phase domain can be described by the following differential equations: ZI dx dV = - (1a)