0045-794987 $3 00 + 0.00 c 1987 Pcrgamon Journals Ltd MATHEMATICAL MODELING OF THE TRANSIENT RESPONSE OF ELECTRIC TRANSMISSION LINES DUE TO CONDUCTOR BREAKAGE GHYSLAINE MCCLURE and RENB TINAWI Department of Civil Engineering, f%ole Polytechnique de Montreal, P.O. Box 6079, Station A, Montreal, QuCbcc, Canada H3C 3A7 Abstract-Nonlinear dynamic analyses are performed using ADINA with four idealizations of a small- scale model of a transmission line section subjected to a conductor breakage condition. Results indicate that higher frequency components of the response must be filtered out in order to achieve numerical stability. Accuracy is obtained provided the effect of the propagating stress wave is integrated frequently enough, both in time and space. Comparisons of the transient response with experimental results rcport- ed by Moxer et a/. (IEEE Trans. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Power Apparatus Systems lW,938-947.1981) confirm the validity of the proposed mathematical models. 1. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA INTRODUCTION 1.1 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Problem definition The design of an aerial transmission line for longitu- dinal loads is an essential task. Many sources of unbalanced loads arise in the life of the line. Most of them act statically or quasi-statically (ice accretion, temperature change, steady wind, maintenance and construction procedures), but some are essentially dynamic (ice shedding, strong turbulent wind, wind- induced vibrations, forces due to flashovers). Other even more severe dynamic loads are associated with exceptional events that cause the failure of a line component (cable breakage, drop of a conductor sus- pension assembly, tower or foundation collapse). Exceptional longitudinal loads are of special concern to the line designer. Therefore structural failure occurring under service loads must not propagate and provoke catastrophic cascading effect along the line. For practical reasons, most line designers treat these special loads as static and account for their dynamic effects by applying impact factors to the calculated response in the final displaced configu- ration. Since the late 1940s, efforts have been concen- trated worldwide, by the power-line industry, in search of realistic criteria to the selection of impact factors. In view of the availability of more appropri- ate numerical tools, there is a need to research these criteria. Full-scale tests are rarely conducted and results from small-scale tests remain difhcult to extrapolate to realistic situations. Reliable mathe- matical models involving nonlinearities as well as structural dynamics would then bc invaluable in better understanding of line behavior, which would inevitably lead to better line design, 1.2 Context of the study The work presented here is an essential part of a larger study on the dynamic behavior of existing high-voltage line sections. The objective is to evalu- ate current design criteria used by the industry for exceptional longitudinal transient loads. The specific problem of cable breakage is examined. However, the authors feel that the modeling considerations dis- cussed here are likely to apply to other dynamic unbalance phenomena. In any mathematical modeling form of engineering design problems, preliminary analyses with simplify- ing assumptions are crucial for building a correct final model in which the analyst has gradually gained confidence. In this paper, the authors will present their experience in conducting preliminary nonlinear dynamic finite element analyses using ADINA for the cable breakage problem related to electric transmission lines. In order to validate the various novel mathemati- cal models proposed in this paper, experimental results reported by Mozer et al. [l] and Mozer [31] will be used for comparison. 2 BRIEF LIT’RRATURE REVIEW RELATED TO CABLE MODELING 2.1 Finite segments andfinite elements Cables are used as structural components in so many engineering applications that researchers in various specialty fields (marine, offshore, civil, aero- nautical and aerospace engineering) can share their experience. Review papers by Choo and Casarella [2], Nath [3] and Migliore and Webster [4, S] sum- marize the approach used for cable dynamics in the marine environment. Finite segment models are fairly popular in this field and Wang [6] has dis- cussed their accuracy in representing various modes of vibrations. Few segments are needed to represent out-of-plane motions (pendulum oscillations), whereas transverse in-plane vibrations and longitu- dinal vibrations (which generate stress waves) are essentially wave propagation problems. The latter 41 CAS 26:1/2-D