Keywords: dynamics, shock loads, overhead lines, cable failure, ice shedding, finite element modelling.

This paper shows how numerical modelling has become an essential tool for the study of the mechanical security of overhead electric power lines. The author summarises the evolution [1,2] and recent advances in the application of nonlinear finite element modelling procedures to predict the dynamic response of overhead transmission lines under shock loads. Examples of the source of such shock loads are: the sudden failure of a line component (conductor, ground wire, insulator string failures), an external shock aimed at removing ice or snow from a cable, or the natural sudden shedding of ice or snow from a cable span section.

The presentation of the general macroscopic modelling approach is done for the case of a sudden conductor failure, which typically serves as a benchmark case in design for overhead line security. The originality of the approach does not lie in the development of new theoretical tools - although we have a few original contributions of this type - but rather in the application of existing theory and advanced modelling tools to this particular problem: we have used ADINA software [3] throughout. In fact, overhead lines can be analysed as a sophisticated, highly nonlinear solid-fluid interactive system. However, the objective in practice is to reduce the level of sophistication to retain the essential features of the problem at hand. The examples presented are kept simple to illustrate the salient features of the models and to focus on the most important aspects of the response.

Two modelling considerations are essential in such problems: firstly, the cable finite element formulation must accommodate very large kinematics and secondly, the cable mesh density and time step selected for direct integration of the incremental equations of motion must allow for adequate sampling of the shock propagation through the integration points of the model.

Since the shock loads considered may yield large dynamic forces in the supports, it becomes important to model the post-elastic behaviour of towers. The recent development of a special isoparametric L-beam (angle shape with equal or unequal legs) element [4] facilitates post-elastic analysis of classical metallic lattice towers.

The modelling approach for cable breakages and suspension string failures has been validated with several experimental results obtained at both the reduced scale [1] and the full scale [5]. Experimental validation for ice shedding problems at the full scale is still incomplete as such tests are very difficult and costly to achieve. It is anticipated that our recent work on ice shedding [6] will evolve into the development of a special iced cable finite element that will integrate failure criteria for the ice deposit.

All the examples presented in the paper are of modest size. However, very large realistic models have been studied (in particular at Hydro-Québec TransÉnergie [5]) in which all intact wires and tower members were meshed in detail. These problems are very demanding numerically and the main limitations are those of the computing platform, which justifies a move towards high performance computing. With these improved capabilities, our future work will address realistic simulations of longitudinal and transverse cascades triggered by shock loads for the design and validation of various anti-cascading towers and line failure containment devices.

1

G. McClure, and R. Tinawi, "Mathematical modeling of the transient response of electric transmission lines due to conductor breakage", Computers & Structures, 26(1/2), 41-56, 1987. doi:10.1016/0045-7949(87)90235-5

2

G. McClure, and M. Lapointe, "Modeling the structural dynamic response of overhead transmission lines", Computers & Structures, vol. 81, 825-834, 2003. doi:10.1016/S0045-7949(02)00472-8

3

ADINA R&D Inc., "ADINA A finite element program for automatic dynamic incremental nonlinear analysis", Watertown, MA 02172, 2003.

4

P.S. Lee and G. McClure, "A general three-dimensional L-section beam finite element for elastoplastic large deformation analysis", Computers & Structures, 84, 215-229, 2006. doi:10.1016/j.compstruc.2005.09.013

5

P. Vincent, C. Huet, M. Charbonneau, P. Guilbault, M. Lapointe, and G. McClure, "Testing and numerical simulation of overhead transmission lines dynamics under component failure conditions", 40th General Session of CIGRÉ, Paris, France, 29 August- 3 Sept., Paper No. B2-308, 2004.

6

T. Kálmán, G. McClure, M. Farzaneh, and L.E. Kollar, "Dynamic behavior of iced cables subjected to mechanical shocks" in "Proceedings of the 6th International Symposium on Cable Dynamics", AIM Ed., Charleston, South Carolina, 339-346, 2005.

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