Evaluation du couplage inductif pour la modelisation des cables et lignes electriques de transmission dans EMTP

Environmental concerns and the lack of space in overpopulated cities can impose a cluttering of powerlines, telecommunication facilities, railway systems and gas pipelines, or the use of a common right-of-way. Equipments that are brought in close proximity to each other can generate mutually induced currents and voltage. This problem is well known as Electromagnetic Compatibility (EMC), an important aspect in equipment design.; To perform EMC studies in the corridors of power networks, a group of partners associated to the improvement of the EMTP-RV (Electromagnetic Transients Program-Restructured Version), have launched the development of CRINOLINE, an EMTP-RV software toolbox. This new project requires modifications in line and cable parameter calculation modules in the EMTP-RV such as taking into account mutual earth return impedance between two equipments of different types. Such a case is the inductive coupling between an overhead line and an underground cable.; The principal objective of this research is to evaluate the mutual earth return impedance and to analyze its incorporation in line and cable EMTP-RV models for structures of different types.; The mutual earth return impedance derives from the electrical field due to the presence of the ground. By considering the quasi-TEM assumptions (Transverse Electromagnetic) taken by Pollaczek to solve Maxwell's equations for this field, we show that for the configurations usually met, these assumptions are respected. However, for distances beyond the order of a hundred meters, depth about a tens meters or for frequencies of a few MHz, assumptions are not valid any more and the results of the evaluation of Pollaczek's integral are questionable.; By correcting the localization of the roots of Pollaczek's integral function for one of the most recent numerical evaluation methods and by bounding the relative error, we propose a new numerical evaluation method of the Pollaczek's integral. This is validated in comparison with the results of the Quasi-Monte Carlo method without truncation.; The limits of the new numerical method are related to those of Lobatto quadrature in Matlab when the steps required for the absolute tolerance needed are extremely small.; In addition, the CPU time for certain configurations is relatively high. The estimate of error bounds is conservative and lengthens the execution time. The new numerical method that we propose will be a whole tool to establish the limits of precision of closed-form approximations.; By analysing series expansions of the electric field expressions introduced by Pollaczek, we derive two new approximate formulas: one for overhead line and buried cable coupling; and another for the buried cables. Moreover, the latter is deduced from a general observation that impedance between buried cables can be deduced from the expression of the impedance between an overhead and underground elements adding two Bessel functions.; New approximate formulas as those of Lucca, CCITT, Saad and the Uribe method, were compared with the new numerical method. It turns out that for the case overhead-underground, the new approximate formula is more precise than others for frequencies lower than approximately 1 kHz, and for short distances (height < 10m and horizontal distance < 3m). However, all these approximate formulas for mutual earth return impedance between overhead line and buried cable are inadequate for frequencies over 10kHz. We propose a hybrid method combining the approximate formulas we recently introduced with Lucca's formula and Lobatto quadrature. This hybrid formula gives relative errors of less than 1% compared to the complete numerical method. Time costs for a typical case of 10000 evaluations of impedance is less than 60 seconds. This hybrid method may be improved by optimizing the use of the approximate formulas and Lobatto quadrature in Matlab. The new approximate formula we propose for cables appears to be as precise as Saad's for...