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IEEE TRANSACTIONS ON MAGNETICS, VOL 34, NO. 5, SEPTEMBER 1998 2513 Simplified Model of the Discharge Path in Electrical Devices by an Iterative FEM Procedure M. Feliziani F. Maradei, E. Santini, C. Santucci University of L'Aquila - Department of Electrical Engineering - 67040 Poggio di Roio, L'Aquila, Italy University of Roma "La Sapienza" - Department of Electrical Engineering - Via Eudossiana 18, 001 84 Rome, Italy Abstract - A simple VEM procedure is proposed to predict approximately the electrostatic discharge path in a complex configuration. The method is based on the FEM solution of the Laplace equation in order to find the maximum electrical field in the examined domain. When the calculated local electric field is greater than the electric strength of the considered material, a partial discharge event is imposed in the numerical procedure and modelled by an eiquipotential segment. The procedure continues iteratively to solve the Laplace equation modifying adequately the boundairy conditions at each iteration to approximate the breakdown discharge path. Details of the FEM implementation and numerical results of the proposed iterative procedure are given. Keywords: ESD, FEM, iterative procedure, local error estimation I. INTRODUCTION The problem of electrostatic discharge (ESD) is of relevant interest in the studies of electromagnetic compatibility, high voltage engineering, electrostatics and electrical machines [l] - [2]. The aim of this work is to propose a model to predict approximately the discharge path on the basis of the electro-geometrical configuration. Therefore, the interest :is not focused on the basic principles of the main charge generation procedures and development of fundamental modelis for the discharge event. Here, an investigation is made to approximate the path of the breakdown discharge in a two-dimensional configuration by a simple iterative proc1:dure based on the FEM solution of the Laplace equation. The main assumption of the proposed technique is rather restrictive: the discharge path is supposed to be coincident, step .by step, with the maximum gradient path. This hypothesis, which is practically nonphysical, is very convenient in the design of the electronic devices when the ESD event must be prevented. In this case interior electronics must be ade:quately separated by the enclosure to prevent second arc discharges in air. The proposed procedure permits to calculate accurately this separation distance between electrodes. Manuscript received Novemlm 3, 1997. Mauro Feliziani, felizian@ing.univaq.it; Francescaromana Maradei, niaradei@elettrica.ing.uniromal .it; Ezio Santini, ezio@elettrica. ing.uniroma1 .it; Carmen Santucci, carmen@elettrica.ing.uniromal .it. The proposed method permits to find the finite elements in the examined domain where the electric field is maximum.
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