Efficient approach for full-wave modelling of grounding systems is provided. First the electric field integral equations are cast in form that is more suitable for grounding analysis and have improved convergence. Then numerical evaluation of the Sommerfeld integrals is substituted by bivariate cubic interpolation procedure of the solutions from pre-computed interpolation grid. This procedure provides substantial improvement of efficiency of the full-wave electromagnetic analysis of grounding systems, while introducing a negligible error in the results.
Słowa kluczowe: grounding systems, Sommerfeld integral, analysis of grounding systems
W artykule opisano efektywne podejście do modelowania systemów uziemiających. W pierwszej części podano równania różniczkowe opisujące pole elektryczne w formie, która jest bardziej odpowiednia dla analizy uziemienia i pozwala na uzyskanie lepszej zbieżności z wynikami eksperymentu. Następnie obliczenia numeryczne całek Sommerfelda zastąpiono dwuzmienną interpolacją sześcienną rozwiązań z wcześniej obliczonej siatki interpolacyjnej. Ta procedura zapewnia znaczną poprawę wydajności pełnej elektromagnetycznej analizy układów uziemienia, jednocześnie wprowadzając nieznaczny błąd w wynikach.
Keywords: układy uziemienia, całka Sommerfelda, analiza układów uziemienia
The frequency dependent and transient characteristics of grounding systems are of interest in many engineering analyses related to electric power safety and lightning protection, where frequencies of interest range from dc to few MHz , and electromagnetic compatibility related studies, with frequencies of interest up to tens of MHz . Different methods for modelling of grounding systems have been developed in the past few decades, based on electric circuit [3, 4], transmission line  and electromagnetic theory . Among them, electromagnetic model provides most accurate results for all frequencies of interest. The most popular electromagnetic model is based on antenna theory and solution of electric field integral equations by the method of moments (MoM) [6, 7]. One difficulty in implementation of the mathematically exact solution for the electric field for semi-infinite conducting medium in practical problems is the numerical evaluation of singular, oscillatory and slow converging Sommerfeld integrals, which is numerically unstable and extremely time consuming procedure. To circumvent this problem in practical analysis, quasi-static [8, 9] or complex-images approximations [10, 11] are often employed, however, the governing approximations limit their validity to a certain upper frequency and system dimensions. Due to the lack of efficient full-wave model, the domain of applicability of these approximations as well as other approximate models has not been rigorously tested for wide range of parameters and complex configurations. Another common problem in the application of antenna theory based methods for analysis of buried conductors is that they may not provide exact solutions for low frequencies approaching 0 Hz. This is either due to improper treatment of the images of currents in conductors , or due to numerical instabilities often referred to as “low frequency breakdown". This paper presents efficien [...]
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