On the evaluation of input impedance and transient impedance for grounding electrodes using antenna theory

The purpose of this paper is to propose a fast, accurate and efficient algorithm for assessment of input impedance and consequently the evaluation of transient impedance of the grounding electrode.

The mathematical model is based on the thin wire antenna theory and related Pocklington integro-differential equation in the frequency domain, which is numerically treated via Galerkin-Bubnov variant of the indirect boundary element method (GB-IBEM). Two different approaches, scattered voltage method (ScVM) and induced electromotive force – boundary element method (IEMF-BEM), for input and transient impedance are discussed in detail. Extensive numerical experiments have been undertaken to analyze numerical sensitivity of the methods.

Although it was widely used so far, the ScVM, was shown to be unsuitable for the grounding impedance assessment because results are dependent on the number of elements used in the numerical solution. On the other hand, the other method, IEMF-BEM is rather stable, with the respect to the number of elements used and with excellent convergence rate. In addition, IEMF-BEM is much simpler to implement as it requires only multiplication of matrices already assembled within the procedure of current distribution calculation, as opposed to the ScVM which requires numerical integration of quasi-singular integrals which, by it self, can be very demanding.

The IEMF-BEM is originally developed by the authors and used for the first time for grounding impedance assessment. It is simple and very efficient and can easily be extended to arbitrary grounding configurations.