WIRE ANTENNA MODEL FOR TRANSIENT ANALYSIS OF SIMPLE GROUNDING SYSTEMS, PART I: THE VERTICAL GROUNDING ELECTRODE

The paper deals with the transient impedance calculation for simple grounding systems. The mathematical modelmodel is based on the thin wire antenna theory. The formulation of the problem is posed in the frequency domain, while the corresponding transient response of the grounding system is obtained by means of the inverse Fourier transform. The current distribution induced along the grounding system due to an injected current is governed by the corresponding frequency domain Pocklington integro-differential equation. The influence of a dissipative half-space is taken into account via the reflection coefficient (RC) appearing within the integral equation kernel. The principal advantage of the RC approach versus rigorous Sommerfeld integral approach is simplicity of the formulation and significantly less computational cost. The Pocklington integral equation is solved by the Galerkin Bubnov indirect boundary element procedure thus providing the current distribution flowing along the grounding system. The outline of the Galerkin Bubnov indirect boundary element method is presented in Part II of this work. Expressing the electric field in terms of the current distribution along the electrodes the feed point voltage is obtained by integrating the normal field component from infinity to the electrode surface. The frequency dependent input impedance is then obtained as a ratio of feed-point voltage and the value of the injected lightning current. The frequency response of the grounding electrode is obtained multiplying the input impedance spectrum with Fourier transform of the injected current waveform. Finally, the transient impedance of the grounding system is calculated by means of the inverse Fourier transform. The vertical and horizontal grounding electrodes, as simple grounding systems, are analyzed in this work. The Part I of this work is related to the vertical 150 Poljak and Doric electrode, while Part II deals with a more demanding case of horizontal electrode.