Limitations on Using Closed-Forms in Modelling Horizontal Grounding Electrodes

This paper investigates the adequacy of using closed-form expressions for the per unit length (pul) parameters of horizontal grounding electrodes. Two distinct approaches are used, and the accuracy is tested against results obtained using the so-called Hybrid Electromagnetic Model (HEM). The validity limits of using closed-forms are discussed based on results obtained for different electrode lengths and soil resistivity values. Both frequency domain (harmonic impedance) and time domain results (GPR) are compared. Harmonic impedance results show that the finite-length conductor based closed-form expressions can provide accurate results in the lower frequency range, the limit increasing with the soil resistivity value. For low resistivity soils, the limit is around 20 kHz. The infinite-length conductor based closed forms are to be avoided as they generally lead to poor results. For a lightning current representative of subsequent strokes, very high frequencies are excited and the finite-length conductor based closed-form GPR results are not accurate. It is shown that they lead to higher peak values, thus providing conservative results.