Modeling of Grounding Grids under Lightning Currents Using a Nonuniform Transmission Line Approach

Modeling a grounding system in the time domain makes it possible to account for the nonlinear phenomenon of soil ionization, which occurs following the injection of a very high-intensity lightning current. Several numerical studies using the Finite-Difference Time-Domain (FDTD) method have focused on modeling grounding systems while considering soil ionization. These works, which have produced excellent agreement with experimental measurements, directly solve Maxwell’s equations in three dimensions (3D), but they remain computationally intensive and numerically complex. In this paper, we propose a model for a grounding grid that offers a simplified implementation while accounting for the various electromagnetic couplings that arise after spatial discretization of the grid, as well as for soil ionization caused by the injection of a high-intensity lightning pulse. This new formulation is developed based on the equations of nonuniform Transmission Lines (nuTL) combined with the Finite-Difference Time-Domain (FDTD) method.

[1] Ametani Akihiro, and al., Guideline for Numerical Electromagnetic Analysis Method, CIGRE Technical Brochure 543, pp. 1-106. 2013.

[2] N. Harid and al., On the Analysis of Impulse Test Results on Grounding Systems, EEE Transactions on Industry Applications, 2015.

[3] A. Mousa, The soil ionization gradient associated with discharge of high currents into concentrated electrodes, IEEE Transactions on Power Delivery, Volume: 9, Issue: 3. 1994.

[4] A. C. Liew and al., Dynamic model of impulse characteristic of concentrated earths, Proc. IEE, 121, (2), pp. 123–135. 1974.

[5] A. Boutadjine, B. Nekhoul and al.,  Realistic modeling of the grounding system transient behavior with frequency dependence, Electric Power Systems Research, volume 203, February 2022, 107644.

[6] C. R. Paul, Analysis of Multiconductor Transmission Lines, John Wiley & Sons, Inc., New York, 1994.

[7] Y. Liu, N. Theethayi, and R. Thottappillil, An Engineering Model for Transient Analysis of Groundig system Under Lightning Strikes: Nonuniform Transmission-Line Approach. IEEE Trans. on Power Delivery. Vol. 20. N° 2. April 2005.

[8] D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method, by Wiley edition. 2013.

[9] K. Otani and al., FDTD Simulation of Grounding Electrodes Considering Soil Ionization, International Conference on Lightning Protection (ICLP), Vienna, Austria. 2012.

[10] IEEE Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Grounding System. Revision of IEEE Std 81-1983.