### Implementation of an analytical formulation for LEMP to assess the lightning performance of a distribution line

#### Abstract

This paper presents the implementation of an analytical formulation to calculate the lightning electromagnetic field (LEMP) assuming a current wave-shape linearly rising with flat top and a transmission Line (TL) returns -stroke model. It is presented also describes the development of the expressions for the image dipoles required to calculate the vertical electric field, the azimuthal magnetic field and, specially, the horizontal electric field. The expressions to calculate the contribution of source dipoles were presented in a previous publication of by other authors. The complete formulation is used to calculate electromagnetic fields and lightning- induced voltages on a typical overhead distribution line. The results were compared with traditional formulas to calculate the LEMP (such as the Rubinstein’s formula) and to calculate induced voltages (such as the Rusck Formula ’s) showing errors less below than 1%. If a more complex wave shape were was used (such as as the Heidler’s one),, errors less thanbelow 5% were found. Additionally, the formula was employed to calculate the flashover rate of a distribution line above a ground with infinite and finite conductivity. It was found eErrors less than 5% were found compared with to the results obtained in the IEEE 1410 Standard. On the other hand, the computation time required to the assessment of an overhead line indirect lightning performance is reduced by half when the analytical formula is used.

#### Keywords

Lightning; lightning induced voltages; distribution lines; analytical formulas; electromagnetic field; flashover rate

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