Quadratic spline formulation of lightning stroke inclination effects on insulator string overvoltages

Digital simulation is imperative for insulation coordination which necessitates evaluation of the various overvoltages likely to beb imposed on systems. In this paper the experimental results of the effects of lightning stroke inclination on the insulator string overvoltages of a 500 kV transmission line have been represented as empirical formulas by quadratic splines. The overvoltages have been obtained as ratios of the overvoltage peaks to the peaks of the stroke currents. The formulas have been derived for practical values of stroke current waveshapes and tower footing resistances. The insulator strings of the phases having the same height may, according to the experimental results, be exposed to equal or unequal overvoltages depending on the lightning strike characteristics. For the former case a single formula has been derived, but for the latter distinctive formulas have been found. These formulas will be useful in the analysis of lightning overvoltages and transmission line outage prediction by digital simulation.