$k$ -factor Test Voltage Function for Oscillating Lightning Impulses in Nonhomogenous Air Gaps

The k-factor function, called the test voltage function, in present standards IEEE Standard 4-2013 and IEC 60060-1, was determined years ago for voltages not higher than 100 kV and with relative overshoots around 15%. This paper presents the results of k-factor tests carried out for greater voltages up to +1.32 MV (equivalent to air-gap distances d = 2.5 m) and many test conditions. These test conditions are relative overvoltages, β^´ up to 35%, different damping ratios: from δ = 0 (overshoot) to δ =35% (oscillating waveform), and different electrical configurations of a nonhomogenous electric field using air gap factors K = 1 (rod plane) up to K =1,45 (rod conductor). The results show that the present k-factor function stated in both standards does not represent insulation behavior for large air-gap distances when the gap factor K is around 1. Only when the gap factor K increases to 2, are the experimental k-factor values closer to the standard k-factor function. A general formula for the k-factor, depending on the oscillation frequency, gap distance, and the electric-field nonhomogeneity, k (f, d ,K) is derived from the performed tests, taking also into account the k-factor results of the recent bibliography.