Developing an approximation to the Heidler function - With an analytical transformation into the frequency domain

IEC 62305 utilises the Heidler function as the standardised lightning current waveshape because it mimics the properties of a real lightning stroke. There is no analytical solution to the integral of the Heidler function and this means that it is not possible to obtain an expression for the Heidler function in the frequency domain. There are several approximations that are used to overcome this shortcoming. This paper proposes a new approximation that is designed in the Laplace domain. Initial results show that the amplitude differs with that of the Heidler function by no more than 3.7%. Furthermore, the first derivative of the approximated current waveshape, dI=dt, differs with that of the Heidler function by 10.5%. This however can be explained by the steepness factor not being calibrated correctly for the same shape Heidler function. The approximation is created in the Laplace domain and therefore it is trivial to plot the frequency spectrum of the approximation. Frequency analysis shows that the approximation agrees with those of other researchers. It is concluded that the initial results are evident of a promising approximation to the Heidler function.