Parameter estimation of positive lightning impulse using curve fitting-based optimization techniques and least squares algorithm

Abstract

Lightning is leads to various adversary effects on energy systems and living beings. These negative effects can be reduced only through a better understanding of their characteristic behaviours of lightning. The present study makes a comprehensive evaluation on the calculation of the function parameters of different mathematical models in the literature for the modelling of lightning impulses using the optimization-based curve-fitting method. For the lightning current waveform, artificial lightning current waveforms at different magnitudes were used at 10/350 μs, experimentally measured from Dresden High Voltage Test Laboratory using current impulse generator. With these waveforms, Pulse, Double Exponential, and Heidler function parameters were calculated using Genetic Algorithm(GA), Particle Swarm Optimization(PSO), and Grey Wolf-Cuckoo Search(GWO–CS) optimization algorithms for modelling lightning impulses. The results were statistically evaluated. The simulation findings reveal that the optimization-based curve fitting approach is simple, solid, and efficient tool for accurately extracting the peak value, current derivative, charge, specific energy and the front and tail times of lightning impulse forms using Pulse, Double Exponential, and Heidler functions. The Pulse function parameters calculated by GWO–CS have a higher accuracy for describing the artificial lightning current waveform at standard deviation-5.134e-2, relative error-2.11e-10, mean absolute error-6.14e-12 and root mean square error- 2.47e-6.