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This paper aims to present the approximation of lightning currents waveshapes by the multi-peaked analytically extended function (MP-AEF) for the experimentally measured channel-base currents in the artificially triggered lightning discharges. Modified transmission line model of lightning return strokes having the channel current both linearly decaying and sinusoidally changing with height (MTLSIN) is used to calculate the lightning electromagnetic field.

MP-AEF’s parameters for the artificially triggered lightning channel-base currents are calculated by using Marquardt least squares method (MLSM). Lightning electromagnetic fields are calculated based on electromagnetic theory relations, thin-wire antenna model of the vertical lightning channel and the assumption of the perfectly conducting ground. MTLSIN model as an engineering model of lightning strokes is used to obtain the electric field results as these are simultaneously measured in rocket-triggered lightning experiments together with the channel-base currents.

MP-AEF approximates multi-peaked pulse waveshapes. Some important function parameters are chosen prior to the approximation procedure, such as current peaks and the corresponding time moments of those peaks, which presents an advantage in comparison to other functions. The desired accuracy of approximation is obtained by choosing an adequate number of function terms. MLSM is used for the estimation of unknown parameters. Using MTLSIN model, the influence of the channel height and return stroke speed on the lightning electromagnetic field waveshape is analyzed in this paper.

MP-AEF may be used for approximation of various multi-peaked waveshapes. It has no errors in the points of maxima which is important for the lightning protection systems design. MTLSIN model may be validated by using simultaneously measured lightning electromagnetic fields at various distances from the channel and for channel heights estimated in the experiments. It is also possible to approximate measured current derivatives by MP-AEF and use them for further computation.

MTLSIN model is proposed in this paper for the evaluation of lightning electromagnetic fields induced by artificially triggered lightning discharges. The procedure is based on the approximation of lightning channel-base currents by the multi-peaked analytically extended function previously proposed by the authors. This function may be used not only for representing lightning currents but also for other waveshapes as current derivatives, electric and magnetic fields and their derivatives, which are all important for the lightning protection design. MTLSIN gives lightning electromagnetic fields results which are in better agreement with measured fields than those obtained by other models from literature.

The purpose of this paper is to present a new function for approximating lightning channel‐base currents which is useful in return stroke modelling and for calculating lightning electromagnetic fields and induced effects in conductive structures, installations and systems.

The derivative and integral of the function are obtained analytically. Function parameters are calculated to approximate theoretically assumed or experimentally measured first stroke channel‐base currents using least‐squares method. The proposed expressions are useful for calculating lightning electromagnetic field using thin wire antenna approximation and lightning stroke models. Analytically obtained Fourier transform of the function is needed in the case of a lossy ground.

The function can approximate both double and one‐rise front waveshapes, so as faster and slower decaying tails. Some important function characteristics can be chosen prior to the approximation procedure, such as the current peak and rise‐time to peak, which is an advantage in comparison to other functions from literature. Parameters can be calculated so to obtain the desired decreasing‐time to half of the peak value; maximum current steepness due to analytically obtained derivative; charge transfer corresponding to the function integral; the specific energy corresponding to integral of the square of the function, etc.

This function can be used also for approximation of other impulse quantities of interest.

The new proposed function for lightning current modelling is suitable for generalization of the procedure for computing electromagnetic fields and induced effects.