Analytical and fractional model for power transmission of lossy transmission line

Abstract

A lossy transmission line can draw current from DC source if DC voltage is applied to constant resistance. This manuscript proposes a fractional modeling of lossy transmission line based on the partial differential equations by employing Kirchoff's current and voltage laws via Fourier analysis. The governing equation of lossy transmission line is fractionalized by means of modern fractional differential operators. The optimal solution of voltage is investigated by means of Fourier sine and Laplace transforms subject to the imposed conditions. The solutions of voltage over the transmission line have been investigated in terms of exponential and gamma functions. The comparative analysis of voltage over the transmission line through Caputo-Fabrizio and Atangana-Baleanu fractional operators has been presented for line losses on the basis of conductance, resistance and inductance for power transmission.