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 that's why surge impedance become uniform on lossy transmission line. This manuscript proposes the analytical and fractional modeling of lossy transmission line based on 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 investigated solutions of voltage over the transmission line have been established in terms of exponential and gamma functions. The comparative analysis of voltage over the transmission line through Caputo-Fabrizio and Atangana-Baleanu fractional operators have been presented for line losses on the conductance, resistance and inductance for the confirmation of the principle of electric power transmission.