Time-Domain Analysis of Fractional-Order Transmission Line Models

Based on transmission line propagation principles, this paper proposes a generalized fractional-order transmission line equation. By introducing the fractional-order parameter β, this equation establishes a theoretical framework capable of simultaneously characterizing both normal and anomalous voltage wave propagation phenomena. When applying the fractional-order Adomian decomposition method for transient analysis, the solution complexity for high-order differential equations is effectively reduced through series decomposition of nonlinear terms. Simulation results demonstrate that as β increases from 0.25 to 1, rapid diffusion phenomena during the initial stage progressively diminish while reflected wave superposition effects become increasingly prominent. This characteristic originates from the continuous regulatory mechanism of fractional derivatives governing wave propagation processes. The proposed equation not only precisely characterizes transmission line transient behavior but also significantly reduces simulation time, decreases data requirements, and lowers computational complexity compared to conventional fractional Laplace algorithms, thereby providing an efficient engineering solution for power system transient analysis.