A Closed Power Equation for Transmission Lines Under Heaviside Non‐Distortion Condition

We analyze the propagation of instantaneous electric power, ( and being voltage and current), along a uniform transmission line. We prove that the partial differential equation governing admits a universal structural closure into a linear equation of telegrapher‐type if and only if the Heaviside non‐distortion condition is satisfied. This identifies the Heaviside state as the essentially unique configuration where closure is an intrinsic algebraic property of the transmission line, distinguishing it from coincidental, state‐dependent closures that may occur for highly specific waveforms. Away from this condition, the energy dynamics can be described by a coupled nonlinear system for the instantaneous power and impedance, , providing a mathematical demonstration of the exclusivity of the Heaviside limit. Additionally, we derive the linear ordinary differential equations of third‐ and fourth‐order satisfied by the complex power in the AC regime, for lines with spatially varying parameters. A perturbative analysis, supported by numerical simulations and a Hilbert‐transform‐based modal diagnostic, quantifies the cumulative phase drift and effective frequency shifts arising from structural departures from the Heaviside state.