Vehicle Speed and Net-Energy Gain on Dynamic Wireless Charging Lanes: An Analytical and Numerical Assessment

Abstract

Vehicle speed affects exposure to a dynamic wireless charging (DWC) lane and propulsion demand. This study develops an analytically tractable homogeneous-lane model that separates received electrical energy, wheel work, drivetrain losses, and auxiliary demand. Under an explicitly assumed affine speed–efficiency relation, net DC-terminal energy per unit distance reduces to a three-coefficient expression. The derivative identifies monotonic speed dependence and interior stationary points; the latter represents reduced depletion rather than positive charging. A convexity argument establishes a constant-speed upper bound for a homogeneous quasi-steady segmented formulation at fixed traversal time. Energy-neutral power and coverage thresholds and deadline- and energy-target-dependent feasible-speed intervals are derived. Numerical calculations evaluate hypothetical 300 and 700 m lanes using an idealized baseline and explicitly assumed non-ideal drivetrain and auxiliary-load scenarios. For the 50 kW reference extension, a 700 m traversal with a 0.5 kWh net-energy target and a 60 s deadline permits approximately 11.667–15.221 m/s. Feasibility can be lost within a deterministic six-factor stress box. Component-wise and reduced-form calculations agree within 8.9 × 10−16 kWh across the verification cases. These results provide a reproducible analytical screening baseline with explicit assumptions; they constitute software verification, not experimental validation or a deployment-ready speed controller.