Estimating Available Traction Power in Multi-Train AC Railway Networks from a Distance-Dependent Power Envelope
For railway operators, this provides a real-time, solver-free estimate of available power to prevent capacity loss and reliability issues due to voltage drops.
The paper addresses the problem of estimating available traction power for multiple trains on AC railway feeders to prevent voltage drops that trigger current limitation. The proposed distance-dependent power envelope method estimates per-train available power with an average error of about 9% across multi-train cases, improving with more trains, and scales online cost with train count rather than network size.
Decarbonisation is raising the electrical load on mainline alternating-current railway feeders that were not designed for sustained, simultaneous high-power demand. When several trains accelerate together on a shared feeder, the contact-line voltage can fall far enough to trigger rolling-stock current limitation or feeder protection, eroding capacity and reliability. Preventing this in real time requires a quantity conventional operation does not expose: a localised, continuously updated estimate of the traction power available to each train given the live network state. A railway power-flow model, with trains represented under a voltage-dependent automatic current-limitation characteristic, shows that the minimum network voltage is governed by the product of power and distance rather than by power alone, yielding a distance-dependent single-train power envelope. This envelope does not add up when several trains share a feeder, so a conservative pairwise screen is generalised to a solver-free multi-train estimate: a calibrated shared-path voltage model returning the minimum section voltage and the per-train available power for any number of trains. Calibration uses two short offline solver runs, one fixing the self-impedance and one the inter-train coupling through a separation-dependent factor. Its current-limitation behaviour follows EN 50388-1, and on matched multi-train cases the estimate tracks the full power flow to within about nine per cent on average across two-, three-, and four-train cases, improving as more trains share the feeder, while its online cost scales with the number of trains rather than the network size.