Railway electrification is accelerating globally as part of decarbonization efforts, but many mainline alternating-current feeders were designed for lower, non-simultaneous power demands. When multiple trains accelerate together on shared infrastructure, contact-line voltage can drop sharply, activating automatic current limitation in rolling stock and triggering feeder protection schemes. These events degrade capacity and reliability while operators lack real-time visibility into available traction power under live network conditions.
A new power-flow model addresses this challenge by representing trains with voltage-dependent automatic current-limitation characteristics aligned to EN 50388-1 standards. The analysis reveals that minimum network voltage depends on the product of power and distance, not power alone—a critical finding that conventional single-train envelopes miss. However, multi-train power envelopes do not simply add, creating a complex interaction problem unsuitable for conventional approaches.
The researchers developed a calibration-based, solver-free estimation framework that delivers per-train available power and minimum section voltage for any number of simultaneous trains. The method requires only two brief offline power-flow solver runs: one to establish self-impedance and one to determine inter-train coupling through a separation-dependent factor. The resulting model uses a shared-path voltage approach scalable to operational networks.
Testing across two-, three-, and four-train scenarios showed the estimate tracks full power-flow solutions to within approximately nine percent accuracy on average, with performance improving as more trains share the feeder. Critically, computational cost scales with the number of trains rather than network size, enabling practical real-time deployment.
This advance equips rail operators with actionable intelligence for managing conflicting power demands dynamically. Real-time available-power estimates permit optimized train acceleration coordination, preventing voltage collapse and protection events while maximizing line capacity. The method bridges the gap between decarbonized railway operations and existing infrastructure limitations.
