Demand Management in Hybrid Locomotives Through Aggregated Models of Supercapacitors and Railway Units

Most European Union governments and numerous railway operators have announced plans to replace most of their diesel units by 2030–2040. However, a significant portion of the rail network remains non-electrified. In some cases, the proposed solution has been to close certain tracks, but this approach entails considerable societal costs for small cities and represents a loss of prior railway investments. Consequently, hybrid locomotives and multiple units (either new or refurbished) emerge as a viable solution during this transitional period to enhance energy efficiency and preserve services on these lines, particularly for freight operations. These hybrid units can operate on both electrified and non-electrified tracks and can also serve as “railway prosumers”, contributing to both storage and generation in fully or partially electrified areas. However, implementing these “prosumer tasks” faces challenges, such as the rapid power demand fluctuations during acceleration and the loss of energy recovery potential during braking in hybrid or fully electric units. These losses may also impact the overall power system. This paper presents an alternative approach to modeling double-layer capacitors (supercapacitors) combined with electrical equivalent models for lithium-ion batteries. The Differential Transformation Method (DTM) is used to solve the non-linear ordinary differential equations governing the supercapacitor model, while parameter optimization is achieved through a grid search approach, demonstrating high accuracy compared with laboratory trials. This framework highlights the potential of hybrid units, as illustrated through simulations that analyze storage sizing, energy management, increased energy recovery, and changes in unit performance. These models facilitate a pre-feasibility evaluation of energy storage systems for hybrid railway applications.