Roman Antonenko

Purpose. The objective of this work is to develop a method for the optimal control of multiple unit electric train with a multi-motor traction electric drive motion that minimizes energy consumption while maintaining a fixed travel time over a given section, taking into account actual traction and braking characteristics, track profile, and the variable number of traction motors in operation. Methodology. The problem is formulated as an isoperimetric optimal control problem with a constraint on the total travel time. To solve it, the dynamic programming method is applied in the discrete “path–speed” state space. The time constraint is accounted for by introducing a Lagrange multiplier, whose optimal value is determined iteratively using the bisection method. The model accounts for the nonlinear traction and braking characteristics of the rolling stock, speed limits along the track, resistance forces, and the influence of the track profile. Particular attention is paid to the correct description of braking modes, including the transition from electric to mechanical braking at low speeds. Additionally, an approach has been developed to optimize the number of active traction motors, which allows the motor load mode to be aligned with their energy efficiency. Findings. The proposed algorithm enables the generation of energy-optimized speed profiles within specified time constraints. It has been established that the use of the dynamic programming method allows for the generation of optimal traction, coasting, and braking modes while accounting for all constraints. Taking into account the optimal number of operating traction motors provides an additional reduction in energy consumption compared to modes with a fixed configuration. According to the results of the numerical experiment, energy consumption was reduced by 30–35 % relative to the suboptimal (aggressive) mode while maintaining the specified travel time. Originality. A generalized approach to optimal train motion control is proposed, combining dynamic programming, adaptive selection of the Lagrange multiplier, and optimal selection of the number of active traction motors along the route of multiple unit electric train. The motion model has been improved by introducing a terminal speed zone and correctly accounting for braking modes, which increases the stability and accuracy of the numerical solution. Practical value. The results obtained can be used in the development of automated train control systems, the optimization of schedules, and the improvement of energy efficiency in the operation of electric traction rolling stock.

Стаття присвячена вирішенню актуальної науково-прикладної проблеми підвищення точності та достовірності математичного моделювання макродинаміки тягового рухомого складу. Головною метою дослідження є розробка узагальненої математичної моделі руху поїзда, яка здатна комплексно описувати нестаціонарні процеси в тяговому електроприводі та зоні фрикційного контакту «колесо-рейка» в режимах тяги і гальмування. В основі запропонованого рішення лежить інтегрований підхід до опису електромеханічних та фрикційних систем із застосуванням трирівневої архітектури моделювання: мікродинаміка на рівні окремої осі, сумація зусиль на рівні секції або візка та макродинаміка поїзда в цілому. В роботі обґрунтовано доцільність застосування оптимізованої одномасової розрахункової схеми механічної частини тягового електроприводу для задач оцінки енергоефективності, розрахунку гальмівних шляхів та загального руху ділянкою.

The global energy transition necessitates innovative solutions to reduce fossil fuel dependence in the railway sector. This paper analyzes the architectural integration of electrochemical On-board Energy Storage Systems into plug-in hybrid traction systems. The objective is to formulate an engineering approach for energy-efficient rolling stock operating on high-voltage networks (3 kilovolts) and autonomous power. The methodology synthesizes circuit designs, focusing on Bidirectional Direct Current converter topologies and Battery Management Systems. It compares Lithium-Ion cells (Lithium Nickel Manganese Cobalt Oxide, Lithium Iron Phosphate, Lithium Titanate Oxide) to identify suitable heavy-duty configurations. The study identifies isolated Bidirectional Direct Current converters, specifically the Dual Active Bridge topology, as critical for safety in high-voltage environments. It substantiates the transition to Silicon Carbide Metal-Oxide-Semiconductor Field-Effect Transistors, reducing switching losses by 50–70 % versus Insulated-Gate Bipolar Transistors. However, switching frequencies must be limited to 1.5–2 kilohertz to comply with EN 50121 Electromagnetic Compatibility standards. The analysis shows mono-chemical Lithium Nickel Manganese Cobalt Oxide batteries are unsuitable due to thermal risks. Instead, a hybrid architecture combining Lithium Iron Phosphate for capacity and Lithium Titanate Oxide for peak power is proposed. Traditional Proportional-Integral-Derivative regulators are deemed insufficient for complex hybrids; the study advocates for Model Predictive Control to optimize energy flow based on route topography. Furthermore, a modular Battery Management System with high precision (1%) is required to maximize battery range. The optimal architecture integrates an isolated Silicon Carbide converter, a hybrid Lithium Iron Phosphate and Lithium Titanate Oxide battery, and Model Predictive Control, ensuring balanced safety, efficiency, and cost.

This study examines the rolling stock that currently employs or could be equipped with plug-in hybrid traction systems. Existing methodologies for selecting energy storage systems often limit their applicability, which creates certain constraints when choosing a solution for hybrid traction systems. As a result of the study, a well-founded preliminary selection of an energy storage system based on expert evaluation and the Harrington desirability function was carried out. Engaging experts in relevant fields makes it possible to obtain up-to-date information on technology development and assess whether parameters meet specific requirements. The application of methods for evaluating expert consensus provides a foundation for using the results in subsequent calculations. Harrington desirability function makes it possible to combine parameters with varying units of measurement and other differences, yielding a single value that can simplify decision-making. Using expert-derived evaluations, weighting coefficients for various parameters were calculated for the defined types of rolling stock. In the current research, three types of energy storage systems were selected for locomotives and multiple-unit rolling stock, meeting the specified conditions. These include battery, supercapacitor-based and flywheel-based storage systems, with overall desirability scores (without weighting coefficients) of 0.638, 0.636, and 0.573, respectively. Modifying the set of parameters, introducing additional constraints, and adjusting weighting coefficients in conjunction with motion optimization tasks makes it possible to adapt the methodology to the requirements for specific projects for constructing or upgrading rolling stock with plug-in hybrid traction systems