Comparative Calculation of the Fuel–Optimal Operating Strategy for Diesel Hybrid Railway Vehicles

Abstract

In contrast to road-based traffic, the track as well as the corresponding duty cycle for railways are known beforehand, which represents a great advantage during the development of operating strategies for hybrid vehicles. Hence the benefits of hybrid vehicles regarding the fuel consumption can be exploited by means of an off-line optimisation. In this article, the fuel-optimal operating strategy is calculated for one specified track using two hybrid railway vehicles with different kinds of energy storage systems: on the one hand, a lithium-ion battery (high-energy storage) and, on the other, a double layer capacitor (high-power storage). For this purpose, control-oriented simulation models are developed for each architecture addressing the main effects contributing to the longitudinal dynamics of the power train. Based on these simulation models, the fuel-optimal operating strategy is calculated by two different approaches: Bellman’s dynamic programming, a wellknown approach in this field, and an innovative sensitivity-based optimisation.

Analysis of Hybrid and Plug-In Hybrid Alternative Propulsion Systems for Regional Diesel-Electric Multiple Unit Trains

“…A backward-looking quasi-static simulation approach [43,58] was adopted in modeling the dynamics of the previously described system architectures. The simulation model was developed in the MATLAB ® /Simulink © environment using the OPEUS Simulink toolbox [59].…”

“…The vehicle resistance R v [N] includes roll resistance and air resistance, modelled using the Davis equation [60], with vehicle-specific coefficients r 0 [N], r 1 [N/(m/s)], and r 2 [N/(m/s) 2 ]; R g [N] is the grade resistance, with g = 9.81 m/s 2 denoting the gravitational acceleration, and γ [rad] the angle of the slope [61]; and the curve resistance R c [N] is calculated using Roeckl's formula [62], with φ [m] denoting the curve radius. With the given wheel diameter, d w [m], and the vehicle velocity, v, the torque at the wheel, T w [Nm], and its rotational speed, ω w [rad/s], can be calculated by [37,43].…”

“…The power from the EM shaft to the wheels is transmitted via the axle gear, with the constant gear ratio i ag and the constant efficiency of the gearbox η ag . The torque T EM [Nm] and the rotational speed ω EM [rad/s] at the mechanical input of the axle gear result from [37,43].…”

“…Based on the operation mode (motor or generator), and with the EM efficiency η EM = f EM (T EM , ω EM ) determined by a linear 2D-interpolation in the efficiency map, the electric power of the electric motor P EM [W] can be determined by [37,43].…”

“…These include its requirements for perfect information on the future duty cycle, the extensive calculation time, frequent switches in power distribution, and the inability to deal with variables that include counters due to its non-causal nature, i.e., propagation backward in time. Therefore, the EMS obtained from the DP is mainly used in defining other causal controllers [41], or as a benchmark in evaluating real-time algorithms [42,43]. The equivalent consumption minimization strategies (ECMS) [44] and Pontryagin's minimum principle (PMP) optimal control strategies [45,46] belong to a group of instantaneous optimization methods that can be used in defining causal controllers.…”