Optimization algorithm for minimizing railway energy consumption in hybrid powertrain architectures: A direct method approach using a novel two-dimensional efficiency map approximation

SEnSOR (Smart Energy Speed Optimizer Rail) is a direct method based optimization algorithm developed at DLR for determining minimum energy speed trajectories for railway vehicles. This paper aims to reduce model error and improve this algorithm for any alternative powertrain architecture. Model simplifications such as projecting the efficiency maps of different train components onto one-dimensional space can lead to inaccuracies and non-optimalities in reality. In this work, 2D section-wise Chua functional representation was used to capture the complete behavior of efficiency maps and discuss its benefits. For this purpose, a new smoothing method was developed. It was observed that there is an average of 6% error in the energy calculation when both, 1D and 2D, models are compared against each other. Previously, solving for different powertrain architectures was time consuming with the requirement of manual modifications to the optimization problem. With a modular approach, the algorithm was modified to flexibly adapt the problem formulation to automatically take into account any changes in powertrain architectures with minimum user input. The benefit is demonstrated by performing optimization on a bi-mode train with three different power sources as developed within the EU-project FCH2RAIL. The advanced algorithm is now capable to adapt to such complex architectures and provide feasible optimization results within a reasonable time.