Review of energy-efficient train control and timetabling

Abstract

The energy consumption of trains is highly efficient due to the low friction between steel wheels and rails, although the efficiency is also influenced largely by the driving strategy applied and the scheduled running times in the timetable. Optimal energy-efficient driving strategies can reduce operating costs significantly and contribute to a further increase of the sustainability of railway transportation. The railway sector hence shows an increasing interest in efficient algorithms for energy-efficient train control, which could be used in real-time Driver Advisory Systems (DAS) or Automatic Train Operation (ATO) systems. This paper gives an extensive literature review on energy-efficient train control (EETC) and the related topic of energy-efficient train timetabling (EETT), from the first simple models from the 1960s of a train running on a level track to the advanced models and algorithms of the last decade dealing with varying gradients and speed limits, and including regenerative braking. Pontryagin's Maximum Principle (PMP) has been applied intensively to derive optimal driving regimes that make up the optimal energy-efficient driving strategy of a train under different conditions. Still, the optimal sequence and switching points of the optimal driving regimes are not trivial in general, which led to a wide range of optimization models and algorithms to compute the optimal train trajectories and more recently to use them to optimize timetables with a trade-off between energy efficiency and travel times.

Design of energy‐efficient train speed profiles considering fixed‐block signaling system

“…To make discussion possible, one needs a method to optimize speed profiles. Importance of such optimization has been long known, and some attempts at it were made, but a breakthrough in this field was achieved about 10 years ago when computing performance has reached a sufficient level; examples are presented in a number of reviews …”

“…Importance of such optimization has been long known, and some attempts at it were made, 4,5 but a breakthrough in this field was achieved about 10 years ago when computing performance has reached a sufficient level; examples are presented in a number of reviews. 6,7 On the other hand, regarding application to real train operation, energy saving was studied or implemented using ATO (Automatic Train Operation), DAS (Driver Advisory System), and so on 3,[8][9][10] ; energy saving can be accomplished with relative ease using speed profile improvement, and one can expect for a big effect within a short time.…”

Optimal Operation of High-Speed Trains Using Hybrid Model Predictive Control

“…The maximum tract input max is a nonincreasing function of speed, which is approximated by a piecewise linear, quadratic, and/or hyperbolic function of speed [15]. Thus it can be described as a group of hyperbolic or parabolic formulas and each formula approximates the actual traction force for a certain speed interval [30], such as…”

“…obtain LP-subproblem LP( ); (5) Π ← Π ∪ LP( ) (6) end for (7) if there are no LP( ) ∈ Π that need to be solved then (8) obtain optimal performance index * 0 ; (9) obtain optimal solution vector * ; (10) obtain optimal control input ( ) ← * ; (11) else (12) while num < Maxnum do (13) for each ∈ [ , 1] do (14) extracting LP( ) from Π; (15) if LP( ) has feasible solution then (16) obtain ( ) and ; (17) else (18) if LP( ) satisfies ( ) ∈ {0, 1} and ( ) < * 0 then (19) * 0 ← ( ) and * ← ; (20) num = num + 1;…”

“…As a summary, Scheepmaker et al [15] presented an extensive review on energy-efficient train control and the related topic of energy-efficient train timetabling, from the first simplest model of a train running on a level track to the advanced models and algorithms of the last decade dealing with varying gradients and speed limits and including regenerative braking. And there have appeared various theories and technologies to realize the efficient and safety train operation, such as the passivity-based cruise control [16], the robust adaptive control [17], and the iterative learning and fault detection approaches [18,19].…”