Review of energy-efficient train control and timetabling

Highlights

• Literature review of energy-efficient train control and timetabling.

• Overview of energy-efficient driving strategies under various conditions.

• Application of Pontryagins Maximum Principle to optimal train control.

• Insight in the relation between energy-efficient train control and timetabling.

• Overview of algorithms for 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.

Introduction

Global warming is an increasingly important topic these days. One of the causes of global warming is the increasing amount of carbon dioxide (CO₂) emissions which comes for a large part from transport. Therefore, the European Union (EU) set targets to decrease these CO₂ emissions. One of the sectors affected by these measures is the railway sector. For the railway sector targets are set by the UIC (International Union of Railways) and CER (Community of European Railway and Infrastructure Companies). The short term target is to decrease CO₂ emissions by 30% over the period 1990 to 2020, with a further decrease by 50% in 2030 (UIC, 2012). Furthermore, energy consumption of railway companies should be decreased in 2030 by 30% compared to 1990. A further incentive for railway undertakings to reduce energy consumption is the reduced operating costs and enlarged competitive advantages involved.

As a consequence, railway companies in Europe have started research on opportunities to decrease energy consumption in order to be sustainable and more profitable in the future. Several ways to achieve this goal are as follows:

• An operator can deploy rolling stock that is more energy-efficient (due to more efficient engines or streamlining).

• An operator may better match the capacities of the trains with the demand, so that fewer empty seats are moved around.

• An operator can deploy measures concerning heating, cooling, lighting, etc. of parked trains during nights in order to save energy.

• Energy-efficient train control (EETC) or eco-driving may be applied, in which a train is driven with the least amount of traction energy, given the timetable.

• The timetable may be constructed in such a way that it allows EETC most effectively, resulting in energy-efficient train timetabling (EETT).

This paper focuses on the last two options: energy-efficient train control (EETC) and energy-efficient train timetabling (EETT). A good overview of different measures in order to decrease energy consumption for urban rail transport can be found in González-Gil, Palacin, Batty, and Powell (2014).

EETC has been and is a hot topic in the literature. Much research effort aims at finding the optimal driving strategies of a train that minimize energy consumption  (Khmelnitsky (2000); Liu and Golovitcher (2003); Albrecht, Howlett, Pudney, Vu, Zhou, 2015b, Albrecht, Howlett, Pudney, Vu, Zhou, 2015c). Most of this research is based on optimal control theory, and in particular on Pontryagin’s Maximum Principle (PMP) (Pontryagin, Boltyanskii, Gamkrelidze, & Mishchenko, 1962), to derive the optimal control. This leads to optimal driving regimes such as maximum acceleration, cruising, coasting and maximum braking, see Fig. 1. The problem is then to find the optimal sequence of these driving regimes and the switching points between the regimes for a range of different circumstances and train types. The optimal driving strategy must then be translated into feasible and understandable advice to train drivers in real-time. This generated considerable research in developing Driver Advisory Systems (DAS) that provide specific speed advice to the train drivers with the main challenge to incorporate the current delays into the advice (Kent, 2009, ON-TIME, 2013, Panou, Tzieropoulos, Emery, 2013). Energy savings between 20–30% have been reported when applying EETC in a DAS compared to normal train operation, for example see Franke, Terwiesch, and Meyer (2000) and ON-TIME (2014a).

The impact of train operation on energy savings depends on the timetable. More recently this led to research on the topic of optimal running time supplements (Scheepmaker & Goverde, 2015). A running time supplement is the extra running time on top of the technically minimum running time between two stations which is included in the timetable primarily to manage disturbances in operations and to recover from small delays. However, if a train is punctual then these supplements can be used for energy-efficient driving. Nevertheless, in practice energy efficiency is not yet considered in the construction of timetables which sometimes leads to allocating most running time supplements before main stations where punctuality is measured at the cost of insufficient supplements or even unrealizable running times earlier on the route. Another recent stream of research considers the synchronization of accelerating and braking trains to support regenerative braking, like T. Albrecht (2004). With regenerative braking, kinetic energy is converted into electricity that is fed back to the power supply system to be used by other (nearby) trains. A more detailed description about the working of regenerative braking and different regenerative braking technologies for urban transport can be found in the review paper of González-Gil, Palacin, and Batty (2013). Energy savings up to 35% have been reported after timetable optimization compared to using the normal timetable, for example see T. Albrecht and Oettich (2002) and Sicre et al. (2010).

This paper provides a thorough review of the literature on energy-efficient train control and timetabling, starting with 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. The focus is on the differences between the mathematical models and algorithms in terms of applicability, accuracy and computation time, and their main conclusions on the structure of the optimal driving strategy.

Our method is based on a literature study focussed on EETC and EETT. We structured the publications based on the frameworks shown in Figs. 2 and 9. Our review paper includes publications up to January 2016. The recent paper by X. Yang, Li, Ning, and Tang (2016) also provides a review of EETC and EETT with a focus on urban rail. In contrast to that paper, we consider general railway systems and focus on the differences in the mathematical problem formulations and solution approaches.

Section 2 introduces a basic EETC problem and outlines the mathematics involved. Section 3 reviews the EETC literature building on the concepts and terminology of the basic model. The application of EETC in EETT is the topic of Section 4, which reviews the related literature on the optimization of running time supplements and the synchronization of accelerating and braking trains. Finally, Section 5 ends this literature review with the main conclusions and an outlook to future research directions of EETC and EETT.