Multiple-phase train trajectory optimization with signalling and operational constraints

Wang, Pengling; Goverde, Rob M.P.

doi:10.1016/j.trc.2016.06.008

Cited by 120 publications

(74 citation statements)

References 27 publications

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“…For the instances with parameter values corresponding to the more accurate models the computations times for the MILP approach were above a minute, while the fastest Pseudospectral method took more than several minutes. P. Wang and Goverde (2016) considered the train trajectory optimization problem for two successive trains without regenerative braking with consideration of general infrastructure (varying gradients and speed limits) and operational constraints, as well as signalling constraints. Operational constraints refer to time and speed restrictions from the actual timetable, while signalling constraints refer to the influences of signal aspects and automatic train protection on train operation.…”

Section: Eett Without Regenerative Brakingmentioning

confidence: 99%

Review of energy-efficient train control and timetabling

Scheepmaker

Goverde

Kroon

2017

European Journal of Operational Research

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329

149

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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.

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Section: Eett Without Regenerative Brakingmentioning

confidence: 99%

Review of energy-efficient train control and timetabling

Scheepmaker

Goverde

Kroon

2017

European Journal of Operational Research

Self Cite

329

149

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“…SOC bt denotes the remaining capacity of the BTs, which is changed with the output/input current i bt . The law of change is portrayed by Equation (15), and the position is chosen as the independent variable to be consistent with tram movement model. Generally, SOC bt should be limited to a range, and the current output/input should not exceed its given boundary.…”

Section: On-board Hybrid Power Plant Modelmentioning

confidence: 99%

“…as equation (43) hp-adaptive pseudospectral method Pseudospectral methods for solving multiple phases train trajectory optimal control problems have been presented in [8,15]. The optimal control problem is transcribed to a discrete nonlinear programming problem at collocation points [35].…”

Section: Multiple Phases Integrated Problemmentioning

confidence: 99%

Integrated Optimization of Speed Profiles and Power Split for a Tram with Hybrid Energy Storage Systems on a Signalized Route

et al. 2018

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Abstract:A tram with on-board hybrid energy storage systems based on batteries and supercapacitors is a new option for the urban traffic system. This configuration enables the tram to operate in both catenary zones and catenary-free zones, and the storage of regenerative braking energy for later usage. This paper presents a multiple phases integrated optimization (MPIO) method for the coordination of speed profiles and power split considering the signal control strategy. The objective is to minimize the equivalent total energy consumption of all the power sources, which includes both the energy from the traction substation and energy storage systems. The constraints contain running time, variable gradients and curves, speed limits, power balance and signal time at some intersections. The integrated optimization problem is formulated as a multiple phases model based on the characters of the signalized route. An integrated calculation framework, using hp-adaptive pseudospectral method, is proposed for the integrated optimization problem. The effectiveness of the method is verified under fixed time signal (FTS) control strategy and tram priority signal (TPS) control strategy. Illustrative results show that this method can be successfully applied for trams with hybrid energy storage systems to improve their energy efficiency.

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“…It is a consensus that a well-designed train control strategy could significantly reduce the energy consumption during the train run. such as dynamic programming method (Effati and Roohparvar, 2006;Franke et al, 2000;Ko et al, 2004;Vasak et al, 2009), linear programming method (Effati and Roohparvar, 2006;Wang et al, 2013Wang et al, , 2014 and pseudospectral method (Wang and Goverde, 2016;Wang et al, 2013Wang et al, , 2014. There are also numerical methods that don't belong to the above-mentioned types.…”

Section: Introductionmentioning

confidence: 99%

“…Regarding this issue, attempts have been made in Yang et al (2012) and Goodwin et al (2016), where the railway is operated under the fixed-block systems, and the solution is obtained by the genetic algorithm. Wang and Goverde (2016) considered the control of an individual train to minimise energy consumption and delay, while the train trajectory is restricted by the time/speed windows at specific locations of the track. A special case of this combined scheduling and control problem is to design the energy-efficient timetable in a metro line, as in Gupta et al (2016), Lo (2014a, 2014b), Su et al (2013), Xu et al (2016), Yang et al 3 It was confirmed in Albrecht et al (2016) that the energy consumption on level track is a strictly decreasing and strictly convex function of journey time.…”

Section: Introductionmentioning

confidence: 99%

A multiphase optimal control method for multi-train control and scheduling on railway lines

Liu

2016

Transportation Research Part B: Methodological

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We consider a combined train control and scheduling problem involving multiple trains in a railway line with a predetermined departure/arrival sequence of the trains at stations and meeting points along the line. The problem is formulated as a multiphase optimal control problem while incorporating complex train running conditions (including undulating track, variable speed restrictions, running resistances, speed-dependent maximum tractive/braking forces) and practical train operation constraints on departure/arrival/running/dwell times.Two case studies are conducted. The first case illustrates the control and scheduling problem of two trains in a small artificial network with three nodes, where one train follows and overtakes the other. The second case optimizes the control and timetable of a single train in a subway line. The case studies demonstrate that the proposed framework can provide an effective approach in solving the combined train scheduling and control problem for reducing energy consumption in railway operations.

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Multiple-phase train trajectory optimization with signalling and operational constraints

Cited by 120 publications

References 27 publications

Review of energy-efficient train control and timetabling

Review of energy-efficient train control and timetabling

Integrated Optimization of Speed Profiles and Power Split for a Tram with Hybrid Energy Storage Systems on a Signalized Route

A multiphase optimal control method for multi-train control and scheduling on railway lines

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