See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/287371342 Train trajectory optimisation of ATO systems for metro lines Article · November 2014 DOI: 10.1109/ITSC.2014.6957953 CITATIONS READS 8 438 8 authors, including: Ning Zhao Stuart Hillmansen University of Birmingham University of Birmingham 25 PUBLICATIONS 180 CITATIONS 94 PUBLICATIONS 1,081 CITATIONS SEE PROFILE SEE PROFILE Paul Weston Zhongbei Tian University of Birmingham University of Birmingham 56 PUBLICATIONS 935 CITATIONS 15 PUBLICATIONS 86 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Fuel Cell Locomotive View project Track circuits View project All content following this page was uploaded by Zhongbei Tian on 30 June 2016. The user has requested enhancement of the downloaded file. SEE PROFILE CONFIDENTIAL. Limited circulation. For review only. Train Trajectory Optimisation of ATO Systems for Metro Lines * Ning Zhao, Clive Roberts, Member, IEEE, Stuart Hillmansen, Paul Western, Lei Chen, Zhongbei Tian, Tingyu Xin, Shuai Su optimality [7]. Rachel Liu describes a Pontryagin maximum principle application to find the optimal train movement sequence to minimise energy usage [8]. However, most of the research works do not consider the control process of ATO systems, which automatically controls the train movements by tracking the target speed trajectory [9-13]. If such a train trajectory was implemented into an ATO system, the train would have to switch the movement mode from motoring to braking or coasting frequently, thus increasing energy usage. Abstract— This paper describes an Enhanced Brute Force Algorithm application to optimise train trajectory (driving speed curve) for Automatic Train Operation (ATO) systems. A multi-train simulator was developed specifically for the study. It can be used to simulate the movement of railway vehicles and calculate the detailed power system energy consumption with different train trajectories when implemented on an AC or DC powered railway line operating with multiple trains. Results are presented using a practical train trajectory and an optimal train trajectory with a full day timetable and passenger flow on the Beijing Yizhuang Metro Line. Analysis of the results shows that by using an optimal train trajectory, the energy consumption around the power network can be significantly reduced within a constrained journey time. Furthermore, the results also show that the developed simulator is able to facilitate the understanding of the railway traction and power system, and that it provides guidance for adjusting the service timetable and driving strategy to minimise energy usage. This paper describes an Enhanced Brute Force Algorithm application for calculating the optimal train trajectory for ATO systems. A multi-train traction and power system energy simulator was developed for this purpose, which is used to simulate the train movements and calculate the detailed power system energy consumption with a full day timetable and passenger flow on the Beijing Yizhuang Metro Line. Both the optimal train trajectory and a practical train trajectory are implemented into the simulator for energy consumption comparisons. I. INTRODUCTION The train trajectory, which is conventionally controlled by the driver but, in modern train control systems, can be calculated and implemented automatically, has a key effect on energy consumption. As energy-efficient driving is becoming a critical issue for railway operators due to rising energy prices and environmental concerns, train trajectory optimisation is increasingly important for modern railway design [1-4]. Researchers have set out a number of different approaches to optimise train operation in recent literature. Hee-Soo Hwang proposes a fuzzy control model to calculate an optimal running pattern through a trade-off between journey time and energy usage [5]. Bwo-Ren Ke proposes a MAX-MIN ant system to optimise the train trajectory for mass rapid transit systems with cable signalling systems [6]. Compared with metaheuristics, exact search provides a more straightforward approach and is guaranteed to find optimal solutions and prove II. MULTI-TRAIN SIMULATOR DEVELOPMENT The developed Multi-Train Simulator is designed to achieve the following requirements: Simulate the detailed movement of railway vehicles around an AC or DC powered railway network; Calculate voltages and currents in the power network when trains are operating; Calculate the delivered power from the substations and the power consumption at the railway vehicles; Analyse the overall energy consumed when specific timetables are operated; Allow the modification of the behaviour of trains within the simulation; *Resrach supported by Beijing Laboratory of Urban Rail Transit and Beijing Key Laboratory of Urban Rail Transit Automation and Control. N. Zhao is with the Birmingham Centre for Railway Research and Education, School of Electronic, Electrical and Computer Engineering, University of Birmingham, Birmingham, UK (corresponding author to provide phone: +44 (0)121 414 7522; fax: +44 (0)121 414 4291; e-mail: [email protected]). C. Roberts, S. Hillmansen, P. Western, L. Chen, Z. Tian, T. Xin are with the Birmingham Centre for Railway Research and Education, School of Electronic, Electrical and Computer Engineering, University of Birmingham, Birmingham, United Kingdom, B15 2TT, (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected] bham.ac.uk). S. Su is with the 2State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiao tong University, P. R. China (e-mail: [email protected]). Identify and quantify energy losses. In order to develop the simulator, it is necessary to consider the fundamental physics of train motion. Lomonossoff’s Equations, which have previously been described in earlier works, are used to solve the dynamic movement equations [14-16]: (1) where Mtr is the effective mass; Ftr is the traction force effort; Fgrad is the force due to the gradient; R is the vehicle resistance, 1 Preprint submitted to 17th International IEEE Conference on Intelligent Transportation Systems. Received June 24, 2014. CONFIDENTIAL. Limited circulation. For review only. which can be calculated by the following equation with constants a, b, c, known as the Davis equation [17]. The constants are empirical and relative to the track and aero-dynamic resistance. ( ) | | typical movement modes for train motion can be obtained, as shown in Figure 1. The traction system characteristics of a Yizhuang Line vehicle are shown in Figure 2. Speed (2) The forward tractive effort control signal will equal zero when the power is shut down, i.e. in coasting mode or braking mode. In that case, no energy usage will be included. Speed limit Motoring mode Cruising mode Coasting mode Braking mode ̇ { ̇ ( ) ( ) ( ) ( ) (3) Figure 1. Four modes of train movement. A number of parameters should be configured into the simulator. Figure 4 shows the system input and output diagram. Fixed parameters that are not changed during the modelling process are considered as constant values, such as route data, power system characteristics and train traction characteristics. Dynamic parameters, such as acceleration rate, train weight and passenger flow, change from time to time corresponding to train speed, schedule, gradient profile and movement mode. An iterative technique is implemented into the simulator to calculate rail traction and power system solutions [18, 19]. where s is the train position; uf and ub are the control signal for forwards effort and backwards braking effort; f(v) and b(v) are the maximum tractive effort and braking effort at the current speed; r(v) is the resistive force at the current vehicle speed; g(s) is the force due to the gradient at the current position. The boundary conditions are given as follows. The initial conditions are: ( ) { (4) ( ) III. TRAIN TRAJECTORY OPTIMISATION and the final conditions are: As shown in Figure 4, different train trajectories can be applied into the simulator. In this study, an optimal train trajectory application is considered. The result will be compared with that of a practical train trajectory. Figure 5 shows the simulation flowchart. ( ) { (5) ( ) Some constraints are imposed: ( ) { [ ] [ ] As show in Figure 6, the journey is divided into a number of sections (dot dash lines) in terms of the line speed limit changes, altitude changes and distance. The train movement mode in each section needs to be optimised in order to minimise the overall energy consumption. Cruising mode will not be considered in the optimisation as it is difficult to track precisely using ATO systems. (6) where v_lim(s) is the train target speed or line speed limit (whichever is smaller) at the current position s. Based on Equation 1, Equation 2 and Equation 3, four Figure 2. Traction system characteristic of a Yizhuang Line vehicle. 2 Preprint submitted to 17th International IEEE Conference on Intelligent Transportation Systems. Received June 24, 2014. CONFIDENTIAL. Limited circulation. For review only. Input data where n is the number of trains to be optimised; Trun is the journey time; Tmax and Tmin are the maximum and minimum permitted scheduled journey times; Erun is the train energy usage, which can be calculated using the following equation: ( ) [ ( )] ( ) (9) ∫ Calculate the movement of first train Arrive at a station No Yes Final station No Yes Read line speed, gradients. Calculate braking distance New movement authority Dwell time where f [v(t)] is the maximum tractive effort at the current vehicle speed v(t). No In this optimisation study, each potential movement sequence is assumed as a candidate solution and has an individual solution domain. The complexity of the domain depends on the assumed search boundary and search interval. A conventional brute force search enumerates all possibilities in the solution domain to find the optimum [21]. This rapidly becomes impractical due to the processing time required for complex problems [22]. The developed enhanced brute force algorithm is able to address this problem by constraining the solution domain [23, 24]. Key : Yes ti Update movement authority Calculate the distance to the limitation of movement authority - time si - train position vi - train speed pi Movement authority simulation st - train engine power i - station position a ac - acceleration rate a co - coasting rate Calculate the distance to the next station and the next speed limit change position a cu - cruising rate a br - braking rate ( Choose mode Acceleration Coasting Cruising ( Braking ) Fixed parameters: Record results to arrays Train control method Route data: Line speed limits Network gradient Station location Network curvature Output figures, store results to database Figure 3. Simulation flowchart [20]. Train traction data: Traction power Regenerative power Resistance (7) ( ) ∑ Motor efficiency (8) (10) ( ) (11) Simulation input: Timetable (TA) Train trajectory (TR) Target speed Coasting point Movement sequence Simulation output: Power system data: Rectifier characteristics Feeder cable resistances Traction return path resistance Conductance to ground Crossbonds resistance Network voltage range The aim of the train trajectory optimisation in this study is to find the most appropriate train movement sequence (TR1 to TRi) to minimise energy usage within a constant journey time. The cost function to be minimised is thus: ∑ ∑ ) Multi-train Simulator Substation energy usage Auxiliary system energy usage Train energy usage Train operation time Train schedule diagram Dynamic parameters: Acceleration rate Train weight Passenger flow Figure 4. Flowchart of the developed simulator. Figure 5. A full train schedule diagram. 3 Preprint submitted to 17th International IEEE Conference on Intelligent Transportation Systems. Received June 24, 2014. CONFIDENTIAL. Limited circulation. For review only. TR1 TR2 TR3 TR4 TR5 TR6 TR7 schedule diagram obtained from the simulator are shown in TABLE I and Figure 5 respectively. TR8 TR9 TR10 TR11 The detailed energy consumption calculated from the simulator is shown in TABLE II. It can be seen that optimal operation can save energy usage by up to 16% with the same timetable. The energy transmission efficiency from the substations to the railway vehicles is approximately 96%. The auxiliary systems, such as lighting, heating and air conditioning, cost 1% of the substation energy usage. TABLE I. SCHEDULED TIMETABLE OF BEIJING YIZHUANG METRO LINE. Figure 6. An example of a Beijing Yizhuang Metro Line train trajectory optimisation. The method initially calculates an estimated movement sequence (TRest) based on the practical train trajectory and constant journey time (Tcon), as shown in Equation 10. The method then only considers the candidate solutions which are close in value to the estimated solution, thereby reducing the solution domain, as shown in Equation 11. The computing time is therefore significantly decreased. The optimal and practical train trajectories are shown in Figure 7. It can be observed that the actual train switches its movement mode from motoring to braking or coasting frequently as the ATO system aims to track the constant cruising speeds. The optimal train trajectory is able to avoid such situations, thereby reducing energy usage. Station Station location, m Dwell time, s Yizhuang railway station 0 Ciqu Operation time, s Up direction Down direction 40 0 0 1334 45 104 103 Ciqu South 2620 35 248 248 Jinghailu 4706 30 423 421 Tongjinanlu 6971 30 601 599 Rongchangdongjie 9309 30 790 791 Rongjingdongjie 10663 30 923 923 Wanyuanjie 11943 30 1052 1052 Yizhuang Park 13481 30 1194 1194 Yizhuangqiao 14474 35 1309 1309 Jiugong 16456 30 1477 1478 Xiaohongmen 18822 30 1660 1664 Xiaocun 20097 30 1793 1800 Songjiazhuang 22728 30 2016 2019 TABLE II. DETAILED ENERGY CONSUMPTION. Parameters Metro operation time, hours Train traction energy consumption, kWh Auxiliary system energy consumption, kWh Substation energy consumption, kWh Figure 7. Beijing Yizhuang Metro Line practical and optimal train trajectory (up direction) IV. SIMULATION AND OPTIMISATION RESULTS Transmission loss, kWh The simulation is designed using the optimal and the practical train trajectories with a full day timetable and passenger flow on the Beijing Yizhuang Metro Line, which is an urban railway line connecting Beijing city centre and Yizhuang district. The scheduled timetable and the full train Energy transmission efficiency Total passenger flow, thousands of people Operation with practical train trajectory Operation with optimal train trajectory 17.7 17.7 83771 70884 (-15%) 823 823 88188 73955 (-16%) 3594 3071 (-15%) 96.0% 95.8% 1128 1128 4 Preprint submitted to 17th International IEEE Conference on Intelligent Transportation Systems. Received June 24, 2014. CONFIDENTIAL. Limited circulation. For review only. As shown in Figure 8, the network energy usage continues to increase from when the first train departs the first station until the line is fully loaded at 7:00. Between 9:00 to 16:00 (off-peak time), the energy usage reduces by half, as the train service interval increases significantly. The last train departs the first station at 22:05. After that, the number of the trains in the network reduces, and thus the energy consumption also reduces. Figure 9 shows the network energy usage per passenger. It can be observed that the number remains relatively stable between 7:00 and 21:00, which indicates that the train service interval plan fits the passenger flow demand. and power system, and furthermore it provides guidance for adjusting the service timetable and driving strategy to minimise energy usage; It was found that increasing the service interval before 7:00 and after 21:00 on the Beijing Yizhuang Metro Line is able to improve energy efficiency, thereby reducing the energy consumption significantly; The choice of train trajectory employed on a line has a direct impact on improving train performance, thereby reducing the energy usage; The enhanced brute force algorithm was shown to be able to provide a good performance to achieve optimal results. ACKNOWLEDGMENT This research is jointly supported by Beijing Laboratory of Urban Rail Transit and Beijing Key Laboratory of Urban Rail Transit Automation and Control. 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