Railway Vertical Alignment Optimisation at Stations to

CONFIDENTIAL. Limited circulation. For review only.

Railway Vertical Alignment Optimisation at Stations to Minimize Energy* T. Xin, C. Roberts, Member, IEEE, J. He, Member, IEEE, S. Hillmansen, N. Zhao, L. Chen, Z. Tian, and S. Su 

Abstract— With the prices of energy and environmental concerns increasing, improving railway operation efficiency as an effective method of reducing energy consumption and operation expense has attracted more attention. In metro systems, the two traditional methods used to minimize energy consumption are optimising the timetable and driving strategy, which has been studied for decades. In this paper, a new approach is proposed to improve energy efficiency by optimising the vertical alignment at stations. Firstly, we develop a simplified route with one station in the middle to analyse the relationship between energy consumption and the parameters of vertical alignment at the station. Secondly, we carry out an optimisation simulation of vertical alignment at Beijing Metro Yizhuang Line No.5 station, which reduces energy consumption by 1.66%. Finally, our one station simulation can be extended to the entire Yizhuang route. The simulation results show that, after adding optimal vertical alignment at stations, the energy consumption and journey time could be reduced by 5.6% and 0.53%, respectively. Above all, optimisation of the vertical alignment at stations is an effective approach to minimize energy consumption and improve energy efficiency. Index Terms—Energy-efficiency, vertical alignment, gradient, metro.

I. INTRODUCTION As the railway industry continues to develop, more passengers and freight are attracted than ever before. As a result, the number of trains in operation is increasing rapidly, energy consumption has increased, and significant amounts of greenhouse gases are emitted into the environment. Considering the growing prices of energy and the environmental issues, operating trains in energy-efficient ways is nowadays more important than ever [1]. In order to improve railway operation efficiency, various methods to reduce energy consumption have been developed, including *Research supported by Beijing Laboratory of Urban Rail Transit and Beijing Key Laboratory of Urban Rail Transit Automation and Control. T. Xin is with Birmingham Centre for Railway Research and Education, University of Birmingham, Birmingham, B15 2TT, U.K. and School of Electrical Engineering, Beijing Jiaotong University, Beijing, 100044, China (corresponding author to provide phone: 44-7923639715; e-mail: [email protected]). C. Roberts, S. Hillmansen, N. Zhao, L. Chen and Z. Tian with Birmingham Centre for Railway Research and Education, University of Birmingham, Birmingham, B15 2TT, U.K. (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). J. He with School of Electrical Engineering, Beijing Jiaotong University, Beijing, 100044, China (e-mail: [email protected]). S. Su with the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 100044, China (e-mail: [email protected]).

regenerative braking systems, a reduction in train resistance between wheels and tracks and peak demand control of power supply [2, 3]. Carbon and recycled materials are also used where safety, reliability and practicality allow. A metro is a type of high-capacity public passenger railway service which is generally built in urban areas and which runs in tunnels. The energy-efficiency of a metro system is determined by many factors, such as the performance of the traction and breaking system, the weight of the train, the track plan and profile, civil speed, the signaling system applied, train control strategy, timetable, etc.[4, 5]. For a railway vehicle, energy is used for accelerating and braking, overcoming electrical and mechanical power losses, overcoming the resistance generated by wind and also friction between wheels and tracks [6]. Two adjacent stations along a metro route are much closer to each other than in long-distance railways. The usual spacing between stations is approximately 1~3 km, and the entire route is much shorter. Hence, a metro train needs to accelerate from standstill to operating speed after departing from a station, and decelerate from commercial speed to come to a stop at the next station much more frequently than a long-distance train. Along the Beijing Metro Yizhuang Line, the journey time between two adjacent stations is 2~4 minutes, and the vehicle operates at a relatively low speed (the operation velocity limit is 80 km/h). As a result, the work done by the traction system to overcome the resistance generated by wind and friction is much smaller than that done to accelerate and decelerate. Hence, most of the energy consumption of the metro is used for accelerating and braking, and saving the energy used for these actions could help to enhance energy-efficiency. A metro route with reasonable vertical alignment at stations could make a contribution to a reduction in energy consumption by storing and transferring energy properly. Generally speaking, the ideal vertical alignment at a station is a parabolic curve, on which the station is set at the top, as shown in Figure 1.

Figure 1. Ideal vertical alignment at a station

On this assumption, when a train runs on an upslope, a portion of the kinetic energy turns into potential energy, and

Preprint submitted to 17th International IEEE Conference on Intelligent Transportation Systems. Received June 21, 2014.

CONFIDENTIAL. Limited circulation. For review only. the train slows down. The traction system does less work to brake than it would on a flat track. When the train departs from the station, the declivity helps the train to accelerate by converting potential energy, which is stored during running through the ascent, to kinetic energy. Part of the energy which would have been used to speed the train up is economized. Compared with a route without optimum vertical alignment, the control strategy switching points move towards the right, which means that, on the optimal route, the train could brake and accelerate later. The train could, therefore, run at a relatively high speed for a longer time, and the journey time is minimized. In the real world, optimisation of the vertical alignment is an auxiliary means to minimize energy. This paper focuses on improving the energy-efficiency of the railway industry by optimising the vertical alignment at stations, the topology of which is determined by the gradient and horizontal length. The paper is organized as follows. In Section II we review some literatures on improving energy-efficiency by optimising the control strategy, the timetable and the infrastructure. In Section III, to study the relationship between energy saving and vertical alignment, a simplified route is proposed and optimisation simulations are carried out using a Single Train Simulator (STS). In Section IV we present the case study based on the Beijing Metro Yizhuang Line. Firstly, we optimise the vertical alignment at No.5 station. The vertical alignments at all stations along Yizhuang Line, except for the first and last stations, are then simulated in the optimal condition. The results illustrate that the proposed method gets a good performance for energy saving. II. LITERATURE REVIEW The most important criterion to evaluate energy-efficiency is energy consumption, which could reflect the timetable, and the total operating expense [4]. The energy consumption depends significantly on the trajectory, and the trajectory has a close relationship with the control strategy and timetable. Hence, optimising the trajectory and timetable is generally the key method of improving railway efficiency. The problems can be formulated as optimal theory, which includes the control strategy and the integrated timetable. Many researchers focus on optimising the control strategy and timetable, and have already achieved good research results [7-10]. A number of studies were conducted to minimize train energy consumption with different optimisation methods, such as numerical optimisation, dynamic programming, and metaheuristics optimisation, which includes Genetic Algorithm (GA) [3] and Ant Colony Optimisation (ACO) [1]. Among these studies, the Pontryagin maximum principle, as the basic theory, is widely applied [11]. Meanwhile, some other methods, such as mixed integer linear programming and the pseudospectral method [12] are also applied. In 1997 Howlett and Cheng [8] studied the energy-efficiency of a train operating on a route with various gradients. Liu and Golovitcher [4] pointed out that the cost of energy consumption makes up a large proportion of the Operation and Maintenance (O&M) costs, and they proposed an analytical solution of the optimal problem with variable gradients and gave a sequence of optimal controls and equations to find the control change points. A time-driven TPS

model was developed by Kim and Chien [3] to simulate train operation, which can be applied to evaluate various performance indicators, such as travel time and energy consumption, for any train operation (e.g. the combination of acceleration, cruising, coasting, braking and standing regimes) and track alignments (e.g. the combination of segments with level, convex and concave terrains). As common sense dictates, the timetable is one of the most important factors which decides the trajectory. To obtain global optimality for the whole system, including the timetable and energy consumption, the relationship between the timetable and driving strategy cannot be neglected [10]. In Su’s study, a numerical algorithm, known as Integrated Energy-Efficient (IEE), was developed to optimise the integrated timetable, containing both the train schedule and the trajectory [13]. Other studies aim at researching the relationship between energy efficiency and the infrastructure. Liu et al. [5] calculated the energy consumption of a train running on various gradients of ascent and declivity under a certain velocity. They verified the conclusion that a concave profile form is the best design to save energy. Further simulations were carried out upon routes of different length [14], and the energy consumptions of three types of trains corresponding to different limited velocities and control strategies were obtained. III. ANALYSIS AND MODELING OF VERTICAL ALIGNMENT A. Analysis of Vertical Alignment The route upon which the track is constructed and the train runs is defined as an alignment, which can be divided into horizontal alignment and vertical alignment according to how it displays in the XY plane, or with the Z component, respectively. The horizontal alignment indicates where the route or track goes physically, whereas the vertical alignment defines the elevation of the route, i.e. the rise and fall. Generally speaking, horizontal alignments are more complex than vertical alignments. However, the design of the vertical alignment has a close relationship with energy-efficiency, because the gradients along an alignment can affect the operation speed, the traction power and the energy consumption. As a result, when designing a railway route, the gradients on new alignments are usually examined more meticulously than horizontal alignments [15]. In the real world, an alignment consists of tangents and curves. A tangent is simply a straight line between two points, which is denoted by grade. The role of curves is to connect these tangents together. Vertical alignments are comprised of vertical tangents and vertical curves, and the vertical curves are almost always parabolic in nature. Vertical tangents, referred to as gradient in STS, are straight lines effectively plotted in the Z-plane or vertically. When designing the vertical alignment, many factors should be considered, such as the characteristics of the train, passenger demand, the possibility of derailment, etc.


CONFIDENTIAL. Limited circulation. For review only.

Figure 2. Vertical alignment model in STS

A simplified route model, which is 1.8 km-long with a station in the middle, was developed in STS with Matlab. Based on the algorithm in STS, the curve factors are ignored. Hence, the ideal vertical alignment at a station could be simplified to a trapezoid, as shown in Figure 2. Length is the horizontal length of the upslope or the declivity, h is the vertical height of the platform, and α is the grade of the upslope or declivity. The vertical alignment proposed in this paper is symmetrical with the station centre. In this model, assume that the train only runs from left side to right side. Gradient is one of the input variables of STS, and energy consumption, journey time, power, acceleration, etc. are the outputs. The relationship between the real grade and gradient is illustrated in equation (1), (1) Based on the ideal assumption, when a train runs on a route with a well-designed vertical alignment at a station, it could just stop at the platform without using any braking or traction. In this process, the total kinetic energy of the train transfers into potential energy and heat dissipation, as described in equation (2), (2) where, m is the mass of the train; v is the train’s velocity when it runs to the foot of the upslope; h is the vertical height of vertical alignment; losses include the work done to overcome the friction between wheels and tracks, air drag, etc. The opposite of the upslope process, after the train departs from a station it runs through the declivity, and potential energy converts to kinetic energy and losses. When the train runs to the foot of the vertical alignment, the desired velocity is reached. B. Optimisation of Vertical Alignment at Stations To find the relationship between the structure of the vertical alignment and the energy consumption, optimisation simulations are carried out on this simplified model in a Single Train Simulator (STS) with Matlab. We suppose that the absolute value of the gradient is varied from 0 to 100‰. Specifically, for the upslope, the gradient changes from 0 to 100‰; whereas, for declivity, it changes from 0 to -100‰.

Figure 3. Energy and power to gradients

Among the output parameters of the STS, we focus on the changing trend of kinetic energy, potential energy, work done by the traction system, the traction and braking power. The two profiles in Figure 3 indicate the different kinds of energy, traction and braking power corresponding to various gradients of vertical alignment. In Figure 3 (a), the black line is the energy consumption; the red line denotes the kinetic energy; and the green line and dashed line denote the potential energy and the energy used for overcoming resistance, respectively. In Figure 3 (b), the blue line and red line denote the traction power and braking power, respectively. 1) Resistance The resistance of a moving train can be calculated by the Davis formula, which has been used for over 80 years and can be described by (3) where, R is the rail vehicle resistance (N), V is the velocity (m/s), and A (N), B (N•s/m) and C (Ns2/m2) are regression coefficients obtained by vehicle tests. In the Davis formula, coefficients A and B account for mass and mechanical resistance, and C accounts for air resistance. The work done for overcoming this resistance could be accounted for by ∫

(4)

where, S is the length of the simulation step. In STS, the whole route is divided into many piecewise constant length parts. 2) Potential energy The potential energy is proportional to the height of the position of the train, described by (5) Hence, the potential energy curves could reflect the various structures of the vertical alignment. From Figure 3(a), we can see that the track slopes up gradually to the station and the potential energy of the train when it arrives at the top of the vertical alignment increases. 3) Kinetic energy and work done by traction system The kinetic energy, which is denoted by Ek, is a quadratic formula of v (6) Only one train is analyzed in this paper, hence regeneration braking is not taken into account. There is no energy transferred from or to the power supply system. From


CONFIDENTIAL. Limited circulation. For review only. Figure 3 (a) we can ascertain that from the train's departure from the initial position to approximately 0.4 km, the work done by the traction system is constantly increasing; whereas between 0.4 km and the top of the vertical alignment, the work done by the traction system is nearly constant, which means that the train begins to coast at 0.4 km. Because regeneration braking is not considered, the work done by the traction system is almost the same, corresponding to various gradients. With an increasing gradient, the station is elevated. More kinetic energy transfers into potential energy which makes a contribution towards decelerating the train. Therefore, the braking system can take action later. In Figure 3 (a) and (b), we can see that the train runs at the speed limit for longer and the braking points, at around 0.6 km, move towards the right. Above all, the greater the gradient of vertical alignment, the longer the train can run at the speed limit, and as a result, the smaller the journey time and energy consumption. After the train departs from the station, the traction system begins to work to speed up the train to the commercial speed limit. As the absolute value of the vertical alignment increases, the traction points move gradually towards the left. In other words, the traction system begins to stop working earlier. It takes a shorter time to reach the speed limit. Hence, when train runs to around 1.05 km, there are differences between the work done by the traction system, which correspond to different gradients. The bigger the gradient, the less energy is consumed along the entire route.

Beijing Metro Yizhuang subway line in China. The Beijing Yizhuang Metro Line, which is an important metro line which connects the Yizhuang Economic Development Zone and Beijing's suburban areas, began operation in 2010. The Yizhuang Line is 23.23 km long with 14 stations, including 6 underground and 8 on the surface [16]. The operational speed limit and the average speed are 80 km/h and 40 km/h, respectively. The average distance between two adjacent stations is 1.74 km. The altitude diagram of the Beijing Metro Yizhuang Line is shown in Figure 5. The blue asterisks are station centres. In STS, simulations are carried out based on the assumption that the train does not stop at the station, but that it runs through the platform length at a low speed, costing the dwell time. Hence, in Figure 5, there is no flat platform.

According to the simulation output data, we could ascertain the impact of vertical alignment on energy consumption and journey time more directly. Figure 4 shows that the bigger the gradient, the less energy and journey time is consumed by a train. In this figure, the blue line and red line denote the entire journey time and energy consumption corresponding to various gradients, respectively.

A. Vertical Alignment Optimisation at One Station To minimize energy consumption, as well as the journey time of the entire trip, vertical alignment optimisation simulations are carried out using station No.5 along the Beijing Metro Yizhuang Line. According to China’s latest Code for the Design of Subway, generally, the maximum gradient of the main line is 30‰; in difficult sections, the maximum gradient can be 35‰; in special topography sections, the maximum gradient can be 40‰. In this paper, we assume that the entire line is built on normal topography conditions, and the maximum gradient at the station is 30‰. In the simulations at station No.5, the gradient and the horizontal length are the two variables. We change the gradient and length from 0 to 30‰ and 100 m to 345 m, respectively, at the same moment. The simulation results are shown in Figure 6.

Figure 5. Beijing Subway Yizhuang Line

Figure 4. Time and energy to gradients

The energy consumption and journey time decrease almost linearly, as the gradient increases. However, when the gradient reaches 92‰ or even greater, the vertical alignment becomes extraordinarily abrupt. The vertical alignment contributes significantly to the acceleration of the train, and the train’s velocity exceeds the limit speed, causing the braking system to take action, which consumes energy. Hence, the energy consumption does not decrease any more after a gradient larger than 92‰. This is the reason why, in Figure 3 (b), there is a burr along the braking profile at about 1.05 km.

(a)

IV. CASE STUDY A case study showing optimisation of vertical alignment is presented in this section, which is based on the data from the


CONFIDENTIAL. Limited circulation. For review only. empiricism, we chose 300 m, which is approximate to 310 m, as the horizontal length of the optimal vertical alignments. On the basis of the real parameters of the Yizhuang Line, the maximum gradient is -19.23‰, or nearly 20‰. In order to change the entire route as little as possible, the gradient of every vertical alignment was set as 20‰ for the upslope and -20‰ for declivity. Assume that every flat platform is 200 m long and the vertical alignment is symmetrical with the platform centre. The ideal vertical alignment illustrated above is added at every station, except the first and last stations. Alongside the simulations set out in the last part, another control strategy is applied in the following simulation, which costs less journey time but consumes more energy.

(b) Figure 6 3D Figures: Journey time and energy vs. gradient and length

Figure 6 (a) illustrates the relationship between journey time, gradient and horizontal length, and (b) denotes the relationship between energy consumption, gradient and horizontal length. The results show that as the gradient and length of vertical alignment at No.5 station increase, the journey time decreases. However, compared with Figure 6 (a), the 3D diagram shown in Figure 6 (b) is not quite smooth. The smallest energy consumption does not correspond to the biggest gradient and length. However, the main trend of energy consumption is still to decrease. The simulation result data demonstrates that the smallest energy consumption corresponds to the vertical alignment where gradient and horizontal length are 30‰ and 310m, respectively. TABLE I. Original route Route 1 Route 2

TABLE TYPE STYLES

Gradient(‰)

Length(m)

Energy(kWh)

Time(s)

0

0

331.04

1773.56

30 30

310 345

325.55 325.95

1769.02 1769.05

In TABLE I, Route1, in which the platform is raised up to 9.3 m, corresponds to the minimum energy consumption. Comparing with the original route without vertical alignment, the energy consumption and journey time are reduced by 1.66% and 0.27%, respectively. Route2, where the platform is raised to 10.35 m, corresponds to the biggest gradient and length of vertical alignment. Energy consumption and journey time are for Route 2 are reduced by 1.54% and 0.25%, respectively. According to the results, we can see that the optimisation of vertical alignment affects the energy consumption more than the journey time. For station No.5, when the vertical alignment is 310 m long, the energy consumption is the smallest. B. Final Route When only one station along the Beijing Metro Yizhuang Route is optimised, the energy consumption can be reduced by nearly 1.7%. There is doubt whether vertical alignment optimisation at more stations could achieve more energy savings. To explore this question further, vertical alignment optimisation was carried out on the entire Metro Yizhuang Line. According to the conclusions above and using

Figure 7. Original route and final route

The simulation results show that, compared with the original route, the stations along the new route are raised up, as shown in Figure 7. In Figure 7, the black asterisks denote new station centres. The energy consumption and journey time of the original route and the optimal route were computed, as shown in TABLE II. TABLE II. Original route Final route Difference

COMPARISION OF RESULTS Energy (kWh) 362.42 342.13 -20.29

journey time(s) 1734.95 1725.78 -9.17

According to the results, on account of adding vertical alignment at stations, the energy consumption and journey time are reduced by 20.29 kWh and 9.17 s, respectively. The optimal route has 5.6% less energy consumption than the original route. However, the vertical alignment does not have a good performance in reducing the journey time; the journey time is only reduced by 0.53%. V. CONCLUSION The main contribution of this paper is to develop a novel optimisation approach to improve the energy-efficiency of the railway industry. By carrying out simulations, it is shown that optimising vertical alignment at stations could reduce the energy consumption and journey time of metro systems. To research the relationship between energy-efficiency and the topology of vertical alignment, a simplified route was built. By varying the vertical alignment at stations, the results show that energy consumption and journey time decrease almost linearly as the gradient increases. The case study is carried out based on real data of the Beijing Metro Yizhuang Line. The


CONFIDENTIAL. Limited circulation. For review only. results show that when only one station is optimized, the energy consumption could be reduced by 1.6% at the most; when optimal vertical alignment is added at all stations, except the first and last stations, the proposed method could reduce energy consumption by 5.6%. When designing new railway lines, optimisation of vertical alignment at stations can be chosen as an auxiliary approach to minimize energy consumption. ACKNOWLEDGMENT This research is jointly supported by Beijing Laboratory of Urban Rail Transit and Beijing Key Laboratory of Urban Rail Transit Automation and Control. REFERENCES [1]. S.F. Lu, S. Hillmansen and C. Roberts, "Single Train Trajectory Optimisation," IEEE Transations on intelligent transportation systems vol. 6, pp. 1-10, May. 2011. [2]. G. Chiriac, L. Cantemir, C. Niţucă, I. Stoichescu, D. Demian and I. Gavrila, "Solutions to Reduce the Electric Energy Consumption and the Operating Cost in Railway Transportation," Railway Pro, vol. 1, pp. 23-29, Feb. 2011. [3]. K.C. Kim, Steven I. Jy "Optimal Train Operation for Minimum Energy Consumption Considering Track Alignment, Speed Limit, and Schedule Adherence," Journal of Transportation Engineering, vol. 137, pp. 665-674, Sep. 2011. [4]. R. Liu and I.M. Golovitcher, "Energy-efficient operation of rail vehicles," Transportation Research Part A: Policy and Practice, vol. 37, pp. 917-932, Apr. 2003. [5]. H. Liu, B. Mao, Y. Ding, W. Jia and S. Lai, "Train Energy-saving Scheme with Evaluation in Urban Mass Transit Systems," Transportation Systems Engineering and Information Technology, vol. 7, pp. 68-73, Oct. 2007. [6]. X.S. Feng, "Optimization of target speeds of high-speed railway trains for traction energy saving and transport efficiency improvement," Energy Policy, vol. 39, pp. 7658-7665, Dec. 2011. [7]. P.G. Howlett, "Optimal Strategies for the Control of a Train," Automatica, vol. 32, pp. 519-532, Apr. 1996. [8]. P.G. Howlett and J. Cheng, "Optimal Driving Strategies for a Train on a Track with Continuously Varying Gradient," Australian Mathematical Society Series B Applied Mathematics, vol. 38, pp. 388-410, Jan. 1997. [9]. K.K. Wong and T.K. Ho, "Coast control for mass rapid transit railways with searching methods," IEE Proceedings - Electric Power Applications, vol. 151, pp. 365, May. 2004. [10]. S. Su, X. Li, T. Tang, Z. Gao and G. Ziyou, "A Subway Train Timetable Optimization Approach Based on Energy-Efficient Operation Strategy," IEEE Transactions on Intelligent Transportation Systems, vol. 14, pp. 883-893, June. 2013. [11]. L.S. Pontryagin, "Optimization in differential games," Russian Mathematical Surveys, vol. 33, pp. 25-32. 1978. [12]. Y. Wang, B. De Schutter, T.J.J. van den Boom and B. Ning, "Optimal trajectory planning for trains – A pseudospectral method and a mixed integer linear programming approach," Transportation Research Part C: Emerging Technologies, vol. 29, pp. 97-114, Apr. 2013. [13]. S. Su, T. Tang, X. Li and Z. Gap, "Optimization of Multitrain Operations in a Subway System," Intelligent Transportation Systems, IEEE Transactions on vol. 15, pp. 673-684, Oct. 2014. [14]. X.D. Hu and J. Zhang, "Research on Optimal Scheme for Energy-saving Slope of Urban Rail Transit," Journal of railway engineering society vol. pp. 27-30, May. 2013. [15]. AREMA. Railway Traction Design. American Railway Engineering and Maintance of Way Assoication, 2003. [16]. X. Li and H.K. Lo, "An energy-efficient scheduling and speed control approach for metro rail operations," Transportation Research Part B: Methodological, vol. 64, pp. 73-89, 6//. 2014. [17]. Su, S., et al., "Energy-efficient train control in urban rail transit systems". Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2014.
