Energy-efficient Train Control Research Articles

Increasing realism in modelling energy losses in railway vehicles and their impact to energy-efficient train control

AbstractThe reduction of energy consumption is an increasingly important topic of the railway system. Energy-efficient train control (EETC) is one solution, which refers to mathematically computing when to accelerate, which cruising speed to hold, how long one should coast over a suitable space, and when to brake. Most approaches in literature and industry greatly simplify a lot of nonlinear effects, such that they ignore mostly the losses due to energy conversion in traction components and auxiliaries. To fill this research gap, a series of increasingly detailed nonlinear losses is described and modelled. We categorize an increasing detail in this representation as four levels. We study the impact of those levels of detail on the energy optimal speed trajectory. To do this, a standard approach based on dynamic programming is used, given constraints on total travel time. This evaluation of multiple test cases highlights the influence of the dynamic losses and the power consumption of auxiliary components on railway trajectories, also compared to multiple benchmarks. The results show how the losses can make up 50% of the total energy consumption for an exemplary trip. Ignoring them would though result in consistent but limited errors in the optimal trajectory. Overall, more complex trajectories can result in less energy consumption when including the complexity of nonlinear losses than when a simpler model is considered. Those effects are stronger when the trajectory includes many acceleration and braking phases.

Energy-Efficient Train Control with Onboard Energy Storage Systems considering Stochastic Regenerative Braking Energy

Energy-Efficient Train Control with Onboard Energy Storage Systems considering Stochastic Regenerative Braking Energy

The optimal solution to the energy-efficient train control in a multi-trains system–Part 2: the optimality and the uniqueness

When a train travels in a multi-trains system, the power flow of other trains and the track grades make up the spatial–temporal area (STA) for the train. Finding the optimal solution for the energy-efficient train control (EETC) problem in STA can help reduce the net energy consumption. This paper studies the analytic method to obtain the optimal solution. In Part 1, the algorithm for the problem was designed. The underlying structure of the algorithm is the connection between three optimal states through optimal feasible strategy. In Part 2, the optimality of the optimal feasible strategy is verified through a generalised local energy functional, and its uniqueness is proved based on the variational method. Additionally, we discuss the influence of external power on the optimal solution of the classical EETC problem. Case studies using data for a real freight railway line are given to illustrate our results.

The optimal solution to the energy-efficient train control in a multi-trains system-part 1: the algorithm design

When a train travels in a multi-trains system, the power flow of other trains and the track grades make up the spatial–temporal area (STA) for the train. Finding the optimal solution for the energy-efficient train control problem in STA can help reduce the net energy consumption. This paper studies the analytic method to obtain the optimal solution. In Part 1, we propose an algorithm specifically designed for this problem. The underlying structure of the algorithm is the connection between three optimal states through the optimal feasible strategy. We propose an algebraic method to calculate the optimal feasible strategy and discuss how it intersects with the speed limit. In Part 2, we will discuss the optimality and uniqueness of the optimal feasible strategy. Case studies using data from a real freight railway line are given to demonstrate the effectiveness of the proposed algorithm.

Research on the cooperative train control method in the metro system for energy saving

PurposeTo address the problem that the current train operation mode that train selects one of several offline pre-generated control schemes before the departure and operates following the scheme after the departure, energy-saving performance of the whole metro system cannot be guaranteed.Design/methodology/approachA cooperative train control framework is formulated to regulate a novel train operation mode. The classic train four-phase control strategy is improved for generating specific energy-efficient control schemes for each train. An improved brute force (BF) algorithm with a two-layer searching idea is designed to solve the optimisation model of energy-efficient train control schemes.FindingsCase studies on the actual metro line in Guangzhou, China verify the effectiveness of the proposed train control methods compared with four-phase control strategy under different kinds of train operation scenarios and calculation parameters. The verification on the computation efficiency as well as accuracy of the proposed algorithm indicates that it meets the requirement of online optimisation.Originality/valueMost existing studies optimised energy-efficient train timetable or train control strategies through an offline process, which has a defect in coping with the disturbance or delays effectively and promptly during real-time train operation. This paper studies an online optimisation of cooperative train control based on the rolling optimisation idea, where energy-efficient train operation can be realised once train running time is determined, thus mitigating the impact of unpredictable operation situations on the energy-saving performance of trains.

A Data-Driven Iterative Learning Approach for Optimizing the Train Control Strategy

The energy-efficient train control (EETC) problem is investigated in this paper. And a soft actor-critic-based method is proposed to optimize the train driving strategy. Firstly, EETC problem is converted to the inverse problem, i.e., minimizing the trip time of the journey with constant energy consumption. Based on the conversion, the EETC problem is reformulated as a finite Markov decision process which can be solved by deep reinforcement learning algorithms. Secondly, an optimization method based on the soft actor-critic (SAC) method is designed to calculate the optimal driving strategy of the train with introducing the reservoir sampling method. Finally, some case studies are conducted to verify the effectiveness and performance of the proposed method. Simulation results demonstrate that a good energy-saving performance can be achieved. In single interval, the SAC-based method can reduce about 1.65% of the energy consumption compared with numerical method. And the energy consumption reduction can be extended to be 6.49% when the proposed approach is applied in multiple intervals.

Direct multiple shooting for computationally efficient train trajectory optimization

Energy efficient train control has been an active field of research for several decades, with Pontryagin’s maximum principle and dynamic programming being the two most common approaches for the computation of optimal trajectories. In this paper, we detail how direct multiple shooting can be used in the same context and highlight its two main advantages: the flexibility in the problem formulation and the availability of computationally efficient open-source software. Using the proposed framework, which is made publicly available, we are able to solve particularly challenging train trajectory optimization problems within only a few seconds.

A data-driven bi-objective matheuristic for energy-optimising timetables in a passenger railway network

Energy-efficient train timetabling (EETT) is essential to achieve the full potential of energy-efficient train control, which can reduce operating costs and contribute to a reduction in CO2 emissions. This article proposes a bi-objective matheuristic to address the EETT problem for a railway network. To our knowledge, this article is the first to suggest using historical data from train operation to model the actual energy consumption, reflecting the different driving behaviours. The matheuristic employs a genetic algorithm (GA) based on NSGA-II. The GA uses a warm-start method to generate the initial population based on a mixed-integer program. A greedy first-come-first-served fail-fast repair heuristic is used to ensure feasibility throughout the evolution of the population. The objectives taken into account are energy consumption and passenger travel time. The matheuristic was applied to a real-world case from a large North European train operating company. The considered network consists of 107 stations and junctions, and 18 periodic timetables for 9 train lines. Our results show that for an entire network, a reduction up to 3.3% in energy consumption and 4.64% in passenger travel time can be achieved. The results are computed in less than a minute, making the approach suitable for integration with a decision support tool.

Train Control and Schedule Integrated Optimization With Reversible Substations

The Carbon Neutralization is a grand strategy to deal with global climate change. As a major energy consumer, urban rail transit (URT) system should contribute corresponding solutions. This paper proposes an energy-efficient train control and schedule integrated optimization method under DC traction power supply system (TPSS) with reversible substation (RSS). The dynamic coupling mechanism between the train movement process and the RSS working mode is analyzed and modeled. Aiming to minimize the total RSS energy consumption for the train traveling over multi-interstation with a given total trip time, the train trajectory and schedule optimization problem is integrated in the same level, and is formulated as a multi-phase optimal control problem (MOCP) to be solved by a pseudo-spectral method (PSM). As a supplement, a customized dynamic programming (DP) method for the problem is introduced to verify the validity of the proposed solution framework. Simulation results under the models of the RSS energy together with conventional rectifier substation energy and vehicle mechanical energy are presented and compared, indicating that the proposed methodology has great energy saving performance for the new-type DC railway system.

Energy-Efficient Model Predictive Train Traction Control With Incorporated Traction System Efficiency

The control system for energy-efficient train operation with the inclusion of a detailed train motion model and train traction system energy efficiency is presented in the paper. A piecewise affine train model is constructed with the parameters obtained for the electromotive train of an industrial manufacturer. The model encompasses intrinsic features of the train system such as linearized resistance force, a set of traction and braking force physical limitations and passengers comfort constraints. The resulting quadratic optimization problem is solved parametrically through dynamic programming giving the off-line precomputed optimal control law that is a function of train speed and traversed path. The on-line computed traction force profile is then tuned with respect to the traction system energy efficiency. The developed control system is evaluated on a detailed real case study scenario put together with a railway operator and the train manufacturer. The presented results show the possibility of significant energy consumption reductions achieved by energy-efficient train control.

Energy‐optimal study integrated speed trajectories, timetable and the layout of neutral sections for high‐speed railway

Speed trajectories, timetable and the layout of neutral sections are the key elements that affect train energy consumption (EC). This paper combines the microscopic energy-efficient train control (EETC), macroscopic energy-efficient train timetabling (EETT) and neutral sections location planning (NSLP), to achieve minimum EC in bi-directional high-speed railway. An integrated model is first established based on neutral sections distribution model, timetable model and a multi-phase model. Then, a double loop genetic algorithm (DLGA) is designed for matching the proposed model. The case studies are conducted by the proposed model and algorithm on the Wuhan-Yueyang rail corridor. A simple case for single-train movement in one section is primarily executed with variable neutral section location, to investigate the impact of neutral section location for train operation. The results indicate that neutral section locating at the coasting (CO) and cruising (CR) zones is the prior choice for energy conservation. Then, three integrated problems (EETC, EETC + EETT and EETC + EETT + NSLP) are carried out to obtain the energy-optimal speed trajectories, timetable and the layout of neutral sections, showing that EETC + EETT + NSLP increases the regenerative energy recycling from 14.2% to 49.1% and achieves 9.2% energy reduction compared with EETC.

Cooperative Eco-Driving of Multi-Train Under dc Traction Network

Cooperative eco-driving of multi-train combined with dc railway system can achieve energy saving at the substation level for the metro system. This article presents an integrated optimization method for eco-driving by combining energy-efficient train control and dc traction power supply system (TPSS) model, to minimize the substation energy consumption. The coupled time-varying TPSS models for single train and multi-train are established, and a novel power flow calculation (PFC) method is proposed, to directly obtain the precise power flow distribution without iterations. Then, customized dynamic programming (DP) algorithms for specific TPSS models are developed, and optimal speed profiles of the tracking train and the preceding train can be respectively obtained by the multi-phase DP method. The former maximizes the utilization of a distributed regenerative braking energy (RBE), and the latter actively generates RBE to be fully utilized. Finally, the performance of the proposed method is analyzed by implementing the numerical experiments with field data from Guangzhou Metro Line 8, and the effectiveness is verified by comparing it with a previous study-based heuristic algorithm (HA). The simulation result indicates that the proposed method can also effectively reduce the lost energy on the catenary, suppress catenary voltage fluctuations, and precise match power during the RBE transmission phase.

Deep reinforcement learning with reference system to handle constraints for energy-efficient train control

Train energy-efficient control involves complicated optimization processes subject to constraints such as speed, time, position and comfort requirements. Conventional optimization techniques are not apt at accumulating numerous solution instances into decision intelligence by learning for consecutively confronted new problems. Deep reinforcement learning (DRL), which can directly output control decisions based on current states, has shown great potentials for next-generation intelligent control . However, if the DRL is directly applied to energy-efficient train control, the received results are almost unsatisfactory. The reason lies in that the agent may get into confusion about how to trade off those constraints, and spend great computational time performing a large number of meaningless explorations. This article attempts to propose an approach of DRL with a reference system (DRL-RS) for proactive constraint handling, where the reference system deals with checking and correcting the agent’s learning progresses to avoid stepping farther and farther onto the erroneous road. The proposed approach is evaluated by the numerical experiments on train control in metro lines. The experimental results demonstrate that the DRL-RS can achieve faster learning convergence, compared with the directly applied DRL. Furthermore, it is possible to reduce more energy consumption than the commonly used genetic algorithm .

Energy-efficient train control using nonlinear bounded regenerative braking

Energy-efficient train control (EETC) has been studied a lot over the last decades, because it contributes to cost savings and reduction of CO2 emissions. The aim of EETC is to minimize total traction energy consumption of a train run given the running time in the timetable. Most research is focused to apply mechanical braking on this problem. However, current trains are able to use regenerative braking, which leads to another optimal driving strategy compared to mechanical braking. Research on EETC with a realistic nonlinear bounded model for regenerative braking or a combination between regenerative and mechanical braking is limited. The aim of this paper is to compare the difference between the EETC with regenerative and/or mechanical braking. First, we derive the optimal control structure for the problems with different braking combinations. Second, we apply the pseudospectral method on different scenarios where we investigate the effect of varying speed limits and gradients on the different driving strategies. Results indicate that compared to pure mechanical braking, combined regenerative and mechanical braking leads to a driving strategy with higher energy savings, a lower optimal cruising speed, a shorter coasting phase and a higher speed at the beginning of the braking phase. In addition, a nonlinear bounded regenerative braking curve leads to a different driving strategy compared to a constant braking rate that is commonly used in literature. We show that regenerative braking at a constant braking rate overestimates the total energy savings.

Pseudospectral optimal train control

In the last decade, pseudospectral methods have become popular for solving optimal control problems. Pseudospectral methods do not need prior knowledge about the optimal control structure and are thus very flexible for problems with complex path constraints, which are common in optimal train control, or train trajectory optimization. Practical optimal train control problems are nonsmooth with discontinuities in the dynamic equations and path constraints corresponding to gradients and speed limits varying along the track. Moreover, optimal train control problems typically include singular solutions with a vanishing Hessian of the associated Hamiltonian. These characteristics make these problems hard to solve and also lead to convergence issues in pseudospectral methods. We propose a computational framework that connects pseudospectral methods with Pontryagin’s Maximum Principle allowing flexible computations, verification and validation of the numerical approximations, and improvements of the continuous solution accuracy. We apply the framework to two basic problems in optimal train control: minimum-time train control and energy-efficient train control, and consider cases with short-distance regional trains and long-distance intercity trains for various scenarios including varying gradients, speed limits, and scheduled running time supplements. The framework confirms the flexibility of the pseudospectral method with regards to state, control and mixed algebraic inequality path constraints, and is able to identify conditions that lead to inconsistencies between the necessary optimality conditions and the numerical approximations of the states, costates, and controls. A new approach is proposed to correct the discrete approximations by incorporating implicit equations from the optimality conditions. In particular, the issue of oscillations in the singular solution for energy-efficient driving as computed by the pseudospectral method has been solved.

The impact of wind on energy-efficient train control

An energy-efficient train trajectory corresponds to the speed profile of a train between two stations that minimizes energy consumption while respecting the scheduled arrival time and operational constraints such as speed limits. Determining this trajectory is a well-known problem in the operations research and transport literature, but has so far been studied without accounting for stochastic variables like weather conditions or train load that in reality vary in each journey. These variables have an impact on the train resistance, which in turn affects the energy consumption. In this paper, we focus on wind variability and propose a train resistance equation that accounts for the impact of wind speed and direction explicitly on the train motion. Based on this equation, we compute the energy-efficient speed profile that exploits the knowledge of wind available before train departure, i.e., wind measurements and forecasts. Specifically, we: (i) construct a distance-speed network that relies on a new non-linear discretization of speed values and embeds the physical train motion relations updated with the wind data, and (ii) compute the energy-efficient trajectory by combining a line-search framework with a dynamic programming shortest path algorithm. Extensive numerical experiments reveal that our “wind-aware” train trajectories present different shape and reduce energy consumption compared to traditional speed profiles computed regardless of any wind information.

Optimal running time supplement distribution in train schedules for energy-efficient train control

Energy-efficient train driving can lead to a significant reduction in both CO2 emissions and energy consumption. A lot of research has been done on the topic of energy-efficient train control that minimizes total traction energy consumption. Furthermore, the running time supplements in the timetable determine the possibilities for energy-efficient train driving. However, research on the distribution of these supplements in order to maximize the potential for energy-efficient train driving is limited. This paper considers the multiple-section train trajectory optimization problem, which aims at finding the optimal distribution of running time supplements over multiple stops for a single train given a total scheduled running time in order to maximize the potential for energy-efficient train driving. In addition, we compare two different methods to compute the energy-efficient train control: an indirect solution method and a direct solution method. We applied both methods to a Dutch case study for an Intercity train between the stations Utrecht Central and Arnhem Central. The running time supplement distribution that minimizes the total energy use for a train has the same cruising speed on each section. Furthermore, the shorter the distance between stops, the larger the relative running time supplement. The indirect solution method generates results very quickly compared to the direct solution method and can be used for real-time control. The direct solution method is able to provide direct feedback on the necessary optimality conditions and does not require a specialized code to generate the optimal speed trajectory profile, therefore, it is useful for exploring new variants of the optimal control problem.

Comparing train driving strategies on multiple key performance indicators

The driving strategy of train drivers has a large impact on the energy consumption. In recent studies the focus was on calculating the optimal eco-driving strategy, and measuring the exact amount of energy used during train runs. However, energy consumption is not the only key performance indicator that affects the operational performance of train or freight operating companies. In this study we define a set of key performance indicators, relevant to train operation, that are specific, measurable, assignable, realistic and time-related, and that are influenced by the driving strategy of the driver. These key performance indicators are safety, timeliness, energy consumption, workload of the driver, the environment, cost of maintenance and brand image. We chose four driving strategies that are most used in daily practice or most studied in the literature to assess these key performance indicators. Per key performance indicator we defined evaluation criteria to measure the impact of a driving strategy. We then defined key characteristics (e.g. track length, gradients), and conditions (e.g. speed restrictions, and load factor) based on which we defined test scenarios for three different train types. We then used the Radau Pseudospectral Method for solving the various optimal train control problems to compute the effect of the driving strategies on most of the key performance indicators. Our findings show amongst others, that a maximal coasting strategy causes the least environmental pollution, and in most scenarios its energy consumption coincided with the optimal energy-efficient train control strategy or it had an energy efficiency close to the optimal one. Furthermore, we found that on other key performance indicators there are differences between the driving strategies (e.g. in cost of maintenance), which should be considered when choosing a preferred driving strategy. Our results enable train and freight operating companies to make an informed decision when choosing a preferred driving strategy for their drivers, or when choosing a Driver Advisory System that supports this preferred driving strategy.

A hierarchical ensemble learning framework for energy-efficient automatic train driving

Railway transportation plays an important role in modern society. As China's massive railway transportation network continues to grow in total mileage and operation density, the energy consumption of trains becomes a serious concern. For any given route, the geographic characteristics are known a priori, but the parameters (e.g., loading and marshaling) of trains vary from one trip to another. An extensive analysis of the train operation data suggests that the control gear operation of trains is the most important factor that affects the energy consumption. Such an observation determines that the problem of energy-efficient train driving has to be addressed by considering both the geographic information and the trip parameters. However, the problem is difficult to solve due to its high dimension, nonlinearity, complex constraints, and time-varying characteristics. Faced with these difficulties, we propose an energy-efficient train control framework based on a hierarchical ensemble learning approach. Through hierarchical refinement, we learn prediction models of speed and gear. The learned models can be used to derive optimized driving operations under real-time requirements. This study uses random forest and bagging - REPTree as classification algorithm and regression algorithm, respectively. We conduct an extensive study on the potential of bagging, decision trees, random forest, and feature selection to design an effective hierarchical ensemble learning framework. The proposed framework was testified through simulation. The average energy consumption of the proposed method is over 7% lower than that of human drivers.

Optimizing the Energy-Efficient Metro Train Timetable and Control Strategy in Off-Peak Hours with Uncertain Passenger Demands

How to reduce the energy consumption of metro trains by optimizing both the timetable and control strategy is a major focus. Due to the complexity and difficulty of the combinatorial operation problem, the commonly-used method to optimize the train operation problem is based on an unchanged dwelling time for all trains at a specific station. Here, we develop a simulation-based method to design an energy-efficient train control strategy under the optimized timetable constraints, which assign the dwelling time margin to the running time. This time margin is caused by dynamically uncertain passenger demands in off-peak hours. Firstly, we formulate a dwelling time calculation model to minimize the passenger boarding and alighting time. Secondly, we design an optimal train control strategy with fixed time and develop a time-based model to describe mass-belt train movement. Finally, based on this simulation module, we present numerical examples based on the real-world operation data from the Beijing metro Line 2, in which the energy consumption of one train can be reduced by 21.9%. These results support the usefulness of the proposed approach.