Energy-efficient Speed Profile Research Articles

A Novel Real-Time Algorithm for Optimizing Train Speed Profiles Under Complex Constraints

Energy-efficient speed profile optimization of train operations is challenging due to complex constraints including passage points and speed limits. Moreover, it is critical to perform real-time re-optimization of speed profiles within a short control period. To speed up the speed profile re-optimization with complex constraints, we introduce various train characteristics into the shortest path problem with time windows (SPPTW) from the literature, and formulate energy-efficient optimization as a train-based SPPTW (TRAIN-SPPTW). This reduces the solution space and leads to reduced computation complexity. To further reduce computational time for solving the Train-SPPTW, we take advantage of the preprocessing + query structure used in existing pulse algorithms (PA) on one hand, and further overcome their limitations in computation efficiency on the other hand by proposing a tour-adaptive partial-bounding pulse algorithm (TPPA) to shorten the total time of the preprocessing and query stages. We use a simulation study on the tracks of the Dongguan-Huizhou intercity railway in China to demonstrate that the proposed TPPA reduces the computational time by at least 60 % compared to three existing algorithms without sacrificing the quality of the solution.

Onboard train speed optimization for energy saving using the prediction of block clearing times under real-time rescheduling

Energy-saving driving is crucial during railway operation, especially in case of disturbances that require timetable rescheduling. This paper presents a method for the dynamic onboard tuning of energy-efficient speed profiles after the real-time train rescheduling process under a fixed block signaling system for mixed traffic. Similar to the idea of connected driver advisory systems, trains constantly communicate with a central traffic management system. After the rescheduling process, this system provides recommended time corridors for the passing of block signals that depend on the predicted clearing times of the block sections. These recommendations are then used for individual energy optimization of single train runs by avoiding unnecessary braking in front of block signals and maximizing cruising distances. The method is tested and evaluated on a representative line segment of the ELVA, the Railway Signaling Lab at RWTH Aachen University under realistic conditions. Energy consumptions are compared for different prediction time horizons at which the recommendations are available to the train's onboard system. In the examined test case of two trains, the energy-consumption could be decreased by up to 53% compared to operation without any rescheduling system. Thus, the proposed method is able to reduce energy consumption significantly.

Energy-Optimal Speed Control for Autonomous Electric Vehicles Up- and Downstream of a Signalized Intersection

Signalized intersections can increase the vehicle stops and consequently increase the energy consumption by forcing stop-and-go dynamics on vehicles. Eco-driving with the help of connectivity is a solution that could avoid multiple stops and improve energy efficiency. In this paper, an eco-driving framework is developed, which finds the energy-efficient speed profile both up- and downstream of a signalized intersection in free-flow situations (eco-FF). The proposed framework utilizes the signal phasing and timing (SPaT) data that are communicated to the vehicle. The energy consumption model used in this framework is a combination of vehicle dynamics and time-dependent auxiliary consumption, which implicitly incorporates the travel time into the function and is validated with real-world test data. It is shown that, by using the proposed eco-FF framework, the vehicle’s energy consumption is notably reduced.

Energy-efficient speed profile: an optimal approach with fixed running time

Tracking the optimal speed profile in electric train operation has been proposed as an efficient and feasible solution for not only reducing energy consumption, but also no at costs to upgrading the existing railway systems. This paper focuses on finding the optimal speed profile based on Pontryagin’s maximum principle (PMP) while ensuring the fixed running time, and comparing energy saving levels in the cases of applying or not applying PMP. The way to determine the fixed running time also differs from works published is to calculate the total trip time equal to scheduled timetable exactly. Calculating accelerating time t a , coasting time t c , braking time t b via values of maximum speed v h , braking speed v b of optimal speed profile. The other hands, v h and v b are determined by solving nonlinear equations with constraint condition: the running time equal to the demand time. Simulation results with data collected from electrified trains of Cat Linh-Ha Dong metro line, Vietnam show that energy reduction for the entire route when PMP utilization is up to 8.7% and running time complied with scheduled timetables.

Dynamic Programming-based Macroscopic Speed Planner for Electric Vehicle Platooning

Vehicle platooning has demonstrated significant energy saving potentials on highway via reduction of aerodynamic drag resistance by closely following a leading vehicle. However, taking full advantage of platooning opportunities for energy saving is a challenging task since accomplishable energy saving benefits depends on many factors such as the leading vehicle speed, relative position to the leading vehicle, platoonable miles with the leading vehicle, and others. This paper proposes a dynamic programming (DP)-based algorithm to optimize the speed profile for an electric vehicle to minimize the energy consumption when traveling on a given route with several platoonable vehicles sharing the same route. The proposed DP-based speed optimization framework was applied to a case study with five potential platooning vehicles over a 65-mile route with a time constraint. Through the case study, it was found that the DP-based optimization algorithm can determine the most energy-efficient speed profile for a given time deadline in a complex platooning environment based on the energy consumption from aerodynamic drag. Compared to the baseline control, the optimal speed profile from the DP optimization results can achieve significant energy saving benefits up to 18.12%.

Energy-efficient speed profile: An optimal approach with fixed running time

Tracking the optimal speed profile in electric train operation has been proposed as an efficient and feasible solution for not only reducing energy consumption, but also no at costs to upgrading the existing railway systems. This paper focuses on finding the optimal speed profile based on Pontryagin's maximum principle (PMP) while ensuring the fixed running time, and comparing energy saving levels in the cases of applying or not applying PMP. The way to determine the fixed running time also differs from works published is to calculate the total trip time equal to scheduled timetable exactly. Calculating accelerating time t a , coasting time t c , braking time t b via values of maximum speed v h , braking speed v b of optimal speed profile. The other hands, v h and v b are determined by solving nonlinear equations with constraint condition: the running time equal to the demand time. Simulation results with data collected from electrified trains of Cat Linh-Ha Dong metro line, Vietnam show that energy reduction for the entire route when PMP utilization is up to 8.7% and running time complied with scheduled timetables.

An Optimal Train Speed Profile Planning Method for Induction Motor Traction System

Optimizing the operating speed curve of trains without adding new energy storage facilities is essential in the energy-saving operation of railways. In this paper, we propose an optimal train speed curve planning method for driving trains more energy efficiently. A refined traction energy evaluation model for induction motor propulsion systems is first presented. The proposed model considers the efficiency of the traction motor at different operating points and the efficiency of the inverter and gearbox. Then, the optimal energy-efficient speed profile problem is transformed into a multistep decision problem and solved using dynamic programming (DP). To verify the effectiveness of the proposed method, a case study was conducted on an actual subway line. The results obtained indicate that the speed curve produced by the proposed method results in a 20% energy consumption saving compared with the speed curve for actual operations. Furthermore, the results of comparison with a genetic algorithm indicate that the DP algorithm is better able to satisfy the constraints of the train traction system. Solving the optimal speed curve using the proposed method and programming the onboard controller of the train according to the optimal speed curve enables the train to be driven with greater energy efficiency.

Enhanced Eco-Approach Control of Connected Electric Vehicles at Signalized Intersection With Queue Discharge Prediction

Long queues of vehicles are often found at signalized intersections, which increases the energy consumption of all the vehicles involved. This paper proposes an enhanced eco-approach control (EEAC) strategy with consideration of the queue ahead for connected electric vehicles (EVs) at a signalized intersection. The discharge movement of the vehicle queue is predicted by an improved queue discharge prediction method (IQDP), which takes both vehicle and driver dynamics into account. Based on the prediction of the queue, the EEAC strategy is designed with a hierarchical framework: the upper-stage uses dynamic programming to find the general trend of the energy-efficient speed profile, which is followed by the lower-stage model predictive controller to computes the explicit solution for a short horizon with guaranteed safe inter-vehicular distance. Finally, numerical simulations are conducted to demonstrate the energy efficiency improvement of the EEAC strategy. Besides, the effects of the queue prediction accuracy on the performance of the EEAC strategy are also investigated.

Energy-Efficient Speed Profile Optimization for High-Speed Railway Considering Neutral Sections

A neutral zone is a section of a railway line without traction current during high-speed train operations and is very common in high-speed railway lines. However, previous studies on energy-efficient speed profile (ESP) optimization did not consider the electric neutral section constraints. Thus, a risk of being unable to drive out of the neutral section because of a low initial speed and a deviation in the energy consumption effect occur. This paper studies the characteristics of the neutral section to optimize the operating curves of high-speed trains. It can aid in trains passing through the neutral section smoothly. The proposed method is feasible and close to reality. By analyzing the actual coasting distance of a train in the neutral section and building its mathematical model, we provide special double-speed limits and stability constraints. Subsequently, by simulating vehicle performance, operating conditions, and the location of the neutral section, a train ESP optimization model is constructed. Moreover, an improved dynamic programming algorithm is proposed, which uses the vehicle maximum traction and braking force to simplify the computation of state transitions. Finally, the numerical results of simulations demonstrate the efficiency of the proposed model and solution methodology. Compared with the solution without neutral section constraints, an energy-efficient effect of 1.43% is achieved. Further, the proposed method performs better with a stability and high-quality solution than the genetic algorithm.

Energy‐efficient approach combining train speed profile and timetable optimisations for metro operations

Rising energy cost and environment-friendly awareness make energy conservation a key issue for metro operation. Reducing traction energy consumption and improving the utilisation of regenerative braking energy are two efficient solutions to conserve energy. Two optimisation models are proposed in this study for metro systems to minimise the energy consumption by exploring energy-efficient speed profile and optimum timetable. An analytical formulation through finding suitable force coefficients and driving regime-switching points is developed to investigate the optimal speed profile of a single train during its movement along complex rail tracks considering gradients, curves, tunnels and speed limits. Moreover, the synchronisation of accelerating and braking trains is much necessarily implemented when a timetable optimisation model is established for the energy-efficient operation by adjusting the dwell times, running times and turnaround times of multiple trains. A combined particle swarm optimisation and genetic algorithm are addressed to solve the model. The case studies from the actual data of a Beijing Metro line are carried out to verify the feasibility and availability of the proposed approach. Their results show that the net energy consumption of trains along the metro line is reduced by 10.99% by combining the optimal speed profiles and timetable.

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.

Energy-efficient speed profile optimization for medium-speed maglev trains

This study addresses the problem of reducing the energy consumption of the medium-speed maglev (MSM) system by optimizing the train speed profile. Auxiliary stopping areas, the nonlinear resistance caused by the linear motor, and the suspension energy consumption are considered in the formulation of the speed profile optimization problem. Next, dynamic programming and mixed-integer linear programming (MILP) approaches that utilize these characteristics are proposed to solve the problem. The numerical results show that both approaches ensure MSM train safety and energy-efficient operation. Furthermore, the MILP approach could be used for emergency trajectory planning due to its shorter computational time.

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.

Co-optimization of speed trajectory and power management for a fuel-cell/battery electric vehicle

With the advent of vehicle connectivity via intelligent transportation systems, the simultaneous optimization of powertrain operation and vehicle dynamics has become an important research problem to improve energy efficiency. However, this problem is still very challenging due to computational loads in terms of time and memory usage, and hence very little effort has been spent to reveal the full potential of co-optimization. Studies in the literature on eco-driving or energy-efficient operation typically preferred using a sequential optimization or eliminating some constraints for fast computation. This paper extends the authors’ previous work of determining energy-efficient speed profiles focused on vehicle dynamics by including additional state and control variables due to vehicle hybridization in application to a fuel-cell/battery electric vehicle. The results from Pontriagyn’s Minimum Principle analysis reveal that the co-optimization can be formulated with one discrete variable describing vehicle operation and another continuous variable for power distribution to reduce computation in implementing Dynamic Programming. Then, the performance of co-optimization and sequential optimization for energy-efficient driving is comprehensively analyzed and compared in terms of energy consumption by each powertrain component, operating modes, and computational cost. The total energy savings by co-optimization range from 5.3% to 24.2% for aggressive driving on a hilly terrain. Meanwhile, on a relatively flat road, the benefit of co-optimization is less significant. Nonetheless, co-optimization achieved 0.5%–5.3% reduction in total energy consumption as compared to sequential optimization.

Multi-train trajectory optimization for energy-efficient timetabling

This paper proposes a novel approach for energy-efficient timetabling by adjusting the running time allocation of given timetables using train trajectory optimization. The approach first converts the arrival and departure times to time window constraints in order to relax the given timetable. Then a train trajectory optimization method is developed to find optimal arrival/departure times and optimal energy-efficient speed profiles within the relaxed time windows. The proposed train trajectory optimization method includes two types, a single-train trajectory optimization (STTO), which focuses on optimizing individual train movements within the relaxed arrival and departure time windows, and a multi-train trajectory optimization (MTTO), which computes multi-train trajectories simultaneously with a shared objective of minimizing multi-train energy consumption and an additional target of eliminating conflicts between trains. The STTO and MTTO are re-formulated as a multiple-phase optimal control problem, which has the advantage of accurately incorporating varying gradients, curves and speed limits and different train routes. The multiple-phase optimal control problem is then solved by a pseudospectral method. The proposed approach is applied in case studies to fine-tune two timetables, for a single-track railway corridor and a double-track corridor of the Dutch railway. The results suggest that the proposed approach is able to improve the energy efficiency of a timetable.

Integrated Optimization on Train Control and Timetable to Minimize Net Energy Consumption of Metro Lines

Energy-efficient metro operation has received increasing attention because of the energy cost and environmental concerns. This paper developed an integrated optimization model on train control and timetable to minimize the net energy consumption. The extents of train motoring and braking as well as timetable configurations such as train headway and interstation runtime are optimized to minimize the net energy consumption with consideration of utilizing regenerative energy. An improved model on train control is proposed to reduce traction energy by allowing coasting on downhill slopes as much as possible. Variations of train mass due to the change of onboard passengers are taken into account. The brute force algorithm is applied to attain energy-efficient speed profiles and an NS-GSA algorithm is designed to attain the optimal extents of motoring/braking and timetable configurations. Case studies on Beijing Metro Line 5 illustrate that the improved train control approach can save traction energy consumption by 20% in the sections with steep downhill slopes, in comparison with the commonly adopted train control sequence in timetable optimization. Moreover, the integrated model is able to significantly prolong the overlapping time between motoring and braking trains, and the net energy consumption is accordingly reduced by 4.97%.

Adaptive Fuzzy Planning of Optimal Speed Profiles for High-Speed Train Operation on the Basis of a Pareto Set

Today, one of the main concerns for railways administrations and operators is reducing energy consumption. Ecodriving design is one of the main approaches to reducing energy consumption with low levels of investment. In this paper, a Pareto set–based adaptive fuzzy approach to trajectory planning is proposed to generate energy-efficient speed profiles for high-speed train operation. First, the Pareto set for high-speed train operation is constructed by using a hybrid evolutionary algorithm based on differential evolution and simulated annealing. Second, by considering that the operational delays are variable because of the uncertainties of line conditions in practice, a system to control adaptive fuzzy predictions is proposed to regulate the coasting point dynamically so as to meet the requirements of punctuality and energy savings. The proposed approach decreases the energy consumption of high-speed trains mainly by changing the coasting point, a technique that make implementation easy and guarantees passenger comfort compared with frequent changes under different operating conditions. Finally, the proposed approach is analyzed by using real operational data from the Wuhan–Guangzhou high-speed railway line in China to assess energy savings and punctuality. The results of simulation illustrate the efficiency of the proposed approach.

Definition of energy-efficient speed profiles within rail traffic by means of supply design models

Nowadays, energy efficiency is a key requirement for railway systems in order to reduce operating costs. One of the main solutions for implementing energy efficiency is the optimization of train speed profiles to minimize tractive energy consumption. From a transportation systems point of view, the definition of optimized speed profiles should consider their possible impact on rail traffic flows, in order to evaluate their feasibility. To do so, an innovative optimization framework for the definition and the evaluation of energy efficient speed profiles, based on supply design modelling, is proposed. The framework operates on two levels: the first level generates energy efficient speed profiles with respect to timetable constraints, infrastructure characteristics and rolling stock features, and the second simulates these speed profiles on the rail network within the specific rail traffic conditions. Through this new integrated view, the evaluation of the proposed optimal speed profiles can fully take into account the operational requirements of the services, such as trains scheduling, absence of or small allowance for delays and respect for buffer times for passenger transfer at connecting stations. A numerical example based on a calibrated simulation model of the suburban S-Bahn S9 line that operates in the Canton of Zurich shows how energy efficient speed profiles can be defined considering the rail traffic influences, thus increasing the quality of the solutions.

局所的な省エネ運転操作を組み合わせた省エネ運転支援システムの開発

局所的な省エネ運転操作を組み合わせた省エネ運転支援システムの開発

Intelligent Train Operation Algorithms for Subway by Expert System and Reinforcement Learning

Current research in automatic train operation concentrates on optimizing an energy-efficient speed profile and designing control algorithms to track the speed profile, which may reduce the comfort of passengers and impair the intelligence of train operation. Different from previous studies, this paper presents two intelligent train operation (ITO) algorithms without using precise train model information and offline optimized speed profiles. The first algorithm, i.e., ITOe, is based on an expert system that contains expert rules and a heuristic expert inference method. Then, in order to minimize the energy consumption of train operation online, an ITOr algorithm based on reinforcement learning (RL) is developed via designing an RL policy, reward, and value function. In addition, from the field data in the Yizhuang Line of the Beijing Subway, we choose the manual driving data with the best performance as ITOm. Finally, we present some numerical examples to test the ITO algorithms on the simulation platform established with actual data. The results indicate that, compared with ITOm, both ITOe and ITOr can improve punctuality and reduce energy consumption on the basis of ensuring passenger comfort. Moreover, ITOr can save about 10% energy consumption more than ITOe. In addition, ITOr is capable of adjusting the trip time dynamically, even in the case of accidents.