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Problem of optimal train control with the aim of minimizing energy consumption is one of the old optimal control problems. During last decades different solutions have been suggested based on different optimization techniques, each including a certain number of constraints or different train configurations, one being the control on the tractive effort available from traction motor. The problem is previously solved using dynamic programming for trains with continuous tractive effort, in which velocity was assumed to be the control variable. The paper at hand presents a solution based on dynamic programming for solving the problem for trains with discrete tractive effort. In this approach, tractive effort is assumed to be the control variable. Moreover a short comparison is made between two approaches regarding accuracy and ease of application in a driver advisory system.

Electric traction system is the most energy efficient traction system in railways. Nevertheless, not all railway networks are electrified, which is due to high maintenance and setup cost of overhead lines. One solution to the problem is battery-driven trains, which can make the best use of the electric traction system while avoiding the high costs of the catenary system. Due to the high power consumption of electric trains, energy management of battery trains are crucial in order to get the best use of batteries. This paper suggests a general algorithm for speed profile optimization of an electric train with an on-board energy storage device, during catenary-free operation on a given line section. The approach is based on discrete dynamic programming, where the train model and the objective function are based on equations of motion rather than electrical equations. This makes the model compatible with all sorts of energy storage devices. Unlike previous approaches which consider trains with throttle levels for tractive effort, the new approach considers trains in which there are no throttles and tractive effort is controlled with a controller (smooth gliding handle with no discrete levels). Furthermore, unlike previous approaches, the control variable is the velocity change instead of the applied tractive effort. The accuracy and performance of the discretized approach is evaluated in comparison to the formal movement equations in a simulated experimented using train data from the Bombardier Electrostar series and track data from the UK.

Regenerative braking is one of the main reasons behind the high levels of energy efficiency achieved in railway electric traction systems. During regenerative braking, the traction motor acts as a generator and restores part of the kinetic energy into electrical energy. To use this energy, it should be either fed back to the power grid or stored on an energy storage system for later use. This paper reviews the application of energy storage devices used in railway systems for increasing the effectiveness of regenerative brakes. Three main storage devices are reviewed in this paper: batteries, supercapacitors and flywheels. Furthermore, two main challenges in application of energy storage systems are briefly discussed. 

Simulation of power consumption in electric trains is categorized in two categories: electrical power simulation and mechanical power simulation. The mechanical power is calculated as speed times tractive effort and it gives an overall view on the total energy consumption of the train during different driving cycles. Detailed calculation of losses in different components in the propulsion system is however done using complex electrical models. In this paper, we introduce a nonlinear regression model generated from validated electrical equations for the calculation of the power loss in the motor converter module of electric trains. The function can be used instead of efficiency maps to evaluate the trains’ performance during the operation or dynamic simulations.

Driver advisory systems, instructing the driver how to control the train in an energy efficient manner, is one the main tools for minimizing energy consumption in the railway sector. There are many driver advisory systems already available in the market, together with significant literature on the mathematical formulation of the problem. However, much less is published on the development of such mathematical formulations, their implementation in real systems, and on the empirical data from their deployment. Moreover, nearly all the designed driver advisory systems are designed as an additional hardware to be added in drivers’ cabin. This paper discusses the design of a mathematical formulation and optimization approach for such a system, together with its implementation into an Android-based prototype, the results from on-board practical experiments, and experiences from the implementation. The system is based on a more realistic train model where energy calculations take into account dynamic losses in different components of the propulsion system, contrary to previous approaches. The experimental evaluation shows a significant increase in accuracy, as compared to a previous approach. Tests on a double-track section of the Mälaren line in Sweden demonstrates a significant potential for energy saving.

Catenary-free operated electric trains, as one of the recent technologies in railwaytransportation, has opened a new field of research: speed profile optimization and energy optimaloperation of catenary-free operated electric trains. A well-formulated solution for this problem shouldconsider the characteristics of the energy storage device using a validated model and method. This paper,discusses the consideration of the battery behavior in the problem of speed profile optimization ofcatenary-free operated electric trains. We combine the single mass point train model with an electricalbattery model and apply a dynamic programming approach to minimize the charge taken from thebattery during the catenary-free operation. The models and the method are validated and evaluatedagainst experimental data gathered from the test runs of an actual battery driven train tested in Essex,UK. The results show a significant potential in energy saving. Moreover, we show that the optimumspeed profiles generated using our approach consume less charge from the battery compared to theprevious approaches.