Xuan Vu

Brief paper: Local energy minimization in optimal train control

The calculation of optimal driving strategies for on-board control of freight trains is a challenging task. In this paper we calculate the critical switching points for a globally optimal strategy on a track with steep gradients using a new local energy minimization principle. The method has been used successfully in Australia to calculate optimal switching points and hence provide in-cab advice to train drivers on long-haul freight trains.

Energy-efficient train control: The two-train separation problem on level track

Abstract When two trains travel in the same direction along the same track it is a common safety requirement that they must be separated by at least one signal. If the signals are located at fixed positions, they divide the track into separate sections and the safety requirement means that two trains cannot occupy the same section at the same time. Safe separation can be ensured by specifying supplementary section clearance times which define the latest allowed exit time for the leading train and the earliest possible entry time for the following train. The clearance times could initially be based on an existing timetable but we will show that adjusting these times can substantially decrease the total energy required by the trains. In this paper we find driving strategies that minimize total energy consumption and allow both trains to finish on time while adhering to the separation constraints imposed by the supplementary clearance times. We establish a new necessary condition to check whether a set of specified clearance times is optimal and discuss a heuristic procedure to find the optimal clearance times and the corresponding speed profiles. We illustrate our methods with a simplified but realistic case study.

Optimal train control: Analysis of a new local optimization principle

It is known that the optimal driving strategy for a train takes the form of a power-speedhold-coast-brake strategy unless the track contains steep grades. In such cases the predominant speedhold mode must be interrupted by phases of power on steep uphill sections and phases of coast on steep downhill sections. The Freightmiser device is used by Pacific National to provide on-board advice to train drivers about energy efficient driving strategies. Freightmiser uses a fast and efficient numerical algorithm to solve a key local energy minimization problem and hence find the optimal switching points. Although the numerical algorithm converges to a feasible solution there is no direct proof that the solution is unique. We explain the basic ideas behind the local energy minimization principle and use an extended perturbation analysis to derive various equivalent forms of the necessary conditions.

Optimal driving strategies for two successive trains on level track subject to a safe separation condition

When two trains travel along the same track in the same direction it is a common safety requirement that they should always be separated by at least one signal. If the signals are located at fixed positions dividing the track into different sections then the two trains cannot occupy the same section of track at the same time. It is desirable to find driving strategies that minimize the total energy consumption and allow the trains to reach their final destinations at the designated times. In this paper we impose a prescribed sequence of intermediate times that ensure adequate separation for two successive trains on level track. By varying these times we find necessary conditions defining the optimal sequence of prescribed intermediate times-a sequence that minimizes total energy consumption.

Using Maximum Power to Save Energy

Some rail operators discourage their drivers from using maximum power on the grounds that it has high fuel flow rates or high energy consumption rates. However, optimal control theory indicates that the most efficient driving strategies should use maximum power. Although the rate of energy use is higher while using maximum power, the duration of power phases is shorter and overall energy use is less. We use realistic examples to show how using more power when accelerating can reduce overall energy use.

Optimal real-time junction scheduling for trains with connected driver advice systems

Abstract Many railways around the world are using driver advice systems to provide real-time advice to drivers on how to control their trains to stay on time with minimum energy use. Standalone driver advice systems use pre-prepared timetables. More recently, driver advice systems are being developed with data connections to central control systems, to allow real-time updating of schedules. Dynamic rescheduling of trains in response to disruptions can be an intractable problem for large networks. Localised junction scheduling, combined with driver advice systems, can reduce time lost at individual junctions by ensuring that trains arrive at the junction with sufficient headways to ensure smooth traffic flows. We have developed a system that combines real-time driving advice calculation with real-time junction scheduling to reduce delays at junctions, and have simulated the operation of this junction scheduling system at Neasden Junction in the UK, where about 10% of trains are slowed at the junction. When an express train was delayed by three minutes early in its journey, the result would have been three trains arriving at the junction within a 60 s interval. The junction scheduling system detected the potential conflicts 20 min before they occurred, and calculated new target times at the junction to resolve the conflicts. The connected driver advice systems responded by calculating new optimal speed profiles to meet the revised arrival times.