An optimal train journey with bounds on energy consumption during specified intermediate time intervals

In order to mitigate consumption of electrical energy during periods of peak demand it is common for electricity system operators to offer financial incentives that encourage large corporate consumers to reduce power usage at designated critical times. For train operators on large rail networks it may be more profitable to limit energy consumption during these times, for selected individual train journeys, rather than always implementing a true optimal strategy that minimizes overall energy consumption. In this paper we use classical methods of constrained optimization to find driving strategies for a single train that minimize energy consumption subject to constraints on energy usage within designated high-demand time intervals during the journey. We illustrate our results by considering a journey with realistic parameters and two different nominal sets of energy consumption constraints.