REDUCING ENERGY DURING SPECIFIED TIME INTERVALS FOR MULTIPLE TRAINS USING SIMPLE TRAIN MODELS

Abstract Electricity supply operators offer financial incentives to encourage large energy users to reduce their power demand during declared periods of increased demand from energy users such as residential homes. This demand flexibility enables electricity system operators to ensure adequate power supply and avoid the construction of peaking power plants. Railway operators can sometimes reduce their power demand during specified peak demand periods without disrupting the train schedules. For trains with infrequent stops, such as intercity trains, it is possible to speed up trains prior to the peak demand period, slow down during the peak demand period, then speed up again after the peak demand period. We use simple train models to develop an optimal strategy that minimizes energy use for a fleet of trains subject to energy-use constraints during specified peak demand intervals. The strategy uses two sets of interacting parameters to find an optimal solution—a Lagrange multiplier for each energy-constrained time interval to control the speed of trains during each interval, and a Lagrange multiplier for each train to control the relative train speeds and ensure each train completes its journey on time.