Optimal Control of Electric Bus Lines

Licentiate thesis, 2021

Bus lines are inherently unstable systems, where any delay tends to be further amplified by the accrued passenger loads encountered at stops downstream. This self-reinforcing mechanism, when combined with the multiple sources of disturbances of an urban environment, can lead to the problem of bus bunching. To mitigate this, various types of control strategies have been proposed and some are routinely employed by transit agencies around the globe to improve service regularity. They range from simple rule-based ad-hoc solutions, to elaborate real-time prediction-based bus velocity control. However, most of these strategies only focus on service-related objectives, and often disregard the potential energy savings that could be achieved through the control intervention. Velocity-based control, in particular, is very suitable for eco-driving strategies, which can increase the energy efficiency of the transit system by adjusting the planned velocity trajectories of the vehicles based on the road and traffic conditions.

This thesis proposes a scalable resolution method for the bus line regularity and eco-driving optimal control problem for electric buses. It is shown how this problem can be recast as a smooth nonlinear program by making some specific modelling choices, thus circumventing the need for integer decision variables to capture bus stop locations and avoiding the infamous complexity of mixed-integer programs. Since this nonlinear program is weakly coupled, a distributed optimization procedure can be used to solve it, through a bi-level decomposition of the optimization problem. As a result, the bulk of the computations needed can be carried out in parallel, possibly aboard each individual bus. The latter option reduces the communication loads as well as the amount of computations that need to be performed centrally, which makes the proposed resolution method scalable in the number of buses. Using the concept of receding horizons to introduce closed-loop control, the optimized control trajectories obtained were applied in a stochastic simulation environment and compared with classical holding and velocity control baselines. We report a faster dissipation of bus bunching by the proposed method as well as energy efficiency improvements of up to 9.3% over the baselines.