Abstract
A <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">co-charging</i> parking system is a charging system in which the chargers are automated, i.e., they can automatically connect to or disconnect from vehicles presented in the parking. This system makes it possible to have less chargers than the number of parking places. This paper studies an optimal scheduling problem aiming at charging all vehicles to required battery level while minimizing the total charging cost. We formulate this scheduling problem as a non-linear optimal control problem with mixed integer constraints and mixed discrete and continuous time. The problem is solved using a Branch and Bound Strategy coupled with Pontryagin Maximum Principle (PMP) and Interior Point Methods (IPMs) for optimal control. The presented method is tested on numerous configurations and shows promising results both in term of precision and in term of convergence rate.
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