Maximise the Regenerative Braking Energy using Linear Programming

Regenerative braking improves the energy efficiency of railway transportation by converting the kinetic energy into the electrical energy. In this paper, Linear Programming (LP) is applied to search for the train braking trajectory with the maximum Regenerative Braking Energy (RBE). LP takes the advantages of simplicity in modelling, efficiency in computation, flexibility in applications. Compared with the previously proposed model in [1], the proposed LP optimisation model takes into account the speed limit constraints during the braking operation. Four case studies have been performed with different speed limits and initial braking speeds. While the maximum allowed braking time takes a key role for the RBE recovery, a threshold exists when the impact of maximum allowed braking time starts to become negligible. It has been demonstrated in this paper that LP is a robust and effective method to locate the optimal braking trajectory with the maximum RBE. The results of the optimisation are of significant interest for urban transportation systems where the regenerative braking is frequently applied. Future work of this paper is to investigate the optimisation of RBE in a more complicated scenario where the gradients are present and the motoring operation of train is allowed.