Optimal mesh discretization of the dynamic programming for hybrid electric vehicles

The maximum fuel economy achievable by a hybrid electric vehicle (HEV) on a specific driving mission can be attained through the identification of the best admissible control policy. In the last years, the Dynamic Programming (DP) algorithm has proved to be capable of identifying the optimal policy once the definition of a proper computational grid is performed. As far as the refinement of the latter is concerned, the results produced by the selected control strategy can be negatively affected by a rough mesh due to approximation errors chains. Still, too fine a grid can lead to unreasonable CPU times. Hence, a method for automatically detecting the optimal mesh discretization with respect to different HEV simulations should be found. In the present paper, a self-adaptive statistical approach based on a proper management of any admissible battery energy variation is developed to significantly improve the calculation times required for HEV architectures while still attaining the best possible accuracy in terms of CO2 emissions as well as total cost of ownership (TCO). For the purpose, a low-throughput battery model has been taken into account so that the number of cells, the curve power limit and the energy content could be accounted for. The proposed method was tested on two parallel HEVs belonging to different categories, specifically a passenger car and a heavy-duty vehicle. The robustness of the method was also assessed for by testing the effects of a variation in the number of control variables within the simulation.