Optimal Energy Management in a Range Extender PHEV Using a Cascaded Dynamic Programming Approach

Dynamic programming is widely used to benchmark the performance of a hybrid electric vehicle. It is also well documented that it is a very computationally heavy procedure depending on the number of states and control inputs in the problem formulation. In this paper we investigate the possibility of reduction in the computational time by splitting the number of states and control inputs between two models and applying dynamic programming individually, using the output of one as an input to the other and hence cascading the two models. A range extended hybrid electric vehicle powertrain architecture is modeled with four states and four control inputs, which is considered as the full model. Further, the states and control inputs of the battery and engine are separated from the other states, splitting them between the two new DP models. The vehicle performance estimated from this ‘cascaded models approach’ is compared with that from the full model. Initial comparisons show a very good match with minor differences in performance and considerable a reduction in computation time from around 6 hours to around a minute.