A Dynamic Programming Algorithm for HEV Powertrains Using Battery Power as State Variable

One of the first steps in powertrain design is to assess its best performance and consumption in a virtual phase. Regarding hybrid electric vehicles (HEVs), it is important to define the best mode profile through a cycle in order to maximize fuel economy. To assist in that task, several off-line optimization algorithms were developed, with Dynamic Programming (DP) being the most common one. The DP algorithm generates the control actions that will result in the most optimal fuel economy of the powertrain for a known driving cycle. Although this method results in the global optimum behavior, the DP tool comes with a high computational cost. The charge-sustaining requirement and the necessity of capturing extremely small variations in the battery state of charge (SOC) makes this state vector an enormous variable. As things move fast in the industry, a rapid tool with the same performance is required. The present work proposes a novel approach in defining the state variables of the DP algorithm with the objective of reducing the computational time at a low cost of accuracy. The commonly used state variable, SOC, is replaced by the cumulative battery power vector discretized twice: the first one being the macro-discretization that runs throughout DP to get associated to control actions, and the second one being the micro-discretization that is responsible for capturing the smallest power demand possible and updating the final SOC profile.