Battery capacity and battery thermal management control have a significant impact on the Hybrid Electric Vehicle (HEV) fuel economy. Additionally, battery temperature has a key influence on the battery health in an HEV. In the past, battery temperature and cooling capacity has not been included while performing optimization studies for power management or optimal battery sizing. This paper presents an application of Dynamic Programming (DP) to HEV optimization with battery thermal constraints. The optimization problem is formulated with 3 state variables, namely, the battery State Of Charge (SOC), the engine speed and the battery bulk temperature. This optimization is critical for determining appropriate battery size and battery thermal management design. The proposed problem has a major challenge in computation time due to the large state space. The paper describes a novel multi-rate DP algorithm to reduce the computational challenges associated with the particular class of large-scale problem where states evolve at very different rates. In HEV applications, the battery thermal dynamics is orders of magnitude slower than powertrain dynamics. The proposed DP algorithm provides a novel way of tackling this problem with multiple time rates for DP with each time rate associated with the fast and slow states separately. Additionally, the paper gives possible numerical techniques to reduce the DP computational time and the time reduction for each technique is shown.
