The process of engine warming-up leads to additional fuel consumption. Energy management strategy considering engine warming-up is expected to further improve the energy economy of hybrid electric vehicles. This study provides a simple yet practical model for engine thermal dynamics. Then, the optimization problem of energy management considering engine warming-up is formulated on the basis of the control-oriented engine thermal dynamics. Thereafter, the optimal solution is derived by using the dynamic programming algorithm. Finally, the proposed engine thermal dynamics and energy management strategy are evaluated through simulation and experiments. Results show that the established engine thermal model effectively captures the main thermal behavior, simulation results reveal a high degree of approximation to experimental results for the engine temperature and fuel consumption, and the energy management strategy with engine temperature can further improve the energy efficiency.

发动机预热过程会导致额外的燃料消耗。考虑发动机预热的能源管理策略有望进一步提高混合动力汽车的能源经济性。这项研究为发动机热动力学提供了一个简单而实用的模型。然后，在面向控制的发动机热力学基础上，提出了考虑发动机预热的能量管理优化问题。此后，通过使用动态规划算法推导出最优解。最后，通过仿真和实验评估所提出的发动机热动力学和能量管理策略。结果表明，建立的发动机热模型有效地捕捉了主要的热行为，