Applying forward dynamic programming to combined energy and thermal management optimization of hybrid electric vehicles

The efficiency of internal combustion engines (ICEs) is well-known to be low at cold starting conditions. Additionally, the energy demand for passenger compartment heating is substantial and either provided by an electrical auxiliary heater or in terms of the engine waste heat. Plug-in hybrid electric vehicles (PHEVs) are prone to suffer from extended warm-up periods due to increased engine off periods as compared to conventional vehicles. Energy management strategies (EMSs) however allow for warm-up applications independent of the drive torque request. Optimal control theory serves as benchmark for EMS, offering a variety of numerical methods. This paper focuses on forward dynamic programming (FDP) accounting for causal system dynamics such as engine temperature. Results confirm, that even though the fuel saving potential of the engine warm-up is significant, it is hardly influenced by means of the EMS. A second implementation variant is proposed to counteract the curse of dimensionality. The presented approach not entirely achieves global optimality, yet yields results close to optimum within reasonable computational times. As opposed to the reference, the proposed method allows accounting for a variety of causal system dynamics leading towards an EMS more close to reality.