In this work, a supervisory control strategy is proposed for parallel hybrid electric vehicles (HEVs). The control strategy is based on the equivalent consumption minimization strategy (ECMS) but it also considers the power consumed by the engine cooling system to optimize the overall fuel economy of the vehicle. To verify its effectiveness, the proposed cooling-sensitive ECMS is implemented on a through-the-road (TTR) HEV, after the mathematical model of the TTR HEV is developed based on power flows, and engine thermal dynamics is also included. Simulations are performed with different drive cycles, and the results show that the cooling-sensitive ECMS is able to improve the fuel economy by 2.7% compared to the baseline ECMS. Furthermore, it is shown that cooling-sensitive ECMS operates in a charge-sustaining manner provided that the equivalence factors are optimally selected
