Comparative Evaluation of ECMS and DP Control Strategies Using Steady-State and Transient Engine Models in Mild Hybrid Electric Vehicles

Transient engine operation in real driving conditions generally leads to higher fuel consumption than that predicted by steady-state maps. For this reason, this work investigates the impact of using steady-state and transient engine representations within Equivalent Consumption Minimization Strategy (ECMS) and Dynamic Programming (DP)-based energy management strategies for a P2 mild hybrid electric vehicle. ECMS makes decisions based on the current operating state, hence providing local optimal solution, whereas DP yields a globally optimal solution by considering the entire driving cycle. This work quantifies the maximum achievable fuel savings using these control strategies considering engine transient operation. In this work, an ECMS controller is proposed that calculates the equivalent fuel consumption precisely by utilizing engine and electric machine efficiencies derived from their current operating points on their operating characteristic maps. In the cost function the term for engine fuel consumption is evaluated in two separate cases, using a steady-state fuel model in one case and a transient engine model in the other. In parallel, a DP benchmark based on Bellman’s backward recursion is formulated using both engine modelling approaches. The findings indicate that the impact extends beyond total fuel consumption to the dynamic behavior of the powertrain as well. Specifically, the root mean square (RMS) and total variation (TV) of engine and motor torques show that including transient model in the cost function leads to different optimal control actions and significantly influences torque smoothness and overall drivetrain stability.