Research on Equivalent Factor Boundary of Equivalent Consumption Minimization Strategy for PHEVs

The equivalent fuel consumption minimum strategy (ECMS) based on the Pontryagin's minimum principle (PMP) enables real-time energy management optimization of plug-in hybrid electric vehicles (PHEVs). However, it remains challenging to accurately determine the equivalent factor (EF). In this study, an analytical expression of the optimal EF boundary is addressed to facilitate more efficient search of the optimal EF. The deterministic expression of the optimal EF boundary is derived from the Hamilton equation of PMP. By combining the optimal EF boundary and differential evolution algorithm, a novel fusion adaptive ECMS (A-ECMS) is proposed to demonstrate the application of the proposed boundary in the framework of model predictive control (MPC). Two different simulations with and without prior knowledge of driving cycle were respectively conducted, and the simulation results verify the feasibility of optimal EF boundary and manifest that the energy savings by the proposed A-ECMS can reach more than 97% of dynamic programing, highlighting the superior performance of the proposed strategy.