The Impact of Penalty Function and Equivalence Factor on the Performance of ECMS Controller in Range Extended Electric Vehicles

This study discusses the role of the equivalence factor and penalty function in improving the performance of energy consumption minimization strategies in Range Extended Electric Vehicles (REEVs). In conventional ECMS, equivalence factors are typically derived from constant efficiency assumptions for simplicity or adaptively adjusted according to driving conditions in adaptive ECMS. In REEVs, however, the battery efficiency exhibits nonlinear behavior in the low SOC range, which directly leads to variability in the equivalence factor within conventional ECMS. This study investigates the influence of the variable equivalence factor on the overall fuel economy. The equivalence factors are usually considered constant or vary adaptively depending on driving cycles. However, the variation in battery efficiency is often neglected. The present study compares the results obtained for both constant and variable battery efficiencies in deriving the equivalence factors. The simulation results show that an improvement of approximately 3% in fuel economy was obtained for UDDS, NEDC, and WLTC driving cycles as a result of applying the variable equivalence factor. Additionally, through an analysis of various penalty function designs, the study highlights their crucial role in optimizing fuel consumption across different driving cycles.