Range-extended new energy vehicles are a type of automobile that combines the advantages of electric vehicles and internal combustion engines (Shi et al. in Mech Syst Signal Process 179, 2022). These vehicles typically use an electric motor as the main propulsion system (Hossain et al. in J Energy Storage 55:105752, 2022), equipped with a small internal combustion engine (usually gasoline or diesel). Under normal conditions, the vehicle primarily relies on battery power, driven by the electric motor, which offers high efficiency and low emissions. When the battery charge drops to a certain level, the internal combustion engine starts and acts as a generator to recharge the battery (Wang et al. in J Power Sources 521, 2022).