Adaptive energy management strategy of plug-in hybrid electric bus

•The strategy of PHEB can be applied online and in real time.•The strategy of PHEB reduces the equivalent fuel consumption.•The strategy of PHEB declines the capacity loss.•Improvements to the strategy considering the time-domain accumulation.•Improvements to the strategy considering bound constraints on the co-state variable. In this study, the online application of a new energy management strategy (EMS) is proposed for a power-split plug-in hybrid electric bus (PHEB) to improve its system's fuel economy and reduce power battery degradation. The new EMS employs Pontryagin's minimum principle (PMP) and the power battery state of charge (SOC) feedback method to adjust the covariates online. A model-free adaptive control (MFAC) EMS was designed and constructed according to the compact form dynamic linearization model to further obtain accurate SOC feedback; the time–domain cumulative as well as covariate upper and lower limit constraints were used to obtain a real-time MFAC-Ⅲ strategy for online applications. The average reduction in battery capacity loss on all ten routes was 8.19 %, resulting from the correlation between the MFAC-III EMS and MFAC EMS; evaluations conducted on both strategies indicated that the MFAC-III outperforms the MFAC strategy in hardware-in-the-loop. [Display omitted]