Universal Bounds Estimation and Efficient Tuning for Equivalent Factor in Real-Time Cost-Optimal Predictive ECMS of PHEVs

Accurate and efficient estimation of the equivalent factor (EF) in equivalent consumption minimization strategy (ECMS) is pivotal for achieving desirable economy effects in plug-in hybrid electric vehicles (PHEV). To this end, a real-time predictive ECMS (PECMS) for cost optimality in series PHEVs is proposed, which aims to minimize the total cost associated with fuel consumption, battery degradation, and electricity usage. A generalized unified constraint for battery power command is developed to establish the minimum feasible control domain in powertrain, thereby reducing control complexity and deriving minimal usable EF bounds. Building upon this unified constraint, a universal approach for estimating EF bounds is introduced, independent of specific control objectives or powertrain configurations. Subsequently, a concise and efficient EF tuning approach based on the golden section method is formulated to estimate the appropriate EF for PECMS in real time. With this EF determination, optimal battery power commands are computed by solving the Hamilton function. Simulation and hardware-in-the-loop test results verify the effectiveness of the proposed strategy in reducing operational cost, accurately estimating EF bounds, and achieving efficient EF tuning in real-time applications.