An offline closed-form optimal predictive power management strategy for plug-in hybrid electric vehicles

This article develops an optimal predictive power management strategy (OP-PMS) for plug-in hybrid electric vehicles (PHEVs) to manage the remaining battery level throughout a defined journey. Apart from using the battery before charging it again at the destination, this approach also supports transit through an Ultra Low Emission Zone (ULEZ), where a PHEV needs to operate in pure electric mode to avoid emissions. This type of PHEV power management strategy (PMS) design problem is a noncausal control problem, where the power demand of the remaining driving cycle and the final battery energy level targets influence the current power management action. Rather than solving the whole optimization problem online, this article presents a simplification that leads to a closed-form analytic solution with parameters that can be computed offline. This article makes three key contributions. First, a novel input-linearization method is developed, which converts the OP-PMS into a convex quadratic programming (QP) problem that captures the essential model nonlinearities using an input transformation and a quadratic cost function. Second, the influence of future power demands and final targets on current energy management policy is explicitly quantified from a dynamic optimal control perspective. Third, the noncausal convex QP is approximated with a closed-form analytic solution that is calculated offline. This leads to a real-time implementable OP-PMS with coefficients that can be precalculated and stored in the engine control unit. To demonstrate the viability of this approach, numerical examples are provided based on a generic PHEV model to verify the efficacy of the proposed OP-PMS.