Analytical Approach for the Power Management of Blended-Mode Plug-In Hybrid Electric Vehicles

This paper focuses on the intrinsic aspects of power management for hybrid electric vehicles (HEVs) and plug-in HEVs (PHEV). A vehicle power distribution density function is used to describe the drive cycle characteristics. An electric driveline loss is introduced to describe the minimum system loss for a given mechanical power output, and a piecewise linear fuel consumption model is used to capture essential characteristics such as idle fuel consumption rate, peak efficiency, and the minimum power to reach peak efficiency. Models are based on the assumption that both machines operate at the optimal speed and torque for a given mechanical power as if they are coupled with an ideal continuous variable transmission (CVT). The power management strategy is represented with a pair of power parameters that describe the power threshold for turning on the engine and the optimum battery power in engine-on operations. The model of a parallel hybrid electric powertrain is constructed to obtain optimal solutions that maximize the fuel economy for a given battery energy depletion and for a general vehicle power distribution density function. One-dimensional loss models of two power sources as approximations to real machines coupled with hypothetic CVTs are introduced to solve the optimization problem analytically. It is found that the optimal minimum engine power is the controlling factor in minimizing the total fuel consumption for the given battery energy depletion targets and that the optimal power is solely determined by powertrain characteristics. Numerical simulations validated the properties of the optimal power solutions obtained through analytic approaches. The significance of the results to real-world HEV and PHEV applications are also discussed.