Zaremba, A., Soto, C., Shakiba-herfeh, M., and Jennings, M., "Power Management of Hybrid Electric Vehicles based on Pareto Optimal Maps," SAE Int. J. Alt. Power. 3(1):56-63, 2014, doi:10.4271/2014-01-1820.
Pareto optimal map concept has been applied to the optimization of the vehicle system control (VSC) strategy for a power-split hybrid electric vehicle (HEV) system. The methodology relies on an inner-loop optimization process to define Pareto maps of the best engine and electric motor/generator operating points given wheel power demand, vehicle speed, and battery power. Selected levels of model fidelity, from simple to very detailed, can be used to generate the Pareto maps. Optimal control is achieved by applying Pontryagin's minimum principle which is based on minimization of the Hamiltonian comprised of the rate of fuel consumption and a co-state variable multiplied by the rate of change of battery SOC. The approach delivers optimal control for lowest fuel consumption over a drive cycle while accounting for all critical vehicle operating constraints, e.g. battery charge balance and power limits, and engine speed and torque limits. The methodology has been verified through comparison with the production VSC strategy of the 2013 HEV Fusion and it shows comparable performance. The approach is effective for evaluation of new system configurations and for early analysis of next generation HEV systems before VSC calibrations are developed.