Analytical Optimal Solution to the Energy Management Problem in Series Hybrid Electric Vehicles

An optimal solution to the energy management problem in hybrid electric vehicles has been extensively addressed in the literature during the last decade, especially with the application of dynamic programming, the Pontryagin minimum principle, or equivalent consumption minimization strategy. However, most of the works consist in finding cycle-specific optimal trajectories, which are far from being general control strategies. The aim of this work is to derive an analytical expression, general and not cycle specific, for the energy management problem that summarizes the optimal controls for a series hybrid electric vehicle. Starting from a simple definition of the powertrain, an explicit formulation is deducted to minimize fuel consumption based on an analytic analysis of the Pontryagin minimum principle. Explicit expressions for control variables and costates are provided. The result is a general control strategy that specifies the optimal generator set usage for a given probability distribution of expected traction demands. This methodology is benchmarked with common methods in the literature (dynamic programming and numerical Pontryagin minimum principle) showing near identical results but with strongly reduced computational time. The general form of this control strategy can also be used to analyze the optimal operation range of the engine, which could be useful for designing purposes.