Analytical Solution to Equivalent Consumption Minimization Strategy for Series Hybrid Electric Vehicles

Analytical optimal solution to the energy management of hybrid electric vehicles is of interest from theoretical and practical perspectives. Particularly, effort has been made to derive analytical solution to the energy management problem for series hybrid electric vehicles using Pontryagin's minimum principle (PMP). However, admissibility of the system input was not fully explored in determining the optimal input candidates. In this paper, the analytical solution for the same problem is found by partitioning the positive power demand set into four subsets, where the solution is derived for each case separately according to the corresponding admissible input set. The analytical solution is verified through comparison with numerical solution for a series hybrid electric wheel loader, and two different drive cycles are considered for this purpose. From the proposed solution, effective equivalence factor bounds are found and used to construct an adaptive equivalent consumption minimization strategy. The proposed strategy and the analytical solution are implemented together for the same vehicle to demonstrate their effectiveness in dealing with real-world applications. Simulations are performed for 12 drive cycles, and the results are compared to the ones achieved by PMP-based optimal control where the optimization is done numerically. Simulation results suggest that the proposed methodology is relatively fast and has satisfactory performance in presence of drive cycle uncertainty. It is observed that the proposed method fulfills charge sustenance, and the achieved fuel consumption figures are very close to the optimal benchmarks found by the non-causal method.