A Comparative Study of Equivalent Factor Optimization Based on Heuristic Algorithms for Hybrid Electric Vehicles

The equivalent consumption minimization strategy (ECMS) is an instantaneous optimization method implemented online for hybrid electric vehicles (HEVs) to improve fuel economy. To fulfill the near-optimal performance of ECMS, equivalent factors (EFs) must be well tuned for different powertrains and driving cycles. This study proposes a hierarchical offline optimization framework which tunes the penalty value of state of charge (SOC) balance in the outer layer and optimizes EFs based on heuristic algorithms in the inner layer. A comprehensive analysis is conducted to evaluate three heuristic algorithms, including the genetic algorithm (GA), the nonlinear-inertia-decreasing particle swarm optimization algorithm (NLPSO), and the novel firefly algorithm (FA). The traversal optimization method (TOM) is chosen as the benchmark. Besides, a sensitivity analysis is carried out to reveal the impact of the penalty value on the battery SOC balance. The simulation results confirm that the battery SOC balance positively relates to the penalty value. However, the biggest penalty value is not always the optimal choice. The comparative results show that the GA and NLPSO can lessen 99.86% and 99.87% of the computational burden but increase the fuel consumption by 4.44% and 4.26%, respectively, compared to TOM. On the other hand, FA can reduce computational time by 99.87% with a 1.85% loss of fuel economy, which is superior to the other two heuristic algorithms in terms of optimality and computational cost.