This paper presents a direct mathematical approach for determining the state of charge (SOC)-dependent equivalent cost factor in hybrid-electric vehicle (HEV) supervisory control problems using globally optimal dynamic programming (DP). It therefore provides a rational basis for designing equivalent cost minimization strategies (ECMS) which achieve near optimal fuel economy (FE). The suggested approach makes use of the Pareto optimality criterion that exists in both ECMS and DP, and as such predicts the optimal equivalence factor for a drive cycle using DP marginal cost. The equivalence factor is then further modified with corrections based on battery SOC, with the aim of making the equivalence factor robust to drive cycle variations. Adaptive logic is also implemented to ensure battery charge sustaining operation at the desired SOC. Simulations performed on parallel and power-split HEV architectures demonstrate the cross-platform applicability of the DP-informed ECMS approach. Fuel economy data resulting from the simulations demonstrate that the robust controller consistently achieves FE within 1% of the global optimum prescribed by DP. Additionally, even when the equivalence factor deviates substantially from the optimal value for a drive cycle, the robust controller can still produce FE within 1–2% of the global optimum. This compares favorably with a traditional ECMS controller based on a constant equivalence factor, which can produce FE 20–30% less than the global optimum under the same conditions. As such, the controller approach detailed should result in ECMS supervisory controllers that can achieve near optimal FE performance, even if component parameters vary from assumed values (e.g., due to manufacturing variation, environmental effects or aging), or actual driving conditions deviate largely from standard drive cycles.
Benchmark fuel economy for a parallel hybrid electric three-wheeler vehicle (rickshaw)