Energy management strategy for a multi-motor PHEV combining DP-derived SOC reference trajectory and numerical torque distribution optimization

This paper proposes a hierarchical energy management strategy for a multi-motor plug-in hybrid electric vehicle (PHEV), combining a dynamic programming (DP)-derived state-of-charge (SOC) reference trajectory with pre-computed motor torque distribution optimization. The upper-layer DP generates a globally optimal SOC trajectory offline under the WLTC cycle, while the lower-layer pre-computed optimization map minimizes electrical energy consumption for real-time P3/P4 torque split execution. This decoupled framework eliminates real-time high-complexity optimization while achieving substantial control precision improvements. Experimental validation on a chassis dynamometer with n = 3 repeated tests (CV <1%) demonstrates a 2.9% fuel economy improvement (6.11 ± 0.05 to 5.935 ± 0.05 L/100 km) over a production-calibrated baseline. The improvement arises from three synergistic mechanisms: DP-guided SOC scheduling enhances engine thermal efficiency (+1.25 percentage points), the pre-computed torque distribution map improves motor optimality (+5% in optimal distribution adherence), and expanded SOC operating range increases high-voltage operation (+16%), reducing electrical losses. The proposed strategy provides a repeatable methodology and practical guidance for calibrating rule-based controllers of hybrid electric vehicles.