Phase-Informed ECMS with Soft SOC Safeguarding for a Virtual Hybrid Agricultural Tractor

Abstract

Abstract

Fuel reductions can be confounded by battery depletion or unreported control corrections. This theoretical study examines phase-informed equivalent-consumption minimization (ECMS) with a soft state-of-charge (SOC) safeguard in an ideal power-split virtual tractor. The model includes planetary kinematics, machine limits, battery resistance and engine execution constraints. Numerical conservation checks verify implementation without providing empirical validation. The frozen adaptive configuration reproduces the submitted 5.676% normalized fuel saving. On 20 independent paths, it achieves 5.951% saving relative to matched load following, with all paths meeting a 10−4 terminal-SOC tolerance. Removing the safeguard leaves no terminal-valid paths. Removing adaptation instead gives 7.091% saving with the same safeguard, while increasing mean interventions from 94.8 to 150.5. Adaptation therefore changes the fuel–intervention trade-off rather than improving fuel economy. Same-parameter cycle, capacity and map audits retain positive valid-pair savings but expose terminal failures and an empty-action demand boundary. A historical approximately 20% full-information diagnostic is reported separately under a favorable map, different electrical limits and relaxed terminal band. The contribution is an auditable comparison of fuel, terminal charge and corrections within a declared virtual platform, without recursive-feasibility guarantees or field-economy predictions.