  Hybrid electric vehicles (HEVs) are becoming increasingly popular because
they can better combine the working characteristics of internal combustion
engines and electric motors. However, the minimum fuel consumption of an HEV
for a battery electrical balance case under a specific assembly condition and a
specific speed curve still needs to be clarified in academia and industry.
Regarding this problem, this work provides the mathematical expression of
constrained optimal fuel consumption (COFC) from the perspective of constrained
reinforcement learning (CRL) for the first time globally. Also, two mainstream
approaches of CRL, constrained variational policy optimization (CVPO) and
Lagrangian-based approaches, are utilized for the first time to obtain the
vehicle's minimum fuel consumption under the battery electrical balance
condition. We conduct case studies on the well-known Prius TOYOTA hybrid system
(THS) under the NEDC condition; we give vital steps to implement CRL approaches
and compare the performance between the CVPO and Lagrangian-based approaches.
Our case study found that CVPO and Lagrangian-based approaches can obtain the
lowest fuel consumption while maintaining the SOC balance constraint. The CVPO
approach converges stable, but the Lagrangian-based approach can obtain the
lowest fuel consumption at 3.95 L/100km, though with more significant
oscillations. This result verifies the effectiveness of our proposed CRL
approaches to the COFC problem.
