Relaxed Model Predictive Control for Energy Management in an Extended Range Electric Vehicle

This work introduces a Relaxed Model Predictive Control (R-MPC) strategy for optimal energy management in an Extended-Range Electric Vehicle (EREV). The study is motivated by the need to achieve high fuel efficiency while maintaining the battery state of charge (SOC) within safe limits under dynamic driving conditions. The proposed controller reformulates the Equivalent Consumption Minimization Strategy (ECMS) into a convex optimization framework that minimizes fuel consumption and penalizes SOC deviation from a reference band. A relaxation technique is applied to the generator on/off decision, replacing the binary variable with a continuous one bounded between zero and one, which eliminates mixed-integer complexity and allows realtime implementation. The R-MPC enforces strict constraints on generator power, slew rate, and battery current, ensuring reliable and stable operation of the hybrid powertrain. Simulation studies are performed across several standard and custom driving cycles using a complete EREV model implemented in Python. Comparative results against the baseline ECMS confirm that the R-MPC achieves lower fuel consumption and improved SOC regulation with smooth generator transitions. The proposed approach provides a practical and optimized convex formulation for predictive control in hybrid electric vehicles, demonstrating a viable pathway toward real-time energy management in future extended-range electric platforms.