Minimizing System Entropy: A Dual-Phase Optimization Approach for EV Charging Scheduling.

To address the electric vehicle (EV) charging scheduling problem in rural distribution networks, this study proposes a novel two-phase optimization strategy that combines particle swarm optimization (PSO) and Q-learning for global optimization and real-time adaptation. In the first stage, PSO is used to generate an initial charging plan that minimizes voltage deviations and line overloads while maximizing user satisfaction. In the second phase, a Q-learning approach dynamically adjusts the plan based on real-time grid conditions and feedback. The strategy reduces the system's entropy by minimizing the uncertainty and disorder in power distribution caused by variable EV charging loads. Experimental results on a 33-bus distribution system under baseline and high-load scenarios demonstrate significant improvements over conventional dispatch methods, with voltage deviation reduced from 5.8% to 1.9%, maximum load factor reduced from 95% to 82%, and average customer satisfaction increased from 75% to 88%. While the computation time increases compared to standalone PSO (66 min vs. 34 min), the enhanced grid stability and customer satisfaction justify the trade-off. By effectively minimizing system entropy and balancing grid reliability with user convenience, the proposed two-phase strategy offers a practical and robust solution for integrating EVs into rural power systems.