Under the background of smart and green transformation in ports, Automated Guided Vehicles (AGVs) have become the main means of horizontal transportation in automated container terminals. To address the problem of unbalanced energy levels and inefficient utilization of charging resources among AGV groups, this paper investigates AGV group energy balancing based on potential game theory and deep reinforcement learning. Considering the AGV group energy level, energy distribution range, and charging station utilization, the distributed AGV charging scheduling problem is transformed into a game-theoretic model among AGVs, and a potential game–based AGV group energy balancing model is proposed. Furthermore, by integrating the Multi-Agent Deep Deterministic Policy Gradient (MADDPG) algorithm with Potential Game Theory (PGT), a MADDPG-PGT algorithm is developed to derive the energy balancing strategy for AGV groups. Numerical simulation experiments are conducted based on the operational tasks of three real container vessels. The simulation results indicate that, regardless of whether the automated container terminal operates during peak or off-peak periods, the proposed method maintains the average energy level of the AGV group at approximately 85%, while constraining the energy distribution range within 80%–90% throughout task execution. This achieves a balanced energy state for the AGV group and effectively reduces the service pressure on charging stations. Comparative results demonstrate that the proposed method outperforms existing approaches in terms of AGV group energy balance, task completion time, and charging station utilization. Under vertical, U-shaped, and horizontal layouts, the MADDPG-PGT algorithm consistently achieves energy balance among AGV groups. Specifically, for small-scale and large-scale task volumes, the horizontal layout yields the best energy balancing performance, while for medium-scale task volumes, the three layouts exhibit similar equilibrium states, collectively enhancing the overall operational efficiency of automated container terminals.