Port terminals, especially their reefer container yards, face surging power demands. Efficient reefer charging is critical for port sustainability and efficiency, as it helps reduce peak energy loads and total energy consumption. This requires consideration of reefer characteristics, temperature control requirements, time-variant energy prices, port power distribution network and environmental factors such as ambient temperature and sunlight. Optimising the charging power and internal temperature of reefers is therefore essential. This study introduces mathematical models to optimise two efficient charging schemes for reefers: flexible power charging and on/off power charging. Internet-of-Things (IoT) technologies can enable tailored optimisation strategies for reefer charging by facilitating information sharing among reefers and the charging planning system. This study also proposes a cyber-physical system for IoT that allows these charging schemes to be implemented. Using data from existing ports, the results demonstrate that the optimised reefer charging plan significantly reduces energy costs and alleviates peak energy consumption, consistently outperforming the baseline policy. In the optimised plan, charging periods are slightly adjusted based on energy price in each period as part of a demand response strategy, and intermittent charging is actively used for peak energy shaving. The study also quantifies the positive impact of roof shade installation. Findings provide actionable insights for refrigerated goods.