Grid-connected hybrid energy systems (HESs) represent a very promising option for addressing the problem of power outages worldwide. The selection of a suitable optimization approach and operational strategy are important aspects of the optimal design and operation of these HESs. This study aimed to find the optimal grid-connected PV/battery system sizes to supply electricity for a residential house in Karbala, Iraq, using two control strategies, load following (LF) and cycle charging (CC). The optimization was performed using HOMER software with and without the multi-year effects. The comparison analysis was carried out by considering the techno-economic and environmental performance of the feasible systems. The simulation results indicate that optimal configuration is achieved by using the CC strategy. Furthermore, the multi-year module affects the optimal results dramatically. Under the CC strategy, the multi-year effects increase the required PV size from 6 kW to 7 kW and the required number of batteries from 18 to 20, leading to an increase in the net present cost from $26,750 to $33,102 and a decrease in CO2 emissions from 7581 kg/year to 7379 kg/year. The results also show that the optimization results are highly affected by the variations of some critical parameters, such as solar radiation, average load, and battery degradation limits. The achievements indicate the higher effectiveness of the multi-year effects and control strategy on the optimal design of HESs.