In recent decades, there has been a substantial surge in the adoption of renewable energy systems (RESs), particularly photovoltaic systems (PVs). However, the increasing integration of PV systems into distribution networks has exposed limitations in traditional control methods, such as cascaded linear control with PID controllers. These limitations manifest in dynamic response, power regulation capability, and adaptability to varying operating conditions. Voltage fluctuations arising from intermittent PV output have become a significant concern. The primary aim of this study is to develop a Model Predictive Control (MPC) scheme capable of generating a control signal based on a cost function. The study also seeks to validate the effectiveness of MPC under diverse scenarios. Additionally, an energy storage system, represented by a battery, is incorporated to support the PV system during periods of low power output. The chosen methodology involves using a Dual Active Bridge converter for charging and discharging the batteries. Including an LCL filter in the design significantly reduces THD from 51% to 2.62%. When comparing the response to changing linear loads, MPC demonstrates faster performance than DQ control, with a response time ahead of 0.23 seconds.