The increasing integration of distributed renewable energy sources into distribution networks results in significant voltage regulation challenges. To address these challenges, we introduce a novel data-driven approach for voltage regulation that utilizes predictive control mechanisms, specifically data-enabled predictive control (DeePC). This method exploits the capabilities of photovoltaic (PV) inverters and battery energy storage systems (BESS) to manage bus voltages within the distribution network. Unlike traditional model-based approaches that require a precise physical model of the network, the DeePC algorithm operates optimally by relying solely on historical data to predict and adjust bus voltages. By employing the DeePC algorithm, the proposed controller maintains voltage profiles and the state of charge (SoC) of BESSs within operational thresholds in an optimal and robust manner. To further reduce the computational complexity, a reformulation of DeePC is developed using scoring functions, where the DeePC algorithm is efficiently approximated via differentiable convex programming. We validate our approach through simulations on the IEEE 34-bus test system, demonstrating its efficiency in maintaining desired voltage levels without the need for a detailed physical system model.