The increasing penetration of renewable energy sources (RESs) and battery energy storage systems (BESSs) in low-voltage distribution networks demands advanced planning strategies to ensure operational efficiency and cost-effectiveness. This paper proposes a hybrid optimization framework for the expansion of low-voltage AC/DC systems, addressing the optimal placement, sizing, and operation of RESs, BESSs, and voltage source converters (VSCs). The methodology combines an Iterated Local Search (ILS) metaheuristic with a nonlinear optimal power flow (OPF) model and incorporates scenario reduction via K-means clustering to capture uncertainties in demand, energy prices, and RES generation. Applied to a 73-node hybrid AC/DC network, the proposed approach reduces energy purchase costs and losses, improves voltage profiles, and enhances component utilization. These results demonstrate the effectiveness of jointly integrating RESs and BESSs in hybrid networks, while maintaining computational efficiency through hybrid optimization and scenario reduction.