The ongoing interest in renewable energy drives efforts to continuously improve these systems. Photovoltaic (PV) battery systems could be optimized by integrating a Digital Twin (DT) in combination with bidirectional charging. The problem with existing PV systems lies in the constantly changing weather conditions and fluctuating electricity prices, which are not effectively utilized, leading to inefficient and costly solutions. We developed an optimization algorithm based on a DT that reduces electricity costs through intelligent charging and discharging of the PV battery system for apartments and residential homes, focusing on balcony power plants. To achieve this, a DT is created that digitally mirrors the physical PV battery system and continuously adapts to the current conditions using consumption, production, and price data in real-time and for forecasting. In comparison with two other self-developed algorithms, one computationally intensive and one very simple, our intelligent algorithm presents a middle ground between fast computation and cost efficiency. The results show a cost reduction of up to 300 euros or 35% for a typical German household.