This paper investigates the reliability of a multi-cell battery system used in the Ground Control Station (GCS) of tethered High-Altitude Platform Systems (tHAPS), assuming the battery cells are series-connected. The model integrates repair and replenishment strategies to enhance battery reliability and ensure uninterrupted power supply to tHAPS. We analyze four practical variants, deriving explicit steady-state probabilities, which offer critical insights into system performance. Despite the inherent lower reliability of series-connected cells, our results demonstrate that effective management of repairs and replenishment significantly improves overall reliability. Additionally, the cost analysis indicates that increasing repair and replenishment rates reduces system costs by minimizing battery failures. The model underscores the importance of proper resource allocation and optimizing costs while maintaining high system reliability.