The development of energy storage battery systems is key to advancing the "dual carbon" goal, but with it come the potential safety hazards of energy storage power stations. Therefore, it is urgent to accurately evaluate the reliability of energy storage battery systems. This paper proposes a method for evaluating the operational reliability of energy storage batteries considering multidimensional performance degradation. First, a Gaussian process-based method for calculating the distribution of voltage characteristics during the performance degradation process of energy storage batteries is proposed. This calculates the probability distribution of voltage characteristics during the charging and discharging cycle, providing an important dimension for characterizing performance degradation. Then, a multidimensional general generation function-based operational reliability evaluation method for energy storage battery systems is proposed. The reliability of individual batteries is calculated through the probability distribution of voltage characteristics and capacity. Then a series parallel relationship function that can consider the topological connection of energy storage batteries is defined to calculate the overall reliability of the battery system. Finally, a numerical simulation based on NASA energy storage battery data shows that the proposed method can achieve accurate reliability evaluation of such battery systems.