The battery system plays an important role in a number of modern power applications. In practice, cell charge imbalance is a very common issue in battery system operations, which may cause serious problems in power efficiency, equipment reliability and safety, etc. To analyze the performance of battery equalization systems, physical experiments with actual devices and computer simulations based on circuit models are typically used. These approaches, however, may be time-consuming and energy-inefficient for larger-scale systems. In this paper, based on the proposed mathematical model for series-connected battery equalization systems, we develop an analytical algorithm to approximate the state of charge (SOC) of battery cells at any time instant during the equalization process, and derive the formulas to calculate critical performance measures of the system. Extensive numerical experiments are carried out to justify the accuracy of the algorithm and formulas developed. In addition, the proposed methods use much less computational time as compared to computer simulations.