Repurposed electric vehicle batteries (REVBs) which refer to the batteries retired from on-road electric vehicles (EVs), have huge potential to be reused in the distribution systems. The optimal configuration of REVBs is the key to the design of the distribution networks and the basis of optimal scheduling. However, the states of REVBs, such as state of health (SOH), state of charge, and remaining useful life (RUL), need to be monitored to avoid hazardous operations and lower the risk of system operation. Therefore, a stochastic degradation model is introduced to describe the capacity degradation, in which the random operation conditions are better reflected. Also, the impact of the optimal operation of REVB on the optimum REVB configuration is constructed in the lower-level, with the REVB configuration on the upper-level. Finally, case studies are conducted by different benchmarks to show the effectiveness and validation of the proposed bi-level model.