Evolution of Discharge DC Internal Resistance and Its Association with Capacity Degradation in a Vanadium Redox Flow Battery During Long-Term Cycling

Long-term degradation of vanadium redox flow batteries (VRFBs) is strongly coupled with the evolution of discharge direct current internal resistance (DCIR). This work employs 213 constant-current cycles on a 4 cm2 single cell to examine the associations between discharge DCIR and capacity, discharge voltage and efficiencies. The average values of the initial 10 cycles were used as the baseline. Multiple statistical approaches, including detrending, differencing, moving-block bootstrap, and internal chronological holdout evaluation were used to assess the influence of shared temporal trends and serial dependence. Self-calculated DCIR matches test records closely with merely 1.03% average relative error. After trend correction, normalized DCIR maintains a strong negative correlation with normalized capacity. The established free-intercept quadratic model achieved the best full-data fitting performance, with an R2 of 0.99593 and a root mean square error (RMSE) of 0.00524. The fitted empirical relationship indicates that equal increments in normalized DCIR are associated with larger concurrent capacity-state reductions in the higher-resistance region. During the internal chronological holdout evaluation, the DCIR-based model yielded an RMSE of 0.00854. These results establish a statistically robust DCIR–capacity relationship over long-term cycling and demonstrate the potential of routinely recorded discharge DCIR as a low-cost concurrent capacity-state indicator, providing a quantitative foundation for its future extension to broader VRFB operating scenarios.