## 6 Conclusions  
The existing retired power battery capacity degradation model makes it difficult to consider the impact of various cycle conditions on battery capacity degradation, especially because there are few studies on retired power battery capacity degradation models involving different \(\Delta\)SOCs. In addition, due to the long and costly cycle tests of retired batteries, test data for different \(\Delta\)SOCs are very limited. In view of the inadequacies and data limitations of existing studies, this paper puts forward three semi-empirical modeling methods to obtain the law of capacity degradation of retired batteries under various working conditions. The above content verifies the feasibility and accuracy of the proposed methods in this paper and then summarizes the practical applicability of the three methods according to the advantages and disadvantages of their respective case studies. 1. The method based on model interval number similarity is suitable for situations where the known test data contain limited \(\Delta SOC\) but the coverage of unknown \(\Delta SOC\) is relatively comprehensive. In detail, the \(\Delta SOC\) of the known data contains two types of measured data, the same average SOC but different DODs and the same can ensure that the capacity degradation of retired batteries can be predicted within a reasonable range under the circumstances of very limited data. Therefore, in practical application scenarios, this method is suitable for a preliminary assessment of the capacity degradation of retired batteries with unknown \(\Delta SOC\);
2. The method based on parameter interval number similarity is suitable for situations where the known test data contain limited \(\Delta SOC\) and the coverage of the unknown \(\Delta SOC\) is not comprehensive enough. In detail, the \(\Delta SOC\) of the known data contains two types of measured data, the same average SOC but different DODs and the same DOD but different average SOCs. This method has good accuracy and can predict the capacity degradation of retired batteries under various cycle conditions. Therefore, in practical application scenarios, this method is suitable for further evaluation of the capacity degradation of retired batteries with unknown \(\Delta SOC\) and for estimating the capacity decline of retired batteries under other cycle conditions in the same \(\Delta SOC\);
3. The improved semi-empirical modeling method based on the least square fitting method is suitable for situations where the \(\Delta SOC\) contained in the known test data is relatively comprehensive. In detail, the \(\Delta SOC\) of known data would contain both the same average SOC but different DODs and the same DOD but different average SOCs. This method has the highest accuracy and can accurately predict the capacity decline of retired batteries under various cycle conditions. Therefore, in the actual application scenario, this method is suitable for the accurate assessment of the capacity decline of retired batteries in an unknown \(\Delta SOC\) and has great significance for the cascade utilization analysis of retired batteries. Conceptualization, W.X. and J.T. ; methodology, W.X., H.C., and J.T. ; software, W.X. ; validation, W.X. and H.C.; formal analysis, W.X. and X.L. ; investigation, H.C. and F.S. ; resources, X.L. ; data curation, J.W. and J.D. ; writing--original draft preparation, W.X. and H.C.; writing--review and editing, X.L. and J.T. ; visualization, J.W. and J.D. ; supervision, J.T. ; project administration, J.T. ; funding acquisition, F.S. and J.D. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by Science and Technology Project of State Grid Corporation of China, \"Research on key technologies for risk assessment of inter-provincial power spot market considering uncertainty of power supply and load\" (Project No. : 5108-202355047A-1-1-ZN). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.