## 4 SOC Estimation Method
### EKF Method
Figure 12a,c show that the fuzzy fusion algorithm had a higher estimation accuracy when the initial SOC error was more accurate (\(|e_{SOC0}|<3\%\)). When \(e_{SOC0}\) was large, the fuzzy fusion algorithm had a larger estimation error than the other algorithms (Figure 12b). However, the initial SOC correction methods, such as the full-charge calibration method or the OCV method (e.g., with a 3 h rest for the LIBs), were used in the practical EV applications. Therefore, an accurate initial SOC could be ensured, improving the feasibility of the fuzzy fusion method for real EVs. Moreover, Figure 12c shows that the SOC estimation accuracy based on the MM-MA method was higher than that based on the 2 RC model, which validates the effectiveness of the proposed MM-MA method to improve the SOC estimation accuracy by improving the model accuracy. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case Name** & **Describe** & **Parameters Setting** \\ \hline Case A & The influence of initial SOC error (\(e_{SOC0}\)) & \(SOH=90\%\), \(I_{drift}=-0.1\)A, \(U_{drift}=5\) mV, \\  & on fuzzy algorithm & ECM\({}_{drift}=-3\) mV, \(e_{OCV}=5\) mV \\ Case B & The influence of model error (ECM\({}_{drift}\)) & \(e_{SOC0}=0.3\%\), SOH \(=95\%\), \(I_{drift}=-0.08\)A, \\  & on fuzzy algorithm & \(U_{drift}=5\) mV, \(e_{OCV}=-5\) mV; \\ Case C & The influence of voltage measurement & \(e_{SOC0}=0.3\%\), SOH \(=90\%\), \(I_{drift}=-0.1\)A, \\  & error (\(U_{drift}\)) on fuzzy algorithm & ECM\({}_{drift}=3\) mV, \(e_{OCV}=5\) mV \\ Case D & The influence of current measurement & \(e_{SOC0}=0.5\%\), SOH \(=95\%\), \(U_{drift}=-5\) mV, \\  & error (\(I_{drift}\)) on fuzzy algorithm & ECM\({}_{drift}=5\) mV, \(e_{OCV}=5\) mV \\ Case E & The influence of the SOH on fuzzy algorithm. & \(e_{SOC0}=0.3\%\), \(I_{drift}=-0.1\)A, \(U_{drift}=5\) mV, \\  & the algorithm. & ECM\({}_{drift}=5\) mV, \(e_{OCV}=5\) mV \\ Case F & The influence of SOC–OCV curve error & \(e_{SOC0}=0.3\%\), SOH \(=95\%\), \(I_{drift}=-0.1\)A, \\  & (\(e_{OCV}\)) on fuzzy algorithm. & ECM\({}_{drift}=-5\) mV\(U_{drift}=5\) mV \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Case and parameter setting. Figure 13 shows the SOC estimation results for Case B, including the relationship between the model error and the SOC error, for the three methods. Figure 13a shows that the SOC accuracy of the fuzzy fusion algorithm exceeded that of the EKF when the model error was large. As shown in Figure 13b, the SOC accuracy of the fuzzy fusion algorithm was lower than the EKF when the model error was very small. Figure 13c shows the relationship between the SOC errors based on three algorithms and model errors of ECM. It was obvious that the accuracy of the fuzzy fusion algorithm was higher than that of both the EKF and AH methods for most conditions, except when the model error was very small \(\left(\text{ECM}_{drift}<10\text{ mV}\right)\). However, even for a very small ECM\({}_{drift}\), the estimation accuracy of the fuzzy fusion algorithm was acceptable. Moreover, the accuracy of the SOC estimation based on the MM-MA method was better than that of the 2 RC model in the whole model error area. In actual EVs, battery aging and adverse environmental temperatures adversely affect the ECM's accurate reflection of the LIB characteristics, resulting in increased model error. From the above results, we can see that the proposed fuzzy fusion algorithm significantly outperformed the EKF and AH methods. Figure 14 compares the SOC estimation results of the three algorithms for Case C. Figure 14a,b show the SOC errors of the three algorithms with small and large voltage sensor error (\(U_{drift}\)). Figure 14c shows the relationship between SOC error based three algorithms and the \(U_{drift}\). It can be seen that the SOC estimation accuracy of the fuzzy fusion algorithm was better than that of the EKF method, except for very small \(U_{drift}\) values. Moreover, the superiority of the fuzzy fusion algorithm increased with the increase of \(U_{drift}\).