## 4 SOC Estimation Method
### EKF Method
However, even for small \(U_{drift}\) values, the accuracy of the fuzzy fusion algorithm was within the acceptable range. Figure 12: SOC estimation results for Case A. (**a**) \(\varepsilon_{SOC0}=0.5\%\); (**b**) \(e_{SOC0}=5.0\%\); and (**c**) root-mean-square error (RMSE) of SOC in different initial SOC errors. Figure 15a depicts the relationship between the RMSE of SOC estimation and the error of the current sensor. We can see that the fuzzy fusion algorithm was better than others in considering the sensor error. Figure 15b shows the relationship between the RMSE of SOC estimation and the SOH. It is clear that the SOC estimation accuracy of the fuzzy fusion algorithm exceeded that of the EKF when the SOH fell from 100% to 80%. Thus, it is deduced that the Comb algorithm is highly adaptable to the capacity decay of an LIB. Figure 15c shows the RMSE of SOC estimation for \(e_{OCV}\) values of \(-100\) to 100 mV. We can see that the fuzzy fusion algorithm was better than the EKF when model and sensor errors were considered. When the current sensor error existed, the SOC obtained by the AH had a larger cumulative error. Therefore, our proposed method was better than that of the EKF and AH in cases D, E, and F.

Figure 14: SOC estimation results for Case C. (**a**) \(U_{drift}=3\) mV; (**b**) \(U_{drift}=50\) mV; and (**c**) RMSE of SOC in different drift voltages. Figure 13: SOC estimation results for Case B. (**a**) \(ECM_{drift}=50\) mV; (**b**) \(ECM_{drift}=-2\) mV; and (**c**) RMSE of SOC in different model errors. The above case study indicated that the EKF was slightly better than the fuzzy fusion algorithm under ideal conditions of no or very small model and sensor errors. However, the results of the fuzzy fusion algorithm were also within the acceptable range for these conditions. Under practical conditions involving significant model, sensor, and SOC-OCV curve errors, the fuzzy fusion algorithm significantly outperformed the EKF and AH. Moreover, the proposed MM-MA method not only improved the accuracy of the model, but also improved the accuracy of the SOC estimation. In an actual BMS, the computation time of the SOC estimation is as important as the estimation accuracy. The computation time of various SOC estimation algorithms was performed in MATLAB 2016a on a computer with INTEL Core i5-4440 CPU (3.1 GHz) and 8 GB RAM. Table 6 lists the calculation results under NEDC in the entire SOC area (0-100%). It is noted that the computation time was the time of SOC estimation in the entire SOC area (0-100%) using our proposed algorithm, based on the current and voltage curves obtained from experiments and the identified model parameters. It can be seen that the computation time of the fuzzy fusion algorithm was only slightly larger than the computation time of EKF. Therefore, the proposed algorithm greatly improved the estimation accuracy, without increasing the complexity, in the case of large model and sensor errors, and it was highly suitable for practical EV applications. Figure 15: RMSE of SOC for cases D, E, and F. (**a**) Case D: RMSE of SOC in different drift currents; (**b**) case E: RMSE of SOC in different SOHs; and (**c**) Case F: RMSE of SOC in different SOC–OCV curve errors. ## 6 Conclusions

In this study, nine ECMs and five commonly used model parameter identification algorithms were compared in the whole SOC area, and the most suitable ECM and matched parameter identification algorithm, in the high and low SOC area, were obtained, respectively. Based on this, a MM-MA method was proposed. To improve the robustness and accuracy of SOC estimation based on MM-MA in practical application, a fuzzy fusion SOC estimation algorithm based on EKF and AH was proposed. The experimental results show that the satisfactory estimation accuracy can still be maintained even when large model errors and sensor errors exist, and that the accuracy and robustness of the fuzzy fusion algorithm is better than that of EKF and AH.