# Research of Adaptive Extended Kalman Filter-Based SOC Estimator for Frequency Regulation ESS
## 3 Performance Verification of SOC Estimation Using Adaptive Extended Kalman Filter
### SOC Estimation of Frequency Regulation ESS Using Extended Kalman Filter  
Assuming that there is no error in the current sensor, SOC estimation using the Coulomb counting method can exhibit a reliable estimation performance. However, all current sensors have minimum error values, and the more expensive and superior the sensor, the smaller the error. Hundreds or thousands of batteries are used in ESSs that operate with high voltage and high current, and the environment is one in which severe noise interference can easily be found in the sensor data. The noise was added as user-defined to the voltage and current data measured by the test equipment to represent the actual noise in the field. At this time, the accuracy of the SOC estimation performance using the Coulomb counting method can be greatly degraded by noise. As the SOC affects the battery stability and cycle life, an accurate SOC estimation is necessary.  
In this study, extensive noise was added to the current of the FR test pattern shown in Section 2.1, and the results are presented in this section. In this way, it is verified that the algorithm can estimate the SOC correctly when noisy current data are input to the EKF algorithm. Figure 6 shows the FR test pattern with added noise, and it can be seen that severe noise is generated in the existing current data. When the noise-containing current is input to the algorithm, the SOC estimation result of the algorithm can be seen in Figure 7, and the SOC calculated by the Coulomb counting method with the noise-free current is used as the reference SOC. The SOC estimation result shows that the SOC calculated by the Coulomb counting method with the noise current is different from the reference SOC, whereas the SOC estimated using the EKF algorithm estimates the reference SOC well.  
Figure 6: Noise current generated in the test pattern of FR ESS.  
Figure 7: _Cont._Again, the initial SOC given as the input of the algorithm was 30%, and it was confirmed whether the reference SOC was well estimated even if the initial SOC was different. Although the initial estimation error of the EKF appears to be more than 30%, owing to the initial SOC error, it can be seen that an SOC estimation error of within 3% in the FR test pattern is immediately obtained by the EKF algorithm. The SOC calculation using the Coulomb counting method may show that the error is reduced or is largely generated depending on the shape of the noise. With the Coulomb counting method, for which the error cannot be corrected by the open-loop method, the noise of the current is represented as the error of the SOC, which causes an incorrect SOC calculation. However, the EKF exhibits a high estimation performance because it estimates the SOC considering noise based on the measured voltage even when the noise current is input.  
Figure 8 compares the voltage estimation when noise-free current is input to the EKF, and the voltage estimation when noisy current is input to the algorithm. Both results confirm that the measured voltage is well estimated. No noise was added to the voltage measurement data, and only noise was present in the current, so there was no significant effect on the voltage estimation.  
Figure 8: Comparison of voltage estimation results in test patterns of FR ESS (EKF vs. EKF that inputs noise current).  
Figure 7: SOC estimation in test pattern of FR ESS. (**a**) SOC estimation in test pattern of FR ESS using EKF; (**b**) Comparison of SOC estimation errors of EKF and Coulomb counting methods.