# 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 Using Adaptive Extended Kalman Filter
Since the value of the noise covariance matrix of the AEKF algorithm is updated according to the data input, the estimation performance of the data with the noise component is superior to that of the conventional EKF. Figure 10: Comparison of voltage estimation at noise voltage input. (**a**) Noise in input voltage data; (**b**) Comparison of voltage estimation of AEKF and EKF when noise data is input. Figure 12 shows the SOC estimation performance of the AEKF algorithm when noise is present in the FR test pattern. Figure 12a shows the noise added to the input current data. Figure 12b compares the SOC estimation performance of EKF and AEKF when these noise currents are input. The initial input SOC of the algorithm is set to 30% in order to confirm that the two algorithms can estimate the reference SOC well. Both algorithms quickly estimate the reference SOC, but it can be seen that the AEKF, which automatically updates the noise covariance matrix, estimates the SOC faster than the EKF. Figure 13 compares the Kalman gain of EKF and AEKF, which change during the SOC estimation process. As the value of the Kalman gain decreases, the algorithm outputs the result by weighting the value estimated by the algorithm rather than the measured value coming into the input. Since noisy data are input, the AEKF is closer to zero than the EKF, and the Kalman gain is lowered. As a result, the AEKF algorithm indicates that there is a lot of noise in the input data, and it can be confirmed that the AEKF algorithm depends more on the estimated value than on the measured value. Figure 11: Variation of noise covariance matrix during voltage estimation. (**a**) Change in noise covariance \(\mathrm{R_{adaptive}}\) of measured values; (**b**) Variation of noise covariance \(\mathrm{Q_{adaptive}}\) in progress equation. Figure 12: SOC estimation of the adaptive extended Kalman filter (AEKF) in a frequency regulation (FR) test pattern; (**a**) Noise generation from input current data; (**b**) SOC estimation comparison of EKF and AEKF. Figure 13: Comparison of Kalman gains for EKF and AEKF during SOC estimation. Figure 14 shows the voltage estimation performance of AEKF when severe noise occurs in voltage data in the FR test pattern. Figure 14a shows the severe noise generated randomly in the voltage data. Figure 14b shows the voltage estimation results of AEKF and EKF. When looking at the estimation result, the EKF estimation result is unstable in the form of noise, although it estimates the actual voltage. This is because the noise covariance of the EKF is used as a fixed value for extensive noise, and the AEKF with the updated noise covariance shows a relatively stable estimation result. Figure 15 shows a comparison of the Kalman gains that change during voltage estimation. The AEKF shows that the Kalman gain converges to near zero owing to the noise of the input data, greatly reducing the weight of the measured value with severe noise. However, because the Kalman gain of EKF has a specific gravity in the measured value relative to AEKF, the noise component of the measured value appears more in the estimated value. Figure 14: Voltage estimation of AEKF in FR test pattern. (**a**) Noise generation from input voltage data; (**b**) Comparison of voltage estimation for EKF and AEKF. In this section, it is verified that the EKF can accurately estimate the SOC and voltage, even in the test pattern of the FR ESS, and it is confirmed that the SOC estimation is excellent considering the noise, even when the noisy current data are input. Although the noise covariance matrices \(\mathbf{Q}\) and \(\mathbf{R}\) are used as fixed values in the EKF, the shape of the estimation result varies depending on how the values are set. On the other hand, the AEKF that automatically adjusts the noise covariance matrices \(\mathbf{Q}\) and \(\mathbf{R}\) by considering the noise generated from the input data within the algorithm shows excellent estimation performance for the input data, including noise, compared to the conventional EKF.