# Research of Adaptive Extended Kalman Filter-Based SOC Estimator for Frequency Regulation ESS
## 2 Design of Operation Algorithm for FR ESS and Power Characteristics Analysis
### Operation Algorithm Design of Frequency Regulation ESS
If the frequency is in the dead band and the SOC is out of the dead band of the SOC, the ESS will charge or discharge a power of 10% (SOC 50-63%, SOC 67-80%) or 15% (SOC 0-50%, SOC 80-100%). The dead frequency band was set to \(\pm\)0.03 Hz based on 60 Hz and the dead band of the SOC was set to \(\pm\)2%. The droop coefficient in steady state was set to 0.00279 in order to calculate the ESS power [2]. Figure 2 shows the test pattern of the FR ESS, which was generated by inputting the frequency of the day when the ESS usage was closest to the annual average (normal pattern) and the frequency of the day when the ESS was used heavily (severe pattern), and the results show the experiment performance after applying the test pattern to the battery. The FR pattern of the ESS was generated based on a nickel cobalt manganese battery that has a 20 Ah capacity, and the frequency for one day was set to the test frequency. The algorithm performs power control and applies to the battery the output power obtained as a result of the algorithm. The SOC is calculated by integrating the power, and it can be seen that the pattern operates based on SOC 65%. Table 1 shows the default value of the frequency regulation algorithm used to generate the test patterns in Figure 2.  
Figure 2: _Cont._  
Table 2 compares the result of normal and severe patterns. In the case of the normal pattern, the battery is charged and discharged about 1.57 times per day based on the nominal energy of the battery, and for the severe pattern, it is charged and discharged 3.38 times a day. When the input frequency was 60.03 Hz or higher, the battery charged energy for the frequency regulation was 96.07 Wh in the normal pattern. When the input frequency was 59.97 Hz or less, the energy discharged was 23.40 Wh. In the severe pattern, a frequency of 60.03 Hz or more was reached, and the energy charged by the battery for frequency regulation was 185.76 Wh, which was about 1.9 times higher than in the normal pattern. The energy discharged when the input frequency was below 59.97 Hz was 135.00 Wh, which was about 5.7 times higher than the normal pattern. In the normal pattern, the SOC was less than 63%, and the energy charged for the SOC recovery was 18.62 Wh. When the SOC of battery was 67% or more, the energy discharged was 91.61 Wh. In the severe pattern, the SOC was less than 63%, and the charged energy to recover the SOC was 60.99 Wh, which was about 3.2 times more than the value in the normal pattern. The energy discharged by a SOC of 67% or more was 111.93 Wh, and 1.2 times more energy was discharged compared with the normal pattern. In the case of the normal pattern, the charge operation was performed more often than the discharge operation and, because of the large amount of charge, the operation was performed to discharge the battery to recover the SOC. The maximum power in the test pattern is 147.57 W for the normal pattern and 98.21 W for the discharge. In the severe pattern, 170.94 W is the maximum charge power and 158.73 W is the maximum discharge power. The average C-rate of the battery during charging in the normal pattern is 0.79 and the average C-rate during discharging is 0.45. The average C-rate observed during charging in the severe pattern is 0.68 and average discharge C-rate is 0.59. The normal pattern showed a maximum frequency of \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Reference Frequency (Hz) & 60 \\ Dead Band (Hz) & \(\pm\)0.03 \\ Center SOC (\%) & 65 \\ SOC Operation Range (\%) & \(\pm\)2 \\ Rated Power (W) & 292 \\ Nominal Energy (Wh) & 73 \\ SOC Recovery Power “\(50<\) SOC \(<80^{\circ}\) (\%) & 10\% (of rated power) \\ SOC Recovery Power “SOC \(<50,80<\) SOC” (\%) & 15\% (of rated power) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Default set value for analysis of frequency regulation algorithm. Figure 2: Operation result of energy-storage system (ESS) for frequency regulation.