# 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  
When the ESS is operated for frequency regulation in the grid, it is very economical. Korea Electric Power Corporation, Korea's only utility for grid operation, is operating a 376 MW as frequency regulation ESS. The frequency changes continuously for a very short time, and in order to maintain this, the ESS is charged and discharged very frequently. It is very difficult to accurately estimate the SOC in such a complex pattern, and it is necessary to find an SOC estimation method that can accurately estimate the SOC of the FR pattern. In this section, the FR algorithm is designed and the power pattern is analyzed for the SOC estimation study. Design of FR algorithm and EKF algorithm was carried out through MATLAB coding, and patterns generated using waveform transform function of MACCOR series 4000 equipment were tested on the battery. The FR ESS monitors the frequency of the system and is sensitive to changes in frequency. Figure 1 shows the operation algorithm of the FR ESS. When the frequency of the system is normal, the FR ESS operates at steady state to maintain the 60 Hz reference frequency of the system in South Korea [2; 9]. A dead frequency band is set and, when the frequency of the system is outside of this range, the ESS is operated to maintain the frequency of the system at 60 Hz. When the grid frequency is in the dead band, the dead band of the SOC required to maintain the SOC is determined, and the suitable operation is performed to maintain the SOC within the operating range. In the event of an accident in which a plant trips, the frequency of the grid system will drop significantly. At this time, an operation of the transient state is performed using the rated power of ESS to recover the frequency. The speed regulation rate (droop) for determining the sensitivity of the ESS power to the frequency change is set differently for the steady state and transient state [2]. When the frequency is recovered after the transient state, the ESS is controlled to return to the steady state. The grid system in South Korea is very stable, and it is rare to experience the transient state in which a plant trips or where the frequency changes rapidly. Therefore, the test pattern for the frequency regulation experiment used in this paper was generated by inputting the frequency when the ESS operates in steady state. Figure 1: Operation algorithm of frequency regulation ESS. The operator of the ESS decides the _Droop_ coefficient to determine how sensitive the ESS will output according to the frequency state. The _Droop_ coefficient can be expressed using Equation (1) below. \[Droop=\frac{\Delta f/f_{\text{ref}}}{\Delta P/P_{\text{rated}}}. \tag{1}\]  
In the above equation, \(f_{\text{ref}}\) is the reference frequency (60 Hz) and \(P_{\text{rated}}\) is the maximum power that the ESS can output. The value \(\Delta f\) is the difference between the reference frequency \(f_{\text{ref}}\) and the current system frequency f. The values \(f_{\text{ref}}\) and \(P_{\text{rated}}\) are the values already known by the user in the process of constructing the ESS, and when the _droop_ coefficient is determined, the proportional coefficient \(K_{\text{d}}\) for calculating the power of the ESS can be calculated by applying the _Droop_ coefficient as follows:  
\[K_{\text{d}}=\frac{\Delta P}{\Delta f}\quad[W/Hz]. \tag{2}\]  
If the proportional coefficient \(K_{\text{d}}\) is determined, the power of the ESS when the frequency is input can be calculated using Equation (3)  
\[P_{\text{ESS}}=K_{\text{d}}\cdot\Delta f\quad[W]. \tag{3}\]  
\(P_{\text{ESS}}\) is the power of the ESS when the frequency is input, and is calculated by multiplying the difference between the reference frequency \(f_{\text{ref}}\) and the incoming system frequency f by \(K_{\text{d}}\). If the frequency deviates from the dead band during steady-state operation, the power of the ESS is calculated in the above equation.