## 3 Design of the Enhanced Dynamic Regulation Reserve Controller
### The Control Strategy of Enhanced Dynamic Regulation (E-dReg)
#### 3.2.2 State-of-Charge (SOC) Limitations of Battery Energy Storage System  
To safeguard the battery energy storage system from situations where the SOC becomes excessively high or low due to prolonged charging or discharging, the proposed dynamic frequency regulation control strategy in this paper dynamically adjusts the output curve selection based on the current SOC of the energy storage system. This real-time scheduling helps prevent overcharging or over-discharging, thereby extending the lifespan of the battery energy storage system. When the frequency of the power system is higher, the energy storage system must be charged to stabilize frequency (absorbing power from the power system), and the SOC may reach \(SOC_{max}\). On the contrary, when the frequency of the power system is lower, the energy storage system must discharge (supplying power to the power system) to stabilize the frequency, and the SOC may reach \(SOC_{min}\). In this paper, upper and lower limits have been imposed on the SOC to ensure that the charging and discharging actions of the energy storage system always operate within a safe range, as represented by Equation (1). Here, \(P_{out}\) denotes the output power, \(SOC_{max}\) represents the current SOC of the energy storage  
Figure 8: Flow chart of enhanced dynamic regulation (E-dReg) control. system, \(SOC_{max}\) denotes the upper limit set for the SOC, and \(SOC_{min}\) denotes the lower limit set for the \(SOC\). \[\left\{ \begin{aligned} P_{out}\geq 0,\ if\ SOC_{now}\geq SOC_{ max}\\ P_{out}\leq 0,\ if\ SOC_{now}\leq SOC_{min}\\ P_{out},\ Else\end{aligned} \right. \tag{1}\]  
In addition to the basic upper and lower limits imposed on the \(SOC\) to protect the energy storage system, the SOC control strategy in the E-dReg control strategy is defined within the range of 85% \(\pm\) 2.5%. The program will assess the current SOC state and choose the most appropriate output/input power ratio slope curve. If the current SOC state is higher, it will select a slope range with a higher output and a lower input; conversely, if the SOC state is lower, it will choose a slope range with a higher input and a lower output. The selection of the output slope for each SOC range is illustrated in Figure 9. Additionally, two new limiting conditions have been added for SOC during the execution of the energy transfer schedule for charging and discharging actions. The limiting conditions for charging and discharging protection are expressed in Equations (2) and (3). When the SOC is less than or equal to 82.5%, the slope for output calculation is determined based on the green segment. For SOC falling within the range of greater than 82.5% but not exceeding 87.5%, the slope for output calculation is based on the red segment. Finally, when the SOC exceeds 87.5%, the slope for output calculation is determined based on the blue segment. \[P_{out}=\left\{ \begin{aligned} 0,\ if\ 0.85\leq SOC_{now}\\ 0,\ if\ 0.8\leq SOC_{now}\leq 0.85\\ P_{load\ shift}^{Target},\ if\ SOC_{now}<0.8\end{aligned} \right. \tag{2}\]  
The inclusion of the charging protection limiting condition is designed to protect against and prevent the controller from repeatedly initiating charging actions at the edge of the target SOC value during the charging schedule period. When executing the charging schedule, if the SOC reaches 85%, the charging action will be stopped. It will only be allowed to resume when the SOC drops below 80%. Here, \(P_{load\ shift}^{Target}\) represents the scheduled amount of energy transfer for that second. \[P_{out}=\left\{ \begin{aligned} 0,\ if\ SOC_{now}\leq 0.1\\ 0,\ if\ 0.1\leq SOC_{now}\leq 0.15\\ P_{load\ shift}^{Target},\ if\ 0.15< SOC_{now}\end{aligned} \right. \tag{3}\]  
Figure 9: Control strategy curve of dynamic frequency regulation considering SOC. The discharge protection limiting condition is designed to protect against and prevent the controller from repeatedly initiating discharge actions at the edge of the target SOC value during the discharge schedule period.