## 3 Design of the Enhanced Dynamic Regulation Reserve Controller
### The Control Strategy of Enhanced Dynamic Regulation (E-dReg)
#### 3.2.3 Charging/Discharging Control Computation  
The E-dReg adds the function of energy transfer on top of the frequency regulation action in dynamic frequency regulation. Therefore, the charging/discharging control calculation of the E-dReg control strategy in this paper is developed and designed based on the technical specifications of dReg0.5. Taking 60.00 Hz as the frequency reference for frequency movement, Table 2 provides a corresponding comparison between the charging/discharging calculation and the output setting values. The control strategy will calculate the charging/discharging control quantity based on the current grid frequency and SOC status, selecting different slope curves for computation. The calculation of the charging/discharging control quantity will be performed using the slope-intercept form to determine the slope and intercept of the curve, as shown in Equation (4). Here, \(P_{out}\) represents the output power, \(m\) represents the slope, \(f_{now}\) represents the current frequency, and \(a\) is a constant representing the intercept of the power axis. \[P_{out}=m(f_{now}-60)+a \tag{4}\]  
When not within the time frame of the energy transfer schedule or without receiving an emergency dispatch directive, the charging/discharging actions of the enhanced dynamic frequency regulation reserve are the same as dynamic frequency regulation, involving only the execution of frequency regulation actions. However, during the energy transfer schedule or upon receiving an emergency dispatch directive, the charging/discharging control quantity at that moment is the sum of the frequency regulation control quantity and the scheduled energy transfer amount, as expressed in Equation (5). Here, \(P_{load\ shift}^{Target}\) represents the dReg0.5 execution capacity for that second, and \(P_{load\ shift}^{Target}\) represents the scheduled energy transfer amount for that second. \[P_{out}=P_{dReg0.5}^{Target}+P_{load\ shift}^{Target} \tag{5}\]  
When dynamic frequency regulation actions and energy transfer are executed simultaneously, a conditional check needs to be added before the output, as shown in Equation (6). \begin{table}
\begin{tabular}{c c c c c}  & **System Frequency** & **Corresponding** & **Power Ratio (\%)** & **Corresponding** \\  & **(Hz)** & **Symbol** & **Power Ratio (\%)** & **Symbol** \\ \hline Full output/input response frequency & 59.50 & \(f_{1}\) & 100 & \(P_{1}\) \\ \hline First response frequency & 59.75 & \(f_{2}\) & 48 & \(P_{2}\) \\ \hline Flexible adjustment range & 59.98 & \(f_{3}\) & 9 & \(P_{3}\) \\ \hline Flexible adjustment range & 60.02 & \(f_{4}\) & \(-9\) & \(P_{4}\) \\ \hline First response frequency & 60.25 & \(f_{5}\) & \(-48\) & \(P_{5}\) \\ \hline Full output/input response frequency & 60.50 & \(f_{6}\) & \(-100\) & \(P_{6}\) \\ \hline \end{tabular}
\end{table} 
Table 2: dReg0.5 charge and discharge calculation corresponding to the output set value. The purpose of this check is to avoid exceeding the daily awarded capacity when the execution capacity of frequency regulation actions is added to the scheduled energy transfer amount. If the sum of both exceeds the daily awarded capacity, the output is limited to the daily awarded capacity to ensure the safe operation of the system. Moreover, assuming a frequency reference of 60.00 Hz, if the current system frequency is below 59.50 Hz or above 60.50 Hz and there is an ongoing energy transfer scheduling action, the action needs to be paused for 900 s and directly switched to dReg0.5 mode. The energy transfer action can only resume after a 900 s delay, as shown in Equation (7). Here, \(P_{Capacity}\) represents the awarded capacity for that hour. \[P_{out}=\left\{ \begin{aligned} & P_{Capacity},\ if\ P_{Capacity}<P_{dReg0.5}^{Target}+P_{load\ shift}^{Target}\\ & P_{dReg0.5}^{Target}+P_{load\ shift}^{Target},\ Else\end{aligned} \right. \tag{6}\]  
\[P_{out}=\left\{ \begin{aligned} & P_{Capacity},\ if\ f_{ now}<59.50 Hz\\ &-P_{Capacity},\ if\ 60.50 Hz<f_{now}\\ & P_{dReg0.5}^{Target}+P_{load\ shift}^{Target},\ Else\end{aligned}