## 2 Proposed Preventive Control Strategy
### Step 3: Selection of Control Methods  
Step 3 is the selection of four parallel control methods. In this step, the system operators have to choose one of the four methods to improve the \(\mathbf{f_{\min}}\). The first one is the GR method. The operation of the GR method is illustrated in Figure 2. For the GR method, the generator re-dispatch or the start-up of additional diesel generator could ensure the sufficient frequency stability. System operators will re-dispatch the online diesel generators to share the same power generation output for each unit at first. If the predicted \(\mathbf{f_{\min}}\) is still below the predetermined threshold, then the preventive control system will be activated by starting another diesel unit and again re-dispatch the online diesel generators. The increase of spinning reserve by activating additional diesel unit certainly can improve frequency stability. This process of starting an additional diesel unit is continued until \(\mathbf{f_{\min}}\) is higher than the predetermined threshold. Then the next process is implemented to obtain the optimal online diesel generator dispatch with sufficient frequency stability and minimal operating cost. For the second stage of GR method, the economic dispatch, including the fuel cost and start-up cost of diesel generators, are considered. Each online diesel generator is re-dispatched according to its fuel-cost curve. If the predicted \(\mathbf{f_{\min}}\) is below the predetermined frequency threshold, then the \(\mathbf{P_{\max}}\) (MW) constraint on each online diesel generator will be updated, by limits the maximum power generation of each diesel generator to increase the overall spinning reserve. Finally, the optimal GR is obtained, which ensures both the sufficient frequency stability and minimal operating cost. The GR method is simple and efficient; however, its main disadvantages are the possible economic and environmental constraints of diesel generators. Therefore, the proposed control scheme further develops other methods by applying energy storage or demand management. The operation of the BESS method is depicted in Figure 3. In the developed BESS method, based on the simulation results and approximate method, it can establish the formulation relationship between \(\mathbf{f_{\min}}\) and the improved frequency nadir \(\mathbf{f_{\min,BESS}}\) (Hz) by BESS. The equation is shown as:  
\[\mathbf{f_{\min,BESS}}=\mathbf{f_{\min}}+\mathbf{k_{\text{BESS}}}\mathbf{P_{\text{BESS}}}, \tag{1}\]  
where \(\mathbf{P_{\text{BESS}}}\) (MW) is the active power output of the BESS; \(\mathbf{k_{\text{BESS}}}\) is the slope of linear regression of Equation (1). Different operating modes have different \(\mathbf{k_{\text{BESS}}}\) values and they are obtained throughout a trained neural network. The offline historical data were used to train the neural network; then the \(\mathbf{P_{\text{BESS,}\textit{opt}}}\) (MW) is determined, which ensures the sufficient frequency stability and minimal requirement of BESS. The frequency nadir is improved and should be higher than the predetermined frequency threshold of power system, which is achieved with the sufficient output capacity of BESS. Figure 3: The operation of the BESS method. Figure 2: The operation of the GR method. On the other hand, the operation of the DLC method is demonstrated in Figure 4. For the DLC method, based on the simulation results and approximate method, the formulation relationship between \(\mathbf{f_{\min}}\) and the improved frequency nadir \(\mathbf{f_{\min,DLC}}\) (Hz) by DLC has been established. The equation is shown as:  
\[\mathbf{f_{\min,DLC}}=\mathbf{f_{\min}}+\mathbf{k_{DLC}}\mathbf{P_{DLC}}, \tag{2}\]  
where the \(\mathbf{P_{DLC}}\) (MW) is the amount of the load shedding and \(\mathbf{k_{DLC}}\) is the slope of linear regression of Equation (2). Different operating modes have different \(\mathbf{k_{DLC}}\) values and they are obtained throughout a trained neural network.