## 4 Simulation Tests
### System Contingency in Single Control Area  
In this subsection, the dynamic frequency performance of the proposed control strategy is investigated under the condition of the step disturbance in a single-area power system. The total capacity of regulation generators in Area 1 is 0.21 p.u. The initial SOCs of all the individual ACs is respectively set as [0.46,0.47,0.48,0.49,0.51,0.52,0.53,0.54]. A step disturbance of a load with 0.21 p.u. at 810s is predefined to emulate the system contingency. A comparison of three control strategies is present to clarify the superiority of the proposed control strategy. For the sake of clarity, the frequency control strategies for comparison are numbered as follows:  
1. Control strategy 1: Conventional secondary frequency control without ACs. 2. Control strategy 2: Secondary frequency control considering generators and ACs with a fixed distribution factor. 3. The proposed coordinated control strategy  
The system frequency responses under control strategy 1, control strategy 2 and the proposed control strategy are shown in Figure 4. Upon the occurrence of system contingency at 810s, there is an apparent tendency of the system frequency to decrease. Due to the inadequate capacity of the regulation generators, the control strategy without ACs has the inability to handle the frequency imbalance caused by step disturbance. Considering numerous ACs supplement the frequency control, frequency stability can be ensured by control strategy 2 and the proposed control strategy. In comparison with control strategy 2, it is observed that the frequency nadir is within the reasonable range (\(\pm\)0.2 Hz) in the proposed control strategy. \begin{table}
\begin{tabular}{c c c} \hline
**Area No.** & **1** & **2** \\ \hline \(D\) (p.u./Hz) & 0.0015 & 0.002 \\ \(2H\) (p.u./Hz) & 0.1667 & 0.2 \\ \(B\) (p.u./Hz) & 0.3483 & 0.2798 \\ \(R\) (Hz/p.u.) & 3 & 3.6 \\ \(T_{g}\) (s) & 0.08 & 0.075 \\ \(T_{c}\) (s) & 0.4 & 0.3 \\ \(T_{tie}\) (p.u./Hz) & 0.25 & 0.25 \\ \(K_{i}\) & 0.05 & 0.05 \\ \hline \end{tabular}
\end{table} 
Table 1: The parameters of a two-area power system. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \(Ra\) (\({}^{\circ}\)C/kW) & 2 \\ \(C\) (kWh/\({}^{\circ}\)C) & 2 \\ \(k_{p}\) (kW/Hz) & 0.114 \\ \(k_{q}\) (kW/Hz) & 0.03 \\ \(T_{out}\) (\({}^{\circ}\)C) & 21 \\ \(T_{min}\) (\({}^{\circ}\)C) & 20 \\ \(T_{max}\) (\({}^{\circ}\)C) & 22 \\ \hline \end{tabular}
\end{table} 
Table 2: The parameters of the inverter ACs. The power output of regulation generators and aggregated ACs under three control strategies are respectively shown in Figures 5 and 6. Under different control strategies, the available regulation capacities of generators are limited in various levels during the time integral [810s-820s]. Among three control strategies, the deficiency of adjustable capacity in control strategy 1 is relatively severe. Comparatively, the capacity deficiency in proposed control strategy is relatively negligible with the participation of individual ACs. Correspondingly, it is observed from Figure 6 that among three control strategies, a sufficient contingency reserve is provided in the proposed control strategy during the transient disturbance. Recall that the frequency performance in the proposed control strategy outperforms the other control strategies as shown in Figure 4. This is mainly attributed to the fact that a hierarchical frequency control scheme is utilized to maximize the available capacity of heterogeneous ACs and relieve the regulation stress of generators. Figure 4: The frequency response under different control schemes. Figure 5: The power output of regulation generators under different control schemes. The simulation results of Case 1 are shown as Table 3. Compared to the control strategy 1 and control strategy 2, the maximum of the frequency deviation in the proposed strategy is scaled down effectively. From the viewpoint of the energy efficiency, the energy saving in the proposed control strategy is 17.6% compared to the control strategy 1.