## 4 Case Study
The statistic simulation result obtained by the DFRL and conventional AGC algorithms is shown in Table 2 and Figure 11. Note that, in Table 2 and Figure 11, the frequency deviation \(\Delta f\) and ACE \(\epsilon_{\text{ACE}}\) are the average absolute values of all areas in all cases in the two-area power system, three-area power system, and four-area power system, respectively. Statistic simulation results (Table 2 and Figure 11) obtained by the DFRL and conventional AGC algorithms show that:  
1. The average absolute values of the frequency deviations obtained by DFRL are less than \(\Delta f_{2}\) (i.e., 0.1 Hz), while the average absolute values of the frequency deviations obtained by 10 conventional AGC algorithms may larger than 0.1 Hz in both Case 1 and Case 2 (Table 2); Therefore, the emergency situation of a large-scale interconnected power system and the curse of dimensionality can simultaneously be reduced by the proposed DFRL. 2. Compared to 10 conventional AGC algorithms, DFRL can obtain the highest control performance with a smaller absolute value of frequency deviation \(\Delta f\) and larger CPS index \(k_{\text{CPS}}\) (Figure 11). 3. Since the deep forest of DFRL can perform representation learning for the states of the power system, the preventive strategy for AGC can be considered effective for a large-scale interconnected power system. Figure 10: Next states of the three-area power system in Case 1. Figure 9: Convergence curves of frequency deviation, area control error (ACE), and control performance standard (CPS) of the training process of deep forest reinforcement learning (DFRL): (**a**) frequency deviation; (**b**) ACE; (**c**) CPS. Figure 11: Statistic simulation results: (**a**) two-area power system; (**b**) three-area power system; (**c**) _China Southern Power Grid_. \begin{table}
\begin{tabular}{l l r r r} \hline \hline
**Power Systems** & **Algorithms** & \(\Delta f\) **(Hz)** & \(\epsilon_{\text{ACE}}\) **(MW)** & \(k_{\text{CPS}}\) **(\%)** \\ \hline \multirow{8}{*}{Two-area} & PI & 0.063 & 27 & 84.82 \\  & PID & 0.050 & 22 & 90.23 \\  & SMC & 0.081 & 35 & 85.54 \\  & ADRC & 0.056 & 24 & 82.34 \\  & FOFID & 0.066 & 28 & 83.29 \\  & FLC & 0.079 & 34 & 91.40 \\  & ANN & 0.065 & 28 & 91.06 \\  & Q learning & 0.091 & 39 & 77.72 \\  & Q(\(\lambda\)) learning & 0.056 & 25 & 78.33 \\  & R(\(\lambda\)) learning & 0.044 & 19 & 82.14 \\  & DFRL & 0.002 & 1 & 99.48 \\ \hline \multirow{8}{*}{Three-area} & PI & 0.075 & 69 & 76.03 \\  & PID & 0.076 & 69 & 86.33 \\  & SMC & 0.184 & 192 & 67.24 \\  & ADRC & 0.095 & 65 & 78.66 \\  & FOPID & 0.188 & 209 & 78.78 \\  & FLC & 0.145 & 365 & 80.82 \\  & ANN & 0.133 & 88 & 83.87 \\  & Q learning & 0.091 & 83 & 81.41 \\  & Q(\(\lambda\)) learning & 0.076 & 128 & 88.13 \\  & R(\(\lambda\)) learning & 0.093 & 209 & 80.84 \\  & DFRL & 0.036 & 28 & 97.07 \\ \hline \multirow{8}{*}{_China Southern_} & PI & 0.072 & 237 & 80.43 \\  & PID & 0.049 & 203 & 82.49 \\  & SMC & 0.187 & 587 & 75.45 \\  & ADRC & 0.059 & 48 & 88.22 \\  & FOPID & 0.093 & 562 & 75.65 \\  & FLC & 0.084 & 568 & 75.62 \\ \multirow{2}{*}{_Power Grid_} & ANN & 0.093 & 242 & 79.65 \\  & Q learning & 0.114 & 384 & 79.03 \\  & Q(\(\lambda\)) learning & 0.111 & 443 & 77.23 \\  & R(\(\lambda\)) learning & 0.111 & 256 & 78.36 \\  & DFRL & 0.041 & 62 & 92.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistic simulation results.