## 4 Case Study
Both the DFRL and the conventional AGC algorithms were simulated for three power systems, i.e., IEEE two-area power system, three-area power system, and the _China Southern Power Grid_ (Figure 7). The parameters of these conventional AGC algorithms are given in Appendix A. These parameters were obtained by genetic algorithm with a simple configuration, i.e., the population size was set to 100, and the maximum number of generations was set to 100. Both conventional AGC algorithms and the proposed DFRL-based controller were applied to 'Area A' in these three power systems. The _China Southern Power Grid_ contains four areas of China, i.e., 'Area A' for the _Guangdong_ Power Grid, 'Area B' for the _Guangxi_ Power Grid, 'Area C' for the _Guizhou_ Power Grid, and 'Area D' for the _Yunnan_ Power Grid [37]. In these three power systems: each control area contains a governor \(1/(1+sT_{\text{g}})\), a generator \(1/(1+sT_{\text{t}})\), and a frequency response model \(K_{\text{p}}/(1+sT_{\text{p}})\); the frequency response coefficient and the droop coefficient are \(B_{i}\) and \(R_{i}\), respectively. Thus, the mathematical model of each generation unit can be described as follows. \[G_{\text{unit}}=\frac{1}{(1+sT_{\text{g}})}\frac{1}{(1+sT_{\text{t}})} \tag{16}\]  
where \(T_{\text{g}}\) and \(T_{\text{t}}\) are the time constants of the governor and generator of each control area, respectively. Also, the generation rate constraint \(k_{\text{GRC}}^{i}\) and adjustable capacity constraint \(P_{\text{max}}^{i}\) are included in the real _China Southern Power Grid_ model. In these three power systems, the \(i\)th area is connected to the \(j\)th area with the alternating current tie-line response model \(2\pi T_{ij}/s\). The parameters of these three power systems are given in Appendix B, Appendix C and Appendix D, respectively. Two large continuous disturbances were designed for these power systems, i.e., 'Case 1' and 'Case 2' (Figure 8). These two large continuous disturbances may lead to the occurrence of emergency situations: (i) A  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Pow.a** & **Stat.b** & **Value** \\ \hline All & StaI.d & \(\left\{\begin{array}{l}\Delta f:(-0.10,-0.08,-0.06,-0.04,-0.02,0.00,0.02,0.04,0.06,0 0.08,0.10)\text{ Hz }\\ k_{\text{CTS}}:(95,96,97,98,99,99,59,99,98,97,96,95)  
large disturbance in the continuous coverage of all active power values represents the system load value space, as designed for 'Case 1'. (ii) Since the power systems are delay systems, a large system load with delay was designed ('Case 2'). The control periods of the algorithms in all cases were set to 4 s, i.e., these algorithms were executed once every 4 s. The number of iterations of the training process of DFRL was set to 300 (Figure 9). Simulation results show that the proposed DFRL method can obtain the best control performance with the smallest frequency deviation. The major reasons for this superior control performance are that: (i) the next state of a power system can be predicted by DFRL, such as the next states of the three-area power system in 'Case 1' (Figure 10); (ii) \(\Delta f\) obtained by conventional Q learning may be larger than 0.03 Hz (Figure 10) when the next state of a power system lacks prediction. The calculation memory of Q learning is 17,688 Bytes, while that of DFRL is 6072 Bytes. Thus, compared to Q learning, the calculation memory of DFRL is reduced by 34.328% in these simulations. The training time for the deep forest of the DFRL algorithm is 35.14 min. The training time for the ANN, Q learning, Q(\(\lambda\)) learning, and R(\(\lambda\)) learning algorithms is less then 10 min. Figure 8: Curves of large continuous disturbances: (**a**) two-area power system; (**b**) three-area power system; and _China Southern Power Grid_. Figure 7: Topological graph of the three power systems: (**a**) Two-area power system; (**b**) Three-area power system; (**c**) _China Southern Power Grid_.