## 4 Experiment Environment
### Case 2: Comparative Analysis of Frequency Control Effects of Different Methods under DoS Attacks
As shown in Figure 14a, the maximum frequency deviation of the bus is about 0.13 Hz, and all the buses enter a stable state at \(t=3\) s. As shown in Figure 14b, the maximum frequency deviation of the bus is about 0.14 Hz, and each bus can maintain a stable state after \(t=3.5\) s. As shown in Figure 14c, the maximum frequency deviation of the bus is about 0.24 Hz, and all the buses enter a stable state after \(t=7\) s.  
As shown in Figure 15a, the maximum frequency deviation of the bus is about 0.14 Hz, and each bus can gradually maintain a stable state at \(t=3.5\) s. As shown in Figure 15b, the maximum frequency deviation of the bus is about 0.14 Hz. The frequency deviations enter the stable interval around \(t=4\) s and fluctuate within the stable interval. As shown in Figure 15c, the maximum frequency deviation of the bus is about 0.21 Hz, and its final state is in an oscillating state, which fluctuates outside the set error band. According to the above experimental results, when the intensity of DoS attacks is small, all three methods can adjust the frequency deviation of power grids to a stable range. Additionally, the frequency control strategies based on convex neural networks and RBF have a slightly shorter stabilization time than the frequency control strategy based on RNN. When the intensity of DoS attacks is high, the proposed control strategy can maintain the frequency deviation within a small range of fluctuations, thereby effectively suppressing the impact of DoS attacks and load change disturbances, while the other two methods are slightly worse. Therefore, this group of experiments verifies that the proposed frequency control strategy based on convex neural networks can accelerate the convergence speed in the control process and improve the performance of the controller. The initialization of vectors \(\mathbf{w}_{a,i}\) and \(\mathbf{w}_{c,i}\) satisfies Assumption 2, and the simulation time is 8 s. The experimental results are shown in Figure 16. This paper simulates the control process of all buses in the IEEE118 bus testing system under the proposed frequency control strategy. However, the IEEE118 bus testing system has a large number of buses; therefore, the frequency deviation data of 20 buses was selected to analyze the control performance as shown in Figure 16a-d.  
As shown in Figure 16, the maximum frequency deviation is generated on bus 1, which is about 0.13 Hz. All buses can maintain a stable state after 3.5 s. Since the load is constantly changing, after the frequency deviation is in the stable range, there is still a certain degree of fluctuations during the time period from \(t=3.5\) s to \(t=8\) s.  
According to the experimental results, the IEEE118 bus testing system verifies that the proposed frequency control strategy can be applied to the frequency control process  
Figure 16: Frequency deviation curve of the IEEE118 bus testing system under the controller, \(\eta_{ji}=0.2\). (a) Frequency deviation curves of bus 1, 6, 11, 16, and 21. (b) Frequency deviation curves of bus 26, 31, 36, 41, and 46. (c) Frequency deviation curves of bus 51, 56, 71, 76, and 81. (d) Frequency deviation curves of bus 86, 91, 96, 101, and 106.