## 4 Case Simulation and Result Analysis
### Voltage Transient Droop Signal Detection Experiment  
In order to verify the applicability of the accelerated stochastic resonance for other categories of power system periodic characteristic signals in strong noise environments, the voltage-dropout signal is used as the simulated fault signal, and the input simulated fault signal is  
\[s(t)=\left(1-v(u(t_{2})-u(t_{1}))\right)\sin(2\pi f_{0}t) \tag{46}\]  
In the formula, \(v=0.8\); \(f_{0}=50\) Hz; \(u(t_{1})\) and \(u(t_{2})\) are the step signals generating sudden changes at the moments of \(t_{1}\) and \(t_{2}\), respectively; \(t_{1}=0.13\); and \(t_{2}=0.07\). Gaussian white noise \(n(t)\) with a noise intensity \(D\) of \(1\) is mixed in, the sampling frequency is \(f_{s}=2000\) Hz, and the number of sampling points is \(L=5000\), so as to obtain the noise-containing voltage-dropout fault signal. Setting the system parameters \(a=1.5\), \(b=1\), \(c=2\), the fourth-order Runge-Kutta algorithm is utilized to calculate the Langevin equation, the waveforms and spectra of the voltage-dropout signals are shown in Figure 19, and the experimental results are shown in Figures 20-22. The purpose of the detection of the voltage transient signal is to determine the voltage transient and voltage recovery moments, so the output signal-to-noise ratio cannot be used as a separate evaluation index to measure the performance of the algorithm [23]; therefore, the number of interrelationships between the input and output signals is introduced as an evaluation index, which is used to measure the phase-matching relationship between the output signal of the stochastic resonance and the original input signal, and the number of interrelationships between input and output signals \(\rho_{SX}\) expression is as follows:  
\[\left\{ \begin{array}{l}R_{SX}(\tau)=\int_{-\infty}^{+\infty}\left[s(t)+n(t) \right]\cdot x(t+\tau)dt\\ \\ \rho_{SX}=\frac{R_{SX}(\tau)}{\sqrt{R_{S}(0)\cdot R_{X}(0)}}\end{array} \right. \tag{47}\]  
where \(R_{S}\) and \(R_{X}\) are the autocorrelation coefficients of the input and output signals of the stochastic resonance system, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(f\)**/Hz** & **SR** & **UBSR** & **ASR** \\ \hline \multirow{4}{*}{(a) \(D=1\)} & 50 & 50 & 50 & 50 \\  & 110 & 110 & 110 & 110 \\  & 150 & 150 & 150 & 150 \\  & 250 & 250 & 250 & 250 \\  & 350 & 350 & 350 & 350 \\ \hline \multirow{4}{*}{(b) \(D=5\)} & 50 & 50 & 50 & 50 \\  & 110 & 110 & 110 & 110 \\  & 150 & 150 & 150 & 150 \\  & 250 & 250 & 250 & 250 \\  & 350 & 350 & 350 & 350 \\ \hline \end{tabular}
\end{table} 
Table 1: Harmonic frequency detection results of three stochastic resonance systems. (a) \(D=1\). (b) \(D=5\). Figure 19: Input noise-containing voltage drop signal waveform and spectrum at \(D=1\). (**a**) Time domain waveform. (**b**) Spectral amplitude. Figure 20: SR detection system output signal waveform and spectrum at \(D=1\). (**a**) Time domain waveform. (**b**) Spectral amplitude. Comparing Figure 19 with Figures 20-22, it can be seen that all three stochastic resonance detection models can realize the conversion of noise energy to signal energy, which in turn suppresses the noise and improves the signal-to-noise ratio. Comparing the output signals of Figures 20-22, it can be seen that under low-intensity noise interference, the non-saturated stochastic resonance improves the amplitude of the system output and has the highest output signal-to-noise ratio, while the classical stochastic resonance system has the middle output signal-to-noise ratio, and the accelerated stochastic resonance system has the middle output signal-to-noise ratio. Figure 21: UBSR detection system output signal waveform and spectrum at \(D=1\). (**a**) Time domain waveform. (**b**) Spectral amplitude. Figure 22: ASR detection system output signal waveform and spectrum at \(D=1\). (**a**) Time domain waveform. (**b**) Spectral amplitude. has the lowest output signal-to-noise ratio, which is in line with the conclusions of the previous derivation.