## 4 Case Simulation and Result Analysis
### Voltage Transient Droop Signal Detection Experiment
However, the output signals of the classical stochastic resonance detection system and the unsaturated stochastic resonance detection system have more obvious waveform distortion in the part of the voltage transient, mainly due to the fact that the voltage transient will make the sinusoidal signal appear harmonics, but the harmonics are relatively very weak, and in the presence of the 50 Hz voltage signal, it cannot affect the shape of the potential well. In the presence of the noise, the harmonic energy is clamped by the noise energy, which is partially transformed into low-frequency energy of random noise, which is evident in the spectrum of the output signal. The accelerated stochastic resonance detection system, due to the larger slope of the potential well wall in the exponential type, makes the displacement span of the particle jumping in the trap smaller, which equivalently weakens the control effect of the random noise on the particle state in the process of jumping, and the waveform distortion of the system is smaller at this time, which also reflects the unique advantages of the accelerated stochastic resonance detection system. The Gaussian white noise \(n(t)\) with a noise intensity \(D\) of 5 is mixed in, the system parameters \(a=1.5\), \(b=1\), \(c=2\) are set, and the fourth-order Runge-Kutta algorithm is utilized for the calculation of the Langevin equation. The voltage transient drop signal waveforms and spectra are shown in Figure 23, and the experimental results are shown in Figures 24-26. Comparing Figure 23 with Figures 24-26, it can be seen that the classical stochastic resonance detection system has no stochastic resonance phenomenon under strong noise interference, the degree of stochastic resonance of the non-saturated stochastic resonance detection system is weaker, and only the accelerated stochastic resonance detection system succeeds in the occurrence of stochastic resonance, which realizes the transformation of the noise energy to the signal energy, suppresses the noise, and improves the signal-to-noise ratio, and the signal main frequency of 50 Hz error-  
Figure 24: SR detection system output signal waveform and spectrum at \(D=5\). (**a**) Time domain waveform. (**b**) Spectral amplitude. Figure 25: UBSR detection system output signal waveform and spectrum at \(D=5\). (**a**) Time domain waveform. (**b**) Spectral amplitude. In order to better measure the accuracy of different stochastic resonance systems in detecting the moment of voltage transient drop, as well as the moment of voltage return, the number of interrelationships between the input and output signals of each stochastic resonance detection system is calculated, and the results are shown in Table 2.  
As can be seen from Table 2, only the accelerated stochastic resonance detection system can better maintain the signal phase and waveform, which can reduce the distortion of the classical stochastic resonance detection system. Although the output signal-to-noise ratio of ASR is lower than that of SR and UBSR in the case of weak noise disturbances, the unique noise immunity and the anti-distortion capability are highlighted in the case of strong noise disturbances.