# Power System Signal-Detection Method Based on the Accelerated Unsaturated Stochastic Resonance Principle

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## Abstract

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## 1. Introduction

## 2. Output Saturation Limits for Classical Stochastic Resonance Models

#### 2.1. Potential Function Model for Bistable Systems

#### 2.2. Output Saturation Limit

## 3. Improved Stochastic Resonance Model with Output Saturation Limits

#### 3.1. Unsaturated Stochastic Resonance Model

#### 3.2. Accelerated Stochastic Resonance Model

## 4. Case Simulation and Result Analysis

#### 4.1. Harmonic Signal Detection Experiment

#### 4.2. Voltage Transient Droop Signal Detection Experiment

#### 4.3. Comparison of Method Computational Efficiency

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Potential function curves under input signal modulation. (

**a**) Potential function curves at quarter-cycle moments. (

**b**) Potential function curve at the moment of the three-quarter cycle.

**Figure 9.**Potential function curves under input signal modulation. (

**a**) Potential function curves at quarter-cycle moments. (

**b**) Potential function curve at the moment of three-quarter cycle.

**Figure 11.**Input noise signal waveform and spectrum at D = 1. (

**a**) Time domain waveform. (

**b**) Spectral amplitude.

**Figure 12.**SR detection system output signal waveform and spectrum at D = 1. (

**a**) Time domain waveform. (

**b**) Spectral amplitude.

**Figure 13.**UBSR detection system output signal waveform and spectrum at D = 1. (

**a**) Time domain waveform. (

**b**) Spectral amplitude.

**Figure 14.**ASR detection system output signal waveform and spectrum at D = 1. (

**a**) Time domain waveform. (

**b**) Spectral amplitude.

**Figure 15.**Input Noise signal waveform and spectrum at D = 5. (

**a**) Time domain waveform. (

**b**) Spectral amplitude.

**Figure 16.**SR detection system output signal waveform and spectrum at D = 5. (

**a**) Time domain waveform. (

**b**) Spectral amplitude.

**Figure 17.**UBSR detection system output signal waveform and spectrum at D = 5. (

**a**) Time domain waveform. (

**b**) Spectral amplitude.

**Figure 18.**ASR detection system output signal waveform and spectrum at D = 5. (

**a**) Time domain waveform. (

**b**) Spectral amplitude.

**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.

**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.

**Figure 23.**Input noise-containing voltage drop signal waveform and spectrum at D = 5. (

**a**) Time domain waveform. (

**b**) Spectral amplitude.

**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.

**Figure 26.**ASR detection system output signal waveform and spectrum at D = 5. (

**a**) Time domain waveform. (

**b**) Spectral amplitude.

**Table 1.**Harmonic frequency detection results of three stochastic resonance systems. (a) $D=1$. (b) $D=5$.

f/Hz | SR | UBSR | ASR | |
---|---|---|---|---|

(a) $D=1$ | 50 | 50 | 50 | 50 |

110 | 110 | 110 | 110 | |

150 | 150 | 150 | 150 | |

250 | 250 | 250 | 250 | |

350 | 350 | 350 | 350 | |

(b) $D=5$ | 50 | 50 | 50 | 50 |

110 | 110 | 110 | 110 | |

150 | 150 | 150 | 150 | |

250 | 250 | 250 | 250 | |

350 | 350 | 350 | 350 |

**Table 2.**Number of correlations between the input and output signals of various stochastic resonance detection systems.

$\mathit{D}=1$ | $\mathit{D}=5$ | |
---|---|---|

SR | 0.6132 | 0.1743 |

UBSR | 0.6439 | 0.3972 |

ASR | 0.9879 | 0.9794 |

Methodologies | Plus Window Interpolation FFT | VMD | EEMD | Empirical Wavelet Tranform | SR | UBSR | ASR |
---|---|---|---|---|---|---|---|

time- consuming/s | 1.032 | 2.3814 | 7.5216 | 2.0105 | 0.8123 | 1.0117 | 1.2361 |

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## Share and Cite

**MDPI and ACS Style**

Sun, S.; Qi, X.; Yuan, Z.; Tang, X.; Li, Z.
Power System Signal-Detection Method Based on the Accelerated Unsaturated Stochastic Resonance Principle. *Appl. Sci.* **2024**, *14*, 4284.
https://doi.org/10.3390/app14104284

**AMA Style**

Sun S, Qi X, Yuan Z, Tang X, Li Z.
Power System Signal-Detection Method Based on the Accelerated Unsaturated Stochastic Resonance Principle. *Applied Sciences*. 2024; 14(10):4284.
https://doi.org/10.3390/app14104284

**Chicago/Turabian Style**

Sun, Shuqin, Xin Qi, Zhenghai Yuan, Xiaojun Tang, and Zaihua Li.
2024. "Power System Signal-Detection Method Based on the Accelerated Unsaturated Stochastic Resonance Principle" *Applied Sciences* 14, no. 10: 4284.
https://doi.org/10.3390/app14104284