# Generative Adversarial Network-Based Scheme for Diagnosing Faults in Cyber-Physical Power Systems

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Knockoff Generation

**Definition**

**1.**

**Definition**

**2.**

**Theorem**

**1.**

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The collected voltage, frequency, and phase angle measurements following an LL fault on bus #1 at $t=1$ second of the simulation.

**Figure 3.**The attained F-Measure values for the kNN classification model w.r.t. each feature selection technique.

**Figure 4.**The attained F-measure values by means of the SVM classification model w.r.t. each dataset.

**Table 1.**The attained F-Measure (FM) values by means of the kNN classification model w.r.t. each dataset.

Dataset | Baseline | InfFS | Relief | MutInfFS | mRMR | ||||
---|---|---|---|---|---|---|---|---|---|

S#1 | S#2 | S#1 | S#2 | S#1 | S#2 | S#1 | S#2 | ||

${\mathcal{A}}_{1}$ | 0.7379 | 0.8527 | 0.8312 | 0.7718 | 0.7963 | 0.7479 | 0.8560 | 0.7758 | 0.8647 |

${\mathcal{A}}_{2}$ | 0.6809 | 0.7847 | 0.8209 | 0.7386 | 0.7858 | 0.7111 | 0.8478 | 0.7468 | 0.8563 |

${\mathcal{A}}_{3}$ | 0.6519 | 0.7149 | 0.7966 | 0.7169 | 0.6973 | 0.6962 | 0.7968 | 0.7279 | 0.7818 |

${\mathcal{A}}_{4}$ | 0.7522 | 0.8828 | 0.8408 | 0.7928 | 0.8052 | 0.7695 | 0.8632 | 0.7956 | 0.8733 |

${\mathcal{A}}_{5}$ | 0.7006 | 0.8020 | 0.8305 | 0.7587 | 0.7887 | 0.7329 | 0.8511 | 0.7599 | 0.8639 |

${\mathcal{A}}_{6}$ | 0.6620 | 0.7418 | 0.7415 | 0.7388 | 0.7019 | 0.7113 | 0.7757 | 0.7432 | 0.7885 |

${\mathcal{A}}_{7}$ | 0.6691 | 0.7754 | 0.8244 | 0.7217 | 0.8149 | 0.6571 | 0.8155 | 0.7658 | 0.8046 |

${\mathcal{A}}_{8}$ | 0.5668 | 0.7274 | 0.8183 | 0.6705 | 0.8070 | 0.5905 | 0.8051 | 0.7157 | 0.7957 |

${\mathcal{A}}_{9}$ | 0.4973 | 0.6535 | 0.7406 | 0.6371 | 0.7331 | 0.6180 | 0.7236 | 0.6828 | 0.7141 |

${\mathcal{A}}_{10}$ | 0.6884 | 0.8125 | 0.8298 | 0.7544 | 0.8194 | 0.7515 | 0.8211 | 0.7910 | 0.8077 |

${\mathcal{A}}_{11}$ | 0.5925 | 0.7317 | 0.8181 | 0.6981 | 0.8106 | 0.6880 | 0.8084 | 0.7391 | 0.7956 |

${\mathcal{A}}_{12}$ | 0.5187 | 0.6799 | 0.7438 | 0.6691 | 0.7343 | 0.6485 | 0.7287 | 0.7090 | 0.7217 |

Avg. | 0.6432 | 0.7633 | 0.8030 | 0.7224 | 0.7743 | 0.6935 | 0.8055 | 0.7460 | 0.8057 |

**Table 2.**The attained F-Measure (FM) values by means of the SVM classification model w.r.t. each dataset.

Dataset | Baseline | InfFS | Relief | MutInfFS | mRMR | ||||
---|---|---|---|---|---|---|---|---|---|

S#1 | S#2 | S#1 | S#2 | S#1 | S#2 | S#1 | S#2 | ||

${\mathcal{A}}_{1}$ | 0.7970 | 0.9143 | 0.9156 | 0.8258 | 0.8936 | 0.7776 | 0.9159 | 0.8696 | 0.9413 |

${\mathcal{A}}_{2}$ | 0.7407 | 0.8898 | 0.9060 | 0.8157 | 0.8877 | 0.7520 | 0.9061 | 0.8600 | 0.9344 |

${\mathcal{A}}_{3}$ | 0.6799 | 0.8768 | 0.8414 | 0.7998 | 0.8084 | 0.7351 | 0.8480 | 0.8516 | 0.8840 |

${\mathcal{A}}_{4}$ | 0.8265 | 0.8780 | 0.9091 | 0.8571 | 0.8973 | 0.8007 | 0.9195 | 0.8864 | 0.9407 |

${\mathcal{A}}_{5}$ | 0.7749 | 0.8527 | 0.9003 | 0.8330 | 0.8901 | 0.7671 | 0.9090 | 0.8701 | 0.9361 |

${\mathcal{A}}_{6}$ | 0.7211 | 0.8481 | 0.8418 | 0.8254 | 0.8219 | 0.7560 | 0.8456 | 0.8611 | 0.8867 |

${\mathcal{A}}_{7}$ | 0.7341 | 0.8259 | 0.8886 | 0.7893 | 0.8694 | 0.7159 | 0.8697 | 0.8546 | 0.9156 |

${\mathcal{A}}_{8}$ | 0.6706 | 0.7977 | 0.8839 | 0.7611 | 0.8640 | 0.6746 | 0.8867 | 0.8377 | 0.9050 |

${\mathcal{A}}_{9}$ | 0.6187 | 0.7856 | 0.8170 | 0.7518 | 0.8000 | 0.6549 | 0.8019 | 0.8259 | 0.8513 |

${\mathcal{A}}_{10}$ | 0.7697 | 0.8373 | 0.8934 | 0.8147 | 0.8766 | 0.7353 | 0.8742 | 0.8823 | 0.9157 |

${\mathcal{A}}_{11}$ | 0.7143 | 0.8206 | 0.8865 | 0.7839 | 0.8668 | 0.6954 | 0.8656 | 0.8595 | 0.9085 |

${\mathcal{A}}_{12}$ | 0.6611 | 0.8030 | 0.8221 | 0.7767 | 0.8054 | 0.6762 | 0.8000 | 0.8568 | 0.8543 |

Avg. | 0.7257 | 0.8441 | 0.8755 | 0.8029 | 0.8569 | 0.7284 | 0.8685 | 0.8656 | 0.9061 |

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**MDPI and ACS Style**

Hassani, H.; Razavi-Far, R.; Saif, M.; Palade, V.
Generative Adversarial Network-Based Scheme for Diagnosing Faults in Cyber-Physical Power Systems. *Sensors* **2021**, *21*, 5173.
https://doi.org/10.3390/s21155173

**AMA Style**

Hassani H, Razavi-Far R, Saif M, Palade V.
Generative Adversarial Network-Based Scheme for Diagnosing Faults in Cyber-Physical Power Systems. *Sensors*. 2021; 21(15):5173.
https://doi.org/10.3390/s21155173

**Chicago/Turabian Style**

Hassani, Hossein, Roozbeh Razavi-Far, Mehrdad Saif, and Vasile Palade.
2021. "Generative Adversarial Network-Based Scheme for Diagnosing Faults in Cyber-Physical Power Systems" *Sensors* 21, no. 15: 5173.
https://doi.org/10.3390/s21155173