# Deep Neural Network with Hilbert–Huang Transform for Smart Fault Detection in Microgrid

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## Abstract

**:**

## 1. Introduction

- An FDM for AC MGs is proposed to provide precise and timely FT, phase, and place data;
- This study combined DNNs and HHT with SVD to solve the MG–FD problem from an information-based standpoint;
- Complete scenarios were performed to decompose the efficiency of the offered method and compare the outcomes with those of other methods.

## 2. Examined MG System

## 3. Hilbert–Huang Transform

#### 3.1. Empirical Mode Decomposition

- For a data set, the number of zero crossings and extremes are assumed to vary or be equivalent to one;
- All points have a zero-average extent for the envelope defined by the local minimum and maximum.

- 3.
- Explore the local maximum and minimum in the sample data, and build a pair of envelopes by connecting them using cubic splines;

- 4.
- Average $\mu \left(\tau \right)$ was determined for the two envelopes. By subtracting it from the basic signal $s\left(\tau \right)$, the primary component ${\upsilon}_{1}\left(\tau \right)$ is obtained as follows;

- 5.
- When ${\upsilon}_{1}\left(\tau \right)$ satisfied the previous two requirements, it would be the initial IMF; otherwise, it would be the main function and stages ‘a’ to ‘c’ are repeated in order to obtain ${\upsilon}_{11}\left(\tau \right)$ as follows:

- 6.
- When sifting is repeated $m$ times, the initial IMF is ${\upsilon}_{1m}\left(\tau \right)$, $im{f}_{1}$;

- 7.
- Leaving $im{f}_{1}$ independent of $s\left(\tau \right)$ and making it ${\zeta}_{1}\left(\tau \right)$, as follows;

- 8.
- ${\zeta}_{1}\left(\tau \right)$ is regarded as the primary signal. Equation (1) to Equation (3) are repeated to calculate the next IMF.

#### 3.2. Hilbert Transform

#### 3.3. Singular Value Decomposition

#### 3.4. Shannon Entropy

## 4. DNN-Driven FD

#### 4.1. Condensed Layer and GRU

#### 4.2. DNN Architecture

#### 4.3. Time-Series Simulation and Training

## 5. Scenarios

#### 5.1. FD Precision and Commutating Time

#### 5.2. Comparative Analysis with Existing FDMs

#### 5.3. DNN Architecture

#### 5.4. Uncertainty of Measurement

#### 5.5. Efficiency on Developed IEEE 34-Bus MG System

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**The final condensed neuron layers of the faulty line detection and FLD–DNNs: (

**a**) faulty phase detection; (

**b**) FLD.

Variable | Operational State | Fault Resistance $\mathbf{\Omega}$ | Fault Place | Topology | Fault Kind |
---|---|---|---|---|---|

Count | 2 | 4 | 9 | 2 | 10 |

Feasible configuration | Islanded or non-islanded | 0.01, 1, 10, or 100 | 10%, 20%, …, or 90% on fault line | Radial or loop | AG, BG, CG, AB, AC, BC, ABG, ACG, BCG, or ABCG |

Variable | Fault line | ${L}_{6}$Load | ${L}_{3}$$\text{}{L}_{4}$Loads | ${L}_{5}$Load | |

Count | 4 | 2 | 2 | 2 | |

Feasible configuration | Line 12, 23, 34, or 56 | [90 kW, −20 kVAr] /[45 kW, −10 kVAr] | [90 kW, 45 kVAr] /[45 kW, 25 kVAr] | [90 kW, −40 kVAr] /[45 kW, −20 kVAr] |

Variable | Operational State | Topology | Event |
---|---|---|---|

Count | 2 | 2 | 34 |

Feasible configuration | Islanded/ non-islanded | Loop/radial | Topology variation, operational state variation, ${L}_{3}$, ${L}_{4}$, ${L}_{5}$ load variation through ±5%, ±10%, ±15%, or ±20%, |

Variable | ${L}_{6}$Load | ${L}_{3}$$\mathrm{and}{L}_{4}$Load | ${L}_{5}$Load |

Count | 2 | 2 | 2 |

Feasible configuration | [90 kW, −20 kVAr] /[45 kW, −10 kVAr] | [90 kW, 45 kVAr] /[45 kW, 25 kVAr] | [90 kW, −40 kVAr] /[45 kW, −2 kVAr] |

Relay | ${\mathit{R}}_{65}$ | ${\mathit{R}}_{56}$ | ${\mathit{R}}_{43}$ | ${\mathit{R}}_{34}$ | ${\mathit{R}}_{32}$ | ${\mathit{R}}_{23}$ | ${\mathit{R}}_{21}$ | ${\mathit{R}}_{12}$ | Average | ||
---|---|---|---|---|---|---|---|---|---|---|---|

Place Error (%) | Test | 5.9 | 1.89 | 5.83 | 4.51 | 8.81 | 10.47 | 4.23 | 5.92 | 5.95 | |

Training | 4.52 | 4.41 | 6.68 | 5.72 | 8.75 | 8.62 | 2.17 | 2.61 | 5.44 | ||

Precision (%) | Fault Phase | Test | 98.62 | 97.31 | 97.24 | 98.77 | 97.01 | 98.96 | 98.25 | 97.64 | 97.98 |

Training | 97.81 | 96.79 | 98.52 | 96.48 | 97.13 | 98.13 | 98.03 | 98.57 | 97.68 | ||

Fault kind | Test | 98.74 | 96.91 | 97.92 | 97.58 | 96.46 | 98.21 | 97.52 | 97.91 | 97.66 | |

Training | 98.42 | 99.34 | 98.02 | 97.87 | 95.48 | 97.31 | 97.59 | 97.74 | 97.72 | ||

Fault versus sound | Test | 99.42 | 99.28 | 99.21 | 99.14 | 99.64 | 99.35 | 99.38 | 99.63 | 99.38 | |

Training | 99.81 | 99.97 | 99.38 | 99.35 | 99.62 | 99.38 | 99.98 | 99.46 | 99.62 |

Procedure | Average Time |
---|---|

DNN identification | 0.37 ms/DNN |

DNN training | 437.48 s/DNN |

HHT and characteristics | 0.5 ms/HHT |

Method | Suggested Method | Random Forest [4] | Decision Tree [3] | Support Vector Machine [3] | Decision Tree [4] | |
---|---|---|---|---|---|---|

Precision (%) | Phase | 97.98 | - | 90.4 | 93.3 | - |

Fault | 99.38 | 99 | 90.4 | 93.3 | 97 | |

Kind | 97.66 | 94 | 90.4 | 93.3 | 85 | |

Error (%) | Place | 5.95 | - | - | - | - |

Number of CLs | 1 | 2 | 3 | ||
---|---|---|---|---|---|

Number of GRULs | 1 | Test (%) | 94.89 | 95.91 | 95.29 |

Training (%) | 95.12 | 95.69 | 95.21 | ||

2 | Test (%) | 95.41 | 95.96 | 95.91 | |

Training (%) | 96.63 | 96.14 | 95.98 | ||

3 | Test (%) | 96.19 | 97.47 | 96.81 | |

Training (%) | 96.28 | 97.61 | 96.88 | ||

4 | Test (%) | 96.12 | 97.92 | 97.45 | |

Training (%) | 97.67 | 98.02 | 97.31 | ||

5 | Test (%) | 96.26 | 96.21 | 95.57 | |

Training (%) | 98.11 | 98.32 | 97.48 |

SNR | Perfect | 30 dB | 40 dB | |
---|---|---|---|---|

Precision (%) | Phase | 97.98 | 97.71 | 97.81 |

Fault | 99.38 | 99.24 | 99.36 | |

Kind | 97.66 | 97.62 | 97.65 | |

Error (%) | Place | 5.95 | 5.98 | 5.97 |

Precision(%) | Phase | 97.69 |

Fault | 99 | |

Kind | 98.12 | |

Error(%) | Place | 6.38 |

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## Share and Cite

**MDPI and ACS Style**

Aqamohammadi, A.R.; Niknam, T.; Shojaeiyan, S.; Siano, P.; Dehghani, M.
Deep Neural Network with Hilbert–Huang Transform for Smart Fault Detection in Microgrid. *Electronics* **2023**, *12*, 499.
https://doi.org/10.3390/electronics12030499

**AMA Style**

Aqamohammadi AR, Niknam T, Shojaeiyan S, Siano P, Dehghani M.
Deep Neural Network with Hilbert–Huang Transform for Smart Fault Detection in Microgrid. *Electronics*. 2023; 12(3):499.
https://doi.org/10.3390/electronics12030499

**Chicago/Turabian Style**

Aqamohammadi, Amir Reza, Taher Niknam, Sattar Shojaeiyan, Pierluigi Siano, and Moslem Dehghani.
2023. "Deep Neural Network with Hilbert–Huang Transform for Smart Fault Detection in Microgrid" *Electronics* 12, no. 3: 499.
https://doi.org/10.3390/electronics12030499