# Fault Detection and Classification of Shunt Compensated Transmission Line Using Discrete Wavelet Transform and Naive Bayes Classifier

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model Studied

**Generator:**Base MVA rating of 300 MVA, 400 kV, frequency =60 Hz, internal Resistance (R

_{in}) = 0.8929 Ω, internal source inductance (L

_{in}) = 16.56 mH, short circuit MVA rating of 100 and base kV of 300 kV.

**Transmission line:**Positive and zero sequence resistance of 0.0279 Ω/km and 0.3046 Ω/km, positive and zero sequence inductance of 0.828 mH/km and 3.820 mH/km, positive and zero sequence capacitance of 11.66 ηF/km and7.03 ηF/km, respectively.

**STATCOM:**Voltage rating of 400 kV with 100 MVA base. The model consists of 48 pulses Voltage Source Converter (VSC).

**Load:**The system consists of an active and reactive power load of 210 MW and 150 MVar respectively.

**Circuit Breakers:**During normal operation, the breaker is considered as closed. For simulation of a fault, the fault is applied for the period of 6/60 to 7/60. The breaker resistance of 0.001 Ω, the Snubber resistances and the capacitance of 1 MΩ and infinite value, are considered for simulation study.

#### Proposed Method of Fault Detection

## 3. Feature Extraction Using Discrete Wavelet Transform

#### 3.1. Feature Extractions

#### 3.1.1. Standard Deviation (SD)

#### 3.1.2. Energy Value (E)

## 4. Fault Classifiers

_{1}-Normal, C

_{2}-LG fault, C

_{3}-LL fault, C

_{4}-LLG fault and C

_{5}-LLLG fault. Moreover, the effectiveness of the method is also tested for occurrence of fault at different locations of thetransmission lines.

#### 4.1. Multi-Layer Perceptron (MLP) Network

_{1}, u

_{2}and u

_{3}), hidden and output layers.

_{j}represents the output of the previous layer neuron, W

_{ij}is the weight between the ith an d jth neuron, and W

_{io}is the input bias of this neuron. In this work, the MLP network is trained using the back propagation method, and the detailed explanation is presented in [26,27].

#### 4.2. Bayes and Naive Bayes Classifiers

_{1}, L

_{2}, …, L

_{n}} of variables in class C = [C

_{1}, C

_{2}, …, C

_{5}]. The classification problem can be defined as,

_{1}, L

_{2}, …, L

_{n}}. To cater this limitation, all features in a class are assumed to be independent, and that results in the Naive Bayes (NB) classifier that reduces the number of parameters to be estimated from 2(2n − 1) to 2n [25,30,31]. NB is a linear classifier that divides the input data set into the training and prediction step for identifying the type of class using Bayes’ theorem. In the training phase, the classifier determines the probability distribution pertaining to the features of any given class is independent. During the prediction phase, our classifier estimates the posterior probability of the test sample data belonging to a respective class. Then the method classifies the samples based on the maximum likelihood of posterior probability. The NB classifier has been widely used because of its simplicity, being easy to implement with a high accuracy and sound theoretical basis that guarantees the optimized results. The probability function defined in (8) can be rewritten with the assumption of independent features as,

_{1}, L

_{2}, L

_{3}, L

_{4}, L

_{5}} = {Normal, LG, LL, LLG, LLLG}, then P(L) denotes the probability distribution over the sesystem states, as represented in Figure 5,

_{i}is the probability of L for being in state L

_{i}. The assumed probability of each disturbance is as follows: P(Normal) = P(L

_{1}) = 0.2, P(LG) = P(L

_{2}) = 0.2, P(LL) = P(L

_{3}) = 0.3, P(LLG) = P(L

_{4}) = 0.2 and P(LLLG) = P(L

_{5}) = 0.2.

#### 4.3. Performance Indices of Classifier

_{P}is the predicted type of fault, and E

_{O}is the expected type of fault.

## 5. Results and Discussion

#### Performance Evaluation of Classifiers

## 6. Comparative Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Three-phase current waveform during a Line to Ground (LG) fault (at 200 km) in Phase A without STATCOM compensation.

**Figure 9.**Three-phase current waveform during the LG fault (at 200 km) in Phase A with STATCOM compensation.

**Figure 10.**Discrete Wavelet Transform (DWT) analysis of Phase A under normal conditions without compensation.

Detailed Coefficient Levels | Frequency Band in kHz |
---|---|

D1 | 20 to 10 |

D2 | 10 to 5 |

D3 | 5 to 2.5 |

D4 | 2.5 to 1.25 |

D5 | 1.25 to 0.625 |

D6 | 0.625 to 0.3125 |

D7 | 0.3125 to 0.15625 |

D8 | 0.15625 to 0.0781 |

Cases | Normal | LG | LLG | LL | LLLG | |
---|---|---|---|---|---|---|

Without STATCOM | SDA | 0.33 | 0.89 | 0.5 | 0.49 | 0.34 |

SDB | 0.33 | 0.05 | 0.48 | 0.49 | 0.35 | |

SDC | 0.33 | 0.06 | 0.02 | 0.02 | 0.31 | |

E-A | 0.58 | 0.08 | 0.01 | 0.01 | 0.43 | |

E-B | 0.23 | 0.89 | 0.5 | 0.51 | 0.24 | |

E-C | 0.19 | 0.02 | 0.49 | 0.48 | 0.33 | |

With STATCOM | SDA | 0.33 | 0.22 | 0.12 | 0.13 | 0.34 |

SDB | 0.34 | 0.56 | 0.46 | 0.44 | 0.34 | |

SDC | 0.33 | 0.22 | 0.42 | 0.43 | 0.32 | |

E-A | 0.54 | 0.39 | 0.03 | 0 | 0.43 | |

E-B | 0.15 | 0.42 | 0.08 | 0.44 | 0.24 | |

E-C | 0.31 | 0.19 | 0.89 | 0.56 | 0.32 |

**Table 3.**Current magnitude during normal conditions and faults at different locations without the STATCOM-compensation.

Without STATCOM | |||||||
---|---|---|---|---|---|---|---|

Fault Distance | Type of Fault | Minimum Current | Maximum Current | ||||

Ia kA | I b kA | I c kA | Ia kA | I b kA | I c kA | ||

No fault | −0.205 | −0.205 | −0.205 | 0.205 | 0.205 | 0.205 | |

100 km | LG | −2.57 | −0.34 | −0.46 | 6.95 | 0.28 | 0.25 |

LL | −4.11 | −12.5 | −0.25 | 12.6 | 4.05 | 0.25 | |

LLG | −4.19 | −12.0 | −0.71 | 1.34 | 4.3 | 0.65 | |

LLLG | −3.88 | −12.0 | −12.4 | 1.52 | 6.76 | 4.3 | |

200 km | LG | −1.23 | −0.27 | −0.39 | 3.67 | 0.19 | 0.18 |

LL | −2.19 | −7.01 | −0.25 | 7.06 | 2.16 | 0.25 | |

LLG | −2.1 | −6.78 | −0.45 | 7.56 | 2.34 | 0.38 | |

LLLG | −1.97 | −7.06 | −7.16 | 8.32 | 3.78 | 2.82 | |

300 km | LG | −0.78 | −0.294 | −0.37 | 2.49 | 0.185 | 0.19 |

LL | −1.56 | −4.78 | −0.25 | 4.93 | 1.47 | 0.25 | |

LLG | −1.51 | −4.85 | −0.51 | 5.08 | 1.62 | 0.37 | |

LLLG | −1.31 | −5.17 | −4.97 | 5.72 | 2.62 | 2.16 |

**Table 4.**Current magnitude during normal conditions and faults at different locations with STATCOM-compensation.

Fault Distance | Type of Fault | With STATCOM | |||||
---|---|---|---|---|---|---|---|

Minimum Current | Maximum Current | ||||||

I a kA | I b kA | I c kA | I a kA | I b kA | I c kA | ||

No f | −1.22 | −2.07 | −2.08 | 2.51 | 1.26 | 1.21 | |

100 km | LG | −3.36 | −1.04 | 1.17 | 6.95 | 1.23 | 0.8 |

LL | −4.57 | −11.7 | −1.24 | 11.8 | 4.58 | 1.07 | |

LLG | −4.74 | −11.4 | −1.3 | 1.26 | 4.82 | 1.18 | |

LLLG | −4.57 | −11.5 | −1.1.9 | 1.43 | 7.02 | 4.91 | |

200 km | LG | −2.20 | −1.12 | −1.23 | 3.97 | 1.23 | 1.08 |

LL | −2.80 | −6.3 | −1.25 | 6.38 | 2.71 | 1.07 | |

LLG | −2.85 | −6.25 | −1.36 | 6.76 | 2.99 | 1.09 | |

LLLG | −2.72 | −6.47 | −6.46 | 4.49 | 4.06 | 3.3 | |

300 km | LG | −1.85 | −1.19 | −1.28 | 3.18 | 1.22 | 0.84 |

LL | −2.22 | −4.56 | −1.27 | 4.61 | 2.22 | 1.07 | |

LLG | −2.33 | −4.61 | −1.38 | 4.88 | 2.41 | 1.17 | |

LLLG | −2.22 | −4.84 | −4.79 | 5.32 | 3.24 | 2.68 |

Without STATCOM | With STATCOM | |||||||
---|---|---|---|---|---|---|---|---|

Condition | Type of Fault | Location km | SD-A (×10 ^{3}) | SD-B (×10 ^{3}) | SD-C (×10 ^{3}) | SD-A (×10 ^{3}) | SD-B (×10 ^{3}) | SD-C (×10 ^{3}) |

Normal | No fault | 100 | 0.177 | 0.177 | 0.177 | 0.875 | 0.877 | 0.866 |

200 | 0.177 | 0.177 | 0.177 | 0.875 | 0.877 | 0.866 | ||

300 | 0.177 | 0.177 | 0.0177 | 0.875 | 0.877 | 0.866 | ||

LG | AG | 100 | 3.087 | 0.166 | 0.204 | 3.394 | 0.8 | 0.797 |

200 | 1.582 | 0.154 | 0.196 | 2.046 | 0.825 | 0.817 | ||

300 | 1.058 | 0.145 | 0.19 | 1.674 | 0.851 | 0.835 | ||

BG | 100 | 0.3 | 3.17 | 0.267 | 0.793 | 3.49 | 0.835 | |

200 | 0.245 | 1.63 | 0.198 | 0.821 | 2.11 | 0.836 | ||

300 | 0.238 | 1.1 | 0.196 | 0.838 | 1.72 | 0.859 | ||

CG | 100 | 0.263 | 0.299 | 2.66 | 0.854 | 0.811 | 3.305 | |

200 | 0.193 | 0.243 | 1.37 | 0.852 | 0.831 | 1.888 | ||

300 | 0.193 | 0.238 | 0.921 | 0.874 | 0.849 | 1.569 | ||

LLG | ABG | 100 | 5.865 | 5.65 | 2.82 | 5.81 | 5.69 | 0.766 |

200 | 3.158 | 3.03 | 2.06 | 3.188 | 3.14 | 0.803 | ||

300 | 2.14 | 2.15 | 2.05 | 2.357 | 2.33 | 0.832 | ||

BCG | 100 | 0.188 | 5.65 | 4.99 | 0.755 | 5.67 | 5.12 | |

200 | 0.17 | 3.06 | 2.71 | 0.799 | 3.14 | 2.87 | ||

300 | 0.161 | 2.09 | 1.84 | 0.834 | 2.35 | 2.16 | ||

CAG | 100 | 5.108 | 0.287 | 5.15 | 5.247 | 0.759 | 5.21 | |

200 | 2.749 | 0.203 | 2.79 | 2.932 | 0.794 | 2.9 | ||

300 | 1.842 | 0.202 | 1.87 | 2.202 | 0.833 | 2.17 | ||

LL | AB | 100 | 5.723 | 5.67 | 0.177 | 5.633 | 5.67 | 0.838 |

200 | 3.097 | 3.04 | 0.177 | 3.085 | 3.11 | 0.842 | ||

300 | 2.105 | 2.05 | 0.177 | 2.279 | 2.3 | 0.849 | ||

BC | 100 | 0.177 | 5.255 | 5.691 | 0.851 | 5.281 | 5.245 | |

200 | 0.177 | 2.868 | 2.832 | 0.856 | 2.944 | 2.905 | ||

300 | 0.177 | 1.964 | 1.929 | 0.86 | 2.204 | 2.164 | ||

CA | 100 | 4.998 | 0.177 | 5.06 | 5.112 | 0.846 | 5.04 | |

200 | 2.693 | 0.177 | 2.75 | 2.85 | 0.852 | 2.8 | ||

300 | 1.8 | 0.177 | 1.86 | 2.131 | 0.858 | 2.09 | ||

LLLG | ABCG | 100 | 6.254 | 6.48 | 5.69 | 6.224 | 6.43 | 5.75 |

200 | 3.368 | 3.51 | 3.1 | 3.397 | 3.37 | 3.19 | ||

300 | 2.263 | 2.39 | 2.1 | 2.493 | 2.58 | 2.36 |

Without STATCOM | With STATCOM | |||||||
---|---|---|---|---|---|---|---|---|

Condition | Type of fault | Location km | E-A (×10 ^{8}) | E-B (×10 ^{8}) | E-C (×10 ^{8}) | E-A (×10 ^{8}) | E-B (×10 ^{8}) | E-C (×10 ^{8}) |

Normal | No fault | 100 | 1.25 | 0.49 | 0.4 | 22.7 | 6.26 | 13.1 |

200 | 1.25 | 0.49 | 0.4 | 22.7 | 6.26 | 13.1 | ||

300 | 1.25 | 0.49 | 0.4 | 22.7 | 6.26 | 13.1 | ||

LG | AG | 100 | 96.4 | 0.56 | 0.51 | 128 | 5.36 | 11.4 |

200 | 25.9 | 0.56 | 0.51 | 56.5 | 5.62 | 12.1 | ||

300 | 12 | 0.51 | 0.46 | 42.7 | 5.85 | 12.3 | ||

BG | 100 | 1.64 | 57.1 | 0.51 | 21.3 | 70.7 | 13.2 | |

200 | 1.44 | 15.3 | 0.41 | 25.8 | 27.5 | 12.3 | ||

300 | 1.5 | 7.08 | 0.37 | 22.3 | 18.8 | 13 | ||

CG | 100 | 1.39 | 0.76 | 72.9 | 21.7 | 5.74 | 97.1 | |

200 | 1.33 | 0.6 | 18.8 | 21.2 | 6.22 | 38.6 | ||

300 | 1.18 | 0.63 | 8.47 | 22.1 | 6.11 | 28.8 | ||

LLG | ABG | 100 | 301 | 223 | 0.71 | 307 | 214 | 11.3 |

200 | 87.1 | 65 | 0.5 | 105 | 64 | 12.8 | ||

300 | 41.8 | 30.4 | 0.45 | 63.8 | 34.3 | 13.6 | ||

BCG | 100 | 1.36 | 184 | 179 | 20.8 | 185 | 200 | |

200 | 1.2 | 54.6 | 53.4 | 21.3 | 58.1 | 67 | ||

300 | 1.18 | 25 | 22.7 | 22.1 | 32.8 | 44.4 | ||

CAG | 100 | 318 | 0.73 | 313 | 326 | 5.17 | 305 | |

200 | 94.6 | 0.51 | 93 | 106 | 5.09 | 94.9 | ||

300 | 41.6 | 0.52 | 41.2 | 66.9 | 5.53 | 56.5 | ||

LL | AB | 100 | 255 | 254 | 4.05 | 265 | 234 | 12.8 |

200 | 74.7 | 73.9 | 0.4 | 92.6 | 68.3 | 12.9 | ||

300 | 35.6 | 35 | 0.4 | 56.8 | 35.8 | 12.9 | ||

BC | 100 | 1.24 | 174 | 169 | 22.4 | 170 | 186 | |

200 | 1.24 | 53 | 50.2 | 22.4 | 49.5 | 62.4 | ||

300 | 1.24 | 23.5 | 22.3 | 22.4 | 30.2 | 40.8 | ||

CA | 100 | 308 | 0.5 | 312 | 314 | 5.8 | 300 | |

200 | 91.5 | 0.49 | 93.4 | 103 | 5.87 | 91.7 | ||

300 | 40.5 | 0.49 | 41.3 | 65.5 | 5.98 | 54.3 | ||

LLLG | ABCG | 100 | 425 | 241 | 315 | 414 | 236 | 315 |

200 | 125 | 70.5 | 94.7 | 130 | 71.9 | 97 | ||

300 | 57.5 | 33.3 | 40.7 | 76.6 | 38.6 | 59.1 |

Classes | C1 | C2 | C3 | C4 | C5 | System State |
---|---|---|---|---|---|---|

C1 | 1 | 0 | 0 | 0 | 0 | Normal |

C2 | 0 | 1 | 0 | 0 | 0 | LG |

C3 | 0 | 0 | 1 | 0 | 0 | LLG |

C4 | 0 | 0 | 0 | 1 | 0 | LL |

C5 | 0 | 0 | 0 | 0 | 1 | LLLG |

Accuracy Rate | Misclassification Rate | ||||||||
---|---|---|---|---|---|---|---|---|---|

MLP | Bayes | Naive Bayes | |||||||

Cases | MLP | Bayes | Naïve Bayes | % Rate | Type of Fault | Rate | Type of Fault | Rate | Type of Fault |

Case-1 | 80 | 20 | 100 | 20 | C3 | 80 | C2-C5 | 0 | 0 |

Case-2 | 60 | 20 | 100 | 40 | C2–C3 | 80 | C2-C5 | 0 | 0 |

Case-3 | 80 | 20 | 100 | 20 | C3 | 80 | C2-C5 | 0 | 0 |

Case-4 | 100 | 20 | 100 | 0 | 0 | 80 | C2-C5 | 0 | 0 |

Kappa Statistics | MAE | RMSE | |||||||
---|---|---|---|---|---|---|---|---|---|

MLP | Bayes | Naive Bayes | MLP | Bayes | Naive Bayes | MLP | Bayes | Naive Bayes | |

Case-1 | 0.75 | 0 | 1 | 0.159 | 0.32 | 0.025 | 0.236 | 0.4 | 0.088 |

Case-2 | 0.5 | 0 | 1 | 0.201 | 0.32 | 0 | 0.292 | 0.4 | 0 |

Case-3 | 0.75 | 0 | 1 | 0.172 | 0.32 | 0.033 | 0.248 | 0.4 | 0.097 |

Case-4 | 1 | 0 | 1 | 0.155 | 0.32 | 0 | 0.227 | 0.4 | 0 |

Cases | %RAE | %RRSE | ||||
---|---|---|---|---|---|---|

MLP | Bayes | Naive Bayes | MLP | Bayes | Naive Bayes | |

Case-1 | 49.89 | 100 | 7.85 | 59.23 | 100 | 22.21 |

Case-2 | 62.86 | 100 | 0 | 73.22 | 100 | 0 |

Case-3 | 53.74 | 100 | 10.29 | 62 | 100 | 24.46 |

Case-4 | 48.46 | 100 | 0 | 56.89 | 100 | 0 |

Type of Fault Considered | |||||||||
---|---|---|---|---|---|---|---|---|---|

Authors | Methods | LG | LL | LLG | LLL | LLLG | Fault Resistance | STATCOM | %Accuracy |

Singh. A.R [1] | Synchronized Measurements | √ | √ | √ | √ | √ | √ | √ | 99.6 |

Ghazizadeh A. [3] | Synchronized Measurements | √ | √ | √ | × | √ | × | √ | 99.07 |

Mishra. S.K [4] | DWT | √ | √ | √ | × | × | √ | √ | - |

Gupta. O.H [8] | Superimposed sequence components-based integrated impedance (SSCII). | √ | √ | √ | √ | √ | √ | SVC | - |

Albasri. F.A [10] | Impedance Measurements | √ | √ | × | √ | × | × | √ | - |

Hussain. S [15] | Unsynchronized Measurements | √ | √ | × | √ | × | √ | √ | 99 |

Proposed Work | DWT &NB | √ | √ | √ | × | √ | √ | √ | 100 |

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**MDPI and ACS Style**

Aker, E.; Othman, M.L.; Veerasamy, V.; Aris, I.b.; Wahab, N.I.A.; Hizam, H.
Fault Detection and Classification of Shunt Compensated Transmission Line Using Discrete Wavelet Transform and Naive Bayes Classifier. *Energies* **2020**, *13*, 243.
https://doi.org/10.3390/en13010243

**AMA Style**

Aker E, Othman ML, Veerasamy V, Aris Ib, Wahab NIA, Hizam H.
Fault Detection and Classification of Shunt Compensated Transmission Line Using Discrete Wavelet Transform and Naive Bayes Classifier. *Energies*. 2020; 13(1):243.
https://doi.org/10.3390/en13010243

**Chicago/Turabian Style**

Aker, Elhadi, Mohammad Lutfi Othman, Veerapandiyan Veerasamy, Ishak bin Aris, Noor Izzri Abdul Wahab, and Hashim Hizam.
2020. "Fault Detection and Classification of Shunt Compensated Transmission Line Using Discrete Wavelet Transform and Naive Bayes Classifier" *Energies* 13, no. 1: 243.
https://doi.org/10.3390/en13010243