# A Single-Terminal Fault Location Method for HVDC Transmission Lines Based on a Hybrid Deep Network

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- CNN-LSTM was used to solve many shortcomings of the single-ended traveling wave method, including high sampling frequency, difficulty to determine wave velocity and identify wave heads when an HIF occurs. It provides high precision and strong robustness to fault types, noise, sampling frequency, and different HVDC topologies in fault location.
- (2)
- VMD-TEO was used for feature engineering, which made the characteristics of the fault signals obvious. It reduced the dependence of deep learning on the number of samples to a certain extent, thereby improving the learning efficiency and accuracy of CNN-LSTM.
- (3)
- A comparison experiment of 1D-CNN and recurrent networks including LSTM, GRU and Bi-GRU as a regressor in the hybrid model explained the reason for choosing LSTM. Compared with feature engineering methods such as WT and HHT, VMD-TEO showed a better performance on the accuracy of fault location through CNN-LSTM.

## 2. Fault Location Based on Traveling Wave Theory

#### 2.1. Feature Engineering and Acquisition of Samples

_{m}

_{0}and i

_{m}

_{1}are the current or voltage of the ground-mode and aerial-mode traveling wave after decoupling, respectively, and i

_{p}and i

_{n}are the fault current or voltage of the corresponding positive and negative electrodes, respectively.

_{max}and x

_{min}are the maximum and minimum values in the sample data, respectively.

#### 2.2. Fault Segment Identification Based on 2D-CNN

_{1}–C

_{6}), six pooling layers (S

_{1}–S

_{6}), a flatten layer (R

_{1}), two dense layers (F

_{1}, F

_{2}), two dropout layers (D

_{1}, D

_{2}), and a softmax layer (F

_{3}). The parameter configuration of each layer in this model is listed in Table 1.

_{i}is the input sample or the feature sample of the previous layer, x

_{j}is the output feature sample, and f is the activation function to be selected.

_{1}) in Figure 4, has a tiling function that can tile neurons on multiple multidimensional feature samples into 1D vectors. The operation of the fully connected layer can be described as:

_{1}, D

_{2}) are set as 0.3 and 0.2, respectively.

#### 2.3. Single-Ended Traveling Wave Method for Fault Location

_{1}and L

_{2}, respectively. As reported in Reference [16], the wave velocity is a frequency-dependent variable. The traveling wave velocities on the overhead line and the cable are v

_{1}(ω) and v

_{2}(ω), respectively. Here ω is the frequency when the traveling wave component reaches the rectifier side. Δt is the time difference between the second traveling wave head and the first traveling wave head identified at the M terminal. The distance from the fault point to the M terminal is x, which is the fault location result.

_{1}< x < L

_{1}+ L

_{2}/2 when the fault occurs at F

_{1}, and L

_{1}+ L

_{2}/2 < x < L

_{1}+ L

_{2}when the fault occurs at F

_{2}. When the fault point is at F

_{1}, the path of the traveling wave is F

_{1}-J-F

_{1}-J-M, i.e., the second traveling wave head recognized by the M terminal is the reflected wave from the fault point. The fault distance can be calculated using the following formula:

_{2}, the path of the traveling wave is F

_{2}-N-F

_{2}-J-M, i.e., the second traveling wave head recognized by the M terminal is the reflected wave from the opposite bus N. The fault distance can be calculated by the following formula:

## 3. Fault Location Based on CNN-LSTM

#### 3.1. Theoretical Background of LSTM

_{t}in the forget gate, state memory unit S

_{t}

_{−1}, and intermediate output h

_{t}

_{−1}together determine the forgotten part of the state memory unit. x

_{t}in the input gate is determined by the sigmoid and tanh functions to jointly determine the vector retained in the state memory unit. Intermediate output h

_{t}is jointly determined by the updated S

_{t}and o

_{t}. The calculation formulas in these processes are expressed as follows:

_{t}, i

_{t}, g

_{t}, o

_{t}, h

_{t}, and S

_{t}are the states of the forget gate, input gate, input node, output gate, intermediate output, and state unit, respectively, W

_{fx}, W

_{fh}, W

_{ix}, W

_{ih}, W

_{gx}, W

_{gh}, W

_{ox}, and W

_{oh}are the matrix weights of the corresponding gate multiplied by input x

_{t}and intermediate output h

_{t}

_{−1}, b

_{f}, b

_{i}, b

_{g}, and b

_{o}are the bias terms of the corresponding gate. ☉ is the bitwise multiplication of the elements in the vector. σ is the sigmoid function, and φ is the tanh function.

#### 3.2. CNN-LSTM Hybrid Model for Fault Location

_{1}) in 2D-CNN and the probability information of the fault segment are calculated by the regressor. The experimental results demonstrate that six LSTM layers should be used in the CNN-LSTM network, and each LSTM layer contains 64 neurons. The dense layer (F

_{4}) uses a neuron. The loss function is mean squared error, and the optimizer is Adam. The proposed hybrid network model can intelligently integrate information from different fault sections and corresponding fault distances, and continuously optimize and update network parameters to make it close to ideal.

## 4. Simulation Results and Analysis

#### 4.1. Simulation Model and Related Parameters

^{−8}, 2.2 × 10

^{−7}, and 1.8 × 10

^{−7}Ω·m, respectively. The relative dielectric constant of the insulator is 2.5 with length of 200 km. The resistance, GMR, and length of the overhead wire are 0.03206 Ω/km, 0.0122834 m, and 300 km, respectively.

#### 4.2. Experimental Result of Traveling Wave Method

_{f}changes, the aerial-mode component of the fault current is shown in Figure 11. When R

_{f}is less than 100 Ω, the fault current amplitude is larger and its variety is more obvious than that when R

_{f}is between 800 and 1200 Ω. Through this analysis, it can be seen that the fault resistance of LIF and HIF ([0, 100 Ω] and [800 Ω, 1200 Ω], respectively) is one of the reasonable circumstances.

- (1)
- The change step size of the fault distance is taken as 1 km.
- (2)
- Transition resistance R
_{f}= 0.0001%, 1%, 2%, 3% … 100% of the maximum transition resistance. - (3)
- Fault types include PG, NG, and PN.

_{d1}= 4.00175 s, t

_{d2}= 4.00233 s. According to the theoretical analysis [7,14], it is assumed that the parameters of the aerial-mode component do not change much, and the influence of frequency on the traveling wave velocity is ignored. Since the HVDC model and parameters in this study are exactly the same as that described in Reference [14], the fixed aerial-mode traveling wave velocities in Reference [14] are used for calculation, where v

_{1}= 293,997.1102 km/s, v

_{2}= 196,333.3333 km/s. The theoretical value of fault distance is 443.063 km, the error distance of fault distance is 6.937 km, and the error percentage is 1.54%. This error does not meet the actual engineering requirements. The possible reason of the error is that fixed traveling wave velocities are adopted while ignoring their frequency variation characteristics.

#### 4.3. Experimental Result of CNN-LSTM

_{s}) and its offset (Δs), respectively. When Δs is large, the number of categories (N) of the fault sections is small. When N is small, the recognition rate for HIF is low. When N is large, the data amount and learning effect of CNN-LSTM are affected. Therefore, the selection of appropriate Δs is very important for accurate fault location.

_{s}is [0, 500]. When Δs = 100, N = 4, the fault sections are [0, 200], [100, 300], [200, 400], and [300, 500]. When Δs = 50, N = 9, the fault sections are [0, 100], [50, 150],…, and [400, 500]. When Δs = 25, N = 19, the fault sections are [0, 50], [25, 75],…, and [450, 500]. Δs is changed, and the classification experiments of HIF and LIF are performed again. With the change in Δs (Δs = 2, 5, 10, 20, 25, and 100), the accuracy percentage of the 2D-CNN classifier is shown in Figure 15. The width of the ribbon in Figure 15 reflects the accuracy range of each fault segment identification, where the edges of the ribbon reflect the maximum and minimum accuracy, and the solid line reflects the average accuracy. When Δs = 25, i.e., N = 19, the classification effect of HIF and LIF is best with accuracies of 99.98% and 99.99%, respectively.

#### 4.4. Influence of Sampling Frequency

_{act}is the actual fault distance, y

_{pred}is the predicted fault distance, N

_{1}and N

_{2}are the number of test samples for HIF and LIF, respectively, and N

_{1}= N

_{2}= 500.

#### 4.5. Influence of Noise

#### 4.6. Comparison of Other Methods

#### 4.7. Other HVDC Model

_{1}and L

_{3}are overhead lines with a length of 150 km, and L

_{2}is a cable with a length of 150 km. The CNN-LSTM model is retrained according to the previous program, and 10 samples are randomly selected for testing, as shown in Table 4. The error interval of the proposed method is in [0.249, 0.379 km]. This error range also meets engineering needs. By the analysis of Table 4, it can be concluded that this fault location method has higher accuracy when considering different HVDC topologies, and is also rarely affected by fault types and fault resistance.

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

HVDC | High voltage direct current |

CNN | Convolutional neural network |

LSTM | Long short-term memory |

VMD | Variational mode decomposition |

TEO | Teager energy operator |

WT | Wavelet transform |

HHT | Hilbert–Huang transform |

VMD-TEO | Variational mode decomposition–Teager energy operator |

EMD | Empirical mode decomposition |

LIF | Low impedance fault |

HIF | High impedance fault |

RNN | Recurrent neural network |

GRU | Gated recurrent unit |

Bi-GRU | Bidirectional gated recurrent unit |

IMF | Intrinsic mode function |

IMF1 | The first intrinsic mode function component |

TEV | Teager energy value |

VSC | Voltage source converter |

NG | Negative ground |

ELU | Exponential linear unit |

PG | Positive ground |

PN | Positive and negative |

## References

- Nanayakkara, O.M.K.K.; Rajapakse, A.D.; Wachal, R. Location of DC line faults in conventional HVDC systems with segments of cables and overhead lines using terminal measurements. IEEE Trans. Power Deliv.
**2012**, 27, 279–288. [Google Scholar] [CrossRef] - Chen, K.; Hu, J.; Zhang, Y.; Yu, Z.; He, J. Fault location in power distribution systems via deep graph convolutional networks. IEEE J. Sel. Areas Commun.
**2020**, 38, 119–131. [Google Scholar] [CrossRef] [Green Version] - Bains, T.P.S.; Sidhu, T.S.; Xu, Z.H.; Voloh, I.; Zadeh, M.R.D. Impedance-based fault location algorithm for ground faults in series-capacitor-compensated transmission lines. IEEE Trans. Power Deliv.
**2018**, 33, 189–199. [Google Scholar] [CrossRef] - Kezunovic, M. Smart Fault Location for Smart Grids. IEEE Trans. Smart Grid
**2011**, 2, 11–22. [Google Scholar] [CrossRef] - Shu, H.C.; Han, Y.M.; Huang, R.; Tang, Y.T.; Cao, P.L.; Yang, B.; Zhang, Y. Fault Model and Travelling Wave Matching Based Single Terminal Fault Location Algorithm for T-Connection Transmission Line: A Yunnan Power Grid Study. Energies
**2020**, 13, 1506. [Google Scholar] [CrossRef] [Green Version] - Lin, S.; He, Z.; Li, X. Travelling wave time-frequency characteristic-based fault location method for transmission lines. IET Gener. Transm. Distrib.
**2012**, 6, 764–772. [Google Scholar] [CrossRef] - Livani, H.; Evrenosoglu, C.Y. A single-ended fault location method for segmented HVDC transmission line. Electr. Power Syst. Res.
**2014**, 107, 190–198. [Google Scholar] [CrossRef] - Spoor, D.; Zhu, H.G. Improved single-ended traveling-wave fault-location algorithm based on experience with conventional substation transducers. IEEE Trans. Power Deliv.
**2006**, 21, 1714–1720. [Google Scholar] [CrossRef] [Green Version] - He, Z.Y.; Liao, K.; Li, X.P.; Lin, S.; Yang, J.W.; Mai, R.K. Natural Frequency-based line fault location in HVDC lines. IEEE Trans. Power Deliv.
**2014**, 29, 851–859. [Google Scholar] [CrossRef] - Zhang, C.; Song, G.; Wang, T.; Yang, L. Single-ended traveling wave fault location method in DC transmission line based on wave front information. IEEE Trans. Power Deliv.
**2019**, 34, 2028–2038. [Google Scholar] [CrossRef] - Borghetti, A.; Bosetti, M.; Di Silvestro, M.; Nucci, C.A.; Paolone, M. Continuous-wavelet transform for fault location in distribution power networks: Definition of mother wavelets inferred from fault originated transients. IEEE Trans. Power Syst.
**2008**, 23, 380–388. [Google Scholar] [CrossRef] - Bernadic, A.; Leonowicz, Z. Fault location in power networks with mixed feeders using the complex space-phasor and Hilbert–Huang transform. Int. J. Electr. Power Energy Syst.
**2012**, 42, 208–219. [Google Scholar] [CrossRef] [Green Version] - Xie, L.; Luo, L.; Li, Y.; Zhang, Y.; Cao, Y. A traveling wave-based fault location method employing VMD-TEO for distribution network. IEEE Trans. Power Deliv.
**2020**, 35, 1987–1998. [Google Scholar] [CrossRef] - Wang, L.; Liu, H.; Le Van, D.; Liu, Y. Novel method for identifying fault location of mixed lines. Energies
**2018**, 11, 1529. [Google Scholar] [CrossRef] [Green Version] - Lan, S.; Chen, M.-J.; Chen, D.-Y. A novel HVDC double-terminal non-synchronous fault location method based on convolutional neural network. IEEE Trans. Power Deliv.
**2019**, 34, 848–857. [Google Scholar] [CrossRef] - Duan, J.; Liu, J.; Lu, H.; Zhao, Z. Fault location method based on traveling-wave instantaneous frequency for HVDC transmission lines. Proc. CSEE.
**2016**, 36, 1842–1848. [Google Scholar] - Zhang, X.; Tai, N.; Wang, Y.; Liu, J. EMTR-based fault location for DC line in VSC-MTDC system using high-frequency currents. IET Gener. Transm. Distrib.
**2017**, 11, 2499–2507. [Google Scholar] [CrossRef] - Moradzadeh, A.; Zakeri, S.; Shoaran, M.; Mohammadi-Ivatloo, B.; Mohammadi, F. Short-term load forecasting of microgrid via hybrid support vector regression and long short-term memory algorithms. Sustainability
**2020**, 12, 7076. [Google Scholar] [CrossRef] - Nguyen, T.T.; Pham, L.H.; Mohammadi, F.; Kien, L.C. Optimal scheduling of large-scale wind-hydro-thermal systems with fixed-head short-term model. Appl. Sci.
**2020**, 10, 2964. [Google Scholar] [CrossRef] - Dash, P.K.; Samantaray, S.R.; Panda, G. Fault classification and section identification of an advanced series-compensated transmission line using support vector machine. IEEE Trans. Power Deliv.
**2007**, 22, 67–73. [Google Scholar] [CrossRef] - Zhang, F.; Liu, Q.; Liu, Y. Novel fault location method for power systems based on attention mechanism and double structure GRU neural network. IEEE Access
**2020**, 8, 75237–75248. [Google Scholar] [CrossRef] - Alves da Silva, A.P.; Lima, A.C.S.; Souza, S.M. Fault location on transmission lines using complex-domain neural networks. Int. J. Electr. Power Energy Syst.
**2012**, 43, 720–727. [Google Scholar] [CrossRef] - Livani, H.; Evrenosoglu, C.Y. A machine learning and wavelet-based fault location method for hybrid transmission lines. IEEE Trans. Smart Grid
**2014**, 5, 51–59. [Google Scholar] [CrossRef] - Shi, Z.; Liang, H.; Dinavahi, V. Direct interval forecast of uncertain wind power based on recurrent neural networks. IEEE Trans. Sustain. Energy
**2018**, 9, 1177–1187. [Google Scholar] [CrossRef] - Ergen, T.; Kozat, S.S. Online training of LSTM networks in distributed systems for variable length data sequences. IEEE Trans. Neural Netw. Learn. Syst.
**2018**, 29, 5159–5165. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ding, M.; Zhou, H.; Xie, H.; Wu, M.; Nakanishi, Y.; Yokoyama, R. A gated recurrent unit neural networks based wind speed error correction model for short-term wind power forecasting. Neurocomputing
**2019**, 365, 54–61. [Google Scholar] [CrossRef] - Zhao, R.; Wang, D.; Yan, R. Machine health monitoring using local feature-based gated recurrent unit networks. IEEE Trans. Ind. Electron.
**2018**, 65, 1539–1548. [Google Scholar] [CrossRef] - LeCun, Y.; Bengio, Y.; Hinton, G. Deep learning. Nature
**2015**, 521, 436–444. [Google Scholar] [CrossRef] - Du, Y.; Li, F.; Li, J.; Zheng, T. Achieving 100x acceleration for N-1 contingency screening with uncertain scenarios using deep convolutional neural network. IEEE Trans. Power Syst.
**2019**, 34, 3303–3305. [Google Scholar] [CrossRef] - Passalis, N.; Tefas, A. Training lightweight deep convolutional neural networks using bag-of-features pooling. IEEE Trans. Neural Netw. Learn. Syst.
**2019**, 30, 1705–1715. [Google Scholar] [CrossRef] - Al Hassan, H.A.; Grainger, B.M.; McDermott, T.E.; Reed, G.F. Fault location identification of a hybrid HVDC-VSC system containing cable and overhead line segments using transient data. In Proceedings of the IEEE PES T&D 2016, Dallas, TX, USA, 3–5 May 2016. [Google Scholar]
- Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q.; Yen, N.C.; Tung, C.C.; Liu, H.H. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. Ser. A
**1998**, 454, 903–998. [Google Scholar] [CrossRef] - Dragomiretskiy, K.; Zosso, D. Variational mode decomposition. IEEE Trans. Signal Process.
**2014**, 62, 531–544. [Google Scholar] [CrossRef] - Li, Y.; Fan, C.; Li, Y.; Wu, Q.; Ming, Y. Improving deep neural network with multiple parametric exponential linear units. Neurocomputing
**2018**, 301, 11–24. [Google Scholar] [CrossRef] [Green Version] - Mohammadi, F.; Nazri, G.-A.; Saif, M. A new topology of a fast proactive hybrid DC circuit breaker for MT-HVDC Grids. Sustainability
**2019**, 11, 4493. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Hybrid two-segment voltage source converter–high voltage direct current (VSC-HVDC) system.

**Figure 2.**Feature engineering analysis results of negative ground (NG) fault occurring at 350 km; (

**a**) fault voltage with noise, (

**b**) fault current with noise, (

**c**) IMF1 of fault voltage by variational mode decomposition (VMD), (

**d**) IMF1 of fault current by VMD, (

**e**) Teager energy values (TEVs) of the first intrinsic mode function (IMF1) in fault voltage, and (

**f**) TEVs of IMF1 in fault current.

**Figure 9.**Voltage source converter (VSC) control system structure; (

**a**) overall controller structure and (

**b**) inner loop controller structure.

**Figure 11.**Fault current at M terminal when the transition resistance R

_{f}changes; (

**a**) PG fault at 50 km, (

**b**) PG fault at 150 km, (

**c**) PG fault at 300 km, and (

**d**) PG fault at 400 km.

**Figure 12.**Partial samples when faults occur at 50, 150, 300 and 400 km. (

**a**–

**d**) Fault current without noise; (

**e**–

**h**) IMF1 of fault current by VMD; (

**i**–

**l**) fault voltage without noise; (

**m**–

**p**) TEVs of IMF1s in fault voltage.

**Figure 13.**Normalized confusion matrix of classification effect; (

**a**) low impedance fault (LIF) and (

**b**) high impedance fault (HIF).

**Figure 14.**Experimental results of signal extraction and singularity detection for a PN fault at 450 km; (

**a**) fault current at terminal M, (

**b**) IMF1 obtained from VMD, (

**c**) TEV of IMF1 with a time window of 40.96 ms, and (

**d**) TEV of IMF1 with a time window of 5 ms.

Layer Types | Kernel/Pool Size | Sub- Sampling Layer | Stride | Number of Kernels | Number of Neurons | Activation Function | Outputs |
---|---|---|---|---|---|---|---|

Input layer | - | - | - | - | - | - | 2 × 4096 × 1 |

C_{1} | 2 × 2 | - | 1 | 16 | - | ELU | 2 × 4096 × 16 |

S_{1} | 2 × 2 | Maximum | 2 | - | - | - | 1 × 2048 × 16 |

C_{2} | 2 × 2 | - | 1 | 16 | - | ELU | 1 × 2048 × 16 |

S_{2} | 1 × 2 | Maximum | 2 | - | - | - | 1 × 1024 × 16 |

C_{3} | 2 × 2 | - | 1 | 32 | - | ELU | 1 × 1024 × 32 |

S_{3} | 1 × 2 | Maximum | 2 | - | - | - | 1 × 512 × 32 |

C_{4} | 2 × 2 | - | 1 | 32 | - | ELU | 1× 512 × 32 |

S_{4} | 1 × 2 | Maximum | 2 | - | - | - | 1 × 256 × 32 |

C_{5} | 2 × 2 | - | 1 | 64 | - | ELU | 1 × 256 × 64 |

S_{5} | 1 × 2 | Average | 2 | - | - | - | 1 × 128 × 64 |

C_{6} | 2 × 2 | - | 1 | 64 | - | ELU | 1 × 128 × 64 |

S_{6} | 1 × 2 | Average | 2 | - | - | - | 1 × 64 × 64 |

R_{1} | - | - | - | - | - | - | 4096 |

F_{1} | - | - | - | - | 200 | ELU | 200 |

D_{1} | - | - | - | - | - | - | 200 |

F_{2} | - | - | - | - | 64 | ELU | 64 |

D_{2} | - | - | - | - | - | - | 64 |

F_{3} | - | - | - | - | N | Softmax | N |

Fault Distance | WT | HHT | VMD-TEO | |||
---|---|---|---|---|---|---|

Distance | Error | Distance | Error | Distance | Error | |

(km) | (km) | (km) | (km) | (km) | (km) | (km) |

50 | 53.797 | 3.797 | 53.386 | 2.386 | 50.137 | 0.137 |

100 | 103.827 | 3.827 | 95.564 | 4.436 | 99.773 | 0.227 |

150 | 153.624 | 3.624 | 153.518 | 3.518 | 150.265 | 0.265 |

200 | 196.671 | 3.329 | 204.447 | 4.447 | 200.272 | 0.272 |

250 | 254.227 | 4.227 | 244.596 | 5.404 | 250.257 | 0.257 |

300 | 305.106 | 5.106 | 304.234 | 4.234 | 300.251 | 0.251 |

400 | 404.534 | 4.534 | 396.522 | 3.478 | 400.197 | 0.197 |

450 | 446.575 | 3.425 | 455.416 | 5.416 | 450.234 | 0.234 |

Fault Distance | 1D-CNN | GRU | Bi-GRU | LSTM | ||||
---|---|---|---|---|---|---|---|---|

Distance | Error | Distance | Error | Distance | Error | Distance | Error | |

(km) | (km) | (km) | (km) | (km) | (km) | (km) | (km) | (km) |

50 | 54.186 | 4.186 | 51.186 | 1.186 | 51.919 | 1.919 | 50.137 | 0.137 |

100 | 104.333 | 4.333 | 101.333 | 1.333 | 98.179 | 1.821 | 99.773 | 0.227 |

150 | 154.221 | 4.221 | 151.221 | 1.221 | 151.978 | 1.978 | 150.265 | 0.265 |

200 | 195.896 | 4.104 | 198.896 | 1.104 | 202.149 | 2.149 | 200.272 | 0.272 |

250 | 254.131 | 4.131 | 251.131 | 1.131 | 252.721 | 2.721 | 250.257 | 0.257 |

300 | 305.213 | 5.213 | 301.213 | 1.213 | 302.497 | 2.497 | 300.251 | 0.251 |

400 | 404.238 | 4.238 | 401.238 | 1.238 | 397.768 | 2.232 | 400.197 | 0.197 |

450 | 445.879 | 4.121 | 448.879 | 1.121 | 452.011 | 2.011 | 450.234 | 0.234 |

Fault Location | Fault Type | Fault Resistance | Distance | Error |
---|---|---|---|---|

(km) | (Ω) | (km) | (km) | |

40 | PG | 900 | 39.739 | 0.261 |

80 | NG | 75 | 80.379 | 0.379 |

120 | PN | 1100 | 119.668 | 0.332 |

150 | PN | 65 | 149.618 | 0.382 |

180 | NG | 29 | 180.317 | 0.317 |

250 | PG | 840 | 249.749 | 0.251 |

310 | NG | 920 | 310.346 | 0.346 |

375 | PN | 1020 | 374.688 | 0.312 |

400 | PG | 1120 | 399.627 | 0.373 |

440 | NG | 54 | 440.249 | 0.249 |

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## Share and Cite

**MDPI and ACS Style**

Wang, L.; He, Y.; Li, L.
A Single-Terminal Fault Location Method for HVDC Transmission Lines Based on a Hybrid Deep Network. *Electronics* **2021**, *10*, 255.
https://doi.org/10.3390/electronics10030255

**AMA Style**

Wang L, He Y, Li L.
A Single-Terminal Fault Location Method for HVDC Transmission Lines Based on a Hybrid Deep Network. *Electronics*. 2021; 10(3):255.
https://doi.org/10.3390/electronics10030255

**Chicago/Turabian Style**

Wang, Lei, Yigang He, and Lie Li.
2021. "A Single-Terminal Fault Location Method for HVDC Transmission Lines Based on a Hybrid Deep Network" *Electronics* 10, no. 3: 255.
https://doi.org/10.3390/electronics10030255