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The fault generated transient traveling waves are wide band signals which cover the whole frequency range. When the frequency characteristic of line parameters is considered, different frequency components of traveling wave will have different attenuation values and wave velocities, which is defined as the dispersion effect of traveling wave. Because of the dispersion effect, the rise or fall time of the wavefront becomes longer, which decreases the singularity of traveling wave and makes it difficult to determine the arrival time and velocity of traveling wave. Furthermore, the dispersion effect seriously affects the accuracy and reliability of fault location. In this paper, a novel double-ended fault location method has been proposed with compensating the dispersion effect of traveling wave in wavelet domain. From the propagation theory of traveling wave, a correction function is established within a certain limit band to compensate the dispersion effect of traveling wave. Based on the determined arrival time and velocity of traveling wave, the fault distance can be calculated precisely by utilizing the proposed method. The simulation experiments have been carried out in ATP/EMTP software, and simulation results demonstrate that, compared with the traditional traveling-wave fault location methods, the proposed method can significantly improve the accuracy of fault location. Moreover, the proposed method is insensitive to different fault conditions, and it is adaptive to both transposed and untransposed transmission lines well.

Power systems have grown rapidly over the last few decades, and the number and length of transmission lines increased. Transmission lines are exposed in the field, and, especially in the mountains and hilly terrains, they are prone to failure. In this scenario, a fast and accurate fault location technique is essential to reduce the restoration time of power systems, which is important with respect to technical and economic issues. Therefore, the study and development of fault location have been motivated since the 1950s [

The traveling-wave-based fault location methods for transmission lines can generally be classified as single- and double-ended methods in terms of their different ways of obtaining the fault information. For many years, the single-ended traveling-wave-based methods were recognized by utilities as a good way to overcome the drawbacks of impedance-based approaches [

For the traveling-wave-based fault location method, the accuracy of fault location lies in the arrival time and velocity of traveling wave. Several methods have been proposed to determine the arrival time of traveling wave [

On the other hand, the wave velocity also directly affects the accuracy of fault location. Some researchers have proposed some methods which are insensitive to the velocity of traveling wave [

When a fault happens, the generated traveling wave contains a lot of frequency components, which can be viewed as very important fault information. Because of the frequency-dependent parameters of transmission line, each component has different velocity and attenuation. This phenomenon is defined as traveling-wave dispersion effect [

The paper is organized as follows. Section

When a fault happens on a transmission line, the generated voltage and current surges will travel towards both ends of the line. This is equivalent to generating a virtual voltage source at the fault point, as shown in Figure

Traveling-wave theory.

Refraction and reflection will occur at the fault point, ends of lines, and other discontinuity points. Thus, the generated reflected and refracted wave will propagate along the transmission line, as shown in Figure

Refection and refraction of traveling wave.

In the double-ended traveling-wave-based method, the distance between a fault point and measuring point at

There is an electromagnetic coupling effect between transmission lines. Therefore, by using a modal transformation matrix, we can decompose the traveling wave between phases into several independent modes. In the case of transposed transmission lines, the parameters of transmission line are balanced and the modal transformation can be defined as constant and real [

For untransposed transmission line, the phase-to-modal transformation matrix is frequency-dependent and unsymmetrical [

Wavelet transform (WT) is a common mathematical tool for digital signal processing. WT has been widely applied in lots of fields, such as time series analysis, speech processing, digital image processing, and power system transient analysis [

Wavelet transform is regarded as a filter. The filter of wavelet transform can be employed as follows:

From the analysis above, wavelet transform can be calculated by using Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT). Therefore, wavelet transform of traveling wave can be employed by using the following equation:

The traveling wave has a lot of frequency components. As a matter of fact, the distributed parameters of transmission line are frequency-dependent, which results in different frequency components having different velocities and attenuation values. This phenomenon is defined as the dispersion effect of traveling wave [

There are two important parameters for the traveling-wave dispersion effect. One is the propagation coefficient, and the other is phase velocity. The propagation coefficient of the

Frequency-dependent parameters of transmission line.

Resistance varied with frequency

Reactance varied with frequency

Attenuation coefficient varied with frequency

Propagation velocity varied with frequency

The propagation coefficient is also described as follows:

The modal attenuation coefficient and phase velocity, which vary with frequencies, are shown in Figures

It can be seen from Figure

In frequency domain, attenuation and wave velocity of traveling wave increase along with frequency. In time domain, the arrival times of different frequency components are not the same. The high-frequency component will arrive at the measuring point first of all, and the low-frequency component will be delayed much more in reaching the measuring point than the high-frequency component. Therefore, all of the detected wavefronts at different measuring points are not ideal step signals; these rise times or fall times get long, which can been seen from Figure

The propagation theory of forward and reverse traveling wave is shown in Figure

The propagation theory of forward and reverse traveling wave.

According to the propagation equation of single conductor line, the voltages

From signal and system theory, the reverse traveling wave

Likewise, the initial surge of traveling wave, which is used for double-ended fault location method, is the frequency response of the signal at the fault point. Suppose that the distance between the fault point and the measuring point is

For fault location,

When a fault happens, the three-phase voltage at

The three-phase voltage is obtained when a fault happens.

The transient three-phase voltages are first decoupled into their independent modal components by using (

At the scale

At the scale

Based on the double-ended fault location theory described in Section

Calculate the propagation function based on Carson formulation, and then calculate the corresponding corrected function

At the scale

Based on the double-ended fault location theory, accurate fault distance,

From the analysis above, it can be observed that the wavelet-transform-based fault location method is described in frequency domain from Step

A model for 500 kV transposed transmission line is constructed in ATP/EMTP, as shown in Figure

Model of transmission line.

500 kV transmission line model

Geometry structure of transmission line

In ATP/EMTP software, the sample rate is set as 1 MHz. The traveling-wave data generated in ATP software is imported into MATLAB software. In MATLAB, the correction method is implemented. In this paper, ^{5} km/s.

When we select several discrete frequencies and calculate the propagation function of each frequency with

When we obtain

Corrected waveforms with the distance of 345 km.

As can be seen from Figure

Comparisons of the wavelet coefficients.

In this paper, we compare the fault location accuracy between the traditional method and the proposed method. The traditional method is based on the wavelet transform (Morlet wavelet function) and it is not corrected by the correction method proposed in this paper. In order to test the applicability of the proposed method, various fault conditions are simulated, respectively. In the simulated experiments, the error of fault location is calculated as a performance index by the following equation:

The transition resistance directly affects the voltage amplitude of the initial traveling wave. In this paper, we set the fault inception angle to analyze the errors of fault location, when the transition resistance varies from 10 Ω to 500 Ω. The distance between the fault point and the measuring terminal is 100 km, the fault type is A-G, and the fault inception angle is 106°. The simulated results are shown in Tables

Error under different transition resistance values (transposed circuit).

Transition resistance | The traditional method | The proposed method | ||
---|---|---|---|---|

Location results | Error | Location results | Error | |

10 | 100.3 | 0.10 | 100.23 | 0.07 |

50 | 99.50 | 0.18 | 99.60 | 0.13 |

100 | 99.34 | 0.22 | 99.62 | 0.12 |

500 | 98.70 | 0.43 | 99.30 | 0.23 |

Error under different transition resistance values (untransposed circuit).

Transition resistance | The traditional method | The proposed method | ||
---|---|---|---|---|

Location results | Error | Location results | Error | |

10 | 100.57 | 0.19 | 100.30 | 0.10 |

50 | 101.20 | 0.40 | 100.56 | 0.19 |

100 | 98.75 | 0.42 | 99.18 | 0.27 |

500 | 101.02 | 0.34 | 100.55 | 0.18 |

The fault inception angle is one of the most effective parameters which influence the accuracy of the traveling-wave-based fault location. In order to test the influence of fault inception angle, the simulated cases are constructed with the fault inception angle varied from 18° to 90°. At the moment, the fault type is A-G, the transition resistance is 10 Ω, and the fault distance is 100 kilometers. The experiment results are shown in Tables

Error under different inception angles (transposed circuit).

Fault inception angle | The traditional method | The proposed method | ||
---|---|---|---|---|

Location results | Error | Location results | Error | |

18° | 100.60 | 0.20 | 100.42 | 0.07 |

36° | 100.31 | 0.10 | 100.22 | 0.10 |

72° | 100.86 | 0.29 | 99.96 | 0.18 |

90° | 100.80 | 0.27 | 100.78 | 0.26 |

Error under different inception angles (untransposed circuit).

Fault inception angle | The traditional method | The proposed method | ||
---|---|---|---|---|

Location results | Error | Location results | Error | |

18° | 100.85 | 0.28 | 100.50 | 0.17 |

36° | 100.62 | 0.21 | 100.40 | 0.13 |

72° | 99.33 | 0.22 | 99.60 | 0.13 |

90° | 100.56 | 0.19 | 100.33 | 0.11 |

To investigate the effect of different fault types based on the proposed method in this paper, several experiments have been implemented and experiment results are shown in Tables

Error under different fault types (transposed circuit).

Fault type | The traditional method | The proposed method | ||
---|---|---|---|---|

Location results | Error | Location results | Error | |

A-G | 100.30 | 0.10 | 100.23 | 0.08 |

B-G | 99.50 | 0.17 | 99.63 | 0.12 |

BC | 99.21 | 0.26 | 100.45 | 0.15 |

BC-G | 100.87 | 0.29 | 100.14 | 0.05 |

ABC-G | 99.25 | 0.25 | 99.45 | 0.18 |

Error under different fault types (untransposed circuit).

Fault type | The traditional method | The proposed method | ||
---|---|---|---|---|

Location results | Error | Location results | Error | |

A-G | 100.57 | 0.19 | 100.30 | 0.10 |

B-G | 99.54 | 0.15 | 99.64 | 0.12 |

BC | 101.05 | 0.35 | 100.85 | 0.28 |

BC-G | 100.78 | 0.26 | 100.23 | 0.08 |

ABC-G | 100.50 | 0.16 | 100.26 | 0.09 |

To investigate the performance of antinoise under different levels, several experiments have been implemented. In these experiments, the transition resistance is 10 Ω with BC-G fault, the fault inception angle is 106°, and the fault distance is 100 kilometers. Since noise has no meaningful information about fault location, it would be rational to define a threshold to reject the noise-associated WT coefficient [

Error under different noise levels (transposed circuit).

Noise (unit: dBw) | The traditional method | The proposed method | ||
---|---|---|---|---|

Location results | Error | Location results | Error | |

10 | 100.78 | 0.26 | 100.14 | 0.05 |

20 | 100.78 | 0.26 | 100.15 | 0.05 |

30 | 99.21 | 0.2633 | 100.30 | 0.10 |

40 | 100.76 | 0.2533 | 100.21 | 0.07 |

The production error of the towers supporting transmission line is very low, and it is within 1 cm. The geometrical parameters of the corner tower and the tower in substation are sometimes different from other towers along the transmission line. The number of the corner towers and the towers in substation is very small and they can be omitted. Therefore, from the point of view of theoretical calculation, we assume that the relative position between line conductors is unchanged. On the other hand, the height of line conductors will sometimes increase when the transmission line passes through a road, village, city, mountain, and so forth. The change is very complicated; it is very difficult to model the real transmission line. In the paper, for analyzing the applicability of the proposed method, the length of the transmission line which is supported by the changed tower is 20 km. In these experiments, the transition resistance is 10 Ω with A-G fault, the fault inception angle is 106°, and the fault distance is 100 kilometers. Simulation results in Table

Error under different tower heights (transposed circuit).

Tower height (mile) | The traditional method | The proposed method | ||
---|---|---|---|---|

Location results | Error | Location results | Error | |

0 | 100.60 | 0.20 | 100.14 | 0.05 |

+5 | 100.47 | 0.16 | 100.22 | 0.07 |

+10 | 99.18 | 0.27 | 100.45 | 0.15 |

+20 | 100.80 | 0.27 | 100.55 | 0.18 |

In this paper, the dispersion characteristic of traveling wave is analyzed in time and frequency domain, respectively. When traveling wave travels along transmission line, the fall or rise time of the wavefront will become long with the increase of propagation distance. Thus, the singularity of the transient wavefront decreases. In this paper, a novel double-ended fault location method has been proposed to overcome the dispersion effect of traveling wave. In the method, a correction algorithm for overcoming the dispersion effect of traveling wave enhances the singularity of the transient traveling wave. The proposed method is tested under various experiment conditions, such as different fault distances, different transition resistances, and different fault inception angles. The simulation experiments demonstrate that the proposed method is better than the traditional traveling-wave-based fault location method. Furthermore, the novel method is suitable for both transposed and untransposed transmission lines. All of the advantages prove that the proposed method is available. However, there are several other parameters which affect the slope of traveling wave, such as the impedance characteristic of traveling-wave measurement equipment and shunt reactor connected to the line. Future work will consider those parameters.

The author declares that there are no competing interests regarding the publication of this paper.

This work was supported by the Fundamental Research Funds for the Central Universities (no. 13MS68) and Hebei Province Natural Science Foundation of China, Youth Science Fund (no. E2013502267).