The distribution network exhibits complex structural characteristics, which makes fault localization a challenging task. Especially when a branch of the multi-branch distribution network fails, the traditional multi-branch fault location algorithm makes it difficult to meet the demands of high-precision fault localization in the multi-branch distribution network system. In this paper, the multi-branch mainline is decomposed into single branch lines, transforming the complex multi-branch fault location problem into a double-ended fault location problem. Based on the different transmission characteristics of the fault-traveling wave in fault lines and non-fault lines, the endpoint reference time difference matrix S and the fault time difference matrix G were established. The time variation rule of the fault-traveling wave arriving at each endpoint before and after a fault was comprehensively utilized. To realize the fault segment location, the least square method was introduced. It was used to find the first-order fitting relation that satisfies the matching relationship between the corresponding row vector and the first-order function in the two matrices, to realize the fault segment location. Then, the time difference matrix is used to determine the traveling wave velocity, which, combined with the double-ended traveling wave location, enables accurate fault location.

With the gradual increase in urbanization and city scale, the demand for electricity in modern society is also rising. As more loads are connected to the distribution network, distribution lines with multiple branches serve the purpose of providing multiple power supplies to cater to the increasing number of loads [

The distribution network has a complex topology, with each mainline containing numerous branches. Typically, traveling wave detection devices are installed at the end of the line rather than at the end of each branch. As a result, directly applying the double-ended traveling wave positioning method to multi-branch distribution networks is challenging [

Reference [

Based on the analysis above, this paper proposes a new method for locating multi-branch faults by fitting the time difference matrix. The complex problem of locating faults in multi-branch lines is simplified by transforming it into a double-ended fault location problem. Additionally, the multi-branch lines are decomposed into mainlines that only consist of simple branches, such as T-branches or three-branches. The fault original traveling wave head in the fault line and non-fault line have different characteristics. To analyze this, we establish the decomposed baseline time difference matrix S and the fault time difference matrix G of the mainline endpoints. We then deeply analyze the time difference variation before and after a fault occurs on both lines. Additionally, we identify any changes in the elements of these matrices before and after a fault occurs. To minimize the impact of wave velocity on line parameters, we determine the wave velocity based on the arrival time of the original fault-traveling wave along the shortest path. This allows us to modify the parameters in matrices S and G. The least square method is used to fit the data of the row vector elements in matrices S and G. This helps determine the best first function match between the two-row vectors, which then determines the fault branch segment. This method is suitable for multi-branch circuits, improving the algorithm’s practicality. The proposed method has been verified for accuracy and reliability through theoretical analysis and simulation.

In the multi-branch distribution network, there are three main types of line faults. These include mainline faults

In summary, multi-branch lines in

After decomposing the multi-branch line into a simple line (T-branch or three-branch line), the problem of locating faults in complex multi-branch lines is transformed into locating faults in double-ended networks [

As shown in

Similarly, we can establish the baseline time difference matrix

When a genuine fault occurs, we can construct the fault-traveling wave time difference matrix

Similarly, the failure time difference matrix

The transmission characteristics of fault-traveling waves are different between the fault and non-fault lines: As shown in

In

If the elements in the matrix S and G of all lines are the same, it can be judged the bus is faulty.

In a multi-branch distribution network, the mainlines containing multiple branches are decomposed into multiple lines containing only simple branches. A simulated fault point is set at the head and tail of each mainline after decomposition, and the endpoint reference time difference matrix

According to the above principles, when the fault

In

By using

A single branch line refers to a branch line that does not have any other branches connected to it. For example, when the fault

When the fault

The original traveling wave head is transmitted along the shortest path, carrying information about the time it takes for the traveling wave from the fault point to reach the detection device [

When a fault point as shown in

In

The velocity of the traveling wave is not solely determined by the speed of light, as it is influenced by line parameters. In this paper, we combine two data points from the fault time difference matrix G that have the minimum time difference for each line. We use these data points to calculate the wave velocity based on the principle of original fault-traveling wave diffuseness along the shortest path. Finally, we average out the sum of wave velocities acquired from each line, as shown in

In the above formula,

Based on the principles mentioned above, the matrix S and G of a non-fault line should be identical under ideal circumstances. However, in practical situations, various measurement errors occur. For instance, factors like interference, lightning strikes, and high-frequency signals can affect the traveling wave acquisition device. As a result, incorrect original traveling wave heads are identified during fault identification. The arrival time of the calibration original traveling wave head shows varying degrees of error. To mitigate this, we introduce the least square method for a one-time fitting to reduce the impact of errors.

The least square method is a mathematical technique used for fitting data. Specifically, the linear least square method determines if the data follows a linear pattern and finds the best function that fits the data by minimizing the sum of squared errors [

The linear least square method is used to find a linear relationship between x and its corresponding y. The equation for this method is:

The undetermined constants a and b in the equation are transformed into linear regression coefficients, which represent the intercept and slope of the line. The goal of the fitting is to determine these regression coefficients based on measured data, to minimize deviation and to make data points as close as possible to the straight line. Deviations can be positive or negative, and their calculation follows this formula:

When S is the smallest in the above equation, the corresponding a represents the fitted curve coefficient. Both a and b must satisfy the following conditions:

In

The first-order fitting relation obtained through the least square method must satisfy the matching relation between the corresponding row vectors and the subfunction (

The multi-branch distribution network, depicted in

The

After a fault occurs, the traveling wave detection device constructs the original time of the fault-traveling wave head using the fault time difference matrix G from mainline 2, as shown in

The row vectors

As shown in

As shown in

To analyze the impact of transition resistance on this multi-branch fault location algorithm, we conducted experiments with different ground fault types and fault points. Specifically, we tested fault resistances of 50, 500, and 1000 Ω, respectively. Additionally, we set the original phase of the faults to 90° and introduced white noise with a signal-to-noise ratio of 40 dB as a jamming signal. The results of fault location are shown in

Point of fault | Fault type | Segment location result | Transition resistance (Ω) | Fault location result (m) | Fault location error (m) |
---|---|---|---|---|---|

Ag | a- |
50 | 176 | 24 | |

500 | 176 | 24 | |||

1000 | 176 | 24 | |||

ABg | b-c | 50 | 1373 | 32 | |

500 | 1353 | 52 | |||

1000 | 1345 | 60 | |||

Arc | d- |
50 | 158 | 42 | |

500 | 134 | 66 | |||

1000 | 122 | 78 | |||

Ag | h- |
50 | 195 | 5 | |

500 | 192 | 8 | |||

1000 | 192 | 8 | |||

ABg | h-i | 50 | 523 | 89 | |

500 | 517 | 95 | |||

1000 | 517 | 95 | |||

Arc | p- |
50 | 719 | 81 | |

500 | 719 | 81 | |||

1000 | 719 | 81 |

It can be acquired from the results in

To analyze the impact of the original fault phase angle on this multi-branch fault location algorithm, we conducted simulations with different ground fault types and fault points. Specifically, we tested three scenarios: 30°, 60°, and 90° fault phase angles. In each scenario, we set the fault resistance to 50 Ω and introduced a white noise interference signal with a signal-to-noise ratio of 40 dB for accurate simulation. The results of fault location are shown in

Point of failure | Fault type | Segment location result | Original fault phase angle (°) | Fault location result (m) | Fault location error (m) |
---|---|---|---|---|---|

Ag | a- |
30 | 277.6 | 22.4 | |

60 | 277.6 | 22.4 | |||

90 | 277.6 | 22.4 | |||

ABg | b-c | 30 | 1254.8 | 25.2 | |

60 | 1254.8 | 25.2 | |||

90 | 1257.6 | 22.4 | |||

Arc | d- |
30 | 236.2 | 63.8 | |

60 | 236.2 | 63.8 | |||

90 | 236.2 | 63.8 | |||

Ag | h- |
30 | 182.8 | 17.2 | |

60 | 182.8 | 17.2 | |||

90 | 182.8 | 17.2 | |||

ABg | h-i | 30 | 484 | 128 | |

60 | 484 | 128 | |||

90 | 484 | 128 | |||

Arc | p- |
30 | 662.9 | 137.1 | |

60 | 662.9 | 137.1 | |||

90 | 662.9 | 137.1 |

It can be acquired from the results in

To analyze the influence of white noise on this fault location algorithm, we added white noise signals to the sampled signal. The signal-to-noise ratios used were 40, 50, and 60 dB. For simulation purposes, we set the fault resistance at 50 Ω and the fault original phase angle at 90°. The results of fault location are shown in

Point of failure | Fault type | Segment location result | Interference white noise (dB) | Fault location result (m) | Fault location error (m) |
---|---|---|---|---|---|

Ag | a- |
40 | 274.8 | 25.2 | |

50 | 274.8 | 25.2 | |||

60 | 274.8 | 25.2 | |||

ABg | b-c | 40 | 1377 | 28 | |

50 | 1257.6 | 22.4 | |||

60 | 1257.6 | 22.4 | |||

Arc | d- |
40 | 273.1 | 26.9 | |

50 | 273.1 | 26.9 | |||

60 | 273.1 | 26.9 | |||

Ag | h- |
40 | 184 | 16 | |

50 | 184 | 16 | |||

60 | 184 | 16 | |||

ABg | h-i | 40 | 750 | 12 | |

50 | 750 | 12 | |||

60 | 750 | 12 | |||

Arc | p- |
40 | 767.5 | 32.5 | |

50 | 767.5 | 32.5 | |||

60 | 770.3 | 29.7 |

It can be acquired from the results in

We analyzed the positioning effects of various methods. Based on the fault locations and types shown in

The fault location problem in the multi-branch distribution network can be addressed by decomposing the multi-branch mainline into multiple mainlines with single branches. This transforms the multi-branch fault location problem into a double-ended fault location problem. To determine the fault segment, we establish an endpoint time difference matrix and a fault time difference matrix based on the propagation features of the fault-traveling wave in both fault and non-fault lines. By comparing the change rules of corresponding elements in these matrices, we can identify the faulty section. Additionally, to improve practicality, we introduce a least square fitting model to reduce errors caused by marking the original traveling wave head, lightning strikes, or high-frequency noise. This method enhances engineering applicability and is suitable for addressing faults in multi-division power grid systems. In summary, this paper proposes a logical and orderly location method that observes matrix features before and after a fault to handle faults in multi-branch lines. However, it relies on improvements in traveling wave acquisition equipment performance and clock synchronization device accuracy.

The authors acknowledge the support of State Grid Hunan Electric Power Research Institute.

This work was funded by the project of State Grid Hunan Electric Power Research Institute (No. SGHNDK00PWJS2210033).

The authors confirm their contribution to the paper as follows: The study conception and design: Hua Leng, Silin He; data collection: Silin He, Jian Qiu; analysis and interpretation of results: Feng Liu, Xinfei Huang; draft manuscript preparation: Xinfei Huang, Jiran Zhu. All authors reviewed the results and approved the final version of the manuscript.

Data supporting this study are included within the article.

The authors declare that they have no conflicts of interest to report regarding the present study.