To locate the fault location accurately and solve the problem quickly is the key to improve the power supply capacity of power grid. This paper presents a fault location method based on SVM fault branch selection algorithm and similarity matching. Firstly, an SVM-based fault branch filter classifier was constructed based on the positive sequence component feature matrix data of each monitoring point, which can accurately select the branch where the current fault is located. Then, based on the positive sequence voltage distribution characteristics, the Euclidean distance and Pearson correlation coefficient (PCC) are used to establish the similarity objective function of fault location. And then, the fault is accurately located by the objective function. Finally, the proposed method is validated by using an IEEE-14 node network. The results show that the proposed method is effective and accurate.
Fast and accurate location of distribution network faults can effectively reduce the time of troubleshooting and blackout, reduce economic losses, and improve power supply reliability [
At present, scholars have done a lot of work on the accurate fault location of the distribution network. The main fault location methods are mainly divided into the traveling wave method and nontraveling wave method (including impedance method, node matrix method, and fitting optimization method). The traveling wave method [
In summary, most of the existing location methods either fail to overcome the influence of transition resistance on the location results or need to know the fault branch and fault type to locate, or the location results are greatly affected by measurement errors and fake fault points or need to traverse all locations of the network to search fault points, which results in a huge amount of calculation when the system scale is large.
To solve these problems, a fault location method based on the SVM fault branch selection and similarity model matching was proposed in this paper. The method utilized the distribution characteristics and their interrelationships of positive sequence voltage variations at each monitoring point to construct fault feature modes that were not affected by fault types and transition resistance. A fault branch selection database was established based on the simulation data and use this data to train SVM-based fault branch selecting classifier. And this SVM classifier is used to determine the branch where the current fault is located. Then, the fault location models of each branch were established with the fault distance parameter
The location, type, and transition resistance of faults are the three variables that determine the voltage of each monitoring point. The schematic diagram of failure in the system is shown in Figure
A fault takes place in a network.
In this paper, the symmetrical component method is used to decompose the positive sequence component, and the positive sequence component is used to analyze the fault electrical characteristics. In three phases, A phase is 120 degrees ahead of B phase, B phase is 120 degrees ahead of C phase, C phase is 120 degrees ahead of A phase, and the components with the same amplitude of three phases are called positive sequence components. The positive sequence driving point impedance
In formula (
Assuming that the positive sequence voltage before system failure of monitoring point
In formula (
Positive sequence voltage variation at monitoring point is defined as
It can be seen from the formula above that the change of positive sequence voltage at the monitoring point is only related to the positive sequence impedance between the monitoring point and the fault point and the positive sequence fault current. The positive sequence impedance between the monitoring point and the fault point represents the relative position information between them. For any fault position in the branch, the positive sequence impedance between the monitoring point and the fault position corresponds to it one to one and is not affected by the fault type and transition resistance.
It is assumed that there are two monitoring points in the system and two faults take place at point F successively, as shown in Figure
Two faults on different branches.
According to formula (
In formula (
From the formulas above, it can be seen that the ratios of positive sequence voltage variations of
Based on the above analysis, a fault location model based on network monitoring point information can be established according to the change characteristics of monitoring points. Assuming that the first and last nodes of the branch where the fault is located are
The calculation formula of positive sequence short-circuit current is standard positive sequence voltage before fault divided by positive sequence driving point impedance at fault position:
In formula (
From the data information uploaded from the monitoring point and the network topology parameters, it can be seen that the fault location
In order to avoid the influence of data amplitude, the sequence of positive sequence voltage variation is standardized in this paper. The standardized processing formula is
Among them,
After standardizing the positive sequence voltage variation sequence of the monitoring points, the fault location model (
In the above formula,
According to the characteristics of positive sequence voltage distribution, the proportional relationship between positive sequence voltage variations at each monitoring point is fixed for faults occurring at the same location. Therefore, a unique
Support vector machine (SVM) makes the linear nonseparable samples in the input space project to the high-dimensional space through nonlinear mapping and becomes the linear separable samples by introducing inner product kernel function [
Define the category tag
The distance from the sampling point to the classification interface is
The optimal classification interface should satisfy the idea of maximum separation, i.e.,
By using the extreme value method of inequality constraints, we can get
The partial derivatives of
If
The samples that with
The kernel classification function is expressed as
For the linear nonseparable case, SVM introduces the relaxation variable
The kernel function used in this paper is sigmoid function:
Based on this, this paper regards the failure of each branch as the same type. At 25%, 50%, and 75% of each branch, the virtual fault points are set up, respectively. The fault simulation is carried out at the virtual fault points. The fault data are processed according to formula (
After determining the branch where the fault is located, this paper uses the similarity matching method to solve the fault location parameter
The Euclidean distance transform is useful for a variety of applications including image processing, computer vision, pattern recognition, shape analysis, and computational geometry [
PCC is a parameter used to measure the linear relationship between distance variables [
The PCC between
Combined with the above Euclidean distance and PCC algorithm, the fault distance objective function established in this paper is shown in the following formula:
In the fault location calculation process, the short-circuit fault is simulated at 25%, 50%, and 75% of each branch in the network, and a fault-based branch selection database is established. Use this database to train the SVM fault branch selection model. Then, based on the current fault information,
Fault location execution flowchart.
The case analysis is based on the IEEE-14 node typical distribution network as a simulation model. The model topology and the parameters of each branch are shown in Figure
The typical distribution network of IEEE-14 nodes.
Fault tests were carried out at 25%, 50%, and 75% of each branch. The fault types included single-phase short-circuit fault, two-phase short-circuit fault, and three-phase short-circuit fault. Table
The positive sequence voltage variation information database of monitoring points.
Node | Branch | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
1 | 1.000 | 0.988 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 |
2 | −1.000 | 1.000 | 0.992 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 |
3 | −1.000 | 0.994 | −1.000 | 1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 |
4 | 1.000 | −1.000 | −1.000 | −1.000 | 0.949 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 |
5 | −1.000 | 0.969 | −1.000 | −1.000 | 1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 |
6 | −1.000 | −1.000 | 1.000 | 1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 |
7 | −1.000 | −1.000 | −1.000 | 0.960 | 1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 |
8 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | 1.000 | 1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 |
9 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | 0.100 | −1.000 | 1.000 | −0.200 | −0.600 | −0.900 | −1.000 | −0.300 |
10 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −0.683 | 1.000 | −0.109 | −0.980 | −1.000 | −0.881 |
11 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −0.231 | 1.000 | −1.000 | −1.000 | −1.000 |
12 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | 1.000 | −0.421 | −0.818 |
13 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −0.114 | 1.000 | −0.291 |
14 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −0.650 | −0.875 | −1.000 | −0.825 | −0.450 | 1.000 |
15 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −0.921 | 0.762 | 1.000 | −1.000 | −1.000 | −0.980 |
16 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | 1.000 | 0.441 | −0.548 |
17 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −0.385 | 0.692 | 1.000 |
18 | −1.000 | −1.000 | −1.000 | −1.000 | 1.000 | 1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 |
19 | −1.000 | −1.000 | −1.000 | 1.000 | −1.000 | −1.000 | 1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 | −1.000 |
20 | −1.000 | −1.000 | −1.000 | 0.105 | −1.000 | −1.000 | −1.000 | −1.000 | 1.000 | −0.196 | −0.600 | −0.910 | −1.000 | −0.302 |
In order to know how many training samples should be sufficient to meet the expected accuracy, the relationship between training set size and test set accuracy was tested before the fault location experiment. The experimental results are shown in Table
The relationship between training set size and test set accuracy.
The number of training samples | Test accuracy (%) |
---|---|
100 | 8.3 |
200 | 38.3 |
300 | 81.7 |
400 | 96.7 |
500 | 100 |
600 | 100 |
700 | 100 |
Then, in each branch, three fault points (60 in total, random position, and random fault type) are randomly selected as the test data of the SVM fault branch selection. The process of generating validation samples is as follows: A random number from 0 to 1 is generated as the fault distance The fault type is selected randomly, in single-phase fault, two-phase fault, and three-phase fault. On branch 1, the failure can be simulated according to the result of random selection, and 1 verification sample is obtained. Repeat the random fault simulation three times on branch 1, and then continue the random fault simulation on the next branch. There are 20 branches in total, so 60 verification samples can be obtained.
The correct rate of branch selection test results is shown in Table
The test results of the SVM-based fault branch selection algorithm.
Branch number | Accuracy rate (%) |
---|---|
1 | 100 |
2 | 100 |
3 | 100 |
4 | 100 |
5 | 100 |
6 | 100 |
7 | 100 |
8 | 100 |
9 | 100 |
10 | 100 |
11 | 100 |
12 | 100 |
13 | 100 |
14 | 100 |
15 | 100 |
16 | 100 |
17 | 100 |
18 | 100 |
19 | 100 |
20 | 100 |
Assuming that single-phase ground fault occurs in branch 10,
Location information of
Node number | 2 | 4 | 5 | 7 | 10 | 14 |
---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 1.33 | 0.03 | |
−1 | −1 | −1 | −1 | 1 | −0.955 |
Establishing the fault distance location model of the No. 10 branch,
Similarity with different fault distances.
In each branch, 10 fault points (200 in total, including single-phase short-circuit fault, two-phase short-circuit fault, and three-phase short-circuit fault) are randomly selected for fault location this verification. Establish fault location models for 20 branches. Use the location error rate to describe the performance of the algorithm. As shown in formula (
The results of the average location error rate of each branch.
Branch number | The average error rate (%) |
---|---|
1 | 3.26 |
2 | 3.62 |
3 | 2.51 |
4 | 3.65 |
5 | 2.53 |
6 | 1.39 |
7 | 1.11 |
8 | 1.50 |
9 | 0.95 |
10 | 0.25 |
11 | 3.50 |
12 | 3.15 |
13 | 2.95 |
14 | 0.00 |
15 | 0.10 |
16 | 0.25 |
17 | 0.11 |
18 | 2.19 |
19 | 3.17 |
20 | 3.84 |
The average location error rate shown by the experimental results can be well controlled within 4%, which satisfies the requirements for the accuracy of fault location results.
The fault location algorithm proposed in this paper only deals with the positive sequence voltage variation of each monitoring point when the fault occurs. The location result is not affected by the fault source type and transition resistance. Firstly, the branch of the fault is determined by the SVM fault branch selection method, which avoids the traversal of the whole network branch, reduces the location range, and reduces the calculation amount. Then, the fault location parameter
This paper builds an IEEE-14 node network to verify the effectiveness of the algorithm. The results of the case show that the method can locate various types of faults, and the average location error of each branch can be well controlled within 4%. The algorithm lays a solid theoretical foundation for the rapid processing of grid faults.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
The authors would like to thank the project “Research on Key Technologies of Compact Flexible Loop Closing Device for Medium Voltage Distribution Network” (J2020081) for their support in this research.