A new method of fault domain identification is proposed based on K-means clustering analysis theories using the wide-area information of power grid. In the method, the node Intelligent Electronic Device (IED) associated domain is defined, and the relationship of positive sequence current fault component for the association domain boundaries is sought, then the conception of positive sequence fault component differential current for node IED association domains is introduced. The information of the positive sequence fault component differential current gathered by node IEDs is selected as the object of K-means clustering. The node IEDs of fault associated domains can be classified into one category, and the node IEDs of non-fault associated domains are classified into another category. With the fault area minimum principle, the group of node IEDs about fault associated domains can be obtained. The overlap of fault associated domains for different nodes is the fault area. A large number of simulations show that the algorithm proposed can identify fault domains with high accuracy and no influence by the operating mode of the system and topological changes.
With the increasingly complex structure and the continuously extended scale of power grid, the traditional backup protection based on local information can not satisfy requirements of complex and various operation modes of power grid. The rapid development of computer technologies and the wide-area measurement technologies make global information being introduced into protection possible. In recent years, extensive researches on wide-area backup protection have carried on at home and abroad, mainly concentrating in tripping strategies and fault areas identification of wide-area protection, etc. [
The wide-area relay protection system given in reference [
In order to further study the application of artificial intelligence algorithm in wide-area backup protection and improve the accuracy of fault identification with wide-area information under different working conditions, a new method for identifying failure areas of power grid based on k-means clustering according to wide-area positive sequence fault component differential current information is proposed on the basis of previous studies.
The K-means clustering algorithm is to cluster based on the objective function of a prototype. In the algorithm, the sum of distances from data to corresponding clustering centers is the optimized objective function and adjusting rules for iterative operations are obtained by finding the extremum solution of the function. The mean value of data samples of each cluster subset is selected as the clustering center of the corresponding cluster. The main idea of the algorithm is to divide data into different classes through iteration processes, and makes the clustering criterion function used to evaluate the clustering performance to achieve its optimum, so that each cluster generated can be compact inside and independent to others. The number k of clusters and a database contains n objects are needed to be input first of all, and then n objects are divided into k clusters, which can make the minimum square error criterion [
1) Select K initial clustering centers:
2) Calculate the distance d from every data to each clustering center, and divide the data to the corresponding cluster
3) Calculate the new clustering center vector
In which, q is the attribute number of data,
4) Repeat processes 2 and 3, until each cluster is no longer changes.
Node IEDs of power grid are installed at substation nodes, corresponding to substations. Each node IED has the same status, whose works are mainly to collect electric information sent from related line IEDs, and upload them to wide-area decision center after preliminary processing. Line IEDs mainly acquire positive sequence current fault component information at installation places, and upload the information to the corresponding grid node IEDs. Fault domains of power grid can be identified by the fault recognition algorithm to process the data uploaded by node IEDs. The associated domain of node IED is defined in this paper. As shown in
The positive sequence fault component differential current of the node IED associated domain is defined as the sum of phasors of all positive sequence fault current components measured at boundary line IEDs. For example, at the node IEDB2, the positive sequence fault component differential current
When a fault occurs at bus B3 in the
assured that the domain ③ is the fault associated domain. Hence, when a single independent fault associated domain appears, the bus in the associated domain is thought to be failed.
Clustering status characteristic values selected in this paper are the RMS
Row vectors of the matrix A correspond to node IED status information, that is clustering objects of K-means.
The wide-area information matrix A of power grid is the input of K-means clustering for the clustering analysis of the associated domain of each grid node. Still the circuit in
where, nodes corresponded to fault domains are IEDB2 and IEDB3, nodes corresponded to non-fault domains are IEDB1, IEDB4 and IEDB5. Characteristic information of associated node IEDs in fault domains are all the whole fault current at fault points in domains with similar vector information. And all characteristic information of associated node IEDs in non-fault domains are merely unbalanced currents with small values and their vector information are similar. But vectors information are different vigorously between node IEDs of fault domain s and non-fault domain. Based on a large number of simulations, wide-area information samples acquired by node IEDs are divided into two groups: the IED class of fault domain associated nodes and the IED class of non-fault domain associated nodes.
In a large multi-station power system, the principle of minimum fault area is satisfied, based on which, the cluster with the least node IED number in clustering results is chosen as the associated node IED class of fault domains in this paper. In the class, the overlapped domain of associated fault domains of each node IED is thought as the fault domain. If there is no overlapped domain, bus failure at associated node is thought to happen in corresponding fault domain. The process of the fault identification based on K-means algorithm is shown in
As shown in
According to the definition above, the positive sequence fault component differential current of the node IED associated domain is referred as the sum of current phasors measured by boundary line IEDs in the associated domain. Calculations of positive sequence fault component differential currents for node IED associated domains of the IEEE-3 machine 9-node system are as shown in
After calculating all positive sequence fault component differential currents of the node IED associated domains, the RMS value ∆Ii1 in first circle and the RMS value ∆Ii2 in second circle of differential currents after fault are selected as wide-area information vector for the i-th node IEDBi. Hence, the node IED wide-area information matrix A
Assume three-phase short circuit fault occurs at line L9, the wave of positive sequence fault component differential currents measured at part node IEDs is shown in
The RMS values ∆Ii1 in first circle and the RMS values ∆Ii2 in second circle of positive sequence fault component differential currents in the associated domain of each node IED are as shown in
Therefore, the wide-area information matrix A
Node IED | Calculations of differential currents in associated domains | Node IED | Calculations of differential currents in associated domains |
---|---|---|---|
IEDB1 | IEDB6 | ||
IEDB2 | IEDB7 | ||
IEDB3 | IEDB8 | ||
IEDB4 | IEDB9 | ||
IEDB5 |
Node IED | ||
---|---|---|
IEDB1 | 0.003262 | 0.00434 |
IEDB2 | 0.04379 | 0.049084 |
IEDB3 | 0.039394 | 0.052657 |
IEDB4 | 4.650301 | 5.788424 |
IEDB5 | 0.019525 | 0.026133 |
IEDB6 | 0.043009 | 0.056496 |
IEDB7 | 4.70755 | 5.794702 |
IEDB8 | 0.043522 | 0.05657 |
IEDB9 | 0.015611 | 0.020266 |
Row vectors of the matrix are objects analyzed according to K-means clustering algorithm. The dimension of sample characteristic values is m =2, the number of data samples is n = 9, and the initial cluster number is h = 2. Select randomly the 1-th and 6-th rows as initial clustering centers, the class centroid coordinate matrix C of two classes is
The distance sum vector in classes is SUMD = [0.00039 0.0008]
The distance matrix D of each data to their class center is
The outline of K-means clustering is as shown in
Clustering results are as shown in
Class 1 | Class 2 |
---|---|
“IEDB7” | “IEDB6” |
“IEDB4” | “IEDB3” |
“IEDB2” | |
“IEDB9” | |
“IEDB1” | |
“IEDB5” | |
“IEDB8” |
According clustering results, the wide-area information of 9 node IEDs are divided into two classes, in which the one with least nodes are identified as the node IED class of fault associated domains according to the algorithm proposed. As in
Assume AC two-phase to ground fault occurs at bus B2, the node IED wide-area information matrix A
Clustering results are as shown in
To test accuracy of the identification algorithm based on K-means, clustering analysis are carried on when faults occur under other fault conditions, results seen in
Class 1 | Class 2 |
---|---|
“IEDB2” | “IEDB6” |
“IEDB7” | |
“IEDB3” | |
“IEDB4” | |
“IEDB9” | |
“IEDB1” | |
“IEDB5” | |
“IEDB8” |
Real fault element | Class 1 | Class 2 | Identification results |
---|---|---|---|
L4 | “IEDB4” “IEDB5” | “IEDB6” “IEDB3” “IEDB9” “IEDB1” “IEDB7” “IEDB8” “IEDB2” | Line L4 |
L1 | “IEDB1” “IEDB2” | “IEDB4” “IEDB5” “IEDB9” “IEDB6” “IEDB7” “IEDB8” “IEDB3” | Line L1 |
B4 | “IEDB4” | “IEDB6” “IEDB5” “IEDB8” “IEDB1” “IEDB3” “IEDB9” “IEDB2” “IEDB7” | Bus B4 |
B8 | “IEDB8” | “IEDB9” “IEDB5” “IEDB6” “IEDB1” “IEDB3” “IEDB4” “IEDB2” “IEDB7” | Bus B8 |
L3is not in operation, B7 faults | “IEDB7” | “IEDB6” “IEDB5” “IEDB8” “IEDB1” “IEDB3” “IEDB4” “IEDB2” “IEDB9” | Bus B7 |
G2 is not in operation, L3 faults | “IEDB3” “IEDB4” | “IEDB6” “IEDB5” “IEDB9” “IEDB1” “IEDB7” “IEDB8” “IEDB2” | Line L3 |
A new method for fault domain identification based on wide-area positive sequence fault component differential currents and K-means algorithm is proposed in this paper. Wide-area information of node IEDs are clustered by K-means according to the fault domain minimum principle to assure the class with least node IEDs to be the associated node class of fault associated domains. The fault identification can be realized by finding the overlapped area of fault associated domains of those node IEDs.
Simulation results show that fault domains can be identified correctly when the operational mode of power grid changes, such as one line or one source is not in operation. Fault domain identification based on wide-area status information and the intelligent algorithm are discussed in this paper, which provides a new way to diagnose faults in grid.
The research work was financially supported by the artificial intelligence key laboratory of Sichuan province ( 2014RYY05,2015RYY01).
Wu, H. and Li, Q.Z. (2017) Fault Identification of Power Grid Based on Wide-Area Differential Cur- rent and K-Means Clustering. Energy and Power Engineering, 9, 19-29. https://doi.org/10.4236/epe.2017.94B003