kNN based fault detection and classification methods for power transmission systems
 Aida Asadi Majd^{1},
 Haidar Samet^{1}Email authorView ORCID ID profile and
 Teymoor Ghanbari^{1}
https://doi.org/10.1186/s416010170063z
© The Author(s) 2017
Received: 20 January 2017
Accepted: 25 July 2017
Published: 15 August 2017
Abstract
This paper deals with two new methods, based on kNN algorithm, for fault detection and classification in distance protection. In these methods, by finding the distance between each sample and its fifth nearest neighbor in a predefault window, the fault occurrence time and the faulty phases are determined. The maximum value of the distances in case of detection and classification procedures is compared with predefined threshold values. The main advantages of these methods are: simplicity, low calculation burden, acceptable accuracy, and speed. The performance of the proposed scheme is tested on a typical system in MATLAB Simulink. Various possible fault types in different fault resistances, fault inception angles, fault locations, short circuit levels, X/R ratios, source load angles are simulated. In addition, the performance of similar six wellknown classification techniques is compared with the proposed classification method using plenty of simulation data.
Keywords
Short circuit faults Fault detection Fault classification K nearest neighbor algorithm1 Introduction
Distance protection is one of the major protections of power systems, utilized for detection, classification, and location of short circuit faults. In the detection stage, any change caused by different normal and abnormal conditions is recognized. Then in the classification stage, the type of faults (Ag, Bg, Cg, ABg, BCg, CAg, AB, BC and CA) is determined.
In the fault location stage, the distance between the fault and the relay is determined. Due to importance of speed and accuracy of fault detection and classification units, too many investigations have been dedicated to these fields.
When a fault occurs in the power system, variables such as current, power, power factor, voltage, impedance, and frequency change. Many detection techniques detect fault occurrence by comparing the postfault values of these variables with their values during system normal operation. Some of fault detection methods are based on Kalman filter [1], first derivative method, Fourier transform (FT), and least squares [2]. Some other methods are based on differential equations [2], travelling waves [3, 4], phasor measurement [5], discrete wavelet transform [6], fuzzy logic, genetic algorithm [7] and neural network [8].
Also, many efforts have been made in the field of fault classification, which can be broadly categorized in two main groups. First, methods that are based on signatures of the signals and definition of some criteria such as: discrete wavelet transform (DWT) [9–13], Fourier transform (FT), Stransform [14], adaptive Kalman filtering [15], sequential components [16, 17], and synchronized voltage and current samples [18]. The second group includes the methods based on artificial intelligence techniques such as: Artificial Neural Networks (ANN) [19–21], fuzzy logic [22, 23], Support Vector Machine (SVM) [24–26], and decisiontree [27].
In this paper, two new methods are presented for detection and classification of faults. A moving window with the length of half cycle of power frequency is considered and the RMS value of the current samples is computed in the window. The RMS value obtained in the last window before fault, in which the fault instant is the last sample, is saved. The current waveforms are divided by the saved RMS value. Then, kNN algorithm is applied to these normalized waveforms and their squares in classification and detection methods, respectively.
In the detection method, a moving window with the length of half cycle is considered. In the window, besides finding the fifth nearest neighbor for each point of the squared normalized currents, the distance between each point and its corresponding neighbor is found. By comparing the maximum distance in each window with an adaptive threshold, the fault is detected.
The classification method has a similar trend, but the kNN algorithm is applied to the instantaneous values of normalized threephase currents and length of the window is three quarters of a cycle.
Various scenarios including different fault types, fault inception angles, fault resistances, fault locations, sources phase angles, X/R ratios, and short circuit levels are used to evaluate the performance of the methods in a simulated typical fivebus power system. Also, in order to evaluate the performance of the proposed classification method, it is compared with six other similar methods. The methods are compared in terms of delay time and accuracy using a data set including 450 different cases. Beside the simplicity, the proposed techniques have small calculation burden and high accuracy. Moreover, the methods performance is preserved in different conditions.
The remainder of this paper is organized as follows: Section 2 presents the understudy power system. In Section 3, basis of kNN and its application for fault detection as well as an improved fault detection algorithm are presented. In Section 4, the proposed classification algorithm is introduced. The simulation results are presented in Section 5. A comparison between the performance of the proposed method and some other similar methods is presented in Section 6. Finally, the main conclusions are presented in Section 7.
2 Simulated power system

Generators: Rated line to line voltage is 20 kV, threephase shortcircuit power is 1000 MVA, frequency is 50 Hz, X/R ratio is 10. Also it is assumed that the angles of sources 1 and 2 are 0 and −10 degree, respectively.

Transformers: Rated power is 600 MVA, voltage ratio is 20/230 kV with deltastargrounded connection, its primary and secondary impedances are 0.06 + j0.3 Ω and 0.397 + j2.12 Ω.

Lines: All of line impedances are 0.02 + j0.15 Ω/km. Lines 1–2, 2–3, 3–4, 4–1, and 5–2 are 200, 70, 120, 40, and 50 km, respectively.

Loads: The active and reactive powers of load 1 are 400 MW and 100 MVAr, respectively. The active and reactive powers of load 2 are 100 MW and 50 MVAr, respectively.
Sampling frequency: It is equal to 10 kHz.
3 The proposed change detection scheme
3.1 kNearest Neighbor algorithm (kNN)
The kNN algorithm is a nonparametric classification method that can achieve high classification accuracy in problems with nonnormal and unknown distributions. For a particular sample, k closest points between the data and the sample are found. Usually, the Euclidean distance is used, where one point’s components are utilized to compare with the components of another point.
The basis of kNN algorithm is a data matrix that consists of N rows and M columns. Parameters N and M are the number of data points and dimension of each data point, respectively. Using the data matrix, a query point is provided and the closest k points are searched within this data matrix that are the closest to this query point.
In general, the Euclidean distance between the query and the rest of the points in the data matrix is calculated. After this operation, N Euclidean distances which symbolize the distances between the query with each corresponding point in the data set are achieved. Then, the k nearest points to the query can be simply searched by sorting the distances in ascending order and retrieving those k points that have the smallest distance between the data set and query.
3.2 The proposed fault detection algorithm
Considering fixed sampling frequency, Euclidean distance between each sample and other samples of a considered sliding window varies when a change occurs. In fact, Euclidean distance represents differences between the samples values. kNN algorithm can derive variation of the Euclidean distance for change detection. In this work, a sliding window with length of half cycle of power frequency is moved on squared normalized current waveform of each phase. Then, kNN algorithm is applied to the samples of each window and the fifth nearest neighbor for each sample and the distance between them is obtained. Finally, the maximum distance is selected for each phase named M_{a,D}, M_{b,D}, and M_{c,D}. Based on different simulations, it is confirmed that the fifth nearest neighbor gives the best accuracy. In addition to the derived fifth neighbor, the distance between each sample and its corresponding fifth neighbor is derived. Considering sampling frequency 10 kHz, there are 100 samples in each half cycle, result in 100 different distances. Among them, the maximum distance is compared with a certain threshold value to detect fault condition.
4 The proposed fault classification scheme
The general approach for fault classification is the same as detection method. However, in the classification method the kNN algorithm is implemented in a window applied to normalized current waveforms with length of three quarters of a cycle, called analysis window. The considered k value and length of analysis window are selected based on different simulations to achieve the best accuracy and speed for the classification.
It is obvious, the distance between each sample of current and its fifth neighbor is a suitable criterion for fault classification. By choosing the maximum distance for each phase (M_{a,C,} M_{b,C}, and M_{c,C}) and comparing it with a threshold value, the type of fault can be determined. It is obvious that the values of M_{a,C,} M_{b,C}, and M_{c,C} are obtained exactly the same as detection method, but in a window with the length of three quarters of a cycle. The best threshold value is selected using different simulations.
 1.For discrimination between two phase faults (LL) and grounded two phase faults (LLg), the means of three phases’ corresponding current samples in the analysis window is obtained and the maximum mean is utilized as follows:$$ Mi=\max \left(\frac{ia+ ib+ ic}{3}\right)\kern0.5em in the analysis window $$
 2.
In order to omit the initial transient behavior of the signal, twenty first samples of the window are not considered.
5 Test cases and simulation results
5.1 Case 1: Various fault types
Results of various fault types
Type  Mi  M_{a,C}  M_{b,C}  M_{c,C} 

Ag  1.2652e + 03  0.5853  0.0711  0.0824 
Bg  1.0727e + 03  0.1017  0.5539  0.0342 
Cg  310.2327  0.0698  0.0986  0.4405 
ABg  1.0528e + 03  0.7518  0.3433  0.0580 
BCg  994.4663  0.0903  0.6393  0.3064 
CAg  878.8438  0.3729  0.0881  0.5971 
AB  0.0286  0.4575  0.4040  0.0444 
BC  0.1351  0.0888  0.4539  0.3813 
CA  0.0488  0.2934  0.0889  0.4018 
ABC  0.0065  0.6779  0.5013  0.4630 
The results for each group of phasetoground, phasetophasetoground, and phasetophase faults are similar. Therefore, hereafter only four types of faults including: Ag, ABg, AB, and ABC are considered.
5.2 Case 2: Various inception instants
Results of various fault inception instants
Inception instant (sec)  Type  Mi  M_{a,C}  M_{b,C}  M_{c,C} 

0.2032  Ag  993.4711  0.5603  0.0610  0.1014 
0.2062  Ag  436.8110  0.4895  0.0658  0.0992 
0.2092  Ag  535.8503  0.7499  0.0713  0.0952 
0.2032  ABg  1.0660e + 03  0.6429  0.3094  0.0894 
0.2062  ABg  944.6056  0.6065  0.2122  0.0889 
0.2092  ABg  512.7830  0.9243  0.3425  0.0805 
0.2032  AB  0.0454  0.4573  0.3848  0.0878 
0.2062  AB  0.0449  0.4300  0.3439  0.0889 
0.2092  AB  0.0450  0.5665  0.4345  0.0860 
0.2032  ABC  0.0059  0.5048  0.4663  0.2638 
0.2062  ABC  0.0047  0.4698  0.2639  0.5052 
0.2092  ABC  0.0040  0.2640  0.5038  0.4723 
5.3 Case 3: Various fault resistances
Results of various fault resistances
Type  Resistance (Ω)  Mi  M_{a,C}  M_{b,C}  M_{c,C} 

Ag  10  898.5760  0.4789  0.0753  0.0771 
Ag  30  561.8625  0.3472  0.0804  0.0493 
Ag  50  405.9855  0.2790  0.0830  0.0482 
Ag  70  316.9368  0.2381  0.0844  0.0474 
Ag  90  259.7276  0.2114  0.0853  0.0469 
ABg  10  779.8930  0.5540  0.3489  0.0568 
ABg  30  508.6675  0.3957  0.2961  0.0538 
ABg  50  375.8039  0.3096  0.2524  0.0456 
ABg  70  297.5452  0.2593  0.2221  0.0454 
ABg  90  246.1880  0.2269  0.2006  0.0453 
AB  10  0.0536  0.4328  0.3798  0.0444 
AB  30  0.0889  0.3280  0.2957  0.0444 
AB  50  0.1022  0.2637  0.2435  0.0444 
AB  70  0.1076  0.2242  0.2110  0.0444 
AB  90  0.1101  0.1981  0.1893  0.0444 
ABC  10  0.0231  0.4989  0.4472  0.3738 
ABC  30  0.0651  0.3610  0.3447  0.2130 
ABC  50  0.0862  0.2903  0.2817  0.1453 
ABC  70  0.0970  0.2471  0.2420  0.1236 
ABC  90  0.1031  0.2185  0.2151  0.1193 
5.4 Case 4: Various fault locations
Results of various fault locations
Type  location (%)  Mi  M_{a,C}  M_{b,C}  M_{c,C} 

Ag  0  1.8356e + 03  0.7890  0.0715  0.0821 
Ag  20  1.5959e + 03  0.7035  0.0711  0.0825 
Ag  40  1.3724e + 03  0.6222  0.0710  0.0821 
Ag  60  1.1608e + 03  0.5493  0.0712  0.0811 
Ag  80  957.3303  0.4802  0.0719  0.0560 
Ag  100  758.6445  0.4136  0.0732  0.0590 
ABg  0  1.5206e + 03  1.0038  0.4373  0.0521 
ABg  20  1.3260e + 03  0.8987  0.3990  0.0543 
ABg  40  1.1418e + 03  0.7994  0.3615  0.0566 
ABg  60  965.7605  0.7050  0.3253  0.0593 
ABg  80  795.2633  0.6144  0.2899  0.0598 
ABg  100  628.0395  0.5265  0.2549  0.0621 
AB  0  0.0251  0.5906  0.5384  0.0444 
AB  20  0.0268  0.5338  0.4784  0.0444 
AB  40  0.0281  0.4819  0.4270  0.0444 
AB  60  0.0289  0.4337  0.3787  0.0444 
AB  80  0.0293  0.3884  0.3327  0.0444 
AB  100  0.0292  0.3450  0.2898  0.0444 
ABC  0  0.0077  0.8967  0.6611  0.6104 
ABC  20  0.0077  0.8034  0.5927  0.5474 
ABC  40  0.0071  0.7180  0.5305  0.4900 
ABC  60  0.0057  0.6387  0.4729  0.4368 
ABC  80  0.0036  0.5640  0.4187  0.3868 
ABC  100  0.0025  0.4926  0.3668  0.3391 
Results of fault locations more than 100%
Fault Type  Resistance  Location (%)  Mi  M_{a,C}  M_{b,C}  M_{c,C} 

ABC  negligible  105  6.1112e08  0.4899  0.3648  0.3372 
ABg  90  105  144.2950  0.1833  0.1639  0.0473 
AC  negligible  110  0.0081  0.1963  0.0888  0.3032 
Ag  90  110  150.6250  0.1693  0.0879  0.0480 
AB  negligible  120  0.0080  0.3385  0.2827  0.0444 
Bg  90  120  144.2091  0.0961  0.1671  0.0666 
From the results, it can be concluded that the performance of the proposed method is preserved even for locations more than 100%. It should be mentioned that the performance of the proposed method degrades for locations more than 120%.
5.5 Case 5: Various sources load angles
The results for various angles, according different inception instant, fault resistances, and fault types verify that proposed method classify the faults in different values of sources load angles. For abbreviation, the results relevant to this case are not presented.
5.6 Case 6: Various X/R ratios
Different X/R ratios impact on the performance of the proposed method is also investigated, considering different inception instant, fault resistances, and fault types. From the results, it can be concluded that accuracy of the proposed method is preserved for different values of X/R ratios.
5.7 Case 7: Various short circuit levels
The performance of the proposed method is also evaluated for various sources short circuit levels. The algorithm also has desirable performance for these cases.
5.8 Case 8: Various load levels
Results of various load levels
Fault  Noload  Load1  Load2  

Type  resistance  Inception instant  100 MW  200 MW  300 MW  400 MW  50 MW  100 MW  
25 MVAr  50 MVAr  75 MVAr  100 MVAr  25 MVAr  50 MVAr  
AB  Negligible  0.2002  Mi  0.0128  0.0124  0.0120  0.0116  0.0112  0.0125  0.0123 
Ma  1.8524  0.8232  0.5531  0.4304  0.3605  2.1232  2.3803  
Mb  1.7653  0.7522  0.4856  0.3686  0.3023  2.0399  2.3048  
Mc  0.0773  0.0921  0.0444  0.0444  0.0444  0.0822  0.0869  
ABg  30  0.2032  Mi  467.5109  450.9092  434.2540  418.0157  402.4154  457.0304  446.9282 
Ma  1.6118  0.7110  0.4746  0.3673  0.3067  1.8174  2.0083  
Mb  0.6028  0.2936  0.2268  0.1966  0.1796  0.6865  0.7655  
Mc  0.1003  0.1102  0.1066  0.0993  0.0946  0.1024  0.1018  
ABC  90  0.2062  Mi  5.1811e09  1.3579e08  1.7955e08  2.7285e08  2.4108e08  2.5092e08  2.5051e08 
Ma  1.1341  0.2924  0.1651  0.1534  0.1483  1.2205  1.1439  
Mb  0.8183  0.3847  0.2699  0.2172  0.1868  0.9138  1.0000  
Mc  0.8122  0.3815  0.2678  0.2161  0.1868  0.9061  0.9907 
5.9 Case 9: Current transformer saturation
Results of two fault cases during current transformer saturation
Fault Type  Mi  M_{a,C}  M_{b,C}  M_{c,C}  

a  AB  9.2980e04  1.0595  1.1337  0.0915 
b  ABC  0.0074  1.2737  1.2458  1.4452 
6 A comparison with other techniques
The performance of the proposed method is compared with six other similar approaches in this Section. All of the methods are evaluated using an identical data set in similar conditions. The six methods are briefly reviewed as follows:
a. Sequence Component [16]: This technique classifies the faults using the phase differences between positive and negative sequences. Also, relative magnitudes of negative and zero sequences from prefault to the fault stage are used to distinguish between phasetophase (LL) and phasetophasetoground (LLg) faults.
b. Alienation Coefficients [28]: In this algorithm, alienation technique is applied to two half successive cycles with the same polarity. The alienation coefficients of the successive cycles as two dependent variables are calculated. This technique is capable of classification using only threephase current waveforms and its delay time is half cycle of power frequency. Also, another version of this approach is presented in [29].
c. Discrete Wavelet Transform [23]: Daubechies family of wavelet transform is used in this technique. Third level output among different decomposed levels is used and the summation of detailed current signals for each phase (S_{a}, S_{b,} and S_{c}) is obtained. If the summation of Sa, S_{b,} and S_{c} is equal to zero, then the fault type is either threephase or LL, otherwise, it is phasetoground (Lg) or LLg fault.
d. Fuzzy Logic [22]: The prerequisite of this technique is fault occurrence time. In this algorithm, using measured current samples, some specific characteristics for the samples are defined for the fault classification. The technique takes three quarters of a cycle to classify the fault.
e. Using RMS Values of current: A simple approach to classify the faults is based on comparing the RMS values of threephase current waveforms with a certain threshold. The RMS values of the phases are obtained using Fourier transform in a half cycle window after fault occurrence. Discrimination between LL and LLg is determined using zero sequence component of current, which is large for LLg and zero for LL.
f. Using RMS Values of Voltage: This technique is exactly the same as previous method for threephase voltage signals. Type of fault is determined when the RMS values of the voltages become less than a certain threshold.

Fault resistances

Fault inception instants

Fault locations

Generators X/R ratios

Phase difference between two generators

Generators short circuit levels

Delay operation time

Error percentage
Comparison between the different methods
Technique  Error Percentage of different fault resistance and occurrence time (%)  Error Percentage of different fault location (%)  Error Percentage of different X/R ratio of sources (%)  Error Percentage of different phase angle of sources (%)  Error Percentage of different short circuit level of sources (%)  Total error percentage (%)  Mean delay time (ms) 

a  10.5  12  10  14  10  10.98  15 
b  22.5  30  22.86  26  25  24.15  10 
c  26  20  25.71  32  37.5  27.07  10 
d  0  0  0  2  2.5  0.49  15 
e  13  10  7.14  46  32.5  17.56  10 
f  28  20  24.29  34  17.5  26.10  10 
Proposed technique  0.5  0  0  8  7.5  1.95  15 
The number of the whole cases considered in this Section is 410; 200 cases for different fault resistances and inception instants, 50 cases for different fault locations, 70 cases for different sources X/R ratios, 50 cases for different sources angles, and 40 cases for different short circuit levels.
In Table 8, error percentages for the above mentioned factors are calculated as the ratio of number of malfunction operations to number of the relevant cases. Then, total error percentage for each method is calculated as ratio of number of whole malfunction operations to number of whole the cases.
Techniques a and d have a delay time 15 ms and techniques b, c, e, and f have a delay time 10 ms. Among the methods with delay time 15 ms, fuzzy logic has a very good performance with only 0.49% error.
The proposed technique has a good performance with error percentage of 1.95% and average delay time of 15 ms. Based on the calculated total error percentage and delay time, it is confirmed that the proposed method has acceptable performance in comparison with other methods.
7 Conclusion
Two simple methods for fault detection and classification are presented in this paper. The methods are based on kNN algorithm. Plenty of simulations were used in order to evaluate the performance of the methods. The performance of the proposed classification method is compared with six other similar methods. From the results, the good accuracy and speed of the methods are confirmed. The classification technique has accuracy about 98% for the considered data set with 15 ms average delay time.
Declarations
Authors’ contributions
All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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