An algorithm for fault detection and classification method for widearea protection in Korean transmission systems is proposed. The modeling of 345kV and 765kV Korean power system transmission networks using the Electro Magnetic Transient Program  Restructured Version (EMTPRV) is presented and the algorithm for fault detection and classification in transmission lines is developed. The proposed algorithm uses the Wavelet Transform (WT) and Singular Value Decomposition (SVD). The Singular value of Approximation coefficient (
SA
) and part Sum of Detail coefficient (
SD
) are introduced. The characteristics of the
SA
and
SD
at the fault conditions are analyzed and used in the algorithm for fault detection and classification. The validation of the proposed algorithm is verified by various simulation results.
1. Introduction
It is critical to secure transmission lines against faults to maintain stable operation of power systems. Fault detection, classification, and the location of transmission lines are very important tasks in protecting electric power systems. Fast fault detection is needed to protect the system components from the harmful effects of a fault. Faulttype classification is needed to analyse the original signal with appropriate signal processing schemes such as the Wavelet Transform (WT). The WT is a mathematical tool used in a wide variety of fields for signal and image processing applications
[1]
. WT is also useful in power system transient analysis, as it is based on the time and frequency domain simultaneously
[2]
. WT can be used on a broad frequency range rather than a specific frequency domain, which makes WT very useful for analysing the transient phenomena in a power system. For this reason, WT has been applied in protection algorithms to detect, classify, and locate faults in power systems. Although WT has good features, typically, it is not used alone in analyses of power system transients, because the transformed signals still contain a large amount of data which requires further processing.
Thus, faulttype classification has been performed with several other methods, such as traveling waves
[3

4]
, adaptive Kalman filtering
[5]
, discrete wavelet transform
[6

7]
, fuzzy logic, neural networks
[8]
, a fusion of different artificial network techniques, and combinations of wavelet and hyperbolics
[9]
. Neural networks have disadvantages in that they require a considerable amount of training effort to obtain good performance, especially under various operating conditions such as systemloading level, fault resistance, and source impedance. Another disadvantage of neuralbased networks is that the results of training may not cover some cases, as the starting point is chosen at random and can end up in minimum times
[10

13]
. Wavelet Singular Entropy (WSE) using WT with Singular Value Decomposition (SVD) and Shannon’s information entropy theory have been proposed
[14

16]
. SVD can be useful to decompose large amounts of data into small square matrices.
In this paper, an algorithm that includes fault detection and classification is proposed for widearea protection. An algorithm for fault detection and classification is presented based on Wavelet Singular Value Decomposition (WSVD) combined with WT and SVD
[17]
. Singular value of Approximation coefficients (
SA
) containing low frequency components and part Sum of Detail coefficients (
SD
) containing high frequency components derived from WSVD are defined, and the mother wavelet is selected as a characteristic of WSVD. The characteristics of
SA
and
SD
are analysed in various fault conditions to detect the faults and classify between those faults. An algorithm is proposed based on the results of
SA
and
SD
to detect and classify various faults. The various simulation results are performed and the results are analysed. In summary, we propose an algorithm which can detect and classify faults in transmission system using WSVD for widearea protection.
2. Modeling of WideArea Transmission System in Korea
The nationwide electrical power transmission network in Korea was modelled using the EMTPRV. The system parameters used in modelling are the real system data in the PSS/E files provided by KEPCO and KPX
[18]
.
The nominal voltages of the power transmission network in Korea are composed of 154 kV, 345 kV, and 765 kV. The target network is all the transmission lines of 345 kV and 765kV in 2008
[19

22]
. The transmission lines of 154 kV are treated as a load. The modelled system is operated based on the peak load condition in summer 2008. The total load is 54,647 MVA (The Active Power is 54,300 MW and the Reactive Power is 6,150 MVar). The total generation is 57,001 MVA (55,070 MW and 14,713 MVar) and the loss of transmission lines over 154 kV is about 2 %.
Fig. 1
shows the widearea transmission system of Korea modelled by EMTPRV
[20]
. Simulations are performed in steady state for 10 seconds in order to validate the performance of the modelled network. Frequencies are measured at the nine buses: Dongseoul No. 1, Sinsiheung No. 3, Asan No. 3, Sinjechun No. 3, Chungyang No. 3, Seodaegu No. 3, Uiryung No. 3, Singoangju No. 3, and Bukbusan No. 3s.
Power system network modeled by EMTPRV.
In the simulated results, the lowest frequency is 59.9931 Hz at Uiryung No. 3, and the highest frequency is 60.0002 Hz at Seodaegu No. 3. As the frequencies vary within less than 0.01 Hz, we can confirm that the modelled network operates in a stable state.
3. Characteristic Analysis of Disturbance Using Wavelet Singular Value Decomposition
 3.1 Wavelet transform
The WT is able to extract time and frequency information at the same time from the original signal
[23

26]
. The Discrete Wavelet Transform (
DWT
) of a signal is defined as:
where
ψ
[
k
] is mother wavelet,
is a scale parameter, and
is the time shift of
ψ
[
k
]
[26]
.
The Results of
DWT
depend on the mother wavelet. One characteristic of the mother wavelet is that the mean value is zero within a certain period of time. The Daubechies 4 (db4) wavelet is usually used as a mother wavelet for transient analysis in power systems.
The WT consists of successive pairs of lowpass and highpass filters. For each pair, the highscale and lowfrequency components are called approximation coefficients of WT, while the lowscale and highfrequency components are called detail coefficients. The approximation coefficient and detail coefficient constitute the WTcoefficient matrix
[24]
.
 3.2 Singular value decomposition
Singular Value Decomposition (SVD) is a powerful and effective tool to extract special features in linear algebra. SVD is a factorization of the matrix. For any matrix
, matrix
A
can be decomposed as:
where
U
is an
m
×
m
orthonormal eigenvector matrix of
AA^{T}
, and
V
is an
n
×
n
orthonormal eigenvector matrix of
A^{T}A
. Then, Σ is an
m
×
n
matrix that can be written as:
Here, S diag(
σ
_{1}
,···
σ_{r}
) = is a diagonal matrix by,
r
×
r
and
σ
is called a singular value that is calculated by SVD. SVD has information about the magnitude of the signal, which be used for analysis
[26

27]
.
 3.3 Wavelet singular value decomposition
Wavelet Singular Value Decomposition (WSVD) is a type of wavelet transform with SVD
[17]
. The approximation and detail coefficients
a1
and
d1
are calculated through the decomposition and reconstruction process on the level 1 DWT with the signal
x
from a moving window of size
n
. The sizes of the
x
,
a1
, and
d1
become
n
as well. The Singular value of Approximation (
SA
) is a singular value to be calculated by (4) using
a1
. The Sum of the absolute value of Detail (
SD
) is calculated by (5) and (6) using
d1
.
Here,
i
is the starting time of sampling of the moving window, and lf is the filter size according to the mother wavelet. In order to suppress the negative effect of the DWT filter caused by applying the moving window techniques,
SD1
is calculated to remove the value at both ends of
d1
during the calculation. The value of
d1
is calculated by a decomposition and reconstruction process of the level 1 DWT of the signal s[n] using Daubechies 4 (db4) as the mother wavelet based on a moving window with a size of 24 (a half cycle). In this process, assuming that the size of the filter is 8 and the highpass filters are HD1, HD2, ···· and HD8, then
d1
[1]

d1
[6]
and
d1
[19]
d1
[24]
do not have a pattern in
d1
because of the influence of duplicated signals for convolution multiplication. However,
d1
[7]

d1
[18]
have a pattern in
d1
because they are not impacted by the signal duplication for convolution multiplication.
Fig. 2
shows a sine waveform of one cycle as an original signal.
a1
and
d1
are the results of the decomposition and reconstruction process of db4 with the level 1 DWT. The
d1
curve shows fluctuation at both ends.
a1 and d1 for a sinusoidal signal
 3.4 Analysis of faulttype characteristics based on WSVD
The various faults are simulated in the model of the 345kV transmission system shown in
Fig. 3
. We model 345kV transmission system using EMTPRV. Lines applied to the system are nontransposed constant parameter model and average parameters of ACSR 480mm
^{2}
– 4 bundled lines, usually used in 345kV transmission system of Korea, are utilized.
Fig. 3
and
Table 1
indicate the transmission system model and parameters of line used, respectively.
345kV transmission system model
Line parameters
The simulation conditions are as follows:

1) Fault types: Single linetoground (SLG) Double linetoground (DLG) Linetoline short circuit (DLL) Threephase fault (3Φ)

2) Distances of faulting position from bus 1 [km] 5, 10, 15, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 285, 290, 295

3) Fault inception angles [°] 0, 30, 45, 60, 90, 120, 135, 150, 180

4) Fault resistances [Ω] Linetoground fault: 20, 50, 100 Linetoline fault: 0, 50, 100 Threephase linetoline fault: 0
The measured original signals are each phase voltage measured at bus 1 or bus 2 after the faults. The sampling frequency is 2.88 kHz, the size of a moving window is 24 (half cycle), and the mother wavelet is db4, which is generally used for analysing transience in electrical power systems
[26

28]
.
Figs. 4
and
5
show the
SA
and
SD
of each simulated fault. In
Figs. 4
and
5
, (a) shows SLG, (b) shows DLL, (c) shows DLG, and (d) shows threephase fault (3Φ).
Variation of the SA by fault type
Variation of the SD by fault type
In the case of SLG, the variations of SA have the same trend as the original voltage signal. The voltage of the faulty phase is decreased, while that of the healthy phases is increased. The difference value between the faulty and the healthy phase is almost double compared with the normal conditions, as shown in
Fig. 4(a)
. The magnitude of
SD
at the faulty phase is generally higher than that of the healthy phase. In the case of DLL, the magnitudes of the original voltages at the faulty phases are smaller than that in the healthy phase. The magnitude of
SD
at the fault phases increase rapidly, as shown in
Fig. 5(b)
. As shown in
Fig. 4(c)
, the result of DLG is very similar to that of DLL, but the magnitude of the healthy phase in case of DLG experiences small variance caused by the faulty phase. In the case of a 3Φ fault, the original voltage magnitude of the faulty phases is decreased rapidly, but the results are relatively low. The magnitudes are shown according to the fault resistance and the fault inception angle. The variation of
SA
is shown in
Fig. 4(d)
, and the
SD
is shown in
Fig. 5(d)
.
 3.5 Characteristic analysis of generator loss
Simulations of generator loss are performed by tripping the Busan C/C, Ulsan C/C, Ulsan T/P, and Kori N/P. The simulation conditions include the tripping generator group, with a maximum voltage of phase and a minimum voltage of phase a, and a total of 42 simulations are conducted. Each group of selected generators is connected to the bus of each generator group, which include 8 units of Busan C/C, 6 units of Ulsan C/C, 3 units of Ulsan T/P, and 4 units of Kori N/P. The measuring point of voltage is the North Busan 3S bus, and the signals are processed with WSVD.
Fig. 6
shows the variation of
SA
and
SD
caused by generator loss.
SA
shows a similar pattern to that of DLL or 3Φ fault.
SD
shows the results to be discriminated with
SA
that are different from those with a 3Φ fault. However, the maximum variation rates of each phase are similar.
Variation of SA and SD by generator loss
 3.6 Characteristic analysis of load shedding
Simulations of load shedding are performed by tripping the loads at North Busan 3S and New Ulsan 3S buses from 5% to 40 % by 5% increments. A total of 32 simulations are performed, considering the magnitude of voltage at the closing point. The measuring point for the voltage signal is at North Busan 3S, and the signals are processed with WSVD.
Fig. 7
shows the variation of
SA
and
SD
by load shedding.
SA
increases by 0.01 p.u. due to the load shedding of 350 MVA. SD shows the results between DLL and 3Φ fault. The variations of SD are doubled compares to the normal state.
Variation of SA and SD by load shedding
4. Algorithm for Fault Detection and Classification
 4.1 Method of the fault detection
The characteristics of
SA
and
SD
according to the fault types were analysed in Section 3. Based on the characteristics,
SD
is selected to detect faults. This is because the variation of
SD
is more severe than that of
SA
when a fault occurs.
Fig. 8
compares the results of WSVD transformation of the 345kV phase voltage signal and that of the same signal with SNR 100 of Additive White Gaussian Noise (AWGN).
SA
and
SD
for the signal only remain unchanged, while those for the signal with AWGN show variations. Apparently,
SD
fluctuates much more than
SA
when noise is added.
Fig. 9
shows the differential value of
SD
with 1 cycle. The maximum differentiated value is 0.6. Therefore, the threshold value to detect a fault in the 345kV transmission line, α, is set to 1 with some margin. The value can be adjusted by considering conditions of the power system and operational requirements.
WSVD signal added AWGN (Additive White Gaussian Noise)
Differential value of SD added AWGN
 4.2 Method of faulttype classification
Several indices are defined to classify fault types based on the aforementioned characteristics of
SA
and
SD
:
NSA
(Normalized maximum
SA
;
ΔSA
),
AR
(Ranked
SA
),
NSD
(Normalized maximum
SD
;
ΔSD
), and
NSS
(Normalized Settled
SD
;
ΔSD
). The zero sequence voltage
V_{0}
is introduced to determine whether the fault is symmetric or asymmetric.
NSA
is the ratio of the absolute value of
SA
in normal conditions to that of the maximum change of
SA
for a cycle after a fault calculated in (7). The (8) calculates the last
NSA
to select the faulty phase. If the value is bigger than the threshold
β
, it becomes 1, but it is otherwise 0.
NSD
is the ratio of the absolute value of
SD
in normal conditions to that of the maximum change of
SD
for a cycle after a fault, as shown in (9). The threshold values associated with
NSD
are
δ
= 0.001,
γ
= 0.5, and
ζ
= 0.75. The threshold value δ identifies linetoline faults, γ double linetoground faults, and
ζ
threephase faults from generator loss.
NSS
is the ratio of the absolute value of
SD
in normal conditions to that of the maximum change of
SD
for a cycle after a fault, as shown in (10).
η
is the threshold value associated with
NSS
, and is set at 0.75. It identifies threephase fault from generator trips.
β, δ, γ, ζ,
and
η
used as threshold values that are related to the ratio values of
SA
and
SD
, and they are not directly associated with the transmission system.
 4.3 Algorithm for fault detection and faulttype classification
The proposed algorithm detects and classifies the fault using the methods described in Sections 1 and 2. 12 types of fault are numbered as shown in
Table 2
.
Figs. 10
and
11
describe the proposed algorithm, and pe in the figures is the sample number for one cycle.
The variable value of each fault type
The variable value of each fault type
Main Flow Chart of the algorithm for fault detection and fault type classification using WSVD
Algorithm for fault detection and type classification using WSVD
5. Simulation and Discussions
 5.1 Simulation conditions
The various faults are simulated in the 345kV transmission system presented in
Fig. 3
, to verify the algorithms. A total of 56,744 simulations are conducted, until the failed cases become 20 times.
Simulation conditions consist of various fault distances, fault types, fault resistances, and fault inception angles, as follows:

 Fault distance: randomly selected, between 1~299 km from bus 1, with a unit of 1 km

 Fault type: randomly selected

 Fault resistance: randomly selected, between 1 and 100 Ω, with a unit of 1 Ω

 Fault inception angle: randomly selected, by starting a fault at random time within 1 cycle, with a unit of 0.1 ms
Faults are simulated using EMTP. The results from EMTP were converted to a format compatible to MATLAB, and WSVD was performed in MATLAB.
 5.2 Simulation results of fault detection and classifycation
Fig. 12
shows the simulation results of fault classifycation for various fault types.
Table 3
shows the results of the simulations. It shows the times of simulation and failure, and success rate of the fault type classification for each fault type. SLG, DLL, and 3Φ fault classified 100% correctly. However, the success rate of DLL classification was 99.88%. The total success rate of fault classification is 99.96%.
Results of fault classification for the various fault types
Verification result of faults classification
Verification result of faults classification
The most failed cases for the fault type classification are DLG faults with the distance of 23 km and 277 km from the bus. The three phase voltage,
SA
and
SD
of this case are shown in
Fig. 13
. In the cases of the DLG fault, if the distance is 23 or 277 km, it shows that the SA of the faulted phase does not rapidly decrease, hence
β
of the faulted phase becomes less than 1. As a result of
NSA1
, the algorithm classifies the SLG fault. However, the fault would be detected, if the detecting period becomes 2 cycles.
The failed case of the fault type classification (DLG, Distance of fault: 23km, Fault Resistance: 54Ω)
6. Conclusion
Modelling of the 345kV and 765kV Korean nationwide power system network in EMTPRV has been described based on real data in PSS/E files provided by KEPCO and KPX. Based on the modelled system, an algorithm for widearea protection in the Korean transmission system has been proposed. The proposed algorithm consists of fault detection and classification. The method for fault detection and classification using WSVD was also discussed. Various simulation conditions were performed to analyse the characteristics at each fault in the 345kV transmission model system. The characteristics in various fault conditions using WSVD were analysed. With the analysis results, NSA, AR, NSD, and NSS were designated with proper values for fault detection and classification. All algorithms for wide area protection, including fault detection and fault type classification are validated through various simulation conditions. The algorithms of fault detection and type classification work perfectly in the simulations.
By using the proposed algorithm, national wide monitoring and supervising system can be monitoring and classifying of the faults in national widearea transmission network as a new way redundantly with the SCADA (Supervisory Control and Data Acquisition) and EMS (Energy Management System) in order to be more reliable operation when the signal can be acquired by PMU on national wide.
Acknowledgements
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. NRF2013R1A1A2009294)
BIO
JaeWon Lee was born in Korea, 1954. He received his B.S. in electrical and computer engineering from Sungkyunkwan University, Suwon, Korea in 1975 and M.S. degree in engineering from Yonsei University, Seoul, Korea in 1989. He is now working toward his Ph.D. degree at Sungkyunkwan University in Korea. He was in charge of facility design, operation and management at Plant Engineering for 25 years. Currently, he is working as a Principal Engineer at Seoul EM Co., Ltd in Korea. His research interests include power system protection, analysis and system design. Mr. Lee is a Registered Professional Engineer in Korea and APEC Engineering Associations.
WonKi Kim was born in Korea, 1987. His research interests include power system transients, protection and stability. He received his B.S and M.S degrees in School of Electrical and Computer Engineering from Sungkyunkwan University, Korea, 2010 and 2012.
YunSik Oh was born in Korea, 1987. At present, he is working on his Ph. D thesis at Sungkyunkwan University. His research interests include power system transients, protection and stability. He received his B.S and M.S degrees in School of Electrical and Computer Engineering from Sungkyunkwan University, Korea, 2011 and 2013.
HunChul Seo was born in Korea, 1982. He received his B.S and M.S degrees in School of Electrical and Computer Engineering from Sungkyunkwan University, Korea, 2004 and 2006. He worked for Korea Electrical Engineering & Science Institute, Seoul, Korea, as a researcher in power system division from 2006 to 2009. He was a postdoctoral fellow in the dept. of electrical engineering, Yeungnam University, Korea, from Sep. 2013 to Jan. 2014. From Mar. 2014, he is an assistant professor with the School of IT Engineering, Yonam Institute of Digital Technology, Korea. His research interests include power system transients, protection and stability.
WonHyeok Jang He received his B.S. and M.S. in Electrical and Computer Engineering from Sungkyunkwan University, Suwon, Korea in 2008 and 2010, respectively. He is now working toward his Ph.D. degree at University of Illinois at UrbanaChampaign. He is a Research Assistant in Electrical and Computer Engineering Department, University of Illinois at UrbanaChampaign. His research interests include power system modeling and analysis.
Yoon Sang Kim obtained B.S., M.S., and Ph.D. degrees in Electrical Engineering from Sungkyunkwan University, Seoul, Korea, in 1993, 1995, and 1999, respectively. He was a member of the Postdoctoral Research Staff of Korea Institute of Science and Technology (KIST), Seoul, Korea. Likewise, he was a Faculty Research Associate in the Department of Electrical Engineering, University of Washington, Seattle. He was a Member of the Senior Research Staff, Samsung Advanced Institute of Technology (SAIT), Suwon, Korea. Since March 2005, he has been a professor at the School of Computer and Science Engineering, Korea University of Technology Education (KOREATECH), Cheonan, Korea. His current research interests include Virtual simulation, PowerIT technology, and devicebased interactive application. Dr. Kim was awarded the Korea Science and Engineering Foundation (KOSEF) Overseas Postdoctoral Fellow in 2000. He is a member of IEEE, IEICE, ICASE, KIPS, and KIEE.
ChulWon Park was born in Korea in 1961. He received his B.S., M.S. and Ph.D. degrees in Electrical Engineering from Sungkyunkwan University(SKK), Seoul, Korea, in 1988, 1990, and 1996, respectively. From 1989 to 1993 he was an associate researcher at Lucky GoldStar Industrial Systems. From 1993 to 1996, he was a senior researcher at PROCOM system and lecturer at S.K.K. University. At present, he is a professor in the Department of Electrical Engineering at GangneungWonju National University, since 1997. His research interests include smart grid, power IT, IED, power system modeling and control, and computer application in power system. He is a member of the KIEE. Dr. Park was awarded Paper Prize of KIEE in 2010.
ChulHwan Kim was born in Korea, 1961. In 1990 he joined Cheju National University, Cheju, Korea, as a fulltime Lecturer. He has been a visiting academic at the University of BATH, UK, in 1996, 1998, and 1999. Since March 1992, he has been a professor in the School of Electrical and Computer Engineering, Sungkyunkwan University, Korea. His research interests include power system protection, artificial intelligence application for protection and control, the modelling / protection of underground cable and EMTP software. He received his B.S and M.S degrees in Electrical Engineering from Sungkyunkwan University, Korea, 1982 and 1984, respectively. He received a Ph.D in Electrical Engineering from Sungkyunkwan University in 1990. Currently, he is a director of Center for Power IT (CPIT) in Sungkyunkwan University.
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