Abstract
The nonlinear operation of metal oxide varistor (MOV)-protected series compensator in transmission lines introduces complications into fault detection approaches. The accuracy of a conventional fault detection schemes is adversely affected by continuous change of the system impedance and load current at the point of a series compensation unit. Thus, this study suggests a method for detecting the faulted phase in MOV-protected series-compensated transmission lines. Primarily, the fault feature is identified using the covariance coefficients of the current samples during the fault period and the current samples during the pre-fault period. Furthermore, a convenience fault detection index is established by applying the cumulative sum technique. Extensive validation through different fault circumstances is accomplished, including different fault positions, resistances, and inception times. The experimental results show that the proposed method performs well with high resistance or impedance faults, faults in noisy conditions, and close-in and far-end faults. The proposed method is simple and efficient for faulty phase detection in MOV-protected series-compensated transmission lines.
THE presence of series compensator devices in power transmission changes the system parameters such as line impedance and load current at the connection point of the series compensation [
An effective method for fault identification in series-compensated transmission lines has been proposed. A previous scheme in [
Given these challenges, a new method is developed for identifying the faulty phases in MOV-protected series-compensated transmission lines. The proposed method compares the covariance indices of samples during the fault period with the same samples during the pre-fault period over several cycles and then establishes a convenience fault detection index by applying the cumulative-sum (CUSUM) techniques. The main contribution of the new method is its ability to detect high-resistance faults and high-impedance faults in MOV-protected lines. Thus, it is considered a development compared to current schemes [
The rest of this paper is defined as follows. The principles of the proposed algorithm is defined in Section II. The simulation and test results are provided in Section III, and the work will be summarized in Section IV.
The basic intention of the covariance coefficient is to quantify the relationship between two random variables and . Therefore, given samples of datasets of variables, the covariance can be obtained as:
(1) |
where is the arithmetic mean of ; and is the arithmetic mean of . is taken to be the phase-current samples during the fault period, while indicates the phase-current samples during the pre-fault interval of the cycle. Therefore, the CUSUM of the covariance samples per cycle is calculated as:
(2) |
where is the samples per cycle; is the instantaneous sample; and is the sampling instant.
Under a safe operation condition, the covariance index stabilizes around a specific value and then changes significantly after the fault inception. This change depends on the relationship between the variables and . In general, the covariance index is used for representing how one variable is related to another. Therefore, the covariance is positive when both variables are increasing in the same manner, and negative when the variables are in an opposite relationship. In a power system network, the current is typically prone to changes in direction. Therefore, the covariance index may be positive or negative according to the power flow direction. In this paper, it is observed that when a fault happens during the power flow direction from the sending-end bus to the receiving-end bus, increases significantly after the fault inception. In contrast, when a fault happens during the power flow direction from the receiving-end to the sending-end, decreases significantly after the fault inception. This feature is used for quantifying a convenience based on the following expressions:
(3) |
(4) |
where is the fault detection index in the case of forward power flow (from sending to receiving end); is the fault detection index during reverse power flow; is the reference covariance index as captured in a healthy state; and are the drifting factors chosen to be 2 and 0.75, respectively; and the subscript k is the instantaneous sample of the fault detection index, . Under a safe operation condition, the output of (3) and (4) are zero. If there is a fault and is positive, increases abruptly after the fault inception. Simultaneously, the output of (4) will continue to be zero. If there is a fault and is negative, decreases abruptly after the fault inception. Meanwhile, the output of (3) will continue to be zero. Consequently, a fault condition will be issued if the following criterion is fulfilled:
(5) |
where Output is the output of (3) and (4).
A power system model built in PSCAD/EMTDC is used for executing the fault tests. The model comprises two power sources (500 kV and 50 Hz) connected through 200 km series-compensated overhead transmission lines. The positive- and negative-sequence impedance of the transmission line is , and the zero-sequence impedance is . The MOV-protected series compensator includes two stages, and each stage includes series capacitance 193.9 with shunt inductance 820.5 and resistance 0.0402 . These components are connected shunt with 83.95 kV arrester. The sampling rate is 4 kHz and the data is transferred to MATLAB to implement the fault detection process.

Fig. 1 Schematic diagram of transmission line.
Phase-to-ground fault (phase a is ground to earth) at 50 km from Bus 1 with a fault resistance of 200 is selected to validate the performance of the proposed method. The fault inception is at s and it continues for 100 ms.

Fig. 2 Performance of proposed method during phase-to-ground fault. (a) Current. (b) CvI. (c) FDI. (d) Output.

Fig. 3 Logic of fault clearance.
To further evaluate the performance of the proposed scheme, we considered phase-to-ground fault with ground resistance of 15 , which is created at 182 km from Bus 1 (out of the coverage of zone 1). The selected fault starts at s and continues until s. This test is performed with an uncompensated line in case 1, and with a compensated line in case 2, respectively.

Fig. 4 Performance of distance protection for uncompensated and compensated lines. (a) Impedance trajectory in Mho distance relay. (b) Performance of Mho distance relay during fault cases.
The fault in case 1 is simulated out of zone 1. The impedance trajectory is outside of zone 1 and is not registered by the distance protection. The fault in case 2 is simulated out of zone 1 with MOV-protected series-compensated transmission line, but the impedance trajectory is observed inside zone 1 due to the presence of the MOV-protected series compensator (overreach operation). As the result, the distance protection issues a trip output at s (about 31.5 ms after the fault inception) as shown in

Fig. 5 Performance of proposed method for uncompensated and compensated lines. (a) CvI. (b) Output.
To verify the performance of the proposed scheme during double phase fault with series compensation, we considered a double-phase-to-ground fault, i.e., phases a and b are grounded to the earth with ground fault resistance of 100 created at 110 km from bus 1. The selected fault starts at s and continued until s.

Fig. 6 Proposed method performance during double line fault under series compensation. (a) Current. (b) FDI. (c) Output.
Different fault scenarios have been designed to thoroughly investigate the capabilities of the proposed method. The first fault scenario is performed by creating a fault by grounding phase b and phase c at 110 km from the sending-end with different ground fault resistances. The fault cases start at s and continue until s.
Close-in faults and direct current (DC) offsets are common causes of current transformer (CT) saturation. The highest DC offset occurs when a fault begins at a fault inception angle (FIA) of -90° or +90°. To evaluate the performance of the proposed method under such conditions, the proposed method is tested by creating a close-in fault with an FIA of 90°. The CT set is selected with a 5 burden and a turn ratio of 1000:5 installed at the sending-end. A three-phase-to-ground fault situated at ( s), which is 10 km from bus 1, is considered to execute the CT saturation test. The fault case is performed with ground fault resistance ( ).

Fig. 7 Performance of proposed method under close-in fault. (a) Current. (b) CvI. (c) FDI. (d) Output.
The fault case is detected correctly with remarkable timing. It is cleared 102.25 ms after the fault begins. This test is repeated several times with different CT burdens.
A noise test is executed by applying double-phase-to-ground fault, i.e., phases a and c are grounded to earth with a ground resistance Rf of 100 . The fault case is carried out 110 km from bus 1. It starts at s and continues until s. Phase a is corrupted with noise of 20 dB, while phases b and c remain clear of noise.

Fig. 8 Performance of proposed method under noise condition. (a) Current. (b) CvI. (c) FDI. (d) Output.
The change of power flow direction is caused by the reversal of the power angle of the voltage source. However, such conditions will also change the covariance from a positive relationship to a negative relationship. This test is executed by changing the sending voltage source angle from 30° (default) to 10°, and the receiving voltage source angle from 10° (default) to 30°. Then, phase-to-ground fault has been applied, where phase b is grounded to earth with a ground resistance of 100 , and the fault case is 10 km away from the series compensation unit. The fault case starts at s and continues until s.

Fig. 9 Performance of proposed method with change of power flow direction. (a) Current. (b) FDI. (c) Output.
The average number of samples that can be obtained within 1 s is a crucial factor in the assessment of the performance of fault detection algorithms. A higher sampling rate allows for a considerable increase in signal resolution. However, it also increases the burden on relays and the microprocessor. The proposed scheme functions properly at different sampling rates ranging from 1 kHz up to 5 kHz. Phases a and b are grounded with a fault resistance of 100 selected to perform this test. The corresponding fault at 110 km from the sending-end, which starts at s and continues for 100 ms. The results are shown in Table V. At higher sampling rates, the response time is reduced. However, there is not a noticeable difference in the response time when the sampling frequency is 4 or 5 kHz. Therefore, 4 kHz is chosen as the sampling frequency for the proposed method.
The high-impedance fault model reported in [

Fig. 10 High-impedance model.
The DC voltage continuously varies around 0.01 ms. Whenever the system voltage is greater than Vp, the current will flow towards the ground. It will reverse when the system voltage is less than Vn. No current will flow when the system voltage is greater than Vn and less than Vp [

Fig. 11 High-impedance fault assessment. (a) Current. (b) FDI. (c) Output.
The IEEE 9-bus system is considered for further investigation of the proposed method.

Fig. 12 IEEE 9-bus system.

Fig. 13 Performance in multi-machine systems. (a) Group a. (b) Group b.
Far-end fault with high impedance or resistance in MOV-protected series-compensated transmission lines is a challenge for many fault detection methods. The proposed method has been compared with schemes in [

Fig. 14 Proposed scheme compared to two schemes in [
Recently, other schemes [

Fig. 15 Performance of proposed method compared to scheme in [
The same fault is repeated for testing the next scheme [

Fig. 16 Performance of proposed method compared with scheme in [
Generally, it is possible to conclude that the proposed method is characterized by the following remarks.
1) The proposed scheme avoids dividing the current signals into positive and negative half-cycles used in two other schemes [
2) The proposed method detects the fault condition based on obtaining the relationship between the current samples during fault intervals and pre-fault intervals, but it is not restricted to a narrow range as in another scheme [
3) The proposed scheme works properly with high-resistance or impedance faults compared with the scheme in [
The proposed method is suggested to identify the faulty phase in MOV-protected series-compensated transmission lines. It relies on calculating the covariance between the current samples over several cycles during the fault period and the pre-fault period. Moreover, the covariance index between these current samples are stable around a specific limit under the safe operation condition, and significant changes arise during the fault period. Then, the CUSUM technique is employed to enlarge the fault feature. As a result, the proposed method can be characterized by: ① less computation, which relies only on the current measurement and does not divide the current signals into positive and negative half-cycles as in conventional cumulative schemes; ② good immunity to noise, which works properly with signal-noise ratio (SNR) up to 20 dB; ③ proper performance with far-end, high-resistance or impedance faults in MOV-protected series-compensated transmission lines; ④ proper performance with different sampling rates from 1 kHz up to 5 kHz; ⑤ remarkable time response, which does not exceed 15 ms in the worst test case.
REFERENCES
A. M. El-Zonkoly and H. Desouki, “Wavelet entropy based algorithm for fault detection and classification in FACTS compensated transmission line,” International Journal of Electrical Power & Energy Systems, vol. 33, no 8, pp. 1368-1374, Oct. 2011. [百度学术]
M. E. Mandour and A. A. Elalaily, “Swivelling characteristic for the protection of series compensated lines,” Electric Power Systems Research, vol. 18, no. 1, pp. 31-35, Jan. 1990. [百度学术]
A. Capar and A. B. Arsoy, “A performance oriented impedance based fault location algorithm for series compensated transmission lines,” International Journal of Electrical Power & Energy Systems, vol. 71, pp. 209-214, Oct. 2015. [百度学术]
R. K. Gajbhiye, B. Gopi, P. Kulkarni et al., “Computationally efficient methodology for analysis of faulted power systems with series-compensated transmission lines: a phase coordinate approach,” IEEE Transactions on Power Delivery, vol. 23, no. 2, pp. 873-880, Apr. 2008. [百度学术]
B. Vyas, R. P. Maheshwari, and B. Das, “Protection of series compensated transmission line: issues and state of art,” Electric Power Systems Research, vol. 107, no. 2, pp. 93-108, Feb. 2014. [百度学术]
O. H. Gupta and M. Tripathy, “Superimposed energy-based fault detection and classification scheme for series-compensated line,” Electric Power Components and Systems, vol. 44, no. 10, pp. 1095-1110, May 2016. [百度学术]
P. Jafarian and M. Sanayepasand, “High-speed superimposed-based protection of series-compensated transmission lines,” IET Generation, Transmission & Distribution, vol. 5, no 12, pp. 1290-1300, Dec. 2011. [百度学术]
N. Perera and A. D. Rajapakse, “Series-compensated double-circuit transmission-line protection using directions of current transients,” IEEE Transactions on Power Delivery, vol. 28, no. 3, pp. 1566-1575, Jul. 2013. [百度学术]
H. Eristi, “Fault diagnosis system for series compensated transmission line based on wavelet transform and adaptive neuro-fuzzy inference system,” Measurement, vol. 46, no. 1, pp. 393-401, Jan. 2013. [百度学术]
M. K. Jena and S. R. Samantaray, “Intelligent relaying scheme for series-compensated double circuit lines using phase angle of differential impedance,” International Journal of Electrical Power & Energy Systems, vol. 70, pp. 17-26, Sept. 2015. [百度学术]
A. Swetapadma, P. K. Mishra, A. Yadav et al., “A non-unit protection scheme for double circuit series capacitor compensated transmission lines,” Electric Power Systems Research, vol. 148, pp. 311-325, Jul. 2017. [百度学术]
V. Malathi, N. S. Marimuthu, S. Baskar et al., “Application of extreme learning machine for series compensated transmission line protection,” Engineering Applications of Artificial Intelligence, vol. 24, no. 5, pp. 880-887, Aug. 2011. [百度学术]
B. Vyas, B. Das, and R. P. Maheshwari, “Improved fault classification in series compensated transmission line: comparative evaluation of Chebyshev neural network training algorithms,” IEEE Transactions on Neural Networks, vol. 27, no. 8, pp. 1631-1642, Aug. 2016. [百度学术]
B. Vyas, B. Das, and R. P. Maheshwari, “An improved scheme for identifying fault zone in a series compensated transmission line using undecimated wavelet transform and Chebyshev neural network,” International Journal of Electrical Power & Energy Systems, vol. 63, pp. 760-768, Dec. 2014. [百度学术]
C. Wang, G. Song, X. Kang et al., “Novel transmission-line pilot protection based on frequency-domain model recognition,” IEEE Transactions on Power Delivery, vol. 30, no. 3, pp. 1243-1250, Jun. 2015. [百度学术]
O. V. Sivov, H. A. Abdelsalam, and E. B. Makram, “Adaptive setting of distance relay for MOV-protected series compensated line considering wind power,” Electric Power Systems Research, vol. 137, pp. 142-154, Aug. 2016. [百度学术]
M. Biswal, “Adaptive distance relay algorithm for double circuit line with series compensation,” Measurement, vol. 53, pp. 206-214, Jul. 2014. [百度学术]
M. R. Noori and S. M. Shahrtash, “Combined fault detector and faulted phase selector for transmission lines based on adaptive cumulative sum method,” IEEE Transactions on Power Delivery, vol. 28, no. 3, pp. 1779-1787, Jul. 2013. [百度学术]
S. R. Mohanty, A. K. Pradhan, and A. Routray, “A cumulative sum-based fault detector for power system relaying application,” IEEE Transactions on Power Delivery, vol. 23, no. 1, pp. 79-86, Jan. 2008. [百度学术]
M. H. Musa, Z. He, L. Fu et al., “Linear regression index-based method for fault detection and classification in power transmission line,” IEEJ Transactions on Electrical and Electronic Engineering, vol. 13, no. 9, pp. 979-987, Jul. 2018. [百度学术]
M. H. H. Musa, Z. He, L. Fu et al., “A correlation coefficient-based algorithm for fault detection and classification in a power transmission line,” IEEJ Transactions on Electrical and Electronic Engineering, vol. 13, no. 7, pp. 1394-1403, Jul. 2018. [百度学术]
I. Hafidz, P. E. Nofi, D. O. Anggriawan et al., “Neuro wavelet algortihm for detecting high impedance faults in extra high voltage transmission systems,” in Proceedings of 2017 2nd International Conference on Sustainable and Renewable Energy Engineering (ICSREE), Hiroshima, Japan, May 2017, pp. 97-100. [百度学术]
W. D. C. Tat and Y. Xia, “A novel technique for high impedance fault identification,” IEEE Transactions on Power Delivery, vol. 13, no. 3, pp. 738-744, Jul. 1998. [百度学术]
A. M. Sharaf and G. Wang, “High impedance fault detection using feature-pattern based relaying,” in Proceedings of IEEE PES Transmission and Distribution Conference and Exposition, Dallas, USA, Sept. 2003, pp. 222-226. [百度学术]