- Email: [email protected]
Equal transfer processes-based distance protection of EHV transmission lines
Electrical Power and Energy Systems 52 (2013) 81–86
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Equal transfer processes-based distance protection of EHV transmission lines Minghao Wen ⇑, Deshu Chen, Xianggen Yin State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Hubei, China
a r t i c l e
i n f o
Article history: Received 4 July 2011 Received in revised form 6 February 2013 Accepted 28 March 2013
Keywords: Coupling capacitor voltage transformer Distance relay Equal transfer process Virtual digital transfer
a b s t r a c t The overreach of the distance protection caused by CCVT is still a serious problem for high-speed line protections. Based on the theory of Equal Transfer Process of Transmission Lines (ETPTLs), a new high-speed distance relay scheme is proposed in order to overcome above problem. The solution is to make the three-phase voltages and currents at the relay location and the voltage at the fault point have the same transfer links by virtue of a new design. Three major steps of the new method are demonstrated: restructuring of the voltage at the fault point, the virtual digital transfer method and solving the R–L differential equation. A variety of ATP simulation tests show that the new method effectively reduces the transient error caused by CCVT and improves the operating speed by a series of technical countermeasures including three major steps, iterative calculations of the fault distance and an inverse time delay setting criterion. The distance measuring error is within 5% at approximately 15 ms after fault occurrence, which is superior to various adaptive protection algorithms based on CCVT transient error estimation or source impedance ratio (SIR). Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Distance protection is the foremost protection to protect the transmission line without needing the channel [1–6]. However, the overreach of the distance protection caused by CCVT is still a serious problem for high-speed line protections. Presently, CCVT is extensively applied to the power systems of 330 kV, 500 kV and above in China. Under normal conditions, the primary power system operates at steady-state. In this case, the transferring accuracy of CCVT is satisfactory. However, the system voltage drops suddenly when a fault occurs on any part of the transmission network. The output of the CCVT cannot trace the input simultaneously due to the very large capacitance and inductance of the CCVT, and the transient process may last for a long period of time. The transient characteristics of CCVT distort the linear transfer relationship between the secondary voltage injected to the protection device and the primary voltage of the line, which may lead to the transient overreach of distance protections and endanger the security and stability of power systems [7–11]. In China, the zone-I setting of the distance protection is set as 0.8 time of the full line impedance. In order to avoid the transient overreach, the protection reach only can be up to 24% of the total length of the line if the protection is required to operate within between 5 ms and ⇑ Corresponding author. Tel./fax: +86 2787540945. E-mail address: [email protected] (M. Wen). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.03.028
10 ms. 56% of the total length can be protected if the operating time is required to be between 10 ms and 20 ms. It has been disclosed that the degree of transient overreach caused by CCVT is in relation to SIR [11]. At present, the usual approach preventing the protection from this type of overreach is to add additional time delay. However, in order to improve the operating speed and the reliability of distance protections, many studies are conducted on CCVT simulation and how to improve the transient response characteristics of CCVT. Some methods are proposed, e.g., transient error est based method. Different time delay strategies are adopted according to the quantity of error. In this case, the operation speed is enhanced compared with the regular distance protection [12]. The measurement error can be estimated by means of the quantity of SIR. This error is small when SIR is relatively small. In this case, time delay to issue the trip signal can be reduced [13]. What’s more, the combination of various digital filter algorithms can be adopted to improve the accuracy of fault measurement by reducing the impact of the transient component of CCVT [14]. These methods, however, only partly improve the accuracy of fault measurement. Therefore, the effect of reducing the time delay of protection tripping is not satisfactory. The most ideal method is the recurrence of the input voltage of CCVT. However, it is very difficult to reconstruct the input signal according to the output signal of a complex circuit. In [15], a simplified model of CCVT and corresponding parameters are used to
82
M. Wen et al. / Electrical Power and Energy Systems 52 (2013) 81–86
correct the measuring error of the secondary voltage, which can reduce the error to some extent. However, the transient measuring error during the first cycle after fault inception is still quite big. The voltage and current signals used by distance protection device do not match the corresponding actual signals of protected line due to the transfer of CCVT, which results in the transient overreach of distance relays. In order to prevent the distance relay from transient overreach, it is necessary to guarantee that the voltage difference between the relay location and the fault point with respect to the current measured by the distance relay can comply with the real transmission line model of taking the distribution parameters into account. It is pointed out by ETPTL[16,17] that the relationship between the distributed voltage and the current of a transmission line does not change if they are transformed by the same linear circuit and still comply with the distribution parameter model of the original transmission line. Generally, CCVT can be regarded as a linear transfer circuit since the intermittent transformer of CCVT always will not saturate. Therefore, for the purpose of allowing the voltage difference between the relay location and the fault point with respect to the current measured by the distance relay to comply with the distributed parameter model of the original transmission line, both the transfer links for the voltage and the current signals at the relay location, as well as that for the voltage at fault point should be consistent. To solve above problems, a fast distance protection scheme that can prevent from the transient overreach caused by CCVT is put forward. Three countermeasures are introduced. Firstly, the voltage at the fault point is restructured. The pre-fault voltage at the fault point is regarded to be close to the bus voltage at the relay location, and the post-fault voltage at this point is regarded as the voltage drop on a fault resistance. Secondly, a virtual digital transfer method is adopted, which can ensure that the current at the relay location and the voltage at the fault point pass the virtual digital transfer link whose transfer characteristic is the same as that of the actual CCVT equipped at the relay point. Thirdly, the R–L differential equation algorithm can be used to solve the fault distance by using the voltage at the relay position, which is transferred by the real CCVT, together with the current through the relay point, which is transferred by the virtual CCVT, and the voltage at the fault point, which is transferred by the virtual CCVT.
neglected and the voltage at the fault point passing the CCVT linear circuit transfer is simply regarded as zero, the transient overreach of the distance relay will possibly occur to a great extent. It is necessary to estimate the voltage at the fault point according to the three-phase voltages and currents at the relay location that can be measured by the distance relays. The process of restructuring the voltage at the fault point can be divided into two stages, namely, the pre-fault one and the postfault one. In general, the pre-fault voltage at the fault point is a sinusoidal steady-state signal. The compensated voltage at a certain point of the protected line is used as the estimation of this voltage since the fault position is unpredictable. Two scenarios should be taken into account during the stage of post-fault. Firstly, the voltage at the fault point can be regarded as zero in the case of bolted faults. Secondly, this voltage at the fault point can be regarded as the voltage drop on the fault resistance in the case of the grounding fault via a fault resistance. The voltage drop on the fault resistance can be expressed as the product of the current passing through the fault resistance multiplied by the fault resistance. According to the usual realization method of distance protection, the current through the fault resistance in the case of the grounding fault via a fault resistance is replaced with zero sequence current measured by the distance relay. The current through the fault resistance in the case of a phase-to-phase fault via fault resistance is replaced with the current of the faulty phase. In this case, the value of the fault resistance can be taken as a variable to solve. Therefore, the post-fault voltage at the fault point can be uniformly set as the voltage drop on the fault resistance, i.e., the product of the fault resistance and the current through the fault resistance. If the solution of this fault resistance is nearly equal to zero, this fault should be a bolted fault.
2.2. Virtual digital CCVT transfer method A virtual digital CCVT transfer method is adopted, which can ensure that the currents at the relay point and the voltage at the fault point pass the virtual digital transfer link whose transfer characteristic is the same as that of the actual CCVT equipped at the relay point. So the problem about the difference between the transfer feature of the voltages at the relay point and that of the currents due to the transient characteristic of CCVT can be solved. The
2. A fast distance protection method 2.1. Restructuring of the voltage at the fault point When the CCVT is not applied to a transmission line, the bus voltage measured by the conventional distance relay is actually the voltage difference between the relay location and the fault point in the case of bolted faults. It is because that the voltage at the fault point is zero in this scenario. Therefore, this voltage and the line current comply with the model of the protected line. When the CCVT is used for a distance relay to measure the voltage, according to ETPTL, the relationship of the voltage difference between the relay location and the fault point with respect to the current measured by the relay cannot comply with the distributed parameter model of the protected line unless the measured current of the distance relay and the voltage at the fault point also pass the CCVT linear transfer circuits which are the same as that for the bus voltage measurement. The voltage at the fault point can be regarded as zero when a bolted fault takes place. However, this voltage does not suddenly drop to zero at the moment of the fault inception if it passes the CCVT linear transfer circuit. Instead, a transient process should exist and last for dozens of milliseconds. If this transient process is
Fig. 1. CCVT circuit: (a) actual circuit; (b) equivalent circuit.
M. Wen et al. / Electrical Power and Energy Systems 52 (2013) 81–86
virtual digital CCVT circuit is identical to the actual CCVT equivalent circuit as shown in Fig. 1b. The more detailed process of the virtual transfer method can refer to literature [16].
83
case of 50 Hz power frequency. A moving data window is used, that is, the oldest one is moved out when a new sample enters this window and the algorithm is re-executed. The calculation procedure is detailed as below.
2.3. Application of R–L differential equation algorithm During the transient course due to fault occurrence, Sub-harmonics and decaying DC components contained in the current samplings have adverse impact on the performance of the phasor based distance protection. The distributed capacitance of the line is not taken into account for the R–L differential equation based distance relaying algorithm. Hence, its high-frequency characteristics are not satisfactory. The virtual transfer method is adopted in the proposed distance protection algorithm. The voltage at the relay location is transformed by CCVT, meanwhile, both the current through the relay location and the voltage at the fault point used by the distance protection algorithm are also processed by the virtual digital transfer links having the same CCVT transfer characteristic. The capacitance and the inductance in CCVT circuit could lead to series resonance at the frequency close to the power frequency, which will restrain the high frequency components of input signals to a great extent. In this case, the shortcomings of R–L differential equation algorithm due to the impact of high frequency components can be overcome. Therefore, the application of R–L differential equation algorithm is promising to achieve relatively good protection performance. The implementation of R–L differential equation algorithm in the new protection scheme is demonstrated by taking the singlephase-to-earth fault as an illustration. When a single phase to earth fault via the fault resistance Rf occurs at point F on the line, we have.
um ðtÞ ¼ uf ðtÞ dðim ðtÞ im0 ðtÞÞ dim0 ðtÞ þ R1 ðim ðtÞ im0 ðtÞÞþL0 þ R0 im0 ðtÞ þ L1 dt dt
Step 1: New samplings of three phase currents are obtained by processing three phase currents with virtual CCVT transferring link. Step 2: Define t0 be the moment of fault occurrence, and tjs be the current calculation moment, we have
tjs ¼ t0 þ 5 ms
ð3Þ
t0 can be determined by the pick-up element, which is implemented with the over-current relay with respect to the superimposed components of phase-phase current together with the zero-sequence over-current relay. Step 3: Define the iteration value to calculate the fault distance be D0 = 0.5 Dl, Dl is the length of the protected line. Step 4: Calculate the samplings of the voltage at the fault point during the period between t0 T and tjs, where T is 100 ms. Step 5: Processing the samplings of the voltage at the fault point during the period between t0 T and tjs by means of virtual CCVT transfer link to obtain the new samplings. Step 6: Substitute the three-phase voltage samplings, together with the samplings of the new three-phase currents, and the voltage at the fault point into R–L differential equation to calculate the fault distance D during this period of time. Step 7: Turn to step 8 if tjs – t0 < 50 ms, else turn to step 10. Step 8: Define
tjs ¼ tjs þ ð20=96Þ ms
ð4Þ
0
Step 9: Let D = D and turn to step 4. Step 10: End.
l ð1Þ where um(t) is the faulty phase voltage at the relay point; im(t) the faulty phase current at the relay point; uf(t) the faulty phase voltage at the fault point F; im0(t) the zero sequence current at the relay point; L1 and R1 the positive sequence inductance and resistance of the line per unit length; L0 and R0 the zero sequence inductance and resistance of the line per unit length; l the distance from the relay point to the fault point F; Rf is the fault resistance.Here, uf(t) is the function of Rf as described in Section 2.1. One-point differential algorithm is adopted to perform the differential calculation, as given by:
dðim ðtÞ im0 ðtÞÞ dt
¼ t¼nDt
½im ðn þ 1Þ im0 ðn þ 1Þ ½im ðnÞ im0 ðnÞ Dt ð2Þ
where Dt is the sampling interval and n is the index of the samplings. If a series of samplings in a certain period are substituted into (1), a series of differential equations are available correspondingly. They can compose of a set of the equations. In this paper, the least square algorithm is used to calculate the distance from the relay point to the fault point. 2.4. Iterative calculations of the fault distance A data window with 5 ms window length starting from the moment of fault inception is used to calculate the fault distance based on the proposed method. The sampling rate is set as 4800 Hz in the
In this way, we have every fault distance calculation result for each sampling instance during the post-fault period of 50 ms time length. 2.5. An inverse time delay setting criterion The inverse time delay setting criterion can be used for the proposed new scheme, as described below: For the small SIR system(SIR < 10), as long as the pick-up element operates, we set Zset = 0.5ZL in the case of tpost-fault = 8 ms, set Zset = 0.8ZL in the case of tpost-fault = 10 ms, and set Zset = 0.95ZL in the case of tpost-fault = 15 ms. ZL is the impedance of the protected line. For the big SIR system(10 < SIR < 20), as long as the pick-up element operates, we set Zset = 0.5ZL in the case of tpost-fault = 12 ms, set Zset = 0.8ZL in the case of tpost-fault = 15 ms, and set Zset = 0.95ZL in the case of tpost-fault = 25 ms. 3. Simulation analysis A variety of simulation tests show that the new method effectively reduces the transient error caused by CCVT. The new method is compared with several existing distance protection schemes to highlight its advantages. The existing distance protections include the conventional differential equation based distance relaying algorithm, half-cycle Fourier Algorithm and full-cycle Fourier Algorithm [18–21]. The impedance measurement calculation methods of various adaptive algorithms in [12,13] are also based on these algorithms.
84
M. Wen et al. / Electrical Power and Energy Systems 52 (2013) 81–86
Fig. 2. The schematic diagram of simulation system.
Table 1 Parameter list of CCVT equivalent circuit. Circuit parameter
Value
Parameter of damper
Value
Parameter of load
Value
L1 H R1 k X Ce lF
142.1274 1.95055 0.078567
Cf lF Lf H rf k X Rf k X
0.015858 639.576 6.0 131.8
Rb k X Lb H
1352.0 3229.3
The tests have been done based on Alternative Transients Program version of EMTP (ATP). The schematic diagram of the 500 kV power system is shown in Fig. 2. Here u(t) and i(t) are voltages and currents sampled by the protection, and D is the line length. The line parameters are D = 100 km, r = 0.027 X/km, x = 0.28 X/km, r0 = 0.195 X/km and x0 = 0.649 X/km. Data for network A are: RA = 0.42 X, LA = 0.106 H, RA0 = 0.188 X, and LA0 = 0.036 H. Data for network B are: RB = 0.63 X, LB = 0.16 H, RB0 = 0.28 X, and LB0 = 0.054 H. The equivalent electromotive forces of networks A and B are EA = 525 kV and EB = 500 kV respectively. The phase angle between them is 30°. The parameters of CCVT are shown in Table 1. The sampling rate is set as 4800 Hz in the case of 50 Hz power frequency.
A data window with 5 ms window length starting from the moment of fault inception is used to calculate the fault distance based on the proposed method (as described in Section 2.4). The timeimpedance curve can be obtained. The horizontal axis in the figure represents the moment at which the data window end is. Here, the fault occurrence is taken as the initial moment. The longitudinal axis stands for the measuring impedance. The measured impedance is expressed in per unit with respect to the actual line impedance between the fault point and the relay location. Similarly, the time-impedance curves can be obtained for other existing distance protections. The least square method with a 5 ms data window is adopted to obtain the fault distance when executing the differential equation based algorithm. For the half-cycle and full-cycle Fourier Algorithms, the phasors of three-phase voltages and currents at the relay location are calculated prior to obtaining the measuring impedance from the fault point to the relay location. For the convenience of comparison and analysis, 4800 Hz sampling rate is adopted for all these four algorithms. Fig. 3 shows the time-impedance curves in the case of SIR = 6, l = 20 km and RF = 0.1 X. The curve begins at 5 ms since the minimum data window of the new method is 5 ms. Similarly, the curve formed by the solving-differential-equation algorithm begins at 5 ms. Besides, the curve formed by the half-cycle Fourier algorithm begins from 10 ms, and the curve formed by the full-cycle Fourier algorithm begins from 20 ms. There are some fluctuations at the initial moment for these four time-impedance curves, and then the measuring impedances all gradually approach 1. Here two time indexes are used to analyze and compare the four distance protection algorithms, namely, the moment t0.9–1.1 corresponding to the measuring impedance with the convergence of 0.9–1.1, and t0.95–1.05 corresponding to the measuring impedance with the convergence of 0.95–1.05. Here we have t0.9–1.1 = 14 ms and t0.95–1.01 = 15 ms for the new method. In comparison, we have t0.9–1.1 = 28 ms and t0.95–1.05 = 58 ms for the solving-differential-equation algorithm, t0.9–1.1 = 31 ms and t0.95–1.05 = 42 ms for the half-cycle Fourier Algorithm,
Fig. 3. Time–impedance curves when SIR = 6: (a) the curve of the new method, (b) the curve of the differential equation algorithm, (c) the curve of the half-cycle Fourier algorithm, (d) the curve of the full-cycle Fourier algorithm.
M. Wen et al. / Electrical Power and Energy Systems 52 (2013) 81–86
85
Table 2 Some typical simulation results (ms).
SGF PPF TPF
t0.9–1.1 t0.95–1.05 t0.9–1.1 t0.95–1.05 t0.9–1.1 t0.95–1.05
l = 20 km SSIR = 6
l = 40 km SSIR = 3
l = 60 km SSIR = 2
l = 80 km SSIR = 1.5
9 14 13 14 14 16
8 9 12 13 14 16
8 8 12 13 13 15
8 13 6 13 8 12
t0.9–1.1 = 32 ms and t0.9–1.05 = 34 ms for the full-cycle Fourier Algorithm. If the setting impedance is 1, in accordance with the relay protection test specification which allows 5% transient overreach, the relay based on the new method can operate at 15 ms. In contrast, the other three distance protections operate with longer time delay. Among which, the full-cycle Fourier Algorithm based method, the fastest one of these three algorithms, needs 34 ms to operate. Actually, for various adaptive protection algorithms based on CCVT transient error estimation or SIR, the degree of the transient error resulting from CCVT, that is, the impedance calculation precision, is estimated according to some indexes. Then, this degree is used to adjust the time delay of the protection adaptively. In this case, the minimum operation time under some fault conditions will inevitably exceed 34 ms. In contrast, the new method is based on ETPTL, which effectively reduces the transient error caused by CCVT and improve the operating speed by a series of technical countermeasures including restructuring the voltage at the fault point, virtual transfer method and R–L differential equation based distance relaying algorithm. Table 2 provides part of typical simulations results. Where, SGF means single phase ground fault, PPF means phase-phase shortcircuit fault, and TPF means three-phase short-circuit fault. Further simulation tests prove that the new method effectively reduces the transient error caused by CCVT, within a 5% distance measuring error at about 15 ms after fault occurrence, which is obviously superior to various adaptive protection algorithms based on CCVT transient error estimation or SIR. Fault distance measuring error can be given by
error ¼ jD lj=l
ð5Þ
D is the actual fault distance measuring value and l is the real value of fault distance. In addition, compared with the regular distance protection algorithm, which guarantees the distance measurement precision by means of a long time delay, the operation speed of the new method is much faster. In order to compare the simulation results between the proposed method and the method in [14], which is called as FPAAbased mho distance relay considering CCVT transient supervision, average operating times for different fault types, SIRs {5, 15}, and different fault locations {0, 75, 90, 100}% have been shown in Table
Table 3 Average operating times (ms) of the proposed method and the FPAA-based relay. Ph–G
Ph–Ph
SIR = 5
0 75 90 100
SIR = 15
SIR = 5
SIR = 15
New
fpaa
New
fpaa
New
fpaa
New
fpaa
8 10 15 NO
10 17 NO NO
12 15 25 NO
27 28 NO NO
8 10 15 NO
11 19 NO NO
12 15 25 NO
26 38 NO NO
NO: no operation.
3. Where, ‘‘new’’ means the proposed method, and ‘‘fpaa’’ means FPAA-based mho distance relay considering CCVT transient supervision. As seen, the proposed method is able to achieve fast operating speed and higher accuracy. 4. Conclusions Based on ETPTL, the reason of CCVT leading to the transient overreach of distance relays is analyzed in this paper. It is pointed out that the transfer link of the voltage and current involved in the distance protection calculation are not consistent. Therefore, the voltage difference between the relay location and the fault point as well as the current measured by the distance relay cannot comply with the model of the protected transmission line. To overcome above problem, a fast distance protection scheme that can be utilized to prevent the transient overreach caused by CCVT is put forward. The results of the simulation tests show that the new method can effectively reduce the transient error caused by CCVT less than ±5% at about 15 ms after fault occurrence, which is obviously superior to various adaptive protection algorithms based on CCVT transient error estimation or SIR. Furthermore, compared with the conventional distance protection algorithms, the operation speed of the new method is much faster. Acknowledgments This work was supported by the National Natural Science Foundation of China (51077061 and 50837002). References [1] Sadeghi Hadi. A novel method for adaptive distance protection of transmission line connected to wind farms. Int J Electr Power Energy Syst 2012;43(1):1376–82. [2] Ghorbani Amir, Khederzadeh Mojtaba, Mozafari Babak. Impact of SVC on the protection of transmission lines. Int J Electr Power Energy Syst 2012;42(1):702–9. [3] Al-Kandari Ahmad, Gilany Mahmoud, Madouh Jamal. An accurate technique for locating faults by distance relays. Int J Electr Power Energy Syst 2011;33(3):477–84. [4] Lin X, Li Z, Ke S, Gao Y. Theoretical fundamentals and implementation of novel self-adaptive distance protection resistant to power swings. IEEE Trans Power Deliv 2010;25(3):1372–83. [5] Ricardo Caneloi dos Santos a. Eduardo cesar senger, transmission lines distance protection using artificial neural networks. Int J Electr Power Energy Syst 2011;33(3):721–30. [6] Xia Jingde, Jiale Suonan, Song Guobing, Wang Li, He Shien, Liu Kai. Transmission line individual phase impedance and related pilot protection. Int J Electr Power Energy Syst 2011;33(9):1563–71. [7] Marti JR, Linares LR, Dommel HW. Current transformers and couplingcapacitor voltage transformers in real-time simulations. IEEE Trans Power Deliv 1997;12(1):164–8. [8] Kezunovic M, Kojoric L, Skendzic V. Digital models of coupling capacitor voltage transformers for protective relay transient studies. IEEE Trans Power Deliv 1992;7(4):1927–35. [9] Fernandes Jr D, Neves WLA, Vasconcelos JCA. Coupling capacitor voltage transformer: a model for electromagnetic transient studies. Electr Power Syst Res 2007;77(2):125–34. [10] Tziouvaras DA, McLaren P, Alexander G. Mathematical models for current, voltage and coupling capacitor voltage transformers. IEEE Trans Power Deliv 2000;15(1):62–72.
86
M. Wen et al. / Electrical Power and Energy Systems 52 (2013) 81–86
[11] Pajuelo E, Ramakrishna G, Sachdev MS. Strengths and limitations of a new phasor estimation technique to reduce CCVT impact in distance protection. Electr Power Syst Res 2010;80(4):417–25. [12] Benteng He, Yiquan Li, Bo ZQ. An Adaptive Distance Relay Based on Transient Error Estimation of ccvt. IEEE Trans Power Deliv 2006;21(4):1856–61. [13] Kasztenny B, Sharples D, Asaro V, Pozzuoli M. Distance relays and capacitive voltage transformers—balancing speed and transient overreach. General Electric Company, GER-3986; 2000. [14] Dadash Zadeh MR, Sidhu TS. FPAA-based mho distance relay considering CVT transient supervision. IET Gen Trans Distrib 2009;3(7):616–27. [15] Izykowski J, Kasztenny B. Dynamic compensation of capacitive voltage transformers. IEEE Trans Power Deliv 1998;13(1):116–22. [16] Wen Minghao, Chen Deshu, Yin Xianggen. Instantaneous value and equal transfer processes-based current differential protection for long transmission lines. IEEE Trans Power Deliv 2012;27(1):289–99.
[17] Minghao Wen. A new scheme of the protection based on the principle of balance of energy with virtual cvts. Proc CSEE 2007;27(24):11–6 [in Chinese]. [18] Elmore WA. Protective relaying theory and applications. 2nd ed. Marcel Dekker Inc.; 2004. [19] Ghorbani Amir, Mozafari Babak, Ranjbar Ali Mohammad. Digital distance protection of transmission lines in the presence of SSSC. Int J Electr Power Energy Syst 2012;43(1):712–9. [20] Zadeh Hassan Khorashadi, Li Zuyi. Adaptive load blinder for distance protection. Int J Electr Power Energy Syst 2011;33(4):861–7. [21] Bakara Ab Halim Abu, Yatimc Fazilah Mat, Yusofb Sallehuddin. Analysis of overload conditions in distance relay under severe system contingencies. Int J Electr Power Energy Syst 2010;32(5):345–50.
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Equal transfer processes-based distance protection of EHV transmission lines Minghao Wen ⇑, Deshu Chen, Xianggen Yin State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Hubei, China
a r t i c l e
i n f o
Article history: Received 4 July 2011 Received in revised form 6 February 2013 Accepted 28 March 2013
Keywords: Coupling capacitor voltage transformer Distance relay Equal transfer process Virtual digital transfer
a b s t r a c t The overreach of the distance protection caused by CCVT is still a serious problem for high-speed line protections. Based on the theory of Equal Transfer Process of Transmission Lines (ETPTLs), a new high-speed distance relay scheme is proposed in order to overcome above problem. The solution is to make the three-phase voltages and currents at the relay location and the voltage at the fault point have the same transfer links by virtue of a new design. Three major steps of the new method are demonstrated: restructuring of the voltage at the fault point, the virtual digital transfer method and solving the R–L differential equation. A variety of ATP simulation tests show that the new method effectively reduces the transient error caused by CCVT and improves the operating speed by a series of technical countermeasures including three major steps, iterative calculations of the fault distance and an inverse time delay setting criterion. The distance measuring error is within 5% at approximately 15 ms after fault occurrence, which is superior to various adaptive protection algorithms based on CCVT transient error estimation or source impedance ratio (SIR). Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Distance protection is the foremost protection to protect the transmission line without needing the channel [1–6]. However, the overreach of the distance protection caused by CCVT is still a serious problem for high-speed line protections. Presently, CCVT is extensively applied to the power systems of 330 kV, 500 kV and above in China. Under normal conditions, the primary power system operates at steady-state. In this case, the transferring accuracy of CCVT is satisfactory. However, the system voltage drops suddenly when a fault occurs on any part of the transmission network. The output of the CCVT cannot trace the input simultaneously due to the very large capacitance and inductance of the CCVT, and the transient process may last for a long period of time. The transient characteristics of CCVT distort the linear transfer relationship between the secondary voltage injected to the protection device and the primary voltage of the line, which may lead to the transient overreach of distance protections and endanger the security and stability of power systems [7–11]. In China, the zone-I setting of the distance protection is set as 0.8 time of the full line impedance. In order to avoid the transient overreach, the protection reach only can be up to 24% of the total length of the line if the protection is required to operate within between 5 ms and ⇑ Corresponding author. Tel./fax: +86 2787540945. E-mail address: [email protected] (M. Wen). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.03.028
10 ms. 56% of the total length can be protected if the operating time is required to be between 10 ms and 20 ms. It has been disclosed that the degree of transient overreach caused by CCVT is in relation to SIR [11]. At present, the usual approach preventing the protection from this type of overreach is to add additional time delay. However, in order to improve the operating speed and the reliability of distance protections, many studies are conducted on CCVT simulation and how to improve the transient response characteristics of CCVT. Some methods are proposed, e.g., transient error est based method. Different time delay strategies are adopted according to the quantity of error. In this case, the operation speed is enhanced compared with the regular distance protection [12]. The measurement error can be estimated by means of the quantity of SIR. This error is small when SIR is relatively small. In this case, time delay to issue the trip signal can be reduced [13]. What’s more, the combination of various digital filter algorithms can be adopted to improve the accuracy of fault measurement by reducing the impact of the transient component of CCVT [14]. These methods, however, only partly improve the accuracy of fault measurement. Therefore, the effect of reducing the time delay of protection tripping is not satisfactory. The most ideal method is the recurrence of the input voltage of CCVT. However, it is very difficult to reconstruct the input signal according to the output signal of a complex circuit. In [15], a simplified model of CCVT and corresponding parameters are used to
82
M. Wen et al. / Electrical Power and Energy Systems 52 (2013) 81–86
correct the measuring error of the secondary voltage, which can reduce the error to some extent. However, the transient measuring error during the first cycle after fault inception is still quite big. The voltage and current signals used by distance protection device do not match the corresponding actual signals of protected line due to the transfer of CCVT, which results in the transient overreach of distance relays. In order to prevent the distance relay from transient overreach, it is necessary to guarantee that the voltage difference between the relay location and the fault point with respect to the current measured by the distance relay can comply with the real transmission line model of taking the distribution parameters into account. It is pointed out by ETPTL[16,17] that the relationship between the distributed voltage and the current of a transmission line does not change if they are transformed by the same linear circuit and still comply with the distribution parameter model of the original transmission line. Generally, CCVT can be regarded as a linear transfer circuit since the intermittent transformer of CCVT always will not saturate. Therefore, for the purpose of allowing the voltage difference between the relay location and the fault point with respect to the current measured by the distance relay to comply with the distributed parameter model of the original transmission line, both the transfer links for the voltage and the current signals at the relay location, as well as that for the voltage at fault point should be consistent. To solve above problems, a fast distance protection scheme that can prevent from the transient overreach caused by CCVT is put forward. Three countermeasures are introduced. Firstly, the voltage at the fault point is restructured. The pre-fault voltage at the fault point is regarded to be close to the bus voltage at the relay location, and the post-fault voltage at this point is regarded as the voltage drop on a fault resistance. Secondly, a virtual digital transfer method is adopted, which can ensure that the current at the relay location and the voltage at the fault point pass the virtual digital transfer link whose transfer characteristic is the same as that of the actual CCVT equipped at the relay point. Thirdly, the R–L differential equation algorithm can be used to solve the fault distance by using the voltage at the relay position, which is transferred by the real CCVT, together with the current through the relay point, which is transferred by the virtual CCVT, and the voltage at the fault point, which is transferred by the virtual CCVT.
neglected and the voltage at the fault point passing the CCVT linear circuit transfer is simply regarded as zero, the transient overreach of the distance relay will possibly occur to a great extent. It is necessary to estimate the voltage at the fault point according to the three-phase voltages and currents at the relay location that can be measured by the distance relays. The process of restructuring the voltage at the fault point can be divided into two stages, namely, the pre-fault one and the postfault one. In general, the pre-fault voltage at the fault point is a sinusoidal steady-state signal. The compensated voltage at a certain point of the protected line is used as the estimation of this voltage since the fault position is unpredictable. Two scenarios should be taken into account during the stage of post-fault. Firstly, the voltage at the fault point can be regarded as zero in the case of bolted faults. Secondly, this voltage at the fault point can be regarded as the voltage drop on the fault resistance in the case of the grounding fault via a fault resistance. The voltage drop on the fault resistance can be expressed as the product of the current passing through the fault resistance multiplied by the fault resistance. According to the usual realization method of distance protection, the current through the fault resistance in the case of the grounding fault via a fault resistance is replaced with zero sequence current measured by the distance relay. The current through the fault resistance in the case of a phase-to-phase fault via fault resistance is replaced with the current of the faulty phase. In this case, the value of the fault resistance can be taken as a variable to solve. Therefore, the post-fault voltage at the fault point can be uniformly set as the voltage drop on the fault resistance, i.e., the product of the fault resistance and the current through the fault resistance. If the solution of this fault resistance is nearly equal to zero, this fault should be a bolted fault.
2.2. Virtual digital CCVT transfer method A virtual digital CCVT transfer method is adopted, which can ensure that the currents at the relay point and the voltage at the fault point pass the virtual digital transfer link whose transfer characteristic is the same as that of the actual CCVT equipped at the relay point. So the problem about the difference between the transfer feature of the voltages at the relay point and that of the currents due to the transient characteristic of CCVT can be solved. The
2. A fast distance protection method 2.1. Restructuring of the voltage at the fault point When the CCVT is not applied to a transmission line, the bus voltage measured by the conventional distance relay is actually the voltage difference between the relay location and the fault point in the case of bolted faults. It is because that the voltage at the fault point is zero in this scenario. Therefore, this voltage and the line current comply with the model of the protected line. When the CCVT is used for a distance relay to measure the voltage, according to ETPTL, the relationship of the voltage difference between the relay location and the fault point with respect to the current measured by the relay cannot comply with the distributed parameter model of the protected line unless the measured current of the distance relay and the voltage at the fault point also pass the CCVT linear transfer circuits which are the same as that for the bus voltage measurement. The voltage at the fault point can be regarded as zero when a bolted fault takes place. However, this voltage does not suddenly drop to zero at the moment of the fault inception if it passes the CCVT linear transfer circuit. Instead, a transient process should exist and last for dozens of milliseconds. If this transient process is
Fig. 1. CCVT circuit: (a) actual circuit; (b) equivalent circuit.
M. Wen et al. / Electrical Power and Energy Systems 52 (2013) 81–86
virtual digital CCVT circuit is identical to the actual CCVT equivalent circuit as shown in Fig. 1b. The more detailed process of the virtual transfer method can refer to literature [16].
83
case of 50 Hz power frequency. A moving data window is used, that is, the oldest one is moved out when a new sample enters this window and the algorithm is re-executed. The calculation procedure is detailed as below.
2.3. Application of R–L differential equation algorithm During the transient course due to fault occurrence, Sub-harmonics and decaying DC components contained in the current samplings have adverse impact on the performance of the phasor based distance protection. The distributed capacitance of the line is not taken into account for the R–L differential equation based distance relaying algorithm. Hence, its high-frequency characteristics are not satisfactory. The virtual transfer method is adopted in the proposed distance protection algorithm. The voltage at the relay location is transformed by CCVT, meanwhile, both the current through the relay location and the voltage at the fault point used by the distance protection algorithm are also processed by the virtual digital transfer links having the same CCVT transfer characteristic. The capacitance and the inductance in CCVT circuit could lead to series resonance at the frequency close to the power frequency, which will restrain the high frequency components of input signals to a great extent. In this case, the shortcomings of R–L differential equation algorithm due to the impact of high frequency components can be overcome. Therefore, the application of R–L differential equation algorithm is promising to achieve relatively good protection performance. The implementation of R–L differential equation algorithm in the new protection scheme is demonstrated by taking the singlephase-to-earth fault as an illustration. When a single phase to earth fault via the fault resistance Rf occurs at point F on the line, we have.
um ðtÞ ¼ uf ðtÞ dðim ðtÞ im0 ðtÞÞ dim0 ðtÞ þ R1 ðim ðtÞ im0 ðtÞÞþL0 þ R0 im0 ðtÞ þ L1 dt dt
Step 1: New samplings of three phase currents are obtained by processing three phase currents with virtual CCVT transferring link. Step 2: Define t0 be the moment of fault occurrence, and tjs be the current calculation moment, we have
tjs ¼ t0 þ 5 ms
ð3Þ
t0 can be determined by the pick-up element, which is implemented with the over-current relay with respect to the superimposed components of phase-phase current together with the zero-sequence over-current relay. Step 3: Define the iteration value to calculate the fault distance be D0 = 0.5 Dl, Dl is the length of the protected line. Step 4: Calculate the samplings of the voltage at the fault point during the period between t0 T and tjs, where T is 100 ms. Step 5: Processing the samplings of the voltage at the fault point during the period between t0 T and tjs by means of virtual CCVT transfer link to obtain the new samplings. Step 6: Substitute the three-phase voltage samplings, together with the samplings of the new three-phase currents, and the voltage at the fault point into R–L differential equation to calculate the fault distance D during this period of time. Step 7: Turn to step 8 if tjs – t0 < 50 ms, else turn to step 10. Step 8: Define
tjs ¼ tjs þ ð20=96Þ ms
ð4Þ
0
Step 9: Let D = D and turn to step 4. Step 10: End.
l ð1Þ where um(t) is the faulty phase voltage at the relay point; im(t) the faulty phase current at the relay point; uf(t) the faulty phase voltage at the fault point F; im0(t) the zero sequence current at the relay point; L1 and R1 the positive sequence inductance and resistance of the line per unit length; L0 and R0 the zero sequence inductance and resistance of the line per unit length; l the distance from the relay point to the fault point F; Rf is the fault resistance.Here, uf(t) is the function of Rf as described in Section 2.1. One-point differential algorithm is adopted to perform the differential calculation, as given by:
dðim ðtÞ im0 ðtÞÞ dt
¼ t¼nDt
½im ðn þ 1Þ im0 ðn þ 1Þ ½im ðnÞ im0 ðnÞ Dt ð2Þ
where Dt is the sampling interval and n is the index of the samplings. If a series of samplings in a certain period are substituted into (1), a series of differential equations are available correspondingly. They can compose of a set of the equations. In this paper, the least square algorithm is used to calculate the distance from the relay point to the fault point. 2.4. Iterative calculations of the fault distance A data window with 5 ms window length starting from the moment of fault inception is used to calculate the fault distance based on the proposed method. The sampling rate is set as 4800 Hz in the
In this way, we have every fault distance calculation result for each sampling instance during the post-fault period of 50 ms time length. 2.5. An inverse time delay setting criterion The inverse time delay setting criterion can be used for the proposed new scheme, as described below: For the small SIR system(SIR < 10), as long as the pick-up element operates, we set Zset = 0.5ZL in the case of tpost-fault = 8 ms, set Zset = 0.8ZL in the case of tpost-fault = 10 ms, and set Zset = 0.95ZL in the case of tpost-fault = 15 ms. ZL is the impedance of the protected line. For the big SIR system(10 < SIR < 20), as long as the pick-up element operates, we set Zset = 0.5ZL in the case of tpost-fault = 12 ms, set Zset = 0.8ZL in the case of tpost-fault = 15 ms, and set Zset = 0.95ZL in the case of tpost-fault = 25 ms. 3. Simulation analysis A variety of simulation tests show that the new method effectively reduces the transient error caused by CCVT. The new method is compared with several existing distance protection schemes to highlight its advantages. The existing distance protections include the conventional differential equation based distance relaying algorithm, half-cycle Fourier Algorithm and full-cycle Fourier Algorithm [18–21]. The impedance measurement calculation methods of various adaptive algorithms in [12,13] are also based on these algorithms.
84
M. Wen et al. / Electrical Power and Energy Systems 52 (2013) 81–86
Fig. 2. The schematic diagram of simulation system.
Table 1 Parameter list of CCVT equivalent circuit. Circuit parameter
Value
Parameter of damper
Value
Parameter of load
Value
L1 H R1 k X Ce lF
142.1274 1.95055 0.078567
Cf lF Lf H rf k X Rf k X
0.015858 639.576 6.0 131.8
Rb k X Lb H
1352.0 3229.3
The tests have been done based on Alternative Transients Program version of EMTP (ATP). The schematic diagram of the 500 kV power system is shown in Fig. 2. Here u(t) and i(t) are voltages and currents sampled by the protection, and D is the line length. The line parameters are D = 100 km, r = 0.027 X/km, x = 0.28 X/km, r0 = 0.195 X/km and x0 = 0.649 X/km. Data for network A are: RA = 0.42 X, LA = 0.106 H, RA0 = 0.188 X, and LA0 = 0.036 H. Data for network B are: RB = 0.63 X, LB = 0.16 H, RB0 = 0.28 X, and LB0 = 0.054 H. The equivalent electromotive forces of networks A and B are EA = 525 kV and EB = 500 kV respectively. The phase angle between them is 30°. The parameters of CCVT are shown in Table 1. The sampling rate is set as 4800 Hz in the case of 50 Hz power frequency.
A data window with 5 ms window length starting from the moment of fault inception is used to calculate the fault distance based on the proposed method (as described in Section 2.4). The timeimpedance curve can be obtained. The horizontal axis in the figure represents the moment at which the data window end is. Here, the fault occurrence is taken as the initial moment. The longitudinal axis stands for the measuring impedance. The measured impedance is expressed in per unit with respect to the actual line impedance between the fault point and the relay location. Similarly, the time-impedance curves can be obtained for other existing distance protections. The least square method with a 5 ms data window is adopted to obtain the fault distance when executing the differential equation based algorithm. For the half-cycle and full-cycle Fourier Algorithms, the phasors of three-phase voltages and currents at the relay location are calculated prior to obtaining the measuring impedance from the fault point to the relay location. For the convenience of comparison and analysis, 4800 Hz sampling rate is adopted for all these four algorithms. Fig. 3 shows the time-impedance curves in the case of SIR = 6, l = 20 km and RF = 0.1 X. The curve begins at 5 ms since the minimum data window of the new method is 5 ms. Similarly, the curve formed by the solving-differential-equation algorithm begins at 5 ms. Besides, the curve formed by the half-cycle Fourier algorithm begins from 10 ms, and the curve formed by the full-cycle Fourier algorithm begins from 20 ms. There are some fluctuations at the initial moment for these four time-impedance curves, and then the measuring impedances all gradually approach 1. Here two time indexes are used to analyze and compare the four distance protection algorithms, namely, the moment t0.9–1.1 corresponding to the measuring impedance with the convergence of 0.9–1.1, and t0.95–1.05 corresponding to the measuring impedance with the convergence of 0.95–1.05. Here we have t0.9–1.1 = 14 ms and t0.95–1.01 = 15 ms for the new method. In comparison, we have t0.9–1.1 = 28 ms and t0.95–1.05 = 58 ms for the solving-differential-equation algorithm, t0.9–1.1 = 31 ms and t0.95–1.05 = 42 ms for the half-cycle Fourier Algorithm,
Fig. 3. Time–impedance curves when SIR = 6: (a) the curve of the new method, (b) the curve of the differential equation algorithm, (c) the curve of the half-cycle Fourier algorithm, (d) the curve of the full-cycle Fourier algorithm.
M. Wen et al. / Electrical Power and Energy Systems 52 (2013) 81–86
85
Table 2 Some typical simulation results (ms).
SGF PPF TPF
t0.9–1.1 t0.95–1.05 t0.9–1.1 t0.95–1.05 t0.9–1.1 t0.95–1.05
l = 20 km SSIR = 6
l = 40 km SSIR = 3
l = 60 km SSIR = 2
l = 80 km SSIR = 1.5
9 14 13 14 14 16
8 9 12 13 14 16
8 8 12 13 13 15
8 13 6 13 8 12
t0.9–1.1 = 32 ms and t0.9–1.05 = 34 ms for the full-cycle Fourier Algorithm. If the setting impedance is 1, in accordance with the relay protection test specification which allows 5% transient overreach, the relay based on the new method can operate at 15 ms. In contrast, the other three distance protections operate with longer time delay. Among which, the full-cycle Fourier Algorithm based method, the fastest one of these three algorithms, needs 34 ms to operate. Actually, for various adaptive protection algorithms based on CCVT transient error estimation or SIR, the degree of the transient error resulting from CCVT, that is, the impedance calculation precision, is estimated according to some indexes. Then, this degree is used to adjust the time delay of the protection adaptively. In this case, the minimum operation time under some fault conditions will inevitably exceed 34 ms. In contrast, the new method is based on ETPTL, which effectively reduces the transient error caused by CCVT and improve the operating speed by a series of technical countermeasures including restructuring the voltage at the fault point, virtual transfer method and R–L differential equation based distance relaying algorithm. Table 2 provides part of typical simulations results. Where, SGF means single phase ground fault, PPF means phase-phase shortcircuit fault, and TPF means three-phase short-circuit fault. Further simulation tests prove that the new method effectively reduces the transient error caused by CCVT, within a 5% distance measuring error at about 15 ms after fault occurrence, which is obviously superior to various adaptive protection algorithms based on CCVT transient error estimation or SIR. Fault distance measuring error can be given by
error ¼ jD lj=l
ð5Þ
D is the actual fault distance measuring value and l is the real value of fault distance. In addition, compared with the regular distance protection algorithm, which guarantees the distance measurement precision by means of a long time delay, the operation speed of the new method is much faster. In order to compare the simulation results between the proposed method and the method in [14], which is called as FPAAbased mho distance relay considering CCVT transient supervision, average operating times for different fault types, SIRs {5, 15}, and different fault locations {0, 75, 90, 100}% have been shown in Table
Table 3 Average operating times (ms) of the proposed method and the FPAA-based relay. Ph–G
Ph–Ph
SIR = 5
0 75 90 100
SIR = 15
SIR = 5
SIR = 15
New
fpaa
New
fpaa
New
fpaa
New
fpaa
8 10 15 NO
10 17 NO NO
12 15 25 NO
27 28 NO NO
8 10 15 NO
11 19 NO NO
12 15 25 NO
26 38 NO NO
NO: no operation.
3. Where, ‘‘new’’ means the proposed method, and ‘‘fpaa’’ means FPAA-based mho distance relay considering CCVT transient supervision. As seen, the proposed method is able to achieve fast operating speed and higher accuracy. 4. Conclusions Based on ETPTL, the reason of CCVT leading to the transient overreach of distance relays is analyzed in this paper. It is pointed out that the transfer link of the voltage and current involved in the distance protection calculation are not consistent. Therefore, the voltage difference between the relay location and the fault point as well as the current measured by the distance relay cannot comply with the model of the protected transmission line. To overcome above problem, a fast distance protection scheme that can be utilized to prevent the transient overreach caused by CCVT is put forward. The results of the simulation tests show that the new method can effectively reduce the transient error caused by CCVT less than ±5% at about 15 ms after fault occurrence, which is obviously superior to various adaptive protection algorithms based on CCVT transient error estimation or SIR. Furthermore, compared with the conventional distance protection algorithms, the operation speed of the new method is much faster. Acknowledgments This work was supported by the National Natural Science Foundation of China (51077061 and 50837002). References [1] Sadeghi Hadi. A novel method for adaptive distance protection of transmission line connected to wind farms. Int J Electr Power Energy Syst 2012;43(1):1376–82. [2] Ghorbani Amir, Khederzadeh Mojtaba, Mozafari Babak. Impact of SVC on the protection of transmission lines. Int J Electr Power Energy Syst 2012;42(1):702–9. [3] Al-Kandari Ahmad, Gilany Mahmoud, Madouh Jamal. An accurate technique for locating faults by distance relays. Int J Electr Power Energy Syst 2011;33(3):477–84. [4] Lin X, Li Z, Ke S, Gao Y. Theoretical fundamentals and implementation of novel self-adaptive distance protection resistant to power swings. IEEE Trans Power Deliv 2010;25(3):1372–83. [5] Ricardo Caneloi dos Santos a. Eduardo cesar senger, transmission lines distance protection using artificial neural networks. Int J Electr Power Energy Syst 2011;33(3):721–30. [6] Xia Jingde, Jiale Suonan, Song Guobing, Wang Li, He Shien, Liu Kai. Transmission line individual phase impedance and related pilot protection. Int J Electr Power Energy Syst 2011;33(9):1563–71. [7] Marti JR, Linares LR, Dommel HW. Current transformers and couplingcapacitor voltage transformers in real-time simulations. IEEE Trans Power Deliv 1997;12(1):164–8. [8] Kezunovic M, Kojoric L, Skendzic V. Digital models of coupling capacitor voltage transformers for protective relay transient studies. IEEE Trans Power Deliv 1992;7(4):1927–35. [9] Fernandes Jr D, Neves WLA, Vasconcelos JCA. Coupling capacitor voltage transformer: a model for electromagnetic transient studies. Electr Power Syst Res 2007;77(2):125–34. [10] Tziouvaras DA, McLaren P, Alexander G. Mathematical models for current, voltage and coupling capacitor voltage transformers. IEEE Trans Power Deliv 2000;15(1):62–72.
86
M. Wen et al. / Electrical Power and Energy Systems 52 (2013) 81–86
[11] Pajuelo E, Ramakrishna G, Sachdev MS. Strengths and limitations of a new phasor estimation technique to reduce CCVT impact in distance protection. Electr Power Syst Res 2010;80(4):417–25. [12] Benteng He, Yiquan Li, Bo ZQ. An Adaptive Distance Relay Based on Transient Error Estimation of ccvt. IEEE Trans Power Deliv 2006;21(4):1856–61. [13] Kasztenny B, Sharples D, Asaro V, Pozzuoli M. Distance relays and capacitive voltage transformers—balancing speed and transient overreach. General Electric Company, GER-3986; 2000. [14] Dadash Zadeh MR, Sidhu TS. FPAA-based mho distance relay considering CVT transient supervision. IET Gen Trans Distrib 2009;3(7):616–27. [15] Izykowski J, Kasztenny B. Dynamic compensation of capacitive voltage transformers. IEEE Trans Power Deliv 1998;13(1):116–22. [16] Wen Minghao, Chen Deshu, Yin Xianggen. Instantaneous value and equal transfer processes-based current differential protection for long transmission lines. IEEE Trans Power Deliv 2012;27(1):289–99.
[17] Minghao Wen. A new scheme of the protection based on the principle of balance of energy with virtual cvts. Proc CSEE 2007;27(24):11–6 [in Chinese]. [18] Elmore WA. Protective relaying theory and applications. 2nd ed. Marcel Dekker Inc.; 2004. [19] Ghorbani Amir, Mozafari Babak, Ranjbar Ali Mohammad. Digital distance protection of transmission lines in the presence of SSSC. Int J Electr Power Energy Syst 2012;43(1):712–9. [20] Zadeh Hassan Khorashadi, Li Zuyi. Adaptive load blinder for distance protection. Int J Electr Power Energy Syst 2011;33(4):861–7. [21] Bakara Ab Halim Abu, Yatimc Fazilah Mat, Yusofb Sallehuddin. Analysis of overload conditions in distance relay under severe system contingencies. Int J Electr Power Energy Syst 2010;32(5):345–50.