Title: Wavelet‐based EMTR method for fault location of VSC‐HVDC transmission lines
Abstract: The Journal of EngineeringVolume 2019, Issue 16 p. 961-966 Session – Poster ABOpen Access Wavelet-based EMTR method for fault location of VSC-HVDC transmission lines Xipeng Zhang, Corresponding Author Xipeng Zhang [email protected] orcid.org/0000-0002-0193-3270 Department of Electrical Engineering, Shanghai Jiao Tong University, Minhang, Shanghai, People's Republic of ChinaSearch for more papers by this authorNengling Tai, Nengling Tai Department of Electrical Engineering, Shanghai Jiao Tong University, Minhang, Shanghai, People's Republic of ChinaSearch for more papers by this authorXiaodong Zheng, Xiaodong Zheng Department of Electrical Engineering, Shanghai Jiao Tong University, Minhang, Shanghai, People's Republic of ChinaSearch for more papers by this authorWentao Huang, Wentao Huang Department of Electrical Engineering, Shanghai Jiao Tong University, Minhang, Shanghai, People's Republic of ChinaSearch for more papers by this author Xipeng Zhang, Corresponding Author Xipeng Zhang [email protected] orcid.org/0000-0002-0193-3270 Department of Electrical Engineering, Shanghai Jiao Tong University, Minhang, Shanghai, People's Republic of ChinaSearch for more papers by this authorNengling Tai, Nengling Tai Department of Electrical Engineering, Shanghai Jiao Tong University, Minhang, Shanghai, People's Republic of ChinaSearch for more papers by this authorXiaodong Zheng, Xiaodong Zheng Department of Electrical Engineering, Shanghai Jiao Tong University, Minhang, Shanghai, People's Republic of ChinaSearch for more papers by this authorWentao Huang, Wentao Huang Department of Electrical Engineering, Shanghai Jiao Tong University, Minhang, Shanghai, People's Republic of ChinaSearch for more papers by this author First published: 07 January 2019 https://doi.org/10.1049/joe.2018.8790Citations: 7AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract A wavelet-based electromagnetic time reversal method for locating faults in voltage source converter-high-voltage direct current (VSC-HVDC) transmission lines is proposed in this study. This principle, firstly, is to use wavelet decomposition to filter the 1-mode fault currents, which are recorded at ends of the transmission line. Secondly, the filtered currents are mirrored on time axes, which called time reversal. Thirdly, the time-reversed currents are set as current sources at ends of the lossless mirror lines. Through assuming a fault at each point of line, the assumed fault currents are calculated, and the RMS of fault current at actual fault location is maximal according to a strict scientific proof. Theoretically, the Wavelet-based Electromagnetic Time Reversal (WEMTR) method is robust against fault types and resistance. A multilevel converter-HVDC system is established in Power Systems Computer-Aided Design (PSCAD)/Electromagnetic Transients including DC (EMTDC) to verify the feasibility of the proposed method, and the transmission line is simulated by frequency independent phase model. The results show that, the fault location can be calculated exactly without high sampling rates. 1 Introduction The technology of flexible high-voltage direct current (HVDC) system promotes the utilisation of renewable and clean energy [1-4]. In China, many projects of flexible HVDC systems have been put into operation. According to the types of converter stations, the flexible HVDC systems can be divided into two, one is the two-level or three-level converter-based system, and the other is modular multilevel converter-based HVDC (MMC-HVDC). MMC–HVDC system has been developed better than the others due to less harmonics and high output voltage. If the transmission line failed, the expensive devices of converter stations may be damaged by overcurrent generated from the fault, in additional, the whole system may be out of operation. Therefore, it is very important to locate the fault quickly and accurately [5, 6]. At present, the methods of fault location for HVDC transmission line are mainly based on the principles of travelling wave and transient calculation. Travelling-wave-based method can locate the fault through one or multiple observers. The single-ended method detects the arrival time for the forward and reflected wave, and the fault location is calculated through the time difference. However, the amplitude of reflected wave is generally small, which is difficult to detect. The multiple-ended method locates the fault based on the detected arrival time of initial forward wave at ends of the line. The multiple-ended method needs precision time synchronisation, and the general sampling frequency is over 500 kHz. In general, the travelling-wave-based method is mainly restricted by the sampling devices and the recognition technology of wavefront [7-9]. In addition, the natural-frequency-based method, derived from the travelling wave principle, is also used for fault location [10]. However, the natural frequency is affected by the fault resistance and the distributed capacitance of the lines, especially of the cables. The transients-calculation-based method uses the transmission equations of lines to locate faults, and it is based on two physical properties: the lowest voltage along the line exits at the fault point, and where the voltage and current are also in phase [11-15]. This method usually employs the equation of the Bergeron line model to calculate the voltage and current along the line. However, the measured transients are influenced by injection current from the AC side. Meanwhile, the calculation of transients is not accurate when employing Bergeron line model. In order to overcome the disadvantages in the above fault location methods, this paper presents a novel fault location principle of electromagnetic time reversal theory. The EMTR-based method originates from the lightning fault location in the space, and its basic principle is Maxwell's equations [16-18]. In this paper, the feasibility of EMTR-based fault location method for transmission lines is proved [19, 20]. The wavelet decomposition is employed to extract the useful signals from 1-mode observed transients. After that, the filtered currents are time reversed and regarded as the current sources at ends of line. Finally, the RMSs of assumed fault currents along the line are calculated, and the peak value among these RMSs indicates the actual fault point. 2 Theory of EMTR 2.1 Time reversal The core of the proposed method in this paper is time reversal, which changes the direction of the time . In practical application, the measured signal is only for a period. If the initial moment t = 0, and the final moment t = T, the signal would be time revered as . 2.2 Theory justification In this section, a single line is applied to prove the feasibility of the proposed method. Fig. 1 a is the additional network after fault occurrence, the total length of the line is L, and the fault is occurred at L 1. The line-to-earth voltage at fault point is uF, and the measured currents and voltages at both ends of the line are iM / iN / uM / uN, which are full-band signals. The positive directions of all observed signals are labelled in Fig. 1 a. The theoretical values of measured voltage and current in frequency domain at end M can be calculated as follows: (1) where Fig. 1Open in figure viewerPowerPoint Theory justification in a single line (a) Additional network after fault occurrence, (b) Calculation of assumed fault current in mirror line U + / I + is the forward voltage and current, and U - / I - is the backward voltage and current. ZC and γ are the wave impedance and propagation coefficient of transmission line, respectively. Besides, w is the angular frequency, and R/L/C is the distributed parameters of resistance, inductor and capacitor, respectively. As shown in Fig. 1 b, a lossless mirror line is established, and the distributed parameters of resistance, inductor and capacitor are 0/-L /-C. Then, the sources are set at ends of the line as (2) Since only the voltage and current are measured and known, the forward current can be derived from them, and the theoretical values for forward current are in (2). Suppose a fault occurred at Lz, and the reflected current were ignored in the mirror line. The fault current at the assumed fault location can be obtained as (3) where, . Let Formula (3) can be rewritten as (4) In (4), and are real values, so the maximum value of is achieved when (5) where n is a natural number. In fact, β 0 /β ≃ 1 if the frequency was higher than 50 Hz, so the formula (5) is simplified as (6) Since the initial forward current will be selected for calculation, θ 1 equals to θ 2. Therefore, the fault location . Furthermore, observed currents of frequency band is employed for fault location, the ultimate result will be unique for . This could be easily proved by contradiction. 3 EMTR-based fault location method for VSC-HVDC As described in the previous section, the measured fault currents are affected not only by the injection currents from AC side, but also by the control and protection system. The priority of EMTR method is to extract the useful signals from transients through appropriate filters. If the measured signal is weak, and the signal-to-noise is small, the wavelet technology can effectively detect the actual signal. The expansion of the wavelet decomposition is where is wavelet function, and is scaling function, and their coefficient can be achieved, respectively, as shown as (7) Fig. 2 presents a flowchart of WEMTR-based fault location method for VSC-HVDC. After a line fault occurred, the observers record the fault current represents the positive-pole current, and is the negative-pole current (n is the serial number of observer). The 1-mode currents are calculated as follows: (8) Fig. 2Open in figure viewerPowerPoint Flow diagram of fault-location based on WEMTR Then, the currents are filtered through wavelet decomposition, and time reversed. Suppose the fault point is at Lx, the assumed fault current at Lx can be calculated, as shown in (9), which is the sum of delayed time reversed currents: (9) where represents the distance between assumed fault point and observer n, and , which is the velocity of travelling wave. Finally, we select the peak value among all , and corresponding L real is the actual fault point. 4 Simulation case study 4.1 Simulation system of MMC-HVDC In this paper, a bipolar MMC-HVDC is established in PACAD/EMTDC. Fig. 3 a shows the structure diagram of the MMC-HVDC system. The rated voltages of AC1 and AC2 are, respectively, 240 and 230 kV, and the frequency is 50 Hz. The power flow passes through the AC side, the transformer, the filter, the converter station and the DC side. The level of MMC converter station is 77, and MMC1 uses controlling strategies of fixed active power and voltage, MMC2 adopts the controlling strategies of the fixed active and reactive power. The rated voltage of DC transmission line is ±320 kV, and the transmission capacity is 1200 MW. Fig. 3Open in figure viewerPowerPoint Simulation system of MMC-HVDC (a) Schematic diagram of the overall system structure, (b) structure of overhead line Fig. 3 b shows the geometrical parameters of the overhead line, and the length of the line is 400 km. In order to simulate the actual line preciously, the phase-domain frequency-dependent line model is adopted in the simulation. The resistance and inductance of the actual lines, due to the presence of skin effect, will change with the frequency. Figs. 4 a and b show the 1-mode resistance, conductance, inductance and capacitance of overhead line in comparison with frequency. As can be seen from the figure, the capacitance and conductance are not affected by frequency, but the resistance increases, while the inductance decreases with increasing frequency. Fig. 4 c shows the value of β0 /β in Section 1.2. For overhead lines, if the frequency was higher than 50 Hz, the value of β0 /β ≃ 1. Fig. 4Open in figure viewerPowerPoint Frequency-dependent distribution parameters of overhead lines (a) 1-mode resistance and conductance, (b) 1-mode inductance and capacitance, (c) Value of β0 /β at different frequencies The fault occurred time is set at 3.5 s in this paper. The currents from 3.497 to 3.503 s are recorded, and there is no need to detect the accurate time of fault occurrence. That is to say, the start time of recorder can be at any one moment of normal operation of the system, and the stop time of recorder can be at the moment that the DC breakers starts to open. The time between the two recorders are synchronised by GPS. The Haar wavelet function is chosen for filtering and decomposition. 4.2 Different fault types Suppose a positive-line-to-ground fault occurred at 100 km from line end M, and the fault resistance is 100 Ω, the 1-mode currents at ends of the line are recorded and displayed in Fig. 5. In the filtering process, the 1-mode currents are filtered through Haar wavelet function, and wavelet component named 'd 1' is stored for further calculation. The filtered 1-mode currents are called . Then, these filtered currents are time reversed as shown in Fig. 5, whose names are . By using the formula (9), we can calculate the RMSs of the fault currents along the line. Besides, the wave speed of 1-mode current is 2.98 km/μs, and the fault is assumed occurred at every point along the line, and the distance interval is 50 m. As shown in Fig. 6, the final result of fault location is 98.75 km. Fig. 5Open in figure viewerPowerPoint Filtering and time reversal of measured currents (a) Filtered and time reversed 1-mode currents at end M, (b) Filtered and time reversed 1-mode currents at end N Fig. 6Open in figure viewerPowerPoint Fault location result for 100 km from end M There are four different fault types: positive-line-to-ground fault (PLG), negative-line-to-ground fault (NLG), line-to-line fault (LL), and line-to-line-to-ground fault (LLG). Different faults are simulated, the fault resistance is set as 100 Ω, and the measured currents are recorded with sampling frequency of 50 kHz. Fig. 7 shows the results of fault location for four kinds of faults occurring at 150 km from the M -end. Table 1 gives the results of different fault types at different fault points. It is obviously that the fault location result is not affected by the fault type, and the relative errors of the results are within 1%. 'err1' represents the absolute errors, and 'err2' is the relative errors. Fig. 7Open in figure viewerPowerPoint Fault location results for different fault types at 150 km from end M Table 1. Fault location results for different fault types PLG, km NLG, km LL, km LLG, km |err1|, km |err2|, % 0 3.30 3.30 3.30 3.30 3.30 0.825 30 33.10 33.10 33.10 33.10 3.10 0.775 60 56.95 56.95 56.95 56.95 3.05 0.762 90 92.70 92.70 92.70 92.70 2.70 0.675 120 116.55 116.55 116.55 116.55 3.45 0.863 150 152.30 152.30 152.30 152.30 2.30 0.575 180 176.15 176.15 176.15 176.15 3.85 0.962 210 211.90 211.90 211.90 211.90 1.90 0.475 240 241.70 241.70 241.70 241.70 1.70 0.425 270 271.50 271.50 271.50 271.50 1.50 0.375 300 301.30 301.30 301.30 301.30 1.30 0.325 330 331.10 331.10 331.10 331.10 1.10 0.275 360 360.90 360.90 360.90 360.90 0.90 0.225 390 390.70 390.70 390.70 390.70 0.70 0.175 400 396.65 396.65 396.65 396.65 3.35 0.838 4.3 Different fault resistances Suppose a fault occurred at middle of the transmission line, with different fault resistances of 0, 100 and 300 Ω, Fig. 8 shows the results of fault location. By analysing the data in Table 2, the results are almost the same with different fault resistances. The larger the fault resistance is, the smaller the transient current is, so the mutation of the measured current decrease with the increase of the fault resistance, which causes the peak value of assumed currents decrease. Fig. 8Open in figure viewerPowerPoint Fault location result for different fault resistance at 200 km from end M Table 2. Fault location results for different fault resistances 300 Ω |err2|, % 100 Ω |err2|/% 0 Ω |err2|/% 0 3.30 3.800 3.30 0.825 15.20 0.825 20 21.15 0.288 21.15 0.288 21.15 0.288 40 39.05 0.238 39.05 0.238 39.05 0.238 60 56.85 0.788 56.95 0.762 56.95 0.762 80 80.75 0.188 80.75 0.188 80.75 0.188 100 104.60 1.150 98.65 0.337 98.65 0.337 120 116.55 0.863 116.55 0.863 116.55 0.863 140 140.35 0.087 140.35 0.087 140.35 0.087 160 164.20 1.050 164.20 1.050 158.25 0.438 180 182.10 0.525 176.15 0.962 176.15 0.962 200 199.95 0.013 199.95 0.013 199.95 0.013 220 223.80 0.950 223.80 0.950 223.80 0.950 240 241.70 0.425 241.70 0.425 241.70 0.425 260 259.50 0.125 259.55 0.112 259.55 0.112 280 283.40 0.850 283.40 0.850 283.40 0.850 300 301.30 0.325 301.30 0.325 301.30 0.325 320 319.10 0.225 319.15 0.213 319.15 0.213 340 343.00 0.750 343.00 0.750 337.05 0.737 360 355.75 1.063 360.90 0.225 360.90 0.225 380 378.70 0.325 378.75 0.313 378.75 0.313 400 396.65 0.838 396.65 0.838 396.65 −0.838 When a metal line-to-line fault occurs at the ends of the line, the capacitance of the MMC's module discharged quickly within a few microseconds, and the measured current contains a large amount injection current from AC side, which will seriously affect the precision of calculation result, as shown in Table 2. In practice, the probability of metal failure occurred at the ends of the line is especially low, therefore the result can be neglected. 4.4 Different sampling frequencies The sampling frequency is limited by the sampling devices. In this paper, the results of the positive-line-to-ground fault with different sampling frequencies of 50, 100 and 200 kHz are compared, and the fault resistance is 300 Ω. The average relative error in Table 3 shows that, the higher the sampling frequency is, the higher the accuracy is. Besides, it is also obvious that, the accuracy of result improves with frequency increase for each specific fault point. Table 3. Fault location results for different sampling rates 200 kHz |err2|, % 100 kHz |err2|, % 50 kHz |err2|, % 0 0.30 0.075 0.30 0.075 3.30 0.825 10 9.25 0.188 9.25 0.188 9.25 0.188 30 30.10 0.025 30.10 0.025 33.10 0.775 50 49.50 0.125 50.95 0.238 50.95 0.238 70 68.85 0.288 68.85 0.288 68.85 0.288 90 89.70 0.075 89.70 0.075 92.70 0.675 110 109.10 0.225 110.55 0.137 104.60 1.350 130 129.95 0.013 128.45 0.388 128.65 0.337 150 150.80 0.200 152.30 0.575 152.20 0.550 170 170.15 0.038 170.15 0.038 170.30 0.075 190 189.55 0.112 188.05 0.487 188.05 0.487 210 210.40 0.100 211.90 0.475 211.90 0.475 230 229.75 0.063 229.75 0.063 229.70 0.075 250 249.15 0.212 250.65 0.163 247.65 0.587 270 270.00 0.000 271.50 0.375 271.50 0.375 290 289.30 0.175 292.40 0.600 289.60 0.100 310 310.25 0.063 310.25 0.063 307.25 0.688 330 331.10 0.275 331.10 0.275 331.10 0.275 350 350.45 0.112 348.95 0.263 348.95 0.263 370 371.30 0.325 372.80 0.700 366.85 0.787 390 389.20 0.200 390.70 0.175 390.70 0.175 400 399.65 0.088 399.65 0.088 396.65 0.838 average error 0.135 — 0.261 — 0.474 If the sampling frequency of 200 kHz is adopted in travelling wave-based method, the inherent error of the travelling-wave-based method is 1500 m, which is larger than the error of the WEMTR-based method. The actual travelling-wave-based method requires the sampling frequency of higher than 500 kHz, which needs more cost. 5 Conclusion This paper presents a novel fault-location method for DC transmission lines based on wavelet-based time reversal theory. The theoretical justification and simulations shows that, through establishing the lossless mirror line, the result is accurate and easy to calculate. After adopting the technology of wavelet decomposition, the influence of injection current from AC side is eliminated. The results are not affected by the fault resistances and fault types. Besides, the higher the sampling frequency, the higher the accuracy is, and when the sampling frequency is 50 kHz, the result is also precise, which reduces the cost. 6 References 1Liu J., Tai N., Fan C. et al.: 'Comments on fault handling and protection technology for VSC-HVDC transmission lines', Autom. Electr. Power Syst., 2015, 39, (20), pp. 158 – 167 2Wu B., Li R., Bie R. et al.: 'Current development and research prospect of VSC-MTDC', Mod. Electr. Power, 2015, 32, (2), pp. 9 – 15 3Zhang J., Zhao C., Sun H. et al.: 'Improved topology of modular multilevel converter and application', Trans. China Electr. Technol. Soc., 2014, 29, (8), pp. 173 – 179 4Liang S., Tian J., Cao D. et al.: 'Control and protection scheme for VSC-HVDC', Autom. Electr. Power Syst., 2013, 37, (15), pp. 59 – 65 5Liu J., Tai N., Fan C. et al.: 'Protection scheme for high-voltage direct-current transmission lines based on transient AC current', IET Gener. Transm. Distrib., 2015, 9, (16), pp. 2633 – 2643 6Xu M., Cai Z., Liu Y. et al.: 'A novel fault location method for HVDC transmission line based on the broadband travelling wave information', Trans. China Electr Technol. Soc., 2013, 28, (1), pp. 259-265. 7Kasun Nanayakkara O., Athula D, Rajapakse et al.: 'Traveling-wave-based line fault location in star-connected multiterminal HVDC systems', IEEE Trans. Power Deliv., 2012, 27, (4), pp. 2286 – 2294. 8Sadegh A., Majid S., Moein A. et al.: 'A traveling-wave-based methodology for wide-area fault location in multiterminal DC systems', IEEE Trans. Power Deliv., 2014, 29, (6), pp. 2552 – 2560. 9Kerf K., Srivastava K., Reza M. et al.: 'Wavelet-based protection strategy for DC faults in multi-terminal VSC HVDC systems', IET Gener. Transm. Distrib., 2011, 5, (4), pp. 496 – 503. 10He Z., Liao K., Li X. et al.: 'Natural frequency-based line fault location in HVDC lines', IEEE Trans. Power Deliv., 2014, 29, (2), pp. 851 – 859. 11Kasun Nanayakkara O., Athula D., Rajapakse et al.: 'Location of DC line faults in conventional HVDC systems with segments of cables and overhead lines using terminal measurements', IEEE Trans. Power Deliv., 2012, 27, (1), pp. 279 – 288. 12Yang J., John E., Fletcherand J. et al.: 'Short-circuit and ground fault analyses and location in VSC-based DC network cables', IEEE Trans. Ind. Electron., 2012, 59, (10), pp. 3827 – 3837. 13Matthias K., Christian M.: 'Analytic approximation of fault current contributions from capacitive components in HVDC cable networks', IEEE Trans. Power Deliv., 2015, 30, (1), pp. 74-81. 14Suonan J., Gao S., Song G.: 'A novel fault-location method for HVDC transmission lines', IEEE Trans. Power Deliv., 2010, 25, (2), pp. 1203 – 1209. 15Mohammad F, Javad Sadeh: 'A novel fault-location method for HVDC transmission lines based on similarity measure of voltage signals', IEEE Trans. Power Delivery, 2013, 28, (4), pp. 2483 – 2490. 16Rosny J., Lerosey G., Fink M.: 'Theory of electromagnetic time-reversal mirrors', IEEE Trans. Antennas Propag., 2010, 58, (10), pp. 3139 – 3149. 17Fink M.: 'Time reversal of ultrasonic fields. I. Basic principles', IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 1992, 39, (5), pp. 555 – 556 18Lugrin G., Parra N., Rubinstein F.: 'On the location of lightning discharges using time reversal of electromagnetic fields', IEEE Trans. Electromagn. Compat., 2014, 56, (1), pp. 149 – 158. 19Razzaghi R., Lugrin G., Manesh H.: 'An efficient method based on the electromagnetic time reversal to locate faults in power networks', IEEE Trans. Power Deliv., 2013, 28, (3), pp. 1663 – 1673. 20Zhang X., Tai N., Wang Y.: 'EMTR-based fault location for DC line in VSC-MTDC system using high-frequency currents', IET. Gener. Transm. Distrib., 2017, 11, (10), pp. 2499 – 2507. Citing Literature Volume2019, Issue16March 2019Pages 961-966 FiguresReferencesRelatedInformation