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379
Chapter-5
Conclusions
In this research work a HVDC model is proposed for the analysis of
various operating conditions. The faults generally occurred on the
transmission line such as AC faults on the rectifier side and inverter
side, the DC line fault on the transmission line at various distances have
been analyzed using Fast Fourier Transforms(FFT), Artificial Neural
Networks (ANN) and Wavelet Transforms(WT). The DC voltage and
current at the rectifier were recorded.
The following observations have been made from the recorded
characteristics of the voltage and current.
During the normal operating condition of the HVDC system, it will
transmit power satisfactorily with both the voltage and currents observed
to be at 1 p.u.
During DC line faults, the line voltage at the rectifier is oscillating
till the fault has been cleared. Similar types of characteristics have been
obtained for all the fault resistances. However the DC line current rises
to 2 p.u. in 0.01sec. The system starts recovering after the clearance of
the fault.
380
During the AC faults on the AC side of the rectifier the DC line
voltage is positive and is oscillating between 2p.u. and 0 p.u. The AC
voltage on the inverter side has no significant impact due to this fault.
However the currents on the AC side are almost zero at the time of fault.
For the analysis and identification of HVDC system faults a
technique based on the reverse voltage travelling wave (RVTW) has been
proposed in this thesis. The RVTW is calculated for all the operating
conditions of the HVDC system. It is observed that the magnitude of the
RVTW is low for normal operating system when compared to that of a
fault condition. The RVTW has been analyzed by using FFT analysis.
It is observed from the FFT plot for various operating conditions of
HVDC that the dominant frequency during the normal operating
condition is around 600Hz and the magnitude of the dominant frequency
is very low when compared to the fault conditions.
The dominant frequency for the DC line fault is inversely
proportional to the location of the fault i.e. as the distance increases the
frequency decreases. The magnitude of the dominant frequency is
observed to be varying with the fault resistance. However, the variation
in the fault resistance has no impact over the frequency. Hence it can be
stated that for the location of the faults the RVTW technique is more
effective.
381
During the AC faults on the AC side of the rectifier the dominant
frequency is observed to be the 2nd harmonic frequency (120Hz) and the
magnitude of frequency component is very much high for all the faults
such as LG, LLG and LLL faults.
During the AC faults on the AC side of the inverter the dominant
frequency is observed to be near the 2nd harmonic frequency (100Hz)
and the magnitude of frequency component is very much high for all the
faults such as LG, LLG and LLL faults.
The RVTW also been analyzed by using Artificial Neural Networks.
For this purpose the RVTW has been sampled at regular intervals of 0.8
milliseconds by considering the local maximum values during this
period. The normalized data from the local maximum values has been
used for training and testing the ANN. From the test results of the ANN,
it is proved that the local maximum values are having a clear edge in
identifying and locating the faults of the HVDC transmission system.
By using the wavelet analysis technique the reverse voltage
travelling wave (RVTW) has been decomposed in to four levels using
daubeches4 wavelet as the mother wavelet. The observations made from
the analysis of level 1 wavelet coefficients are:
During the normal operating conditions, the energy of the wavelet
coefficients is less than 4.
382
The energy of the wavelet coefficients for DC line faults is more
than 100 for various fault resistance.
The energy of the wavelet coefficient is in between 5 to 50 for the
AC faults both on the rectifier and inverter side.
Hence the faults on the HVDC transmission system can be
classified by considering the energy of the level 1 wavelet coefficients. For
the location of the faults on the HVDC transmission line the time interval
between the first two peaks of level 1 coefficients of RVTW has been used.
Among all the techniques for the classification and location of
faults in HVDC transmission system the wavelet based classification and
location techniques are proved to be more efficient and accurate.
However ANN based techniques are also competent in identifying and
locating the faults on HVDV transmission system. The major draw backs
of ANN based techniques is that they require huge amount of data and
computing time for training. The performance of the ANN is mostly
dependent on the quantity of data used for training the network. It is
observed from the comparison of the above three techniques for the
location of faults on the DC transmission line, the technique using the
wavelet coefficients is very much efficient than FFT and ANN.
Converter transformers are the major components of HVDC system
which are the interface between AC and DC systems. Therefore it is
383
subjected to more amount of stress. The integrity of the transformer
mainly depends on the insulation. As the transformer is subjected to
various types of stresses such as lightening and switching, to achieve the
satisfactory operation and to identify various types of faults in the
transformer a most reliable and effective testing technique should be
adopted. A 315 MVA, single Phase, three winding converter transformer
has been considered for this analysis. From the configuration of the
windings in the transformer the internal inductances and capacitances
have been calculated. This equivalent circuit has been used for the
generation of neutral currents for various test conditions of the
transformer. The faults such as - turn to turn fault, turn to ground fault,
winding to winding fault, have been created on the converter transformer
model and the neutral current has been stored. The neutral current has
been analyzed using FFT, ANN and wavelet techniques.
From FFT plot of the neutral current signal, it is observed that the
DC component available during the normal operating condition is low
when compared to that of other operating conditions. The DC component
during the fault condition is more predominant. It is observed that in
case of turn to ground fault the DC component in the neutral current
depends on the position of the fault. However the magnitude of the DC
component for the section to section fault is independent of the location
of fault.
384
The neutral current obtained during normal operating condition
has been decomposed into various frequency components and the
neutral current has been reconstructed using Gabor wavelet. This
method can be adopted for de-noising of the neutral current signal.
The neutral current data for various operating conditions has been
analyzed using ANN. The ANN training and testing data has been
generated by taking the local maximum value of the neutral currents
considered for a duration of 6.4 s. The results show that the ANN based
technique based on the local maximum value is more capable of
classifying the types of faults in the converter transformer.
The neutral current obtained from the HVDC transformer model
also been analyzed by using wavelet transform technique. The data has
been analyzed by using debauches wavelet and decomposed in 8 levels.
The normalized output of the low pass filter is used to train the ANN
using feed forward back propagation algorithm. The results show that
wavelet based techniques for the classification of faults in converter
transformer is most efficient and effective than the ANN based
techniques.
To validate the above analysis a typical winding structure has been
considered for experimental study. The following conclusions were drawn
from the experimental study. The digital recording of neutral currents in
the HV and taping windings of a 61MVA, 11kV/220kV transformer has
385
been carried out by applying a Low voltage impulse at one of the terminal
for various test conditions of the winding. However the core has been
removed. The changes in the neutral current characteristics depend
primarily on the extent of failure. The neutral currents are recorded
using digital oscilloscope for healthy winding and also by shorting several
pairs of discs and turns in succession. The recorded neutral currents are
analyzed by using FFT and wavelet transform and different plots
obtained for each case have been presented. The absolute 8th level
wavelet coefficients have been normalized and are used to train and test
the ANN. The test results of the ANN have been presented. From the
experimental analysis it is observed that to obtain more accuracy more
amounts of data required for the training of ANN.
Hence it can be concluded that the wavelet transform technique is
a more efficient tool in the classification and location of faults in HVDC
system. In this thesis the HVDC system faults i.e. the faults in the
transmission line, converter transformer were analyzed by using FFT,
ANN and Wavelet Transform (WT) Techniques and the analysis based on
the wavelet transform technique has been identified as a most efficient
tool in the classification and location of faults. By just knowing the
length of the transmission line and time between the first two peaks of
the reverse voltage travelling wave, considering the velocity of the wave as
light velocity the location of the fault on the long DC transmission line
386
can be determined. It is also possible to de-noise the signal using wavelet
transform technique to obtain more accurate fault location.
387
Scope of Future work
This dissertation has made an extensive effort in analyzing various
faults associated with HVDC system. The faults such as single line to
ground fault, double line to ground fault and symmetrical faults on AC
side of rectifier and inverter, DC line faults were extensively studied in
this dissertation. The faults associated with the converter transformer
such as inter turn faults, inter winding faults and ground faults were
analyzed by using different fault analysis techniques.
Further work can be extended in the following areas:
The modeling of bi-polar HVDC system and analysis of faults in bi-
polar HVDC system.
The VSC HVDC model response for various fault conditions and
identification of faults.
For the detailed analysis of the converter transformer, it is required
to divide the transformer windings into more number of sections in order
to get more amounts of data to train the neural network to have better
accuracy. The future work can be extended in developing the transformer
model by considering the core into account. For the power frequency
388
simulation of the converter transformer it is required to consider the core
of the transformer.
The analysis of the converter transformer based on the adoptive
wavelet technique which may provide a better solution in identifying the
type of the fault prevailing in the converter transformer.
The converter transformer can also be analyzed by using coherence
function which may give more accurate results in identifying and locating
the converter transformer faults.
The same techniques may also be implemented in reactors for
identification and location of faults.
389
REFERENCES
[1] K.R. Padiyar, “HVDC Power Transmission Systems Technology and
System Interactions”, New Age International (P) Limited, Publishers,
New Delhi, 2002.
[b] S.S Rao, “EHVAC and HVDC transmission”, Khanna Publications,
[2] Philip Christopher Gregory, "Bayesian logical data analysis for the
physical sciences: a comparative approach with Mathematica
support", Cambridge University Press, 2005, pp. 412-415.
[3] Christopher M. Bishop, "Neural Networks for Pattern Recognition"
Oxford University Press, 1955.
[4] Mikhled Alfaouri and Khaled Daqrouq, "ECG Signal Denoising By
Wavelet Transform Thresholding", American Journal of Applied
Sciences 5 (3), 2008, pp. 276-281.
[5] http://www02.abb.com/global/seitp/seitp202.nsf/0/a521beb 28a
c88e75c12572250046e16a/$file/HVDC+history.pdf
[6] M. A. Rahman, B. Jeyasurya, "A state-of-the-art Review of
Transformer Protection Algorithms", IEEE Trans on Power Delivery,
Vol. 3, No 2, April 1988, pp 534-544.
[7] D. Robertson, O. Camps, and J. Mayer, “Wavelets and power
system transients”, SPIE international symposium on optical
engineering in aerospace sensing, Apr. 1994, pp. 474-487.
[8] P.F . Ribeiro, “Wavelet transform: an advanced tool for analysing
non-stationary harmonic distortion in power system”, Proceedings
of IEEE ICHPS, VI, Bologna, Sep. 21-23, 1994.
[9] Pham, V.L. Wong, K.P., “Wavelet-transform-based algorithm for
harmonic analysis of power system waveforms”, IEE Proceedings of
Generation, Transmission and Distribution, Vol. 146, No. 3, May
1999, pp. 249 –254.
390
[10] Pham, V.L. Wong, K.P, “Antidistortion method for wavelet transform
filter banks and non-stationary power system waveform”, IEE
Proceedings of Generation, Transmission and Distribution, Vol.
148, No. 2, Mar. 2001, pp. 117 –122.
[11] Van Long Pham, Kit Po Wong, Watson, N., Arrillaga, J, “Sub-
harmonic state estimation in power systems”, IEEE Power
Engineering Society Winter Meeting, 2000, Vol. 2, pp. 1168 –1173.
[12] Tongxin Zheng; Makram, E.B.; Girgis, A.A.; “Power system
transient and harmonic studies using wavelet transform Matlab
toolbox”, IEEE Transactions on Power Delivery, Vol. 14, No. 4,
Oct.1999, pp. 1461 –1468.
[13] Gu, Y.H.; Bollen, M.H.J, “Time-frequency and time-scale domain
analysis of voltage disturbances”, IEEE detection and localization.
Transactions on Power Delivery, Vol. 15, No. 4, Oct.2000, pp. 1279-
1284.
[14] Ren Zhen; Huang Qungu; Guan Lin; Huang Wenying, “A new
method for power systems frequency tracking based on trapezoid
wavelet transform”, International Conference on Advances in Power
System Control, Operation and Management, 2000, Vol. 2, pp. 364
–369.
[15] Shyh-Jier Huang; Cheng-Tao Hsieh, “Application of continuous
wavelet transform for study of voltage flicker-generated signals”,
IEEE Transactions on Aerospace and Electronic Systems, Vol. 36,
No. 3 P art: 1, Jul. 2000, pp. 925 –932.
[16] Ming-Tang Chen; Sakis Meliopoulos, A.P. “Wavelet-based algorithm
for voltage flicker analysis”, Proceedings Ninth International
Conference on Harmonics and Quality of Power, 2000, Vol. 2, pp.
732–738.
[17] Santoso, S.; Powers, E.J.; Grady, W.M.; “Electric power quality
disturbance detection using wavelet analysis”, IEEE-SP Proceedings
391
of International Symposium on Time-Frequency and Time-Scale
Analysis, 1994, pp. 166 –169.
[18] Santoso, S.; Powers, E.J.; Grady, W.M.; Hofmann, P. “Power quality
assessment via wavelet transform analysis”, Transactions on Power
Delivery, IEEE, Vol. 11, No. 2, Apr. 1996, pp. 924 –930.
[19] Santoso, S.; Powers, E.J.; Grady, W.M.; Parsons, A.C.; “Power
quality disturbance waveform recognition using wavelet-based
neural classifier. I. Theoretical foundation”, IEEE Transactions on
Power Delivery, Vol. 15, No. 1, Jan. 2000, pp. 222 –228.
[20] Santoso, S.; Powers, E.J.; Grady, W.M.; Parsons, A.C.; “Power
quality disturbance waveform recognition using wavelet-based
neural classifier. II. Application”, IEEE Transactions on Power
Delivery, Vol. 15, No. 1, Jan. 2000, pp. 229 –235.
[21] Santoso, S.; Powers, E.J.; Grady, W.M. “Power quality disturbance
data compression using wavelet transform methods”, IEEE
Transactions on Power Delivery, Vol. 12, No. 3, Jul. 1997, pp. 1250
–1257.
[22] Chung, J.; Powers, E.J.; Grady, W.M.; Bhatt, S.C., “New robust
voltage sag disturbance detector using an adaptive prediction error
filter”, IEEE Power Engineering Society Summer Meeting, 1999,
Vol. 1, pp. 512 –517.
[23] Gaouda, A.M.; Salama, M.M.A.; Sultan, M.R.; Chikhani, A.Y.
“Power quality detection and classification using wavelet-multi-
resolution signal decomposition”, IEEE Transactions on Power
Delivery, Vol. 14, No. 4 , Oct. 1999, pp. 1469 –1476.
[24] Cano Plata, E.A.; Tacca, H.E. “Power quality assessment and load
identification”, Proceedings. Ninth International Conference on
Harmonics and Quality of Power, 2000, Vol. 3, pp. 840 –845.
[25] Kawada, M.; Tungkanawanich, A.; Kawasaki, Z.-I.; Matsu-Ura, K.,
“Detection of wide-band E-M signals emitted from partial discharge
392
occurring in GIS using wavelet transform”, IEEE Transactions on
Power Delivery, Vol. 15, No. 2, Apr. 2000, pp. 467 –471.
[26] Shim, I.; Soragan, J.J.; Siew, W.H.; Sludden, K.; Gale, P.F., “Robust
partial discharge measurement in MV cable networks using
discrete wavelet transforms”, IEEE Power Engineering Society
Winter Meeting, 2000., Vol. 1 , pp. 718 –723.
[27] Li, Z.M.; Feng, Y.P.; Chen, J.Q.; Zheng, X.G., “Wavelet analysis
used in UHF partial discharge detection in GIS (gas insulated
substations)”, International Conference 8th International
Conference on Power System Technology, Beijing, China, 1998.
Proceedings, Vol. 1, pp. 163 –166.
[28] S. J. Yao, Y. H. Song, L. Z. Zhang and X. Y. Cheng, “Wavelet
transform and neural networks for short-term electrical load
forecasting”, Energy Conversion and Management, Vol. 41, No. 18,
Dec. 2000, pp. 1975-1988.
[29] Huang, C.-M.; Yang, H.-T. “Evolving wavelet-based networks for
short-term load forecasting”, IEE Proceedings of Generation,
Transmission and Distribution, Vol. 148, No. 3, May 2001, pp. 222
–228.
[30] In-Keun Yu ; Chang-Il Kim ; Y. H. Song, “A Novel Short-Term Load
Forecasting Technique Using Wavelet Transform Analysis”, Electric
Machines and Power Systems, Taylor & Francis Inc., 2000, pp.
537–549.
[31] Weon-Ki Yoon; Devaney, M.J., “Power measurement using the
wavelet transform”, IEEE Transactions on Instrumentation and
Measurement, Vol. 47 No. 5, Oct. 1998, pp. 1205 –1210.
[32] Weon-Ki Yoon; Devaney, M.J. “Reactive power measurement using
the wavelet transform”, IEEE Transactions on Instrumentation and
Measurement, Vol. 49 No. 2, Apr. 2000, pp. 246 –252.
393
[33] Hamid, E.Y.; Kawasaki, Z.-I. “Wavelet packet transform for RMS
values and power measurements”, IEEE Power Engineering Review,
Vol. 21, No. 9, Sept. 2001, pp. 49 –51.
[34] Jiang, F.; Bo, Z.Q.; Redfern, M.A.; Weller, G.; Chen, Z.; Dong
Xinzhou, “Application of wavelet transform in transient protection-
case study: busbar protection”, Seventh International Conference
on (IEE) Developments in Power System Protection, 2001, pp. 197 –
200.
[35] Chang, C.S.; Feng, T.; Khambadkone, A.M.; Kumar, S. “Remote
short-circuit current determination in DC railway systems using
wavelet transform”, IEE Proceedings of Electric Power Applications,
Vol. 147, No. 6, Nov. 2000, pp. 520 –526.
[36] Chang, C.S.; Kumar, S.; Liu, B.; Khambadkone, A., “Real-time
detection using wavelet transform and neural network of short-
circuit faults within a train in DC transit systems”, IEE Proceedings
of Electric Power Applications, Vol. 148, No. 3, May 2001, pp. 251-
256.
[37] Wu Guopei; Guan, L.; Ren Zhen; Huang Qungu, “A Novel method
for large turbine generator protection based on wavelet
transformation”, International Conference on Advances in Power
System Control, Operation and Management, 2000. Vol. 1, pp. 254
–258.
[38] Lin Tao; Ying Xianggeng; Chen Deshu, “Study on wavelet analysis
and its application to numerical protection for large synchronous
generator”, Proceedings of International Conference on Power
System Technology, 1998, Vol. 2, pp. 1121 –1129.
[39] Zhongming Ye; Bin Wu, “Online rotor bar breakage detection of
three phase induction motors by wavelet packet decomposition and
artificial neural network”, IEEE 32nd Annual Conference on Power
Electronics Specialists, 2001, Vol. 4, pp. 2209 –2216.
394
[40] Wang, J.; McInerny, S.; Haskew, T. “Insulation fault detection in a
PWM controlled induction motor experimental design and
preliminary results”, Proceedings of Ninth International Conference
on Harmonics and Quality of Power, 2000, Vol. 2, pp. 487–492.
[41] Zhang, X.H.; Cao, Y.N.; Li, Y.L. “A new project for motor fault
detection and protection”, IEE Seventh International Conference on
Developments in Power System Protection, 2001, pp. 145 –148.
[42] Eren, L.; Devaney, M.J. “Motor bearing damage detection via
wavelet analysis of the starting current transient”, Proceedings of
the 18th IEEE Instrumentation and Measurement Technology
Conference, 2001, Vol. 3, pp. 1797 –1800.
[43] Jiang, F.; Bo, Z.Q.; Chin, P.S.M.; Redfern, M.A.; Chen, Z. “Power
transformer protection based on transient detection using discrete
wavelet transform (DWT)”, IEEE Power Engineering Society Winter
Meeting, 2000, Vol. 3, pp. 1856 –1861.
[44] Vanaja, R.; Udayakumar, K., “A new paradigm for impulse testing
of power transformers”, IEEE Power Engineering Society Winter
Meeting, 2000, Vol. 3, pp. 2206 –2210.
[45] Pandey, S.K.; Satish, L. “Multi-resolution signal decomposition: a
new tool for fault detection in power transformers during impulse
tests”, IEEE Transactions on Power Delivery, Vol. 13 No. 4, Oct.
1998, pp. 1194 –1200.
[46] Gomez-Morante, M.; Nicoletti, D.W. “A wavelet-based differential
transformer protection”, IEEE Transactions on Power Delivery, Vol.
14, No. 4, Oct. 1999, pp. 1351 –1358.
[47] Shaohua Jiao; Wanshun Liu; Peipu Su; Qixun Yang; Zhenhua
Zhang; Jianfei Liu, “A new principle of discrimination between
inrush current and internal short circuit of transformer based on
fuzzy sets”, Proceedings of International Conference on Power
System Technology, 1998, Vol. 2, pp. 1086 –1090.
395
[48] Mao, P.L.; Aggarwal, R.K. “A novel approach to the classification of
the transient phenomena in power transformers using combined
wavelet transform and neural network”, IEEE Transactions on
Power Delivery, Vol. 16, No. 4, Oct 2001, pp. 654 –660.
[49] Magnago, F.H.; Abur, A., “Fault location using wavelets”, IEEE
Transactions on Power Delivery, Vol.13, No. 4, Oct. 1998, pp. 1475
–1480.
[50] Magnago, F.H.; Abur, A., “A new fault location technique for radial
distribution systems based on high frequency signals”, IEEE Power
Engineering Society Summer Meeting, 1999, Vol. 1, pp. 426 –431.
[51] Abur and F. H. Magnago, “Use of time delays between modal
components in wavelet based fault location”, International Journal
of Electrical Power & Energy Systems, Vol. 22, No. 6, Aug. 2000,
pp. 397-403.
[52] Silveira, P.M.; Seara, R.; Zurn, H.H. “An approach using wavelet
transform for fault type identification in digital relaying”, IEEE
Power Engineering Society Summer Meeting, 1999, Vol. 2, pp. 937
–942.
[53] W. Zhao, Y. H. Song and W. R. Chen, “Improved GPS travelling
wave fault locator for power cables by using wavelet analysis”,
International Journal of Electrical Power & Energy Systems, Vol.
23, No. 5, Jun. 2001, pp.403-411.
[54] Zhao, Y.H. Song and Y. Min, “Wavelet analysis based scheme for
fault detection and classification in underground power cable
systems”, Electric Power Systems Research, Vol. 53, No 1, 2000,
pp. 23-30.
[55] Dong Xinzhou; Ge Yaozhong; Xu Bingyin, “Fault position relay
based on current travelling waves and wavelets”, IEEE Power
Engineering Society Winter Meeting, 2000, Vol. 3, pp. 1997-2004.
[56] Chaari, O.; Meunier, M.; Brouaye, F. “Wavelets: a new tool for the
resonant grounded power distribution systems relaying”, IEEE
396
Transactions on Power Delivery, Vol. 11, No. 3, Jul. 1996, pp. 1301
–1308.
[57] David Chan Tat Wai; Xia Yibin, “A novel technique for high
impedance fault identification”, IEEE Transactions on Power
Delivery, Vol. 13, No. 3, Jul. 1998, pp. 738 –744.
[58] Solanki, M.; Song, Y.H.; Potts, S.; Perks, A., “Transient protection of
transmission line using wavelet transform”, IEE Seventh
International Conference on Developments in Power System
Protection, 2001, pp.299 –302.
[59] S. Hanninen, M. Lehtonen, T. Hakola, R. Rantanen, “Comparison of
wavelet and differential equation algorithms in earth fault distance
computation”, Proceedings of Conference on Power System
Computation, Norway 1999.
[60] Charytoniuk, W.; Wei-Jen Lee; Mo-Shing Chen; Cultrera, J.;
Theodore Maffetone, “Arcing fault detection in underground
distribution networks- feasibility study”, IEEE Transactions on
Industry Applications, Vol. 36, No. 6, Nov.-Dec. 2000, pp. 1756–
1761.
[61] Shi, T.H.; Zhang, H.; Liu, P.; Zhang, D.J.; Wu, Q.H., “Accelerated
trip of power transmission line based on bi-orthogonal wavelet
analysis”, IEEE Power Engineering Society Summer Meeting, 2000,
Vol. 3, pp. 1333 –1337.
[62] K. Yu and Y. H. Song, “Development of novel adaptive single-pole
auto-reclosure schemes for extra high voltage transmission systems
using wavelet transform analysis”, Electric Power Systems
Research, Vol. 47, No. 1, Oct. 1998, pp. 11-19.
[63] I.K. Yu and Y.H. Song, “Wavelet analysis and neural networks
based adaptive single-pole auto-reclosure scheme for EHV
transmission systems”, International Journal of Electrical Power
and Energy Systems, Jul. 1998, pp. 465-474.
397
[64] Yu, I.K.; Song, Y.H., “Wavelet transform and neural network
approach to developing adaptive single-pole auto-reclosing schemes
for EHV transmission systems”, IEEE Power Engineering Review,
Vol. 18, No. 11, Nov. 1998, pp. 62 –64.
[65] Li Youyi; Dong Xinzhou; Bo, Z.Q.; Chin, N.F.; Ge Yaozhang,
“Adaptive reclosure using high frequency fault transients”, IEE
Seventh International Conference on Developments in Power
System Protection, 2001, pp. 375-378.
[66] Robertson, D.C.; Camps, O.I.; Mayer, J.S.; Gish, W.B., “Wavelets
and electromagnetic power system transients”, IEEE Transactions
on Power Delivery, Vol. 11, No. 2, Apr. 1996, pp. 1050 –1058.
[67] Galli, Anthony Wayne, Gerald T. Heydt. “Analysis of electrical
transients in power systems via a novel wavelet recursion method”,
Thesis at Purdue University Graduate School, Oct. 1997.
[68] Wilkinson, W.A.; Cox, M.D. “Discrete wavelet analysis of power
system transients”, IEEE Transactions on Power Systems, Vol. 11,
No. 4, Nov. 1996, pp. 2038 – 2044.
[69] Heydt, G.T.; Galli, A.W. “Transient power quality problems analyzed
using wavelets”, IEEE Transactions on Power Delivery, Vol. 12, No.
2, Apr. 1997, pp. 908 –915.
[70] Meliopoulos, A.P.S.; Chien-Hsing Lee, “An alternative method for
transient analysis via wavelets”, IEEE Transactions on Power
Delivery, Vol. 15, No. 1, Jan. 2000, pp. 114 –121.
[71] Xianguing Liu; Pei Liu; Shijie Cheng, “A wavelet transform based
scheme for power transformer inrush identification”, IEEE Power
Engineering Society Winter Meeting, 2000, Vol. 3, pp. 1862 –1867.
[72] Qi Li; Chan, D.T.W. “Investigation of transformer inrush current
using a dyadic wavelet”, Proceedings of International Conference on
Energy Management and Power Delivery, 1998, Vol. 2, pp. 426 –
429.
398
[73] Abur, A.; Ozgun, O.; Magnago, F.H. “Accurate modeling and
simulation of transmission line transients using frequency
dependent modal transformations”, IEEE Power Engineering
Society Winter Meeting, 2001, Vol. 3, pp. 1443 –1448.
[74] Magnago, F.H.; Abur, A., “Wavelet-based simulation of transients
along transmission lines with frequency dependent parameters”,
IEEE Power Engineering Society Summer Meeting, 2000, Vol. 2, pp.
689 –694.
[75] Bathurst, G.N.; Smith, B.C.; Watson, N.R.; Arrillaga, J, “Modelling
of HVDC transmission systems in the harmonic domain” Power
Delivery, IEEE Transactions on Volume 14, Issue 3, Jul 1999 pp
1075-1080.
[76] Bathurst, G.N.; Watson, N.R.; Arrillaga, J., “Modeling of bipolar
HVDC links in the harmonic domain”, Power Delivery, IEEE
Transactions, Volume 15, Issue 3, Jul 2000, pp. 1034-1038.
[77] Strobl B, G. Herold, “Harmonic Transfer Through Converters “, EPE
2001, pp. 1-10
[78] Yonyg He Liu; Perera, L.B.; Arrillaga, J.; Watson, N.R, “A Back to
Back HVDC Link With Multilevel Current Reinjection Converters”
Power Delivery, IEEE Transactions Volume 22, Issue 3, July 2007
pp. 1904-1909.
[79] Li Guangkai, Li Gengyin, Liang Haifeng, Yin Ming, “Research on
hybrid HVDC”, Power System Technology, 2004. Power Con 2004,
Volume: 2, pp. 1607- 1612.
[80] Naidoo, D. Ijumba, N.M., “HVDC line protection for the proposed
future HVDC systems”, Power System Technology, 2004. PowerCon
2004. Volume: 2, pp. 1327-1332.
[81] Takeda, H.; Ayakawa, H.; Tsumenaga, M.; Sanpei, M., “New
protection method for HVDC lines including cables”, Power
Delivery, IEEE Transactions, Volume 10, Issue 4, Oct 1995, pp.
2035 - 2039
399
[82] Kato, Y.; Watanabe, A.; Konishi, H.; Kawai, T.; Inoue, Y.; Irokawa,
H., “Neutral Line Protection System for HVDC Transmission”, Power
Delivery, IEEE Transactions, Volume 1, Issue 3, July 1986, pp. 326
- 331
[83] Senthil, J. Padiyar, K.R. Sachchidanand, “A simulator study of
recovery of HVDC links following AC system faults” ACE'90.
Proceedings of [XVI Annual Convention and Exhibition of the IEEE
In India] pp. 45-49
[84] Darwish, H.A.; Taalab, A.-M.I.; Rahman, M.A, “Performance of
HVDC converter protection during internal faults” Power
Engineering Society General Meeting, 2006. IEEE Volume, Issue, 0-
0 0 Page(s):7
[85] Hua Li Fuchang Lin Junjia He Yuxin Lu Huisheng Ye Zhigang
Zhang, “Analysis and Simulation of Monopolar Grounding Fault in
Bipolar HVDC Transmission System”, Power Engineering Society
General Meeting, 2007, IEEE. pp. 1-5
[86] Xi-Mei Liu, Wan-Yun Wei, Fei Yu, "SVM Theory and Its Application
in Fault Diagnosis of HVDC System," Third International
Conference on Natural Computation (ICNC 2007), Vol. 1, pp.665-
669,
[87] Bhattacharya, S.; Dommel, H.W, “A new commutation margin
control representation for digital simulation of HVDC system
transients”, Power Systems, IEEE Transactions, Volume 3, Issue 3,
Aug 1988, pp. 127 – 1132.
[88] Lidong Zhang Dofnas, L., “A novel method to mitigate commutation
failures in HVDC systems”, Power System Technology, 2002.
Proceedings. PowerCon 2002. Volume: 1, pp. 51- 56.
[89] Lingxue Lin Yao Zhang Qing Zhong Zhiwei Liao, “Studies of
Commutation Failures in HVDC System Based on Hypersim”,
PowerCon 2006, pp. 1-7.
400
[90] ABB Utilities, Ludvika, Sweden; “A novel method to mitigate
commutation failures in HVDC systems”, Power Systems
Technology 2002. Proceedings. Powerconn 2002. Volume: 1, pp.
51- 56.
[91] Johnson, R.K. Klemm, N.S. De Laneuville, H. Koetschau, S.G.
Wild, G., “Power modulation of Sidney HVDC scheme. I. RAS
control concept, realization and field tests”, power Delivery, IEEE
Transactions, Oct 1989, Vol. 4, No. 4, pp. 2145-2152.
[92] Hara, S. Hirose, M. Hatano, M. Kinoshita, S. Ito, H. Ibuki, K.,
“Fault protection of metallic return circuit of Kii channel HVDC
system”, AC-DC Power Transmission, 2001. Seventh International
Conference on (Conf. Publ. No. 485), pp. 132- 137.
[93] Kristmundsson, G.M.; Carroll, D.P., “The effect of AC system
frequency spectrum on commutation failure in HVDC inverters”,
Power Delivery, IEEE Transactions, Volume 5, Issue 2, Apr 1990,
pp. 1121 – 1128.
[94] Magnago, F.H. Abur, A., “Fault location using wavelets”, Power
Delivery, IEEE Transaction, Oct 1998, Vol. 13, No. 4, pp. 1475-
1480
[95] Ilaria Bartolini, Paolo Ciaccia, Florian Waas, “Using the wavelet
transform to learn from user feedback (2000)”, In Proceedings of
the First DELOS Network of Excellence Workshop on Information
Seeking, Searching and Querying in Digital Libraries, Zurich,
Switzerland, December 2000, pp 1-6.
[96] Gaouda, A.M. El-Saadany, E.F. Salama, M.M.A. Sood, V.K.
Chikhani, A.Y.; “Disturbance monitoring in HVDC systems using
wavelet multi-resolution analysis” Electric Utility Deregulation and
Restructuring and Power Technologies, 2000. Proceedings. DRPT
2000. pp 678-684.
[97] Gouda, A. M. El-Saadany, E. F. Salama, M. M. A. Sood, V. K.
Chikhani, A. Y., “Monitoring HVDC Systems Using Wavelet Multi-
401
resolution Analysis” Power Engineering Review , IEEE. Nov. 2001
Vol. 21, Issue:11, pp. 54-55
[98] Shang, L. Herold, G. Jaeger, J. Krebs, R. Kumar, A.; “High-speed
fault identification and protection for HVDC line using wavelet
technique” Power Tech Proceedings, 2001 IEEE Porto Volume: 3, on
page(s): 5 pp. vol.3.
[99] Shang, L. Herold, G. Jaeger, J. Krebs, R. Kumar, A. “Analysis
and identification of HVDC system faults using wavelet modulus
maxima “, AC-DC Power Transmission, 2001. Seventh International
Conference on (Conf. Publ. No. 485), Publication Date: 28-30 Nov.
2001 pp 315- 320.
[100] Johan Driesen and Ronnie Belmas., “Time-frequency analysis in
power measurement using complex wavelets” Circuits and Systems,
2002.ISCAS 2002. IEEE International Symposium, Vol. 5, pp. 681-
684
[101] K.Harish Kashyap, U.Jayachandra Sheonoy, “Classification of
power system faults using wavelet transforms and probabilistic
neural networks”, Circuits and Systems,. IEEE International
Symposium, ISCAS 2002. Vol. 3, pp. 423- 426.
[102] Chilukuri, M.V. Dash, P.K. Khincha, H.P., “Fault analysis of
FACTS using phase-corrected wavelet transform and pattern
recognition approach”, TENCON 2003. Conference on Convergent
Technologies for Asia-Pacific region, Oct. 2003, Vol. 3, pp. 986- 992
[103] Dong Xinzhou, GE Yaozhong, Xu Bingyin., “Fault position relay
based on current travelling waves and wavelets”, Power Engineering
Society Winter Meeting 2000,IEEE. Jan 2000, Vol. 3, pp. 1997-
2004
[104] Ping Chen; Bingyin Xu; Jing Li; “Travelling Wave Based Fault
Locating System for HVDC Transmission Lines”, Power System
Technology, 2006. PowerCon 2006.
402
[105] Wang Yuhong Ren Zhen Li Qunzhan, “Wavelets Selection for
Commutation Failure Detection in HVDC System” TENCON 2006.
2006 IEEE Region 10 Conference, Nov. 2006, pp 1-4.
[106] Elhaffar, A. Elkalashy, N.I. Lehtonen, M., “Experimental
Investigations on Multi-end Fault Location System based on
Current Travelling Waves”, Power Tech.2007 IEEE Lausanne., July
2007, pp. 1141-1146
[107] Yuhong Wang; Qunzhan Li; Xiaoqiong He; Cao Wen, “Commutation
failure recognition in HVDC systems using wavelet and shannon
entropy”, Electrical and Computer Engineering, 2008. CCECE
2008, Volume , Issue , 4-7 May 2008, pp. 001897 - 001902
[108] A.Borghetti, M. Bosetti, M.Di Silvestro, C.A. Nucci and M.Paolone,
“Continuous-Wavelet Transform for Fault Location in Distribution
Power Networks: Definition of Mother Wavelets Inferred From Fault
Originated Transients”, Power Systems , IEEE Transactions, May
2008, Vol. 23, Issue:2, pp. 380-388
[109] Rashmi Aspi Keswani, "Identification of Fault in HVDC Converters
Using Wavelet Based Multi-Resolution Analysis," ICETET, pp.954-
959, 2008 First International Conference on Emerging Trends in
Engineering and Technology, 2008.
[110] magnus öhrström*, martin geidl, lennart söder*, göran andersson,
“Evaluation of Travelling Wave Based Protection Schemes for
Implementation in Medium Voltage Distribution Systems”
[111] Lai,L.L.; Ndeh-Che,F.; Chari,T.; Rajroop, P.J.; Chandrasekharaiah,
H.S. “HVDC systems fault diagnosis with neural networks” Power
Electronics and Applications, 1993., Fifth European Conference on
vol.8, 13-16 Sep 1993 pp.145-150.
[112] Lai, L.L. “Application of neural networks to fault classification and
protection” Advances in Power System Control, Operation and
Management, 1997. APSCOM-97. Fourth International Conference
on (Conf. Publ. No. 450) Vol. 1, No. 11-14, Nov 1997 pp.72 – 76.
403
[113] Narendra K. G.; Sood V. K.; Khorasani K.; Patel R.; “Application of a
Radial Basis Function (RBF) Neural Network for fault diagnosis in a
HVDC system”, IEEE transactions on power systems ISSN 0885-
8950 CODEN ITPSEG 1998, vol. 13, no1, pp. 177-183.
[114] R. Malewski, T. Mc Comb and M. M. C. Collins, "Measuring
Properties of Fast Digitizers Employed For Recording HV Impulses",
IEEE Trans Instrument Measurement, Vol. IH-32, No. 1, 1983, pp.
17-22.
[115] R. Hanique "A Transfer Function is a Reliable Tool for Comparison
of Full and Chopped Lightning Impulse Tests" IEEE Trans on Power
Delivery, Vol. 9, July 1994, pp. 1261-1266.
[116] J. Bak-Jeno;en, B. Bak-Jensen, S. D. Mikkelsen, "Detection Of
Faults And Ageing Phenomena In Transformers By Transfer
Function", IEEE Trans on Power Delivery, Vol. 10, No. 1, Jan 1995,
pp 308-314.
[117] E. Rahim Pour, J. Christian, Kurt Feser, "Transfer Function
Method to Diagnose Axial Displacement And Radial Deformation Of
Transformer Windings", IEEE Trans on Power Delivery, Vol. 18, No
2, April 2003.
[118] J. Christian, Kurt Feser, "Procedures for Detecting Winding
Displacements in Power Transformers by the Transfer Function
Method", IEEE Trans on Power Delivery, Vol. 19, Jan 2004, pp 214-
219.
[119] Chang Qing Zhang, R. Eugene Stuffle, Linda R. Stuffle, "Analytical
Method for Transformer Fault Detection", M. S. E. Jhesis, Idaho
State University, 1991, pp 1541-1545.
[120] James J. Dukarm, ''Transformer Oil Diagnosis Using Fuzzy and
Neural Networks", IEEE Trans 1993, pp 329-332.
[121] Y. Zhang, X. Ding, Y. liu, P. J. Griffin" An Artificial Neural Network
approach to Transformer Fault Diagnosis" IEEE Trans on Power
Delivery, Vol. 11, No 4, October 1996, pp 1836-1841.
404
[122] N. K Patel, R. K Khubchandani, "ANN Based Power Transformer
Fault Diagnosis", IE (I) Joumal-EL, Vol. 85, June 2004, pp 60-63.
[123] T. Nogami, Yoshihide Yokoi, Hideo Ichiba, Yoshihiro Atsumi, "Gas
Discrimination Method For Detecting Transformer Faults By Neural
Network", IEEE Trans. Elec. Insul., Vol. 4, 1994, pp 3800-3805.
[124] S. Birlasekaran and G. Ledwich, “Use of FIT and ANN Techniques
In Monitoring Of Transformer Fault Gases", International
Symposium on Electrical Insulating Materials, Japan, September
27-30, 1998, pp 75-78.
[125] Luis G. Perez, Alferd J. Flechsig, Jack L. Meador, Zoran Obradovic "
Training An Artificial Neural Network To Discriminate Between
Magnetizing Inrush And Internal Faults" IEEE Trans on Power
Delivery, Vol. 9, No. 1, Jan 1994, pp 434441.
[126] M. R Zaman and M. A Rahman "Experimental Testing Of The
Artificial Neural Network B~-j Protection Of Power Transformers"
IEEE Trans on Power Delivery, Vol. 13, No 2, April 1998, pp 510-
516.
[127] H T. Yang, W. Y. Chang and C. L. Huang "A New Neural Network
Approach To Online Fault Section Estimation Using Information Of
Protective Relays And Circuit Breakers" IEEE Trans Power Delivery,
Vol. 9, Jan 1994, pp 220-229.
[128] HWang, K L. Butler "Modeling of Transformer Internal Short Circuit
Faults Using Neural Network Techniques".
[129] P. Alves da Silva, A. H. F. Insfran, P.M. da Silveria, G. Lambert
Torres, "Neural Networks for Fault Location in Substations", IEEE
Trans on Power Delivery, Vol. 11, No 1, Jan 1996, pp 234-239.
[130] J. Mazon, I. Zamora, 1. Gracia, K. J. Sagastabeitia, J. R. Saenz,
“Selecting ANN Structures To Find Transmission Faults”, Vol. 14,
No 3, July 2001, pp 7-8.
[131] Ghendy Cardoso, Jr., 1. G. Rolim and H. H. Ziim, "Application of
Neural Network Modules to Electric Power System Fault Section
405
Estimation", IEEE Trans on power Delivery, Vol. 19, No 3, July
2004, pp 1034-1041.
[132] David C. Yu, James C. Cummins, Zhuding Wang, Hong-Jun Yoon
and Ljubomir A. Kojovic, "Correction Of Current Transformer
Distorted Secondary Currents Due To Saturation Using Artificial
Neural Networks", IEEE Trans on Power Delivery, Vol. 16, No 2,
April 2001, pp 189-194.
[133] Gaganpreet Chawla, Mohinder S. Sachdev, G. Ramakrishna,
"Artificial Neural Network Application for Power System Protection",
IEEE Trans on Power Delivery, Vol. 1, No 2, May 2005, pp 1954-
1957.
[134] Michael Negnevitsky, Vsevolod Pavlovsky, "Neural Networks
Approach to Online Identification of Multiple Failures of Protection
Systems" IEEE Trans on Power Delivery, Vol. 20, No 2, April 2005,
pp 588-594.
[135] P. Werle, A. Akbari, H. Borsi, E. Gockenbach, "Partial Discharge
Localisation on Power Transformer using Neural Networks
combined with Sectional Winding Transfer Functions as Knowledge
Base" International Symposyum on electric insulating materials
(ISEIM), Himeji, Japan, 2001, pp. N-179.
[136] Li. Yongli, Gu. Fuhai, He. Jiali, "A Study On The Fault
Identification Of Transformers Using The Neural Network", IEEE
Trans on Power Delivery, Vol. 2, 18-21 Aug.1998, pp 1058-1061.
[137] Dr. A. S. Zadgaonkar, A. S. Thoke, "Application of Artificial Neural
Network to Power Transformer Protection (short- circuits and
overloads)" Electrical Review Magazine, November 2002, pp 13-17.
[138] McDermid, W. Glodjo, A. Bromley, J.C. Manitoba Hydro, and
Winnipeg, Man, “ Analysis of winding failures in HVDC converter
transformers “, Electrical Insulation Conference and Electrical
Manufacturing & Coil Winding Conference, Cincinnati, OH 1999.
Proceedings, pp.653-657.
406
[139] [140] W. McDermid D.H. Grant A. Glodjo and J.C. Bromley,
"Analysis of Converter Transformer Failures and Application of
Periodic On-line Partial Discharge Measurements", Electrical
Insulation Conference and Electrical Manufacturing & Coil Winding
Conference, 2001. Proceedings, pp.577-582.
[140] [141] Grant, D.H. McDermid, W. Manitoba Hydro and Winnipeg,
Man, “Assessment of thermal aging of HVDC converter transformer
insulation”, Conference Record of the 2004 IEEE International
Symposium on Electrical Insulation on 19-22 Sept. 2004, pp. 230 –
232.
[141] [142] R. Leelaruji, J. Setréus, and G. Olguin, “Availability
Assessment of the HVDC Converter Transformer System”,
Probabilistic Methods Applied to Power Systems, 2008. PMAPS '08.
Proceedings of the 10th International Conference on 25-29 May
2008, pp. 1 - 8
[142] LI, Yong, NAKAMURA, Kazuo, LUO, Longfu and LIU Fusheng,
"Analysis of Characteristic Parameters of Auto-compensation and
Harmonic-shielding Converter Transformer for HVDC Transmission
System", The International Conference on Electrical Engineering
2008, July 6-10, 2008, OKINAWA, JAPAN, pp. 1-6.
[143] [144] G. Bhuvaneswari, Senior Member, IEEE, and B. C. Mahanta,
"Analysis of Converter Transformer Failure in HVDC Systems and
Possible Solutions", IEEE Transactions on Power Delivery, April
2009, Vol.24, No.2, pp.814-821.
[144] M. S. Naidu, V. Kamaraju "High Voltage Engineering" Second
Edition TATA Mc Graw Hill press, 1996, PP339-342.
[145] Ryszard Malewski, Bertrand Poulin, "Impulse Testing of Power
Transformer using the Transfer Function Method", IEEE Trans on
Power Delivery, Vol. 3, No 2, April 1988, pp 476-489.
[146] Syed M. Islam & Gerard Ledwich, "Locating Transformer Faults
through Sensitivity Analysis of High Frequency Modeling Using
407
Transfer Function Approach", IEEE International symposium of an
Electrical Insulation Material, Qurbec Canada, June 16-19, 1996,
pp 38-41.
[147] Patrick Bastard, Pierre Bertrand, Michel Meunier, "A Transformer
Model for Winding Fault Studies", IEEE Trans on Power Delivery,
Vol. 9, N02, April 1994, pp 690-699.
[148] V. Brabdwajn, H. W. Dommel, I. I. Dommel, "Matrix Representation
of Three Phase N-winding Transformers", IEEE Trans on P.A.S,
June 1982, pp 1369-1378.
[149] H. Wang, K. L. Butler, "Finite Element Analysis of Internal Winding
Faults In Distribution Transformer", IEEE Trans on Power Delivery,
Vol. 16, No 3, July 2001, pp 422-428.
[150] H. Wang, K. L. Butler, "Modeling Transformers with Internal
Incipient Faults", IEEE Trans on Power Delivery, Vol. 17, No 2,
April 2002, pp 500-509.
[151] P. T. N. Vaessen, E. Hanique, "A New Frequency Response Analysis
Method for Power Transformer", IEEE Trans Power delivery, Vol. 7,
January 1998, pp 384-391.
[152] Juan A. Martinez, Bruce A. Mork, "Transformer Modeling for Low
and MidFrequency Transients- A Review", IEEE Trans on Power
Delivery, Vol. 20, No 2, April 2005, pp 1625-1632.
[153] Simon Ryder, "Frequency Response Analysis for Diagnostic Testing
of Power Transformers", Electricity today Magazine article pp 1 to 8.
[154] Jong - Wook Kim, Byung Koo Park, Seung Cheol Jeong, Sang Woo
Kim, PooGyeon Park, "Fault Diagnosis Of Power Transformer Using
An Improved Frequency -Response Analysis", IEEE Trans on Power
Delivery, Vol. 20, No 1, Jan 2005, pp 169-178.
[155] Littler, T.B.; Morrow, D.J. “Wavelets for the analysis and
compression of power system disturbances”, IEEE Transactions on
Power Delivery, Vol. 14, No. 2, Apr. 1999, pp. 358 –364.
408
[156] E. Styvaktakis, M.H.J. Bollen, I.Y.H. Gu, “A fault location technique
using high frequency fault clearing transients”, IEEE Power Eng.
Rev. 19, May 1999, pp. 50-60.
[157] K R Padiyar, "HVDC Power Transmission Systems (Technology and
system interactions)"New Age International (P) Limited, Publishers,
New Delhi.
[158] Edward Wilson Kimbark, “Direct Current Transmission”, Vol.1,
Wiley-Interscience, a Division of John Wiley & Sons, Inc, New York,
1971.
[159] Jos Arrillaga, Y H Liu, N R Watson, ”Flexible Power
Transmission(The HVDC optons)”, John wiley & Sons Ltd.,
England.
409
RESEARCH PUBLICATIONS FROM THIS THESIS
[1] P Krishna Murthy, J. Amarnath, S. Kamakshaiah and B.P.
Singh,“Wavelet Transform approach for Detection and Location of
Faults in HVDC System”, IEEE Region 10 colloquium and the third
ICIIS, Kharagpur, India, December 8-10, 2008, pp. 1-6
[2] P Krishna Murthy, J. Amarnath, S. Kamakshaiah and B.P. Singh,
“HVDC transmission System fault Diagnosis and location using
Artificial Neural Networks” International Conference on Energy and
Environment, EnviroEnergy 2009, March 19-21, 2009, pp. 847-
851.
[3] P Krishna Murthy, J. Amarnath, S. Kamakshaiah and B.P. Singh,
“Internal Fault Diagnosis of HVDC Converter Transformer using
wavelet Transform Technique”, 16th International Symposium on
High Voltage(ISH-2009), Capetown, South Africa, 24th – 28th Aug
2009. pp. 1611-1614.
[4] P Krishna Murthy, J. Amarnath, S. Kamakshaiah and B.P. Singh,
“Classification of internal faults of a converter transformer using
Wavelet Transforms”, Third International Conference on Power
Systems (ICPS-2009), Kharagpur, India, 27-29 December, 2009.
(Accepted for oral presentation)
[5] P Krishna Murthy, J. Amarnath, S. Kamakshaiah and B.P. Singh,
“Location of faults in HVDC converter transformer using wavelet
techniques”, TRAFOTECH-2010. Accepted for presentation
[6] Pannala Krishna Murthy, J. Amarnath, S. Kamakshaiah and B.
Murali Krishna, “Recognition of faults in HVDC system by wavelet
analysis” J. Curr.Sci. 12(1), (2008), Pp. 33-42.
410
[7] P Krishna Murthy, J. Amarnath and B.P. Singh, “Reconstruction of
HVDC Converter Transformer Neutral Current using Gabor
Wavelet”, Indian Electrical and Electronics Manufacturers
Association (IEEMA JOURNAL), JUNE 2009, pp.118-121.
[8] P Krishna Murthy, J. Amarnath, S. Kamakshaiah and B.P. Singh,
“ANN Based Internal Fault Diagnosis of HVDC converter
Transformer” International Journal of Applied Engineering
Research (IJAER)" Vol.4 No.6, 2009, pp 867-876.
[9] P Krishna Murthy, J. Amarnath, and S. Kamakshaiah, “HVDC
transmission line fault location using FFT analysis”, International
Journal of Applied Engineering Research (IJAER) Communicated.
411
ANNEXURE - I
Specifications of HVDC system model
AC Terminal equipment:
5000MVA equivalent at Rectifier:
VL = 500 kV
f = 60 Hz
Connection: Y Grounded
Source inductance= 98.03 mH
Parallel RL Branch connected in series with the AC source:
R = 26.07
L = 48.86 mH
10000MVA equivalent at Inverter:
VL = 345 kV
f = 50 Hz
Connection: Y Grounded
Source inductance= 28.0 mH
Parallel RL Branch connected in series with the AC source:
R = 6.205
L = 13.96 mH
412
AC filters:
60Hz, 600MVAR AC filter bank at rectifier
150 MVAR shunt capacitor bank
Tuned filters
11th Harmonic filter, 150 MVAR, Q =100.
13th Harmonic filter, 150 MVAR, Q =100.
24th Harmonic filter, 150 MVAR, Q =3.
50Hz, 600MVAR AC filter bank at Invertor
150 MVAR shunt capacitor bank
Tuned filters
11th Harmonic filter, 150 MVAR, Q =100.
13th Harmonic filter, 150 MVAR, Q =100.
24th Harmonic filter, 150 MVAR, Q =3.
Converter Transformers:
Converter Transformer at rectifier:
Rating: 1200MVA
f = 60Hz
HVAC winding Equivalent circuit Parameters:
VL = 500 kV
Tap = 0.9 (fixed)
R1 = 0.0025 (p.u.)
L1 = 0 (p.u.)
Connection: Y ground
HVDC winding Equivalent circuit Parameters:
V2 = 200 kV
R2 = 0.0025 (p.u.)
L2 = 0.24 (p.u.)
Connection: Y
413
HVDC winding Equivalent circuit Parameters:
V2 = 200 kV
R2 = 0.0025 (p.u.)
L2 = 0.24 (p.u.)
Connection:
Magnetizing Resistance (Rm) = 500 (p.u.)
Magnetizing Reactance (Lm) = 500 (p.u.)
Converter Transformer at Inverter:
Rating: 1200MVA
f = 50Hz
HVAC winding Equivalent circuit Parameters:
VL = 345 kV
Tap = 0.96 (fixed)
R1 = 0.0025 (p.u.)
L1 = 0 (p.u.)
Connection: Y ground
HVDC winding Equivalent circuit Parameters:
V2 = 200 kV
HVDC – winding – 1 Equivalent circuit Parameters:
V2 = 200 kV
R2 = 0.0025 (p.u.)
L2 = 0.24 (p.u.)
Connection: Y
HVDC winding - 2 Equivalent circuit Parameters:
V2 = 200 kV
R2 = 0.0025 (p.u.)
L2 = 0.24 (p.u.)
Connection:
Magnetizing Resistance (Rm) = 500 (p.u.)
Magnetizing Reactance (Lm) = 500 (p.u.)
414
Each Six Pulse Thyristor Bridge Ratings:
No. of Bridge arms: 3
Snubbed Resistance: Rs = 2000
Snubber Capacitance Cs= 0.1 f
Ron=1 m
Lon=0 H
Forward Voltage Vf= 0 V
Smothing Reactors:
R = 1
L = 0.5 H
HVDC transmission Line Parameters:
Distributed Parameter Line
f = 60 Hz
R = 0.015 /kM
L = 0.0792 mH/kM
C = 14.4 nf/kM
Line length = 300 kM
415
ANNEXURE – II
The digitalized reverse voltage travelling wave obtained during the
following operating conditions of the HVDC system:
Normal operating condition
DC fault at 50 kM away from the rectifier with a fault resistance of
1.
LG fault on the AC side of the inverter
Time (ms) no fault (V) DC fault(V) LG fault (V)
1.00E-05 14.94 14.96 14.96
2.00E-05 14.88 14.88 14.88
3.00E-05 14.83 14.86 14.86
4.00E-05 14.78 14.80 14.80
5.00E-05 14.70 14.71 14.71
6.00E-05 14.54 14.55 14.55
7.00E-05 14.38 14.39 14.39
8.00E-05 14.22 14.22 14.22
9.00E-05 14.09 14.09 14.09
1.00E-04 13.95 13.95 13.95
1.10E-04 13.83 13.83 13.83
1.20E-04 13.76 13.76 13.76
1.30E-04 13.73 13.70 13.70
1.40E-04 13.72 13.71 13.71
1.50E-04 13.78 13.08 13.76
1.60E-04 13.90 11.07 13.76
1.70E-04 14.04 8.48 13.65
1.80E-04 14.23 5.97 13.45
1.90E-04 14.38 3.52 13.12
2.00E-04 14.56 1.12 12.69
2.10E-04 14.63 -1.27 12.12
2.20E-04 14.68 -3.68 11.46
2.30E-04 14.68 -6.10 10.69
2.40E-04 14.63 -8.54 9.82
2.50E-04 14.53 -11.01 8.88
2.60E-04 14.38 -13.50 7.89
2.70E-04 14.25 -15.98 6.88
2.80E-04 14.07 -18.45 5.81
2.90E-04 13.89 -20.92 4.74
3.00E-04 13.71 -23.38 3.66
3.10E-04 13.53 -25.83 2.58
3.20E-04 13.34 -28.28 1.49
3.30E-04 13.15 -30.70 0.40
3.40E-04 12.95 -33.12 -0.69
3.50E-04 12.79 -35.51 -1.75
3.60E-04 12.60 -37.90 -2.82
3.70E-04 12.46 -40.26 -3.85
3.80E-04 12.30 -42.57 -4.88
3.90E-04 12.21 -44.86 -5.85
4.00E-04 12.14 -47.08 -6.77
4.10E-04 12.13 -49.07 -7.64
4.20E-04 12.16 -50.32 -8.45
4.30E-04 12.25 -50.52 -9.21
4.40E-04 12.40 -50.00 -9.89
4.50E-04 12.56 -49.34 -10.55
4.60E-04 12.77 -48.75 -11.16
416
4.70E-04 12.96 -48.21 -11.78
4.80E-04 13.17 -47.76 -12.38
4.90E-04 13.35 -47.37 -13.00
5.00E-04 13.49 -47.06 -13.65
5.10E-04 13.62 -46.81 -14.32
5.20E-04 13.67 -46.66 -15.05
5.30E-04 13.70 -46.58 -15.80
5.40E-04 13.70 -57.41 -16.58
5.50E-04 13.68 -116.96 -17.38
5.60E-04 13.64 -217.18 -18.19
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418
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419
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420
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421
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9.09E-03 12.80 -550.07 -483.30
9.10E-03 12.78 -546.07 -483.47
9.11E-03 12.79 -542.62 -483.62
9.12E-03 12.78 -539.62 -483.77
9.13E-03 12.79 -537.01 -483.82
9.14E-03 12.81 -534.83 -483.84
9.15E-03 12.84 -533.01 -483.83
9.16E-03 12.88 -531.55 -483.79
9.17E-03 12.95 -530.40 -483.75
9.18E-03 13.01 -529.52 -483.70
9.19E-03 13.10 -528.88 -483.67
9.20E-03 13.18 -528.40 -483.64
9.21E-03 13.29 -528.09 -483.63
9.22E-03 13.40 -527.85 -483.62
9.23E-03 13.52 -527.72 -483.61
9.24E-03 13.62 -527.64 -483.62
9.25E-03 13.69 -527.58 -483.61
9.26E-03 13.69 -527.53 -483.60
9.27E-03 13.68 -527.45 -483.57
9.28E-03 13.65 -527.36 -483.53
9.29E-03 13.63 -527.16 -483.46
9.30E-03 13.61 -526.88 -483.40
9.31E-03 13.60 -526.48 -483.32
9.32E-03 13.65 -525.96 -483.23
9.33E-03 13.70 -525.35 -483.16
9.34E-03 13.81 -524.59 -483.11
9.35E-03 13.92 -523.70 -483.06
9.36E-03 14.01 -522.67 -483.04
9.37E-03 14.13 -521.43 -483.02
9.38E-03 14.26 -519.99 -483.03
9.39E-03 14.36 -518.36 -483.04
9.40E-03 14.48 -516.51 -483.02
9.41E-03 14.58 -514.51 -482.99
9.42E-03 14.70 -512.34 -482.92
9.43E-03 14.83 -510.02 -482.86
9.44E-03 14.98 -507.61 -482.87
9.45E-03 15.14 -505.12 -482.99
9.46E-03 15.32 -502.58 -483.12
9.47E-03 15.52 -500.00 -483.24
9.48E-03 15.70 -497.41 -483.35
9.49E-03 15.85 -494.84 -483.44
9.50E-03 15.96 -492.33 -483.53
9.51E-03 16.05 -489.85 -483.59
9.52E-03 16.07 -487.47 -483.66
9.53E-03 16.03 -485.19 -483.68
9.54E-03 15.91 -482.96 -483.71
9.55E-03 15.75 -480.83 -483.68
9.56E-03 15.55 -478.76 -483.66
9.57E-03 15.33 -476.76 -483.63
9.58E-03 15.08 -474.85 -483.65
9.59E-03 14.85 -472.99 -483.66
9.60E-03 14.59 -471.21 -483.76
9.61E-03 14.33 -469.54 -483.90
9.62E-03 14.09 -467.96 -484.11
9.63E-03 13.87 -466.52 -484.42
9.64E-03 13.67 -465.20 -484.75
9.65E-03 13.49 -464.01 -485.17
9.66E-03 13.32 -462.96 -485.60
9.67E-03 13.16 -462.03 -486.07
9.68E-03 12.97 -461.23 -486.56
9.69E-03 12.81 -460.51 -487.02
9.70E-03 12.63 -459.86 -487.46
9.71E-03 12.48 -459.23 -487.86
9.72E-03 12.36 -458.61 -488.20
9.73E-03 12.24 -458.00 -488.49
9.74E-03 12.14 -457.40 -488.72
9.75E-03 12.08 -456.80 -488.89
9.76E-03 12.01 -456.19 -488.98
9.77E-03 11.98 -455.58 -489.01
9.78E-03 11.95 -454.99 -488.98
9.79E-03 11.92 -454.40 -488.90
9.80E-03 11.88 -453.83 -488.73
9.81E-03 11.83 -453.24 -488.51
9.82E-03 11.77 -452.65 -488.23
9.83E-03 11.69 -452.04 -487.89
9.84E-03 11.57 -451.42 -487.52
9.85E-03 11.45 -450.77 -487.14
9.86E-03 11.32 -450.09 -486.76
9.87E-03 11.17 -449.37 -486.38
9.88E-03 11.04 -448.56 -486.03
9.89E-03 10.89 -447.62 -485.73
9.90E-03 10.78 -446.45 -485.48
9.91E-03 10.69 -444.94 -485.23
9.92E-03 10.63 -442.84 -485.02
427
9.93E-03 10.58 -439.84 -484.82
9.94E-03 10.53 -435.63 -484.63
9.95E-03 10.51 -429.73 -484.44
9.96E-03 10.47 -421.78 -484.25
9.97E-03 10.45 -411.58 -484.08
9.98E-03 10.43 -399.12 -483.95
9.99E-03 10.43 -384.79 -483.87
1.00E-02 10.43 -369.25 -483.80
1.00E-02 10.44 -353.55 -483.76
1.00E-02 10.49 -338.77 -483.70
1.00E-02 10.53 -325.97 -483.64
1.00E-02 10.62 -316.00 -483.55
1.01E-02 10.74 -309.29 -483.42
1.01E-02 10.88 -305.82 -483.28
1.01E-02 11.01 -305.27 -483.10
1.01E-02 11.08 -307.06 -482.85
1.01E-02 11.14 -310.46 -482.58
1.01E-02 11.20 -314.85 -482.22
1.01E-02 11.23 -319.61 -481.76
1.01E-02 11.23 -324.34 -481.15
1.01E-02 11.21 -328.90 -480.44
1.01E-02 11.21 -333.26 -479.63
1.02E-02 11.20 -337.27 -478.78
1.02E-02 11.21 -340.85 -477.90
1.02E-02 11.28 -343.94 -477.02
1.02E-02 11.39 -346.41 -476.11
1.02E-02 11.52 -348.13 -475.22
1.02E-02 11.67 -348.81 -474.33
1.02E-02 11.83 -348.07 -473.49
1.02E-02 12.02 -345.56 -472.66
1.02E-02 12.21 -340.92 -471.82
1.02E-02 12.44 -333.92 -471.01
1.03E-02 12.65 -324.61 -470.18
ANNEXURE - III
DC Line Fault Data (Reverse Voltage Travelling wave
The digitalized reverse voltage travelling wave obtained during the DC line
fault at various distances with various fault resistances.