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ANALYSIS AND IDENTIFICATION OF HVDC SYSTEM FAULTS USING WAVELET MODULUSMAXIMA

L. Shang, G. Herold; J. Jaeger, R. Krebs, A. Kumar

Friedrich-Alexander University of Erlangen–Nuremberg; Siemens AG, Germany

ABSTRACT

In this paper, different HVDC system faults are analysedand the rationing criteria based on wavelet modulusmaxima for the identification of the HVDC system faultsare proposed. The simulation results are discussed. Theresults show that the application of wavelet techniqueleads to a proper and more reliable solution for faultidentification. The results also provide a good basis for the new high-speed protection of HVDC lines.

KEYWORD

HVDC fault, HVDC line protection, Identification,wavelet, wavelet modulus maxima

1. INTRODUCTION

The detection and fast clearance of faults in HVDC linesare important for a safe operation of power systems. The

protection principle based on travelling wave theory provides the fastest protection. Long HVDC linescannot be sufficiently modelled with concentrated

parameters as assumed in traditional protection systems.Therefore, long HVDC lines have to be represented asdistributed elements and a protection for long HVDClines should be developed based on travelling wavetheory.

According to travelling wave theory, voltage and currenttravelling waves appear on the line when fault occurs.The fault generated travelling waves contain sufficientfault information that can be used for high-speed faultidentification and line protection. In AC transmissionlines, the amplitude of fault generated travelling waveschanges with the voltage angles. There is a problem for the travelling wave protection when faults occur near voltage zerocrossing. However, there is no such problemfor DC transmission lines so that travelling wave

protection is ideally suited for HVDC lines.

In HVDC systems, commutation failures in theconverter station and single-phase short circuit faults atthe AC side are similar to HVDC line faults. It is animportant requirement of HVDC line protection thatdifferent fault types be identified and the correctdecision be made as fast as possible.

However, a fast and reliable fault identification is still a big challenge. It is not easy to identify HVDC faults byusing pure frequency domain based methods or pure

time domain based methods. The pure frequency domain based methods are not suitable for the time-varyingtransients and the pure time domain based methods arevery easily influenced by noise.

The wavelet transform provides a new approach for analysing time-varying transients. It has the capability of analysing signals simultaneously in time and frequencydomain. Moreover, it can adjust analysis windowsautomatically according to frequency, namely, shorter windows for higher frequency and vice visa. Hence it issuitable for characteristic identification and travellingwave protection [1-3]. However, wavelet based fastidentification and protection in HVDC systems is arelatively new field.

In this paper, the behaviour of different faults in HVDC power systems will be analysed through wavelettransform and the identification criteria based onwavelet techniques will be proposed. Based on theabove investigations, the high-speed HVDC line

protection will be developed. The simulations arecarried out with MATLAB . The results show that thewavelet techniques lead to a new way for the faultidentification and the protection in HVDC systems.

2. FAULTS IN HVDC SYSTEMS

For the analysis and the identification of HVDC systemfaults, different cases are studied. A standard model of 12-pulse HVDC system under the MATLAB environment is used for the simulation. Figure 1 showsthe simulation model in which a 1000 MW (500 kV,2kA) DC line is used to transmit power from a 500 kV,5000 MVA, 60 Hz network to a 345 kV, 10 000 MVA,50 Hz network. The DC line is 300 km long and the

speed of the travelling wave is 296112 km/s.Figure 2 shows the voltages and currents of DC line atthe rectifier terminal when (a) DC line short circuit, (b)commutation failure at the inverter station, (c) single-

phase short circuit on the AC side of inverter station,and (d) normal operation condition as a reference case.

From Figure 2, we can see that different types of faultslead to similar transient processes. It is not easy toidentify the faults and to make correct protectiondecision fast within 3-5ms by using traditional methods.It is even more difficult if there is noise.

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Figure 1. Simulation model

Figure 2. Faults in HVDC systems

3. WAVELET TRANSFORM

The Wavelet transform transfers a time varying signalinto a time-scale plane and thus can represent theoriginal signal with time as well as frequencyinformation. Each scale in wavelet transformcorresponds to a certain frequency band and the timewindow widths are changed with scale or frequencyautomatically. Such multiresolution property is

particularly suitable for analysing transient signals.Another important reason why wavelet transform is

attractive for engineers is because there are fastcalculation algorithms based on filter bank structure.

There are different algorithm structures for the wavelettransform. Considering a better time location and a

better information keeping, we use the a’trous structure but without down-sampling blocks following the high- pass filters. Figure 3 shows our filter bank where H 0 andH1 are low-pass filters and high-pass filters respectively.

The outputs of high-pass filters are the wavelettransform of the original signal, called as waveletcoefficients.

Figure 3. Wavelet filter bank

The absolute local maximum values of waveletcoefficients are called wavelet modulus maxima. If themother wavelet is the first derivative of a smoothfunction, the edge of a signal can be represented well byits wavelet modulus maxima. Under above condition,the wavelet modulus maxima occur at an edge point, the

polarity of the maxima shows the change direction of theedge, and the amplitude represents the changingintensity of the edge. It is proved that the waveletmodulus maxima satisfy the following relation.

( ) α Ast xW ≤

max(1)

Where, W max x(t ) is the wavelet modulus maxima of signal x(t ), A is a constant, s is scale and α is Lipschitzexponent.

This relation means that the wavelet modulus maxima of an edge ( α = 0 or α > 0) remain unchanged or increasein value while the wavelet modulus maxima caused bywhite noise ( α < 0) decrease in value when scaleincreases. Additionally, the number of wavelet modulusmaxima caused by white noise decrease sharply when

scale increase [4]. This makes a strong denoisingfunction possible. The simulation results show that thewavelet modulus maxima represent the edges well evenwhen signals are mixed with 15% noise [5].

3 WAVELET ANALYSIS OF HVDC SYSTEMFAULTS

The transients of the study cases above will be analysedthrough wavelet transform. Each case is sampled at 80kHz and 512 samples are taken for wavelet transform in4 scales. The Mallat wavelet is used as the mother

wavelet. HVDC line currents, HVDC line voltages andcorresponding reverse voltage travelling waves are usedas the input signals of the wavelet filter bank. Reverse

(b)

(a)(c)

Network I Network II

Rectifier Inverter

M N(b)

(a)(c)

Network I Network II

Rectifier Inverter

M N

H1( z )

H0( z )

H1( z 2)

H0( z 2)

H1( z 4)

H0( z 4)

H1( z 8)

H0( z 8)

)(4k d

)(1k x

k x

)(3k x

)(4k x

)( 2k x

)(3k d

)(2k d

)(1k d (scale 1)

(scale 2)

(scale 3)

(scale 4)

H1( z )

H0( z )

H1( z 2)

H0( z 2)

H1( z 4)

H0( z 4)

H1( z 8)

H0( z 8)

)(4k d

)(1k x

)(1k x

k x k x

)(3k x )(3k x

)(4k x )(4k x

)( 2k x )( 2k x

)(3k d

)(2k d

)(1k d (scale 1)

(scale 2)

(scale 3)

(scale 4)

DC Current (kA) DC Voltage (kV)

time (s) time (s)

(a) DC line short circuit

time (s) time (s)

(b) Commutation failure at the inverter station

time (s) time (s)

(c) AC single-phase short circuit at the inverter station

time (s) time (s)

(d) Normal operation condition

0. 45 0. 5 0 .5 5 0. 6 0 .6 5

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voltage travelling waves are calculated with Equation(2).

2/)( DC c DC r i Z uu −= (2)

Where r u is reverse voltage travelling wave, DC u and

DC i are the DC voltage and DC current respectively, and

c Z is the surge impedance of the HVDC line.

3.1 NORMAL OPERATIONS

The DC current and DC voltage are steady with smallchanges around the rated values during the normaloperation conditions. Figure 4 shows the DC current atthe terminal M and its wavelet modulus maxima in four scales. Figure 5 and Figure 6 display the DC voltage andthe reverse voltage travelling wave at the terminal Mand their wavelet modulus maxima in four scales. Thewavelet modulus maxima occur regularly and with smallvalues: less than 0.04 for DC current, less than 40 for DC voltage and less than 20 for reverse voltagetravelling wave.

3.2 HVDC LINE FAULTS

HVDC line faults at different locations with differentfault resistances are simulated. One of the HVDC linefaults occurs at 100 km from terminal M and with zerofault resistance. Figure 7 shows the DC current at theterminal M and its wavelet modulus maxima in four scales. Figure 8 and Figure 9 display the DC voltage and

the reverse voltage travelling wave at the terminal Mand their wavelet modulus maxima in four scales.

It can be seen that:• The wavelet modulus maxima occur at every

arriving and reflection instant of the travellingwaves. The polarities appear regularly: positiveand negative in turns. The values of the waveletmodulus maxima are much larger than ones duringthe normal operation conditions.

• The negative wavelet modulus maxima of DCcurrent are relative small. They are too small tomeasure the time delay for the fault location,

although the positive ones are large enough for thefault detection.• The wavelet modulus maxima of the DC voltage

provide a secure fault detection and time location.• The wavelet modulus maxima of the reverse

voltage travelling wave provide a similar effect asthe DC voltage. Notice that the reverse voltagetravelling wave is nearly equal to zero duringnormal operation conditions, and it can be moreeasily processed than the DC voltage.

• The first four values of the wavelet modulusmaxima of the reverse voltage travelling wave areabout 1000. The fault can be securely detected if the pick-up value is set to 100.

3.3 COMMUTATION FAILURES

Figure 10 shows the wavelet modulus maxima of thereverse voltage travelling wave at the terminal M duringa commutation failure at the inverter station.

It can be seen that:• All wavelet modulus maxima are less than 40.• The polarities of the wavelet modulus maxima

remain the same 3ms after the disturbance arrivesat terminal M. During this time, the values of thewavelet modulus maxima are less than 15.

• The commutation failure can be identified clearlyfrom the HVDC line fault and the normal operationwith the setting (e.g. 100) value and the polaritychange.

3.4 AC SINGLE-PHASE FAULTS

Figure 11 shows the wavelet modulus maxima of thereverse voltage travelling wave at the terminal M duringan AC single-phase fault at the inverter station.

Similar to the commutation failure, all wavelet modulusmaxima in AC single-phase fault are less than 40, the

polarities of modulus maxima remain the same for 3ms.Therefore, the AC fault can also be identified surelyfrom the HVDC line fault and the normal operation withthe setting (e.g. 100) value and the polarity change.

Unlike the commutation failure, the wavelet modulusmaxima in AC single-phase fault occur with moredensity and relative larger value specially 3ms after thedisturbance arrives at terminal M, and the polarities

become positive and negative in turns after the unified polarity changes. Considering a fast identification in3ms, the difference of the wavelet modulus maxima can

be better used. Figure 12 shows the energy during 3mson each scale. It can be seen that the difference betweena commutation failure and an AC fault can bediscriminated with the energy.

4 WAVELET IDENTIFICATION OF HVDCSYSTEM FAULTS

With the help of the above analysis of HVDC faultsthrough wavelet transform, the criteria for theidentification can be obtained.

• For HVDC line fault identification, the amplitudeof the first wavelet modulus maxima of reversevoltage travelling wave, denoted as || max r U W ,

should be larger than the setting value setting K .

The setting can be taken as 100 for 500 kV HVDClines.

setting r K U W >|| max (3)

• For identifying commutation failures and AC faults

from the normal operation condition, the pattern of polarity change is used. During the normaloperations, the polarities regularly change positive

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and negative in turns. It will be a commutationfailure or an AC fault if the polarities remain thesame for 3ms.

• For differentiation between a commutation failureand an AC fault, the energy of the wavelet modulusmaxima on the scale 4 during 3ms are used. The

energy, denoted as )( max r U W E , should be larger than the setting value

setting E . The setting can be

taken as 40 for 500 kV HVDC lines.

setting r E U W E >)( max (4)

Based on the identification of HVDC faults, a new high-speed HVDC line protection can be developed. In this

protection, the fault location can be also obtained at thesame time as the fault identification. The fault locationis calculated according to Equation 5. The key here isthe measurement of the time delay ∆ t. Considering that

the reflection from the fault location (reflection factor isnegative) is different than the reflection from the lineterminal (reflection factor is positive), we measure thetime delay between the first two opposite polaritywavelet modulus maxima.. Namely, if the first isnegative, the next one should be taken with positive

polarity.

2t v

L∆×

= (5)

Where L is fault distance in km from the measuring point, t ∆ is the time delay in s and v is travelling wavespeed in km/s.

For example, a DC line fault with 60 ohm faultresistance occurs at 200 km from terminal M. The firstmodulus maxima is 723, larger than the setting (100) sothat the DC line fault is detected. In this case, thereflected travelling wave from the terminal N arrives atthe terminal M earlier than the reflection from faultlocation. With the help of the polarity, it is easy toidentify them. The time delay between the first twoopposite polarity wavelet modulus maxima (herecorresponding to the first and the third modulusmaxima) is 0.0013 s, thus the fault is located 199.87 kmaway from terminal M, as shown in Figure 13. The fault

is detected and located correctly.

5 CONCLUSION

For high-speed HVDC line protection based ontravelling waves, methods for transient signal analysisare necessary. Particularly, the identification withsimilar HVDC transients caused by faults is decisive.The wavelet transform provides a new possibility for this. In this paper, the different HVDC system faults areanalysed and the criteria for the identification and theline protection are proposed. The simulation resultsshow that the proposed approach based on the waveletmodulus maxima can make a definite identification of HVDC line faults, commutation failures and AC single-

phase faults. The application of wavelet techniques leadsto a faster, easier and more reliable solution for theidentification of HVDC system faults and thedevelopment of new high-speed protections of HVDClines.

Figure 4. DC current during normal operation

Figure 5. DC voltage during normal operation

0.5 0.501 0.502 0.503 0.504 0.505 0.5061.98

1.99

2

2.01 HVDC line current

k A

0.5 0.501 0.502 0.503 0.504 0.505 0.506-0.05

0

0.05

s c a l e

4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-0.02

0

0.02

s c a l e 3

0.5 0.501 0.502 0.503 0.504 0.505 0.506-0.01

0

0.01

s c a l e 2

0.5 0.501 0.502 0.503 0.504 0.505 0.506-5

0

5x 10 -3

s c a l e

1

Wavelet modulus maxima

0.5 0.501 0.502 0.503 0.504 0.505 0.5061.98

1.99

2

2.01 HVDC line current

k A

0.5 0.501 0.502 0.503 0.504 0.505 0.506-0.05

0

0.05

s c a l e

4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-0.02

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0

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0

5x 10 -3

s c a l e

1


0.5 0.501 0.502 0.503 0.504 0.505 0.506490

500

510520

HVDC line voltage

k V

0.5 0.501 0.502 0.503 0.504 0.505 0.506-50

0

50

s c a l e 4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-50

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50

s c a l e

3

0.5 0.501 0.502 0.503 0.504 0.505 0.506-10

0

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s c a l e 2

0.5 0.501 0.502 0.503 0.504 0.505 0.506-5

0

5

s c a l e 1

Wavelet modulus maxima0.5 0.501 0.502 0.503 0.504 0.505 0.506490

500

510520

HVDC line voltage

k V

0.5 0.501 0.502 0.503 0.504 0.505 0.506-50

0

50

s c a l e 4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-50

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3

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0

10

s c a l e 2

0.5 0.501 0.502 0.503 0.504 0.505 0.506-5

0

5

s c a l e 1


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Figure 6. Reverse voltage travelling wave duringnormal operation

Figure 7. DC current during HVDC line fault

Figure 8. DC voltage during HVDC line fault

Figure 9. Reverse voltage traveling wave during HVDCline fault

0.5 0.501 0.502 0.503 0.504 0.505 0.50610

15

20

25HVDC line reverse voltage travelling wave

k V

0.5 0.501 0.502 0.503 0.504 0.505 0.506-20

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20

s c a l e 4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-20

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s c a l e 1


0.5 0.501 0.502 0.503 0.504 0.505 0.50610

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20


k V

0.5 0.501 0.502 0.503 0.504 0.505 0.506-20

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s c a l e 4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-20

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0.5 0.501 0.502 0.503 0.504 0.505 0.506-5

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s c a l e 1


0.5 0.501 0.502 0.503 0.504 0.505 0.506-1000

0

1000HVDC line voltage

k V

0.5 0.501 0.502 0.503 0.504 0.505 0.506-5000

0

5000

s c a l e 4

time (s)

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-2000

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s c a l e 1


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0

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k V

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5000

s c a l e 4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-5000

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246

HVDC line current

k A

0.5 0.501 0.502 0.503 0.504 0.505 0.506-1

01

s c a l e 4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-0.5

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HVDC line current

k A

0.5 0.501 0.502 0.503 0.504 0.505 0.5060

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HVDC line current

k A

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-500

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k V

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s c a l e 1


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Figure 10. Reverse voltage travelling wave duringcommutation failure

Figure 11. Reverse voltage travelling wave during ACsingle-phase fault

Figure 12. Energy of the wavelet modulus maxima

Figure 13. A DC line fault: 200km from terminal M

REFERENCES

[1] Magnago, F.H. and Abur, A., 1998, “Fault locationusing wavelets”, IEEE Trans. on Power Delivery,13-4 , 1475-1480.

[2] Dong, X. Zh., Ge, Y. Zh. and Xu, B. y., 2000,“Fault position relay based on current travellingwaves and wavelets”, IEEE PES 2000 Winter Meeting, 23-27.

[3] Shang, L., Herold, G. and Jaeger, J., 2000, “A newapproach to high-speed protection for transmissionline using wavelet technique”, PSP 2000, 85-90.

[4] Mallat, S. and Hwang, W. L., 1992, “Singularitydetection and processing”, IEEE Trans. onInformation Theory , 38-2, 617-643.

[5] Shang, L., Herold, G. and Jaeger, J., 2001, “High-speed protection for transmission line based ontransient signal analysis using wavelets”, IEEDPSP 2001, 173-176.

1 2 3 40

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Energy of the wavelet modulus maxima

AC fault

Commutation failure

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Energy of the wavelet modulus maxima

AC fault

Commutation failure

0.5 0.501 0.502 0.503 0.504 0.505 0.506-100

0


k V

0.5 0.501 0.502 0.503 0.504 0.505 0.506-50

0

50

s c a l e 4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-20

0

20

s c a l e

3

0.5 0.501 0.502 0.503 0.504 0.505 0.506-10

0

10

s c a l e 2

0.5 0.501 0.502 0.503 0.504 0.505 0.506-5

0

5

s c a l e 1


0.5 0.501 0.502 0.503 0.504 0.505 0.506-100

0


k V

0.5 0.501 0.502 0.503 0.504 0.505 0.506-50

0

50

s c a l e 4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-20

0

20

s c a l e

3

0.5 0.501 0.502 0.503 0.504 0.505 0.506-10

0

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0.5 0.501 0.502 0.503 0.504 0.505 0.506-5

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0.5 0.5005 0.501 0.5015 0.502 0.5025-1000

0

HVDC line reverse voltage travelling wave

k V

time (s)

time (s)


-723 +591

∆ t = 0.0013s LMF = 199.87km

0.5 0.5005 0.501 0.5015 0.502 0.5025-500

0

500

0.5 0.5005 0.501 0.5015 0.502 0.5025-1000

0

0.5 0.5005 0.501 0.5015 0.502 0.5025-1000

0

HVDC line reverse voltage travelling wave

k V

time (s)

time (s)


-723 +591

∆ t = 0.0013s LMF = 199.87km

0.5 0.5005 0.501 0.5015 0.502 0.5025-500

0

500

0.5 0.5005 0.501 0.5015 0.502 0.5025-500

0

500

0.5 0.501 0.502 0.503 0.504 0.505 0.506-400-200

0200

HVDC line reverse voltage travelling waver

k V

0.5 0.501 0.502 0.503 0.504 0.505 0.506-50

0

50

s c a l e

4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-50

0

50

s c a l e 3

0.5 0.501 0.502 0.503 0.504 0.505 0.506-20

0

20

s c a l e 2

0.5 0.501 0.502 0.503 0.504 0.505 0.506-5

0

5

s c a l e 1

Wavelet modulus maxima0.5 0.501 0.502 0.503 0.504 0.505 0.506-400

-2000

200HVDC line reverse voltage travelling waver

k V

0.5 0.501 0.502 0.503 0.504 0.505 0.506-50

0

50

s c a l e

4

time (s)

0.5 0.501 0.502 0.503 0.504 0.505 0.506-50

0

50

s c a l e 3

0.5 0.501 0.502 0.503 0.504 0.505 0.506-20

0

20

s c a l e 2

0.5 0.501 0.502 0.503 0.504 0.505 0.506-5

0

5

s c a l e 1


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