Partial Discharge Location in Power Cables Using a Phase Difference Method

1738 R. Mardiana and C. Q. Su: Partial Discharge Location in Power Cables using a Phase Difference Method

1070-9878/10/$25.00 © 2010 IEEE

Partial Discharge Location in Power Cables using a Phase Difference Method

Redy Mardiana and Charles Q. Su

The Petroleum Institute Department of Electrical Engineering

PO Box 2533, Abu Dhabi, UAE

ABSTRACT This paper presents a new partial discharge (PD) location technique for power cables. Unlike commonly used time-domain reflectometry (TDR) methods, this technique is based on the analysis of phase difference between the direct and reflected waves of a PD pulse measured at the cable end. The phase difference at various frequencies can be obtained from the cross Fourier spectral density function. After implementing a phase unwrapping algorithm, the defect is located. This technique has been tested using the Electromagnetic Transient Program (EMTP) on the model of a 20 kV, 1-km underground cable. The simulation takes into account the frequency-dependent parameters of the cable and the measurement accuracy of the A/D converter (8-bit). The signal-to-noise ratio (SNR) varies from 10 dB to -5 dB for all computer simulations. The statistical results are given to demonstrate the performance of the proposed technique.

Index Terms — Partial discharges, PD location, phase difference, cable insulation.

1 INTRODUCTION

PARTIAL discharge is recognized as a precursor of premature degradation of insulating dielectric materials in power cables. The PD activity in power cables is caused by various defects, such as voids, shield protrusions, contaminants, advanced stage of water trees, etc. PD will gradually degrade and erode the dielectric materials, eventually leading to insulation breakdown [1-2]. As a result, finding the defect sites is an effective diagnostic tool for in service power cables. Over the years, many studies have been directed towards the development of a single-end PD locating system, and numerous research results have been reported [3-9]. Among these, the time-domain reflectometry (TDR) method is commonly used in the field [3-8]. The TDR method estimates the arrival time interval between the direct and reflected waves of a PD pulse to locate the defect in the cable. The estimation of arrival time interval is carried out using pulse peak detection, 50% pulse peak detection, threshold detection, etc. [6, 10]. It is well know that, when using the TDR method, the frequency-dependent attenuation of power cable affects the accuracy of PD location [10-11]. A PD pulse generates two waves of the same amplitude traveling in opposite directions towards the cable ends. The direct wave is distorted as a result of propagation through the cable, while the reflected wave is distorted as a result of propagation through the cable as well as the terminal reflections. As the two waves travel unequal length of cable, the shapes of the direct and reflected waves will differ. With increasing distance propagated, the peak of the wave lags further, i.e., the waveform rise time increases.

The reflected wave suffers more from noise and attenuation and its amplitude becomes smaller as it travels along the cable. This condition affects the estimation of arrival time interval, because the determination of the point on the waves between which the time should be measured becomes more complicated. This causes an error in the PD location estimation [10-11].

To overcome the problem of the TDR method, this paper presents a new partial discharge location technique which can more accurately pinpoint the PD location in power cables. This technique is based on the analysis of phase difference between the direct and reflected waves of a PD pulse. The phase difference at various frequencies can be obtained from the cross Fourier spectral density function. After implementing a phase unwrapping algorithm, the defect can be located. This technique is tested using the EMTP on the model of a 20 kV, 1-km underground cable which takes into account the frequency-dependent parameters [12-13]. The PD pulse is measured by a sensor connected to the cable end with the other end opened. Additive noise, which could complicate the analysis, is superimposed on the PD pulse. The signal-to-noise ratio (SNR) varies and represents small to large noise levels for all computer simulations.

2 PD MEASURING SYSTEM The PD measuring system in the phase difference method is

basically the same as the TDR method. The only difference is the signal processing of PD pulse. A simplified PD measuring system is shown in Figure 1. The PD instrument is connected to the test cable at end A by means of an HV capacitor. The remote end B is left open. The instrument contains a band pass filter and a high gain, wideband amplifier which is followed Manuscript received on 20 April 2010, in final form 5 August 2010.

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 17, No. 6; December 2010 1739 by a digitizer (A/D) and a microcomputer (PC) for digital signal processing [14].

The PD is simulated by injecting a narrow pulse at the distance d from the measuring end [14-15]. The proposed PD pulse shape is described in Subsection 5.1. The measured PD pulse at the measuring end can be expressed as

0( ) ( ) ( ) ( ) ( ) (1)

t

y t h t s t h s tξ

ξ ξ=

= ⊗ = −∑ where h(t) is the impulse response of the instrument, s(t) is the PD signal received by the instrument, ⊗ denotes the linear convolution operation, and y(t) is the measured PD pulse. The measured signal is then digitized by the A/D converter. The recorded PD signal stored in the PC, denoted as x(t), contains the PD pulse and additive noise (such as environmental, electronic, etc) [14].

3 PULSE SEPARATION A PD at the distance d from the measuring end of a cable

generates two pulses. One pulse travels at a specific propagation velocity along the cable towards the measuring end A. The other travels in the opposite direction towards the remote end B. Once reaching the remote end, it is reflected and arrives later at the measuring end as illustrated in Figure 2a. The first pulse is referred as direct wave, while the second pulse is reflected wave. The reflected wave has therefore traveled an additional distance of 2(L-d) (where L is the cable length). The arrival time interval between the direct and reflected waves is given by

2 12( ) (2)L dt t t

v−

Δ = − =

where t1 is the arrival time of the direct wave, t2 is the arrival time of the reflected wave, and v is the propagation velocity.

In the proposed technique, it is necessary to separate between the direct and reflected wave before the phase difference can be derived. Let T= L/v be the maximum traveling time for a pulse to travel from cable end A to end B. The recorded PD signal x(t) is then divided into two windows

and each window has a length of T as shown in Figure 2b. The first window contains the direct wave denoted as x1(t), while the second window contains the reflected wave denoted as x2(t). The new arrival time interval between the direct and reflected waves is now given by

2 1 . (3)dt t t TΔ = − − Inserting equation (2) into equation (3), the new arrival time interval becomes

2 . (4)dL dt

v−

Δ =

The formula in equation (4) is the same as that for the two-end PD location system.

4 DETAIL OF PHASE DIFFERENCE METHOD

The basic idea of the proposed PD location technique is to calculate the phase difference at each frequency of Fourier spectra between the direct and reflected waves. Both the waves in the recorded PD signal x(t) must be separated before the calculation of phase difference is carried out.

4.1 PD LOCATION ESTIMATION Consider x1(t) as the time-domain direct wave and x2(t) as

the time-domain reflected wave. Assuming a total record length of T for each wave, then deriving the signals in the

Figure 2. The direct and reflected waves; (a) before pulse separation and (b) after pulse separation

Figure 1. Block diagram of the PD measuring system.


frequency domain using the Fourier transformation (FT) [16], we have

21 1

0

22 2

0

( ) ( )

( ) ( ) . (5)

Tj ft

Tj ft

X f x t e dt

X f x t e dt

π

π

−

−

=

=

∫

∫ The cross Fourier spectral density function of both signals is defined as

12 1 2( ) ( ). ( ) (6)G f X f X f∗= where * denotes the complex conjugate. The G12(f) will be a complex number such that

( )12 Re Im 12( ) ( ) ( ) ( ) (7)j fG f G f jG f G f e φ− Δ= − =

where

( )1/ 22 212 Re Im

Im

Re

( ) ( ) ( )

( )( ) arctan . (8)( )

G f G f G f

G ffG f

φ

= +

⎛ ⎞Δ = ⎜ ⎟

⎝ ⎠ The term Δφ(f) in equation (8) corresponds to the phase difference between signals x1(t) and x2(t). This phase difference is a function of frequency f. The relation between the phase difference and the arrival time interval Δtd is expressed as [6]

( ) 2 . (9)d df t f tφ ω πΔ = Δ = Δ Replacing Δtd with equation (4), we obtain

2( ) 2 . (10)L df fv

φ π −Δ = ×

Rearranging equation (10), the estimate of PD location becomes a function of frequency

1 ( )( ) . (11)2 2

v fd f Lf

φπ

⎛ ⎞Δ= −⎜ ⎟

⎝ ⎠ The final estimate of PD location d̂ can be obtained from the mean value of d(f).

4.2 PHASE UNWRAPPING As given in equation (10), the phase difference depends on

the PD location. To illustrate the relation between the phase difference and the PD location, a computer simulation has been made. The length of the cable is assumed to be L = 1000 m and the PD propagation velocity is v = 1.783×108 m/s. For the sake of simplicity, the frequency is limited to a range of 0–5 MHz. Figure 3 shows the phase difference as a function of frequency for three different PD locations. In practice, the phase difference varies only from -π to π radian, because the phase difference is resulted from a trigonometric function as defined in equation (8). Because of large frequency bandwidth, the phase difference goes through more than a cycle with increasing frequency as shown in the Figures 3a, 3b and 3c. This means there is more than one frequency which have the same phase difference value and, from equation (11), this will provide ambiguous location of the PD. The cycles of the phase difference are referred to fringes. As the PD location moves towards the middle of the cable (d = L/2), the number of fringes decreases.

It should be noted that if the phase difference is not wrapped in the interval of [-π, π] radian, then it will cover a range of

2 2 (12)m mπ π φ π π− − ≤ Δ ≤ +

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−2

0

2

Frequency (MHz)P

hase

Diff

eren

ce (

radi

an)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−2

0

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−2

0

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−100

−50

0

50

100

150

(a)

(b)

(c)

(d)

d = 100 m

d = 800 m

d = 300 m

d = 100 m d = 300 m

d = 800 m

Figure 3. The phase difference as a function of frequency for three different PD locations, (a) defect at d =100 m, (b) defect at d =300 m, (c) defect at d=800 m, and (d) the phase difference after implementing the phase unwrapping algorithm.

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 17, No. 6; December 2010 1741 where m is the number of fringes. The number of fringes can be obtained by rearranging equation (10) as follows

( ) 22 . (13)

f mL dm f

v

φ πΔ = ×−

= ×

For instance, for the defect at d = 300 m and frequency range up to f = 5 MHz, the number of fringes is equal to m = 11. The maximum number of fringes is obtained when d = 0 and f = fc (Nyquist frequency).

It is obvious that to eliminate the ambiguity of PD location, the phase difference must be unwrapped. In other words, the phase difference must be rearranged to have a unique value for each frequency as shown in Figure 3d. This can be done by implementing a phase unwrapping algorithm. The objective of phase unwrapping algorithm is to remove the discontinuities or phase jumps that appear in the phase difference function. The algorithm applies a module 2π operation (i.e., by adding ±2nπ radian, where n = 1, 2,.., m) to the phase difference in equation (8) until the following condition is fulfilled

1( ) ( ) . (14)i if fφ φ π−Δ −Δ ≤

The simple and popular phase unwrapping algorithm can be found in [17].

4.3 FLOWCHART OF PD LOCATION Figure 4 shows the flowchart of the PD location technique

based on the phase difference method. The PD signal s(t) is received by the instrument. The signal is convoluted by the impulse response of the instrument model h(t) using equation (1). The output from this convolution is the measured signal y(t). The additive noise w(t) is introduced at the output of the instrument which could complicate the analysis. The signal is then digittized by the 8-bit A/D converter. The output from the A/D converter is the recorded PD pulse x(t). The recorded PD pulse is split into two windows using the pulse separation procedure as described in Section 3. The first window contains the direct wave x1(t) and the second window contains the reflected wave x2(t). Both the direct and reflected waves are transformed into frequency domain signals using the Fourier transformation (FT). The output of this transformation is X1(f) and X2(f) for the direct and reflected waves, respectively. The cross Fourier spectral density is obtained using equation (6), while the phase difference Δφ(f) is obtained using equation (8). Up to this point, the phase difference is wrapped in the interval of [-π, π] radian. Next, the phase unwrapping algorithm is employed to remove the discontinuities that appear in the phase difference. The estimate of PD location as a function of frequency d(f) is calculated using equation (11). The final estimate of PD location d̂ can be obtained from the mean value of d(f).

5 SIMULATION RESULTS

To evaluate the performance of the proposed technique, a thorough computer simulation is carried out. The PD pulse propagation in a cable is simulated using the Electromagnetic Transient Program (EMTP). The cable model has a length of L = 1000 m and is a 20 kV underground cable with cross linked polyethylene (XLPE) insulation. The cable model takes into account the frequency-dependent parameters [12-13]. The detailed cable geometry is given in the Appendix. The cable sheath is assumed to be return path, so that the PD pulse travels along cable conductor and sheath [3, 9]. The propagation velocity is calibrated by injecting a pulse at measuring end of the cable and then the time interval between the first peak and the second peak is measured. The resulted propagation velocity is v = 1.783×108 m/s.

The instrument is modeled by an 8-th order IIR bandpass filter with a bandwidth of 100 kHz to 30 MHz and 3 dB attenuation at cut-off frequency [14]. The digitizer (A/D) has an 8-bit vertical resolution and sampling frequency of 100 MHz. The time window T is equal to 1000 m / 1.783×108 m/s = 5.61 μs or 561 samples. The additive noise is modeled by the Gaussian noise [14, 18] and the signal-to-noise ratio varies from 10 dB to -5 dB. This simulation is very close to a practical PD measurement system.

Figure 4. Flowchart of the proposed PD location technique.


5.1 PD MODEL A typical PD pulse is generated at the defect site. The PD

signal is commonly represented by a Gaussian or exponential pulse. In this simulation, the PD pulse is modeled by a current source having double-exponential form [9]

01 2

( ) exp exp (15)t tI t Iτ τ

⎛ ⎞⎛ ⎞ ⎛ ⎞= − − + −⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠

with the wavefront τ1 = 4 ns and wavetail τ2 = 12 ns. The current multiplier I0 is 6 mA which is equal to a charge of about Q = 50 pC. Figure 5 shows the waveform of the simulated PD pulse and its comparison with other PD pulse shapes [18-19].

5.2 PD LOCATION ANALYSIS As an example, a PD at location d = 300 m is analyzed.

Figure 6 shows the measured PD pulse with three different signal-to-noise ratios (SNRs) i.e., 10 dB, 0 dB, and -5 dB. These SNRs represent small, moderate, and large noise, respectively. When the noise is small, the direct and reflected waves are clearly seen. On the other hand, when the noise is large, the reflected wave is not easy to be distinguished from the noise. Intuitively, the closer the defect is to the measuring end, the more distortion the reflected wave would suffer as it travels almost twice the cable length before it is received by the instrument.

To simplify the explanation of signal processing, the analysis is focused on the PD pulse with the SNR = 10 dB. In the proposed technique, the PD pulse must be split into the direct and reflected waves by means of the pulse separation procedure as illustrated in Figure 2. This can be done as follows; (a) firstly, the direct wave must be identified and then it is chopped with the window length of T; (b) the following time window T is allocated to cover the reflected wave. Therefore, the reflected wave may not need to be identified and distinguished from the noise, even if the SNR is -5dB. It is important to note that it is not critical to determine the starting point of the time window T, because the starting point can be shifted to any point

without affecting the simulation results. However, the length of time window must be calculated beforehand. Figure 7 shows the recorded PD pulse after pulse separation.

The two windows which contain the direct and reflected

waves, respectively, are transformed into frequency domain using the Fourier transformation (FT). The Fourier spectrum and phase difference as a function of frequency can be derived using the cross Fourier spectral density function as shown in Figure 8. The phase difference is wrapped in the interval of [-π, π] radian and the fringes are clearly seen mainly at low frequencies as shown in Figure 8c. For the

0 1 2 3 4 5

0

50

100

150

200

250

Am

plitu

de (

Dig

ital U

nit)

Time (μs)

0 1 2 3 4 5

0

50

100

150

200

250

Am

plitu

de (

Dig

ital U

nit)

Time (μs)

(a)

(b)

Figure 7. The recorded PD waveform after pulse separation; (a) the direct wave and (b) the reflected wave. This waveform is the output from the A/Dconverter.

0 2 4 6 8 10−50

0

50

100

0 2 4 6 8 10−50

0

50

100

0 2 4 6 8 10−50

0

50

100

Am

plitu

de (

mV

)

Time (μs)

SNR = 10 dB

SNR = 0 dB

SNR = −5 dB

Figure 6. The PD pulse with different SNRs for the defect at d = 300 m.

0 10 20 30 40 50 60 70 800

0.2

0.4

0.6

0.8

1

Time (ns)

Cur

rent

(R

elat

ive

Uni

t)

ProposedRef.[18]Ref.[19]

Figure 5. The waveform of PD model.

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 17, No. 6; December 2010 1743 higher frequencies (e.g., above 10 MHz), the phase difference seems to scatter. This is because, in that frequency range, the cross Fourier spectrum is relatively low and the noise dominates the signal.

The phase unwrapping algorithm as described in Subsection

4.2 is applied to the phase difference. Figure 9a shows the unwrapped phase difference for the entire frequency range. It can be seen that the unwrapped phase difference at higher frequencies still has a tendency to increase linearly as frequency increases. The estimate of PD location as a

function of frequency can be obtained from the unwrapped phase difference using equation (11) and the result is shown in Figure 9b. The final estimate of PD location is the mean value of d(f), d̂ = 301.19 m.

5.3 STATISTICAL RESULTS The performance of the proposed technique is evaluated

quantitatively. A total of 100 PD signals at a given location and SNR is generated. For the given PD location and SNR, the mean location and average error are calculated. The average error of PD location is defined as

1

1 ˆAverage Error (16)n

ii

d dn =

= −∑ where d is the true location, d̂ is the estimated location, and n = 100. The statistical result for various PD locations and SNRs is shown in Figure 10. The correlations between the true and mean locations are very high indicating that the proposed technique has a high accuracy. The effect of noise on the PD location estimation is shown in Figure 11. Obviously, the larger the noise level, the higher the average error. However, in all cases, the average error is less than 3 m.

From these statistical results, it can be concluded that the phase difference method does not need to determine the point on the waves which is important for the measurement of the arrival time interval. This is an advantage of the phase difference method over the TDR method.

0 100 200 300 400 500 600 700 800 900 10000

200

400

600

800

1000

True Location (m)

Mea

n Lo

catio

n (m

)

0 100 200 300 400 500 600 700 800 900 10000

200

400

600

800

1000

True Location (m)

Mea

n Lo

catio

n (m

)

0 100 200 300 400 500 600 700 800 900 10000

200

400

600

800

1000

True Location (m)

Mea

n Lo

catio

n (m

)

Corr.Coef = 0.99999954

Corr.Coef = 0.99999946

Corr.Coef = 0.99999942

(a)

(b)

(c)

Figure 10. The statistical results for various PD locations and noise levels, (a) SNR = 10 dB, (b) SNR = 0 dB, and (c) SNR = -5 dB.

0 5 10 15 20 25 300

100

200

300

400

500

Frequency (MHz)

Pha

se D

iffer

ence

(ra

dian

)

0 5 10 15 20 25 30294

296

298

300

302

304

Frequency (MHz)

Est

imat

ed L

ocat

ion

(m)

(b)

(a)

Figure 9. (a) The unwrapped phase difference and (b) the estimate of PDlocation d(f) as a function of frequency. The dashed line indicates the truePD location at d = 300 m.

0 5 10 15 20 25 300

100

200

300

400

Frequency (MHz)

Cro

ss F

ourie

r S

pect

rum

(Rel

ativ

e un

it)

0 5 10 15 20 25 30

−2

0

2

Frequency (MHz)

Pha

se D

iffer

ence

(ra

dian

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−2

0

2

Frequency (MHz)

Pha

se D

iffer

ence

(ra

dian

)

(a)

(b)

(c)

Figure 8. The output of cross Fourier Spectral density function; (a) thecross Fourier spectrum, (b) the phase difference, and (c) zoom in of panel(b) for the frequency range up to 5 MHz.


It is worth noting that when the defect is very close to the

measuring end, the first reflected wave is more likely to overlap with the second reflected wave, since both the waves become wider as they travel almost twice the cable length. Similarly, when the PD location is very close to the remote end, the direct and reflected waves will overlap, since they experience similar traveling distances which are close to the cable length. This pulse overlapping makes the pulse separation difficult and can produce unrealistic location results, i.e., the error is much higher. As clearly shown in Figure 11, the average error is high when the defects are very close to the cable ends. This pulse overlapping also complicates the PD location estimation in the TDR method [8, 14]. In this simulation, the PD must be located in the range of 3 m ≤ d ≤ 997 m from the measuring end in order the proposed technique to locate the PD properly.

5.4 PERFORMANCE ON DIFFERENT PD PULSE SHAPES

To analyze the effect of PD pulse shapes on the location accuracy, three different PD models are used for comparison. The mathematical formula for the PD models follows equation (15). Table 1 shows the parameters of the models and Figure 12 shows the corresponding waveforms. Note that the first model has been applied in the previous subsection.

The same test procedure has been carried out to evaluate the performance of the proposed technique. The result of average errors for various PD locations and SNRs is plotted in Figure 13. It is shown that, similar to Figure 11, the location error gradually improves as the defect site is further away from the measuring end, except at the site where is very close to the remote end. The location error slightly increases when the wavefront and the wavetail time constants of the pulse are reduced (i.e., the PD pulse width is shorter). This is understood, because lesser PD signal information is obtained

for shorter PD pulse width at the given sampling frequency. However, this condition does not reduce the location accuracy appreciably.

6 CONCLUSION A new technique for locating PD sources in power cables has

been presented in the paper. The proposed technique estimates the phase difference of each Fourier frequency between the direct and reflected waves of a PD pulse. The PD location is determined after the phase unwrapping algorithm is implemented. The proposed technique does not need to estimate the arrival time interval, so that the problem of the estimation error of arrival time interval in the TDR method can be avoided.

0 100 200 300 400 500 600 700 800 900 1000

1.5

2

2.5

3

PD Location (m)

Ave

rage

Err

or (

m)

0 100 200 300 400 500 600 700 800 900 10001.5

2

2.5

3

PD Location (m)

Ave

rage

Err

or (

m)

0 100 200 300 400 500 600 700 800 900 10001.5

2

2.5

3

PD Location (m)

Ave

rage

Err

or (

m)

Model 1Model 2Model 3



(a)

(b)

(c)

Figure 13. The average error of three PD models for various PD locations and noise levels, (a) SNR = 10 dB, (b) SNR = 0 dB, and (c) SNR = -5 dB.

0 10 20 30 40 50 60 70 800

0.2

0.4

0.6

0.8

1

Time (ns)

Cur

rent

(R

elat

ive

Uni

t)


Figure 12. The waveforms of three different PD models.

0 100 200 300 400 500 600 700 800 900 1000

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

PD Location (m)

Ave

rage

Err

or (

m)

SNR = 10 dBSNR = 0 dBSNR = −5 dB

Figure 11. The average error for various PD locations with different noiselevels.

Table 1. Parameters of PD Models. Model τ1 (ns) τ2 (ns) I0 (mA) Q (pC)

1 4 12 6 50 2 2 10 5.4 50 3 1 5 11 50

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 17, No. 6; December 2010 1745

The performance of the proposed technique has been evaluated quantitatively through computer simulations. A PD pulse with additive noise was generated at various locations. The statistical results for different PD locations demonstrate that proposed technique has high location accuracy and its accuracy does not significantly affected by the PD pulse shapes. Further investigations will be done on in-service power cables at site.

APPENDIX Figure A.1 depicts the geometry and physical data of a 20

kV underground cable. The metallic sheath is considered as the return path in the EMTP simulation.

r1 = 11.85 mm; r2 = 18.15 mm r3 = 19.70 mm; r4 = 22.00 mm Inner Insulation εr = 2.3 (XLPE) Outer Insulation εr = 8.0 (Extruded PVC) All relative permeability μr = 1.0 Core: Aluminum with resistivity = 2.82 x 10-8 Ω.m Sheath: Copper with resistivity = 1.72 x 10-8 Ω.m

Figure A.2 shows the frequency-dependent impedances of the cable core-sheath. Note that these impedances are independent on grounding connections [12].

ACKNOWLEDGMENT This research work was supported by the Abu Dhabi Gas

Industries Ltd. (GASCO). The authors wish to gratefully acknowledge their support.

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[14] Z. Du, P. K. Willet, and M. S. Mashikian, “Performance limits of PD location based on time-domain reflectometry”, IEEE Trans. Dielectr. Electr. Insul., Vol. 4, pp. 182-188, 1997.

[15] M. Vakilian, T.R. Blackburn, R. E. James, and B. Phung, “Semiconducting layer as an attractive PD detection sensor of XLPE cable”, IEEE Trans. Dielectr. Electr. Insul, Vol. 13, pp. 885-891, 2006.

[16] A. G. Piersol, “Time delay estimation using phase data”, IEEE Trans. Acoust. Speech. Signal Process., Vol. 29, pp. 471-477, 1981.

[17] A.V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, Prentice Hall, Englewood Cliffs, NJ, Ch.12, 1989.

[18] N. Oussalah, Y. Zebboudj, and S. A. Boggs, “Partial discharge pulse propagation in shielded power cable and implications for detection sensitivity”, IEEE Electr. Insul. Mag., Vol. 23, No. 6, pp. 5-10, 2007.

[19] T.K. Abdel-Galil, A.H. El-Hag, A.M.. Gaouda, M.M.A. Salama, and R. Bartnikas, “De-noising of partial discharge signal using eigen-decomposistion technique”, IEEE Trans. Dielectr. Electr. Insul., Vol. 15, pp. 1657-1662, 2008.

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Figure A.2. (a) Resistance, (b) reactance, and (c) susceptance of cable.

Figure A.1. Cable geometry used in the simulation.


Redy Mardiana (M’02) received the B.E. and M.E. degrees from Bandung Institute of Technology, Indonesia in 1992 and 1997, respectively, and the Ph.D. degree from the Osaka University, Japan in 2002. He served as a research fellow at the National Institute of Information and Communications Technology, Tokyo, Japan for two years (2002-2003). Since 2004 he has worked as assistant professor at the high voltage

laboratory, Department of Electrical Engineering, Bandung Institute of Technology. He served as the chairman of the 14th Asian Conference on Electrical Discharge (ACED), 2008. He joined the Petroleum Institute in January 2010. He has published more than 60 international journal and conference papers. His research interests include condition monitoring of high-voltage insulation and lightning detection and protection. He is a member of SAEJ, Japan.

Charles Q. Su (SM’91) received the B.Sc. degree from Huazhong University of Science and Technology in1969, the M.Sc. degree from Wuhan University in 1981 and the Ph.D. degree from the University of New South Wales, Sydney in 1990. He was a tests and operations engineer from 1970-1978, an Honorary Research Associate with the University of Western Australia in 1985 and a Lecturer at the University of New South Wales in 1990. From 1991 to

2001, he worked as a Senior Lecturer and Associate Professor at Monash University, Australia. He was also the Head of High Voltage and Condition Monitoring Group in the Department of Electrical and Computer Systems Engineering in charge of the HV Laboratory. In 2002, he took up the position of Chief Technologist in Singapore Power, the national electricity company of Singapore and worked for five years. He was also a Senior Fellow in Singapore National University in 1998, a Guest Professor at the Technical University of Denmark in 1999 and North China Electrical Power University, Beijing in 2000. Since 2007, He has been a Professor with the Petroleum Institute, Abu Dhabi. His main research interests include insulation condition monitoring, partial discharge detection, reliability-centered maintenance, fuzzy logic incipient fault diagnosis of electrical plant, high voltage insulation tests, high frequency modeling of transformer and generator windings, pattern recognition using artificial intelligence and teaching innovation in engineering education. He holds two Australian patents and has published around 150 journal and conference papers. He published a book (co-authored with Prof. R.E. James) in the IET Power and Energy Series. He is a member of the Institute of Engineering and Technology (Fellow), and CIGRE SC A2.

Documents

Partial Discharge Location in Power Cables Using a Phase Difference Method