A Frequency Domain Method for Partial Discharge Location in Underground Power Cables �

Redy Mardiana and Ahmad Fajar Firdaus

Department of Electrical Engineering, The Petroleum Institute PO Box 2533, Sas Al Nakhl, Umm Al Naar

Abu Dhabi, United Arab Emirates

�������—A frequency domain method to determine the location of partial discharges (PD) from one-end of underground power cable is presented in this paper. This method is developed based on the phase difference between the direct and reflected waves of a PD pulse. The phase difference as a function of frequency is obtained using the cross Fourier spectral density function. The defect in the cable can be located after implementing a phase unwrapping algorithm. Laboratory experiments using a model of a 3.3 kV, 50m underground cable have been carried out and the statistical results are presented as well. The comparison results with the time domain methods are also given to demonstrate the effectiveness of the proposed method.

Keywords-partial discharge; PD location; phase difference; cable insulation

I. INTRODUCTION

Partial discharge (PD) is a symptom of insulation status in power cables. Partial discharges are produced when a power cable containing insulation defects is stressed with AC voltage. The PD activity will gradually degrade and erode the insulating materials of a power cable and greatly shorten its lifetime [1]. Therefore, finding the defect sites is a powerful and useful tool for the maintenance and operation of power cables to prevent unexpected discontinuities of power system. The methods to pinpoint the defect can be based on the measurements from one or both ends of the cable. In the former case, the time-domain reflectometry (TDR) method is commonly used. The PD pulse is measured by a sensor connected to the cable end with the other end opened. This TDR method exploits the characteristics of the direct and reflected waves of a single PD pulse. Many studies which are directed towards the development of single-end PD locating systems have been reported [2-4]. In the latter case, the PD pulse is detected by two sensors, one at each cable end. The data acquisition from the sensors has simultaneous detection and sampling. Given the pulse propagation velocity and cable length, the PD location can be derived from the difference in time-of-arrival (DTOA) of the same PD pulse received by the sensors [5, 6]. In both cases, the estimation of time-of-arrival are carried out in time domain using pulse peak detection, 50% peak detection, threshold detection, cross-correlation, maximum likelihood, etc., [5-7], and the signal processing is performed in time domain.

The PD pulse generated at the defect site is characterized as a fast pulse having rise and decay time in the range of nanoseconds. This characteristic is not preserved when the pulse is travelling along the cable because of the frequency-dependent parameters of

the cable. These parameters cause attenuation and dispersion to the original PD pulse [5-7]. Attenuation is due to losses in the solid dielectric and the resistance of conductor and sheath. Normally, the attenuation severity increases with frequency. As a result, the PD pulse will lose its frequency content and its pulse amplitude is reduced. Dispersion is due to the different frequencies composing a PD pulse travel along the cable at different velocities; therefore, the pulse will spread in time domain. With increasing distance propagated, the pulse peak becomes smaller and lags further, i.e., the signal to noise ratio becomes low and the pulse rise time increases. These conditions affect the estimation of time-of-arrival because the determination of the point on the pulse where the time should be measured becomes more complicated. As a consequence, the time-of-arrival estimation becomes less accurate, resulting in inaccurate PD location estimation [7, 8].

This paper focuses on a method to locate the PD from one-end of the cable in which the estimation of the time-of-arrival of PD signals is not required. The signal processing of this method is carried out in the frequency domain. The PD location can be estimated from the phase difference between the direct and reflected waves of a PD pulse at the cable terminal. The cross Fourier spectral density function is applied to obtain the phase difference at various frequencies. After implementing a phase unwrapping algorithm, the defect can be located. This technique was first introduced by the authors in [9], where the scheme was verified by only computer simulation. In this paper, the proposed scheme is tested in the high voltage laboratory using the actual 3.3 kV, 50-m underground cable. The PD pulse from signal calibrator is injected at a defect location and its direct and reflected waves are measured at the cable end, keeping the other end open circuited. The statistical results along with the comparison with the time domain methods are also presented to validate the effectiveness of the proposed scheme.

II. PD MEASURING SYSTEM

In the laboratory experiments, the simplified PD measuring system to evaluate the phase difference method is shown in Figure 1. This system is basically the same as in the TDR method. The only difference is the signal processing of PD pulse. The PD instrument which consists of analog-to-digital (A/D) converter and personal computer (PC) is connected to the test cable at the measuring end A. The remote end B is left open.

The PD is simulated by injecting a narrow pulse at the defect location. This pulse is generated from signal calibrator. The defect is located at a distance from the measuring end [10, 11]. The measured signal is then digitized by the A/D converter. The recorded PD signal stored in the PC, denoted as ��� , contains the PD pulse and additive noise (such as environmental, electronic, etc). The digital signal processing is carried out in the PC.

III. PULSE SEPARATION

After A PD at the distance 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 remaining one 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 2(a). 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 ���� , where ��isthe cable length. The arrival time interval between the direct and reflected waves is given by

2 1

2( ) (2)

� � � ���

� � � �

where �� is the arrival time of the direct wave, �� is the arrival time of the reflected wave, and � is the propagation velocity of the cable.

In the proposed technique, it is necessary to separate between the direct and reflected wave before the phase difference can be derived. Let ��� ��� be the maximum traveling time for a pulse to travel from cable end A to end B. The recorded PD signal ��� is then divided into two windows and each window has a length of � as shown in Figure 2(b). The first window contains the direct wave denoted as ���� ,while the second window contains the reflected wave denoted as ���� �� The new arrival time interval between the direct and reflected waves is now given by

2 1 . (3)� � � �� � � �

Inserting equation (2) into equation (3), the new arrival time interval becomes

2. (4)

� ���

� �

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

IV. 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 ��� must be separated before the calculation of phase difference is carried out.

��� ����������������������

Consider ���� as the time-domain direct wave and ���� as the time-domain reflected wave. Assuming a total record length of � for each wave, the signals in the frequency domain is derived using the Fourier transformation (FT) [12], as shown below:

2

1 1

0

2

2 2

0

( ) ( )

( ) ( ) . (5)

�� �

�� �

! � � " �

! � � " �

�

�

�

�

�

�

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

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.

12 1 2( ) ( ). ( ) (6)# ! ! ��

where * denotes the complex conjugate. The #��� will be a complex number such that

( )

12 Re Im 12( ) ( ) ( ) ( ) (7)� # # �# # " �� �� � �

where

1/ 22 2

12 Re Im

Im

Re

( ) ( ) ( )

( )( ) arctan . (8)

( )

# # #

# #

�

� �

� � � � �

� �

The term ��� in equation (8) corresponds to the phase difference between signals ���� and ���� . This phase difference is a function of frequency .

The relation between the phase difference and the arrival time interval �� is expressed as

( ) 2 . (9) � �� � �� � � � �

Replacing ���with equation (4), we obtain

2( ) 2 . (10)

� �

� � �� � �

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

1 ( )( ) . (11)

2 2

� �

��

� �� �� �

� �

There are two alternatives to obtain the final estimate of PD location ̂ . The first alternative, the estimated PD location can be obtained from the mean value of � . The second alternative, the estimated PD location can be obtained using a linear regression. This regression is used to obtain the slope (gradient) of the phase difference given by

� )(��� (12)

Then from equation (11), the final estimate of PD location becomes

).2

(2

1ˆ���� �� (13)

��� $%�&'����� ������������

Figure 3 shows the flowchart of the PD location technique based on the phase difference method. The PD signal is

received by the instrument. The signal is then digitized by the 8-bit A/D converter. The output from the A/D converter is the recorded PD pulse ��� � 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 ���� and the second window contains the reflected wave ���� ��Both the direct and reflected waves are transformed into frequency domain signals using the Fourier transformation (FT). The output of this transformation is !�� and !�� for the direct and reflected waves, respectively. The cross Fourier spectral density is obtained using equation (6), while the phase difference ��� is obtained using equation (8). Up to this point, the phase difference is wrapped in the interval of [-�, �]radian. Next, the phase unwrapping algorithm is employed to remove the discontinuities that appear in the phase difference. The simple and popular phase unwrapping algorithm can be found in [13]. The estimate of PD location as a function of frequency � is calculated using equation (11). The final estimate of PD location ̂ can be obtained from either the mean value of � � or the linear regression as written in equation (13)��

V. EXPERIMENT AND RESULTS

To evaluate the performance of the proposed technique, laboratory experiments are carried out. The cable model has a length of � = 50 m and is a 3.3 kV underground cable with cross linked polyethylene (XLPE) insulation. The cable is three-core copper conductor. Each core has 150 mm2 diameter and 2.4 mm insulation thickness. Only one core conductor is

Figure 3. Flowchart of the PD location using phase difference method.

used to test the PD location. The core conductor of the cable is excited by the signal calibrator at 20 meters from one end (or equivalent to 30 meters from another end). In other words, two PD locations can be analyzed (i.e., = 20 m and = 30 m). The signal calibrator can be adjusted to generate a certain charge. Here, two PD charges; 50 pC and 1 nC are simulated. The cable sheath is grounded and assumed to be return path, so that the PD pulse travels along cable conductor and sheath. The propagation velocity is calibrated beforehand by injecting the calibration signal at the 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 � = 1.852 �108 m/s. The digitizer (A/D) has an 8-bit vertical resolution and sampling frequency of 100 MHz. The time window � is equal to 50 m / 1.852 �108 m/s = 0.27 �s or 27 samples. This laboratory test is very close to a practical PD measurement system.

(�� ��������������%)����

For example, a PD signal with a charge of 1 nC is injected at location equals 20 m from the measuring end. Figure 4(a) shows total recorded PD pulse. Only the first two waves are considered for the analysis. 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 �; (b) the following time window � is allocated to cover the reflected wave. Therefore, the reflected wave may not need to

be identified and distinguished from the noise. It is important to note that it is not critical to determine the starting point of the time window �, because the starting point can be shifted to any point without affecting the PD location results. However, the length of time window must be calculated beforehand. Figure 4(b) and 4(c) show the direct wave and the first reflected wave, respectively, 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 5. The phase difference is wrapped in the interval of [-�, �] radian and the fringes are clearly seen mainly at low frequencies as shown in Figure 5(b). For the higher frequencies (e.g., above 20 MHz), the phase difference seems to be scattered. This is because the cross Fourier spectrum is relatively low or very low signal-to-noise ratio in that frequency range. Therefore, hereafter only the frequencies below 20 MHz are used to estimate the PD location.

The phase unwrapping algorithm is then applied to the phase difference� Figure 6(a) shows the unwrapped phase difference for the frequency range up to 20 MHz. It can be seen that the unwrapped phase difference has a tendency to increase linearly as frequency increases. The slope � of phase difference using a linear regression is indicated. The estimated slope is � equals 0.259 radian/MHz. Figure 6(b) shows the estimate of PD location as a function of frequency� from equation (11). The final estimate of PD location using the mean value of � is ̂ = 21.06m, meanwhile if it is using the

linear regression is ̂ = 21.18 m.

From the above result, it can be concluded that the phase difference method does not need to determine the point on the

−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6−0.5

0

0.5

1

1.5

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0

0.5

1

1.5

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plit

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it)

0.1 0.15 0.2 0.25 0.3−0.5

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Time (μs)

(a)

(b)

(c)

Figure 4. (a) The recorded PD pulse train, (b) the direct wave after pulseseparation, and (c) the first reflected wave after pulse separation.

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

Frequency (MHz)

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Frequency (MHz)

Ph

ase

Diffe

ren

ce

(ra

dia

n)

(a)

(b)

Figure 5. The output of cross Fourier Spectral density function; (a) the crossFourier spectrum and (b) the phase difference.

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.

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The performance of the proposed technique is evaluated quantitatively. A total of 5 PD signals at a given location and charge is generated. For the given PD location and charge, the mean location and average error are calculated. The average error of PD location is defined as

1

1 ˆAverage Error (14)�

��

� �

� ��

where is the true PD location, ̂ is the estimated location, and � = 5.

The results from the proposed method are compared with those from three time domain methods, which are based on the time-of-arrival measurements:

a. Peak detection: The highest point of the initial PD pulse is taken to mark the time-of-arrival.

b. 50% Peak detection: Similar to the peak detection, but the time when the initial pulse reaches 50% of its peak amplitude is taken to be the time-of-arrival.

c. Threshold detection: The time at which the PD pulse exceeds a certain threshold is marked as the time-of-arrival. The threshold level is chosen relative to the noise level, making it always as low as the noise permits without too many false triggers. For comparison, here the threshold level is set 10% from the peak.

The statistical results and their comparison of PD location for different PD locations and charges are shown in Table 1. The location estimate by means of the phase difference method consists of using the mean value (PDM-MV) and the linear regression (PDM-LR). The table shows that the phase difference method has better accuracy in which the location estimates are closer to the true locations. Figure 7 shows the related average errors by various methods. The location error improves as the PD site is further away from the measuring end. This improvement is consistent with the results from computer simulation [11, 12]. It is clearly seen that the phase difference method has lower errors indicating that the proposed method has better performance compared to the time domain methods. In general, the phase difference method with the mean value (PDM-MV) has better location accuracy than the method with the linear regression (PDM-LR).

Table 1: Estimated PD location by various methods for different defect locations and charges.

True Location

Charge Estimated Location (m)

Peak 50% Peak Threshold PDM-MV PDM-LR

20 m 50 pC 21.11 21.48 21.30 20.89 21.081 nC 21.30 22.04 21.67 21.08 21.20

30 m 50 pC 30.19 30.56 30.93 30.45 30.591 nC 30.37 30.56 30.93 30.27 30.26

VI. CONCLUSIONS

A frequency domain analysis method for determining the location of 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.

Figure 7. The average error by various methods for different defect locationsand charges.

0 5 10 15 200

1

2

3

4

5

6

Frequency (MHz)

Ph

ase

Diffe

ren

ce

(ra

dia

n)

0 5 10 15 2017

18

19

20

21

22

23

Frequency (MHz)

Lo

ca

tio

n E

stim

ate

(m

)

Unwrapped Phase

Linear Regression

Calculated Location

True Location

(a)

(b)

Figure 6. (a) The unwrapped phase difference along with its estimatedslope from linear regression; (b) the estimate of PD location as a function offrequency. The dashed line indicates the true PD location at = 20 m.

Laboratory experiments have been carried out to evaluate quantitatively the performance of the proposed technique. The technique has been applied to locate PD locations using a 3.3 kV, 50-m underground cable. The PD pulse was generated at different locations and charges. The statistical results demonstrate that proposed technique has good location accuracy and it is found that the accuracy does not significantly affected by the PD charges. The comparison results with time domain methods show that the proposed method has better location accuracy. In general, the phase difference method with the mean value (PDM-MV) has less error than the method with the linear regression (PDM-LR).

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