estimating the location of partial discharges in cables

44 IEEE Transac t ions on E lec t r i ca l In su la t ion Vol. 27 No. 1, F e b r u a r y 1002

Estimating the Location of Partial Discharges in Cables

J. P. Steiner,, P. H. Reynolds Biddle Instruments, Blue Bell, PA

and w. L. Weeks Purdue University, School of Electrical Engineering,

West Lafayette, IN

A B S T R A C T There are seve ra l a l t e r n a t i v e t e c h n i q u e s that c a n be used to estimate the loca t ion of partial d i scha rge in cables; however , c e r t a i n t echn ica l obs t ac l e s need to be o v e r c o m e before accep- t a n c e of this t y p e of testing b e c o m e s widesp read . A rev iew of the t h e o r y of s ignal propagation in p o w e r cab le s is presented a l o n g w i t h i t s relation to p a r t i a l d i scha rge site location. F u n d a m e n t a l limitations affect the de tec t ab i l i t y and loca t ion a c c u r a c y of p a r t i a l discharges i n p o w e r cables. The sources of these errors are discussed a l o n g w i t h methods that min imize their effects. The a d v a n t a g e s and d i sadvan tages of a l t e r n a t i v e methods for loca t ing p a r t i a l d i scha rge sites are presented along w i t h a ca l ib ra t ion method that i m p r o v e s the a c c u r a c y of these methods.

1. I N T R O D U C T I O N

NDERGROUND power cables are used extensively for U power delivery and many of these cables have been in service for extended periods of time. The most widely used insulation in these cables is polyethylene and this material is known to degrade as it ages. One recognized aging mechanism in polyethylene cables is water treeing; sometimes, near the end of the life of a cable, a water tree changes into a n electrical tree, leading to rapid failure of the insulation. Various methods have been proposed for detecting water trees in situ. A correlation has been found between the dielectric losses of aged cables and their reduced breakdown strength [l]. High field ac loss a t harmonic frequencies of the excitation also appear to be correlated in wet, aged cable specimens [Z]. Japanese researchers have developed on-line measurement methods to monitor the presence of water trees [3, 41. It has been

predicted that low level partial discharge (PD) may be present in water trees even before they convert into electrical trees [5]. The presence of low level electrical activity in water trees was recently reported [6].

During the manufacture of power cables the final step is a quality control procedure in which voltage is applied to the completed cable and PD is measured. If the measured PD level is above a prescribed limit, the cable is rejected. It would seem that a similar, in s i tu test would be appropriate to determine whether the aged cable has reached the end of its service life. Unfortunately, once an electrical tree becomes active there is only a brief time available to detect it before the cable fails; therefore, it is extremely difficult to implement a testing program which might detect electrical trees prior to failure.

During the past decade, technology has become avail-

0018-9367 $1.00 @ 1992 IEEE

IEEE Transactions on Electrical Insulation Vol. 27 No. 1 , February 1992 45

able for detecting and locating low level P D in power cables. However, the research programs studying aging mechanisms in polyethylene cables have not taken full advantage of this new technology and so it is not c1ea.r whether measurable P D is present in aged cables. As the technology associated with P D detection and location in power cables matures, various difficulties are being over- come and fundamental limitations are becoming clear, While it is not presently certain whether measurable P D is actually present in aged power cables, the minimum detectable levels are becoming defined. In the following, cable characteristics which limit the performance of the measurement are discussed.

2. CABLE PROPAGATION CHARACTERISTICS

NY measurement is ultimately limited by the noise A corrupting it. Though the noise imposes the fundamental limitation, it is the characteristics of the cable and of the measurement circuit which determine the levels of noise which are intolerable. Most P D location methods use the broadband P D pulses received a t one (or both) of the cable terminations, and the performance of the methods depend on the fidelity of these signals. Howev- er, coaxial power cables are optimized for power delivery, not signal propagation, consequently the measured signals have poor fidelity. The poor signal fidelity, due to the propagation characteristics of the power cable, places limits on the performance attainable by these methods.

2.1 ATTENUATION

The primary cause of signal distortion in coaxial power cables is the frequency dependent loss caused by the semiconducting material used for the strand and insulation screens. The attenuation in the cable ~ ( w ) , as a function of frequency, is given by

.(U) = exp[-a(w)z] (1)

where z is the length of cable through which the signal travels and a ( w ) is the frequency dependent attenuation parameter. At high frequencies this attenuation becomes severe and, as shown in Figure 1, most of the high frequency energy is lost in longer cables. This high attenuation of the signals in longer cables imposes a limit on the sensitivity of P D measurements.

There are some fundamental limitations to the measurement of P D which can be stated in terms of a relationship between the bandwidth and the attainable sensitivity [7]. These results can also be stated in terms of a

0

-0.001

6 z 2 -0.002

I -0.005

-0.006 ' ' ' 1 1 1 1 1 1 1 ' ' L * , ' L " ' "-"" ' ' 1 1 1 1 1 1 1 ' ''A id io4 16 io6 io7 io8

Frequency, Hz

Figure 1. Loss characteristics of an XLPE, 15 kV, 1/0 coaxial power cable with a tape shield. Data obtained from measurements of the attenuation on a 505 m sample using sinusoidal excitation.

fundamental lower bound on the estimation of the charge. The bound is referred to as the Cramer-Rao lower bound and is expressed in terms of the minimum variance of any estimator used to estimate the charge in a P D pulse. Whenever a measurement is made, noise limits its ultimate sensitivity and the Cramer-Rao lower bound de- fines this ultimate limit in terms of the variance of the noise corrupting the estimate. The variance given by the Cramer-Rao lower bound can be realized by an optimum estimator; however, it is usually difficult, if not impossible, to determine the optimum estimator.

To calculate the Cramer-Rao lower bound it is necessary to make assumptions about the statistical nature of the noise corrupting the measurement. If the noise is from a stationary, Gaussian random process with power spectral density N ( w ) , then the bound on the variance of the estimate of the amplitude is given by

where a is the unknown, nonrandom amplitude of the unit amplitude pulse s ( t ) , S(w) is the Fourier transform of s ( t ) , and ii is the estimate of a [8]. The result in Equa- tion (2) can be interpreted as the reciprocal of an inte- grated signal-to-noise ratio (SNR). The amplitude is the appropriate parameter to estimate because an estimate

46 Steiner et al.: Partial Discharges in Cables

of the charge, on the basis of a unit charge pulse, reduces to an estimate of a scale factor (amplitude). The Gauss- ian noise assumption is appropriate since the predomi- nant types of noise corrupting the measurement (the thermal noise in the system and AM band radio broadcasts) are adequately modeled as Gaussian. Furthermore, the Gaussian assumption makes the calculation of the lower bound tractable. The bound can be calculated if the amplitude is considered random but this requires making assumptions about the statistical nature of the PD amplitude. For purposes of this exposition the amplitude will be considered fixed a t the minimum detection level because this is the value of interest.

The result in Equation (2) applies directly to single input measurements. Multiple input systems, such as a balanced system, are capable of eliminating external interference. For a balanced system the result still applies, but the noise term in Equation (2) is the residual interference due to unbalance plus the thermal noise.

The actual quantity of interest is the charge, and Equa- tion (2) can be restated in terms of a lower bound on the estimation of the charge [9]. Following Boggs and Stone [7], the PD pulse is assumed to have a Gaussian pulse shape

(3) t 2

s ( t ) = aexp[--1

where a is the amplitude to be estimated. The Gaussian assumption for the pulse shape should not be confused with any statistical assumption about the PD, it is merely a convenient mathematical tool for expressing the results in a closed form.

2 To”

For purposes of analysis and comparison to the true charge, a dc coupled system is assumed since the true charge cannot be exactly calculated unless the PD current waveform contains its dc component. This can be seen from the definition of charge

00

Q = / i(t) d t = I (w) lw=0 (4) -W

which is the dc term of z(t)

The charge in this calculation is assumed to be the actual charge and not an apparent charge. While this is unrealistic from a practical standpoint, discussing the lower bound in terms of an apparent charge unnecessar- ily complicates matters. Since the relationship between the charge and the apparent charge is a scale factor, the results are still valid. Inclusion of this scale factor simply reduces the sensitivity by the amount of this scale factor. Also, so that the result can be easily expressed in closed

50

8 f 30 v1

3 a c

10 8

-10 -10 0 10 20 30

Input SNR, dB

Figure 2.

Output S N R vs. input S N R of L M M S E , autocorrelation, and peak value charge estimators.

0.9

Frequency, Hz

Figure 3. Ratio of velocity of propagation in an XLPE, 15 kV, 1/0 cable to the natural velocity of propagation in polyethylene. Data obtained from measurements of the delay on a 505 m sample using sinusoidal excitation.

form, the noise will be assumed to be white Gaussian noise, i.e., only thermal noise is present with value No/2. The charge in the pulse can be calculated to be

(5)

IEEE nansactions on Electrical Insulation Vol. 27 No. 1 , February 1992 47

where Zo is the characteristic impedance of the cable and the rms duration of the pulse is given by

The output SNR, SNR,,t, of the estimator is given by

E(&)’ a’€, SNRout = - -- - var(8) N0/2 (7)

where I, is the energy of the unit amplitude pulse. The noise N0/2 is defined as kT,, where k is Boltzmann’s constant and T,, is the equivalent noise temperature of the entire system. The effective noise temperature includes contributions to the thermal noise from the cable, measurement impedance and amplifier. Using these assumptions, the minimum measurable charge is given by

where B is the rms bandwidth of the P D pulse and is given by

( 9 )

The term SNROut, is a subjectively chosen quantity that describes the quality of the measurement in terms of a minimum acceptable SNR.

This calculation assumes a matched impedance load on the cable so that maximum energy is transferred from the cable to the detector. Most commercially available P D detectors have circuit topologies that reduce the available signal level. This loss of signal energy can also be described by a scale factor which, when included, further reduces the sensitivity.

As an example of the application of Equation (8), consider a 35 52 power cable having a length which limits the pulse bandwidth to 5 MHz. Furthermore, assume that the system has a noise figure of 4.0 so that N0/2 = 32x lo-’’ and that a measurement result with SNRout = 20 d B is the minimum acceptable result. Given these values, the minimum charge that can be measured is 0.014 pC. This particular result represents the theoretical minimum charge that can be measured if the optimum estimator is used in a 3552, matched impedance system.

The result in Equation (8) should only be viewed as approximate since it assumes white noise and a Gaussian pulse shape. In practice, the noise corrupting the measurement is not white and the propagation characteristics of the cable determine the shape of the pulse. However, using Equation (2) it is possible t o calculate numerically more precise lower bounds if accurate models (or estimates) are used for the pulse shape and noise.

Even if Gaussian noise is assumed it is still difficult to find a n optimum estimator for PD. The difficulties with determining an optimum estimator are related to the available information about the received signal. To determine the optimum estimator, it is necessary to know the exact propagation characteristics of the cable, the length of cable through which the PD pulses have traveled, the exact arrival time of the P D pulse, the statistical distribution of the charge and the statistical characteristics of the Gaussian noise. None of this information is available and either has to be estimated or assumed. Imprecise information about these quantities will cause additional loss in performance, however, this loss will be moderate since estimators can be found which are nearly optimum.

One possible estimator, that is nearly optimum, is the linear minimum mean square error (LMMSE) estimator of the amplitude [9-111. This particular estimator is based on a linear filter which is optimum in the class of all linear estimators. The filter is given by

where N(u) is the power spectral density of the noise, ri is the arrival time of the i t h pulse with amplitude ai and the superscript * means the complex conjugate. The scale factor 77 is given by

- where aa is the mean square value of the random variable ai that is being estimated. S(U) is, in essence, the Fourier transform of the propagation characteristic of the cable because the P D pulse, at its origin, is essentially a delta function, which means that the cable determines the shape of the received pulse. The estimate of a; is then determined as

6; = F- [X (U) H o p t (U)] It =o (12)

where F-’ refers t o the inverse Fourier transform. The received PD, pulse X(U), corrupted by noise is given, in the time domain, by

z ( t ) = aiS( t ) + n(t) (13)

If the noise is Gaussian then the LMMSE estimator is the optimum estimator. However, even if the noise is not Gaussian, this estimator is the optimum linear estimator. The aforementioned difficulties associated with estimating the amplitude still apply to this solution since this estimator requires a significant amount of unknown information.

48

HIGH VOLTAGE CABLE

9 - b

- COUPLER

Figure 4. HV cable termination. Typical terminations are matched to the impedance of the cable under test and have a Gaussian high-pass characteristic.

The variance of the estimate is not the only measure of error that is important. Bias errors in the measurement can also be important and are defined as

B(6) = E(" - a) (14)

where E is the expectation operator, a is the actual value of the quantity being estimated, and 6 is its estimate. Bias errors in estimates are distinct from the variance of the estimate. The variance describes the random fluctu- ation of the estimate while the bias describes the nonrandom, fixed error. In this case, the bias error can take the form of an unwanted scale factor. For example, an incorrect choice of the pulse shape (cable characteristics) can cause a scaling error in the estimate. This implies that the appropriate S ( w ) needs to be used in the filter described by Equation (10) and this requires that the solution be adaptive in the sense that S(w) must correspond to the particular length of cable through which the P D pulse traveled.

While the LMMSE estimate is a near optimum estimator of the charge i t requires a complicated and numerically intensive computation. A simpler method that yields good results can be used. This second method, the autocorrelation estimator, is an ad hoc technique and is very simple to implement [ll]. This technique is based upon a maximum likelihood argument used in a different context, and it should be noted that this estimator is not a maximum likelihood estimator for this case [9]. The estimate is formed by evaluating the autocorrelation function a t zero delay, removing the bias due to the noise, and taking the square root of the result. The value of the

Steiner et al.: Partial Discharges

time autocorrelation function a t zero delay is

TI2

y = / 2 ( t ) d t - T I 2

in Cables

defined by

(15)

where the P D pulse is assumed to be contained in the interval -T /2 , T / 2 .

It is convenient in this analysis to omit the 1/T factor from the usual definition of the time autocorrelation function. The resulting value will be an estimate of the sum of the noise energy and the energy in the PD pulse. Taking the expected value yields

E(ylai) = ai&, + Tu2 (16) where u2 is the variance of the noise and is the energy in the signal pulse s ( t ) . The term Tu2 is an unwanted bias term and is removed from the calculation before further processing. The final step is t o calculate the square root of the result after removal of the bias. The estimate of the amplitude is then

where acal ,b is a reference level obtained through calibration. This estimate also has a bias. The bias is equal to the square root of the attenuation of the energy caused by the cable losses.

The measurements in Figure 2 illustrate the relative performance of three different estimators obtained using an eight bit quantizer, a P D calibrator, and a variable power noise source. The measure of performance is the SNR defined as

In these measurements the rms error is due only to the variance of the estimator because the digitizer operated in its linear region. The input signal was maintained a t a fixed level of 10% of the full scale input level of the digitizer. The input noise was broadband and was ad- justable so that the input SNR could be varied between -10 and 30 dB. Figure 2 shows the effectiveness of both the LMMSE and autocorrelation estimators in noisy measurements while the peak value estimator, defined as the peak of the pulse, tracks the input SNR. The autocorrelation estimate performs better than the LMMSE estimate a t low SNR because the pulse arrival time also must be estimated.

2.2 DISPERSION

In addition to the high attenuation suffered by a PD pulse, as it propagates along the cable, its phase also

IEEE Transactions on Electrical Insulation Vol. 2 7 No. 1, February 1982 49

becomes distorted. The phase change @(U) caused by propagation through the cable is given by

@(U) = exp[iD(w)z] (19)

where z is the length of cable through which the signal travels. The frequency dependent phase parameter P ( w ) determines the propagation velocity of the cable. If the phase parameter is strictly a linear function of frequency, then the cable is considered t o be a linear phase channel and there is a single value for the velocity

1

and is called the natural velocity of propagation. The constants C and L are the cable’s per unit length ca- pacitance and inductance, respectively. For power cables the phase function deviates from this ideal behavior and the cable is considered to be dispersive. Pulses traveling through a dispersive medium become distorted even in the absence of any frequency dependent attenuation losses. This distortion further diminishes the accuracy of modeling PD pulses as Gaussian pulses.

The phase distortion occurs because the different frequency components of the P D pulse travel a t different velocities. The effect of this dispersion is to spread the pulse in time, making i t difficult to choose a reference point on the waveform that can be used to measure the pulse’s arrival time. This dispersive property also makes it difficult to assign a simple pulse propagation velocity to power cables. A ratio of the velocity of propagation c in a power cable to the natural velocity of propagation v in polyethylene as a function of frequency is shown in Fig- ure 3. The change in velocity, over the frequency range shown, is quite dramatic and is influenced strongly by the properties of the semiconducting shields. The dispersive character shown in Figure 3 is for a specific cable; however, similar behavior should be expected in other power cables and has been theoretically predicted [12].

Some qualitative comments can be made about the propagation characteristics of power cables based on the work in [12]. For frequencies < 15 kHz, the surrounding ground has a dramatic effect on the propagation characteristics. For frequencies > 15 kHz, the ground return has relatively little influence. The propagation velocity is nearly flat, to within a few percent, for frequencies in the range 0.1 to 50 MHz. At frequencies > 100 MHz the velocity rapidly approaches the natural velocity of the dielectric. The work in [12] considered a cable with a solid shield. Many power cables have helically wound concentric neutrals that only approximate a full shield. In this case, significant energy propagates in the region external to the concentric neutrals (ground), even a t the

higher frequencies, causing further distortion of the signal. These qualitative remarks suggest that P D location methods should only use frequencies in excess of 100 kHz to reduce the errors due to dispersion. The da ta of Fig- ure 3 bear this out with only a 3% change in velocity over the 0.1 to 10 MHz range.

Other factors can influence the propaga.tion velocity of power cables. In [12] it was found that the composition of the semiconducting material used in the shields is not uniform along the length of the cable. Since the velocity is heavily influenced by the semiconducting shields, this adds the further dimension that the velocity is not uniform along the length of the cable, even for a single frequency. Other factors that can cause errors are the temperature dependence of the permittivity of the insulation and more significantly, the temperature dependence of the semiconductor’s properties. These can cause errors if time delay measurements are made a t one temperature and interpreted using velocities determined a t another temperature. However, since power cables are usually buried a t a depth where temperature fluctuations are small, this effect is not significant. An additional effect occurs when power cables age. Water is often ab- sorbed into the dielectric and this absorption is not uniform along the length or through the cross section. The permittivity of water, at room temperature, is M 80 and can significantly alter the equivalent permittivity of the cable, again affecting the velocity. Although these effects are relatively minor, in combination they can amount to a location error of several meters which is unacceptable. Large errors can occur if the cable system has different types of cable spliced in along its length making the velocity change in a stepwise fashion.

3. SIGNAL PROPAGATION

UNDAMENTAL to the methods used to locate P D in ca- F bles is the modeling of the pulse propagation along the conductors. A thorough understanding of propagation in cables is necessary t o design algorithms to estimate the parameters of the P D pulse. An effective model is determined by modeling the P D as a point current source exciting the cable a t some interior location. To determine the equations for propagation, consider this point current source to be located a t a position z = c on a transmission line of length L . .This transmission line has a characteristic impedance Zo and is terminated by arbitrary impedances Z1 and Zz located a t position z = 0 and z = L, respectively. There are two solutions for pulse propagation generated by a n interior current source [9]. The two solutions apply to the respective regions on either side of the current source located a t z = c. The Fourier


transforms of the solutions for the respective regions are in Region 1

direct term and the second term in the brackets is referred to as the reflected term.

The signal parameter of interest is the position within the cable from which the P D emanates. The parameter

(exp['Y(w)(z - + exp[-?'(w)(z + 2)1) estimates that yield this quantity are called delay estimates and are estimates of the times of arrival of the pulses due to the PD. More specifically, the required pa-

I(-w)ZO(-w)(l + Pz(-w) exp[27(-w)(z - L)1) 2(1 - Pl( -w)PZ(-w) exp[-27(-w)Ll)

Vl(-w,.) =

(21) and in Region 2

(exp[-r(-w)(z - .)I+ P d W ) exp[--r(-w)(z + 2 - 2L)H

The term I ( w ) is the Fourier transform of the P D current pulse exciting the cable. The quantities p l ( w ) and pz(w) are the voltage reflection coefficients a t the ends of the cable defined by

and

rameter estimates are the time delay of the pulse and its first reflection.

To understand the estimation procedure, consider a simple case of lossless, nondispersive propagation with a matched impedance a t the receiving end of the cable. The matched impedance termination a t the receiver is not necessary if only the first two arriving pulses are used. However, to simplify the explanation, a matched termination is assumed. In this case the cable is a linear phase system with the propagation phase function given by

(27) 1

P(w) = --w = m w

(24) where the velocity U is constant. The noiseless received . . . .

In general, the characteristic impedance of the cable is a function of frequency, as are the termination impedances. The propagation parameter ~ ( w ) is also, in general, a

signal s ( w ) , due t o a P D a t z = z is described in the frequency domain as

(28) I(W)ZO

function of frequency and is given by S ( W ) = V l ( W , O ) = - 2 Hl(-w)

= 4 w ) + iP(-w) (25)

The frequency dependent attenuation parameter a ( w ) ,

The linear filter H l ( w ) describes the propagation through the and is given by

determines the loss characteristics of the cable and is re- sponsible for the high frequency losses in the cable. The

H l ( w ) = exp[-iwz/v] + exp[-iw(2L- x ) / v ] (29)

frequency dependent phase parameter P ( w ) , determines the propagation velocity of the cable.

The equations for the two regions provide a complete solution including all reflections. Most algorithms use only the first few reflections to locate P D sites. To convert the complete solution into an approximate solution, Equation (21) and (22) expanded into a series to retrieve the first few reflections. The case of most interest is the voltage VI a t the termination position z = 0 when the reflection coefficients are p1 = 0 and pz = 1. This corresponds to an instrument measuring the voltage a t the position z = 0 due t o a P D located a t z = c on a cable terminated in its characteristic impedance a t z = 0 and left open circuited at the other end z = L. This same solution applies to the first two terms of the expansion when the instrument end also has a reflection coefficient of 1. The solution is given as

where L is the total length of the cable and c is the length of cable between the receiver and the P D site. This Equa- tion is a special case of the solution given in Equation (21) and has a simple explanation. Each of the exponential terms corresponds to a time delayed impulse with the time delay corresponding t o the propagation delay from the P D site to the receiver. This is easily seen by calculating the inverse Fourier transform of H l ( w ) which is

F 4 [ H 1 ( w ) ] = 6 1- 7 + 6 [1- - 2 L - 2 ] (30)

If the digitizer begins recording a t the instant that the P D pulse occurs, then the first impulse (delta function) is the direct arriving pulse and arrives a t time given bv

2

U T1 = -

The second impulse is the reflected term that arrives a t

where the characteristic impedance is considered real V a l -

ued. The first term in the brackets is referred to as the The location of the P D site is deduced from an estimate of the time difference, AT between the direct pulse and


the reflected pulse and is given by dispersion. It can be shown that dispersion causes a bias error in many of the delay estimators since these estimators make assumptions about the phase characteristics of the cable such as a propagation velocity that is constant for all frequencies which is not true for power cables. The

(33) 2 ( L - x)

AT = 1-2 - TI = - U

The position of the P D site is then calculated as 3 bias is defined as

B[?] = E(? - T ) (35) L - a = :VAT 2 (34)

The position calculated in Equation (34) is the distance of the PD site from the open circuit end of the cable.

where ? is the estimate of the delay. Without dispersion the P D pulse is simply displaced in time by an

is present, a small amount of phase delay is added that manifests itself as an additional small displacement of the pulse in time. Dispersion distorts the pulse so it is difficult to describe precisely how the pulse is displaced, but it is often seen as a shift in the location of the pulse’s

The cable propagation velocity is the only piece of in-

is not known, it can be measured by performing a calibration experiment t o determine the electrical length of the cable which is then used to calculate the propagation velocity based on the known length of the cable.

formation required to locate the P D site. If this quantity amount to the propagation When dispersion

4. LOCATION METHODS

HERE are a variety of time delay estimators which T can be used to locate P D in cables [9,13-161. These techniques range from very simple level crossing, time of arrival estimators [15] to more sophisticated signal subspace methods [9] , nonlinear maximum likelihood techniques [14] and generalized cross correlators [9 ,13,18] . Most methods for locating P D in cables require significant numerical computation. The main disadvantages of these techniques are that they require sophisticated computer hardware to compute the results and only a small portion (< 1%) of the available da t a can be processed. However, they are capable of combating noise and reducing the bias errors due to limited resolution. With this type of implementation it is theoretically possible to reach the fundamental lower bounds of the measurement performance.

One of the most effective methods is the maximum likelihood technique presented in [14]. This technique is capable of significantly reducing resolution bias errors in measurements of P D sites located near the ends of a cable. It is still limited by this bias but performs significantly better than other methods. A similar technique, the signal subspace method [9], has similar capabilities and asymptotically is equivalent to a maximum likelihood method [17]. The main drawback of these techniques is the enormous computational effort required in their implementation.

Each of these methods has its particular strength such as simplicity of implementation or the ability to enhance the measurement. However, each of these methods suffers the same failing, a bias error in the delay estimate due to

peak, a tilting of the rising edge, and a more pronounced spreading of the trailing edge of the pulse.

4.1 LEVEL CROSSING METHOD

The simplest method for determining the time delay is to use the time a t which the received signal crosses some predetermined amplitude threshold (level crossing) [15]. The threshold is chosen t o be some small level near the zero baseline of the signal. A timer is started when the direct arriving pulse crosses the threshold and is then st.opped when the reflected pulse crosses the same threshold. The time difference is then translated into a location, using for example Equation (34). This method displays the measurement results as a histogram of the P D site locations. Since the P D pulses arrive a t random times, the histogram method effectively mitigates errors associated with multiple, closely spaced sites. The advantage of this technique is its simplicity; i t is very cost-effective to implement. Furthermore, this method has the advantage that results can be accumulated in real time without the need for time-consuming intervention by a computer to perform calculations.

Basically this is the same approach used in time domain reflectometry (TDR) when the operator views the pulses on the T D R screen and measures the time delays between pulses. The difference between this approach and TDR is that it is automated and that the T D R pulses are generated by the P D process rather than by the measuring instrument. This method has limited application because of the difficulty in determining the appropriate threshold for distorted, noisy, or unknown waveforms. If the signal is distorted with excessive ringing, the oscillations will cause false triggering of the timing circuits. If noise is


present, i t can cause false triggering of the timer, especially in cases where low level P D is measured. If two pulses are closely spaced and overlapping, the timer will begin counting but will not have a trigger to stop. The cable is dispersive and consequently neither the front edge of the pulse or the pulse shape is preserved causing further errors. In typical power cables, attenuation is heavy and thus the reflected pulse is often much lower in amplitude than the direct pulse. These nonideal propagation characteristics contribute to the difficulty of obtaining delay estimates using a predetermined amplitude threshold as a trigger reference for the two pulses. P D of both polarities occur a.nd the detection impedance is high pass in nature so each received pulse has components of both polarities regardless of the initial polarity. This further compounds the difficulties associated with implementing circuitry to respond properly to arbitrary polarities. The baseline, or some small level near i t , is an inappropriate reference point on the pulse waveform because any of these problems can cause large errors in the location estimate. In general, the peak of the pulse waveform is also an unsuit- able reference point on the waveform because of the shifts in the peak resulting from nonideal propagation characteristics. The basic difficulty associated with this method is the lack of a reference point on the pulse waveform that can be used as a time delay measurement reference.

This Equation has an impulse function a t the time origin and a t time delays symmetric about the origin. Auto- correlation functions always have their maximum a t the origin so the impulse a t the origin conveys no information. The location of the P D site is deduced from an estimate of the time delay r from the origin to either of the impulses symmetrically located about the origin

2(L - x) IT( = -

U (39)

The position of the P D site is calculated as

1 2

L - x = -u(rl (40)

and is the distance from the open circuit end of the cable to the P D site.

For best performance it is necessary that the receiving end of the cable be terminated in its characteristic impedance. A practical implementation of a matched termination for measuring P D is shown in Figure 4. There will always be unwanted reflections from the receiver because it is difficult to terminate a cable in a matched impedance when HV is present. However, using this circuit, it is possible to make the reflection coefficient a t the receiver small across the limited band of frequencies required for these measurements.

Autocorrelation provides excellent results for many sit- uations but has some failings. The impedance mismatch-

4.2 AUTOCORRELATION

One simple numerical method for locating P D in a cable is to calculate the autocorrelation function of the received waveform [9]. The time autocorrelation function Rss(r) is defined as

R s s ( ~ ) = - s ( t ) s ( t + T ) ~ T (36) T ' J where s ( t ) is the P D signal previously defined and T is the measurement observation time (record length). In the frequency domain Raa(r) is called the energy spectral density and is given by

j ' [ R s s ( 7 ) 1 =

J1(w)z~'2 (1 + exp[-2iw(L- x ) / v + exp[2 iw(~ - x ) / u ]

The term in the brackets is the magnitude squared of NI in Equation (29). This result is interpreted by calculating the inverse Fourier transform of the terms in the brackets giving

4 (37)

es a t the ends of the cable cause the autocorrelation function to be a superposition of the direct term, the first reflected term, and any secondary reflections. The delay term of interest will have contributions from all these reflections. The secondary reflected terms in the superposition are highly dispersed and have phase shifts incurred during reflection from the receiver. These secondary reflections cause the desired delay term to accumulate delay errors from the dispersion and phase shifts.

The received signal used in the calculation of the autocorrelation function has noise and the autocorrelation function of the noise superposes with the desired autocorrelation function. If the noise is wide-band thermal noise, the added term is concentrated around the origin and is of little consequence. When the noise is from external interference entering a t the cable terminations, the noise contributes terms a t delays corresponding to the cable ends. The contribution from the noise correlation function can obscure P D sites near the ends of the cable and if strong enough can obscure sites located far within the interior of the cable.

When PD is located near the end of a long power cable, the pulse resolution of the measurement may not be large (38)

IEEE Transactions on Electrical Insulation Vol. 27 No. 1, February 1992 53

enough to locate the P D site. Since the measurement is made from only one cable termination, the method relies on the directly propagated P D pulse and its reflection from the open circuit end of the cable. If the P D site is located near the end of the cable, the arrival times of the direct pulse and reflected pulse are nearly the same and it becomes difficult to differentiate between a single pulse and two closely spaced pulses. The two pulses will be interpreted as one and attributed to a P D a t the cable termination. When this occurs, the measuring system h said to be resolution limited since it cannot resolve both pulses. The region of the cable in which the direct pulse and reflected pulse are not resolved is called the blind spot of the cable. This type of measurement resolution limitation can be described in terms of a delay bias error [9] and is called type I resolution bias. As a rule of thumb, the two pulses are resolvable if the P D site is located a distance from the end of the cable equal to a propagation delay (equivalent distance) that is the reciprocal of the bandwidth of the received P D signals. Typical bandwidths for practical lengths of cable are no more than 10 MHz (100 ns reciprocal), so any P D sites within 15 m (assuming a propagation delay of 6.56 ns/m) of either end of the cable will appear as a P D a t the termination of the cable. Long cables have even smaller bandwidths further reducing the resolution.

4.3 MATCHED FILTER

An improvement in the autocorrelation technique is possible using matched filtering [9]. This technique cross correlates a calibration waveform with the received signal. Mathematically this operation is defined by

M ( t ) = S ( T ) h Z ( t - T ) d T (41) --M 7

where s ( t ) is the received P D signal previously defined and h 2 ( t ) is a time reversed version of a calibration waveform similar to the P D signals but including only the direct propagation term

In the frequency domain the matched filtering operation is described by

M ( w ) =

' ( w ) z ~ Hz(w)(exp[-iwz/vl + exp[- iw(2~ - . ) /VI) 2

(43) This result is interpreted by calculating the inverse Fouri- er transform of the terms within the brackets giving

1 (44) 2L - x

F - l [ M ( w ) ] M q t - ;) + a(t - -

This is the same result found in Equation (30) so the P D site is located using Equation (31) through (34). As before, the position of the P D site is the distance from the open circuit end of the cable to the PD site.

In this simple analysis the term I ( w ) H z ( w ) was ignored because, by supposition, the filter H z ( w ) is matched to the shape of I ( w ) and does not contribute to the delay (in the absence of dispersion). The term I ( w ) H z ( w ) is in essence the autocorrelation function of the direct arriving P D pulse. In fact, the inverse Fourier transform of M ( w ) is the superposition of time shifted autocorrelation functions

where R d i r e c t ( T ) is the autocorrelation function of the direct arriving P D pulse. The advantage of this technique is directly related to the autocorrelation function interpretation. By definition the autocorrelation function has its maximum a t the time origin. This means that the positions of peaks of the time shifted version correspond to the correct time delays. The inability to choose a consis- tent position on a waveform as the time reference causes the level crossing technique to be highly ina.ccurate. In contrast, the autocorrelation method has an inherent time reference, the peaks of the autocorrelation function. In the matched filter method, the times of arrival are the times a t which the output correlation function attains its maximums. This approach yields excellent time delay estimates provided that the signal shape is accurately known beforehand because the problems associated with selecting a proper threshold are eliminated. This technique also performs adequately in the presence of noise.

A calibration experiment can provide an adequate wave- fo,rm for use as the matched filter. The received signals travel through unknown amounts of cable so the shape will be slightly different than the calibrating signal. This inaccuracy in pulse shape causes a bias error in the delay estimate because of dispersion. However, the major problem with this method is due t o multiple pulses arriving a t almost the same time. The matched filter provides only slightly better results than the level crossing method and the same performance of the autocorrelation method.

In the presence of external interference, the matched filter provides slightly better results than the autocorrelation method. The matched filter can suppress noise outside its bandwidth thus improving performance. Al- so, the autocorrelation method concentrates the noise a t a single delay, obscuring sites near this delay; the matched filter does not.


There are generalizations to the matched filter approach that can improve the measurement in the presence of external interference [9]. If external interference is present, then using a filter similar to that in Equation (10) for H z ( w ) gives essentially the same results as Equation 41 except that the interference is attenuated. The filter is similar to a Wiener filter and is given by

where X is a parameter that controls the pulse resolution of the filter and N ( w ) is the noise previously defined [lo]. The scale factor ( is given by

- a2 l 2

( = 1 + - [ 9 u2XIS(w)l2 + N ( w )

where the term is the mean square value of the ampli- tudes. The interpretation of this filter is aided by considering the denominator of Equation (46). At frequencies where the noise power is large, the denominator becomes large so the filter attenuates the noise. The effect is to remove the interference. An additional benefit of this method is that the resulting amplitude of the filtered P D signal is an optimum estimate of the charge in the pulse. It is possible to make this filter behave as a deconvolution filter by adjusting the factor X to reduce the type I resolution bias, but this will only reduce the bias by a factor of 2 to 3 [9,18]. The penalty for using deconvolution is an increase in the variance of the delay estimate. This reduces the resolution of multiple sites.

4.4 CROSS CORRELATION

The cross-correlation method uses signals received a t both ends of the cable and is effective in eliminating type I resolution bias in measurements of P D sites located near the ends of a cable [9,13]. Consider the same simple, lossless, linear phase case as before except now the cable is terminated in matched loads a t both ends. The time cross-correlation function is defined as

Rdls2(T) = ']3l(t)s2(i+ T T ) d T (48) 0

where the signals s1 and s2 are the signals received a t the two ends of the cable. In the frequency domain R s l s s ( r ) is called the cross-energy spectral density and is given by

This result is interpreted by calculating the inverse Fouri- er transform of the term in the brackets giving

R s l s s ( ~ ) x 6 T - - [ In this method the location of the P D site is deduced from an estimate of the time delay T from the origin of the cross correlation t o the impulse displaced from the origin

The position of the P D site is then calculated as

1 x = - ( L 2 - T V ) (52)

and is the distance from the end a t which s1 is measured to the P D site. This method does not rely on any reflections and thus does not have a type I resolution bias, thus the cable has no blind spot.

Cross correlation provides a significantly higher SNR than single-ended methods. The improvement derives from the fact that single ended methods rely on a highly attenuated reflection. The improvement is seen by com- paring autocorrelation with cross correlation. In autocorrelation the portion of the correlation function that is used for the delay estimate suffers an attenuation of

n,(w) = exp[-2a(w)(L - x)] (53)

In cross correlation the portion of the correlation function that is used for the delay estimate suffers an attenuation of

n c ( w ) = exp[-a(w)( l - x)] exp[-a(w)x] (54)

Taking the ratio gives the loss in SNR

(55)

This result makes perfect sense because the reflected term has t o travel the entire length of the cable to get back to the receiver. For long cables this loss can be so significant that the reflected pulse is not detectable.

The received signals used to calculate the cross- correlation function have noise and, similar to the autocorrelation method, the noise correlation function superposes with the desired correlation function. If the noise is wide-band thermal noise, generated in the receivers, there is no added term because the noise terms in the two channels are independent. When the noise is from external interference entering a t the cable terminations, the noise contributes terms at delays corresponding to the cable ends. Just as in the autocorrelation method, the noise correlation function

IEEE l'kansactions on Electrical Insulation Vol. 27 No. 1, February 1992 55

Figure 5. Block diagram of a generalized cross correlator showing the prefilters used to eliminate interference.

' I

can obscure P D sites near the ends of the cable and if strong enough can obscure sites located far within the interior of the cable.

Cross correlation can be combined with a variety of noise reduction techniques t o enhance its performance in the presence of external interference. Using filters in both channels similar to the one in Equation (46) yields a correlator that is referred to as the Wiener generalized cross correlator [19]. A block diagram of the generalized cross correlator is shown in Figure 5. The prefilters are used to eliminate undesirable interference in each channel prior to cross correlating. The filter in each channel is given by

This type of correlator is especially effective in eliminating narrowband interference from radio broadcasts. An example of the efficacy of this approach is shown in Fig- ure 6 and 7. The result in Figure 6 shows the cross- correlation function of two P D pulses (one received a t either end) corrupted by correlated, multitone, narrowband interference. The presence of the P D site is obscured. If these same signals are prefiltered prior to cross correlating, the interference in nearly eliminated and the P D site is easily identified as can be seen in Figure 7.

The main drawback of cross correlation is the require- ment that both ends of the cable need to be instrumented. The instrumentation a t both ends must be time synchro- nized and there must be a communications link between the two ends. Although technically possible, the implementation would not be cost-effective for in situ measurements. However, for laboratory and factory testing, this is the preferred method because of the variety of noise reduction methods that can be easily incorporated, in addition to its superior resolution bias reduction and dra- matically increased sensitivity. Furthermore, most com- mercial da t a acquisition equipment has provision for two channels of input so little extra investment is required for data acquisition equipment.

i i i 1 I 0.75

05

0.25

0

-0.25

-05

250 350 450 550 650 750

Distance, meters

Figure 6. Cross-correlation function of signals con- taminated by narrowband interference. The cross-correlation function of the PD signal is totally obscured.

1

0.75

- 0.5 'E3 8

v 0 02s c l 0

3 -0.25

U -05

-0.75

-2 !i

-1 250 350 450 550 650 750

Distance, meters Figure 7 .

Normalized cross-correlation function calculated using the same signals as in Figure 6 but processed using a Wiener generalized cross correlator. The cross-correlation function of the PD signal is no longer obscured by the interference.

4.5 MULTIPLE SITES

Correlation based methods can use averaging to reduce


the effects of noise. However, when averaging is used another type of resolution error occurs. The correlation function has its peak centered a t the time delay corre-

to increase the resolution. Resolution is not limited to in- crements of the sampling frequency; it is possible to inter- polate between points to within fractions of the sampling

sponding to the P D site. Correlation functions are similar in width to the P D pulses used in their calculation. Resolution problems occur if two P D sites are located within close proximity to each other. In this case the correlation functions overlap and it is not possible to dis- tinguish two individual correlation functions; they appear as one. This is another distinct type of resolution limitation of the measurement and is called type I1 resolution bias. As a rule of thumb, the two sites are resolvable if the sites are separated by a propagation delay (equivalent distance) that is the reciprocal of the bandwidth of the received P D signals. As shown in Figure 1, power cables severely bandlimit the received signals. Typical bandwidths for practical lengths of cable are < 10 MHz (100 ns reciprocal). This means that P D sites must be

- - rate. As an example, consider a cross correlation estimate of a 0.025 pC P D with a 10 MHz bandwidth and a 14 dB SNR. It can be shown that the standard devia- tion of this estimate is 7 ns [9]. Stronger PD signals have smaller variances further increasing the resolution. The resolution for this example is 1 m, a 15x increase; 500 sites could be located in a 500 m cable, but multiple sites within any 1 m length will appear as a single site. This approach was used to detect the presence of two closely spaced P D sites in a 54 m, 15 kV power cable. The delay histogram was formed from individual cross correlation based delay estimates. Both P D sites are easily identified using the delay histogram in Figure 8 even though they are only separated by 2 m. The alternative method for measuring time delays with cross-correlation functions is

separated by 15 m (assuming a propagation delay of 6.56 ns/m), and only 33 P D sites can be resolved in a 500 m length of cable. The resolution performance decreases as the cable length increases.

to use signal averaging. However, a bandwidth in excess of 70 MHz is required to achieve this same resolution with a signal averaged cross-correlation function and this is impossible with this length cable.

I 4.6 REMOVING BIAS DUE TO DIS P E RSlO N

ir d B U Dispersion, when considered together with the frequen-

cy dependent loss, makes it extremely difficult to estimate precisely the location of a P D site in a power cable. None of the aforementioned delay estimators is capable of removing the delay bias caused by the propagation characteristics of the cable. Other difficulties also arise when trying to locate the absolute position of the PD

49 50 51 52 53 54 55 56 57 site. These difficulties are not related to the bias caused by the cable propagation characteristics but to the lack of knowledge about the cable. Records of the paths of installed cables and their exact lengths are rarely main-

200

100

0

Distance, meters

Figure 8. v

Delay histogram of two PD sites in a 82 m, XLPE, 15 kV power cable located 2.1 m apart.

Fortunately, there is a simple method that reduces greatly the effects of this resolution limit. If the location of the P D site is calculated from each data record and sorted into a histogram, the resolution can be increased substantially. Ideally, the histogram consists of single impulses, each corresponding to a separate P D site. However, the estimates of the time delays are noisy and this noise is described by the variance of the estimates. When the histogram is formed, the variance of the estimate is a measure of the width of the histogram of the estimates. Better delay estimates (smaller variance) result in narrower histograms and thus better resolution. The estimator with the smallest variance should be used

tained. It is common that the length of the cable may only be known to within lo%, if a t all; this affects the accuracy of the velocity if i t is measured. Even if the exact length is known and the path is precisely traced, varia- tions in the depth of burial may cause unacceptable errors when the path of the cable is traced along the surface of the ground.

Fortunately, there is a simple solution to the problems associated with determining the absolute location of the P D site. The solution is to calibrate the measurement a t positions along the cable [9,16,20,21]. The technique is very simple and involves four steps. A schematic of the method is shown in Figure 9. In this Figure it is assumed that (L1 < Lz < L3) and that the line length (Lg - Ll) is much smaller than the length, LTOT, of the


I CALIBRATION I I CALIBRATION I "A "A

A CABLE UNDER A

I I I 1

I I I I

MEASUREMENT

I I I - I I I I I 0 L1 L 2 L s L m

DISTANCE

Figure 9. Schematic of PD location recalibration. Recal- ibration can be performed with or without HV applied to the cable. The diagram depicts a single antenna placed at two different positions.

cable under test. First, with HV applied, determine the time delay 72 to the P D site using any suitable method. Using the best velocity information available, determine the approximate prelocation of the P D site based on 72. The second step is to inject a P D calibration signal into the cable, using an antenna, a t location L1 near to the prelocation site. Then calculate the time delay 71, to the calibration antenna with the same method used to determine 72. This can be performed with or without HV applied to the cable, whichever is most convenient. The third step is to measure precisely the distance from L1 to a second calibration position L3, move the antenna to the new position, inject a similar signal at L3 and measure the time delay 73. In this analysis it is assumed that (71 < TZ < 73) but this relationship is not necessary; the technique can be modified. The fourth step is to calculate the absolute position. One approach is to calculate a velocity veal, using

(57) L3 - L1

v c d = ~

7 3 - 7 1

and then calculate the absolute position as

LZ = L1 + v c a 1 ( ~ 2 - 71)

Lz = L1-t (L3 - L1)-

( 5 8 )

(59)

or 7 2 - 71

73 - 71 which locates the P D site relative to the first calibration position in terms of the directly measurable quantities. It is possible to find variants of this method using obvious modifications.

This calibration procedure is highly effective in removing bias errors associated with the imperfect velocity in-

formation. Using the proper delay estimator, the variance of the time delay estimate becomes small leaving the bias as the major source of error. This technique is successful because the three time delays are determined for almost identical lengths of cable so all of the bias errors are nearly the same. This can most easily be seen by considering Equation (59) and assuming that the bias error is ap- proximately due to a scale factor which modifies the time delay. Since each time delay 7 has the same scaling factor the bias cancels by taking the ratio. Furthermore, assuming that the bias error does not cancel and causes an error E by defining the new reference line ( L 1 , L3) , the absolute error c(Lz - L1) is reduced greatly because ( L z - L1) is small compared to the total cable length. Typical errors may be 1% which is 5 m on a 500 m length of cable. If the error is maintained a t 1% and the new reference line is 10 m, the error becomes 0.1 m.

The first use of this technique was on a 294 m cable con- taining a manufacturing defect a t Essex Wire [21]. Cross correlation was used to determine the delay estimate and the calibration signals were created by removing a small portion of the insulation screen to create a P D signal rather than using an antenna. The location accuracy was better than 10 cm. It is also possible to inject calibration pulses nondestructively into the cable using an antenna [9,20]. The signals shown in Figure 10 are pulses induced on a coaxial line using this method. Using a properly de- signed antenna, pulses have been induced on buried URD cables and have yielded accuracies of 30 cm.

4.7 NEUTRAL CORROSION

Another difficulty encountered during the in situ measurement of P D is the corrosion of the neutral wires in aged cables. If the neutral corrosion is extensive the cable may appear to have a n open circuit (or high impedance) a.t the point where the neutrals are missing. It is extremely difficult to measure broadband signals traveling down a cable with open neutrals since most of the signal energy reflects back from the point where the neutrals are missing. Low frequency signals can propagate past these points because a significant portion of the low frequency signals travel in the surrounding ground [12]. However, as previously mentioned, low frequency signals cannot be used effectively t o locate low level P D in cables. Even if the neutral wires are not completely corroded, partial corrosion can distort the signal enough that it is difficult to locate the P D site.

5. CONCLUSIONS

A N Y of the technical difficulties associated with lo- M cating P D sites in cables have been solved. As solu-


l f 0.6

> Q 0 2 U 1 U .-. d g -0.2

-o*6 -1 0 i 200 400 600 800 10oO

Time, ns 1

o-6 I Q 0.2 '0

- 1 " ~ ~ " " ' " " ' ' ~ ' " ' ' ~ ' ~ ~ ' 0 200 400 600 800 10oO

Time, ns Figure 10.

Signals induced on a coaxial cable using a recalibration antenna. The two signals are received at opposite ends of the cable. The two signals have opposite polarities because the pulse is induced inductively.

tions to the technical problems are found, certain limitations of the measurements become clear. The fundamental limitations of the methods are caused by the back- ground noise in the system and the propagation characteristics of the cable. It is meaningless to state a single number for the minimum detectable level of a PD in a cable; each case will be different. However, it is possible to approximate the minimum detectable level by calculation, if information about the cable system and noise are available.

Some technical issues and questions remain unanswered. The most important question is whether measurable PD is present in aged cables for a sufficient time prior to failure. If P D is detectable for only a brief time before failure, implementation of a utility-wide test plan would be impossible.

Cable manufacturers have a long history of quality control testing upon which to base their P D testing proce- dures. Since in situ testing of P D is a relatively new technology, there is no equivalent data base. Two questions immediately become apparent:

1. What voltages should be used for these measurements?

2. What magnitude of P D should be considered innocu- ous to the cable?

Implementing a complete measurement system capable of reaching the fundamental limitations of the measurement will be expensive. To provide reliable results, the analysis system should be able t o process a t least hun- dreds if not thousands of P D events in an expedient fashion and this will require a signal processor. The power source for this system will have to be PD free, portable, and capable of energizing long lengths of cable. A cost- effective power source meeting these requirements may have to be unconventional and use emerging technolo- gies. For example, the power source might be a very low frequency (VLF) test set or an oscillating wave test set.

Assuming that these P D measurements provide mean- ingful results, the question remains whether utilities will accept this technology with ita limitations. Since there is no known solution to the problem of neutral corrosion, will the utilities invest in a technology that only applies to a portion of their cable installations? A complete test system will be a large capital investment; however, the major cost is in implementing the test program. In North Amer- ica, some utilities have several hundred thousand meters cif cable installed with the nominal length of a typical circuit being 150 m. The economic overhead associated with periodically testing each cable could be large.

Despite the questions raised about the application of this technology to the utility industry, it is ready for the move into dielectric research laboratories and quality control facilities of cable manufacturers. This technology promises to improve significantly P D detection levels while providing manufacturers and researchers access to the sites of naturally occurring insulation defects.

IEEE Transactions on Electrical Insulation Vol. 2 7 No. 1, February 1992 59

ACKNOWLEDGEMENT [ll] J . P. Steiner, W. L. Weeks, “Digital Estimation of Partial Discharge,” CEIDP Annual Report, (IEEE Conf Record 87 CH2462:0), pp. 73-78, Gaithersburg Md., 1987.

Portions of this work were performed a t Purdue Uni- versity, West Lafayette, Ind., and were supported by Es- sex Wire. Also, the authors gratefully acknowledge the reviewers for their helpful comments.

[I21 Y. Diao, Propagation of Wideband Signals in Power Cables, Ph. D. Thesis, Purdue University, School of Elec. Eng., West Lafayette, Ind., Dec., 1984.

REFERENCES

[l] M. Kruger, R. Feurstein, A. Fils, “New Very Low Frequency Methods for Testing Extruded Cables”, IEEE International Symposium on Electrical Insula- tion, pp. 286-289, 1990.

[2] M. Nagao, T . Tokoro, A. Yokoyama, M. Kosa- ki, “New Approach to Diagnostic Method of Water Trees” , IEEE International Symposium on Electrical Insulation, pp. 296-299, 1990.

[3] T. Nakayama, “On-Line Cable Monitor Developed in Japan”, Conference Record 91- WM-255-0-PWRD, IEEE/PES Winter Power Meeting, New York NY, 1990.

[4] A. Iga, M. Aihara, J. Fujiwara, J . Kawai, “Applica- tion of G P T to Tan Delta Measuring Apparatus for Distribution Cable in Hot Line”, Conference Record 91-WM-251-9-PWRD1 IEEE/PES Winter Power Meeting, New York NY, 1990.

[5] R. Bartnikas, R. M Eichhorn, ed., Engineering Di- electrics, Volume IIA, “Electrical Properties of Solid Insulating Materials: Molecular Structure and Elec- trical Behavior”, S T P 783, ASTM Press, Philadel- phia, Pa., pp. 405, 1983.

[6] M. 0. Pace, F. F Dyer, T . V. Blalock, B. E. Williams, S. W. Milam, I. Alexeff, “New Water Tree Monitor- ing Technique”, 1990 IEEE Conference on Electrical Insulation and Dielectric Phenomena, pp. 391-397, 1990.

[7] S. A. Boggs, G. C. Stone, “Fundamental Limits in the Measurement and Detection of Corona and Par- tial Discharge”, IEEE Transactions on Electrical In- sulation, Vol. 17, pp. 143-150, 1982.

181 H. L. Van Trees, Detection, Estimation and Mod- ulation Theory, Part I, pp. 309, Wiley, New York, 1968.

[9] J . P. Steiner, Digital Measurement of Partial Dis- charge, Ph.D. Thesis, Chapters 3-4, Purdue Univer- sity, School of Elec. Eng., West Lafayette Ind, 1988.

[lo] L. E. Franks, Signal Theory, Dowden and Culver, Chapter 9, Stroudsburg Pa., 1981.

[13] W. L. Weeks, J. P. Steiner, “Instrumentation for the Detection and Location of Incipient Faults on Pow- er Cables”, IEEE Transactions on Power Apparatus and Systems, Vol. 101, pp. 2328-2335, No. 7, July, 1982.

[14] C. H. Knapp, R. Banzal, M. S. Mashikian, R. B. Northrop, “Signal Processing Techniques for Partial Discharge Site Location in Shielded Power Cables”, IEEE Trans. on Power Delivery, Vol. 5, No. 2, pp.

[15] M. Beyer, W . Kamm, H. Borsi, H., and K. Feser, “New Method for Detection and Location of Dis- tributed Partial Discharges (Cable Faults) in High Voltage Cables Under External Interference”, IEEE Transactions on Power Apparatus and Systems, Vol. 101, pp. 3421-3438, No. 9, Sept., 1982.

[16] M. S. Mashikian, R. Banzal, R. B. Northrop, “Loca- tion and Characterization of Partial Discharge Sites in Shielded Power Cables”, IEEE Transactions on Power Apparatus and Systems, Vol. 5, No. 2, pp.

[17] R. 0. Schmidt, A Signal Subspace Approach to Multiple Emitter Location and Spectral Estimation, Ph.D. Thesis, Stanford Univ, Stanford, Calif., Nov., 1981.

181 J . P. Steiner, E. S. Furgason, W. L. Weeks, WO- bust Deconvolution of Correlation Functions,” IEEE Ultrasonics Symposium Proc. No. 87CH2492-7, pp. 1031-1035, Denver Colo., 1987.

1’91 A. Hero, and S. Schwartz, “A new Generalized Cross Correlator”, IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. 33, pp. 38-45, No. 1, Feb., 1985.

859-865, 1990.

833-839, 1990.

[20] J. P. Steiner, W. L. Weeks, “Detection and Location of Pips in Power Cables”, Report to Essex Wire and Detroit Edison, Nov., 1986.

[21] W. L. Weeks, J. P. Steiner, “Recent Experiences in Partial Discharge Location,” Report to Essex Wire, March 27, 1985.

This paper is based on a presentation given at the 1990 Volta Colloquium on Partial Discharge Measurements, Como, Italy, 4-6 September 1990.

Manuscript was received on 15 March 1991, in revised form 8 August 1991.

estimating the location of partial discharges in cables

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