Partial Discharge Localization for a Transformer Based on ... - CiteSeerX

Partial Discharge Localization for a Transformer Based on Frequency Spectrum Analysis Shuzhen Xu, Steven D. Mitchell and Richard H. Middleton School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, N.S.W. 2308. Australia. 1. Abstract Partial discharge (PD) is a major source of insulation failure in power transformers. The location of a PD source is of crucial importance in both the maintenance and repair of a transformer. This paper applies the knowledge that the poles of a PD current frequency spectrum do not change, whilst the zeros vary with the position of a PD source within the winding. An algorithm based on this approach has been developed for the localization of PDs. The algorithm adopts the wellknown ladder network to model the transformer winding, then estimates the parameters of this model from the poles of the PD current frequency spectrum. This provides the necessary information to be able to calculate a PD signal from different source locations within the model. Finally, the position of a PD source can then be estimated by a comparison of the measured and calculated PD signals. Simulation and experimentation results are demonstrated in the paper. 2. Introduction Partial discharge (PD) measurement is a powerful technique used to detect an incipient insulation fault in a power transformer. Research is being carried out to detect, locate and classify the type of PD. Techniques for the localisation of PD sources are of major importance in on-site maintenance and repair [1]. Early work on PD location for transformers assumed the transformer behaved like a capacitance network at high frequencies [2], but further studies [3] indicate this is only valid over a limited frequency range. The attenuation of higher frequency components of the coupled PD signal’s energy as a simple function of PD position along the transformer winding, has been used [1,4] for PD localisation. However, practical PD tests show that the frequency spectra of a current response in a transformer are so complicated that they don’t demonstrate any “straightforward” pattern [5,6]. Therefore, a lot of recent effort has been channelled into the study of the frequency spectrum of the PD current detected at the neutral terminal, with the aim of PD localisation [5-9]. It is believed that although the signal detected at the neutral terminal is a highly distorted representation of the original PD pulse, it does contain very useful information about the site of origin and nature of the discharge.

The objective of this paper is to develop a PD localisation method by analysing the frequency spectrum of the measured PD current signal. It is assumed that the original discharge pulse is a current source, and has a unitary distribution over the frequency range of interest. Therefore, the detected PD signal can be considered as the impulse response of the studied system, with an unknown discharge site-of-origin. The paper uses the knowledge that the poles of a PD current frequency response do not change with the location of the PD. On the other hand, the zeros of the frequency response do vary with the position of a PD source within the winding. An algorithm based on this approach has been developed that can estimate the discharge position within the transformer winding. The algorithm initially estimates the parameters of a high-frequency transformer model based on the poles of the PD current frequency spectrum. This parameter estimation is accomplished by using a two-stage approach involving linear least squares optimization and a genetic algorithm. The site of origin of the PD can then be estimated by calculating the terminal PD current waveform based on different source locations within the transformer model, and comparing these with the observed waveform. To verify the validity of the estimation, simulation and laboratory experiments have been conducted on an 11kV/415V distribution transformer. 3. Background Theory A PD generated within a transformer winding can have an associated frequency range between a few kHz to hundreds MHz. Over this range a ladder network model as in Figure 1 may be employed. Gs Cs I0

i1 L s Cg Gg

r

V1

Gs i2 Ls

Cg Gg

Gs

V2

Cs

Cs

r

in L s Cg

Rg

Cg

Gg

VN

r Cg

Figure 1. A Ladder network model for a transformer winding, PD at Node 2

Note that mutual inductances have not been explicitly depicted in Figure 1. The PD occurrence can be simulated as a current pulse injected into

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Gg

the network. To obtain the output current through the neutral point in such a circuit, it is very convenient to use state-space equations as follows:

x& = Ax + Bu

(1)

y = C1 x + C 2 x& with

x = [i1 (t ), i2 (t ),L , i N (t ),V1 (t ),V2 (t ),L ,V N (t )]T é0 ù - L-1 N ù , B = ê -1 ú ú Q -1G ûú ëQ K û C1 = [1,0, L ,0,-Gs ,0, L ,0] ; é- L-1 R A = ê -1 ëêQ M

C 2 = [0,0, L ,0,-C s ,0, L ,0] ;

K = [0, L ,0,0, L ,1( r ) , L ,0] , Note that the position of 1 in vector K is decided by the input position.

L , Q and G are the inductance, capacitance and admittance matrices of this system. They are given by:é L M 12 M 13 L L M 1N ê M 12 L M 12 O M ê ê M 13 M 12 L O O M L=ê ê M O O O O M 13 ê M O O O M 12 ê êë M 1N L M 13 M 12 L

ù ú ú ú ú ú ú ú úû

é(Cg + 2Cs ) - Cs 0 LL 0 ù ê - Cs (Cg + 2Cs ) O ú ê ú ú O O Q=ê 0 O ê ú - Cs ú M O O ê êë 0 - Cs (Cg + Cs + CB )úû

Y ( s ) = (C1 + C 2 s )( sI - A) -1 B, U ( s) » 1

(3)

In Eq. 3 only the matrix B is related to the position of the input (PD current source location). It can be seen that the matrix A is not affected by the position of the PD current source. Also, the occurrence of a discharge does not affect the system structure. Therefore, the poles of the system, which are the eigenvalues of the matrix A, are completely determined by the system itself. Only the zeros contain information related to the PD site-of-origin. In another words, the poles of the frequency spectrum of any detected PD current signal may be used for system identification (parameters Ls , C s , C g and r of the model), whereas the zeros of the transfer function may be used for PD localization. 3.1

Parameter Estimation from Detected PD Current Based on the theory discussed above, the procedure for estimating transformer parameters from detected PD current is composed of three steps. These are as follows: 1) Obtain the frequency spectrum Y (s ) of the terminal PD current signal. 2) Estimate the poles of the system from the calculated frequency spectrum. 3) Estimate the parameters in the model, as depicted in Figure 1, from the estimated poles. Step 1 can be achieved easily through the use of a Fast Fourier Transform (FFT). In the second step, the frequency spectrum, which is the frequency response of the system, is modeled by a transfer function [10] as follows: b ( s) (4) Y (s) = a ( s) where b (s ) and a (s ) are polynomials and defined by b ( s ) = b m s m + b m -1 s m -1 + L + b1 s + b0 (5)

GS 0 L 0 ù é- (2GS + Gg ) ê ú GS - (2GS + Gg ) O ê ú ú G=ê O O 0 O ê ú M O O GS ú ê êë GS - (GS + Gg )úû 0

a ( s ) = a n s n + a n -1 s n -1 + L + a 1 s + 1

Note that CB is the bushing capacitance. The frequency response can be calculated by taking the Laplace Transform of Eq. (1).

Y (s) = (C1 + C 2 s )( sI - A) -1 B U ( s)

response of the system and Eq. 2 may be written as:

(2)

Since the PD current source is assumed to have a unitary distribution, the frequency spectrum of the detected PD can be considered as the frequency

(6)

Substituting Eq.5 and Eq.6 into Eq.4, the following equation is obtained: (7) Y ( s ) = X ( s )q Where X ( s ) = - s nY ( s ) L - sY ( s ) s m L s 1 and

[

q = [a n L a1 bm L b1 b0 ] .

]

Then the coefficients can be obtained through applying a least square optimization. After that, it is not difficult to get the poles of the system, which are the roots of polynomial a (s ) .

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Step 3 is a nonlinear optimization problem. The objective function is to minimise the difference between the eigenvalues of matrix A and the calculated poles. The eigenvalues and poles are sorted by frequency in descending order. é- L-1 R - L-1 N ù eig ( A) = eig ( ê -1 ú ) (8) Q -1G ûú ëêQ M = poles = roots (a ( s )) There are a wide variety of non-linear optimization algorithms available. This paper has tried nonlinear least squares (NONLSQ) and a genetic algorithm (GA) approach. It has found that with the high number of parameters and the nature of the problem, several local minimums appear. For these reasons, NONLSQ has difficulties and often does not converge to the global minimum point. However GA, with its evolution based survival of the fittest approach to parameter optimization, provides quite good results. More details on genetic algorithms can be found in the reference [11]. 3.2 Estimation of PD source location After all the parameters in the model are obtained, the output signal can be calculated for a PD initiated at any node location. This is accomplished first of all by utilizing equation 2 with the appropriate B matrix and an inverse Fourier transform (IFFT). Then, the Crosscorrelation of each of the calculated output signals based on all possible PD site-of-origins, with the original measured one, is used to locate the PD position. The matching procedure can be performed in the frequency domain by extracting feature vectors like the position of zeros in the frequency response, or the time domain by using the whole signal waveform. In practice we would suggest the use of the time domain for the following reasons. There are significant inaccuracies introduced at higher frequencies due to skin and eddy current effects. In the frequency domain only a few data points are located within the accurately modeled low frequency end of the spectrum. The lack of a precise model for the transformer winding at high frequencies reduces the reliability of the data as it approaches the higher end of the spectrum. In the time domain, the high frequency inaccuracies will only effect the early samples ensuring that the more accurately modeled data, the low frequency end, will dominate the correlation, which enhances the effectiveness of the matching procedure.

discharges (at different site-of origins), are calculated by using the Electromagnetic Transient Program (EMTP) software. The calculated current signals are then fed into a software implementation of the algorithm for PD localization as previously described. The first PD current used is that with the source located at the 2nd section node away from the neutral point. Figure 2 is the resulting transfer function model fit of the signal frequency spectrum, which in this case, is the impulse response. It can be observed that the fit is quite satisfactory. The cross-correlation of the simulated PD current with the calculated currents based on the estimated model, is shown in Figure.3. According to the maximum correlation rule, the source position of the first PD is determined to be at section 1 or section 2 of the ladder from the measuring point. To demonstrate the validity of the algorithm for this case, the analysis is repeated for 5 discharges and the results of localization are shown in Figure.3 and Table.2. Figure.4 is a comparison between the measured frequency spectrum and the estimated frequency spectrum. Good matching between them has been obtained, particularly at low frequencies. The error at high frequencies is due in part to a relatively low order TF model. The TF order selection was restricted because of the wide frequency band of interest used in the least squares optimization[10]. Further research in this area is ongoing. Table 1 - The predefined and estimated values of elements

Def Est

L (mH) 16.2 17.7

R (ohm) 3.1 2.83

Cs (pF) 30 28

the circuit

Cg (pF) 1232 1159

Table. 2 Comparison between the actual position and the estimated position of the PD

PD Sites-of-origin PD1 PD2 PD3 PD4 PD5

Real position 17% 34% 50% 67% 83%

Estimated position 20% 37% 50% 63% 87%

4. Simulation The simulation study has been carried out on a simple 12 unit ladder network as shown in Figure 1 with predefined circuit elements as listed in Table 1. The various PD currents that flow through the neutral point due to the Dirac-shaped

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frequency spectrum of measured PD data fitted data with TF model

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measurement setup is given in Figure.5. A 1GHz Agilent Infinium oscilloscope was used to record all of the data. The CT used was a Lilco 13W5000 Core (10 Primary turns/ 10 Secondary turns).

Amplitude

1

0.1

0.01

1E-3

1E-4 10000

100000

frequency (Hz)

Figure 2. The estimated result of the TF modeling versus the frequency spectrum of the simulated PD current origin 1 origin 2 origin 3 origin 4 origin 5

1.0 0.9

correlation

0.8 0.7

Figure.5 Simplified reciprocity based measurement set-up

0.6 0.5 0.4 0.3 0.2

0.0

0.2

0.4

0.6

0.8

1.0

normalized position

Figure.3 The correlation between the simulated and calculated PD currents with different source positions ( 0%-neutral point; 100%-bushing point)

origin 1

100 0.01 1E-6 100

origin 2

Amplitude

0.01 1E-6 100

origin 3

0.01 1E-6 100

origin 4

1E-6

Though not ideal, to simplify testing and to improve sensitivity, this paper has utilized reciprocity theory to obtain a PD current with an impulse voltage source. According to electrical circuit theory [13], for a reciprocal network with two ports, if voltage excitation at port1 and current excitation at port 2 are the same, the responses of the voltage at port 2 and current at port 1 remain the same, i.e., V1 = I 2 Þ V2 = I 1 . To ensure the validity of the reciprocity approach for the transformer winding, a comparison of the frequency responses when using both voltage and current sources with interchanged excitation and response ports, has been measured and is shown in Figure 6. The measured results demonstrate an excellent correlation. Reciprocity based measurements on the transformer winding will yield accurate results. + voltage source - current source

origin 5

0.1 1E-9 50000

100000

150000

200000

250000

frequency (Hz)

300000

350000

400000

+measured -estimated

Figure.4. The comparison between the frequency spectrum of the simulated and calculated PD currents with respect to the estimated position.

5. Experimental Investigation A 3-phase distribution transformer (11kV/430V,200kVA), which has been removed from it’s vessel, is utilized for the experimental investigation. The High-Voltage side is disconnected to provide an independent singlephase winding. Three equidistant clamps have been mounted along the high voltage winding, and between each clamp are two winding sections. The

1

Amplitude

0

0.1

10

100

1000

10000

100000

1000000

frequency

Figure.6 The frequency response curves of the transformer winding when subjected to voltage and current impulses with interchanged excitation and response ports.

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‘PD current’ data is taken from various clamp positions and fed into the PD localisation algorithm. The sampling period was 0.1ms. The resulting transfer function model of the frequency spectrum of one of the measured PD currents is depicted in Figure.7. This is stage 2 of the localization algorithm. Since the winding has 8 sections, the ladder network model is set to 8 units. The estimated values of the parameters at every section are shown in Table.3. M12 to M18 are the mutual inductance between each of the sections. The frequency influence on these parameters will make direct verification difficult. However, the grounding capacitance of the winding was measured at 42Hz using an impedance meter with a resulting value of approximately 400pF. The estimated total grounding capacitance is This result is C ga = C g ´ 8 = 435.1 pF . reasonably consistent with that measured. Table.3 The calculated parameters of the winding

L (H) R (ohm) Cs (F) Cg (F) M12 (H) M13 (H) M14 (H) M15 (H) M16 (H) M17 (H) M18 (H)

1.1401 12498 4.0054e-14 5.439e-11 1.0363 0.98723 0.86867 0.78593 0.54532 0.59637 0.41314

One such reason could be the influence of the A and C windings on the single B phase winding which was used for all measurements. Effects such as mutual capacitance and inductance between the outside windings and the winding under test have not been taken into consideration in the model. Another reason for the offset could be the frequency dependence of the inductance L and the resistance R. This influence, though considered, is not easily modeled and will be the focus of further investigation. Figure. 9 is a comparison between the measured and calculated PD currents with their estimated positions. 6. Conclusion: An algorithm for transformer partial discharge localisation has been developed in this paper. The approach is based upon frequency spectrum analysis of PD current signals. The algorithm initially estimates the parameters of the transformer from the poles of the discharge frequency spectrum. The position of a PD source can then be deduced by calculating the PD current waveforms with the source simulated at various locations within the transformer. These waveforms are then compared to the observed waveform to determine the closest match. This algorithm does not require any predetermined information about the transformer. The PD site-of-origin is determined purely from a measured PD current. Simulation and experimentation both show promising results. Table. 4 the comparison between actual position and the estimated position of measured PD

+spectrum of measured PD -fitted data with TF model

Amplitude

0.01

PD Site-of-origin PD1 PD2 PD3 PD4

Real position 25% 50% 75% 100%

Estimated position 12.5% 25% 50% 62.5% origin 1 origin 2 origin 3 origin 4

1E-3

0.8 1000

10000

100000

0.6

frequency (Hz)

Figure 7. The resulting TF model of the frequency spectrum of a measured PD current.

The correlation between the measured PD currents and the calculated currents, back from the estimated model, are given in Figure. 8. Using a maximum match rule, the final results for all the PD currents are given in Table. 4. The results are very interesting. There is a distinct offset away from the bushing between the estimated and true PD source. There are a number of possibilities for this offset and the work on this area is ongoing.

correlation

0.4 0.2

0.0

-0.2 -0.4 0.0

0.2

0.4

0.6

0.8

1.0

normalized position

Figure.8 The correlation between the measured and the calculated PD currents with differing source positions ( 0%neutral point; 100%-bushing point)

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2

measured PD current estimated PD current

origin 1

1 0

origin 2

1

Current

0 1

origin 3

0

origin 4

0.4 0.2 0.0 -0.2 -0.4 2000

4000

points

Figure.9 The comparison between the measured and calculated PD currents with their estimated positions.

7. Acknowledgments The authors would like to thank Energy Australia for providing the distribution transformer and the Australian Research Council and Pacific Power International for supporting this research.

Power Transformers Using Neural Networks Combined with Sectional Winding Transfer Functions as Knowledge Base’, p579-582. [9] [10] R.H. Middleton, G.C. Goodwin, Digital Control and Estimation, Prentice Hall, Englewood Cliffs, N.J., 1990. [11] T. Back, D.B. Fogel, Z.Michalewicz, Evolutionary Computation 1: Basic Algorithm and Operators, Institute of Physics Publishing, Bristol and Philadelphia, 1984. [12] James S. Walsh, Graham C. Goodwin, Frequency Localising Basis Functions for Wideband Identification, 2003. [13] Lawrence P.Huelsman, Basic Electrical Theory. [14] Francisco de Leon, Adam Semlyen, Complete Transformer Model for Electromagnetic Transients, IEEE Transactions on Power Delivery, Vol.9, No.1, Jan.1994, p231-237. [15] G.B.Gharehpetian, H.Mohseni, K.Moller, Hybrid Modelling of Inhomogeneous Transformer Windings for Very Fast Transient Over-voltage Studies, IEEE Trans. On Power Delivery, Vol.13, No.1, January 1998, p157-163.

8. References: [1] J.P. Steiner, W. L. Weeks, A new method for locating partial discharges in transformer, p275281. [2] R. E. James, J. Austin and P. Marshall, Application of Capacitive network winding representation to the location of partial discharge in transformers, Electrical Engineering Trans. I. E. Australia, pp.95-103, 1977. [3] R. E. James, B. T. Phung, Q. Su, ‘Application of Digital Filtering Techniques to the Determination of Partial Discharge Location in Transformers’, IEEE Trans. Electrical Insulation, Vol. 24, No.4, August, 1989. [4] Yafei Zhou, A. I. Gardiner, G. A. Mathieson, Y. Qin, ‘New Methods of Partial Discharge Measurement for the Assessment and Monitoring of Insulation in Large Machines’, p111-114. [5] Z.D. Wang, P.A. Crossley, K. J. Cornick, ‘A Simulation Model for Propagation of Partial Discharge Pulse in Transformer’, ….., p151-155, 1998. [6] Xuzhu Dong, Deheng Zhu, Changchang Wang, Kexiong Tan, Yilu Liu, ‘Simulation of Transformer PD Pulse Propagation and Monitoring for 500kV Subsation’, IEEE Trans. On Dielectric and Electrical Insulation, Vol.6, No.6, Dec. 1999, p803-813. [7] Z.D. Wang, P. A. Crossley, K. J. Cornick, ‘Partial Discharge Location in Power Transformers Using the Spectra of the Terminal Current Signals’, High Voltage Engineering Symposium, IEE, p5.58.s10-5.61.s10, Aug., 1999. [8] P. Werle, A. Akobari, H. Borsi, E. Gockenbach, ‘Partial Discharge Localisation on

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