PARTIAL DISCHARGE PATTERN ANALYSIS WITH CORRELATION COEFFICIENTS C. Chang and Q. Su Center for Electrical Power Engineering Department of Electrical & Computer Systems Engineering Monash University, Clayton VIC 3168 Australia ABSTRACT Partial discharges (PDs) are localized electrical discharge that partially bridges the insulation between conductors. The continuous impact of PDs may reduce the remaining lifetime of high voltage (HV) equipment. In order to ensure reliable operation of HV equipment, it is important to identify the type of defect and monitor its activity within the insulation system. The extraction of fingerprints from various PD patterns is an important step for PD source recognition. Among those extractable parameters, the correlation coefficient is used to measure the similarity and dissimilarity of various distribution variables. With a new PD measuring and analysis system, correlation coefficients between positive and negative half cycles of individual distributions and those between phase resolved (PRPD) and pulse height resolved (PHPD) patterns are calculated and analyzed leading to some useful conclusions. 1. INTRODUCTION 2. PD MEASURING SYSTEM PD signal is one of the most important quantities to be With the measuring system shown in figure 2.1, the used to examine the status of many electrical insulation defects listed in table 1 were tested in this apparatus because PD measurement is a sensitive investigation. The non-destructive test was carried out method for testing and monitoring the insulation with the applied voltage started from sample’s condition of HV equipment. An important object of inception level. PD test is to identify PD source of different type. Previous work has proved that statistical parameters Defect Type Description are useful to characterize the PDs . However the 1 Corona discharge in air progress in computer measurement techniques has 2 Oil-impregnated pressboard made it possible to accurately record and store a large 3 Ground wall discharge in an epoxy amount of PD data. Meanwhile sophisticated digital resin stator bar data acquisition systems not only enable fast Table 1. Defect types for PD source identification computation of various discharge parameters during the measurement but also make PD pattern analysis HF Filter available on the run. At the meanwhile some advanced algorithms can be employed to extract parameters of interest for characterizing even monitoring the PD U~ Ck Ca activity. In this paper, PD distribution pattern originated from PD source of three different types are CC Measuring System compared and investigated. Obviously, different type CD of insulation defect produces different discharge patterns. There are many types of patterns that can be used for PD source identification. If the degree of Fig.2.1 PD measuring system similarity and dissimilarity among these distribution patterns can be presented and included in a database, U~ high-voltage supply identification of the defect type from the observed PD CC connecting cable pattern may be possible . Based on the property CD coupling device and preamplifier of correlation coefficient, PD distribution pattern from Ck test object different source has been studied. Ca coupling capacitor. During test, PD pulses were measured according to Maximum PD - Phase their amplitudes using a new discharge detector 2500 2000 . PD distribution pattern analysis including 1500 phase resolved and pulse height resolved patterns, Maximum PD/Second 1000 were performed. 500 0 45 90 135 180 225 270 315 360 -500 3. PD DISTRIBTUION PATTTERNS -1000 -1500 -2000 For pattern recognition purposes, the information -2500 contained in the discharge distributions must be -3000 Degree quantified. The description of these quantified Figure 3.3 Maximum PD magnitude – phase distribution shapes can be carried through by various statistical parameters. It is practically useful to 3.2 PHPD Distribution Patterns integrate PD data for further analysis . As it is understood that the important parameters to Three discharge intensity spectra may be used to characterize PDs are phase angle ϕ, PD magnitude q describe the nature of PD distribution. With this so- and PD number n. PD distribution patterns are called PHPD approach, it scrutinizes the discharge composed of these three parameters. However there patterns in relation to the level of discharge are other parameters that are often used to characterize magnitude. Like PRPD approach and based on the PD, such as the maximum and average value of quantization level of the measuring system, the range integrated distribution parameters. of discharge magnitude is again equally divided into 200 windows. Over the entire measuring period, 3.1 PRPD Distribution Patterns distribution variables such as number of PD events, average voltage and maximum voltage are calculated PRPD pattern analysis investigates the discharge as functions of discharge magnitude window. After patterns in relation to voltage ac cycle, which is being quantified, figure 3.4 presents the distribution equally divided into 200 windows. Figure 3.1, 3.2 and pattern of PD number in relation to magnitude 3.3 illustrate PRPD distribution patterns from a window index while figure 3.5 and 3.6 show sample of oil impregnated pressboard. Over the entire distribution patterns of average and maximum applied period, the integrated parameters were calculated and voltage varied with discharge magnitude window plotted as a function of the phase window. . PD Pulse Rate - Phase PD Number - PD Magnitude 30 100 25 80 PD Number/Second 20 PD Number 60 15 10 40 5 20 0 0 45 90 135 180 225 270 315 360 0 0 25 50 75 100 125 150 175 200 Degree PD Magnitude Figure 3.1 PD repetition rate – phase Figure 3.4 Repetition rate – magnitude window Average PD - Phase Average Voltage - PD Magnitude 1500 8 1000 6 Average PD/Second 4 Applied Voltage (KV) 500 2 0 45 90 135 180 225 270 315 360 0 25 50 75 100 125 150 175 200 -500 -2 -4 -1000 -6 -1500 -8 Degree PD Magnitude Figure 3.2 Average PD magnitude – phase Figure 3.5. Average voltage – magnitude window Maximum Voltage - PD Magnitude PD Pulse Rate - Phase 40 8 6 PD Number/Second 30 4 applied Voltage (KV) 2 20 0 25 50 75 100 125 150 175 200 10 -2 -4 0 0 45 90 135 180 225 270 315 360 -6 Degree -8 PD Number - PD Magnitude 20 PD Magnitude Figure 3.6. Maximum voltage – magnitude window 0 25 50 75 100 125 150 175 200 PD Number -20 3.3 Correlation Coefficients -40 Correlation coefficient (CC) is employed to determine -60 whether two ranges of data move together. In this case -80 it can be used to describe whether large values of one PD Magnitude half-cycle data are associated with small values of the Fig 4.2 Repetition rate - window index at 2.2 KV other. It is defined as follow: Average PD - Phase 150 CC = ∑ x • y −∑ x •∑ y n i i i i 100 Average PD/Second (∑ x − (∑ x ) n) • (∑ y − (∑ y ) 2 2 2 2 i i i i n) 50 0 45 90 135 180 225 270 315 360 -50 Here x and y represent the two distribution variables -100 and i is the window index of either positive or -150 negative half cycle of a distribution. Correlation -200 coefficient has the value range between –1 and +1. If Degree one variable tends to increase as the other decreases, 1.0 Average Voltage - PD Magnitude the correlation coefficient is negative. Conversely, if 0.8 0.6 the two variables tend to increase or decrease together Normalised Voltage 0.4 the correlation coefficient is positive. 0.2 0.0 25 50 75 100 125 150 175 200 -0.2 4. FEATURE EXTRACTION -0.4 -0.6 -0.8 Correlation coefficients among various corresponding -1.0 PD Magnitude distribution patterns may be calculated within the Fig 4.3 Average value – window index at 2.2 KV system as shown in figure 4.1. Distribution patterns of the pressboard sample under different voltages are Maximum PD - Phase demonstrated from figure 4.2 to 4.7 when using PD 200 repetition rate, average and maximum integration 100 Maximum PD/Second value as distribution variable respectively. 0 45 90 135 180 225 270 315 360 -100 -200 -300 -400 Degree Maximum Voltage - PD Magnitude 8 6 applied Voltage (KV) 4 2 0 25 50 75 100 125 150 175 200 -2 -4 -6 -8 PD Magnitude Figure 4.1. Correlation coefficient calculation Fig 4.4 Maximum value – window index at 2.2 KV PD Pulse Rate - Phase With the measuring system arrangement of Figure 2.1, 30 correlation coefficients of defect sample listed in table 25 1 were computed under different voltages. The PD Number/Second 20 correlation coefficients of interest in this case are as follows: 15 10 5 (1) Between positive and negative half cycle of the 0 0 45 90 135 180 225 270 315 360 same distribution. Degree (2) Between positive half cycle of PRPD and the PD Number - PD Magnitude 60 corresponding positive half cycle of PHPD 40 distribution. 20 (3) Between negative half cycle of PRPD and the PD Number 0 25 50 75 100 125 150 175 200 corresponding negative half cycle of PHPD -20 distribution. -40 As illustrated in figure 4.8, correlation coefficients of -60 -80 PD Magnitude various distribution variables of PRPD and PHPD Fig 4.5 Repetition rate - window index at 4.5 kV vary with applied voltage. It is clearly seen that three distribution variables of PRPD increase along with the Average PD - Phase increase of voltage. This implies that PRPD 1500 distribution patterns improve the symmetry between 1000 positive and negative half cycle when voltage Average PD/Second 500 increased. However, as for average and maximum 0 45 90 135 180 225 270 315 360 distribution variables of PHPD, the symmetry stops -500 improving when voltage increased to 4.8 kV or above. -1000 The move is obviously driven by the significant -1500 increase of discharge magnitude in one half cycle of Degree the distribution when voltage is reached to the level. Average Voltage - PD Magnitude 8 6 Applied Voltage (KV) 4 2 0 25 50 75 100 125 150 175 200 -2 -4 -6 -8 PD Magnitude Fig 4.6 Average value – window index at 4.5 kV Maximum PD - Phase 2500 2000 1500 Maximum PD/Second 1000 500 0 45 90 135 180 225 270 315 360 -500 -1000 -1500 -2000 -2500 -3000 Degree Maximum Voltage - PD Magnitude 8 6 applied Voltage (KV) 4 2 0 25 50 75 100 125 150 175 200 -2 -4 -6 -8 PD Magnitude Fig 4.8 Distribution variables vs. voltage with Fig 4.7 Maximum value – window index at 4.5 kV A oil-impregnated pressboard sample Box plot is a graphical display that simultaneously describes several important features of a data set, such as center, spread, departure from symmetry, and identification of observations that lie unusually far from the bulk of the data. It not only consists of a rectangular box representing the inter-quartile range of the data as well as indicating the lowest and highest observations. There is a line drawn across the box at the median of the data set and whiskers that extended from each end of a box. The lower whisker is a line from the first quartile to the smallest data point within 1.5 inter-quartile ranges from the first quartile. The upper whisker is a line from the third quartile to the largest data pint within 1.5 inter-quartile ranges from the third quartile. Box plots are particularly useful in graphical comparisons among data sets, because they have high visual impact and are easy to understand. For example, figure 4.9 shows, in each category, comparative box plots for three distribution variables. Inspection of the display reveals that there is less variability for number and average distribution variables in PRPD. Therefore, box plots of figure 4.9 give a graphical summary of three distribution variables used in this investigation, which help to have a close look over the data range of selected distribution variables thus identify the accepted range as well as the extreme value. 5. CLASSIFICATION USING MLPs Multilayer perceptrons (MLPs) extend the perceptron with hidden layers. Figure 5.1 shows a one hidden layer MLP with m inputs, p hidden processing elements (PEs) and n outputs. The correlation coefficients from various distribution patterns may be investigated using MLP with m=12, p=6 and n=2. Every PE in hidden and output layers is a nonlinear tanh PE with bias set to 0.5. W11 I1 W11 W12 Y1 W12 I2 Wn1 Wn2 W1p Yn Wnp Im Wpm Fig5.1 A MLP with one hidden layer (m-p-n) The multilayer perceptron are trained with error- correction learning. Using delta rule, the error was Fig. 4.9 Statistical characteristics of calculated computed at each PE. The error between the network CC of three distribution variables output and the desired value is a measure for the successful classification of listed discharge defects in 7. REFERENCES table 1 . The cost function may be used for this purpose and defined as:  C. Chang and Q. Su, “Comparison Between Pattern Recognition Techniques For Partial 1 N (5.1) Discharge Identification”, Proceedings of J (t ) = ∑ (d i (t ) − yi (t )) 2 2 i =1 Australasian University Power Engineering Conference, Hobart, Australia, Sep. 1998 Here d is the desired output value and y is the actual  D. Wenzel, H. Borsi, E. Gockenbach, “A output value. N is the number of exemplar and t is the Measuring System Based on Modern Signal time from the beginning of the training. The cost Processing methods for Partial Discharge function shown in figure 5.2 indicates the success of Recognition and localization On-Site”, IEEE discharge classification through fingerprints composed Symposium on Electrical insulation, pp. 20-23, by correlation coefficients. 1998  C. Chang, Q. Su, “Partial Discharge Distribution Patterns Analysis Using Combined Statistical Parameters”, IEEE PES Winter Meeting 2000, Singapore, January 24-28, 2000.  C. Chang, Q. Su, “Analysis of Partial Discharge Patterns from a Rod to Plane Arrangement”, IEEE Symposium on Electrical insulation, April 2-5, 2000  Q. Su, “Partial Discharge Measurements on Generators Using a Noise Gating System”, Australasian Universities Power Engineering Conference, September. 26-29 1999. Darwin, Figure 5.2 Quadratic cost function J(t) Australia  C. Chang, Q. Su, “Statistical Characteristics of 6. CONCLUSION Partial Discharges from a Rod to Plane Arrangement”, Australasian Universities Power Due to the complexity of PD phenomena, statistical Engineering Conference, September. 26-29 1999, parameters of various distribution patterns may be Darwin, Australia. used to identify PD source of different type.  Q. Su, C. Chang, and R. Tychsen “Travelling Correlation coefficients can be computed from various Wave Propagation of Partial Discharges along distribution patterns of PRPD and PHPD. Meanwhile, Generator Stator Windings”, International it is important to understand that correlation Conference on Properties and Application of coefficients vary with criteria such as defect location, Dielectric Materials, 25-30 May 1997, Seoul, geometry, applied external stress etc. The moving Korea, pp. 1132-1135. trend as well as the variability of correlation  Gallant and White, “On Learning Derivatives of coefficients may be closely examined and compared an Unknown Function with MLPs”, Neural using both trend line and box plot. Being trained with Networks 5 (1), 129-138, 1992. extracted fingerprints, A MLP neural network has successfully identified the PD source of different type.