The Applications of Weibull Function to Partial Discharge Analysis and Insulation Ageing: A Review

A. S. Deshpande Research Scholar, Electrical Dept.,

VJTI, Mumbai, India

asdamolsd@gmail.com

A. S. Patil M. Tech Student, Electrical Dept.,

VJTI, Mumbai, India.

abhi.patil03@gmail.com

Dr. A. N. Cheeran

Professor, Electrical Dept., VJTI,

Mumbai, India ancheeran@vjti.org.in

Abstract— Partial Discharge (PD) is a locally confined electrical breakdown within the high voltage insulating system that only partially bridges the distance between two electrodes. PD from different sources produce different PD pulse height distribution (PDHD) patterns. PD source/type identification is approached by resorting to the stochastic analysis of PDHD shape. PDH data resulting from a single PD source and multiple sources are often characterized using the Weibull distribution. Moreover, the mixed weibull distribution is also applied to multiple defects and is found successful to assess electrical ageing progression of insulation systems. The shape and scale parameter of the weibull function are important for the characterization of the type of PD phenomenon and hence the PD identification and life-time analysis. A comprehensive survey of PD analysis using weibull distribution with respect to PD source identification, insulation ageing, reliability analysis etc has been presented in this paper. The survey shows that, much of the work has been carried out on model voids. Research has to be extended to obtain a figure of merit for PD of single and multiple discharges and for complex PD patterns observed in practical insulation systems.

Keywords- High Voltage Insulation, Weibull Distribution, Partial Discharge, Electrical insulation aging, Reliability.

I. INTRODUCTION Electrical discharge which do not completely bridge the

electrodes, are called partial discharge (PD). PD may occur internal to insulation, or on the surface or at sharp points & corners called as corona discharges. A PD phenomenon is a complex stochastic process because it exhibits significant statistical variability in properties like pulse amplitude, shape, and time of occurrence [1]. Even though PD is localized to a particular region and is self-quenching, it usually causes progressive deterioration of the insulation which may eventually lead to breakdown. PD detection and diagnosis is thus an important tool for quality assessment electrical-insulation. It is considered as an indicator of insulation integrity and performance.

It is very commonly seen in practical insulation systems, that there are more than one PD sources acting simultaneously. The patterns obtained with PD detectors

contain characteristic features of the source/class of the respective partial discharge process involved. For this reason, PD pattern recognition is important for PD phenomena identification. Several techniques, such as neural networks method [2], fractals analysis [3] and centour score method [4] etc have been adopted for pattern recognition and PD phenomena identification [5-7].

In contrary with a deterministic approach, probabilistic analyses appear to be more appropriate to model the discharge behavior initiated from unknown sources. The diagnosis of insulation systems by PD analysis finds considerable support from stochastic processing of PD data. Both PD mechanisms and PD pattern identification can be inferred by appropriate stochastic models involving PD height (amplitude) and phase distributions. Analysis of Partial Discharge Height Distribution (PDHD) patterns may provide characteristic statistical parameters to determine the discharge source as well as the degradation process. Different types of PD sources produce different types of PDHD patterns. Proper interpretation of the observed discharge patterns, for e.g. on-line PD monitoring, can be used to determine the discharge source, i.e. defect type as well as the physical phenomena behind it.

The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering and also most popular for modeling stochastic deterioration [8].

Research shows that the Weibull distribution provides a potential model to quantify the characteristics of the observed patterns [9, 10]. The parameters of the Weibull function can be related to the PD standard quantities and can constitute a useful tool for the identification of different PD phenomena [9].

Contin, et. al. [11] used Fuzzy classifiers for classification of PD signals. The feature vector was constructed by including Weibull parameters. This classifier resulted in a cluster of signals homogeneous in terms of stochastic features of the PD pulses.

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This paper initially discusses the PD phenomena identification and separation. Remaining sections discuss about different aspects of PD analysis with the use of weibull distribution.

II. PD PHENOMENA IDENTIFICATION USING WEIBULL DISTRIBUTION

The PDH values resulting from a single PD source can be characterized by the two-parameter Weibull function. Equations (1) and (2) are the expressions of the cumulative distribution and the probability density function for two parameter weibull function.

(1)

(2)

Here α and β are the scale and shape parameters, and q is the charge magnitude. The quality of fitting the two-parameter weibull distribution for the PD originating from single source is as shown in fig. 1 [9]. The quality of fit can be verified by means of appropriate tests like Cramer-von-Mises test.

Fig. 1 Weibull distribution applied to PDH data for a single PD source.

When two types of PD phenomena are active simultaneously occurring in voids inside the insulation, deviations from the two-parameter Weibull function generally is observed as shown in fig 2 [9]. The behavior displayed by fig. 2 was explained by the appearance of a second PD phenomenon superimposing on the previous one. Five parameter Weibull distribution fits well for such discharges, whose cumulative distribution is given by,

F(q) = p. F1(q) + (1-p).F2(q) (3)

where q is the charge magnitude and Fl(q) and F2(q) are the cumulative distributions of the two sub-populations (the expressions of Fl(q) and F2(q) are given by eq.(l)).

Equation (1) is characterized by 2 parameters, that is, α and β, while the additive model (eq.(3)) is characterized by 5 parameters, that is, α1, α2, β1, β2 and probability p.

Fig.2 Weibull distribution applied to PDH data for multiple PD sources.

III. PD ANALYSIS USING SHAPE AND SCALE PARAMETERS OF WEIBULL FUNCTION

The estimation of the Weibull parameters enables calculation of standard average quantities used for PD analysis such as mean, integrated charge height per cycle, mean number of discharges per cycle, mean value of charge height transferred by each pulse, maximum discharge height etc [9, 10, 12]. The parameters of the weibull function, α and β, can be estimated by the means of Maximum Likelihood Method and Least Square Method. Based upon the values of β, the type of discharge can be interpreted [10,12-15]. Thus, β parameter can be used to distinguish and study different types of discharges.

Fig. 3 and 4 [16] shows the variation of the scale and the shape parameters with respect to applied voltage. These results show clearly the PD phenomena separation.

Nimbole et. al., 2008 [17] presents a diagnosis of insulation using linear prediction method. Long term prediction of future of α and β for different samples over time was studied and analyzed. The performance is compared with Artificial Neural Network and shown that the neural network model is less efficient in predicting the shape and scale parameter in comparison with linear predictive model.

Application of weibull distribution along with gives more precise results for identifying PD of different types with the help of the scale parameter (α) and shape parameter (β) and some statistical parameters like skewness and kurtosis [18, 19]. The Weibull-like function also provides the best performance in terms of quality of fit, separation and identification of single and combined PD sources [13].

IV. INSULTION DEGRADATION AND AGEING The ageing of dielectrics is characterized by an irreversible

deterioration and it affects the performance and lifetime of the

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equipment. So monitoring of electrical ageing is also an important issue in high voltage insulation systems. Diagnosis of insulation ageing is carried out by studying the variations of both the probability function parameters ( and ) and the standard average quantities with ageing time and/or voltage [10]. Figure 5 [10] shows the time behavior of the shape and scale parameter of the Weibull function, for positive (+) and negative (-) discharges, relevant to a sample specimen. Scale parameter increase with ageing time, whereas, the shape parameter decreases for both positive and negative discharges as seen in Fig. 5.

Fig. 3 Behavior of the shape parameter derived from combined and single PD tests, as function of applied voltage (Positive polarity).

Fig. 4 Behavior of the scale parameter derived from combined and single PD tests, as function of applied voltage (Positive polarity).

M. Nedjar et. al., 2007 [20] investigated electrical ageing of polyurethane under AC voltage. This material is used as insulating material in the electrical machines. Weibull statistical analysis of the time to breakdown was performed to govern the degradation of polyurethane caused by partial discharges.

Since reliability, life-time, condition monitoring have become hot and essential topics now-a-days, some recent work brings new methods in picture like multi layer perceptions (MLP-BP), adaptive neuro-fuzzy inference system (ANFIS), principle component analysis-linear inference system (PCA-

LDA) etc. These methods are used along with weibull distribution for evaluation of degradation of electrical tree [21].

Fig. 5 Time behavior of the shape and scale parameter of the Weibull function, for positive (+) and negative (-) discharges, relevant to a sample specimen.

Moreover, it is necessary to apply different strategies in the form of condition-based maintenance for reliability analysis. Asset managers are in need of tools to assist them in decision making on appropriate replacement and/or maintenance strategies. Figure 6 illustrates such an approach to manipulate acquired data for condition based maintenance [22].

Fig. 6 Data manipulation for condition based maintenance.

CONCLUSION

Weibull distribution is a powerful tool for PD identification and to assess insulation ageing. An attempt has been made to review work done in PD analysis using weibull distribution till today and to discuss different analytical aspects of PD which can be studied using weibull.

The parameters of the Weibull function, can be correlated to the PD activity and constitute a useful tool for insulation diagnosis based on PD measurements. Shape parameter is one such identification index which is invariant with the PD source location in the insulation system.

From this review, the authors came to a conclusion that weibull functions can be used successfully for single and multiple PD source detection. The work done till now is mostly carried out on model voids, using some experimental set up. More work needs to be carried on practical experimental data obtained on high voltage machines like transformer, rotating

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machines etc. Also, there is a need to study variation in values of alpha and beta for different types of discharges found in such machines like slot discharge, delamination, gap discharge, end winding discharge etc. Use of Neural Networks along with weibull function can prove even better for PD pattern recognition. There is a possibility to get some fruitful results using weibull distribution in conjunction with Pulse Sequence Analysis which will help for physical interpretation of discharges.

Emphasis should be given to diagnosis of insulation systems with regard to hazard function, reliability etc, to monitor failure rate and life time of any high voltage equipment/system.

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