energies Article
Evaluation of Electrical Tree Degradation in Cross-Linked Polyethylene Cable Using Weibull Process of Propagation Time Donguk Jang 1 and Seonghee Park 2, * 1 2
*
Metropolitan Transportation Research Center, Korea Railroad Research Institute, Uiwang 16105, Korea;
[email protected] ICT Fusion Green Energy Center, Wonkwang University, Iksan 54538, Korea Correspondence:
[email protected]; Tel.: +82-31-460-5412
Academic Editor: Fengshou Gu Received: 25 September 2017; Accepted: 3 November 2017; Published: 7 November 2017
Abstract: The main purpose of this paper is to evaluate electrical tree degradation for cross-linked polyethylene (XLPE) cable insulation for three difference models. In order to show the distribution characteristics using phase resolved partial discharge (PD), we acquire data by using a PD detecting system. These acquired data presented four 2D distributions such as phase angle-average discharge distribution, pulse magnitude-pulse number distribution, phase angle-pulse number distribution, and phase angle-maximum discharge derived from the distribution of PD. From the analysis of these distributions, each of the tree models are proved to hold its unique characteristics and the results were then applied as basic specific qualities. In order to evaluate the progresses of an electrical tree, we proposed methods using parameters by means of Weibull distribution to the time of tree propagation. We measured the time of tree propagation for 16 specimens of each artificial tree models from initiation stage, middle stage, and final stage respectively, using these breakdown data, we estimated the shape parameter, scale parameter, and mean time to failure. It is possible to analyze the difference in lifetime between the initial stage, the middle stage, and the final stage, and could be used to predict the lifetime of an XLPE cable from these results. Keywords: partial discharge; Weibull analysis; XLPE cable; electric tree; propagation time
1. Introduction Maintenance technology for diagnosing electric power equipment has shifted from time-based maintenance to both condition-based and reliability-centered maintenance in Korea. Among various methods of implementing condition-based diagnosis, partial discharge (PD) diagnosis method is most widely used because it is easy to derive parameters for insulation diagnosis. This is thanks to sufficient information on the insulation condition of the electric power equipment that is contained in signals arising from the occurrence of PD in the power equipment [1,2]. Construction of a number of electric railroads incorporating high-speed rail has recently taken place, and a lot of railway sections involving long tunnels have also been constructed in Korea. Whereas insulated cables are rarely utilized in the general sections of electric railroads due to the overhead catenary lines being used there, the minimalized construction of insulated cables in tunnel sections is operated from the perspective of the cross-sectional area of a tunnel on the grounds of construction costs. So, feeder wires are installed inside tunnels as insulated cables on overhead catenary lines. The condition diagnosis and degradation evaluation of the insulated cables installed in tunnels emerge as important factors. Electrical treeing in cable insulation is a pre-breakdown phenomenon for insulation failure and the main factor in the insulation degradation of solid insulators. Therefore, discerning any electrical
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Electrical treeing in cable insulation is a pre-breakdown phenomenon for insulation failure and the main factor in the insulation degradation of solid insulators. Therefore, discerning any electrical tree tree and and investigation investigation its its propagation propagation status status is is undoubtedly undoubtedly most most crucial crucial because because itit is is directly directly related related to to the the lifespan lifespan of of the the equipment equipment [3–11]. [3–11]. To determinethe thepropagation propagation of electrical this paper came with three types of To determine of electrical trees,trees, this paper came up withup three types of simulated simulated electrical tree specimens and presented a method of revealing it by estimating the electrical tree specimens and presented a method of revealing it by estimating the shape andshape scale and scale parameters using distribution the Weibull[12–19]. distribution [12–19]. As a Weibull methoddistribution of using Weibull parameters using the Weibull As a method of using analysis, distribution analysis, discharge to sizes were the employed to uncover the propagation of electrical partial discharge sizespartial were employed uncover propagation of electrical trees by estimating the trees the shape and parameters step bycharacteristics. step and analyze their by change shapeby andestimating scale parameters step by stepscale and analyze their change In addition, using characteristics. In each addition, bythe using 16 specimens eachof model, thepropagation failure time in themeasured event of any 16 specimens for model, failure time in thefor event any tree was and tree propagation was measured and presented. The failure times were then identified and presented. The failure times were then identified and categorized into three relevant tree propagation categorized intoestimating three relevant tree propagation stages, thereby estimating the stages, thereby the shape parameters, the scale parameters andthe theshape meanparameters, time to failures scale parameters and the mean time to failures (MTTF) at each stage. (MTTF) at each stage. 2. 2. Test Test Specimens and Experimental Setup 2.1. Artificial Artificial Electrical Electrical Tree Tree Model Model 2.1. The specimens tree discharge were secured by cutting somesome Cross-linked The specimens for forthe theartificial artificialelectrical electrical tree discharge were secured by cutting CrossPolyethylene (XLPE)(XLPE) insulating material portions off a Korea powerpower distribution cable with linked Polyethylene insulating material portions off a Korea distribution cablerating with voltagevoltage 13.2 kV, three types of tree of models were made shown in Figure rating 13.2 kV,different three different types tree models wereas made as shown in 1. Figure 1. needle electrode
8 mm
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needle electrode
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ground electrode
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Figure 1. Artificial electric tree models: (a) tree model 1 was only needle electrode; (b) tree model 2 Figure 1. Artificial electric tree models: (a) tree model 1 was only needle electrode; (b) tree model 2 with with void void on on needle needle electrode electrode surface; surface; (c) (c) tree tree model model 33with withmetal metalparticle particlebetween betweenneedle needleand andground ground electrode [18–20]. electrode [18–20].
Each specimen was made by inserting a needle into the relevant insulating material after heating Each specimen was made by inserting a needle into the relevant insulating material after heating it to 100 °C in order to inhibit the occurrence of any nonessential electric discharge due to the complete it to 100 ◦ C in order to inhibit the occurrence of any nonessential electric discharge due to the complete adherence of the interface between the needle and the insulating material during the needle insertion. adherence of the interface between the needle and the insulating material during the needle insertion. The made specimens were tested in the insulation oil condition in order to prevent any surface The made specimens were tested in the insulation oil condition in order to prevent any surface discharge that could possibly occur on surface and outside. discharge that could possibly occur on surface and outside. 2.2. Experimental Method and Data Processing 2.2. Experimental Method and Data Processing 2.2.1. 2.2.1. Partial Partial Discharge Discharge Measurement Measurement The experimentalapparatus apparatusfor for occurrence of and PD the andobtainment the obtainment of relevant data The experimental thethe occurrence of PD of relevant data consists consists of a PD-free transformer, a PD pulse acquisition, storage, a display system and a microscope of a PD-free transformer, a PD pulse acquisition, storage, a display system and a microscope for for observing electrical as shown in Figure The apparatus is designed a way so that observing electrical treestrees as shown in Figure 2. The2.apparatus is designed in suchina such way so that voltage voltage application, data acquisition data processing are allwith possible withdischarge it. Partialpulses discharge application, data acquisition and data and processing are all possible it. Partial were pulses were detected using a PD detector (Biddle Instruments, Dallas, TX, USA), and the data from was detected using a PD detector (Biddle Instruments, Dallas, TX, USA), and the data was derived derived from the Φ-q-n distribution. Data format acquired from PD detector is 8 × 512 matrix which the Φ-q-n distribution. Data format acquired from PD detector is 8 × 512 matrix which the phase
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angle of one cycle is divided into 64 sections and pulse count is calculated by dividing the discharge the phase angle of one cycle is divided into 64 sections and pulse count is calculated by dividing the Energies 2017, 10, 1789 3 of 14 magnitude into 64 sections based on the maximum discharge magnitude. PD statistical distributions discharge magnitude into 64 sections based on the maximum discharge magnitude. PD statistical are calculated and investigated from these data format. distributions are calculated investigated theseand data format. the phase angle of one cycleand is divided into 64from sections pulse count is calculated by dividing the discharge magnitude into 64 sections based on the maximum discharge magnitude. PD statistical Optical distributions aremicroscope calculated and investigated from these data format. Monitor & CCD
HV (applied voltage) HV (applied voltage)
Optical microscope & CCD
Artificial tree models
Artificial tree models
Monitor
Save image
Save image
PD detector
PD detector
Using PC for PD data acquisition
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Figure 2. This is the(a) test process of the experimental setup to detect the(b) partial discharge (PD): (a) test Figure 2. This is the test process of the experimental setup to detect the partial discharge (PD): (a) test process; (b) (b) Partial Partial discharge discharge detector detector system. system. process; Figure 2. This is the test process of the experimental setup to detect the partial discharge (PD): (a) test process; (b) Partial discharge detector system.
2.2.2. Observation of Tree Propagation 2.2.2. Observation of Tree Propagation 2.2.2. Observation of Tree Propagationand growth of tree, an optical microscope (Olympus, Tokyo, In order to check the occurrence In order to check the occurrence and growth of tree, an optical microscope (Olympus, Tokyo, Japan) Japan) In was installed aboveoccurrence test specimens immersed in an theoptical oil tank as shown in FigureTokyo, 3b. The order to check and growth ofoil tree, microscope was installed above test the specimens immersed in the tank as shown in Figure(Olympus, 3b. The microscope microscope was connected to the Charge Coupled (CCD) camera3b. as shown Japan) was installed above test computer specimensthrough immersed in the oil tankDevice as shown in Figure The was connected to the computer through Charge Coupled Device (CCD) camera as shown in Figure 3a. in microscope Figure 3a. The image ofcomputer tree was through able to be observed and Device recorded on computer. wasgrowth connected to the Charge Coupled (CCD) camera as shown The growth image of tree was able to be observed and recorded on computer. in Figure 3a. The growth image of tree was able to be observed and recorded on computer. CCD CCD
PD PD measuring measuring unit unit
Microscope Monitor Microscope Monitor Tree specimen Tree specimen
Oil tank Oil tank
(a) (a)
Save image & growth Save image tree &ofgrowth of PC tree PC
PD free PD free transformer transformer
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Figure 3. This is diagram of the tree image observation process and setup to see the tree propagation Figure 3. This is diagram of the tree image observation process and setup to see the tree propagation Figure 3. This is diagram of the tree image observation process and setup to see the tree propagation image: (a)(a) Tree Microscope andCharge Charge Coupled Device (CCD) with image: Treeimage imageobservation observation process; process; (b) (b) Microscope and Coupled Device (CCD) with image: (a) Tree image observation process; (b) Microscope and Charge Coupled Device (CCD) with test specimen. test specimen. test specimen.
2.2.3. Tree Growth 2.2.3. Tree Growthand andDegradation Degradation Stage Stage 2.2.3. Tree Growth and Degradation Stage InIn the used in in this thisexperiment, experiment,PD PDinception inception voltage (PDIV) thecase caseofofthe theneedle-plane needle-plane structure structure used voltage (PDIV) In the case of the needle-plane structure used in this experiment, PD inception voltage (PDIV) was was measured byPD PDpulse pulsemagnitude, magnitude,but but the background noise was measuredabout about16 16kV. kV.The ThePDIV PDIV was was judged judged by the background noise measured about 16 kV. The PDIV was judged by PD magnitude, theInbackground noise was was 2 pC test laboratory, PDIV was when PD pulse was 5 5pC. paper, applied was 2 pC inintest laboratory, PDIV was set when PDpulse pulse wasabove abovebut pC. Inthis this paper, applied 2voltage pC in test laboratory, PDIV wastree set when PDand pulse was above 5 pC.toIn this paper, applied voltage voltage was setto13.2 to13.2kV kVduring during tree growth, tree could be rapidly according was set growth, and tree could bemade made toprogress progress rapidly according was set to13.2 kV during tree growth, and tree could be made to progress rapidly according to the the voltageafter after PDwas was occurred. to to the voltage PD occurred. is important thing investigate properties properties of artificial tree models voltage PD wasthing occurred. It It isafter important totoinvestigate of tree treepropagation propagationfor forthree three artificial tree models because it could find out the correlation with the lifetime depending on sources of defect the treetree It is important thing to investigate properties of tree propagation for three artificial tree models because it could find out the correlation with the lifetime depending on sources of defect the occurred. We assume that the degradation stage of the tree was divided into initiation, middle and because it could find out the correlation with the lifetime depending on sources of defect the occurred. We assume that the degradation stage of the tree was divided into initiation, middle tree and final respectivelyfor for0.6~0.9 0.6~0.9mm, mm,1.5~1.8 1.5~1.8 mm mm and growth length. final respectively and above above2.4 2.4mm mmbased basedononthe thetree tree growth length. 3. Experimental Results 3. Experimental Results
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occurred. We assume that the degradation stage of the tree was divided into initiation, middle and final respectively for 0.6~0.9 mm, 1.5~1.8 mm and above 2.4 mm based on the tree growth length. Energies 2017, 10, 1789
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3. Experimental Results 3.1. Partial Discharge Distributions for Tree Model 1 3.1. Partial Discharge Distributions for Tree Model 1 Figure 4 show the partial discharge distributions during the tree propagation in tree model 1. In Figure 4 show partialindischarge the tree in tree is model the case of model 1, the as shown Figure 3,distributions if AC voltageduring is applied, the propagation breakdown voltage lower1. In the case of as shown in Figure 3, if voltage is applied, thein breakdown voltage is (the voltage at model which 1,corona occurs is lower) in AC general when the needle the needle-to-plane lower (theisvoltage at than which corona is lower) in tree general when in the needle-to-plane electrode negative when it isoccurs positive, and the growth is the fastneedle when the needle is positive, electrode is negativefailure than when is positive, and the treewhen growth fast when the needle is positive, therefore, insulation may itoccur much more easily theisneedle electrode has entered the therefore, insulation failure may occur much more easily when the needle electrode has entered the positive half cycle. For these particular reasons, it can be concluded that any discharge pulse positive half cycle. in Forthe these particular reasons, it can be concluded that any discharge pulse occurring occurring is larger positive half cycle. is larger in the positive half cycle. 100
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Figure Figure4. 4.Statistical Statisticaldistributions distributionsof ofPD PDfor fortree treemodel model1:1:(a) (a)Hn(q) Hn(q)distribution; distribution;(b) (b)Hn(Φ) Hn(Φ)distribution; distribution; (c) Hq n(Φ) distribution; (d) Hqmax(Φ) distribution. (c) Hqn (Φ) distribution; (d) Hqmax (Φ) distribution.
The distribution of pulse repetition rate of PD tends to decrease as the electrical tree propagation The distribution of pulse repetition rate of PD tends to decrease as the electrical tree propagation proceeds from the initiation stage towards the final stage, whereas in the cases of the PD—related proceeds from the initiation stage towards the final stage, whereas in the cases of the PD—related distributions, Hqn (Φ) and Hqmax (Φ), their values tend to increase as the electrical tree propagation distributions, Hq (Φ) and Hqmax (Φ), their values tend to increase as the electrical tree propagation proceeds towards nthe final stage of its propagation. This reveals that the quantity of electric discharge proceeds towards the final stage of its propagation. This reveals that the quantity of electric discharge is is a more important factor than the frequency of discharge occurrence in understanding the a more important factor than the frequency of discharge occurrence in understanding the characteristics characteristics of both the insulation degradation and failure. of both the insulation degradation and failure. 3.2. Partial Discharge Distributions for Tree Model 2 Figure 5a–d show electric discharge distributions during the tree propagation in model 2. Much like in the case of model 1, the repetition rate of PD is more frequent in the positive half cycle than in the negative half cycle in model 2. PD magnitude has shown to be greater in the positive half cycle than in the negative half cycle. Both the mean and largest PD magnitude are greater in the positive half cycle. This seems to be the result of the existence of a void in the needle tip in model 2, unlike in
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3.2. Partial Discharge Distributions for Tree Model 2 Figure 5a–d show electric discharge distributions during the tree propagation in model 2. Much like in the case of model 1, the repetition rate of PD is more frequent in the positive half cycle than Energies 2017, in 10,the 1789negative half cycle in model 2. PD magnitude has shown to be greater in the positive 5 of 14 half cycle than in the negative half cycle. Both the mean and largest PD magnitude are greater in the positive half cycle.1.This to be thealso result of thethe existence of a void in the needle tipthere in model the case of model Thisseems phenomenon shown same characteristics even when was a2, unlike inforeign the case of model 1. This 3. phenomenon alsosimilar showncharacteristics the same characteristics there metallic material in model Model 2 shows in the PD even pulsewhen repetition was its a metallic material in model Model 2stage, showsthe similar characteristics in final the PD pulse rate, growth foreign is clearly classified into the3.initiation middle stage, and the stage in repetition rate, its growth is clearly classified into the initiation stage, the middle stage, and the final terms of the PD magnitude. In addition, as the tree propagation proceeds further towards the last stage in magnitude. addition, as the tree the propagation proceeds further towards stage, theterms data of onthe thePD discharge pulseInabove 300 pC shows greater PD pulse repetition rate. the last stage, the data on the discharge pulse above 300 pC shows the greater PD pulse repetition rate. 100
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Figure 5. Statistical distributions of PD for tree model 2: (a) Hn(q) distribution; (b) Hn(Φ) distribution; Figure 5. Statistical distributions of PD for tree model 2: (a) Hn(q) distribution; (b) Hn(Φ) distribution; (c) Hqn(Φ) distribution; (d) Hqmax(Φ) distribution. (c) Hqn (Φ) distribution; (d) Hqmax (Φ) distribution.
3.3. Partial Discharge Distributions for Tree Model 3 3.3. Partial Discharge Distributions for Tree Model 3 The electric discharge size characteristically does not grow when the electrical tree propagates. The electric discharge size characteristically does not grow when the electrical tree propagates. Figure 6 shows PD distributions during the tree propagation in Tree Model 3. Many electric Figure 6 shows PD distributions during the tree propagation in Tree Model 3. Many electric discharges discharges occurred in the negative half cycle, thus displaying a high frequency of its occurrence, occurred in the negative half cycle, thus displaying a high frequency of its occurrence, whereas the whereas the positive half cycle showed definitely high values in electric discharge size in Tree Model positive half cycle showed definitely high values in electric discharge size in Tree Model 3. The PD 3. The PD magnitude was discovered to be greatest in Model 3 and seems to be a phenomenon magnitude was discovered to be greatest in Model 3 and seems to be a phenomenon appearing as appearing as a result of an electric field being concentrated near the metallic foreign material. a result of an electric field being concentrated near the metallic foreign material. However, both the However, both the PD repetition rate and magnitude are characteristically shown to be greater during the initiation and middle stages rather than during the final stage. These are considered due to the influence of the metallic foreign material. More specifically, they are considered to be a phenomena appearing not only due to the complicated occurrence of the electric discharge from the needle tip, electric discharge together with a metallic foreign material, and electric discharge starting from the metallic foreign material but also due to the reinforcement of an electric field nearby under the influence of the metallic foreign material.
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PD repetition rate and magnitude are characteristically shown to be greater during the initiation and middle stages rather than during the final stage. These are considered due to the influence of the metallic foreign material. More specifically, they are considered to be a phenomena appearing not only due to the complicated occurrence of the electric discharge from the needle tip, electric discharge together with a metallic foreign material, and electric discharge starting from the metallic foreign material but also due to the reinforcement Energies 2017, 10, 1789 6 of of 14 an electric field nearby under the influence of the metallic foreign material. 100
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Figure 6. Statistical distributions of PD for tree model 3: (a) Hn(q) distribution; (b) Hn(Φ) distribution; Figure 6. Statistical distributions of PD for tree model 3: (a) Hn(q) distribution; (b) Hn(Φ) distribution; (c) Hqn(Φ) distribution; (d) Hqmax(Φ) distribution. (c) Hqn (Φ) distribution; (d) Hqmax (Φ) distribution.
3.4. Tendeny of Statistical Distributions of PD According to Tree Propagation 3.4. Tendeny of Statistical Distributions of PD According to Tree Propagation Figure 7a–d show the variation of mean value of statistical distributions of PD in order to Figure 7a–d show the variation of mean value of statistical distributions of PD in order to investigate PD tendency according to tree propagation stage for each artificial tree models. investigate PD tendency according to tree propagation stage for each artificial tree models. The distribution of Hn(q) and Hn(Φ) show the tendency that the variation rate of distribution The distribution of Hn(q) and Hn(Φ) show the tendency that the variation rate of distribution decreases and the distribution of Hqn(Φ) and Hqmax(Φ) increase as growing tree propagation at decreases and the distribution of Hqn (Φ) and Hqmax (Φ) increase as growing tree propagation at positive and negative cycles in case of model 1. For the case of model 2 as shown in Figure 7b, positive and negative cycles in case of model 1. For the case of model 2 as shown in Figure 7b, variation variation ratio tends to increasing as growing the tree propagation in every statistical distributions, ratio tends to increasing as growing the tree propagation in every statistical distributions, but it is but it is similar variation rate during middle to final stage for Hn(Φ) distribution. In case of model 3, similar variation rate during middle to final stage for Hn(Φ) distribution. In case of model 3, we get the we get the tendency that variation ratio of mean value for Hn(Φ) distribution is increasing from tendency that variation ratio of mean value for Hn(Φ) distribution is increasing from initiation toward initiation toward middle stage, but rather decreasing as growing progress of final stage. In addition, middle stage, but rather decreasing as growing progress of final stage. In addition, the tendency the tendency of variation for Hqn (Φ) and Hqmax (Φ) distributions gradually shows decrease as of variation for Hqn (Φ) and Hqmax (Φ) distributions gradually shows decrease as progress to final progress to final stage, and variation rate at the time to the final stage is larger than at the time from stage, and variation rate at the time to the final stage is larger than at the time from initiation to the initiation to the middle stage. middle stage.
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Model 1 Model 2 Model 3
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Figure 7. Mean of statistical distributions of PD for tree models: (a) Hn(q) distribution; (b) Hn(Φ) Figure 7. Mean of statistical distributions of PD for tree models: (a) Hn(q) distribution; (b) Hn(Φ) distribution; (c) Hqn(Φ) distribution; (d) Hqmax(Φ) distribution. distribution; (c) Hqn (Φ) distribution; (d) Hqmax (Φ) distribution.
3.5. Evaluation of the Degradation Degree of XLPE Cable Using Weibull Analysis 3.5. Evaluation of the Degradation Degree of XLPE Cable Using Weibull Analysis 3.5.1. Weibull Analysis 3.5.1. Weibull Analysis The degradation degree of the electrical trees is an important evaluation element because it is The degradation degree of the electrical trees is an important evaluation element because it is directly related to the lifetime of the cable. Several methods to classify PD sources or insulation directly related to the lifetime of the cable. Several methods to classify PD sources or insulation diagnosis were proposed like fuzzy theory, artificial neural network (ANN), fractal model, statistical diagnosis were proposed like fuzzy theory, artificial neural network (ANN), fractal model, statistical methods, and backpropagation. In previous papers, we proposed methods to identify partial methods, and backpropagation. In previous papers, we proposed methods to identify partial discharge discharge sources and diagnosis using ANN, adaptive network based fuzzy inference system and sources and diagnosisanalysis using ANN, adaptive network fuzzy inference system principle principle component linear discriminant systembased [16–19]. In order to evaluate theand degradation component analysis linear discriminant systemthis [16–19]. order to evaluate the degradation degree of degree of the electrical trees more accurately, paperIn has processed the electrical tree propagation the electrical trees more accurately, this paper has processed the electrical tree propagation time by time by means of the Weibull distribution. meansWeibull of the Weibull analysisdistribution. offers a mathematical approach for the tree propagation time analysis. The Weibull analysis offers a shown mathematical approach for the tree propagation time analysis. cumulative Weibull function is in Equation (1): The cumulative Weibull function is shown in Equation (1): 𝑡 𝛽 (1) " [−( F(𝑡; 𝛼, 𝛽) = 1 − exp ) ]# t𝛼 β F(t; α, β) = 1 − exp − (1) α and β is the shape parameter. Scale Here, t is tree propagation time, α is the scale parameter, parameter and shape parameter are derived by using least square estimation method. Here, t is tree propagation time, α is the scale parameter, and β is the shape parameter. Scale andofshape parameter arePropagation derived by Time using least square estimation method. 3.5.2.parameter Examination the Electrical Tree Figure 8 shows the failure times during the electrical 3.5.2. Examination of the Electrical Tree Propagation Time tree propagation for 16 specimens in each model. The tree propagation time was discovered to be shortest when there was any void in the Figure shows 2), thewhereas failure times during the electrical tree propagation forwas 16 specimens in each needle tip 8(Model the tree propagation was slowest when there metallic foreign model. The tree propagation time was discovered to be shortest when there was any void in the needle
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tip (Model 2), whereas the tree propagation was slowest when there was metallic foreign material (Model In Model 3, it was confirmed that although electricthe tree propagation tended to tended be fast material3).(Model 3). In Model 3, it was confirmed that the although electric tree propagation when was any kindwas of metallic foreign materialforeign during material the initiation stage, propagation from to be there fast when there any kind of metallic during theitsinitiation stage, its the metallic foreign material until the occurrence of insulation failureofproceeded slowly that the propagation from the metallic foreign material until the occurrence insulation so failure proceeded insulation failure later thanoccurred in any other so slowly that theoccurred insulation failure latercase. than in any other case. 800
Failure time[min.]
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Figure 8. 8. Time Time of of failure failure according according to to tree treemodels. models. Figure
Each failure time was measured after classifying the electrical tree propagation stages into three Each failure time was measured after classifying the electrical tree propagation stages into three stages in order to estimate the parameters and the mean lifetime at each stage through the tree stages in order to estimate the parameters and the mean lifetime at each stage through the tree occurrence testing of electrical tree model specimens. The propagation stages of each electrical tree occurrence testing of electrical tree model specimens. The propagation stages of each electrical tree were restricted into the time of its 30% growth as the initiation stage, the time of its 60% growth as were restricted into the time of its 30% growth as the initiation stage, the time of its 60% growth as the the middle stage, and the time of insulation failure as the failure stage (i.e., final stage). middle stage, and the time of insulation failure as the failure stage (i.e., final stage). Table 1 reveals the growth times for each electrical tree propagation stage of Model 1. The Table 1 reveals the growth times for each electrical tree propagation stage of Model 1. estimated Weibull distributions and parameters are as shown in Figure 9 and Table 2 respectively. The estimated Weibull distributions and parameters are as shown in Figure 9 and Table 2 respectively. Table 1. Time to failure of tree model 1. Specimen Number
Initiation (Min.)
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Figure 9. Time to failure of the Weibull distribution of tree model 1 (divided by three progress: initiation, middle, failure).
stages in order to estimate the parameters and the mean lifetime at each stage through the tree occurrence testing of electrical tree model specimens. The propagation stages of each electrical tree were restricted into the time of its 30% growth as the initiation stage, the time of its 60% growth as the middle stage, and the time of insulation failure as the failure stage (i.e., final stage). 1 1789 reveals the growth times for each electrical tree propagation stage of Model 1. The Energies Table 2017, 10, 9 of 14 estimated Weibull distributions and parameters are as shown in Figure 9 and Table 2 respectively.
Figure9. 9. Time to failure of the Weibull distribution of model tree model 1 (divided byprogress: three progress: Figure Time to failure of the Weibull distribution of tree 1 (divided by three initiation, initiation, middle, failure). middle, failure).
Table 2. Shape and scale parameter of tree model 1. Initiation
Parameter Grouping subpopulation 1 subpopulation 2
Middle
Failure
Shape
Scale (Min.)
MTTF (Min.)
Shape
Scale (Min.)
MTTF (Min.)
Shape
Scale (Min.)
MTTF (Min.)
6.3 7.5
37 70
41
8.4 3.3
124 212
137
8 4.6
271 495
302
Figure 8 displays the results of applying failure time data based on the classification of the propagation stages in Electrical Tree Model 1 to the Weibull function. It means that some parts of the measurement data have different forms of distributions, and the shape and scale parameters for each population must be estimated by applying the data to the five-parameter Weibull function. What we can confirm through these measurement results is that three of the 16 trees show different propagation aspects. In general, the propagation of bush-type trees proceeds slowly. Three measurement data represented the propagation of bush-type trees, and the remaining data showed a mixed form of both branch and bush types. Table 2 displays the shape and scale parameters for each tree propagation stage of Electrical Tree Model 1. All the shape parameters for Population 1 were estimated to have a value of 1 or higher, this means that the tree propagation proceeded in the form of their wear-out failure due to their degradation. The time difference between the tree propagation stages of the scale parameters for the data on different tree propagation forms, i.e., mutually different populations, was 96 min between the initiation and middle stages and 147 min between the middle and final stages in Population 1, whereas it was 142 min between the initiation and middle stages and 283 min between the middle and final stages in Population 2. The mean lifetime was 96 min between the initiation and middle stages and 165 min between the middle and final stages. Table 3 displays the time of each tree propagation stage for each specimen in Electrical Tree Model 2. Figure 10 reveals the results from applying the failure time data based on the classification of the tree propagation stages in Model 2 to the Weibull function. One of the measured specimens in Model 2 shows a different form of tree propagation in comparison with the other specimens. In general,
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necessary to use the two-parameter estimation method, not the five-parameter estimation method in the case three of Model 2. of data are required for analyzing the Weibull function. Thus, it is necessary to at least pieces use the two-parameter estimation method, not the five-parameter estimation method in the case of Table 3. Time to failure of tree model 2. Model 2.
Specimen Number Initiation (Min.) Middle (Min.) Table 3. Time to failure of tree model 2. 1 32 63 2 26 Specimen Number Initiation (Min.) Middle51(Min.) 3 1 29 60 32 63 4 2 33 66 26 51 5 3 36 72 29 60 33 66 6 4 32 63 36 72 7 5 24 45 6 32 63 8 7 31 62 24 45 9 8 37 74 31 62 37 74 10 9 34 63 10 34 63 11 53 105 11 53 105 1212 33 67 33 67 1313 29 57 29 57 28 56 1414 28 56 32 66 1515 32 66 16 31 58 16 31 58 Average time 33 64 Average time 33 64
Failure (Min.) 210 170 Failure (Min.) 195 210 220 170 240 195 220 210 240 155 210 205 155 245 205 245 225 225 350 350 220 220 190 190 185 185 215 215 205 205 215 215
Figure 10. Time to failure of the Weibull distribution of tree model 2 (divided by three progress: Figure 10. Time to failure of the Weibull distribution of tree model 2 (divided by three progress: initiation, middle, failure). initiation, middle, failure).
By using the two-parameter estimation method, the shape parameters were estimated to be 7.5, By using the two-parameter estimation method, the shape parameters were estimated to be 7.03, and 7.64 according to the relevant time, the scale parameters were estimated to be 24, 68, and 7.5, 7.03, and 7.64 according to the relevant time, the scale parameters were estimated to be 24, 68, 226 min, and MTTF to be 32, 64, and 212 min. and 226 min, and MTTF to be 32, 64, and 212 min. In model 2, the tree propagation proceeds very fast during the initiation stage but the tree In model 2, the tree propagation proceeds very fast during the initiation stage but the tree propagation speed is similar to those from other models after the middle stage, this is considered to propagation speed is similar to those from other models after the middle stage, this is considered to be because the tree propagates fast at an early stage due to the influence of the void at the end tip of be because the tree propagates fast at an early stage due to the influence of the void at the end tip of Model 2, but shows a general tree propagation aspect later. However, even if the tree propagation
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Model 2, but shows a general tree propagation aspect later. However, even if the tree propagation characteristics of Model 2 show similar aspects, what is important is that the time to failure in Model 2 is much shorter in comparison with the other models, this is vital information for understanding the lifetime of the electrical tree according to each defect. Table 4 is the respective values of the shape parameters, scale parameters, and MTTF in Model 2. The difference in the mean lifetime between the initiation and middle stages was 32 min, and that between the middle and final stages was calculated to be 148 min. When compared with Model 1, the tree propagation time between the initiation and middle stages was shown to be shorter than that in Model 1, however the tree propagation time between the middle and final stages is similar to that of Population 1. Table 4. Shape and scale parameter of tree model 2. Initiation
Middle
Shape
Scale (Min.)
MTTF (Min.)
7.5
34
32
Failure
Shape
Scale (Min.)
MTTF (Min.)
Shape
Scale (Min.)
MTTF (Min.)
7.03
68
64
7.64
226
212
Table 5 displays the failure time data on each tree propagation stage in Electrical Tree Model 3, and Figure 11 shows the results from applying the failure time data based on the classification of the tree propagation stages in Model 3 to the Weibull function. Like in the case of the specimens of Model 1, some of the measurement specimens of Model 3 also reveal different tree propagation aspects in comparison with the other specimens. The shape and scale parameters for each group were estimated by applying the five-parameter estimation method. Table 5. Time to failure of tree model 3. Specimen Number
Initiation (Min.)
Middle (Min.)
Failure (Min.)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
45 45 60 40 43 52 50 75 50 120 50 48 100 55 40 50
130 125 170 120 130 155 152 225 147 355 150 140 208 160 120 150
285 280 380 270 290 345 335 495 325 790 330 310 640 355 265 330
Average time
58
165
377
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Figure 11. Time to failure of the Weibull distribution of tree model 3 (divided by three progress: Figure 11. Time to failure of the Weibull distribution of tree model 3 (divided by three progress: initiation, middle, failure). initiation, middle, failure).
Table 6 shows the shape parameters, the scale parameters and the MTTF in Model 3, which were Table 6 shows the shape the scale parameters andtime the MTTF in Model 3, which respectively estimated from parameters, the measured failure times. The difference between the were tree respectively estimated from the measured failure times. The time difference between the 206 tree propagation stages in Population 1 was 100 min between the initiation and middle stages and propagation stages in Population 1 was 100 min between the initiation and middle stages and 206 min min between the middle and final stages, whereas the time difference between tree propagation between the middle and final whereasthe theinitiation time difference between treeand propagation stages in stages in Population 2 was 195stages, min between and middle stages 206 min between Population 2 was 195 min between the initiation and middle stages and 206 min between the middle the middle and final stages. It can be confirmed from the parameter estimation results in Population stages. It can confirmed from the estimation results inisPopulation 2 that if a 2and thatfinal if a bush-type treebe propagates during the parameter initiation stage, its propagation therefore very slow bush-type tree propagates during the initiation stage, its propagation is therefore very slow and that and that the tree propagates much more slowly in Model 3 containing needle-like foreign materials. the tree propagates much more slowly in Model 3 containing needle-like foreign materials. Table 6. Shape and scale parameter of tree model 3. Table 6. Shape and scale parameter of tree model 3.
Parameter Parameter Grouping Shape Grouping Subpopulation 1 Subpopulation 1 Subpopulation 2 Subpopulation 2
Initiation
Middle
Failure
InitiationMTTF Middle Failure Scale Scale MTTF Scale Shape Shape Scale Scale MTTF Scale MTTF (Min.) Shape (Min.) (Min.) Shape (Min.) (Min.) Shape (Min.) (Min.) (Min.) (Min.) (Min.) 10.8 50 9.1 150 9.3 329 56 161 10.8 50 9.1 150 9.3 329 2.92.9 9898 2.9 293 4.1 700 56 161 2.9 293 4.1 700
MTTF MTTF (Min.) (Min.)
367
367
4. Discussion 4. Discussion When fully analyzing the failure types according to the relevant time, it can be confirmed that When fully analyzing the failure types according to the relevant time, it can be confirmed that the the failure rate increases according to the relevant time in each of the three models. In other words, failure rate increases according to the relevant time in each of the three models. In other words, all the all the shape parameters have a value of 1 or higher, it can be seen from this that all the three models shape parameters have a value of 1 or higher, it can be seen from this that all the three models show show a wear-out failure. A curve with this form of an increasing failure rate (IFR) is characterized by a wear-out failure. A curve with this form of an increasing failure rate (IFR) is characterized by the the concentrated occurrence of failures anywhere due to the equipment wear-out or aging, in which concentrated occurrence of failures anywhere due to the equipment wear-out or aging, in which case case doing preventive maintenance immediately prior to the concentrated occurrence of any failure doing preventive maintenance immediately prior to the concentrated occurrence of any failure can can prevent such failure in advance. prevent such failure in advance. It can be confirmed through the results of the analyses conducted up until now that both the It can be confirmed through the results of the analyses conducted up until now that both the reliability and the failure rate appear to be different according to the relevant time through electrical reliability and the failure rate appear to be different according to the relevant time through electrical tree-type defects, which are a failure mechanism. These can provide a lot of information for working tree-type defects, which are a failure mechanism. These can provide a lot of information for working out and implementing appropriate measures against failures. In other words, the time for equipment replacement can be determined during the initiation stage of tree propagation or even after the middle stage by applying the data obtained from the partial discharge signals to the data learned in
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out and implementing appropriate measures against failures. In other words, the time for equipment replacement can be determined during the initiation stage of tree propagation or even after the middle stage by applying the data obtained from the partial discharge signals to the data learned in advance, thereby discerning the actual causes of the occurrence of partial discharge and, if such causes are attributable to any electrical tree, by also analyzing the causes of the electrical tree. It is possible to configure a system for providing feedback as part of the design stage for discovering the causes of electrical trees through the analysis of the Weibull function and comprehensively examining the respective problems in the manufacturing process and using and installing the equipment, thereby finding out the causes of such problems. F. Steennis et al. presented about prediction of lifetime aspects for XLPE cable and paper-insulated lead-covered cable using Weibull analysis [20]. From this paper, we are able to use Weibull distribution and PD activities to determine evaluation of degradation and to confirm applicability in field. It would be possible to apply the analysis data obtained by using Weibull analysis usefully as basic data for configuring this system. 5. Conclusions This paper analyzed the electrical tree propagation-based characteristics of the distributions of partial discharge signals occurring in cable insulation materials and has presented a degradation evaluation method, the results of this study are as follows: 1. 2.
3.
This paper analyzed the characteristics of the partial discharge distributions at each tree propagation stage in each simulated electrical tree model. Shape and scale parameters tended to increase as the electrical tree degradation proceeded in Tree Models 1 and 2, whereas the values of shape and scale parameters tended to decrease when the electrical tree propagation proceeded towards the final stage in Model 3. The failure time of each specimen was measured in order to determine the degradation degree of the electrical trees by means of F(t) which uses the relevant time as a variable. The failure times in each model were measured and written by the degradation stage, and the shape parameters, the scale parameters and MTTF for each model and each stage were also estimated by means of these measurement results. The time difference between the degradation stages could be calculated, and the remaining lifetime of trees was estimated by means of such time differences.
It is considered that the research performed in this study can be utilized as basic research data for insulation diagnosis and the lifespan estimation of not only power cables but also electric power equipment which uses any different types of insulating material. It is also considered that the data based on this study can be utilized for determining the lifespan estimation and maintenance stages in the continuous monitoring and diagnosis system. Acknowledgments: This study was supported by R&D Project of Korea Railroad Research Institute. I would really like to thank to Kangwon Lee who works at KRRI for gave me advice and helped me revise this paper. Author Contributions: Donguk Jang and Seonghee Park conceived experiments and discussed results. Seonghee Park performed the experiments and analyzed the Weibull distribution. Donguk Jang analyzed PD experiment results and wrote this paper. Conflicts of Interest: The authors declare no conflict of interest.
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