the implementation of needle-plane electrode configuration and test methods · pdf...

International Journal on Electrical Engineering and Informatics - Volume 5, Number 2, June 2013

The Implementation of Needle-Plane Electrode Configuration and Test Methods for Partial Discharge Inception Voltage Characteristic

Measurement of Mineral Oil

Ferdinand Sipahutar1,3, Suwarno1, Ahmad Azhari Kemma1,3, Norasage Pattanadech2, Fari Pratomosiwi2, and Michael Muhr2

1School of Electrical Engineering and Informatics, Institut Teknologi Bandung,

Jl. Ganesha 10, Bandung Indonesia 2Institute of High Voltage Engineering and System Management, TU Graz,

Inffeldgasse 18, A - 8010 Graz, Austria 3PT PLN (Persero), Jakarta, Indonesia

Abstract: The investigation of the Partial Discharge Inception Voltage characteristic is performed by many researchers using the needle-plane electrode configuration and various test methods. This was conducted due to the capability of Partial Discharge Inception Voltage characteristic to represent or determine the condition of insulating liquid. This paper discusses the implementation of the needle-plane electrode configuration and two test methods to find out the characteristics of Partial Discharge in Partial Discharge Inception Voltage level of mineral oil. For this purposes, the mineral oil which used was Nynas Nitro 4000x with water content less than 10 ppm. In experiment, the test circuit was set up according to IEC 60270. The Ramp Method as the first test procedure was conducted in this experiment according to IEC 61294 with ramp rate of rise test voltage 1 kV/s until Partial Discharge Inception Voltage occurred. Meanwhile, a Combine Method as the second test procedure was used as comparative Partial Discharge Inception Voltage test technique. With this combine method, the test voltage was applied to the test object with rate of rise test voltage 1 kV/s until 70% of the Partial Discharge Inception Voltage value obtained from the ramp method. Then the test voltage was increased in steps with 1 kV/step with step duration of 1 minute until Partial Discharge Inception Voltage obtained with apparent charge ≥ 100 pC. The rest time between consecutive tests was 5 minutes. The needle tip radius that used as high voltage electrode were 10 µm and 20 µm, meanwhile brass plane electrode with diameter 75mm and 50mm was used as the grounded electrode. The gap distance between the needle electrodes toward ground electrode was fixed at 50 mm. The calculation of electric field stress of the needle-plane electrode configuration was done by using simulation of Finite Element Method (FEM). Based on the Partial Discharge Inception Voltage test result, the needle electrodes with tip radius 10 µm will produce electric field stress that higher than other needle tip, meanwhile the Partial Discharge Inception Voltage is lower which tested using both test method. By using the combine method, the Partial Discharge Inception Voltage value, charge quantity and the number of Partial Discharge will be lower than the ramp method. The results also showed that the Partial Discharge pulse currents using both test method was about 0.2 – 0.85 mA. The time duration of Partial Discharge pulse was in the range of 1.01 – 8.38 µs and the rise time were between 68 - 301 ns. It was found that the Partial Discharge Inception Voltage test result agree with the Weibull distribution Keywords: Partial Discharge Inception Voltage; Electrode; Ramp method; Combine method; Weibull; CDF; PDF ; CV; Finite element method

Received: February 15th, 2013. Accepted: May 31th, 2013

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1. Introduction Monitoring of the transformer oil is important to be kept due to the occurrences of Partial Discharge will generate stress within the liquid insulation. Actually, there are many factors that may affect the quality of the mineral oil that usually used as the insulation for transformer. The moisture effect, particle, thermal stress and electrical stress are several factors that should be eliminated. The Partial Discharge events in liquid insulation may lead complete breakdown, especially while the degradation of the insulations material occur [1-2]. Therefore, to maintain the condition of transformer oil, the continuity monitoring is needed. One of the methods that used to monitoring oil condition in transformer is Partial Discharge measurement. This method is an important diagnostic technique and used as non-destructive test for the insulation of high voltage [1]. The occurrence of Partial Discharge in mineral oil is strongly associated with the cavity formation within the mineral oil. The evolution of these cavities will induce the rise of series Partial Discharge pulses of ascending magnitude. Such Partial Discharge Pulses can be used as an indicator to determine the value of the Partial Discharge Inception Voltage (PDIV) in insulating liquid [3]. The information of the Partial Discharge Inception Voltage characteristic in mineral oil that obtained from measurement can be used as useful indicator to monitor the degradation of the insulation of high voltage components [4]. In many case, Partial Discharge Inception Voltage is an alternatively important indicator that most researchers use for representing the integrity of the liquid insulation [5].The definition of Partial Discharge Inception Voltage of an insulating liquid according to the IEC 61294 is the lowest voltage at which an apparent charge occurs equal or exceeding 100 pC when the sample is tested under the specified conditions [6]. Some researchers report that the characteristic features of partial discharge phenomena greatly depend on experimental conditions such as electrode geometry, shape and amplitude of applied voltage, liquid nature and purity [7]. Therefore, the electrode geometry and shape have an important role for Partial Discharge Inception Voltage measurement. The electrode geometry and shape will affect the Partial Discharge Inception Voltage measurement which is related to the deployment of electric field stress around the electrode and especially at the tip. This factors also being a reason for investigation of Partial Discharge Inception Voltage characteristic of the liquid insulation by using the needle-plane electrode configuration that has been used by many research groups as seen in [8, 9, 10]. The highest electric field was obtained at the tip of needle electrode [11]. There are doubts about the effectiveness of ramp method as the test procedure which recommended by IEC61294 [12]. The advantage of Ramp Method is short test duration to obtain Partial Discharge Inception Voltage value but may have a highly chance to lead breakdown events. The Combine Method as the comparator of the Ramp Method can used for Partial Discharge Inception Voltage measurement and able to reduce the chance of the breakdown events than Ramp Method. But the combine method requires long test duration to obtain Partial Discharge Inception Voltage value. The discussion about distribution pattern of partial discharge data is also important to perform. This is done to determine the characteristic of test data obtained by experiment. So the probability of data such as cumulative distribution function (cdf) and probability density function (pdf) of Partial Discharge can be known. Based on numerical analysis, partial discharge fit to the two parameter of Weibull function [13]. This Weibull distribution is widely used for data analysis due to its relative simplicity and flexibility. Besides of that, this paper proposes the CDF and PDF of Partial Discharge Inception Voltage value so it can be used to determine the occurrence probability of Partial Discharge Inception Voltage value. In this case, the Partial Discharge Inception Voltage data was analyzed by using simple formula that used to determine the distribution of Breakdown Voltage (BDV) data [14]. 2. Experiment Setup and Data Analysis The experiments were divided into two parts. First, we simulated the electric field simulation of the electrode configuration system by FEM simulation. Second, we carried out laboratory scale experiment. The moisture content in this measurement was kept less than 10

Ferdinand Sipahutar, et al.

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ppm which was measured by using Karl Fischer Coulometer. A. Electrode Configuration The measurement of Partial Discharge Inception Voltage was performed in a test vessel. Tungsten needle electrode with tip radius 10 µm and 20 µm were used as high voltage electrode. The length of needle electrode is 45 ± 0.5 mm. Brass plane electrodes with 75 mm and 50 mm diameter were used as the grounded electrode. The gap distance between the needle - plane electrode was fixed at 50 mm. Figure 1, depicts the electrode configuration for Partial Discharge Inception Voltage measurement.

75 mm50 mm

Tip radius Tip radius

10 µm 20 µm

Needle Electrode

50 mm 50 mm

Tip radius Tip radius

10 µm 20 µm

Figure 1. Electrode configuration for Partial Discharge Inception Voltage (PDIV) measurement B. Testing Circuit The test circuit for Partial Discharge Inception Voltage measurement was set up according to IEC 60270 [15]. The discharge was measured with Power Diagnostics ICM and Oscilloscope Yokogawa DLM series at the same time. With ICM, we recorded the Partial Discharge Inception Voltage and Partial Discharge patterns. The coupling device was connected to the coupling capacitances and to the ICM. This configuration was chosen to depict the real condition of electrical system. In addition, this configuration was used to avoid the possible destruction of measuring equipment in case of the breakdown occurs. Meanwhile with oscilloscope, we used to recorded the Partial Discharge pulse current signal.The shunt resistor was directly connected to the oscilloscope via 50 ohm matching impedance. Figure 2, illustrates the test circuit of Partial Discharge Inception Voltage measurement.

Coaxial cable 50 Ω

Coaxial cable 50 Ω

Coupling Capacitances

Coupling Devices

Current limiting resistor

Voltage Regulator MatchingImpedanceG

Insulation Condition

Coaxial cable 50 Ω

Test Vessel

(16 litre oil)

Pre‐amplifier

Personal Computer

C

Step Up

C

Capacitive voltage divider 200 kV Shunt Resistor

Oscilloscope

Figure 2. Test circuit for Partial Discharge Inception Voltage (PDIV) measurement

The Implementation of Needle-Plane Electrode Configuration and Test

207

C. Testing Procedure The Ramp Method (as specified in IEC 61294) and the Combine Method were used to investigate Partial Discharge Inception Voltage characteristic of mineral oil. According to IEC 61294, Partial Discharge Inception Voltage measurement is done by applying the ramp test voltage with rate of rise test voltage 1 kV/s until the first discharge with its apparent charge ≥ 100 pC occur. The measurement of Partial Discharge Inception Voltage was conducted ten times for every test object. The combine method procedure is a method to generate Partial Discharge Inception Voltage by means of increasing the voltage with the rate of rise test voltage 1 kV/s until 70% of average Partial Discharge Inception Voltage value that obtained from Ramp Method. Then, the voltage was increased in steps with rate of rise test voltage 1 kV/step until the Partial Discharge Inception Voltage value (100 pC detection) occurred. After the Partial Discharge Inception Voltage value was achieved, the test voltage was decreased until zero. The rest time between consecutive tests was 5 minutes. Figure 3, describes the test procedure of Partial Discharge Inception Voltage measurement using ramp method and combine method.

1 minute

70 % of average PDIV

1 kV/s

PDIV (Charge =100 pC)

5 minute

1 kV/s

1 kV/s

zerovolt zerovoltzero volt

1 kV/s 1 kV/s

PDIV PDIV PDIV

1 minute

PDIV pulse

PDIV

PDIV (Charge = 100 pC)

zero volt

1st 2nd 3rd 10th

b)a) Figure 3. Test procedure of Partial Discharge Inception Voltage measurement according to a)

IEC 61294, b) Combine Method

D. Data Analysis The plot of Partial Discharge Inception Voltage test results is an useful information to forecast the possibility of failures. Some action and appropriate plans to manage and controls such failures can be conducted by using data plot. Weibull analysis is widely used for data plot and data analysis due to its relative simplicity and flexible. In addition, the failure analysis and forecasting of small number of population data can be conducted using Weibull analysis [16]. In many case, Weibull analysis is applied to analyze breakdown voltage and partial discharge data. The guide for statistical analysis of electrical insulation breakdown data can be seen in [17]. Based on numerical analysis, partial discharge is fit with Weibull distribution of two parameter [18]. In this thesis, PDIV characteristics test results were analyzed using Weibull distribution to obtain the cumulative distribution function (cdf) and the probability density function (pdf). The formula for data analysis is complied with IEEE 930-2004. The Weibull statistical analysis of Partial Discharge Inception Voltage characteristics test results is conducted using the following formula.

; , 1 (1) The F(t;α,β) is defined as the cumulative distribution function, α is defined as a scale parameter, β is defined a shape parameter that related to the range of Partial Discharge Inception Voltage, whilst t is defined as a measured variable and in this case is Partial Discharge Inception Voltage value.


208

Simple approximation : , ..

. 100% (2) The F(i;n) is defined as an estimation of CDF, i is defined as the rank order of data, and n is defined as weights of small data sets. The expressions for the CDF is present the probability of Partial Discharge Inception Voltage occurring with the rising of test voltage. The probability density function of Weibull distribution can be calculated using the formula as follows [19].

. . exp (3)

The f(x) is defined as probability density function, α is defined as scale parameter, is defined as shape parameter, x is defined as measured variable. For calculation, we determine:

ln (4)

where ln (ti) is the natural logarithm. For each probability of PDIV value, we expressed a percentage of value:

ln ln 1 , (5)

The weighted average of Xi and Yi is calculated using the equations as follows: ∑

∑ and ∑

∑ (6)

By using equation (2-17) the β and α parameter can be calculated as follows:

∑ ∑ –

exp } (7)

The lower and upper bounds of the 90% confidence interval for the percentile:

exp / and exp / (8) For fitting data, the Kolmogorof-Simirnov method is introduced because is appropriate for small samples [20]. P0 (Xi) = P0 (X ≤ Xi) = CDF (Xi) (9) ; 1 … (10) D+ = Fn – Fo and D- = Fo – Fn-1 (11) D = Maximum of all D+ and D- ( ≥ 0) ; for i = 1, ….. n (12) According to the Kolmogorof-Simirnov method, Fo(Xi) is defined as the CDF evaluated at Xi, Fn(Xi) is defined as a empirical distribution function, D or ks is defined as the distance test, n is defined as the number of data, and X is defined as the data value. The test error α = 0.05, CV(0.05), was used for fitting data.


209

Table 1. shows the critical value of Kolmogorof-Simirnov error. Table 1. Kolmogorov-Simirnov Critical Value (CV) for α (0.20 and 0.05) [20]

Number of sample CV (0.20) CV (0.05) 4 0.494 0.624 5 0.446 0.564 6 7 8 9

10

0.411 0.381 0.358 0.339 0.322

0.521 0.486 0.457 0.432 0.411

3. Test Results and Discussion According to the simulation results, we can see that the electric field stress for plane diameter 75 mm is higher than plane diameter 50 mm which tested using the needle electrode tip radius 10 µm and 20 µm respectively as shown in table 2. From table 2, we can conclude that small tip radius will generates high electric field stress and will influencing the inception voltage of the partial discharge. Figure 4 shows the comparison of the Partial Discharge Inception Voltage value and standard deviation for all electrode configurations which tested using both test methods. The quantity of charge can be seen on Figure 5. The test results show that the average Partial Discharge charge (QIEC) of the needle electrode with tip radius 20 µm which higher than Partial Discharge charge of the needle electrode with tip radius 10 µm and this is related to the increasing of Partial Discharge Inception Voltage value.

Table 2. The maximum electric field stress based on simulation

results at the needle tip using input 100 volt

Needle Tip Radius Electric Field Stress (kV) [Plane Diameter 50 mm]

Electric Field Stress (kV) [Plane Diameter 75 mm]

10 µm 13.7 15 20 µm 8.1 8.8

Figure 4.Test results of average PDIV, Standard Deviation and Electric Field Stress from different test procedure and needle tip radius

0

10

20

30

40

50

75 50 75 50PDIV

(kV

), St

d D

evia

tion

(kV

), El

ectri

c Fi

eld

Stre

ss (k

V/c

m)

Test Method - Ground ElectrodePDIV [Needle Tip 10 µm]PDIV [Needle Tip 20 µm]Standard Deviation [Needle Tip 10 µm]

Ramp Method Combine Method


210

From Figure 4 we can see that the needle electrode with tip radius 10 µm generates lower Partial Discharge Inception Voltage than needle electrode with tip radius 20 µm. These results are in accordance with the maximum electric field stress that simulated for both tip radii. The simulation results show that the value of electric field stress of the needle electrode with tip radius 10 μm is nearly two times of needle electrode with tip radius 20 μm as stated in the Table 2. The different of Partial Discharge Inception Voltage level may cause by the randomness evolving of cavity within mineral oil and local heating process that influenced by the electric field stress of the different needle tip dimensions. The electric field stress affects also the aggressiveness of ions movement within mineral oil. This movement caused by the high electric field stresses could evoke the kinetic energy for ions. When the movement of ions toward area is near to the tip of the needle electrode, the possibility of discharge is high. Figure 4 also presents the standard deviation of Partial Discharge Inception Voltage value of the needle electrode with tip radius 20 µm that higher than needle tip radius 10 µm by using ramp method and combine method. This result indicates that the use of needle tip radius 10 µm for Partial Discharge Inception Voltage measurement of mineral oil under room temperature is better than using needle electrode with tip radius 20 µm. In addition, the combine method is more sensitive to detect Partial Discharge Inception Voltage than ramp method. The reason of this sensitivity is related to the development of cavities that requires sufficient energy to discharge which influenced by local heating due to electric field stress. Under the constant test voltage for 1 minute (in accordance with combine method), the discharge possibly occur when cavities are already formed. Unlike the case of IEC 61294 test procedures, with rate of rise test voltage 1 kV/s, the cavity establishment is not progressing well. Therefore, the Partial Discharge Inception Voltage with charge ≥ 100 pC will be only detected when the electric field stress is higher than combine method and occasionally occur near to the breakdown limit. Hence, the measurement of Partial Discharge Inception Voltage using the combine method is more secure from breakdown events than ramp method. According to the test results, the standard deviation of Partial Discharge Inception Voltage value is better when using the needle electrode with tip radius 10 µm than the needle electrode with tip radius 20 µm. Therefore, the using of the needle electrode with tip radius 10 µm is highly recommended than the needle electrode tip radius 20 µm.

Figure 5.Test results of average Partial Discharge Charge (Qiec) from different test procedure and needle tip radius

From Figure 5 we can see that the Partial Discharge charge (Qiec) is strongly influenced by the Partial Discharge Inception Voltage value that related to the electric field stress. When the

050

100150200250300350400450500

75 50 75 50

Ave

rage

PD

IV (k

V) a

nd A

vera

ge P

D C

harg

e (p

C)

Test Method - Ground ElectrodePDIV [Needle Tip 10 µm] PDIV [Needle Tip 20 µm]Qiec - Ramp Method [Needle Tip 10 µm] Qiec - Ramp Method [Needle Tip 20 µm]



211

electric field stress inside the mineral oil is high, then the Partial Discharge Inception Voltage value is easy to obtained especially using the needle electrode tip radius 10 µm and plane diameter 75 mm. With high electric field stress, the Partial Discharge charge production will high. According to the test results, we can see the test method also influence the Partial Discharge Inception Voltage and Partial Discharge charge value. This results is caused by the combine method is easy to obtain the Partial Discharge Inception Voltage value in low voltage. Therefore, the generation of Partial Discharge charge will also influence by the Partial Discharge Inception Voltage value which related to the electric field stress. Besides of the Partial Discharge Inception Voltage and Partial Discharge charge value, the characteristic of Partial Discharge such as pulse current, duration of pulse current, and also the rise time of Partial Discharge current can be obtained. Table 3 depicts the characteristic of Partial Discharge current. Table 3. The maximum electric field stress based on simulation results at the needle tip using

input 100 volt From table 3 we can see the characteristic of Partial Discharge current such as pulse current, pulse duration and the rise time. According to the test results, high electric field stress will generates high Partial Discharge pulse current. The configuration of the needle electrode with tip radius 10 µm toward the ground plane electrode with tip radius 75 mm will produce Partial Discharge pulse current which higher than plane electrode diameter 50 mm tested using both test methods. Moreover, Partial Discharge pulse duration and Partial Discharge rise time is shorter than the cofiguration of the needle electrode tip radius 10 µm and 20 µm toward the ground plane diameter 50 mm. In addition, we can see also that the needle electrode with tip radius 20 µm will generates Partial Discharge pulse current, Partial Discharge pulse duration and Partial Discharge rise time which higher than the needle electrode with tip radius 10 µm for appropriate configuration. We can conclude also that the test methods will influence the value and range of Partial Discharge pulse current, Partial Discharge pulse duration and also Partial Discharge rise time. Figure 6a and 6b represent the cumulative distribution function and probability density function of Partial Discharge Inception Voltage value of ramp method and combine method respectively. The numerical analysis of Partial Discharge Inception Voltage value of ramp method and combine method is in accordance with the Weibull distribution. The compliance of data to the Weibull distribution for each test method is proved by using Kolmogorov-Simirnov (KS) method. The congruence of Partial Discharge Inception Voltage data to the Weibull distribution is indicated by D+ and D- parameter. While the maximum value of D+ or D- less than critical value of KS that presented in the table 1, then hypothesis of dataagrees with the Weibull distribution is accepted. The Confidence Interval (CI) for lower and upper bounds is 90% confidence limit for the percentiles 0.1%, 1%, 5%, 10%, 30%, and 95%. The higher

Needle tip

radius (µm)

Ground Plane Electrode (mm)


75 mm 50 mm 75 mm 50 mm

Gap

Dis

tanc

e 50

mm

Puls

e C

urre

nt 10 0.39-0.46 0.27-0.47 0.29-0.37 0.2-0.32

20 0.54-0.85 0.41-0.65 0.34-0.51 0.36-0.44

Puls

e D

urat

ion 10 1.40-2.57 1.39-3.67 1.06-2.01 1.08-2.26

20 2.79-8.38 2.69-6.99 1.01-2.78 1.25-2.23

Ris

e Ti

me 10 73-180 83-227 68.8-173.6 71-153

20 151-276 107-301 90.4-172.8 131-188


212

frequently density function of PDIV value using ramp method for plane diameter 75 mm and 50 mm is in the 31.2 – 34.3 kV for needle tip 10 µm and 39.5 – 40.2 kV for needle tip 20 µm. Meanwhile, for combine method, the higher frequently density function lies in the 25.4 - 26.2 kV for needle tip 10 µm and 31.2 - 34 kV for needle tip 20 µm. The probability density function of Partial Discharge Inception Voltage value can be used as information to determine the frequently density of the occurrence of Partial Discharge Inception Voltage. Table 4 shows, the pdf for all electrode configurations.

a)

b) Figure 6. Weibull CDF and PDF of Partial Discharge Inception Voltage value for Plane

diameter 50 mm (a) Ramp Method b) Combine Method

Table 4. The highest value of probability density function of PDIV for all the needle-plane electrode configurations

Conclusion The electrode geometry such as the needle tip radius, the shape of ground electrode and also the gap distance will influence the Partial Discharge Inception Voltage characteristic (inception voltage, Partial Discharge charge, Partial Discharge current) of mineral oil. Besides

Test Method Plane 75 mm Plane 50 mm

Needle tip 10 µm Needle tip 20 µm Needle tip 10 µm Needle tip 20 µm

Ramp Method 33.6 % (31.2 kV) 16.10 % (39.5 kV) 16.18% (34.3 kV)

13.44% (40.2 kV)

Combine Method 38.7 % (25.4 kV) 19.31 % (31.2 kV) 34.96% (26.2

kV) 22.44% (34 kV)

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

14 24 34 44 54

Prob

ability Den

sity Fun

ction (%)

Cumulative distribu

tion

function

(%)

Partial Discharge Inception Voltage (kV) ‐ Ramp Method

cdf data points [needle 10 µm]

upper confidence bound [needle 10 µm]

lower confidence bound [needle 20 µm]




pdf data points [needle 10 µm]


10 µm [α = 34.1715, β = 15.1088, D+ = 0.1764] 20 µm [α = 42.2330, β = 10.4032, D+ = 0.1830]

[Confidence Interval (CI) =90%]

0%

10%

20%

30%

40%

0%

20%

40%

60%

80%

100%

16.0 26.0 36.0

Prob

ability Den

sity Fun

ction (%)

Cumulative distribu

tion functio

n (%)

Partial Discharge Inception Voltage (kV) ‐ Combine Method









10 µm [α = 28.3766, β = 27.1657, D+ = 0.2796] 20 µm [α = 33.7061, β = 21.1148, D+ = 0.2991]

[Confidence Interval (CI) =90%]


213

of that, the test method for Partial Discharge Inception Voltage measurement is also an important parameter to be considered. According to the test results, the combine method procedure is more sensitive to detect Partial Discharge Inception Voltage at low voltage and more secure from breakdown events than the ramp method which recommended by IEC 61294. In addition, the standard deviation of Partial Discharge Inception Voltage value for all the needle electrode tip radius 10 µm that tested using both test methods is better than the needle electrode tip radius 20 µm. Therefore we can conclude that the combine method is feasible to be used in Partial Discharge Inception Voltage measurement and according to the test results, the needle electrode with tip radius 10 µm is recommended for Partial Discharge Inception Voltage measurement of mineral oil. In addition, the configuration of the needle electrode tip radius 10 µm and plane diameter 75 mm, is strongly recommended due to its good performance and its feasibility for Partial Discharge Inception Voltage characteristic measurement of mineral oil. Finally, the test results for Partial Discharge Inception Voltage obtained from experiment test agree with Weibull distribution and by using the cdf and pdf value, the frequently density of the occurrence of Partial Discharge Inception Voltage can be known. It found that the highest frequently density function of Partial Discharge Inception Voltage value using ramp method for plane diameter 75 mm and 50 mm is in the 31.2 – 34.3 kV for needle tip radius 10 µm and 39.5 – 40.2 kV for needle tip 20 µm. Meanwhile, for combine method, the higher frequently density function lies in the 25.4 - 26.2 kV for needle tip radius 10 µm and 31.2 - 34 kV for needle tip 20 µm. References [1] Muhr.M, Schwarz.R, Pack.S, Koerbler.B., 2004. Unconventional Partial Discharge

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