00055716.pdf

IEEE Transactions on Electrical Insulation Vol. 25 No. 3, June 1990 453

Measurements of Partial Discharges by Computer and Analysis of Partial

Discharge Distribution by the Monte Carlo Method

M. Hikita, K. Yamada', A. Nakamura, T. Mizutani, A. Oohasi2,

and M. leda3 Department of Electrical Engineering,

Nagoya University, Nagoya, Japan

ABSTRACT An attempt is made to elucidate the mechanism of partial discharge (PD) occurring in the CIGRE Method I1 (CM-11) electrode system, which is a representative closed-void model system. We developed a computer-aided PD measuring system. This allows us to obtain phase information of all PD pulses, together with their amplitudes, so that a statistical analysis of these data can be discussed. Measurements of PD are made for the CM-I1 electrode system. Effects of the pressure and gas inside the void on the PD are examined. Taking into account the experimental results, we propose a model for the PD mechanism. This model assumes that the statistical time lag of discharge depends on the overvoltage and that the residual voltage depends on the PD magnitude. A Monte Carlo simulation of the PD distribution is made on the basis of this model. The computed results agree well with the experimental data and the appearance of swarming pulsive micro discharges. The physics of the model also are discussed.

INTRODUCTION

variety of organic polymers have been used as electri- A cal insulating materials for electric power apparatus and cables. A large amount of work has been done on degradation of the insulating materials caused by partial discharges (PD) occurring at various defects in the polymer insulator itself and at the interface between electrodes and the insulating materials [l]. PD degradation is one of the most significant factors deciding the life of the insulation system. Much remains unknown about the mechanisms of the PD degradation. In order to clarify

the mechanism of PD degradation, a deeper understanding of the fundamental properties of PD is essential [2].

For the study of PD phenomena, various types of measurement have been used such as observation of waveform of PD pulse, high-speed photographic measurements of discharge column, and analysis of the discharge spectrum. Very few attempts, however, have been made to use statistical analysis of a large volume of data on PD pulses [31.

Computer-aided PD measurement systems enable the

0018-Q367/90/0600-453$1.00 @ 1990 IEEE

. . . . .-.. ,

454 Hikita: Partial Discharge Distribution by the Monte Carlo Method

Sphere E l e c t r o d e and that has considered that the sparking voltage v, of the void gap and the residual voltage v, are simultaneously distributed. The physics of PD in our model is also Stainless S t e e l Ball (@Set)

Copper Pipe (75mm,@4) qualitatively discussed. n I

Kap ton (OB125nn t)

\ Plane E l e c t r o d e Stainless Steel (@to)

Figure 1. Structure of CIGRE Method I1 electrode system.

measurement of all PD pulse amplitudes, as well as the phase angle information, i.e., at which phase angle each PD pulse takes place. The PD pulse amplitude distribution obtained by this method is expected to include significant information on the PD phenomena. The measurements and the statistical analysis of the correlation between PD pulse-height distribution and the phase angle of the applied voltage is a good prospect for a new and useful means of PD study [3].

From this point of view, we have made measurements of PD pulses using the CIGRE Method I1 (CM-11) electrode system, developed a computer system, and examined the statistical properties of partial discharges. Okamoto et al. [4] made a simulation of PD characteristics including the phase angle of the applied voltage. This reference probably has been the only one concerning such PD simulation. Their model assumed Whitehead’s equivalent circuit and introduced a probability distribution of the discharge time lag. The authors [4] approximated a sinusoidal voltage waveform as a triangular waveform because it simplified the calculation.

In this paper, we propose a model for a PD mechanism which assumes that the statistical time lag of the discharge is dependent on overvoltage of a void gap and the residual voltage depends upon the charge of preced- ing PD. With Monte Carlo simulation of PD characteristics, the model can explain, to some extent, the PD distribution and occurrence of swarming pulsive microdischarges (SPMD) measured for CM-I1 electrode system. There seems no other report except the present one that has made Monte Carlo simulation of the PD distribution with the phase angle information of an applied voltage,

EXPERl M ENTAL

ELECTRODE S Y S T E M

IGURE 1 illustrates the CIGRE Method I1 electrode F system, which is an improved type of CIGRE Method I (CM-I) electrode and is expected to be accepted by CI- GRE SC15 as a standard test electrode for internal PD measurements [5] . The electrode system used had a cylin- drical void of 125 pn in thickness and 3 cm in diameter. The sample used was a board made of 1 mm thick epoxy resin. The void was filled with dry air a t atmospheric pressure for the standard measurements. The PD inception voltage was about 4 kV of rms value. Ac voltage of 7 kV at 60 H a was applied to the test electrode through this experiment. PD pulse amplitude distribution was measured at a given aging time for 60 s, corresponding to 3600 cycles, by using the developed system. In order to examine the effects of pressure and gas content inside a void, further measurements were made for different gas pressures and for different ratios of oxygen and nitrogen content in the gaseous mixture.

On the other hand, the CM-I1 electrode system is de- signed so that the wall does not influence the PD characteristics. This is one of the main reasons why CM-I1 electrode system is recognized as a standard test electrode for the evaluation of a sample against internal PD. It has been reported that for the case of relatively low voltage application no tree-like surface discharges took place on the sample surface [6], and that PD occurred over the sample surface within a radius of 2.4 to 3 mm right below the upper electrode [7] . The electrode system is thus considered appropriate for the fundamental study of internal PD.

For a usual small-void system such as CM-I electrodes, the wall surrounding a void strongly affects the internal PD, which makes the understanding of the mechanism more difficult.

M E A S U R E M E N T S S Y S T E M

The details of the developed computer-aided PD measuring system (CAPDMS) to accomplish the statistical analysis of PD distribution are given below. The measuring system can record the number of PD pulses and the


magnitude of each pulse occurring in a given period, as well as the phase angle information, i.e., where the PD pulse has occurred in one cycle of the applied ac voltage.

SYMBOL LIST

- N

d

6

x

the capacitance of a void [F] the capacitance seen from the discharge gap C ,

the capacitances of the insulator in parallel and in series with the void [F] gap distance or sample thickness [m] frequency of applied voltage [H,] the current flowing through the resistance z of the discharge column [A] PD pulse amplitude distribution =xi n($,, q j ) , the relation between the magnitude of charge and the number of PD pulses ( q - n characteristics) = ( l / T ) E i n ( & , q , ) , the phase angle dependence of average discharge occurrence density ($ - fi characteristics) [ 1 /SI = ( l / T ) E i , j n($,,qj), the averagenumberof PD pulses occurring per s [l/s]

PI

- N / f [1 /cycle1 = d Q / d 6 the probability density function of Q ( 6 ) gas pressure in a void [Pa] apparent charge [C] = ( l / T ) C j qjn($i,q,), the phase angle dependence of average discharge current ($ - + characteristics) [ C / s ]

phase angle dependence of the average magnitude of PD pulse ($ - i j / i i characteristics) [C/number] the probability that the discharge starts at phase 6 = 6 after the gap voltage reaches vsm at $ = 60

= ( l / T ) E i , j q,n($i,qj), the average discharge current [C/s]

period of PD measurements normalized gap instantaneous voltage the peak value of the gap voltage [VI and the peak value of the applied voltage [VI, respectively residual voltage [VI and the minimum residual

discharge inception voltage of a gap [VI the normalized critical gap voltage at which discharge eventually occurs at infinite time normalized gap overvolt age permittivities of the sample and air, respectively

phase angle of the applied alternating voltage

phase angle of the applied voltage at which PD occurs [deg] phase angle of the applied voltage for positive PD and for negative PD at which SPMD starts to occur, respectively number of occurrence of discharge per unit phase angle [l/deg] a proportional constant relating X and AV

voltage IV]

[F/mI

[degl

Figure 2 shows the test circuit for PD measurements. Ac HV generated by a transformer was applied to a test electrode system which is parallel with a coupling capac- itor Ck. The PD pulses are detected across a RC detection impedance. Applied alternating voltage is divided by 1000, which is used later to obtain the signal for the phase information. Two signals are transmitted to the analog to digital (A/D) converter by optical fibers to avoid electrical noise. The A/D converter holds the peak level of each detected P D pulse and then digitizes it by 7 bits to 128 divisions between +5 and -5 V. The signals are transmitted to the main memory of mini-computer MEL- COM 70/25 by direct memory access (DMA), giving 10 ps as the minimum time interval for data acquisition of the system.

The A/D converter generates low level rectangular pulses with 1 ps width using the signal transmitted from the divided applied voltage. The output pulse, used for the phase position of the applied voltage, divides one cycle of ac voltage into 128 time windows of the order of 1 ps. The first time window is assigned when the applied voltage crosses 0 V from the negative to positive half cycle. The window number a t which a PD pulse takes place, gives the phase angle of the voltage cycle.

Figure 3 shows the concept of how to acquire the PD data by the CAPDMS mentioned above. The two dimensional array n(4, q ) is stored in the main memory as shown in Figure 3, where n is the number of PD pulses having occurred in phase angle 4 with a magnitude q. For example, when a P D pulse occurs a t a phase angle 4; with a magnitude of q j , the content of memory corresponding to the element of the array n(di, q j ) is increased by one. This method therefore makes it possible to measure the phase characteristics of PD pulses for a very long period. After taking the data in a given time, the stored data in the main memory unit is transferred to the cartridge disk. This measurement sequence can be automatically repeated for the number of measurement cycles previously set. After measurement, the data stored on the cartridge disk are transferred to the floppy disk.

The data thus obtained are input via the floppy disk to the FACOM M-382 in Nagoya University Computa- tion Center, after which various types of data analysis are made. The software developed allows one to deal with a large volume of data and to obtain various important parameters related to PD, such as the total number of PD pulses n, total apparent charge C q transferred by discharges, the phase angle characteristics, and so on. Since CAPDMS can take phase angle information of each P D pulse, one can draw three-dimensional graphics of the phase angle distribution of the number and magnitude of


Cd=2 OOpF

Rd=5kR

R =235R

R =165R

Cx'=2. 2pF

Cd ' =200pF

1 2

FACOM

M-382 T

Results

NAGOYA UNIVERSITY Vo 1 tme ter

3

0 0

Zero cross detective signal

Differential Attamtor amp-

Detected PD pulse signal

Figure 2. Test circuit for partial discharge measurements.

PD pulses, 4 - q - n (voltage phase angle, magnitude of PD pulse, number of PD pulses), along with the distributions of discharge magnitude vs. number of PD pulses ( q - n), and three types of phase distributions such as phase angle vs. pulse density (4 - f i ) , phase angle dependence of average discharge current (4 - i j ) , and phase angle vs. average charge per P D pulse (4 - q / f i ) .

EXP ER1 M ENTAL RESULTS

IGURE 4 shows a typical result of the temporal change F of the characteristics and distributions of P D for the CM-I1 electrode system for 7 kV a t 60 Hz. The upper Figures show 4 - q - n characteristics with the applied voltage phase 4 along the t axis, the magnitude of PD pulse along the y axis, and the number of P D along the z axis. In every lower Figure of Figure 4(a) to (e), showing 4-q distribution, the high density of dots indicates a high repetition rate of P D pulses. A sinusoidal waveform in the Figure represents an applied voltage waveform. Figure 4 also indicates the average number of PD pulses % occurring per alternating cycle of an applied voltage and the average discharge current G ( n A ) . At 25 h of the aging, the magnitude of PD pulses becomes smaller than that a t 30 min of aging. As the aging time increases further, PD pulses occurring a t phase angle near 90' and 270' or later parts of the phase begin to disappear, and both and decrease. No pulses with more than 10 DC. which is the minimum detection sensitivitv of charge

MELCOM

Software

Phase angle is divided into L [S 128) sections

Q)

c? 3

-8 2

C .-

> U .d

V l m .- c 0 wz !i

0

Phase angle of applied voltage # ( d e g )

Figure 3. Concept of PD data acquisition to the computer memory.

for our CAPDMS, appears t o be detected a t 312 h after the initiation of voltage application. This is because the P D pulses turned into so-called swarming pulsive mi- crodischarnes (SPMD'I which are characterized bv much r - 7 " " \

IEEE Transactions on Electrical Insulation Vol. 25 No . 3, June 1990 45 7

(I [ P C I . I O 1 0 [ P C I 1 1 0 ' 0 ( P C ) . I O 1

5 0 0

100

300

200

IO0

- 0 L -

-100

-200

- 3 0 0

-400

-500

Q = 6 7 . 0 nA

500

400

100

200

I O 0

I

-100

-200

-100

- 4 0 0

- 5 0 0

s =21.3/cyc QC=74.5 nA

N =11.8/cycle

6 =24.8 nA

200

,le

-400

-500

0

(I [ P C I ,101 0 ( P C I * I O ' 500

100

300

200

I 0 0

- 0 L I

-100

-200

-300

-400

-500

500 E =o.o4/cycle

400 1 ij =0.04nA 300 J

200 -

100 -

-200

- 3 0 0

-400

-500

Figure 4. Experimental results on temporal change of q5 - q - n and q5 - q characteristics of PD for CIGRE Method I1 electrode system for applying 7 kV a t 60 Hz. x, is the average number of PD pulses per cycle, and is the average charge per pulse. Data acquisition time T is 60 s for each figure. L is the number of divisions of time window in one cycle.

smaller charge of each pulse and much higher repetition rate, in comparison with the ordinary PD pulses. It is

reported that SPMD take place in such electrode system as open-void and CM-I systems when the content of gas


air: Jbu'I'orr

1 I

-90 - 4 0 -3 40 80

IO0

80

60

' 40

0 -

20

0

-60

- B O

100

80

60

' 40

20

0

e

0 -

: -20 a I

0 - 4 0

-60

-80

-100

IO0 e

BO

60

' 40

0 -

20

0

-60

-80

-100

le

J \

Figure 5. Effects of gas pressure inside a void on r$ - q - n and r$ - q characteristics for dry air at 100 kPa (left), 75 (center), and 48 kPa (right).

inside a void becomes rich of nitrogen due to consumption of oxygen by the reaction with a sample [8]. It is also seen from 4 - q characteristics a t 30 min and 25 h that PD occur a t phase angle of both 90 and 270", which are the ac voltage peaks. This phenomenon can be interpreted in terms of existence of time lag of discharge: the difference between the time when the voltage of the discharge gap, including the void, reaches the discharge inception voltage and the time when discharge actually takes place.

CM-I1 electrode, measurements were made a t 7 kV for different gas pressures of 100, 75 and 48 kPa of dry air. The results are shown in Figure 5. There seems to be no distinct difference among P D characteristics for three different gas pressures. Since discharge inception voltage decreases with gas pressure, the phase a t which PD begins to occur shifts toward earlier phase, leading to an increase in the average current Q as shown in Figure 5.

EFFECTS OF PARTIAL PRESSURE The number of PD pulses with smaller charge quantity is larger a t 25 h than a t 20 min, although the occurrence of PD pulses extend over the same width of the phase RATIO OF 0, AND Nz region, The phenomenon is considered to result not only from the time lag of discharge but also due to changes in the discharge inception voltage of the gap, the residual voltage, and the area of discharge. We will discuss this later.

EFFECTS OF GAS PRESSURE INSIDE VOID ON PD DISTRIBUTION

Kako et al. [9] has reported that for CM-I electrode system the gas pressure inside the closed void decreases with increasing aging time. In order to examine the effects of gas pressure inside a void on PD characteristics for

Izeki et al. [8] suggested that nitrogen-rich atmosphere in a void, due to consumption of oxygen, gives rise to SPMD. The effects of partial pressure ratio of oxygen and nitrogen inside a void on P D distribution for the test electrode system are also investigated. Figure 6 shows the results for compound gas consisting of dry air and nitrogen gas with different ratios of partial pressures, 150:610, 60:700 and 20:740, corresponding to 4, 1.7, and 0.6% of the mixture proportion of 0 2 , respectively. As can be seen, decreasing the ratio of 0 2 / N z l decreases the number of PD pulses with larger charge quantity. When the ratio is 20:740 ( 0 2 : 0.6%), the characteristics become to


m t r o , IO,, .

air: 60'rorr air-: Lu'l'orr N 2 :740Torr

( 0 2 : 0.6%)

N2 :700Torr

( o2 : 1.7 % )

air: 150Torr N2:610Torr

N500/ (02: 4 % 1

- 8 0 -63 -c 40 80 -90 - 4 5 - 3 4c 80 - 8 0 -40 - 0 40 20

0 t P C 1 . I O 1 0 [ P C I . l o 1

IO0

80

60 0 L

= 10

20

0

G -20 e U

0 -40

-60

-80

-100

IO0

le 80

60 0 - 1, 40

20

0

" -20

0 -40

-60

- e -

-80

- i o 0

I O 0

E O

60 0 - . 40

20

0

" -20

D - 4 0

-60

- e I

- 8 0

- IO0

le

Figure 6. Effects of partial pressure ratios of oxygen and nitrogen inside a void on 4 - q - n and 4 - q characteristics. Ratios of dry air and nitrogen gas are 150:610 (left), 60:700 (center), and 20:740 (right), respectively.

resemble in shape with those a t 96 h as shown in Fig- ure 4, in which SPMD took place, consistent with Izeki's suggestion. When the partial pressure po of oxygen is high, there seems almost no change in the PD characteristics. The shape of distribution begins to change when the partial pressure of oxygen goes down to a critical value. It was also observed that further decrease of po brought the ordinary PD pulses into SPMD. Note that the PD distribution pattern similar to that for 25 h aging time shown in Figure 4 were observed over a relatively long period from 10 to 60 h after the initiation of voltage application. On the other hand, no matter what the compound ratio of dry air and nitrogen gas was, any PD distribution similar to that a t 25 h aging time could not be observed. The reason for that is that the degradation of the sample surface and/or the resultant residual materials affect the PD characteristics for long time aging.

Figure 7. Whitehead's equivalent circuit for PD. C, is the capacitance of a void, and c, and c b are, respectively, the capacitances of insulation in parallel and in series with a void.

rive the theoretical PD distribution using Monte Carlo

Actual P D pulse occurrence distribution is considered to depend on various factors such as discharge inception voltage v, of a gap, residual voltage v,, statistical time lag T of discharge, discharge area, leakage resistance of a void gap, and so on. For simplicity, Whitehead's equivalent circuit for FD shown in Figure 7 is used in our I for the CM-I1 electrode system. This Section will de- simulation. The simulation model considers a probability

SIMULATION OF PARTIAL DISCHARGE DISTRIBUTION

N the previous Section, we have shown PD distribution


distribution function for wa(r), w, and r. We assume that the discharge area is constant no matter how big the discharge is and that the leakage resistance of a void gap can be neglected. At first, some appropriate probability distribution functions are assigned to the parameters. The simulation is done using random number which follows the distribution function so that one can obtain various PD characteristics such as 4 - q - n. The applied voltage used here is sinusoidal.

Figure 8. Relation between sparking voltage 'U. and residual voltage ' u ~ of a gap.

Figure 9. Phase relations of various parameters concerning occurrence of SPMD.

Throughout the calculation, we normalize the gap instantaneous voltage w when no discharge occurs as

w = s in4 (1)

Note that all voltages used in the simulation are normalized by Equation (1). The apparent charge q of discharge is known, and given by

= C,(% - 0,)

where c, is the capacitance of a void, cm and c b are, respectively, the capacitances of the insulator parallel and

100

2 50

E O L 5 -50

h

v

Figure 10. Experimental results of various phase characteristics of SPMD at aging time of 650 h. Detection sensitivity is 0.3 pC for measurements of SPMD.

t 2 -100

-150

in series with the void. C, = 1, Equation (2) becomes

Since this simulation assumes

q = v , - w,

The FACOM Fortran SSL 11, a scientific subroutine li- brary, is used to generate random numbers.

.(3)

MODEL FOR PARTIAL DISCHARGE OCCURRENCE MECHANISM

DISCHARGE TIME LAG r

When a linearly rising voltage is applied to a discharge gap set up between metal electrodes, there is scatter in discharge inception voltage due to the statistical time lag. Hayashi [lo] reported that if the probability of the discharge initiation is proportional to overvoltage Av of a gap, the theoretical calculation agrees with experimental results. Similarly, our simulation assumes that the number X of occurrence of discharge per unit phase angle is proportional to overvoltage Aw. Let v,, be the critical gap voltage a t which discharge eventually occurs at infinite time. Suppose the gap voltage w becomes vnm at an applied voltage phase angle q5 = 00. Noting that all voltages given are normalized


1 l000

0

- 5 0 5 v (VI

4 - 9 - "

9 - n

2

I

> - 0

3 40 - I

-2

- 3

- 4 -5 Y

w w m m J J 3 3 e e o

90 180 270 360 z PHRSE ( O E G I

0 a0

0

U - 0 W yl \ >

-80 >

gap voltage

Figure 11. Simulation of PD distributions during a period of 3600 cycles of the applied voltage for XU = 5 . 6 ~ lO-'/deg.

using Equation (l), the gap overvoltage AV at q5 = 8 is expressed by (in case of AV > 0)

Let Q ( T ) be the probability that the discharge begins to occur by q5 = 8 after the gap voltage reaches v,, at q5 = 80. The probability dQ(8) that discharge begins to

(4) AV = v(8) - vsm = sin 8 - sin eo

462 Hikita: Partial Discharge Distribution b y the Monte Carlo Method

We assume that the residual voltage v, decreases with increasing AV. The following equation between V, and Au is thus obtained o m

- >

5 : e o -

- U ? -

-. w w ( n o - 2 . J a > c e o . ,

-AV

11 (13) 03(sin80) - 02(cos 6,)

Q ( 4 , e o ) 1 - ~XP[M 2 occur after dB from the phase 4 by which no discharge takes place, is thus given by

1

(5) where 0 is the time lag of discharge in unit phase, given by

When the number of occurrence of discharge per unit o=e-eo (14) phase angle X is proportional to the gap overvoltage AV,

Transformation of Equation (13) and replacement of Q A = XOAV (6) with U gives

where Xu is a constant and a fitting parameter to the experimental result. Equation (5) is then rewritten as (15)

Q3(sin e,) 02(cos e,) - In( 1 - U) - -

6 2 X O

cos e cos eo - ( e - (e - Bo)3(sin e,)

6 + gap voltage

Figure 12. Simulation of PD distributions for Xo = 5.6 x 103/deg.

Approximation of Equation (9) using Equation (12) gives

IEEE Transactions on Electrical Insulation Vol. 25 No. 3, June 1990

- 320-

463

- - $ - q / n

t c

0 m-

160 1

c z

Izeki et al. [ll] measured the discharge area, and the average values of v, and v, for the CM-I electrode system. The authors concluded that the discharge area S of SPMD is almost the same as that of ordinary PD, and that v, is nearly equal to v, a t the onset of SPMD. Similar to the report, our simulation assumes that SPMD takes place for CM-I1 electrode system not because of division of the discharge area, but because of the decrease of time lag of discharge leading to a decrease in A V . In this case,

where vp is the peak value of the gap voltage when no discharge occurs (Figure 9). As shown in the previous Section, the ordinary PD form turned into SPMD after 150 h from the application of 7 kV a t 60 He for the CM-I1 electrode system. Figure 10 shows the experimental result of the phase characteristics of SPMD at aging time of 650 h. Substituting the values e,+ = 345' and 8,- = 165' which are obtained from Figure 10 one can get

(18) v, x v, x (16) v, = 0 . 3 7 ~ ~ If v, and v, are equal and constant, regardless of phase a t which PD occur and regardless of the polarity of PD,

Next, let vp be the peak value of a voltage applied between the electrodes, one obtains from Figure 7


large overvoltage - AV 1 -

+ + small overvoltage

- AV2

A + + +

Figure 14. Conceptual illustration of growth of electron avalanche for different overvoltages AV, and Avz, where AV, > AVZ.

Figure 15. Simplified equivalent circuit for discharges of a void gap. C,, is the capacitance seen from the discharge gap C,, Z is the resistance of the discharge column and v , is the voltage across the gap.

c b

(C, + Cb) vp =

If we express c b and c, by the simple equation

C = &S/d (20)

where E is the permittivity, d the gap distance or the thickness of a sample, and S is the area, then

c b = 3.3~,S/ l (mm) (21)

C, = ~,S/125(pm) (22) where the relative permittivity of epoxy resin is 3.3. Us- ing Equations (19)' (21) and (22)' one can obtain

i Figure 16.

Predicted current vs. voltage characteristics for discharge column of PD.

t Figure 17.

Predicted current i and voltage vfp of the resistance 2 as a function of time.

up = 0.29Vp (23)

under our experimental conditions. Since the applied voltage in our experiments is 7 kV, Equation (23) gives vp = 2870 V and hence v, = 1060 V following Equa- tion (18). Paschen's curve [12] gives about l kV to the discharge onset voltage for nitrogen in case of our experimental conditions; p = 100 kPa and d = 125 pm, that is, the product of pd = 1.25 kPa cm. The voltage estimated here is in good agreement with 'U, obtained above, and also agrees with the reported breakdown voltage of 1000 V measured for 100 pm gap between metal electrodes at atmospheric pressure in nitrogen [ 131. From the above considerations, we assume v,, = 1000 V. In case of an applied voltage of 7 kV, the normalized voltage 'U,, = 0.35.


b Figure 18.

Equivalent circuit of PD considering that discharge area is divided into a number small areas. R, is the surface resistance of a sample, and G,, is the discharge gap for a simulation of surface discharges along the sample surface.

MINIMUM RESIDUAL VOLTAGE v,.,;~

Assuming that for the CM-I1 electrode system the discharge extends up to a state corresponding to maximum normal glow discharge, the normal glow maintaining voltage is taken as v,.,in. Because the maintaining voltage is close to the minimum sparking voltage, which is about 300 V for nitrogen and air, we take v,,;~ = 300 V. Nor- malization of the voltage gives v,.~;,, = 0.1.

RESULT OF SIMULATION IGURES 11 and 12 show typical results of the com- F puted PD distributions during a period of 3600 cy-

cles of the applied voltage for two different values of Ao. Note that in these Figures as the magnitude of charge V ( V ) is used instead of q(C) . This is because in the simulation the voltage waveform is normalized as v = s in4 (Equation (l)), and thus q is expressed by q = 'U, - v,. (Equation (2)). On the other hand, for comparison, Fig- ure 13 shows the measured PD occurrence distributions a t the beginning stage of aging. Comparison of Figure 11 (A, = 5 . 6 ~ lO-l/deg) with Figure 13 indicates that our simulation gives similar PD distribution to that obtained by the experiments. The results of the simulation also in- dicate that when the parameter A0 deciding the number of occurrence of discharge per unit phase angle increases, as shown in Figure 12 (A" = 5.6 x 103/deg), the various kinds of phase characteristics computed become to resemble those of the experimental results for SPMD shown in Figure 10. As shown above, it is concluded that the simulation based upon the described PD model gives a reasonable agreement with the PD characteristics a t early aging time and also in the case of SPMD for a dry-air void system. The simulation assumes that the coefficient A0 is constant in one alternating voltage cycle. It is noticed, however, that

this assumption cannot explain the obtained experimental results of the PD distribution where the ordinary pulsive PD and SPMD are observed simultaneously in one alternating cycle. This discrepancy suggests that Xu is not constant but varies with phase angle of the alternating voltage cycle. Physically, there is a possibility that the mixture proportion of 0 2 present in the void decreases due to electron attachment to oxygen molecule after the first PD pulse takes place a t the beginning of each alternating half cycle. The modified simulation, with A0

varying, is under investigation.

A CONSIDERATION ON PHYSICS OF PARTIAL

DISCHARGE MECHANISM

DISCHARGE TIME LAG HERE is a theory that for electronegative gas such as T SFG and air, transforming neutral molecules into neg-

ative ions due to electron attachment plays an important role in gas breakdown, in addition to the electron-impact ionization process [14]. The theory says that equilibrium of the two processes gives a condition for sparking discharge. Since oxygen included in air is strongly electronegative, the impact ionization coefficient of air apparently goes down due to the electron attachment. The apparent decrease of the impact ionization coefficient is considered to give rise to a decrease of the discharge onset probability resulting in the statistical time lag. For CM-I1 electrode system, as shown in the previous Section, SPMD takes place when gas in a void is rich in nitrogen. It is suggested that SPMD occurs through consumption of oxygen in a void due to reaction with the sample during long time voltage application [15]. Because nitrogen does not suffer from electron attachment, there is no decrease in the impact ionization coefficient, leading to an increase of the discharge onset probability as a result of the decrease of the discharge time lag. We have already shown that when a small quantity of oxygen exists in a void, a part of PD is turned into SPMD, and further increase in the applied voltage leads to broadening of the phase region where the discharge form is SPMD. This phenomena can be explained as follows: Because the reaction rate of electron detachment is much slower than that of electron attachment for oxygen, the number of oxygen molecules (Oz), which are target particles for electron attachment, decreases through the transformation into O-' by several discharges occurring a t the beginning of a discharge cycle. When the number of oxygen molecules is small a t the beginning, the reaction rate of electron detachment greatly decreases, resulting in high discharge onset probability, as a consequence


of the change in PD form into SPMD in the later phase region in one cycle. Because the rate of increase of overvoltage increases with applied voltage, the repetition rate of PD increases. This leads to a prominent decrease in number of oxygen molecules due to electron attachment, resulting in an increase of discharge onset probability a t earlier phases, as a consequence, the occurrence of SPMD extends over a wider phase region. In a discharge inter- mission period, electron detachment proceeds. At the onset of discharge of the next cycle, the number of oxygen molecules recovers. In order to explain the experimental result that ordinary PD and SPMD occur simultaneously in a half cycle of the app!ied voltage, our simulation leads to the suggestion that the discharge onset probability of nitrogen must be four times higher than that of air. If one considers the generation growth process of discharge due to electron impact ionization, there is a possibility that the above difference by a factor of four can be explained, since the discharge onset probability is expected to have impact ionization coefficient with an exponential form. At any rate, the quantitative estimation of the decrease of the discharge onset probability due to the electron attachment to oxygen is required with the electron detachment process considered. Further examination is also necessary on the assumption made in our model that the number of occurrence of discharge per unit phase angle is proportional to the overvoltage of the gap.

RESIDUAL VOLTAGE

It is generally recognized that PD stops when a reverse field is formed by the accumulation of charges on an insulation surface and thus discharge cannot be sustained. However, in our model, only this consideration does not give a satisfactory explanation to the residual voltage. AI- though including several assumptions, three attempts are made to qualitatively explain how the residual voltage is determined. The first two (1 and 2) consider the growth of discharge and the third (3) considers the division of discharge area.

(1) EXAMINATION O F v, FROM THE GROWTH OF DISCHARGE

Suppose that PD arise from a simple electron avalanche occurring in a gap. I t is expected that as the overvoltage a t the onset of discharge is higher, the electron avalanche grows to a larger size until the electric field in the gap becomes so small that electrons are unable to ionize gas molecules. This consideration is conceptually illustrated in Figure 14. For higher overvoltages, therefore the gap voltage, which is the residual voltage, is thought to become smaller when electrons and ions in the gap reach both electrodes after discharge stops.

(2) EXAMINATION OF v, FROM DISCHARGE GROWTH ABILITY

Let us illustrate the discharge in a void by a more simplified equivalent circuit as shown in Figure 15. In this Figure, C,,, the capacitance seen from the discharge gap C,, is given by

Cgr = Cg + CmCb/(Cm + Cb) (24)

and z is the resistance of discharge column and is expected to show a negative resistance characteristics as shown in Figure 16. Well-known current vs. voltage (i-v) characteristics of discharge channels a t low pressures for steady state do not hold directly for temporary discharges such as PD a t atmospheric pressure. There is however, a possibility that the i - vg characteristics correspond to the transition state from the former glow state to the normal glow state. When the switch S gets closed (Fig- ure 15), which means the onset of discharge, the current i(t) flowing through z is expressed as

i(t) = -C,,(dv,(t)/dt) (25)

The waveforms of i(t) and v g ( t ) are shown in Figure 17. If one considers the growth process of discharge, the current given by Equation (25) could no longer be supplied at a certain point and hence discharge would stop. Thus, a t the time when the slope d i ( t ) / d t exceeds the current growth of the discharge, the discharge stops, and the gap voltage becomes the residual voltage. Higher overvoltage at the onset of discharge, therefore, is considered to bring faster growth of discharge current, leading to lower residual voltage.

(3) EXAMINATION OF v, FROM DIVISION OF DISCHARGE AREA

Although we have so far assumed that the discharge area is constant, it is reasonable to consider that discharge with higher charge level makes the discharge area broader. Let us assume now that discharge does not always occur over an entire area below the electrode, but is divided into a number of small areas. The equivalent circuit for PD is illustrated in Figure 18, where R,, (n = 1 , 2 , 3 . . .) is the surface resistance of a sample, and the discharge gap G,, parallel with R,, is given for a simulation of surface discharge along the direction of a sample surface. As the overvoltage AV becomes higher, the discharge area gets larger because the discharge along the surface direction adds to it. Figure 18 also indicates that discharges at many gaps C,, and C,, are more likely to occur at higher overvoltages. After discharges stop, charges existing in the area dif- fuse over an entire sample surface with the a constant determined by the product of the surface resistance of the

IEEE Transactions on Electrical Insulation Vol. 25 No. 3, June lQQ0 467

sample and the capacitance per unit area. The diffusion process provides all C,, and Can with an uniform charge distribution. The gap voltage a t steady state gives rise to the residual voltage U,. It follows that as AV increases, z), apparently decreases. On the other hand, when the repetition rate of PD is higher than the time constant T , the charge distribution on the sample surface is no longer uniform. This case will give complicated influences on the PD occurrence. Because the overvoltage is thought to be lower with high nitrogen concentration, the discharge area becomes small, so that the discharge is divided into many smaller areas. In this case, U, apparently gets closer to U,,, which gives rise to SPMD. As already discussed in this sub-section, if it is assumed that the PD area is divided, we can also apply our simula tion model by considering the apparent residual voltage. Finally, it should be noted that the discussion we made in this section contains several intuitive assumptions. Fur- ther detail examination including the quantitative estimation is required.

CONCLUSION EASUREMENTS of PD were made for the CM-I1 elec- M trode system, a representative closed-void model elec-

trode system by using the developed computer system. Measuring temporal change of the PD pulse distribution, the statistical properties including the phase information of PD characteristics were examined. Effects of the pressure and gas inside the void on the PD properties were also examined. Results obtained are summarized as follows: 1.As aging time increased, the PD pulses occurring a t

the slower phase and those with the greater magnitude of charges began to disappear earlier. Finally, the PD pulses turned into the so-called swarming pulsive microdischarges (SPMD).

2. The PD distribution began to change when the partial pressure of oxygen present in the void went down to a critical value. Further decrease of partial pressure of oxygen brought the PD pulses into SPMD.

Taking into account the experimental results, a model for the mechanism of PD was proposed. The model assumes that the statistical time lag of discharge depends linearly on the overvoltage and that the residual voltage depends on the charge of PD. With Monte Carlo simulation of the PD distribution, it was shown that the computed results well explains the experimental data on the PD distribution and the appearance of SPMD. The physics of the model was also discussed. Conse- quently, it was suggested that the electron attachment in oxygen gas greatly influences the time lag of the discharge, and that the size and area of the discharge give significant contributions to the residual voltage.

ACKNOWLEDGMENTS HE authors are grateful to Mr. Yutaka Higashimura T of Hitachi Research Laboratory, Hitachi Ltd. for pro-

viding CIGRE Method I1 electrode system and to Japan Ciba-Geigy Co. for providing epoxy resin samples. This work was supported in part of a Grant-in Aid for Sci- entific Research from the Ministry of Education, Science and Culture.

REFERENCES

[l] J . H. Mason, “Di~charges”, IEEE Trans. on Elec. Insul., Vol. 13, pp. 211-238, 1978.

[2] J . C . Devins, “The Physics of Partial Discharges in Solid Dielectrics”, IEEE Trans. on Elec. Insul., Vol. 19, pp. 475-495, 1984.

[3] T. Tanaka and T . Okamoto, “A Minicomputer Based Partial Discharge Measurement of Partial Discharge in Insulation Structures”, Conf. Rec. of 1978 Int. Symp. on Elect. Insul. pp. 86-89, 1978.

[4] T . Okamoto and T . Tanaka, “Analysis of Partial Discharge Characteristics by an Equivalent Circuit with Fluctuating Discharge Time Lag”, Trans. of IEE Japan, Vol. 105A pp. 269-275, 1985.

[5] W. R. Kodoll, H. C. Karner, T. Tanaka and M. Ieda, “Internal Partial Discharge Resistivity Testing” , CI- GRE 15-04, International Conf. on Large High Volt- age Electric Systems, 1988.

[6] Y. Kitamura, “Internal Partial Discharge Character- istics Using New CIGRE Method Electrode System”, IEE Japan Elect. Insul. Mater. EIM-86-5, 1986.

[7] N. Izeki, F. Tatsuda and Y. Matsuzaki, “Measure- ments of Area of Partial Discharge and A tan 6 - Voltage Characteristics Using Risadue Method”, 1985 National Convention Record IEE of Japan # 315, 1985.

[8] N. Izeki and F. Tatsuda, “Behavior of Void Dis- charges in Short Gap Spaces”, 4th Intern. Symp. on High Voltage Engineering, 22-04, 1983.

[9] Y. Kako and Y. Higashimura, “Study on the Charac- teristics of Internal Pressure and Surface Resistance of Void Enclosed in Epoxy Resin due to Internal Par- tial Discharges”, Trans. of IEE Japan, Vol. 105A, pp. 555-561, 1985.

[lo] M. Hayashi, “Statistical Fluctuation of Discharge”, Oyobutsuri, the Japan Soc. of Appl. Phys., Vol. 40, pp. 1133-1138, 1971.

468 Hikita: Partial Discharge Distribution b y the Monte Carlo Method

[ll] N. Izeki, “Partial Discharge Characteristics of Closed Void for CIGRE Method I Electrode”, 1985 National Convention Record of IEE Japan, # 314, 1985.

[15] K. Yamada, M. Hikita, A. Oohashi, and M. Ieda, “A Consideration on Swarming Pulsive Microdischarges in CIGRE Method I1 Electrode System”, Proc. of the 18th Symp. on Elec. Insul. Materials, IEE Japan, pp.

[12] T. W. Dakin, “Breakdown of Gases in Uniform Fields 177-180, 1985. Paschen Curves for Nitrogen, Air and Sulfur Hex- afluoride”, Electra, Vol. 32, p. 61, 1974. ’ Present address: Toshiba Corporation

Department of Electrical Engineering, Aichi Institute of [I31 M. Kando, “Very Short Gap ac Breakdown Charac- teristics Due to a High-speed Power Cut-Off Method”, T ~ ~ ~ ~ . of IEE japan, vol. 1 0 2 ~ , pp. 319-326, 1982.

Technology, Toyota

’ Present address: Aichi Institute of Technology, Toyota

Manuscript was received on 11 May, in revised form 23 Oct. 1989 [14] K. Horii, “Study of Gas Discharges in a Long Gap”,

Oyobutsuri the Japan Soc. of Appl. Phys. Vol. 40, pp. 1126-1127, 1971.

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