NBS

PUBLICATIONS

NBSIR 82-2629 A11101 45276=1

1981 Annual Report: Optical

Measurements for Interfacial

Conduction and Breakdown

j

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Washington, DC 20234

January 1 983

i

I

Prepared for: Department of Energy

Division of Electric Energy Systems

Washington, DC 20585

national bureau

OF STANDARDS

LIBRARY ^APR 8 J 9a3

NBSIR 82-2629

t I

* 1981 ANNUAL REPORT: OPTICAL

MEASUREMENTS FOR INTERFACIAL

CONDUCTION AND BREAKDOWN

R. E. Hebner, Jr., E. F. Kelley, and J. N. Hagler

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Washington, DC 20234

January 1 983

Prepared for: Department of Energy

Division of Electric Energy Systems

Washington, DC 20585

U.S. DEPARTMENT OF COMMERCE, Malcolm Baidrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

TABLE OF CONTENTS

Page

LIST OF FIGURES iv

LIST OF TABLES vii

Executive Summary viii

Abstract ix

I. INTRODUCTION . 1

II. RESEARCH PLAN 1

III. INTERFACIAL PHENOMENA 3

A. EFFECTS OF SURFACE AND SPACE CHARGE 3

1. Surface Charge on Interface 3

2. Cylindrical Space Charge 3etween Spheres 10

B. BREAKDOWN LOCATION — CONTAMINATED OIL 17

IV. ELECTRIC FIELD MEASUREMENTS — SPACE CHARGE 24

A. THEORY 24

B. EQUIPMENT 31

C. SPACE CHARGE IN NITROBENZENE 31

D. ELECTRIC FIELDS IN TRANSFORMER OIL 41

1. Contaminated (Wash) Oil, Room Temperature 41

2. Contaminated (Failed) Oil, Elevated Temperature 47

3. Clean Oil, Elevated Temperatures , AC, DC 50

V. CONCLUSION 65

VI. REFERENCES 69

LIST OF FIGURES

Page

Fig. 1. Surface charge at the interface of two regions of differing

permittivity between parallel plates having a potential

difference of V 5

Fig. 2. Surface charge density along the interface, p (z) 11

Fig. 3. Equipotential lines between parallel plates for a uniform

interfacial surface charge density, p (z), and with no voltage

applied to the plates, V = 0 ... 1 12

Fig. 4. Equipotential lines between parallel plates for the nonuniform

interfacial surface charge density, p (z), and with V = 0 ... 12

2 Fig. 5. Cylindrical space charge between two spheres. The upper

sphere is at $ = +V and the lower sphere is at 4

) = -V 13

Fig. 6 . Geometry and coordinates used in the program PLTMG 15

Fig. 7. Triangulation employed by program PLTMG 18

Fig. 8 . Equipotential lines obtained via PLTMG with no space charge

present 19

Fig. 9. Equipotential lines obtained via PLTMG with space charge

present (see eq 16) 20

Fig. 10. Summary of breakdown voltage measurements using contaminated

oil. The open circles indicate breakdown away from the

interface while the solid circles denote interfacial

breakdown. The squares represent data on oil only (no paper

in the system) 23

Fig. 11. Microscope photographs showing removal of bubbles in the paper

used for interfaces. The line in the upper left photograph

denotes 0.5 mm (500 um) 25

Fig. 12. The relative field strength expressed as a function of relative

transmitted light intensity and previous fringe number N . . . . 27

Fig. 13. Exact and approximate calculations are presented as a function

of relative intensity I/I m <l. The approximate form for

the relative field is good to 10% up to I/I m~0.8, whereas

the forms of the sensitivity function g(I/I m ) show a deviation

of 10% near I/I m

= 0.25 30

Fig. 14. Apparatus. An expanded laser beam provides illumination of

the cell which is placed in an oil tank between crossed

polarizers. A telescope provides proper image magnification,

and neutral density filters are used" to regulate the light

intensity. The transmitted light is measured by a computerbased, intensified, si 1 i con-vi di con detector 32

iv
LIST OF FIGURES (cont.)

Page

Fig. 15. The intensity profile I (z ) generated by the computerized

detection system is produced by scanning the viewed detector

area and integrating the intensity for each scan parallel

to the y axis 33

Fig. 16. Relative intensity profiles for impulse voltage applied to a nitrobenzene Kerr cell. The extent to which the profiles

deviate from being uniform from plate to plate provides a measure of the nonuniformity of the field. The smaller,

higher frequency modulations of the profiles are due to

nonuniformities in the light sources and small changes within

the liquid 35

Fig. 17. Relative intensity profiles at the peak of the 60-Hz ac waveform

vs several peak voltage levels. Note that distortions do not

become obvious until the fringe number n exceeds one. The

numbers near the profiles denote the fringe number 36

Fig. 18. Relative intensity profiles at the negative peak of the 60-Hz ac waveform vs peak voltage level. The numbers near the profiles

denote fringe number 37

Fig. 19. Relative electric field at the positive or negative peak of the

60-Hz waveform as a function of position for the voltages in

figures 17 and 18 38

Fig. 20. Space-charge density in nitrobenzene. These approximate curves

are inferred from the relative electric field plots in figure 19.

Note that the highest density shown refers to 3.7 xlO^

molecules, assuming one charge per molecule 39

Fig. 21. Positive-negative zero-crossing profiles compared with the

n = 1 profile. The grounded electrode is at the left 40

Fig. 22. The height of the transmittance peaks at the positive to

negative zero crossing as measured at the plates as a function

of the peak voltage squared. The grounded electrode is at the

left. (V 2 is used as the abscissa rather than V or V

4 in order

to keep in line with customary Kerr-effect plots.) 42

Fig. 23. The change in relative intensity selected voltages between a negative and a positive peak. The peak applied voltage was about 22 kV 43

Fig. 24. Comparison of the measured intensity averaging 10 detector

records and 100 detector records 44

Fig. 25. Intensity profiles taken at the positive peak and negative

peak of the 60-Hz waveform. 10,000 scans were averaged to

produce the profiles. The peak voltage was 70.5 kV 45

v
LIST OF FIGURES (cont.)

Page

Fig. 26. Comparison of the average positive and negative peak

profiles with typical standard deviation associated

with these measurements 46

Fig. 27. Relative electric field for the positive and negative peaks

and associated standard deviation 48

Fig. 28. The normalized field as a function of position between parallel

plates in transformer oil at four different temperatures.

The data at 68°C suggests that the space-charge density

may be making a significant (~5%) contribution to the

electric field 49

Fig. 29. Intensity profiles for aligned polarizers. These are only

used to establish the magnitude of I mand not the shape. The

intensity after voltage application has decreased probably due

to increased particulate contamination and/or malfunction of

illuminating laser 51

Fig. 30. Comparison before and after voltage is applied to the curves

used to establish the I m profile and the background curves.

The numbers in parentheses refer to the profile number in

table 5 52

Fig. 31. Unprocessed (raw) data at 41 kVPP of 60-Hz waveform and

zero-voltage backgrounds. Each curve is an accumulation of

1000 scans 53

Fig. 32. The incident intensity profile I m

(z) 56

Fig. 33. The net, average Kerr profile I (z ) 56

Fig. 34. The relative intensity profile I(z)/Im

(z) 57

Fig. 35. Relative electric field E(z)/Em ; ±5% limits are shown

about the average in the magnified view 58

Fig. 36. Relative field for 86°C 61

Fig. 37. Relative field for 95°C 62

Fig. 38. Relative field for 107°C 63

Fig. 39. Intensity profiles at various voltages for 107°C oil compared

to background signal levels 64

Fig. 40. Comparison of the 60-Hz intensity profiles taken at the

positive peak (PP), the positive-negative zero crossing (PNZC),

and the zero-voltage background revdals no significant space

charge as would be found with observations of the 60-Hz

zero crossing in nitrobenzene . 66

vi
LIST OF FIGURES (cont.)

Page

Fig. 41. Intensity profiles under application of dc. No polarity

dependence of shape is obvious as would be expected if the

deviations from intensity uniformity were arising from spacecharge field distortions 67

Fig. 42. Relative field profiles at 107°C under application of dc show

slight intensification at each plate 68

LIST OF TABLES

Page

Table 1. Space charge in gap between spheres 16

Table 2. Percent increase (decrease) in field

density, gap d = 2 16

Table 3. Clean oil data 21

Table 4. Summary of particulate contamination 47

Table 5. Data collection sequence 54

Table 6. Data handling 59
Executive Summary

Power system apparatus employs composite insulation. For example,

in a transformer, paper pressboard and transformer oil provide the necessary

electrical insulation. Economic considerations provide incentives to reduce

the size of the apparatus, yet retain the same voltage rating. This serves

to increase the electric field stress on the composite insulation which

increases the probability of failure unless steps are taken to make the

insulation more reliable. In order to improve the electrical characteristics

of composite insulation, it is important to determine what factors influence

its electrical breakdown.

Space or surface charge and contaminants affect the breakdown strength

of single component insulation and composite insulation systems. Charge

distributions modify the electric field from what would be calculated from

geometrical considerations alone and thereby produce regions of field

intensification which can increase breakdown probability. Particle or chemical contaminants may also decrease the electrical strength of a system.

These factors need to be investigated throughout the temperature range

which can exist in practical apparatus.

Before space-charge measurements are performed on composite insulation

systems via electro-optical techniques, it is necessary to understand the

role of space charge in transformer oil by itself under a variety of

contaminants and temperatures. Kerr-effect measurements are reported here

for contaminated transformer oil from room temperature to 68°C, and for

clean oil the measurements are extended to 107°C. In all the observed

cases, the field intensifications due to space charge are less than 10% of

the average field and usually less than 5%.

In order to supplement the space-charge measurements in composite

insulation systems, mathematical and computer modeling of space and surface

charge was included in order to anticipate the effects of charges.

Substantial charge densities were found to be necessary in order to modify

the electric field in such a way that a change in the breakdown strength

could be anticipated.

Breakdown tests were performed on a paper-oil interfacial system where

a paper sample is held parallel to the field and touching both electrodes.

This study helps to understand what factors influence the reduction of

breakdown strength and should give insight to the electro-optical measurements.

It was determined that the handling of the paper samples was critical to the

tendency for the breakdown to occur along the paper. When contaminated oil was used, it appeared that large particle contaminants lowered the breakdown

strength but did not cause the breakdown to prefer the interface.

The work done so far has served to eliminate factors which would readily

account for a lower electrical strength of composite insulation than the strength

of each component insulant by itself. This information focuses attention on other factors such as water and particle contamination as being possible sources

of space charge or failure, and it forces our attention to higher temperatures.

vi i i
1981 ANNUAL REPORT: OPTICAL MEASUREMENTS

FOR INTERFACIAL CONDUCTION AND BREAKDOWN

R. E. Hebner, Jr., E. F. Kelley, and J. N. Hagler

Abstract

This report presents measurements and calculations contributing to

the understanding of space and surface charges in practical insulation

systems. Calculations are presented which indicate the size of charge

densities necessary to appreciably modify the electric field from what

would be calculated from geometrical considerations alone. Experimental

data is also presented which locates the breakdown in an electrode

system with a paper sample bridging the gap between the electrodes. It is found that with careful handling, the breakdown does not necessarily

occur along the interface even if heavily contaminated oil is used.

The effects of space charge in the bulk liquid are el ectro-opti cally

examined in nitrobenzene and transformer oil. Several levels of

contamination in transformer oil are investigated. Whereas much space

charge can be observed in nitrobenzene, very little space charge, if

any, can be observed in the transformer oil samples even at temperatures

near 100°C.

Key words: breakdown; composite insulation; dielectrics; electric field

calculation; electro-optics; high voltage; insulation; interfaces;

Kerr effect; liquids; solids.
I. INTRODUCTION

The objectives of this investigation are to develop apparatus and

appropriate procedures for the optical measurement of interfacial electric

field and space-charge density of materials for electric power equipment

and systems; to understand the interfacial prebreakdown and breakdown

processes in specific insulating systems; and to demonstrate the

applicability of the developed instrumentation and procedures in

future development and design of systems involving liquid-solid

dielectrics.

Because space-charge effects are evident in gaseous composite

systems [1,2], it is tempting to extend those results to explain the

behavior of liquids. The results reported here caution presuming too

much of a role of space charge in modifying the prebreakdown electric

fields in liquid and liquid/solid systems. Specific experimental models

using transformer oil, paper, or pressboard are studied so that these

results are applicable to the power industry.

This report first discusses the quantitative effects of surface

charge on an interface in modifying the electric field. This extends

the mathematical modeling done in the last annual report in that an estimation technique is developed to place an upper bound on field

distortions. Additionally, computer solutions to the electrostatic

problem of a charged interface are presented.

An experimental study is next presented which indicates the

contribution of the interface to breakdown. This work extends previous

results in that it includes the effects of contaminated transformer oil

and documents the handling of the paper interface.

Finally, electro-optical measurements are presented which contrast

the space-charge effects found in nitrobenzene with the findings in

transformer oil. The transformer oil measurements were extended to

include contaminated transformer oil, and the clean transformer oil

measurements were extended to over 100°C.

II. RESEARCH PLAN

Power system apparatus employs solid insulation for structural

support and electrical insulation. As in the case of many transformers,

an insulating liquid fills the remaining volume of the apparatus. In

order to reduce the size of the apparatus (with obvious economic advantages),

yet retain the same voltage capability, the composite insulation must

be subjected to higher electrical stresses. Unless steps are taken to

increase the breakdown strength, such a reduction in size will increase

the probability of failure of the apparatus. This economic incentive

strongly suggests that the behavior of composite insulation systems be

characterized at a fundamental level.

The presence of space or surface charge in a composite insulation system

will change the electric field from what it would be if such charge were

absent. Thus if a uniform field (as provided by the geometry of two parallel

1
plates) were modified by space charge while the voltage on the plates is held

constant, the uniformity of the field would be destroyed and field intensification would occur in some region between the plates. The probability of

breakdown would be increased due to the increase in the local electric field,

and the apparatus would be more likely to fail. For this reason, it is

important that the role of space charge in composite insulation systems be

determined, its source be identified, and its control be attempted. Other

factors such as particle or chemical contamination may influence either

the breakdown probability or the existence of space charge in composite

insulation systems. Hence such contaminants need to be investigated.

To obtain fundamental understanding of interfacial breakdown, mathematical

modeling is combined with experiments. In the mathematical model phase of the

study, the distortion of the electric field, in typical geometries due to

interfacial space charge, is calculated. Experimental techniques to measure

the electric field are also being developed to verify the applicability of

the mathematical model to practical systems. Electro-optical measurements,

in this case based on the Kerr effect, were selected because they offer high

temporal and spatial resolution and do not perturb the system under

investigation. Additionally, in order to be directly applicable to practical

power system apparatus, these experimental observations must cover the range

of temperature possible in such apparatus, i.e. , from room temperature to over 150°C.

Before the field modifying effects of an interface can be inferred

from electro-optical measurement, it is necessary to document the spacecharge behavior in transformer oil alone over a range of temperatures and

contaminations. Only after such characterizations are made upon the oil can the effects of an interface be distinguished from the nature of oil.

This is the emphasis of the electro-optical measurements reported here.

The measurement of breakdown characteristics of an interfacial system

is carried out upon a paper-oil system where the paper is held parallel to

the electric field and touching both electrodes. This system is subjected

to various handling procedures to identify the factors which contribute to

the breakdown probability. Both clean and contaminated oil are used.

The purpose of such an investigation is to isolate those factors which

contribute to decreasing the breakdown strength of a composite system.

Earlier in this work, some effort was directed toward understanding

die! ectrophoretic phenomena because it was presumed that di el ectrophoretic

forces on particles and/or bubbles may make a significant contribution to

interfacial breakdown. Although that work was very well done and expanded

the understanding and the control of di el ectrophoreti c effects, our investigation failed to establish a direct connection between these

effects and interfacial breakdown. That phase of the investigation,

therefore, was not continued.

In summary, the research proceeds by studying model systems in

which interfacial breakdown is produced. Techniques are being developed

to measure and to calculate the electric field distribution in the

vicinity of the interfaces. This approach is intended to provide a quantitative understanding of interfacial breakdown. It is anticipated

that this improved understanding will lead to improved tests on, and
standards for, insulating materials and systems. In addition, this work

should yield measurement techniques which will help other researchers in

the development of improved apparatus.

III. INTERFACIAL PHENOMENA

A. EFFECTS OF SURFACE AND SPACE CHARGE

It may be speculated that a primary cause of breakdown (flashover)

is the intensification of the electric field due to an accumulation of

space or surface charge within a system. However, carefully controlled

experiments have shown that this flashover can occur quite far from

where charge is assumed to be accumulating [3].

Here we present the results of the investigation into the role

which space and surface charge play in enhancing an electric field.

Using mathematical models, we have estimated the enhancement of the

magnitude of the electric field in two situations.

Section 1 contains an analysis of the effect of accumulation of

surface charge on an interface placed at right angles to (and between)

two parallel electrodes upon which a potential difference has been

applied. Different dielectric materials are assumed on either side of

the interface. Such a model would be suggested by sandwiching a thick

pressboard spacer between parallel plates where the spacer only fills

half the region between the plates. The remaining half might be filled

with transformer oil. Or it could describe a solid-gas interfacial

system. In either case, the effect of surface charge is of interest.

We use Fourier series techniques to obtain an estimate of the field

enhancement due to the surface charge and show that this enhancement

decreases exponentially with the distance from the interface.

In section 2, we outline the results of a preliminary investigation

into the effect of introducing a thin cylinder of charge into the gap

between two spheres. Such a model is useful in considering the effects

of charged particles electrohydrody namical ly confined in a columnar

region between two electrodes [4]. This study was carried out using

a computer code (resident at NBS) for solving two dimensional elliptic

boundary value problems. We derive the following result: given two

spheres each of radius 8 cm separated by a gap of 2 cm with a potential

difference of 20 kV placed upon them, and with a thin cylinder of charge

(total charge 1.2 x 10 4 pC) introduced in the gap; then the enhancement

3 cm from the axis of symmetry is at most 2%.

1. Surface Charge on Interface

As a first example of the effect of space or surface charge accumulation

on the electric field, consider the following problem: two parallel

electrodes are located at z = 0 (cm) and z = 1 (cm). The space between

the electrodes is divided into two regions: the region y <0 is filled

with an insulator with permittivity q = qe0 and the region y > 0

is filled with an insulator ^ = <

2

€

o* (Thus, we assume an interface

located at y

= 0.

)

3
Assume further that a potential difference V is placed across the

plates and a surface charge density p(z ) exists on the interface (see

fig. 1 ). (The derivation of the series solution presented below was considered first in [3].)

Laplace's equation for the potential <j> in the regions bounded by

the electrodes is

V

2

* (y,z) = o, (l)

with the following boundary conditions:

*(y,o) = o, <j> (y , i ) = v. (2)

lim <f>(y,z) * », (3)

y

+±0°

<j> is continuous at (0,z) for 0 < z <1, (4)

e

1

<f)y

(0",z) - e2

^y

{0 +

iz) = p (z ) (5)

for 0 < z < 1 .

Here, <\>y denotes the partial derivative of $ with respect to y.

First, assume V = 0. We solve eqs (1) - (3) separately in the

regions y < 0 and y > 0 and use conditions (4) and (5) to find the

general solution.

Using the usual procedure of separation of variables and eqs (1) - (3), we obtain solutions to Laplace's equation

r e

_niiy si n(nnz ) , y > 0

4>n(y>z) =

( e

niiy si n(nnz ), y <0.

So, for y > 0, the resulting potential may be written as

oo 4>(y,z) = l

a ne‘

niiy sin(n7iz ), (6)

n=l

and for y < 0,

<f>(y ,z ) = [ b

n e

n-ny sin (me ), (7)

n=l

4
54

Surface

charge

at

the

interface

of

two

regions

of

differing

permittivity

between

parallel

plates

having

a

potential

difference

of

V.
for some sequences (a n ) and (b n

).

The orthogonality conditions for the sequence of functions sin(nnz),

n=l ,2,. . on 0 < z <1 is

l

/ 1/2 i-f m = n

/ sin(nnz )sin(nwz )dz = ; . (8)

0

( 0 if m * n

Let y

+ 0 +

in eq (6) and y-*- 0" in eq (7). The continuity condition

(4) says that these two limits must be identical for each z, 0 < z <1.

Thus

l a n sin(miz) s

[ b„ sin(nnz).

n=l n=l

Integrating each of these series against sin(nuz), n = 1,2,... and

using the orthogonality relations (8) yields a n = b n , n = 1,2,... . So,

for some numbers C n , n = 1,2, ...the potential may be expressed as

o° <My,z) = I C

n e"

niT

l y l Sin(miz ). (9)

n=l

Note that the potential <j)(y,z) is a symmetric function about the y

axis, i.e. , 4>(y,z) = <K-y,z). In particular, 4>y

(0 “ ,z ) = - 4> (0 +

,z ) for

0 < z < 1. We obtain, using eq (5),

<j>y(0“,z) = p(z )/(e

1 +e

2 ) for 0 < z < 1. (10)

To obtain the coefficients C n , differentiate the series in eq (9)

term by term with respect to y for yO and let y-K3”. Then

<IV(0“,z) = l

n7rC n sin(nnz),

y n=l

or

oo p(z)/(q+£2) = l

niT c n sin l 112 )*

n=l

Integrating each side against sin(nuz), n = 1,2,.... and using eq (8) once again, we obtain

l

/ [p(z )/(ei+C2)]sin(nnz ) = nirC n/2.

o

6
This allows us to express the C n in terms of the charge density

1

C n = (G/mr) / p(z )si n(nnz )dz , (11a)

o

where

G = 2/(e]+e2 ). (lib)

This completes the derivation in the case where the potential is "zero"

on both electrodes. If the potential on the top electrode is now assumed

to be V, then we easily obtain the solution

<l>(y,z) = Vz + l C

n eH y l Sin(nnz ),

n=l

( 12 )

where the C n 's are given by (11).

Before considering some of the consequences of this derivation, we

recall briefly some elementary mathematical facts. The proofs of these

assertions are standard and can be found in many books which discuss

Fourier series and infinite series. (For example, see [5,6].)

(1)

The sum of a geometric series: If | x| < 1, then

I x

n = x/(l-x).

n=l

OO CO Q

r\

(2)

The Schwartz inequality: If \a

n

^ < 00 and \ b J- <

00 then

n=l n=l

I I a nb n | < »

n=l

and

I l a

n*

3 „l <

( l

a

n

2

> 1/2

( l 01/2 • n=l n=l n=l

(3)

Parseval's identity:

Since the sequence of functions sin(nnz), n=l,2,... is a complete

orthogonal system on 0 < z <1, the following holds:

If

l

/ | f

2

(z ) | dz < ® , o and if

7
1

a n = / f (z )sin(nnz )dz , n = 1, 2,... , o then

i

/ |f 2 (z)|dz = 2 I |a

n | 2

. o n=l

We are now ready to proceed with our estimate of the magnitude of

the electric field E 0 due to the surface charge. So let us assume

that both electrodes satisfy <j> = 0. Also we impose the restriction that

the surface charge density p(z) is square integrable on the interval

0 < z < 1 , i . e.

l

/ p

2

(z )dz <

00

. 0

Def i ni ng

a n = / p(z )sin(niTZ )dz

0

then the coefficients (eq (11)) in the expansion for the potential

may be written as

C n = 2a n/[mr(ei + £2 )] = Ga n/mr,

and the potential becomes

<l>(y,z) = (G/tt) l (a

n /n)e _n l y l sin(nnz ). (13)

n=l

Since the potential is symmetric about the y axis, we restrict the

remainder of this discussion to the region y > 0. Differentiating the

series (13) term by term yields the negative of the electric field

components produced by the charge density

fy(y,z) = - G l

a

n e“

n7iy sin(miz ),

n=l

and

00 <^(y,z) = G l a

ne“

n7iy cos(n-nz ).

n=l

Noting that the electric field due to the charge density is

E 0 (Uy

| 2+I*z | 2

) 1/2

. (W)

we can obtain an upper bound for E 0. Since |sin(mtz)|<l

and |cos(mr)|< 1, E 0

is bounded by

8
n=l

Using the Schwartz inequality this can be written as

E

0

< (^)G I Un |e' my -

CO oo E 0

< (/2)G( I

a

n

2 )i^(

l (e'

2lI^) n

) 1/2. n=l n=l

Using Parseval 's identity and the expression for the sum of a geometric

series, the decaying exponential bound for E 0 can be seen

where, as previously defined, G = 2/(e]_+e2).

To illustrate the uses of this estimate, we consider the following

experimental situation: a potential of 25 kV is applied to the top

electrode and various surface charge densities are assumed on the interface.

The right side is vacuum 03 = ^0 » dncl The permittivity of the

insulator is e\ = 20 eg.

Of course, in an experimental situation the extent of the electrodes

and the interface is finite. However, our mathematical model can serve

as an indicator of the possible field enhancement. Let us apply here our estimate (15) to two different surface charge densities on the interface.

Case 1 : A uniform space-charge density. Assume p]_(z) = p 0 , for

0 < z < 1, where p 0 = 10~ 5 C/m 2

. If no surface charge were present, then

the electric field would have a constant magnitude E = 25 kV/cm. The

integration over the square of the charge density in eq (15) simply

gives p 0 , so the change in the magnitude of the electric field satisfies

(at the point (y,z) between the electrodes with y > 0)

For y

= 0.5 cm, for instance, we obtain E 0

< 0.22 kV/cm and E 0

/E < 0.009.

Thus, at a point 0.5 cm from the interface, the field enhancement is

less than 1%. For y =1 cm, we obtain

E q

< G (/ p2

(z )dz ) 1/2[e _1iy /(l-e' 2lTy

) 1/2

], (15)

0

E 0

< (1 . 076 )[e“ 71^/(l-e“ 2lT^ ) /

1/2

] (kV/cm)

E 0

< 0.047 kV/cm and E 0/E < 0.002,

so the field enhancement is at most 0.2%.

Case 2: A nonuniform space-charge density. Assume

P2 ( z )

0, 0 < z < 1/3

(1.5z - 0.5)po , 1/3 < z < 1,

9
c o where pq = 10

-3 C/m . Figure 2 shows the graph of P 2 U).

Most of the charge is concentrated near the top electrode. A simple

calculation shows that

1 [/ pZ (z)dz] 1/2 = (/2}p0

/3 < 0.5po. 0

A simple analysis as in case (1) shows that Eo/E < 0.5% on the line

y

= 0.5 cm and Eo/E < 0.1% on the line y

= 1 cm. Figure 3 shows

equi potential lines for the case where p(z) = pi(z), and figure 4

shows these lines when p(z ) = P2(z). The 1 i ne y

= 0 is centered

in each picture.

2. Cylindrical Space Charge Between Spheres

In this section, we use a computer model to study the following

electrostatic problem: a potential difference is placed on two spheres

separated by a small gap. A thin cylinder of charge is assumed in

the gap between the spheres (see fig. 5). We are interested in the

change in the magnitude of the electric field due to this charge.

More precisely, two spheres of each of radius R have their centers

at the points (0,0, c) and (0,0, -c) with R < c but so that the gap between

the spheres, d = 2(c-R), is "small." A potential <j> = + V is put on the

top sphere, and 4> = - V on the bottom. We assume further that a thin

cylinder of space charge exists in the gap and that the space charge

density p, at a distance r from the z-axis, is given by

P(r)

A cos^( irr/2a) , for 0 < r < a, |z| < c,

and r

2+(z-c) 2 > R

2

0, otherwise. (16)

where A and a are small relative to R. A standard calculation shows

that the total charge in this cylinder is (ignoring the slightly spherical

shape of the top and bottom of the cylinder)

c-R 2u a / / / A cos2(Trr/2a)rdrd6dz (17)

R-c 0 0

= [3(tt 2 -4)/2tt] a

2 Ad = 0.934a^Ad ,

so that we can control the total amount of charge in the cylinder by adjusting

A once a and d are known.

To study the solution to this problem we used a program which solves

two-dimensional elliptic boundary value problems with fairly general

boundary conditions over fairly general bounded geometries using an adaptive finite element technique [7].

10
(Z) ‘A11SN30 30HVH0

11

Surface

charge

density

along

the

interface.
0

CD

03

+-> E O

l. > oM— — C

13 SZ

+-> 03o -a

4- c

03

03

M

a.

03 •>— L- oo

03 c

o_ 0 » a o c

O) OJ II 0 cn

+-> 03

O) .3= " n U lo

a>

00 O) 4-> aj o 03 C 03 I

•r- 4- CL

13 <D i— 00 —

03 +-> •f-

+-> 03

O

C -i- +-> 0 U

+->03-0 0 4-0

03 L- *r— i— 0 i— 3 +-> Q.

O’

C O.

LlJ 03

CO

03

12

Fig.

4.

Equipotential

lines

between

parallel

plates

for

the

nonumform

interfacial

surface

charge

density, P

(z),

and

with V- U.
Fig. 5. Cylindrical space charge between two spheres. The upper

sphere is at <J> = +V and the lower sphere is at <j> = -V.

13
Using the cylindrical symmetry in this problem, Poisson's equation in the

variables r and z reduces to

- ( 4>rr

<t

) r/ r ^zz ) = )/^o» (18)

where p(r) is given by (16).

The specific geometry and dimensionless spacing we chose is shown in

figure 6; specifically, R = 8, C = 9, d = 2, and we used a = 0.5. For the

boundary conditions we use

/ +V on the top semicircle

$ = -V on the bottom semicircle (19)

3 <j>/ 3n =

0 , for r = 0 and -1 < z <1 (20)

4> =

<P induced on the lines from

(8,9) to (13,9), (13,9) to (13,-9) and

(13,-9) to (8,-9). (21)

Some explanation is in order about conditions (20) and (21). In (20), n denotes the unit outer normal to the region and (20) is equivalent to

stipulating that the equi potenti al lines intersect the z axis at right

angles. The three lines on the boundary and referenced in condition

(21) are assumed to be far enough away from the z axis that the potential

is unaffected by moderate amounts of space charge centered along the

axis of symmetry. Specifically, we use 10 terms of the series of Legendre

functions for the potential where no space charge is present. (Note: We

checked our solution using 10 terms with one using 30 or more terms, and

found no significant difference in our results.)

A word of caution is necessary before we present our results. The

values for the field vectors were generated by the computer program.

This program generates the graph of the potential <j>(r,z) as being

piecewise linear, and the field vector at the point (r,z) is found by

computing the normal to the plane which coincides with the graph of <j>(r,z)

at the point (r ,z , <j>(r,z ) )• This procedure, we believe, has reasonable

accuracy in this case, but certainly suffers somewhat from the inherent

loss of accuracy in a numerical differentiation procedure.

Table 1 shows the total charge and the maximum charge density in

the gap between the spheres as specified in eq (16). Various radii and

spacing are chosen where it is assumed that a potential of 10 kV is

placed on the top sphere and -10 kV on the bottom sphere. Table 2 shows

the percent increase or decrease in field intensity at a point with

dimensionless coordinates r and z. To obtain coordinates in centimeters

for each of the various situations, multiply the r and z coordinates by

d/2, where d is the spacing between the spheres.

The main conclusion to be observed from these tables is that at a distance three units from the axis of symmetry only a small ( i . e. , less

than 2%) enhancement of the electric field occurs.

14
Fig. 6. Geometry and coordinates used in the program PLTMG.

15
Table 1. Space charge in gap between spheres

Spaci ng

spheres

between

(cm)

Radi i of

spheres (cm)

Total

charge (pC)

Maximum charge

density

(pC/cm^)

1 4 6.04 x 10 3 1.03 x 105

2 8 1.21 x 10 4 2.58 x 10 4

5 20 3.02 x 10 4 4.13 x 10 3

Table 2. Percent increase (decrease) in field density,

gap d = 2

z r = 1.5 2.0 2.5 3.0

1.5

/ (3.96)

1.0 (15.2) (11) (14.2) 1.5

0.5 (24.6) (5.5) (8.5) 0.9

0.0 12.2 5.9 3.9 1.1

-0.5 16 5 4.6 5.3 1.2

-1.0 11.6 7.2 3.8 1.1

-1.5 1.9

16
Figures 7 through 9 were drawn using the program PLTMG. The first of

these shows a typical high level triangulation used in the finite element

calculation. Figure 8 shows equi potenti al lines for the case where no space charge is present and figure 9 shows equipotential lines for the

case with space charge to which the data above refers.

The analyses presented here show that even for large charge densities

the resulting perturbations of the ideal geometric field are surprisingly

small. Especially for distances beyond the gap spacing, we find that

field modifications are typically less than 10% in the case of a cylinder

of charge between spherical electrodes and less than 1% for sheets of

charge between parallel plates.

B. BREAKDOWN LOCATION — CONTAMINATED OIL

On the basis of the above discussion it is clear that substantial

amounts of space or surface charge are required before a significant

modification of the electric field arises. Such a result indicates that

when breakdown occurs at an interface, it may not be because of field

distortions arising from space charge, but some other phenomena may

increase the probability of breakdown at the interface. This is not to

say that space charge does not exist or cannot influence breakdown in some

way other than a modification of the field.

A previous report [8] showed that for a clean, well -characterized

system, breakdown does not necessarily occur at an oil-paper interface.

Equivalently, it was shown that the presence of an interface does not

necessarily reduce the breakdown strength of a system. Such results

strongly indicated that space-charge field intensifications were not

present in carefully cleaned and prepared interfacial systems or that

they made no difference. The question of liquid purity became important

at this point and prompted us to repeat these interfacial breakdown tests

using contaminated oil.

The electrodes used for this study were two discs (diameter 2.5 cm)

with rounded edges which provided a uniform field. The discs were split

along their diameter to clamp the paper sample parallel to the electric

field. 60-Hz ac voltage was applied at a ramping rate of 3 kV/s until

the electrode system broke down. The paper samples were sufficiently

thin so that the split edge did not significantly enhance the field where

the paper was clamped. The fact that the split electrode edge did not

enhance the breakdown probability appreciably was shown by separating the

electrode split halves the thickness of the paper (0.007 cm), and running

several breakdowns without any paper in the system. The position of the

breakdowns continued to distribute themselves randomly about the uniform

field region and not prefer the small split. This indicated that the

split electrode geometry would not be responsible for driving the breakdown

to the paper interface when the paper is installed.

Obtaining statistically meaningful data is a time-consuming process

since the breakdown usually destroys the interface. When the breakdown

occurs at the interface it burns away a portion of the paper. However,

even if the breakdown does not occur at the interface, the shockwave from

17
18

Fig.

7.

Trianguldtion

employed

by

program

PLTMG.
19

Fig.

8.

Equi

potential

lines

obtained

via

PLTMG

with

no

space

charge

present.
20

Equipotential

lines

obtained

via

PLTMG

with

space

charge

present

(see

eq

16

).
the breakdown usually rips the paper. Thus, the apparatus must be opened

and a new interface installed after each breakdown. To minimize the

amount of time expended, we felt that surveying interfacial breakdowns

under several different conditions with relatively few breakdowns for

each condition was preferred to many breakdowns under only one condition.

Even so, it took more than 150 breakdown tests before the handling procedures

could be established and consistent data obtained. These results strongly

suggest that there is no fundamental electric field perturbation introduced

by the paper interface, but that the interface's contribution to lowering

the breakdown voltage possibly rests in either entrapped gasses in the

interface material (bubbles) or dirt, or both.

To determine the influence of oil purity on breakdown location,

measurements were first performed using clean oil (mechanically filtered

and degassed) and then severely contaminated oil was used. The contaminated

oil had been removed from a commercial transformer which had failed. The

data obtained using clean oil is presented in table 3.

Table 3. Clean oil data

Condition

No interface

Interface present

Interface present

but breakdown not

at interface

Interface present

and breakdown at

i nterface

Number of

breakdowns recorded

15

10

7

3

Breakdown voltage

(2.5 mm gap)

76 ± 10 kV

68 ± 11 kV

74 ± 7 kV

56 ± 9 kv

The variations associated with the breakdown voltages are the standard

deviations about the mean value. Throughout these experiments, whether

or not the breakdown occurs at the interface is determined in two ways:

optical observations during breakdown and observation of burned areas on the interface. The results in table 3 show that 70% of the time the

breakdown did not occur at the interface, and the breakdown voltage was essentially the same as the breakdown voltage without an interface. The

30% of the time the breakdowns occurred at the interface, the breakdown

voltage was substantially lower than without an interface. Because of

the difficulty in handling the paper interface, we hypothesize that the

breakdowns at the interface were caused either, by bubbles embedded in

the paper or perhaps by particles introduced with the paper or a combination of both.

21
The results obtained using contaminted oil are shown in figure 10.

The contaminated oil contained small particles which would eventually

precipitate out of the oil. Since the particles presumably influence

breakdown, the oil reservoir was initially shaken to suspend these

particles. The first five breakdowns or "shots" were made without an interface present, and the resulting average breakdown voltage was

53 ± 7 kV — significantly below the 76 ± 10 kV recorded for clean oil.

The second five measurements were taken with a paper interface present

and provided a higher breakdown voltage, 65 ± 12 kV, where three of the

five breakdowns occurred at the interface. Suspecting that the suspended

particles were dominating the breakdown behavior, the system was allowed

to sit overnight, which would permit the larger particles to precipitate

out from the oil. The next morning five breakdowns were recorded without

an interface whereby the average breakdown voltage was 74 ± 7 kV — about

the same as for clean oil.

At this point a series f 10 shots was taken, five with an interface

and five without. Only now the oil reservoir was shaken before each

shot so that the oil in the cell contained the larger particles which

had previously precipitated out. Using this method the breakdowns without

an interface occurred at an average of 34 ± 5 kV and with an interface

at 39 ± 8 kV ~ essentially the same. Note, however, only two of the

breakdowns occurred at the interface. From these data, it is postulated

that although the oil contamination, especially particulate contamination,

decreases the breakdown voltage of the system, it does not have a dramatic

effect on the interfacial phenomena since the breakdown, as before,

does not necessarily occur at the interface even with heavily contaminated

oil.

The first 100 or so breakdowns are not reported in table 3 or figure 10. When interfaces were installed during these shots, they

always broke down at much lower voltages compared to the breakdown voltage

without an interface. The procedure used to load the interface into the

cell was as follows: a paper interface which had been under oil in a vacuum was placed in the split electrode system and then sealed in the cell.

The cell was evacuated for at least one minute and then loaded with oil

while the vacuum was maintained above the oil. After the cell was filled

with oil, the system was brought to atmospheric pressure with dry nitrogen.

A problem arises during the filling process. When the oil enters the

cell under vacuum, it outgasses, producing small bubbles, some of which

lodge upon the interface. These bubbles are suspected of lodging in the

fiber structure of the paper interface thereby weakening its ability to

withstand voltage. The above hypothesis fits the observations well, for

the loading procedure can be changed so that the interface is found to

withstand as much voltage as the liquid, at least 50% of the time and

perhaps more.

The procedure which resulted in the most breakdown resistant

interfaces was: to load a new interface into the cell and to evacuate

the cell for one minute. Because the oiled paper supply was stored under

vacuum, it is possible to get a few bubbles on or near the interface only

during installation. These bubbles are easily removed during the cell's

evacuation. The cell was pressurized with dry nitrogen to atmospheric

pressure and then slowly filled with oil to avoid producing small bubbles.

22
to

r*.

o

in

co

o

CO

in

in

(A>|) e6ej|0A uMop^eaig

23

Breakdown

Number

(Contaminated

Oil)

).

Summary

of

breakdown

voltage

measurements

using

contaminated

oil.

The

open

circles

indicate

breakdown

away

from

the

interface

while

tite

solid

circles

denote

interfacial

breakdown.

The

squares

represent

data

on

oil

only

(no

paper
The bubbles which managed to attach themselves to the interface during

loading were always sufficiently large that they could be pushed away by

slowly circulating the oil through the cell and along the interface. The

difference between this procedure and the first is that the interface is

pressurized after all the bubbles have been removed from its surface.

When the cell is loaded with the oil under vacuum, we postulate that

small bubbles impregnate the interface. If the oil were degassed, we would expect even these bubbles to be dissolved if enough time were

allowed. However, since the breakdown occurs shortly after loading

the cell, the procedure which produces the fewest number of bubbles in

the paper is suspected of producing the most breakdown resistant interface.

The data reported here (in table 3 and fig. 10), therefore, employed the

second loading process where the interface is pressurized and the cell

is loaded with oil at atmospheric pressure.

To illustrate the problem of bubbles, we show several microscope

photographs of the paper material used in figure 11. The top left

photograph, A, shows the oil soaked paper before subjecting it to a vacuum. The top right photograph, B, shows the effects of vacuum pumping

for a few minutes. The vacuum pumping clearly makes a great difference

in the number of bubbles remaining in the paper. The bottom left

photograph, C, shows that extended vacuum pumping (several hours) removes

more, but not all, of the bubbles; note the one bubble marked. Overnight

this bubble dissolved into the liquid and is not observed in the bottom

right photograph, D, taken the next morning. These results point to the

physical characteristics of the paper interface as a critical element in

the interfacial breakdown.

IV. ELECTRIC FIELD MEASUREMENTS — SPACE CHARGE

In this section we review Kerr-effect electro-optical, field

measurements, and the equipment used to make those measurements. The

space charge in nitrobenzene which develops between parallel plates is

then observed and quantified. These methods are then applied to the

measurement of space charge in transformer oil. Dramatically different

results are observed for transformer oil than for nitrobenzene.

A. THEORY

The electric field measurements reported here are made using the

electro-optic Kerr effect. Such measurements provide non-contact means

of observing the electric field, since only light is used to probe the

field region of interest. Kerr-effect measurements are described in

detail elsewhere, so only a brief description will be given here [9].

Certain liquids, when subjected to electric fields, become

bi ref ri ngent , meaning that polarized light will pass through the liquid

at different speeds depending upon the polarization angle relative to

the field direction. Light polarized parallel to the field will move

more slowly than light polarized perpendicular to the field. If parallel

plates are used to provide a uniform field in a cell filled with a liquid

exhibiting a Kerr effect, and if the cell is placed between crossed

polarizers so that the uniform field direction is at an angle of 45° with

24
25

Fig,

11,

Microscope

photographs

showing

removal

of

bubbles

in

the

paper

used

for

interfaces.

The

line

in

the

upper

left

photograph

denotes

0,5

fnm

(500

pm).
respect to the polarization axes, then the transmitted light will be

found to be a function of the field between the plates E and the length

of the plates l

I/I m = si n 2 ( ttBE 2 £) , (22)

where I is the transmitted intensity of the observed light ray, I m

is

the maximum amount of light which can be transmitted along that ray path

(as if the polarizer were aligned), and B is the Kerr constant of the

liquid used. At room temperatures, the Kerr constant for nitrobenzene is

B = 3.2 x 10" 10 cm/V 2

, and typically for transformer oil B = 3.2 x 10“ 13 cm/V 2 For uniform fields, the electric field is related to the applied voltage

by E = V/d, where d is the plate spacing. Fringe fields are neglected

throughout this report since they contribute less than a 1% correction [10].

Whenever the entire area surrounding the plates is illuminated, a two-dimensional Kerr pattern is produced. The light and dark regions found

in such a Kerr pattern are usually described in terms of fringe numbers

n = (E/E m ) 2 =

0,2, 4, 6, for dark fringes

1,3, 5, 7, for light fringes

non-integer for between fringes.

(23)

where E m

= (2Bt)” 1/2 is the field intensity required to produce the

first fringe. E m contains the Kerr-effect sensitivity information and

the plate length. Then eq (22) may be written in terms of the fringe

number or a relative electric field

I/I m

= sin 2 (mr/2) = si n

2 [( tt/ 2) (E/E m ) 2

]. (24)

In order to infer the electric field strength from the light intensity

information, it is necessary to keep track of the fringe number. By

introducing the previous fringe number, an integer

N = int(n) , (25)

(where n-1 < N < n) , eq (24) may then be inverted to express the relative

field strength in terms of the light intensity

E/E m

= {2[N- i nt ( N/2 ) ] + (-1 ) N

(2/ir) sintt I/IJ 1/2

] [ 1/2

. (26)

A plot of this function is shown in figure 12. Whenever a parall el -pi ate

geometry Kerr pattern shows several fringes (as is the usual case with

nitrobenzene) the field strength may be determined using eq (26).

Consider a paral 1 el -pi ate geometry where the plates are parallel to the

x-y plane and placed with surfaces at z = ±d/2 giving a plate separation

or gap of d. Let the length of the plates be £ in the x-di recti on which

also will be the direction of the light beam. This system is placed between

crossed polarizers. Because of the Kerr effect, a two-dimensional pattern

will be observed in the y-z plane. That is, for each ray (y,z) parallel

to the x-axis there will be an observed intensity I(y,z) which is related

26
RELATIVE

INTENSITY,

I/I

RELATIVE FIELD, E/Em

o -* ro

FRINGE NUMBER, n

Fig. 12. The relative field strength expressed as a function of relative

transmitted light intensity and previous fringe number N*

27
to the incident intensity I m

(y,z) by eq (24). Describing the incident

intensity I m(y,z) in this manner allows us to account for imperfections

in the optical system or light source (usually a laser) which produces a nonuniform incident beam. For this reason reference is usually made to

the relative transmitted light intensity I (y ,z )/I m (y ,z ) to avoid the

problems arising from imperfections.

There are two factors which determine the electric field E(y,z).

The voltage applied to the plates gives

where the plate at z = d/2 is the cathode and z = -d/2 is the anode.

Secondly, space charge can influence the electric field according to

Poisson's equation. By symmetry and assuming a linear, isotropic medium,

the space charge density can, at most, be a function of z so that Poisson's

equation may be written as a simple derivative of the electric field

where e = <e0 is the dielectric constant of the liquid, where < is the

electric susceptibility and e Q = 8. 85 x 10" 14 F/cm is the permittivity

of free space. The plus (minus) sign is used if the direction of the

field is (is not) in the direction of increasing z. If there is no space

charge between the plates, then p = 0, dE/dz = 0, and the electric field

is uniform E(z) = V/d = constant. In such a case, the relative transmitted

intensity will be uniform, given by eq (22), I (y ,z )/I m (y ,z ) is constant.

Thus, any nonuniformity of the electric field because of space charge will

be manifested by a nonuniformity in the transmitted light.

With liquids like nitrobenzene which exhibit a large Kerr coefficient,

it is easy to observe space-charge field modifications because a sufficiently

large field can be applied to the liquid which will produce many fringes.

Space-charge field distortions will become manifest by the presence of

several fringes in regions where the relative intensity would be uniform

if the field were uniform. However, if a liquid does not exhibit a large Kerr coefficient, then it may not be possible to observe the first

bright fringe (n = 1) before the liquid between the plates breaks down.

Such is the case with transformer oil if the plates are not made awkwardly

long so that E m

= (2B£)~ 1/2 is less than the breakdown field.

For example, if we assume E mis on the order of the breakdown fields

in transformer oil under the application of dc, say, E m

= 100 kV/cm, then

the required plate length would be l = l/2B(E m ) 2 ~ 160 cm — not a very

practicable length. For the transformer oil experiments reported here, the

plate length was £ = 30 cm which would imply a field of E^ = (2Bz)” 1/2 = 228 kV/cm

for the first fringe. Breakdown fields, however, are typically 100 kV/cm

so that E/E m= 0.44 at the most. This results in a relative light

intensity of I/I m= 0.09. For such low relative light intensities

(I/I m < 0.1), an examination of figure 12 suggests there may be problems

of measurement, since the relative field E/E mis a sensitive function

of the relative intensity I/I m. Let us examine this further.

d/2

/ E(y ,z )dz = V,

-d/2

(27)

P = p(z ) = ±edE/dz , (28)

28
Because we are limiting ourselves to small relative intensities

(N =0), eq (26) which expresses E/E m

in terms of I /

m reduces to

E/Em

= {(2/ir)sin" 1 [(I/I

rn

) 1/2]}1 /2

. (29)

Provided the relative intensity is small (I/Im << 1), the above relation

simplifies even further to

E/E m - (2/ir) 1/2 (I/I m ) 1/I+

. (30)

Our above concern for sensitivity is expressed in the differential

relationship

dE/E

m

- (l/8Tr)l/2(l/lm

)-3/4d i/i m# (31)

The negative power of the relative intensity becomes large as the intensity

reduces to zero, and this might lead one to believe that 1 ow-1 i ght- level

Kerr measurements are impracticable. This is not the case, however,

because we are mainly interested in the sensitivity of measuring a field

dE/E (not dE/Em ) as determined by a deviation in the measured light

dl/I (not dl/l m ). To put this another way, whenever an intensity

I(y,z) is measured it will exhibit the same intensity profile I m (y,z),

that is, I(y,z )/I m(y,z ) = constant, only if the field is not changed

from its uniform structure by space charge. If there is space charge,

then we can expect some change dl(y,z) in the light intensity which can

be related to the change in the field dE due to space charge. Thus the

quantity of interest is dE/E related to dl/I by a sensitivity function

g(I/I m ). Using eq (24) the general relationship dE/E = g(I/Im

)dI/I

becomes

dE/E = (l/2ir)(I/I

ni ) 1/2 (l-I/Im

)i /2 (E/E

IT1 )” 2dI/I, (32)

where E/Emis given by eq (26). Since we have restricted ourselves to

n < 1 , we can use eq (29) for E/E m

to obtain

dE/E = ( 1 )( I/Im ) 1/2 (l-I/I

rn

) -1/2

{ S in _l

[( I/Im ) l/2

]>

-1 dI/I. (33)

Here g

( I /

m ) is restricted to I/I m < 1. Further restricting ourselves

to small intensities so that I /

m « 1 , we obtain the simple relation

dE/E = (l/4)dl/l. (34)

Here g ( I / I m ) = 1/4. This shows that for low light levels in the Kerr

effect, a small change in the electric field will manifest itself by a factor of four larger change in the light intensity. The comparison of

the exact coefficient of dl/I in eq (33) to the approximate coefficient

in eq (34) is expressed in figure 13 along with a comparison of the exact

and approximate expressions for E/Em

in eqs (29) and (30), respectively.

Clearly, for intensities I /

m < 0.1, eqs (34) and (30) hold rather

well and the small -I approximation is useful for even an extended range

of I /

m

values. Therefore, throughout the transformer oil work we will use the approximate expressions eq (30) for estimating the relative

field E/E m from the relative intensity I /

m> because usually the relative

intensity is I /

m

= 0.1 or below unless breakdown fields are explored.

29
RELATIVE

FIELD,

E/E

,

OR

g(l/l
Even for relatively large intensities I/I m ~ 0.8, the absolute error

in using the approximate form of relative field is about 10%. If the

field were distorted 10% at these levels, our error in estimating the

amount of distortion would only be 1% as a result of using the approximate

expression.

B. EQUIPMENT

The diagram of the apparatus is shown in figure 14, and the type of

information obtained with the commercially available detector system

is shown in figure 15. The first part of the detector is an electrostatically-focused image intensifier which illuminates a silicon target.

The target is a microscopic array of photodiodes separated by ~8 urn. A 25-um diameter electron beam scans this array to read the charge

on the photodiodes and recharge them. Light causes the photodiodes to

reduce the amount of charge remaining on them which is detected by the

electron beam current. This current information is integrated for one line of scan, digitized and stored in the computer's memory. The resulting

intensity profile I(z) can

4 be position resolved into about 500 parts each

with a dynamic range of 10 and ±2% linearity. Such a detector resolution

often exceeds the resolution provided by the image producing optics.

The detector can be pulsed and synchronized with the 60-Hz line allowing

accumulative scanning for many 60-Hz waveforms. A computer console

controls the scanning of the detector as well as the data collection,

storage, manipulation, and output. Because of the sensitivity of the

detector even in pulsed mode, neutral density filters are needed to

decrease the input light levels.

When the apparatus is used to observe Kerr fringes in nitrobenzene,

the procedure is much like conventional photography. Since both bright

and dark fringes are present, the intensity profiles are easily interpreted

to produce electric field profiles. Additionally, the low viscosity of

nitrobenzene and other optical properties provide relatively stable

intensity profiles which are not dramatically affected by turbulence

during steady-state high-voltage operation, either 60 Hz or dc. Such

luxuries are not afforded using transformer oil as the Kerr fluid.

The properties of transformer oil -- apparently an index of refraction

which is very sensitive to temperature — cause it to manifest turbulence

by intensity fluctuations. This and the low light levels associated with

the Kerr response requires complicated data-handl i ng methods to acquire

rel i abl e data.

C. SPACE CHARGE IN NITROBENZENE

The nitrobenzene test cell, in which the nitrobenzene is dehydrated

and filtered during the course of the measurements, had parallel plates

9.5 cm square and separated by 0.6 cm. The nitrobenzene is pumped through

powdered alumina to remove much of the water and a mechanical filter

which removes most of the particles over 2 urn in diameter. Because fluid

motion degrades the image, the filtration is only performed before each

measurement sequence and not during the accumulation of data.

31
COMPUTER

CONTROL

tp- o V- O <- 4-> X

4->

X pj

d <T3 X>

X o X U -r- X-

•r— a> *f— r—

d

4-> 00 Op- o X 00 •r- X O O O X _X

•iV- CT 4->

X E o X

CM o r*

e= q; o

>3 X2 1 r— X a x cc

•l—

a XI >—

x • 2 X o X x

LLi to 4-> E cn v.

O

0) O) •r- 0)

X 4—

N X 02 V. 00 U

•1

0- r,3 X

CC > -X OJ

O

X 4-) o C Q. -O E aj < ~ X

4->

O

o_

X

X

00

— O.

X

00 cO ow X I— OO X 4-> U

OJ o OJ c~ Q. -Q c X x

•I— P- X)

X

W <T3 x

00

C

nj -r~ X X X

1)

U

X 03 C I

iT3 Q- CLX OO X -r- > -o o

L. 00 CL !-x

aj +-> CL'

o •>- u h00X >, , 4-> OJ -r- +J oo ,— >I X c

OJ

O

4->

O

x jr <c a) < u x

00 oo c

rO «

V.

X +J X X <+- SC

I— oo

O) • > (/) 00 L- L. X '— <U +->

4-> 1—

M

O

03 <U •>— <D O U O C X X

CL

D r—

X

O-JC o = < -p

O0 " O X x a) 4_) 00 C 03 i- _o

32
AREA VIEWED

BY DETECTOR

2 2

Fig. 15. The intensity profile I (z ) generated by the computerized

detection system is produced by scanning the viewed detector

area and integrating the intensity for each scan

paral 1 el to the y axi s

33
To analyze the 60-Hz ac Kerr patterns, the distortions of the electric

field arising from the fringe fields are determined. In an ideal parallelplate Kerr cell, i.e., where the field is confined entirely between the

plates of length l and separation d, the Kerr fringe number n is given

by eq (23). However, because of the fringe fields extending beyond the

plates, there is some question as to whether or not these fringe fields

will produce a significant distortion in the Kerr pattern. The change

in fringe number An associated with a field distortion AE can be

determined from eq (23) to be

AE/E = An/2n (35)

This field distortion arising from the fringe field can be measured using

the detection system.

In figure 16, several intensity-profiles are shown for impulse voltages.

The profile for 41 kV, for example, shows an intensity change of Al/I m

« 0.3

on the average. Since the intensity is related to the fringe number by

eq (24), this change in intensity gives rise to a fringe shift of An = 0.2.

Using a fringe number of n = 27 ± 3, the effective field distortion becomes

AE/E = 0.004 or 0.4%. Not only does this low distortion illustrate the

approximately uniform field provided by this system, but it also provides

an example of the measurement precision. In the following 60-Hz ac data,

the fringe number is less than 10 so that the fringe-field contribution

(~ 0.4%) will not be evident. Thus, any nonuniformity may be attributed to

electric field distortions due to space charge.

The 60-Hz ac data is obtained by recording an intensity profile for

1 ys at some selected point on the 60-Hz waveform. The profiles for

100 consecutive waveforms are added to form the final intensity profile

for that position on the waveform. In figures 17 and 18, profiles are displayed for the positive and negative peaks, respectively. Each profile

shows the fringe pattern associated with the peak voltage. Because the

intensity is not uniform between the plates, it is clear that there is

space-charge distortion of the field. Since the relative field strength

E/E mis related to the fringe number n via eq (23), figure 19 shows the

relative field between the plates as inferred from the intensity profiles.

For both positive and negative peaks, a space-charge threshold may be seen near n = 1 or E = E m

. There is a pronounced decrease in the field

near the anode and a slight increase in the field near the cathode. Also

noteworthy is the fact that the space-charge density seems to saturate as the applied field increases. The charge density, proportional to the

field gradient as shown by eq (28), may now be determined.

Figure 20 shows the approximate charge density p measured at the

positive peak as a function of applied voltage. Here it is assumed that

E m

= 12.7 kV/cm and < = 35 for nitrobenzene. These curves are rough

indications of space-charge behavior, not precision calculations based on

eq (28); however, a saturation space charge of -400 nC/cm3 or more is

i ndi cated.

Any net light intensity at the positive-negative zero crossing (PNZC)

of the 60-Hz waveform reveals that the space charge decays more slowly

than the voltage decay of the waveform [8]. Figure 21 shows PNZC profiles

34
z= -d/2 z=d/2

POSITION

Fig. 16. Relative intensity profiles for impulse voltage applied to a nitrobenzene Kerr cell. The extent to which the profiles

deviate from being uniform from plate to plate provides a measure of the nonuniformity of the field. The smaller,

higher frequency modulations of the profiles are due to

nonuniformities in the light sources and small changes within

the liquid.

35
FOR

POSITIVE

PEAKS

60Hz

AC

1 VOLTAGE

22. 5kV

2 1.4kV

18. 7kV

16. 8kV

15. 2kV

13.0kV

10.3kV

8. IkV

8. IkV

6.0kV

4.0kV

1.8kV

z= -d/2

POSITION

z = d/2

Fig. 17. Relative intensity profiles at the peak of the 60-Hz ac waveform

vs several peak voltage levels. Note that distortions do not

become obvious until the fringe number n exceeds one. The

numbers near the profiles denote the fringe number .

36

CATHODE
RELATIVE

INTENSITY

I(z)/I

m

FOR

NEGATIVE

PEAKS

60Hz

AC

1 VOLTAGE

z=-d/2 . z=d/2

POSITION

2 1.6kV

20.0kV

18.8kV

17.2kV

15. IkV

12.8kV

10. 7kV

7.6kV

7.6kV

4.2kV

2.5kV

LUQ

O

Z

<

Fig. 18. Relative intensity profiles at the negative peak of the 60-Hz ac waveform vs peak voltage level. The numbers near the profiles

denote fringe number.

37
RELATIVE

ELECTRIC

FIELD,

E/E

m

60-Hz

AC

POSITION

Fig. 19. Relative electric field at the positive or negative peak of the

60-Hz waveform as a function of position for the voltages in

figures 17 and 18.

38

FRINGE

NUMBER
SPACE

CHARGE

DENSITY,

p

(C

/cm3

)

Fig. 20. Space-charge density in nitrobenzene. These approximate curves

are inferred from the relative electric field plots in figure 19.

Note that the highest density shown refers to 3.7 xl0

1^ molecules, assuming one charge per molecule.

39

NUMBER

OF

CHARGES

PER
INTENSITY

(COUNTS)

3x 10

z = -d/2 z = d/2

POSITION

Fig. 21. Positive-negative zero-crossing profiles compared with the |

n = 1 profile. The grounded electrode is at the left.

40
as compared to the n = 1 profile. Note the peaks near the plates. It is

instructive to examine the voltage dependence of these peaks to see if

saturation of space charge at the PNZC also occurs. Figure 22 shows a plot of these intensity peaks as a function of voltage squared. A

saturation of space charge is clear as a plateau is approached for higher

voltages.

As a further illustration of space charge, it is instructive to record

the intensity profiles at selected points from the negative peak, through

the zero crossing to the positive peak (see fig. 23). These profiles are

not significantly different from those shown in figures 17 and 18.

Differences between the positive peaks of figures 17 and 23 may be a result of increases in space charge due to contamination from water

diffusing out of the nylon walls of the cell or a result of the lack of

precision associated with setting the voltage.

D. ELECTRIC FIELDS IN TRANSFORMER OIL

1. Contaminated (Wash) Oil, Room Temperature

Electro-optical measurements of the electric field were made in

transformer oil employed previously as a wash for radiators used in

power transformers after their construction was completed. One problem

which is more significant in transformer oil than in nitrobenzene is

the degeneration of the intensity profile due to turbulence. Each time

the detector records a profile, it stores the intensity data in memory.

The number of records which are averaged to produce an intensity profile

may be controlled. Figure 24 shows the effect of increasing the number

of records per profile from 10 to 100. The intensity profiles are produced

by applying ac 66.8 kV peak to plates with length l = 30 cm and separation

d = 0.64 cm. Timing was such that the positive peak of the 60-Hz waveform

was observed. If the intensity per record, at any point z, were normally

distributed with a standard deviation of a, one would expect that N scans would show a standard deviation an = a//H. Such a situation is not

observed presumably because the observation time, even for 10,000 scans,

may not be sufficient to obtain a normal distribution because of long-time

turbulence fluctuations or flow pattern changes within the cell due to

heating. To reduce the effects of turbulence, each intensity profile

below is a composite of 10,000 scans which requires 2.8 min to accumulate.

Figure 25 shows intensity profiles at 70.5 kV peak voltage 60-Hz ac —

six positive peak (PP) profiles and three negative peak (NP) profiles.

These data have not been adjusted by subtracting a background signal.

The “glitch" at the left side of the NP profiles is an artifact of the

detector. Figure 26 shows the averaged data with background profiles

subtracted. The error bar represents the standard deviation associated

with the profiles. There does not appear to be any measurable distortion

in these profiles, i.e., it appears that space charge has no effect on the field distribution. To check this conclusion, it is important to

examine the relative field strength E/E m and not just the intensity profiles.

An estimate of the incident profile is made by aligning the polarizers

and recording the I m

(z) profile. This turns out not to be an adequate

means to establish the true I m

(z) profile because of the imperfections

41
1.8x10

LO

O

(S11MD00) A1ISN31N 

42

L. c aj ai o d "O

•r— +-> S_

4-> o u 4-> c 03 Z o a •r— +-> 4- OO i- J- cu <T3 > > a

•I— V) •a v4_) 03 o

•p- La CNJ

CO VI o cu +->>(/) U +J cl +-> CU Z 0

rO t ia

rcu I— d a.

cu

da

+-> +-> T3 -P

D

cu

+->

d

<U

L

u

-a

d aj LU

ra +-> Z d >4- 3 +-> i+- CO +-> o its a; cc rO L- V- 1 03 cr> w < CU "O CL OJ

T3 V. CU V) jj

D

L.

d v) LC

CU 3 1— ta

CJ VI C ITS

W * V) L 05

ra cu . d TJ 4-> E -a <o =

+-> cu 0

•r- V)p o +j LU E its ra d </) VI 3 +-> 3 a e cn

ra c

cru

00 V) <

L- •!—

4_> 00

ra

r

CU +J i 00 CD"D •>- r— 0) o ra a $

_J

d 4.

+-> <-> +J O0 1—3 0 O 4- o o c > V) (- > O 4-

oj

•r- r"

d

4->

M <aN c

C“

a > t- cd cu CL —

•r- > a

0) CU 0) d J-> cc . o

ra 4-> +-> a) CDi 4- d OJ 4_ 1) 0

1—

C

O -P • CNJ

CNJ• CD • r— U_ 1
RELATIVE

INTENSITY

I(z)/I

m

(z)

TIME

NEGATIVE PEAK t /T POSITIVE PEAK

POSITION POSITION

Fig. 23. The change in relative intensity selected voltages between a negative and a positive peak. The peak applied voltage was

about 22 kV.

43
INTENSITY

(COUNTS)

£

INTENSITY

(COUNTS)

Fig. 24. Comparison of the measured intensity averaging 10 detector

records and 100 detector records

44
INTENSITY

(COUNTS)

INTENSITY

(COUNTS)

Fig. 25. Intensity profiles taken at the positive peak and negative

peak of the 60-Hz waveform. 10,000 scans were averaged to

produce the profiles. The peak voltage was 70.5 kV.

45
I

I

(N LZ N

fa -a

a; a) CL 4-> “O fa a>

IIN negati

n

assoc

o o

e +->

o

H

C/D

O

Q.

<T3 rg

ai > > 1) •r- -a

4-J

•'—

00 o_ o .-a C-'O

c

a> -a

<a oo

VOJ r— > <a

<a u

a> jc

CL

CNJ

-a

4- SZ O +J

l/> 00

aj

fa -i— — 4— E O

O i_ O CL

II N

• LO

CM

• cn

X

CO

^ sanaoad aovaaAv

(SlNnOO) A±ISN3±NI

46

with

these

measurements.
in the optical elements. A more sophisticated process is needed which

will be presented and used in later data presentations. The determination

of E(z)/Em

is accomplished via the approximation in eq (30) and the results

are shown in figure 27. Thus the error bar in figure 27 represents the

standard deviation of the field measurements and is about 3% of the relative

field value. These data were taken with a field of 110 kV/cm. The cell

readily broke down with fields of 129 kV/cm, so we were operating near the

breakdown field strength.

The conclusion reached here is that even for room-temperature transformer

oil which is heavily contaminated, space-charge field distortions are less than 3%.

2. Contaminated (Failed) Oil, Elevated Temperature

Although the oil used in the previous investigation was contaminated,

there was some concern whether or not the typical contaminants were found

in it. Some transformer oil was then tested which came from a transformer

which had failed. Electro-optical Kerr-effect measurements were made on this oil at room and elevated temperatures. The contamination level of

this oil is summarized in table 4.

Table 4. Summary of particulate contamination

Particle size 3

urn Number of particles/ml

Contaminated oil Normal oil

3 - 150

50 - 150

1221

60

40 - 70

0.1 - 0.2

3 About 90-98% of the particulates were cellulose (from the paper

or pressboard in the apparatus) with the remaining being iron

or copper.

An analysis similar to that performed previously was made for the

intensity profiles taken at several temperatures. For these data, however,

100 scans were averaged for each I(z) profile and three I(z) profiles

were combined to give the resulting I(z) profile from which E(z) is

determined. The resulting E(z) profile was composed of an average of

300 profiles taken at the positive peak of the 60- Hz waveform. This was done at each temperature. Throughout these measurements, a voltage of

about 42 kV was applied to the parallel plates with a gap of d = 0.64 cm

so that the applied field was 66 kV/cm — well under the usual breakdown

voltages. Figure 28 summarizes the electric field measurements in the

contaminated oil. The electric-field profiles shown here are normalized

to emphasize and more easily quantify the relative distortions. At room temperature, this oil exhibited no measurable field distortion, that is,

the electric field was uniform to within ±2% of its average value.

Near 53°C, the field was again uniform to within about ±3% of its

average value. Near 57°C the field was again uniform to within about

±3%; there may, however, have been some enhancement at the anode and

a decrease of the electric field strength at the cathode.

47
RELATIVE

E

FIELD

E/E

0.7

0.6

0.5

• ••• NEGATIVE PEAK

POSITIVE PEAK

z = -d/2 z = d /2

POSITION

Fig. 27. Relative electric field for the positive and negative peaks

and associated standard deviation .

48
NORMALIZED

ELECTRIC

FIELD

-d/2 0 d/2

(ANODE) (CATHODE)

POSITION, z

Fig. 28. The normalized field as a function of position between parallel

plates in transformer oil at four different temperatures.

The data at 68°C suggests that 'the space-charge density

may be making a significant (~5%) contribution to the

electric field.

49
For the temperature near 68°C an apparent distortion was observed

in the electric field profile. The maximum 6% or more change in the

field from one plate to the other was about 5% of the average electric

field between the plates. If this is space-charge field distortion,

and not an artifact of the apparatus, then the space-charge density

which could produce such a distortion would be about -1 nC/cm 3. It must

be stressed that this is a preliminary measurement and must be further

substantiated before confidence in such a result is establ i sired. In comparison, the amounts of space charge which are found in nitrobenzene

are easily a factor of 400 times larger than the value listed above

for oil (see fig. 20 ).

With this possible indication of space charge, it was desirable to

make measurements at even higher temperatures -- 100°C and higher.

However, the cell was made from high-pressure, laminated phenolic plate

(paper base, grade xx) and could not withstand the application of high

voltage at 100°C. (The failure was probably due to water vapor.)

However, profiles were obtained at 75°C and room temperature. These

profiles were similar to those shown in figure 28, only with an opposite

slope. Such a result suggests that even the 6% field distortions

indicated by the data in figure 28 may not be real but an artifact of

the measurement.

3. Clean Oil, Elevated Temperatures, AC, DC

To extend these measurements above 100° C, several materials were

tested in transformer oil up to 170°C under the application of high voltage.

On the basis of these tests, a new cell, cell holder, positioning device,

and tank were designed. The cell was made of stainless steel with

machinable glass ceramic, acetal or polytetraf 1 uoroethy 1 ene (PTFE) plastic

high voltage feed-throughs and electrode supports and silicone rubber

and/or PTFE seals. The insulated, aluminum, oil tank has a sealed top

and vents to the laboratory air through an activated charcoal filter to

eliminate hot-oil odors. The cell can be positioned in the tank by means

of controls outside the tank. Up to 6600 W of heat may be applied to

the tank.

At this point a "standard" procedure was established to record the

profile data. We summarize the main features in table 5. The profiles

(denoted by memory number in table 5) associated with an actual run are displayed in figures 29 through 31. These data were taken at an oil

temperature of 76°C. Each curve is a composite of 1000 scans of the

detector. When voltage is applied, the phase is adjusted so that the

detector (on for 6 us) obtains the intensity profile for the positive

peak (PP) of the 60-Hz waveform.

In order to determine the electric field E(z)/Em , it is necessary to

know the relative intensity I(z)/I m

(z). It is not adequate to align the

polarizers and determine I m

(z ) because the polarizers are not perfect

and small perturbations in the intensity pattern -- almost invisible to

the eye — become important. Measurements with the polarizers aligned,

however, provide a value for the magnitude of I m

. The profile shape of

I m

(z) is obtained by slightly rotating the polarizers from their crossed

position to obtain a measurable intensity. The intensity profile does

50
16

x

10

<N

l

CM

"5

i

i

CO CO CO CM O

(SlNflOO) 01.-rAllSN3i.NI

51

Fig.

29.

Intensity

profiles

for

aligned

polarizers.

These

are

only

used

to

establish

the

magnitude

of

I

m

and

not

the

shape.

The

intensity

after

voltage

application

has

decreased

probably

due

to

increased

particulate

contamination

and/or

malfunction

of

illuminating

laser.
INTENSITY

(COUNTS)

INTENSITY

(COUNTS) (2)

( 13)

( 3 )

( 14)

( 5 )

POSITION, z

( 14)

(ID

( 5 )

( 4 , 12)

POSITION, z

Fig. 30. Comparison before and after voltage is applied to the curves

used to establish the I m profile and the background curves. The numbers in parentheses refer to the profile number in

table 5. 52
INTENSITY

(COUNTS)

«

INTENSITY

(COUNTS)

fig. 31. Unprocessed (raw) data at 41 kVPP of 60 -te waveform and

zero-voltage backgrounds. Each curve is an accumulation of

1000 scans.

53
Table 5. Data collection sequence

Profile

No. Symbol

Fi gure

No. Description

MI AP (#1 NDF29 Polarizers are aligned and

M2 40° 30

a 1.0 neutral density

filter is placed at NDF-1

in figure 14. This filter

is removed after this

profile is obtained.

Polarizers almost crossed.

M3 50° II Polarizers almost crossed.

m SCB or NSB II A shutter is closed ahead

M5 ZVB II

of the detector to determine

the detector background, and/or

the illumination is blocked

to give a no-signal background.

With the shutter open

M6 Vl 31

a background is obtained

with no voltage applied.

Polarizers are crossed.

A profile is obtained with

M7 ZVB ll the voltage on, then off,

M8 V

1

II for a sequence of at least

M9 ZVB ll three times; four are shown

MID V

1

ll here.

Mil ZVB ll M12 Vl

ll Ml 3 ZVB ll

V

2 ,V 3 , etc. The above on-off sequence

is repeated for each

voltage level or phase

(for 60-Hz).

Ml 4 SCB or NSB 30 As above.

Ml 5 40° (1 Ml 6 5D° II

Ml 7 AP (#1NDF

29 As above Ml
not change in shape significantly for ±10° about the crossed polarizer

setting. Because of a scale error the polarizers are crossed when

polarizer P2 (see fig. 14) is set at 47.5° with respect to the vertical

plates. The incident profile I m (z) is determined from the 40° and 50°

profiles before and after the application of voltage (profiles M2, M3,

M15, M16) by first subtracting off the zero-volts background (ZVB,

intensity through crossed polarizers, e.g. , profile M5), then normalizing

each curve to 1, averaging the four profiles, and then multiplying the

result by the average magnitude of the AP profiles — the magnitude of I m

. The result is shown in figure 32. Any average of a profile is made

along the "level" portion of the profile, i.e., the level region defined

by where the the profile breaks off its steep intensification from low

background levels. (If the 40°-50° profiles are dramatically different

after the data is collected than before, the profiles taken before the

voltage data may be ignored since this would indicate that the application

of voltage modified the intensity distribution. Whenever this is the case,

it is also obvious in the ZVB profiles — the ZVB profiles change after

the voltage has been applied but they do not change from that point onward.)

To obtain the net signal profile for the Kerr effect at some voltage,

the three or, in this case, four voltage profiles (profiles M6, M8, M10,

M12) are averaged and the average background (an average of ZVB, profiles

M7, M9, Mil, M13) is subtracted from it; the result is in figure 33.

Usually the profile is set to zero at the assumed position of the plates

(z = ±d/2) so the place location can be determined easily throughout the

remaining data handling (see fig. 33). The relative intensity profile

I(z)/I m (z) is obtained by a pointwise division of the two profiles

(see fig. 34). It is only the information contained between -d/2 < z < d/2

that is of interest. Finally, using the approximate relation between

E/E mand I /

m expressed in eq (30), E(z)/E m may be calculated (see fig. 35).

The data handling process is summarized in table 6.

It is rather evident that there is a possible intensity shift problem

during the course of an experiment. This is evident in the dramatic

change of intensity of the al igned-polarizer profiles in figure 29. Some

of this is due to the gradual introduction of particles into the gap

during the voltage application. The fact that the oil is well-filtered

before the application of voltage is evidenced by the lack of forward

light scattering from the laser beam as it passes through the cell.

While the voltage is applied, particles (diameters > 2 urn) accumulate

in the gap. These particles serve to scatter the light, increasing

the background in the areas shadowed by the plates (fig. 31) and serve

to depolarize the light, increasing the light transmitted through crossed

polarizers (fig. 32).

An additional problem is the intermittent failure of the laser which

could explain why the I(z) profiles in figure 32 are not all at the same

level (though they are the same shape). In either case, it is not really

important that we obtain absolute measurements at this time. If we needed to know the absolute space-charge density to ±10%, then it would

be important to know the I/I m accurately. However, since we are trying

to obtain only an indication of space charge, approximate magnitudes are sufficient. The profile shapes, not their absolute magnitude, are important

to detect the presence of space charge.

55
INTENSITY

(COUNTS)

INTENSITY

(COUNTS)

Fig. 32. The incident intensity profile I m

(z).

-d/2 0 d/2

POSITION, z

Fig. 33. The net, average Kerr profile I (z )

56
m

|/l ‘A1ISN31NI 3AllV13y

57

Fig.

34.

The

relative

intensity

profile

I

(z

)

/1

(z

).
RELATIVE

FIELD,

E/E

m

RELATIVE

FIELD,

E/E

0.3

Fig. 35. Relative electric field E(z)/Em ; ±5% limits are shown about

the average in the magnified view.

58
Table 6. Data handling

Resul t Figure Operation

I n Magnitude

I m

P rofi le 32

(M18)

Raw I(z) Average

( M19

)

ZVB Average

( M20)

I (z ) Net 33

(M21)

T(z )/Im (z ) 34

(M22

)

E(z )/E m 35

(M23)

Subtract background (ZVB) from AP curves, obtain average values

over level portion (-d/2 <z < d/2),

average the values from before and

and after the run. Im(D/10 = AVE (M1-M4-(M5-M4)/10) * 12.5 x 10 6

I m (2)/10 = AVE(M17-M14-(M13-M14)/10) = 9.10 x 10 6

I Iml = (Im(10) + Im(2))/2 = 1.08 x 10 8

.

Subtract backgrounds (ZVB) from 40° and

50° curves (before and after run), normalize

and average the four curves, multiply by

I In I • Ml 8 = I m

(z) = |Im |[N0RM(M2) + N0RM(M3)

+ N0RM(M15 ) + N0RM( M16 ) ]/4

where, e.g., N0RM(M2) = M2/AVE(M2) where

average is made over level portion

(-d/z < z < d/2).

Obtain average of voltage-on profiles.

Ml 9 = ( M6 + M8 + M10 + M12 )/4

Obtain average of voltage-off profiles.

M20 = (M7 + M9 + Mil + M13)/4

Subtracting the average of the voltageon and voltage-off profiles is equivalent

to averaging the subtraction of the

voltage-on/off profiles.

M21 = M19 - M20

Set I(z) = 0 at z = ±d/2 to mark plates.

Perform pointwise division of I by I m

M22 = M21/M18

Perform pointwise operation on I/I^ according

to eq (30).

M2 3 = (0.40528 * M22 ) (1/4)

The average value with standard deviation

(-d/2 < z < d/2) is 0.245 ±0.004 (1.67%).

The maximum E/En

is 0.261 (6.4% high from

average), the minimum is 0.239 (2.3% low

from average).

59
Now that we have established the electric field profile shown in

figure 35, several comments are in order. First, if the nonuniformity of

the field is due to space charge, then the field nonuniformities can be

confined to less than 10% of the applied field. Second, the small peak

to the left of z = d/2 is characteristic of a reflection off a plate or part of a diffraction pattern arising from optical alignment problems.

It would be reasonable to ignore the peak on that basis thus reducing the

field nonuniformity, but we will not do so since it has not been definitely

established that such a peak is not due to space charge. Third, the overall

slope of the profile is opposite to that obtained previously on contaminated

oil -- compare figure 36 with figure 29. Either the nature of the space

charge was different or the slope is due to systematic effects. Because of

the data to follow, it is suspected that there are yet systematic problems

associated with optical alignment which give rise to a nonuniform intensity

profile which can be mistaken as a space charge.

In figures 36 through 38 we show E(z)/E m profiles for the positive

peak (PP) of a 60-Hz waveform at oil temperatures of 86°C, 95°C, and 107°C

respectively. Each curve in these figures represents an accumulation of

I (z ) for 3000 to 4000 cycles of the 60-Hz waveform. In figure 36, the

86°C E/E m profile shows an enhancement at the cathode as we saw in the

76°C (fig. 35). Similarly, all the field nonuniformities can be contained

within 10% of field maximum. In the 95°C data (fig. 37), we see a sharper

apparent field enhancement at the cathode. It can, however, no longer be

confined to 10% of the field maximum. If this were a trend and not a result of optical alignment, then at higher temperatures we would expect

more enhancement — an enhancement which would not depend upon small

changes in alignment. The cell's position was changed during the course

of these experiments, if not by thermal expansion of parts then by direct

alignment changes. The 107°C E/E m profiles in figure 38 show some enhancement at the cathode -- especially for the lower voltages — but

there is essentially no enhancement at the highest fields. This result

suggests that the previous field nonuniformities are due to systematic

effects and not due to space charge.

Referring to figure 38, there seems to be a trend toward field

enhancement at lower voltages. However, when the intensity profiles are examined (fig. 39), we find that the low-voltage profiles are near background levels — levels which could easily exhibit the nonuniformity

of the polarizer's parallelism. Therefore, these low-intensity data

cannot be trusted.

Another possible source of error is nonuniform optical activity of the

cel 1 -tank-pol ariz er system. It is conceivable that multiple reflections

between non-parallel window surfaces, temperature dependent optical

activity of windows, reflections off the plate surfaces, and/or index of

refraction changes due to nonuniform heating of the oil between the

plate could make the system nonuniformly sensitive to the polarization

direction of the light passing through the cell. Such possibilities must

be investigated before more sensitive measurements can be made; however,

this hypothesis is verified to some extent since the profile shape seems sensitive to the alignment of the system with the laser beam.

60
RELATIVE

FIELD,

E/Em

RELATIVE

FIELD,

E/Em

Fig. 36. Relative field for 86°C.

61
RELATIVE

FIELD,

E/E

m

RELATIVE

FIELD,

E/E

E

Fig. 37. Relative field for 95°C.

62
RELATIVE

FIELD,

E/E

RELATIVE

FIELD,

E/E

POSITION, z

Fig. 38. Relative field for 107°C .

63
INTENSITY

(COUNTS)

"

INTENSITY

(COUNTS)

-d/2 0 d/2

POSITION, z

Fig. 39. Intensity profiles at various voltages for 107°C oil compared

to background signal levels.

64
Previously we noted (figs. 21,22) that space charge in nitrobenzene

persisted through the zero crossing of the 60-Hz waveform. Tin's is not

observed in the 107°C data at the positive-negative zero crossing (PNZC)

of the 42k V 60-Hz waveform (see fig. 40). This also indicates that

space charge may not be present in transformer oil.

The results taken for dc show dramatic intensification near the plates

(fig. 41); however, the non-symmetri c profile shows no polarity sensitivity

which tends to rule out space charge in favor of optical alignment or activity problems. With increasing temperatures, the E/Em profiles are U-shaped and rather symmetrical. However, the maximum distortion of the

field at the highest voltage is still less than 10% of the field

maximum (see fig. 42).

V. CONCLUSION

In this report we calculated the field modifications due to space

or surface charges. Next, we examined data which showed that an interfacial system need not break down at the interface even in a contaminated system, and we discussed how the condition of the paper

influences breakdown. We then turned our attention to space charge in

liquids, and characterized the space charge found in nitrobenzene at

60-Hz ac. A saturation space charge of over -400 nC/crn 3 could be

measured el ectro-opti cal ly at the cathode. Finally, these electro-optical

measurement techniques were applied to transformer oil. There it was found that no field distortions greater than ±5% of the average field

could be attributed to space charge. This was true for clean or contaminated transformer oil from room temperature to 100°C or above.

These results will be refined and carried to higher temperatures;

nonuniform electrode geometries, and interfaces in the future to quantify

the contribution of space charge to the electrical characteristics of

insulating liquids under practical conditions.

65
INTENSITY

(COUNTS)

in

INTENSITY

(COUNTS)

-d/2 0 d/2

POSITION, z

Fig. 40. Comparison of the 60-Hz intensity profiles taken at the positive

peak (PP), the positive-negative zero crossing (PNZC), and the

zero-voltage background reveals no significant space charge as would be found with observations of the 60-te zero crossing in

nitrobenzene.
X

D

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67

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41.

Intensity

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under

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of

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No

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of

shape

is

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as

would

be

expected

if

the

deviations

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intensity

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were

arising

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distortions.
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68
VI. REFERENCES

[1] J. E. Thompson, J. Lin, K. Mikkelson, and M. Kristiansen, ElectroOptical Surface Flashover Measurements, Appl . Phys. Let. Vol . 37,

No. 6, 15 Sep. 1980, p. '574-576.

[2] J. E. Thompson, J. Lin, K. Mikkelson, and M. Kristiansen, Investigations

of Fast Insulator Surface Flashover in Vacuum, IEEE Trans, on Plasma Science, Vol. PS-8, No. 3, Sept. 1980, pp. 191-197.

[3] R. E. Hebner, Jr., E. F. Kelley, J. E. Thompson, T. S. Sudarshan, and

T. B. Jones, 1980 Annual Report: Optical measurements for interfacial

conduction and breakdown, Nat. Bur. Stand. (U.S.), NBSIR 81-2275,

83 pages (May 1981).

[4] T. J. Lanoue, Insulation Studies for Power Frequency Improvement,

Report on Contract ET-78-C-01-3058, U.S. Dept, of Energy, 1980.

[5] A. Zygmund, Trigonometric Series Vol. I , pp. 16, 19

(Cambridge U. Press 1959).

[6] P. Morse and H. Feshbach, Methods of Theoretical Physics , Part I, pp. 82, 456 (McGraw Hill Book Co., 1953).

[7] Fortran subroutine PLTMG developed by R. Bank and A. Scherman

of the University of Texas, and amplified and modified by

J. Blue and C. Wilson of NBS.

[8] E. F. Kelley and R. E. Hebner, Breakdown between bare electrodes

with an oil-paper interface," Nat. Bur. Stand. (U.S.), NBSIR 80-2071,

33 pages (June 1980).

[9] E. C. Cassidy, R. E. Hebner, Jr., M. Zahn, and R. J. Sojka,

Kerr-Effect Studies of an Insulating Liquid Under Varied HighVoltage Conditions, IEEE Trans. Elec. Insul., Vol. E I - 9 , No. 2,

June 1974, pp. 43-56.

[10]

P. D. Thacher, Optical Effects of Fringing Fields in Kerr Cells,

IEEE Trans. Elec. Insul., Vol. EI-11, No. 2, June 1976, pp. 40-50.

(A rather complete analysis is given here to determine perturbati ons

in the uniform-field Kerr patterns because of fringing fields of

real vs. ideal plates as well as the effects of windows in the cell.)

69

NBS-114A (rev. 2 -ac) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 82-2629

2. Performing Organ. Report No.

3. Publication Date January 1983 4.

TITLE AND SUBTITLE

1981 ANNUAL REPORT: OPTICAL MEASUREMENTS

FOR INTERFACIAL CONDUCTION AND BREAKDOWN

5.

AUTHOR(S)

R. E. h'ebner, Jr., E. F. Kelley, and J. N. Hagler

6. PERFORMING ORGANIZATION (If joint or other than N8S. see in struction s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Con tract/ Grant No.

8. Type of Report & Period Covered

Final

9.

SPONSORING ORGANI ZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Preparecf for

Department of Energy

Division of Electric Energy Systems

Washington, DC 20585

10.

SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here)

This report presents measurements and calculations contributing to

the understanding of space and surface charges in practical insulation

systems. Calculations are presented which indicate the size of charge

densities necessary to appreciably modify the electric field from what

would be calculated from geometrical considerations alone. Experimental

data is also presented which locates the breakdown in an electrode

system with a paper sample bridging the gap between the electrodes. It is found that with careful handling, the breakdown does not necessarily

occur along the interface even if heavily contaminated oil is used.

The effects of space charge in the bulk liquid are el ectro-optically

examined in nitrobenzene and transformer oil. Several levels of

contamination in transformer oil are investigated. Whereas much space

charge can be observed in nitrobenzene, very little space charge, if

any, can be observed in the transformer oil samples even at temperatures

near 100°C.

12.

KEY WORDS (Six to twelve entries; alphabetical order • caoitalize only proper names; and separate key words by semicolons)

breakdown; composite insulation; dielectrics; electric field calculation;

electro-optics; high voltage; insulation; interfaces; Kerr effect; liquids; solids

13. AVAILABILITY

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