NISTIR 88-3886

Research for Electric Energy

Systems - - An Annual Report

R. J. Van Brunt, Editor

U.S. DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

(Formerly National Bureau of Standards)

Center for Electronics and Electrical Engineering

Electrosystems Division

Gaithersburg, MD 20899

December 1987

Issued November 1988

Prepared for

Department of Energy

Division of Electric Energy Systems

1000 independence Avenue, SW

Washington, DC 20585

NISTIR 88-3886

Research for Electric Energy

Systems - - An Annual Report

R. J. Van Brunt, Editor

U.S. DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

(Formerly National Bureau of Standards)

Center for Electronics and Electrical Engineering

Electrosystems Division

Gaithersburg, MD 20899

December 1987

Issued November 1988

National Bureau of Standards became the

National Institute of Standards and Technology

on August 23, 1988, when the Omnibus Trade and

Competitiveness Act was signed. NIST retains

all NBS functions. Its new programs will encourage

improved use of technology by U.S. industry.

Prepared for

Department of Energy

Division of Electric Energy Systems

1000 Independence Avenue, SW

Washington, DC 20585

U.S. DEPARTMENT OF COMMERCE

C. William Verity, Secretary

NATIONAL INSTITUTE OF STANDARDS

AND TECHNOLOGY

Ernest Ambler, Director

TABLE OF CONTENTS

Foreword iv

Abstract v

1. INTRODUCTION 1

2. ELECTRIC FIELD MEASUREMENTS 1

2.1 Introduction 1 2.2 Ion Mobility 2

2.3 Experimental Arrangement 2

2.4 Theoretical Time-of -Flight Spectrum 4

2.5 Experimental Results 9

3. GASEOUS DIELECTRICS RESEARCH 14

3.1 Introduction 14

3.2 Transfer of F" in Collisions of SFg with Fluorinated Gases and

S0 2

: Temperature Dependence and Implications for Electrical

Discharges in SF6 15

3.3 Electron Transport, Ionization, Attachment, and Dissociation

Coefficients in SF 6 and Its Mixtures 19

3.4 Zonal Model for Corona- Induced Decomposition of Dielectric

Gases 29

3.5 Analysis of Dielectric Strength Data for Binary Electronegative

Gas Mixtures 35

4. INTERFACIAL PHENOMENA IN LIQUIDS 41

4.1 Introduction 41

4.2 Image - Preserving Optical Delay 42

4.3 Partial Discharge Initiation 44

4.4 Streamer Initiation and Collapse Under Pressure 46

5. CHARACTERIZING TRANSIENT MEASUREMENTS BY USE OF THE STEP RESPONSE

AND THE CONVOLUTION INTEGRAL 52

5.1 Introduction 52

5.2 Discussion of Proposed Method 54

5.3 Experimental Method 55

5.4 Convolution Calculations 59

5.5 Discussion 68

5.6 Conclusions 73

6. REFERENCES 74

iii
Foreword

This report summarizes the progress of four technical investigations

conducted during FY 87. Although reasonable efforts have been made to ensure

the reliability of the data presented, it must be emphasized that this is an

interim progress report and that further experimentation and analysis may be

performed before the conclusions from any of these investigations are formally

published. It is therefore possible that some of the observations presented

in this report will be modified, expanded, or clarified by our subsequent

research

.

iv
RESEARCH FOR ELECTRIC ENERGY SYSTEMS AN ANNUAL REPORT

Richard J. Van Brunt, Editor

Abstract

This report documents the technical progress in the four investigations which

make up the project "Support of Research Projects for Electrical Energy

Systems", Department of Energy Task Order Number 137, funded by the U.S.

Department of Energy and performed by the Electrosystems Division of the

National Institute of Standards and Technology (NIST) . The first

investigation covers the measurement of ions in the vicinity of dc highvoltage transmission lines and in biological exposure facilities designed to

simulate power line environments. Two techniques for measuring ion mobilities

in air were evaluated, namely a pulsed time-of- flight (TOF) drift- tube and an

AC TOF drift- tube. The problems associated with extracting reliable

mobilities from TOF data are discussed. The second investigation addresses

concerns with electrical breakdown and chemical decomposition of commonly used

gaseous dielectrics like SF6

. For this investigation, the results from a

number of separate activities are reported. Examples of results from direct

measurement of the temperature dependences of the rate coefficients for F‘

transfer reactions between SFg and various discharge generated contaminants

like S0F 4 , SOF 2 , S0 2 , SF 4 , and SiF4 are presented. Also covered is an

analysis of the electron transport and swarm parameters in SF 6 using numerical

solutions of the Boltzmann transport equation to find an improved "complete"

set of electron-collision cross sections that were then used to compute

electron- impact rate coefficients for SF 6 dissociation in SF 6 /N 2 , SF 6 /0 2 , and

SF 6 /Ne mixtures as a function of electric field- to-gas density ratio, E/N.

Another study presents preliminary results obtained from a "three zone" type

chemical kinetics model for oxidation of SF 6 in a glow- type corona discharge

which accounts for observed oxyfluoride yields when water vapor is present in

the gas at trace levels. And finally, the further development of a

theoretical model to evaluate the consistency among electron collision cross

section, swarm, and dielectric strength data for binary electronegative gas

mixtures is included. For the investigation on interfacial phenomena in

liquids, results include a description of an image -preserving optical delay

(IPOD) together with fast electrical pulse detection to observe correlations

between the partial discharge current pulses and development of optically

opaque regions near a point electrode. Results of an investigation of the

streamer initiation and collapse in hexane under pressure are also detailed.

Finally, in the investigation concerned with measurement of high-voltage

transients, a detailed evaluation is given of the performance of different

free standing dividers for measurement of fast impulses. The focus is on use

of step response determination and application of convolution techniques to

interpretation of waveforms recorded during transient measurements.

v

1 . INTRODUCTION

Under an Interagency Agreement between the U.S. Department of Energy

(DOE) and the NIST, the Electrosystems Division of NIST, has been providing

technical support to DOE on a number of tasks concerned with research on

electrical energy systems. This document summarizes the technical

accomplishments of this program during fiscal year 1987.

Section 2 of this report describes the work in ac electric and magnetic

fields and dc field and ion measurements. Section 3 summarizes the work

performed under task 3 on the development of the measurement techniques and

the accumulation of fundamental data needed for gaseous dielectrics research.

Section 4 describes the development of techniques to measure interfacial

phenomena in liquids. The final technical project, which deals with the

measurement of nanosecond breakdown in power system dielectrics, is summarized

in section 5.

2. ELECTRIC FIELD MEASUREMENTS

Task 01

Martin Misakian and William Anderson

Electrosystems Division

National Institute of Standards and Technology

2.1 Introduction

The objectives of this project are to develop methods to evaluate and

calibrate instruments which are used, or are being developed, to characterize

the electrical parameters in the vicinity of power lines and in laboratory

apparatus designed to simulate the power line environment. Electrical

measurement support is also provided for DOE- funded efforts to determine if

there are biological effects due to ac fields and dc fields with ions.

The electrical parameters of interest include the electric field

strength, magnetic flux density, ion current and charge densities, ion

mobility and ion species. Recent laboratory studies have focused on the

measurement of ion mobilities at atmospheric pressure using drift-tubes; some

results of these studies are described in the following sections. In

addition, during 1987 the first draft of a new IEEE standard for measuring dc

electric fields and ion related quantities was prepared at NIST in

collaboration with members of the DC Fields and Ions Working Group. Other

activities in 1987 include: the preparation of a chapter (Exposure Systems

and Measurements) of a National Council on Radiation Protection and

Measurements report on ELF field effects; a site visit to the Battelle Pacific

Northwest Laboratories to characterize electrical parameters in several

bioeffects exposure systems; and the issuance of the IEEE and the

International Electrotechnical Commission standards which provide guidance for

measuring power frequency electric and magnetic fields. The final drafts of

these standards were prepared at NIST and include the results of NIST studies.

1
2 . 2 Ion Mobility

The mobility of an ion as it moves through a gas under the influence of a weak electric field is defined as the ratio of the ion drift velocity to the

electric field strength. Corrections for pressure and temperature are

normally made to obtain a "reduced mobility." The motivation for measuring

ion mobilities, within the context of possible bioeffects due to dc power

lines, is that mobility values provide, in some cases, a rough measure of ion

mass [1,2]. Ideally, the ion species is of interest when considering the

possibility of bioeffects due to exposure to ions from dc power lines, but

sampling ions at atmospheric pressure with a mass spectrometer is difficult

and requires a complex apparatus [3]. Ion mobility spectra can be measured at

atmospheric pressure with less complicated instrumentation and ascertaining

that the mobility spectra remain unchanged during a bioeffects study may be

as important as knowing that the electric field strength or ion current

density remain constant. Mobility spectra would also be useful in

determining whether an equivalence might exist between bioeffects studies

conducted in different laboratories.

Ion mobility can be determined by measuring the time required for an ion

to travel a given distance in a known dc electric field. A device that has

been used extensively for this measurement is the drift tube. Following

earlier studies with a prototype parallel-plate drift tube [4]

,

two

cylindrical drift tubes have been fabricated and used for ion mobility

measurements in room air ionized by corona. The design of the drift tubes

differs from those normally used for mobility measurements in that metal guard

rings with insulating spacers and alignment rods have been replaced with an

insulating cylinder on which guard rings have been coated. One drift tube is

of the pulsed time -of - flight type [5] and the other is an ac time-of -flight

device [6]. The guard ring design was used for establishing an approximately

uniform electric field for the mobility measurements after earlier attempts to

apply a uniform resistive coating to the inside wall of an insulating tube

failed

.

2 . 3 Experimental Arrangement

Schematic views of the two cylindrical drift tubes are shown in figure 1

.

Both drift tubes are fabricated from commercially available "machinable glass"

rods that have been bored to form tubes with an inside diameter of 5.65 cm.

The inside walls of the tubes are then coated with a commercial conductive

ink. After drying, guard rings 1 cm in width (end guard rings are 0.5 cm) are

formed by cutting -0.05 cm wide circular grooves with a lathe. The tubes are

fired to make the rings permanent. An approximately uniform electric field is

established along the axis of the cylinder by grading the potential of the

guard rings using a resistive voltage divider [7],

Figure 1(a) shows a drift tube designed to operate in a pulsed time-of

flight (TOF) mode. Briefly, ions arriving from the right are prevented entry

into the drift tube by the shutter (double mesh, 12 wires/cm, 90%

transparency) which is biased shut with a small voltage supplied to the

outside mesh. The ions are produced in untreated room air by wires in corona,

using an apparatus that has been previously described [8]. Ions enter the

2
nr

(a)

-H.V

To Electrometer

Insulator

Shutters

(b)

Figure 1. Schematic views of drift tubes made of insulating cylinders

and conductive guard rings on inside walls. (a) pulsed time -of

flight drift tube with movable collector electrode (b) ac time-offlight drift tube. The inside diameter of each tube is 5.65 cm.

3
drift tube and travel to the collector after the shutter is pulsed open for a

fraction of a millisecond. Because more than one species of ions is present

in the approximately disk- shaped volume of ions that passes through the

shutter, the ions will separate into groups with the same drift velocity or

mobility as they traverse the length of the drift tube. A shield grid (single

mesh, 28 wires/cm, 90% transparency) before the collector prevents the

induction of current in the collector circuit until the ions pass through the

shield grid. The current induced in the collector circuit as the ions travel

between the shield and collector is monitored and exhibits maxima and minima

as a function of time because of the different time-of- flights of the

different ion species. The current induced in the collector is converted to a voltage using a current- to-voltage operational amplifier-circuit. This

signal is sampled with a signal averager to obtain a relatively noise- free

spectrum. The length of the drift region is variable so that the distance the

ions travel can be made nominally 4 cm or 8 cm. By obtaining TOF spectra at

two drift distances, it is possible to eliminate so called "end effects" when

computing the TOF of a given ion peak.

Figure 2(a) is a block diagram showing the drift tube, signal averager,

and pulse generator for gating the shutter. It is noted that the signal

averager is emulated, with some cost saving, using a personal computer with a

commercially available data acquisition board and software.

Figure 1(b) shows a schematic view of an ac TOF drift tube similar in

principle to that employed by Tyndall and Powell [6]. The shutters at each

end of the drift tube are biased closed and are opened periodically with

sinusoidal voltages applied to the inner mesh of each shutter. Ions that have

TOF's between the shutters equal to half the period of the ac voltage will

pass through both shutters to yield a steady-state current which is measured

with an electrometer. Measurement of ion current as a function of frequency

results in current maxima at specific frequencies for ions with different

mobilities. The mobility of an ion, K, is given by the expression

K = 2L2 F/V , (1)

where F is the frequency of the current maximum, L is the length of .the drift

space and V is the voltage across the drift tube.

Figure 2(b) is a block diagram showing an automated system, under the

control of a minicomputer, that is used for obtaining TOF spectra. A

programmable function generator provides the sinusoidal voltages to the

shutters via small transformers. As the frequency is varied under control of

the computer, the current is measured with the electrometer. The values of

the frequency and the associated ion current are stored in the computer for

later printout.

2.4 Theoretical Time-of -Flight Spectrum

V

An approximate expression for the pulsed TOF spectrum of a single ion

species, appropriate for a cylindrical drift tube, is derived. It is assumed

that there are no reactions between the ions and the air molecules in the

drift space and there are no fringing field effects at the ends of the drift

4
?

(a)

?

(b)

Figure 2. Block diagrams of pulsed TOF and ac TOF drift tube measurement

systems (a) pulsed TOF system includes pulse generator for gating

shutter open (normally closed with bias voltage) and signal

averager which averages the signal from the drift tube collector

circuit (b) ac TOF system includes programmable function generator

for producing a sinusoidal voltage under the control of a minicomputer. As the frequency of the gating voltage to the

shutter is advanced, ion current values detected with the

electrometer are measured and stored in the computer with the

corresponding frequencies.

5
« space. Assuming an infinitesimally short shutter pulse width, the diffusion

broadened ion current arriving at the shield at time t is given by [5]

f(t) = (C/th

) [vd + (L/t)] exp [ - (L - vd

t) 2 /4DLt], (2)

where C is a constant, vd

is the ion drift velocity, L is the distance between

the shutter and shield meshes and Dl is the longitudinal diffusion coefficient

which is given, for our electric field conditions, by the Einstein equation

DL = KkT/e. (3)

In Eq. (3), K is the mobility, k is the Boltzman constant, T is the

temperature in degrees Kelvin, and e is the ionic charge. Assuming a

rectangularly shaped shutter pulse of width, w, the ion current is increased

and the peak of the TOP spectrum is shifted to longer times. The diffusionbroadened, pulse-width-broadened, ion current passing through the shield mesh

as a function of time is given by F(t), where [9]

F(t)dt

• t

f(t' )dt'

.

J t-w

( 4 )

The current, i(t), induced in the collector circuit by the ionic charge as it

travels between the shield and the collector is given by [10]

i(t) = q(t)vd

'/s, (5)

where q(t) is the ionic charge moving between the shield and collector with

drift velocity, vd

'

;

s is the spacing between shield and collector. The ionic

charge, q(t), between the shield and collector is found from integrals of the

form

q( t) F( t ' ) dt

( 6 )

where t 0 is the TOF of the ions that first reach and pass through the shield

mesh. Because the first ions to pass through the shield mesh will reach the

collector at some time, t c , and be eliminated, and because some ions will

still be present in the shield-collector space after the last ions pass

through the mesh at time, tf, the expression for q(t) will change. For

6
t Q<t<tc , q ( t)

t c<t<tf , q ( t)

t>tf, q ( t)

t

JtW

F( t ' ) dt

t

F( t

' ) dt

o

rc f

F(t' )dt'

t 0+(t-tc )

t +(t-t \ r o c'

F(t ' )dt '

,

<4

( 7 )

Figure 3 shows schematically the positions of f(t) , F(t), and i(t) along the

time axis with the peak heights of each function normalized to the same value

.

By choosing trial values of v^ in Eq. (2), fits can be attempted of an

experimental TOF spectrum using Eqs . (2) -(7).

As noted above, Eqs. (2) through (7) are obtained assuming that there are

no fringing electric field effects at the ends of the drift tube and that the

leading and trailing edges of the ion cloud that passes through the shutter

coincide with the gating pulse. In addition, it is assumed that Coulomb

repulsion between the ions and space charge distortion of the drift field have

negligible effect on the TOF spectrum. These assumptions are briefly

examined.

When the shutter is pulsed-open, the amplitude of the voltage pulse is

chosen to make the electric field in the shutter nearly the same as that in

the drift region. This reduces the effect of the fringing fields for a

fraction of a millisecond. However, during most of the ion TOF, the drift

field near the shutter will be significantly perturbed because there exists an

electric field in the shutter that differs in magnitude and direction. A

simplified, but conservative two-dimensional model calculation of the

perturbed electric field and ion TOF along a path midway between two shutter

wires indicates that the trailing edge of the ion cloud which passes through

the shutter would have its TOF retarded by about 1.4% for L equal to 4 cm and

about 0.7% for L equal to 8 cm for the electric fields in our drift tube.

Comparable results are expected for trajectories that will not pass midway

between the shutter wires because the longer path length near the wires is

compensated for by the stronger electric field and drift velocity. Because

the shutter mesh actually consists of crossed wires, the retardation of the

trailing edge of the ion cloud should be less.

The effect of fringing electric fields on the drift velocity, as the ions

approach the shield, is reduced by making the electric field between the

shield and collector the same as in the drift space. A numerical twodimensional calculation of the perturbed electric field and ion TOF along a path midway between two shield wires indicates that the TOF is increased by

less than 0.02% for a path length of 4 cm. The reduction of the drift

7
APPROXIMATE THEORY

FOR PULSED TIME OF FLIGHT DATA:

ONE ION SPECIES

i(t) = C 2 q(t)

Figure 3. The ion current arriving at the shield mesh as a function of time

is described by F(t). The current signal in the collector circuit,

i(t), is proportional to the charge moving between the shield and

collector. C : and C 2 are constants.

8
velocity should be less for the crossed-wire mesh actually used for the

shield.

A parallel-plate apparatus which can produce a known charge density [8]

is used to introduce ions into the drift tube. The number density of the ions

that enter the drift tube is approximately 2 x 10 s ions/cm3

. This density is

sufficiently low that the effects of Coulomb repulsion between the ions and

space charge distortion of the drift field can be ignored [11].

A theoretical expression for the mobility spectrum obtained with the ac

TOF drift tube is not readily developed because the shape of the gating

voltage applied to the shutters makes it difficult to characterize the "open"

condition compared to the pulse -waveform. Other disadvantages with the

sinusoidal waveform for measuring ion mobilities at atmospheric pressure are

readily apparent. From Eq. (1), and the typical operating parameters

V = 2.0 kV, L = 0.06 m, K * 1.5 X 10" 4 m

2 /Vs, F is about 42 Hz. At such low

frequencies and for the ac voltage amplitudes required to adequately open the

shutters, the duration of the "open" condition can be several milliseconds.

The long duration results in a very broad spectrum making it difficult to

identify the frequency in Eq . (1). Because more than one ion species is

normally present in the spectrum, the long opening of the shutters also

results in the loss of resolution of the individual current maxima.

2.5 Experimental Results

Pulse TOF Spectra . Examples of TOF spectra of ions produced by corona in

untreated laboratory air are shown in figures 4 through 7. The electric field

in the drift space was near 24.8 kV/m in all cases. Figure 4 shows TOF

spectra as a function of shutter pulse width and for a drift space of 4 cm.

During the first -0.3 ms, no ions are able to pass through the shutter because

their TOF's through the shutter exceeds the pulse width. As the pulse width

is increased, the ions with the largest mobility (shortest TOF) appear first.

Ions with smaller mobilities can be seen as the pulse width is increased.

Thus, depending on pulse width, the shutter can act as a mobility filter,

affecting the abundances of the various ion species in the TOF spectrum. In

addition, the data indicate that corrections to the axis are necessary

because the different ions enter the drift space at different times. For

example, about 0.3 ms should be subtracted from the time axis for the fastest

ions. The value of w in Eq . (4) should also be adjusted to the effective

pulse width. Corrections for the slower ion species cannot be made from the

data in figure 4 because the pulse width associated with their first

appearance cannot be clearly determined. However, the drift velocities of the

different ion peaks can be estimated by obtaining TOF spectra at 4 cm and

8 cm, and dividing the difference in distances by the difference in the

corresponding TOF's.

Figure 5 shows positive ion spectra obtained on different days. The data

indicate that the number of ion species produced by corona in uncontrolled

air, as well as their relative abundances, can vary with time. These results

suggest that some attempt be made to control the composition of the air used

to produce ions in an animal bioeffects exposure system. In addition, as

noted earlier, periodic monitoring of the ion TOF spectrum in a bioeffects

9
Figure 4. TOF spectra of positive ions as a function shutter pulse width.

Ions with small drift velocities fail to clear the shutter until

the pulse width is made sufficiently long.

10
•J V

A

/

SEPTEMIjpD n

L\> \\y

J

W

AlinilCT is

1

. II

: \

-v

. 1

1

rv.. ...

A

! 1

; 1 AUGUST 10

5.0 15.0 25.0 35.0

TIME OF FLIGHT (ms)

45.0

I

I

j

I

j

i

I

|

i

i

Figure 5. TOF spectra of positive ions measured on different days. The

changes in the spectra reflect changes in the air composition.

Figure 6. Example of negative TOF spectrum. By increasing the ion time-off light, peaks corresponding to ions with different drift velocities

are seen.

11
exposure system is necessary to confirm that the composition of the ions has

not changed.

Figure 6 shows TOF spectra of negative ions produced by corona in room

air. What appears to be two overlapping peaks when the length of the drift

tube is 4 cm, is observed to be more than three peaks when the time -of- flight

is extended by increasing the length of the drift region and reducing the

electric field strength. In addition, the complex and variable spectra in

figures 4 through 6 are as expected based on earlier observations of the

number of ion species produced by corona in air [12] and the lack of control

of the air composition.

Attempts to fit the experimental data using the theory developed earlier

have yielded mixed results. Figure 7 shows an experimental fast-peak of a

positive ion TOF spectrum for L - 8 cm and the calculated peak taking into

account diffusion, pulse -width broadening, and the passage of the ions through

the shield-collector region [Eqs. (2) - (7)]. The time axis has been adjusted

for delay of the ions passing through the shutter. The theoretical curve is

obtained by choosing a drift velocity in Eq . (2) that gives a peak with an

onset that should match the experimental one.

When the theoretical drift velocity is compared with that determined by

measuring the difference in TOF's for drift distance of nominally 4 and 8 cm,

the drift velocity values agree to within about 0.5%. Slightly poorer

agreement (difference < 1%) occurs when theoretical drift velocity is

calculated for L - 4 cm. It should be noted that drift velocities, determined

from the "raw data", i.e. without fitting the data, result in errors of 8% and

4% for measurements at L =* 8 cm and L = 4 cm respectively. However, there

exists a discrepancy of about 0.3 ms between the theoretical and experimental

peak positions in figure 7. Originally it was thought that the experimental

peak consisted of two or more closely spaced ion peaks with nearly the same

mobility. While there is clearly overlap between adjacent peaks, the good

agreement between the theoretical and experimental drift velocities suggests

that the 0.3 ms discrepancy may be, in part, an instrumental effect. One

possible explanation, which will be checked shortly, is the effects of

charging the collector electrode in the drift tube which reduces the, electric

field in the shield-collector region. This could displace the experimental

peak to a longer-time-of-flight as seen in figure 7.

A.C. TOF Spectra . Figure 8 shows an example of a positive ion TOF

spectrum obtained with the ac TOF drift tube; the electric field strength in

the drift space was near 32.6 kV/m. The inset shows a pulsed TOF spectrum

recorded at nearly the same time as the ac data was obtained. As anticipated

from the earlier discussion, no structure representing the different ion

species can be discerned in the ac TOF spectrum and the mobility value

corresponding to the peak ion current is not readily interpreted. Thus, the ac

TOF technique for measuring ion mobilities does not appear suitable for

obtaining spectra at atmospheric pressure. However, preliminary measurements

using a modified ac waveform consisting of pulses of constant width and

alternating polarity shows considerable promise for measuring ion mobilities

and will be examined in the coming year.

12
POSITIVE

ION

CURRENT

(arb.

units)

T T

TOF (seconds)

58 . AC TOF spectrum for positive ions. ~

Inset shows pulsed TOF spectrum 3

recorded at nearly the same time. ®

h-z

HI

(T

CC3

O

o

LU>

COO

a.

Figure 7. Attempt to fit theoretical TOF peak,

using eqs . (2) - (7)

,

to experimental

peak for L equal to 8 cm. The

difference between theory and

experiment may indicate an

instrumental effect (see text)

.

13
3. GASEOUS DIELECTRICS RESEARCH

Task 03

Richard J. Van Brunt, Sanjay V. Kulkarni , and Arthur V. Phelps

Electrosystems Division

National Institute of Standards and Technology

3.1 Introduction

The objectives of this project are the development of measurement

capabilities and the providing of fundamental data as part of the Department

of Energy's basic research concerned with the development and evaluation of

advanced compressed- gas - insulation technology.

To reduce space requirements and improve the efficiency of high-voltage

transmission systems, the electric power industry has turned toward more

extensive use of compressed-gas insulation. To design meaningful tests of

system performance and establish specifications for the quality of materials

used in such systems, more information is needed about the fundamental

physical and chemical processes which lead to insulation deterioration and

electrical breakdown. The research includes applications of gas

chromatography-mass spectrometry to characterize corona discharge by-products;

and the acquisition of fundamental data, e.g., reaction rate coefficients,

corona inception voltages, production rates of corona by-products, the

effects of contaminants on discharge initiation, and the rates of discharge

induced decomposition of the gas.

This report highlights four significant technical activities. The first

is concerned with the measurements of rate constants for F" transfer from SFg

to fluorinated gases and S0 2 produced by electrical discharges in SF 6

. The

implications of these processes on ion transport and SF6 oxidation in corona

discharges are also considered. The results have been published during the

past year in both conference [13] and archival [14] papers. The second

activity concerns the determination of a new "complete" set of electron

collision cross sections for SF6 and the use of these cross sections to

compute electron transport, ionization, attachment, and dissociation

coefficients in SF 6 and its mixtures with N 2 , 0 2 , and Ne . The results of this

work have also been submitted for archival publication [15], Information

acquired from the first two activities were used in the third activity on

development of a theoretical, three-zone chemical kinetics model for

predicting oxyfluoride production from point-plane glow- type corona discharges

in SF 6 /H 2 0 mixtures. Preliminary results of this work were presented in an

invited paper at the 5th International Symposium on Gaseous Dielectrics [16].

The fourth activity involved calculation and analysis of dielectric strength

data for the binary electronegative gas mixtures SF6 /C0 2 , SF6 /Argon, SF 6 /Neon,

and SF 6 /Helium. Information from this activity was presented in two

conference papers [17,18]. In this report we provide a brief summary of the

more significant findings from these activities.

14
3.2 Transfer of F" in Collisions of SFg with Fluorinated Gases and S0 2

: Temperature Dependence and Implications for Electrical Discharges in

sf6

The reactivity of SFg towards S0 2 , S0F2 , S0 2 F 2 , S0F4 , SF 4 , and SiF 4 has

been investigated using the technique of pulsed electron beam high-pressure

mass spectrometry. These studies were initiated in order to probe the complex

anionic chemistry occurring during electrical discharges in SF6 and to

determine the influence of trace level decomposition products upon the

identity and reactivity of the negative charge carriers present in the

discharge. Although no reaction of any type was observed with S0F 2 and S0 2 F 2 , efficient F' transfer of the type SFg + A -* AF“ + SF s was found to occur in

all of the other systems including the S0 2 F" + S0F4 pair, which was studied

separately. The reaction of SFg with S0 2 also yields two other products,

SFg and S0 2 F2

' With the exception of the SFg + SiF 4 reaction, all of the

processes exhibited a negative temperature coefficient in that the rate

constants for F” transfer decreased substantially with increasing temperature.

The reaction SFg + SiF4

-*• SiFg + SFs was found to proceed with a rate constant

of 5.6 ± 0.8 x 10" Cm

3 /s throughout the temperature range studies (298 - 510 K) , which corresponds to a collision efficiency of unity. The other

transfer reactions were found to approach unit collision efficiency only at

reduced temperatures (< 300K) . Typical results are shown in Fig. 9.

The present data, combined with the existing literature, establish the

following F" affinity scale; (F" affinity defined as the energy requirement

for the dissociation AF

-

-*• A + F'); (S0 2 F 2 , S0F 2 ) <SF s <SF 4 <S0 2 <S0F 4 <SiF 4 suggest an absolute value of 40 ± 3 kcal/mol for the F‘ affinity of SF s which

indicates that SFg is reactive towards several of the major stable byproducts from electrical discharges in SF6

. This is verified by the data in

Fig. 10 showing observed growth and decay of major negative ions from SF 6 previously subjected to a corona discharge. The data shown in this figure

correspond to normalized ion intensities observed as a function of time

following pulsed ionization at a temperature of 293 K from a sample containing

0.05 mole fraction of corona- decomposed SF 6 in CH 4

. Shown in Fig. 11 are

similar data from the same decomposed SF s sample undiluted in CH 4

.

It is obvious from these data that the negative ions SFg and SFg

initially produced by electron attachment in SF 6 rapidly react away leaving

SiFg and SOFg as terminal negative ions. These ions result predominantly from

reactions of SFg with S0F 4 and SiF 4 which are present in the SF 6 at trace

levels and result from the decomposition of SF 6 in the discharge [19,20]. The

present results are of relevance in any attempt to model negative ion

transport in SF 6

. They indicate, especially for SF 6 ions in high-pressure

drift tubes or corona discharges, that rapid ion conversion processes

involving interactions of SF6 negative ions with trace contaminants that have

higher F' affinities than SFg will convert SFg into other types of charge

carriers within a relatively short distance (or time) compared to total drift

distances or transit times. We have shown [14], for example, by solving the

standard second-order rate equations for F" transfer processes in negative

corona- decomposed SF6 at 200 kPa (2 atm) that 90% of the SFg produced

initially in the active corona-discharge region will be replaced by other

anions after only 20 /is of transit time.

15
(o.OlX'OUl

16

Figure

9.

Temperature

dependence

of

rate

constants

k(cm

3

/s)

for

SFI

+

S0

9

and

SFI

+

S0F

4

.
NORMALIZED

INTENSITIES

O.OOI

0.01 r

2 3 4 5

TIME (MILLISECONDS )

Figure 10. Normalized ion intensities observed as a function of time following

pulsed ionization at 293 K of a sample of 0.05 mole fraction SF 6 in

CH 4 after decomposition of the SF6 in a negative corona discharge.

17
NORMALIZED

INTENSITIES

TIME (MILLISECONDS )

Figure 11. Normalized ion intensities observed as a function of time following

pulsed ionization at 293 K of the same sample of SF6 for which data

are shown in Figure 14, but undiluted by CH 4

. Pressure is 0.9

Torr

.

18
3.3 Electron Transport, Ionization, Attachment, and Dissociation

Coefficients in SF6 and Its Mixtures

An improved set of electron-collision cross sections was derived for SF 6 and used to calculate transport, ionization, attachment, and dissociation

coefficients for pure SF6 and mixtures of SF6 with N2 , 0 2 , and Ne . Our

recommended SF6 cross-section set is shown in Fig. 12 which displays cross

sections versus electron energy for momentum transfer, ionization, attachment,

and vibrational and electronic excitation. A requirement imposed on the

cross-section set was that the electron kinetic-energy distributions obtained

as functions of E/N from numerical solutions of the Boltzmann transport

equation using this set yield electron transport and ionization and attachment

coefficients that are in satisfactory agreement with the data from reliable

measurements on both pure SF6 and its mixtures as shown in Fig. 13. Here E is

the electric field strength and N is the gas number density. The transport

coefficients of particular interest are the drift velocity (W) and the

longitudinal and transverse diffusion coefficients over mobility (Dl//z and

D-p/zi respectively.)

The SF6 cross sections differ from previously published sets primarily at

very low electron energies and at high energies. At energies below 0.03 eV

the attachment cross section was adjusted to fit recent data from electron

swarm experiments, while the elastic momentum- transfer cross section was

increased to the theoretical limit. At high energies, an allowance was made

for the excitation of highly excited levels as observed in electron-beam

experiments. The individual cross sections agree where possible with

directly measured or theoretically calculated cross sections. Where no

reliable data were available on the absolute magnitudes of cross sections,

they were at least required to be consistent with observed thresholds and

energy dependences.

With this cross-section set, electron kinetic - energy distributions were

computed from numerical solutions of the electron- transport (Boltzmann)

equation using the two-term, spherical harmonic expansion approximation to

obtain electron transport and reaction coefficients as functions of E/N and

the fractional concentration of SF6 in the gas mixtures SF 6 /N 2 , SF 6 /0 2 , and

SF 6 /Ne. The critical E/N = (E/N) c at which the ionization and attachment

rates are equal were also determined and compared with various available

experimental data. This corresponds to a necessary condition for electrical

breakdown in the gas for a uniform electric field and is considered to be a

measure of dielectric strength.

The computer code used for solving the electron Boltzmann transport

equation for the electron kinetic-energy distributions which were then used to

compute transport, swarm, and reaction coefficients is a modified version [21]

of that used previously for calculation of temporal ionization coefficients.

The code accounts for the gradients resulting from steady-state spatial growth

or decay, due to ionization and attachment. In general, any swarm

coefficient, aj/N, corresponding to a process with cross section Qj(e), where

e is the electron kinetic energy, is computed from the electron kinetic - energy

distribution function f(e) using the relationship

19
CROSS

SECTION

(m

2)

ELECTRON ENERGY (eV)

Figure 12. Electron-SF6 collision cross sections versus electron energy.

Cross-section symbols are: - effective momentum transfer;

Qa(SFg), Qa (SF£ ) , and Qa (F, Fj , SF;) - electron_ attachment ; QVIB

vibrational excitation; - total ionization; (j = 1,2,3) - electronic excitation.

20
ATTACHMENT

AND

IONIZATION

DIFFUSION/MOBILITY

COEFFICIENT

(m

2)

(V)

E/N (Td)

Figure 13. Transport, attachment and ionization coefficients for electrons in

pure SF 6 . The symbols are: W - drift velocity; D]_/

p

and Dj//j. - longitudinal and transverse diffusion coefficients over mobility;

a^_/N - ionization coefficient; rj a

/N - attachment coefficient. The

calculated swarm and transport coefficients are indicated by the

solid lines. For comparison we show: results of Aschwanden

(Ref. 34) - closed circles (o)

,

closed triangles (A)

,

closed

squares (a) , and open squares () and, closed inverted triangles

()

;

data of Siddagangappa et al. (Ref. 48) - open tilted triangles

( ) - data of Verhaart (Ref. 35) - open inverted triangles (V)

;

data of Naidu and Prasad (Ref. 49) - closed diamonds ( ) ; data of

McAfee (Ref. 50) - open diamonds ( ); data of Hayashi (Ref. 51) - open triangles (A) - data of Bhalla and Craggs (Ref. 52) - open

circles (o)

.

21

DRIFT

VELOCITY

(m/s)
aj/N = kj/W ( 1 )

where W is the electron drift velocity kj is a rate coefficient given by

k. - (2/m ) H

[q (Of(Odc,

J e Jo J

( 2 )

and me is the electron mass. It is assumed here that f(e) satisfies the

normalization requirement

~CX>

[ f(€)£ H

d£ - 1. (3)

J 0

Shown in Fig. 13 by the solid lines are the calculated ionization

coefficient (cr^/N) , attachment coefficient (rj a

/N = aa/N) , drift velocity, and

longitudinal and transverse diffusion coefficients over mobility for pure SF 6

. In the case of pure SF6 , the computer code used to solve the transport

equation yielded satisfactory solutions only for E/N greater than 150 Td

(1 Td = 10 21 Vm2 ). For E/N values below 150 Td, attempts to carry out the

iterative determination of the attachment coefficients, i.e., spatial decay

coefficients, resulted in oscillatory nonconvergent solutions and/or negative

electron energy distributions. We proposed [15] that this failure is due to

an inherent limitation of the two- term spherical-harmonic approximation, since

this approximation cannot properly account for anisotropies in the electron

energy distribution with respect to the electric - field direction for cases

like SF 6 where there is a high attachment cross section near zero energy.

There are indications that this limitation can be removed by using multi -term

representations of the distribution function [22].

The E/N dependence of the SF 6 elec tron- impact dissociation rate'

coefficients k^({Q^}j), where 1 =* 1,2,3, . .

.

j

is a particular set of

cross sections for dissociative electronic excitation processes, were

calculated using:

(€)f(€)€d€

.

(4)

In this equation e t ^ is the threshold energy for the i th process.

For the calculation of SF6 dissociation rates, it was assumed, consistent

with available experimental data [23], that ionization always leads to

dissociation, i.e., SF£ is the largest ion that can be formed. It was also

assumed that SF6 behaves like other large fluorinated molecules for which

there is experimental evidence [24] that electronic excitation always leads to

dissociation. This assumption is supported by measurements [25,26] of uv and

22
optical emissions from SF 6 excited by electron impact that show either broad,

unstructured emission or a predominance of atomic fluorine emission at

energies sufficient for electronic excitation.

The calculated dissociation rate coefficients versus E/N for {Q^lj

corresponding to the subsets of cross sections for dissociative attachment,,

dissociative ionization, and electronic excitation, as well as the total for

all dissociation processes are shown in Fig. 14. Extrapolations of present

results indicated by the dashed lines in Fig. 14 are seen to be roughly

consistent with the only other known calculation of these rate coefficients by

Masek et al. [27] at 100 Td. It is seen from Fig. 14 that in the E/N range of

10 2 to 10 3 Td, the total SF6 dissociation rate is dominated by electronic

excitation processes leading to neutral fragment formation. It is therefore

these processes that can be expected to control the rate of SF 6 decomposition

in electrical discharges in which E/N > (E/N) c (see Refs 4 and 7).

It is necessary to point out that, both for pure SF6 and its mixtures, we

have neglected the effect of contributions to the gas mixture from products of

dissociation or subsequent chemical reactions in obtaining solutions to the

Boltzmann transport equation, i.e., the gas decomposition is assumed to be

sufficiently small that the products of dissociation do not significantly

influence the electron kinetic - energy distribution. It should be cautioned,

therefore, that when applying the present results to modelling of chemical

processes in electrical discharges, there are cases for which this assumption

of constant composition will not be valid, as for example in low-pressure

microwave discharges in which most of the gas is dissociated. This assumption

should be reasonable, however, for localized high-pressure corona or glow- type

discharges [ 19 ]

.

For the mixtures SF 6 /0 2 , SF6 /N2 , and SF 6 /Ne, we show respectively in

Figs. 15, 16, and 17 examples of calculated results for the normalized

dissociation coefficients o^/fX] at (E/N) c , where [X] is the concentration of

the dissociating molecular species of interest. The corresponding rate

coefficients, k^, can be found using Eq . (1) with the calculated W shown for

E/N = (E/N) c in each case. Also shown in these figures are predicted (E/N) c values as a function of mixture ratio in comparison where possible with

available experimental data. The agreement between the predicted and measured

values are seen to be quite good. No measured data for (E/N) c exist for the

SF 6 /0 2 mixture.

In the case of SF 6 /N2 mixtures contributions to SF 6 dissociation may

occur due to energy transfer in collisions of metastable excited N 2 molecules

with SF6 , the maximum effect of these contributions was calculated and is

indicated by the curve in Fig. 15 for [a^(SF 6 ) + a t (N 2 )]/NF, where a t (N 2 ) is

the sum of the excitation coefficients for the triplet excited states of N 2

. It is assumed here that all nitrogen triplet states excited by electron

collision are quenched only by dissociative excitation transfer to SF 6

. It is

known that the lowest A

3 Z£ metastable state of N 2 is not efficiently quenched

by SF 6 , although there is evidence that the higher lying B

3 IIg(v = 2) state is

electronically quenched [28]. Analysis of results for total SF 6 decomposition

23
CALCULATED

SF

e

DISSOCIATION

RATE

k

d

(cm^/s)

Figure 14. Calculated electron- impact SF 6 dissociation rate coefficients for

total dissociation (closed circles - o) , total electronic

excitation (closed triangles - A) , total dissociative ionization

(closed squares - EJ) , and total dissociative attachment (closed

inverted triangles -V) versus E/N in comparison with previous

calculation of Masek et al. (Ref. 27) at E/N = 100 Td (open points

o, A, V). The dashed line represents an extrapolation of the

present calculated results.

24
(E/N)

c

[1<T

21

V

m

2

]

DISSOCIATION

COEFFICIENT

(m

eg

10 5

C/5 E

§

>

t

O

O

LU

>

hLL

CCQ

Figure 15. Calculated dissociation coefficients for SF 6 with (dotted curve)

and without (solid curve) excitation transfer from N 2 and the drift

velocities (dashed curve) at the critical fields, (E/N) c , and

(E/N) c (dot-dashed curve) versus the fractional SF 6 content F in

SF 6 /N2 mixtures in comparison with the indicated experimental

results of Aschwanden (Ref. 34) and Verhaart (Ref. 35).

25
(E/N)

c

[10"

21

V

m

2]

DISSOCIATION

COEFFICIENT

(m

CVi

CO

E

§

>

O

O

-j

SJJ >

iLJL CCQ

Figure 16. Calculated dissociation coefficients for SF 6 (solid curve) and 0 2 (dashed curve) and electron drift velocity (dotted curve) at the

critical fields, (E/N) c , and (E/N) c (dot-dashed curve) versus the

fractional SF 6 concentration F in SF 6 /0 2 mixtures.

26
(E/N)

c

flO

'

21

V

m

2

]

DISSOCIATION

COEFFICIENT

(m

10 6

10 5

10 4

10 3

0.2 0.4 0.6 0.8

F = [SFe ]/(lNeMSF6 ]>

1.0

CO

E

§

O

o

—I

LLJ >

hU_

CCQ

Figure 17. Calculated dissociation coefficients for SF 6 with (dashed curve)

and without (solid curve) excitation transfer from Ne and electron

drift velocities at (E/N) c and (E/N) c (dot-dashed curve) versus the

fractional SF6 content F in SF 6 /Ne mixtures. The calculated (E/N) c are compared with the indicated breakdown data of Aschwanden,

Ref. 34.

27
rates in glow- type corona discharges [29] in SF6 /N 2 mixtures also suggest that

contributions to SF6 dissociation by excitation transfer from N 2 is of minor

importance

.

As in the case of SF 6 /N2 , the maximum effect of excitation transfer on

SF 6 dissociation for SF 6 /Ne mixtures was calculated and is indicated by the

upper dashed curve in Fig. 17 corresponding to the quantity (a^(SF6 ) +

a t (Ne))/NF where at (Ne) is the sum of the coefficients for excitation to the

metastable states of neon. The effect of excitation transfer on SF6 dissociation is seen to be relatively small for F > 0.01. An analysis of

experimental observations of the products from SF6 dissociation in SF 6 /Ne

mixtures by Siddagangappa et al. [29] shows that the dissociation of SF 6 by

collisions with excited Ne cannot be ruled out.

In the case of SF6 /0 2 mixtures the calculation includes the contribution

to electron attachment from three-body formation of 0 2 as discussed in Refs 30

and 31. It was found, however, that neglecting this process had no

significant effect on the results shown in Fig. 16, except for pure or nearly

pure 0 2

. Three-body attachment is expected to be less significant than

dissociative attachment because of its relatively low magnitude and low

effective energy range [31,32]. The electron-attachment rate in SF 6 /0 2 is

dominated by SF

g for F > 0.04. The possible influence of collisional electron

detachment from oxygen negative ions has not been included here. There are

experimental results, although generally not in good agreement [33],

indicating that electron detachment in the interactions of O' , 0 2 , O 3 , and O 4 with 0 2 may occur with significant probability at the (E/N) c values considered

here

.

In addition to the coefficient for dissociation of SF6 normalized to F,

we also calculated, as shown in Fig. 8 , the coefficient for 0 2 dissociation

normalized to the fractional 0 2 concentration, (1 - F) . Again, both

q^(SF 6 )/NF and a^(0 2 ) /N( 1 - F) apply only at (E/N) c for each mixture ratio. The

0 2 dissociation coefficients are subject to the uncertainties discussed in

Ref. 30.

The measured (E/N) c data for SF6 /N 2 and SF6 /Ne were obtained from Refs 34

and 35, and the drif t-velocity data for SF 6 /N 2 at (E/N) c was given in Ref. 34.

At the present time no measured results have been obtained on dissociation

coefficients for any of the mixtures considered here. It should be noted that

the dissociation coefficients, or rates, are essential information in any

attempt to theoretically predict the rate of SF6 decomposition in electrical

discharges [16,19,29]. The results from this calculation were used in the

model described in the next section to predict the rate of oxyfluoride

formation in negative glow- type, point-plane corona discharges in pressurized

SF 6 containing trace amounts of water vapor.

The SF 6 cross-section set determined in the present work should be useful

in the calculations of (E/N) c and transport and swarm parameters for other gas

mixtures containing SF 6

. The dissociation coefficients presented here are the

first ever to be calculated for SF 6 and SF 6 mixed with N 2 , 0 2 , and neon.

28
3.4 Zonal Model for Corona- Induced Decomposition of Dielectric Gases

A three-zone model for chemical decomposition of electronegative gases in

negative point-plane corona discharges was proposed [16] and shown to be

useful in predicting discharge by-product yields and the dependences of these

yields on discharge current and gas mixture composition. The principal

assumption of this model is that the gas in which a highly localized negative

corona occurs can be partitioned into three zones of differing chemical

activity, namely the glow region, ion-drift region, and main gas volume as

depicted in Fig. 18.

The glow region corresponds to the relatively small volume which is

observed [29] to be of approximate uniform luminosity near the tip of the

point electrode. It is assumed to be the region of greatest chemical activity

in which the mean electric field- to-gas density ratio, E/N, is approximately

equal to, or slightly exceeds the critical value (E/N) c at which the electronimpact ionization and attachment rates are equal. This assumption is

justified by recent measurements performed in similar constricted glow-type

discharges in SF6 [36]. Consistent with optical observations [29], the glow

region is also assumed to be spherical of radius R and volume r c , where r c is

much smaller than the main gas volume r t ; typically t c /r^ < 10" 9.

The chemistry in the glow is dominated by fast reactions primarily

involving free radials or ions produced directly or indirectly by electron

collisions. The rate constants for bimolecular reactions are required to be

in excess of about 10" 15 cm3 /s in order that the processes in the glow can go

to completion, i.e., the reaction times are short compared to times required

for molecular diffusion out of r c

. Dissociation of the gas by electron

collisions is also confined to r c , since for r > R, the energetic electrons

needed to initiate gas decomposition rapidly thermalize and are removed by

attachment. Also, consistent with observations [19], the rate-controlling

processes for gas decomposition in the glow are the electron- impact

dissociation processes, the rates for which were calculated by the method

discussed in the previous section. Table 1 lists the reactions and

corresponding rates that were used in the model for the glow region. The rate

constants for the various bimolecular processes involving free radicals were

derived from several sources [37-39].

The ion-drift region is the interelectrode region in which charge is

predominantly carried by negative ions and the chemistry is dominated by ionmolecule reactions of the type considered above in Sec. 3.2. The reactions

that occur in this zone can be important in influencing the yields of some

gaseous by-products observed from discharge - induced decomposition. The

present model considers, for example, the F' transfer reaction [14,20]

SF, S0F 4 S0F 5 + SF 5 , kj = 2.0 x 10‘ 10 cm3 /s (5)

in predicting the rate for S0F 4 production. There is evidence [20] that in

many cases this is the predominant S0F 4 destruction mechanism. Given here is

29
GLOW

REGION

05 03

05C

5-1 o X 5-( 4-5 O

05

05 & 05 4J c

03

X r—I 45 C4

*r-l i $ 4-1 c

T3 •H

05O

4-5 Pu

03 - O 05 o >

U)

cn 4-5 o3 0360

>*, 05

4->

C > c

•H *»-t 4J

05

C

03

O

*—^ ^

CQ *r-l 0) U)o 6

0) rC

o>

cuEO

0)

05 60 T> C

•r-t <0 U E4

05 cn

(-w

4-1 4i •4 O

'O 4-4

4-1 ^ O 05 03

cn o e e o

•r-i 05 60 C

05

O

ffi

N

OO

054

60

•rH pH

30
18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

Table 1 . Proposed Reaction Scheme for Glow Region

e + SFg SFg + F + e

e + SFg SF4 + 2F + e ^1 8 = 2.4 X 10 2 1/s

e + H2 0 -*• H + OH + e ^1 9 = 1.9 1/s

SFs + SFs - SF 4 + SFg ^2 0 - 5.0 X 10 2 1/s

SFg + SFg S 2 Fjq k2 i = 5.0 X 10- 13 cm3 /s

SFs + F - SFg ^2 2 = 1.0 X 10“ 12 cm3 /s

F + F - F 2 k2 3 = 2.0 X io - 10 cm3 /s

F + H 2 0 - OH + HF ^2 4 = 2.0 X 10“ 1 6 cm3 /s

SF4 + OH SOF3 + HF ^2 5 = 1.1 X 10- 11 cm3 /s

F + SOF3 - SOF4 k2 6 = 3.6 X 10“ 13 cm3 /s

F + H HF k2 7 = 2.0 X 10 -1

1

cm3 /s

S0F3 + OH - S0 2 F 2 + HF ^2 8 = 1.0 X 10“ 13 cm3 /s

H + H - H 2 ^2 9 - 1.0 X 10“ 15 cm3 /s

OH + OH - H 2 0 + 0 ^3 0 = 1.0 X 10“ 15 cm3 /s

OH + F -+ FOH ^3 1 = 2.0 X 10“ 12 cm3 /s

OH + SF5 - S0F 4 + HF ^3 2 = 5.0 X 10“ 13 cm 3 /s

OH + 0 0 2-l- H ^3 3 = 1.6 X 10“ 12 cm3 /s

0 + SFg -» S0F4 + F ^3 4 = 3.3 X 10' 11 cm3 /s

H + OH -»• H 2 0 k 3 g = 2.0 X 10" 11 cm 3 /s

^3 6 = 5.0 X 10“ 13 cm3 /s

31
the thermal value for the rate constant k x that applies at low E/N. The rate

equation for S0F 4 production that includes the effect of reaction (5) can be

written as

r d[ S0F 4 ] ikJSOFJ exp{(-k 1 [S0F 4 ]/v - k')Z 0 ) - 1 = r

t

( 6 ) dt evr

t

(k x[ S0F4 ] /v - k')

V /

where i is the discharge current, e is the electronic charge, v is the mean

drift velocity of SFg , Z 0 is the distance between r c and the anode, r t is the

production rate for S0F4 within r c , and k' is a decay constant for a

competing SFg deactivation process that can also occur in the ion-drift zone.

For the purposes of the present discussion, it is sufficient to note that at

t = 0, d[S0F4 ]/dt is initially given by r t , and after a sufficiently long time

it approaches a lower constant value of r t -i/er t that represents the limit

where all SFg is destroyed by reaction (5)

.

This latter condition is likely

to be reached for the experimental situations considered here.

The main gas volume is a region of slow chemistry involving relatively

stable species like SF 4 and SF2 that diffuse out of the glow region and

undergo slow reactions on the walls of the gas-containing vessel or with gasphase contaminants like 0 2 and H 2 0. It will be assumed here for convenience

that the vessel which defines r t is a sphere centered at r c with a radius Rw , where Rw » R. It has been shown by Van Brunt and Siddagangappa [20] from

mass spectrometric measurements made using the mixture SF 6 /0 2 /H 2 0 enriched

with either 18 0 2 or H 2 18 0, that S0F2 and S0 2 F 2 are formed from negative corona

preferentially by reactions involving H 2 0 and 0 2 respectively. The relative

insensitivity of S0F 2 and S0 2 F 2 yields to [H 2 0] and [0 2 ] suggest that these

products are predominantly formed by the slow gas -phase reactions

( 7 )

and

( 8 )

that occur in the main gas volume. The rate for reaction (7) has been

measured by Sauers and coworkers [40], and for reaction (8) an upper limit was

determined by Plumb and Ryan [38]. The gas-phase hydrolysis processes

( 9 )

32
and

SOF 4 + H2 0 S0 2 F 2 + 2HF k5 = 2.0 x 10 21 cm3 /s, ( 10 )

also occur in the main gas volume and can affect the relative oxyfluoride

yields after sufficiently long times. It has been shown by Van Brunt and

Sauers [41] however, that reactions (9) and (10) are too slow to be of

importance for the experimental situations under consideration here.

The model allows for diffusion of reactive species into and out of the

different zones, and involves finding numerical solutions to the set of rate

equations associated with the reactions mentioned above and in Table 1 coupled

with the differential equations for diffusion. The numerical solutions were

obtained using a chemical kinetics computer code recently developed at the

National Institute of Standards and Technology [42].

Shown in Fig. 19 are examples of calculated S0F 2 and S0F 4 yields -versus - time (or equivalently, net charge transported, Q = it) from the proposed model

in comparison with experimental data of Van Brunt [19]. The prediction for

S0F 4 includes the effect of reaction (6) in the ion-drift zone. The

concentrations for SF6 and H 2 0 were held constant at the indicated values.

The concentrations of the intermediates SFs and F are seen to reach constant

values almost immediately as required for the steady-state condition. The

relatively good agreement between calculated and experimental results was

achieved in part by adjusting the relative contribution of reaction (19) to

the SF6 dissociation rate and by treating the volume ratio r c /r t as an

adjustable parameter which was varied within a range restricted by the

uncertainty associated with the optical measurement of R, namely

R = (1.5 ± 0.5) x 10 2 cm. The rate of S0 2 F 2 production derived from the

calculation was five orders of magnitude below the measured rate reported by

Van Brunt [19]. This is expected since S0 2 F 2 is believed to be formed mainly

by reaction (8) involving molecular oxygen which was not included in this

model. A proper accounting for S0 2 F 2 production requires not only the

presence of 0 2 , but also the inclusion of SF 6 dissociation channels leading to

formation of the lower valence sulfur fluorides SF 3 and SF 2

.

An investigation of the sensitivity of the model predictions to

variations and uncertainties in the various parameters used is underway. A

preliminary examination of the special case considered here showed that the

electron- impact dissociation rate is indeed the rate controlling factor in

oxyfluoride production, and S0F2 production, in particular, is very sensitive

to the relative contribution of reaction (19) to the total dissociation. In

the present case, the required contribution from reaction (19) leading to SF 4 as opposed to SF 5 formation is less than 1% of the total. The model predicts

that both S0F 2 and S0F 4 production rates increase almost in direct proportion

to the current as observed. Although S0F2 production based on this model is

insensitive to variations in [H 2 0] as required, the predictions for S0F 4 are

33
»

Figure 19. Comparison of predicted (solid and dashed lines) and measured (open

and solid points) S0F 4 and S0F 2 yields versus charge transported

(Q _ it) from decomposition of 200 kPa SF 6 containing 200 ppmv H 2 0

in a 40 /iA negative corona. Also shown are the predicted steadystate levels of SF s and F in the glow region of the discharge.

34
relatively more dependent on [H 2 0] than the experimental observations would

suggest. For the scheme given in Table 1, it was found that reaction (33) is

the dominant S0F4 formation mechanism with reaction (25) providing most of the

OH. Direct dissociation of H2 0 appears to be relatively unimportant. The

role of H2 0 in SOF4 production requires further investigations; but based on

the case considered here, it would appear that the influence of H2 0 on S0F 4 yield depends on the relative competition between reaction (33) and other

mechanisms that can remove OH, especially reaction (31)

.

3.5 Analysis of Dielectric Strength Data for Binary Electronegative Gas

Mixtures

The motivation for this activity was to test a theoretical model that has

been proposed [43] to analyze dielectric strength data for binary gas mixtures

with the purpose of determining the consistency of these data with relevant

information about swarm and electron-collision cross sections for the

individual gas constituents. The model was previously used successfully to

evaluate dielectric strength data for the gas mixtures SF 6 /N 2 , CCi 2 F 2 /N 2 , and

CCJ? 2 F 2 /SF6 [43]. In the present work the model was applied to the mixtures

SF6 /C0 2 , SF6 /Ar , SF6 /Ne, and SF6 /He [17].

Since details of the model have been described elsewhere [43], only an

outline of the main assumptions is given here; namely: 1) the intrinsic

dielectric strength of an electronegative gas mixture, i.e., the critical

electric field-to-gas density ratio (E/N) c ra , is defined by the criterion

am

** ^m* where am and rj m are respectively the electron- impact ionization and

attachment coefficients for the mixture; 2) the electron energy- distribution

functions for the mixture are Maxwellian; 3) the mean electron energy in a binary gas mixture £ m is given by a weighted sum of the mean energies of the

component gases A and B,

? m(F,E/N) - g(F) i A(E/N) + [1 - g(F) ] e

fi (E/N) , g(F) > 0, (11)

where g(F) is the weighting function and F is the gas mixture ratio

F = [ A] / ( [A] + [B] ) , 0 < F < 1; ( 12 )

and 4) the dependence of the mean energies l

and £g on E/N can be determined

by comparing experimentally measured ionization coefficients of the

constituent gases with the corresponding coefficients computed for a

Maxwellian distribution function using electron collision cross-sections for

momentum transfer and ionization as input data, i.e.,

[(E/N)(a /N)] - (0. E/N) (a /N) , i - A, B; 0. > 0

-L LJ 1 (13)

35
For the mixtures studies here, the E/N-range was subdivided into j

sectors, where in each sector the experimental values for (a^/N) in Eq . (13)

were represented by a linear approximation:

(a./N)

r exp

a. . + b. . ij(E/N) 1, 2, 3 (14)

The F dependence of (E/N) c ra is found by solving Eq. (11) for E/N, once

£ m (F) has been determined using the breakdown criterion am = rj m , and once the

E/N dependencies of and eg are known from Eq . (13). The correction factors

Pi in Eq. (13) are used to obtain a least squares fit between predicted and

experimentally measured (E/N) c m

values. Large deviations of Pi from unity

indicate either a failure of the Maxwellian approximation or significant

inconsistencies among the breakdown, swarm and cross-section data, or a

combination of both problems.

Figures 20 and 21 show the (E/N) c ra results obtained from this

"Maxwellian" model in comparison with results from numerical solutions of the

Boltzmann Equation as discussed in section 3.1 above for the binary gas

mixtures SF6 /Ar and SF6 /C0 2 respectively. The calculations in these figures

are compared with data from different measurements [34,44-46]. It is seen

that in both cases the agreement among the various calculations and

experimental data is quite good.

Although the Maxwellian model appears to give satisfactory results for

the SF6 /C0 2 and SF6 /Ar mixtures assuming an equal weighting function for mean

energies, i.e., g(F) =- F, this is not the case for the SF6 /Ne and SF 6 /He

mixtures. This is indicated in Table 2 which shows that the Pi parameters for

SF 6 /Ne and SF6 /He deviate significantly from unity and the root-mean- square

deviations between the Maxwellian and corresponding experimental data are

considerably higher than for SF 6 /C0 2 and SF 6 /Ar.

The cause of the failure of the Maxwellian approximation for SF 6 /He and

SF 6 /Ne was initially suggested [17] to be the consequence of unaccounted for

Penning ionization processes, i.e.,

He* 4- SFg -*• He + SFg + e,

where He* corresponds to helium in a metastable excited state that exceeds the

ionization energy of SF 6

. Unfortunately, nothing is known about the rate for

this process. The maximum possible influence of Penning ionization on the

critical field, (E/N) c m , for SF 6 /He and SF6 /Ne was determined from numerical

Boltzmann type calculations assuming either that no Penning ionization occurs,

or that all He atoms excited to metastable states are quenched by ionizing

collisions. The latter case is equivalent to assuming that collisions which

produce metastable excitation also produce ionization. The results of this

calculation for SF6 /He are displayed in Fig. 22 in comparison with available

experimental data [44,45]. It is evident that Penning ionization has an

insignificant effect on (E/N) c m

in this case except in nearly pure helium. A

similar conclusion can be drawn from the calculations of Kline, et al. [ 47 ].

36
(E/N)

c

[1CT

21

V

m

2]

Figure 20. Critical electric field-to-gas density ratio, (E/N) c , as a function

of the fractional SF 6 content in an SF6 /Ar gas mixture. Shown are

the results of calculations based on the Maxwellian approximation

and numerical solutions to the Boltzmann transport equation in

comparison with various indicated experimental data.

37
(E/N)

c

[10“

21

V

m

2]

Figure 21. Critical electric field-to-gas density ratio, (E/N) c , as a

function of the fractional SF6 content in an SF 6 /C0 2 gas mixture

Shown are the results of calculations based on the Maxwellian

approximation and numerical solutions to the Boltzmann transport

equation in comparison with various indicated experimental data.

38
(E/N)

c

[10~

21

Vm

2]

Figure 22. Critical electric field- to-gas density ratio, (E/N) c , as a function

of the fractional SF6 content in an SF 6 /He gas mixture calculated

from numerical solutions to the Boltzmann transport equation

assuming 1) no Penning ionization of SF6 by metastable He, and 2)

the maximum effect of Penning ionization whereby all He excitated

to metastable states are quenched in an ionization process. Shown

for comparison are various indicated data from experiments

.

39
It can therefore be concluded from this investigation that the omission

of Penning ionization in the Maxwellian model does not account for its failure

when applied to either SF6 /Ne or SF6 /He. It was discovered from calculations

of the mean electron energies that the cause of failure lies with the

assumption g(F) = F. For these mixtures, g(F) must be a much more rapidly

varying function of F, perhaps of the form (1 - e"£^) where [A] in Eq . (12)

corresponds to SF6 and ( is a constant. This is expected because the lowest

excited states of He and Ne are quite high (greater than 19 and 14 eV

respectively) , which means that they are not very effective in " thermalizing"

electrons, i.e., in reducing electron kinetic energy in the gas via inelastic

collisions. This is in contrast to SF s which has many low-lying excited

states. Therefore SF6 is a much better electron thermalizer than either Ne or

He, and the addition of only a relatively small amount of SF 6 to these gases

will have a disproportionately large effect on the reduction of e m . Thus, the

assumption of g(F) = F in Eq . (11) is not realistic in these cases.

Further investigations into the limits of the Maxwellian model for

determining consistency among dielectric strength, electron swarm, and

collision cross-section data are underway. The method appears to show promise

in providing an analytical procedure for helping to determine the reliability

of data on the uniform- field dielectric strength of numerous gas mixtures,

especially those for which there exists only limited information on electron

collision processes.

Table 2. Correction factors 0^ - £3 (Eq. 13) and root-mean- square

deviations found in fitting the Maxwellian model to (E/N) c for the

various binary mixtures containing SF 6

.

Gas Mixture

0a(SF6 ) RMS deviation (V 2 m

4

) (for g(F) = F)

SF 6 /C0 2 0.8 1.0 0. 74E-40

SF 6 /Argon 0.9 1.03 0. 14E-39

SF 6 /Neon 0.7 1.0 0 . 1 IE- 38

SF 6 /Helium 1.1 4.7 0.88E-39

40
4. INTERFACIAL PHENOMENA IN LIQUIDS

Task 04

Edward F. Kelley

Electrosystems Division

National Institute of Standards and Technology

4.1 Introduction

The objective of this research is to understand the mechanisms of failure

in practical insulation found in power apparatus. Electrical insulation

schemes in practical apparatus generally involve composites of different media

such as solids and liquids. For example, transformer windings are often

wrapped with layers of paper and separated with pressboard and the entire

assembly placed in a liquid insulant such as transformer oil. In order to

minimize the destruction of, or damage to, such apparatus, it is necessary to

develop a complete understanding of the failure mechanisms for all the range

of stresses to which the apparatus is subjected. These include stresses which

occur both during ordinary operation when the apparatus undergoes slow

degradation due to aging, during extreme operation, including peak usage

periods, and the times when the apparatus is subjected to surges or impulses

from a variety of sources.

Understanding of the failure mechanisms will permit designers of

apparatus and component- insulation materials to appreciate the inherent

limitations of the media and the entire systems. For instance, if it were

determined that sub-micron particles (conducting or non-conducting) were

responsible for partial discharge initiation, it would not be likely that

systems could practically be designed to eliminate such contamination.

However, if research were to demonstrate that partial discharge activity was

caused by micron-sized conducting particles, then designs which eliminate such

contamination could be of interest. Such contaminents would be symptomatic of

the assembled system and would not depend upon some fundamental property of

the insulation (unless the liquid or solid were of poor quality and

contaminated)

.

To illustrate an aspect of liquid breakdown which relates to the more

fundamental characteristics of liquids in general and independent of the

apparatus, consider fast breakdown. It has been shown that liquid insulation

can break down at a lower voltage than expected when subjected to steep- front

pulses. We can explain this behavior with our understanding of streamer

structure and development, and such behavior is recognized as a fundamental

property of the liquid insulation. Liquid quality can modify some of the

details of the behavior, but no amount of purification will eliminate the

problem associated with fast breakdown.

Such research on breakdown phenomena in liquids focuses on what we must

live with and what we can avoid if we need to. But in order to be able to

make these claims, we need to understand the processes involved at more

fundamental levels than are presently known. If one is able to model the

processes involved in terms of the liquid properties, then one can reach the

necessary level of understanding to recognize the limits or boundaries which

41
are imposed by the insulation media. This does not refer to a gross empirical

model, but to a model which derives its parameterization from the properties

of the liquids used. The aim of such research serves to establish frontiers

and to identify clearly the causes of degradation and failure.

In Table 3 we list a number of aspects of liquid-solid insulation which

are know to affect performance. This list is not intended to be complete, but

is included to outline the diversity of phenomena which characterize the

acceptability of insulation systems. The list also serves to provide

orientation to our research. The areas of free -charge field enhancement and

breakdown streamer initiation and growth have received attention from this

laboratory in the past. The work reported here concentrates on partial

discharge phenomena and experimental apparatus which assists in their

observations. The details of these results are discussed below.

4.2 Image -Preserving Optical Delay

General

An optical imaging system has been invented to perform photographic

observation of random, transient phenomena. An electrical signal arising from

the transient phenomenon is used to trigger an image -converter camera as soon

as possible after the signal is produced. By means of the image -preserving

optical delay, the image associated with the phenomena is delayed from

reaching the camera for a longer period of time than it takes the camera to

begin taking pictures. Therefore, the first few frames show photographs of

any events which occurred before the transient was created. In this way we

can obtain photographs of random events before they happen, after they occur.

Results Summary

The need for an image -preserving optical delay (IPOD) arises when

information is desired concerning the development of a very fast, random

phenomena. Processes such as electrical breakdown or partial discharges in

insulation studies are random, and the critical information concerning the

process often occurs prior to the electrical event. For example, if one

wanted to understand how lightning is generated, the information regarding the

initiation and development of the process is not readily obtainable after the

lightning has occurred. The information which is needed is a documentation of

the phenomena prior to the lightning strike. In electrical breakdown

processes in general, it is the prebreakdown events that are often of

interest. These events may only last a few microseconds or less prior to the

breakdown. If one happens to have the recording camera operative exactly at

the right moment, then the prebreakdown phenomena can be photographed.

However, to routinely take a picture of the processes which precede such a

random event, it is necessary to delay the image from reaching the

photographic recording device until it is possible to trigger the photographic

system (open the "shutter"). In the case of an image converter camera (ICC)

it may require 100 ns to trigger the electronics to make the camera operate

and it is a simple matter to arrange for the electrical breakdown to trigger

such a camera. If the image information coming from the region between the

electrodes can be delayed longer than the required 100 ns, then the camera,

42
Table 3. Aspects of* Liquid-Solid Insulation Correlating Performance

SPACE- CHARGE AND SURFACE -CHARGE FIELD ENHANCEMENTS

Chemical nature and temperature of liquid affects space -charge content

possibly enhancing electric field increasing discharge activity.

PARTIAL DISCHARGE DEGRADATION

LIQUID DEGRADATION:

CHEMICAL CHANGES:

Increasing conductivity.

Production of new molecular charge carriers can increase

conduction which produces heating and accelerates aging

process

.

Increasing space-charge field enhancement.

Chemical byproducts can contribute to generation of space

charge in liquid increasing probability of further partial

discharge activity or even breakdown.

Production of corrosive byproducts.

Leads to more rapid degradation of insulation components

.

PARTICULATE CHANGES

:

Increasing probability of more partial discharges.

Increasing probability of streamer initiation and breakdown.

Contamination of solid surfaces thereby increasing their

probability of discharge activity.

SOLID DEGRADATION:

Permanent damage resulting in channels or voids.

COINCIDENCE WITH IMPULSE

Serves as initiation site for impulse breakdown streamer.

BREAKDOWN STREAMER INITIATION AND GROWTH CHARACTERISTICS

Similar problems as with partial discharges although damage is more

serious. Streamer structure can be controlled somewhat by liquid used.

NATURAL CHEMICAL DEGRADATION

Impurities and contaminants in media can change insulation properties

over a long period of time even if the material is not subjected to use.

ELECTROCHEMICAL DEGRADATION

Subjection of media to electric fields can cause chemically induced

changes from nature of charge carriers and processes at electrode

surfaces

.

THERMAL DEGRADATION

Conductivity of media and electrohydrodynamic motion of liquid provide

heating thereby enhancing chemical degradation.

ELECTROHYDRODYNAMIC MOTION

Liquid motion contributes to reducing temperature of hotter areas and to

diluting contaminants generated by partial discharges -- both are

benefits. Liquid motion can sweep particulate impurities into high field

regions increasing the probability of discharge activity.

43
looking back in time, will be able to photograph the phenomena which occurred

just before the breakdown event responsible for triggering the camera.

An array of ten 2. 5 -cm diameter flat mirrors symmetrically located about

a central 5 -cm diameter flat mirror is placed on the optical axis at the focal

point of a spherical concave mirror having a diameter of 15 cm and focal

length f of 152 cm. The light from an object placed a distance 2f from the

concave mirror can be continuously refocused through the system by aligning

the mirrors appropriately. The image is formed a distance of 2f from the

concave mirror with a total magnification of unity. Such a system will

provide a 160-ns delay in the light and provide a resolution of 10 line pairs

per millimeter (lp/mm). The delay unit is less than 2 m in length and 0.2 m

in width. In Fig. 23 we show a simplified drawing of the delay in an

experiment to observe electrical breakdown. The image converter camera is

triggered by means of a pulse transformer which senses the moment of

breakdown.

A delay of 390 ns can be arranged by replacing the spherical concave

mirror with a mirror having a 365 cm focal length. The penalty is a loss of

resolution. Using the same flat-mirror array, the resolution will be about 5

line pairs per millimeter (lp/mm). Such a poor resolution is less than the

maximum 10- lp/mm resolution of the image-converter camera. To prevent a loss

in image quality using the longer focal- length mirror, it is possible to

magnify the image before it enters the delay, and then reduce it at the image

converter camera. By extension, the magnification can be increased up to

approximately 100X in order to provide high-magnification, high-speed

photographs of transient phenomena initiation.

4.3 Partial Discharge Initiation

General

A collaborative experiment with the University of Tennessee successfully

monitored the initiation and evolution of partial discharges in transformer

oil subjected to dc . By means of the image-preserving optical delay we were

able to photograph the initiation of a partial discharge and follow -its

development. The current supplied to the partial discharge was simultaneously

monitored by a specially designed amplifier. This is the first time that the

initiation of a partial discharge has been photographed. There were no

surprises in that the structure of the partial discharge was similar to the

structure of a streamer produced by the application of an impulse voltage.

Results Summary

An immediate application of the image -preserving optical delay (IPOD) was

to photograph partial discharges in liquids under the application of dc . The

objective of this collaborative experiment with the University of Tennessee

was to combine their electronics expertise in making fast current

measurements of a partial discharge (PD) with the capabilities at NIST to take

high-speed photographs back in time. The result was to monitor the current

supplied to a PD and simultaneously photograph the evolution of the partial

discharge from its inception through its growth.

44
FLAT

MIRROR

45

Figure

23.

Schematic

of

use

of

image

-preserving

optical

delay

in

liquid

breakdown

experiment.
In order to accomplish this simultaneous measurement not only was a

sensitive amplifier needed, but an amplifier with a fast through-put so that

when coupled with two pulse generators it was possible to fire the image - converter camera (ICC) and a Pockels-cell shutter (PCS) all within 150 ns

after the PD initiated. The PCS was necessary to limit the light striking the

ICC to the time period necessary to make the exposure. Since cw laser light

was needed to illuminate the tip of the needle electrode during the

application of dc , without the PCS too much light would impinge on the

photosensitive surface of the ICC and fog the film.

The results showed that the PD grows uniformly while the current supplied

to the PD is principally in the form of pulses. This was observed for both

the negative and positive PD. Figure 24 illustrates the uniform growth

characteristics in contrast with the discreet nature of the supplied current.

This feature of uniform growth despite pulsed current is true for the

initiation and growth of discharges in liquids under the application of

impulse voltages.

By using high-magnification (75X) , we attempted to observe any particles

which might be responsible for the initiation of the PD. The resolution was

limited to approximately 5 /xm due to the optical system employed. No

particles of that size were observed in the vicinity of the point which could

cause PD initiation. If particles, even ones smaller than 1 /xm, do not serve

as initiation sites for PD's, then further research is needed to fully

understand the charge- inj ection process at high fields.

In a future experiment it is anticipated that an examination will be made

of the effects of pressure on the initiation and growth of partial discharges

in attempts to correlate the current signature with growth structure.

Provided an improved optical system is possible, we also anticipate exploring

to determine the phenomena at the limits of optical resolution.

4.4 Streamer Initiation and Collapse Under Pressure

General

A collaborative experiment was conducted with the University of Tennessee

on the initiation of streamers in liquid under the application of impulse

voltages applied to a needle - sphere gap. A square pulse was applied having a

peak voltage so that the streamer would not grow to breakdown before the pulse

was chopped to zero. With the application of pressure, the initial streamer

was observed to collapse and disappear while the voltage remained on the

needle tip. When the voltage was chopped, a new streamer appeared which

resembled the structure of the anode streamers, the branches of which did not

follow the previous branches of the cathode tree which injected the charge in

the liquid. An estimate of the amount of charge injected and the charge

diffusion time is shown to be consistent with the high resistivity of hexane.

46
b.

c.

d.

i i i i i i i 1 2 3 4 5 6 7

Time (ms)

Time (ms)

1 2

oic

a>

4)E

(S

0)w

75 Time ( // s

)

47

Figure

24.

Uniform

partial

discharge

growth

despite

pulsed

current

supplied
Results Summary

The photographic results of the structure of partial discharges conducted

in the previous study (see 4.3) shows a similarity to the initiation phase of

streamers in liquids under the application of impulse voltages. To explore

the similarities further, a needle-sphere electrode system having a gap of

5 mm is placed in hexane and is subjected to a square pulse having a rise -time

of order 100 ns and a selectable chop time from 10 /jls to 100 ns • The current

supplied to the resulting streamer is monitored while the growth of the

streamer is photographed by an image -converter camera (ICC) . Because of the

nature of the impulse generator used much of the current waveform information

is contaminated by noise associated with the generation of the pulse.

However, a remarkable phenomena is observed in the streamer structure. At

atmospheric pressure (0.1 MPa), the cathode streamer displays its

characteristic bush- like shape - an almost spherical structure which increases

in size until a faster filamentary event emanates from the bush and bridges

the gap causing breakdown. Reducing the voltage will cause the bush to

appear, but it does not grow to breakdown. As the hydrostatic pressure

increases, it becomes more difficult to initiate the cathode streamer or bush,

and one generally finds that the bush tends to become more branched and less

filled. In addition, once a voltage is reached where the cathode streamer

initiates, it is observed to collapse within a few microseconds because of the

pressure even though the voltage remains on the needle. If the voltage is

sustained, the cathode bush will eventually collapse completely leaving only

traces of its existence. The charges which were responsible for the growth of

the bush (or streamer) are left in the liquid and do not diffuse quickly into

the surrounding liquid. This can be verified by chopping the voltage to zero.

The needle is now at zero (ground) potential and there are negative charges in

the liquid. Another streamer develops quickly which permits these negative

charges to be removed from the liquid into the tip of the needle. The

observed streamer is very similar to the filamentary streamers created when

the needle is the anode. This "reversed" streamer is approximately the same

size as the cathode streamer which deposited the charge, but its shape is very

different

.

In Fig. 25 we show moderately magnified ICC photographs of the -timeevolution of the streamers. In these photographs, the first frame is in the

lower left hand corner and the last frame is in the upper right hand corner.

The height of each frame is approximately 1.2 mm, and the tip radius of

curvature is approximately 40 nm - I n Fig. 25a the time between photographs is

2 ns and the entire process of the disintegration of the cathode bush and the

creation of the anode-type tree can be seen. The first frame is taken after

the voltage is applied and the voltage is chopped between the fourth and the

fifth frames. It is interesting to note how the cathode streamer collapses.

The collapse begins nearest the needle and extends to the end of the streamer.

This is readily seen in Fig. 25b. The between fram is 210 ns. The creation

of the "reversed" anode- like tree occurs rapidly. In Fig. 25c the time

between frames is 50 ns and the process is completed within that time

interval

.

We can make an estimate of the amount of charge deposited in the liquid

by this pressure - induced collapse process. We have established in an earlier

48
e

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•rH fa

fa 03

03 -a

}-l • 03 03 03 c 3-4 3.

0) 3

bO 03

O

03 03 un

5-i 03

3-4 -o a o c

03 3-4 -

03 03

03 T3 03 03 c e a 3 03 03 3-i r-H 03 fa

•—1

•fa o C o T3 03

•fa 03 fa 3 3

03 CT fa S •fa 03

03 hJ -q

03

3-4 03 fa • 3.

03 0303

O

fa i—^ t-H O 3 CN a

03 /—

N

X 03

X

a b0

03 03

3-i fa 03

b£) -fa 03 O O S

fa > 03 O 3-4 £ fa fa

fa

O r+

03 b0 03

3-4

C 03

03 •fa 5 s a fa

03 fa 03 O O rCl X b£l U 03 C 3.

•fa 3-4 c 03 CN

ca 03

3-1

C ^

fa 3 03

LD

CN

03U3

bO

fa

49

(after

chop).
paper that these streamers act as if they are extensions of the electrodes and

have the characteristics of conductors [53]. In that paper, a model was

developed whereby the spherical structure of the streamer (especially the

cathode bush) can be approximated by a sphere at the potential of the needle.

A simple approximation to the resulting potential is obtained by choosing an

appropriate point charge which would produce a quasi-spherical equipotential

of about the same size. We adapt that model to the present situation as

follows: Consider a sphere which is roughly the same size as the cathode bush

before it collapses entirely. From Fig. 25 we could use a diameter of 0.75

mm. The sphere has a radius R and the gap between the bottom of the sphere

and the grounded electrode is G. The grounded electrode is actually a sphere

in this experiment, but because of its comparatively large radius of curvature

(1.3 cm) and the fact that this is only an order-of -magnitude calculation, we

assume it acts like a plane to simplify the calculation. If V is the

potential on the quasi-point-charge sphere, the method of point- image -charges

can be used to obtain the size of the charge needed to create an equipotential

similar to this imaginary sphere. The charge is given by

q - 47reV(h 2 - G

2 )/2G. (1)

Here e is the permittivity of the liquid (1.9 cq) anc* h is the height of the

charge q above the ground plane:

h - a + 0 - G/3 , (2)

where

a - (S + 7P) 1 /3 t 0 - (S - 7P) 1 / 3

,

S = (8/27)G 3 + 2G 2 R + 2GR2

,

P = ( 32/27)G s R + ( 140/27)G 4 R

2 + 8G 3 R3 + 4G 2 R4

For small spheres high above the ground plane, the location of the charge is

approximately at the center of the sphere: h = G + R. Using a radius of

R = 0.375 mm, a gap beneath the sphere of G = 4.25 mm, and a voltage of

V = 130 kV, we find that a charge of q = 11 nC at approximately the -center of

the sphere would produce an equipotential which would match the voltage which

is applied to the tip (h = 4.624 mm, vs the center at 4.625 mm). In Fig. 26

we show a diagram of this model drawn to scale. It may well be argued that

there is a contribution to the field from the needle electrode, but in this

calculation it is ignored for simplicity since we are interested in an

estimate of the charge deposited in the liquid. Assuming this charge is

evenly distributed through this spherical volume, we have a charge density of

49 /iC/cm 3

.

The fact that such a high charge density can exist for a number of

microseconds without dispersing can be seen from a simple calculation

involving the conductivity of the liquid. In this calculation we will ignore

any external field for the purposes of simplicity. Consider an isotropic,

linear, resistive medium with conductivity a. For such an ohmic liquid the

current density is proportional to the electric field

50
T

1 mm

i

G

51
J a E. (3)

The time rate -of -change of charge leaving the quasi-point-charge sphere with

surface area I! is simply the outflow of the current density through the

surface of the sphere, which by the divergence theorem of Gauss is the volume

integral of the divergence of the current density:

- dq/dt

• * «

• II

«/ % % % « 2

J dxdydz

.

(4)

Since the divergence of J and E are related by ohms law, Eq . (3), and since

the divergence of the electric field is proportional to the charge density

(Maxwell's equations), V*E = p/e, the volume integral is proportional to the

charge contained within the surface, and the rate equation reduces to

dq/dt = - q {a/e). (5)

Thus, the charge is seen to deplete from the region of the sphere

exponentially with a characteristic time constant of r = e/o. To require that

the time constant be long compared to 20 ps amounts to requiring a

conductivity such that a « 0.84 pS (or a resistivity 1/a » 120 Mftcm)

.

Comparing this to typical values of conductivity for liquid hydrocarbons of

10“ 12 S or less, it is reasonable to postulate that the charge will remain

essentially motionless after the collapse of the bush [54]. Clearly this

simple model neglects charge migration and other complications; it only serves

to provide us with a means of checking the reasonability of the estimate.

The results presented here suggest further experimentation. By using

liquids such as water which have much higher conductivities, we should be able

to see an extension of the "reversed" tree beyond the collapse of the cathode

bush depending upon how long we wait for the chop or decay of the voltage.

5. CHARACTERIZING TRANSIENT MEASUREMENTS BY USE OF THE STEP RESPONSE

AND THE CONVOLUTION INTEGRAL

Task 05

R. H. McKnight, J. Lagnese and Y. Zhang

Electrosystems Division

National Institute of Standards and Technology

5.1 Introduction

The measurement of high-voltage transients requires a means of reducing

the high voltage signal to levels which are compatible with data recording

equipment. The measurement devices which accomplish this reduction are known

generically as voltage dividers and they should ideally scale the signal to a smaller value without distortion. These dividers, however, invariably

52
introduce some distortion of the input signal, due primarily to inadequate

bandwidth or aberrations such as overshoot. This distortion may be negligible

or totally unacceptable, depending on the allowable error associated with the

particular measurement requirement. One example of the type of distortion

encountered in cascading systems is the effect on rise time, which can be

calculated for certain conditions by using the well known root-mean- square

expression, r e ff = J r l 2 + r 2 2 + ... where the individual rise times are those

of the cascaded system [55]

.

It should be noted that this calculation is

frequently applied inappropriately, since it applies only to systems (and

pulses) which have monotonic transitions. For many applications, freestanding voltage dividers are used and the examples presented in this paper

are primarily of this type of divider. As will be pointed out, however, the

method has general applicability to other voltage measuring systems.

If the divider system is assumed to be linear, then the general methods

of linear- system analysis can be applied to characterize the system. Two

equivalent approaches involve either time-domain or frequency- domain analysis.

In the frequency- domain [56], the divider is characterized by the following

equation

r Vin(“> Aii(cd) A 12 (

Ca> ) v0 («)

lin( w )

w J A. 2 i (w) A2 2 ( u )

L J

The voltage transfer function, H(w)

,

is defined for zero output current,

I 0 = 0, i.e.

,

H(w) = V0 (w)/Vi(w) | x (w) _ 0 - 1/AnCw). (2)

The conventionally defined divider ratio is given by

N-An (0) = lim AnCw) . (3)

w -* 0

if the limit exists. For some dividers, capacitive dividers for example, the

limit does not exist and the ratio is defined for a region of little change in

A x l (w)

.

In general, the elements of the matrix are complex numbers containing

both amplitude and phase information. Clearly, one of the requirements in

analyzing the divider in terms of its frequency response is the ability to

measure that response. In practical terms, this is not an easy task [55]. It

certainly is not practical to provide a complete response curve, so that some

limits must be applied and these limits must be based on an understanding of

the divider response. Commercial network analyzers can be used to provide

quickly both amplitude and phase information about a given circuit.

Unfortunately, these analyzers are not usually available in laboratories where

transient measurements are to be made.

53
In the time-domain, the divider characteristics are incorporated in the

impulse response. Under the assumption that the system is linear, causal and

time -shift invariant, the input and output voltage are related through the

convolution integral (also known as Duhamel's integral), given in Eq . (4)

[58].

v(t) = Jv(s) g(t-s)ds = ^tJ*v(s) [u(t-s) ]ds (4)

where g(t-s) is the system impulse response and u(t-s) is the step response.

It is generally not feasible to measure the impulse response directly.

Because of the impulse and step response relationship indicated in Eq . (4),

the step response can be used to characterize the system. This approach is

attractive for many laboratories, since a transient recording device is

required to make measurements and can also be used to record the step

response, if the bandwidth, sampling rate, etc., are adequate. Step (or

square wave) responses are frequently used in the laboratory to align

compensated probes and, as noted below, are used to determine divider

characteristics qualitatively.

The use of the step response to characterize systems for high voltage

measurements is detailed as a part of both IEEE (IEEE 4) [59] and IEC (IEC 60-

1 to 4) [60] standards concerned with the measurement of standard pulses used

in the electrical power industry. In each, various parameters are obtained

from a measured step response and are used to predict whether a given

measuring system is adequate to provide a measurement within the uncertainty

limits specified by the standards. The step response is not used directly in

the actual measurement, and there has been much discussion, both published and

in working group meetings about the usefulness of the step response parameters

in the existing standards [61,62,63]. The appropriate interpretation of the

step response itself in real measuring systems was also extensively debated

prior to and during the process of developing the existing standards

[64,65,66,67]. Different parameters obtained from experimental step responses

have been proposed as alternatives in the existing standards, but have not

been adopted and also have generated much discussion [62]. A proposed

revision to the IEC standard recommends that the accuracy of the measurement

be determined by use of a measuring system that has been compared to a

reference system maintained by the appropriate national laboratory [68].

5.2 Discussion of Proposed Method

Described below is the use of experimentally determined step responses

along with analytic waveforms to determine the suitability of a particular

measuring system for making measurements of interest and to present examples

of the application of the method. The method involves the convolution of the

experimental step response with analytic waveforms which represent the ideal

waveform expected in the experimental arrangement. For example, for the full

lightning waveform, this would be a double exponential with appropriate time

constants. The same waveform would be used for canonical EMP waveforms, with

an appropriate change in time constants. Actual waveforms obtained from a measuring system which was known to introduce negligible errors could also be

used in the calculation. The use of this method has been discussed at various

54
times and in working group meetings and one application is presented in a

paper describing comparisons of two dividers [69]. Two earlier communications

describe convolution calculations and their application to measurement

analysis [70,71]

.

Values of waveform parameters such as peak-value and front- time, which

is approximately the 30-90% transition time for standard, or chopped lightning

waveforms (defined in the existing IEC and IEEE standards) , or risetime

(appropriately defined) and peak value for an arbitrary waveform, can be

determined for both the input and calculated output waveform. By comparing

the values, the error introduced by the measuring system can be estimated.

This estimate should not be considered as constituting a number which can be

used to make a correction. Rather, it represents an uncertainty bound on the

actual measurement and is an estimate of the best measurement that can be

made with a given system for the assumed waveform. Systematic errors, random

noise, and other confounding factors will further degrade the quality of the

measurement. However, this method does allow a direct indication as to

whether or not the dynamic response of a measuring system is adequate for the

measurement as represented by the step response used in the convolution.

5.3 Experimental Method

One necessary component of the evaluation method described here is an

experimentally determined step response. Methods for obtaining the step

response of free-standing divider systems are given in [59,60] and one

recommended method is indicated in figure 27. Here the divider assembly and

the associated leads are brought to a steady-state voltage, typically less

than 1 kV, and the system is then shorted to ground through a fast-acting

switch. Conventionally, this switch is a small mercury-wetted relay which has

closure times of the order of 1 ns. The output of the divider system then is

the step response. As noted earlier, there has been extensive discussion in

the literature and at various meetings about the relationship of the step

response, determined using the method shown above, and the actual measurement

made in a laboratory experiment. These concerns are based on several

objections, including the change in geometry when the divider is attached to

the test generator and object, the impedance mismatch between the transmission

line formed by the line connecting the divider to the signal to be measured,

the traveling wave aspect of the leads connecting system components, and the

effect of source impedance, both in the step response measurement and the test

itself. These concerns add uncertainty to the measurement, but are not (with

the possible exception of the source impedance) a cause of inadequate dynamic

response in the divider system.

As part of recent studies to determine sources of error introduced when

two dividers are being compared for purposes of calibration, step responses

for a range of different conditions were measured for two free standing

dividers designed to measure standard and chopped- lightning impulses as

defined in IEC and IEEE standards [72]. An example of the range of responses

obtained for one of these dividers is shown in Fig. 28.

The parameter changed in these measurements was the value of the damping

resistor, RD, shown in Fig. 27. The oscillations seen in the step response

55
I56

Figure

27.

Configuration

for

obtaining

step

response

of

free

standing

divider

(Ref.

58).

R[)

is

a

damping

resistor,

while

R^p

limits

the

current

flow

from

supply

V

during

the

period

the

relay

shorts

to

ground.
result primarily from the inductance and capacitance associated with the

external lead, and the stray capacitance- to-ground of the divider itself

including the capacitive grading ring attached to the top of the divider.

Selected parameters obtained from the step response measurements as defined in

the IEC and IEEE standards for two dividers, designated NBS1 and NBS3, with

different^response characteristics are listed in Table 4. The definitions of

these parameters are not presented here, and the numbers listed in Table 4 are

given only for the purpose of illustrating the effect of the damping resistor

on divider response.

Table 4. Effect of Damping Resistor on Divider Response

Rd

Tn

(Unit Step Response

)

Ta (Partial Step Response) Overshoot

( ohms

)

(ns) (ns) (%)

NBS

1

0 23 27 39

50 29 30 28

150 33 36 14

250 41 44 6

400 52 53 2

NBS3

0 19 17 24

150 23 20 11

350 28 29 3

550 36 36 1

For voltage measurement systems installed in devices such as gas

insulated power equipment or pulse-power systems, as compared to free standing

devices, the main difficulty in applying step response measurement methodology

is that of producing a fast step in the equipment. Such steps have been

produced by charging the system and then shorting- to - ground through an

existing switch or through a switch installed for the test. In some test

lines or specific geometries, it may be possible to apply a step from an

external generator and observe the wave propagating on the line by means of

the installed sensor. An example of this approach, done in a test line

designed to evaluate fast sensors, is shown in Fig. 29, where the directly

measured input signal and the output from a small resistive divider with

overshoot are shown for comparison [73]. Sensors used to measure transients

in gas - insulated power equipment and pulse-power systems, for example, have

been subjected to step- response evaluation and several examples have been

published. Input and output step waveforms for voltage dividers designed for

use in gas insulated equipment are shown in [74]. A fast current probe, a

subnanosecond attenuator, and a fast divider are similarly characterized in

[75,76,77]. These "evaluations" are qualitative, and basically attempt to

show that the step - response of the system has a transition time much faster

than the anticipated signal to be measured, as well as some modest degree of

57
a

o

m

a

os

cn a —

o- o

a <r o II

II Q

Qi

a

Od "N

m

a

. o

5-i m

<u CM

X)

«T—

1

II >

*rH T—

1

X! Q

cd

«—

H

00 / N 03 <r Z

4-1 „ O a

a; o

w m

c T—

1

oa II w

05 a

Cd a

0) ,•—

s

4-> CO

00 'w'

coCM

<D

5-1 3

QO

•rH

C-Ih

3SNOdS3H d31S Q3ZnVlAlldON
overshoot, and so would contribute a negligible error in the actual

measurement

.

5.4 Convolution Calculations

The functional form of the double exponential voltage waveform used in

these calculations is given in Eq. (5), while the parameters a and p for four

different waveforms are given in Table 5.

v(t) - A(exp (-at) - exp(-/3t)) (5)

Table 5. Parameter Values for Selected Waveforms

Waveform a

(s" 1 ) P

(s" 1 )

Standard 1.2x50 1 . 39xl0 4 2.71x10®

Standard 0.9x50 1 . 39xl0 4 3.61x10®

Fast waveform 1 1.39xl0 6 66.3x10®

Fast waveform 2 4 . 0x10® 476x10®

In (5), A is a normalizing factor. The designation of the waveforms by a

"TlxT2" statement refers in the case of the standard lightning waveforms to

approximate front time and the time for the waveform to decay to 50% of the

peak value measured from the peak. The two fast waveforms are used to

represent particular waveforms of interest to workers studying the effects of

fast transients on various equipment. The first is roughly a "50x500 ns"

waveform, while the second is a canonical waveform frequently used in EMP

calculations. Two different standard lightning waveforms were used. One had

front and fall times near the 1.2x50 microsecond waveform of the standard,

while the second had a faster front time. In addition to the full waveform,

chopped waveforms were also used in the calculations. For these, the standard

waveforms were disrupted at some fraction of the peak value and brought

linearly to zero in a chosen time, typically 50 or 100 ns.

The experimentally determined step responses shown previously and a

digitized representation of the input waveform were used in the convolution

calculations. The calculation is straightforward and can be done on a

personal computer. An example of a convolution is displayed in Fig. 30 where

both input and output waveforms are shown for the NBS1 divider configured for

near critical damping. This represents the slowest front time measured for

59
aanindwv

60

Figure

29.

Input

step

(solid)

and

output

signal

(dashed)

from

a

small

resistive

divider

located

in

a

coaxial

test

line.

The

input

signal

was

produced

by

a

fast

cable

pulser.
the divider. In Fig. 30 and all comparison figures, the input waveform has

been normalized to have a peak value of 1.

Similar calculations for a chopped waveform and the same divider

configuration are shown in Fig. 31. These calculations illustrate the

distortion introduced in the output waveform as a result of the inadequate

dynamic response of the divider. As is well known, the chopped waveform is

significantly more difficult to measure accurately than is the full lightning

waveform. Front times and peak values (normalized) obtained from a set of

calculations for two dividers NBS1 and NBS3 are summarized in Table 6.

Two different chopped waveforms were used for illustration. The values

presented with front times of about 1 microsecond were calculated using the

1.2x50 waveform chopped at 0.9 of the peak value. Those with the shorter

front times represent a chop at 0.75 of the peak value of the 0.9x50 waveform.

This waveform represents an extreme condition, and would not realistically be

used in measurements. These calculations illustrate the errors that can be

expected as a divider's dynamic response becomes inadequate.

For full- lightning impulses, these results indicate the two dividers

would be expected to provide accurate measurements. Front- times show larger

differences, in part due to uncertainty in calculating front times when there

are superimposed oscillations. For the chopped- lightning measurements, the

differences become much more significant. In particular, for the early chop

on the faster waveform, the NBS1 divider would be expected to show a

significant error, but as noted above, a waveform like this would probably not

be used in actual measurements. In a recently completed international

comparison of impulse measuring systems, experimental results were obtained

which were consistent with these calculations [78].

Convolutions clearly show that superficial deductions based on

observations of step response measurements may be misleading. For example, a theoretical step response was devised in which there was significant overshoot

and severe oscillations of varing frequency. The three step responses used in

the calculations are shown in Fig. 32. The overshoot is extreme (about 80

percent) , while the resonant frequencies of the system ranged from 5 to

16 MHz. Figures 33 and 34 show convolutions of the two extreme cases.

Clearly, both the step response of the measuring system and the waveform to be

measured are important in the calculation. The high-frequency oscillations

seen in Fig. 33(a) do not contribute distortion, since there is little

spectral power-density in the waveform to be measured at this frequency. As

the resonant frequency of the system decreases, there is more overlap between

the frequency space representing the signal and the divider response. The

effects consequently become more severe.

These calculations also present a problem which is of practical concern

in the measuring laboratory and one which is inadequately dealt with in the

present standards. The oscillations on the front of the output make a

calculation of the time parameters, subject to considerable error, such as

transition times based on percentages of the waveform, (front time or rise

time) .

61
Table 6. Calculation of Distortion Introduced by Various

Divider Configurations

Full Lightning Impulse

Actual Calculated Actual Calculated

Divider Rd(fl) Front Time Front Time Max Max

NBS1 0 1 . 2 fJLS 1.27/xs 1.0 0.996

NBS

1

250 1.2 1.26 1.0 0.998

NBS1 500 1.2 1.27 1.0 0.995

NBS3 0 1.2 1.29 1.0 0.996

NBS3 250 1.2 1.21 1.0 1.0

NBS3 550 1.2 1.21 1.0 1.0

NBS1 0 0.9 0.96 1.0 0.994

NBS 1 250 0.9 0.95 1.0 0.996

NBS 1 500 0.9 0.96 1.0 0.992

NBS3 0 0.9 0.97 1.0 0.993

NBS3 250 0.9 0.92 1.0 1.0

NBS3 550 0.9 0.92 1.0 1.0

Chopped Lightning Impulse

Divider Rd(fl)

Actual

Front Time

Calculated

Front Time

Actual

Max

Calculated

Max

NBS1 0 1 . 04fxs 1 . 02ms 1.0 0,975

NBS1 250 1.04 0.95 1.0 0.962

NBS 1 500 1.04 0.95 1.0 0.958

NBS3 0 1.04 1.02 1.0 0.973

NBS3 250 1.04 1.00 1.0 0.987

NBS3 550 1.04 0.99 1.0 0.984

NBS 1 0 0.42 0.38 1.0 0.947

NBS 1 250 0.42 0.37 1.0 0.898

NBS 1 500 0.42 0.37 1.0 0.886

NBS3 0 0.42 0.39 1.0 0.938

NBS3 250 0.42 0.39 1.0 0.947

NBS3 550 0.42 0.39 1.0 0.944

62
aanindwv

63

Figure

30.

Convolution

of

the

measured

step

response

for

NBS1

configured

to

be

near

critically

damped

(E

in

Fig.

28)

with

the

1.2x50

waveform.

Input

waveform

is

solid,

output

dashed.
aanindwv

64

Figure

31.

Convolution

of

the

same

step

as

in

Fig.

30

with

a

chopped

waveform.

Chop

was

at

90%

of

the

full

waveform

peak

and

the

chop

was

a

linear

50

ns

ramp

to

zero.

The

input

waveform

was

renormalized

to

1

for
AMPLITUDE

(b)

65

igure

32.

Empirical

step

responses

calculated

to

show

effects

of

ring

frequency.

Overshoot

in

each

case

was

approximately

80

percent,

and

the

ring

frequencies

were

approximately

(a)

16

Mhz

;

(b)

8

Mhz

;

(c)

4.8

Mhz.

The

settling

time

was

slightly

more

than

1
aanindwv.

66

Figure

33.

Convolutions

of

step

shown

in

32

(a)

with

a

chopped

waveform

constructed

by

chopping

the

0.9x50

waveform

at

90

percent

of

t

e

peak.

The

chop

was

a

linear

100

ns

ramp.
CO

c

hsamndwv

67

Figure

34.

Convolution

of

step

32

(c)

with

the

wavefom

of

Fig.

33.
The limitations posed by the use of conventional free-standing dividers

to measure pulses faster than those typically used by the power community is

shown in Fig. 35. Here, the waveform is the fast waveform 1 from Table 5, and

the step response is that of the NBS3 divider configured with no damping

resistor. The resulting oscillatory output makes this measurement useless.

In contrast, Fig. 36 shows the same waveform with a critically damped

response. This calculation presents one of the interesting results to appear

in the convolution study. Despite the very large error introduced in the

front -time of the waveform due to the inadequate divider response, the error

in the peak value is much smaller. Of course, faster dividers can be

constructed for these waveforms, but as the required voltage increases this

becomes more difficult.

As an example of the distortion that can be introduced in the peak value

of a waveform, consider the convolution of fast waveform 2 (Table 5) with the

step response of the small resistive divider (shown in Fig. 29) illustrated in

figure 37. Although the step response of the divider is almost adequate to

follow the waveform, the overshoot produces a significant error. This is an

example of a situation where the convolution can be used to judge if the

potential error is excessive for the intended measurement.

An additional question about the use of the step response is how the

closure speed of the switch involved in the measurement affects the measured

step response. A series of convolutions have been done in which ramps of

different 0-100% rise times ranging from 1 to 60 ns (for this calculation)

were used with an arbitrarily chosen experimental step response for NBS1. The

measured step response and its convolution with a ramp step of 60 ns is shown

in Fig. 38. Although the distortion of the step response shown in Fig. 38 is

significant, the calculations indicated that for this step response,

transition times as long as 20 ns had little effect on the step response.

This implies that for many dividers designed to measure standard lightning

impulses, switches other than the fast mercury relays could be used. This

may decrease some of the "noise" problems encountered due to radiation effects

associated with fast rise times [56].

5.5 Discussion

In contrast to a calculation method which uses unrealistic signals such

as ramps, the convolution method presented can show the effect of the use of a

given measuring system, represented by its step response, to measure a signal

of a shape which is closely related to the actual signals of interest. The use

of this method and the plotting of input and output waveforms is instructive

in that the distortion is clearly seen. Intuition may be a poor substitute

for calculation, as is evidenced in figure 33, where a highly oscillatory step

response has little effect on a chopped lighting- impulse waveform.

It should be emphasized that this method does not address some of the

questions raised in historical debate about the step response itself and the

methods of obtaining it. The measurement must be done properly, and the

individual experimenter must have sufficient expertise and knowledge to insure

this. The damping conditions resulting from the internal impedance of the

test generator and any external damping resistance in general are not known.

68
gamiidiAiv

69

Figure

35.

Convolution

of

fast

waveform

1

(Table

5)

with

an

undamped

step

response

for

NBS3.

Observed

overshoot

is

approximately

15

percent.
aanindiAiv

70

Figure

36.

Fast

waveform

1

convolved

with

a

critically

damped

step

response

for

NBS3

.
aamndwv

71

Figure

37.

Fast

waveform

2

(Table

5)

convolved

with

the

step

response

of

the

resistive

divider

shown

in

Fig.

29.
3anindwv

72

Figure

38.

Distortion

of

critically

damped

step

for

NBS1

by

convolution

with

60

ns

(0-100%)

ramp.

Solid

curve

is

undistorted

step,

dashed

result

of

calculation.
As a result, only bounds can be placed on the measurement using this method.

Considerations of requirements on the data recording system are beyond the

context of the present work and are not discussed here.

5.6 Conclusions

The examples of convolution calculations shown above illustrate a method

of evaluating a measurement system and are not intended to be exhaustive.

Each laboratory would have to measure the step response of its own system by

devising a method to produce a step to which the measuring system will

respond. For free-standing dividers, the methods outlined in the standards

listed previously or those discussed in the literature will suffice. Earlier

technical problems, encountered with producing a step with a fast transition

time at a high enough voltage to produce any adequate signal to register on

the relatively insensitive impulse oscilloscopes, have all but disappeared

with the advent of fast, versatile, digital waveform recorders with low level

inputs. Frequently, the present day problem is one of attenuating the signal

to usable levels during testing.

Waveforms of the type expected in the experiment can be calculated using

a simple analytic form as illustrated here, or by using a look-up table in the

calculation. An experimentally determined waveform, recorded by a divider

known to introduce little distortion, could also be used.

As noted earlier, this approach should not be considered as a method

from which correction factors can be obtained for a given measurement. It

does appear to be useful however, in providing an evaluation of the

application of a given measurement method of known experimental step response

to the measurement of well characterized impulse waveforms.

73
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74
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79
N BS-H4A (rev. 2-ec

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

SHEET (See instructions) NISTIR 88-3886 728 November 1988

4. TITLE AND SUBTITLE

Research for Electric Energy Systems -- An Annual Report

5. AUTHOR(S)

Richard J. Van Brunt, editor

6. PERFORMING ORGANIZATION (If joint or other than NBS. see in struction s) 7. Contract/Grant No.

NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

GAITHERSBURG, MD 20899

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

U.S. Department of Energy

Division of Electric Energy Systems

1000 Independence Avenue, N.W.

Washington, D.C. 20585

10. SUPPLEMENTARY NOTES

j 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 summarizes the technical accomplishments during fiscal year 1987 from

a U.S. Department of Energy sponsored program at the National Bureau of Standards to

provide technical support for DOE’s research on electrical energy systems. Major

activities associated with each of the four subtasks that constitute the program are

highlighted. These include research on: 1) electric field and ion measurements;

2) fundamental physical and chemical processes in commonly used gaseous dielectrics like

SF^; 3) development of advanced methods for observing and catagorizing prebreakdown

interfacial phenomena in liquid dielectrics; and 4) evaluation of advanced methods for

characterizing transient measurements by use of step response and convolution integrals

as they apply to free standing dividers.

12.

KEY WORDS (Six to twelve entries; alphabet! cal order; capitalize only proper names; and separate key words by semicolons)

convolutions; collision cross sections; dividers; drift tubes; insulation; ion mobilities;

ion-molecule reactions; liquid dielectrics; optical delay; partial discharges; step

response; sulfur hexafluoride

13.

AVAILABILITY

^ U n I i mi ted

For Official Distribution, Do Not Release to NTIS

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