NATL INST OF STAND & TECH

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IMBSIR 84-2881

High-Current Measurement

Techniques

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosvstems Division

Washington, DC 20234

May 1984

QC

103

,156

34-286

1934

l w

Prepared for: 'andia National Laboratories

Ibuquerque, New Mexico 87185

NBSIR 84-2881

NATIONAL T.'j Or STA':n-‘

. USHARY

HIGH-CURRENT MEASUREMENT

TECHNIQUES

J. D. Ramboz and D. R. Flach

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Washington, DC 20234

May 1984

Prepared for: Sandia National Laboratories

Albuquerque, New Mexico 87185

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

TABLE OF CONTENTS

Page

LIST OF FIGURES iv

LIST OF TABLES iv

Abstract 1

1. INTRODUCTION 1

2. ROGOWSKI COIL MEASUREMENTS 3

2.1 Comparison Bridge Circuitry 3

2.2 Positional Sensitivity Tests 5 2.3 Gap Separation Sensitivity 7 2.4 Return Conductor Proximity Effects 9

2.5 Effects of Ferromagnet i c Materials in Coil Proximity 10

2.6 Relative Coil Sensitivity 11

3. HIGH-CURRENT SHUNT MEASUREMENT RESULTS 11

4. DYNAMIC TESTS ON A DIGITAL OSCILLOSCOPE MEASUREMENT SYSTEM 14

4.1 Sinewave Testing 14

4.2 Step Function Testing 16

5. CONCLUSIONS 17

6. ACKNOWLEDGMENTS 17

7.

REFERENCES 17
LIST OF FIGURES

Page

Figure 1. Bridge circuit for comparing the output voltage ex to

the reference voltage en

3

Figure 2. Decrease of coil sensitivity for gap separations and

three positions of the high-current conductor (coil A) 8

Figure 3. Measurement results of the effective bits as a function

of signal frequency (without averaging) 14

Figure 4. Measurement results of the effective bits as a function

of signal frequency (with averaging) 15

Figure 5. Differential linearity error (in LSBs) versus code BIN

(decimal) 15

Figure 6. Analog plot of step response (vertically expanded) 16

LIST OF TABLES

Page

Table 1. Coil identification, size and type (Size refers to the

inside diameter of the toroid "window") 2

Table 2. Test results for the positional sensitivity tests for coil A . . . 6

Table 3. Diameters of coil windows and high-current conductor,

and the percentages of the window occupied by the

conductor 6

Table 4. Rotational sensitivity test results for a 4.4-cm by

10.2-cm rectangular bar centered in coil A window 7

Table 5. Test results for coil A when split coil is opened in

increments of 1.3 cm (0.5 inch) 8

Table 6. Return conductor proximity effects. Test results of

percent change in coil sensitivity as a function of

distance to return current conductor 9

Table 7. Effect of ferromagnet ic plate in proximity of coil 10

Table 8. Sensitivity of each coil relative to the NBS reference

coil. Sensitivity given to four significant digits

followed by one standard deviation where meaningful data

exi sted ' 11

Table 9. Shunt measurement results to assess the proximity

effects of the return high-current conductor 12

Table 10. Effects of ferromagnetic material in the proximity of

the shunt. Also shown are effects due to coaxial cable

location and "compensation" network pickup 13

iv
HIGH-CURRENT *€ASUREMENT TECHNIQUES

J. D. Ramboz and D. R. Flach

Abstract

"he measurement of very nigh ac currents presents soecial prob'e^s in

the selection of current sensors, instrumentation, and techniques, "his

report discusses initial test results for Rogowski coils and high-capacity

current shunts often used to measure large ac currents. Eight Rogowski

coils of three sizes and ratings were tested at a nominal current of

1000 A. The coils were comoared against an N3S orecision air-core mutua'

inductor to obtain a measure of complex sensitivity, pcsitiona’

sensitivity, gap-separation sensitivity (for the split-coil types', and

proximity effects of the return conductor and of ferromagnet ic mate*"' a'

The shunt was tested to assess the oroximity effects of the return

conductor and of ferromagneti c material. It was concluded that tne

particular Rogowski coils tested would not have measurement uncertainties

of less than a few percent unless extreme care was ta<en in tneir

calibration ana subsequent use. "he measurements for the shunt suggest

somewhat less proximity effect than those for the coils. A digit a

1 oscilloscope was evaluated for possible use as a transient recorder.

"

n e elective number of bits, the differential linearity, and the response to a steo function were determined.

keywords: ac current measurement; calibration; current shunts; digita'

oscilloscope; high current; Rogowski coils.

1. INTRODUCTION

The goal of this overall effort is to study the feasibility of accurate

-easurement of very nigh currents, uc to ^CO,3CO a^oe^es, nav' n g snort durations

in the millisecond time 'Intervals. Sucn currents are ^sed in welding

processes. Deve'cpment of "eas^re-ent tecnn'-oues, ceve'lopmert o~ measurement

apparatus, ana the evaluation of ootn oarcware and software usea for tne

measurement and eva : uation of hign-pu’seo c^r^e^ts a^e being pursued.

"n^s 'eocrt d'scusses the -irst efforts to assess so~e of the

characteristics of commercial high-current ~easuri r'g instruments, namely

Rogowski -type air-core coils [1]', arc separately, a

n ' go-current, 1 ow- 'moedance

shunt. Test currents used were steady-state sinusoidal and ''"'ted t: 2CCO amperes. Also investigated was a aigital-osci ' loscope measurement systewn'lch ~ay prove useful as a transient '’ecor; 1'

C jpq display device for '/.refforts.

"he Rogowski co'"s investigated were com-erpia' ur'ts arc a r e of 3 —t

‘

toroidal design. All nave an air core arc generate an output /oltage r rapt ' . proportional to the time r ate-of -change of ourr-ert, as

wnere eo is the coi 1

1 s output voltage, N is toe nuroer of tj r ns to re to ' , : is the magnetic f.^x proGuced by a current in a conductor ana t is t~e. "o can also be expressed in VKS units as

Numbers in or ack et s refer to the '"’terature ref erases listed 3t v- : this report.
e

o

u q

WN

2v

di

dt »

where y 0 is the permeability of the core, W is the core width, N is the number

of turns on the toroid, a and b are the inside and outside diameters of the

toroid, i is the current and t is time [2]. As can be seen, the output is the

time derivative of the current scaled by a constant. An electronic integrating

circuit is used to process the coil's output. The output of the integrator is

then directly proportional to current.

A variety of coils were selected for test. Two basic types were available;

one was of a fixed geometry and the other was a split, hinged arrangement such

that the toroid could be opened, placed around a current-carrying conductor, and

snapped shut to its operating position. The table below gives the dimensions of

the coils and the types. The coils are each arbitrarily designated by a letter

which is used hereafter to identify the coil.

Table 1. Coil identification, size and type

(Size refers to the inside diameter of the toroid "window".)

Designation Size Type

cm i nches

A 12.7 5.0 Split

B 12.7 5.0 Split

C 12.7 5.0 Fixed

D 6.4 2.5 Split

E 6.4 2.5 Spl it

F 6.4 2.5 Spl it

G 6.4 2.5 Fixed

H 2.5 1.0 Split

One high-current shunt was tested to assess such effects as proximity to

high-current return conductors, proximity to ferromagnetic materials, and output

potential lead placement. The shunt tested has a nominal resistance of

10 ohms and a maximum current rating of 30,000 amperes with a duty cycle of

0.5%.

The oscilloscope tested utilizes digital sampling and storage techniques to

record an electrical event. The oscilloscope can be remotely operated via an IEEE 488 bus by a suitable controller. Parameters such as noise, signal-tonoise ratio, differential linearity, and step response were measured.

The test results for the Rogowski coils show that current measurement could

be relied upon to within a few percent over a wide variety of conditions. For

measurements with uncertainties in the range of a few tenths of one percent,

very tight control of the testing and calibration conditions would have to be

maintained. The test results for the shunt indicate that care must be taken

regarding the routing of both the high-current conductors and the potential

output leads in order to keep errors below a few tenths of one percent.

2
Oscilloscope tests indicate that the unit tested met the manuf acturer '

specifications, but even so, might serve only in a limited way for the further

precision measurement of pulsed currents.

2. ROGOWSKI COIL MEASUREMENTS

2.1 Comparison Bridge Circuitry

A ratio transformer bridge was configured as shown in figure 1. The

primary current I was sensed by two coils and a step-down current transformer.

The reference coil, made by NBS, feeds its output to an accompanying set of

electronics, which gives an output voltage en

. The coil under test feeds its

output to its set of electronics producing an output voltage ex

. Both en and ex are directly proportional to the current I flowing through the two

coils. Current I also flows through a 5000:5 ampere step-down current

transformer which, with the use of a 0.1-ohm shunt, gives a measure of primary

current

Figure 1. Bridge circuit for comparing the output voltage ex to the reference

voltage en

.

The complex ratio of the two voltages can be derived from the ratio

transformer setting k the value of R, and the value of C, when the bridge is

balanced. The voltage ratio magnitude le x /e n can be expressed as

e

n [(1-k) 2 + ( RC)

2

] 172

where w is 2-rf and all other terms are as described above. The frequency f

normally set to about 50 Hz to avoid 1 i ne-frequency beat problems.

3
The phase solution can be expressed as

4

> = tan _1 [(l/k)/coRC] + tt/2 radians. ( 2 )

The NBS mutual inductor electronics package has a precision voltage divider

and phase adjustment built into it. These controls were set so that the

magnitudes of the voltages ex and en were approximately equal. This then

makes k = 0.5 nominally and gives the bridge maximum sensitivity. The phase

adjustment on the electronics package has a small and limited range used for

final bridge balancing. The gross phase balance is accomplished by selecting

proper values for R and C. A typical value for R was 10,000 ohms, while values

for C ranged from about 0.0001 to 0.02 yF, depending on which coil was being

tested. The final phase angle is then the sum of the phase shifts as determined

by eq (2) and the phase setting of the mutual inductor electronics.

The absolute sensitivity of the coil under test was not measured. The

desired information from the test was what changes occurred in the coil's output

for changes in test configuration (coil position relative to the center

conductor, for example). Because only changes of the measurand were being

sought, gains and phase shifts due to the electronics and residual phase errors

of the bridge become unimportant. As described in each test portion of this

report, a reference test condition was selected and all other measurements for

that group of data were related to the data of the referenced condition.

The bridge could easily be balanced with a resolution of the ratio

transformer setting of 1 part in 50,000 giving a voltage ratio resolution of

about 0.002%. Typically, balances were made to only 1 part in 5000 because the

changes due to varying test conditions did not warrant the extra resolution.

Phase balance resolution was about ±0.03 mrad for most of the tests.

For proper operation of the bridge, it is necessary that the output

voltages en and ex be of approximately opposite phase. This was generally

accomplished by physically arranging the orientation of the coil on the

high-current center conductor. For the split-coils, this phase could be

reversed by physically reversing the coil so that the current would be flowing

in the opposite direction through the coils' windows. On the solid coils, it was necessary to either reverse the coils' orientation or reverse the electrical

output of the test electronics. Because none of the coils tested gave any

markings of coil polarity (i.e., no "marked terminal" as is common practice of

current transformers) , this determination of polarity was one of trial and error.

The test current I was typically set to 1000 amperes, and, for some tests,

ranged from 100 to 2000 amperes. A digital voltmeter measured the voltage Vf across the 0.1-ohm shunt as shown in figure 1. It was unnecessary to test at exact primary currents inasmuch as none of the sensing coils, electronics,

bridge, etc. were grossly nonlinear. As long as ratio of the two coils' outputs

was being measured with the bridge, the primary current could be varied

considerably with no serious degradation of the test results.

The laboratory data recorded for each test included the following

i nformation:

4
Test coil identification

Data and time of test

Test current (I)

NBS/mutual inductor electronics divider setting

NBS/mutual inductor electronics phase shifter setting

Bridge resistance (R)

Bridge capacitance (C)

Ratio transformer setting (k)

Frequency (f)

Test condition, position, orientation, etc.

The information was generally evaluated so that solutions to eqs (1) and

(2) were done by computer assistance. (The program and documentation are available upon request.)

2.2 Positional Sensitivity Tests

A series of tests was performed on each of several current-sensing coils to

determine the effects of the position of the high-current conductor relative to

the sensing coil. The coil was mounted on a 3.2-cm (1.25-inch) diameter rod

which was the high-current conductor. This passed at right angles through the

coil's window. For the larger diameter coils (coils A through G), it was possible to move the coil to several positions to determine if the location of

the conductor had any effect on the output.

When testing the 12.7-cm (5-inch) coils, data was collected in 17 separate

positions: eight positions when the inside of the coil rested against the

center conductor at angular intervals of 45°; eight positions midway radially

between the center of the coil and the inside edge at angular intervals of 45°;

and one position at the center of the window.

Fewer positional possibilities exist for the smaller diameter coils (coils

D through G). The 6.4-cm (2.5-inch) coils were tested similarly to the 12.7-cm

coils except only the outside eight positions and the central position were

used, eliminating the eight intermediate radial positions. The 3.2-cm center

conductor occupies a larger proportion of the window for the 6.4-cm coils than

for the 12.7-cm coils leaving fewer meaningful positions available.

For the 2.5-cm (1-inch) coil (coil H), no positional tests were done

because a 2.5-cm conductor was used which allowed no relative movement.

A smaller conductor could not be used for the test currents of 1000 amperes

because of conductor heating.

The output from the coi 1 -under-test was compared to a reference coil by a ratio transformer bridge previously discussed. The voltage ratios (also

proportional to the current sensitivity ratio) of the two coils were measured

for a variety of test coil positions discussed above. For the final analysis,

the data for each of the positions were compared to the data obtained at the

center of the coil and the percentage difference calculated. Table 2 below

gives the results for the coils tested. The maximum difference for any two

positions is noted as well as the maximum difference for any position relative

to the central position.

5
Table 2. Test results for the positional sensitivity tests for coil A.

Coil Designation Maximum Difference

(%)

Maximum Difference

Relative to Center

(%)

12.7 cm (5 inch) split (A) 7.2 -4.0

(B) 3.7 +2.4

12.7 cm (5 inch) fixed (C) 1.1 -0.9

6.4 cm (2.,5 inch) split (D) 1.9 -1.3

(E) 1.4 +1.4

(F) 1.6 -0.9

6.4 cm (2.,5 inch) fixed (G) 0.6 +0.5

2.5 cm (1 inch

)

split (H) — —

The largest differences were measured on the larger coils, namely the

12.7-cm coils, with accordingly smaller differences measured for the smaller

coils. In all instances, the split coils showed larger differences than the

fixed coils.

It should be noted that the manufacturer of the coils states that the

high-current conductor should occupy at least 40% of the coil's window area. This condition was not met during these tests. It is apparent that as the

high-current conductor becomes a larger proportion of the window area, less

relative positioning can occur until at the limit of equal diameters, no difference can exist. Table 3 below shows the diameters for the windows, the

high-current conductor, and the percentage of the window area which is occupied

by the high-current conductor.

Table 3. Diameters of coil windows and high-current conductor,

and the percentages of the window occupied by the conductor.

Coil Designation Inside

Di ameter

cm inch

High-Current

Conductor

cm inch

% of Window

Occupi ed

A,B,C Split & Fixed 12.7 5 3.2 1.25 6

D,E,F,G Split & Fixed 6.4 2.5 3.2 1.25 25

H Split 2.5 1 2.5 1 100

The high-current conductor occupied less than 40% of the window area for

all coils except coil H. The diameter necessary for the conductor to be at least 40% of the window area can be calculated from the following expression

(for circular cross-sectional conductors):

d c > 0.632 dw , (3)

where dc

is the diameter of the high-current conductor, and dw is the

diameter of the window. The minimum diameters dc to satisfy the 40%

6
requirement for coils A, B, and C would be 8 cm, for coils D, E, F, and G would

be 4 cm, and 0.6 cm for coil H.

The results shown in table 2 indicate less positional sensitivity for the

6.4-cm coils than for the larger 12.7-cm coils. The amount of window occupied

for the larger coil is only about 6% as compared to 25% for the smaller 6.4 cm coils. It is presumed that the differences in position continue to decrease as the percentages of occupied window approaches 100%. A note of caution: one cannot state from the above data that the smaller coils have less positional

sensitivity without further testing.

Additional tests were performed to assess the positional sensitivity of

coil A when rotated about a 4.4 by 10.2-cm (1.75 by 4 inches) rectangular bar as

a high-current conductor. The coil was centered about this bar and then rotated

in 45° increments and measurements made. The results are shown in table 4

below. The data indicate that a maximum change of about 1.4% occurs at 90° and

at 270°. Also note that for other di ametri cal ly opposed positions (namely, 0°

and 180°, 45° and 225°, 135° and 315°), the changes are very nearly equal. The

rectangular bar used as a high-current conductor occupied about 31% of the

window area.

Table 4. Rotational sensitivity test results for a 4.4-cm by 10.2-cm

rectangular bar centered in coil A window.

( Degrees)

Rotational

Position

% Change from

Output at 0°

0 0.0

45 -0.4

90 -1.4

135 -1.3

180 -0.1

225 -0.7

270 -1.4

315 -1.0

2.3 Gap Separation Sensitivity

A group of measurements was made on two of the 12.7-cm coils to determine

the effects of the split coil not being completely shut. The coil was placed in

three positions about the high-current conductor which passed throuqh the coil's

window. In the "upper" position, the conductor was located so that the top of

the conductor rested against the inside top of the coil directly adjacent to the

split opening of the coil. The second position was located in the center of the

window. The "lower" position was selected such that the bottom of the conductor

was resting against the lower inside of the coil directly adjacent to the hinged

split. The coil was placed in the upper position and remained there while the

split coil was opened in increments of 1.3 cm (0.5 inch) from closed to 12.7 cm

(5 inches). The coil output was compared to the NBS reference coil for each oaD

setting. The same procedure was followed for the center and lower positions of

the conductor. The ratio and phase angle of the coil's output relative to the

NBS reference coil were calculated. Table 5 below gives the test results and

figure 2 shows the gap setting data plotted for coil A.

7
DECREASED COIL SENSITIVITY

CU £

cL

c U L c

L C

* U

L

C

• U

L C

c

• U

U L

L

C •

u * Upper Posi tion

c * Center Position U U

L

- L * Lower Posi tion

U

U

50 0 2 4 6 8 10 12 14

CAP SEPARATION, cn Figure 2. Decrease of coil sensitivity for gap separations

of the high-current conductor (coil A).

Table 5. Test results for coil A when split coil

in increments of 1.3 cm (0.5 inch).

and three positions

is opened

Gap Opening % Decrease of Coil Output

cm Inches Upper Position Center Position Lower Position

0 0 0.0 0.0 0.0

1.3 0.5 6.7 2.8 3.1

2.5 1 14.4 6.8 7.4

3.8 1.5 20.1 9.1 11.0

5.1 2 24.6 12.2 15.2

6.4 2.5 29.5 16.0 18.4

7.6 3 33.1 18.4 22.6

8.9 3.5 37.0 21.4 26.0

10.2 4 38.8 24.3 30.3

11.4 4.5 41.0 27.3 32.6

12.7 5 42.9 30.0 36.5

The gap can open to approximately 18 cm (7 inches); however, when this was first done, a ground wire broke in the region of the hinge mechanism and the

coil became sensitive to the proximity of nearby objects, such as hand motion

near the coil, etc. The coil ground was repaired and the gap opening was thereafter limited to about 12.7 cm (5 inches).

Similar data were obtained from the 12.7-cm split coil designated as coil B. The high-current conductor was about 3.2 cm in diameter. The least

sensitive position to gap opening was in the center of the window. The most

sensitive of the three positions tested was at the "upper" side of the window

nearest the split. It should be noted that wide-gap settings are abnormal to

the coils use. The wide-gap measurements confirmed a fair degree of linearity

of sensitivity decrease with gap opening, therefore, data from the wide-gap

measurements could be used for linear extrapolation to small-gap openings. The

extrapolated sensitivity decrease for small -gap separations is about 0.1% per

0.025 cm (0.01 inch).

8
Gap opening tests were run with a high-current conductor occupying only

about 6% of the window area; it is felt that the sensitivity to gap opening

would be somewhat less had a larger conductor been used. Also, these tests were performed in the NBS 12,000-ampere current cage where rather symmetrical

electric fields exist; in situations where distorted fields are present, gap

opening sensitivity could be much worse.

2.4 Return Conductor Proximity Effects

Five coils were tested for external field effects by using a flexible,

2.5-cm diameter high-current conductor. The conductor was passed through the

coil's window at an arbitrary position. This position was left unchanged for

the set of measurements on any one coil. The distance between the conductor in

the window and the return high-current conductor was varied from a distance of

about 51 cm (20 inches) to about 5 to 10 cm (2 to 4 inches) minimum, depending

on the particular coil being tested.

The coils selected for these tests ranged from the smallest to the largest

(2.5 cm to 12.7 cm) and consisted of one fixed coil and one split coil from each

size group. The output at the most distant position of the return conductor was

used as the reference value to which all other data were compared for each

coil. The test results are shown in table 6. The percentage change in output

is shown in columns for each coil tested. Data is presented vertically against

distance between high-current conductors.

Table 6. Return conductor proximity effects. Test results of

percent change in coil sensitivity as a function of

distance to return current conductor.

Approximate Percent Change Referenced to Most Di st ant

Di stance Between 2.5 cm 6.4 cm 6.4 cm 12.7 cm 12.7 cm High Current Conductors Spl it Fi xed Split Fixed Split

cm Inches Coil H Coil G Coil D Coil C Coil A

74 29 0.0

51 20 -0.2 0.0

48 19 +0.2 0.0

46 18 0 . 0 , 0.0

43 17

41 16 0.0 - 0.7

38 15 +0.3 +0.2

36 14

33 13 - 0.1

31 12 -0.5 +0.4 +0.1

28 11 -0.7

26 10 +0.4

23 9 -0.8 + 1 . 2 , 0.0

20 8 +0.3

18 7 -0.9 +0.7 -0.6

15 6 + 3.3

13 5 -1.4 -0.5 +0.8 - 4.3

10 4 - 1.9 +0.3 - 8.0

7.6 3 -0.5 +0.3

5.1 2 -2.9 +0.7

2.5 1

9
especaHy evident for the 12.7-on split airtsSs’thTg^-S’fiJS coil.

was that

obtllneVw^^^lhTcJil^arorienLd^boSi

the Je^e

^ ^

two opDosite sides S thl

ab0“t

J the high-current conductor such

perpendicularl^^As ca'n b^s^^Tth' Y^^^M^IhroS^he^Ind^

s bs "

;-r to the high-current conductor " »

passing through

« “Stirsv

the coil's window.

irsf ;:,rs“P r

S‘sS: si" =~ L-s' • -

changes ca^be^d^^^ -hes), larger

2.5 Effects of Ferromagnetic Materials in Coil Proximity

JaraHel'to llSIpIlssiss-

?he coiK

’ 6

^

W3S br ° U9ht a,0n 9 side the co11 a “ane

overaH Effect

sar1es of measurements are shown in table 7. The

percent in the worst cale ThI Lvt S"k"’ leSS than a few tenths of one

Plate was in the Jolls

3

proximity'

“

the ,argeSt cha"9es “he" the —a ^ e /7

‘—Effect of ferrom agnetic plate in proximity of coil.

Coil Designation Percent Change Referenced to Wo

Ferrous Material

Perpendicul ar Horizontal

Perpendicul ar Vertical

Parallel

6.4 cm, fixed. Coil G

6.4 cm, split. Coil D 12.7 cm, fixed. Coil C

12.7 cm, split. Coil A

-0.04

-0.24

0.00

• 1.8

-0.08

-0.56

0.00

•3.1

-0.32

10
2.6 Relative Coil Sensitivity

The data for each of the seven coils were evaluated for their individual

sensitivity as compared to the NBS reference coil. The values represent a factor of the uncalibrated NBS coil's sensitivity. Using such data, relative

comparisons can be made, one coil with respect to another, to determine how

consistently the coils are manufactured. Table 8 gives the data.

For coils A through G, the mean sensitivity ratio relative to the NBS

reference coil was 0.3790 with a one standard deviation of ±0.0051 (±1.4%) about

the mean. The maximum difference between any two coils of the group A through G was about 3%. Coil H is a high sensitivity coil whose output was approximately

7.5 times greater than the other coils. For coils A through C, the value shown

in percent following the sensitivity ratio is a one standard deviation limit for

the data from which the mean sensitivity ratio was calculated.

Table 8 . Sensitivity of each coil relative to the NBS reference coil.

Sensitivity given to four significant digits followed by one standard deviation where meaningful data existed.

Coil Designation Sensitivity3 Ratio Relative to NBS Coil

Co i 1 A (12.7 cm.» split) 0.3831 ±1..1%, 0. 3942 b ±0.3%

Coi 1 B (12.7 cm., split) 0.3841 ±0..3%

Coi 1 C (12.7 cm,, fixed) 0.3705 ±0.. 1 %

Coi 1 D (6.4 cm. split) 0.3760

Coil E (6.4 cm. spl it) 0.3751

Coi 1 F (6.4 cm. split) 0.3825

Coi 1 G (6.4 cm. fixed) 0.3815

Coi 1 H (2.5 cm. split) 2.806 c

a Value obtained with use of 3.2-cm round conductor in all tests unless

otherwise noted.

b High-current conductor dimensions used were 4.4 x 10.2 cm.

c High-current conductor was 2.5-cm diameter.

3. HIGH-CURRENT SHUNT MEASUREMENT RESULTS

Preliminary measurements were made on a 30,000 ampere shunt which has a nominal value of resistance of 10 microhms. It is rated at a duty cycle of 0.5^

for a period of one second. The maximum steady state current is rated at 1,500 amperes.

Tests were performed to assess 1) the proximity effects of the return

high-current conductor, and 2 ) the proximity effects of ferrcmagnet i c mater’ 3 ’,

(i.e., steel plates, etc.). To test for the proximity effects of the return

high-current conductor, the shunt was connected into a 1,000 ampere circuit witn

flexible 2.5-cm cables. A flat loop was configured having an approximate

diameter of 50 cm. The loop was made decreasingly smaller in increments inc

measurements were made of the complex voltage ratio of the shunt's output

compared to the output of the NBS reference coil through its accompanying

electronics.

11
The basic ratio transformer bridge shown in figure 1 was used to measure

the magnitude of the voltage ratio and the phase angle. A high input impedance

amplifier having a gain of 10 was used to provide more voltage from the shunt's

output and its output was fed to the bridge circuit as voltage ex .

Table 9 gives the measured results of the return conductor proximity

effects. The percentage change in voltage ratio is referenced to the value

measured at a separation of conductors of 51 cm (20 inches). The phase angle

difference is also referenced to the value measured at the 51-cm separation.

The changes were relatively small from the initial separation of 51 cm to

20 cm, however, as the separation became less than 20 cm, the phase angle showed

significant changes and the percentage change in ratio began to decrease

rapidly. The ratio changed in a rather smooth function, finally decreasing

about -0.46% from its initial value. The change in phase difference, however,

increased rather smoothly until the separation was nearly zero, then suddenly

reversed when zero separation was reached.

Table 9. Shunt measurement results to assess the proximity

effects of the return high current conductor.

Approximate Distance Between Change Phase Angle Difference

Shunt and Return Conductor Referenced to 51 cm Referenced to 51 cm cm inches Separation (percent) Separation (mrad)

51 20 0.00 0.0

46 18 +0.02 +0.2

41 16 +0.03 +0.3

36 14 +0.04 0.0

31 12 +0.05 +0.3

25 10 +0.05 +0.6

20 8 +0.04 +0.8

15 6 +0.01 +2.6

10 4 -0.05 +4.4

7.6 3 -0.10 +6.9

5.1 2 -0.18 +10.5

2.5 1 -0.27 +14.3

0 0 -0.46 -4.2

The configuration for the measurement of ferromagnet ic proximity effects

used the same bridge measurement arrangement as discussed above. Basically, a reference measurement was made to establish some arbitrary value for ratio and

phase. This reference condition was an open 51-cm loop of high-current

conductor with the shunt connected in one side of the loop. A 24- by 52-cm

steel plate was then brought into the vicinity of the shunt and loop and a new bridge balance obtained. The differences from the initial conditions were then

calculated. Table 10 gives the measurement results. Also shown are the results

of two other tests: one to assess the effects of the location of the coaxial

cable coming from the shunt and crossing the high-current conductor, and the

other to evaluate the pickup effects of the "compensation" network and enclosure

which is attached to the coaxial cable coming from the shunt.

12
Table 10. Effects of ferromagnetic material in the proximity

of the shunt. Also shown are effects due to coaxial

cable location and "compensation 11 network pickup.

Change in Ratio

Relative to Reference

Condition Listed (percent)

Difference in Phase Angle

Relative to Reference

Condition Listed (mrad)

Test Condition

0.00 (ref) 0.00 (ref) 51-cm open flat loop, no ferromagnetic material

present.

+0.07 -0.2 Ferromagnetic plate flat

on loop.

+0.15 -2.3 Ferromagnetic plate

upright in loop 25 cm

from shunt.

+0.34 -6.9 Ferromagnetic plate

upright against end of

shunt.

-0.28 +8.7 Ferromagnetic plate flat

on shunt.

0.00 (ref) 0.0 (ref) 51-cm open loop, coaxial

cable perpendicul ar to

and on return conductor.

+0.04 +0.6 Coaxial cable

perpendicular to and 23 cm above return

conductor

+0.10 +0.6 Coaxial cable parallel to

and 23 cm above return

conductor

+0.11 -4.5 Coaxial cable parallel to

and on return conductor

for a length of 38 cm.

0.00 (ref) 0.0 (ref) Network enclosure

magnetically shielded.

0.00 +0.8 Network enclosure

magnetically shielded on five sides - small

magnetic "leaks."

+0.11 +20.9 Network enclosure placed

next to return conductor,

no magnetic shielding.

The effect of ferromagnetic material in the general proximity of the shunt

gave measurable changes, but were not considered too great in comparison to i few tenths of one percent unless the material came very close to the shunt.

13
The coaxial voltage-sensing lead coming from the shunt is sensitive to

pickup when placed near the high-current conductor, especially if it is parallel

to the conductor. It should be kept at least 20 cm from the conductor and, if

necessary to be that close, be oriented at right angles to the conductor. (The

manufacturer recommends that this lead be kept 2 or 3 ft away from high-current

conductors.

)

The compensation network which is enclosed in a small aluminum box is very

sensitive to stray pickup if anywhere near a high-current conductor. Distances

up to 60 to 100 cm showed significant pickup. Simple magnetic shielding

(placing the "box" in a steel enclosure) reduced the pickup to barely measurable

levels.

4. DYNAMIC TESTS ON A DIGITAL OSCILLOSCOPE MEASUREMENT SYSTEM

4.1 Sinewave Testing

The digital -osci 1 loscope measurement system was tested for its

signal -to-noi se (S/N) ratio using a sinusoidal source as the input stimulus over

the frequency range from 1 kHz to 10 MHz. A sinewave fitted to the digitized

output data was used to determine the rms noise N from the result of subtracting

the digitized data from the fitted sinewave data. The measurement errors are graphically shown in figure 3 in terms of the "effective number of bits." There were about seven effective bits over a frequency range of 1 kHz to 1 MHz and

then the number dropped to about five bits at 10 MHz. The waveform storage

option of the oscilloscope provides a resolution of 10 bits, and a perfect

instrument would show a result of 10 effective bits in this test. The effective

number of bits n is computed from

n = 10 - log

2 q77Y2") >

where Q

= 1 LSB, or it can also be computed from

n = (S/N - 1.8)/6 . EFFECTIVE BITS VS. FREQUENCY

NO AVERACINC

CURVE FIT flETHOO RANCE -15 V FS 1-100 KHZ

- 5 v fs i-i0 nuz

501 DATA POINTS

t KHZ 10 KHZ 100 KHZ 1 MHZ 10 MHZ Figure 3. Measurement results of the effective bits as a function of signal

frequency (without averaging).

The noise N can be reduced by averaging each data point, which is easily

done with the oscilloscope, and figure 4 shows the results for a 64-point

average. Fast Fourier Transforms were applied to the output data to compute the

14
S/N ratios for the 64-point averages. This method is computationally faster and

gives substantially the same results as obtained using the curve fitting

technique. Averaging (as was carried out here) improved the performance by one

to two bits.

EFFECTIVE BITS VS. FREQUENCY

0 -NO AVERACINC

0 - G4/P0INT

FFT nETHOO

RANGE- 14 V FS TO 1 00 KHZ

- 2V 1-10 MHZ

Figure 4. Measurement results of the effective bits as a function of signal

frequency (with averaging).

A differential linearity error test based on a sinewave input was also

performed. Figure 5 shows a plot of the data obtained from this test. The

number of sample points taken was 100,200 (one hundred thousand two hundred) and

the test took several minutes to run. The statistical nature of this test gives

a high confidence level of 99.9% that no code will exceed an error of 0.5 LSB.

(An ideal digitizer has a quantization error of ±0.5 LSB.) Differential

linearity errors at the end points (near codes 0 and 1023) should be disregarded

since they are caused by a 5% overranging of the input signal. For the

confidence level of 99.9%, there should be no more than 1 point out of the 1023

points exceeding ±0.5 LSB. However, as figure 5 shows, there are at least 16

points exceeding ±0.5 LSB.

INPUT 07 KHZ. 1.14 VOLTS/OIV

LSB ' S/D 1 V . 0 US/DIV, Cn 1. DC INPUT 180200 SAMPLE POINTS

Figure 5. Differential linearity error (in LSBs) versus code BIN ' dec’^a ' )

15
The computation of differential linearity error, as shown in figure 5, is

determined by

( actual number of occurrences of Ith code

total number of sample points . ideal probability of 1th code

The reader is guided to reference 3 for a fuller explanation.

4.2 Step Function Testing

NBS has under development a fast-settling, step-like generator which is

designed to rapidly change (rise/fall) from one voltage level to a second

voltage level within an error band of ±0.02% in 50 ns or less [4]. The results

of a positive rise-time test are shown in figure 6, and a 7-point moving average

was applied to smooth the data. For the time base rate shown in figure 6, a nearly perfect step from the NBS generator was applied to the input. The term

SGD is the step generator drive frequency, and 400 sample points are shown out

of a 501-point record. The starting voltage level was approximately -4 volts,

and the ending voltage level was approximately +4 volts. The ordinate of

figure 6 is plotted in units of LSBs and is only a portion of the 0 to 1023-bit

full-scale range which corresponds to 10 volts full-scale. The 8-volt step

represents (8/10) x 1024 = 819 bits where only a small expanded portion is shown

in figure 6. The approximate 20-bit overshoot out of the 819 bit change

represents about 2.4% overshoot. The time required for the voltage to settle

was about 5 us.

'0 LSB'S/OJV. STEP RESPONSE

OC COUPLED INPUT

950

Figure 6. Analog plot of step response (vertically expanded).

16
5.

CONCLUSIONS

The measurement results suggest that high-pulsed currents can be measured

by the coils tested with uncertainties of no less than a few percent unless

extreme care is taken in calibration and subsequent use of these coils.

Sensitivity changes due to positional orientation, proximity effects,

differences from one coil to the next, and gap openings preclude precision

measurements in the order of a few tenths of one percent. In all instances, the

fixed coils are generally less sensitive to the effects of orientation and

proximity than are the split coils. Rogowski coils can be made which are virtually insensitive to many of these types of effects, such as the coil used

as a reference made by NBS.

The measurements made with the high-current shunt suggest that it is

perhaps less sensitive to some of the same overall effects seen in the coil

measurements. However, large errors can be introduced by improper placement or shielding of the potential lead from the shunt and the enclosure of the

compensation network. Much more work would have to be done to completely

qualify these and other effects at very high currents.

Test results from limited measurements made on the digital oscilloscope

indicate performance within the manuf acturer ' s specifications. Even so, this

instrument will probably find limited use in the ultimate system for the

calibration of very high current sensors. A sampling, multichannel device

having better resolution will be required.

6.

ACKNOWLEDGMENTS

The authors wish to express appreciation to Mr. T. M. Souders and

Dr. R. E. Hebner for their technical contributions, and to

Mrs. Elizabeth Matthews who assisted in the laboratory. Thanks also to

Mrs. Barbara Frey who prepared the manuscript.

7.

REFERENCES

[1] Rogowski, W., Steinhaus, W., Die Messung der magnetischen Spannung, Arch.

Elektrotechn. vol . 1, pp. 141-150, 1912.

[2] Di Capua, M. S., Rogowski coils, fluxmeters and resistors for pulsed

current measurements; Mcknight, R. H. and Hebner, R. E., eds., Nat. Bur.

Stand. (U.S.), Spec. Publ. 628 (June 1982).

[3] Peetz, B. E., Dynamic testing of waveform recorders, IEEE Trans, on Instr.

and Meas., Vol. IM-32 (March 1983).

[4] Schoenwetter, H. K., A programmable precision voltage-step qenerator for

testing waveform recorders, Conf. Proc. IEEE Instr. and Meas. Tech.

(Jan 17-18, 1984).

17
NBS-114A (REV. 2*8C ) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See/nstructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 84-2881

2. Performing Organ. Report No. 3. Publication Date

May 1984

4. TITLE AND SUBTITLE

HIGH-CURRENT MEASUREMENT TECHNIQUES

5. AUTHOR(S)

J. D. Ramboz and D. R. Flach

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions

)

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

3. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant in formation . If document includes a significant

bibliography or literature survey, mention it here)

The measurement of very high ac currents presents special problems in the selection of

current sensors, instrumentation, and techniques. This report discusses initial test

results for Rogowski coils and high-capacity current shunts often used to measure

large ac currents. Eight Rogowski coils of three sizes and ratings were tested at

a nominal current of 1000 A. The coils were compared against an NBS precision air- core mutual inductor to obtain a measure of complex sensitivity, positional sensitivity

gap-separation sensitivity (for the split-coil types), and proximity effects of the

return conductor and of ferromagnetic material. The shunt was tested to assess the

proximity effects of the return conductor and of ferromagnetic material. It was concluded that the particular Rogowski coils tested would not have measurement

uncertainties of less than a few percent unless extreme care was taken in their

calibration and subsequent use. The measurements for the shunt suggest somewhat less

proximity effect than those for the coils. A digital oscilloscope was evaluated for

possible use as a transient recorder. The effective number of bits, the differential

linearity, and the response to a step function were determined.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semi colon s) ac current measurement; calibration; current shunts; digital oscilloscope; high

current; Rogowski coils.

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