A11100 T=lS33b

- _ fTT

NBS

PUBLICATIONS

- NBSIR 81-2410

Measurement of Ion Current

Density At Ground Level in the

Vicinity of High Voltage DC

Transmission Lines

U.S. DEPARTMENT OF COMMERCE

National Bureau cf Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

December 1 931

100

. U56

31-2010

1981

Lc. 2 A

Department of Energy

Office of Electric Energy Systems

12th Street & Pennsylvania Ave., IM.W.

Mail Stop 3344

Washington, DC 20461

NBSIR 81-2410

MEASUREMENT OF ION CURRENT

DENSITY AT GROUND LEVEL IN THE

VICINITY OF HIGH VOLTAGE DC

TRANSMISSION LINES

NATIONAL BUKSAt)

8TAWDAtl>3 LIBRARY Jan 2 5 1982

not dec. . dc(00

(j cry no , %i- to

l<izi

a.

^

R. H. McKnight, F. R. Kotter, and M. Misakian

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

December 1 981

Prepared for Department of Energy

Office of Electric Energy Systems

12th Street & Pennsylvania Ave., N.W.

Mail Stop 3344

Washington, DC 20461

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

TABLE OF CONTENTS

Page

LIST OF FIGURES iv

Abstract 1

1. INTRODUCTION 1

2. EXPERIMENTAL PROCEDURE 3

2.1 General 3

2.2 AC Measurements 4

2.3 DC Measurements 4

3. RESULTS AND DISCUSSION 8

3.1 AC Measurements 8

3.2 DC Fields Plus Ions. 10

3.3 Analysis of DC Results 13

3.4 Location of Ground Plane 16

4. MODELS FOR A WILSON PLATE NOT IN THE GROUND PLANE 17

4.1 Current Density Measurements: 60-Hz Electric Fields . 17

5. CONCLUSIONS 21

6. REFERENCES 22
LIST OF FIGURES

* Page

Figure 1. Schematic view of apparatus 5

Figure 2. Dimensions of "Wilson plates" used in

the present study 6

Figure 3. Percentage current density increase for

plates A-D 7

Figure 4. Wilson plate measurement errors obtained

with 60-Hz electric fields as function of

guard ring width and elevation above the ground

.plane 9

Figure 5. Percentage increase in current density as function of Wilson plate elevation and spacecharge contribution to electric field 11

Figure 6. Percentage increase of current density as a function

of space-charge density near the ground plane ... 12

Figure 7. Errors in Wilson plate current density

measurements as a function of guard ring

width and elevation above the ground plane ..... 14

Figure 8. Schematic view of flux lines terminating on a sensor plate located above the ground plane .... 15

Figure 9. Comparison of experimental values with

model calculations for a prolate spheroidal

boss 18

Figure 10. (a) Representation of a guarded Wilson plate

located in the ground plane, (b) Schematic

view of a spherical current sensor* modeled in

the text 19

iv
MEASUREMENT OF ION CURRENT DENSITY AT GROUND LEVEL

IN THE VICINITY OF HIGH VOLTAGE DC TRANSMISSION LINES

R. H. Mcknight, F. R. Kotter, and M. Misakian

Sensors for measuring vertical current density at

ground level near high voltage dc (HVDC) transmission lines

are subject to error when the sensor is not in the ground plane.

The magnitude of this error, for guarded and unguarded sensors,

has been investigated using both dc electric fields with space

charge and ac electric fields in a parallel plate facility. For

conditions like those expected under HVDC transmission lines,

the results obtained using ac and dc methods agreed to within

experimental uncertainty. The measured errors are as large as 25 percent for guarded sensors and significantly larger for

unguarded sensors. Data for various sensor elevations and

guarding are presented in graphs to aid the designer.

Key words: high voltage dc; measurement errors; transmission

lines; vertical current density; Wilson plates.

1. INTRODUCTION

It is not economically feasible to design high voltage dc (HVDC)

transmission lines with conductors of sufficiently large diameter

that minor surface defects and adhering foreign particles will not

result in significant corona generation at normal operating voltages.

In the usual operating mode, the transmission line consists of two

conductors (or conductor bundles) of opposite polarity and balanced

with respect to ground. In the immediate vicinity of the negative

conductor, the positive ions in the corona discharge are attracted

to the conductor and neutralized. The same is true for the negative

ions near the positive conductor. Ions of the same polarity as the

conductor are repelled and tend to migrate along electrostatic field

lines to the other conductor or to ground depending on their initial

locations.

The ions produced are so-called small ions with mobilities of

the order of 10 _ 4 m2/V*s. Some recombination occurs during migration

and some ions grow in size by attachment to other molecules and

aerosols. Wind forces acting on the ions can predominate over the

electrical forces and carry larger ions over considerable distances

well out of significant influence of the electric field. Thus, both

conduction and convection currents exist in the presence of wind.

In theory at least, these components of the total current density

can be independently, although indirectly, measured. Measurements

of the wind speed (u) and the net space-charge density (p) permit

calculation of the convection current density, jn (j u = up).

Similarly, measurements of the electric field (E) and of the

1
conductivity (x) permit calculation of the conduction current

density, j e ( j e

= *E).

No techniques have been developed for direct measurement of

either the conduction or convection components of the current density

at an arbitrary point in space; however, in principle at least,

measurement of the vertical component of the conduction current density

at the ground surface is quite simple [l]. 1

Measurements of the current density at ground level are of

value in estimating the electric potential to which insulated persons

or objects which intercept the ion current can be elevated. Under

conditions where the current density can be considered conduction

current density (j e ) only, a measurement of the electric field (E)

and an assumption regarding the value of the weighted average ion

mobility (K) permits an estimate of the ion density

Pp (pp = j e /KE) of a given polarity.

Current to a conducting plate lying in the ground plane, but

insulated from ground, can be measured with electrometer circuits

which require negligible rise of the probe plate potential above the

ground reference. Current-density measuring devices of this type

have been used for many years in atmospheric electricity research

under the name "Wilson plates" [3-6]. The current density levels

of interest in that area of research are orders of magnitude lower

than those frequently encountered in the vicinity of HVDC transmission

lines. The larger current simply eases the requirement on the current

measuring instrument when ion currents from power lines are to be

measured.

The accuracy customarily sought in Wilson plate measurements

of atmospheric electricity has not been high, since there is more

interest in changes due to weather, diurnal variations, etc., than in

absolute magnitudes [7]. The principal sources *of error (excluding

instrumental uncertainty) identified and discussed in the atmospheric

research literature are: (1) the change in the plate potential

resulting from the flow of charge to it, (2) the displacement current

introduced by moving clouds of space charge, and (3) the lack of

coplanarity between the Wilson plate and the local ground plane [8].

The first two items have been studied, but the coplanarity requirement

apparently has not been investigated by atmospheric scientists. One

earlier study, concerned with currents induced in objects located

under ac transmission lines, does deal with the question of unguarded

plates under ac conditions [9].

It is important to ascertain how large these various sources of

error are so that reliable estimates can be made of the uncertainty

in measurements made near HVDC transmission lines. If the sources of

^Numbers in brackets refer to the references listed at the end of this

report.

2
error are well understood, then corrections can be made to data

which will improve the overall accuracy of the measurement.

This report focuses on the third type of error mentioned above.

Specifically, miniature, Wilson-plate-type, current sensors are used under

controlled laboratory conditions to explore the errors which result from

use of guarded and unguarded plates at various elevations above the ground.

Data were obtained for both ac and dc fields of varying intensity.

2. EXPERIMENTAL PROCEDURE

2.1 General

The vertical conduction current density (j e ) at the surface of a Wilson plate is given by

j e = PpKE (D

where the various symbols have been previously defined. The actual

current measured with the plate is the integral of j e over the surface

of the plate. If the sensing plate is raised above the ground plane,

then the electric field distribution at the surface of the plate

changes. In particular, as is well known from the theory of

electrostatics, the field increases due to geometrical enhancement, and

if K and pp remain constant, the measured j e will increase. This results

in an error in the measure of j e which is due to the spatial location of

the sensor.

In an analogous fashion, a Wilson plate sensor exposed to an ac field will have induced in it a displacement current which is also

proportional to the integral of the electric field over the surface

of the plate. For the ac conditions, an increase in the displacement

current would be observed as the sensor is raised above the ground

plane. This increase is due to the geometrical enhancement of the

field by the sensor just as for the situation with dc fields and ions.

One would expect that the effect of raising the current sensor

out of the ground plane would be the same for the measurement of

displacement current in a space-charge free region at 60 Hz as for

measurement of the ion current with direct voltage if the following

assumptions are valid: (1) in the dc case the ions follow the field

lines, and (2) the presence of the space charge in this case does

not distort the field pattern.

In this experiment, measurements were made both for ac fields

and for dc fields with space charge. The measurements of displacement

current at 60 Hz can be made with greater precision and accuracy than

comparable measurements with dc conduction currents. The ac measurements

can also be made with a much simpler experimental arrangement than

that required for the dc field plus ions. If, as is shown to be the

3
case later, there is agreement between measurements taken using the

two methods then the ac technique can be used to determine the behavior

of a given sensor. ,

The facility used for producing ion currents in the presence of

a dc field is shown schematically in figure 1 and has been previously

described in detail [10]. The apparatus permits the establishment of

controllable levels of ion current density (j e ) between the parallel

plates in the presence of a dc electric field which can be varied

independent of the current density. The electric field and spacecharge density in the region between the plates can be calculated in

terms of experi mental ly determined quantities. The facility can also

be operated with 60-Hz excitation with no space charge.

The current-sensing plates used in these studies are illustrated

in figure 2. They were constructed from 0.157 -cm thick copper-clad

fiber glass sheets. On six of them a central section of the copper

was isolated from an outer band (henceforth referred to as a guard

ring) by a narrow slot (about 0.5 irm wide) milled through the copper

as indicated. The nominal dimensions are tabulated in the figure.

2.2 AC Measurements

Using 4 kV, 60-Hz excitation of the parallel-plate structure,

with a plate separation of approximately 0.5 meter, data were taken

with each of the plates listed in figure 2. These data consisted of

the displacement current to the plates as a function of height above

the ground plane. Figure 3 is representati ve of the data obtained

with one set (A-D) of plates [11]. Plotted here is the percentage

increase in displacement current above that measured with the sensor

in the ground plate. The value of a guard ring in reducing this

increase is evidenced by the substantially greater slope observed for

the unguarded sensor. The ac data were very reproducible and the

data shown are typical of those obtained in a single run.

The maximum uncertainty in these results is a few percentage

points. However, relative values are considered correct to within a few tenths of one percent. The important sources of uncertainty are

the effects of the leads to the plates and perturbati ons of objects

nearby the parallel plate system. Manually inserted spacers, all of

which were smaller in cross section than the sensor plate, were used

to raise the sensor plates above the ground plate. It was determined

that the spacer size did not affect the results.

2.3 DC Measurements

The parallel plate system was also operated to produce a dc

field plus ions. In these measurements the electric field and current

density at the ground plate were varied over a wide range and data

4
CAP

Figure 1. Schematic view of apparatus. The configuration shown is

appropriate for generating an electric field with positive

space charge. The top and bottom plates of the parallel

plate structure are located in the planes z = 0 and z = 1.

The corona wires are oriented parallel to one another and

are perpendicular to the plane of the figure. Operation of

the apparatus is described in detail in Ref. 10.

5
Plate

Nominal

Dimensions

(cm]

Designation a b

A kT 15

B 10 5.0

C 10 2.5

D 10 10

A' 8.5 7.5

B' 8.5 5.0

C' 8.5 2.5

D' 8.5 8.5

D,D'- No guard ring

t Slot to pass

miniature coax cable

Figure 2. Wilson plates used in the present study.

6
Current

Density

Increase

(

Percent

)

Wilson Plate Elevation (d) Above Ground Plane (cm)

Figure 3. Percentage increase in 60-Hz displacement current

density for plates A-D (fig. 2) as function of

Wilson plate elevation above ground plane. Smooth

lines connect related data points.

7
were acquired for some of the sensors shown in figure 2. Current

densities ranged from 50 nA to 3 yA and field values were varied

from 4 to 35 kV/m.

This system is much less stable and reproducible when operated

in a dc mode than with ac excitation. As a result, special measures

had to be taken to obtain useful results.

For the parallel plate system operating to produce a dc conduction

current, it was not possible to reproduce operating conditions during

a data run unless the various electrode voltages were left unchanged.

For the purpose of this study, a current-sensing plate was slowly

raised, by means of a motor drive, out of the plane of the ground

electrode in figure 1. Its elevation above the plane was determined

using a cathetometer . In this way, a stable operating condition

could be maintained as the elevation of the plate was varied.

The current to the sensing plate was measured with a commercial

electrometer which drove a strip chart recorder. One observer marked

the chart at times when predetermi ned elevations were reached as indicated by a second observer using the cathetometer. A second

current probe mounted on the ground plate of the assembly was used

to monitor the ion current density being introduced into the parallelplate structure and small adjustments of the voltages applied to the

ion-generating section were made, when necessary, to maintain a constant current to this probe during a series of observations.

Under these conditions, the electric field and current density at the

ground plate were constant during a data run.

Even under the controlled conditions and with the precautions

indicated above, the variability associated with the ion production

and transport made it impossible to obtain the same precision achieved

in the ac measurements. Some indication of the spread in data acquired

is evident in figure 6.

3. RESULTS AND DISCUSSION

3.1 AC Measurements

The percent increase of current density shown in figure 3 can be

thought of as a measurement error as the Wilson plate is elevated

above the ground plane. Figure 4 summarizes such measurement errors in

normalized form for all the Wilson plate probes using 60-Hz electric

fields. The curves presented here are smooth curves drawn through

points taken from data similar to that shown in figure 3. The data

are shown in terms of parameters related to the geometry and location

of the sensor plate. The importance of even a small guard ring is

clearly evident. The width of the guard ring becomes much less

important as the sensor is brought near the ground plane (larger

a/d). For small a/d values, which correspond to larger elevations

8
Measurement

Error

(Percent)

Normalized Wilson Plate Dimension (a/d)

Figure 4. Wilson plate measurement errors obtained with 60-Hz electric

fields as a function of guard ring width and elevation above

the ground plane.

9
for a given sensor, a wider guard ring can reduce the error by several

percent. It is worth noting that for a one-meter square Wilson plate

2 cm above the ground plane (a/d = 50), the error for a guard ring as wide as 0.20 m is still of the order of 4 percent.

Deno [9] experimentally determined the enhancement factors for

an unguarded plate above the ground surface under a 60-Hz high voltage

test line. Direct comparison of his results with those reported

here are possible only for a/d = 16, where he observed an enhancement

of about 36 percent--to be compared with the 38 percent extrapolated

from the figure 4 data. This is considered good agreement, especially

in view of the fact that his experiment was designed to explore the

problem of metal roofs with a resultant emphasis on lower values of

a/d.

3.2 DC Fields Plus Ions

The precision of the dc current density measurements, as indicated

above, was considerably less than that obtained with an ac field.

However, it was sufficient to conclude that, except for the case of a probe without a guard ring, for low values of space-charge

density the ac and dc results were the same within the accuracy of

the measurements. Figure 5 shows some typical data of the percentage

increase in current density versus probe height above the ground

plane for two different dc operating conditions. An earlier ac result is included for comparison. The data in figure 5 are presented

for two different values of the parameter AE/Eg which is proportional

to space-charge density in the neighborhood of the ground plane.

Here aE is Eg - E] where Eg and E] are the calculated values [10]

of the unperturbed electric field strength at the ground plane

and one centimeter above the ground plane, respecti vely . The variable

AE/Eg then serves as a convenient measure of the contribution of

the space charge near the current sensor to the electric field (and

thus to the current density) at the surface of the sensor--rel ati ve

to the total electric field existing at that surface. In general,

the agreement between ac and dc results diminishes, however, as the

space-charge density is increased. This is clearly seen for the two cases shown in the figure.

In figure 6 the percent increase in ion current density for a selected current sensor for a wide range of values of AE/Eg is

indicated. The scatter in the data alluded to earlier is evident here.

Each point represents a current density increase calculated from data

such as that shown in figure 3 for different electrical operating

conditions. Each of these operating conditions is characteri zed by a known set of applied potentials, plate spacing, average current

density to the ground plate,' and a measured electric field at the

ground plate (fig. 1). This information is used to determine AE/Eg.

In general, for a given field, as the current density increases, tne

parameter AE/Eg increases.

10
60

Figure 5

Wilson Plate Elevation (d) Above Ground Plane (cm)

Percentage increase in current density as function of Wilson

plate (probe A) elevation and space-charge contribution to

electric field. o - AE/Eg = 0.004; x - AE/Eg = 0.024;

A - ac values.

11
Normalized Change In Electric Field (AE/Eg)

Figure 6. Percentage increase of current density as function of spacecharge density near the ground plane for probe A and a/d = 12.5

(see fig. 2). While there is much scatter in the data, an upward trend is evident.

12
3.3 Analysis of DC Results

An accurate theoretical description of the ion current intercepted by the model Wilson plates has not been developed because of

cost and time factors. It is worthwhile, however, to discuss

qualitatively the results observed for different values of AE/Eg.

If the contribution to the total electric field from the space charge

is very small, the electric field is nearly uniform, and the dc current

density data should agree with the 60-Hz results as the Wilson plate

is raised above the ground plane. That is, the ions will travel

along electric field lines and be collected by the sensing element;

the increase in the ion current as the height is increased will be

functionally the same as that for the number of field lines terminating

on the sensing element. Because the charge density is initially

small, the increase of the electric field (as the sensing element is

raised) at and near the sensing element due to the charge density

can be considered small and neglected.

When the space charge makes a large contribution to the electric

field, the change in electric field at the Wilson plate surface as the probe is elevated differs from the ac case. Qualitatively the data

in figure 5 suggest that the field strength increases at a faster

rate, as a function of probe elevation, than in the space-charge

free case because the now significant charge density is increased

due to the field perturbati on. This means that a more rapid increase

in measurement error should be observed for larger charge densities

and the figure 6 data confirm this expectation. Additional comparisons

between the dc and ac results are shown in figure 7. The solid

curves are identical with those of figure 4 and show the results of

the ac measurements series. The individual points plotted show the

results of the dc series of measurements using AE/Eg as a parameter.

Except for the case of the unguarded sensor, the dc data points for

AE/Eg < 0.004 lie very close to the corresponding ac curves;

however, that is not true for data points corre'spondi ng to larger

values of that parameter.

Reliable measurements of the polar charge density in the

vicinity of HVDC transmission lines are not yet available; however,

the results of two independent calculations are in hand [12,13].

These agree reasonably well with one another and predict values for

the parameter AE/Eg (scaled to a one-meter square Wilson plate

with aE being the field difference over a 10-cm distance) in the

range 0.002 to 0.006. On this basis it is concluded that the ac curves of figure 4 for guarded Wilson plates may be applicable to

measurements in the vicinity of HVDC transmission lines.

It should be noted that with the unguarded sensor, the dc data

points in figure 7 for all values of AE/Eg lie well below the

ac curve. The explanation for this is readily evident from a consideration of the field pattern shown in figure 8. Field lines

which terminate on the underside of the sensing plate contribute

13
Measurement

Error

(Percent)

0 10 20 30 40 50

Normalized Wilson Plate Dimension (a/d)

Figure 7. Errors in Wilson plate current density measurements as a function of guard ring width and elevation above the ground

plane. The solid curves are results of measurements with

alternating current. The AE/Eg parameter (see main text)

values for the dc data plotted are as follows: + - 0.004;

A - 0.014; V - 0.024; o - 0.004.

14
Figure 8. Schematic view of flux lines terminating on a sensor plate

located above the ground plane.

15
to the induced current (the ac case) but ions which traverse these

field lines (the dc case) are prevented from reaching the sensing

plate by the insulating support. If the resistivity of the

insulation is sufficiently high, presumably a charge will accumulate

on the surface of the insulation and distort the field. If the

resistivity is not so high as to permit significant charge

accumulation, the ion current associated with this fringing field

will divide between the sensing plate and the ground plane. In

either case the results for the unguarded plate with ac cannot be

expected to apply when the plate is used for measurement of ion

current. This same effect would of course apply to the guarded

sensors as well, but since most field lines which terminate on the

underside are near the edge, their effect will be negated by 'the

guard ring. If the unguarded sensor had been constructed entirely

of a conducting material, the ac and ion current measurements would

be expected to agree.

3.4 Location of Ground Plane

Even when care is taken to assure that the plane of the current

sensor very nearly coincides with the ground surface, a question

arises with respect to the location of the "effective" ground

plane. At first thought this might be expected to be a function

of the nature of the soil and of its water content. However, as the analysis given below indicates, only in exceptional situations,

e.g., if the sensor were to lie on solid rock, would there be

justification for differentiating between the surface of the ground

and the effective ground plane in measurements of the normal

component of current density at the ground level.

Consider the "true" ground plane to lie a distance, h, below

and parallel to the ground surface and assume that the soil between

the two planes is homogeneous. Then the ground surface becomes an equipotential surface which differs from "true" ground potential by

a voltage, Eh. A grounded Wilson-plate-type current sensor then

distorts the field at the ground surface--the extent of the distortion

being directly related to the potential difference between the Wilson

plate and the plane in which it lies.

The electric field strength in the soil is E = jp s where

j is the current density and p s the soil resistivity. Experimentally determined representati ve values of soil resistivity given

in an IEEE standard [14] range from a minimum of 3.4 to a maximum

of 4580 ohmmeters. If one assumes a uni form- current density of

10~6 A/m^ incident on a ground surface where the resistivity has

the approximate value, 4600 ohmmeters, the field in the soil is

0.00460 V/m. If the true ground plane is a meter below the ground

surface, the grounded Wilson plate differs in potential from the

surface on which it rests by 4.6 millivolts.

16 .
This seems to be a worst case and indicates that the resulting

field distortion is negligible, and the error introduced is likewise

negligible. Note that in the case of a Wilson plate off the ground

surface only 2 cm in' a field of 10 kV/m, the plate potential differs

from the space potential by 200 volts. For a guarded one meter Wilson

plate the error so introduced (from fig. 4) is about 4 percent.

4. MODELS FOR A WILSON PLATE NOT IN THE GROUND PLANE

As noted in the previous section, accurate model calculations

which predict the experimental results observed during the present

study cannot be readily performed. Two simplified models are developed

in this section, however, which qualitatively predict some of the

observed results.

4.1 Current Density Measurements: 60-Hz Electric Fields

An accurate theoretical treatment for the problem of induced

currents in the model Wilson plates has not been attempted. However,

an estimate of the expected error can be obtained from a consideration

of the field perturbation produced by an oblate spheroidal boss on the surface of a plane on which a uniform electric field is incident.

The enhancement of the field at the center of the surface of such a boss has been tabulated as a function of the ellipsoidal parameters

[15]. Figure 9 provides a comparison of the experimental results

obtained using the small Wilson plates with calculations for two

rather arbitrarily chosen spheroids used as approximations to the

actual geometry. The geometry of the boss relative to the Wilson

plate is shown in the figure. These results are considered

of value in that they provide order-of-magni tude confirmation that

the experimental results obtained are in agreement with those which

can be expected from theoretical considerations. A theoretical

model which provides an explanation of the trends observed in the

measurements is developed below.

A Wilson plate located in the ground plane is shown schematically

in figure 10(a) and is modeled approximately as a grounded conducting

sphere with an isolated sensing element shown in figure 10(b). The

sphere is located in the zero potential plane of a uniform 60-Hz

electric field produced with parallel plates that are infinitely far

away. Raising the Wilson plate above the ground plane is simulated

by elevating the sphere above the zero potential plane, z = 0. A

general expression for the electric field at the surface of a sphere

in a uniform field is given by [16]

E s = [($-Y)/a + 3E 0 cose] sin at, ( 1 )

where $ is the space potential at the center of the sphere prior

to the introduction of the sphere, V is the potential of the sphere,

17
Normalized Wilson Plate Dimension (a/d or 2a/ yS)

Figure 9. Comparison of experimental values with calculations for a prolate spheroidal boss. In the calculations presented, 8 = d

and two values of a were chosen: a = a/2, a' = 3a/4. For the

experimental results shown, the data are indicated as

A - a = 8.5 cm; o - a = 10 cm. Calculated curves shown as ....

18
(a)

Figure 10. (a) Representation of a guarded Wilson plate located in the

ground plane, (b) Schematic view of a spherical current sensor,

modeled in the text.

19 •
a is the sphere radius, E 0 is the peak value of the electric field,

8 is the polar angle in spherical coordinates, and sin wt

indicates the sinusoidal time dependence of the potentials and

field. For a grounded sphere located in the zero potential plane,

eq (1) reduces to

E = 3E 0 cos 0 sin u>t . (2)

As the sphere is raised above the zero potential plane, eq (1) becomes

E s = [$/a + 3E 0 cose] sin wt . (3)

When the sphere is raised, we assume that the equipotential surface

remains flat, but theoretically the surface will be distorted near the

sphere. Because the field is uniform, $ can be replaced with h E 0

where h is the distance above the ground plane. Equation (3) can

then be put into the form

E s = 3 E 0 (sin wt) [cos e + yh] (4)

where y = (l/3a). The factor in brackets in eq (4) describes how

the field at a point on the surface of the sensing element is enhanced

as the sphere, simulating the Wilson plate, is raised above the

ground plane.

Noting that the surface charge density on the sensing element

of the sphere is given by a = e 0E s , where z 0

is* the permittivity of

free space, it is possible to show [17] that the current induced in the

sensing element defined by the angle 9 0 (fig. 10(b)) is given as

a function of height by

I = 27Tcoa^e 0

E 0 (cos wt) [h( 1 -cos8Q )/a +. (3/2) sin 2e 0

] . (5)

Noting that the sensing area is given in spherical coordinates as

sin8 d9d$ = 27Ta 2

(1 -COS8

q

)

,

( 6 )

the current density, I/A, can be put into the form

20 .
J = J o [l+0(0o

)h] (7)

where J 0is the current density when h = 0

J

0

= (3/2)oj£0

Eqsin 2e 0 (cos o>t)/(l -cos0 Q

)

,

( 8 )

and B ( ©o ) is given by

B(0O) = 2 ( 1 -cos0 Q) / ( 3a sin 2

0 o

). (9)

The normalized rate of change of J as h is increased (i.e., as the

"Wilson plate" is raised above ground plane) is just

Equations (9) and (10) predict that a graph of normalized current density

(J/Jo) versus height above the ground plane (h) will (1) have a constant

slope for a given guard ring width (fixed 8 0 ), and (2) show a greater

slope (measurement error) if a Wilson plate with a smaller guard ring is

used above the ground plane (e.g., 3 (60° )>b

(

30° ) ) . Both predictions

have been observed experimentally (fig. 3) suggesting that the approximations

used in developing the model are not unreasonable. An expression analogous

to eq. (10) for the dc case with space charge could not be developed.

As a result of these studies it is concluded that, in general,

unguarded Wilson-plate-type current sensors should be used only

if the sensor plane can be made to coincide very closely with the

ground surface. More flexibility is available if the sensing plate

is guarded. Figure 4 can then be used in the design of a current

sensor as follows:

A decision as to the minimum elevation above the ground

plane and the maximum lateral plate dimensions which are practical determines the value of a/d. The guard ring

width required to reduce the error resulting from the non- zero value of d to a value considered acceptable can then

be estimated by interpolation between the curves given.

It is also noteworthy that under most conditions there need be

no concern over the question as to how far below the surface of the

21

1 dJ

( 10 )

5. CONCLUSIONS
ground the "true" ground surface lies. Finally, it was found that

data which predict the Wilson plate measurement errors of 60-Hz

displacement currents above the ground plane are also appropriate

for predicting measurement errors for conduction current under

HVDC transmission lines.

6. REFERENCES

[1] In the atmospheric electricity literature experiments are reported which appear to indicate that in turbulent air there

may be a significant vertical component of convection (or

"advection") current to sensors located in the ground plane. See

W. P. Aspi nail, "Mechanical -Transfer Currents of Atmospheric

Electricity, J. Geophys. Res. Vol . 77 (1 972), pp. 3196-3203.

For further discussion of this phenomenon, see Ref. 2.

[2] L. H. Dayaratna and W. C. A. Hutchinson, Atmospheric

Electrical Mechanical Transfer Currents to Plate Antennas

in Electrical Processes in Atmospheres (Proc. of 5th Int.

Conf. on Atmos. Elect.) Ed by H. Dolezalek and R. Reiter.

Pub. D. Steinkopff, Darmstadt, Germany (1977), pp 225-230.

[3] C. T. R. Wilson, On the Measurement of the Air-Earth Current

and on the Origin of Atmospheric Electricity, Proc. Camb.

Phil. Soc., Vol. 13 (1906), pp. 363-382.

[4] J. A. Chalmers, Atmospheric Electricity, Pergamon Press,

Oxford, Eng. (2nd ed. 1967), pp. 218-219.

[5] H. Israel, Atmospheric Electricity, (Translated from the

2nd German edition) U.S. Dept, of Commerce, Natl. Tech. Info.

Service, Springfield, Va. (1 973), Vol. 1*1, pp. 628-631 .

[6] T. D. Bracken, A. S. Capon, and D. V. Montgomery, Ground Level

Electric Fields and Ion Currents on the Cel ilo-Sylmar

±400 kV DC Intertie During Fair Weather, IEEE Trans.,

Vol. PAS-97 (1978), pp. 370-378.

[7] H. Israel, Loc. Cit., p. 485.

[8] H. Israel, Ibid, p. 479ff and p. 628ff.

[9] D. W. Deno, Calculating Electrostatic Effects of Overhead

Transmission Lines, IEEE. Trans., Vol. PAS-93 (1974), pp. 1458-1471.

[10]

M. Misakian, Generation and Measurement of DC Electric Fields

With Space Charge, J. Appl . Phys., Vol. 52, pp. 3135-3144, 1981 .

22
[ 11 ] Data obtained with parallel plate separations as small as 10 cm

are in agreement with the results shown in figure 3. This means

that perturbations of the surface charge distribution on the

top plate by the Wilson plate are negligible for our experimental

conditions.

[12] T. D. Bracken - private communication.

[13] Y. A. Morozov and B. G. Yakobson, Calculation of Electric

Field Intensity, Concentration of Aerial Ions and Ion Current

• Density on Overhead DC Power Lines in Problems of Electrical

Safety in the National Economy, All-Union Central Scientific

Research Institute of Work Safety, Moscow, 1973, U.S. Department of Energy Translation 21, p. 36.

[14] IEEE Std #142-1972, Recommended Practice for Grounding of

Industrial and Commercial Power Systems, p. 87.

[15] P. Moon and D. E. Spencer, Field Theory for Engineers,

D. van Nostrand Co. Inc., New York, N.Y., 1961, p. 287 ff.

[16] See Ref. 15, p. 225 ff.

[17] M. M-isakian, F. R. Kotter, and R. L. Kahler, Miniature ELF

Electric Field Probe, Rev. Sci . Instrum, Vol . 49, pp. 933-935,

1978.

23
NBS-114A Rrv. 2 -ac> U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions

)

1. PUBLICATION OR

REPORT NO.

MBS I R 81-2410

2. Performing Organ. Report No 3. Publication Date December 1981

4. TITLE AND SUBTITLE

Measurement of Ion Current Density at Ground Level in the Vicinity of High

Voltage DC Transmission Lines

5. AUTHOR(S)

R. H. McKnight, F. R. Kotter, M. Misakian

S. PERFORMING ORGANIZATION (If joint or other than NB$, see instructions;

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8 . Type of Report & Period Covere

9.

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

Department of Energy

Office of Electric Energy Systems

12th Street & Pennsylvania Ave., N.W.

Washington, D.C. 20461

10.

SUPPLEMENTARY NOTES

J

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

11.

ABSTRACT (A 200-word or less factual summary of most s i gn i fi can t in formation. If document includes a si gnificant

bi bliography or literature survey , mention it here)

Sensors for measuring vertical current density at

ground level near high voltage dc (HVDC) transmission lines

are subject to error when the sensor is not in the ground plane.

The magnitude of this error, for guarded and unguarded sensors,

has been investigated using both dc electric fields with space

charge and ac electric fields in a parallel plate facility. For

conditions like those expected under HVDC transmission lines,

the results obtained using ac and dc methods agreed to within

experimental uncertainty. The measured errors are as large as 25 percent for guarded sensors and significantly larger for

unguarded sensors. Data for various sensor elevations and

guarding are presented in graphs to aid the designer.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) high voltage dc; measurement errors; transmission lines;

vertical current density; Wilson plates.

13. AVAILABILITY

[X]Unl i mi tea ECU For Official Distribution. Do Not Release to NTIS

' Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

[Xj Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGE)

27

15. Price

$7.50

USCOMM-DC 6043-F