power frequency magnetic fields might affect biological systems, power engineers have been trying to find transmission line geometries that will reduce fields.
1430
IEEE Transactions on Power Delivery, Vol. 8, No. 3, July 1993 THE PERFORMANCE OF REDUCED MAGNETIC FIELD POWER LINES
THEORY AND MEASUIWENTS ON AN OPERATING LINE R.G. Olsen, Senior Member IEEE D.C. James School of Electrical Engineering & Computer Science Washington State University Pullman WA 99164-2752
Abstract - Because of the recent concerns that power frequency magnetic fields might affect biological systems, power engineers have been trying to find transmission line geometries that will reduce fields. One of the reduced field geometries that has been in existence for many years is the so-called double circuit, low reactance line. Such a line if balanced (i.e. positive sequence currents) can have fields that are a factor of three lower than a single circuit line on the right-of-way Off the right-of-way much greater reduction is achieved because the field attenuates much faster. However, it has been found through analytical studies that magnetic fields are very sensitive to small deviations from positive sequence currents due to load unbalance; therefore the field reduction is not as great as predicted for a balanced line, especially off the right-of-way. This paper reports the results of a measurement and a theoretical program to study the magnetic field performance of a double circuit 230-kV line with only one circuit energized and with both circuits paralleled in a low reactance configuration. As expected, the measurements show that the reduced field line is more sensitive to deviations from balanced currents.
V.L. Chartier, Fellow IEEE Bonneville Power Administration Division of Laboratories PO Box 491 Vancouver WA 98666 phased as a "low reactance" single circuit line shown in Fig. 1. Off the right-of-way much greater reduction is possible if the line is perfectly balanced because the magnetic field decays as the inverse of the distance cubed rather than the inverse of the distance squared which is the case for the conventional single circuit line. Unfortunately, it has been found through analytical studies that the magnetic fields from these reduced field lines are very sensitive to current balance if a portion of the return current flows in the earth (i.e. the system is grounded) [61. As a result, the performance predicted under balanced current conditions may be degraded under operating conditions. This is a serious limitation because the operating conditions are not under the control of the transmission line designer. The purpose of this paper is to examine the influence of small current fluctuations due to load balance changes on the performance of a reduced magnetic field 230-kV transmission line. The fluctuations referred to here are to be distinguished from the gross changes which occur in average load currents as the total system load changes. Computer models and measurements were used to evaluate the magnetic field performance of the operating line.
Keywords: Magnetic fields, EMF, ELF fields, Power line fields. 1.0 INTRODUCTION
Power frequency magnetic fields generated by overhead power lines have been of current interest because of concerns they might affect biological In response, research programs to systems [l]. characterize these fields and to investigate the possible relation between them and health effects are being conducted [21. A lot of work has also been conducted in recent years to develop instrumentation to measure power system magnetic fields; to improve the analytical models for predicting these fields; and to find transmission lines with reduced fields. Most of the theoretical models assume that power line currents are positive sequence (i.e. equal phase current magnitude and phase angles separated by 120') which has been found to be adequate for most single circuit transmission lines. However, certain line geometries have been proposed to reduce magnetic fields [3,4,51. One line geometry that has been in existence for over 30 years that can reduce magnetic fields by a factor of three on the right-of-way is the so-called double circuit, low reactance line if it is
92 SM 458-0 PWRD A paper recommended and approved by the IEEE Transmission and Distribution Committee of the IEEE Power Engineering Society for presentation at the IEEE/PES 1992 Summer Meeting, Seattle, WA, July 12-16,1992. Manuscript submitted August 29, 1991; made available for printing June 22, 1992
\\\\\I 1 , \ , \ \ \ \ \ \ \ \ \ \ \
;;} c cr
Electrical Ph8Slng Connections
?,?!
\ \ \ \ \ \ \ \ \ \ \ \ ~
Figure 9 lhre. Phe.0 Low R.ai~tance Connfigurmtion
Fig. 1
Double Circuit Geometry Phased and Operated as a Single Circuit Low Reactance Line
The definitions in this paper are chosen to be consistent with those used in the EPRI pilot study of residential power frequency magnetic field 171. Specifically, the vector sum of all currents on power line conductors (including the neutral wire if any) is defined as the "net current". The "return current" is defined as all current which travels in conductors at "ground potential". Thus, it includes the portion of the net current that flows in the neutral wire or grounded shield wires (if any) plus the ground current of a grounded system. If the net current is zero there is no earth return current. One special case of "zero net current" is that of balanced (i.e. positive sequence) currents on the phase conductors and zero currents on the neutral and shield wires.
0885-8977/93$03.000 1992 IEEE
143 1 2.0
THEORY OF OVERHEAD POWER LINE MAGNETIC FIELDS
A is the free space wavelength ( A = 3x108/f meters) [8,91. Note that (2-1) and ( 2 - 2 ) consist of a first
2.1
THE LOW FREQUENCY MAGNETIC FIELD OF AN ARRAY OF HORIZONTAL CONDUCTORS ABOVE EARTH
term that expresses the direct contribution from current in the conductor while the second term accounts for its image counterpart. The image is located at a "complex depth" which is proportional to the skin depth of the earth. The total magnetic field of n parallel conductors is simply the superposition of the fields from n conductors. N
The calculations of the magnetic fields of infinitely long horizontal conductors above a homogeneous earth has been the subject of considerable study [8,91. A useful approximation to the RMS fields of a conductor which carries power system frequency current is [ l o l l :
C
Bxn= -2 In
[T
(y+d +a) -
(2-11
(mG) A]
N
RTn
cn
(2-4)
Bxn n=l
~x =
(y-dn)
B
=I B
(2-5)
yn
n=1 2.2 POWER SERIES REPRESENTATION FOR THE LOW FREQUENCY MAGNETIC FIELDS OF AN ARRAY OF HORIZONTAL CONDUCTORS ABOVE EARTH (2-3)
Bzn = 0
In is the RMS phasor current in the nth conductor in amperes, (hn,dn) and (x,y) are the locations of the nth conductor and the field point respectively in meters
where
a = 6 = 503(pg/f)0'5
To gain insight into schemes for minimizing the magnetic fields from N phase conductors, it is useful to reconfigure (2-1) and (2-2) by using simplifying assumptions along with a Taylor series expansion. If typical values for earth resistivity (10-1000 S2.m) and power system frequency (60 Hz) are considered, it can be shown that the earth's skin depth ranges from 200 to 200Om. Since the depth of the image current in (2-1) and (2-2) is roughly equal to fi times the skin depth, the relative magnitude of the image current .contribution to the magnetic field is far less than the contribution from the current in the conductor for field points located within a typical right-of-way. Thus, in the right of way, i t is not unreasonable to neglect the image current contribution to the magnetic field. Further, the first terms in equations (2-1) and (2-2)can expanded in a Taylor series with y=O. If it is assumed that:
(meters) dn = da
6
is the skin depth of the earth where p
g
+
6n
is the g
earth resistivity in Q*meters and f is the power system frequency in Hertz. The geometry of the problem is illustrated in Figure 2.
where d is the average height of the conductors, that a
and that Ra>> (6,(, (hnl,then the dominant terms of the series expansions for (2-4)and (2-5) are: 2sin(+1 Bx(x,y) =
~
Ra
- -sin(2g)
c
2(1 + 2 sin2[$)IN
In
n=l
6,I,
+
Ra2
n=l
Ra
Definition
of
CinlA
Geometric
Variables
fc
MnA-1
Equations (2-1) and (2-2) are valid for field points above the earth's surface and whose distance away from the conductors (R ) is less than A/20 where cn
sin(2$)
+~
'a2
+ etc.
n=l
' a 2
M-nnntir
(2-6)
N hnIn + terms proportional to (l/Ff;)
Fig. 2
(mG)
c
n=l
2-7 1
6,1~ + terms proportional to (1ma3 + etc.
n=l
where sin(+) = d /Ra and c o s ( + ) = x m a
1432 Note that the first and second/third terms of each series are of order 1/R and 1/R2 respectively. 2.3 REDUCED MAGNETIC FIELD CONFIGURATIONS to reduce the magnetic field In order contribution from the array of conductors, consider the case where the first three terms of the Taylor series expansions (2-6) and (2-7) are set equal to zero:
may not be satisfied and this may have a significant influence on the magnetic field. This topology (referred to here as Type I) has magnetic fields which may decay as slowly as 1/R . It should be noted that a
most transmission lines in the United States are A history of the connected with type I topology. reasons for this is given in [111.
I.
N
1In= 0
(2-8)
n=1 N
1hnIn= 0
(2-9)
n=l N
16,I,=
0
(2-10)
n=1
Fig. 3
Common Three Phase Line Terminations
Clearly, the first term (i.e. the l/Ra term) can
Also, note that the 1/Ra2 terms (i.e. the second
be forced to zero by requiring that no net current flow in the conductor array. This condition can be forced by using an ungrounded system topology as shown in section 2.4. Under this condition the magnetic fields decay at least as fast as 1/Ra2. To reduce the
and third terms of (2-6)and (2-7)) are forced to zero by assuming that current splits equally in paralleled phase conductors. As will be shown later, this is not always a valid assumption but is used here to gain insight to the importance of net current on the performance of six conductor single circuit power lines phased for low reactance. The effect of unbalance and unequal current splitting on the performance of reduced magnetic field power lines (e.g. low reactance lines), raises two basic questions: 1) How does a grounded (Type I) system's performance compare to that of an ungrounded (Type 11) system under normal operating conditions? 2) If current does not split equally in paralleled phase conductors, what effect does that have on the These questions contribution from the 1/Ra2 term?
magnetic field further requires that certain geometric and current constraints be observed in addition to the no net current condition. Mathematically, these additional constraints are given by equations (2-9) and (2-10). Some examples of three phase power lines which satisfy the geometric constraints are discussed in [61. One of these is a double circuit power line operated as a single circuit line and phased for "low reactance". This line is illustrated in Figure 1. In order to cancel the l/Ra terms of the field, the current in the two conductors which comprise each phase must split equally. The actual splitting is determined by the line impedances and may not be equal. If it2is not, the cancellation is not complete and the l/Ra terms remain. When the currents are balanced and split equally in paralleled phase conductors, the geometry satisfies (2-9) an$ (2-10) and the fields decay at least as fast as l/Ra . This property along with field cancellation creates what is being called a "reduced magnetic field" line and is of great interest at the present time. 2.4
EFFECTS OF NON-ZERO NET CURRENT AND UNEQUAL CURRENT SPLITTING ON THREE CONDUCTOR AND SIX CONDUCTOR LOW REACTANCE SINGLE CIRCUIT CONFIGURATIONS
According to the definition used here and in reference [71, balanced conditions exist when (2-8) holds. One of the factors which affects whether or not unbalanced loading will result in return current is system topology. Three common line terminations (grounded wye, open wye and delta) are shown in Figure 3. The topology of the second and third of these (i.e. Type 11) forces equation (2-8) to be satisfied even in the presence of non-symmetric line configurations and loads. As shown in the last section, Type I1 topology causes the magnetic fields to decay at least as fast as l/Ra2 without regard to the relative amplitudes and phase angles of the In individual phase currents or the line geometry. the first topology (i.e. grounded wye), however, (2-8)
will now be answered by computer simulation. The first configuration considered is the three conductor "North Circuit" which consists of the three "north" conductors shown in Figure 5 of section 4.1. The other three conductors were grounded at a single point. Under zero net current conditions (which is ensured for type I1 grounding) the magnetic field according to (2-6) decays at least as fast as 1/R: and (2-7). However, in a Type I (grounded wye) system, net current can flow and the l/Ra term of equation (2-6) and (2-7) contributes to the magnetic field. The second configuration considered is the low reactance line which consists of all six conductors shown in Figure 5 with the assumption that the current splits equally in paralleled phase conductors. In a Type I1 system, the magnetic field will decay at least as fast as 1/R '. However, if the low reactance line is a grounded system (Type I, grounded wye), then net current can flow and the l/Ra term will contribute to the field. The third configuration considered is the same low reactance line with currents that do not necessarily split equally in paralleled phase conductors. For the zero net current condition the 1/Ra2 term will contribute to the magnetic field but the l/Ra will to flow.
not
because net current is not allowed
For the grounded wye system both the l/Ra
and 1/Ra2 terms will contribute to the magnetic field.
1433 Configurations one, two, and three as described above are summarized in Table I. Cases 1, 4. 7, represent the "balanced" case defined as the condition where line current is only "positive sequence" (i.e. equal current amplitudes with 120' phase spacing). Clearly, equation (2-8) is satisfied (i.e. net current equal to zero) in this case for both grounded and ungrounded systems. Although Table I summarizes which lower order terms will contribute to the magnetic field, it does not provide a means to quantify the magnitude of those contributions. One way to do this is through use of computer simulation (MAGFLDI as discussed in section 3. It should be emphasized that this program uses the exact equations ( 2 . 1 ) and (2.2) rather than (2.6) and (2.7). In order to use the program, it is necessary to define conductor geometries, line. currents, system topology (i. e. grounded or ungrounded systems) and locations where the magnetic field is to be calculated. For this exercise, the conductor geometries are shown in section 4.1, Figure 5 and Unbalanced phase currents will be set to 1000A. loading as described in section 3 will be Type Ground Case CKT. 1
Single
2
"
3
"
4
L.R.
5
It
6
I'
7
L.R.
8
9
Table I
"
Equal
1
(L5-L95)/L50
(XI
(L=-POS SEQ)/WS SEQ
case
O m
60m
2 3
3.63 17.98
3. 8 18. 0
-0.063 0.549
-0.04 0.56
5
8.80 9.31
33.59 144.97
-0.006 1.634
2.11 131.13
3.79 11.41
3.69 142.25
-0.236 1.590
-19.01 149.36
6 8
9
Om
(XI
60 m
Order of
Currents
System
I or I1
Pos. Seq.
N/A
I1 I
Zero Net
N/A
Non-Zero Net
N/A
I or I1 Pos. Seq. I1 Zero Net I Non-Zero Net
Y Y
I or I1 I1 .
E
I
Pos. Seq. Zero Net Non-Zero Net
Y
1:
Y Y Y -
Effects of Current Unbalance and Unequal Current Split on the Performance of Conventional and Reduced Magnetic Field Configurations
simulated with random current amplitoude fluctuations of 2 2% and phase fluctuations of 2 2 . When assumed, unequal current splitting between paralleled phase conductors will be simulated by using 510A for North facing and 490A for South facing conductors. Two measures of the effect of current fluctuations are calculated. The first, (L5-L95)/L50, is a measure of the variation in magnetic field as the curroent is randomly varied within the 22% amplitude, 22 phase limits. Lx is the value exceeded by x% of the magnetic field probability distribution. The second, (L50-POS SEQ)/POS SEQ is a measure of how much the average field under random fluctuation currents differs from the value for the magnetic field if the current is purely "positive sequence". "POS SEQ" is the value of magnetic field for a positive sequence current. Table I1 shows results from the MAGFLD program as calculated for distances of 0 and 60m extending North from the power line (section 4.1, Figure 5). Since the positive sequence current case is used as a basis for comparison, cases 1, 4, and 7 are not studied here. Several things are clear from Table 11. First, the magnetic fields of ungrounded system topologies (cases 2, 5, and 8 ) are not as sensitive to current
(3-11
where ; I n \
L en
is the nominal current in the nth
conductor and Ain, A$n random
variables.
are zero mean Ain
and
A@n
independent
have
uniform
probability densities with maximum values specified by the user. For this paper, MAGFLD as described in [121 was modified to predict the "resultant" field (i.e. the square root of the sum of the squares of the rectangular components as defined in section 7.1). This was done because the measured field is also a "resultant" field. 4.0
MEASUREMENT OF MAGNETIC FIELDS FROM A THREE CONDUCTOR SINGLE CIRCUIT AND FROM A SIX CONDUCTOR 'LOWREACTANCE SINGLE CIRCUIT TRANSMISSION LINE
As shown in section 2.3, one scheme for reducing magnetic fields from overhead power lines is to use a double circuit line phased as a single circuit low reactance line. In the balanced case with equal current .splitting, theory showed that the magnetic field for the low reactance line would drop off as l/Ra3, compared , ..to 1/Ra2 for conventional three conductor configurations. However, the l/Ra3 performance is degraded under normal operating conditions when unbalanced loading on a grounded wye system results in net current. These results cause 1 ) Given a several basic questions to be raised:
1434 grounded wye low reactance wire configuration, what is the relationship between currents and magnetic fields 2 ) Do low under actual operating conditions? reactance lines produce significantly lower magnetic fields than conventional three wire geometries? 3) Does the computer model (MAGFLD) accurately describe the actual field levels under unbalanced conditions when the net current is non-zero? In order to address these questions, an experiment was devised to measure magnetic fields and phase currents from both a conventional three conductor single circuit line and a six conductor low reactance single circuit line which are in a grounded wye system. An overview of the experiment and a description of the instrumentation used to measure line current and magnetic field is given in this section.
r4'
ERM Mapnmtio Flold Probn
4.1 DESCRIPTION OF THE TEST SITE T 3 2 m (247
In order to directly measure the effects of current unbalance, a 230 kV double circuit transmission line connected on both ends to grounded wye transformers was instrumented with devices specifically designed to measure low frequency magnetic fields and line sensors to measure conductor current. The site was located in Renton, Washington near the corner of S . Grady Way and Shattuck. The elevated profile view of Figure 4 shows the transmission line oriented in a East-West direction Darallelinn S . Gradv ~- Wav.
-
~mm~m cny L I ~ M
WL) lhnmmlmmlonCorridor
a
I NI
,jll
11/11
SCL Soah Rmnlon-SouthSub 2 5 0 h
a
S C L Eolhml No.1 250kv S C L Bolhml No2 250kv
0
Ill
Fig. 4 Elevated Profile View of Renton, WA Test Site This particular line [Talbot Hill-O'brien) was originally constructed as a 230 kV double circuit with three conductors facing North and three facing South as shown in Figure 5. Although the South facing conductors are in place, the South circuit was never completed and was, therefore, not energized. Measurements were made on two transmission line conductor configurations during two periods. From February 23 to March 4, 1991, the line was operated with only the three North facing conductors energized. This testing period will be referred to as "North Circuit". From March 4 to March 13, 1991, the line was reconfigured as a single circuit low reactance line. In this configuration, all six conductors were energized. This testing period will be referred to as "low reactance" AS shown i n Figure 5, current probes are located on all three North facing conductors and the bottom South facing conductor while magnetic field probes are located along the x-axis at 0 , 7.32 (24.1, 15.24 (50'1, 28.35 (93'1, 47.85 (157'). and 67.06 [220')m (ft).
4.2 INSTRUMENTATION Recording equipment used at the Renton test site consisted of two separate systems: NITECH Plus 1 Line Monitoring and ERM Magnetic Field Wave Capture.
W . W m (220')
Fig. 5
Cross Section Geometry for Renton, WA, Test Site The NITECH system consists of donut sensors (power donuts) and a ground station recorder (data logger) [141. Each donut sensor clamps directly onto a given conductor and measures line current, voltage, and temperature. This information is transmitted via an FM signal to the NITECH ground station and magnetically recorded with a portable IBM PC. For the Renton experiment, the NITECH system was configured to record line currents at five minute intervals. Recorded data consisted of line current amplitudes sampled once every 10 seconds then averaged over five minute intervals. These time averaged data were then magnetically recorded with a portable IBM PC. The magnetic field wave capture system was designed by ERM, Inc. for EPRI [151. The system is designed to measure magnetic fields from 0.01 mG to 1000 mG over a frequency range from 60 to 780 Hz. It consists of up to 30 magnetic field probes and an industrial grade IBM PC AT to retrieve and process the data. Each probe contains three coils. Each coil measures the magnetic field in a given direction. The coils are orientated in a Cartesian [x,y,z)reference frame and measure time varying magnetic fields via the voltage induced in the coils by those fields. In each data retrieval cycle magnetic field waveshapes were digitized, recorded and processed. Simultaneously, current samples from the NITECH system were recorded to identify the instantaneous current at the time of magnetic field recording. This retrieval process occurred in less than 500 ms and was repeated regularly at five minute intervals. As can be seen, two sets of measured current data were recorded. Both sets were analyzed and found to be the same. Resident software for the ERM system allows the user to record a variety of information about the magnetic field such as: time histories, histograms, true RMS, and a fast fourier analysis provides magnetic field frequency spectra. For purposes of this report, the ERM system was configured to extract the RMS value of the 60 Hz field component and did so for three spatial fields at the six probe locations. 5.0 STUDY OF BACKGROUND MAGNETIC FIELDS In an ideal test site, the electrical source under study (i.e. the primary source) would be located great distances away from other low frequency electrical sources in order to minimize the corruptive effect that these additional sources have on the magnetic field. Unfortunately, it is not always possible to choose such an ideal site. In these cases, it is necessary to characterize the "background fields" from these "other sources". In selecting a suitable test site for this work, it was necessary to find a power line with a double
1435 circuit geometry that could be reconfigured as a single circuit low reactance line. In addition, the computer equipment used to process and store the data required a distribution service drop (i.e. 120 or 240 AC source). These constraints made it difficult to choose an isolated test site located away from other electrical sources. The chosen test site proved to be a reasonable compromise between satisfying experimental constraints and minimizing background field. In selecting the exact site, care was taken to position the ERM probes as far as possible from other overhead power lines and from known buried sources. After testing of the North circuit was completed (March 4, 19911, the line was de-energized while line crews reconfigured the line as a low reactance line. During this time (approximately 5 hours), the ERM system continued to measure magnetic field while the primary source was de-energized. These measurements are used to characterize the background magnetic,field at the site. Figure 6 shows ERM magnetic field data from each of the six probes during the de-energized period. RENTON ELF MF TEST SITU LINE DEAD RESULTANTBACKGROUND MAGNETIC FIELD
2% 21
1
E,
I
Unfortunately, the background data shown in Table 111 cannot be subtracted from the line data since phase was not measured and the background field was not constant. 6.0 CURRENT MEASUREMENTS
Since there is a casual relationship between current and magnetic field as shown in section 2.0, it is important to accurately characterize the currents responsible for measured magnetic fields. Therefore, the intent of this section is to analyze the measured current in order to extract information necessary for the computer simulation and then compare the predicted and measured magnetic fields. 6.1 Time Variation of Currents As explained in section 4.2, current data were measured by four donut sensors and recorded at five minute intervals. Consider the "instantaneous" current data (i.e. samples of the current amplitude at five minute intervals) as recorded on February 23, 1991 by the ERM system and shown in Figure 7 as a "current time history". RENTON ELF MF TEST SITUN. CKT ONLY PHASE CURREM MAGNWJDE
MARCH 4,1991
1.81.6-
FE823 1901
1.4-
P
121-
0 80 60.4-
DISTANCESIN METERS
'
0
Fig. 7
average values
I
ERM Probe Di;t.mce
0.0
B
Y
0.23
0.32
7.32
1.49
15.24
0.51
I
BZ
BPes
(mG1 0.44
0.49
0.29
1.60
1.54
0.22
1.64
28.35
0.10
1.04
0.19
1.06
47.85
0.06
0.89
0.16
0.90
67.06
0.07
0.81
0.19
0.84
Table 111 Background Magnetic Field as Measured With Talbot Hill-O'Brien 230 kV De-energized
I
& ' &
'E&
'1&"12bO'li00'1600 TIME (HRS)
le00 2mo PM, z4m
Phase Current Amplitude as Recorded by the ERM System During North Circuit Testing
Note that the line current's variation can be separated into two parts. First, the gross changes of each phase current roughly tracks the hourly load changes in approximately the same manner. Secondly, random short term load fluctuations account for the jaggedness of the curves and the short term changes in the differences between phase currents in Figure 7. These differences are a few percent of the total current. It is these random variations that are of interest here because they represent changes in the current balance state of groundea systems. In the next section, they will be isolated from the gross current variations due to predictable load changes. 6.2
0.17
'2h'
Using Average Phase Current as a Normalization Factor
The amplitude of each 60 Hertz current in Figure 7 can be written as:
I s(t) is the slower but larger variation which n
Line
has the same shape for each current (i.e. the larger variations are coherent) but possibly a different amplitude. On the other hand, fn(t) represents the faster but smaller random fluctuations which result from short term changes in the load balance. These
1436 are different for each conductor and are assumed to have zero mean. The magnetic field will show a similar behavior as illustrated in equation (6-2).
Where G is the (primarily) geometric conversion factor between current and magnetic field which can be determined from (2-1) and (2-2). The sliding short term average of the nth phase current in (6-1) is
In avg(t)
= Ins(t)
(6-3)
due to hourly load changes and short term fluctuations while the "South Bottom" sensor was used in the low reactance testing to determine whether or not that phase current split equally between the electrically parallel North Top and South Bottom conductors. Consider first the current fluctuation computed for the North circuit. Figure 8 shows the cumulative distributions derived from conductor current data that was recorded from February 23 to February 25, 1991. Though the North circuit testing encompassed a larger number of days, the cumulative distribution function does not change even if a larger sample set is considered (i.e the current fluctuations are relatively stable). RENTON ELF MF TEST SITE/ N Cm ONLY CURRENTAWUWDE FLUCTUATION
where the sliding average is defined as e5
21
t +T (6-4)
In(t)dt
75 70
q
\
55
t-T In (6-41, T is chosen to be large enough that each fn(t) averages to zero and small enough that s(t) is essentially unaffected by the averaging. average of these time averaged phase currents is
The
-A
(6-5) Fig. 8 If (6-5) is used to normalize the magnetic field in (6-21, the result is
1 - CIn N n=1
1
- C I n
(6-6)
N
n=1
6.3
Amplitude Distribution Fluctuations
of
Phase
Current
At this point it is necessary to define the term "current fluctuation". Current fluctuation is a measure of how a phase conductor's current magnitude deviates from the average current as defined in (6-5). For purposes of this paper, current fluctuation will be quantified by equation (6-7) which yields percentile difference with respect to average current.
Now consider current measurements taken at the Renton, WA test site. Since the test site was used to measure magnetic fields from configurations that energized first three then six conductors, a total of four NITECH power donuts were used to measure conductor current. No more than four were used because only four were available. The location of the donuts is shown in Figure 4 of section 4.1. The North sensors were used to measure changing phase currents
Phase Current Fluctuation as Computed from Measured Average Currents During North Circuit Testing
Percent fluctuation from (6-7) is shown on the x axis while the y axis denotes percent exceeded. To explain this figure, consider the curve labelled "N. Bottom" (North Bottom). Looking at the curve from left to right, note that 95% of the current data exceeds a level of about -3.7% while only 5% of the data exceeds -0.9%. Also, note that the median value is located at 50% exceeded. Basically this means that 50% of the data exceeded the - 2.5% level and 50% did This is the median o r L50 value. The North Bottom conductor's practical minimum (L95 corresponds
e.
to -3.7% The first term of (6-6)is now independent of time and the only changes in this normalized magnetic field come from the small current fluctuations.
I
-3
and the practical maximum (L
corresponds
to a level of -0.9%. In viewing Figure 8, note that each conductor's median (Ls0) is different but that the range between the L5 and Lg5 levels is approximately the same 4%). The significance of these findings will be discussed later. Consider, next, the current fluctuation distribution for the low reactance testing as shown in Figure 9. In this case, four curves that correspond to the four NITECH power donuts are plotted. Current data used to construct Figure 9 was recorded from March 8 to March 10, 1991. Again, the distributions do not change if a larger data set is used. The most interesting feature of this graph is that current in the parallel connection of the S. Bottom and N. Top conductors did not split equally. Two questions can be asked about the data First, are the presented in Figures 8 and 9. differences in the phase current data real or can they be explained by experimental error in the NITECH system? Second, is the non equal split of the current between the two paralleled conductors real or again the result of experimental error? The best answer to the first question is that recent calibration of the NITECH donuts at the Bonneville Power Administration indicates their
1437 RENTON ELF MF TEST SITE' LOW REACTANCE CURRENl AMPLITUDE FLXTUATION
7.0 MAGNETIC FIELD MEASUREMENTS 7.1
Normalized Magnetic Field Measurements
As stated previously in section 4.2. the Renton site was instrumented with a total of six ERM probes located along a horizontal profile from the centerline (Om) extending North to 67.08m. Data from the three orthogonally oriented coils (x,y,z) in each probe was used to calculate a resultant magnetic field as defined in (7-1). r
,112
Phase Current Fluctuation as Computed from Average Currents During Low Reactance Testing accuracy to be better than 1%. The differences between the median levels of the curves in Figures 8 and 9 exceed 1% and thus appear to be real differences. The second question can be answered in the same way. Thus it appears that conductor current deviations from the average current are non-zero mean and vary over a range (L -L ) of about 4%. Fig. 9
95
6.4
5
Extraction of Nominal Currents to Use in the Computer Simulation
The magnetic field data to which predictions will be compared have been normalized as in (6-6) and referred to 1000A. Thus the average of the phase currents used in the MAGFLD simulation of the fields must also be 1000A. The particular nominal values of the individual phase current amplitudes to be used in MAGFLD can then be determined from the L50 values in Figures 8 and 9. Specifically, the North circuit phase currents are respectively 0.9%, 1.6%, and -2.5% above 1000A. This results in nominal current magnitudes of 1009 A for the N. Top, 1016 A for the N. Mid, and 975 A for the S. Bottom conductor. These currwts are defined as nominal currents (i.e. In of sections 2.1 and 3.0) for use in MAGFLD. In the absence of phay infopation, the nominal phases are chosen to be 0 , -120 , and 120' respectively. A similar exercise can be carried out for the low reactance case. Around its nominal value, the conductor current has random fluctuations caused by unpredictable variations in system load balance. Note, for example, that each curve for the North circuit in Figure 8 can be almost linearly approximated.between its L and L5 95 level. This corresponds to a uniformly distributed probability density function for the current. This is identical to probability density function that MAGFLD uses to choose random sets of unbalanced current. In MAGFLD, this random variation component is defined as plus or minus percentage variation. For example, a conductor whose nominal current is lOOA but whose L and L values correspond 95
to 98 and 102, respectively, could be simulated using a f 2% current magnitude variation. Current data from Figures 8 and 9 reveals that average current fluctuation is approximately _C 2%. This is the value used in the simulation. The value chosen for phase deviation will be discussed in section 7.1.
In order to remove the dependence on predictable load variation (i.e.variation in time due to changing demand), the time varying resultant magnetic field was normalized by the average phase current as in equation (6-61, section 6.2. The variation in the normalized field (B:zfm(x,y,t)) is primarily due to load balance changes. This is evident in Figure 10 which shows the normalized measured magnetic field from the low reactance circuit during March 8, 1991. Note that the field generally decreases as the radial distance increases (i.e. where the 0 meter probe is at centerline) and that aside from random fluctuations the normalized field of each probe is roughly constant over the 24 hour period. The only exception to this is RENTON ELF MF TEST SnVLOW REACTANCE NORMALED MAGNmC FIELD 30,
20-
"
MARCH 8.1991
x)
Fig. 10
Normalized Magnetic Field Data from Low Reactance Testing the field at 7.3m. This is due to the buried source of background field which was discussed in section 5.0. Note, for example, that the 7.3 meter field is the only field which does not follow the time history of the others. This is good evidence of a different field source. Figure 11 shows the normalized measured North circuit magnetic field recorded during February 23, 1991. The most notable feature of these data is that the 7.3 meter field is greater than the 0 meter field. This is due to the background field of the buried source. Since the normalized field is not truly constant but varies somewhat with time, statistical analysis can be called upon to quantify means and exceedance levels associated with each probe location. Again the Lg5. L50, and L notation will be used to distinguish practical minimum, median and practical maximum, respectively. The statistics from the normalized data
1438 magnitude random fluctuation (6-81 of f 2% was derived from Figure 8 and the random phase angle fluctuation was chosen to be t 2O. The justification for using a random current fluctuation of f 2% was explicitly stated in section 6.4, however, since statistics regarding 5elative phase angle were not available, the use of 2 2 phase variation needs further explanation. It was selected because it yielded the best match between the range of measured values (Lzeas) ? : L and the predicted range of values (Lred- Liied). It
FEBRUARY 23.1991
w-
DISTANCES IN METERS
I
15.2
-I
30-
-
284
--X I
47.8
10-
87.1
.....- ,. ..._, Fig. 11
Normalized Magnetic Field Data from North Circuit Testing can then be directly compared to the computer simulation from MAGFLD. 7.2
Comparison of Measured and Predicted Magnetic Fields Using nominal currents as described in section
6 . 4 , MAGFLD can be used to calculate magnetic fields
along the horizontal profile for the Renton experiment as described in section 4.1. The simulation results and normalized measured magnetic field statistics associated with the North circuit are shown in Figure 12. RENTON ELF MF SIMULATION/ N. CKl ONLY MONTE CARLO ANALYSIS +I- W,?DEO) ERYMTA
E
1,, 35
,
o , , , , , , , , , , , , , , , , , , , , , , , , ,
,
,
,
10 5
410
-5
5
10 15 20.25 30 35 40 45 50 % 60 SS 70 DISTANCE FROM CENTERLINE (METERS)
SIMUUTON
-
Fig. 12
NOMINAL
- l.95
-
W
..... I5
Predicted and Measured Magnetic Fields for the North Circuit
The measured magnetic fields are plotted as a vertical line which extends from the practical minimum (L951 to the practical maximum (L5) values. The horizontal dash on this level signifies the median (Ls0) value. These data points correspond to probe locations of 0, 7.32 (24'1, 15.25 (50'1, 28.36 (93'1, 47.85 (157'1, and 67.08 (220')m (ftl. The curves from the computer simulation can be described as follows. The solid curve labelled "nominal" is calculated from the nominal currents as derived from Table I V and normalized to an average current of l O O O A per phase. The other three curves represent simulation results from MAGFLD's Monte Carlo analysis. The Lg5. L50 and L
curves mark the practical minimum the practical
maximum and the median respectively. These curves were generated by allowing phase currents to deviate in a random manner from nominal currents. The current
will be shown later that the Sois also appropriate for the low reactance case. There is general agreement between measured and predicted mean levels and ranges for the North circuit except for the measurement at 7.3m. As discussed in sections 5.0 and 7.1, there is good reason to believe that this discrepancy is primarily caused by a buried conductor near this probe. Further support for this statement will be given in section 7.3. Equivalent results for the low reactance circuit are shown in Figure 13. In this case the measured and predicted values do not have the same degree of agreement as did the North circuit data. Nevertheless, it is clear that the magnetic fields for the low reactance circuit are roughly a factor Of three smaller than those for the North circuit only. It is also clear that the practical range of values is a larger percentage of the average field level for the low reactance case than for the North circuit case. This is consistent with the discussion of sensitivity to current fluctuations in section 2.4. It is interesting to note that the disagreement between theory and measurement is not as great at 7.32111as it was for the North circuit case. Nevertheless, the measured range of practical values is much wider than for the other measurement points. This is consistent with the existence of a buried source and can also be observed in Figure 10. It should also be noted that the Ls0 and nominal This is in values in Figure 13 are quite close. apparent contrast to the result for case 9 as shown in tables I and 11. The reason is that the "nominal" currents used in calculating Figure 13 are not balanced (and hence not the positive sequence currents of tables I and 11). Rather, they are chosen to be equal to the Ls0 current values of Figure 9. Had balanced currents been used, the nominal magnetic field would have been much lower and the result consistent with tables I and 11. More specifically, the ratio of North Circuit to low reactance magnetic field would vary from nearly three at the centerline to nearlv eieht 60m from the line. Overall, measured values for the low reactance circuit exceed those predicted. There is sufficient evidence from section 5.0 to conclude that background fields are responsible for the general disagreement between measured and predicted values. However, since phase information is not available, it is a difficult task to actually quantify the extent of the corruption. This problem will be given further consideration in the next section. 7.3 Observations
In section 4 . 0 , a question relating to the overall performance of low reactance circuits versus conventional three wire geometries was posed. Do low reactance lines produce significantly lower magnetic fields? As noted in the previous section, the answer to this question is yes. This can be clearly seen by comparing Figures 12 and 13. The measured magnetic fields from the low reactance circuit are approximately a factor of three smaller than the North circuit fields. This is quite a significant reduction in the fields. The reduction
1439 RENTON ELF MF SIMULATIONILOW REACTANCE
MO"€ -0
WIBu\s
+/-I%,
2DEG.)
ERMDATA RESULTANT FIELD
i-
of the discrepancies between measured and predicted fields. For example the 6.25 mG field at x=O could (with appropriate background phase) be reduced to 5.3 mG which is within the range of predicted values. Similarly, the 5.75 mG field at x=7.32m could be reduced to as little as 4.15 mG which is at the upper edge of the predicted range of values. The remaining measurements can be reduced to within the predicted range by using the same method. 8.0 CONCLUSIONS
DISTANCEFROM CENTERLINE (METERS)
siMuunm
-
L
Fig. 13
NOMINAL
-w
-
......
I
I
Predicted and Measured Magnetic Fields for the Low Reactance Circuit.
is not due simply to the fact that half of the current has been moved to the South circuit, approximately six meters further from the measurement points. To illustrate this, consider a six wire double circuit geometry phased in a single circuit "super bundle" arrangement. Using the now familiar wire configuration from the Renton site, parallel connections are made between N.Top-S.Top,N.Mid-S.Mid, and N.Bottom-S.Bottom. The only difference between this case which is called a "super bundle" and the low reactance case is that the A and C phases of the South circuit are interchanged. Computer simulations for the North circuit, low reactance and super bundle configurations using positive sequence current of lOOOA per phase (i.e. 500A per conductor for the low reactance and super bundle geometries) have been made [111. The predicted values for the super bundle circuit are comparable to those predicted for the North circuit. In short, the relative phasing of the paralleled conductors is very important when attempting to reduce magnetic fields. Consider, once again, the comparison between North and low reactance circuits as depicted in Figures 12 and 13. As mentioned, there is general agreement between measured and predicted values for the North circuit (except at 7.32m) but measured values for the low reactance circuit exceed predicted values at every probe location. It seems reasonable that the background fields discussed in section 5.0 can be used to explain this difference. To show this it should be noted that the background levels in Figure 6 are given directly in (mG) while measured results from the North and low. reactance circuits of Figures 12 and 13 are normalized to 1000A. In order to compare the measured fields with the background fields, it is necessary to un-normalize the measured fields. Since the average current was approximately 250A, the measured fields of Figures 12 and 13 should be decreased by a factor of 4 before comparison to the background fields can be made. For the North circuit data, an average background correction of 0.44 mG could easily bring the 15 mG = (60 mG/kA)xO.25 kA field within the range of predicted fields if the phase of the background field is appropriate. The same cannot be said for the field point at 7.32m because the measured 17.5 mG field could only be reduced to approximately 16.0 mG, well above the predicted average field of 13 mG. The remaining discrepancy is attributed either to currents induced in the buried conductor by the 230 kV power line or to changes in the background field levels during the North circuit measurements. For the low reactance line configuration measurements, the background field could explain all
The currents on an operating transmission line can be separated into a larger slowly varying component which follows the system load and a smaller rapidly varying random component which is determined by system load balance. The small random component may have a significant impact on the performance of transmission lines designed to have reduced magnetic fields. The magnetic fields of a transmission line can be expanded into a power series in the inverse distance ( l / R a ) from the line. The 1/R term is proportional to net current. Reduced magnetic field lines are designed to force the (l/Ra) and (1/R 12. terms to zero. The design is made under the assumption that the transmission line current is only a positive sequence current. This type of current is balanced and has zero net current. The remaining terms are (1/R l3 or higher order. The magnetic fields of reduced magnetic field lines are sensitive to random current fluctuations due and to system load changes. Specifically, both (laa) (l/Ra)'
terms can be reintroduced to the magnetic
field in the presence of non-zero net current and current unbalance. Three phase lines with ungrounded load topologies such as delta or open wye perform better because the ( l / R a ) terms are forced to zero by the topology (i.e. the net current must be zero). The magnetic fields of lines with grounded topologies may be more than 100% greater than predicted with positive sequence currents if the small fluctuating currents are only 2% of the total current. The unequal splitting of phase currents on six conductor low reactance lines causes a degradation in magnetic field reduction. This, however, is not nearly as serious a problem as the influence of non-zero net current. Measurements on an operating 230kV transmission line indicate that typical current fluctuations are approximately bounded by f2fb in amplitude and f2 degrees in phase. Measurements on operating single circuit 230KV three conductor and six conductor low reactance lines show that the latter has magnetic fields three times smaller than the former. The same measurements show that the six conductor low reactance configuration is considerably more sensitive to small current fluctuations than the three conductor configuration. Modeling of this reduction using only positive sequence currents gives reduction predictions which range from three near the line to eight 60m from the line. The computer program MAGFLD can be used to predict the magnetic fields of power lines with known currents and with randomly fluctuating currents superimposed on known currents. 9.0
ACKNOWLEDGEMENTS
Funding and support of this project was provided by Bonneville Power Administration (BPAI and Puget Sound Power & Light Company (PSPL). In particular, we would like to thank BPA's Rick Stearns and Larry
1440 Dickson. Mr. Stearns provided the test equipment used at the Renton site. Mr. Dickson served as the Instrumentation Craftsman in charge of implementation and operation of all test equipment. Next we would like to thank PSPL's Dale Easley, Ron Raczkowski, and Dave Rembert. Mr. Easley worked on contractual agreements which provided: funding for analysis, test location, and use of PSPL's 230 kV Talbot Hill-O'brien transmission line. Mr. Raczkowski coordinated with Metro Rapid Transit for use of the ground site and developed a detailed set of instructions which allowed line crews to reconfigure the line. Mr. Rembert scheduled line crews that installed NITECH power donuts and reconfigured the line as a low reactance single circuit. 10.0 REFERENCES 1.
M. Granger Morgan, "Electric and Magnetic Fields from 60 Hertz Electric Power: What do we know about possible health risks?" 1989. available from the Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213.
2.
T. Moore, "Exploring the Options for Magnetic Field Management", EPRI Journal, Vol. 15, No. 7, October/November 1990, pp. 5-19.
3.
L.E. Zaffanella, "Electric and Magnetic Fields Lecture" 1988 EPRI High Voltage Transmission Line Design Seminar Notes, EPRI High Voltage Transmission Research Facility, Lenox, MA.
4.
V.L. Chartier, "EMF Reduction through Line Design," presented at the 1990 BPA Engineering Conference, March 7-8, 1990, Monarch Motor Hotel, Portland, OR.
5.
W.T. Kaune and L.E. Zaffanella, "Analysis of Magnetic Fields Produced Far From Electric Power Lines," presented at the 1991 IEEE Transmission and Distribution Conference, Dallas, TX.
6.
R.G: Olsen, "Sources of Power Frequency Magnetic Fields", presented at the 1990 IEEE Power Engineering Society Summer Meeting, Minneapolis, MN .
7.
L.E. Zaffanella, "Pilot Study of Residential Power Frequency Magnetic Fields", Final report to EPRI on RP 2942, September, 1989.
8.
J.R. Wait and K.P. Spies, "On the Image Representation of Quasi-Static Fields of a Line Current Source Above the Ground", Canadian Journal of Physics, Vol. 47, PP . 2731-2733, 1969.
9.
R.G. Olsen and T.A. Pankaskie, "On the Exact, Carson and Image Theories for Wires at or Above the Earth's Interface", IEEE Trans., Vol. PAS-102, April 1982, pp. 769-778.
10. R.G. Olsen, R.S. Baishiki and D. Den0 (Principal authors), "Magnetic Fields from Electric Power Lines -- Theory and Comparison to Measurements", IEEE Trans., Vol. PWRD-3, NO. 4, PP. 2172-2186, October 1988. 11. Westinghouse, Electrical Transmission and Distribution Reference Book, 2nd Ed., p. 643, 1950. 12.
R.G. Olsen, D.C. James, and V.L. Chartier, "The Performance of Reduced Magnetic Field Power Lines: Theory and Measurements on an Operating Line." A report to the Puget Sound Power and Light Co., Bellevue, WA, June 15, 1991.
13.
IEEE Committee Report, "Measurements of Power Fresuencv Fields Awav from Power Lines." - Magnetic IEEE Trans., Vol. PWRD-6, No. 2, pp. 901-91i, April 1991.
14. Nitech, "Plus-lD, Portable Distribution Line Monitoring System," available from NITECH, 72 Chambers St., Fairfield, CT 06430-9998. 15. F.M. Dietrich, F. Sicree, "Measurement of Power System Magnetic Fields by Waveform Capture," forthcoming EPRI report. Robert G. Olsen (S165-M'73-SM'85) was born in Brooklyn, NY, on April 9, 1946. He received the B.S.E.E. degree from Rutgers University, New Brunswick, NJ, in 1968 and the M.S.E.E. and Ph.D. degrees from the University of Colorado, Boulder, in 1970 and 1974, respectively. From 1971 to 1973 he was employed by Westinghouse Goeresearch Laboratory in Boulder, CO, where he worked on underground electromagnetic propagation problems. Since 1973 he has been with the School of Electrical Engineering and Computer Science, Washington State University, Pullman. During the first half of 1980 he was on leave as an NSF Fellow at the GTE Laboratories in Waltham, MA, where he conducted research on optical fiber propagation. During the 1984-1985 academic year he was on leave at ASEA Research and Innovation in Vasteras, Sweden, where he worked on problems in computer modeling of high-voltage components and electromagnetic interference. His present research interests are in electromagnetic interference, electromagnetic compatibility, and power line electromagnetics. Dr. Olsen is a member of Eta Kappa Nu, Tau Beta Pi, Sigma Xi, and Phi Kappa Phi. Vernon L. Chartier (SJ62-M'64-SM'72-F80)was born in Fort Morgan, CO on February 14, 1939. He received the B.S. degrees in electrical engineering and business from the University of Colorado, Boulder in 1963. From 1963-1975, he was with the Advanced Systems Technology Department of the Westinghouse Electric Corporation, where he was engineer-in-charge of the Apple Grove 750-kV Project and was this Department's principal consultant to the electric utility industry on the effects of corona and electromagnetic fields associated with high voltage transmission lines. In 1975, he joined the Division of Laboratories of the Bonneville Power Administration where he has been associated with the Lyons 1200-kV Project and other high voltage research projects. He is presently the Chief High Voltage Phenomena Engineer at BPA. Mr. Chartier is a member of the USNC of IEC, Technical Advisor to the USNC of IEC on matters pertaining to CISPR Subcommittee C on High Voltage Lines and Traction Systems, past chairman of the IEEE/PES Transmission and Distribution Committee, member of the PES Awards Committee, Chairman of PES Fellows Committee, member of IEEE Electromagnetic Society, member of ANSI C63, Expert Advisor to CIGRE Study Committee No. 36 (Interference), member of CIGRE, member of the Acoustical Society of America, member of Bioelectromagnetics Society, advisor to several EPRI EMI/EMF projects, and is a Registered Professional engineer in the Commonwealth of Pennsylvania. David C. James was born in 1966 in Kooskia, ID. Mr. James received his B.S. Degree in Electrical Engineering from the University of Idaho,Moscow, ID, in 1989 and his M.S. Degree in Electrical Engineering from Washington State University, Pullman, WA, in 1991. He is currently working as a transmission engineer at The Washington Water Power Company in Spokane, WA.
1441 Discussion K. C. Jaffa (PacifiCorp/Utah Power, Salt Lake City, UT): As pointed out in the paper, a limitation of using a double-circuit low-reactance configuration as a single circuit line to reduce the magnetic field is that the “operating conditions are not under the control of the transmission line designer.” Specifically, these lines are very sensitive to small unbalances or uneven current splitting between individual conductors. This paper discusses this in detail. I would like to add a few comments and pose a couple of questions directed towards future research in this area. A transmission designer normally estimates field levels assuming balanced conditions and even current splitting between conductors. The designer needs to then have some understanding as to how these estimates may differ from actual conditions. Thus, it would be interesting to compare the field measurements and simulations to the estimates that are typically made by line designers. Did the authors make a comparison to typical calculations? In this particular case was the field lower or higher than expected? What was the magnitude of the
differences are multiplied by the much larger positive sequence current so that positive sequence LEF effects can be as significant as zero sequence LEF effects at distances as large as 400 meters [2]. While the LEF is more sensitive to unbalance than the magnetic flux density [3], I believe that caution should still be applied when making these types of assumptions in magnetic flux density equations until it is shown whether the assumptions are valid. The following values were calculated based on one of our 230-kV double circuit lines assuming a field point of one meter above ground.
’
ft
0
58.5
39.1 - 77.3 (67 - 132%)
0 - 19.5 (0, - 33%)
15.9 - 19.9 (27 - 34%)
200
208.4
187 - 233 (90 - 112%)
0 - 19.5 (0 - 9.4%)
15.9 - 19.9 (7.6 9.5%)
-
On single circuit H-frame lines, a specific set of current unbalances These differences are comparable to the +2% variations in current. usually results in a lower field on one side of the line and a higher Could the authors please comment on the impacts of these distance field on the other side compared to balanced conditions. This would assumptions in context of the levels of positive and zero sequence lead one to believe that if lower field levels were measured on one side current magnitudes? of the test line at a specific time then higher levels should be Finally, I would like to point out that the discussion on net current measured on the other side, however a double circuit configuration in section 2.4 and the various line terminations is not applicable to used as a single circuit line may behave differently. Based on this lines with multi-grounded shield wires. In this case, I, + I, + I, may work, do the authors have any additional insight into the effects of equal zero and there can be a current in the order of 1 to 2% on the unbalance and current splitting on the field levels that exist on one shield wire. side of the line compared to the other side? Thank you for taking the time to respond to these comments. Your It is also helpful for a designer to understand as much as possible paper opens up some very interesting topics for future research. about the prediction of current splitting and unbalances if accurate field estimates are to be made. Maw Frazier did some preliminary References work on this subject as part of the EPRI/AGA pipeline studies [l]. Based on a limited set of measurements, he showed that transmission [ l ] M. Frazier, Power Line-Induced AC Potential on Natural Gas line unbalance may be composed of two components, a random and Pipelines for Complex Rights-of-Way Configurations-Volume deterministic component. The random component was postulated to 1:Engineering Analysis, EPRI, EL-3106, 1983. be due to the variability of load balance while the deterministic [2] K. C . Jaffa and J. B. Stewart, Discussion of paper “The Calculacomponent could be predicted by the impedance differences seen by tion of Magnetic Coupling From Overhead Transmission Lines,” each conductor. The impedance differences can be broken down into IEEE Transactionson Power Apparatus and Supply, Vol. PAS-100, resistive, inductive and capacitive components. He also pointed out August 1981, pp. 3857-3858. that the length of the line was important. [3] J. R. Stewart, S. J. Dale, and K. W. Klein, “Magnetic Field In this particular case, Figure 9 of the paper shows a significant Reduction Using High Phase Order Lines,” Paper no. 92 WM difference ( > l.S%) between the current magnitude of the north-top 284-0 PWRD, presented at the IEEE/PES Winter Power Meetconductor and the south-bottom conductor of the same phase. It ing, January 1992. would be interesting to examine this data in light of the theories Manuscript received August 3, 1992. postulated by Man, Frazier. To do this, information would be necessary regarding the length of the line, the conductor locations and characteristics, etc. Could the authors provide this information? I would also appreciate any comments the authors may have on this theory and realize that a complete answer is beyond the scope of this R.G. OLSEN, D.C. JAMES, AND V.L. CHARTIER : paper. It appears that the north circuit is the power source with jumpers carrying power to the south circuit and the data in Figure 9 shows that The authors would like to thank Mr. Jaffa for his comments We the current on the top north circuit is greater than the current on the hope that our response to his insightful discussion will enhance the bottom south circuit. This could lead one to wonder if the jumpering usefulness of this work. method could have also contributed to this difference. Could the authors provide more information on how the conductors were jumpered and discuss any impacts which the jumper impedances could Mr. Jaffa asks for a comparison of the fields predicted by have had on the current splitting? It would be interesting to have transmission line designers who assume balanced conditions and some idea of the individual contributions to the total unbalance made even current splitting with the actual conditions found on this by the effects of the jumpers, individual conductor impedances and the transmission line studied in this paper. We will answer this question load characteristics. This insight would be helpful in extending this by providing idealized data assuming balanced and evenly split study to other transmission line designs. currents to compare with data in Figure 13 of the paper for the In the derivation of equations (2-6) and (2-7), various assumptions actual low reactance line These data are given in Table I. were made. I assume that the magnetic field due to the image current was ignored. In addition, it appears that it was assumed that R,, = R, It is clear that the difference is not too large for field points close to and that R, P 16”1, IhJ I believe that one should be very cautious the line (i.e 38% between the L50 and balanced/equally split results about assumptions when small differences can have significant effects. For instance, it was thought that the longitudinal electric field (LEF at 100 feet) but that the same difference can be very large (i.e. -responsible for magnetic field induction) at a large distance from a 2600% at 500 feet) further away. It is also true, however, that the power line was mostly due to zero-sequence current as opposed to larger differences occur where the fields will be much lower and in positive sequence currents since the geometric differences are small at many cases smaller than background fields. In fact, one of the large distances. This has been shown to not be the case [2]. While it is problems we had with our experiment was background fields on the true that small geometric differences by themselves may not be significant at large distances, it is important to realize that these small order of 1-2 mG. We should note that a similar comparison for the
1442
Distance (feet)
Balanced and Equally Split Currents
from analysis of current measurements. We firther agree that perhaps the deterministic part could be predicted in the absence of current measurements given enough information about the system. We do not think that we had enough information about our system to do so. For example, we did not have any information about any large fixed single phase loads connected to distribution lines fed by this line. These are likely to affect the deterministic part of the unbalance.
Simulation of Figure 13
100
2.1 mG
1.8 mG
2.9 mG
4.4mG
200
.36 mG
.56 mG
1.4 mG
2.3 mG
300
. I 1 mG
35mG
.9mG
1.6mG
400
.05 mG
.25 mG
.69 mG
1.2 mG
500
.02 mG
.21 mG
.55mG
.93 mG
TABLE I - Comparison of Ideal and Actual Data single circuit data shown in Figure 12 shows it to be less sensitive to unbalanced currents. Mr. Jaffa is correct to point out that for a given unbalance condition, the fields may decrease on one side of the transmission line but increase on the other side. Our theoretical studies show, however, that if the fields are averaged over all possible unbalance conditions, the averaged fields turn out to be approximately symmetric, This result assumes that there is not a deterministic unbalance such as we will discuss in the next paragraph. We were unable to study this problem with our measurements because the opposite side of the line was along a busy street. It would be interesting to see the results of such a study. We agree with Mr. Jaffa that the unbalance has both deterministic and a random part. We were able to isolate the deterministic part
We also have theorized that the jumpers used create the low reactance line might have been responsible for the unequal current splitting. We were not, however, able to conclusively show that this was or was not so by comparing typical junction resistances and the extra inductance of the additional line lengths. We can only say that the jumpers were installed with every attempt to minimize the additional contact resistance. Mr. Jaffa is correct in assuming that image currents were neglected and that certain other approximations were made in deriving (2-6) and (2-7). We agree completely that one should be cautious about approximations when small differences can have significant effects. We respond by noting that the purpose of (2-6) and (2-7) was to provide $&& about why double circuit low reactance lines work as they do rather than to provide a basis for calculations. In no case were any of the calculations done for this paper based on these equations. In all cases (2-1) and (2-2) were used for the very reason mentioned by Mr. Jaffa. We also agree that the positive sequence term may dominate despite its larger magnetic field decay rate because the positive sequence current is much larger than the zero sequence current. We appreciate Mr. JaEa’s comments on shield wires. We did not consider these because our test line did not have shield wires. This would be a good topic for a future research project. Manuscript received September 25, 1992.
