Download Radial and Longitudinal Temperature Gradients in Bare

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Radial and Longitudinal Temperature Gradients in Bare Stranded Conductors
with High Current Densities
B. CLAIRMONT
D.A. DOUGLASS
J. INGLESIAS
Z. PETER
EPRI
PDC, Inc.
RedElectrica
Kinectrics, Inc.
USA
USA
Spain
Canada
SUMMARY
At low current densities (< 2 amp/mm2), the radial and longitudinal temperature variation in bare
stranded transmission line conductors can be ignored. At higher current densities, and therefore higher
operating temperatures, however, the radial and axial variation in temperature must be considered.
When the conductor core is hotter than the surface, the sag and possible loss of tensile strength due to
annealing can be underestimated. When the conductor temperature varies along the line from span to
span, locally high temperatures can be overlooked and the average line section temperature wrongly
estimated for line survey measurements.
Conventional and High-Temperature Low-Sag (HTLS) bare stranded conductors are constructed
similarly. One or more layers of round or trapezoidal aluminium strands are wound helically around a
steel or composite core. The core exists primarily for mechanical strength and to limit conductor
expansion at high operating temperatures while the aluminium strands carry almost all the electrical
current (e.g. 98% to 99%). Given the 20 to 45 mm overall diameter of transmission line conductors,
the variation in current density between aluminium layers due to “skin effect” is typically less than
10% and 40% to 60% the Joule heat is generated in the inner aluminium layers. The flow of this heat
to the conductor surface produces a radial temperature drop.
Experiments were undertaken to test an improved calculation model for radial temperature drop.
These included a simulation of aluminium strand layer contact with machined aluminium plates and
thermocouple measurements on ACSR conductors with 3 and 4 layers of aluminium. The results
indicate that radial temperature drop is significant (10oC to 30oC) especially when the aluminium
layers are carrying little or no tension due to plastic or thermal elongation.
The axial conductor temperature variation along an overhead line was modelled mathematically. It is
concluded that there is almost no temperature equalization along overhead lines with bare stranded
overhead conductors. The temperature measured at a single location within a line section may be quite
different from the average conductor temperature in any line section. In certain spans, shielded by
terrain or foliage, short sections of conductor can be damaged by higher than expected temperatures.
KEYWORDS
Thermal Ratings, High Temperature Sag, Radial Temperature Drop, Longitudinal Temperature
Variation, Aluminum strand layers, Effective radial thermal conductivity.
[email protected]
INTRODUCTION & BACKGROUND
The design and rating of overhead transmission lines has changed dramatically in recent years. Bare
stranded transmission conductors are being operated at much higher current densities and temperatures
and new types of high temperature conductor have been introduced. Where in the past, it was not
unusual to design overhead lines for a maximum operating conductor temperature of 50oC, in recent
years, lines are being designed or re-designed to allow conventional steel-cored ACSR conductors to
operate at 100oC or more and commercially available HTLS conductors at 200oC or more.
Since bare overhead stranded conductors used in transmission lines normally have at least two layers
of aluminum strands, the flow of heat generated in these inner layers of aluminum cause a temperature
drop from the inside of the conductor to the outside. This temperature difference is referred to in this
paper as the conductor’s radial temperature drop. At high current densities, the higher temperature of
the core can increase sags or accelerate aging. Weather conditions do not directly affect the radial
drop but can change the aluminum electrical resistance by changing its average temperature.
Unless tapped, overhead transmission line conductors carry the same current between substation
terminations. Thus the heat generated per unit length is the same all along the line. Similarly, air
temperature and solar heating are usually similar along an overhead line unless it is very long or
changes elevation sharply. Thus the heat input from Ohmic losses and solar heating are essentially
constant along the line. The wind speed and direction relative to the conductor can, however, vary
sharply from span to span, especially with low speed turbulent winds. Although aluminum is an
excellent thermal conductor, the small crossection area of a typical bare overhead conductor makes the
axial thermal resistance high and allows little or no axial heat transfer. As a result, sheltered spans can
be significantly hotter than open sections of the line when the line current density is high. As with
radial heat conduction, the difference in temperature between spans at low current density is usually
negligible.
The current density required to produce the line’s maximum allowable temperature depends upon the
outside diameter of the conductor and the assumed weather conditions. For a small, 200 mm2, twolayer conductor, the current density at surface temperature of 100C may be in the range of 1
amps/mm2 while the current density of an 800 mm2 three-layer conductor may only be the The range
of current densities found in bare overhead conductors is usually
HEAT BALANCE FOR BARE OVERHEAD CONDUCTORS
Even if a bare overhead conductor carries no current, during the day absorption of solar heat is
sufficient to raise the conductor temperature 5oC to 10oC above the temperature of the surrounding air.
This conductor temperature is normally referred to as the solar temperature of the conductor. At night
the solar temperature is essentially equal to the air temperature.
Air temperature and solar heat intensity vary little from span to span, so the conductor temperature
along the line varies no more than a few degrees if there is no current. When there is current, heat is
generated through Ohmic losses. The heat generated is equal to the resistance of the conductor times
the square of the current through it. At low current levels, the bare conductor temperature may be only
slightly above the solar temperature but at high current levels the bare conductor can be quite high.
For example, for a 405 mm2 bare stranded aluminum conductor, a current of 1500 amps produces a
temperature rise above solar temperature of between 35oC and 115oC.
These calculations which involve the heat balance at the surface of the conductor are normally
performed using one of the standard methods such as CIGRE Technical Brochure 207 and all assume a
unit length of conductor exposed to the same weather conditions.
Weather conditions, particularly wind speed and direction, vary along transmission lines. At high
current loads, one would expect the conductor temperature to vary along the line as well.
Similarly, with bare stranded conductors having 2 or more layers of aluminum strands, a significant
portion of the Ohmic heat is produced in the inner layers of the conductor and must be conducted to
the surface layer in order to be part of the heat balance there. At high current levels, especially for
2
three and four layers of aluminum strands, one would expect that the temperature of the inner layers in
higher than the surface.
This paper concerns both mathematical calculations and experimental measurements of the variation in
conductor temperature both axially along the line and radially within the conductor.
RADIAL HEAT FLOW IN BARE CONDUCTORS
1
 Do
Di 2
RI
TC  TS 
  2

 ln
2    kr  2 Do  Di 2  Di
2
CIGRE Technical Brochure 207 suggests a
rather simple algebraic equation for the
calculation of radial temperature drop as shown
in the adjacent equation. In ACSR conductors,
98 to 99% of the heat is generated in the
aluminum strands so the conductor is modeled
as a solid hollow cylinder with uniform heat
generation in the aluminum layers and an
effective radial thermal conductivity (kr). The
reference brochure recommends using a value
of 2 watts/m-oC but that is too high for stranded
ACSR and other high temperature conductors
operating at high current and temperature levels.


 
Where:
TC= Core temperature [oC]
TS = Outer layer temperature [oC]
R = Resistance [Ohms/m]
I = Current in conductor [amps]
Di=core diameter [mm]
Do=outside diameter [mm]
kr=eff. radial therm. cond [watts/m- oC]
EFFECTIVE RADIAL THERMAL CONDUCTIVITY
The thermal conductivity of aluminum is 237 W/m- oC [2]. The conventional (e.g. ACSR, AAC,
ACAR etc) and HTLS conductors (ACCR, ACSS etc.) contain both aluminum strands and core strands
(steel, aluminum oxide, carbon fibre etc) with air gaps between the circular or trapezoidal aluminum
strands. Due to its heterogeneous structure, heat conduction analysis for bare overhead conductors is
more complex than if it were simply homogenous (e.g. solid aluminum bar). Air gaps hinder heat
conduction, while contact surfaces between strands increase thermal resistance. The heat is conducted
through contact surfaces between strands and through triangular air voids between layers. As shown in
the preceding equation, this problem is dealt with by introducing a new transport coefficient, the
effective radial thermal conductivity (also known as “apparent”, “resultant” or effective conductivity
in the literature [3].
The effective radial thermal conductivity must be determined by modeling or by measurements. The
relevant literature [3] offers certain theoretical models for estimating the equivalent thermal
conductivity. Some of these models needs input from measurements and mostly offer a rough
estimation for the equivalent thermal conductivity.
Flat plate experiment
Figure 1 Effective radial thermal
conductivity increases with
pressure between the machined
aluminum plates.
Effective Thermal Conductivity from Machined Plate Experiment
Effective rectangular thermal conductivity [watts/m-C]
2.5
Measurements of radial temperature
gradients are difficult in multi-layer
stranded conductors. The strands are
small and thermocouple placement is
difficult.
Control of inter-layer
pressure is difficult since tension
distributions between strand layers
and between aluminum and steel core
strands is difficult to control.
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
Pressure Between Plates [kiloPascals]
4
4.5
5
In
order
to
simplify
such
measurements and gain insight into
3
the heat flow phenomena between aluminum layers, flat aluminum plates were machined to simulate
strand layers. The effect of tension in the conductor aluminum strand layers was simulated by placing
weights on the stacked plates.
The Impact of Pressure on Conductivity
As the pressure between the plates is increased, the conductivity increased as shown in Figure 1 where
the thermal conductivity increases by a factor of about 2 as the weights are increased. One would
therefore expect that the radial temperature drop decreases with the radial pressure between the strand
layers and that the trapezoidal strands would yield lower radial temperature drops than round strands
when under pressure.
EXPERIMENTS WITH TENSIONED, STRANDED CONDUCTOR
Measurements of radial temperature differences with thermocouples placed within bare stranded
conductors are difficult because the dimensions are small and if it difficult to secure the location of the
TCs given the high currents and temperatures generated.
Prior Experiments
There have been quite a few laboratory experiments undertaken to determine the radial temperature
variation in bare stranded overhead conductors. Reference [8] reports temperature gradients measured
on tensioned new and aged ACSR conductors. The measurements were obtained from indoor and
outdoor laboratory test at various temperatures exceeding 300°C. The measurements in this study were
taken at stead-state conditions under steady wind (0, 0.6 and 2.4 m/sec) and tension (22 kN)
conditions. It was found that the temperature difference between core and surface of ACSR conductor
is in order of 10% for new conductor and 20% for aged conductors, depending on conductor
construction and age [8]. The measured temperature gradient in conductors was in the range of 20 to
50 °C, in general. The derived equivalent thermal conductivity is shown in Table 1.
It was concluded by Reference [4] that the radial equivalent thermal conductivity in conductors is
independent of generated heat and increases with increasing conductor tension and increasing air
pressure.
Thermocouple Placement, Tension Control and Forced Cooling
As shown in Figure 2, Thermocouples were placed between strands in the same layer. Small shifts in
the position of the thermocouples can cause significant measurement errors. The steel core of the
conductor was gripped separately from the surrounding aluminum layers so that the tension in the
aluminum layers can be adjusted independently of the steel core. The external convection rate of the
experimental conductor can be changed by turning fans on and off. Changes in wind speed sharply
affected the surface temperature but not the temperature drop from core to surface.
Radial Temperature Measurements
Using the preceding experimental set-up, measurements were made on three large conductors:



Lapwing 45/7 805 mm2 ACSR
Cumberland 42/19 975 mm2 (3-layer) ACSR/TW
Santee 64/19 1330 mm2 (4-layer) ACSR/TW
These laboratory tests are limited to large conductors but consider both round strand and trapezoidal
strand aluminum.
4
Table 1 Summary of Previous Radial Temperature Measurements
Source/
Reference
Alcan* [5]
Alcan* [5]
Kaiser* [5]
Dale/PTI [5]
Dale/PTI [5]
Dale/PTI [5]
OHRD* [8]
OHRD* [8]
OHRD* [8]
OHRD* [8]
OHRD* [8]
Z.Peter [10]
V.T. Morgan [6]
V.T. Morgan [6]
V.T. Morgan [6]
V.T. Morgan [6]
V.T. Morgan [6]
V.T. Morgan [6]
Conductor Condition
ACSR,
round
ACSR,
round
ACSR,
round
ACSR,
round
ACSR,
round
SDC
ACSR,
round
ACSR,
round
ACSR,
round
ACSR,
round
ACSR,
round
ACSR,
round
ACSR,
round
ACSR,
round
ACSR,
round
ACSR,
round
ACSR,
compact
ACSR,
round
new
old
new
old
old
new
new
new
new
Area
(mm2)
402.84,
Condor
689.14,
Bersimis
523.68,
Curlew
402.84,
Drake
Dove
Stranding
Tension
(kN)
Span
(m)
Radial Thermal
Conductivity
(W/mK)
54/7
-
15
3.7
42/7
-
15
2.5
54/7
Low
1.2
1.2-2.1
26/7
2.22
6
2.4-2.6
1985
26/7
2.22
145, outdoor
2.6
1985
2.22
6
2.1
1985
54/7
22.24
indoor
1.4
1977
26/7
22.24
indoor
2.3
1977
26/7
22.24
indoor
2.3
1977
26/7
22.24
365, outdoor
3.0
1977
26/7
22.24
122, outdoor
3.6
1977
45/7
Low
indoor
644.54
402.84,
Condor
402.84,
Drake
402.84,
Drake
402.84,
Drake
402.84,
Drake
689.14,
Bersimis
new
596.41
54/7
28.78
outdoor
new
519.39
54/7
5
indoor
new
519.39
54/7
20
indoor
new
179.38
30/7
Low
new
170.26
18/7
Low
new
417.03
54/7
Low
-
3.5-5.7
AVG=4.6
0.74-5.2
AVG=2.22
0.64-1.6
AVG=1.06
1.05-1.12
AVG=1.1
1.16-4.68
AVG=3.39
4.18-5.89
AVG=4.70
1.15-6.94
AVG=2.46
Year
2006
1985
1985
1985
1985
1985
1985
The conductors were placed in the laboratory test span shown in Figure 2. A special collet was
manufactured and welded to the aluminum strands at one end of the span. This allowed the aluminum
strand layer tension to be controlled separately from the steel core.
To offer a degree of control over the
tension in the aluminum strand layers,
(0 to 2000 lbs) all of the aluminum
strands were welded into a drilled
aluminum thick-walled tube end-fitting
which fits over the steel core at one
end of the test span.
Figure 2 Experimental Set-up to control aluminum layer tension separately.
5
Radial Temperature Difference as a Function of Current Density
with Tension in Aluminum Strand Layers
Radial Temperature Drop Core to Surface - deg C
30
Dashed lines indicate the
calculated radial temperature
drop for a radial thermal
conductivity of 1.5
25
20
Lapwing DT-C
15
Cumberland DT-C
Santee DT-C
10
5
0
1.00
1.50
2.00
2.50
3.00
3.50
Current Density - Amps/mm2
Figure 3 - Radial temperature drop versus current density for Lapwing,
Cumberland, and Santee ACSR with 2 kN tension in the aluminum layers.
Radial Temperature Difference as a Function of Current Density
with Slack Aluminum Strand Layers
Radial Temperature Drop Core to Surface - deg C
30
25
Lapwing DT-C
20
Cumberland DT-C
Santee DT-C
15
10
Dashed lines indicate the
calculated radial temperature
drop for a radial thermal
conductivity of 0.7 w/m-C
5
0
1.00
1.50
2.00
2.50
3.00
Current Density - Amps/mm2
3.50
Large conductors such
as these are less efficient
in
convecting
and
radiating heat to the
surrounding air than
small
conductors.
Therefore the current
densities required to
produce a given surface
temperature are lower.
For example, at a current
density of 3 amps/mm2,
400 mm2 and 800 mm2
conductors
produce
surface temperatures of
120°C and 180 °C,
respectively.
As shown in Figure 3
and Figure 4, the radial
temperature drop for
each of the tested
conductors
increased
with current density and
that the tests where there
was
little
or
no
aluminum
tension
yielded
radial
temperature drops which
were about twice as high
as occurred with tension
in the aluminum layers.
The
dashed
lines
indicated
reasonable
agreement
between
calculations using the
simplified equation with
thermal conductivities of
0.7 and 1.5 watts/m-°C,
for untensioned and
tension
aluminum
strands, respectively.
Figure 4 - Radial temperature drop versus current density for Lapwing,
Cumberland, and Santee ACSR with no tension in the aluminum layers.
Axial Temperature Variation
We can investigate the longitudinal variation of conductor temperature by ignoring any radial variation
and deriving the following differential equation for axial heat transfer within the bare stranded
conductor. If there is no axial variation along the conductor,
d 2T
k x  A  2  qconv  qrad  R (T )  I 2 then the heat balance between heat input from solar heating
dx
and Ohmic losses equals the heat lost by convection and radiation. The
convection and radiation terms in the equation can be represented by linear functions of T-Ts.
6
Figure 5 - Numerical model of axial temperature variation along a current-carrying bare stranded
conductor.
Examples of Temperature Equalization
160
160
150
150
Conductor Temperature - deg C
Conductor Temperature - deg C
Bare overhead conductors carrying ordinary rated current levels of about 1 amp/mm2, produce about
50 watts/meter due to Ohmic heating. Very little of the heat generated within the conductor is
transmitted axially, even when the temperature varies due to varying wind cooling as shown in Figure
6 (for a 10 meter and 1 meter shielded section). The conductor temperature is determined by the local
weather conditions with very little axial heat flow between conductor sections at different temperature.
140
130
120
110
140
130
120
110
100
100
15
17
19
21
23
25
27
29
31
33
Distance Along Conductor - meters
TCss
TC10
35
18
18.5
19
19.5
20
20.5
21
21.5
22
22.5
23
Distance Along Conductor - meters
TC-ZeroAxialConductivity
TC-NormalThermalConductivity
Figure 6 - Calculated temperature distribution for 10 & 1 meter long sheltered sections of conductor.
Wind speed is 1.6 mps at all points outside the 1 meter section where it is only 0.6 mps.
The Impact of Current Density
Even with the line subject to full summer solar heating, the conductor temperature varies little along
the line with varying wind speed and direction. At high current densities, however, the conductor
temperature can vary greatly along the line.
The tension in each line section varies with the average temperature of the line section. The lower
tension produced in hot spans is equalized by adjacent cooler spans but the temperature of each is not
affected by the hotter or cooler temperature of adjacent spans.
Effective Average Perpendicular Wind Speed
The average effective perpendicular wind speed of a line section is defined as that wind speed
perpendicular to the conductor which yields the same tension and average temperature as the actual
wind along the line section.
7
Conclusions
At current densities above 1 to 2 amp/mm2, the conventional concept of specifying or measuring a
single temperature for bare stranded overhead conductors should be reconsidered. The temperature of
the conductor core wires can be significantly higher than the surface and the average temperature of
the conductor crossection can vary from span to span along the line.
The specific current density, above which such effects become important, is a function of the
conductor diameter. A current density of 2 amps/mm2 is required in a 200 mm2 conductor to produce
the same surface temperature as a current density 1 amp/mm2 in an 800 mm2 conductor.
The simplified radial temperature drop calculation equation provided in Technical Brochure 207 is in
reasonable agreement with laboratory measurements made with large ACSR conductors (800 to 1300
mm2). The effective radial thermal conductivity value for tested conductors with tension in the
aluminum strand layers is found to be in the range of 1.5. When the same conductor samples were
tested with slack aluminum strand layers, the conductivity was found to be in the range of 0.7 watts/m°C.
The temperature drop in typical transmission conductors (e.g. 20 to 40 mm diameter) can be as high as
10 to 20oC even with light tension in the aluminum layers and 20 to 40 oC when the aluminum strands
are slack (no tension). When there is no tension in the aluminum layers, it appears that the radial
temperature drop occurs for both round and trapezoidally shaped aluminum strands.
Ignoring the higher core temperature of bare stranded conductors can lead to underestimation of
conductor sag and material degradation. Even at moderate current densities, the longitudinal variation
of conductor temperature from span to span needs to be considered when performing field surveys
with lines “in-service”.
BIBLIOGRAPHY
[1] CIGRE WG 22.12, “Thermal Behaviour of Overhead Conductors”, Technical Brochure 207, August 2002.
[2] Frank P. Incropera, David P. DeWitt: Heat and Mass Transfer, 5th ed. John Wiley & Sons, 2002, pp.410-412,
905.
[3]
L. I. Kiss, “Thermo-physical properties in heat conduction”, Lecture notes, Université de Liège, LAS,
1996.
[4]
V.T. Morgan, “Effects of axial tension and reduced air pressure on the radial thermal conductivity of a
stranded conductor”, IEEE Transaction on Power Delivery, Vol. 8, No.2, April 1993.
[5]
D. A. Douglass, “Radial and axial temperature gradients in bare stranded conductor”, IEEE Transaction
on Power Delivery, Vol. PWRD-1, No.2, April 1986.
[6]
V.T. Morgan, D. K. Geddey, “Temperature distribution within ACSR conductors”, Cigre 22-101, 1992
Session, August 30- September 5.
[7]
W. Z. Black, S. S. Collins, J. F. Hall, “Theoretical model for temperature gradients within bare overhead
conductors”, IEEE Transaction on Power Delivery, Vol. 3, No.2, April 1988.
[8]
G. J. Clarke, “Summary report on the effects of high operating temperatures on conductors and
hardware behaviour”, Ontario Hydro Research Division Report No. 77-177-H, April 25, 1977.
[9]
D. A. Douglass, L.A. Kirkpatrick, “AC Resistance of ACSR – Magnetic and Temperature Effects”,
IEEE Transaction on Power Apparatus and Systems, Vol. PAS-104, No. 6, June 1985.
ACKNOWLEDGEMENT
The authors acknowledge the many technical contributions of Dr. V.T. Morgan.
8