1
Dynamic Line Loading of Transmission Line:
An Application Guideline
Benjamin W. Allen, Member, IEEE, and Dr. P. K. Sen, Senior Member, IEEE

Abstract-- Dynamic modeling approach to determine the
II. STATIC LINE RATINGS
transmission lines current carrying capacity is becoming a
common approach in the industry. IEEE Std. 738 is based on
static, worst-case temperature, wind, emissivity, air density,
viscosity, and conductivity conditions and results often in
conservative ratings.
Dynamic line ratings take into account real-time weather
data, conductor tension data, and ambient temperature to
maximize the limit of current that can be pushed through a
line. This is becoming increasingly important in today’s
energy economy, as the existing electric power infrastructure
is being utilized to its limit. Electric utilities are looking for
innovative methods to increase the capacity of their power
system without spending large amounts of capital.
This paper will address this issue. A spreadsheet analysis
and an interactive program is written to perform the
calculations and make a comparison of various methods and
provide the results in a graphical form. System operator can
use this information in operating the system efficiently and
reliably.
Static current carrying capacity is the steady-state
conductor ratings that are established through IEEE Std. 738
in the US and IEC Std. 60287 for use in most of the rest of the
world. The conductor ratings established through the
applications of these standards dictate the amount of energy
that can be transmitted over a transmission line. These ratings
are typically very conservative and assume near worst-case
conditions. From historical data, wind speed averages across
the US are consistently significantly above this [4], and it is
likely that during a large portion of the year, most areas of the
US experience temperatures below 78°F. The conservative
values produced from traditional static ratings have brought
forward the concept of dynamic line ratings.
Index Terms— Dynamic Line Ratings, Transmission Line,
Conductor Selection, Emergency Loading.
III. WHAT ARE DYNAMIC LINE RATINGS?
Dynamic line ratings differ from their static rating
counterparts in that they are dynamic and can be adjusted on a
minute-to-minute basis, as opposed to being a constant under
any conditions.
IV. ANALYSIS OF VARIABLES EFFECTING LINE RATINGS
I. INTRODUCTION
T
ransmission line current carrying capacity is determined
using the basic heat transfer equations. Under steady-state
conditions, heat generated within a material (in this case, the
conductor) is equal to the heat dissipated out of the material.
With overhead conductors, heat is generated through resistive
losses in the conductor (I 2R losses) and through the sun, while
heat dissipation is depends on radiation and convection [1].
With heat transfer being in equilibrium, the conductor
temperature remains unchanged.
Under transient conditions, however, the conductor
temperature is constantly changing. The rate at which this
temperature change occurs is directly correlated to the mass
and heat capacity of the conductor. According to the IEEE
Std. 738, for transient periods less than one minute, the heat
capacity of any steel in an ACSR conductor may be ignored.
During transients lasting more than one minute, however, the
heat capacity of the entire conductor (both steel and aluminum
strands) must be considered [1].
B. W. Allen is with Colorado School of Mines, Golden, CO 80402 USA
(e-mail: beallen@mines.edu).
Dr. P. K. Sen is with Colorado School of Mines, Golden, CO 80402 USA
(e-mail: psen@mines.edu).
When calculating line ratings per the IEEE Std. 738, a
number of variables are considered. These methods
incorporate conductor characteristics, maximum allowable
conductor temperature, wind speed, wind direction,
transmission line orientation, ambient temperature, day of the
year, time of the day, elevation, latitude, absorptivity, and
emissivity. While all of these variables have an effect on the
conductor rating, some variables have little influence, while
other variables effect ratings greatly. This paper will perform
the analysis of each variable and its degree of influence on the
conductor rating or do a parametric evaluation. As an
example, Figures below display the line ratings on July 1, vs.
January 1. Steady-state variables used are shown in Table I.
The base time used was 5:00pm, as this is typically during
peak demand and allows for a realistic scenario for when a
dynamic rating system could be implemented.
TABLE I
STEADY STATE VARIABLES ASSUMED IN ANALYSIS
Variable
Assumed Value
Conductor
26/7 Drake, 795 kcmil
AL Strand Diameter
0.1749 in.
Steel Strand Diameter
0.1360 in.
DC Resistance (25°C)
0.0214 Ω/1000ft.
AC Resistance (75°C)
0.0263 Ω/1000ft.
Conductor Diameter
1.108 in.
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Maximum Operating Temp.
Ambient Temperature (January)
Ambient Temperature (July)
Atmospheric Conditions
Wind Speed and Direction
Line Angle from N-S
Solar Absorptivity (α)
Emissivity (ε)
Elevation
Latitude
Time
75°C
43.2°F (6.2°C)
88.2°F (31.2°C)
Clear
2 ft/s at 45°
0°
0.5
0.5
5280 ft
39.78°
5:00 pm
The values for all variables stated above are based on seasonal
local conditions found in Denver, Colorado. As a basis of
comparison, rated ampacity under these conditions for a Drake
conductor on January 1 is 1,003.1 A and 754.9 A on July.
A. Conductor Characteristics
The most obvious and influential factor that determines the
maximum ampacity of a transmission line is the conductor that
is chosen. Overhead conductors are available in multiple
types, sizes, and configurations. In overhead distribution,
Aluminum Conductor Steel Reinforced (ACSR) cables are
most commonly used. The physical characteristics of a
conductor that effect rated ampacity include the resistance and
diameter. In a transient state, the number and size of the
aluminum and steel cords that make up the conductor
determine the heat capacity of the conductor, which in turn
determines the thermal time constant, τ. The thermal time
constant determines the rate and time that it takes for the
conductor to arrive at a new steady-state temperature when a
step-change in current is experienced.
only increases 7.3% (0.70 A/kcmil). Increasing from a
2156 kcmil Bluebird conductor to the 2312 kcmil Thrasher
conductor results in an increase in area of 7.2%, but an
increase in ampacity of only 3.2% (0.37 A/kcmil). This
decrease in marginal return can be explained by skin effect
and the use of a larger steel center which carries a higher
resistance than aluminum.
On a final note, the resistance of a conductor changes with
temperature. An increase in temperature results in an increase
in resistance. Since resistive power losses are a source of heat
absorbed by the conductor steel and aluminum, a vicious cycle
can form where an increase in temperature results in higher
losses, which in turn further raise the temperature of the
conductor.
B. Maximum Allowable Temperature
The maximum temperature of the overhead conductor is a
major factor in the conductor’s rated ampacity. As seen in
Figure 2, a 10°C increase in maximum temperature results in
an ampacity of 1066.6 A in January (+5.9% over base case)
and 846.7 A (+10.8%) in July.
Figure 2: Effect of Maximum Rated Ampacity vs. Conductor Temperature
Figure 1: Effect of Maximum Rated Ampacity vs. Conductor Size
As the physical properties of a given conductor are constant
and the conductor used in a given transmission line is not
likely to be changed without significant expense, the
conductor characteristics must be carefully chosen during the
planning stages of a transmission line. It is important to note
that the relationship between ampacity and conductor size is
not linear. As an example, using the July case, upgrading a 4/0
Penguin conductor to a 336.4 kcmil Linnet conductor results
in a 58.7% increase in area but only a 46.6% increase in
ampacity. This equates to a gain of 1.475 A per kcmil. If
upgrading from a 795 kcmil Drake conductor to a 900 kcmil
Canary conductor, the area increases by 13.2%, but ampacity
According to one manufacturer, overhead conductors can be
pushed to a maximum temperature of 100°C for a total of
1500 hours over the life of the conductor [5]. Using 100°C as
a conductor temperature, ampacities of 1151.2 A (+12.9%)
and 962.5 A (+21.6%) are achieved in January and July,
respectively. From this, it can be inferred that during
emergency situations, transmission capacity is more
effectively expanded during the winter months than during the
summer months.
C. Wind Speed
Under base rating conditions, wind speed was assumed to be
2 ft/s (1.37 mph). During a situation where the wind is
completely calm, rated ampacity is greatly reduced to 422.1 A
(-44.1%) in January and 209.8 A (-72.2%) in July. It is
important to note that the 2 ft/s wind speed used in the base
case is low compared to normal averages. In Denver, wind
speed averages 12.6 ft/s (8.6 mph) over the course of a year
[4]. At this wind speed, rated ampacities are increased to
1593.5 A (+58.9%) and 1238.9 A (+65.1%) in January and
July, respectively.
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Figure 3: Effect of Rated Ampacity vs. Wind Speed
When observing the correlation between the wind speed and
rated ampacity as seen in Figure 3, it is observed that the
marginal increase in ampacity for every mile per hour increase
in wind speed diminishes greatly past 20 mph. This infers that
the largest percent change in ampacity rating occurs during
wind speeds between zero and 20 mph. After this point, it still
produces a substantial yet lessened increase in rated ampacity.
On a more interesting note, the Rural Utility Service (RUS)
recommends that all transmission lines be designed to meet
extreme wind conditions loading [6]. In Denver, extreme wind
is considered to be 90 mph [6]. Under these conditions, rated
ampacity would be increased to 3145.8 A (+213.6%) in
January and to 2486.2 A (+229.3%) in July. From these
observations, it is obvious that wind speed is very influential
in the ampacity rating of an overhead conductor.
D. Wind Direction
Another variable related to wind that effects the rated
ampacity of a conductor is the direction of the wind relative to
the conductor. With the base rating assuming an angle of 45°
between the conductor and wind, rated ampacity of the
conductor was calculated to be 1003.1 A in January and
754.9 A in July. With an angle of 0° between the conductor
and the wind (parallel to conductor), rated ampacity is 737.4 A
(-26.5%) and 525.3 A (-30.4%) in January and July,
respectively. When the wind is perpendicular to the conductor,
rated ampacity increases to 1072.4 A (+6.9%) in January and
813.2 A (+7.7%) in July. Figure 4 shows the correlation
between rated ampacity and wind angle from 0 to 90 degrees.
Wind angle has a minor effect on rated ampacity between a
wind angle of 45 and 90 degrees, but can have a significant
effect between 0 and 45 degrees.
Figure 4: Effect of Maximum Rated Ampacity vs. Wind Angle
E. Orientation of Transmission Line
The orientation of the transmission line is defined as the
angle of the transmission line with respect to a North-South
contour. A line running east-west (an angle of 90 degrees)
carries a rated ampacity of 1035.6 A (+3.2%) in January and
805.0 A (+6.6%) in July. Figure 5 shows the rated ampacity as
a function of line angle.
Figure 5: Effect of Maximum Rated Ampacity vs. Line Angle
Over the range of possible line angles, a small change in
ampacity occurs. With relation to other variables, the line
angle has a minimal effect on the rated ampacity of a
conductor. It is interesting to note that the line angle has a
greater maximum effect during the summer months.
F. Ambient Temperature
The ambient temperature of a location has an effect on
multiple variables, including the convective heat transfer,
radiated heat transfer, density of air, dynamic viscosity of air,
and the thermal conductivity of air. Because of the importance
of these variables, ambient temperature plays an important
role in the rated ampacity of an overhead conductor. Figure 6
shows the relationship between ambient temperature and rated
ampacity. Assuming a maximum conductor temperature of
176°F (75°C), there is a near-linear relationship between
ambient temperature and rated ampacity between temperatures
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of -40°F (-40°C) and 86°F (30°C). Additionally, at 59°F
(15°C), a realistic temperature possibility through the year,
rated ampacity of a conductor in July (905.0 A) is 3.3% less
than in January (935.2 A). This shows that ambient
temperature has approximately the same influence on rated
conductor ampacity throughout the year.
affects the solar azimuth, solar declination, and the effective
angle of incidence of the sun’s rays.
Figure 7: Effect of Maximum Rated Ampacity vs. Day of the Year
Figure 6: Effect of Maximum Rated Ampacity vs. Ambient Temperature
It is clearly seen that rated ampacity is typically lower in the
summer months than during the winter months. If a summer
temperature of 86°F (30°C) is experienced, rated ampacity of
the Drake conductor would be 767.5 A. If an especially hot
day of 104°F (40°C) occurs, the rated ampacity would be
reduced to 657.2 A. This 10°C increase in temperature reduces
the rated ampacity by 14.4%. This can be especially alarming
as typical residential loading is driven by air conditioning
units that would experience a higher coincidence factor during
the hotter day. A higher coincidence factor results in more
current in the overhead conductor which is already
experiencing a reduced ampacity rating.
In the winter months, the opposite effect occurs. Assuming
a high temperature of 32°F (0°C) is expected, a Drake
conductor would be rated for an ampacity of 1048.1 A. If the
temperature were to drop to 14°F (-10°C), rated ampacity
would be 1115.7 A, an increase of 6.5%. If residential and
commercial heating was powered through electricity, a
decrease in temperature would naturally have a positive effect
on the conductor’s ability to handle an increased heating load.
As a final comparison, assuming normal temperature
extremes of -4°F (-20°C) and 104°F (40°C) in Denver, rated
ampacities of the conductor would vary from 1154.7 A at -4°F
to 657.2 A at 104°F, a decrease of 43.1% from the minimum
temperature rating. Considering this, ambient temperature has
a significant impact on the rated ampacity of a conductor
throughout normal temperature extrema.
G. Day of the Year
Another important variable that can affect the ampacity
rating of a conductor is the day of the year. Assuming an
ambient temperature of 60°F occurring every day of the year,
Figure 7 shows that the day of the year has a minimal effect by
itself on the ampacity rating. In the summer months, rated
ampacity at 60°F is 900.1 A, while in the rest of the year, rated
ampacity is 930.7 A, a difference of 3.3%. The day of the year
The assumption that the temperature is a constant 60°F
throughout the year is unrealistic, however. To make a
realistic analysis of rated conductor ampacity throughout the
year, average daily temperature data was obtained from the
National Weather Service for Denver, Colorado [7]. When
average temperature is considered, the maximum rated
ampacity of a Drake conductor occurs during December and
January (43°F) and is 1004.0 A. Minimum rated ampacity
occurs during mid-July (90°F) and is 745.4 A (-25.8%).
Using the methods found in IEEE Standard 738 to calculate
the ampacity rating of an overhead conductor, the variable
related to the day of the year has a minimal effect on
conductor ampacity (-3.3%) when considered alone. It is only
when the average maximum ambient temperature is taken into
account that they day of the year has a significant effect on the
rated ampacity of a conductor (-25.8%).
H. Time of the Day
Throughout the course of the day, the position of the sun
changes in the sky and affects the solar azimuth and the
effective angle of incidence of the sun’s rays. Similar to the
day of the year, the time of the day affects rated ampacity in a
very similar, yet more pronounced pattern. During the winter
months, rated ampacity is the highest of the day at 1050.8 A
during the hours of 6pm and 6am, and is lowest during the
hours of 8am to 4pm at 977.8 A (-6.9%). During the summer
months, days are longer, shortening the period of maximum
rated ampacity to the hours of 7pm to 5am. Interestingly, the
period of minimum rated ampacity is slightly shortened to the
hours of 8:30am to 3:30pm. Transition period between
minimum and maximum is lengthened. In the summer,
maximum rated ampacity is 849.8 A while the minimum is
728.1 A (-14.3%). An important observation from Figure 8 is
that both the duration and change in ampacity is larger during
the summer months.
If a typical ambient temperature profile were included in
conjunction with the time of day, the difference between the
minimum and maximum would be increased. Again, this is the
result of the heavy influence that ambient temperature has on
the rated ampacity of an overhead conductor.
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ampacity. As seen in Table II and Figure 9, elevation can
reduce the rated ampacity of a conductor by as much as 16.1%
in extreme cases, but more realistically reduces the rating by
0-3%.
J. Latitude
Latitude is another variable that does not affect a dynamic
line rating but does effect the base rating, as latitude will
remain constant once the transmission line has been
constructed. Latitude has an effect on the altitude of the sun,
solar azimuth, and the effective angle of incidence of the sun’s
rays. As seen in Figure 10, latitude has a negligible effect on
the rated conductor ampacity during July, but has an
increasing effect on rated ampacity in January in the upper
latitudes.
Figure 8: Effect of Maximum Rated Ampacity vs. Time of Day
I. Elevation
In substations, it is typical to derate equipment based on the
elevation of the substation. Table 4-10 in RUS Bulletin
1724E-300 dictates that equipment that is air cooled must be
rated with a correction factor related to elevation [8]. A
portion of this table is reproduced below for comparison,
using 3300ft as a base elevation in July for the IEEE 738
values.
TABLE II
COMPARISON OF ELEVATION CORRECTION FACTORS
Elevation
RUS Factor [8]
IEEE 738
0m (sea level)
1.000
1.040
1000m (3300 ft)
1.000
1.000
1800m (6000 ft)
0.985
0.970
3000m (10,000 ft)
0.960
0.927
4200m (14,000 ft)
0.935
0.888
6000m (20,000 ft)
0.900
0.839
An interesting comparison to make is between the RUS
guide and IEEE Standard 738’s methods. IEEE Standard 738
is more conservative in the effect that elevation has on
conductor ampacity.
Figure 9: Effect of Maximum Rated Ampacity vs. Elevation
Elevation is not relevant to dynamic line ratings as it does
not change. It does, however, have a small effect on the rated
Figure 10: Effect of Maximum Rated Ampacity vs. Latitude
During July, the maximum rated conductor ampacity was
782.9 A at the equator. The minimum rated ampacity was
752.4 A at a latitude of 50° North. This equates to a 3.9%
difference between the extrema during July. In January, the
maximum rated conductor ampacity was 1050.7 A at the
North Pole while the minimum rated ampacity was 993.9 A at
the equator, a difference of 5.4%. It is interesting to note that
during January, the ampacity extrema occur at different
latitudes than the extrema in July. This is a result of the effect
that latitude and time of year have on the altitude of the sun
and solar azimuth variables. However, as latitude is dependent
on the geographical location of the transmission line, it is
something that need only be considered as a constant.
K. Absorptivity and Emissivity
Absorptivity is the ratio of the incident solar radiation
absorbed by a body to the incident solar radiation directed at
the body [9]. Emissivity is a ratio that represents a body’s
ability to emit energy through radiation. A higher absorptivity
value will cause the conductor to absorb more energy, thus
reducing its rated ampacity, while a higher emissivity will
allow the conductor to emit more energy, thus increasing its
rated ampacity. Common values used when determining the
rated ampacity of a conductor when absorptivity and
emissivity are unknown are either 0.5 for both absorptivity
and emissivity, or 0.9 for absorptivity and 0.7 for emissivity
[1].
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Using base values of 0.5 for absorptivity and emissivity,
rated ampacity is 1003.1 A in January and 755.0 A in July.
Decreasing absorptivity to the minimum value 0.23 results in
rated ampacities of 1027.0 A (+2.4%) and 805.3 A (+6.7%) in
January and July, respectively. Increasing absorptivity to the
maximum value of 0.91 decreases rated ampacities in January
and July to 965.7 A (-3.7%) and 671.3 A (-11.0%),
respectively. The percent changes in rated ampacity are
greater in the July case than the January case. This infers that
solar absorptivity is a more important variable in the summer
than in the winter. This is due to the effect that the absorptivity
has on the amount of heat energy absorbed by the conductor
from the sun.
If emissivity is decreased to 0.23, the minimum value, the
rated ampacities of the conductor become 933.6 A (-6.9%) in
January and 688.7 A (-8.9%) in July. With the maximum
emissivity of 0.91, rating ampacities increase to 1100.3 A
(+9.7%) and 845.7 A (+12.0%) in January and July,
respectively.
Figure 11: Effect of Maximum Rated Ampacity vs. Absorptivity and
Emissivity
The effect of absorptivity and emissivity is linear in nature,
as seen in Figure 11. The slope of these lines is steeper during
the summer months than in winter. It is important to note that
absorptivity and emissivity of the conductor will increase over
time and with atmospheric pollution, but does not happen
quickly [1]. This may be over the course of many years, and
because of this, absorptivity and emissivity should be treated
as constants when implementing a dynamic rating system.
V. REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
IEEE Standard for Calculating the Current-Temperature of Bare
Overhead Conductors, IEEE Standard 738-2006.
Phoenix Cable http://www.phoenixwc.com/documents/Bare/ACSRAluminumConductorSteelReinforced.pdf. [Accessed: February 2012]
Southwire Cable
http://www.southwire.com/ProductCatalog/XTEInterfaceServlet?content
Key=prodcatsheet21. [Accessed: February 2012]
http://www.ncdc.noaa.gov/oa/climate/online/ccd/avgwind.html.
[Accessed: February 2012]
http://www.southwire.com/support/RevisingACSRCapacityAssumptions
.htm. [Accessed: February 2012]
Design Manual for High Voltage Transmission Lines, RUS Bulletin
1724E-200, May 2009.
[7]
[8]
http://www.crh.noaa.gov/product.php?site=bou&product=rer&issuedby
=bou. [Accessed: February 2012]
Design Guide for Rural Substations, RUS Bulletin 1724E-300, June
2001. [Accessed: February 2012]