ES1002 : Workshop March 22nd-23rd 2011
Dynamic thermal rating of power transmission
lines and renewable resources
Jiri Hosek
Institute of Atmospheric Physics
Bocni II / 1401, 141 31 Prague 4, hosek@ufa.cas.cz
Abstract— Power transmission lines are often operated close to
their thermal limits, while modern renewable energy sources have
been booming for more than two decades and have caused a
significant decentralization of electricity production. A possible
solution is to construct a new power transmission line, or to
reconductor an old line. However, such upgrades require a
significant investment, and take a long time to deploy. An
alternative to expensive upgrades is to uprate the power lines.
The static rating of existing lines can be upgraded using more
accurate assessment of the climatic conditions along the
transmission corridor, or the lines can be rated in real time using
a dynamic thermal rating (DTR) system.
Dynamic thermal rating of power transmission lines can provide
a significant increase of transmission capacity compared to the
more traditional static rating. The most important inputs to
weather-based DTR systems are measured or forecast
meteorological data. This information can be obtained in form of
instantaneous or averaged values, and with various
sampling/update intervals. Due to the random character of the
updates with instantaneous weather data, the averaged inputs
appear to be a better choice, providing more accurate estimates of
conductor ampacity and temperature. The analysis of update
intervals of the weather data shows that 10-minute interval is
sufficient to provide accurate ampacity estimates, while longer
intervals cause significant errors in ampacity determination.
I. INTRODUCTION
The most significant restriction on electric power
transmission through overhead lines is the thermal limit of the
conductor. High conductor temperatures cause deeper
conductor sag, and subsequently may result in clearance
violations. Another negative consequence is conductor
annealing, which can weaken the conductor and cause its
irreversible elongation. To avoid these problems, currentcarrying conductors are rated in terms of the maximum current
they can safely transport, without a substantial risk of thermal
overload. This rated current is known as ampacity.
Two main approaches can be used for thermal rating of
power transmission conductors. Static rating usually considers
a worst case scenario of ambient conditions for calculating the
steady-state ampacity: high ambient temperature, low wind
speed, and high solar radiation. However, even such
conservative ratings may not suffice under true worst-case
conditions (e.g. extreme ambient temperatures combined with
full solar radiation and no wind). Under such conditions, the
actual ampacity may be even lower than the declared static
rating, leading to a thermal overload of the conductor. This
usually happen with a probability of few percent, depending on
the rating assumptions and climate of the site.
The second method - dynamic thermal rating (DTR) of
transmission lines - represents a significant improvement over
the more traditional static rating. This is because DTR uses
actual operating conditions, rather than assumed conservative
conditions or historical averages. Dynamic methods provide
ampacity either directly, based on actual measurements of
conductor conditions (e.g. temperature or sag), or indirectly,
using ambient weather conditions.
A system that involves DTR and on-line monitoring was
proposed for example by Douglas [1]. In this system, weather
data were recorded every 2-5 minutes and a short-term,
emergency ampacity rating was evaluated every 5-60 minutes.
The weather parameters that are usually measured for DTR
purposes include ambient air temperature, wind speed and
direction, and solar radiation; the latter can be easily
calculated for clear-sky days, if measurements are not
available. In some cases, the conductor temperature is also
measured. As conductor temperature varies in time and space
[2], ampacity cannot be exactly determined but only estimated.
By their very nature, DTR systems are associated with a risk
that the estimated ampacity is higher than its actual value.
Analysis of this risk depends on the particular type of DTR
system. In weather-based DTR systems, ampacity is
determined using a conductor thermal model which uses
observed or forecast meteorological data.
The information from DTR can be used to increase the
normal and emergency operating flexibility of power
transmission systems [3], [4]. This is especially useful if
important part of electricity production is associated with
weather-based renewable energy sources, such as wind
turbines and solar plants, as new wind and solar farms are
often built in remote areas that often lack suitable power grid
connections. In addition to that, their energy production
correlates with weather, as do the dynamic rating of power
lines.
II. THERMAL MODELS FOR POWER LINE RATING
The basic principle of weather-based DTR calculations is
the evaluation of the heat balance equation of the conductor
qs  I 2 RTc   qc  qr  mC p
dTc
0 ,
dt
(1)
where qs and I2R(Tc) are, respectively, the heat gain due to
solar radiation and Joule heating, while qc and qr are the heat
ES1002 : Workshop March 22nd-23rd 2011
loss due to convection and long wave radiation. All four heat
terms are expressed in W/m. The term mCp is the heat capacity
of the conductor in J/m°C.
The ampacity of a conductor can be calculated for steadystate conditions, under the assumption that the conductor
temperature has already reached equilibrium and the derivative
dTc/dt is set to zero. The remaining equation can be solved for
I using a specified function for R(T c), with Tc set to the
maximum safe conductor temperature. Under varying current
and/or ambient conditions the conductor temperature should
be calculated as transient, keeping the derivative dT c/dt at its
actual value. The heat balance equation then needs to be
solved numerically at each time step. The transient thermal
rating is calculated with respect to a specific time period.
Two methodologies are most commonly used for
calculating current/temperature of overhead conductors. These
are the IEEE standard [5] and the CIGRE method [6]. The two
approaches were compared in a study by Schmidt [7], that
found no significant differences in their results.
The calculations of ampacity and conductor temperature in
this study have been performed using a thermal model based
on the IEEE standard 738-2006 [5]. The model allows for
steady-state calculations of the conductor temperature and
ampacity, as well as transient calculations of conductor
temperature in the event of changing ambient parameters,
and/or current. The main meteorological inputs to the model
are wind velocity and ambient air temperature. Incoming solar
radiation can be obtained from measuring instruments or from
an NWP model. Alternatively, it can be calculated using the
time of day, and assuming clear sky conditions. The most
important cooling factor is the convective heat transfer due to
wind. For negligible wind speed, natural convection is
considered in the calculation of qc; for more significant wind
speeds, forced convective heat loss is used.
ampactity calculations were carried out for two common
conductor types: Finch and Linnet, both aluminum conductors
steel reinforced. The bigger conductor has static rating set to
1093A, while the smaller second one can only transport 529A.
The static ratings are specified for 75°C conductor temperature
and 2ft/s wind speed.
The first task was to explore differences of calculations
based on instant and average values of meteorological
parameters. For the averaged inputs, the 99th percentile
naturally decreased with averaging interval due to the
smoothing effects, while in case of instantaneous values it rose
as random extremes could cause higher conductor
temperatures when the updates of wind and temperature were
sparse. Also, the mean absolute error comparing to the most
detailed simulation was significantly higher for instantaneous
case.
For the specified averaging intervals, the transient
temperature of conductor energized with nominal rating
current was calculated. The results of calculations with larger
update interval were compared to the shortest 1 minute
calculation taken as a best solution. As expected, longest
averaging interval caused significant smoothing in the
simulated conductor temperature with occasional errors of
more than 10 °C. The 10-minute interval, on the other hand,
hardly caused errors higher than couple of °C. The table I
surveys overall statistics of the transient calculations for
nominal current.
III. TIME RESOLUTION EFFECTS IN DYNAMIC THERMAL RATING
The ampacity series were obtained for both conductors
using steady state calculations of thermal model, as there is no
need for transient approach when the temperature is fixed. The
maximum temperature for the ampacity calculations was set to
typical value of 75 °C.
The simulated ampacity of conductor Finch shows that in
the given period the power line would be able to transport
around 2070A on average – thus 89% more current than the
static rating. In slightly less than 1% of time the ampacity does
not reach the static rating threshold. Similar values are
obtained for the smaller conductor Linnet, the average gain of
ampacity being 82% and lower-than-static ampacity
occurrence being almost 1%. As expected the mean absolute
error increase with averaging interval, being almost double for
the case of hourly updates comparing to the 10-minute
averages.
To keep the static-rating level of risk that the ampacity
would be smaller than specified, 99th percentile of
corresponding differences should be subtracted from the
original ampacity. It means that for hourly updated
CALCULATIONS
For the specified purpose, the thermal model was applied
using real wind speed and direction series averaged at various
time intervals. As a test data we chose high resolution
measurements at Dlouha Louka (880 m a.s.l.) in Ore
Mountains. The measurements were taken at a top of a
meteorological mast at 50 m above ground. The sensor used
was ultrasonic anemometer METEK USA-1 giving all three
components of wind velocity and temperature. The data were
taken in the period from 18.6.1999 to 2.10.1999, covering the
least windy and warmest season of the year. The availability of
data reached 87.6% with total 135112 one-minute records.
The shortest time interval possible for the current version
of DTR calculation was set to 1 minute, as shorter interval of
changes in external parameters would require further modeling
of heat transfer inside the conductor. Besides 1 minute
interval, the calculations were carried out for typical 10, 30
and 60 minute intervals. The conductor temperature and
TABLE I
STATISTICS OF CONDUCTOR TEMPERATURES CALCULATED USING AVERAGED
AND INSTANTANEOUS VALUES COMPARED TO 1-MINUTE SERIES
ES1002 : Workshop March 22nd-23rd 2011
calculations for Finch we are losing about 40% of ampacity
surplus, while 10-minute updates cause only 26% loss. More
detailed view on ampacity differences caused by various
frequency of updates of meteorological inputs gives histogram
on Figure 1.
Fig. 1. Histogram of differences in ampacity [A] between one-minuteupdated time series and those with longer update periods for conductor Finch.
However, since the typical time constant for selected
conductors is about 10 minutes, one-minute variation in
ampacity might not be of much importance. For this purpose,
the line was supplied with a current based on ampacities with
different time interval of updates and the transient temperature
was calculated for the conductor Finch using one-minute series
of wind and temperature. The differences of conductor
temperature from initial fixed 75 °C represent the error
induced by sparse updating of the inputs. The histogram of
calculated conductor temperatures is displayed on Figure 2.
Any such system is based on thermal model of conductors,
which needs meteorological inputs.
In order to study effects of update interval of the inputs, a
widespread thermal model was applied to high frequency wind
speed, wind direction and air temperature measurements. The
results showed that averaged values of wind and air
temperature are a better choice for input to the thermal model
than instantaneous values. As expected, the model error rises
with longer averaging and update intervals that are used for
wind speed and temperature. Acceptable model error is found
in results when 10-minute or shorter averages of
meteorological inputs are used. As a result, longer sampling
intervals can contribute to conductor aging, should the
calculated ampacities be fully realized in system operation.
The recommended values of conductor temperature are
exceeded in 1% of studied time period when 60-minute
averaging intervals are used, compared to only 0.01% for 10minute intervals.
Based on the above-mentioned results, the use of 10minute averaged values of meteorological inputs is
recommended for dynamic thermal rating systems. In any case,
averaged values are preferable to instantaneous measurements
or predictions.
V. ACKNOWLEDGMENT
This work has been supported by the Natural Sciences and
Engineering Research Council of Canada (NSERC).
VI. REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Fig. 2. Histogram of conductor temperatures [°C] between one-minuteupdated time series and those with longer update periods for conductor Finch.
IV. CONCLUSIONS
Dynamic rating of power lines allows intelligent
management of power grid, especially when important part of
energy is produced from weather-based renewable resources.
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transmission circuits', IEEE Transactions of Power Delivery, 1996, 11,
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