There are several ways to obtain an estimation of the temperature of an electric power cable. First, there are Standards provided by the two main international electric institutions, CIGRE (Conseil International des Grands Réseaux Électriques) [
1] and IEEE (Institute of Electrical and Electronics Engineers) [
2], which explain how to relate the current and the temperature based on the thermal balance of the conductor.
2.2. Numerical Simulation
The main problems when trying to use infrared thermometers with power lines is the distance to the conductor and the unknown value of the conductor’s emissivity. On the one hand, there is a minimal safety distance between the conductor and the tower where the infrared thermometer would be placed. On the other hand, there is a maximum allowable distance for the infrared thermometer to have a good reading and a small spot size.
To increase the spot size and extend the possible distance between the thermometer and the conductor, a sphere was attached to the conductor. The sphere was simulated to check its influence on the conductor temperature and its cooling effect due to convection and radiation. The objective was to design a sphere of the same material as the external layers of the conductor (aluminum in this case) which was big enough for the spot size of the infrared thermometer but small enough to have controllable cooling effects. Additionally, attaching a specific manufactured sphere would solve the unknown emissivity problem.
Several diameters of the sphere were simulated and the cooling effect of the sphere acting as a fin was modelled. The domain included the conductor, with its iron core and aluminum layers, the aluminum sphere attached to the conductor, and the surrounding air volume. It was 1 m long and 0.2 m high and wide, with periodic boundary conditions at the front and the back of the conductor length to simulate an indefinitely long cable. The goals of the numerical model were the following:
To recreate all the electrical and environmental conditions and obtain a realistic model of the behavior of the conductor and the sphere under operating conditions.
To validate the results of the modelled conductor temperature with values obtained from the estimation of the temperature of the conductor under different conditions according to the Standards.
To confirm and obtain a first approximation of the cooling effect of the sphere acting as a fin.
This last goal was important because the surface of the sphere in contact with the air increases the convection and radiation cooling. The physical phenomena simulated in the model were the following:
The alternating current and the electromagnetic field associated with the conductor.
Heat transfer effects resulting from conduction inside the cable and the sphere, natural and forced convection with the air surrounding both solids, solar heating, and cooling radiation to the atmosphere.
Therefore, the most important heat gain and loss mechanisms of the system were included in the numerical method. To include all these effects, the model was implemented by means of coupled physics solved by Ansys Workbench®. First the electromagnetic field was solved using Maxwell® software and then the heat power generated inside the solids were translated into the computational fluid dynamic software Ansys Fluent®, where all the other physical and environmental conditions were recreated, and the temperature profile was calculated.
The model boundary conditions were the ambient temperature, the speed and direction of the wind, solar radiation and current. The main characteristics of the implemented numerical model were steady state analysis with gravity and variable air density, solar and surface to surface (S2S) radiation models, k- turbulence model, periodic conditions to simulate an indefinite long conductor and 890,784 elements. The thermo-physical properties of the conductor were the ones provided by the manufacturer and the value of the sphere emissivity was obtained from the estimation done by the Spanish Metrology Center (CEM).
Figure 1 presents the boundary conditions of the model and a temperature profile of the conductor and the sphere where the cooling effect of the sphere can be seen.
Figure 2 shows an air velocity field surrounding the sphere resulting from the combined natural and forced convection. Three sphere diameters were simulated with different weather and line conditions and the results are summarized in
Table 1. In
Figure 3, the cooling effect of the sphere increasing with its diameter is clearly shown. The smallest simulated diameter was chosen to manufacture the sphere to minimize the cooling effect but to maintain a practical spot size for the pyrometer.
2.3. Infrared System Build Up
The two main components of the infrared system are the infrared thermometer and the sphere. To choose the thermometer, the criteria were available spot size, temperature range and cost. The minimum distance should be around 1 m, considering the length of the insulators typically attached to the tower and the spot size at that distance should not be bigger than 3 cm considering the size of the attached sphere.
Maximum allowable conductor temperature depends on the type of conductor but it is common to specify or as the maximum operational temperature so the needed temperature range would vary from a few degrees Celsius to around one hundred. The lower values of temperature measurements would not be an inconvenience because the maximum sag and ampacity values are fixed by the maximum allowable temperature, i.e., cold conductors are not the problem. Cost was also critical because this system should be a realistic alternative to the contact temperature instruments, which can be found for a few thousand euros.
The infrared thermometer chosen to fill these conditions was the commercial thermometer Optris CSLaser-SF50 model, with a temperature range between −30 and 1000 , spectral range between 8 m and 14 m and an optical resolution of 50:1. The sphere had 60 mm of diameter with a hole of 21.8 mm of diameter and it was made of aluminum with a surface emissivity in the range of 0.95–0.98.
To obtain a value for the emissivity as accurate as possible, the sphere and two cables, one new and other used, were sent to the Spanish Metrology Center (CEM). The idea was to check the emissivity changes due to the conductor’s aging and to estimate the emissivity of the sphere which would be placed on the conductor. The measurement procedure was as follows:
Equipment
For infrared temperature measurements, a LAND C300 type pyrometer with the serial number 40002068 and the calibration certificate number 132525001 was used. The detection range of the pyrometer was 8–14 m with a spot size of 4.5 mm diameter at 50 cm distance.
For contact temperature measurements, a Pt100 ISOTECH model with the serial number 191140/1 and the calibration certificate number 132564001 was used. It was connected to a thermometry bridge ASL F700 model with internal resistance with the serial number 005865/09 and the calibration certificate number 141034002.
Measurement Methods
To reach the different working temperatures, several methods were used:
: The samples were introduced into a dewar with ice and waited until stabilization.
: Laboratory controlled temperature was used .
and : A heating wire rolled over the samples was used.
The samples were partially painted with a high emissivity painting (Nextel
®). Contact temperature was measured with the calibrated Pt100 and the radiation temperature was measured with the pyrometer in the painted and the unpainted parts of the samples. Variations in the temperature measurements were used to obtain the values for the emissivity modifying its value from the pyrometer.
Figure 4b,c show pictures of the samples with the high emissivity painting and
Figure 4a shows a picture of the infrared temperature measurements. Temperature measurements were made at
,
,
and
for the new and used conductors and the sphere.
Contact temperature values from the Pt100,
, and radiation temperature values from the pyrometer,
, in painted and unpainted zones are summarized in
Table 2.
is the temperature stability during the measurements and
U the calibration and measurement expanded uncertainty for
of probability. Columns 9, 10 and 11 of
Table 2 indicate the differences between the contact temperature measurements and the radiation temperature measurements for
= 1 (painted part) and
(unpainted part) and the difference between the two radiation temperature measurements.
Figure 5a–c show the contact and radiation temperature measurements for the 3 samples with their uncertainties. As can be seen in
Figure 5a, the maximum temperature difference between the more accurate measurements (contact and infrared in painted zone) and the unpainted infrared temperature measurements corresponds to the new conductor.
Differences for used conductor and the sphere are less than in the measured nominal temperature range but up to in the case of the new conductor. This means that the emissivities for the old conductor and the sphere are close to 1 but for the new conductor is very low. New conductors have very shiny and polished surfaces with high reflectivity values which make the infrared temperature measurements more complicated. Aging and soiling of the conductor and the sphere contribute to increase the value of the emissivity making the estimations of infrared temperature measurements to improve with time if the emissivity values are corrected in the infrared thermometer.
Sample’s emissivity can be estimated using the pyrometer as the standard and changing the emissivity value of the equipment to reproduce the temperature differences obtained. In
Table 3 the values of the estimated emissivities are summarized.
Once the infrared thermometer and the sphere were characterized, the next step was to build a test facility to check the system behavior. An electric loop was installed in an outdoor facility to control the line parameters and measure the weather conditions with a weather station placed in site. The facility was performed with a high current and low voltage system to facilitate the operating conditions.
Figure 6 shows two details of the facility.
Two contact temperature sensors were placed, one close to the sphere and the other in the middle of the conductor, to check the temperature difference due to the cooling effect of the sphere and to compare with the infrared thermometer measurements. The contact probes were Pt100 type and the electronic transductors were calibrated with a resistance box provided by CEM. Finally, the sphere and the infrared thermometer were placed in the field, in an electric substation sited in the north of Spain, in collaboration with the electric distribution company, Viesgo, as can be seen in
Figure 7.