Нагрев токоведущих частей при длительном протекании тока
DETERMINING HIGH VOLTAGE CABLE CONDUCTOR TEMPERATURES.
Guy Van der Veken.
Euromold, Belgium.
INTRODUCTION.
Type tests on MV cable accessories are described in CENELEC HD628 and HD629 documents.
Some of the tests described require elevated conductor temperatures within strict limits (e.g. 5K to 10K above the maximum permissible operating temperature of the extruded cable insulation).
To accomplish this, over the allowed range of ambiant temperatures, the heating current is to be regulated.
Due to the presence of high test-voltages acrossthe cable’s insulation, the on-line measurement
Guy Van der Veken.
Euromold, Belgium.
INTRODUCTION.
Type tests on MV cable accessories are described in CENELEC HD628 and HD629 documents.
Some of the tests described require elevated conductor temperatures within strict limits (e.g. 5K to 10K above the maximum permissible operating temperature of the extruded cable insulation).
To accomplish this, over the allowed range of ambiant temperatures, the heating current is to be regulated.
Due to the presence of high test-voltages acrossthe cable’s insulation, the on-line measurement
INVESTIGATIONS.
Following points have been evaluated: 1) Validity of the methods as described. 2) Uncertainty of the results obtained. 3) Comparison of the two methods.
For this purpose, following variables have been examined:
a) Thermocouple materials.
b) Thermocouple execution.
c) Thermocouple placement.
d) Effect of conductor cross-section. e) Number of thermocouples used.
Uncertainty factors evaluated include:
a) Uncertainty of the measuring equipments. b) Uncertainty of the measurements.
c) Uncertainty of the calculated temperature.
RESULT
Evaluation of the data leads to following conclusions:
1) The method 2, using jacket temperature measurement, results in the lowest deviation.
2) Uncertainty of the temperature determined
(± 3K for small crossections to ± 5K for large crosssections) is found to be high when compared to the temperature range given (5K).
Following points have been evaluated: 1) Validity of the methods as described. 2) Uncertainty of the results obtained. 3) Comparison of the two methods.
For this purpose, following variables have been examined:
a) Thermocouple materials.
b) Thermocouple execution.
c) Thermocouple placement.
d) Effect of conductor cross-section. e) Number of thermocouples used.
Uncertainty factors evaluated include:
a) Uncertainty of the measuring equipments. b) Uncertainty of the measurements.
c) Uncertainty of the calculated temperature.
RESULT
Evaluation of the data leads to following conclusions:
1) The method 2, using jacket temperature measurement, results in the lowest deviation.
2) Uncertainty of the temperature determined
(± 3K for small crossections to ± 5K for large crosssections) is found to be high when compared to the temperature range given (5K).
of the conductor temperature on the
is not possible using standard
techniques.
3 methods for determining the cable
are given in the document HD628:
1) Method 1 using the relationship between the conductor temperature, the heating current and the ambiant temperature.
2) Method 2 using the relationship between the conductor temperature, the heating current and the cable-jacket temperature.
(These two methods require a preceding calibration of the cable, to establish these relationships.)
3) Method 3 using a parallel loop of same cable in the same environment that is heated with the same current, but is not carrying high voltage.
is not possible using standard
techniques.
3 methods for determining the cable
are given in the document HD628:
1) Method 1 using the relationship between the conductor temperature, the heating current and the ambiant temperature.
2) Method 2 using the relationship between the conductor temperature, the heating current and the cable-jacket temperature.
(These two methods require a preceding calibration of the cable, to establish these relationships.)
3) Method 3 using a parallel loop of same cable in the same environment that is heated with the same current, but is not carrying high voltage.
Cable insulation eccentricity and diameter monitor
RESEARCH.
In order to make a choice between the aforemen- tioned methods, we investigated the following ele- ments:
1. Checking the existing methods.
2. Which method gives the most accurate con- ductor temperature.
3. Is the 5K range feasible? In order to check this, we carried out an uncertainty study according to standard XP X07-020 of 1996.
The tests.
The test configuration. To carry out the no- voltage pre-test (calibration of the cable), the test configuration in figure 2 was used.
At each measurement point, 1 thermocouple (cali- brated) of each thermocouple group (see next paragraph) was attached. This enables us to es- tablish which thermocouple group gives the most accurate temperature reading and whether there are major temperature differences between the different thermocouple groups.
In order to make a choice between the aforemen- tioned methods, we investigated the following ele- ments:
1. Checking the existing methods.
2. Which method gives the most accurate con- ductor temperature.
3. Is the 5K range feasible? In order to check this, we carried out an uncertainty study according to standard XP X07-020 of 1996.
The tests.
At each measurement point, 1 thermocouple (cali- brated) of each thermocouple group (see next paragraph) was attached. This enables us to es- tablish which thermocouple group gives the most accurate temperature reading and whether there are major temperature differences between the different thermocouple groups.
Increased temperature
Cooling
10K
Environ- ment-
Time
2 hrs
3 hrs
8 hrs
will carry out a no-voltage pre-test (calibration) i.e.:st
A 1 method enables us to obtain the relationship
between the conductor temperature, the ambient
temperature and the current.
nd
With a 2
tween the conductor temperature, the cable-jacket temperature and the current.
Specific test.
The heat-cycle test is one of the tests in which we use an increased conductor temperature. This test consists of 128 cycles. Each cycle (see figure 1) lasts for 8 hours and consists of the following steps:
* Heat the cable so that the conductor temperature is within the increased temperature zone for at least 2 hours.
* Leave the cable to cool down naturally for at least 3 hours, until the temperature difference between the conductor and the environment is maximum 10K.
temperature and the current.
nd
With a 2
tween the conductor temperature, the cable-jacket temperature and the current.
Specific test.
The heat-cycle test is one of the tests in which we use an increased conductor temperature. This test consists of 128 cycles. Each cycle (see figure 1) lasts for 8 hours and consists of the following steps:
* Heat the cable so that the conductor temperature is within the increased temperature zone for at least 2 hours.
* Leave the cable to cool down naturally for at least 3 hours, until the temperature difference between the conductor and the environment is maximum 10K.
method, we obtain the relationship be-
MP1
current 70cm 90cm source
MP4 Figure 2: Test configuration.
current 70cm 90cm source
MP4 Figure 2: Test configuration.
MP2
70cm
MP3
70cm
MP3
make the conductor visible) is closed and the jacket is put back in its original position.
Jacket Insulation
Thermocouple
Conductor
Figure 7: Presentation of the thermocouple posi- tioning with the window method.
Calibration. During calibration, the following measurement values are registered every 5 min- utes: current, jacket-, environment- and conductor- temperature. The thermocouples used are de-scribed in paragraph “The thermocouple groups”. The test configuration used is given in figure 2 and the positioning of the thermocouples is described in the previous paragraph. Calibration was carried out for Al cables with a 50mm2, 240mm2 and 630mm2 section. With this choice, we cover a wide range of high voltage cables regarding the cable section. In addition, it gives us a good idea of the better method for determining the conductor tem- perature and of the uncertainty about the conduc- tor temperature we can expect when testing with an increased temperature.
The uncertainty.
To determine the uncertainty of the conductor temperature, we used the French standard XP X07-020 of 1996. This standard is based on estab- lishing the variances on the variables needed for determining the conductor temperature, i.e. vari- ance on current, ambient temperature and jacket temperature. A factor we must certainly take into account is the variance on the model. This is the difference between the conductor temperature measured during calibration and the calculated conductor temperature on the basis of the meas- ured current and the measured jacket temperature (or ambient temperature according to the method used). Once these variances are known, we can establish the variance on the conductor tempera- ture. Then, the uncertainty is indicated by:
∆θconductor = k * (V[θconductor])1/2. (with ∆θconductor : un-certainty on the conductor; k: widening factor;
V[θconductor]: variance on the conductor tempera- ture.)
Jacket Insulation
Thermocouple
Conductor
Figure 7: Presentation of the thermocouple posi- tioning with the window method.
Calibration. During calibration, the following measurement values are registered every 5 min- utes: current, jacket-, environment- and conductor- temperature. The thermocouples used are de-scribed in paragraph “The thermocouple groups”. The test configuration used is given in figure 2 and the positioning of the thermocouples is described in the previous paragraph. Calibration was carried out for Al cables with a 50mm2, 240mm2 and 630mm2 section. With this choice, we cover a wide range of high voltage cables regarding the cable section. In addition, it gives us a good idea of the better method for determining the conductor tem- perature and of the uncertainty about the conduc- tor temperature we can expect when testing with an increased temperature.
The uncertainty.
To determine the uncertainty of the conductor temperature, we used the French standard XP X07-020 of 1996. This standard is based on estab- lishing the variances on the variables needed for determining the conductor temperature, i.e. vari- ance on current, ambient temperature and jacket temperature. A factor we must certainly take into account is the variance on the model. This is the difference between the conductor temperature measured during calibration and the calculated conductor temperature on the basis of the meas- ured current and the measured jacket temperature (or ambient temperature according to the method used). Once these variances are known, we can establish the variance on the conductor tempera- ture. Then, the uncertainty is indicated by:
∆θconductor = k * (V[θconductor])1/2. (with ∆θconductor : un-certainty on the conductor; k: widening factor;
V[θconductor]: variance on the conductor tempera- ture.)
The thermocouple groups. Thermocouple group 1 (= Cenelec method): J-type, point soldered (fig- ure 3). Thermocouple group 2 (= point method): J- type, unsoldered (figure 4). Thermocouple group 3: (window mehtod): J-type, twisted, soldered (figure 5). Thermocouple group 4: strip thermocouple (this is a thermocouple that is attached onto a copper layer, making it possible to measure the jacket temperature with these thermocouples).
Figure 3: Cenelec method.
Figure 4: Point method.
Figure 5: Window method.
Figure 4: Point method.
Figure 5: Window method.
junction
conductor
junction
conductor
junction
Positioning of the thermocouples. The thermo- couples in groups 1 and 2 are connected to the conductor through a small hole, drilled in the cable (see figure 6). This figure also shows how the thermocouple must be positioned, i.e. where the thermocouple wire comes out of the cable, it will be bent. When taping the thermocouple, this bend will provide a pressure point.
Jacket
Insulation
Conductor
Insulation
Conductor
Figure 6: Presentation of the thermocouple posi- tioning with the drilled method.
The thermocouples in group 3 are in contact with the conductor by inserting them between the dif- ferent conductor wires (see figure 7). When the thermocouple is put in place, the window (rectan- gular cut-out in the cable-jacket and insulation to
The thermocouples in group 3 are in contact with the conductor by inserting them between the dif- ferent conductor wires (see figure 7). When the thermocouple is put in place, the window (rectan- gular cut-out in the cable-jacket and insulation to
Thermocouple
RESULTS.
Cenelec ↔ Points ↔ Window.
The results are discussed on the basis of figures. They are the result of the calculations based on the values measured during the tests. However, it is impossible to explain for each figure where all the values come from.
Method 1 ↔ method 2.
When looking at figure 8, we can clearly see that the variance on the model with method 1 (θConductorbased on θEnvironment) is always bigger than with method 2 (θConductor based on θJacket).
Method 1 ↔ method 2.
When looking at figure 8, we can clearly see that the variance on the model with method 1 (θConductorbased on θEnvironment) is always bigger than with method 2 (θConductor based on θJacket).
In this paragraph, we will only consider the results obtained with method 2 (θConductor based on θJacket). The reason for this is given in the previous para- graph.
124°C 122°C 120°C 118°C 116°C 114°C 112°C 110°C 108°C 106°C 104°C
Cenelec Points Window Cenelec Points Window Cenelec Points Window
Cable 50mm2 Cable 240mm2 Cable 630mm2
Cable 50mm2 Cable 240mm2 Cable 630mm2
Temperature of conductor Uncertainty
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
502
2402 6302
CENELEC
Method 2
CENELEC
Method 2
502 2402 6302
POINTS
POINTS
502 2402 6302
WINDOW
WINDOW
Method 1
Figure 8: The variances on the model.
This greater variance on the model has a direct impact on the total uncertainty ∆θConductor (see fig- ure 9). Here too, we see that method 1 always gives greater values.
This greater variance on the model has a direct impact on the total uncertainty ∆θConductor (see fig- ure 9). Here too, we see that method 1 always gives greater values.
Figure 10: Representation of the average conduc- tor temperatures and the uncertainties for the dif- ferent cables and thermocouple positioning.
When looking at this graph, we notice the follow- ing:
* The conductor temperature is highest when the thermocouples are positioned according to the point method (for all three cables).
* The point and window methods are two equiva- lent methods: they have nearly the same conduc- tor temperature and uncertainty.
* The conductor temperatures calculated on the basis of the Cenelec method are 6 to 10°C lower than the conductor temperature calculated on the basis of the point and window methods.
* The uncertainty on the conductor temperature is approximately identical with the 3 methods (Cenelec, points, window).
So we can conclude that the positioning of the thermocouples is better with the point or window method.
Impact of the partial factors
From paragraph "Method 1 ↔ method 2" we know that method 2 is the most appropriate to determineθConductor. Paragraph "Cenelec ↔ points ↔ win- dow" gives us the positioning of the thermocouples (points or window). When discussing the results, we will only consider these methods.
With method 2, V[θConductor]Jacket (= variance on the conductor temperature, whereby the conductor temperature is established on the basis of the jacket temperature) is determined as follows:
When looking at this graph, we notice the follow- ing:
* The conductor temperature is highest when the thermocouples are positioned according to the point method (for all three cables).
* The point and window methods are two equiva- lent methods: they have nearly the same conduc- tor temperature and uncertainty.
* The conductor temperatures calculated on the basis of the Cenelec method are 6 to 10°C lower than the conductor temperature calculated on the basis of the point and window methods.
* The uncertainty on the conductor temperature is approximately identical with the 3 methods (Cenelec, points, window).
So we can conclude that the positioning of the thermocouples is better with the point or window method.
Impact of the partial factors
From paragraph "Method 1 ↔ method 2" we know that method 2 is the most appropriate to determineθConductor. Paragraph "Cenelec ↔ points ↔ win- dow" gives us the positioning of the thermocouples (points or window). When discussing the results, we will only consider these methods.
With method 2, V[θConductor]Jacket (= variance on the conductor temperature, whereby the conductor temperature is established on the basis of the jacket temperature) is determined as follows:
6
5
4
3
2
1
0
5
4
3
2
1
0
502
Method 1
Method 1
2402 6302
CENELEC
Method 2
CENELEC
Method 2
502 2402 6302
POINTS
POINTS
502 2402 6302
WINDOW
WINDOW
Figure 9: The uncertainties in graph.
We can conclude from figures 8 and 9 that method 2 (θconductor based on θJacket) should be preferred for determining θConductor as this method gives us the smallest variance on the model and the smallest uncertainty.
We can conclude from figures 8 and 9 that method 2 (θconductor based on θJacket) should be preferred for determining θConductor as this method gives us the smallest variance on the model and the smallest uncertainty.
∆θConductor (°C)
Variance on model (°C2)
θCond and ∆θCond
Factor 3 26%
Factor 2 3%
50mm2 - Window
V[θCond] = 2.71 °C2∆θCond,Jacket = +/- 3.3 °C
Factor 4 9%
Factor 1 
Factor 2 
Factor 3 
Factor 4
Factor 1 62%
22
∂θ=+
∂θ
V[ ] .V[ ] .V[I]
Cond Jacket ∂θ
Cond
∂I. +
∂I. +
θ+2. Cond . Cond . V[θ
Cond
θ
∂θ ∂θ
]V[I]V[function]
Jacket
Jacket
.V [θJacket.V [I ] = factor 2
Jacket
.V [θJacket.V [I ] = factor 2
Jacket
∂θ
Jacket
∂I
Whereby:
( ∂θCond )2∂ θ Jacket
∂I2.(∂θCond ).(∂θCond ). V[θJacket]. V[I]=factor3
∂θJacket ∂IV [function] = factor 4
Factors 1, 2, 3, 4 are represented in fig. 11.a → f.
∂I2.(∂θCond ).(∂θCond ). V[θJacket]. V[I]=factor3
∂θJacket ∂IV [function] = factor 4
Factors 1, 2, 3, 4 are represented in fig. 11.a → f.
∂θCond( )2
]
= factor 1
Figure 11b: Percentage of the partial factors for the 50mm2-Al cable (window method).
240mm2 - Points
V[θCond] = 3.26 °C2∆θCond,Jacket = +/- 3.62 °C
Factor 4 35%
Factor 3 19%
Factor 2 2%
Factor 1 Factor 2 
Factor 3 
Factor 4
Factor 1 44%
50mm2 - Points
Factor 4 11%
Factor 2 3%
Factor 1
Factor 4 11%
Factor 2 3%
Factor 1
V[θCond] = 2.9 °C2∆θCond,Jacket = +/- 3.41 °C
Factor 3 26%
Factor 2 
Factor 3 
Factor 4
Factor 1 60%
Figure 11a: Percentage of the partial factors for the50mm2-Al cable (point method).
Figure 11c: Percentage of the partial factors for the 240mm2-Al cable (point method).
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