PD-29
DIELECTRIC HEATING IN INSULATING MATERIALS AT HIGH DC
AND AC VOLTAGES SUPERIMPOSED BY HIGH FREQUENCY HIGH
VOLTAGES
*
Matthias Birle and Carsten Leu
Ilmenau University of technology, Centre for electrical power engineering,
Research group of high voltage technology, Germany
*Email: matthias.birle@tu-ilmenau.de
Abstract: In this paper the measuring of the dielectric heating of insulating materials
stressed by high direct voltages and high power-frequency voltages superimposed by
high-frequency high-voltages (so called mixed-voltages) is described. First results are
presented. High-frequency high-voltage stress results in an intense heating caused by
higher dielectric losses commensurate to the frequency, the permittivity and the dielectric
dissipation factor of the material. The aim of the paper is to make a statement regarding
to the influence of superimposed high-frequency voltages on the dielectric heating of
nonpolar and polar polymers in steady state operation. Insulating materials in HVDC
systems and other power electronic high-voltage systems are stressed by mixedvoltages, high direct voltages, high power-frequency voltages and high-frequency
alternating voltages in different forms. To ensure a reliable and sustainable electrical
power supply, all components of the systems have to withstand the new demands
concerning the dielectric stress. Superimposed alternating voltages are repetitive pulses
or a ripple with different frequencies depending on the system configuration and
operation mode. For this stress, no design criteria for insulation materials or standards for
testing exist. Furthermore commercial test equipment for superimposed voltage tests,
especially high-frequency test voltages are not available. The test voltages up to several
10 kV are realized by a test system consisting of an innovative high-frequency highvoltage generator combined with conventional high-voltage AC- and DC- test equipment.
A constant sinusoidal high-frequency voltage up to 50 kV in a frequency range from 1 kHz
to 50 kHz is superimposed on a high 50 Hz alternating voltage or a high direct voltage in
different ratios. The correct measurement of the mixed-voltages is realized by special
high-voltage dividers. The test assembly is made by a temperature decoupled electric
field strength control of the samples where the heat transport mechanism is quantifiable.
1
INTRODUCTION
The conversion of electrical energy into an optimal
form for transmission, storage and consumers
usage is done by power electronic components
increasingly. Due to the switching operations of the
valves, high direct voltages and power-frequency
voltages are superimposed by ripple or repetitive
transients. These voltage forms are called mixedvoltages. The form and amplitude of mixed-voltage
depends on the principle of the inverter, the used
filter configuration and the load characteristic [2].
In this paper the temperature measurement of
dielectrically heated samples during mixed-voltage
stress is presented. Two important facts are in the
foreground of the investigations:
1. Generation of mixed-voltages as test voltages
with adjustable high-frequency components by
the use of a novel high-frequency high-voltage
generator.
2. Innovative test assembly for mixed-voltages,
but especially suitable for high-frequency
voltages, where the temperature of a sample
can be measured during voltage stress and
heat transfer mechanisms are quantifiable.
High-frequency high-voltage stress and the
associated high power losses can lead to life time
reduction respective insulation systems [4]. The
worst case is the failure of electrical equipment like
the example of the Eagle Pass installation [6].
Due to the use of sinusoidal voltage forms and the
special test set up, a mathematical treatment of the
measured temperature curves and complex
calculation for the dielectric losses are possible.
The measured temperature curves at mixedvoltage stress show the influence of the
subordinated voltage on the dielectric heating for
different polymers.
Experimental investigations of the breakdown of
polymers at mixed-voltage stress show that the
breakdown voltage is caused by dielectric heating
due to the high-frequency voltage components [1].
To describe the power losses at voltages with a
plurality of frequencies mathematically, a
theoretical approach is presented in [5].
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PD-29
2
Due to the increasing heating of the sample and
the associated temperature gradient, natural
convection occurs and the temperature curve
approaches to a maximum temperature max (see
Figure 1). The steady state is reached, if the
generated heat Q is equal to the dissipation heat
Qc by convection.
THEORETICAL BACKGROUND
The dielectric losses PDL, which are caused by an
alternating electrical field E are derived from the
electrical equivalent circuit for a lossy dielectric
(RC - circuit). For sinusoidal alternating voltages
PDL is given in Equation 1 where f = frequency,
εr’’ = loss factor and V = volume.
(1)
The quantity of the heat Q of a sample with the
mass m and the heat capacity c at a temperature
gradient of  is:
(2)
The heat dissipation by convection is
(3)
Figure 1: Qualitative temperature curve of the
heating of a sample, only internal heating and
convection
where  = heat transfer coefficient, AC = effective
surface for convection and t = time.
3
In a test set-up with a sample stressed by an
electrical field, where heat radiation and heat
conduction dissipation mechanisms can be
neglected compared to convection, the following
equation is valid:
The generation of the mixed-voltages to use them
as a test voltage is realized by the interconnection
of conventional high-voltage test systems with a
novel high-frequency high-voltage generator
(herein after referred as HFHV-generator) as
described in [3]. Figure 2 shows the high-voltage
circuit for the generation of a mixed-voltage
consisting of a high direct voltage and a highfrequency voltage (herein after referred as
DC + HF - voltage) schematically. An example of
the generated DC + HF - voltage is shown in
Figure 3.
(4)
The solution of the differential equation is:
(
(
)
(5)
)
With:
Figure 4 shows the high-voltage circuit for the
generation of the mixed-voltage consisting of a
power-frequency voltage and a high-frequency
voltage
(herein
after
referred
as
AC + HF - voltage). In Figure 5 an example of the
generated AC + HF - voltage is shown.
(6)
the temperature function is:
(
(
)
)
GENERATION OF MIXED-VOLTAGES AND
VOLTAGE MEASUREMENT
(7)
To protect the elements of the test systems and to
ensure a useful voltage distribution in the circuits,
decoupling elements Ld, Rd and Cd are used.
The qualitative temperature function in correlation
to Equation 7 is shown in Figure 1.
The buildup and the function of the HFHVgenerator are presented in [3] detailed. It is based
on the principle of resonance and generates a
constant sinusoidal high-frequency high-voltage in
the range of 1 kHz to 50 kHz with amplitude up to
70 kV, depending on the load. All capacitances
and inductances in the circuit affect the resonant
frequency of the HFHV-generator. This results in
different frequencies at different high-voltage
circuits (Figure 2 and Figure 4).
At the time t = 0 the temperature gradient Δ is
zero. The sample is at ambient temperature. This
case can be approached adiabatically. The
temperature curve in this case results in a rising
straight and given by Equation 8 (see Figure 1)
where the mass density is :
(8)
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PD-29
Figure 2: High-voltage circuit for the generation of
a mixed-voltage (DC + HF - voltage), EUT: equipment under test, FM: rotational voltmeter
Figure 4: High-voltage circuit for the generation of
a mixed-voltage (AC + HF - voltage), EUT: equipment under test
Figure 3: Example of generated DC + HF - voltage
(2,5 kHz)
Figure 5: Example of generated AC + HF - voltage
(50 Hz and 2,7 kHz)
The capacity of the test object has an influence on
the resonant frequency, also. Here, the frequency
variation due to the different sample materials is
only a few 100 Hz. Furthermore, the HFHVgenerator is used to stress the samples with a
constant sinusoidal high-frequency high-voltage
only. Thus higher frequencies are possible. The
used voltage forms and their resulting frequencies
are compared in Table 1.
Another method to measure high-voltages with
high frequencies or a plurality of frequencies is to
use a divider according to Zaengl. The used selfconstructed Zaengl-divider is characterized by
linear transfer behaviour over a wide frequency
range so that an accurate measurement of mixedvoltages with several frequencies is possible.
Therefore the Zaengl-divider is constructed of lowloss and temperature-stable capacitors and
resistors. The current rating of the divider must be
designed for the high alternating current
(depending on capacity and frequency up to
several hundred mA). The measurement of the
DC + HF - voltage is performed by a measurement
system where the high-frequency high-voltage is
measured with an capacitive divider (Cmeas,
Figure 2) and the direct voltage is measured by a
rotational voltmeter, which has its upper limit
frequency at 20 Hz. Both measurement signals are
merged subsequent.
Table 1: Voltage forms and resulting frequencies:
Voltage form
DC + HF - voltage
AC + HF - voltage
Sinusoidal HF voltage
Frequency
8,7 kHz
50 Hz + 17 kHz
22 kHz
The precise measurement of the generated mixedvoltages is important for the validity of the
investigations. The dielectric heating increases
with the square of the voltage (see Equation 1,
Chapter 2). An accurate measurement of the
voltage has to be guaranteed.
4
TEST SETUP
4.1 Test Vessel
The aim of the investigations is to measure the
dielectric heating of an insulating material sample
during high-voltage stress. The dielectric heating of
the sample is take place under two important
conditions. First, the dielectric heating is caused by
a constant sinusoidal voltage and a homogeneous
electrical field. Second, the heat transfer to the
ambient gas is the main heat dissipation
mechanism and heat conduction in solid materials
and radiation can be neglected. Then the
equations of Chapter 2 are valid for the measured
temperature curves and the temperature curve
For the measurement of high-frequency highvoltages solid-insulated high-voltage dividers are
only suitable for transient high frequency signals
and not for steady state high frequency signals.
Dielectric heating occurs in solid- and liquidinsulated high-voltage dividers also. Thus they can
vary their divider ratio in steady state operation.
Gas-insulated
dividers
(compressed
gas
capacitors) maintain a constant divider ratio in
steady state operation at high frequencies, due to
the insignificant loss factor of the used gaseous
dielectric.
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PD-29
at the DC + HF - voltage. The lower copper
electrode (4) is connected with the high-voltage
bushing by a thin conductive bar (6). The heat
conduction resistance at the contact of the lower
copper electrode (4) and conductive bar (6) is very
large. The upper copper electrode (4) is connected
with the ground side bushing by the shield of the
temperature sensor (5). The temperature is
measured directly on the surface of the upper thin
copper electrode (4).
shown in Figure 1, Chapter 2 can be expected. No
additional heat input into the sample other than the
dielectric heating of the sample is allowed. This
relates to other insulating materials which can be
warmed up by dielectric heating. Partial discharges
have to be completely avoided, also. At highfrequency high-voltages they result in an intense
local temperature increasing and strong erosion of
the sample. Figure 6 shows a sectional view of the
test vessel with a sample (schematically) that fulfils
these conditions.
As ambient medium (9) SF6 gas at a pressure of
3 bar absolute is used. It prevents partial
discharges completely and dielectric heating in the
gas is not significant. Dielectric solids and liquids
as embedding material would cause an additional
heat input into the system by dielectric heating and
result in a difficult mathematical treatment.
7
5
2
1
4
The shield ring assembly (3), the shield of the
temperature sensor (5) and the bushings (7)
and (8) are made of high-grade steel. The thermal
conductivity of high-grade steel is considerable
smaller compared to copper and aluminium. The
heat transport mechanism by thermal conductivity
through the solid materials is suppressed. The
pressure vessel (10) is made of an insulating
material, which has low thermal conductivity and
heat capacity.
3
6
10
8
9
Figure 6: Test vessel (schematic, sectional view),
1-sample, 2- stressed region of the sample,
3-shield ring assembly, 4-thin copper electrodes,
5-temperature sensor with earthed screen, 6-feed,
7-bushing (ground),
8- bushing (high-voltage),
9-SF6 gas, 10-pressure vessel
4.2 Sample materials
In this paper, the dielectric heating of polymers is
studied. Polymers in power energy technologies
are used for cables (cross-linked Polyethylene),
capacitors (Polypropylene) and construction
elements
(Polyamide,
Polyoxymethylen,
Polytetrafluorethylen, and Polyvinylchloride).
The thickness of the sample over the diameter is
not constant. Two thin copper electrodes (4)
contact the sample surface at the thicker middle
volume (2). These electrodes are necessary for the
displacement current of a few 10 to 100 mA at
higher frequencies. Thus, the volume (2) in the
sample is stressed by a homogeneous electric
field. The outer volume of the sample body is
thinner. Here, the electrical field stress in the
sample body is much lower, since electrical field
displacement is occurring in the area between the
sample and the shield ring (3). This is caused by
the difference between the permittivity’s of SF6 and
the solid sample. Thus, there is no heat input from
the outer volume of the sample into the stressed
volume (2).
They are classified into polar and non-polar
polymers. In contrast to non-polar polymers, polar
polymers feature orientation polarization. This
results in a higher permittivity εr, a higher
dissipation factor tan  and thus a higher loss
factor εr'' (εr'' = εr  tan ). Hence the dielectric
losses of polar materials are higher than the
dielectric losses of non-polar materials. Table 2
compares the measured materials, and shows the
loss factor εr'' for different frequencies at 25° C.
Table 2: Comparison of the measured materials,
their polarity and loss factor εr'' (εr'' = εr  tan ):
Material
The triple point (SF6-Gas (9), copper electrodes (4)
and sample (1)) is optimized by the shield rings (3)
so that no partial discharges occur. The shield
rings (3) do not contact the sample, since they
represent a high heat capacity and heat
conduction in the shield rings is not desired. The
creepage distance between the two copper
electrodes (4) has to be long enough, since the
surface resistance is fundamental for the flashover
PVC
PP
PE
Polarity
polar
non-polar
non-polar
Loss factor at 25°C
8,7 kHz 17 kHz
50 Hz
0,186
0,084
0,085
0,0011
0,001
0,001
0,0004
0,0004
0,0004
The sample thickness of 3 mm at the
homogeneous electrically stressed volume (see
Figure 6 (2)) is equal for all materials. The used
mixed-voltage configurations with subordinated
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The measured temperature curves show a linear
increase which rises exponentially to a final value
like
the
mathematical
characterization
in
Chapter 2. The marks in the diagram do not
represent the total number of measurement points
per curve.
voltages in the range of 10 kV to 50 kV lead to
electrical field strengths that are comparable to
those in power engineering equipment.
4.3 Test procedure
First, the dielectric heating at constant sinusoidal
voltage without a subordinated direct or powerfrequency voltage for the three different
frequencies shown in Table 1 has been measured.
Thereafter, the measurements were carried out for
mixed-voltage. At mixed-voltages the subordinated
voltage was set (power-frequency voltage or direct
voltage) and then immediately the high-frequency
high-voltage was adjusted to its value within one
second. The temperature measurement with a
sample rate of 1 Hz starts as soon as the highfrequency high-voltage is increased.
The voltage amplitude at PE compared to PVC and
PP is set at 10 kV for all measurements. For
smaller voltage amplitudes at PE no precise
temperature increasing is measurable. Higher
voltage amplitudes of the superimposed highfrequency voltage at PVC and PP have been
avoided because of the danger of damaging the
sample. The maximum temperatures of PVC are
different to the temperatures of PE. This is caused
by the fact that PVC is a polar material, orientation
polarization occurs and the loss factor is significant
higher (see Table 2)
Depending on the heating of the samples the
thermal steady state is achieved after about
30 minutes. Before a new measurement is
performed, the entire system is cooled down to
ambient temperature. For statistical confidence the
temperature
measurements
at
different
configurations where carried out several times.
5
RESULTS
In Figure 7, the temperature curves of PE and PVC
for different frequencies are presented.
Figure 8: Measured temperature increase of PE,
PP and PVC at DC + HF – voltage
Figure 9: Measured temperature increase of PE,
PP and PVC at AC + HF - voltage
Figure 7: Measured temperature increase of PE
and PVC at constant sinusoidal voltage with
different frequencies and amplitudes of 10 kV (PE)
and 6 kV (PVC)
The temperature curves at DC + HF - voltage for
PVC, PP and PE are presented in Figure 8. The
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PD-29
superimposed high-frequency voltage and the loss
factor of the materials are decisive for the dielectric
heating.
corresponding temperature curves at sinusoidal
voltage with same frequency and same amplitude
are shown in the diagram also. It can be seen that
the heating of the sample at DC + HF - voltage is
the same as for sinusoidal high-frequency voltage
stress with same frequency and amplitude.
At mixed-voltage forms (power-frequency voltage
superimposed by high-frequency voltage) and for
the polar material PVC, the measured
temperatures show, that the configuration of the
mixed voltage has an influence on the dielectric
heating. The power losses depend on the involved
voltage amplitudes and their frequencies
respectively. That means, the dielectric heating
and the maximum temperature respectively
increase with the voltage and frequency of the
subordinated and superimposed voltage form. At
non-polar materials (PE and PP) this effect was not
measureable, because of the small loss factor at
power-frequency.
The temperature curves at AC + HF - voltage are
shown in Figure 9. It can be seen that in the case
of PE and PP for both voltage forms the
temperature curves are equal. In contrast, for PVC
and mixed voltage configuration (20 kV – 50 Hz
and 6 kV – 17 kHz) the maximum temperature is
higher compared to sinusoidal voltage with
amplitude 6 kV and frequency 17 kHz. This is
caused by the fact that for PVC a temperature
increase at power-frequency is measurable also,
due to the high loss factor of PVC at powerfrequency. The power losses of PVC at 6 kV and
17 kHz only about fourteen times greater than at
20 kV and 50 Hz (see Table 2 and calculate
Equation 1). The maximum temperature of a PVC
sample at alternating voltage with an amplitude of
20 kV and a frequency of 50 Hz is 1,2° K (see
Figure 9).
6
For non-polar materials and at mixed-voltages with
high-frequency
components
up
to
10 %
(application field strengths) a thermal breakdown
can be excluded. In this case the temperaturedependent life time reduction is extremely low.
7
CONCLUSION
REFERENCES
[1] Birle, M.; Leu, C.; "Breakdown of polymer
dielectrics at high direct and alternating
voltages superimposed by high frequency high
voltages", 11th IEEE Conference on Solid
Dielectrics, July 2013.
In this paper, the dielectric heating of polymers at
mixed-voltage stress is presented. The used
mixed-voltages are high power-frequency voltages
and high direct voltages, superimposed by
constant sinusoidal high-frequency high-voltages
in the range of several kHz.
[2] Cigré Broshure 447 – Components Testing of
VSC System for HVDC Applications, Working
Group B4.48, February 2011.
An innovative test assembly was build up where
material samples (Polyethylene, Polypropylene
and Polyvinylchloride) are stressed by a
homogeneous electrical field. A direct temperature
measurement of the sample during voltage stress
is realized. The peculiarity is that the heat transfer
mechanisms of the test assembly are quantifiable,
because of the sample geometry, the sample
connections, the shield assemblies and the used
materials. A thermally decoupled electrical field
strength control restricts the heat transfer by
conduction in the solid elements. Thus a correct
measurement of the actual sample temperature
under voltage stress is realized. The reproducible
measured temperature curves show the expected
and calculable characteristic temperature increase.
[3] Birle, M; Leu, C.; Bauer, S.; “Design and
application of a High-Frequency High-Voltage
Generator”, XVII International Symposium on
High Voltage Engineering ISH, August 2011.
[4] Koltunowicz, T.L.; Kochetov, R.; Bajracharya,
G.; Djairam, D.; Smit, J.J., "Repetitive transient
aging, the influence of repetition frequency",
Electrical Insulation Conference (EIC), 2011,
vol., no., pp.444,448, 5-8 June 2011.
[5] Sonerud, B.;
Bengtsson, T.;
Blennow, J.;
Gubanski, S.M.; "Dielectric heating in insulating
materials subjected to voltage waveforms with
high harmonic content", Dielectrics and
Electrical Insulation, IEEE Transactions on ,
vol.16, no.4, pp.926-933, August 2009.
For mixed-voltage forms (high direct voltage
superimposed by high-frequency voltage) with a
total electrical field strength of 15 kV/mm the
dielectric heating is equal to the dielectric heating
of a sinusoidal high-frequency voltage with same
frequency and same amplitude like the
superimposed voltage. For these electric field
strengths, the subordinated direct voltage has no
impact on the dielectric heating due to a
superimposed
high-frequency
voltage.
The
frequency components, the amplitude of the
[6] Paulsson L., Ekehov B., Halén S., Larsson T.,
Palmqvist L., Edris A., Kidd D., Keri A., and
Mehraban B., “High frequency impacts in a
converter-based, back-to-back tie; The Eagle
Pass installation”, IEEE Trans. Power, Del., vol.
18, no. 4, pp. 1410–1415, Oct. 2003.
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