Introduction Very low frequency (VLF) AC voltage testing in the frequency range from 0.01 to 1 Hz is increasingly being used for both high voltage (Hi-Pot) acceptance and condition assessment of installed large capacitance power components [IEEE standards, IEC standard, etc.]. The main advantage of such tests is the low amount of reactive power needed compared to testing at power frequency. Today, equipment for VLF afterlaying tests are becoming available at voltages up to 400 kV. In addition, diagnostic parameters as for example partial discharge activity and dielectric losses, are regularly measured using VLF voltages.

1.  Some practical examples and experiences from
the use of VLF for AC breakdown and diagnostic
testing are summarized in chapter 4.
Theoretical background
Permittivity and dielectric loss
At AC voltage, the resulting dielectric loss is usually
deduced by considering a parallel plate capacitor with
a complex permittivity . The resulting
dielectric loss factor tanδ is the sum of contributions
from both dielectric polarization and losses due to
conductivity σ :
tanδ = tanδ1
(1)
Figure 1 - Permittivity and dissipation factor versus frequency
and temperature
This means that electrical conduction may become
the dominant loss mechanism at very low frequencies.
The applied voltage magnitude and particularly
the temperature of the insulation may therefore
strongly affect the dielectric loss at VLF voltages.
On the other hand, the time constant of the dielectric
relaxation mechanisms will become lower at •••
Introduction
Very low frequency (VLF) AC voltage testing in the
frequency range from 0.01 to 1 Hz is increasingly
being used for both high voltage (Hi-Pot) acceptance
and condition assessment of installed large
capacitance power components [IEEE standards,
IEC standard, etc.].
The main advantage of such tests is the low amount
of reactive power needed compared to testing at
power frequency. Today, equipment for VLF after-
laying tests are becoming available at voltages up
to 400 kV. In addition, diagnostic parameters as
for example partial discharge activity and dielectric
losses, are regularly measured using VLF voltages.
Scope and outline of the work
The main purpose of WG D1.48 was to review the
present knowledge regarding the effects of VLF
voltage testing on electrical properties and ageing
mechanisms of high voltage insulation systems,
aiming at facilitating development of methods and
useful evaluation criteria for both acceptance and
maintenance VLF-tests.
The Technical Brochure consists of three main parts.
 The theoretical part in chapter 2 gives an overview
of how permittivity, dielectric loss and electric field
distribution within insulation systems is expected
to vary with the frequency of the applied voltage
in the range from DC to AC power frequencies.
It presents the general principles of dielectric loss
and partial discharge measurements, as well as
mechanisms of ageing and initiation of electric
breakdown.
 Chapter 3 describes the different ways of
generating VLF test voltages and the methods
available for both withstand and diagnostic testing.
Members
E. ILDSTAD, Convenor (NO), F. MAUSETH, Secretary (NO), M. BAUR (AT),
T. BLACKBURN (AU), J. BLENNOW (SE), J. CASTELLON (FR), A. CAVALLINI (IT),
J. HOLBØLL (DK), N. HOZUMI (JP), H. MAYER (AU), P. MOHAUPT (AT),
F. PETZOLD (DE), C. SUMEREDER (AT)
Electrical properties of insulating
materials under VLF voltage
751WG D1.48
technical brochure
No. 302 - February 2019 ELECTRA 93

2. sufficiently low, causing local heating and melting of
the surrounding polymer.
The most important defects limiting the breakdown
strength of practical high voltage insulation systems
comprises cavities, particle inclusions, interface
irregularities, sharp edges at the electrode, etc.
The overall question addressed in this report is how
the physical and chemical erosion and degradation
process leading to tree initiation and subsequently
electrical breakdown is affected by VLF testing.
Electrical treeing
In case of electric tree formation, it is important to
consider the voltage or the electric field distribution
along the tree structure. As a first approximation, we
will here consider a simplified RC-model, presented
in Fig. 3. In this model, the tree channel is considered
a cylinder with radius r and a total channel resistance
of R, connected in series with the capacitance C of
the non-treed insulation section. In a real electric
tree, surface deposits of carbon determine the value
of this resistance, and its value is expected to reduce
as function of time due to partial discharge activity
and material degradation.
Figure 3 - Simplified RC-Model for a propagating electrical tree,
considered as a resistive tree channel in series with a capacitive
non-treed insulation between the tree tip and the ground electrode
Due to the thin tree channel it is a good approximation
to consider the capacitance C of the non-treed
insulation to be independent of the non-treed
insulation distance [2]. In the case of a channel with
a tip radius of 2 µm, the value of the capacitance
becomes C = 4.9∙10-4
pF. •••
Figure 4 - Ratio of voltage across the tree channel, versus total tree
channel resistance R at 50, 10 and 0.1 Hz [3]
higher temperatures, shifting the maximum losses
towards a higher frequency, as illustrated in Fig. 1.
Partial discharge activity
At low frequencies, the electric field distribution within
an insulation system becomes more determined by
the conductivity of the materials, and the classic
capacitive abc-model needs to be modified. The first
approximate approach is to add insulation resistances
in parallel with the capacitances, as shown in Fig. 2.
Figure 2 - Extended abc-equivalent circuit for modelling
of partial discharges [1]
Due to the insulation conductivity σ, it is expected
that the number of PD pulses per voltage period will
be reduced at VLF-testing below a certain frequency.
As a rule of thumb, the applied voltage frequency
should be approximately higher than
(2)
where σ is the highest conductivity of the insulation
system.
In case of n equal partial discharges occurring per
half period, the power dissipated by the discharges
increase proportional with frequency
(3)
where qa is the apparent partial discharge magnitude,
Ui is the effective applied ac voltage at PD inception
and f is the voltage frequency. Thus, PD activity is
expected to result in a rate of degradation proportional
to the frequency of the applied voltage.
Ageing and electric breakdown of
polymers
In most cases, electric breakdown in polymers is
a progressive, cumulative process involving the
initiation and growth of tiny tubular channels forming
electrical trees during dry service conditions. In case
of ageing in wet environments, water trees grows
due to the combined effect of water condensation
and electric field. Electrical breakdown finally occurs
when the resistance of the tree structure becomes
751WG D1.48
technical brochure
No. 302 - February 2019 ELECTRA 95

3. mechanical strength of the polymer will enhance
formation water filled tree shaped structures,
particularly following the amorphous regions of the
polymer. Due to the high electric conductivity of such
channels compared to the surrounding non-treed
insulation, high dielectric loss values is expected in
case of low frequency testing, particularly if water
trees bridge the insulation wall.
Short term VLF testing is of these reasons expected
not to enhance the formation of water trees.
Methods of generating VLF test
voltages
The report briefly gives an overview of the principle
of the four most common VLF test techniques
currently available, addressing limitations and future
possibilities.
Amplitude modulated VLF voltage
Here, a conventional high voltage transformer, fed
by a motor driven regulating transformer is used
to generate an amplitude modulated AC voltage.
The rectifiers connected to the high voltage side
are switched on at selected moments to create a
sinusoidal VLF voltage.
However, the motor-driven regulating transformer
limits the application to low power and low voltage.
Controlled DC charging and discharging
This principle is based upon combining high-voltage
transformers and two HVDC Greinacher cascades.
A sinusoidal VLF output voltage is obtained using a
complex control algorithm for the power module, DC
units and the discharge elements. The advantage of
this method is that there are no mechanically operated
parts. Choosing a sufficiently high frequency for the
power module, the dimensions and weight of the
transformers and cascades will be reduced. However,
due to the high complexity of the discharge elements
and the control algorithm, this concept cannot easily
be scaled to higher voltage levels.
Differential Resonance Technology (DRT)
This method exploits the property of both resonance
and superposition of two voltages at slightly different
high frequency adding to form a low frequency
voltage at the desired beat frequency. The beat
frequency oscillation consists of the carrier frequency
in the range of 1 kHz, whose amplitude is modulated
by the desired test frequency of, e.g., 0.1 Hz or
higher. Therein, a resonant circuit tuned to the carrier
frequency allows for the simple generation of the •••
The graph presented in Fig. 4 shows that the effect
of reducing the frequency, is that more of the applied
voltage will be across the non-treed insulation and
less stress along the tree structure. Thus, at lower
frequencies, the degree of branching will be reduced
compared to that at higher frequencies. Result
from laboratory experiments, presented in Fig. 5,
verify this expected frequency dependent shape of
electrical trees.
a) Bush shaped electrical b) Branch / filament type of
tree at 50 Hz,10kV tree at 0.1 Hz,14kV
Figure 5 - Typical electrical trees formed from needle tips in XLPE
at 50 and 0.1 Hz voltage[3]
At 50 Hz, rounded-off bush type-shaped trees were
formed, while more filament type of trees were
formed at 0.1 Hz.
Water treeing
Water trees are caused by the synergic effect of
humidity and electric stress. They typically grow very
slowly in the direction of the electric field and in wet
service conditions it may take 10-15 years to bridge
the insulation of a 12 kV XLPE. Examples of typical
water trees are shown in Fig. 6.
a) Vented- and b) bow-tie trees
Figure 6 - Typical Water trees formed in XLPE cables
during service stress at 50 Hz
Water trees are not associated with partial discharges
or emission of light during its initiation and growth.
At 50 Hz AC voltage water trees have, however,
been found to grow in all known polymeric insulation
at electric field stresses down to about 1 kV/mm.
While it has not been possible to detect water trees
formation in case of DC voltage application.
From a theoretical point of view, it is common to
explain formation of water trees by the combined and
slow action of condensation of water and Maxwell
forces acting on enclosed water droplets within the
insulation. Any chemical reactions reducing the
751WG D1.48
technical brochure
No. 302 - February 2019 ELECTRA 97

4. insulation, space charge measurements showed
that the exponential space charge accumulation at
the interfaces followed a time constant of about 2.5
days. This is in good agreement with Eq. (2) using
the average conductivity for the layered insulation.
This strongly indicates that no major electric field
distortions is expected within XLPE cable insulation
during VLF 0.1 Hz testing.
In case of testing cable systems with accessories,
it is important to consider the conductivity of field
grading materials, particularly in case of dielectric
loss and PD measurements.
Dielectric losses
Resultsfrommeasurementsoflowfrequencydielectric
loss of XLPE cable samples have demonstrated that
conduction becomes the dominant loss mechanisms
at temperatures above approximately 50 °C [5].
In case of aged cable samples, the dissipation factor
at 0.1 Hz was, as illustrated in Figure 8, found to
increase significantly with the applied test voltage
[6]. A non-linearity strongly indicating water tree
degradation.
Some condition assessment criteria for service aged
XLPE cables are summarized in [7].
Partial discharges
PD diagnostic at VLF tests is still a challenging task
due to noise interference from the switching devices
within the VLF test sets, particularly at the highest
system voltages requiring higher sensitivity.
As an example, Figure 9 shows typical results from
laboratory PD measurements using test voltage in
the frequency range of 0.01 – 100 Hz and samples
of polycarbonate containing cavities [8]. The results
reveal a reduced number of partial discharges per
period when reducing the frequency. An effect •••
necessary high voltages. By changing the modulation
frequency, VLF voltages at several hundred kV can
be generated in the frequency range from 0.1 Hz up
to 10 Hz.
Cosine-rectangular VLF technology
This type of generator is based upon power electronic
switching or bipolar charging, using built-in positive
and negative HVDC sources, resulting in a square
shaped VLF output voltage.
The significant and most important property of the
cosine-rectangular VLF technology is, however, the
shape of the power recovery during polarity reversal. It
is common to aim at a slope close to that at a frequency
of 50 Hz. Thus, the field stress during polarity reversal
is comparable that at operating frequency.
Selected results from VLF testing
The brochure reviews some practical experience
from VLF testing, mainly from applications on XLPE
cable systems and electrical machines.
Interface charging and electric field
distribution
At low frequencies, the electric field distribution is
expected to be affected by the conductivity of the
insulation, according to Eq. (2). Results summarized
in Fig. 7 indicate that space charge accumulation
in XLPE cable insulations increases at frequencies
below 0.02 Hz [4].
In addition to frequency and duration of voltage
application, different combinations of electrode
materials (e.g. semi-conductor) are important
factors determining the space charge injection and
distribution under AC electric stress.
In case of applying DC voltage to layered XLPE
Figure 7 - Relationship between frequency of the applied electrical
stress and space charge build-up in the bulk of XLPE at room
temperature [4]
Figure 8 - Measured dissipation factors at 0.1 Hz versus test voltage
in kV applied to different type of service aged XLPE cables [6]
751WG D1.48
technical brochure
No. 302 - February 2019 ELECTRA 99

5. It is important to relate the expected endurance at
0.1 Hz voltage testing to that at 50-60 Hz service
stress, considering similar type of defects. A
comprehensive comparison of such breakdown
values are summarized in Fig. 11 [10]. The results
show that in most cases breakdown at VLF (0.1
Hz) testing occur at voltage levels 1-4 times higher
than that at 50 Hz AC voltage. Voids are particularly
difficult to detect.
As shown in Fig. 12, there is a strong correlation
between breakdown at power frequency AC and VLF
voltages [11]. On average, the 0.1 Hz VLF breakdown
values of water treed cables are found to be about
two times higher than breakdown values at 50 Hz AC.
Figure 12 - AC 50 Hz (lower red) and VLF 0.1 Hz
(upper blue) breakdown voltages of water tree
degraded cable samples as a function of non-treed
insulation thickness. Filled and unfilled symbols
represents results from service and laboratory aged
cables, respectively [11]. •••
which was explained using the model of Fig. 2
including charge decay after a discharge.
In most cases, small differences are found between
PD inception voltage, PD magnitudes and the phase-
resolved PD patterns measured at 0.1 Hz and 50 Hz.
In case of testing 12 kV service-aged XLPE cable
samples with cold-shrink joints, a clear frequency
dependence was , however, observed [9]. The results
presented in Fig. 10 show that at frequencies below
0.2 Hz both the PD inception and extinction voltages
were found to be below the service stress at 50 Hz.
This indicates a frequency dependent electric field
distribution within the joints, making it challenging
to correlate PD results obtained at VLF to that at
operating frequency.
Electric breakdown under VLF testing
By electric withstand testing, it is in general possible
to only locate the weakest sites. It can however give
an indication to whether the test object is in good or
bad condition.
Figure 9 - Total number of PDs per voltage cycle and right; average
PD magnitude for insulated cavities [8]
Figure 10 - PD inception (PDIV) and extinction (PDEV) voltage
for a cold-shrink 12 kV cable joint as a function of frequency [9].
Closed Void
Conductive
Protrusion
Insulating
Contaminant
XLPE
Insulation
Conductive
Contaminant
Conductive
Contaminant
Conductive
Contaminant
Insulating
Contaminant
Cut in Cable
Insulation Insufficient
Compression of I/F
Water
droplet
Rubber-
XLPE
Interface
DC
VLF
OSW
Rubber-
XLPE
Interface
Figure 11 - Ratio of breakdown value obtained at different type of
test voltage relative to AC voltage for several types of defects in
cables and accessories [10]
Figure 12 - AC 50 Hz (lower red) and VLF 0.1 Hz (upper blue)
breakdown voltages of water tree degraded cable samples as
a function of non-treed insulation thickness. Filled and unfilled
symbols represents results from service and laboratory aged cables,
respectively [11]
751WG D1.48
technical brochure
No. 302 - February 2019 ELECTRA 101

6. shows that electric breakdown of XLPE cables
occur at voltage levels 1-4 times higher than that
at 50 Hz AC voltage. Voids are particularly difficult
to detect by VLF withstand voltage testing. In case
of water tree-degraded cables, the breakdown
at VLF voltage varies from 50 to 200% of that at
power frequency.
References
[1] P. K. Olsen, F. Mauseth, and E. Ildstad, “The effect of DC
superimposed AC voltage on partial discharges in dielectric
bounded cavities”, presented at the 2014 International
Conference on High Voltage Engineering and Application
(ICHVE), 2014
[2] J. Lekner, “Capacitance coefficients of two spheres”,
Electrostat., vol. 69, pp. 11-14, 2011.
[3] E.Ildstad, K. Fauskanger and J. Holto, “Electrical Treeing
from Needle Implants in XLPE during Very Low Frequency
(VLF) Voltage Testing” IEEE ICSD, Bologna, Italy, June
2013.
[4] X. Wang, N. Yoshimura, Y. Tanaka, K. Murata, and T. Takada,
“Space charge characteristics in cross-linking polyethylene
under electrical stress from DC to power frequency”, J. Phys.
D: Appl. Phys. , vol. 31, pp. 2057-2064, 1998.
[5] C. Dang and S. Pelissou, “Some technical consideration
on very low frequency cable diagnostic”, presented at the
Transmission and Distribution Conference and Exposition,
2003.
[6] J. C. Hernández-Mejía, R. Harley, N. Hampton, and R.
Hartlein, “Characterization of Ageing for MV Power Cables
Using Low Frequency Tan d Diagnostic Measurements”,
IEEE Trans. Diel. and El. Insul., pp. 862-870, 2009.
[7] IEEE Guide for Field Testing of Shielded Power Cable
Systems Using Very Low Frequency (less than 1 Hz), 2013.
[8] C. Forssén and H. Edin, “Partial discharges in a cavity
at variable applied frequency part 2: measurements and
modeling”, IEEE Trans. Diel. and El. Insul., vol. 15, no. 6, pp.
1610-1616, 2008.
[9] F. Mauseth, H. Tollefsen, and S. Hvidsten, “Effect of Test
Voltage Frequency on PD Inception on Service Aged Cable
Joint”, presented at the IEEE Int. Conf. on High Voltage Eng.,
Poznan, Poland, 2014.
[10] K. Uchida, H. Tanaka, and K. Hirotsu, “Study on Detection
for the Defects of XLPE Cable Lines”, IEEE Trans. on Power
Delivery, vol. 11, no. 2, pp. 663-668, 1996.
[11] K. Uchida, M. Nakade, D. Inoue, H. Sakakibara, and M. Yagi,
“Life Estimation of Water Tree Deteriorated XLPE Cables
by VLF(Very Low Frequency) Voltage Withstand Test”,
presented at the PES T&D 2002, 2002. 
Conclusions
The data collected by the literature survey is
discussed with respect to known practical experience
and theoretical considerations. The main purpose of
addressing the physical mechanisms of space charge
formation and degradation has been to provide a
base for evaluation of possibilities and limitations
regarding application of VLF tests, both as high
voltage acceptance/after laying tests and diagnostic
tools. It is concluded that:
 In case of VLF (0,1 Hz) testing of high voltage
insulation systems, the risk of space charge
accumulation is very low, and the electric
field distribution becomes similar to that at
power frequency, provided the conductivity of
the insulating materials is lower than about:
σ < 1·10-16
Ω-1
m-1
.
 During VLF testing of installed cable systems it is
important to address the electric field distribution
within the accessories, as it may become
frequency-dependent, due to higher and non-linear
conductivity of field grading materials compared to
that of the insulation.
 At VLF voltages, the rate of electrical treeing
and gradual degradation is reduced compared to
that at power frequency. Mainly due to the lower
number of Partial discharges per time unit and
reduced voltage drop across voids and electrical
tree channels. More knowledge is, however,
needed to improve comparison and interpretation
of results from partial discharge measurements at
VLF test voltages with that at service stresses.
 For condition assessment of insulation systems,
low frequency measurements of permittivity and
dielectric loss factors is a useful diagnostic tool -
revealing critical changes in conductivity and other
material parameters. For example, VLF testing
of severely water tree degraded XLPE cables is
indicated by high and increased value of dielectric
loss with increasing test voltage.
 Experience from VLF (0.1 Hz) breakdown testing
BROCHURE N° 751
(en anglais seulement)
(in English only)
Disponible sur / Available on:
www.e-cigre.org
Prix non-Membres / Non-Member Price:
90 €
Purchase (non-members)
Free download (members)
751WG D1.48
technical brochure
No. 302 - February 2019 ELECTRA 103