Estimation of Partial Discharge Inception Voltages due to

3rd IASME/WSEAS Int. Conf. on Energy & Environment, University of Cambridge, UK, February 23-25, 2008
Estimation of Partial Discharge Inception Voltages due to Voids in Power
M.U. Zuberi, A. Masood, M.F. Khan, Ekram Husain & A. Anwar
Department of Electrical Engineering, Z.H. College of Engineering and Technology
Aligarh Muslim University, Aligarh 202002
Abstract - In this paper we report a technique for estimating the Partial Discharge (PD) inception voltages in case of
discharges occurring at in voids in power cables in the ambient medium of air. Since occurrence of PD is a
phenomenon dependent on upon many factors such as the type of gas in the void, the gas pressure, surface properties
of the void, size and shape of the void, location of the void, dielectric constant of the surrounding medium etc; these
parameters have to be taken into account. The computed values are valid in the pressure range of 0.067 kPa to
101.333 kPa and for gaps ranging from 0.001 cm to 11.0 cm. Computations are accurate to ± 3.5 % in the pt′ range
of 0.0133 – 1400 kPa-cm.
Keywords - Partial Discharge, Electrical Insulation, Void Discharges, Inception Voltage, Power Cables.
1. Introduction
Quality of insulation is essential for successful and
reliable operation of any power apparatus. Minor flaws
and irregularities such as voids, surface imperfections in
the insulation are however inevitable and lead to partial
discharge which are characterized by an electrical
breakdown at localized regions of the electrical
insulation. [1]-[3]. The localization of the discharge may
be the consequence of an electric field enhancement
restricted to region that is relatively small compared with
the dimensions of the space or gap between the
conductors. The field enhancement can be associated
with abrupt changes in the nature of the insulating
medium that may be caused by voids in solid dielectrics
or gas filled spaces at dielectric or gas filled spaces at
dielectric-conductor or dielectric-dielectric interface.
Discharges within cavities (voids) in solid insulating
system [4] have long been associated with gradual
degradation and dielectric failure. The correlation
between cavity discharge and degradation has been
established for rotating machines [5], power cables [6]
encapsulated transformers and many other solid
dielectric systems so that the correlation between cavity
discharge and degradation is now well established. Gas
filled cavities can originate in a wide range of solid
dielectric systems through many mechanism including
differential thermal expansion(composite systems)
incomplete impregnation or excessive mechanical
stress(fiber reinforced systems) or improper process
control (epoxy castings).Cavities can also originate over
a lifetime of operation as a result of environmental
For PD tests, some existing standards have already
evolved from the ‘representation of the worst working
ISSN: 1790-5095
Page 345
conditions’ to the requirement of a ‘quality of the
insulation system’. This procedure requires a high
quality for the design and construction of the insulating
structures by controlling their electric field strength at
any point. However, in most of the cases it is in fact
impossible to estimate the real dimensions of the PD
source and of the cavity where it has been produced.
Even more difficult is the evaluation of the chemical or
physical deterioration that it will produce during long
operating times. Since it has not been possible to
establish a definite relationship between the discharge
intensity and the in-service life of electrical insulating
systems employed in cables and power apparatus, the
conventional wisdom has always been to insist on the
total absence of PD under operating conditions, which in
turn favored the establishment and universal acceptance
of standardized go/no-go PD tests. In an attempt to
quantify the use of partial discharges in evaluating the
quality of any insulation system, the lowest voltage at
which such events is detected, the partial discharge
inception voltage (PDIV) is proposed in [7].
The question arises as to how the PDIV depends on
pressure as the pressure in the void decreases to near the
Paschen minimum or below [8].
In the present work a technique has been developed to
evaluate the partial discharge inception voltages in case
of discharges occurring in voids in single core power
cables. The estimation of partial discharge voltages is
based on the analysis of Townsend breakdown criterion
and is valid for the whole range of Paschen’s curve
available. These formulations can be applied for
estimating the PD inception voltages in case of
discharges occurring in voids with sufficient accuracy
for various cable sizes and pressures.
ISBN: 978-960-6766-43-5
3rd IASME/WSEAS Int. Conf. on Energy & Environment, University of Cambridge, UK, February 23-25, 2008
2. Present Approach
On the basis of the Townsend breakdown criterion γ[exp
(αt′) – 1] = 1, breakdown voltage Vb is given as:
Vb =
Bpt '
ln[ Apt ' / ln(1 + 1 / γ )]
where p is pressure, t′ is gap spacing and γ is the
secondary ionization coefficient. The constants A and B
can be evaluated from the Townsend equation [9], [10]
for the primary ionization coefficient,
α = A p exp [–Bp/E]
where A is the saturation ionization in the gas at a
particular E/p (electric stress/pressure) and B is related to
the excitation and ionization energies [10] ,[11].
In the absence of secondary ionization coefficientγ, for
the whole range of E/p, equation (1) is of little use for
the evaluation of sparking potentials for the whole pt′
range. It is this drawback in Townsend’s equation which
prevents the use of equation (1) for practical
Since, reasonably accurate breakdown voltages for the
gas under consideration in our case are available [12] for
a wide range of pt′ values; it is possible to use these
Equation (1) can be written as:
Vb =
Bpt '
ln (pt ' ) + k
k = ln[A / ln(1 + 1/γ)]
The values of A and B in equation (2) for air [9], [10] are
given in Table 1.
Table 1
Values of Constants A and B for Air
Ionisation /kPa-cm
V /kPa-cm
Using breakdown voltages Vb from [11] and the values
of A and B from Table 1, k is computed and obtained
[12] as a function of pt′ as shown in Table 2.
Table 2
Computed k as a function of pt′
0.0133 -0.2
0.20 - 100
100 - 1400
4.6295[corresponding to
pt′ = 100 kPa-cm in
k=3.5134 (pt′)0.0599]
Equation (3) is re-written as:
Eg =
ln( pt ' ) + k
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3. Estimation of Pd-Inception Voltages in
Voids in a Single Core Cable
The schematic of a single-core cable of conductor and
sheath radii of Rc and Rs respectively with a cavity of
thickness t′ located at a distance d from the conductor
center is shown in Fig. 1.
Fig 1: Cross section of a Coaxial Cable
The expression for the inception voltage inside the gas
filled cavity [13] is given as.
Vi =
S −1
Eg R ⎡ ⎡⎛ Rs ⎞⎛
t' ⎞ ⎤⎤
⎢ln ⎢⎜⎜ ⎟⎟⎜1 + ⎟ ⎥ ⎥ .
S ⎣⎢ ⎣⎢⎝ Rc ⎠⎝ R ⎠ ⎦⎥ ⎦⎥
In the above equations Eg is the breakdown strength of
the gas inside the void. The value of S depends upon the
shape of the cavity. For a cylindrical void having a large
radius to depth ratio,
S = ξr
whereas for spherical voids [14] S is given by
3ξ r
1 + 2ξ r
ξ r denotes the relative permittivity of the dielectric
Substituting Eg from equation (5) into equation (6), Vi is
written as:
⎫ R ⎡ ⎡⎛ Rs ⎞⎛
t' ⎞
Vi = ⎨
⎬ ⎢ln ⎢⎜⎜ ⎟⎟⎜1 + ⎟
⎩ ln( pt ') + k ⎭ S ⎢⎣ ⎢⎣⎝ Rc ⎠⎝ R ⎠
S −1
⎥⎦ ⎥⎦
where k = M (pt′) N, M and N are constants as given in
Table 2 for different p t′ ranges.
For obtaining critical t′ for minimum inception voltage,
equation (8) can be differentiated with respect to t′ and
equated to zero. The value of t′ thus obtained can be
used in equation (8) to compute the critical inception
voltage Vic.
ISBN: 978-960-6766-43-5
3rd IASME/WSEAS Int. Conf. on Energy & Environment, University of Cambridge, UK, February 23-25, 2008
4. Discussion & Conclusions
Inception Voltage Vi, kV-peak
10 0 0 0
10 0 0
10 0
S phe ric a l
C ylindric a l
0 .0 0 0 1
0 .0 0 1
0 .0 1
0 .1
Cavity thickness t', cm
Fig. 2: Variation in computed values of PDIV with cavity
thickness for discharges in cavities of various shapes
Inception Voltage, kV-peak
10 0 0 0
10 0 0
t' = 0.0005 c m
t' = 0.001 c m
10 0
t' = 0.005 c m
10 0
10 0 0
Pressure, kPa
Fig. 3: Variation in computed values of PDIV with
pressure for discharges in cylindrical cavities of various
Inception Voltage Vi, kV-peak
10 0
R = 1.5 c m
R = 2.5 c m
R = 3.5 c m
0 .1
0 .0 1
0 .1
10 0
10 0 0
Pressure x cavity thickness pt', kPa-cm
On the basis of Paschen’s curve and analysis of
Townsend breakdown equation it is possible to compute
PD inception voltage for discharges occurring in voids in
power cables at different pressure and thickness of
insulation. This approach is of great use to researchers in
deciding their experimental parameters and help in
deciding safe working stress for longer life.
Fig. 2 gives a plot of the variation of PDIV with cavity
size for spherical and cylindrical shaped cavities while
other parameters are held constant. It is seen that the
PDIV occurs at lower values as the cavity size increases.
Furthermore, spherical cavities have a higher PDIV as
compared to cylindrical cavities for the same cavity size.
For a given cavity size, shape and location, the PDIV
can be expressed a s function of pressure. The computed
values of Vi with pressure for cylindrical cavities of
various thickness are plotted in Fig. 3. It is seen that Vi
exhibits a minimum which is the critical inception
voltage Vic for a given t′. It is also observed that the
minimum is occurring at lower and lower pressures as
the thickness of the cavity is increased.
Fig.4 illustrates the variation of PDIV with pt’ as the
location of the void is changed in the cable insulation.
The PDIV curves are found to follow the shape of the
Paschen’s curve. It is also obvious from the figure that
PDIV is minimum for voids located at the conductor
surface where the stress is maximum and increases as the
void location is moved towards the sheath.
In a practical system, the cavity thickness at sheath
surface are expected to be much larger than the cavity
thickness at or near the conductor surface and
correspondingly may have a lower inception voltage as
given in Fig 2.
In actual insulation, a number of voids of different shape
and dimension are present at random and the critical
discharges start at the most favorable site i.e. where
stress concentration is maximum.
The analysis presented does not address the surface
roughness condition, which may exist in voids. Also
deviations may exist because the values of breakdown
voltages obtained from Paschen’s curve are valid for
stress between metal-metal surfaces, whereas in case of
partial discharge occurrence the electric stress is between
dielectric-dielectric surfaces. It may suggest the
Paschen’s breakdown voltage value is obtained from
This method of estimation may be used for predicting
PDIV in case of discharges occurring at interface as well
as voids under uniform field conditions with sufficient
accuracy and has been utilized for predicting PDIV in
the ambient medium of air [16] and N2 [17].
Fig. 4: Variation in computed values of PDIV with
cavity location for discharges in cylindrical cavities
ISSN: 1790-5095
Page 347
ISBN: 978-960-6766-43-5
3rd IASME/WSEAS Int. Conf. on Energy & Environment, University of Cambridge, UK, February 23-25, 2008
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ISSN: 1790-5095
Page 348
E. Husain, A. Anwar, M. U. Zuberi & A.
Masood “A Mathematical Technique for Estimation
of Partial Discharge Inception Voltage at Different
Pressures”, Proc. 2003 IASTED International
Conference on Transmission, Distribution &
Automation, pp 509-513.
M. U. Zuberi, A. Masood, E. Husain & A.
Anwar “Estimation of Discharge Inception Voltages
at Different Pressures in the Ambient Medium of
N2”, Accepted for publication at IEEE PES
Transmission & Distribution Conference and
Exposition, Chicago, USA from April 21-24, 2008.
ISBN: 978-960-6766-43-5