The University of Manchester Research
Optimization of a High Frequency Current Transformer
sensor for Partial Discharge Detection using Finite
Element Analysis
DOI:
10.1109/JSEN.2016.2600272
Document Version
Accepted author manuscript
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Citation for published version (APA):
Zachariades, C., Shuttleworth, R., Giussani, R., & MacKinlay, R. (2016). Optimization of a High Frequency Current
Transformer sensor for Partial Discharge Detection using Finite Element Analysis. IEEE Sensors Journal, 16(20),
7526 - 7533. https://doi.org/10.1109/JSEN.2016.2600272
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Journal
1
IEEE SENSORS JOURNAL
Abstract— High Frequency Current Transformer (HFCT)
sensors are widely used for Partial Discharge detection due to
their versatility, high sensitivity and wide bandwidth. This paper
reports on a Finite Element Analysis (FEA) methodology that can
be employed to optimize HFCT performance. The FEA model
consists of accurate 3D representations of the sensor components.
Two different FEA software modules were used in order to cover
the wide operating frequency range of the sensor. The simulation
computes the frequency response of the sensor in the range
0.3 MHz - 50 MHz for various HFCT geometric and material
parameters, specifically the number of winding turns, spacer
thickness, aperture size and core material. A prototype HFCT
was constructed and the measured response compared with that
of the simulation. The shapes of the responses were similar, with
the simulated sensitivity being higher than the measured
sensitivity by 1 dB on average. The measured low frequency cut-
off of the sensor was found to be only 0.05 MHz lower than that
of the simulation.
Index Terms— condition monitoring, FEA, finite element
analysis, frequency response, HFCT, high frequency current
transformer, partial discharge, sensor.
I. I
NTRODUCTION
artial Discharge (PD) monitoring is a widely employed
technique for diagnosing the condition of electrical
insulation. It can be used to assess the condition of High
Voltage plant assets including rotating machines, switchgear,
transformers and cables [1]. Monitoring can be performed
continuously or at regular intervals (spot-testing), while the
asset is on-line or supplied from an external source, and can be
combined with other monitoring methods to provide a holistic
monitoring solution [2].
To detect PD, a variety of sensors can be used for different
Manuscript received June 27, 2016; revised August 11, 2016; accepted
August 11, 2016. This work was co-funded by the UK’s Innovation Agency,
Innovate UK. Paper no. Sensors-15356-2016.
C. Zachariades is with the University of Manchester and High Voltage
Partial Discharge Ltd, Salford, M50 2UW, UK (e-mail: christos@hvpd.co.uk).
R. Shuttleworth is with the University of Manchester (e-mail:
roger.shuttleworth@manchester.ac.uk), Manchester, M13 9PL, UK.
R. Giussani (e-mail: riccardo.giussani@hvpd.co.uk) and R. Mackinlay are
with High Voltage Partial Discharge Ltd, Salford, M50 2UW, UK.
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier .
applications. These include High Voltage Coupling
Capacitors, Rogowski Coils, Transient Earth Voltage
detectors, Acoustic and RF sensors. One of the most versatile
PD sensors is the High Frequency Current Transformer
(HFCT). The HFCT usually consists of a wound, toroidal,
ferrite core which is placed around an unscreened cable
conductor or earth sheath to inductively detect PD [3]. The
HFCT often has a split-core design, making it easy to install
and suitable for retrofit installations. Also, HFCTs have good
sensitivity and wide bandwidth making them ideal for remote
monitoring [4].
When designing an inductive sensor, such as an HFCT, it is
common to use equivalent circuits [5] or simplified models [6]
to optimize its parameters. The aim of the study described here
is to determine the suitability of Finite Element Analysis
(FEA) in investigating the performance of a HFCT sensor. By
using FEA, optimization of the sensor parameters can be
performed in the virtual domain, avoiding the need for
expensive and time consuming production of multiple
prototypes. To achieve this, an accurate 3D simulation of a
prototype sensor was constructed and the frequency response
of the simulation examined as its various parameters were
changed. The results from the simulation were compared with
test results to determine the accuracy of the methodology.
From this work an understanding of how the various HFCT
parameters affect the response was gained.
II. S
IMULATION METHODOLOGY
The performance of a HFCT sensor is primarily judged by
how its sensitivity (transfer impedance) varies with frequency.
The model described in the following sections was designed
so that S-p
arameters can be computed. From the S-parameters
the transfer impedance can then be derived. Additionally, the
simulation closely resembles the arrangement used for testing
the HFCT (Section IV.A). This allows straight forward
comparison of experimental and simulated results.
A. Model
A three-dimensional model of the HFCT was initially
assembled in Solidworks. For the metallic parts of the sensor,
the existing 3D CAD models were used. The models for the
core and spacers were created from the mechanical drawings
of those parts. No dimensional approximations were made
Optimization of a High Frequency Current
Transformer sensor for Partial Discharge
Detection using Finite Element Analysis
Christos Zachariades, Roger Shuttleworth, Member, IEEE, Riccardo Giussani, Member, IEEE,
Ross MacKinlay
P
1530-437X (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2016.2600272, IEEE Sensors
Journal
2 IEEE SENSORS JOURNAL
when simulating the insulated wire wrapped around the core.
The wire had a radial insulation thickness of 0.3 mm and an
overall diameter of 1.6 mm. Special care was taken to model
the winding termination point as accurately as possible.
In order to reduce the number of elements required for the
discretization, a few features of the casing were suppressed to
simplify the model. These included the bolt holes, bolts, clasp,
and other cosmetic recesses for the attachment of labels. The
omission of these features should not affect the accuracy of
the overall model since they are located on the external
surfaces of the grounded metallic casing. The simplified 3D
model of the sensor is shown in Fig. 1.
The Solidworks sensor model was imported into COMSOL
Multiphysics where it was placed in the middle of a virtual
box with dimensions 0.4 m × 0.4 m × 0.2 m (Fig. 2). The box
serves a dual purpose. It defines the computation domain and
its boundaries provide a low impedance return path for the
current. The domain internally consists of air while its walls
are defined to be lossless conducting boundaries in order to
facilitate current conservation for the simulation. A vertical
conductor passes through the center of the box and the HFCT.
Where the conductor meets the upper and lower box surfaces,
it meets the center conductors of two short coaxial cables,
modelled as RG223. The screens of the two coaxial cables are
electrically connected to the box. Another coaxial cable takes
the signal from the BNC connector of the sensor to the nearest
box boundary. The coaxial cables allow the implementation of
boundary conditions required for model excitation and
measurement of S-parameters (Section II.C).
B. Materials
The material properties required for the computation are the
electrical conductivity, the relative permittivity and the
relative permeability. These properties are shown in Table I.
Most of the material properties do not change significantly
over the frequency range covered by the simulation. An
exception however is the permeability of the ferrite core of the
sensor. The relative magnetic permeability changes with
frequency and plays an important part in the behavior of the
sensor. To take into account the changing permeability, the
real and imaginary permeability plots were sourced from the
supplier. These unfortunately did not extend to the end of the
required frequency range, stopping at 4 MHz, and so
permeability plots from other studies were identified which
show the permeability of the same ferrite material at higher
frequencies [7]. The combined plots were digitized and
imported into COMSOL where they were used to define
interpolation functions of real and imaginary permeability
against frequency (Fig. 3).
It is worth noting that the permittivity and conductivity of
the ferrite also change with frequency [8] but the changes are
relatively minor compared to the same properties of other
TABLE I
M
ATERIAL PROPERTIES FOR COMPUTATION
Component Material
Conductivity
(S/m)
Relative
permittivity
Relative
permeability
Winding
conductor
Copper
5.998 × 10
7
1.0 1.0
Winding
insulation
PVC 0 3.0 1.0
Transmission
line insulation
Polyethylene 0 2.4 1.0
Core Ferrite 0 15.0
j
µµ
′ ′′
−
**
Spacer
Nylon
0
4.0
1.0
Casing
Aluminium
3.774 × 10
7
1.0
1.0
Box
Air
0 - 0.01*
1.0
1.0
* The conductivity of air was increased to a small non-
zero value for frequencies
between 0.3 MHz and 0.6 MHz to speed convergence.
**
µ
′
is the real and
µ
′′
the imaginary permeability defined as interpolation functions.
Fig.
1
. HFCT model (20 winding turns) with the top part of the casing
removed. The main components of the sensor are shown.
Fig. 3
. Plots of real and imaginar
y ferrite permeability against frequency.
The plots were digitized and imported into COMSOL Multiphysics where
they were used to define interpolation functions that specify the behavior of
the ferrite for the simulation.
Fig. 2
. Computation dom
ain including the HFCT geometry. The outer
boundaries of the domain provide a low impedance return path for the
current. Short coaxial cables facilita
te the excitation of the model.
1530-437X (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2016.2600272, IEEE Sensors
Journal
ZACHARIADES et al.: OPTIMIZATION OF A HIGH FREQUENCY CURRENT TRANSFORMER SENSOR 3
materials in the model. It was therefore decided to treat these
ferrite properties as being constant over the frequency range
for simplicity.
C. Physics
COMSOL Multiphysics offers three modules that are
appropriate for modelling at known frequencies, the AC/DC
module, the RF module and the Wave Optics module. The
decision on which of these modules to use depends mainly on
the electrical size of the object being studied, the frequency
and the memory limitations of the computing hardware. The
frequency range of interest, between 0.3 MHz and 50 MHz,
dictates that one of the AC/DC or RF modules should be used.
COMSOL recommends using the AC/DC module when the
characteristic length,
c
L
, of the object being analyzed is much
smaller than the wavelength,
λ
, in free space:
100
c
L
λ
<
(1)
Alternatively, the RF module should be used when the
characteristic length is comparable to the wavelength [9]:
10
100
c
L
λ
λ
<<
(2)
The various dimensions of the HFCT parts and the
frequencies of interest however, put the model at the boundary
between the regions of applicability of the AC/DC and RF
modules. Hence, it was decided to use the AC/DC module for
frequencies between 0.3 MHz and 5 MHz and the RF module
for frequencies between 5 MHz and 50 MHz.
For the lower end of the frequency range, the Magnetic
Fields interface was used which solves a frequency-domain
form of Ampere’s Law for the magnetic and electric fields and
the induced current:
( ) ( )
21
00 e
j
ωσ ω ε µ
−
− +∇× ∇× − =Α ΑM J
(3)
where
ω
is angular frequency,
σ
is electrical conductivity,
0
ε
and
0
µ
are the permittivity and permeability of free space
respectively,
A
is the magnetic vector potential,
M
is the
magnetization of the material and
e
J
is the electric current
density. For higher frequencies, the Electromagnetic Waves
interface was used which solves a similar equation for the
electric field,
E
:
( )
2
1
2
00
0
rr
j
c
ωσ
µε
ωε
−
∇× ∇× − − =
ΕΕ
(4)
where
0
c
is the speed of light in vacuum,
r
ε
is relative
permittivity,
r
µ
is relative permeability. The governing
equations are formed assuming that the materials are linear
isotropic i.e. the polarization depends linearly on the electric
field and therefore the permittivity is constant.
At non-zero operating frequencies the current flowing in
materials with finite conductivity is pushed towards the outer
surface due to the skin effect. The effect becomes more
pronounced as frequency increases and can be exploited to
reduce the computation resources required to simulate the
metallic domains of the model, such as the winding conductor
and the casing. The saving in computation resources is
achieved by assuming that the current flows only on the
surface of the metallic objects of the model using the
Impedance Boundary Condition (IBC):
( )
0
0
ˆˆ
0
r
r
j
µµ
σ
εε
ω
×+− ⋅ =
−
n H E nEn
(5)
where
H
is the magnetic field intensity and
ˆ
n
is the vector
normal to the surface.
By using the IBC the interior of metallic domains can be
excluded from the simulation i.e. it does not need to be
discretized. When using the IBC, resistive losses due to the
finite conductivity of the material can still be accurately
computed providing the characteristic size,
c
L
, of the object is
much larger than the skin depth,
δ
[10]:
10
c
L
δ
>
(6)
The skin depth is defined as the distance from the surface
over which the majority (≈ 63%) of the current is flowing
[11]. As relatively low frequencies were used in the
simulation, the permittivity of metals was considered to be
unity and their permeability was considered to be real valued.
Hence the skin depth becomes:
0
1
f
δ
π µσ
=
⋅⋅ ⋅
(7)
where
f
is the frequency. The IBC was used on the casing of
the HFCT and the winding conductor for frequencies above 5
MHz.
An additional constitutive relationship was added to the
ferrite domain to account for magnetic losses. In essence the
governing equations were modified to include a complex
magnetic permeability in the form:
r
j
µµµ
′ ′′
−
=
(8)
where
µ
′
is the real and
µ
′′
the imaginary permeability
defined as interpolation functions (Fig. 3).
The outer boundaries of the computation domain and the
shields of the coaxial cables were set to Magnetic Insulation
(9) or Perfect Electric Conductor (PEC) (10) depending on the
frequency. In both cases, they are considered to be lossless
metallic surfaces, since the tangential components of magnetic
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Journal
4 IEEE SENSORS JOURNAL
potential or electric field are set to zero:
ˆ
0×=nA
(9)
ˆ
0×=
nE
(10)
Finally, the ends of the three coaxial cables were set to the
Coaxial Lumped Port Boundary Condition which supports the
calculation of S-parameters (Fig. 4). Excitation is specified in
terms of voltage for Port 1 only. In other words, energy enters
the model through Port 1 at the top of the computation domain
and exits through Ports 2 and 3. All ports were 50 Ω
terminated.
D. Discretization
When creating the geometric mesh a compromise must be
made between the solution accuracy and the computational
resource availability. As the number of elements increases the
accuracy of the solution also increases but so does the memory
required to solve the problem. Using a combination of
knowledge regarding the geometric discretization error and
engineering judgement the mesh can be refined to achieve a
fast simulation with a high enough accuracy.
COMSOL by default uses second-order Lagrangian
elements to discretize the geometry. An empirical rule of
thumb is to use five such elements per wavelength [12-14].
Since the study examines the behavior of the sensor over a
range of frequencies, the wavelength varies. Although it is
possible to parametrize the mesh size based on frequency to
reduce memory requirements, this was not applicable to this
study. Other factors took precedence when deciding on
optimum mesh size. This is because the shortest wavelength
for the simulation at 50 MHz is 6 m which is much longer than
the dimensions of any components in the model. For example,
to ensure the quality of the mesh, at least two second-order
elements were used per 90
o
arc [15] which, given the radii of
the various components, are already much shorter than
required. Also, the model contains components with large size
differences which therefore need manual meshing for accurate
representation.
Another parameter to be considered when discretizing the
geometry is the skin depth,
δ
, defined in equation (7). If
δ
is
comparable to the characteristic length of the object it is
advised to use a boundary layer mesh to resolve the field
variations inside a domain [12]. This type of mesh was used to
discretize the winding conductor for frequencies below 5 MHz
for when its interior is included in the simulation.
Part of the discretized geometry can be seen in Fig. 5 which
shows that the mean density varies between parts. The most
important mesh parameters are the following:
• Number of elements: 4.2 - 7.3 million
• Minimum element size: 0.12 mm
• Maximum element size: 12 mm
The number of elements varied between simulations
because the dimensions of some parts were changed in order
to investigate their effect on the frequency response of the
sensor.
The simulations were performed on a workstation with an
Intel
®
Xeon
®
E5-2667 v2 Processor (8 cores/16 threads) and
256 GB of DDR3 memory. The maximum total time taken to
run the two simulations (AC/DC and RF) covering the entire
frequency range was 17 hours and 45 minutes while memory
utilisation reached 187 GB.
III. S
IMULATION RESULTS
Before proceeding to examine the frequency response of the
sensor, it was necessary to check whether the simulation
performs as intended. Fig. 6 shows the magnetic flux density
plotted on a plane in the middle of the computation domain.
The magnetic field lines, visualized as an arrow plot, form
concentric circles around the current carrying wire. They have
a clockwise direction since the current is flowing from the top
of the model towards the bottom (into the page). The function
of the ferrite core is also evident from Fig. 6. The low
reluctance path provides efficient flux linkage between the
current carrying wire and the sensor winding.
Fig. 4
. Port and impedance bo
undary conditions. Energy enters the model
through Port 1 and exits through Ports 2 and 3.
Fig. 5
. Discretized HFCT geometry. Manual meshing was used for different
parts of the model to improve element quality.
