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Article
Electric Field Simulations and Analysis for High
Voltage High Power Medium Frequency Transformer
Pei Huang 1 , Chengxiong Mao 1, * and Dan Wang 2
1
2
*
State Key Laboratory of Advanced Electromagnetic Engineering and Technology,
Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China;
[email protected]
School of Electrical & Electronic Engineering, Huazhong University of Science and Technology,
1037 Luoyu Road, Wuhan 430074, China; [email protected]
Correspondence: [email protected]; Tel.: +86-27-8754-2669
Academic Editor: Gabriele Grandi
Received: 26 December 2016; Accepted: 10 March 2017; Published: 16 March 2017
Abstract: The electronic power transformer (EPT) raises concerns for its notable size and volume
reduction compared with traditional line frequency transformers. Medium frequency transformers
(MFTs) are important components in high voltage and high power energy conversion systems such
as EPTs. High voltage and high power make the reliable insulation design of MFT more difficult.
In this paper, the influence of wire type and interleaved winding structure on the electric field
distribution of MFT is discussed in detail. The electric field distributions for six kinds of typical
non-interleaved windings with different wire types are researched using a 2-D finite element method
(FEM). The electric field distributions for one non-interleaved winding and two interleaved windings
are also studied using 2-D FEM. Furthermore, the maximum electric field intensities are obtained
and compared. The results show that, in this case study, compared with foil conductor, smaller
maximum electric field intensity can be achieved using litz wire in secondary winding. Besides,
interleaving can increase the maximum electric field intensity when insulation distance is constant.
The proposed method of studying the electric field distribution and analysis results are expected to
make a contribution to the improvement of electric field distribution in transformers.
Keywords: medium frequency transformer (MFT); electronic power transformer (EPT); insulation
design; electric field intensity; finite element method (FEM); wire type; interleaved winding
1. Introduction
Medium frequency transformers (MFTs) are usually critical elements in high voltage, high power
energy conversion systems, including electronic power transformer (EPT) [1,2], solid state transformers
(SST) [3], power electronic transformers (PET) [4], and power electronic traction transformers (PETT) [5].
These energy conversion systems are especially suitable for converters of power systems, wind
farms [1], and traction converters, and they are expected to play an important role in future smart grid.
Previous works regarding MFT can be found in literatures [6–11]. Literature [6] presents
an improved thermal model for multi-layer winding consisting of litz-wire and the analytical
calculation of maximum electric field strength in the core window area. Literature [7] proposes a design
methodology of medium-frequency power transformer that accounts for a tuned leakage inductance
of the transformer, core and winding losses mitigation, thermal management, and high isolation
requirements. In literature [8], two optimized transformer concepts, differing in their core material
and cooling strategies, are constructed, aiming for different power density/efficiency goals, and the
author proposes that the research on the effectiveness of the utilized isolation strategies concerning
long term operation and different operation conditions should be addressed in order to make the
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SST technology an attractive replacement for line frequency transformers [8]. Literature [9] provides
a step-by-step design for MFTs with high isolation requirement, and the required design considerations,
including isolation and thermal management, are explained in detail. In literature [10], the inductance
optimization is studied, and a high voltage insulation is carefully designed to support 15 kV for SST
application. Literature [11] analyzes the voltage stress appearing in cascaded converters, in time
and frequency domains. The simulations of the electric field distributions in these transformer are
presented, and the impact of the converter topology on the insulation stress is highlighted. The highest
electric fields appear in the MFT of the converter cells’ dc-dc converters, which provide galvanic
isolation within the SST [11]. Durable insulation is especially important for high power high voltage
transformers since high electric stress leads to partial discharge and the breakdown of transformers [12],
and the breakdown of transformers usually leads to costly repair or replacement [13].
The concentrated research on electric field distribution and insulation design of transformers can
be found in literatures [12,14–18]. Literature [12] focuses on the transient electric field characteristics
in oil-pressboard composite insulation under voltage polarity reversal. The research adopted the Kerr
electro-optic effect technique to conduct real-time measurement of the oil electric fields at the polarity
reversal time of 10, 60, and 120 s respectively, and several important research results are provided.
Literature [14] presents a study of the parameters that affect the breakdown voltage in the insulation
supports of a standard dip and bake dry-type transformer. Besides, the modifications to the design of
currently used insulating support are estimated to reduce its length without increasing the possibility
of breakdown. In literature [15], a lumped parameter equivalent model is developed by dividing
transformer windings into several blocks, then a 2-D asymmetrical electric field finite-element analysis
is performed to determine electric fields through the windings. Literature [16] presents a detailed
analysis of both near and far stray magnetic fields of dry type distribution transformers, and the
results of 3-D simulations are compared with the measurements and show good accuracy, allowing
for design to be based on simulations. Literature [17] deals with the design improvements on graded
insulation of power transformers using transient electric field analysis and a visualization technique.
Literature [18] considers the algorithm of design for an insulation system of a high-voltage combined
instrument transformer using the field method. The author’s software SHIELDS was used to optimize
the number, dimensions, and position of each electrostatic control shield in the insulation of the voltage
and current parts.
The contributions of this paper include: (1) The influence of wire type on electric field distribution
of MFT is discussed in detail, which has not been studied by previous researchers. Three kinds of wire
types are widely used in MFTs, including litz wire, foil conductor and flat copper wire. The electric
field distributions of six kinds of non-interleaved windings using different wire types are researched
and compared using 2-D finite element method (FEM) [19]. (2) The influence of interleaved winding
structure on electric field distribution of MFT is discussed in detail, which has not been researched in
previous works. Interleaved winding structure can reduce the leakage inductance of transformers,
and it has been widely adopted in transformer design [20]. The electric field distributions for two kinds
of interleaved windings and one non-interleaved winding are studied and compared using 2-D FEM.
The proposed method of studying the electric field distribution and analysis results are expected to
make a contribution to the improvement of electric field distribution in transformers. Though the
proposed method is applied to MFT in this paper, the method is general and it is also applicable for
power transformers.
The case study in this paper is performed based on a 1.5 kV, 35 kW, 1 kHz core-type MFT used
in a subunit of 10 kV EPT [21]. EPT is a new type of power transformer. Some new functions can be
obtained by EPT, including providing high quality electric energy to the consumer and improving
the dynamic performance of the power grid [2]. The main circuit structure of the 10 kV EPT can be
found in [2]. The harmonic content and efficiency are two important indicators for EPT. The switching
losses increase and the efficiency decreases with increasing switching frequency. The 1 kHz switching
frequency is adopted since it can fulfill the design requirement of harmonic content for high voltage
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high
power
EPT,
and
desirable
efficiency
can
bebe
achieved.
Therefore,
the
switching
frequency
forfor
the
high
power
EPT,
and
desirable
efficiency
can
achieved.
Therefore,
the
switching
frequency
the
high
EPT,
and
desirable
can
be achieved.
Therefore,
the
switching
frequency
for of
the
MFT
ispower
1 kHz.
The
MFT
works
inefficiency
a dc-dc
converter
asas
shown
inin
Figure
1, 1,
and
the
working
voltage
MFT
is
1 kHz.
The
MFT
works
in
a dc-dc
converter
shown
Figure
and
the
working
voltage
of
MFT
is 1iskHz.
The
MFT wave
works
in
a low
dc-dc
converterripple.
as
shown in Figure 1, and the working voltage of
this
MFT
1 kHz
square
with
frequency
this
MFT
is
1 kHz
square
wave
with
low
frequency
ripple.
this MFT is 1 kHz square wave with low frequency ripple.
MFT
MFT
Figure 1. The topology of dc-dc converter.
Figure
1. 1.
The
topology
ofof
dc-dc
converter.
Figure
The
topology
dc-dc
converter.
This
paper
organized
follow:
Section
introduces
the
FEM
model
the
MFT.
Section
This
Thispaper
paperisis
isorganized
organizedasas
asfollow:
follow:Section
Section2 22introduces
introducesthe
theFEM
FEMmodel
modelofof
ofthe
theMFT.
MFT.Section
Section3 33
presents
the
six
kinds
of
typical
non-interleaved
windings
with
different
wireand
types
and
their
presents
the
sixsix
kinds
ofof
typical
non-interleaved
windings
with
different
wire
types
their
electric
presents
the
kinds
typical
non-interleaved
windings
with
different
wire
types
and
their
electric
electric
field
distribution
results
using
2-D
FEM.
Section
4
presents
one
non-interleaved
winding
field
fielddistribution
distributionresults
resultsusing
using2-D
2-DFEM.
FEM.Section
Section4 4presents
presentsone
onenon-interleaved
non-interleavedwinding
windingand
andtwo
two
and
two interleaved
windings
and their
electric
field results
distribution
results
using
2-D in
FEM.
Finally,
interleaved
windings
and
their
electric
field
distribution
using
2-D
FEM.
Finally,
Section
5, 5,
interleaved
windings
and
their
electric
field
distribution
results
using
2-D
FEM.
Finally,
in
Section
in
Section
5,
the
suggestions
on
insulation
design
of
MFT
are
provided
based
on
the
FEM
results
and
the
suggestions
onon
insulation
design
ofof
MFT
are
provided
based
onon
the
FEM
results
and
discussion
the
suggestions
insulation
design
MFT
are
provided
based
the
FEM
results
and
discussion
Sections
indiscussion
Sections
3 in
and
4. 4. 3 and 4.
in
Sections
3 and
Finite
Element
Modeling
MFT
2.2.
Finite
Element
Modeling
ofof
MFT
2.
Finite
Element
Modeling
of
MFT
2-D
finite
element
method
(FEM)
adopted
obtain
the
electric
field
distribution
MFT
2-D
2-Dfinite
finiteelement
elementmethod
method(FEM)
(FEM)isis
isadopted
adoptedtoto
toobtain
obtainthe
theelectric
electricfield
fielddistribution
distributionofof
ofMFT
MFTinin
in
this
paper,
using
the
finite
element
simulation
software
ANSYS
(Maxwell
16.0,
ANSYS,
Pittsburgh,
this
thispaper,
paper,using
usingthe
thefinite
finiteelement
elementsimulation
simulationsoftware
softwareANSYS
ANSYS(Maxwell
(Maxwell16.0,
16.0,ANSYS,
ANSYS,Pittsburgh,
Pittsburgh,
PA,
USA).
The
case
study
performed
based
kW
MFT
used
kV
EPT.
The
maximum
PA,
USA).
The
case
study
isis
performed
based
onon
a a35
kW
MFT
used
inin
a a10
kV
EPT.
The
maximum
PA,
USA).
The
case
study
is
performed
based
on
a 35
35
kW
MFT
used
in
a 10
10
kV
EPT.
The
maximum
working
voltage
of
this
EPT
is
10
kV,
thus,
the
target
insulation
voltage
for
this
MFT
is
10
kV,
and
safety
working
kV,
and
workingvoltage
voltageofofthis
thisEPT
EPTis is1010kV,
kV,thus,
thus,the
thetarget
targetinsulation
insulationvoltage
voltageforforthis
thisMFT
MFTis is1010
kV,
and
factor
[7]
should
be
considered
when
determining
the
insulation
distance.
The
structure
of
the
core
safety
factor
[7][7]
should
bebe
considered
when
determining
the
insulation
distance.
The
structure
ofof
the
safety
factor
should
considered
when
determining
the
insulation
distance.
The
structure
the
type
MFT
isMFT
shown
in Figure
2a.
The2a.
2-D
electrostatic
finite element
model
ofmodel
this
MFT
established,
core
is isshown
ininFigure
2-D
finite
ofofis
this
MFT
coretype
typeMFT
shown
Figure
2a.The
The
2-Delectrostatic
electrostatic
finiteelement
element
model
this
MFTis is
and
the meshed
2-D
model2-D
is2-D
shown
inisFigure
2b.
The
core
material
ismaterial
silicon
steel
with steel
a steel
thickness
established,
and
the
meshed
model
shown
inin
Figure
2b.
The
core
is is
silicon
with
established,
and
the
meshed
model
is
shown
Figure
2b.
The
core
material
silicon
with
of
0.18
mm.
The
400
Hz
B-H
curve
data
is
used
due
to
the
lack
of
1
kHz
B-H
curve
data.
A
winding
a thickness
ofof
0.18
mm.
The
400
Hz
B-H
curve
data
is is
used
due
toto
the
lack
ofof
1 kHz
B-H
curve
data.
a thickness
0.18
mm.
The
400
Hz
B-H
curve
data
used
due
the
lack
1 kHz
B-H
curve
data.
scheme
isscheme
shown
inis
Figure
2b.
The
foil
conductors
are adopted
inadopted
low voltage
(LV)
winding,
Adesign
winding
design
is
shown
in
Figure
2b.
The
foil
conductors
are
adopted
inin
low
voltage
(LV)
A
winding
design
scheme
shown
in
Figure
2b.
The
foil
conductors
are
low
voltage
(LV)
and
the
flat
copper
wires
are
adopted
in
high
voltage
(HV)
winding.
The
specifications
and
parameters
winding,
voltage
(HV)
winding.
The
specifications
and
winding,and
andthe
theflat
flatcopper
copperwires
wiresare
areadopted
adoptedininhigh
high
voltage
(HV)
winding.
The
specifications
and
of
this 35 kW
MFT
are
shown
inshown
Table
1.
The
LV
iswinding
arranged
near
the near
core
column
to
reduce
parameters
ofof
this
3535
kW
MFT
are
inin
Table
1. winding
The
LV
winding
is is
arranged
the
core
column
parameters
this
kW
MFT
are
shown
Table
1.
The
LV
arranged
near
the
core
column
insulation
distance distance
between
core
andcore
windings.
tothe
reduce
the
insulation
between
and
windings.
to
reduce
the
insulation
distance
between
core
and
windings.
(a)(a)
(b)(b)
Figure
2. 2.
Instructions
ofof
this
MFT:
(a)(a)
Structure
ofof
the
modeled
MFT;
(b)(b)
Meshed
2-D
model.
Figure
Instructions
this
MFT:
Structure
the
modeled
MFT;
Meshed
2-D
model.
Figure 2. Instructions of this MFT: (a) Structure of the modeled MFT; (b) Meshed 2-D model.
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Table 1. Specifications and parameters of the 35 kW MFT.
Table 1. Specifications and parameters of the 35 kW MFT.
Table 1. Specifications and parametersSymbol
of the 35 kW MFT.
Parameter
Parameter
Number
of Phase
Parameter
Number
Phase
Operationof
frequency
Operation
frequency
Number
of Phase
Power
Operation
frequency
Power
Maximum primary voltage
Power voltage
Maximum
primary
Maximum
secondary
voltage
Maximum
primary voltage
Maximum
secondary
voltage
Rms primary
current
Maximum
secondary
voltage
Rms
primary
Rms
primarycurrent
current
Rms
secondary
current
Rms
secondarycurrent
current
Rms
secondary
Primary/secondary
turn
numbers
Primary/secondary
turn
numbers
Primary/secondary
turn numbers
Size
of
the
foil
conductor
Size of the foil conductor
Size of
of the flat
foil conductor
Size
wire
Size ofthe
the flat copper
copper wire
Size
of
the
flat
copper
wire
Max.
length
of
elements
for
Max. length of elements forcore
core
Max.
length
ofelements
elements
for
core
Max.
lengthofof
elements
for
winding
Max.
length
for
winding
Max. length of elements for winding
Value
Symbol
Value
N
1
SymbolN
Value 1
f
1 kHz
N fP
1 135kHz
kW
f P
1 kHz
35
Upmax
1.5kW
kV
P Upmax
35 kW
1.5
kV
U
smax
385
V
Upmax
1.5 kV
U
smax
385
V
Usmax Ip
385 V26.3 A
26.3
Ip Ip
26.3 A
Is
102 A
A
Is Is
102 A102 A
Np/Ns
120/32
Np/Ns
120/32
Np/Ns
120/32 mm
Width/Length
0.4
mm/110
Width/Length
0.4 mm/110 mm
Width/Length
0.42mm/110
mm
Width/Length 2 mm/5
mm/5
Width/Length
mm mm
Width/Length
mm/5
mm
null null
302mm
30 mm
30
mm
nullnull
0.1
mm
null
0.1 mm
null
0.1 mm
3.3.Windings
Windingswith
withDifferent
DifferentWire
WireTypes
Types
3. Windings with Different Wire Types
3.1.
3.1.Windings
Windingswith
withDifferent
DifferentWire
WireTypes
Types
3.1. Windings with Different Wire Types
Litz
Litzwire,
wire, foil
foil conductor,
conductor, and
and flat
flat copper
copper wire
wire are
are three
three kinds
kinds of
of suitable
suitable wire
wire types
types for
for MFTs.
MFTs.
Litz
wire,
foil
conductor,
and
flat
copper
wire
are
three
kinds
of
suitable
wire
types
for
MFTs.
Six
wire
Sixkinds
kindsof
oftypical
typicalnon-interleaved
non-interleavedwindings
windings N-1,
N-1, N-2,
N-2, N-3,
N-3, N-4,
N-4, N-5,
N-5,and
andN-6
N-6with
withdifferent
different
wire
Six
kinds
of
typical
non-interleaved
windings
N-1,
N-2,
N-3,
N-4,
N-5,
and
N-6
with
different
wire
types
are
shown
in
Figures
3a–c
and
4a–c
respectively.
In
the
context
of
foil
conductors
adopted
in
the
types are shown in Figures 3a–c and 4a–c respectively. In the context of foil conductors adopted
in
types
are
shown
in
Figures
3a–c
and
4a–c
respectively.
In
the
context
of
foil
conductors
adopted
in
secondary
winding,
the
three
non-interleaved
windings
N-1,
N-2,
and
N-3
are
shown
in
Figure
3a–c.
the secondary winding, the three non-interleaved windings N-1, N-2, and N-3 are shown in Figure 3a–
the
winding,
the
three non-interleaved
windings
N-1,
N-2,
and
N-3 are shown
in
FigureN-4,
3a–
In
context
litz
wires
adopted
in the
secondary
winding,
thethe
three
non-interleaved
windings
c. the
Insecondary
the
context
litz
wires
adopted
in the
secondary
winding,
three
non-interleaved
windings
Nc.4,In
the
context
litz
wires
adopted
in
the
secondary
winding,
the
three
non-interleaved
windings
NN-5,
and
N-6
are
shown
in
Figure
4a–c.
The
wire
types
adopted
in
the
six
kinds
of
windings
are
N-5, and N-6 are shown in Figure 4a–c. The wire types adopted in the six kinds of windings are
4,
N-5, and in
N-6
are 2.
shown
in Figure 4a–c. The wire types adopted in the six kinds of windings are
expounded
expounded
inTable
Table
2.
expounded in Table 2.
(a)
(a)
(b)
(b)
(c)
(c)
Figure 3. Winding arrangements for different windings: (a) N-1; (b) N-2; (c) N-3.
Figure 3. Winding arrangements for different windings: (a) N-1; (b) N-2; (c) N-3.
Figure 3. Winding arrangements for different windings: (a) N-1; (b) N-2; (c) N-3.
(a)
(a)
(b)
(b)
(c)
(c)
Figure 4. Winding arrangements for different windings: (a) N-4; (b) N-5; (c) N-6.
Figure 4. Winding arrangements for different windings: (a) N-4; (b) N-5; (c) N-6.
Figure 4. Winding arrangements for different windings: (a) N-4; (b) N-5; (c) N-6.
N-3 (litz-foil)
N-4 (flat-litz)
N-5 (foil-litz)
N-6 (litz-litz)
Litz wire
Flat copper wire
Foil conductor
Litz wire
Foil conductor
Litz wire
Litz wire
Litz wire
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3.2. Electric Field Distribution of Different Windings
2-D finite element models
of the
six winding
structures
established using ANSYS software.
Table
2. Wire
types of the
six kinds are
of windings.
The insulation distances between winding layers are 1 mm and 0.3 mm for HV and LV winding layers
respectively, and the insulation
distance between
HV and LV windings
is 1.5 mm. A maximum
Winding Type
HV Winding
LV Winding
excitation voltage of 1500N-1
V and
384
V
are
given
to
HV
and
LV
windings
respectively.
The excitation
(flat-foil)
Flat copper wire
Foil conductor
voltage decreases from one
to the next turn,
from up to down
from outer to inner. Figures
N-2turn
(foil-foil)
Foil conductor
Foiland
conductor
N-3 (litz-foil)
Litzof
wire
Foil conductor
5a–c and 6a–c show the electric
field distributions
the six windings.
(flat-litz)
wire
wire
As can be seen in N-4
Figures
5a–c and Flat
6a–c,copper
for foil
conductorLitz
winding
and flat copper wire
N-5 (foil-litz)
Foil conductor
Litz wire
winding, the peak value N-6
of electric
of the conductors, while for
(litz-litz)field intensity
Litz occurs
wire on the corner
Litz wire
litz wire winding, the peak value of electric field intensity occurs on the middle edge of the
conductors.
electric
field intensities
3.2. Electric The
Fieldmaximum
Distribution
of Different
Windings Emax of the six winding structures are compared in
Table 3. The three windings with the maximum Emax are the windings using foil conductors in
2-D finite
element
modelsN-1,
of the
sixand
winding
structures
are established
using
ANSYS
software.
secondary
winding,
including
N-2,
N-3, while
the three
windings with
the
minimum
Emax
The
insulation
distances
between
winding
layers
are
1
mm
and
0.3
mm
for
HV
and
LV
winding
are the windings using litz wires in secondary winding, including N-4, N-5, and N-6. According to
layers
respectively,
and the electric
insulation
distance
between
LV windings
1.5 study,
mm. Acompared
maximum
the
results
of the maximum
field
intensities
of theHV
sixand
windings,
in thisiscase
excitation
voltage
of 1500
V andmaximum
384 V are given
to field
HV and
LV windings
respectively.
The
with
the foil
conductor,
smaller
electric
intensity
can be achieved
using
litzexcitation
wire in
voltage
decreases
from
one
turn
to
the
next
turn,
from
up
to
down
and
from
outer
to
inner.
Figures
5a–c
secondary winding. It is therefore advisable to choose litz wire in secondary winding to achieve
a
and
6a–c
show
the
electric
field
distributions
of
the
six
windings.
lower Emax.
Energies 2017, 10, 371
(a)
(b)
(c)
Figure 5. Electric field distribution for different windings: (a) N-1; (b) N-2; (c) N-3.
Figure 5. Electric field distribution for different windings: (a) N-1; (b) N-2; (c) N-3.
6 of 11
Energies 2017, 10, 371
6 of 11
Energies 2017, 10, 371
6 of 11
As can be seen in Figures 5a–c and 6a–c, for foil conductor winding and flat copper wire winding,
the peak value of electric field intensity occurs on the corner of the conductors, while for litz wire
winding, the peak value of electric field intensity occurs on the middle edge of the conductors.
The maximum electric field intensities Emax of the six winding structures are compared in Table 3.
The three windings with the maximum Emax are the windings using foil conductors in secondary
winding, including N-1, N-2, and N-3, while the three windings with the minimum Emax are the
windings using litz wires in secondary winding, including N-4, N-5, and N-6. According to the results
of the maximum electric field intensities of the six windings, in this case study, compared with the
(c)
foil conductor, smaller maximum electric field intensity
can be achieved using litz wire in secondary
winding. It is therefore advisable to choose litz wire in secondary winding to achieve a lower Emax .
Figure 5. Electric field distribution for different windings: (a) N-1; (b) N-2; (c) N-3.
(a)
(b)
(c)
Figure 6. Electric field distribution for different windings: (a) N-4; (b) N-5; (c) N-6.
Figure 6. Electric field distribution for different windings: (a) N-4; (b) N-5; (c) N-6.
Table 3. Maximum electric field intensities.
Table 3. Maximum electric field intensities.
Winding Type
N-1Winding
(flat-foil)Type
N-1 (flat-foil)
N-2 (foil-foil)
N-2
(foil-foil)
N-3 (litz-foil)
N-3 (litz-foil)
Emax (V/m)
Winding Type
E
(V/m)
Winding
Type
5
max
9.7331 × 10
N-4
(flat-litz)
5
(flat-litz)
9.7331
×510 N-5N-4
7.5013
× 10
(foil-litz)
5
N-5
(foil-litz)
7.5013
×
10
6
1.2080 × 10
N-6 (litz-litz)
1.2080 × 106
N-6 (litz-litz)
Emax (V/m)
E6.6153
max (V/m)
× 105
5 5
6.6153
× ×1010
6.5078
5 5
6.5078
× ×1010
7.1469
7.1469 × 105
Energies 2017, 10, 371
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Energies 2017, 10, 371
7 of 11
Furthermore, the electric field intensities on predefined paths are studied. As it can be seen in
Furthermore,
electric electric
field intensities
on predefined
are studied.
AsHV
it can
in
Figures
5 and 6, the the
maximum
field intensities
arise inpaths
the region
between
andbe
LVseen
windings.
Figures
5
and
6,
the
maximum
electric
field
intensities
arise
in
the
region
between
HV
and
LV
Therefore,
two
Energies
2017,paths
10, 371between HV and LV windings are predefined. Path 1 is a straight line near
7 ofthe
11 LV
windings.
Therefore,
two paths
between
LV windings
are up
predefined.
Path 1 of
is athe
straight
line
winding
that
begins from
the top
of theHV
LVand
winding
and ends
to the bottom
LV winding,
near the
LV
winding
begins
from
the
top of
LV
winding
and2b.
ends
up2toisthe
bottom
of
thenear
LV
Furthermore,
the
electric
field
intensities
on
predefined
paths
arePath
studied.
it can be
seen
in the
which
is 0.1
mm
awaythat
from
the LV
winding,
asthe
shown
in Figure
aAs
straight
line
winding,
which
is 0.1
away fromelectric
the LVfield
winding,
as shown
2b. Path
2 is a HV
straight
Figures
5 and
6, mm
the maximum
intensities
arise in
inFigure
the region
between
and line
LV
HV winding that begins from the top of the HV winding and ends up to the bottom of the HV winding,
Therefore,
pathsfrom
between
HV and
LVHV
windings
are and
predefined.
1 is bottom
a straight
near windings.
the HV winding
thattwo
begins
the top
of the
winding
ends upPath
to the
ofline
the
which is 0.1 mm away from the HV winding, as shown in Figure 2b.
near the LV
winding
ofwinding,
the LV winding
and in
ends
up to2b.
the bottom of the LV
HV winding,
which
is 0.1that
mmbegins
awayfrom
fromthe
thetop
HV
as shown
Figure
For
non-interleaved
windings
N-1 (flat-foil),
N-4 (flat-litz),
theFigure
electric
field
intensities
online
path 1
winding,
which is 0.1 windings
mm away N-1
from(flat-foil),
the LV winding,
as shown
2b.
Path
2 is a straight
For non-interleaved
N-4 (flat-litz),
theinelectric
field
intensities
on path
1
are shown
in
Figure
7a.
The
local
maximum
electric
field
intensity
on
path
1
for
winding
N-4
is
near theinHV
winding
that begins
from the top
of thefield
HV winding
bottom N-4
of the
are shown
Figure
7a. The
local maximum
electric
intensityand
onends
pathup
1 to
forthe
winding
is
generally
higher
than
that
of
winding
N-1.
For
non-interleaved
windings
N-1
(flat-foil),
N-4
(flat-litz),
HV winding,
which
is of
0.1winding
mm away
from
the
HV winding, aswindings
shown in N-1
Figure
2b.
generally
higher than
that
N-1.
For
non-interleaved
(flat-foil),
N-4 (flat-litz),
the
electric
field
intensities
on
path
2
are
shown
in
Figure
7b.
The
local
maximum
electric
field
intensity
For
non-interleaved
windings
N-1
(flat-foil),
N-4
(flat-litz),
the
electric
field
intensities
on path
1
the electric field intensities on path 2 are shown in Figure 7b. The local maximum
electric
field
are
shown
in
Figure
7a.
The
local
maximum
electric
field
intensity
on
path
1
for
winding
N-4
is
on
path
2
for
winding
N-1
is
generally
higher
than
that
of
winding
N-4
in
most
region.
The
main
intensity on path 2 for winding N-1 is generally higher than that of winding N-4 in most region. The
generally
higher
than thatN-1
of winding
N-1.
For
non-interleaved
windings
N-1
(flat-foil),
N-4conductor
(flat-litz), for
difference
between
windings
and
N-4
is
that,
the
wire
type
of
the
LV
winding
is
foil
main difference between windings N-1 and N-4 is that, the wire type of the LV winding is foil
the N-1,
electric
field
intensities
on
path 2N-4.
are shown
in Figure
7b.
Thestudy,
local the
maximum
electric field
winding
litz
wire
winding
in this
case
conductor
forwhile
winding
N-1, for
while
litz wire
forTherefore,
winding N-4.
Therefore,
in this foil
caseconductor
study, theadopted
foil
intensity on path 2 for winding N-1 is generally higher than that of winding N-4 in most region. The
inconductor
the LV winding
can
relieve
the
local
maximum
electric
field
intensity
in
the
regions
near
the LV
adopted in the LV winding can relieve the local maximum electric field intensity in the
main difference between windings N-1 and N-4 is that, the wire type of the LV winding is foil
windings,
while
wire adopted
in the
winding
local maximum
regions near
thethe
LVlitz
windings,
while the
litz LV
wire
adoptedcan
in relieve
the LV the
winding
can relieve electric
the localfield
conductor for winding N-1, while litz wire for winding N-4. Therefore, in this case study, the foil
intensity
in
the
regions
near
the
HV
winding.
maximum
electric
field
intensity
in
the
regions
near
the
HV
winding.
conductor adopted in the LV winding can relieve the local maximum electric field intensity in the
regions near the LV windings, while the litz wire adopted in the LV winding can relieve the local
maximum electric field intensity in the regions near the HV winding.
(a)
(b)
Figure 7. Electric field intensities
on path 1 and path 2 for winding N-1 (flat-foil)
winding N-4
(a)
(b) andand
Figure 7. Electric field intensities
on path 1 and path 2 for winding N-1 (flat-foil)
winding N-4
(flat-litz): (a) Electric field intensities on path 1; (b) Electric field intensities on path 2.
(flat-litz):
(a)
Electric
field
intensities
on
path
1;
(b)
Electric
field
intensities
on
path
2.
Figure 7. Electric field intensities on path 1 and path 2 for winding N-1 (flat-foil) and winding N-4
(flat-litz): (a) Electric field intensities on path 1; (b) Electric field intensities on path 2.
4. Interleaved and Non-Interleaved Windings
4. Interleaved and Non-Interleaved Windings
4. Interleaved and Non-Interleaved Windings
4.1. Interleaved and Non-Interleaved Windings
4.1. Interleaved and Non-Interleaved Windings
4.1.
Interleaved
andthe
Non-Interleaved
Figure
8a shows
structure of Windings
a typical non-interleaved winding N-1. The foil conductors are
Figure 8a shows the structure of a typical non-interleaved winding N-1. The foil conductors are
adopted in
LV winding,
the flat copper
wires
are used in HV
winding.
illuminates
Figure
8a shows and
the structure
of a typical
non-interleaved
winding
N-1.Figure
The foil8b,c
conductors
are
adopted
in LV winding,
and of
theinterleaved
flat copperwindings,
wires areI-1
used inI-2
HV
winding. Figure
illuminates
the structures
two
kinds
respectively.
It can 8b,c
be
seen
that the the
adopted inofLV
winding,
and the flat copper
wires are and
used in HV
winding. Figure
8b,c
illuminates
structures
ofoftwo
of interleaved
I-1 and I-2 respectively. It can be seen that the wire
wire the
types
the kinds
three
windings
thewindings,
same.windings,
structures
of two
kinds ofare
interleaved
I-1 and I-2 respectively. It can be seen that the
types wire
of the
three
windings
are
the
same.
types of the three windings are the same.
(a)
(b)
(a)
(b)
Figure 8. Cont.
Energies 2017, 10, 371
8 of 11
Energies 2017, 10, 371
8 of 11
(c)
Figure 8. Winding arrangements (partial) for three windings: (a) Non-interleaved winding N-1; (b)
Figure 8. Winding arrangements (partial) for three windings: (a) Non-interleaved winding N-1;
Interleaved winding I-1; (c) Interleaved winding I-2.
(b) Interleaved winding I-1; (c) Interleaved winding I-2.
4.2. Electric Field Distribution of Different Windings
4.2. Electric Field Distribution of Different Windings
2-D finite element models of the three windings are established in ANSYS software. The
insulation
distances
between
winding
is 1 are
mmestablished
and 0.3 mminfor
HV and
LV winding
layers
2-D
finite element
models
of the
three layers
windings
ANSYS
software.
The insulation
respectively,
the insulation
between
HV for
andHV
LV and
windings
is 1.5 mm.
A maximum
distances
betweenand
winding
layers isdistance
1 mm and
0.3 mm
LV winding
layers
respectively,
excitation
voltage
of 1500
V and 384
are given
to HV and
LV mm.
windings
respectively.
The excitation
and the
insulation
distance
between
HVVand
LV windings
is 1.5
A maximum
excitation
voltage of
voltage decreases from one turn to the next turn, from up to down, and from outer to inner. Figure 9a–c
1500 V and 384 V are given to HV and LV windings respectively. The excitation voltage decreases from
shows the electric field distributions of the three windings respectively. The maximum electric field
one turn to the next turn, from up to down, and from outer to inner. Figure 9a–c shows the electric
intensities Emax of the three windings are compared in Table 4. The interleaved winding I-1 achieves
field distributions
of the three windings respectively. The maximum electric field intensities Emax of
the maximum Emax, and the non-interleaved winding N-1 achieves the minimum Emax among the three
the three
windings
are compared in Table 4. The interleaved winding I-1 achieves the maximum Emax ,
windings.
and the non-interleaved winding N-1 achieves the minimum Emax among the three windings.
Table 4. Maximum electric field intensities.
Table 4. Maximum electric field intensities.
Winding Type
Emax (V/m)
Non-interleaved N-1
9.7331 × 105
Winding Type
Emax (V/m)6
Interleaved I-1
1.7234 × 10
5
Non-interleaved
9.7331
Interleaved I-2N-1
1.7203×× 10
106
Interleaved I-1
1.7234 × 106
6
Interleaved
I-2turn to the1.7203
× 10from
The excitation voltage decreases
from one
next turn,
up to down, and from outer
to inner. Comparing non-interleaved winding N-1 with interleaved winding I-2, the voltage of the
thirdexcitation
column isvoltage
much lower
than that
of one
the first
outer from
to inner)
HV winding.
The
decreases
from
turncolumn
to the (from
next turn,
up for
to down,
and from
Therefore, the voltage difference between the HV and LV windings for winding N-1 is much smaller
outer to inner. Comparing non-interleaved winding N-1 with interleaved winding I-2, the voltage of
than winding I-2, and the Emax of winding N-1 is smaller than that of winding I-2. Comparing
the third column is much lower than that of the first column (from outer to inner) for HV winding.
interleaved winding I-2 with interleaved winding I-1, the voltage of the fifth foil conductor is higher
Therefore,
difference
between
theouter
HV and
LV windings
for winding
N-1 isthe
much
smaller
than the
thatvoltage
of eighth
foil conductor
(from
to inner)
for LV winding.
Therefore,
voltage
than winding
I-2,
and
the
E
of
winding
N-1
is
smaller
than
that
of
winding
I-2.
Comparing
difference between the HVmax
and LV windings for winding I-2 is smaller than winding I-1, and the Emax
interleaved
winding
withthan
interleaved
winding
the voltage
the fifth
foilmaximum
conductor
is higher
of winding
I-2 isI-2
smaller
that of winding
I-1.I-1,
According
to theofresults
of the
electric
fieldofintensities
the three windings,
in this
case study,
non-interleaved
winding,
than that
eighth foilofconductor
(from outer
to inner)
for LVcompared
winding.with
Therefore,
the voltage
difference
interleaved
windings
achieve higher
maximum
electric
field
intensity.
Thus,
canofresult
between
the HV and
LV windings
for winding
I-2 is
smaller
than
winding
I-1,interleaving
and the Emax
winding
in
the
increase
of
the
maximum
electric
field
intensity
when
insulation
distance
is
constant.
I-2 is smaller than that of winding I-1. According to the results of the maximum electric field intensities
of the three windings, in this case study, compared with non-interleaved winding, interleaved windings
achieve higher maximum electric field intensity. Thus, interleaving can result in the increase of the
maximum electric field intensity when insulation distance is constant.
Furthermore, the electric field intensities on path 1 and path 2 for the non-interleaved winding N-1,
interleaved windings I-1 and I-2 are investigated. The path 1 and path 2 are placed in the region where
the electric field intensity reaches the maximum. For non-interleaved winding N-1, path 1 and path 2
are placed as shown in Figure 2b. For interleaved windings I-1, path 1 and path 2 are placed between
the eighth foil conductor of the LV winding and the first column of the HV winding (from outer to
inner). For interleaved windings I-2, path 1 and path 2 are placed between the first column of the HV
winding and the fifth foil conductor of the LV winding (from outer to inner).
Energies 2017, 10, 371
9 of 11
Energies 2017, 10, 371
9 of 11
(a)
(b)
(c)
Figure 9. Electric field distribution for three windings: (a) Non-interleaved winding N-1; (b)
Figure 9. Electric field distribution for three windings: (a) Non-interleaved winding N-1; (b) Interleaved
Interleaved winding I-1; (c) Interleaved winding I-2.
winding I-1; (c) Interleaved winding I-2.
Furthermore, the electric field intensities on path 1 and path 2 for the non-interleaved winding
The
electric field
intensities
onI-2
path
and 2 for theThe
three
windings
are2shown
in Figure
N-1, interleaved
windings
I-1 and
are 1investigated.
path
1 and path
are placed
in the 10a,b.
region
The
electric
field
intensities
on
path
1
and
2
of
interleaved
winding
I-1
and
I-2
are
much
higher
where the electric field intensity reaches the maximum. For non-interleaved winding N-1, path than
1 and
those
of
the
non-interleaved
winding
N-1.
According
to
the
simulation
results
of
the
three
windings,
path 2 are placed as shown in Figure 2b. For interleaved windings I-1, path 1 and path 2 are placed
inbetween
this casethe
study,
interleaving
influences
field
eighth
foil conductor
of thethe
LVelectric
winding
andintensity.
the first column of the HV winding (from
outer to inner). For interleaved windings I-2, path 1 and path 2 are placed between the first column
of the HV winding and the fifth foil conductor of the LV winding (from outer to inner).
The electric field intensities on path 1 and 2 for the three windings are shown in Figure 10a,b.
The electric field intensities on path 1 and 2 of interleaved winding I-1 and I-2 are much higher than
those of the non-interleaved winding N-1. According to the simulation results of the three windings,
in this case study, interleaving influences the electric field intensity.
Energies 2017, 10, 371
Energies 2017, 10, 371
10 of 11
10 of 11
(a)
(b)
Figure 10. Electric field intensities on path 1 and path 2 for windings N-1, I-1 and I-2: (a) Electric field
Figure 10. Electric field intensities on path 1 and path 2 for windings N-1, I-1 and I-2: (a) Electric field
intensities on path 1; (b) Electric field intensities on path 2.
intensities on path 1; (b) Electric field intensities on path 2.
5. Conclusions
5. Conclusions
First, the electric field distributions for six kinds of non-interleaved windings with different wire
First, the electric field distributions for six kinds of non-interleaved windings with different wire
types are studied using 2-D FEM, and the results show that, compared with foil conductor, smaller
types are studied using 2-D FEM, and the results show that, compared with foil conductor, smaller
maximum electric field intensity can be achieved using litz wire in secondary winding, and it is
maximum electric field intensity can be achieved using litz wire in secondary winding, and it is
advisable to choose litz wire in secondary winding to achieve a lower maximum electric field
advisable to choose litz wire in secondary winding to achieve a lower maximum electric field intensity.
intensity. Second, the electric field distributions for three different winding structures (one nonSecond, the electric field distributions for three different winding structures (one non-interleaved
interleaved winding and two interleaved windings) are also investigated using 2-D FEM, and the
winding and two interleaved windings) are also investigated using 2-D FEM, and the results show
results show that interleaving can increase the maximum electric field intensity when insulation
that interleaving can increase the maximum electric field intensity when insulation distance is
distance is constant. Therefore, a change of insulation distance is advisable if interleaved winding is
constant. Therefore, a change of insulation distance is advisable if interleaved winding is adopted.
adopted. The proposed method of studying the electric field distribution and analysis results are
The proposed method of studying the electric field distribution and analysis results are expected to
expected to make a contribution to the improvement of electric field distribution in transformers.
make a contribution to the improvement of electric field distribution in transformers. Though they are
Though they are applied to MFT in this paper, the method is general and it is also applicable for
applied to MFT in this paper, the method is general and it is also applicable for power transformers.
power transformers.
Acknowledgments: This work was supported in part by the National Natural Science Foundation of China under
Acknowledgments:
work
was supported
in part
by the of
National
Natural Science Foundation of China
Grant no. 51277083, This
and the
National
Basic Research
Program
China (2015CB251301).
under Grant no. 51277083, and the National Basic Research Program of China (2015CB251301).
Author Contributions: Chengxiong Mao and Dan Wang proposed the idea and supervised the research;
Pei Huang
performed the
simulationsMao
and wrote
the paper;
authors the
contributed
the review of
theresearch;
paper.
Author
Contributions:
Chengxiong
and Dan
Wang all
proposed
idea andto supervised
the
Pei
Huangof
performed
the simulations
and no
wrote
the paper;
all authors contributed to the review of the paper.
Conflicts
Interest: The
authors declare
conflict
of interest.
Conflicts of Interest: The authors declare no conflict of interest.
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