electronics
Article
High Frequency Transformer’s Parasitic Capacitance
Minimization for Photovoltaic (PV) High-Frequency
Link-Based Medium Voltage (MV) Inverter
Himanshu 1 , Harsimran Singh 2 , Pandiyan Sathish Kumar 1 , Muhammad Umair Ali 1
Ho Yeong Lee 1 , Muhammad Adil Khan 1 , Gwan Soo Park 1 and Hee-Je Kim 1, *
1
2
*
ID
,
School of Electrical Engineering, Pusan National University, Busandaehak-ro 63 beon-gil 2, Busan 46241,
Korea; himanshuhimanshu820@gmail.com (H.); sathishnano2013@gmail.com (P.S.K.);
umairali.m99@gmail.com (M.U.A.); hyl@pusan.ac.kr (H.Y.L.); engradilee@gmail.com (M.A.K.);
gspark@pusan.ac.kr (G.S.P.)
Institute of Robotics and Mechatronics, German Aerospace Center (DLR), 82234 Wessling, Germany;
harsimran.smit@gmail.com
Correspondence: heeje@pusan.ac.kr; Tel.: +82-51-510-2364
Received: 18 June 2018; Accepted: 6 August 2018; Published: 8 August 2018
Abstract: The high-frequency-based medium voltage (MV) inverter is used in renewable energy
power sources for power transmission. However, power quality is compromised as a result of
the increase in common mode noise currents by the high inter-winding parasitic capacitance in
high-frequency link transformers. This fast voltage transient response leads to harmonic distortion
and transformer overheating, which causes power supply failure or many other electrical hazards.
This paper presents a comparative study between conventional and modified toroid transformer
designs for isolated power supply. A half bridge high-frequency (10 kHz) MV DC–AC inverter
was designed along with power source; a 680 W solar module renewable system was built.
An FEM-simulation with Matlab-FFT analysis was used to determine the core flux distribution and to
calculate the total harmonics distortion (THD). A GWInstek LCR meter and Fluke VT04A measured
the inter-winding capacitance and temperature in all four transformer prototypes, respectively.
The modified design of a toroid ferrite core transformer offers more resistance to temperature increase
without the use of any cooling agent or external circuitry, while reducing the parasitic capacitance
by 87%. Experiments were conducted along with a mathematical derivation of the inter-winding
capacitance to confirm the validity of the approach.
Keywords: high-frequency-based MV inverter; transformer’s parasitic capacitance; total harmonic
distortion; toroidal transformer; sector windings
1. Introduction
A transformer plays a vital role in energy conversion and is at the heart of the electric power
system. The transformer size decreases with increasing frequency, which allows for the building of
smaller, less expensive, and compact portable electrical devices [1,2]. Therefore, high frequency power
transformers are preferred over traditional frequency transformers (50–60 Hz) in the power electronic
fields, such as switching power supplies; converters; and inverters, including medium voltage (MV)
inverters, which offer a step-up transformer-less solution to interconnect photovoltaic (PV) arrays to
the MV grid [3–8].
Green energy is a priority of many researchers because of population and industrial growth,
which are leading the world towards an extensive rise of global warming threats and visible climate
change. Therefore, renewable energy sources are in high demand, particularly solar and wind energy.
Electronics 2018, 7, 142; doi:10.3390/electronics7080142
www.mdpi.com/journal/electronics
Electronics 2018, 7, 142
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These sources
Electronics
2018, 7, x are
projected to fulfill 50% of the energy requirement by the year 2050 [9]. On2 the
of 16
other hand, the intermittent nature of these power sources is a major limitation to connecting them
straight to electrical/electronic
national
This
criticalcan
obstacle
can be overcome
using
electrical/electronic
systems or systems
national or
grids.
Thisgrids.
critical
obstacle
be overcome
using external
external
devices,
such
as
energy
storage,
converters,
and
inverters
(see
Figure
1)
[10–13].
As
a
result
of
devices, such as energy storage, converters, and inverters (see Figure 1) [10–13]. As a result of the high
the
high
penetration
of
these
high-frequency-based
MV
inverters
into
the
renewable
energy
power
penetration of these high-frequency-based MV inverters into the renewable energy power plants,
plants,demands
energy demands
befor
fulfilled
for industries
home
power requirements.
However,
energy
could be could
fulfilled
industries
and homeand
power
requirements.
However, these
highthese
high-frequency
links,
for
example,
high-frequency
transformer,
H-bridge
inverter
dead
time,
frequency links, for example, high-frequency transformer, H-bridge inverter dead time, and non-linear
and non-linear
harmonic
This
can cause
serious
to the equipment
load,
generates load,
high generates
harmonichigh
content.
This content.
can cause
serious
damage
to damage
the equipment
including
including overheating,
powerfailure,
supplyor
failure,
or electric
shock hazards
[14,15].
Consequently,
to protect
overheating,
power supply
electric
shock hazards
[14,15].
Consequently,
to protect
the
the
component
and
the
connected
loads
from
overheating
and
to
provide
a
power
supply
without
any
component and the connected loads from overheating and to provide a power
without any
disturbances,the
thepower
powerquality
qualityofofthese
theseMV
MVinverters
invertersneeds
needsto
tobe
betaken
takeninto
intoconsideration
consideration[16–19]
[16–19].
disturbances,
.
Figure 1. Renewable energy source on and off grid system.
Figure 1. Renewable energy source on and off grid system.
An electromagnetic interference (EMI) in inverters can affect the power quality of transients, both
An electromagnetic interference (EMI) in inverters can affect the power quality of transients,
short time and longtime deviation, which can cause harmonics. In these devices, harmonics can be
both short time and longtime deviation, which can cause harmonics. In these devices, harmonics can
categorized into two classes: common and differential conduction modes (CCM and DCM) [20–22]. The
be categorized into two classes: common and differential conduction modes (CCM and DCM) [20–22].
high-frequency transformer is one of the sources of EMI and contributes to the common mode
The high-frequency transformer is one of the sources of EMI and contributes to the common mode
harmonics because of the intrinsic coupling capacitance, and electric and magnetic fields [23]. The duty
harmonics because of the intrinsic coupling capacitance, and electric and magnetic fields [23]. The duty
cycle is inversely proportional to the harmonics. Therefore, DCM operations of pulse-width
cycle is inversely proportional to the harmonics. Therefore, DCM operations of pulse-width modulation
modulation (PWM) converters increase the harmonics, which adds power losses in transformer
(PWM) converters increase the harmonics, which adds power losses in transformer windings. Similarly,
windings. Similarly, high-frequency operation causes skin and proximity effects that elevate the
high-frequency operation causes skin and proximity effects that elevate the harmonic losses, winding
harmonic losses, winding power losses, and rapid growth in the operating temperature [24,25]. On the
power losses, and rapid growth in the operating temperature [24,25]. On the other hand, high frequency
other hand, high frequency winding losses and lowering the leakage inductance has been a major
winding losses and lowering the leakage inductance has been a major research focus, while the winding
research focus, while the winding capacitance requires equally serious attention during the design of
capacitance requires equally serious attention during the design of transformers. Capacitive coupling
transformers. Capacitive coupling is one of the paths that can carry high frequency noise; premature
is one of the paths that can carry high frequency noise; premature resonance; electrostatic coupling
resonance; electrostatic coupling to other circuits; and fast transient voltages from primary to secondary
to other circuits; and fast transient voltages from primary to secondary circuitry, which produces
circuitry, which produces common mode noise currents and an increase in transformer temperature in
common mode noise currents and an increase in transformer temperature in the device, resulting in a
the device, resulting in a deterioration of the overall system operation, noise, health, and safety threats.
deterioration of the overall system operation, noise, health, and safety threats.
This capacitive coupling is an eruption effect of a transformer parasitic, rooted by a wide range of
This capacitive coupling is an eruption effect of a transformer parasitic, rooted by a wide range of
capacitance across the transformer, which circulates as a result of winding arrangements. Therefore,
capacitance across the transformer, which circulates as a result of winding arrangements. Therefore,
the key to overcoming this critical hurdle is lowering the inter-winding capacitance. Conventional
the key to overcoming this critical hurdle is lowering the inter-winding capacitance. Conventional
methods to reduce the emergence of capacitive coupling at the transformer include increasing the
methods to reduce the emergence of capacitive coupling at the transformer include increasing the
insulation between the primary and secondary winding or increasing the distance between the primary
insulation between the primary and secondary winding or increasing the distance between the primary
and secondary winding by winding them on opposite sides of the toroidal core. These changes in the
and secondary winding by winding them on opposite sides of the toroidal core. These changes in the
transformer will, however, cause other drawbacks, such as high leakage inductance, larger physical
transformer will, however, cause other drawbacks, such as high leakage inductance, larger physical
size, and poor inductive coupling. Accordingly, conventional methods are not completely effective in
improving the power quality. On the other hand, previous studies [26–32] examined the techniques on
smart transformers fuzzy logic based transformers by winding using fiber optic sensors and certain oils
Electronics 2018, 7, 142
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Electronics 2018, 7, x
3 of 16
size, and
inductive They,
coupling.
Accordingly,
methods are
effective in and
for cooling
thepoor
transformer.
however,
were conventional
arranged specifically
fornot
thecompletely
coupling capacitance
improving
the
power
quality.
On
the
other
hand,
previous
studies
[26–32]
examined
the
techniques
on
temperature control and showed no significant difference when compared with the less expensive
smart transformers
conventional
solutions. fuzzy logic based transformers by winding using fiber optic sensors and certain
oils for cooling the transformer. They, however, were arranged specifically for the coupling capacitance
The leakage inductance and primary/secondary capacitance are mutually exclusive and are
and temperature control and showed no significant difference when compared with the less expensive
governed by the distance between the windings and the unwounded core. As a result of this, it is
conventional solutions.
difficult to achieve both low capacitive coupling and a high degree of inductive coupling in a power
The leakage inductance and primary/secondary capacitance are mutually exclusive and are
transformer
[33,34].
circumvent
this
this study,core.
the conventional
toroid
governed
by theTo
distance
between
theinherent
windingstradeoff
and thein
unwounded
As a result of this,
it isferrite
core transformer
was modified
an additional
3Dand
printed
(PLA)
mold, which
separates
difficult to achieve
both lowby
capacitive
coupling
a highpolylactic
degree of acid
inductive
coupling
in a power
the primary
and [33,34].
secondary
windings,this
and
helps tradeoff
to implement
unique
winding.
Although
transformer
To circumvent
inherent
in this study,
the sector
conventional
toroid
ferrite the
distance
windings
will introduce
leakage
thereacid
is some
capacitance
corebetween
transformer
was modified
by an additional
3D inductance,
printed polylactic
(PLA)gain
mold,inwhich
separatesdue to
the primary
and secondary
windings, and
to implement
unique and
sectorwinding
winding.arrangements
Although the have
the dielectric
constant
of PLA. However,
the helps
magnetic
core geometry
distance
between
will introduce
leakage inductance,
is some
gain in capacitance
due toof the
a large
influence
on windings
self-capacitance
and leakage
inductancethere
of the
transformer
and because
the dielectric
constant
of PLA.
However,
the magnetic
geometryarrangements.
and winding arrangements
addition
of a mold,
it enables
access
to various
types core
of winding
This paperhave
reports a
a
large
influence
on
self-capacitance
and
leakage
inductance
of
the
transformer
and
of the
comparative analysis on the high frequency-link MV inverter for power-qualitybecause
improvement
by
addition of a mold, it enables access to various types of winding arrangements. This paper reports
effective subtraction of capacitive coupling and reducing the temperature increase without using any
a comparative analysis on the high frequency-link MV inverter for power-quality improvement by
extra circuitry or cooling agents.
effective subtraction of capacitive coupling and reducing the temperature increase without using any
extra circuitry or cooling agents.
2. High-Frequency Link Based MV Inverter Design Consideration
2. High-Frequency Link Based MV Inverter Design Consideration
2.1. Toroid Ferrite Core
2.1. Toroid Ferrite Core
To utilize the intrinsic ferrite material properties, it is essential to use a ring configuration of the
To utilize the intrinsic ferrite material properties, it is essential to use a ring configuration
ferrite core. Therefore, the toroid core was used in this paper, as it is commonly used for high-frequency
of the ferrite core. Therefore, the toroid core was used in this paper, as it is commonly used for
square/sine
wave-based applications, such as power input filters, ground-fault interrupters, commonhigh-frequency square/sine wave-based applications, such as power input filters, ground-fault
modeinterrupters,
filters, and common-mode
pulse and broadband
filters.
filters, and
pulse and broadband filters.
A 77 A
material
ferrite
toroid
was
used
MVinverter
inverterhigh-frequency
high-frequency
transformer.
77 material ferrite toroid was usedasasthe
thecore
core for
for MV
linklink
transformer.
FigureFigure
2 presents
a schematic
diagram
andisisdefined
defined
outer
diameter
(A), inner
2 presents
a schematic
diagramofofthe
the core
core and
byby
its its
outer
diameter
(A), inner
diameter
(B),
and
thickness
(C)
(See
Table
1).
Figure
3
shows
how
the
increasing
temperature
affects
diameter (B), and thickness (C) (See Table 1). Figure 3 shows how the increasing temperature affects
the properties
core properties
Table
2 presents
toroidferrite77
ferrite77 core
core material’s
properties.
the core
andand
Table
2 presents
toroid
material’selectrical
electrical
properties.
Figure
2. Ferrite 77 material core dimensions (courtesy: Fair-Rite products Corp).
Figure 2. Ferrite 77 material core dimensions (courtesy: Fair-Rite products Corp).
Table
1. Ferrite
7777
toroid
(courtesy:Fair-Rite
Fair-Rite
products
Corp).
Table
1. Ferrite
toroidcore
coredimensions
dimensions (courtesy:
products
Corp).
Dim
A
A
B B
C C
Dim
mm
mm
61.00
61.00
35.55
35.55
12.70
12.70
Mm
tol Nominal
Mm tol
Nominal
±1.30
2.400
±1.30
2.400
±0.85
1.4001.400
±0.85
±0.50
±0.50
0.5000.500
Electronics 2018, 7, 142
Electronics 2018, 7, x
4 of 15
4 of 16
Table 2.
Table
2. Ferrite 77 toroid
toroid core
core electrical
electrical properties
properties (courtesy:
(courtesy: Fair-Rite
Fair-Rite products
products Corp).
Corp).
Electrical
Electrical Properties
Properties
A
L (nH)
2950 ± 25%
AL (nH)
2950 ± 25%
22)
A
E
(cm
1.58000
1.58000
AE (cm )
−
−11)
∑I/A
(cm
9.20
9.20
)
∑I/A
I
(cm)
14.50
Iee(cm)
14.50
22.80000
Vee (cm
(cm33))
V
22.80000
Figure 3. Temperature effects on Ferrite 77 material properties (courtesy: Fair-Rite products Corp).
Figure 3. Temperature effects on Ferrite 77 material properties (courtesy: Fair-Rite products Corp).
2.2. Harmonic Current Contribution on Transformer Losses and Temperature Rise
2.2. Harmonic Current Contribution on Transformer Losses and Temperature Rise
Total
widely-used notion
notion to
to define
define the
theharmonic
harmoniccontent
contentinin
Total harmonics
harmonics distortion
distortion (THD)
(THD) is
is aa widely-used
alternating
signals.
This
value
is
defined
as
the
ratio
sum
of
the
powers
of
all
harmonic
components
alternating signals. This value is defined as the ratio sum of the powers of all harmonic components toto
the
used for
for low,
low, medium,
medium,and
andhigh
highvoltage
voltagesystems,
systems,
thepower
powerof
of the
the fundamental
fundamental frequency.
frequency. THD
THD is
is used
where
I and
THDV, and can be calculated using the
wherethe
thecurrent
currentand
andvoltage
voltagedistortion
distortionisisdefined
definedasasTHD
THD
I and THDV , and can be calculated using
following
Equations
(1)–(2).
the following Equations (1)–(2).
=

THDv = 
H
∑
!1
| |
2
|Vh |2
| | × 100%

/|V1 | × 100%
(1)
(1)
h 6 =1
(2)
! 1 | | × 100%
2
h
THD I =  ∑ Ii
/| I1 | × 100%
(2)
where h is the harmonic content order, and Vhh6=and
Ih are the voltage and current amplitude of order “h”
1
harmonic component, respectively. V1 and I1 are the voltage and current amplitude of the fundamental
where h is the harmonic content order, and Vh and Ih are the voltage and current amplitude of order “h”
component, respectively.
harmonic component, respectively. V 1 and I1 are the voltage and current amplitude of the fundamental
The International Electrotechnical Commission (IEC) 61727 imposes the limits for harmonics in
component, respectively.
the current—Electromagnetic compatibility (EMC)-Part 3–2: Limits for harmonics current emission.
The International Electrotechnical Commission (IEC) 61727 imposes the limits for harmonics in
The IEEE Single Phase Harmonics Task Force (P1495) has set similar limitations. U.S. and European
the current—Electromagnetic compatibility (EMC)-Part 3–2: Limits for harmonics current emission.
power systems are different from each other in many standards. Therefore, the United States should be
The IEEE Single Phase Harmonics Task Force (P1495) has set similar limitations. U.S. and European
different than the IEC stance. Thus, there is a flexibility to follow the certain standard (Table 3).
power systems are different from each other in many standards. Therefore, the United States should
be different than the IEC stance. Thus, there is a flexibility to follow the certain standard (Table 3).
=
H
2
Table 3. Current and Voltage total harmonic distortion allowing values and their associated risks
(courtesy: Interpreting European norm (EN) 50160 and International Electrotechnical Commission (IEC)
standard 61727). THD—total harmonics distortion.
Electronics 2018, 7, 142
THDV
<8%
THDI
<5%
Risk
normal situation
considerable
5 of 15
Table 3. Current and Voltage
total harmonic
allowing
values and their associated risks
8–15%
5–50%distortion
Minor
harmonic
(courtesy: Interpreting European norm (EN) 50160 and
International
pollution with Electrotechnical Commission
(IEC) standard 61727). THD—total harmonics distortion.
malfunctions
possibility
THDV
THDI
<8%
8–15%
>15%
<5%>15%
situation
considerable
>50% normal
major
harmonic
5–50%
Minor harmonic pollution with malfunctions possibility
pollution with
>50%
major harmonic pollution with malfunctions probability
Risk
malfunctions
probability
The losses in transformers can be classified as load loss (impedance loss), no-load loss (excitation
loss),
and
totalinloss
(no-load +can
load-loss).
Loadasloss
can
be (impedance
subdivided loss),
further
into stray
magnetic
The
losses
transformers
be classified
load
loss
no-load
loss (excitation
losses
in
the
core,
eddy
currents,
and
resistive
losses
in
the
windings.
loss), and total loss (no-load + load-loss). Load loss can be subdivided further into stray magnetic losses
in the core, eddy currents, and resistive losses in the windings.
h=hmax
h = hmax 2 2
Ih2h 2
pt = p f h∑

=1 I h h
pt = p f
(3)
(3)
h =1
wherePPf is
theeddy
eddycurrent
current
loss
the
fundamental
frequency,
and
f and
Ih are
fractions
of total
the
where
loss
atat
the
fundamental
frequency,
and
f and
Ih are
the the
fractions
of the
f isthe
totalload
RMScurrent
load current
the harmonic
number
h.
RMS
at the at
harmonic
number
h.
2.3.Circuit
CircuitOperation
Operation
2.3.
Figure44shows,
shows,AAsingle-phase
single-phase
half
bridge
kHz)
is comprised
of two
power
MOSFET
Figure
half
bridge
(10(10
kHz)
is comprised
of two
power
MOSFET
(IRF(IRF
250)
250)
(Texas
Instruments,
Dallas,
TX,
USA),
S1
and
S2,
which
are
driven
by
a
DSP
F28335
(Texas
(Texas Instruments, Dallas, TX, USA), S1 and S2, which are driven by a DSP F28335 (Texas Instruments,
Instruments,
Dallas,
TX,
USA) chip
to generate
a pulse width
modulated
waveform
andD1
feedback
Dallas,
TX, USA)
chip to
generate
a pulse
width modulated
waveform
and feedback
diodes,
and D2.
diodes,
andfreewheeling
D2. These are
called
freewheeling
withtotwo
DC bus
toTwo-stage
stabilize
These
areD1
called
diodes
with
two DC busdiodes
capacitors
stabilize
thecapacitors
DC voltage.
the DCconversions
voltage. Two-stage
with thetransformer.
help of the high-frequency
power
with the power
help ofconversions
the high-frequency
High-frequency transformer.
operation is
High-frequency
operation
is
possible
at
the
first
DC/DC
stage
and
at
the second
modified
possible at the first DC/DC stage and at the second stage modified amplitude
of stage
converted
highamplitude
of
converted
high-frequency
AC
voltage
by
high-frequency
transformer
secondary,
which
is
frequency AC voltage by high-frequency transformer secondary, which is connected to high-frequency
connected
to
high-frequency
rectifier
AC/DC
and
an
output
inverter,
which
converts
the
DC
voltage
rectifier AC/DC and an output inverter, which converts the DC voltage to the required frequency AC
to the required
frequency
voltage
the case of utility grid 50/60 Hz.
voltage
in the case
of utilityAC
grid
50/60 in
Hz.
Figure 4. Circuit layout for photovoltaic (PV) high-frequency-based medium voltage (MV) inverter
Figure 4. Circuit layout for photovoltaic (PV) high-frequency-based medium voltage (MV) inverter system.
system.
3. Fabrication
This study examined a new design for the high-frequency link of an MV inverter, which mitigates
the temperature increase occurring as a result of harmful harmonics by reducing the capacitive coupling
at the high-frequency transformer. Four toroid core transformers with conventional and modified
configurations, with 180◦ and 360◦ sector windings, were fabricated, and their THD, self-induced
capacitance, and temperature were measured and compared. The transformer windings for all four
3. Fabrication
3. Fabrication
This study examined a new design for the high-frequency link of an MV inverter, which mitigates
This study examined a new design for the high-frequency link of an MV inverter, which mitigates
the temperature increase occurring as a result of harmful harmonics by reducing the capacitive
the temperature increase occurring as a result of harmful harmonics by reducing the capacitive
coupling at the high-frequency transformer. Four toroid core transformers with conventional and
Electronics 2018,
7, 142
6 ofand
15
coupling
at the
high-frequency transformer. Four toroid core transformers with conventional
modified configurations, with 180° and 360° sector windings, were fabricated, and their THD, selfmodified configurations, with 180° and 360° sector windings, were fabricated, and their THD, selfinduced capacitance, and temperature were measured and compared. The transformer windings for all
induced capacitance, and temperature were measured and compared. The transformer windings for all
configurations
werewere
wound
manually.
TheThe
corecore
material,
dimensions,
copper
wire,
andand
a number
of
four
configurations
wound
manually.
material,
dimensions,
copper
wire,
a number
four configurations were wound manually. The core material, dimensions, copper wire, and a number
ofwinding
windingturns
turnswere
werethe
thesame
samefor
forthe
theconventional
conventionaland
andmodified
modifiedconfiguration,
configuration,as
aslisted
listedin
inTable
Table3.3.
of winding turns were the same for the conventional and modified configuration, as listed in Table 3.
Thedifference
differencebetween
between the
the conventional
conventional and
and modified configuration was
The
was aa two-part
two-partmold
moldthat
thatwas
was
The difference between the conventional and modified configuration was a two-part mold that was
mountedover
overthe
thesecondary
secondary windings
windings and
and ferrite core. The primary
mounted
primary winding
winding was
wasthen
thenwound
woundover
over
mounted over the secondary windings and ferrite core. The primary winding was then wound over
thisadditional
additionalpiece
pieceof
ofhardware,
hardware, which
which altered the dimensions
this
dimensions of
of the
the primary
primarywinding
windingand
andprovided
provided
this additional piece of hardware, which altered the dimensions of the primary winding and provided
scopeto
tounique
uniquewinding
winding arrangements.
arrangements. The
The mold was printed using
scope
using aa 3D
3D printer
printerwith
withaaPLA
PLAfilament
filament
scope to unique winding arrangements. The mold was printed using a 3D printer with a PLA filament
material.This
Thiswas
wascomprised
comprised
two
parts,
and
bottom,
each
with
a width
of mm
0.5 mm
material.
ofof
two
parts,
toptop
and
bottom,
each
with
a width
of 0.5
eacheach
withwith
very
material. This was comprised of two parts, top and bottom, each with a width of 0.5 mm each with very
very negligible
extra weight
and[35,36].
cost [35,36].
negligible
extra weight
and cost
negligible extra weight and cost [35,36].
3.1.Case
Case1:1:Conventional
ConventionalToroid
ToroidCore
CoreTransformer
Transformerwith
with180°
180◦Sector
SectorWindings
Windings
3.1.
3.1. Case 1: Conventional Toroid Core Transformer with 180° Sector Windings
◦
thisconfiguration,
configuration,the
the entire
entire secondary
secondary winding
InInthis
winding is
is distributed
distributedover
overthe
the180
180°sector
sectorof
ofthe
thetoroid
toroid
In
this
configuration,
the
entire
secondary
winding
is
distributed
over
the
180°
sector
of
the
toroid
corein
inaaback-and-forth
back-and-forthmanner.
manner. The
The other
other half
half of
of the
core
the toroid
toroid core
core is
is wound
woundwith
withprimary
primarywindings
windingsinin
core
in a back-and-forth
manner.
The other
half of the toroid core is wound with primary windings in
similar
manner,as
asshown
shown
inFigure
Figure
aasimilar
manner,
in
5.5.
a similar manner, as shown in Figure 5.
Figure. 5. The 180°
(A) flux pattern in core; (B) 2D model; (C) 3D model.
◦ conventional(A)
Figure
Figure.5.5.The
The180
180°conventional
conventional (A)flux
fluxpattern
patterninincore;
core;(B)
(B)2D
2Dmodel;
model;(C)
(C)3D
3Dmodel.
model.
3.2. Case 2: Modified Toroid Core Transformer with 180°◦ Sector Windings
3.2.Case
Case2:2:Modified
ModifiedToroid
ToroidCore
CoreTransformer
Transformer with
with 180°
180 Sector
SectorWindings
Windings
3.2.
In this
configuration,
the
secondary
winding
is distributed
over
the 180°
sector
of the
toroid
core
◦ sector
thisconfiguration,
configuration,the
thesecondary
secondary
winding
is distributed
over
180
of the
toroid
InInthis
winding
is distributed
over
thethe
180°
sector
of the
toroid
core
incore
a back-and-forth
manner,
just
as
in
the
previous
case.
The
two
parts
of
the
3D
printed
mold
using
in a back-and-forth
manner,
as in
the previous
case.
The
twoofparts
of the
3D printed
moldaa
in a back-and-forth
manner,
just asjust
in the
previous
case. The
two
parts
the 3D
printed
mold using
PLA
filament
material
were
mounted
over
the
ferrite
toroid
core
and
secondary
windings,
to
usingfilament
a PLA filament
were mounted
ferrite
toroid
coreand
andsecondary
secondary windings,
PLA
materialmaterial
were mounted
over over
the the
ferrite
toroid
core
windings, toto
completely
encapsulate
them.
Owing
to
the
assembly
of
the
mold, the secondary
secondary windingisiscompletely
completely
completelyencapsulate
encapsulatethem.
them. Owing
Owing to
to the
the assembly
assembly of
of the
the mold,
completely
mold, the
the secondarywinding
winding is completely
hidden,
which
leaves
an
entire
360°
span
for
the
primary
winding.
The
initial
experiments
were
carried
hidden,which
whichleaves
leavesan
anentire
entire 360°
360◦ span
span for
for the
the primary
primary winding.
hidden,
winding. The
The initial
initial experiments
experimentswere
werecarried
carried
out
with
the
primary
windings
over
the
360°
sector
and
180°
sector
of thethe
core.
On thethe
other
hand,
the
◦ sector
◦ sector
outwith
withthe
theprimary
primarywindings
windingsover
overthe
the360°
360sector
and
180sector
core.
other
hand,
out
and
180°
of of
the core.
OnOn
the other
hand,
the
lowest leakage inductance was achieved when the primary had a 180°◦ sector winding without
the lowest
leakage
inductance
achieved
when
primaryhad
hadaa 180°
180 sector winding
lowest
leakage
inductance
waswas
achieved
when
thetheprimary
winding without
without
overlapping the secondary winding, as shown in Figure 6.
overlappingthe
thesecondary
secondarywinding,
winding,as
asshown
shownininFigure
Figure6.6.
overlapping
Figure 6. The 180°
(A) flux pattern in core; (B) 2D model; (C) 3D model.
◦ modified (A)
Figure
flux pattern in
in core;
core; (B)
(B)2D
2Dmodel;
model;(C)
(C)3D
3Dmodel.
model.
Figure6.6.The
The180
180° modified
modified
3.3. Case 3: A Conventional 360◦ Wound Toroid Core Transformer
In this case, the secondary winding is distributed over the entire 360◦ sector of the toroid ferrite
core. The primary winding is also distributed over the 360◦ sector on top of the secondary winding
(Figure 7).
Electronics 2018, 7, x
7 of 16
3.3. Case 3: A Conventional 360° Wound Toroid Core Transformer
3.3. Case 3: A Conventional 360° Wound Toroid Core Transformer
In this case, the secondary winding is distributed over the entire 360° sector of the toroid ferrite
In this case, the secondary winding is distributed over the entire 360° sector of the toroid ferrite
core.
The primary
is also distributed over the 360° sector on top of the secondary winding
Electronics
7, 142winding
7 of 15
core.
The2018,
primary
winding is also distributed over the 360° sector on top of the secondary winding
(Figure 7).
(Figure 7).
Figure 7. The 360°
conventional (A) 2D model; (B) flux distribution; (C) 3D model.
◦ conventional
Figure
7. 7.
The
360
Figure
The
360°
conventional(A)
(A)2D
2Dmodel;
model;(B)
(B)flux
fluxdistribution;
distribution; (C)
(C) 3D
3D model.
model.
3.4. Case 4: A Modified 360° Wound
Toroid Core Transformer
3.4.Case
Case4:4:AAModified
Modified360°
360◦Wound
WoundToroid
ToroidCore
CoreTransformer
Transformer
3.4.
InIn
thisthis
case,
the secondary
winding
is distributed
over 360°
sector
the toroid
core
in a back-andcase,
secondary
winding
is distributed
over
360◦ofof
sector
of the
toroid
in a
In this
case,
thethe
secondary
winding
is distributed
over 360°
sector
the toroid
core
in a core
back-andforth
manner,
as
in
the
former
case.
The
toroid
ferrite
core
along
with
the
secondary
winding
is
back-and-forth
as in the
former
case. The
toroid
with the secondary
forth
manner, asmanner,
in the former
case.
The toroid
ferrite
coreferrite
along core
withalong
the secondary
winding is
encapsulated
with
the
3D
printed
mold,
over
which
the
primary
winding
is
wound
around
a
360°
span
winding is encapsulated
the mold,
3D printed
mold, over
which the
primary
is wound
around
encapsulated
with the 3Dwith
printed
over which
the primary
winding
is winding
wound around
a 360°
span
◦8).
(Figure
a
360
span
(Figure
8).
(Figure 8).
Figure 8. The 360° modified (A) 2D model; (B) flux distribution; (C) 3D model.
Figure 8. The 360° modified (A) 2D model; (B) flux distribution; (C) 3D model.
Figure 8. The 360◦ modified (A) 2D model; (B) flux distribution; (C) 3D model.
4. Calculation of the Transformer Inter-Winding Capacitance
4. Calculation of the Transformer Inter-Winding Capacitance
4. Calculation of the Transformer Inter-Winding Capacitance
The general structure (2D, 3D, and flux flow in core) of the four designed transformer’s prototypes
The general structure (2D, 3D, and flux flow in core) of the four designed transformer’s prototypes
Theare
general
structure
(2D,
3D, and flux
flow(3).
in core)
ofsection,
the fourprototype
designed transformer’s
prototypes
under test
illustrated
in the
fabrication
section
In this
transformer calculations
under test are illustrated in the fabrication section (3). In this section, prototype transformer calculations
under
test
are
illustrated
in
the
fabrication
section
(3).
In
this
section,
prototype
transformer
calculations
were carried out for inter-winding capacitance. Figure 9 shows the conceptual structure of case 1 and
were carried out for inter-winding capacitance. Figure 9 shows the conceptual structure of case 1 and
were
carried out for
inter-winding
capacitance.capacitance
Figure 9 shows
the conceptual
structure
of case 1 and
case
2 transformer
prototypes
for inter-winding
calculation.
Likewise,
the capacitance
for
case 2 transformer prototypes for inter-winding capacitance calculation. Likewise, the capacitance for
case
2
transformer
prototypes
for
inter-winding
capacitance
calculation.
Likewise,
the
capacitance
for
other prototypes can be evaluated in a similar manner.
other prototypes can be evaluated in a similar manner.
other prototypes can be evaluated in a similar manner.
Ferrite core material 77 has a negligible effect on parasitic capacitance; therefore, only winding
configurations were taken into account. For the sake of simplicity, only one winding of the secondary
side, which is wound on the ferrite core, is considered for calculation of inter-winding capacitance.
The same position of the secondary winding is considered for all four cases.
The distance between the inner secondary winding and inner primary windings can be expressed
as follows:
s
π
πi
r1in,i = r1 2 + r2 2 − 2r1 r2 cos( +
)
(4)
2
np
where r1 is the distance from the center of the core to the inner primary windings, r2 is the distance
from the center of the core to the outer primary windings, r3 is the distance from the center of the core
to the inner secondary windings, r4 is the distance from the center of the core to the outer secondary
windings (Figure 9), and np is the total number of primary turns. In all four cases, r3 and r4 values
are the same, as secondary winding is wounded on the ferrite core and core dimension is same for
all transformer prototypes. On the other hand, r1 and r2 values will vary with respect to each case,
for example, r1 , for case 4 (r1, 4 ) and case 2 (r1, 2 ) will be same, but they are less than case 3 (r1, 3 ), which
Electronics 2018, 7, 142
8 of 15
in turn is less than case 1 (r1, 1 ). The details of r1 , r2 , r3 , r4 for the four different configurations are given
as follows:
A : r1, 4 = r1, 2 < r1, 3 < r1, 1
B : r2, 1 < r2, 3 < r2, 2 = r2, 4
C : r3, 1 = r3, 2 = r3, 3 = r3, 4
D : r4, 1 = r4, 2 = r4, 3 = r4, 4
Electronics 2018, 7, x
9 of 16
The static capacitance between the inner primary and inner secondary is as follows:
C1in,i =
,
∈∈∘
◦dπl1
∈∈∘◦dπl1
= q
2r21in,i ,
22 r1 2 + r2 2 − 2 r1 r2 cos( π2 +
2
πi
np )
(5)
(5)
where Є∘◦ is
free space,
space, ddisisthe
thediameter
diameterof
ofthe
thewire
wireused
usedfor
forprimary
primaryand
andsecondary
secondary
is the permittivity of free
windings, and l11 is
is the
the overlapped
overlapped length.
length.
Assuming that the voltage potential distribution along the primary turn varies linearly,
linearly,
i
1Vp
np − 1
The total stored energy between the inner primary and secondary is as follows:
The total stored energy between the inner primary and secondary is as follows:
Vp [i ] =
E1in
!
1n −1
2
1 p
i
= 2 ∑ C1in,i (,
Vp )
1
2 i =0
np − 1
(6)
(6)
(7)
(7)
Similarly,
the capacitance
capacitance between
between the
the inner
innerprimary–outer
primary–outersecondary,
secondary,outer
outerprimary–outer
primary–outer
Similarly, the
secondary,
and
outer
primary–outer
secondary
can
be
calculated.
Equations
(4)–(7)
can
be
used
to find
secondary, and outer primary–outer secondary can be calculated. Equations (4)–(7) can be
used
to
the
and and
energy
for the
other
three
cases
as as
well
(Table
4).4).
The
simulation
was
findcapacitance
the capacitance
energy
for the
other
three
cases
well
(Table
The
simulation
wasrun
runon
MATLAB
to calculate
thethe
capacitance
of simplicity
simplicityand
andtotoignore
ignorethe
the
on MATLAB
to calculate
capacitanceininallallfour
fourcases.
cases. For
For the
the sake
sake of
repetitive
process
of
inter-winding
capacitance
calculations,
only
one
winding
in
the
same
position
repetitive process of inter-winding capacitance calculations, only one winding in the same positionof
the
secondary
side
is considered
forfor
allall
four
cases.
ToTo
seesee
thethe
effect
ofof
inter-winding
capacitance,
we
of the
secondary
side
is considered
four
cases.
effect
inter-winding
capacitance,
Electronics
2018,
7,
x
◦
choose
three
primary
winding
for
180°
conventional
and
modified
configurations
instead
of
116,
and
we choose three primary winding for 180 conventional and modified configurations instead of 116, 68 of 16
primary
windings
for 360°
and modified
configurations
instead
of 220.of 220.
and 6 primary
windings
forconventional
360◦ conventional
and modified
configurations
instead
Table 4. Detailed parameters of the transformer prototypes. PLA—polylactic acid.
Prototypes Physical Properties
Copper Wire standard
Primary Turns
Secondary Turns
Core Material (Table 1)
Core shape
Permittivity (F/m)
Case 1
Case 2
Case 3
Case 4
24 AWG
24 AWG
24 AWG
24 AWG
116
116
220
220
116
116
220
220
Ferrite 77
Ferrite 77
Ferrite77
Ferrite 77
Ring
Ring
Ring
Ring
8.85 × 10−12
8.4190×10−12 8.85×10−12 8.419 × 10−12
(Air)
(Air + PLA)
(Air)
(Air + PLA)
Inner Radius (mm)
17.775
15.275
17.775
15.275
Outer Radius (mm)
30.5
32.5
30.5
32.5
Primary Voltage (V)
24
24
24
24
Secondary Voltage (V)
~24
~24
~24
~24
Frequency (kHz)
1–30
1–30
1–30
1–30
17.265
14.765
16.755
14.765
30.5
32.5
31.01
32.5
17.265
17.265
17.265
17.265
Figure 9. Toroidal transformer with 180◦ sectored
presentation
30.5 winding, Conceptual
30.5
30.5 of transformer
30.5
Figurefrom
9. Toroidal
transformer
with 180°
winding,
Conceptual
presentation of transformer
prototypes
left to right
conventional
andsectored
modified.
PLA—polylactic
acid.
fromTable
left to5right
and modified.
PLA—polylactic
It canprototypes
be seen from
thatconventional
the inter-winding
capacitance
would beacid.
highest for case 3, followed
by that for case 1, case 4, and case 2. These analytical calculations hold well with the experimental data
Ferrite core
material which
77 hasisashown
negligible
effect
parasitic capacitance; therefore, only winding
for inter-winding
capacitance,
in the
nexton
section.
configurations were taken into account. For the sake of simplicity, only one winding of the secondary
side, which is wound on the ferrite core, is considered for calculation of inter-winding capacitance. The
Electronics 2018, 7, 142
9 of 15
Table 4. Detailed parameters of the transformer prototypes. PLA—polylactic acid.
Prototypes Physical Properties
Case 1
Case 2
Case 3
Case 4
Copper Wire standard
Primary Turns
Secondary Turns
Core Material (Table 1)
Core shape
24 AWG
116
116
Ferrite 77
Ring
8.85 × 10−12
(Air)
17.775
30.5
24
~24
1–30
17.265
30.5
17.265
30.5
24 AWG
116
116
Ferrite 77
Ring
8.4190×10−12
(Air + PLA)
15.275
32.5
24
~24
1–30
14.765
32.5
17.265
30.5
24 AWG
220
220
Ferrite77
Ring
8.85×10−12
(Air)
17.775
30.5
24
~24
1–30
16.755
31.01
17.265
30.5
24 AWG
220
220
Ferrite 77
Ring
8.419 × 10−12
(Air + PLA)
15.275
32.5
24
~24
1–30
14.765
32.5
17.265
30.5
Permittivity (F/m)
Inner Radius (mm)
Outer Radius (mm)
Primary Voltage (V)
Secondary Voltage (V)
Frequency (kHz)
r1
r2
r3
r4
It can be seen from Table 5 that the inter-winding capacitance would be highest for case 3, followed
by that for case 1, case 4, and case 2. These analytical calculations hold well with the experimental data
for inter-winding capacitance, which is shown in the next section.
Table 5. Theoratical analysis of all presented prototypes, calculated energy, and inter-winding capacitance.
Case 1
Energy (J)
Percentage %
E1
E2
E3
E4
Etotal
Capacitanceeq (F)
5.63 × 10−10
35.4
3.87 × 10−10
24.3
3.54 × 10−10
22.3
2.87 × 10−10
18
1.59 × 10−10
100
2.76 × 10−12
E4
Etotal
Capacitanceeq (F)
Case 2
E1
Energy (J)
Percentage %
10−10
5.31 ×
33.9
E2
10−10
3.74 ×
23.9
E3
10−10
3.66 ×
23.4
10−10
2.94 ×
18.8
10−9
1.57 ×
100
2.72 × 10−12
Case 3
E1
Energy (J)
Percentage %
10−10
5.69 ×
35.5
E2
10−10
3.87 ×
24.2
E3
10−10
3.56 ×
22.2
E4
10−10
2.90 ×
18.1
Etotal
10−9
1.60 ×
100
Capacitanceeq (F)
2.78 × 10−12
Case 4
E1
Energy (J)
Percentage %
10−10
5.29 ×
33.6
E2
10−10
3.73 ×
23.7
E3
10−10
3.73 ×
23.7
E4
10−10
3.00 ×
19
Etotal
10−9
1.57 ×
100
Capacitanceeq (F)
2.73 × 10−12
5. Experimental Setup
The high-frequency transformer temperature, capacitive coupling, and leakage inductance
were measured using a Fluke VT04A (Fluke, Everett, WA, USA) Thermometer and GWInstek LCR
(GWINSTEK, New Taipei City, Tucheng Dist., Taiwan) meter. The experiments were conducted at
constant ambient room temperature, on the high-frequency link of a 1 kW half bridge MV inverter.
Two 38 V, 350 W standalone solar modules connected in parallel served as input for the developed
inverter. Owing to the addition of a 3D printed mold and sector winding, it was possible to have
different winding arrangements. A number of modified toroid high-frequency transformers have been
developed with different sector windings, such as 45◦ , 90◦ , 120◦ , 180◦ , 270◦ , and 360◦ . Figure 10
presents a block diagram of the experimental setup. The input and output waveforms of the
constant ambient room temperature, on the high-frequency link of a 1 kW half bridge MV inverter. Two
38 V, 350 W standalone solar modules connected in parallel served as input for the developed inverter.
Owing to the addition of a 3D printed mold and sector winding, it was possible to have different
winding arrangements. A number of modified toroid high-frequency transformers have been
Electronics 2018, 7, 142
10 of 15
developed
with different sector windings, such as 45°, 90°, 120°, 180°, 270°, and 360°. Figure 10
presents
a block diagram of the experimental setup. The input and output waveforms of the transformer were
stored,
and the harmonic
contents
present
in thecontents
waveform
wereinanalyzed
by Matlab-FFT
(MathWorks,
transformer
were stored,
and the
harmonic
present
the waveform
were analyzed
by
Matlab-FFT
(MathWorks,
Natick,
MA,
USA).
Natick, MA, USA).
FigureFigure
10. Block
diagram
for for
thethe
testing
prototypesPV
PV
high
frequency
based
MV inverter
10. Block
diagram
testingprocess
process for
for prototypes
high
frequency
based
MV inverter
systems.
THD—
total harmonics
distortion.
systems.
THD—total
harmonics
distortion.
6. Results
and Discussion
6. Results
and Discussion
◦
Forcomparative
the comparative
analysis,
wedesigned
designed aa conventional
conventional toroid
transformer
withwith
the same
180 180°
For the
analysis,
we
toroid
transformer
the same
◦
and sector
360 sector
windings
samecore
coredimension.
dimension. The
experimental
studies
statedstated
and 360°
windings
andand
thethe
same
Thecomparative
comparative
experimental
studies
that the proposed modified design succeeded in lowering the inter-winding capacitance (approximately
87%) and controlling temperature increase issues (less than 30◦ ) when compared with conventional
designs; detailed discussion based on sectored winding is shown below. Table 6 compares the THD
of the aforementioned transformer prototypes. By comparative analysis of normative Table 3 and
experimental result Table 6, it is clearly visible that all the prototypes have a minimum risk. Although,
modified designs have registered more or less similar distortion compared with conventional designs.
Table 6. Voltage and current THD for all prototypes.
Source Input Voltage (V)
24
24
24
24
THDV %
Case
1
2
3
4
THDI %
Primary
Secondary
Primary
Secondary
45.53
34.70
11.92
9.81
22.34
22.15
16.33
14.94
5.6
12.22
48.19
43.06
7.20
11.85
49.56
44.32
6.1. Toroidal Transformer with 180◦ Sectored Winding
Inter-winding Capacitance: Large inter-winding capacitance causes a significant amount of common
mode noise at high-frequency operations. Figure 11 shows the comparison for parasitic capacitance
from 1 to 30 kHz frequency at a high-frequency-based MV inverter. It is clearly visible that the
proposed modified design has minimized the parasitic capacitance close to 20 pF, which is much
lower than the conventional design. This was because of the mold, which helped increase the distance
between the windings.
Inter-winding Capacitance: Large inter-winding capacitance causes a significant amount of common
mode noise at high-frequency operations. Figure 11 shows the comparison for parasitic capacitance
from 1 to 30 kHz frequency at a high-frequency-based MV inverter. It is clearly visible that the proposed
modified design has minimized the parasitic capacitance close to 20 pF, which is much lower than the
conventional design. This was because of the mold, which helped increase the distance between the
Electronics 2018,
7, 142
11 of 15
windings.
Figure 11. Toroidal
transformers
sectored
winding, parasitic
parasitic coupling
capacitance
comparison
Figure 11. Toroidal
transformers
at 180at◦ 180°
sectored
winding,
coupling
capacitance
comparison
between the conventional and modified design of high-frequency link based MV inverter systems.
between the conventional and modified design of high-frequency link based MV inverter systems.
Leakage Inductance: In a sectored wound transformer, when the winding covers only 180°, leakage
path changes
core. According
theory, we expected
inductance
be higher
Leakageflux
Inductance:
Inina the
sectored
woundtotransformer,
whenthe
theleakage
winding
coverstoonly
180◦in, leakage
modified
design
when
compared
with
the
conventional
design
because
of
the
distance
between
flux path changes in the core. According to theory, we expected the leakage inductance to be higher
windings created by the PLA mold. However, the 3D printed mold using PLA filament was mounted
in modified
design when compared with the conventional design because of the distance between
over the ferrite toroid core and secondary windings to completely encapsulate them and provided
windings created
the PLA
mold.
However,
3D printed
using
PLA
filament
was mounted
scope to by
increase
the mean
length
turn of thethe
primary
winding, mold
which is
required
to reduce
the leakage
inductance.
This
theory
supported bywindings
the experiment
results [37]. Figure
12 demonstrates
over the ferrite
toroid
core
andis secondary
to completely
encapsulate
them that
andthe
provided
modified
design
recorded
less
leakage
inductance
than
the
conventional
design.
scope to increase the mean length turn of the primary winding, which is required to reduce the leakage
inductance.
This7,theory
is supported by the experiment results [37]. Figure 12 demonstrates
that the
Electronics
1212ofof1616
Electronics
2018,2018,
x 7, x
modified design recorded less leakage inductance than the conventional design.
◦ sectored winding, leakage inductance comparison between
Figure 12.
Toroidal
transformers
at 180
Figure
12. Toroidal
transformers
at 180°
sectored winding, leakage inductance comparison between the
Figure
12.
Toroidal
transformers
at
180°
sectored
winding,
leakage
inductance
comparison
between the
conventional
and
modifieddesign
design of
linklink
based
MV
inverter
systems.
the conventional
and
modified
ofhigh-frequency
high-frequency
based
MV inverter
systems.
conventional and modified design of high-frequency link based MV inverter systems.
Temperature: By comparing modified and conventional transformers on full load, it is clearly visible
Temperature:
ByBy
comparing
modified
and
conventional
transformers
on full
itvisible
is clearly
that
lowering
the
interwinding
capacitance
and
harmonicstransformers
distortion
helped
significantly
in
controlling
Temperature:
comparing
modified
and
conventional
on full
load,
it isload,
clearly
visible
that
lowering
the
interwinding
capacitance
and
harmonics
distortion
helped
significantly
the temperature
rise issue incapacitance
the transformer
13). distortion helped significantly in controlling in
that lowering
the interwinding
and (Figure
harmonics
controlling
the temperature
rise
in the transformer
the temperature
rise issue in
theissue
transformer
(Figure 13). (Figure 13).
Figure 13. Toroidal transformers at 180° sectored winding, temperature comparison between the
conventional and modified transformer design.
Figure 13. Toroidal transformers at 180° sectored winding, temperature comparison between the
Figure 13. Toroidal transformers at 180◦ sectored winding, temperature comparison between the
6.2.
Toroidal Transformer
with
360° Sectored
Winding
conventional
and modified
transformer
design.
conventional and modified transformer design.
The primary winding is on top of the secondary winding for the entire 360°, leakage flux is
produced by the current in the windings, which are opposite in direction and equal in magnitude
(The =
), thus
magnetizing
or leakage
cancels itself
in thefor
core.
primary
winding
is on top
of the flux
secondary
winding
the entire 360°, leakage flux is
Capacitance:
Larger values
self-capacitance
of the transformer,
which
occur
producedInter-winding
by the current
in the windings,
whichofare
opposite in direction
and equal in
magnitude
between
and secondary
windings,
a vital
roleininthe
large
primary current distortions. Self(
=
),primary
thus magnetizing
or leakage
fluxplay
cancels
itself
core.
capacitance
value
of the proposed
prototypeofhas
largely reduced
(40occur
pF)
Inter-winding
Capacitance:
Largermodified
values transformer
of self-capacitance
thebeen
transformer,
which
6.2. Toroidal Transformer with 360° Sectored Winding
Electronics 2018, 7, 142
12 of 15
6.2. Toroidal Transformer with 360◦ Sectored Winding
The primary winding is on top of the secondary winding for the entire 360◦ , leakage flux is
produced by the current in the windings, which are opposite in direction and equal in magnitude
(N1 I1 = N2 I2 ), thus magnetizing or leakage flux cancels itself in the core.
Inter-winding Capacitance: Larger values of self-capacitance of the transformer, which occur
between primary and secondary windings, play a vital role in large primary current distortions.
Self-capacitance value of the proposed modified transformer prototype has been largely reduced
(40 pF) with the help of 3D designed cover, spaces between windings, and proposed different winding
arrangements compared with the conventional prototype. In Figure 14, winding capacitance for
both conventional and modified transformers were plotted. It is noted that the modified design
Electronics 2018,
7, x
13 of 16
succeeded
in 7,minimizing
the transformer self-capacitance by approximately 87% compared with
Electronics 2018,
x
13 of 16
conventional designs.
Figure 14. Toroidal transformers at 360°
sectored winding, parasitic coupling capacitance comparison
◦
Figure
winding,
parasitic
coupling
capacitance
comparison
Figure14.
14.Toroidal
Toroidaltransformers
transformersatat360
360°sectored
sectored
winding,
parasitic
coupling
capacitance
comparison
between the conventional and modified design of high-frequency link based MV inverter systems.
between
betweenthe
theconventional
conventionaland
andmodified
modifieddesign
designofofhigh-frequency
high-frequencylink
linkbased
basedMV
MVinverter
invertersystems.
systems.
Leakage Inductance: The leakage inductance and primary/secondary capacitance are mutually
Leakage Inductance:
Inductance: The
Theleakage
leakageinductance
inductanceand
and primary/secondarycapacitance
capacitanceareare
mutually
Leakage
mutually
exclusive
and are governed
by the distance
between primary/secondary
the windings and unwounded core.
Therefore,
it
exclusive and
and are
aregoverned
governed by
by thedistance
distance between
between the
the windings and
and unwounded core.
core. Therefore,
Therefore, it
exclusive
is difficult to achieve
both lowthe
capacitive coupling
and awindings
high degree ofunwounded
inductive coupling
in a power
achieve
both
low
capacitive
coupling
andand
a high
degree
of inductive
coupling in a power
itis
isdifficult
difficulttoto
achieve
both
low
capacitive
coupling
a high
degree
of inductive
in a
transformer.
However,
the magnetic
core geometry
and winding
arrangements
have acoupling
large influence
transformer.
However,
the
magnetic
core
geometry
and
winding
arrangements
have
a large
influence
power
transformer.
However,
the
magnetic
core
geometry
and
winding
arrangements
have
a
large
on self-capacitance and leakage inductance of the transformer and because of the addition of a mold, it
on self-capacitance
and leakage
of the transformer
and because
of the addition
of a mold,
influence
on self-capacitance
and inductance
leakage
inductance
of the transformer
and because
of the
addition
of it
enables access
to various types
of winding
arrangements.
Thus, the modified
design
has
successfully
enables
access
to
various
types
of
winding
arrangements.
Thus,
the
modified
design
has
successfully
alowered
mold, it enables
access to various
types ofand
winding
arrangements.
Thus,difference
the modified
designleakage
has
the inter-winding
capacitance
achieves
the minimum
between
lowered thelowered
inter-winding
capacitance
and achieves
the minimum
difference
between
leakage
successfully
the
inter-winding
capacitance
and
achieves
the
minimum
difference
between
inductance. The experimental results are shown in Figure 15.
inductance.
The experimental
results are
shown
Figure
leakage
inductance.
The experimental
results
are in
shown
in 15.
Figure 15.
◦ sectored winding, leakage inductance comparison of modified
Figure
atat
360
Figure15.
15.Toroidal
Toroidaltransformers
transformers
360°
sectored winding, leakage inductance comparison of modified
Figure
15.
Toroidal
transformers
at
360°
sectored winding,
leakagesystems.
inductance comparison of modified
and
andconventional
conventionaldesign
designofofhigh-frequency
high-frequencylink-based
link-basedMV
MVinverter
inverter systems.
and conventional design of high-frequency link-based MV inverter systems.
Temperature: Modified
Modified design
design shows
significant
control
inintemperature
rise
by lowering
the interTemperature:
showssignificant
significantcontrol
controlin
temperature
rise
lowering
Temperature: Modified
design shows
temperature
rise
by by
lowering
the the
interwinding
capacitance
and
controlled
leakage
inductance
over
conventional
designs
(Figure
16).
inter-winding
capacitance
and controlled
leakage
inductance
conventional
designs
(Figure
winding capacitance
and controlled
leakage
inductance
over over
conventional
designs
(Figure
16). 16).
An MV inverter high-frequency link-modified toroid transformer was designed differently from
An MV inverter high-frequency link-modified toroid transformer was designed differently from
the conventional toroid designs. Both modified prototypes, case 2 and 4, showed extremely low
the conventional toroid designs. Both modified prototypes, case 2 and 4, showed extremely low
coupling capacitance, that is, 20 pF and 40 pF, respectively. The toroidal transformer at 180° sectored
coupling capacitance, that is, 20 pF and 40 pF, respectively. The toroidal transformer at 180° sectored
winding has registered higher leakage inductance, which can be utilized in other topologies, such as
winding has registered higher leakage inductance, which can be utilized in other topologies, such as
dual active bridge topologies. The experimental results matched the calculated analysis quite well. Thus,
dual active bridge topologies. The experimental results matched the calculated analysis quite well. Thus,
Electronics 2018, 7, 142
13 of 15
An MV inverter high-frequency link-modified toroid transformer was designed differently from
the conventional toroid designs. Both modified prototypes, case 2 and 4, showed extremely low
coupling capacitance, that is, 20 pF and 40 pF, respectively. The toroidal transformer at 180◦ sectored
winding has registered higher leakage inductance, which can be utilized in other topologies, such as
dual active bridge topologies. The experimental results matched the calculated analysis quite well.
Electronics
2018,
x
14 of 16
Thus,
the7,feasibility
of the converter was validated.
Figure
16. Toroidal
transformers
winding,temperature
temperature
comparison
between
Figure
16. Toroidal
transformersatat360°
360◦ sectored
sectored winding,
comparison
between
the the
conventional
and and
modified
design
of of
high-frequency
MVinverter
inverter
systems.
conventional
modified
design
high-frequency link-based
link-based MV
systems.
7. Conclusions
7. Conclusions
Overall,
the MV
inverter
withthe
theproposed
proposed modified
design
has has
a minimized
total total
Overall,
the MV
inverter
with
modifiedtransformer
transformer
design
a minimized
circuit
input–output
capacitance
to
approximately
20
pF,
while
the
temperature
increase
was
kept
circuit input–output capacitance to approximately 20 pF, while the temperature increase was kept
◦ C, without using any extra circuitry or cooling agent. The modified design is certainly a
belowbelow
29.5 29.5
°C, without
using any extra circuitry or cooling agent. The modified design is certainly a
powerful
solution
to
reduce
thedistortion
distortion in
This
leads
to anto
improved
power quality
powerful solution to reduce the
inthe
thewaveform.
waveform.
This
leads
an improved
power of
quality
renewable power sources and an increase in the operational lifetime of the devices and loads involved
of renewable power sources and an increase in the operational lifetime of the devices and loads
in power systems. Hence, the MV inverter with the modified design transformer is more robust than
involved in power systems. Hence, the MV inverter with the modified design transformer is more
other available power inverters of the same power rate. These experimental measurements, which
robustagree
thanwith
other
available power inverters of the same power rate. These experimental measurements,
the mathematical derivation, prove that the transformer shape and winding arrangements
whichhave
agree
with
the on
mathematical
derivation,
prove
that the
transformer
andwhen
winding
a huge
impact
the inter-winding
capacitance,
and cannot
be ignored
in powershape
inverters
arrangements
haveimprovement
a huge impact
the inter-winding capacitance, and cannot be ignored in power
power quality
is ofon
concern.
inverters when
power
quality
improvement
is ofthe
concern.
Finally, the overall result achieved with
prototype provides a very high resistance to the
common the
mode
noise current
by rapid
transients,provides
which makes
the MV
inverter
feasibleto the
Finally,
overall
result caused
achieved
withvoltage
the prototype
a very
high
resistance
for
renewable
energy
sources
applications.
For
future
research,
a
study
of
the
optimal
design
method
common mode noise current caused by rapid voltage transients, which makes the MV inverter feasible
on advanced
prototypes
with
higher inductive
with more
THD
will be conducted.
for renewable
energy
sources
applications.
For coupling
future research,
a controlled
study of the
optimal
design method
on advanced
prototypes
with
higher
inductive
coupling
with
more
controlled
THD
will
be conducted.
Author Contributions: H.-J.K., G.S.P., H.S., and H. conceptualized the idea of this research project. H.-J.K.
and
G.S.P. developed the proposal to the funding body. Finally, the project was awarded the funding. H., P.S., and
H.S.
discuss the design
for the
MV inverter
high-frequency
toroid transformer.
H. this
and H.Y.L.
developed
3D and
Author
Contributions:
H.-J.K.,
G.S.P.,
H.S., and
H. conceptualized
the idea of
research
project.the
H.-J.K.
design model including material selection. The fabrication and integration of the experimental setup were mostly
G.S.P.carried
developed
the
to and
the M.U.A.,
fundingunder
body.the
Finally,
the project
was
awarded
the funding.
H., P.S.,and
and H.S.
out by
theproposal
H., M.A.K.
supervision
of H.J.K.
and
G.S.P. Mathematics
derivation
real-time
data for
wasthe
analyzed
by H.S.high-frequency
and H. The papertoroid
was written
by H. and
discuss
the design
MV inverter
transformer.
H.H.J.K.
and H.Y.L. developed the 3D design
This
researchselection.
was supported
by Basic Research
Laboratoryof
through
the National Research
Foundations
modelFunding:
including
material
The fabrication
and integration
the experimental
setup were
mostly carried
of Korea. Funded by the Ministry of Science, ICT, and Future Planning (NRF-2015R1A4A1041584).
out by the H., M.A.K. and M.U.A., under the supervision of H.J.K. and G.S.P. Mathematics derivation and realConflicts of Interest: The authors declare no conflict of interest.
time data was analyzed by H.S. and H. The paper was written by H. and H.J.K.
Funding: This research was supported by Basic Research Laboratory through the National Research Foundations
of Korea. Funded by the Ministry of Science, ICT, and Future Planning (NRF-2015R1A4A1041584).
Conflicts of interest: The authors declare no conflict of interest.
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article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).