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Toroidal Transformer Design Optimization

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[UCI]I804:21016-000000138716
Dissertation for the degree of Doctor of Philosophy
Toroidal Transformer Design Optimization for The
Application of High-Frequency
Power Converters
Himanshu
Department of Electrical and Computer Engineering
The Graduate School
Pusan National University
February 2019
i
iii
Contents
Contents ·································································································· i
Contents of Table ······················································································iv
Contents of Figure ····················································································· v
1. INTRODUCTION ················································································ 1
1.1. Introduction ·················································································· 4
1.2. References ···················································································· 4
2. BASIC PRINCIPLES AND THEORY OF TRANSFORMERS ························· 8
2.1. Principal of Operation ······································································ 8
2.2 Operation of Transformer
2.2.1 Equivalent Circuit of a Transformer………………………………………….13
2.3. Types of Transformer………………………………………………………………17
2.3.1 Transformer in Power Systems………………………………………………19
2.3.2 Special Types of Transformer……………………………………………..…21
2.3.2.1 Instrumental Transformer ………………………………………......21
2.3.2.2 Autotransformer…………………………………………………….26
2.3.2.3 Transformer Taps ……………………………………………….....26
2.3.3 Transformer Connection………………………………………………….…28
2.4 Technical Points of Transformer ………………………………………………….33
2.4.1 Transformer Temperature Control ………………………………………..33
2.4.1.1 Renown Transformer Temperature Control Methods ……………….35
2.5. Core Material and Shapes…………………………………………………………40
2.6 Losses in Transformers…………………………………………………………....41
iv
2.7. Definition of Power Converter ···························································· 51
2.6. Total Harmonics Distortion in Power Systems ········································· 53
2.7. References ··················································································· 58
3. Toroidal Transformer Design Optimization················································· 62
3.1. Toroid Ferrite Core ········································································· 62
3.2. Minimization of Parasitic Capacitance in Toroidal Transformer ····················· 64
3.2.1 Fabrication…………………………………………………………………..64
3.2.1.1 Case 1: Conventional Toroid Core Tranformer with 1800 Sector Winding
3.2.1.2 Case 2: Modified Toroid Core Transformer with 1800 Sector Winding
3.2.1.3 Case 3: Conventional 3600 Wound Toroid Core Transformer
3.2.1.4 Case 4: Modified 3600 Wound Toroid Core Transformer
3.3. Enlargement of leakage inductance in Toroidal Transformer …………………..67
3.3.1 Leakage inductance in Toroidal Transformer……………………………….68
3.3.2 Sectored winding effects on Toroidal Transformer leakage inductance …....68
3.3.3 High permeability material effect on Toroidal Transformer leakage inductance
3.3.3.1 What is Ferrofluid……………………………………………………....70
3.4 B-H curve for transformer core material (ferromagnetic 77 material)……..71
3.4.1 Determination of B-H Curve of Core Material of Transformer ………71
3.4.2 DC Magnetization Curve …………………………………………….71
3.4.3 Hysteresis Loop……………………………………………………….73
3.3.4 B-H curve for ferrite 77 material, core which have used in all prototypes in our
toroidal transformer design………………………………………………………..75
3.5. References…………………………………………………………………...…75
4. TEST PLATFORM ………………………………………………………………….78
4.1. High Frequency Toroid Transformer’s Parasitic Capacitance Minimization for Standalone solar
v
Photovoltaic (PV) High-Frequency Link-Based Inverter……………………..……78
4.1.1 Renewable Energy Source On and Off Grid System……………………….78
4.1.2 Circuit Operation……………………………………………………………79
4.1.3 Calculation of the Toroid Transformer Inter-Winding Capacitance………..80
4.1.4 Experimental Setup…………………………………………………………85
4.1.5 Results and Discussion……………………………………………………...88
5. CONCLUSIONS………………………………………………………………94
Abstract (Korean)……………………………………………………………………....95
Acknowledgements……………………………………………………………………..97
vi
Contents of Table
Table 1: Ferrite Core Comparative Geometry Consideration ··············································· 41
Table 2. Current and Voltage total harmonic distortion allowing values and their associated risks…..55
Table 3. Proposed Transformer waveforms. ·································································· 58
Table 4: Ferrite 77 toroid core dimensions (Courtesy: Fair-Rite products Corp.). ······················ .63
Table 5: Ferrite 77 toroid core electrical properties (Courtesy: Fair-Rite products Corp.)…....63
Table 6: Leakage inductance with different unwound angles……………………………….…..69
Table 7: Detailed parameters of the transformer prototypes………………………….…………83
Table 8: Theoretical analysis of all presented prototypes, Calculated energy, and inter-winding
capacitance…………………………………………………………………………………….……...84
Table 9: Voltage and current THD for all prototypes……………………………………….……88
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Content of Figures
Figure 1Renewable Energy Source On and Off Grid system………….……………………………………2
Figure 2 A Typical Voltage Transformer…………………………..……..………………………………….9
Figure 3: Single Phase Voltage Transformer…………………………. ………………………………..….10
Figure 4: Single Phase Voltage Transformer Construction……..…..…………………………………..….11
Figure 5: Equivalent circuit of a transformer………………………………………………………………13
Figure 6: Shorten Equivalent circuit of a transformer…………………….…………………………….…14
Figure 7: Electric Power System……………..………………….………………………………………....20
Figure 8. Current Transformer…………………………………………………………………….….……22
Figure 9. Potential or Voltage Transformer………..…………………………………………………........23
Figure 10 Block Diagram for HVDC System……………………………..…………………..……….…..25
Figure 11 Detailed Diagram for HVDC System …………………………………………………….…....25
Figure 12. Typical on-load tap changer……...……………………………………………………….…....27
Figure 13. Three-Phase Transformer Connection. …….…………………………………………….……28
Figure 14. The Y-Y Connection of Transformer……………………………………….………..….……..29
Figure 15. The delta-delta Connection of Transformer …………………………...……………..…….….31
Figure 16. The Wye-Delta Connection of Transformer.………………………………………………..….32
Figure 17. The Delta-Wye Connection of Transformer……………………………………………….…...33
Figure18. Oil Transformer with Air Convection Cooled Heat Exchangers………………………….…….34
Figure 19. Forced Air-Cooled Transformer……..………………………………………………..…..…….36
Figure 20. Oil Air Natural (ONAN) Cooling of Transformer …………………… ………………….……37
viii
Figure 21. Oil Natural Air Forced (ONAF) Cooling of Transformer …………………………………………..38
Figure 22. Oil Natural Air Forced (OFAF) Cooling of Transformer ……………………...…………………....39
Figure 23. Oil Natural Air Forced (OFWF) Cooling of Transformer ………………………………………….39
Figure 24. Skin effect – Isolated conductor………………………………………………………………….…49
Figure 25. Proximity effect – Opposite Currents ……………………..……………………………………….50
Figure 26. Proximity effect – Same Currents……………………………………………………………….…51
Figure 27: Ferrite 77 material core dimensions; (Courtesy: Fair-Rite products Corp.)………………………..63
Figure 28: Temperature effects on Ferrite 77 material properties; (Courtesy: Fair-Rite products Corp.)……..64
Figure. 29. 180° conventional (a) Flux pattern in core (b) 2D model (c) 3D model.………………..…….…..65
Figure. 30. 180° Modified (a) Flux pattern in core (b) 2D model (c) 3D model………………………..…….66
Figure. 31. 360° conventional (a) 2D model (b) Flux distribution (c) 3-D model.………………………..….66
Figure 32. 3600 Modified (a) 2D model (b) Flux distribution (c) Original design (d) 3-D model.…………..67
Figure 33. DC magnetization curve………………………………………………………………………….72
Figure 34. Hysteresis loop……………………………………………………………………………………74
Figure 35. Connection diagram of circuit to trace B − H curve measurement……………………………….75
Figure 36. B-H curve ………………………………………………………………………………………..76
Figure 37. Initial permeability vs H………………………………………………………………………….76
Figure 38 Major to minor loops of BH curve for transformer core material………………………..…….…77
Figure 39. Renewable Energy Source On and Off Grid System……………..………………………………79
Figure 40: Circuit layout for PV high frequency based inverter system(24V)………….…………………..80
Figure 41. Toroidal transformer with 1800 sectored winding, Conceptual presentation of transformer prototypes
ix
from left to right conventional and modified…….…………………………………………..………………81
Figure 42. Block diagram and real time setup for the testing process for prototypes PV high frequency link-based
inverter systems……………………………………………………………………………………………...87
Figure 43. Toroidal transformers at 1800 sectored winding, Parasitic Coupling Capacitance comparison between
the conventional and modified design of high-frequency link-based inverter systems …………….………89
Figure 44. Toroidal transformers at 1800 sectored winding, Leakage inductance comparison between the
conventional and modified design of high-frequency link-based inverter systems....……………………...90
Figure 45. Toroidal transformers at 1800 sectored winding, Temperature comparison between the conventional and
modified transformer design…………………………………………………………………………..……90
Figure 46. Toroidal transformers at 360° sectored winding, parasitic coupling capacitance comparison between the
conventional and modified design of high-frequency link based inverter systems.……………..………...91
Figure 47. Toroidal transformers at 3600 sectored winding, Leakage inductance comparison of modified and
conventional design of high-frequency link based inverter systems…………………………………...….92
Figure 48. Toroidal transformers at 3600 sectored winding, Temperature comparison between the conventional and
Modified design of high-frequency link based inverter systems…………………………………….…...93
x
Toroidal Transformer Design Optimization for The
Application of High-Frequency
Power Converters
by Himanshu
Department of Electrical and Computer Engineering
The Graduate School
Pusan National University
Abstract
The high-frequency-based 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) small power DC–AC Voltage
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
1
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.
2
CHAPTER 1
INTRODUCTION
Over A transformer plays a vital role in energy conversion and is at the heart of any electric
power system. The transformer size decreases with increasing frequency which achieves to
build smaller, less expensive and compact portable electrical devices [1-2]. Therefore, high
frequency power transformers are preferred over traditional frequency transformers (50-60Hz)
in the power electronic fields, such as switching power supplies, convertors, 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 due to 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 great demand, particularly solar and wind
energy. These sources are projected to fulfil 50% of the energy requirement by the year 2050
[9]. On the other hand, the intermittent nature of these power sources is a major limitation to
connecting them straight to electrical/electronic systems or national grids. This critical obstacle
can be overcome using external devices, such as energy storage, convertors, and inverters (see
Figure 1) [10-13]. Due to the high penetration of these high frequency based MV inverters into
the renewable energy power plants, energy demands might be fulfilled for industries and home
power requirements. But these high frequency links, e.g., high frequency transformer, H-bridge
inverter dead time, and non-linear load generates high harmonic content. It can cause serious
damage to the equipment including overheating, power supply failure or electric shock hazards
[14-15]. Therefore, to protect the component and the connected loads from overheating and
1
provide a power supply without any disturbances, the power quality of these MV inverters need
to be taken into consideration [16-19].
Figure 1: Renewable Energy Source On and Off Grid system
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 categorized into two classes: common and differential conduction modes (CCM and
DCM) [20-22]. The high frequency transformer is one of the sources of EMI and contributes
to the common mode harmonics because of the intrinsic coupling capacitance, electric and
magnetic fields [23]. The duty cycle is inversely proportional to the harmonics. Therefore,
DCM operations of PWM converters increase the harmonics, which adds power losses in
transformer windings. Similarly, high-frequency operation causes skin and proximity effects
that elevate the harmonic losses, winding power losses and rapid growth in the operating
temperature [24-25]. On the other hand, high frequency winding losses and lowering the
leakage inductance have been a major research focus, while the winding capacitance requires
2
equally serious attention during the design of transformers. Capacitive coupling is one of the
paths that can carry high frequency noise, premature resonance, electrostatic coupling to other
circuits and fast transient voltages from primary to secondary circuitry, which produces
common mode noise currents and an increase in transformer temperature in the device,
resulting in a 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 capacitance across the transformer and circulates due to winding arrangements.
Therefore, 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 insulation between the primary and secondary winding or by increasing
the distance between the primary and secondary winding by winding them on opposite sides
of the toroidal core. On the other hand, these changes in transformer will 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 some
certain oils for cooling the transformer. They, however, were arranged specifically for the
coupling capacitance and temperature control and showed no significant difference when
compared to the less expensive conventional solutions.
3
The leakage inductance and primary/secondary capacitance are mutually exclusive and are
governed by the distance between the windings and unwounded core. Therefore, it is difficult
to achieve both low capacitive coupling and a high degree of inductive coupling in a power
transformer [33-34]. To circumvent this inherent tradeoff in this study, the conventional
toroid ferrite core transformer was modified by an additional 3D printed Polylactic acid (PLA)
mold, which separates the primary and secondary windings, and helps implementing unique
sector winding. Although the distance between windings will introduce leakage inductance,
there is some gain in capacitance due to the dielectric constant of PLA. However, the
magnetic core geometry and winding arrangements have a large influence on self-capacitance
and leakage inductance of the transformer and due to the addition of a mold; it enables access
to various types of winding arrangements. This paper reports comparative analysis on the
high frequency-link MV inverter for power-quality improvement by effective subtraction of
capacitive coupling and reducing the temperature increase without using any extra circuitry
or cooling agents.
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CHAPTER 2
BASIC PRINCIPLES AND THEORY OF TRANSFORMERS
This chapter gives the brief introduction to all the necessary topics that are required to understand
the thesis. This includes discussion on basic relationships and principles of magnetics, theory of
transformers, discussion on losses in the transformers, and basics of power converters.
2.1. Principal of Operation
One of the main reasons that we use alternating AC voltages and currents in our homes and
workplace’s is that AC supplies can be easily generated at a convenient voltage, transformed
(hence the name transformer) into much higher voltages and then distributed around the country
using a national grid of pylons and cables over very long distances.
The reason for transforming the voltage to a much higher level is that higher distribution voltages
implies lower currents for the same power and therefore lower I2*R losses along the networked
grid of cables. These higher AC transmission voltages and currents can then be reduced to a much
lower, safer and usable voltage level where it can be used to supply electrical equipment in our
homes and workplaces, and all this is possible thanks to the basic Voltage Transformer.
8
Figure 2: A Typical Voltage Transformer
The Voltage Transformer can be thought of as an electrical component rather than an electronic
component. A transformer basically is very simple static (or stationary) electro-magnetic passive
electrical device that works on the principle of Faraday’s law of induction by converting electrical
energy from one value to another.
The transformer does this by linking together two or more electrical circuits using a common
oscillating magnetic circuit which is produced by the transformer itself. A transformer operates on
the principals of “electromagnetic induction”, in the form of Mutual Induction.
Mutual induction is the process by which a coil of wire magnetically induces a voltage into another
coil located in close proximity to it. Then we can say that transformers work in the “magnetic
domain”, and transformers get their name from the fact that they “transform” one voltage or current
level into another.
2.2 Principle of Working
9
Transformers are capable of either increasing or decreasing the voltage and current levels of their
supply, without modifying its frequency, or the amount of electrical power being transferred from
one winding to another via the magnetic circuit.
A single phase voltage transformer basically consists of two electrical coils of wire, one called the
“Primary Winding” and another called the “Secondary Winding”. For this tutorial we will define
the “primary” side of the transformer as the side that usually takes power, and the “secondary” as
the side that usually delivers power. In a single-phase voltage transformer the primary is usually
the side with the higher voltage.
These two coils are not in electrical contact with each other but are instead wrapped together
around a common closed magnetic iron circuit called the “core”. This soft iron core is not solid
but made up of individual laminations connected together to help reduce the core’s losses.
The two coil windings are electrically isolated from each other but are magnetically linked through
the common core allowing electrical power to be transferred from one coil to the other. When an
electric current passed through the primary winding, a magnetic field is developed which induces
a voltage into the secondary winding as shown.
10
Figure 3: Single Phase Voltage Transformer
In other words, for a transformer there is no direct electrical connection between the two coil
windings, thereby giving it the name also of an Isolation Transformer. Generally, the primary
winding of a transformer is connected to the input voltage supply and converts or transforms the
electrical power into a magnetic field. While the job of the secondary winding is to convert this
alternating magnetic field into electrical power producing the required output voltage as shown.
Figure 4: Single Phase Voltage Transformer Construction
•
Where:
•
VP - is the Primary Voltage
VS - is the Secondary Voltage
NP - is the Number of Primary Windings
NS - is the Number of Secondary Windings
Φ(phi) - is the Flux Linkage
Primary winding of transformer - produces magnetic flux when it is connected to electrical
source.
•
•
•
•
•
•
•
Secondary winding of transformer – output winding. The flux, produced by primary winding,
passes through the core and will link with the secondary winding.
Magnetic Core of transformer - the flux produced by the primary winding, that will pass
through this low reluctance path linked with secondary winding and create a closed magnetic
circuit.
11
•
•
Notice that the two coil windings are not electrically connected but are only linked
magnetically. A single-phase transformer can operate to either increase or decrease the
voltage applied to the primary winding. When a transformer is used to “increase” the voltage
on its secondary winding with respect to the primary, it is called a Step-up transformer. When
it is used to “decrease” the voltage on the secondary winding with respect to the primary it is
called a Step-down transformer.
However, a third condition exists in which a transformer produces the same voltage on its
secondary as is applied to its primary winding. In other words, its output is identical with
respect to voltage, current and power transferred. This type of transformer is called an
“Impedance Transformer” and is mainly used for impedance matching or the isolation of
adjoining electrical circuits.
•
•
•
•
The difference in voltage between the primary and the secondary windings is achieved by
changing the number of coil turns in the primary winding ( NP ) compared to the number of
coil turns on the secondary winding ( NS ).
As the transformer is basically a linear device, a ratio now exists between the number of turns
of the primary coil divided by the number of turns of the secondary coil. This ratio, called the
ratio of transformation, more commonly known as a transformers “turns ratio”, ( TR ). This
turns ratio value dictates the operation of the transformer and the corresponding voltage
available on the secondary winding.
It is necessary to know the ratio of the number of turns of wire on the primary winding
compared to the secondary winding. The turns ratio, which has no units, compares the two
windings in order and is written with a colon, such as 3:1 (3-to-1). This means in this example,
that if there are 3 volts on the primary winding there will be 1 volt on the secondary winding,
3 volts-to-1 volt. Then we can see that if the ratio between the number of turns changes the
resulting voltages must also change by the same ratio, and this is true.
Transformers are all about “ratios”. The ratio of the primary to the secondary, the ratio of the
input to the output, and the turns ratio of any given transformer will be the same as its voltage
ratio. In other words for a transformer: “turns ratio = voltage ratio”. The actual number of
turns of wire on any winding is generally not important, just the turns ratio and this
relationship is given as:
A Transformers Turns Ratio
NP/NS = VP/VS = n = Turns Ratio
12
………….1
Transformer’s self-capacitance can be calculated using Equs number (8) [58].
1
1
๐ถ๐‘ = ( ๐‘ค2 ๐ฟ ) = 4๐œ‹2 ๐‘“2 ๐ฟ [๐‘“๐‘Ž๐‘Ÿ๐‘Ž๐‘‘๐‘ ]
๐‘Ÿ
(2)
๐‘Ÿ
๏ƒฏ The temperature rise of the modified and regular design transformer in oC can be calculated
as follows:
๐‘‡๐‘ก = 450(๐‘ƒ๐‘ก๐‘œ๐‘ก๐‘Ž๐‘™ ⁄๐ด๐‘ก )0.826
(3)
Where Ptotal is the total loss in W,
2.2 Operation of Transformer
2.3.1. Equivalent circuit of a transformer
The equivalent circuit is used to simplify circuit analysis and helpful in predetermining the
behavior of the transformer under the various conditions of operation. In figure below are full
description of a transformer:
13
Figure 5: Equivalent circuit of a transformer
where: ๐‘…1 and ๐‘…2 ′ - the primary and secondary winding resistances (denoted respectively). The
resistances cause voltage drops as ๐ผ1๐‘…1 and ๐ผ2๐‘…2 and also copper losses ๐ผ1 2๐‘…1 and ๐ผ2 2๐‘…2.
๐‘‹1๐œŽ, ๐‘‹2๐œŽ ′ − leakage flux in both primary and secondary side give rise to leakage reactance at
both side (denoted respectively).
๐‘…๐น๐‘’ – the iron-core resistance having the value corresponding to power loss in the magnetic
circuit:
Δ๐‘ƒ
= Δ๐‘ƒ๐น๐‘’ = ๐‘…๐น๐‘’๐ผ1๐น๐‘’ 2 (4)
๐‘‹1โ„Ž – magnetizing reactance of primary circuit corresponding to mutual flux and representing
primary Electromotive force (emf- described later)
Figure 6: Shorten Equivalent circuit of a transformer
14
Figure 6 is a reduced version from circuit above (figure 5), it represents the impedance Z which
is combined from reactance and resistance of transformer. From this reduced circuit we can
easily describe the operation of transformer by following equations:
๐‘0 = ๐‘…๐น๐‘’.๐‘—๐‘‹1โ„Ž ๐‘…๐น๐‘’+๐‘—๐‘‹1โ„Ž (5)
๐‘1 = ๐‘…1 + ๐‘—๐‘‹1๐œŽ (6)
๐‘′2 = ๐‘…′2 + ๐‘—๐‘‹2๐œŽ ′ (7)
๐‘ˆ1 = ๐‘1๐ผ1 + ๐‘0๐ผ0 (8)
๐‘ˆ′2 = −๐‘′2๐ผ′2 + ๐‘0๐ผ0 (9)
๐‘- All values are denoted as impedances for primary, iron-core, secondary winding
(respectively). ๐‘ˆ1 − Voltage on primary winding; ๐‘ˆ′2 − Voltage on secondary winding. Note:
All equations above are represented in phasor form.
2.2.2 Electromotive force in windings
EMF Equation of transformer can be determined very simple. In fact, in power transformer, one
alternating electrical source is applied to the primary winding and due to this, magnetizing
current flowing through the primary winding, which produces alternating flux in the core of
transformer. However, this flux links with both primary and secondary windings. Since this flux
is alternating in nature, there must be a rate of change of flux. This phenomenal is related to
Faraday’s law and can be described by following equations:
๐‘ˆ๐‘– = ๐‘ ๐‘‘๐œ™ ๐‘‘๐‘ก
(10)
15
where ๐œ™ is the instantaneous alternating flux and it can be represented as:
๐œ™ = ๐œ™โ„Ž๐‘š๐‘ ๐‘–๐‘›๐œ”๐‘ก
(11)
Using equation 11 we`ll find
๐‘ˆ๐‘– ๐‘ˆ๐‘– = ๐‘๐œ™โ„Ž๐‘š๐œ” โˆ™ ๐‘๐‘œ๐‘ ๐œ”๐‘ก
(12)
RMS value of induced emf in whole primary winding ๐‘ˆ๐‘–1 is:
๐‘ˆ๐‘–1 = 4,44๐‘“๐‘1๐œ™๐œ‡๐‘š๐‘Ž๐‘ฅ
(13)
Similarly, RMS induced emf in secondary winding (๐‘ˆ๐‘–2) can be given as:
๐‘ˆ๐‘–2 = 4,44๐‘“๐‘2๐œ™๐œ‡๐‘š๐‘Ž๐‘ฅ
(14)
where: ๐‘ˆ๐‘–1, ๐‘ˆ๐‘–2- Voltages generated by EMF in primary and secondary windings (denoted
respectively) f – frequency of applied AC source ๐‘1, ๐‘2 – Number of turn of coils in primary
and secondary windings (denoted respectively) ๐œ™๐œ‡๐‘š๐‘Ž๐‘ฅ– The maximum rate change in flux
generated by magnetic circuit. Note:
The convention of ๐‘ˆ๐‘– in all equations are effective values! Finally, from the above equations 13
and 14 we have general equation of electromotive force for transformer.
๐‘ = ๐‘1 ๐‘2 = ๐‘ˆ๐‘–1 ๐‘ˆ๐‘–2
(15)
This constant (p) is called transformation ratio of transformer. • If N2>N1, i.e. p > 1, then the
transformer is step up transformer. • If N2 < N1, i.e. p < 1, then the transformer is step down
transformer.
16
2.3 Types of Transformers
In this part, we are not discussing in detail about each type of transformer, so I described in general
types of transformer according to their usages, shapes, use etc..
Core- Type Transformer
In core-type transformer, the windings are given to a considerable part of the core. The coils used
for this transformer are form-wound and are of cylindrical type. Such a type of transformer can be
applicable for small sized and large sized transformers. In the small sized type, the core will be
rectangular in shape and the coils used are cylindrical. The figure below shows the large sized type.
You can see that the round or cylindrical coils are wound in such a way as to fit over a cruciform
core section. In the case of circular cylindrical coils, they have a fair advantage of having good
mechanical strength. The cylindrical coils will have different layers and each layer will be
insulated from the other with the help of materials like paper, cloth, micarta board and so on.
Shell-Type Transformer
In shell-type transformers, the core surrounds a considerable portion of the windings. The
comparison is shown in the figure below.The coils are form-wound but are multi layer disc type
usually wound in the form of pancakes. Paper is used to insulate the different layers of the multilayer discs. The whole winding consists of discs stacked with insulation spaces between the coils.
These insulation spaces form the horizontal cooling and insulating ducts. Such a transformer may
have the shape of a simple rectangle or may also have a distributed form
17
Step up Transformer & Step-down Transformer –
They are used for stepping up and down the voltage level of power in transmission and distribution
power system network.
Three Phase Transformer & Single-Phase Transformer –
Former, as a rule, is used in three phase power system, as it is more cost effective than later.
However, when size matters, it is preferable to use a bank of three single-phase transformer, as it
is easier to transport than one single three-phase transformer unit.
Electrical Power Transformer, Distribution Transformer – Power Transformer is transferring
energy between high voltage and very high voltage systems, i.e. between generators and
transmission systems and between transmission systems and distribution systems. Also, they are
used in transmission network for stepping up or down the voltage level. It operates mainly during
high or peak loads and has maximum efficiency at or near full load. Distribution transformer steps
down the voltage for distribution purpose to domestic or commercial users. It has good voltage
regulation and operates 24 hours a day with maximum efficiency at 50% of full load.
Indoor Transformer & Outdoor Transformer –
Transformers that are designed for installing at indoor are indoor transformers and transformers
designed for installing at outdoor are outdoor transformers. o Oil Cooled & Dry Type Transformer
- In oil cooled transformer the cooling medium is transformer oil whereas in dry type transformers
air is used as the cooling medium instead of oil.
Phase-Shifting Transformer- A phase-shifting transformer is a device for controlling the power
flow through specific lines in a complex power transmission network. Purposes of Phase-Shifting
transformers:
a) To control the power flow between two large independent power systems;
18
b) To change the effective phase displacement between the input voltage and the output voltage
of a transmission line, thus controlling the amount of active power that can flow in the line.
2.3.1. Transformers in Power Systems (Transmission and Distribution systems)
Transmission refers to the bulk transfer of power by high-voltage links between central generation
and load centers. Distribution, on the other hand, describes the conveyance of this power to
consumers by means of lower voltage networks. Modern transformers used in transmission and
distribution systems have very high efficiencies up to 90%-99%. This means that they can transmit
up to 90%-99% of the electrical energy input to them when stepping up or stepping down the
voltage.
Transmission: Generators usually produce voltages in the range 11–25kV, which is increased by
transformers to the main transmission voltage. At substations, the connections between the various
components of the system, such as lines and transformers, are made and the switching of these
components is carried out. Large amounts of power are transmitted from the generating stations to
the load-centre substations, for example at 400kV and 275kV in Britain, and at 765, 500 and 345kV
in the USA.
Distribution Systems: Distribution networks differ from transmission networks in several ways,
quite apart from their voltage levels. The number of branches and sources is much higher in
distribution networks and the general structure or topology is different. A typical system consists
of a step-down (e.g. 132/11kV) on-load tap-changing transformer at a bulk supply point feeding a
19
number of circuits which can vary in length from a few hundred metres to several kilometres. A
series of step-down three-phase transformers, for example, 11kV/433V in Britain or 4.16kV/220V
in the USA, are spaced along the route and from these are supplied the consumer three-phase, fourwire networks which give 240V, or, in the USA, 110V, single-phase supplies to houses and similar
loads.
Figure 7: Electric Power System
A large number of transformers of different classes and sizes are needed in the transmission and
distribution network, with a wide range of operating voltages. The last transformation step into the
consumer mains voltage (in Europe 400/230V) is done by the distribution transformer. Distribution
transformers operated and owned by electricity distribution companies are responsible for
supplying about 70% of low voltage electricity to final users.
Voltage levels are classified as:
• Extra high voltage: transmission grid(>150kV) typically 220–400kV(ultra high>400kV)
• High voltage >70 kV up to 150 kV
• Medium voltage >1 kV up to 70 kV (typically up to 36 kV)
• Low voltage < 1kV (e.g. 110V, 240V, 690 V)
20
2.3.2. Special Types of Transformers
2.3.2.1. Instrument transformers
Instrument transformer is an electrical device used to transform current as well as voltage level.
Sometimes, they are also called as isolation transformers. Instrument transformers are commonly
used to safely isolate the secondary winding when the primary has high current supply and high
voltage so that the measuring instrument relays or energy meters, which are connected to the
secondary side of the transformer will not get damaged. The instrument transformer is divided into
two types: Current Transformer (CT) and Potential Transformer (PT)
Current Transformer (CT) The CT is used for measuring and for the protection. The primary
of a current transformer typically has only one turn, it never has more than a very few turns, while
the secondary can have a great many turns, depending upon how much the current must be stepped
down. In a lot of cases, the primary of a current transformer is a single wire or bus bar, and the
secondary is wound on a laminated magnetic core, placed around the conductor in which the
current needs to be measured (Figure 8).
21
Figure 8. Current Transformer
Potential Transformers (PT) The potential transformer is also called as the voltage transformer.
The main function of the Potential transformer (PT) is to step down the voltage level to a safe limit
or value. They are used with voltmeters, wattmeters, watt-hour meters, power-factor meters,
frequency meters, synchronizing apparatus, protective and regulating relays, and under voltage
and overvoltage trip coils of circuit breakers. One potential transformer may be used for a number
22
of instruments if the total current required by the instruments connected to the secondary winding
does not exceed the transformer rating
Figure 9. Potential or Voltage Transformer
Power Transformer is generally used in AC (HV, EHV) Substation for transferring electrical
energy between HV, IV & LV at a constant frequency.
A Converter transformer is generally used in HVDC system. We know that in a HVDC system
Power Electronic circuits are used to convert AC to DC (Rectifier circuits) or convert DC to AC
(Inverter Circuits). Both of these circuits are also called converter circuits. A transformer that has
one of its windings connected to one of these circuits, as a dedicated transformer, is a Converter
Transformer.
Basically a converter transformer in a HVDC system:
23
1. Supply AC voltages into two separate circuits feeding the rectifier bridges with a phase shift of
30 electrical degrees for reduction of low order harmonics esp. 5th & 7th harmonics.
2. Acts as a galvanic barrier between AC and DC systems to prevent DC potential entering into
the AC system.
3. Provides Reactive Impedance in the AC supply to reduce short circuit currents and to control
the rate of rise in valve current during commutation.
Major Difference between Power Transformer & Converter Transformer:
1. Main duct in HVDC transformers require more PB (Pressboard) barriers than normal AC
transformers as DC voltage is taken mainly by PB.
2. Converter Transformers are specially designed to withstand the current harmonics caused by
the power electronic converter. These types of transformers are usually made with multiple
secondary windings that are phase shifted (e.g. Dyn11d0) for achieving 12-, 18-, 24-pulse
operation of the converter/rectifier. The higher pulse numbers the better harmonic reduction
towards the supply network. The harmonic cancellation however means additional stress to the
transformer active part because of additional energy losses. The balance of impedances between
the multiple secondary windings is an important design parameter when making phase shifted
transformers. Closer Tolerance in Impedance is required between three phases and also between
upper & lower bridges (star-star, star-delta circuits). Normal transformers: ± 10%, Converter
Transformer: ± 6% on special tolerance and 2-3% variation between units.
3. Taping range of OLTC is large in Converter Transformer as compared with Power Transformer.
24
4. With stepwise change in load current during commutation from one valve to another, the
induced voltages will be fairly high to create circulating currents. So stray losses are increased
compared to conventional power transformers.
5. High percentage of harmonic currents in the load current causes higher load losses in converter
transformer compared to power transformers.
6. High levels of vibration, increased sound level & marginal increase in no-load loss in converter
transformer compared to power transformers.
7. Creepage distance of bushings is normally 40mm/kV in converter transformers as compared to
25mm/kv in power transformers.
Figure 10 Block Diagram for HVDC System
Figure 11 Detailed Diagram for HVDC System
25
2.3.2.2. Autotransformers
An Autotransformer is a transformer with only one winding wound on a laminated core. They are
less costly and smaller for small voltage changes than standard transformers. Autotransformers
transfer much of the power directly through a wire connection. Moreover, less current flows
through the shunt winding, whereas most of the current passes through the lower voltage series
winding at the top. This type of transformers has two main applications on distribution systems:
Voltage regulators: The regulator is an autotransformer with adjustable taps, which, as a rule, is
able to regulate the voltage by ± 10%.
Step banks: Generally, autotransformers are often used instead of traditional transformers on step
banks and even substation transformers, where the relative voltage change is moderate
2.3.2.3. Transformer Taps
Most power transformers have taps on the primary or secondary windings to change the number
of turns and, consequently, the output voltage. The percentage of voltage variation, above or below
normal, between different tap positions varies in different transformers. Taps on oil-cooled
transformers are brought to an oil-filled tap changer, which is externally located or brought to a
tap changer, located under the oil inside the tank. Taps on dry-type transformers are brought to
insulated terminal boards, which is located inside the metal housing, accessible by removing a
panel. Tap changers connected to the primary or secondary side windings of the transformer
depending on: - Current rating of the transformer; - Insulation levels present; - Type of winding
26
within the transformer (eg. Star, delta or autotransformer); - Position of tap changer in the winding;
- Cost; - Physical size.
Tap changers are divided into two types:
• On-load (OLTC) • Off-load/de-energized (DECT).
Off-load tap-changing (manual tap changing) mechanisms require the transformer to be isolated
before its tap settings can be adjusted, and is normally the case with smaller distribution
transformers. However, since the off-load tap changer causes interruption in the supply on-load
tap changers are more preferred today in power system.
The on-load tap-changer (automatic changing) allows to select the ratio change when the
transformer is in service. This means that the transformer ratio may be changed while the power
(current) is still flowing through it. On-load tap changers generally consist of a diverter switch and
a selector switch operating as a unit to effect transfer current from one voltage tap to the next. The
resistors in the diverter switch are typically a few ohms.
Figure 12. Typical on-load tap changer
27
2.3.3 Transformer connections
Three-phase transformer connections
Three-phase connections can be made either by using three single-phase transformers or by using
a three-phase transformer. Advantages of the three-phase transformer are: o it costs less; o the
weight is less; o it requires less floor space; o has lower losses than three single-phase transformers.
The methods of connecting windings will be the same, whether using the one three-phase
transformer or three separate single-phase transformers. The two general methods of connecting
three-phase transformers are shown in figure 13.
Figure 13. Three-Phase Transformer Connection
The method shown in at figure 9 a is known as a delta connection and figure 9b as the star or wye
connection. Differences between wye and delta connection in that wye connection has two phases
28
in series. And the common point “O” of the three windings is called the neutral because equal
voltages exist between this point and any of the three phases. 22
Wye–Wye Connections of Transformer
For high-voltage transmission systems, the use of the wye-connected transformer is more
economical because the voltage across the phase of each winding is a factor of 1.73 less than the
voltage between the lines. If the neutral point is grounded, there is no need to insulate it for the
line voltage.
Figure 14. The Y-Y Connection of Transformer
Figure 14 shows a bank of three transformers connected in Y on both the primary and secondary
sides. If the ratio of transformation of each transformer is K, then the same ratio will exist between
29
the line voltages on the both sides. This connection will give satisfactory service only if the threephase load is balanced; when the load is unbalanced, the electrical neutral will shift from its exact
center to a point that will make the line to neutral voltages unequal.
Advantages of the Y-Y connection:
The primary and secondary circuits are in phase; i.e., there are no phase angle displacements
introduced by the Y-Y connection. This is an important advantage when transformers are used to
interconnect systems of different voltages in a cascading manner. For example, suppose there are
four systems operating at 500, 230, 138, and 69kV that need to be interconnected. Substations can
be constructed using Y-Y transformer connections to interconnect any two of these voltages. The
500 kV system can be tied with the 69 kV 23 system through a single 500 to 69 kV transformation
or through a series of cascading transformations at 230, 138, and 69 kV.
If the neutral end of a Y-connected winding is grounded, then it is possible to use reduced levels
of insulation at the neutral end of the winding. A winding, which is connected across the phases,
requires full insulation throughout the winding.
Disadvantages of the Y-Y connection: o The presence of third (and other zero-sequence)
harmonics at an ungrounded neutral can cause overvoltage conditions at light load. When
constructing a Y-Y transformer using single-phase transformers connected in a bank, the measured
line-to-neutral voltages are not 57.7% of the system phase-to-phase voltage at no load but are about
68% and very quickly decrease as the bank is loaded. The effective values of voltages at different
frequencies combine by taking the square root of the sum of the voltages squared. With sinusoidal
phaseto-phase voltage, the third-harmonic component of the phase-to-neutral voltage is about 60%,
so the effective voltage across the winding is calculated as follows: ๐ธ = √[0.5772 + (0.6 × 0.577)
2 = 68%. (31)
30
Delta–Delta Connection The delta–delta connection has an economic advantage over the wye–
wye connection for lowvoltage, high-current requirements because the winding current is reduced
by a factor of 1.73 to 58% of that in the wye–wye connection. Another advantage of this connection,
if composed of three single-phase transformers, is that one transformer can be removed and the
remaining two phases operated at 86.6% of their rating in the open delta(if one transformer fails it
may switched out of the line and operation continued at a reduced power level) connection.
The principle disadvantage of the delta–delta connection is that the neutral is not available. As a
result, the phases cannot be grounded except at the corners. The insulation design is costlier
because this type of three-phase transformer connection has higher ground voltages during system
fault or transient voltages. Supplying an artificial neutral to the system with a grounding
transformer can help to control these voltages. The delta-connection insulation costs increase with
increasing voltage. Therefore, this type of connection is usually limited to a maximum system
voltage of 345 kV
31
Figure 15. The delta-delta Connection of Transformer
Wye–Delta and Delta–Wye Connections
The wye-delta or delta-wye connections have less objectionable features than any other
connections. In general, these combine most of the advantages of the wye–wye and delta–delta
connections. Complete voltage and current symmetry is maintained by the presence of the delta.
The exciting third-harmonic current circulates within the delta winding, and no third-harmonic
voltage appears in the phase voltages on the wye side. The high-voltage windings can be connected
wye, and the neutral can be brought out for grounding to minimize the cost of the insulation.
Differences in magnetizing current, voltage ratio, or impedance between the single-phase units
are regulated by a small circulating current in the delta. All of these factors result in unbalanced
phase voltages on the delta, which causes a current to circulate within the delta.
Figure 16. The Wye-Delta Connection of Transformer
Although the delta–wye connection has most of the advantages of the wye–wye and delta– delta,
it still has several disadvantages. This connection introduces a 30r phase shift between the primary
and secondary windings, which must be matched for a parallel operation. A delta–wye bank cannot
32
be operated with only two phases in an emergency. If the delta is on the primary side and should
accidentally open, the unexcited leg on the wye side can resonate with the line capacitance
Figure 17. The Delta-Wye Connection of Transformer
The three-phase Delta-Wye connections are shown in Figure 12. This type of connections is used
where it is necessary to step up the voltage, as for example, at the beginning of a high-tension
transmission system.
2.4 Technical Points of Transformers
2.4.1 Transformer Temperature Control
Usually the efficiency of power transformers is more than 99% and because of this the input and
output powers are almost the same. Because of the small amount of inefficiency, losses occur
inside the transformer. These losses are losses such as losses in conductors, losses in electrical
steel due to the changing flux, which is carried, and losses in metallic tank walls and other metallic
structures cause by the stray time varying flux. These losses lead to temperatures increases, which
must be controlled by cooling. The primary cooling media for transformers is oil and air. In oil33
cooled transformers, the coils and core are immersed in an oil-filled tank. The oil is then circulated
through radiators or other types of heat exchanger so that the ultimate cooling medium is the
surrounding air or possibly water for some types of heat exchangers. In small distribution
transformers, the tank surface in contact with the air provides enough cooling surface so that
radiators are not needed. Sometime in these units, the tank surface area is augmented by means of
fins or corrugations
Figure 18. Oil Transformer with Air Convection Cooled Heat Exchangers
The cooling medium in contact with the coils and core must provide adequate dielectric strength
to prevent electrical breakdown or discharge between components at different voltage levels. For
this reason, oil immersion is common in higher voltage transformers since oil has a 27 higher
breakdown than air. Often one can rely on the natural convection of oil though the windings, driven
by buoyancy effects, to provide adequate cooling so that pumping is not necessary. Air is a more
34
efficient cooling medium when it is blown by means of fans through the windings for air-cooled
units. In some applications, the choice of oil or air is dictated by safety considerations such as the
possibility of fires. For units inside buildings, air-cooling is common because of the reduced fire
hazard. While transformer oil is combustible, there is usually tittle danger of fire since the
transformer tank is often sealed from the outside air or the oil surface is blanketed with an inert
gas such as nitrogen. Although the flash point of oils is quite high, if excessive heating or sparking
occurs inside an oil-filled tank, combustible gasses could be released. Environment also plays a
big role in the choice of coolants. Mineral oil used in transformers is known to be detrimental to
the environment if there is an accident. For transformers such as those used on planes or trains or
units designed to be transportable for emergency use, air-cooling is preferred. For units that are
not so restricted, oil is the preferred cooling medium, in general oil cooled transformers are used
in everyday units, from large generator or substation units to distribution units on telephone poles.
There are other cooling media, which find limited use in certain application, such as sulfur
hexafluoride gas, which is usually pressurized. This is a relatively inert gas and it has a higher
breakdown strength than air, it is generally used in high-voltage units where oil cannot be used
and where air does not provide enough dielectric strength. Usually, the standard transformer oil is
used in oil-cooled transformers. Nevertheless, there are other types of oil are also used for
specialized usage. For example, silicon oil. It can be used at a higher temperature than the standard
transformer oil and at a reduced fired hazard.
2.4.1.1 Renown Transformer Temperature Control Methods
Dry type transformers
35
This method can be divided in two types:
(A) Air Natural (AN) Air natural or self-air cooled transformer is generally used for small ratings
transformers up to 3 MVA. Basically, this method uses the natural air flow surrounding the
transformer as cooling medium.
(B) Air forced (AF) Natural air-cooling method is adequate to use for transformers rated more than
3 MVA. Therefore, blowers or fans are required to force the air towards the core and windings so,
hot air is gained cooled due to the outside natural conventional air. However, the air forced must
be filtered to prevent the accumulation of dust particles in ventilation ducts. This method can be
used for transformers up to 15 MVA. In figure below, we can see the example of forced air-cooled
transformer
Figure 19. Forced Air-Cooled Transformer
Oil immersed transformers
36
Generally, the transformer winding and core are immersed in the mineral oil, which has good electrical
insulating property to block the current flow through the oil and high thermal conductivity.
This method can be divided into four types:
(A) Oil Natural Air Natural (ONAN) This cooling method may be used for transformers up to about 30MVA.
In this method, the heat generated in the core and winding is transferred to the oil. The heated oil moves
in the upward direction and flows from the upper portion of the transformer tank according to the
principle of convection. The heat from the oil will dissipate in the atmosphere due to the natural air flow
around the transformer. In this case, the oil in transformer will keep circulating because of natural
convection and will dissipate heat in atmosphere due to natural conduction. In figure below is shown an
example of oil natural air natural cooling of transformer
Figure 20. Oil Air Natural (ONAN) Cooling of Transformer
Oil Natural Air Forced (ONAF)
Generally, this method of transformer cooling is useful for large transformers up to about 60 MVA. The
heat dissipation can be improved by applying forced air on the dissipating surface. Heat dissipation rate
37
is faster and more in ONAF transformer cooling method than ONAN cooling system. In this manner, fans
are mounted near to the radiator and can be provided with an automatic starting arrangement, which
turns on when temperature increases beyond certain value.
Figure 21. Oil Natural Air Forced (ONAF) Cooling of Transformer
Oil Forced Air Forced (OFAF).
Oil Forced Air Forced (OFAF) cooling method is provided for higher rating transformers at substations or
power stations. In this method, oil is circulated with the help of a pump, and then compressed air is forced
to pass on the heat exchanger with the help of high-speed fans. Furthermore, the heat exchangers can be
mounted separately from the transformer tank and connected through pipes at top and bottom as shown
in the figure below.
38
Figure 22. Oil Natural Air Forced (OFAF) Cooling of Transformer
Oil Forced Water Forced (OFWF).
We know that ambient temperature of water is much less than the atmospheric air in same weather
condition. Thus, water may be used as better heat exchanger medium than air. The oil is forced to flow
through the heat exchanger with the help of a pump, where the heat is dissipated in the water, which is
also forced to flow. The heated water is taken away to cool in separate coolers. Generally, this type of
cooling is used for very large transformers with very high power rating above 500 MVA.
Figure 23. Oil Natural Air Forced (OFWF) Cooling of Transformer
39
2.2 Core Material and Shapes
Magnetic cores of various types play a key role in many of the components used in switched
mode power supplies. Core materials and geometries are a basic design consideration. Depending
on the circuit requirements, degree of sophistication, manufacturing techniques, assembly
equipment available and costs, the designer has a wide array of magnetic cores at his disposal. The
list includes: ferrite cores, permalloy powder cores, Kool Mµ® powder cores, 50 Ni/50 Fe powder
cores, tape wound cores, cut cores, bobbin cores, laminations and powdered iron cores.
The correct choice of core materials will optimize power supply performance. In metal
ferromagnetic materials, eddy current losses increase rapidly with frequency and are controlled by
using thin laminations, thin-gauge strips of material, or by powdering and insulating metallic
particles used to produce the core. Practical and theoretical factors limit the effectiveness of this
approach. Ferrite materials have one paramount advantage — very high electrical resistivity,
which means that eddy current losses are much lower than metals. As operating frequencies
increase, ferrites become a practical and useful magnetic material since ferromagnetic types cannot
be made progressively thinner or smaller to reduce eddy current losses to acceptable levels. While
ferrites do provide low core losses at higher frequencies, they have, as previously mentioned,
relatively low saturation levels; therefore, for a given flux density, a larger core cross-section is
needed. This added core area increases copper losses (AC and DC); however, at 20 KHz and higher,
the reduction in core loss obtained when using a ferrite is greater that the subsequent increase in
copper losses. Additionally, fewer turns are needed at higher frequencies to support a given voltage;
hence, the copper losses are kept down. For the lower range of power and switcher frequencies,
nickel-alloy ferromagnetic cores have relatively high electrical resistivity; laminated, or strip
40
wound cores fabricated from thin strip, can be effective up to the 20 KHz range (or higher if
designed and operated at low flux density levels). Tables 2 and 3 summarize the various types of
cores with respect to materials and shape characteristics. These tables provide a basis for magnetic
core selection. The correct choice of core depends on circuit requirements such as frequency,
power level, circuit configuration, and environmental conditions. Our applications engineering
staff will be happy to assist you in choosing the optimum core for your application. The advantages
and disadvantages of the various types of core materials and geometries in transformers, inductors,
and filters are reviewed table 1.
Table 1: Ferrite Core Comparative Geometry Consideration
2.6 Losses in Transformer
Since magnetic lines of force in a transformer are constantly changing in value and
direction, heat is developed because of the hysteresis of the magnetic material (friction of the
molecules). This heat must be removed; therefore, it represents an energy loss of the transformer.
High temperatures in a transformer will drastically shorten the life of insulating materials used in
the windings and structures. For every 8 degrees Celsius (°C) temperature rise, life of the
transformer is cut by one-half; therefore, maintenance of cooling systems is critical. Losses of
41
energy, which appears as heat due both to hysteresis and to eddy currents in the magnetic path, is
known as core losses. Since these losses are due to alternating magnetic fields, they occur in a
transformer whenever the primary is energized, even though no load is on the secondary winding
Losses in transformers Like every existing machine, transformers also can`t work without
energy losses. The transformer has no moving parts and therefore the mechanical losses are absent
in it. Transformer losses are classified as no-load losses and load losses. These types of losses are
common to all types of transformers, regardless of transformer application or power rating.
However, there are two other types of losses: extra losses created by the non-ideal quality of power
and auxiliary (or cooling) losses, which may apply particularly to larger transformers, caused by
the use of cooling equipment such as fans and pumps.
No-load Losses
No-load losses (also called iron loss or core loss) are constant and occur 24 hours a day,
365 days a year, regardless of the load, from this the term no-load losses. They present in the
transformer core whenever the transformer is energized. They are categorized as shown below:
Hysteresis losses caused by the frictional movement of magnetic domains in the core
laminations being magnetized and demagnetized by alternation of the magnetic field. These losses
are responsible for 50% to 80% of total no-load losses and depend on the type of material used to
build a core. Silicon steel has much lower hysteresis than normal steel but amorphous metal has
much better performance than silicon steel. Hysteresis losses can be reduced by material
processing such as cold rolling, laser treatment or grain orientation.
42
Eddy current losses caused by varying magnetic fields inducing eddy currents in the
laminations and thus generating heat and usually they are responsible for 20–50% of total no load
losses. Eddy current losses can be reduced by building the core from thin laminated sheets
insulated from each other by a thin varnish layer to reduce eddy currents.
Less significant stray and dielectric losses occur in the transformer core and these losses
usually account for no more than 1% of total no-load losses
Load Losses
Load losses (also called copper losses or short-circuit losses) occur in the resistance of the
winding of the transformer when it carries the load current. The total loss of copper in the
transformer is obtained by adding both primary and secondary copper losses.Load losses vary
according to the transformer loading. These losses include:
Ohmic heat loss (sometimes called as copper loss) occurs in transformer windings and
caused by the resistance of the conductor. The magnitude of this loss increases with the square of
the load current (๐ผ๐‘™๐‘œ๐‘Ž๐‘‘ 2 ) and is proportional to the resistance of the winding (๐‘…๐‘ค๐‘–๐‘›๐‘‘๐‘–๐‘›๐‘”). Ohmic
heat loss can be reduced by increasing the cross-sectional area of the conductor or by reducing the
winding length of conductor (R=๐œŒ๐‘™ ๐‘† ).
Conductor eddy current losses caused by alternating current and occur in the windings
(due to magnetic fields). Eddy currents can be reduced by reducing the cross-section of the
conductor, so stranded conductors with the separate strands isolated against each other are used to
achieve the required low resistance while controlling eddy current loss.
Extra losses
43
Extra losses caused by unbalanced harmonics and reactive power.
Harmonics: Non-linear loads, such as power electronic devices, such as variable speed
drives on motor systems, computers, UPS systems, TV sets and compact fluorescent lamps, cause
harmonic currents on the network. Harmonic voltages are generated in the impedance of the
network by the harmonic load currents. Harmonics increase both load and no-load losses due to
increased skin effect, eddy current, stray and hysteresis losses.
Unbalance: Transformers subject to negative sequence voltage transform them in the same
way as positive sequence voltages. The behavior with respect to homo-polar voltages depends on
the primary and secondary connections and, more particularly, the presence of a neutral conductor.
If, for example, one side has a three-phase four-wire connection, neutral current can flow. If at the
other side of the winding is delta-connection, the homo-polar current is transformed into a
circulating (and heat-causing) current in the delta. The associated homo-polar magnetic flux passes
through constructional parts of the transformer causing by parasitic losses in parts such as the tank,
sometimes requiring an additional derating.
Extra losses due to current distortion: The most important of these losses is that due to eddy
current losses in the winding, it can be very large and consequently most calculation models ignore
the other harmonic-induced losses. The precise impact of a harmonic current on load loss depends
on the harmonic frequency and the way the transformer is designed. In general, the eddy current
loss increases by the square of the frequency and the square of the load 33 current. So, if the load
current contains 20% fifth harmonic, the eddy current loss due to the harmonic current component
would be 5 2∗0.2 2 multiplied by the eddy current loss at the fundamental frequency, meaning that
the eddy current loss would have doubled.
44
To avoid excessive heating in transformer supplying harmonic currents, two approaches
are used: a) Reducing the maximum apparent power transferred by the transformer, often called
derating. To estimate the required de-rating of the transformer, the load’s de-rating factor can be
calculated. This method, used commonly in Europe, is to estimate by how much a standard
transformer should be de-rated so that the total loss on harmonic load does not exceed the
fundamental design loss. This de-rating parameter is known as “factor K”.
K-factor rating is an index of the transformer’s ability to operate within the temperature
limits due to harmonic content. A K-factor of 1.0 indicates a linear load (no harmonics). A higher
K-factor indicates greater harmonic heating effects. The K-factor is a number derived from a
numerical calculation based on the summation of harmonic currents generated by a non-linear load.
Higher the K-factor, the more significant the harmonic current content.
โ„Ž=๐‘š๐‘Ž๐‘ฅ
๐พ_๐น๐‘Ž๐‘๐‘ก๐‘œ๐‘Ÿ = ∑
๐ผโ„Ž2 โ„Ž2 (๐‘๐‘ข)
โ„Ž=1
Where h is the harmonic number, Ih is the fraction of total RMS load current at harmonic
number h.
ANSI/IEEE C57.12.90-1987 and ANSI/IEEE C57.12.91-1979 classify losses in
transformers. They are load loss (impedance loss); no-load loss (excitation loss); and total loss
(no-load + load-loss). Load loss further subdivides into stray magnetic losses in the core, eddy
currents, and resistive losses in the windings.
PLL =I2R + PEC+PSL
(4)
Where PLL is total load loss, PEC is winding eddy current loss, PSL is stray loss and I2R is resistive loss.
ANSI/IEEE C57.110-1986 confirms that transformer faces abnormal winding temperature rise when
45
harmonic load is present. Winding eddy current loss is the most concern when transformer
supplying nonsinusoidal load current, because it increases approximately with the square of the
frequency [50]. The total eddy current loss, Pt, is given by Equs (5)-(6) shows relation between
K-Factor and winding eddy current loss.
โ„Ž=โ„Ž
Pt = Pf ∑โ„Ž=1 ๐‘š๐‘Ž๐‘ฅ ๐ผโ„Ž2 โ„Ž2
๐‘ƒ
โ„Ž=โ„Ž
K-Factor = ๐‘ƒ๐‘ก = ∑โ„Ž=1 ๐‘š๐‘Ž๐‘ฅ ๐ผโ„Ž2 โ„Ž2
๐‘“
(5)
(6)
Where, Pf is the eddy current loss at the fundamental frequency f and Ih is the fraction of the total RMS load
current at harmonic number h.
C.. K-factor and harmonic loss factor for winding eddy current
The relationship between the harmonic loss factor and the Underwriters laboratories (UL) Kfactor [42]-[44] is given by:
=MAX I2
∑H
H
H=1
)FHL
I2R
K_Factor = (
(7)
Where, FHL is the harmonic loss factor for winding eddy currents, h is the harmonic order, hmax is the highest
significant harmonic number, Ih is the RMS current at harmonic “h” (amperes), and IR is the RMS
fundamental load current (ampere).
The harmonic loss factor is a function of the harmonic current distribution and is independent of
the relative magnitude. The UL K-factor is dependent on both the magnitude and distribution of
the harmonic current.
D. Self- capacitance and Temperature rise
46
Transformer’s self-capacitance can be calculated using Equs (8).
1
1
๐ถ๐‘ = ( ๐‘ค 2 ๐ฟ ) = 4๐œ‹2 ๐‘“2 ๐ฟ [๐‘“๐‘Ž๐‘Ÿ๐‘Ž๐‘‘๐‘ ]
๐‘Ÿ
(8)
๐‘Ÿ
Where CP is primary capacitance, fr is resonant frequency and L represents primary inductance of
transformer or inductor.
Heat dissipation and the increase in temperature depends on many factors. For the specific
requirement of a thermal design of transformers, easy to use expressions are renown with the
designers. The temperature rise of the modified and conventional design transformer in oC can be
calculated as follows:
๐‘‡๐‘ก = 450(๐‘ƒ๐‘ก๐‘œ๐‘ก๐‘Ž๐‘™ ⁄๐ด๐‘ก )0.826
๐ด๐‘ก = ๐พ๐‘ ๐‘ก (๐ด๐‘ก ๐ด๐‘ค )0.5
(9)
(10)
Where Ptotal is the total loss in W, At is the surface area of transformer in, and Kst is a constant related to
core structure, besides is equal to 41.3 for a laminated core.
Transformer Rating Capacity (or rating) of a transformer is limited by the temperature that the
insulation can tolerate. Ratings can be increased by reducing core and copper losses, by increasing
the rate of heat dissipation (better cooling), or by improving transformer insulation so it will
withstand higher temperatures. A physically larger transformer can dissipate more heat, due to the
increased area and increased volume of oil. A transformer is only as strong as its weakest link, and
the weakest link is the paper insulation, which begins to degrade around 100 °C. This means that
a transformer must be operated with the “hottest spot” cooler than this degradation temperature,
or service life is greatly reduced. Reclamation typically orders transformers larger than required,
which aids in heat removal and increases transformer life. Ratings of transformers are obtained by
simply multiplying the current times the voltage. Small transformers are rated in “VA,” volts times
47
amperes. As size increases, 1 kilovoltampere (kVA) means 1,000 voltamperes, 1 megavoltampere
(MVA) means 1 million voltamperes. Large GSUs may be rated in hundreds of MVAs. A GSU
transformer can cost well over a million dollars and take 18 months to 2 years or longer to obtain.
Each one is designed for a specific application. If one fails, this may mean a unit or whole plant
could be down for as long 2 years, costing multiple millions of dollars in lost generation, in
addition to the replacement cost of the transformer itself. This is one reason that proper
maintenance is critical.
Conductor Losses
The inherent resistance of the conductor is the main cause for this type of loss.Basically, this is I
R loss, where I is the current flowing through the conductor, and R is the AC resistance at high
frequencies. The increase in conductor losses is appreciable when the winding conductor thickness
becomes comparable to the 'skin depth' of the high frequency currents.
1. Skin Effect,
2. Proximity Effect,
3. End Effects,
4. Core Gap Effects.
In the following section, we are going to discuss these effects
Skin Effect
This is the fundamental effect at higher frequencies. A current I(t) flowing through a conductor
induces a magnetic flux 0it), which causes eddy currents inside the conductor. According to the
Lenz's law, these eddy currents oppose their cause, i.e., I(t). So the net current density inside the
conductor starts decreasing as the frequency increases.
48
So the high frequency currents do not penetrate to the center of the conductor and there will not
be proper utilization of the conductor besides these losses. However by using litz wire (generally
having a number of insulated strands), we can increase the eddy current path resistance many times.
Braiding or weaving of insulated strands of wire together forms Litz wire in a way that causes each
strand to spend equal time at the surface and each location in the cross-section and will take care
of the skin effect losses. This makes all the strands to carry equal amount of current. The size
(AWG) of the strand depends on the operating frequency
Figure 24. Skin effect – Isolated conductor
Proximity Effect This is another type of loss when a conductor is in the vicinity of other current
carrying conductors. Eddy currents are induced in the conductor by the currents flowing in the
proximity conductors, in turn causes the losses in the conductor. When the 27 windings are multilayered, the proximity effect is the dominant conductor loss at higher frequencies. Proximity effect
is a phenomenon that can greatly increase magnetic winding losses over DC resistance or skin
effect alone. In other words, we can say that both Skin Effect and Proximity Effect are due to the
eddy currents induced inside the conductor: one because of the current carried by itself and the
49
other because of the current in the near by conductors. Decreasing the number of layers needed
could minimize proximity Effect (this can be done by increasing the number of windings per layer).
Harmonic analysis must be used in calculating the Proximity loss or the loss estimates are off by
many orders of magnitude.
End Effects More current tends to flow through the outer (end) windings compared to the middle
(inner) windings because of the non-uniform magnetic fields in transformer or inductor windings.
This can be observed in ETD, E and P core and is absent in toroidal cores as the windings are
distributed uniformly
Core Gap Effects The presence of discrete air gaps in a core creates non-axial magnetic fields,
which intersect the windings inducing additional eddy current losses. The presence of air gap
makes the end windings (windings near to the air gap) to carry more current than the neighboring
conductors as the flux leaving the magnetic material is maximum. These 28 effects are often a
major loss mechanism in transformer and inductors with gapped core. We have not tried using
gapped core to increase the efficiency. It is not only difficult but also almost impossible to account
the losses separately. We are considering the first two types of losses (Skin and Proximity Effects)
which are responsible for the losses in the conductors at high frequencies. Typical current
distributions for proximity effect with current flow both in and the same direction and in opposite
directions were shown in Figures 2.10 and 2.11
50
Figure 25. Proximity effect – Opposite Currents
Proximity Effect is not only more serious than skin effect, but also the analysis of its losses is
obscure and mathematically difficult. We can say that the core loss and proximity effect are the
two most considerations in high frequency magnetics design. Proximity effect limits the high
frequency current density as the operating flux density of the core is limited by the core loss at
high frequencies. Even conductors not carrying any 29 amount of current experience eddy current
losses when they are in an external AC magnetic field. In every conductive element inside a
transformer, inductor, or any AC magnetic device. Skin and Proximity effects are extremely
important.
Figure 26. Proximity effect – Same Currents
2.7. Definition of Power Converter
The task of a power converter is to process and control the flow of electrical energy by
supplying voltages and currents in a form that is optimally suited for user loads. Energy
conversions were initially achieved using electromechanical converters (which were mainly
rotating machines). Today, with the development and the massive production of power
semiconductors, static power converters are used in numerous application domains and especially
51
in particle accelerators. Their weight and volume are smaller and their static and dynamic
performance are better.
The primary task of power electronics is to process and control the flow of electric energy by
supplying voltages and currents in a form that is optimally suited for user loads. Modern power
electronic converters are involved in a very broad spectrum of applications like switched-mode
power supplies, active power filters, electrical-machine-motion-control, renewable energy
conversion systems distributed power generation, flexible AC transmission systems, and vehicular
technology, etc.
Power electronic converters can be found wherever there is a need to modify the electrical energy
form with classical electronics in which electrical currents and voltage are used to carry
information, whereas with power electronics, they carry power. Some examples of uses for power
electronic systems are DC/DC converters used in many mobile devices, such as cell phones or
PDAs, and AC/DC converters in computers and televisions. Large scale power electronics are used
to control hundreds of megawatt of power flow across our nation. Some of those converters are
discussed below
A power converter is an electrical or electro-mechanical device for converting electrical energy. It
may be converting AC to or from DC, or the voltage or frequency, or some combination of these.
One way of classifying power conversion systems is according to whether the input and output are
alternating current (AC) or direct current (DC):
•
AC to DC
52
•
DC to AC
•
DC to DC
•
AC to AC
However, modern power converters are made with many conversion stages. For example,
an UPS (uninterruptible power supply) is made with two stages, first an AC to DC conversion to
make a DC voltage, where the batteries are connected, followed by a DC to AC conversion, which
supplies the load. Amongst the many devices that are used for this purpose are:
Switched-mode power supply
•
Rectifier
•
Inverter
•
Motor generator set
•
DC-DC Converter
•
Converter
Electrical power conversion is a special field of electrical engineering. Power electronics is the
application of solid-state electronics for the control and conversion of electric power.
2.8 Total Harmonics Distortion in Power Systems
Harmonic distortion is one of the major reasons for a transformer overheating and often
exists when the transformers serve nonlinear load [6-10]. Harmonic distortion has attracted
considerable attention since power electronic devices were introduced to improve the efficiency
53
and robust controllability of the power electric systems [11-13]. Therefore, the electronics
equipment, which counts as harmonic sources, will be used progressively in the near future [1416].
The mitigation of harmonic distortion is required urgently to overcome the major
challenges in electric power systems [17]. Thus far, the established mitigation techniques are
hybrid, passive, and active harmonic mitigation, namely triangle-comparison PWM control, line
reactors, and tuned harmonic filters [18-20]. All the established methods have their own positive
and negative factors, and they cannot give an ideal solution for the harmonic distortion problems.
These methods use other extra circuitry and are more expensive techniques that are incompatible
with practical applications [21-22].
Harmonic distortion is one of the major reasons for a transformer overheating and often
exists when the transformers serve nonlinear load [6-10]. Harmonic distortion has attracted
considerable attention since power electronic devices were introduced to improve the efficiency
and robust controllability of the power electric systems [11-13]. Therefore, the electronics
equipment, which counts as harmonic sources, will be used progressively in the near future [1416].
The mitigation of harmonic distortion is required urgently to overcome the major
challenges in electric power systems [17]. Thus far, the established mitigation techniques are
hybrid, passive, and active harmonic mitigation, namely triangle-comparison PWM control, line
reactors, and tuned harmonic filters [18-20]. All the established methods have their own positive
and negative factors, and they cannot give an ideal solution for the harmonic distortion problems.
54
These methods use other extra circuitry and are more expensive techniques that are incompatible
with
Table 2. Current and Voltage total harmonic distortion allowing values and their associated risks
(COURTESY: INTERPRETING IEEE STD. 519).
practical applications [21-22].
1⁄
2
๐ป
2
๐‘‡๐ป๐ท๐‘ฃ = [(∑ |๐‘‰๐‘–โ„Ž | )
⁄|๐‘‰๐‘–๐‘™ |] × 100%
โ„Ž≠1
2
1⁄
2
โ„Ž
๐‘‡๐ป๐ท๐ผ = [(∑๐ป
โ„Ž≠1 |๐ผ๐‘– | )
⁄|๐‘‰๐‘–๐‘™ |] × 100%
where, H is the highest harmonic order considered (H=25 for this paper). Harmonic
components very close to zero are ignored in calculations and only odd harmonics, such as 3, 5, 7,
9, and 11 were considered
55
THDv
THDI
Risk
<5%
< 10 %
normal situation
5–8%
10 – 50 %
considerable harmonic pollution with
malfunctions possibility
>8%
> 50 %
major harmonic pollution with malfunctions
probability
Sources of Harmonics
Harmonics are currents and voltages at frequencies that are integer multiples of the fundamental
power frequency. As a result, power lines contain pure undistorted 50-Hz or 60-Hz sine wave
voltages as well as other signals. The sine wave is distorted and consequently harmonics of the 50Hz or 60-Hz fundamental are found. At higher frequencies, switching transients appear from
rectifiers, motor drives and other sources. In addition, at frequencies above 50 kHz, strong HF
signals from radio, TV and computers are superimposed on the line and appear across the primary
winding of a transformer.
These extra signals, called noise or distortion, appear in two ways on the power lines. At
frequencies above 1 MHz, noise is mostly common mode, which refers to both line and neutral
containing an equal amount of amplitude and phase distortion. For frequencies below 1 MHz, the
major component of the noise is typically differential mode, where the noise on line and neutral
56
sides is equal in amplitude and opposite in phase. Differential-mode noise generates a real noise
voltage difference between line and neutral.
If all these harmonics and noise on the line are detrimental and dangerous, why isn't there some
sort of control over the power quality leaving the generation station? As a matter of fact, there is.
The power leaving the plant and fed into the power grids is clean, green and sinusoidal in nature.
It is rare that the lowly state of power found downstream is related to the source generator. We
must look elsewhere for the source, not to the generation of power.
The harmonics generated downstream can find their way back onto the utility lines and affect all
power users on the system, and ultimately adversely affect the operation of utility and distribution
power transformers all down the line. All loads in common with the transformer secondary share
the effects of the harmonics — so it's a community issue.
Most harmonics originate from the generation of harmonic currents caused by nonlinear load
signatures. A nonlinear load is characteristic in products such as computers, printers, lighting and
motor controllers, and much of today's solid-state equipment. With the advent of power
semiconductors and the use of switching power supplies, the problem has become more severe in
the last few decades. Most of these products didn't exist 30 years ago, thus the trouble is recent
and a direct result of technological innovation.
A nonlinear load draws current in a non-sinusoidal manner, despite the fact the voltage may be
perfectly sinusoidal (Fig. 1). Nonlinear loads draw current during a portion of the incoming voltage
waveform, not continuously as with a light bulb. Current is drawn in bursts or planned abrupt
57
pulses, as required by the product. The result is distorted current wave shapes, the harmonic content
of which can flow back and contaminate other parts of the power supply (Fig. 2).
Harmonics and the resulting harmonic distortion are a constant repetitive occurrence within a
product. Sometimes transients on the line are confused with harmonics, but they are not the same.
Transients typically are not related to normal operating conditions and are a random occurrence
with no repeatable time signature or frequency.
Table 3. Proposed Transformer waveforms.
Source Voltage
Design
(same for all
Designs)
Primary
Secondary
Voltage
Voltage
Primary
Current
Secondary
Current
Conventional 180º
Modified 180º
Conventional 360º
Modified 360º
2.7 References
[1] Robert M. Del Vecchio, Bertrand Poulin, Pierre T. Feghali, Dilipkumar M. Shah, and Rajendra Ahuja,
2001, “Transformer Design Principles” with application to core-form power transformers, CRC Press.
58
[2] Andreas Sumper, Angelo Baggini, 2012, "Electrical Energy Efficiency: Technologies and Application",
John Wiley & Sons, Inc
[3] https://www.usbr.gov/tsc/techreferences/mands/mands-pdfs/Trnsfrmr.pdf
[4] T.A Short, 2004, "Handbook of Electric Power Distribution", CRC Press
[5] John J. Winder,Jr, 2002, “Power Transformers : Principles and Applications”
[6] https://electricalnotes.wordpress.com/2012/07/17/parallel-operation-of-transformers/
[7] http://circuitglobe.com/cooling-of-transfomer-and-methods-of-cooling.html
[8] James H.Harlow, 2004, “Electric Power Transformer engineering”
[9] motor.feld.cvut.cz/SP1
[10] http://ecetutorials.com/transformer/transfomer-cooling-methods/
[11] George McPherson, published by John Wiley & Sons Inc, 1981, “An Introduction to Electrical
Machines and Transformers”.
[12] Weedy, B.M., “Electric Power Systems”. 5th ed. Wiley, 2012. Figures: [1]
https://www.google.cz/search?q=Power+Transformer&client=firefoxbab&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiIsoi4pPPTAhXEtxoKHbPsCOcQ_AUICig
B&biw=1366&bih=659#imgrc=kEAAAT7a4GhP8M [2]
https://www.google.cz/search?q=Power+transformer+wiki&client=firefoxbab&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjFhe68pfPTAhVMWxoKHXU5D2gQ_AUI
BigB&biw=1366&bih=659#tbm=isch&q=Transformer+construction&imgrc=tfT91RP_T0sVlM
[13] https://www.electrical4u.com/what-is-transformer-definition-working-principle-oftransformer/ 45 [12]
https://www.google.cz/search?q=electric+power+system&client=firefoxbab&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjWptrmpIjUAhUJjSwKHWEuAXIQ_AUI
CigB&biw=1366&bih=659#imgrc=7q1PM75FmaSHfM:
59
[14]
https://www.mag-inc.com/Media/Magnetics/File-
Library/Product%20Literature/General%20Information/ps-01.pdf?ext=.pdf
[15]https://www.google.cz/search?q=current+transformer&client=firefoxb&source=lnms&tbm=isch&sa=X&ved=0
ahUKEwjozrrnz9bTAhWIbFAKHQNJAtgQ_AUICC
gB&biw=1366&bih=659#tbm=isch&q=current+transformer+with+secondary+wound+around+t
he+primary+conductor+&imgrc=E3B_zY09h2dn5M
[16] T.A Short, 2004, "Handbook of Electric Power Distribution", CRC Press
[17] https://www.google.cz/search?q=on+load+tap+changer&client=firefoxbab&source=lnms&tbm=isch&sa=X&ved=0ahUKEwj73anwnfTTAhVmGZoKHWTDBo0Q_AU
ICigB&biw=1366&bih=659#imgrc=brOUAiZXGFnFvM:
[18] ttps://www.google.cz/search?q=Figure+17+%E2%80%93+ThreePhase+Connections.&client=firefoxbab&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiN8NXpievTAhXrDZoKHcYgAuMQ_AUI
CigB&biw=1366&bih=659#imgrc=xxhyAQBunv0qiM
[19], [20], [21], [22][23]. http://www.electrical-engineering-assignment.com/three-phasetransformerconnections [23]https://www.google.cz/search?q=oil+transformator&client=firefoxbab&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiS1MGCovTTAhVCiSwKHd0RBlsQ_AUI
CigB&biw=1366&bih=659#imgrc=ECIsH64JowIwNM:
[24] https://www.google.cz/search?q=Forced+aircooled+transformer&client=firefoxb&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjxv_aiovTTAhVnMZoKHRe
XAJ8Q_AUICi gB&biw=1366&bih=659#imgrc=60AETeL4dVd5oM:
[25], [26], [27], [28] http://circuitglobe.com/cooling-of-transfomer-and-methods-of-cooling.html Table: [1]
K.Karsai, D.Kerenyi, L.kiss, 1987, “Large Power transformers”
[29]http://epc.web.cern.ch/content/what-power-converter
[30]https://cds.cern.ch/record/2038603/files/15-43-Aguglia.pdf
60
31https://www.elprocus.com/power-electronic-converters/
32 B.Waltrip; en al. “Inductance Measurement Using an LCR Meter and a Current Transformer”
Interface,IEEE, Ottawa, Canada.16-19 May 2005.
33 McLyman C. W. T.; “Transformer and Inductor Design Handbook.” Beijing, China: China Elect.
Power Press,pp 370–372. 2008
34 Shayan Tariq Jan, Raheel Afzal and Akif Zia Khan. “Transformer Failures, Causes & Impact” in
International Conference Data
Mining, Civil and Mechanical Engineering (ICDMCME’2015),
Bali, Indonesia, Feb. 1-2, 2015
35 Grady W. Mack and Surya Santoso. “Understanding power system harmonics.” IEEE Power Engg.
Review 21, 8-11 2001
36 Salih; Salih Mohammed, Kaleid Waleed Abid and Munther Nayef. “Practical Analysis of Harmonics
Effects on Transformer.” Elixir Renewable Energy Engg. Pp. 70 2014
37
Choi Sewan, Prasad N. Enjeti and Ira J. Pitel. Polyphase “Transformer arrangements with reduced
kVA capacities for harmonic current reduction in rectifier-type utility interface.” IEEE Transactions
on Power Electronics, Vol 11, pp. 680-690 1996.
38 D.A. Barkas, C.S. Psomopoulos, G.C. Ioannidi, S.D. Kaminaris and P. Malastetas. “Experimental and
theoretical investigation of harmonic distortion in high voltage 3-phase transformers.” in MedPower,
Athens, Greece, 2-5 Nov. 2014.
39 Biricik Samet, Özgür Cemal Özerdem.”Experimental study and comparative analysis of transformer
harmonic behaviour under linear and nonlinear load conditions.” In Environment and Electrical
Engineering (EEEIC), Rome, Italy, 8-11 May 2011.
40 Bo Wang, Jie Cai, Xiong Du, and Luowei Zhou. „Review of Power Semiconductor Device Reliability
for Power Converters.” CPSS Transactions on Power Electronics and Applications Vol 2, pp. 101-117,
2017
41 P. Sathishkumar, P., Punyabrahma, R,. Sri Muthu Mrinalini, and G. R. Jayanth "A resonating reflectorbased optical system for motion measurement in microcantilever arrays" Review of Scientific
Instruments, Vol. 86, pp. 096106, 2015
61
42 Force Task and G. Chang. “Characteristics and modeling of harmonic sources-power electronic
devices.” IEEE Power Engineering Review21,Vol 8, pp. 62-64 2001
43 Hudgins and Jerry L. “Power electronic devices in the future.” IEEE Journal of Emerging and Selected
Topics in Power Electronics1, Vol. 1, pp.11-17. 2013
44 Sathishkumar, P., Himanshu, Shengxu Piao., Muhammad Adil Khan.,Do-Hyun Kim, Min-Soo
Kim,Dong-Keun Jeong, Cheewoo Lee and Hee-Je Kim.“A Blended SPS-ESPS Control DAB-IBDC
Converter for a Standalone Solar Power System.“ Energies Vol 10(9),pp. 1431, 2017.
45 Biczel Piotr, Andrzej Jasinski and Jacek Lachecki. “Power electronic devices in modern power systems.”
in EUROCON, 2007. The International Conference on" Computer as a Tool". IEEE, Warsaw, Poland,
9-12 Sept. 2007
46 F II and I. IEEE recommended practices and requirements for harmonic control in electrical power
systems.1993.
CHAPTER 3
Toroidal Transformer Design Optimization
3.1 Toroid Ferrite Core
A. Toroid ferrite Core
62
To utilize the intrinsic ferrite material properties, it is essential to use a ring configuration of the f
errite core. Therefore, the toroid core was used in this paper, as it is commonly used for highfrequency square/ sine wave-based applications, such as power input filters, groundfault interrupters, common-mode filters, and pulse and broadband filters.
Figure 27: Ferrite 77 material core dimensions; (Courtesy: Fair-Rite products Corp.)
A 77 material ferrite toroid was used as the core for MV inverter high-frequency link
transformer. Figure 2 presents a schematic diagram of the core and is defined by its outer
diameter (A), inner diameter (B), thickness (C). Figure 3 shows how the increasing temperature
effects the core properties.
Table 4: Ferrite 77 toroid core dimensions (Courtesy: Fair-Rite products Corp.).
Nomi
Dim
mm
tol
mm
nal
inch
A
61.00
±1.30
2.400
B
35.55
±0.85
1.400
C
12.70
±0.50
0.50
0
Table 5: Ferrite 77 toroid core electrical properties (Courtesy: Fair-Rite products Corp.)
63
Electrical Properties
AL (nH)
2950 ± 25%
AE(cm2)
1.58000
∑I/A(cm-1)
9.20
Ie (cm)
14.50
Ve (cm3)
22.80000
๏ƒฏ
Figure 28: Temperature effects on Ferrite 77 material properties; (Courtesy: Fair-Rite pro
ducts Corp.)
3.2. Minimization of Parasitic Capacitance in Toroidal Transformer
high frequency winding losses and lowering the leakage inductance have been a major
research focus, while the winding capacitance requires equally serious attention during the
design of transformers. Capacitive coupling is one of the paths that can carry high frequency
noise, premature resonance, electrostatic coupling to other circuits and fast transient voltages
from primary to secondary circuitry, which produces common mode noise currents and an
increase in transformer temperature in the device, resulting in a deterioration of the overall
system operation, noise, health, and safety threats
3.2.1 Fabrication
64
This study examined a new design for the high frequency link of a MV inverter, which mitigat
es the temperature increase due to harmful harmonics by reducing the capacitive coupling at th
e high frequency transformer. Four toroid core transformers with conventional and modified c
onfigurations, having 180o and 360o sector windings, were fabricated, and their THD, self-ind
uced capacitance and temperature were measured and compared. The transformer windings for
all four configurations were wound manually. The core material, dimensions, copper wire, an
d number of winding turns were the same for the conventional and modified configuration, as l
isted in Table 3. The difference between the conventional and modified configuration was a tw
o-part mold that was mounted over the secondary windings and ferrite core. The primary wind
ing was then wound over this additional piece of hardware, which altered the dimensions of th
e primary winding and provided scope to unique winding arrangements. The mold was printed
using a 3D printer with a PLA filament material. This was comprised of two parts, top and bot
tom, each having a width of 0.5 mm each with very negligible extra weight and cost [35-36].
A. Case 1: Conventional toroid core transformer with 180° sector windings
In this configuration, the entire secondary winding is distributed over the 180° sector of the tor
oid core in a back-and-forth manner. The other half of the toroid core is wound with primary w
indings in a similar manner, as shown in Figure 5.
Figure. 29. 180° conventional (a) Flux pattern in core (b) 2D model (c) 3D model.
B. Case 2: Modified toroid core transformer with 180° sector windings
65
In this configuration, the secondary winding is distributed over the 180° sector of the toroid co
re in a back-and-forth manner, just as in the previous case. The two parts of the 3D printed mo
ld using a PLA filament material were mounted over the ferrite toroid core and secondary win
dings, to completely encapsulate them. Owing to the assembly of the mold, the secondary win
ding is completely hidden, which leaves an entire 360° span for the primary winding. The initi
al experiments were carried out with the primary windings over the 360° sector and 180° secto
r of the core. On the other ha, the lowest leakage inductance was achieved when the primary h
ad a 180° sector winding without overlapping the secondary winding, as shown in Figure 6.
Figure. 30. 180° Modified (a) Flux pattern in core (b) 2D model (c) 3D model
๏ƒฏ
C. 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).
66
Figure. 31. 360° conventional (a) 2D model (b) Flux distribution (c) 3-D model.
๏ƒฏ
D. Case 4: A modified 360° wound toroid core transformer
In this case, the secondary winding is distributed over 360° sector of the toroid core in a back-andforth manner, as in the former case. The toroid ferrite core along with the secondary winding is
encapsulated with the 3D printed mold, over which the primary winding is wound around a 360°
span (Figure 8).
Figure 32. 3600 Modified (a) 2D model (b) Flux distribution (c) Original design (d) 3-D
model.
3.3 Enlargement of leakage inductance in Toroidal Transformer
E and I core combination transformers generally used for power converter application, which
requires higher leakage inductance. However, the designer has to compromise with more losses,
size, and weight. On the other hand, comparatively, combination of shape and core material
such as ferrite toroidal transformer deliver better electrical performance and provides great
benefits. Instrument and current transformer commonly use toroid’s. Ferrite toroidal transformer
registers less loss, a smaller size, less weight including a less leakage inductance and less
67
electromagnetic noise compared with other shapes such as standard E and I stacked geometry
transformers.
3.3.1 Leakage inductance in Toroidal Transformer
To extrapolate these advantages of ferrite toroid core transformer and utilize them in additional
power conversion application as isolated core (E and I) are in use. In order to achieve that
designers need to succeed in dealing with major problems, which generates nosie in toroid core
transformers namely very high interwinding capacitance and extremely low leakage inductance.
3.3.2 Sectored winding effects on Toroidal Transformer leakage inductance
Sectored Wound Toroidal Transformers In sectored wound transformers, i.e., when the windings
do not cover the entire 360โ—ฆ, the leakage flux follows a completely different path. Fig. 3 shows
the top view of the leakage flux distribution. One can see that in this case the path of the leakage
flux includes a section of the core. The amount of leakage flux that a winding links depends on
the sector that is not wound. From Fig. 3, it is possible to see that many lines of flux only
partially link the winding. We make the remark that the shape of the leakage flux does not
change significantly as the angle of the wound sector varies. However, the intensity of the
leakage flux increases substantially as the unwound angle increases. It should be mentioned that
the flux in the core contributes very little to the leakage inductance since the energy stored
depends on the square of the magnetic field strength H, which is very small in the core due to its
high permeability.
68
Sectored winding is influential on toroid transformer leakage inductance. Toroid core registers
no air gap as it is closed concentric shape. Toroid core needs no bobbin for windings, therefore
one winding wound on total core and second winding wound on first winding therefore
electromagnetic coupling between winding and core is highest and flux finds no path to flee in
air. Resultantly very low leakage inductance in toroid transformer. However, flux will find way
to escape by sectored wound transformer. Francisco de Leon et al. published different measured
leakage inductance with different unwound angles (Table 6).
Table 6: Leakage inductance with different unwound angles
Point
Angle
ษต1 = ษต2
L
(measured)
[µH] N=97
0
0
L0=9.3
1
15
17.6
2
30
56.7
3
45
151
4
65
320
5
80
499
6
100
777
7
120
1032
8
180
2600
69
3.3.3 High permeability material effect on Toroidal Transformer leakage inductance
Leakage flux is not only dependent on geometry of the magnetic circuit, material permeability
plays a vital role for magnetic inefficiency as well. Flux follow the least resistant path similarly
other flow phenomenon. Therefore, magnetic flux prefers to jump on high permeability magnetic
area, regardless flow via the desired channels. This figure shows the graphs obtained Nethe, et al.,
showing the effects of air gap size on the force of a magnetic design, as well as the effects of gap
relative permeability and for various gap distance and ferrofluid permeabilities, respectively. Note
that the improvements from permeability reach a maximum point, then increased permeability has
a negative effect on overall performance as increment in leakage flux.
3.3.3.1 What is Ferrofluid
Ferrofluid is liquid magnets, Fluid is in liquid is state, however according to presence and absence
of magnetic field immediately particles orient along the filed lines. Ferrofluid liquid magnetically
permeable as it contains iron particles. Ferrofluid yield homogenous composition and steady
throughout their life span. Figure
shows crude molecular sketch of a ferrofluid. Particles
agglomeration avert even in strong magnetic field due to surfactant with a chemical polarity.
Ferrofluid devices are used in many applications few names Audio speaker s non-evaporative
applications, Audio speakers, Biomedical devices. However constantly getting attention from
researcher to utilize this unique property in many more other applications. A measure of
permeability often used to describe materials is relative permeability, µr, defined as [1]
µr =
70
µ
µ0
Where µ is the material’s permeability and µ0 is the permeability of air (4π×10−7 Henries/meter)
[1]. The relative permeability of a ferrofluid, to some extent, can be engineered to specification,
but is limited by the amount of carrier fluid and surfactant required.
3.4 B-H curve for transformer core material (ferromagnetic 77 material)
3.4.1 Determination of B-H Curve of Core Material of Transformer
Aim To determine of B-H curve of core material of transformer. Theory The rms voltage induced
in a transformer is given by
E = 4.44φmfN
(1)
where, φm is maximum value of the flux in the core, f is operating frequency and N is number of
turns in the coil. This flux in the coil is given by
φm = BmAc
(2)
where, Bm is the maximum flux density in core and Ac is the cross-sectional area of the core.
So we have
E = 4.44BmAcfN
(3)
The value of induced voltage E is thus dependent upon Bm which can be setup in the core.
3.4.2 DC Magnetization Curve
We know from Biot-Savart’s law that a current carrying conductor produces magnetic field.
“Magnetic field strength” H is proportional to the current which produces the field. From Ampere’s
71
Circuital law, it can be proved that H is proportional to current I. If a current carrying coil produces
magnetic flux which traverses an average length of l in complete flux path,
Hl = NI
(4)
In a magnetic circuit, this field is represented by magnetomotive force. It is analogous to the
electromotive force in electrical circuit. This field is responsible to “set up” certain flux, which in turn gives
rise to certain flux density B. Note that, here H is cause and B is its effect.
The amount of flux which can be setup in a material is determined by an inherent property of the material,
called as permeability, denoted by µ
B = µH
(5)
Let us consider materials used in the laminations of transformers. They are called ferromagnetic
materials. A piece of ferromagnetic material is composed of several “domains”. In each domain,
magnetic moments of all atoms are aligned in one direction. In general, the domains are randomly
oriented. When external magnetic field H is applied to a material, all the domains align in a particular d
Figure 33: DC magnetization curve
irection, setting up “net flux”
72
in the material. Due to domain alignment B (i.e. the magnitude of B) increases. However, after a certain
value of B, the slope of B − H curve starts reducing as shown in Fig. 1; O − S1 represents the linear region
and S1 − S2 represents the “saturation region”. Note that dB dH O−S1 > dB dH S1−S2 (6) 1
In other words, for same increment in B, one has to apply more excitation in saturation region than in
linear region. This is called as DC Magnetization Curve as both B and H have same sign. It is interesting to
see what hapens when the external magnetic “excitation” is removed or reduced to zero. Discussion in
the following section, applies to this case and also the case of AC circuits in general [17].
3.4.3 Hysteresis Loop
Removing external magnetic field is equivalent to reducing H from Hmax to 0. Due to this, the domains
which were aligned in the direction of external field, “become free” of the external magnetic force.
However, now they do not attain completely random orientation as they had at (B = 0, H = 0). Some
domains maintain the direction of external magnetic field. This results in remnant magnetic flux density
Br. In short, while H traverses the trajectory 0 − Hmax − 0; magnetic flux density B traverses 0 − Bmax −
Br, as shown in Fig. 2. In order to reduce flux density to zero we have to apply external magnetic field in
the opposite direction or on the negative H−axis. If external field is increased in the opposite direction,
the behavior of magnetic material is seen analogous to that of the positive quadrant. Complete B − H
curve for is shown in Fig. 2. It is also called as “Hysteresis loop1” traced by the flux density in the material.
We cannot “measure” B and H directly. Further if we have transformer, we only have terminal
measurements at our disposal. Hence, it is required to “process” the signals to get values of B and H. From
Faraday’s law,[16]
V = N dφ/ dt
(7)
73
Also, from equation 2, B is directly proportional to flux φ. A signal proportional to B can be obtained by
integrating the voltage signal. The voltage can be integrated approximately by using an RC circuit. Care
should be taken in the choice of R and C values. The transfer function of the circuit is given by
Vc(s)/ Vin(s) = G(s) = 1/ 1 + sτ
Figure 34: Hysteresis loop
The time constant τ = RC should be chosen such that, in frequency domain (1 + jωτ ) ≈ jωτ 1The term
Hysteresis is used for a system which has memory or causal systems. In this case, the material remembers
last value of applied field in terms of B. 2[17]
Transformer under test current shunt to power scope to power scope
74
Figure 35: Connection diagram of circuit to trace B − H curve measurement
Equation 4 tells that H is proportional to current. The two signals can be given to two channels of a digital
storage oscilloscope. B − H curve of the material can be seen by plotting using Lissajous2 plot settings of
the oscilloscope
3.3.4 B-H curve for ferrite 77 material, core which have used in all prototypes in our toroidal
transformer design.
In figure 36, major curve of B-H plots for core material 77 which we have used in our transformers.
Which have been carried out on very high current at saturated situation. The magnetic strength
(figure 37) of an electromagnet depends upon the number of turns of the coil, the current flowing
through the coil or the type of core material being used. In our experiments, we have used same
core material(ferrite 77 material), number of turns and same power supply with same nonlinear
load. Therefore for transformers core material B-H curve could be major to minor loops (Figure
38) according listed parameters above.
75
Figure. 36 B-H curve
Figure 37. Initial permeability vs H
76
Figure 38 Major to minor loops of BH curve for transformer core material
References
[5] R. M. V. Del, B. Poulin, P. T. Feghali, D. M. Shah, and R. Ahuja, Transformer Design Principles—With
Application to Core-Form Power Transformers. New York: Gordon and Breach, 2001.
[6] M. Heathcote, J & P Transformer Book, 12th ed. London, U.K.: Butterworth–Heinemann, 1998.
[7] M. van der Veen, Modern High-end Valve Amplifiers: Based on Toroidal Output Transformers.
Dorchester, U.K.: Elektor Electronics Publishing, 1999.
[8] A. A. Halacsy, “Reactance and eddy current loss in toroidal transformatoric devices-II,” AIEE Trans.
Power App. Syst, vol. 81, no. 3, pp. 1017–1019, Apr. 1962.
[9] R. Prieto, J. A. Cobos, V. Bataller, O. Garcia, and J. Uceda, “Study of toroidal transformers by means of
2D approaches,” presented at the IEEE 28th Ann. Power Electron. Specialists Conf., St. Louis, MO, Jun.
22–27, 1997.
[10] R. Prieto, V. Bataller, J. A. Cobos, and J. Uceda, “Influence of the winding strategy in toroidal
transformers,” in Proc. IEEE 24th Annu. Conf. Ind. Electron. Soc., Sep. 1998, vol. 1, pp. 359–364.
[11] J. P. Myers, K. A. Weaver, W. R. Wieserman, and U. Poulsen, “O cores—A new approach,” in Proc.
Elect. Insul. Conf. Elect. Manuf. Coil Winding Technol. Conf., Sep. 23–25, 2003, pp. 193–198.
77
[12] P. Gómez, F. d. León, and I. Hernández, “Impulse response analysis of toroidal core distribution
transformers for dielectric design,” IEEE Trans. Power Del., vol. 26, no. 2, pp. 1231–1238, Apr. 2011.
[13] IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power
Systems, IEEE Std. 242-1986, Feb. 1986.
[14] “Comsol Multiphysics, AC/DC User’s Guid,” Comsol AB Group, 2006, pp. 1–156. [15] A. Goldman,
Handbook of Modern Ferromagnetic Materials. Norwell, MA: Kluwer, 1999, vol. I, pp. 64–135.
[15] A. E. Fitzgerald, C. Kingslay, and S. Umans, Electric Machinery. New Delhi: Tata McGraw Hill, 2002
[16] Methods for determining the magnetic properties of magnetic steel sheet and strip with 25 cm
Epstein frame, European Commission Std. 118-87, 1988. [Online]. Available:
http://bookshop.europa.eu/en/euronorm-118-87-pbCB4887670/
[16] Standard Test Method for Alternating-Current Magnetic Properties of Materials at Power
Frequencies Using Wattmeter-Ammeter-Voltmeter Method and 25-cm Epstein Test Frame, ASTM
International Std. A343/A343M
Chapter 4
TEST PLATFORM
4.1. High Frequency Toroid Transformer’s Parasitic Capacitance Minimization for Standalone
solar Photovoltaic (PV) High-Frequency Link-Based Medium Voltage (MV) Inverter
4.1.1 Renewable Energy Source On and Off Grid System
78
Figure 39. Renewable Energy Source On and Off Grid System
4.1.2 Circuit operation
A single-phase half bridge (10 kHz) is comprised of two power MOSFET (IRF 250), S1 and S2,
which are driven by a DSP F28335 chip to generate a pulse width modulated waveform and
feedback diodes, D1 and D2. These are called Freewheeling diodes with two DC bus capacitors to
stabilize the DC voltage. Two-stage power conversions by the frequency transformer. High
frequency operation is possible at the first DC/DC stage and at the second stage modified
amplitude of converted high frequency AC voltage by high frequency transformer secondary,
which is connected to high frequency rectifier AC/DC, and an output inverter, which converts the
DC voltage to the required frequency AC voltage in the case of utility grid 50/60 Hz.
79
Figure 40: Circuit layout for PV high frequency based inverter system.
4.1.3 Calculation of the Toroid Transformer Inter-Winding Capacitance
The general structure (2D, 3D and flux flow in core) of the four designed transformer’s prototypes
under test are illustrated in the fabrication section In this section, prototype transformer
calculations were carried out for inter-winding capacitance. Figure 9 shows the conceptual
structure of case 1 and case 2 transformer prototypes for inter-winding capacitance calculation.
Likewise, the capacitance for other prototypes can be evaluated in a similar manner.
80
Figure 41. Toroidal transformer with 1800 sectored winding, Conceptual presentation of transformer
prototypes from left to right conventional and modified
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 4 cases.
The distance between the inner secondary winding and inner primary windings can be expressed
as follows:
๐œ‹
๐œ‹๐‘–
๐‘Ÿ1๐‘–๐‘›,๐‘– = √๐‘Ÿ1 2 + ๐‘Ÿ2 2 − 2 ๐‘Ÿ1 ๐‘Ÿ2 cos( 2 + ๐‘› )
๐‘
(4)
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 ๐‘Ÿ3 and ๐‘Ÿ4 values are the same, as
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secondary winding is wounded on the ferrite core and core dimension is same for all transformer prototypes.
๐‘Ÿ1 and ๐‘Ÿ2 values will vary with respect to each case, e.g., ๐‘Ÿ1, for case 4 (๐‘Ÿ1,4) and case 2 (๐‘Ÿ1,2) will be same,
but they are less than case 3 (๐‘Ÿ1,3 ) which in turn is less than case 1 (๐‘Ÿ1,1). The details of ๐‘Ÿ1 , ๐‘Ÿ2 , ๐‘Ÿ3 , ๐‘Ÿ4 for the
four different configurations are given as follows:
A:
๐‘Ÿ1,4 = ๐‘Ÿ1,2 < ๐‘Ÿ1,3 < ๐‘Ÿ1,1
B:
๐‘Ÿ2,1 < ๐‘Ÿ 2,3 < ๐‘Ÿ2,2 = ๐‘Ÿ2,4
C:
๐‘Ÿ3,1 = ๐‘Ÿ3,2 = ๐‘Ÿ3,3 = ๐‘Ÿ3,4
D:
๐‘Ÿ4,1 = ๐‘Ÿ4,2 = ๐‘Ÿ4,3 = ๐‘Ÿ4,4
The static capacitance between the inner primary and inner secondary is:
๐ถ1๐‘–๐‘›,๐‘– =
∈โˆ˜๐‘‘๐œ‹๐‘™1
2๐‘Ÿ1๐‘–๐‘›,๐‘–
=
∈โˆ˜๐‘‘๐œ‹๐‘™1
๐œ‹
๐œ‹๐‘–
2√๐‘Ÿ1 2 +๐‘Ÿ2 2 −2 ๐‘Ÿ1 ๐‘Ÿ2 cos( + )
2 ๐‘›
(5)
๐‘
where ∈โˆ˜ is the permittivity of free space, d is the diameter of the wire used for primary and
secondary windings and l1 is the overlapped length.
Assuming that the voltage potential distribution along the primary turn varies linearly,
๐‘‰๐‘ [๐‘–] = ๐‘›
๐‘–
๐‘ −1
๐‘‰๐‘
(6)
The total stored energy between the inner primary and secondary is,
1
๐ธ1๐‘–๐‘› = 2 ∑
๐‘›๐‘ −1
๐‘–=0
(๐ถ1๐‘–๐‘›,๐‘– ( ๐‘›
๐‘–
๐‘ −1
๐‘‰๐‘ )2 )
(7)
Similarly, the capacitance between the inner primary - outer secondary, outer primary - outer secondary,
and outer primary - outer secondary can be calculated. (4) – (7) can be used to find the capacitance and
energy for the other 3 cases as well (Table 4). The simulation was run on MATLAB to calculate the
capacitance in all four cases. For the sake of simplicity and to ignore the repetitive process of inter-winding
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capacitance calculations, only one winding in the same position of the secondary side is considered for all
4 cases. To see the effect of inter-winding capacitance, we choose 3 primary winding for 1800 conventional
and modified configurations instead of 116 and 6 primary winding for 3600 conventional and modified
configurations instead of 220.
Table 7: Detailed parameters of the transformer prototypes
Prototypes
Physical
Properties
Case 1
Copper
24AWG
24AWG
24AWG
24AWG
Primary Turns
116
116
220
220
Secondary
116
116
220
220
Ferrite
Ferrite
Ferrite
Ferrite
-77
-77
-77
-77
Ring
Ring
Ring
Ring
Case2
Case 3
Case 4
Wire standard
Turns
Core Material (Table 1)
Core shape
Permittivity (F/m)
8.85×10-12
(Air)
8.4190 ×10-12
(Air + PLA)
8.85×10-12
(Air)
Inner Radius(mm)
17.775
15.275
17.775
Outer Radius(mm)
30.5
32.5
30.5
83
8.419×10-12
(Air+PLA)
15.275
32.5
Primary Voltage(V)
24
24
24
24
Secondary Voltage(V)
~ 24
~ 24
~ 24
~ 24
1-30
1-30
1-30
1-30
๐’“๐Ÿ
17.265
14.765
16.755
14.765
๐’“๐Ÿ
30.5
32.5
31.01
32.5
๐’“๐Ÿ‘
17.265
17.265
17.265
17.265
๐’“๐Ÿ’
30.5
Frequency (kHz)
30.5
30.5
30.5
t can be seen from the Table 5 that the inter-winding capacitance would be highest for case 3, followed
by case 1, case 4 and case 2. These analytical calculations hold well with the experimental data for interwinding capacitance, which is shown in the next section.
Table 8: Theoretical analysis of all presented prototypes, Calculated energy, and inter-winding
capacitance
Case 1:
E1
E2
E3
E4
Etotal
Capacitanceeq (F)
Energy (J)
5.63×10-10
3.87×10-10
3.54×10-10
2.87×10-10
1.59×10-10
2.76×10-12
Percentage %
35.4
24.3
22.3
18
100
Case 2:
84
E1
E2
E3
E4
Etotal
Capacitanceeq
(F)
Energy (J)
5.31×10-10
3.74×10-10
3.66×10-10
2.94×10-10
1.57×10-9
2.72×10-12
Percentage %
33.9
23.9
23.4
18.8
100
E1
E2
E3
E4
Etotal
Capacitanceeq
(F)
Energy (J)
5.69×10-10
3.87×10-10
3.56×10-10
2.90×10-10
1.60×10-9
2.78×10-12
Percentage %
35.5
24.2
22.2
18.1
100
E1
E2
E3
E4
Etotal
Capacitanceeq
(F)
Energy (J)
5.29×10-10
3.73×10-10
3.73×10-10
3.00×10-10
1.57×10-9
2.73×10-12
Percentage %
33.6
23.7
23.7
19
100
Case 3:
Case 4:
4.1.4
Experimental Setup
The high-frequency transformer temperature and capacitive coupling - leakage inductance was
measured using a Fluke VT04A Thermometer and GWInstek LCR meter. The experiments were
conducted at constant ambient room temperature, on the high-frequency link of a 1kW half bridge
inverter. Two 38V, 350W standalone solar modules connected in parallel, which serves 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 450, 900, 1200, 1800,
2700, and 3600. Figure 10 presents a block diagram of the experimental setup. The input and output
85
waveforms of the transformer were stored, and the harmonic contents present in the waveform were
analyzed by Matlab-FFT.
86
Figure 42. Block diagram and real time setup for the testing process for prototypes PV high
frequency based medium voltage (MV- 24V) inverter systems
87
4.1.5 Result and Discussion
For the comparative analysis, we designed a conventional toroid transformer with the same 1800
and 3600 sector windings and with the same core dimension. The comparative experimental studies
stated that the proposed modified design succeeded in lowering the interwinding capacitance
(approximately 87%) and controlling temperature increase issues (less than 300) 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 to conventional designs.
Table 9: Voltage and current THD for all prototypes
Source
input
Voltage
(V)
Case
THDvoltage %
THDcurrent %
Primary
Secondary
Primary
Secondary
24
1
45.53
22.34
5.6
7.20
24
2
34.70
22.15
12.22
11.85
24
3
11.92
16.33
48.19
49.56
24
4
9.81
14.94
43.06
44.32
88
Toroidal transformer with 1800 sectored winding
Inter-winding Capacitance:
Large inter-winding capacitance causes a significant amount of common mode noise at highfrequency 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 conventional design.
Figure 43. Toroidal transformers at 1800 sectored winding, Parasitic Coupling Capacitance
comparison between the conventional and modified design of high-frequency link based inverter
systems.
Leakage Inductance: In a sectored wound transformer, when the winding covers only 1800
leakage flux path changes in the core. According to theory we expected the leakage inductance
to be higher in modified design when compared to conventional design due to the distance
between windings created by the PLA mold. However, the 3D printed mold using PLA filament
was mounted over the ferrite toroid core and secondary windings to completely encapsulate
them and provided scope to increase the mean length turn of the primary winding which is
89
required to reduce the leakage inductance. This theory is supported by experiment results [37].
Figure 44. demonstrates that modified design recorded less leakage inductance than
conventional design.
Figure 38. Toroidal transformers at 1800 sectored winding, Leakage inductance comparison
between the 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 that lowering the interwinding capacitance and harmonics distortion helped significantly
in controlling the temperature rise issue in the transformer
Figure 45. Toroidal transformers at 1800 sectored winding, Temperature comparison between
the conventional and modified transformer design
90
. 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
(๐‘1 ๐ผ1 = ๐‘2 ๐ผ2 ), 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 succeeded in minimizing the transformer self-capacitance by approximately 87%
compared with conventional designs.
Figure 46. Toroidal transformers at 360° sectored winding, parasitic coupling capacitance
comparison between the conventional and modified design of high-frequency link based MV
inverter systems.
Leakage Inductance: The leakage inductance and primary/secondary capacitance are mutually
exclusive and are governed by the distance between the windings and unwounded core.
91
Therefore, it is difficult to achieve both low capacitive coupling and a high degree of inductive
coupling in a power transformer. However, the magnetic core geometry and winding
arrangements have a large influence on self-capacitance and leakage inductance of the
transformer and because of the addition of a mold, it enables access to various types of winding
arrangements. Thus, the modified design has successfully lowered the inter-winding capacitance
and achieves the minimum difference between leakage inductance. The experimental results are
shown in Figure 47.
Leakage Inductance: The leakage inductance and primary/secondary capacitance are mutually
exclusive and are governed by the distance between the windings and unwounded core.
Therefore, it is difficult to achieve both low capacitive coupling and a high degree of inductive
coupling in a power transformer. However, the magnetic core geometry and winding
arrangements have a large influence on self-capacitance and leakage inductance of the
transformer. The addition of a mold enables access to various types of winding arrangements.
Thus, the modified design has successfully lowered the interwinding capacitance and the
minimum difference between leakage inductance. Experimental results are shown in Figure 41.
92
Figure 47. Toroidal transformers at 3600 sectored winding, Leakage inductance comparison of
modified and conventional design of high-frequency link based inverter systems
Temperature: Modified design shows significant control in temperature rise by lowering the
inter-winding capacitance and controlled leakage inductance over conventional designs (Figure
48).
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, 20pF, and 40pF, respectively. The toroidal transformer at 1800 sectored
winding has registered higher leakage inductance, which can be utilized in other topologies,
such as dual active bridge topologies. The experiments matched the analysis results well in the
circuit operation section, with the feasibility of the converter validated.
Figure 48. Toroidal transformers at 3600 sectored winding, Temperature comparison between
the conventional and Modified design of high-frequency link based MV inverter systems
93
Chapter 5
Conclusions
Overall, the MV inverter with the proposed modified transformer design has a minimized total
circuit input-output capacitance to approximately 20pF, whilst the temperature increase was kept
below 29.5°C, without using any extra circuitry or cooling agent. The modified design is
certainly a powerful solution to reduce the distortion in the waveform. This leads to an improved
power quality of renewable power sources and an increase in the operational lifetime of the
devices and loads involved in power systems. Hence, MV inverter with the modified design
transformer is more robust than other available power inverters of the same power rate. These
experimental measurements, which agree with the mathematical derivation, prove that the
transformer shape and winding arrangements have a huge impact on the inter-winding
capacitance and cannot be ignored in power inverters when power quality improvement is of
concern.
Finally, the overall result achieved with the prototype provides a very high resistance to the
common mode noise current caused by rapid voltage transients, which makes the MV inverter
feasible for renewable energy sources applications. For future research, a study of the optimal
design method on advanced prototypes with higher inductive coupling with more controlled
THD will be conducted.
94
๊ณ ์ฃผํŒŒ ์ „๋ ฅ ๋ณ€ํ™˜๊ธฐ์˜ ์ ์šฉ์„์œ„ํ•œ ํ† ๋กœ ์ด๋‹ฌ ๋ณ€์••๊ธฐ ์„ค๊ณ„ ์ตœ์ ํ™”
ํžˆ๋งŒ ์Šˆ
๋ถ€์‚ฐ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› ์ „๊ธฐ์ „์ž์ปดํ“จํ„ฐ๊ณตํ•™๊ณผ
์š”์•ฝ
๊ณ ์ฃผํŒŒ ๊ธฐ๋ฐ˜์˜ ์ธ๋ฒ„ํ„ฐ๋Š” ๋™๋ ฅ ์ „๋‹ฌ์„ ์œ„ํ•œ ์žฌ์ƒ ๊ฐ€๋Šฅ ์—๋„ˆ์ง€ ์›์œผ๋กœ ์‚ฌ์šฉ๋ฉ๋‹ˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ๊ณ ์ฃผํŒŒ
๋งํฌ ๋ณ€์••๊ธฐ์—์„œ ๋ฐœ์ƒํ•˜๋Š” ๊ถŒ์„  ๊ฐ„ ๋†’์€ ๊ธฐ์ƒ ์ปคํŒจ์‹œํ„ด์Šค์— ์˜ํ•œ ๊ณตํ†ต ๋ชจ๋“œ ๋…ธ์ด์ฆˆ ์ „๋ฅ˜์˜ ์ฆ๊ฐ€๋กœ
์ธํ•ด ์ „๋ ฅ ํ’ˆ์งˆ์ด ์ €ํ•˜๋ฉ๋‹ˆ๋‹ค. ์ด ๋น ๋ฅธ ์ „์•• ๊ณผ๋„ ์‘๋‹ต์€ ๊ณ ์กฐํŒŒ ์™œ๊ณก ๋ฐ ๋ณ€์••๊ธฐ ๊ณผ์—ด๋กœ ์ด์–ด์ง€๋ฉฐ,
์ด๋Š” ์ „์› ๊ณต๊ธ‰ ์žฅ์น˜ ๊ณ ์žฅ ๋˜๋Š” ๊ธฐํƒ€ ์—ฌ๋Ÿฌ ๊ฐ€์ง€ ์ „๊ธฐ ์œ„ํ—˜ ์š”์ธ์„ ์œ ๋ฐœํ•ฉ๋‹ˆ๋‹ค. ์ด ๋…ผ๋ฌธ์€ ์ ˆ์—ฐ
์ „์› ๊ณต๊ธ‰ ์žฅ์น˜์— ๋Œ€ํ•œ ๊ธฐ์กด ๋ฐ ์ œ์•ˆ ๋œ ํ† ๋กœ์ด๋“œ ๋ณ€์••๊ธฐ ์„ค๊ณ„ ๊ฐ„์˜ ๋น„๊ต ์—ฐ๊ตฌ๋ฅผ ์ œ์‹œํ•ฉ๋‹ˆ๋‹ค.
ํ•˜ํ”„ ๋ธŒ๋ฆฌ์ง€ ๊ณ ์ฃผํŒŒ (10 kHz) ์†Œ์šฉ๋Ÿ‰ DC-AC ์ธ๋ฒ„ํ„ฐ๊ฐ€ ์ „์›๊ณผ ํ•จ๊ป˜ ์„ค๊ณ„๋˜์—ˆ์Šต๋‹ˆ๋‹ค. 680 W ํƒœ์–‘
๊ด‘ ๋ชจ๋“ˆ ์žฌ์ƒ ์‹œ์Šคํ…œ์ด ๊ตฌ์ถ•๋˜์—ˆ์Šต๋‹ˆ๋‹ค. Matlab-FFT ๋ถ„์„์„ ์‚ฌ์šฉํ•œ FEM ์‹œ๋ฎฌ๋ ˆ์ด์…˜์„ ์‚ฌ์šฉํ•˜์—ฌ
95
์ฝ”์–ด์˜ ์ž์† ๋ถ„ํฌ๋ฅผ ๊ฒฐ์ •ํ•˜๊ณ  ์ด ๊ณ ์กฐํŒŒ ์™œ๊ณก (THD)์„ ๊ณ„์‚ฐํ–ˆ์Šต๋‹ˆ๋‹ค. GWInstek LCR ๋ฏธํ„ฐ์™€ Fluke
VT04A ๋Š” ๋„ค ๊ฐœ์˜ ๋ณ€์••๊ธฐ ํ”„๋กœํ†  ํƒ€์ž… ๋ชจ๋‘์—์„œ ๊ถŒ์„  ๊ฐ„ ์ •์ „ ์šฉ๋Ÿ‰๊ณผ ์˜จ๋„๋ฅผ ์ธก์ •ํ–ˆ์Šต๋‹ˆ๋‹ค.
ํ† ๋กœ์ด๋“œ ํ˜• ์ฝ”์–ด ๋ณ€์••๊ธฐ์˜ ์ˆ˜์ • ๋œ ์„ค๊ณ„๋Š” ๋ƒ‰๊ฐ์ œ ๋˜๋Š” ์™ธ๋ถ€ ํšŒ๋กœ๋ฅผ ์‚ฌ์šฉํ•˜์ง€ ์•Š๊ณ ๋„ ์˜จ๋„
์ƒ์Šน์— ๋Œ€ํ•œ ์ €ํ•ญ๋ ฅ์„ ํ–ฅ์ƒ์‹œํ‚ค๋ฉด์„œ ๊ธฐ์ƒ ์ปคํŒจ์‹œํ„ด์Šค๋ฅผ 87 % ์ค„์ž…๋‹ˆ๋‹ค. ์ ‘๊ทผ๋ฒ•์˜ ํƒ€๋‹น์„ฑ์„
ํ™•์ธํ•˜๊ธฐ ์œ„ํ•ด ๊ถŒ์„  ๊ฐ„ ์šฉ๋Ÿ‰์˜ ์ˆ˜ํ•™์  ์œ ๋„์™€ ํ•จ๊ป˜ ์‹คํ—˜์„ ์ˆ˜ํ–‰ํ–ˆ์Šต๋‹ˆ๋‹ค.
96
Acknowledgements
I would like to thank all whom had direct or indirect role towards my success in various
levels. First and foremost, I would like to express utmost appreciation and gratitude to Prof. HeeJe Kim, my supervisor, for his meritorious guidance, endless support and encouragement
throughout the course of study. His meticulous attentions to details, incisive but constructive
criticisms and insightful comments have helped my research career and personality. I am
thankful to him for the great amount of freedom I was granted during my work and the dedicated
support for new projects. With deep sense of gratitude, I would like to express my words of
gratitude to Dr. Sunkara Srinivasa Rao and Tulsi Verma for their moral support and help me in
settle down, when I came down firstly to this beautiful land of Busan, South Korea and adjust to
research environment of Pusan National University.
Besides my advisor, I would like to thank the rest of my thesis committee: Prof. JangMok Kim, Prof. Sung-shin Kim, Prof. Kandasamy Prabakar and Prof. Jin-Ahn Jeon, for their
insightful comments and encouragement, but also for the hard question which incented me to
widen my research from various perspectives
My sincere thanks also goes to Dr. H.Singh Dr. Sathis Kumar, Dr. Dinah Punnoose and
Dr. Chandu V. V. Muralee Gopi, Prof Arinadam Biswas and Prof K.N. Hui, who inspired and
supported me throughout my Ph. D. course . Without they precious support it would not be
possible to conduct this research.
97
I wish to express my boundless thanks to my lab members Dr. Thao, Dr. Sathishkumar,
Do-Hyun Kim, Qiu, Anada, Naresh, Saif, Umair, Min-Soo Kim, , Vamsi@Hima, Umair, Sadam
Hussain, Ishfaq, Imran Khan, Duraga, Sarvar,Altaf, Sai, Ronak,Guru, Jason Park, Cho-In-Ho,
Young-Seok Lee, Eswar@Anitha, Gopi, Bala, Rajendra, Devi, Aravinddhu, Raj Mohan,
Archana, Vivek, Malar, Nagaraju, and Prasanna, Adil, Kamran , Waquar etc.
Finally, I am very happy to dedicate this PhD and would like to thank to my all foster
families few names Mr. Ramesh Chandra and Ms. Sarla Bai,Mr. Kailash Shohani, Maureen and
Rog, David and Carol. And friends who became more than family in this Ph. D. experience few
names (alphabetic order) Anand Muthu, Bali, Callum, Do haa ann.(Rick), Gaurav, Karthick,
Raihan Choudhary, Sathis Kumar and Younseok Sa. My deep gratitude for their support during
my studies and I could not ask for a better family member like you people. They make me
understand my capabilities thanks for your affection and support given in all the difficulties
which I have faced during my PhD course. I think thanks is not enough to them, but I can keep
you people in my heart forever.
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