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Transcript of The Thesis Industrial Electronics Applications (Design and Simulation of Coreless Induction Furnace)
ALEXANDRIA UNIVERSITY FACULTY OF ENGINEERING
INDUSTRIAL ELECTRONICS APPLICATIONS (DESIGN AND SIMULATION
OF
CORELESS INDUCTION FURNACE)
A Thesis
Presented to the Graduate School of
Faculty of Engineering, Alexandria University
In Partial Fulfillment of the
Requirements of the Degree
Of
Master of Science
In
Electrical Engineering
By
Eng. Ahmed Mohamed El-Sharkawy
2008
INDUSTRIAL ELECTRONICS APPLICATIONS
(DESIGN AND SIMULATION
OF
CORELESS INDUCTION FURNACE)
Presented by
Eng. Ahmed Mohamed El-Sharkawy
For The Degree of Master of Science
In
Electrical Engineering
Examiners' Committee Approved
Prof. Dr.: Mohamed Abdullah Al-Khazendar ………………
Head of Electrical Department
Faculty of Engineering, Tanta University
Prof. Dr.: Mohamed Magdy Ahmed ………………
Electrical Department
Faculty of Engineering, Alexandria University
Prof. Dr.: Mohamed Yousry Gamal El-Deen ………………
Electrical Department
Faculty of Engineering, Alexandria University
Prof. Dr.: Hossam Mohamed Fahmy Ghanem ………………
Vice dean of graduated studies and research Faculty of Engineering, Alexandria University
Date: 10/5/2008
Advisors' Committee
Prof. Dr. Mohamed Magdy Ahmed ….…………………
Dr. Mahmoud Ibrahim Masaoud ……….……………
i
Acknowledgment First of all, thanks to Allah for giving me the will, the patience and the
determination that helped me to finish this thesis.
I would like to express my sincere appreciation to my supervisor
Prof. Dr. Mohamed Magdy Ahmed for his much appreciated support, valuable
suggestions, constant guidance and patience. Also I would like to thank
Dr. Mahmoud Msaoud for his supervision.
Finally, I'm greatly indebted to my parents, my wife, and my mother in law for
their continuous support and encouragement.
ii
ABSTRACT Induction heating is widely used in metal industry because of its good heating
efficiency, high production rate, and clean working environments. The development of
high-frequency power supplies provided means of using induction furnaces for melting
metals in continuous casting plants. Conventional induction furnaces are usually of the
coreless or channel type.
This thesis deals principally with the design of coreless induction furnaces. Both
mechanical and electrical requirements for induction furnace have been presented. The
mechanical aspect gives consideration to the geometrical parameters while the electrical
aspect deals with the furnace power requirement to make it functional. A model for an
induction furnace has been introduced. Two power supply systems using series and
parallel resonant inverters to feed the coreless induction furnaces have been presented.
MATLAB computer programs to simulate the complete systems for both open loop and
closed loop systems have been created. To verify the design and the simulation results a
comparison between simulation and actual results for both types of inverters has been
done. A full investigation has been presented for both types of inverters in order to
compromise between them.
iii
Table of Content
Content Page Acknowledgement i Abstract ii Table of Content iii List of Tables v List of Figures vi CHAPTER 1 Introduction 1 1.1 Applications of induction heating 1 1.2 Induction Furnaces’ Historical Perspective 2 1.3 Types of Induction furnaces 3 1.4 Thesis Objective 3 1.5 Thesis Layout 4 CHAPTER 2 Induction Heating 5 2.1 Introduction 5 2.2 Basics of induction heating 6 2.3 Factors affecting induction heating 7
a) b)
Electromagnetic induction Skin effect
8 9
2.4 Coreless induction furnace 10 2.4.1 System components 13
CHAPTER 3 Design of Coreless Induction Furnace 14 3.1 Introduction 14 3.2 Selection of furnace size, and power rating 15 3.3 Selection of induction frequency 16
3.3.1 Induced current depth 16 3.3.2 Meniscus height and metal stirring 18
3.4 Design analysis 21 3.4.1 Geometrical parameters 21 3.4.2 Heat energy parameters 22 3.4.3 Electrical parameters 23
CHAPTER 4 Power Supplies in induction melting systems 29 4.1 Introduction 29 4.2 Solid state power converters 30
4.2.1 AC to DC rectifier 31 4.2.1.1 Effect of static converters on power lines 32
iv
4.2.2 DC to AC medium frequency inverter 35 4.2.2.1 Switching losses 35 4.2.2.2 Resonant pulse converters 36
4.3 Current fed inverter with parallel capacitor bank 40 4.3.1 Thyristor's turn-off time 41
4.4 Voltage fed inverter with series capacitor bank 43 4.5 DC filter circuit 44 CHAPTER 5 Simulation and Results 46 5.1 Introduction 46 5.2 Furnace design 46
5.2.1 Geometrical parameters 46 5.2.2 Heat energy parameters 48 5.2.3 Electrical parameters 48
5.3 Simulation parameters 49 5.4 Parallel resonant inverter 49
5.4.1 Open loop system 50 5.4.2 Closed loop system 54 5.4.3 Comparison between simulation and actual results 56
5.5 Series resonant inverter 58 5.5.1 Open loop system 59 5.5.2 Closed loop system 63 5.5.3 Comparison between simulation and experimental results. 65
5.6 Comparison between parallel and series resonant inverter systems.
67
CHAPTER 6 Conclusion and Future Work 71 6.1 Conclusion 71 6.2 Future Work 72
References 73 Arabic summary 75
v
List of Tables
Table PageTable 4.1 Power factor of full wave rectifiers 33 Table 5.1 Thermal parameters of iron 46 Table 5.2 Geometrical parameters of the furnace 47 Table 5.3 Heat energy parameters of the furnace 48 Table 5.4 Electrical parameters of the furnace 49 Table 5.5 Results of open loop system simulation 50 Table 5.6 Comparison between simulated and actual parameters 57 Table 5.7 Comparison between simulated and actual values of furnace
voltage and inverter current for different values of power 58
Table 5.8 Results of open loop system simulation 59 Table 5.9 Electrical parameter of the prototype furnace 66 Table 5.10 Comparison between simulated and experimental values of
furnace voltage and inverter current at different frequencies 66
Table 5.11 Comparison between parallel and series resonant systems' consumed power, efficiency and THD
68
Table 5.12 Comparison between parallel and series resonant systems 70
vi
List of Figures
Figure PageFig. 2.1 The direction of the electromagnetic field produced around a
wire carrying an alternating current 6
Fig. 2.2 Eddy current distributions in the conductive material 6 Fig. 2.3 The resulting induced circulating current 7 Fig. 2.4 a) Equivalent circuit of transformer
b) Secondary short c) Induction heating basis
8 8 8
Fig. 2.5 Distribution chart of current density and skin depth 10 Fig. 2.6 Effect of frequency on the current depth. 10 Fig. 2.7 Typical solenoid induction coil used in a coreless induction
furnace 11
Fig. 2.8 The electromagnetic field generated by a solenoid induction coil a) with no load in the furnace and b) with a load inside the furnace
12
Fig. 2.9 Plot of the electromagnetic field and the energy transferred to the load.
12
Fig. 2.10 An overview of the typical components of a coreless induction furnace system.
13
Fig. 2.11 Block diagram of induction furnace system. 13 Fig. 3.1 Typical Components of a coreless Induction Furnace 14 Fig. 3.2 Induced current depth do in a cylindrical load with diameter D 16 Fig. 3.3 Typical induced current depth Vs frequencies 17 Fig. 3.4 The ratio D/do Vs the efficiency 18 Fig. 3.5 Meniscus height to the diameter of melt 18 Fig. 3.6 Depth of current penetration 19 Fig. 3.7 Light and heavy stirring 20 Fig. 3.8 Relation between the induction frequency and furnace size for
different melting conditions 21
Fig. 3.9 A melted cylindrical load 24 Fig. 3.10 The equivalent circuit of the furnace with load based on
transformer concept 26
Fig. 4.1 Principle diagram of line frequency melting furnace 29 Fig. 4.2 Block diagram of a medium frequency melting system 30 Fig. 4.3 Uncontrolled six-pulse rectifier 31 Fig. 4.4 Uncontrolled twelve-pulse rectifier 32
vii
Fig. 4.5 Amplitude Spectrum of the Twelve Pulse Rectifier 33 Fig. 4.6 Voltage notch due to phase current switchover in a) full wave
rectifier and b) phase controlled bridge 34
Fig. 4.7 Single phase full-bridge inverter. 35 Fig. 4.8 Resonant Circuits a) the series resonant circuit and b) the
parallel resonant circuit 36
Fig. 4.9 Frequency Curve of series resonant inverter 38 Fig. 4.10 Frequency Curve of parallel resonant inverter 39
Fig. 4.11 Medium frequency melting system utilizing current-fed converter
40
Fig. 4.12 Parallel resonant inverter with load commutation 41 Fig. 4.13 a) The phasor diagram of the parallel resonant inverter, and
b) The equivalent circuit 42 42
Fig. 4.14 SCR's turn off time Vs the operating frequency, fo = 250 Hz 43 Fig. 4.15 Medium frequency melting system with full bridge voltage fed
converter 44
Fig. 4.16 a) DC-voltage filter circuit and b) DC-current filter circuit 45 Fig. 5.1 The Geometric shape of the furnace 47 Fig. 5.2 The dimensions of conducting tube 48 Fig 5.3 Open Loop Parallel resonant inverter system 50 Fig. 5.4 Inverter current and furnace voltage at different firing angles 51 Fig. 5.5 Inverter current and furnace voltage at α=0° 51 Fig. 5.6 The DC voltage (Vdc) at α=0° 52 Fig. 5.7 Inverter current, furnace voltage and Vdc at α=30° 52 Fig. 5.8 Inverter current, furnace voltage and Vdc at α=60° 52 Fig. 5.9 Inverter current, furnace voltage at f=254 Hz 53 Fig. 5.10 Output power at fo and at f=254 Hz 53 Fig. 5.11 Reactive power at fo and at f=254 Hz 54 Fig. 5.12 Configuration of the closed loop system 54 Fig. 5.13 The output power compared with the reference power. 55 Fig. 5.14 The inverter current response for step change in the reference
power. 55
Fig. 5.15 The furnace voltage response for step change in the reference power
56
Fig. 5.16 The firing angle response for step change in the reference power
56
Fig. 5.17 The Single line diagram of ABB induction furnace 57
viii
Fig. 5.18 Furnace voltage and inverter current a) actual b) simulation 58
Fig. 5.19 Open Loop Series Resonant Inverter System 59 Fig. 5.20 The inverter current and voltage at different operating
frequencies (fo =250 Hz). 60
Fig. 5.21 The output power (Po) and total impedance (Z) at different operating frequencies.
60
Fig. 5.22 The inverter current and voltage at f=fo=250 Hz. 61 Fig. 5.23 The inverter current and voltage at f=246 Hz. 61 Fig. 5.24 Output power at fo and at f=246 Hz 62 Fig. 5.25 Reactive power at fo and at f=246 Hz 62 Fig. 5.26 VDC at two different capacitor values 62 Fig. 5.27 Pout at two different capacitor values 63 Fig. 5.28 Configuration of the closed loop system 63 Fig. 5.29 The output power compared with the reference power. 64 Fig. 5.30 Phase shift change with the change in the reference power. 64 Fig. 5.31 The reactive power response to the change in the reference
power. 65
Fig. 5.32 The single line diagram of the prototype furnace. 65 Fig. 5.33 Typical setup of the prototype furnace. 66 Fig. 5.34 Inverter voltage and current at resonant frequency
a) experimental b) simulation 67
Fig. 5.35 Inverter voltage and current at frequency lower than fo a) experimental b) simulation
67
Fig. 5.36 Supply current and voltage of the parallel resonant system 69 Fig. 5.37 Supply current and voltage of the series resonant system 69 Fig. 5.38 Output power of a) series resonant system and b) parallel
resonant system at different values of frequency 69
CHAPTER 1 INTRODUCTION
1
CHAPTER 1
INTRODUCTION Induction heating is a non-contact heating process which is used to bond, harden or
soften metals or other conductive materials. For many modern manufacturing processes,
induction heating offers an attractive combination of speed, consistency and control.
Induction heating has a good heating efficiency, high production rate and clean working
environments.
The basic principles of induction heating have been understood and applied to
manufacturing since the 1920s. During World War II, the technology developed rapidly to
meet urgent wartime requirements for a fast, and reliable process to harden metal engine
parts. More recently, the focus on lean manufacturing techniques and emphasis on
improved quality control have led to a rediscovery of induction technology, along with the
development of precisely controlled solid state induction power supplies. In the most
common heating methods, a torch or open flame is directly applied to the metal part, but
with induction heating, heat is actually "induced" within the part itself by circulating
electrical currents.
Since heat is transferred to the product via electromagnetic waves and the part
never comes into direct contact with any flame, there is no product contamination and
when properly set up, the process becomes very repeatable and controllable [1].
1.1 APPLICATIONS OF INDUCTION HEATING Typical applications of induction heating are melting of metals, heating of metals,
brazing and welding and all sorts of surface treatments. However, by using electric
conductive recipients (e.g. graphite) also other materials like glass can be heated.
Brazing is an assembly technique where two pieces are joined together by means of
a third material that is brought to its melting temperature. In the connection zone both
pieces are heated up to a temperature higher than the melting temperature of the third
material. Induction is frequently applied because of the precise localization of the heating.
Moreover the heating happens very quickly which makes that the oxidation or structural or
compositional changes can be controlled. Brazing under inert atmosphere is possible.
Induction heating is suited for high production speeds in automated production lines.
CHAPTER 1 INTRODUCTION
2
Surface hardening techniques are suitable for steel with a carbon percentage of at
least 0.3 %, where the work piece is heated up to approximately 900°C and after that it is
chilled. This technique is used for the hardening of gear wheels, crankshafts, valve stems,
saw blades, spades, rails, and many other things. The inductive process has the advantage
that the treatment can be localized very accurately. Moreover, the chemical composition of
the surface layer doesn’t change, which is the case for other surface hardening techniques.
Because of the selective heating, less energy is required than for a complete heating of the
product and distortion can be avoided. Typical values for inductive hardening are high
power density (1.5 - 5 kW/cm²) and short treatment time (2 seconds). Inductive hardening
is especially applied in automated production processes with sufficient production volume.
With induction heating, a constant and high production quality can be reached. The energy
consumption and the production losses are lower than for conventional techniques.
Induction furnaces are used extensively in the metal industry for melting of metals
and as holding furnaces. An induction coreless furnace essentially consists of a crucible
with refractory lining, that contains the material to be melted and that is surrounded by the
water-cooled induction coil. There are applications at 50 Hz as well as mid-frequency
applications. The power range (up to 10 MW and more) and the specific power (up to 1200
kW/ton) are extremely high, therefore, the melting can occur very quickly. Low-frequency
induction crucible furnaces (50 Hz) are usually applied for big applications (large power
and large capacity), while Mid-frequency furnaces are rather used in smaller applications.
Mid-frequency furnaces offer more flexibility and are more compact. In general there is a
trend towards using mid-frequency furnaces at the expense of low-frequency furnaces [2].
1.2 INDUCTION FURNACES’ HISTORICAL PERSPECTIVE In the early nineteenth century, the phenomenon of induction heating was applied
to the experimental melting of metals. The early furnace consisted of circular hearth or
trough, which contained the molten metal of an annular ring. This formed a short circuited
single turn secondary winding of a transformer which was energized by a supply of
alternating current at normal line frequency. This design has inherent defects, such as
mechanical force set up by the current flowing in the molten metal which tended to cause
contraction and could result in the interruption of the current, thereby posing operational
difficulties. This effect was called ‘pinch effect’ [3], and a lot of attempts to solve it were
not successful until the early of 1900’s, when Ajax Wyatt removed the difficulty by
CHAPTER 1 INTRODUCTION
3
placing the secondary channel in the vertical plane. The weight of the metal in the bath was
then sufficient to overcome the mechanical forces, which caused the pinch effect.
It was later that a new approach was made by E. F. Northrup, who substituted a
crucible containing the metal charge in place of the channel surrounded with a multi-turn
coil through which current was passed at high frequency [4].
The developments of these types of furnaces were extremely rapid, and many
hundreds of thousands of kilowatts of capacity are installed throughout the world today.
1.3 TYPES OF INDUCTION FURNACES There are two types of Induction furnaces; coreless induction furnace and channel
induction furnace. Coreless induction furnace is the concern of this thesis and was briefed
in section (1.1). Channel induction furnace is mainly used as holding furnace which is used
as reservoir for melted metals, keeping and controlling the temperature of the melted
metals [5].
An investigation was done on a novel configuration for an induction melting
furnace which is a combination of conventional channel and coreless induction furnaces
[6].
1.4 THESIS OBJECTIVE This thesis discusses the induction heating principles and applications. Coreless
induction furnace is considered to be one of induction heating important applications in
industry.
The main objective of this thesis is to design and simulate a complete system of a
coreless induction furnace which consists of the furnace and its power supply (rectifier, dc-
link and inverter). Both series and parallel resonant inverters are used to supply the electric
power to the induction furnace. The thesis studies both inverters in order to compromise
between them.
1.5 THESIS LAYOUT The thesis consists of six chapters that describe the design of a coreless induction
furnace and simulate the complete system using a MATLAB program. The organization is
as follows:
Chapter 1, Introduction.
CHAPTER 1 INTRODUCTION
4
Chapter 2, Induction heating. This chapter presents a detailed discussion of
induction heating, its basics, and the factors affecting it. Later, an introduction about
coreless induction furnace is introduced, and then the components of the induction furnace
system are presented.
Chapter 3, Design of coreless induction furnace. In this chapter factors that
affecting the design of the furnace are discussed. These factors include induced current
depth, metal stirring, meniscus height and the operating frequency. After this discussion,
the design analysis of the furnace is explained where the geometrical, energy and electrical
parameters of the furnace are determined.
Chapter 4, Power supplies in induction melting systems. This chapter discusses the
types of power supplies of the coreless induction furnace system, and then solid state
converters are discussed in details. The current fed inverter and the voltage fed inverter are
presented as they are the most common configurations used in industry.
Chapter 5, Simulation and results. In this chapter the design procedure that was
introduced in the previous chapters is implemented. MATLAB programs are introduced to
simulate the complete system. The simulation results of the current fed inverter are verified
by comparing them with those of an actual system manufactured by ABB Company and
the simulation results of the voltage fed inverter are verified by comparing them with those
of a prototype furnace that exists in the laboratory of the faculty of engineering. The
simulation results of the parallel resonant inverter are discussed first, then the results of the
series resonant inverter. Finally a comparison between both types is introduced.
Chapter 6, Conclusion and future work. In this chapter a conclusion of the work is
presented with some recommendations for the future work.
CHAPTER 2 INDUCTION HEATING
5
CHAPTER 2
INDUCTION HEATING
2.1 INTRODUCTION
All induction heating applied systems are developed using electromagnetic
induction which was first discovered by Michael Faraday in 1831. Electromagnetic
induction refers to the phenomenon by which electric current is generated in a closed
circuit by the fluctuation of current in another circuit placed next to it. The basic principle
of induction heating, which is an applied form of Faraday’s discovery, is the fact that AC
current flowing through a circuit affects the magnetic movement of a secondary circuit
located near it. The fluctuation of current inside the primary circuit provided the answer as
to how the mysterious current is generated in the neighboring secondary circuit. Faraday’s
discovery led to the development of electric motors, generators, transformers, and wireless
communications devices. Its application, however, has not been flawless. Heat loss, which
occurs during the induction heating process, was a major headache undermining the overall
functionality of a system. Researchers sought to minimize heat loss by laminating the
magnetic frames placed inside the motor or transformer. Faraday’s Law was followed by a
series of more advanced discoveries such as Lentz’s Law. This law explains the fact that
inductive current flows inverse to the direction of changes in induction magnetic
movement.
Heat loss, occurring in the process of electromagnetic induction, could be turned
into productive heat energy in an electric heating system by applying this law. Many
industries have benefited from this new breakthrough by implementing induction heating
for furnacing, and welding. In these applications, induction heating has made it easier to
set the heating parameters without the need of an additional external power source. This
substantially reduces heat loss while maintaining a more convenient working environment.
Absence of any physical contact to heating devices precludes unpleasant electrical
accidents. High energy density is achieved by generating sufficient heat energy within a
relatively short period of time.
The demand for better quality, safe and less energy consuming products is rising.
Products using induction heating include induction furnaces, surface hardening apparatus
and bonding of metals devices [7].
CHAPTER 2 INDUCTION HEATING
6
2.2 BASICS OF INDUCTION HEATING An understanding of the operating principals of induction furnaces, as one of the
important applications of induction heating, must begin with a basic understanding of
induction heating and how it works. In the most basic sense, consider a wire traveling
through space with an alternating current (I) flowing through it at some frequency (f). An
electromagnetic field is produced around the wire in a direction determined by the “right
hand rule” as shown in Fig. 2.1. Since the current is alternating, it will continuously
reverse directions in the wire, thus the electromagnetic field will alternate with the
direction of the current. When the generated changing electromagnetic field tries to pass
through an electrically conductive material, each line of flux produces a circulating eddy
current in the material as shown in Fig. 2.2.
Fig. 2.1 The direction of the electromagnetic field produced around a wire carrying an alternating current
Fig. 2.2 Eddy current distributions in the conductive material
CHAPTER 2 INDUCTION HEATING
7
The induced eddy currents generate an equal opposing field that cancels out the
field trying to pass through it. The result is no net field through the material. With the
amplitude and direction of each individual eddy current, the circulating currents within the
electrically conductive medium internally cancel each other out, and the net effect is an
induced current that flows around the perimeter of the material as shown in Fig. 2.3. The
induced current flows around the material results in the watt generation that heats the
material. The amount of watts generated in the material is equal to the actual current flows,
in amps, squared times the resistance of the path, in ohms, through which the current is
flowing. This is referred to as ( RI 2 ) heating [8].
2.3 FACTORS AFFECTING INDUCTION HEATING Induction heating is comprised of two basic factors: the electromagnetic induction,
and the skin effect. The fundamental theory of Induction heating, however, is similar to
that of a transformer. Figure 2.4 illustrates a very basic system, consisting of inductive
heating coil and current, to explain the electromagnetic induction and the skin effect.
Figure 2.4.a shows the simplest form of a transformer, where the secondary current
is in direct proportion to the primary current according to the turns ratio. The primary and
secondary losses are caused mainly by the resistance of windings and the link coefficient
between the two circuits is 1.
When the coil of the secondary is turned only once and short-circuited, there is a
substantial heat loss due to the increased load current (secondary current), this is
demonstrated in Fig. 2.4.b. Figure 2.4.c shows a system where the energy supplied from
the source is of the same amount as the combined loss of the primary and secondary. In
these figures, the inductive coil of the primary has many turns while the secondary is
Fig. 2.3 The resulting induced circulating current
Resulting induced circulating current
CHAPTER 2 INDUCTION HEATING
8
turned only once and short-circuited. The inductive heating coil and the load are insulated
from each other by a small aperture. As the primary purpose of induction heating is to
maximize the heat energy generated in the secondary, the aperture of the inductive heating
coil is designed to be as small as possible and the secondary is made with a substance
featuring low resistance and high permeability. Nonferrous metals undermine energy
efficiency because of their properties of high resistance and low permeability [7].
a) Electromagnetic Induction
As shown in Fig. 2.4.c, when the AC current (i) enters a coil with specific number
of turns (N), a magnetic field is formed around the coil according to Ampere’s Law.
∫ = NiHdl (2.1)
Where, H is the magnetic flux intensity.
An object put into the magnetic field causes a change in the velocity of the
magnetic movement. The density of the magnetic field wanes as the object gets closer to
the center from the surface. According to Lentz’s Law, the current generated on the surface
of a conductive object has an opposite relationship with the current on the inducting circuit
Fig. 2.4.a Equivalent circuit of transformer
Fig. 2.4.b Secondary short
Fig. 2.4.c Induction heating basis
CHAPTER 2 INDUCTION HEATING
9
as described in equation (2.2). The current on the surface of the object generates an eddy
current.
dtdNE ϕ
−= (2.2)
Where, E is the induced e.m.f and ϕ is the magnetic flux.
As a result, the electric energy caused by the induced current and eddy current is
converted to heat energy as shown in equation (2.3).
RERIP
22 == (2.3)
It should be noted that additional heat energy due to hysteresis will be generated in
ferromagnetic objects. In this thesis, this additional energy is ignored because it is far small
(less than 10%) than the energy generated by induction current [7].
b) Skin Effect
The higher the frequency of the current administered to the coil, the more intensive
is the induced current flowing around the surface of the load. The density of the induced
current diminishes when flowing closer to the center as shown in equations (2.4) and (2.5).
This is called the skin effect or Kelvin effect. From this effect, one can easily infer that the
heat energy converted from electric energy is concentrated on the skin depth (surface of the
object). odx
ox eii /−= (2.4)
Where, x : Distance from the skin (surface) of the object,
xi : Current density at x.
oi : Current density on skin depth (x=0)
od : A constant determined by the frequency (current depth or skin depth)
fdo µπ
ρ= (2.5)
Where, :ρ Resistivity of charge material
:µ Permeability of charge material
:f Frequency of supply
Equation (2.5) states that the skin depth is determined by the resistivity and
permeability of the object and the frequency of the supply. Figure 2.5 shows the
CHAPTER 2 INDUCTION HEATING
10
distribution chart of current density in relation to skin depth. The effect of frequency on the
current depth is shown in Fig. 2.6 [9].
2.4 CORELESS INDUCTION FURNACE In most cases, when people think of furnaces it is typical to envision a device that
utilizes a heat source such as gas or electrical elements that radiate energy to the surface of
a part to be heated. The energy will then conduct through the part based upon its surface
temperature and thermal conductivity. This limits the rate at which the part can be raised in
temperature. The temperature of the heat source also limits the final temperature that the
part can be heated to. With these limitations in mind, Coreless induction furnaces have
proven to be a valuable tool for reliably producing molten metal that is consistent,
homogenous, and uniform in temperature for the investment casting industry. Rather than
just a furnace, a coreless induction furnace is actually an energy transfer device. In the
coreless induction furnace, energy is transferred directly from an induction coil into the
material to be melted through the electromagnetic field produced by the induction coil. In
this type of devices, the maximum process temperature can be virtually unlimited, since
Fig. 2.5 Distribution chart of current density and skin depth
a) High Frequency b) Low Frequency
do do
Fig. 2.6 Effect of frequency on the current depth.
CHAPTER 2 INDUCTION HEATING
11
there is no external heat source and the energy is generated within the material being
heated. With electric induction, fast melt turn around times can be achieved, providing in
very high system production capabilities. This being the case, it is very important to gain
an understanding of the coreless induction furnace and the principals of its operation [8]. In a coreless induction furnace, the electromagnetic field is generated by a solenoid
induction coil. This coil is typically manufactured with a copper tube wound with a
carefully selected tubing profile and number of turns on the coil. Figure 2.7 shows an
assembly of a typical coreless induction furnace coil. It is manufactured from high
electrical conductivity copper tubing for low power transmission resistance within the coil
to minimize ( RI 2 ) losses. The tube profile has a hollow center for passing low-
conductivity water. This water is used to remove both the generated ( RI 2 ) losses in the
winding as well as the thermal energy conducted from the hot metal through the refractory
system back to the winding.
When an AC voltage is applied to the coil terminals, an alternating current passes
through the coil winding. The current in each turn generates an electromagnetic field
around it as shown previously in Fig. 2.1. With the turns stacked the solenoid coil produces
an electromagnetic field as shown in Figs 2.8 (a) and (b).
Fig. 2.7 Typical solenoid induction coil used in
a coreless induction furnace
CHAPTER 2 INDUCTION HEATING
12
When a load (electrically conductive material) is placed inside the coil, the field
that tries to pass through it induces eddy currents within it that cancel out the field as
shown in Fig. 2.8.b. This is accomplished through the same principle as previously
discussed and shown in Figs. 2.2 and 2.3. The result is an induced current flowing around
the outer perimeter of the load. The amount of energy transferred to the load is
proportional to the induced current squared times the resistance of the path through which
the current is flowing ( RI 2 ). Figure 2.9 shows the transferred energy density in a typical
coreless induction furnace. The load in this case is a molten metal within the furnace
crucible [8].
Fig. 2.8 The electromagnetic field generated by a solenoid induction coil a) with no load in the furnace and b) with a load inside the furnace
(a)
Fig. 2.9 Plot of the electromagnetic field and the energy transferred to the load.
(b)
CHAPTER 2 INDUCTION HEATING
13
2.4.1 System components A coreless induction furnace consists of a complete system of components
necessary for proper, reliable, and safe furnace operation. The main components required
are a furnace, power supply, power transmission system (bus and/or water-cooled cables),
and a water cooling system. Optional equipment may be required such as a hydraulic
system for hydraulic tilt furnaces, and possibly a computer control system for automated
pouring, control system and monitoring, as well as data acquisition and storage. Figure
2.10 shows an overview of the typical components of a coreless induction furnace system
[8], and Fig. 2.11 shows the block diagram of induction furnace system [10]; the details of
this system will be discussed in chapters 4 and 5.
Fig. 2.10 An overview of the typical components of a coreless induction furnace system.
Fig. 2.11 Block diagram of induction furnace system.
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
14
CHAPTER 3
DESIGN OF CORELESS INDUCTION FURNACE 3.1 INTRODUCTION
The coreless induction furnace consists basically of a crucible, inductor coil, shell,
cooling system and tilting mechanism. The crucible is formed from refractory material,
which the furnace coil is lined with. This crucible holds the charge material and
subsequently the melt. The choice of refractory material depends on the type of charge, i.e.
acidic, basic or neutral. The durability of the crucible depends on the grain size, ramming
technique, charge analysis and rate of heating and cooling the furnace [11]. Figure 3.1
shows typical components of a coreless induction furnace [8].
The inductor coil is a tubular copper coil with specific number of turns. An
alternating current (AC) passes through it and magnetic flux is generated within the
conductor. The generated magnetic flux induces eddy currents that enable the heating and
subsequently the melting process in the crucible. In order to eliminate electrical
breakdown, the turns are insulated by wrapping with mica tape, this serve as a good
insulator.
The shell is the outer part of the furnace. This houses the crucible and the inductor
coil, and has higher thermal capacity. It is made of rectangular parallelepiped with low
Fig. 3.1 Typical Components of a coreless Induction Furnace
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
15
carbon steel plate and joined at the corners by edge carriers from angular pieces and strips
of non-magnetic metal.
The cooling system is a through-one-way- flow system with the tubular copper coil
connected to water source through flexible rubber hoses. The inlet is from the top while the
outlet is at the bottom. The cooling process is important because the circuit of the furnace
appears resistive, and the real power is not only consumed in the charged material but also
in the resistance of the coil. This coil loss as well as the loss of heat conducted from the
charge through the refractory crucible requires the coil to be cooled with water as the
cooling medium to prevent undue temperature rise of the copper coil.
Tilting of the furnace is to effect pouring of the molten metal as a last operational
activity before casting. The tilting operation is achieved by a hydraulic circuit using
hydraulic pump and pistons. The furnace is tilted to achieve a maximum angle of 90
degrees for complete pouring of the molten metal [11].
3.2 SELECTION OF FURNACE SIZE, AND POWER RATING The capacity of the furnace is usually determined by the size of the pour required,
but some times a furnace capacity may need to be larger than the pour size. The size and
shape of the charge material to be melted can require a larger opening in the furnace. If
borings, turnings or chips are to be melted, the furnace may require an adequate residual
molten heel left in the furnace in order to efficiently melt. Another factor that can influence
furnace size is power density. If the required melt rate requires a power level that can result
in excessive molten metal meniscus and stirring, the furnace capacity may need to be
increased.
It is important to select the proper power rating for the system. There are many
factors that influence the selection of furnace power. The first is the capacity to be melted,
the type of the material to be melted (Iron, Aluminum, Tin ...) and the desired melt cycle
time. To raise the temperature of a solid material to the pouring temperature, energy must
be put into it based upon the characteristics of its solid specific heat, latent heat of fusion,
and liquid specific heat. The latent heat of fusion is the energy required to push the
material through its phase change from the solid to liquid state [8].
An improperly designed system that has an undersized power supply will reduce
the efficiency of the overall system and reduce the weight of metal that can be melted per
kWh applied. This could, in extreme cases, result in the inability for the system to reach
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
16
the required pour temperature. It should be noted that, the larger the furnace, the higher the
thermal losses [8].
3.3 SELECTION OF INDUCTION FREQUENCY The frequency affects both the coupling efficiency of the electromagnetic field to
the charge and the stirring characteristics of the molten metal in the furnace. For optimal
furnace performance, the selection of the system operating induction frequency is very
important. There are several factors that weigh heavily in selecting the proper frequency
for the application. These are as follows:
1. The physical size of the pieces of material to be melted.
2. The electrical resistivity of the material to be melted.
3. Whether the furnace will be operated to melt from an empty crucible or with a molten
heel left in the furnace.
4. The geometry of the crucible used in the furnace to contain the molten metal.
5. The desired molten metal stirring characteristics.
3.3.1 Induced Current Depth The depth at which induced current flows in an electrically conductive material, as
shown in Fig. 3.2, is a function of the resistivity of the material and the induction
frequency [8]. Equation (2.5) can be used to approximate the depth of the induced current
(do) in a material with a resistivity of ( ρ ), a permeability of (µ) and operating at a
frequency (f).
Fig. 3.2 induced current depth do in a cylindrical load with diameter D
Induced current around the outside perimeter of a cylindrical load
do
D
I
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
17
Figure 3.3 shows a graph of the approximate induced current depth in ferrous alloy
at various induction frequencies for a molten condition.
The induced current depth is extremely important in frequency selection because
the electrical efficiency of the system is a direct result of how well the charge material
couples with the electromagnetic field. The better it couples with the field, the more
efficient it will be. The optimal coupling efficiency of a furnace can be determined by
calculating its D/do ratio. This ratio is the diameter of the part to be melted divided by the
calculated induced current depth. The higher this ratio is, the better the coupling efficiency
of the furnace. Figure 3.4 is a graph showing the coupling efficiency for an induction
furnace versus its D/do ratio.
It is evident that the D/do ratio should always be greater than 5 on a system and
preferably not less than 10, if possible, to keep the efficiency high, as shown in Fig. 3.4. It
is impossible to directly melt chips, borings, or turnings using induction, as the D/do ratio
will be close to zero with no coupling efficiency. Therefore chips, turnings, and borings
must be melted with the assistance of a molten heel. In the case of a molten heel, the melt
Frequency Vs Current Depth
0
10
20
30
40
50
60
70
0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250
F (Hz)
do (m
m)
Fig. 3.3 Typical induced current depth Vs frequency
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
18
diameter in the crucible can be used as the load diameter (D) when calculating the D/do
ratio, thus increasing the coupling efficiency for a reasonable chip melting [8].
3.3.2 Meniscus Height and Metal Stirring Figure 3.5 shows the meniscus height (MH) of the metal which represents the
potential energy of the melt. Meniscus height is caused by the interaction of the magnetic
field from the induction coil and the current that flowing in the molten metal. This force is
equal to the vector product of the magnetic flux density multiplied by the current density of
the melt (B×J). This force is acting on the surface of the metal at the top of the melt
opposes gravity and causes the formation of the meniscus. As both B and J are proportional
to the current flowing through the coil, the meniscus height is proportional to the current
flowing through the coil squared. As kW = I2R, where R is the resistance of the coil and the
melt, the meniscus height is proportional to the kilowatts applied to the furnace and
inversely proportional to the resistance of the furnace coil and the melt.
Fig. 3.4 The ratio D/do Vs the efficiency
Effic
ienc
y
D/do ratio
dm Fig. 3.5 Meniscus height to diameter of melt
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
19
In the furnace, the flow of metal is accelerated only when current is flowing in the
melt. Thus, the accelerated flow only occurs in the region defined as the depth of current
penetration. This depth of penetration is equal to the size of a pipe connected to a reservoir.
A large depth of current penetration would be a large pipe and a very small depth of
current penetration is a very small pipe as shown in Fig. 3.6.
Obviously, for the same meniscus height (pressure of water available), the larger
the depth of current penetration (the larger the diameter of pipe), the greater the flow (of
water).
To carry this analogy further, if these pipes are considered as hoses feeding into a
swimming pool, the size of the swimming pool would be related to the size of the furnace.
Thus a very small hose being placed into the pool, like a small depth of penetration with a
given furnace size, would result in very light stirring. However, a large fire hose being
placed inside the pool, like a large depth of penetration for a given furnace size, would
obviously result in very high stirring as shown in Fig. 3.7.
When the math is done on this process, it is found that the stirring is not linearly
proportional to the meniscus height, but is much more dependent on the frequency itself.
Equation (3.1) gives the level of stirring in a given factors that include power, frequency,
furnace size and alloy being melted.
Fig. 3.6 Depth of current penetration
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
20
AfSG
dkW
SI
m
ρ60000
= (3.1)
Where SI = Stirring index (from 40 to 55 for iron)
kW = kilowatts
dm = Diameter of melt in inches
SG = Specific gravity of the bath
ρ = metal resistivity (µΩ-cm)
A = (π dm2) / 4
f = frequency
The easier way to determine the proper induction frequency is to use the chart
shown in Fig. 3.8, which describes the relation between the induction frequency and the
furnace size for different melting conditions [12]. An ideal melting (ideal stirring) can be
determined when the frequency and the furnace size is interacted on the center line in the
green zone.
Fig. 3.7 Light and heavy stirring
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
21
3.4 DESIGN ANALYSIS The analysis is based on 4 tons capacity of molten iron. Referring to Fig. 3.8, for
the 4 ton capacity, the proper induction frequency is around 250 Hz.
3.4.1 Geometrical Parameters [11] The shape of the crucible is cylindrical. The internal diameter of the crucible (the
diameter of melt) and the height of melt are determined by the furnace capacity with
considerations that the ratio:
)0.26.1( →=c
m
DH
(3.2)
Where =mH height of molten metal (m)
=cD diameter of crucible (m)
Volume of metal charge is given by:
4
2mm
mHd
Vπ
= (3.3)
Where dm = diameter of molten metal (m) = Dc
Also, V
mMVρ
= (3.4)
Where M = the mass of charge in kg
Vρ = the density of charge material in kg/m3
Fig. 3.8 Relation between the induction frequency and furnace size for different melting conditions
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
22
The thickness of the refractory lining of the crucible can be determined from the
relation:
TBr 084.0= (3.5)
Where T = furnace capacity in tones
The internal diameter of the inductor can be calculated from the equation:
)(2 insrcin BBDD ++= (3.6)
Where Bins = thickness of insulation layer (5.5≤Bins≤6 mm)
Height of inductor coil is given by:
min HH )2.11.1( →= (3.7)
The height of furnace from bottom of the bath to the pouring spout is:
tsmf bhHH ++= (3.8)
Where hs = height of slag formed
bt = thickness of bottom refractory lining = 20 cm for 4 ton capacity
The slag height is calculated thus:
2
4
m
ss d
Vh
π= (3.9)
Where Vs = volume of slag in one heat, taken (practically) as 4% of total charge m3.
3.4.2 Heat Energy Parameters The required theoretical heat energy, Qth, consumed during the first period of melt
is given by [11]:
)(JouleQQQQQQ exensshmth −+++= (3.10)
Where, =mQ amount of heat energy to melt 4 tons of charge material.
=shQ amount of heat energy to superheat the melt to temperature of superheat.
=sQ heat required to melt slag forming materials.
=enQ energy required for endothermic process.
=exQ amount of heat energy liberated to the surroundings as a result of exothermic
reactions.
Theoretically Qen ≅ Q
ex.
Therefore,
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
23
)(JouleQQQQ sshmth ++= (3.11)
and,
ptm LMCQ +−= )( 01 θθ (3.12)
where, M = mass of charge, kg.
C = specific heat capacity of charge material, J/kg.k°
Lpt
= latent heat of fusion, J/kg
θ1 = melting temperature of charge, k°
θ0 = ambient temperature, 25°C (298 k°)
Similarly,
shmsh MCQ θ= (3.13)
where, Cm = average heat capacity of molten metal, J/kg.k°
θsh
= amount of superheat temperature, taken as 330
and,
sss GKQ = (3.14)
Where, Ks = quantity of slag formed in (kg), taken as 4% of furnace capacity;
Gs = heat energy for slag = 300 kJ/kg.
3.4.3 Electrical Parameters Figure 3.9 shows a melted cylindrical load put inside the furnace, the total heat
energy induced in it, can be calculated as follows [13]:
Assume an element path of thickness dx at distance x from the vertical axis, and a
sinusoidal flux tm ωϕϕ sin= , where
ABmm ⋅=ϕ (3.15)
and, 2xA π=
Then
tBx m ωπϕ sin2= (3.16)
The induced e.m.f (e)
tBxdtde m ωωπϕ cos2== (3.17)
The effective value of this e.m.f (E) in the element path is
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
24
2maxe
E =
22 22
mBxfE π= (3.18)
If ρ is the resistivity of the material, the resistance of each elemental path is,
dxHx
AlR
m
πρρ 2== (3.19)
The eddy current flows in the metal can be calculated from the equation:
REI m =
dxBHfx
I mmm ρ
π2
= (3.20)
Since the current flows on the outer layer of the metal (skin depth), equations (3.19)
and (3.20) can be rewritten as:
om
m
dHd
Rπρ
= , and
Fig. 3.9 A melted cylindrical load
dm
Hm
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
25
ommm
m dBHfd
Iρ
π8
=
Where f
do µπρ
=
Therefore,
fH
dR
m
m
µπρ
πρ= (3.21)
fBHfd
I mmmm µπ
ρρ
π8
= (3.22)
The total eddy current loss in the charge is
RIP m2= (3.23)
Substituting from (3.21) and (3.22) in (3.23) the eddy current loss can be written in a form:
fBdHf
P mmm
µπρ
ρπ
8
2323
= (3.24)
Where, µ is the permeability of charge material which is equal to µo µr, where µo is the
permeability of free space = 4π×10-7 and µr is the relative permeability. Since at
about 1100 °C temperature, the permeability of the iron is equal to that of air, i.e.,
µ = 4π×10-7 [10], so in equations (3.21) through (3.24), µ =µo.
Bm = maximum flux density (Tesla)
R = Resistance of charge material (load) = RL
Im = current flowing in metal (A)
From equation (3.24)
ommm ddHf
PB 323
8π
ρ= (3.25)
The power (P) can be calculated from the theoretical heat energy Qth calculated
from equation (3.11) as:
tQ
P th= [11] (3.26)
Where t = the total time of melting in seconds
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
26
As mentioned in chapter 2, the induction furnace can be considered as a
transformer with single turn short circuited secondary. Figure 3.10 shows the equivalent
circuit of the furnace coil with load based on the transformer concept [10], from which
22
)( om
coil INI
I +⎥⎦⎤
⎢⎣⎡= (3.27)
Multiplying both sides by N, equation (3.27) can be written as
22 )()( omcoil NIINI +=
Since HlNI o = ,
Then 22 )()(1 HlII
N mcoil
+= , and µBH =
Fig. 3.10 The equivalent circuit of the furnace with load based on transformer concept
Ll
N:1
NLM
RL L2 L1
Req
Leq
Rc LM
Rc
N2RL
Icoil
Icoil
Im
Im/N
Io
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
27
2
2
2)(1
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
µlB
II
N mm
coil
(3.28)
Since the self inductance of the coil is
Ml NLLL +=1
Therefore,
Ml NLLL −= 1 (3.29)
Wherel
ANL ro
2
1µµ
= , 4
2inD
Aπ
= and l = Hin
The voltage across the load is equal to
ωMoLm NLIRN
NI
=2
The referred load resistance Rch = N2 RL , therefore,
ωo
LmM NI
RNINL
2
=
ωlHRI
NL chmM =
and ro
BHµµ
= , so
ωµµ
ωµµ
lBRI
lB
RINL
m
rochm
ro
m
chmM
2
2
==
Substituting in equation (3.29)
ωµµµµ
lBRI
lAN
Lm
rochmrol
22
−= (3.30)
Due to the construction of the furnace, large air gaps are present. Thus, no
saturation takes place [14]. In other words, Since all magnetic energy is stored in air gaps,
insulation between conductors, and within the conductor as shown in Figs 2.8 and 2.9,
where µr is essentially 1.0 and constant, therefore µ =µo [15].
So,
fHBRI
HDN
Linm
ochm
in
inol π
µπµ2
24
22
−= (3.31)
CHAPTER 3 DESIGN OF CORELESS INDUCTION FURNACE
28
The resistance of copper coil inductor at ambient temperature is given by
t
ccc A
lR
ρ= (3.32)
Where ρc = resistivity of copper = 1.72 ×10-7 Ω m at 25 °C
lc = total length of copper tube = π Din N
At = cross sectional area of conducting tube
Also,
tcoil AJI = (3.33)
Where J = current density (ranges from 20 to 40 A/mm2 for water cooled tubing conductor)
Since Io is very small compared with Im/N, NLM can be neglected with respect to
Rch. Therefore, the equivalent resistance chceq RRR += and the equivalent inductance
leq LL =
Coil loss due to resistance is
ccoilc RIP 2= (3.34)
Furnace efficiency can be represented by the following equation
cch
ch
RRR
Eff+
==η (3.35)
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
29
CHAPTER 4
POWER SUPPLIES IN INDUCTION
MELTING SYSTEMS 4.1 INTRODUCTION
The simplest way to construct an induction melting system is to supply the current
into the induction coil directly from the electrical source. Most large induction furnaces
until the end of the 1970's operated on fixed industrial frequencies of 60 or 50 Hz. A bank
of capacitors compensated for the low power factor of the induction coil as shown in Fig
4.1. The power factor could be adjusted by switching the capacitors and, therefore, varying
the impedance of the electrical load. Power regulation is carried out by switching the
transformer taps and capacitors thereby changing the coil current. The highest power level
is achieved when the resonance frequency of the coil and capacitor network is equal to the
frequency of the feeding line. Switching is usually performed using electromechanical
contactors and transformer tap-changers.
Line frequency power supplies limit the generation of high melting power density in
several ways. The frequency is fixed and therefore, the depth of penetration is relatively
high resulting in low resistance of the molten bath. Because the current at low frequency
penetrates deep into the molten bath, the electromagnetic forces push a large amount of
metal causing severe stirring. The magnitude of coil current is also limited because the line
frequency induction furnace is essentially a single phase device causing a severe imbalance
on the feeding power. Electromechanical devices such as contactors for capacitors
Fig. 4.1 Principle diagram of line frequency melting furnace
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
30
switching and transformer tap-changers for power control require regular maintenance and
decrease system reliability, and finally the regulation of power in steps limits the ability of
power control [16].
4.2 SOLID STATE POWER CONVERTERS The solution to the problems limiting the application of line frequency power supplies
in large melting installations became available relatively recently with the development of
large silicon controlled rectifiers (SCR's) capable of commutating high currents. Using
these SCR's, it becomes possible to construct inverters with an equivalent output power of
10,000 kW operating on output frequencies of several hundred Hertz. Operating at medium
frequencies allows limiting stirring to values required by metallurgy while significantly
increased the melting power density and, therefore, reducing melt time.
The solid state power converter also resolves the phase balancing problem. Input 3-,
6- or 12-phase line voltages are rectified before being inverted into single phase medium
frequency electric current. The power converter consists of three major sections as shown
in Fig. 4.2 [16]:
1- AC to DC rectifier and DC filter.
2- DC to AC medium frequency inverter.
3- Bank of tuning capacitors.
Fig. 4.2 Block diagram of a medium frequency melting system
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
31
4.2.1 AC to DC rectifier Solid state rectifier converts three-phase line AC voltage into six-pulse DC voltage.
The basis of all rectifiers is a typical three-phase, six-semiconductor bridge. The
semiconductors may be diodes, SCRs, IGBTs, or GTOs.
Rectifiers may be implemented using 6-pulse or 12-pulse rectification scheme. A 6-
pulse rectifier consists of one six-semiconductor bridge rectifier as shown in Fig. 4. 3. A
12-pulse rectifier contains two rectifiers, where the line voltages feeding each rectifier are
shifted 30°. This phase shift is achieved by connecting one rectifier to a (delta) secondary
winding and another rectifier to a (wye) secondary winding as shown in Fig. 4.4 [17].
SCR rectifiers may operate in full rectification or phase control mode. In full
rectification mode, the SCRs are permanently gated "fired", therefore, they act very much
as diodes, where the switching between conducting phases happens naturally as the voltage
across the SCR becomes positive. In the phase control mode, the gating of SCRs is
delayed, therefore, the switching between phases is forced by the delay angle (α).
Fig. 4.3 Uncontrolled six-pulse rectifier
0° 360° 90°
1
0.5
0.5
1
ωt180°90° 270°
U12 U13 U23 U21 U31 U32 U12 U13 U23ud(t)
Ud
Switch
0° 360° 90° ωt180°90° 270°
SV1 SV2 SV3 SV1
SV4SV6SV5 SV5
IL1
0° 360° 90° ωt180°90° 270°
+Id
-Id
U10
V1 V2 V3
V4 V5 V6
L1
L2
L3U23
IdLd
ud(t)
1 : 1
I'L1 IL1U'10
U12
U10
U'20
U'30
U20
U30
1
2
3
U31
0° 0°
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
32
4.2.1.1 Effect of static converters on power lines.
1) Power factor of the static converters
If during one cycle, a part of the energy is negative and returned from the load back
to the line, the power factor is less than unity. The power factor is represented as the
product of two components; distortion power factor and displacement power factor.
Distortion power factor depends on the amount of harmonic distortions introduced
into the line defined by value of the total harmonic distortion (THD) which is a percentage
ratio of the geometrical sum of all higher harmonic currents to the fundamental current
[17].
1
2
I
ITHD n∑
= (4.1)
The distortion power factor (DPF) can be defined as:
211THD
DPF+
= (4.2)
The displacement power factor of full wave rectifiers is unity. In phase control
rectifiers, the output DC voltage is reduced by delayed firing of the SCRs. Such a delay in
firing results not only in lower average DC voltage but also greater ripples on the DC bus
Fig. 4.4 Uncontrolled twelve-pulse rectifier
V1 V2 V3
V4 V5 V6
U23
IdLd
ud(t)
I' L1,1
U12
V7 V8 V9
V10 V11 V12
U56
Id
U45
IdLd
U'10
U'20
U'30
IL1,2
1
2
3
6
5
4U10
U20
U30
U64
U'10
U'20
U'30
IL1,1U10
U20
U30
L1
L2
L3
U31
I'L1,2
IL1
1 : 1
3:1
0° +30°
0° 0°
udI(t)
udII(t)
0° 360° 90°
1
0.5
0.5
1
ωt180°90° 270°
ud(t)Ud
U65 U45 U46 U56U23 U21 U31 U32 U12 U13 U23 U12 U13U54 U64 U54 U64
IL1,2
0° 360° 90° ωt180°90° 270°
+Id
-Id
U10
IL1,1
0° 360° 90° ωt180°90° 270°
+Id
-Id
U10
IL1
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
33
Table 4.1 Power factor of full wave rectifiers
and phase displacement between current and voltage of the line. Table 4.1 shows the power
factor of full wave rectifiers [17].
Number of pluses Power factor
6 95.49 %
12 98.86 %
24 99.71 %
48 99.85 %
2) Current harmonics generated by static power converters
As previously shown in Figs 4.3 and 4.4, the waveforms of the line current feeding
the power converters are represented by step functions. Increasing the number of rectified
pulses makes the steps smaller and the curve smoother. When two 6-pulse rectifiers are
connected to the same transformer with two secondary sets of windings, one with a "delta"
connection and one with a "wye" connection, opposite polarity of some harmonics in these
two sets of windings will cause them to eliminate each other and will not propagate into
the AC line. Theoretically, the 12-pulse rectifier does not have 5th, 7th, 17th, and 19th
harmonics. This concept is shown in Fig. 4.5.
Fig. 4.5 Amplitude Spectrum of the Twelve Pulse Rectifier
=
ωt
b) YY-Connection
TT/2n
5 7
11 13
17 19
23 25
1/5
1/7
1/11
1/13
1/171/19
1/231/25
-20%
-14%
9%
7,6%
n
5 7 11 13 17 19 23 25
1/5
1/7
1/11
1/131/17
1/19 1/231/25
20%
10%
ω t T/2 T
a) YD-Connection
IL1,1
+
In/I1
In/I1
IL1,2
10%
ωt
n
5 7 11 13 17 19 23 25
1/11
1/13
1/23 1/25
20%
TT/2
IL1
c) YD + YY-Connection
In/I1
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
34
3) Line voltage notching
As described previously, rectification is achieved by current switching between AC
line phases via rectifying devices (diodes or SCRs).
The switching may happen naturally when the voltage difference becomes positive
for full wave rectification or delayed by gating the rectifier SCR after the phase transition.
The line current cannot be switched over instantaneously because the electrical energy
stored in the line and transformer inductances needs time to dissipate. While, one-phase
current tapers down, the current in the second phase ramps up. The time of this overlap
depends on the inductance of the line and transformer connected to the rectifier. During
such an overlap, the rectifier actually shorts one phase to another, therefore, the voltage on
the two phases equalizes for the duration of the semiconductor switchover, creating a notch
in voltage waveforms.
In case of full wave rectification, the switchover initiates when voltages between
phases are equal, therefore, notches on line voltage are shallow but wide as shown in Fig.
4.6 (a).
In a phase control situation, the switchover initiates with a delay and voltages
between phases are different, therefore, equalizing the phase voltage produces severe
notching: one positive and one negative as shown in Fig. 4.6 (b) [17].
Fig. 4.6 Voltage notch due to phase current switchover in a) full wave rectifier b) phase controlled bridge
(a) (b)
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
35
4.2.2 DC to AC medium frequency inverter DC to AC converters are known as inverters. The function of an inverter is to change
a DC input voltage to a symmetrical AC output voltage of desired magnitude and
frequency. A variable output voltage can be obtained by varying the input DC voltage and
maintaining the gain of the inverter constant. On other hand, if the DC input voltage is
fixed and uncontrollable, a variable output voltage can be obtained by varying the gain of
the inverter which is accomplished by Pulse Width Modulation (PWM) control within the
inverter. The inverter gain is the ratio of the AC output voltage to the DC input voltage.
Inverters can be broadly classified into two types; single phase inverters and three
phase inverters. Inverters can be built in using different types of semiconductor devices
(SCRs, IGBTs, or GTOs). Figure 4.7 shows a single phase full-bridge inverter.
An inverter is called a voltage fed inverter if the input voltage remains constant, a
current fed inverter if the input current is maintained constant, and a variable DC-linked
inverter if the input voltage is controllable [18].
4.2.2.1 Switching losses
The switching devices in converters with a PWM control can be gated to synthesize
the desired shape of the output voltage and/or current. However, the devices are turned
"on" and "off" at the load current with a high di/dt value. The switches are subjected to a
high-voltage stress, and the switching power loss of a device increases linearly with
switching frequency. The turn-on and turn-off loss could be a significant portion of the
total power loss [18].
Fig. 4.7 Single phase full-bridge inverter d
Q3Q1
Q2 Q4
I
Id Iinverter
Vinverter Lo
ad
VDC
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
36
Raising the switching frequency helps to build a smaller and lighter converter, but as
presented earlier, switching loss undermines the efficiency of the entire power system in
converting energy, as more losses are generated at a higher frequency. Switching loss can
be partly avoided by connecting a simple snubber circuit parallel to the switching circuit.
However, the total amount of switching loss generated in the system remains the same. The
loss avoided, has in fact, just moved to the snubber circuit [7].
The disadvantages of PWM control can be eliminated or minimized if the switching
devices are turned on and off when the voltage across a device and /or its current becomes
zero. The voltage and current are forced to pass through zero crossing by creating an LC-
resonant circuit, thereby calling a resonant pulse converter [18].
4.2.2.2 Resonant Pulse Converters
The resonant circuit of a resonant converter consists of a capacitor, an inductor, and a
resistor. Two types of resonant converters are generally used: a parallel resonant circuit
(current fed inverter with parallel capacitor bank) and a series resonant circuit (voltage fed
inverter with series capacitor bank). Figure 4.8 shows these two common types. When
power is connected, electric energy is stored in the inductor as illustrated in equation (4.5),
and transferred to the capacitor. Equation (4.6) simplifies the calculation of the amount of
energy stored in the capacitor to be sent to the inductor. Resonance occurs while the
inductor and the capacitor exchange the energy.
The total amount of energy stored in the circuit during resonance remains unchanged.
This total amount is the same as the amount of energy stored at peak in the inductor or
capacitor.
For series resonant circuits:
Fig. 4.8 Resonant Circuits a) the series resonant circuit and b) the parallel resonant circuit
R
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
37
)sin(2 tIi ω= (4.3)
)cos(21 tCIdti
CVc ω
ω∫ −== (4.4)
)(sin21 222 tLILiEL ω== (4.5)
)(cos)(cos21 222
2
22 tLIt
CICVE CC ωωω
=== (4.6)
CILIttLIEE CL 2
22222 ))(cos)((sin
ωωω ==+=+ (4.7)
As some energy is lost due to resistance in the resonance process, the total amount of
energy stored in the inductor decrements in each resonant exchange. The resonance
frequency, which is the speed of energy transfer, is determined by capacitance (C) and
inductance (L) as shown in equation (4.11). The inductive reactance and the capacitive
reactance are given by equations (4.8), and (4.9), respectively. The magnitude of
impedance in a series resonant circuit is given by equation (4.10).
)(2 Ω== LfjLjX L πω (4.8)
)(2
11Ω==
CfjCjX C πω
(4.9)
)(1 22 Ω⎟
⎠⎞
⎜⎝⎛ −+=
CLRZ
ωω (4.10)
At the resonance frequency, the inductive reactance of equation (4.8) and the
capacitive reactance of equation (4.9) become the same, i.e. the voltage of the power
source and the current in the circuit stay at the same level. The resonance frequency can be
summarized as shown in equation (4.11). The current in the circuit reaches its peak when
the source frequency becomes equal to the resonance frequency. It decreases when the
source frequency gets higher or lower than the resonance frequency.
CL
fCf
Lf o πππ
21
212 =⇒= (4.11)
And the selection ratio (the quality factor) of a series resonant circuit is given by
equation (4.12).
CL
RCRRL
Qo
o 11===
ωω
(4.12)
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
38
Equation (4.12) shows that the smaller the resistance than the inductance, when the
source frequency gets closer to the resonance frequency, the sharper the frequency curve of
Fig. 4.9 and the bigger the value of Q. The numerator is proportional to the energy
accumulated in the inductor during resonance and the denominator is proportional to the
average amount of energy consumed in resistance in each cycle. The frequency curve of
Fig 4.9 demonstrates the relationship between current/output energy and source frequency
when the source voltage of the resonant circuit is constant. The current and output energy
reaches its maximum value at resonance frequency. In the area where the switching
frequency is lower than the resonance frequency, the inductive reactance has a direct
relationship with the switching frequency. In other words, the lower the frequency, the
smaller the inductive reactance, and according to equation (4.9), the capacitive reactance is
in inverse relationship with the frequency. As the reactance becomes more capacitive, the
current becomes more leading to the voltage. When the switching frequency increases,
impedance gets smaller, increasing the amount of output energy. In the opposite situation,
a lower switching frequency leads to higher impedance, causing the output energy to
decrease. In the area where the switching frequency is higher than the resonance
frequency, the higher the switching frequency, the bigger the inductive reactance. Here, the
value of the capacitive reactance becomes smaller according to equation (4.9). The higher
inductive reactance causes the current to be more lagging to the voltage. In this situation, a
higher switching frequency is accompanied by an increase of impedance causing the output
energy to be lower. When the switching frequency goes down towards the resonance, the
impedance is decreased, raising the output energy [7].
Fig. 4.9 Frequency curve of series resonant inverter
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
39
The parallel resonant circuit of Fig. 4.8 (b) is considered to be the dual of the series
resonant circuit. The magnitude of impedance in a parallel resonant circuit is given by
equation (4.13).
)()( 2222
Ω+−
=LRLCR
LRZωω
ω (4.13)
It should be noted that a parallel resonant circuit has the highest impedance at
resonance, whereas the series resonant circuit has the lowest impedance at resonance.
The selection ratio (the quality factor) of a parallel resonant circuit is given by
equation (4.14).
CRL
R
RV
XV
Q oo
L ωω
=== 2
2
(4.14)
The numerator of equation (4.14) is proportional the average amount of energy
consumed in resistance and the denominator is proportional to the energy accumulated in
the inductor during resonance in each cycle. The frequency curve appears the same as that
of series resonance, but voltage replaces current. Figure 4.10 demonstrates the relationship
between voltage/output energy and source frequency when the source current of the
resonant circuit is constant. The voltage and output energy reaches its maximum value at
resonance frequency. In the area where the switching frequency is lower than the
resonance frequency, the lower the frequency, the higher the inductive reactance. As the
reactance becomes more inductive, the voltage becomes more leading to the current. In the
area where the switching frequency is higher than the resonance frequency, the higher the
switching frequency, the higher the capacitive reactance. The higher capacitive reactance
causes the voltage to be more lagging to the current [7].
Fig. 4.10 Frequency curve of parallel resonant inverter
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
40
4.3 CURRENT FED INVERTER WITH PARALLEL CAPACITOR
BANK. In the current fed inverter, the power factor correction capacitor bank is connected in
parallel to the furnace coil as shown in Fig. 4.11. Both the capacitor bank and the coil are
placed into the diagonal of a full bridge inverter. This connection allows the reactive
component of the coil current to bypass the inverter SCR's, and to have load commutation
of the thyristors. However, the inverter is exposed to the full furnace voltage.
The values of inverter voltage may be higher or lower than the DC voltage on the
rectifier. Therefore, DC rectifier and inverter sections must be decoupled by reactors. The
reactors supply the inverter with constant DC current. They are acting as a filter and
reservoir of energy. The inverter converts DC current into square wave current injected
into parallel resonant circuit.
The furnace power in current-fed inverter system is controlled by varying both
inverter switching frequency and DC voltage. When inverter voltage falls below DC
rectifier potential, the output power cannot be controlled by variation in inverter
commutation frequency alone. Additional control of the injected DC current is carried out
by regulating the conduction phase angle of the rectifier SCR's. Such regulation will
introduce distortion into the feeding electrical line unless filters are provided.
The main advantage of the parallel resonant inverter is that only part of the coil
current is passed via SCR's, therefore, saving the number of semiconductor devices. The
inverter controls only part of the coil current. This, however, limits the controllability of
Fig. 4.11 Medium frequency melting system utilizing current-fed converter
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
41
the inverter. Using smoothing DC reactors as temporary energy accumulators causes
difficulties in starting the inverter. The energy in the reactors is kinetic energy exists only
when the DC current flows from the rectifier to the inverter. To accumulate the necessary
energy in the smoothing DC reactor, a special starter network is used.
The advantage of lower current in the inverter SCR's is offset by a high voltage to
which these SCR's are exposed. This often requires number of SCR's in series [16]. For a
given output power the volt ampere rating of the inverter SCR's and the rating of the
compensating capacitor increases as the operating frequency increases, therefore, the
inverter should be operated as close to resonance as possible in order to deliver the rated
output power and minimize the total kVA of the system [20].
4.3.1 Thyristor's Turn-off Time There are several techniques for SCR's commutation, one of which is the load
commutating technique, which is common in use in induction heating application. As
shown previously, the capacitor is connected in parallel to the furnace coil and one of the
purposes of the capacitor is to have load commutation of the thyristors. The thyristors pairs
Q1Q2 and Q3Q4, shown in Fig. 4.12, are switched alternately for π angle to impress a square
current wave at the output. The fundamental component of load current leads the nearly
sinusoidal load voltage wave by angleβ°, causing load commutation. Since β= ω tq, the
minimum value of β should be sufficient to turn off the thyristors during time tq [19],
therefore, the operating frequency should always reside above the resonant frequency of
the tuned circuit [20].
Fig. 4.12 Parallel resonant inverter with load commutation
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
42
V IR
IL
IC
IQ I
β
Fig. 4.13 a) The phasor diagram of the parallel resonant inverter, and b) The equivalent circuit
(a)
V
IC IL IR
R L C
I
(b)
Circuit Analysis
Figure 4.13 shows the phasor diagram of the parallel resonant inverter and the
equivalent circuit.
The general equations of the inverter can be given as [19]:
RVI R = (4.15)
LjVI L ω
= (4.16)
cVjIC ω= (4.17)
R
Q
II
=βtan (4.18)
R
LC
III −
=βtan
RV
LVCV ωω
β−
=tan
LRCRω
ωβ −=tan
02
2)2(tan =+−Lf
RCRftf q πππ (4.19)
Where off ⟩
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
43
Equation (4.19) shows that the turn off time for the inverter SCR's decreases as the
operating frequency decreases towards the resonant frequency, and as previously stipulated
the inverter should always operate above resonance such that the minimum turn off time
requirement for the devices is satisfied [19]. Figure 4.14 illustrates equation (4.19) for
furnace coil of 0.1915 mH inductance and 0.0267 Ω resistance and parallel capacitor of
2118.2 µf, which gives resonance frequency of 250 Hz.
SCR's Turn off time
0
5
10
15
20
25
30
35
40
45
50
55
60
250 250.2 250.4 250.6 250.8 251 251.2 251.4 251.6 251.8 252
Frequency (Hz)
t q (u
s)
4.4 VOLTAGE FED INVERTER WITH SERIES CAPACITOR BANK From the standpoint of electric circuit theory, voltage-fed series resonant inverters
represent a duality circuit of the current-fed parallel resonant inverters. The current
smoothing reactors in DC line are replaced by DC voltage filter capacitors and the output
parallel resonant circuit is replaced by a series resonant circuit as shown in Fig. 4.15. The
voltage on the inverter is constant and equal to the output voltage of the AC to DC rectifier
and the full coil current flows though the inverter SCR's and tuning capacitor bank. Such a
configuration provides excellent controllability of the system. By controlling the switching
frequency of the inverter SCR's, it is possible to rapidly change the amount of energy
circulating in the resonant circuit.
The potential electrical energy in DC filter capacitor bank may be indefinitely
maintained regardless of inverter status. During each cycle, the reactive power is flowing
Fig 4.14 SCR's turn off time Vs the operating frequency, fo = 250 Hz
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
44
either from the filter to the furnace via the SCR's or from the furnace to the filter via anti-
parallel diodes. Due to good controllability of the inverter section, there is no need to
control DC voltage. Since phase control is not applied to the rectifier, minimum harmonic
distortion is injected into the feeding line, also no AC line filters are required. The series
voltage-fed inverter can be easily started. The DC filter capacitor is charged to the
operation without the need to start the inverter and, likewise, upon stopping the inverter,
energy is maintained in the filter capacitor, ready for immediate use [16].
The output power of the series inverter increases as the operating frequency is
increased towards the resonance frequency. Therefore the output power of the inverter can
be controlled by controlling the operating frequency. The turn off time available for the
inverter SCR's decreases as the operating frequency increased and becomes zero at the
resonant frequency, therefore the series resonant inverter should always be operated below
the resonant frequency such that the minimum turn off time for the SCR's is satisfied [20].
4.5 DC FILTER CIRCUIT There are two types of DC filter circuits; the DC voltage filter and the DC current
filter. The DC-voltage filter circuit delivers a constant voltage at its output terminals that
can be a variable DC when the filter circuit is supplied by a controlled rectifier. The DC-
current filter circuit delivers a constant current at its output terminals that can also be
variable, when the filter circuit is supplied by a controlled rectifier.
The Inductor in the DC-voltage filter is considerably smaller (about 1%) than the
inductor in a DC-current filter circuit. However the DC-voltage filter also requires a
Fig. 4.15 Medium frequency melting system with full bridge voltage fed converter
CHAPTER 4 POWER SUPPLIES IN INDUCTION MELTING SYSTEMS
45
massive additional capacitor bank in addition to the inductor to achieve the required
filtering action.
Figure 4.16 shows the DC-voltage and DC-current filter circuits for both voltage
fed inverters and current fed inverters respectively.
Id
t
VDC
t
+
-
Id
Id
Ld
VDC
t
VoVDC
t
+
-
VDC Vo
+
-
L<<Ld(a)
Fig. 4.16 a) DC-voltage filter circuit and b) DC-current filter circuit
(b)
CHAPTER 5 SIMULATION AND RESULTS
46
CHAPTER 5
SIMULATION AND RESULTS 5.1 INTRODUCTION
In this chapter, the induction furnace's design analysis which was discussed in chapter
3 will be applied for an induction furnace with 4 ton capacity of iron as a charge material
to be melted. This design includes the geometrical, thermal and electrical parameters of the
furnace. To verify the design results, a digital simulation programs using MATLAB will be
presented for parallel resonant inverter as well as for series resonant inverter. The
simulation results will be compared with actual and experimental results for the parallel
resonant inverter and the series resonant inverter respectively. A comparison between
parallel resonant inverter and series resonant inverter will be discussed on the aspects of
consumed power, efficiency, harmonics produced in the system, and other aspects.
5.2 FURNACE DESIGN The thermal parameters of iron, which is considered as a charge material is shown in
table 5.1 [21], [22], [23], [24], [25] and [26].
5.2.1 Geometrical Parameters The geometrical parameters, shown in Fig. 5.1, were determined by applying
equations (3.2) through (3.9). The results are tabled in table 5.2.
item
Parameter Value unit
1 Specific Heat Capacity 460 kJ/kg.k°
2 Melting Temperature 1573 k°
3 Latent Heat 267 kJ/kg
4 Electrical resistivity 0.1 µΩ-m
5 Temperature coefficient 0.005671 --
6 Density 7000 kg/m3
Table 5.1 Thermal parameters of iron
CHAPTER 5 SIMULATION AND RESULTS
47
item
Parameter Value unit
1 Volume of the charge (Vm) 0.5714 m3
2 Diameter of melt (dm) 76.90 cm
3 Height of melt (Hm) 123 cm
4 Thickness of the refractory lining (Br) 16.8 cm
5 Internal diameter of the inductor (Din) 111.5 cm
6 Height of inductor coil (Hin) 135.3 cm
7 Height of furnace from bottom of the bath to the pouring
spout (Hf) 147.96 cm
Table 5.2 Geometrical parameters of the furnace
Fig. 5.1 the Geometric shape of the furnace
Hm
dm
Hin Hf
Din
Br
Pouring Spout
Coil segments
CHAPTER 5 SIMULATION AND RESULTS
48
5.2.2 Heat Energy Parameters By applying equations (3.10) through (3.14), the results shown in table 5.3 were
determined.
item
Parameter Value unit
1 Amount of heat energy to melt 4 ton of charge material (Qm) 2162.3 MJ
2 Amount of heat energy to superheat the melt to temperature of
superheat (Qsh) 1109.5 MJ
3 Heat required to melt slag forming materials (Qs) 48 MJ
4 Total energy (Qth) 3319.8 MJ
5.2.3 Electrical Parameters The coil was assumed to be a rectangular hollow tube with dimensions shown in Fig.
5.2. By using chart shown in Fig. 3.8 and equations (3.15) through (3.35), the results
shown in table 5.4 were determined.
45 mm
34 mm
40 mm29 mm
Fig. 5.2 The dimensions of conducting tube
Table 5.3 Heat Energy parameters of the furnace
CHAPTER 5 SIMULATION AND RESULTS
49
Item
Parameter value unit
1 Operating frequency (f) 250 Hz
2 Resistance of charge material (RL) 0.05115 mΩ
3 Induced current depth (do) 2.64 cm
4 Current flowing in metal (Im) 232.57 kA
5 Flux density (Bm) 0.0231 Tesla
6 Coil tube cross sectional area (a) 814 mm2
7 Power required to melt the charge in 20 minutes (P) 2.766 MW
8 Coil current (Icoil) 11.803 kA
9 Number of turns of the coil (N) 20 turns
10 Coil resistance (RC) 1.5 mΩ
11 Equivalent resistance (Req) 21.90 mΩ
12 Equivalent inductance (Leq) 0.19014 mH
13 Parallel Capacitance (Cp) for parallel resonant inverter 2120 µf
14 Series Capacitance (Cs) for series resonant inverter 2131.5 µf
5.3 SIMULATION PARAMETERS The furnace coil is represented by a series inductance and resistance, which are Leq
and Req respectively. Req is the sum of the coil resistance RC and the charge resistance
referred to coil side Rch. The capacitor is connected either in parallel or in series with the
previous combination according to the inverter type. The value of the parallel connected
capacitor of the parallel resonant inverter is Cp and the value of the series connected
capacitor of the series resonant inverter is Cs. The furnace was assumed to be totally filled
by a molten metal; therefore Leq and Req are assumed to be constants.
5.4 PARALLEL RESONANT INVERTER In this section a detailed discussion of the results of the parallel resonant inverter is
presented. First the open loop system will be presented, followed by the closed loop system
and finally a comparison between simulation and actual results will be discussed. For
simplicity, the thyristors used in the simulation are GTO type, therefore the turn off time of
the thyristors was neglected, and also the start circuit was not included.
Table 5.4 Electrical parameters of the furnace
CHAPTER 5 SIMULATION AND RESULTS
50
5.4.1 Open Loop System Figure 5.3 shows the arrangements of the open loop parallel resonant inverter
system, which consists of a power supply, six pulse converter with six pulse generator, DC
link reactor, inverter and furnace coil with parallel capacitor. There is no control on the firing angle of the converter, i.e. there is no feed back
from the output voltage and/or power to control the firing angle value.
The simulation was run for different firing angles with input voltage Vm = 2400 volt
and 10.8 mH reactor. Table 5.5 shows a summary of simulation results (inverter current,
furnace current, furnace voltage, furnace power and total harmonic distortion "THD") for
different firing angles.
Table 5.5 Results of Open Loop system simulation
i Firing angle (α)
Iinverter (A)
Ifurance (kA)
Vfurnace (volt)
Pfurnace (kW) THD
1 0 968.8 11.78 3530 3078 0.3120 2 30 835.3 10.21 3057 2295 0.3160 3 45 696.0 8.32 2492 1562 0.3199 4 60 526.1 7.84 2350 1099.8 0.8002 5 90 71.12 1.11 333.3 17.92 0.9784
Req
Leq
Cp
reactor
0
alpha deg
v+-
Vca
Vc
v+-
Vbc
Vb
v+-
Vab
Va
+
-
V
U
GTO
Inverter
g
A
B
C
+
-
Converter
0
alpha_deg
AB
BC
CA
Block
pulses
6-Pulse Generator
Fig 5.3 Open Loop Parallel resonant inverter system
Vfurnace
Iinverter
CHAPTER 5 SIMULATION AND RESULTS
51
Figures 5.4 through 5.8 show the simulation results at resonant frequency f=250
Hz. Table 5.5 shows that inverter current and furnace voltage decrease as the firing angle
increases as shown in Fig. 5.4.
Figure 5.5 shows the waveforms of the inverter current (Iinverter) and the furnace
voltage(Vfurnace) at firing angle (α) =0°. It is clear that Iinverter and Vfurnace are in phase.
Fig. 5.4 Inverter current and furnace voltage at different firing angles
0
500
1000
1500
2000
2500
3000
3500
4000
0 15 30 45 60 75 90Firing angle
Iinverter(A)
Vfurnace(V)
Fig. 5.5 Inverter current and furnace voltage at α=0°
Vfurnace Iinverter
CHAPTER 5 SIMULATION AND RESULTS
52
Figure 5.6 shows the DC voltgae (Vdc) at α=0°, while Fig. 5.7 shows Iinverter,,
Vfurnace, and Vdc atα=30°, and those at α=60° are shown in Fig. 5.8.
Fig. 5.8 Inverter current, furnace voltage and Vdc at α=60°
Fig. 5.7 Inverter current, furnace voltage and Vdc at α=30°
Fig. 5.6 The DC voltage (Vdc) at α=0°
Vdc Vfurnace Iinverter
Vdc Vfurnace Iinverter
CHAPTER 5 SIMULATION AND RESULTS
53
Figures 5.9 through 5.11 show the simulation results at a frequency higher than the
resonance frequency f=254 Hz. It is clear that the inverter current and furnace voltage are
not in phase at f>fo (the voltage is lagging the current) as shown in Fig. 5.9.
It should be noticed that the power at f> fo is higher than the power at fo as shown in
Fig. 5.10. At frequencies above (or below) the resonant frequency, the load voltage
decreases, consequently the supply current increases due to the increase of the voltage
difference between rectifier and inverter voltages. The increase of the supply current
increases the output power.
Figure 5.11 shows the reactive power of the system at f=254 Hz and at fo. It is clear
that the reactive power at fo is almost zero, and it gets higher as f is getting higher.
Fig. 5.10 Output power at fo and at f=254 Hz
Fig. 5.9 Inverter current, furnace voltage at f=254 Hz
Pout in (Watt) at f= 254 Hz
Pout in (Watt) at fo= 250 Hz
CHAPTER 5 SIMULATION AND RESULTS
54
5.4.2 Closed Loop System Figure 5.12 shows the configuration of the closed loop system where the firing
angle of the converter is controlled using a PI controller. The input to this controller is the
difference between the output power (furnace power) and a reference power (required
power). The operating frequency of the inverter is constant (250 Hz).
Fig. 5.11 Reactive power at fo and at f=254 Hz
Q in (VAR) at f= 254 Hz
Q in (VAR) at fo= 250 Hz
Req
Leq
Cp v
+
-
v2reactor
v+-
Vca
Vc
v+-
Vbc
Vb
v+-
Vab
Va
Reference Power
Furnace Power
Ref erence PowerAlf a
PI Controller
V
I
PQ
Output Power
+
-
V
U
GTO
Inverter
i+ -
Ct1
g
A
B
C
+
-
Converter
0
alpha_deg
AB
BC
CA
Block
pulses
6-Pulse Generator
Fig. 5.12 Configuration of the closed loop system
CHAPTER 5 SIMULATION AND RESULTS
55
Figures 5.13 through 5.16 show the simulation results of a closed loop system at
different reference output power.
Figure 5.13 shows the output power response when the reference power was
suddenly changed from 1 MW to 2.5 MW at a time of 0.15 ms. The controller parameters
were adjusted to allow the output power follows the reference power with minimum
settling time, minimum overshoot and zero steady state error.
The corresponding inverter current, furnace voltage and firing angle responses are
shown in Figs. 5.14, 5.15, and 5.16 respectively.
Fig. 5.13 The output power compared with the reference power
Fig. 5.16 Closed Loop Parallel resonant inverter system
Iinverter
Poutput
Preference
Fig. 5.14 The inverter current response for step change in the reference power.
CHAPTER 5 SIMULATION AND RESULTS
56
5.4.3 Comparison Between Simulation and Actual Results To verify the design and simulation results, a comparison between these results and
those of an actual induction furnace will be carried out. The actual furnace is manufactured
by ABB Company in Germany. It is 4 ton capacity working at resonance frequency of 250
Hz, with 3 MW maximum power, 3000 volt maximum voltage and 1500 A maximum
current. The power supply is 12-pulse converter fed from step down transformer Y/Y/∆,
11000/900/900 voltage, which provides two outputs shifted by 30°. Figure 5.17 shows the
single line diagram of the actual furnace.
A comparison between electrical and geometrical parameters of the designed
furnace and the actual one is shown in tables 5.6. From this table, it can be seen that the
design parameters are close to the actual ones.
Fig. 5.16 The firing angle response for step change in the reference power
Fig. 5.15 The furnace voltage response for step change in the reference power
V furnace
Firing angle
CHAPTER 5 SIMULATION AND RESULTS
57
i Parameter Simulated value Actual value
1 Number of turns of the coil (N) 20 turns 20 turns 2 Equivalent inductance (Leq) 0.1901 mH 0.192 mH 3 Capacitance (Cp) 2120 µf 2118.2 µf 4 The volume of the charge (Vm) 0.5714 m3 0.5714 m3
5 The diameter of melt (dm) 76.90 cm 85 cm 6 The height of melt (Hm) 123 cm 107 cm
7 The thickness of the refractory lining (Br)
16.8 cm 10.5 cm
8 The internal diameter of the inductor (Din)
111.5 cm 107 cm
9 The height of inductor coil (Hin) 135.3 cm 131.5 cm
Figure 5.18 (a) and (b) show the actual and simulation furnace voltage and inverter
current respectively. From which it is clear that the voltage is lagging the current with an
Table 5.6 Comparison between simulated and actual parameters
Fig. 5.17 The Single line diagram of ABB induction furnace
CHAPTER 5 SIMULATION AND RESULTS
58
angle enough to sustain the thyristors turn off time. When the simulation was run with
operating frequency higher than the resonant frequency, the same result was obtained.
Table 5.7 shows a comparison between the values of the furnace voltage and the
inverter current of the actual application and the simulated one for different values of
reference power assuming that the furnace is totally filled with molten metal.
Actual Simulation Percentage of error (E)Power
(MW) Vfurnace (V) Iinverter (A) Vfurnace (V) Iinverter (A) Evolt % Ecurrent %
0.5 1191 493 1198 474.5 0.59 3.75
1.0 1678 702 1692 662.5 0.83 5.63
1.5 2045 861 2062 824.1 0.83 4.29
2.0 2367 995 2387 941.9 0.84 5.63
2.5 2643 1076 2668 1043 0.95 3.16
5.5 SERIES RESONANT INVERTER In this section, detailed discussion of the series resonant inverter results is presented.
First the open loop system, then the closed loop system and finally a comparison between
simulation and experimental results will be discussed. As in parallel resonant inverter, the
thyristors used in simulation are GTO type.
(a) (b)
Fig. 5.18 Furnace voltage and inverter current a) actual b) simulation
Table 5.7 Comparison between simulated and actual values of furnace voltage and inverter current for different values of power
CHAPTER 5 SIMULATION AND RESULTS
59
L
Req
Cs
DC Link Reactor
DC LinkCapacitor
f
Freq
+
-
V
U
inverter
Vc
Vb
Va
Va
Vb
Vc
+
-
Diode Rectifier
5.5.1 Open Loop System Figure 5.19 shows the arrangements of the open loop series resonant inverter
system, which consists of power supply, Diode rectifier, DC link parallel capacitor with
series small value reactor (1 % of the parallel resonant system reactor), inverter and
furnace coil with series capacitor. There is no control on the inverter operating frequency,
i.e. there is no feed back from the output power to control the value of the operating
frequency of the inverter.
The simulation was run for different frequencies with input voltage Vm = 179.6 volt.
The reactor value is 0.108 mH, and the capacitor (c) value is 1.2 farad. The value of
capacitor was selected, to minimize the ripples in the DC voltage. Table 5.8 shows a
summary of results (inverter current, furnace voltage, furnace power and total harmonic
distortion "THD") for different operating frequencies.
Table 5.8 Results of open loop system simulation
i Operating
frequency (f) Iinverter
(kA)
Vinverter (volt)
Vfurnace (volt)
Poutput (kW)
THD
1 242 8.34 274.1 2415 1535 0.3007 2 244 9.15 270.6 2671 1851 0.2984 3 246 9.89 266.1 2912 2155 0.2963 4 248 10.39 263.4 3082 2385 0.2938 5 250 10.65 262.0 3184 2500 0.2935
Fig. 5.19 Open Loop Series Resonant Inverter System
Vinverter
Inverter
CHAPTER 5 SIMULATION AND RESULTS
60
Figure 5.20 shows inverter current and voltage at different operating frequencies (fo
=250 Hz).
Figure 5.21 shows the output power (Po) and total impedance (Z) at different
operating frequencies (fo =250 Hz). It is clear that, the output power decreases and the
impedance increases as the frequency decreases compared with the resonant frequency.
Figure 5.22 shows the inverter current and voltage at f=fo=250 Hz. It is clear that
the voltage and the current are in phase, while the voltage is lagging the current when the
operating frequency is lower than fo as shown in Fig. 5.23. The current waveform in Figs.
5.22 and 5.23 was multiplied by a reduction factor of 0.05 so that the two waveforms are
comparable.
Fig. 5.20 The inverter current and voltage at different operating frequencies (fo =250 Hz)
0.02
0.022
0.024
0.026
0.028
0.03
0.032
0.034
240 242 244 246 248 250 252f operating (Hz)
Impe
danc
e
1200
1500
1800
2100
2400
2700
outp
ut p
ower
Z(ohm)P o (kW )
Fig. 5.21 The output power (Po) and total impedance (Z) at different operating frequencies
0
50
100
150
200
250
300
240 242 244 246 248 250 252f o pera ting (Hz)
Vin
verte
r
8
9
10
11
12
Iinve
rter
V (volt)I (kA)
CHAPTER 5 SIMULATION AND RESULTS
61
The output power of the system decreases when the operating frequency decreases
compared with the resonant frequency, while the reactive power increases "becomes more
capacitive" when the operating frequency is lower than the resonance frequency. These
two results are shown in Figs. 5.24 and 5.25 respectively.
The value of the capacitor filter was selected to minimize the ripples in the DC
voltage as possible. Figure 5.26 shows the DC voltage at two different values of capacitor
0.2 farad and 1.2 farad. It can be seen that the ripples in the DC voltage decrease as the
capacitor value increases. Figure 5.27 shows the output power response at two different
values of capacitor 0.2 farad and 1.2 farad. It is clear that the oscillations decreases as the
capacitor value increases.
Vinverter Iinverter
Fig. 5.22 The inverter current and voltage at f=fo=250 Hz.
Vinverter Iinverter
Fig. 5.23 The inverter current and voltage at f=246 Hz.
CHAPTER 5 SIMULATION AND RESULTS
62
Fig. 5.24 Output power at fo and at f=246 Hz
Fig. 5.25 Reactive power at fo and at f=246 Hz
Q at f=fo=250 Hz
Q at f =246 Hz
Fig. 5.26 VDC at two different capacitor values
Pout at f=fo=250 Hz
Pout at f=246 Hz
VDC at C=0.2 Farad VDC at C=1.2 Farad
CHAPTER 5 SIMULATION AND RESULTS
63
5.5.2 Closed Loop System Figure 5.28 shows the configuration of the closed loop system where the operating
frequency is controlled using a PI controller. The input to this controller is the difference
between the output power (furnace power) and the reference power (required power).
Figures 5.29 through 5.31 show the simulation results of a closed loop system at
different reference output power. The simulation was run for time of 1 ms. At a time of 0.5
ms the reference power was suddenly increased from 1.5 MW to 2.5 MW. The controller
Fig. 5.27 Pout at two different capacitor values
P
L
Req
Cs
DC Link Reactor
DC LinkCapacitor v
+
-
v2
Freq
+
-
V
U
inverter
Vc
Vb
Va
Act_Power
Ref erence_PowerFreq1
PI_Controller V
I
PQ
P&Q P Reference
Va
Vb
Vc
+
-
Diode Rectifier
i+ -
Ct1
Fig. 5.28 Configuration of the closed loop system
CHAPTER 5 SIMULATION AND RESULTS
64
parameters were adjusted to allow the output power follows the reference power with
minimum settling time, minimum overshoot and zero steady state error as shown in Fig.
5.29.
When the reference power changes, the controller tries to adjust the frequency to
make the output power follows the reference power; this operation has an influence on the
phase shift between the voltage and the current of the inverter as shown in Fig. 5.30.
As the phase shift changes with the change of reference power, the reactive power,
which depends on the phase shift between the voltage and the current, will change
dramatically. The corresponding change of the reactive power is shown in Fig. 5.31 when
the reference power changes.
Output Power
Reference Power
Fig. 5.29 The output power compared with the reference power.
Fig. 5.30 Phase shift change with the change in the reference power.
Vinverter Iinverter
CHAPTER 5 SIMULATION AND RESULTS
65
5.5.3 Comparison between Simulation and Experimental results To verify the design and simulation results, a comparison between these results and
those of a prototype induction furnace will be carried out. The prototype furnace is
manufactured locally. It is 4 kg capacity working at resonance frequency of 3.623 kHz.
The power supply is full converter fed from step down single phase transformer 220/27
voltage. Figures 5.32 and 5.33 show the single line diagram of the prototype furnace and
the typical setup respectively.
Reactive Power
Fig. 5.32 The single line diagram of the prototype furnace.
Fig. 5.31 The reactive power response to the change in the reference power.
CHAPTER 5 SIMULATION AND RESULTS
66
The parameters of the prototype furnace are shown in table 5.9.
item
Parameter value unit
1 The operating frequency (f) 3623 Hz 2 Equivalent resistance (Req) 0.245 Ω 3 Equivalent inductance (Leq) 64.325 µH 4 Series Capacitance (Cs) 30 µf
Table 5.10 shows a comparison between the inverter voltage and current for both
simulation and prototype results.
Experimental Simulation Percentage of error (E) Frequency
kHz Vinverter (V) Iinverter (A) Vinverter (V) Iinverter (A) Evolt % Ecurrent %
3.623 09.80 40.0 10.66 39.18 8.7 2.05
3.200 14.50 32.64 15.32 31.82 5.6 2.51
2.800 16.78 20.5 17.50 19.94 4.3 2.73
Table 5.9 Electrical parameter of the prototype furnace
Table 5.10 Comparison between simulated and experimental values of furnace voltage and inverter current at different frequencies
Fig. 5.33 Typical setup of the prototype furnace.
CHAPTER 5 SIMULATION AND RESULTS
67
Figure 5.34 (a) and (b) shows the experimental and the simulated furnace voltage
and inverter current at resonant frequency. Figure 5.35 (a) and (b) shows the experimental
and the simulated inverter voltage and current at frequency lower than the resonant
frequency (f=3546 Hz). It is clear that the voltage and the current are in phase at the
resonant frequency while the voltage is lagging the current when the operating frequency is
lower than the resonant frequency.
5.6 COMPARISON BETWEEN PARALLEL AND SERIES
RESONANT INVERTER SYSTEMS. On the previous sections, the parallel and series resonant inverter systems were
demonstrated and discussed in details. In this section a comparison between both systems
will be carried out.
As shown previously, the supply voltage of the series resonant system is lower than
that of the parallel one, while the inverter current of the series system is higher than that of
Fig. 5.35 Inverter voltage and current at frequency lower than fo a) experimental b) simulation
(a) (b)
Fig. 5.34 Inverter voltage and current at resonant frequency a) experimental b) simulation
Iinverter
Vinverter
(b) (a)
(b)
CHAPTER 5 SIMULATION AND RESULTS
68
the parallel one. It should be noted that, all the system components are subjected to the
high current in the series resonant system while only the furnace is subjected to the high
current in the parallel resonant system.
The actual parallel resonant system has a starting circuit in order to accumulate the
necessary energy in the DC link reactor, while in series system, the starting is simple and
does not need a starting circuit as discussed previously in chapter 4.
Table 5.11 shows a comparison between the consumed power, overall efficiency
and the total harmonic distortion (THD) of the supply current for the two systems at three
different levels of reference power. It is clear that the consumed power of the parallel
resonant inverter system is higher than the one of the series resonant inverter system, and
the efficiency of the series resonant inverter system is higher than that of the parallel
resonant inverter system. On other hand, as the series resonant inverter system uses a full
rectification converter, it produces lower harmonics to the supply and the supply voltage is
notching free. It should be noted that, the difference between the THD of the two systems
is not significant at low firing angles, but the THD of the parallel system increases
dramatically as the firing angle increases as shown previously in table 5.5.
Figure 5.36 and 5.37 show the supply voltage and current waveforms for parallel
and series resonant inverter systems respectively. It can be seen that the supply voltage has
a severe notching in the parallel resonant inverter system which doesn't exist in the supply
voltage of the series resonant inverter system. It is also clear that the parallel resonant
inverter system produces higher harmonics than that of the series resonant inverter system.
The series resonant system gives its maximum power at the resonant frequency,
while the minimum power of the parallel resonant system is given at resonant frequency as
shown in Fig. 5.38 (a) and (b) respectively.
Consumed Power (MW) Efficiency % THD Ref Power
(MW) Parallel Series Parallel Series Parallel Series
2.00 2.508 2.235 79.40 88.46 0.3132 0.2995
2.25 2.813 2.787 80.14 82.67 0.3110 0.2960
2.50 3.125 3.013 80.70 83.01 0.3095 0.2944
Table 5.11 Comparison between parallel and series resonant systems' consumed power, efficiency and THD
CHAPTER 5 SIMULATION AND RESULTS
69
In order to sustain the thyristors turn off time, the operating frequency should be
higher than the resonant frequency in the parallel resonant system while it should be lower
than the resonant frequency in the series resonant system.
Fig. 5.37 Supply current and voltage of the series resonant system
Fig. 5.36 Supply current and voltage of the parallel resonant system
(a) (b)
Time
Vsupply Isupply
Time
Vsupply Isupply
Fig. 3.38 Output power of a) Series resonant system and b) Parallel resonant system at different values of frequency
CHAPTER 5 SIMULATION AND RESULTS
70
The control technique of the series resonant system depends only on the control of
operating frequency of the inverter; while both; the controlled rectifier's firing angle and
the operating frequency are controlled in the parallel resonant inverter.
As previously shown the THD of the parallel system increases as the firing angle
increases, therefore, the power factor of the system is getting worse as the firing angle
increases. The power factor of the series resonant system is about 0.95 as the THD is
ranging around 0.3 as shown in table 5.11, while it varies from 0.7 to 0.95 depending on
the controlled rectifier's firing angle of the parallel resonant system.
Series resonant system is simple in design than the parallel resonant system, which
means lower cost in terms of money.
Table 5.12 summaries all the previous points as a comparison between series and
parallel resonant systems.
Feature Parallel Resonant Inverter Series Resonant Inverter
THD Depends on the firing angle Low Voltage High Low Current Low High Starting technique Complicated Simple
Operating frequency Higher than fo (to sustain thyristor toff )
Lower than fo (to sustain thyristor toff )
System power factor 0.7-0.95 (depends on the firing angle)
0.95
Setup Complicated Simple Line rectifier Phase control Full rectification
Control technique Phase control and frequency control Frequency control
Voltage notching Exists Notching free
As a conclusion from previous comparison, it is clear that the series resonant
system is better than the parallel resonant system. The only restriction on the series
resonant inverter system is the high furnace current that passes through the whole system
components.
Table 5.12 Comparison between parallel and series resonant systems
CHAPTER 6 CONCLUSION AND FUTURE WORK
71
CHAPTER 6
CONCLUSION AND FUTURE WORK
6.1 CONCLUSION In the production of mineral resources, the melting of metals has become one of the
tremendous industrial practices in the forefront. Induction furnaces are used extensively in
the metal industry for melting metals and as holding furnaces.
A coreless induction furnace system consists of a complete system of components
necessary for proper, reliable, and safe furnace operation. The main components required
are a furnace, power supply, power transmission system, and a water cooling system.
An understanding of the operating principals of induction furnaces must begin with
a basic understanding of induction heating and how it works. It was found that all
induction heating applied systems are developed using electromagnetic induction. The
basic principle of induction heating is the fact that AC current flowing through a circuit
affects the magnetic movement of a secondary circuit located near it.
Rather than just a furnace, a coreless induction furnace is actually an energy
transfer device where energy is transferred directly from an induction coil into the material
to be melted through the electromagnetic field produced by the induction coil.
The capacity of the furnace is determined by the size of the pour required, the size
and shape of the charge material to be melted, and the power density. There are many
factors that influence the selection of furnace power, the first is the capacity to be melted,
the type of the material to be melted (Iron, Aluminum, Tin ...) and the desired melt cycle
time. For optimal furnace performance, the selection of the system operating induction
frequency is very important, as it affects both the coupling efficiency of the
electromagnetic field to the charge and the stirring characteristics of the molten metal in
the furnace.
The geometrical parameters of the furnace such as diameter of melt, the height of
melt, and diameter of coil are determined directly by the furnace capacity. The heat energy
required to melt the charge material depends on the solid specific heat, latent heat of
fusion, and liquid specific heat of the charge material. From which, the power required to
melt the material can be determined. The electrical parameters of the furnace such as
number of turns of coil, inductance of the coil, resistance of the coil and the maximum flux
CHAPTER 6 CONCLUSION AND FUTURE WORK
72
density are determined based on transformer concept, where the furnace is represented by a
transformer with (N) turns primary and one tune secondary that is short circuited.
The possible power supplies of the coreless induction furnace are current fed
inverter with parallel capacitor bank, which depends on the concept of parallel resonant
circuit, and voltage fed inverter with series capacitor bank, which depends on the concept
of series resonant circuit. Both systems are the most common types of power supplies used
in industry as they produce minimum switching losses.
Compromising between series and parallel resonant inverter systems shows that
series resonant inverter system is better than parallel resonant inverter system in the
aspects of efficiency, power factor, harmonics introduced to the supply current, control
technique, and cost. The only restriction on the series resonant inverter system is the high
current of the furnace which passes through the whole system components therefore high
current rating thyristors and circuit breakers must be used in this system.
6.2 FUTURE WORK Fault diagnosis can be considered as an extension to this work. Fault diagnosis is to
specify the faulty thyristor/thyristors directly from the shape of the current/voltage
waveforms at the time of fault. This will help in quick removal of faults in real
applications.
The furnace acoustic noise could be studied as a point of comparison between
series and parallel inverter resonant systems.
References
73
REFERENCES [1] Unbiased Induction Heating Expertise,
http://www.inductionatmospheres.com/induction_heating.html#Anchor-HO-52727
[2] J. Callebaut and Laborelec "Power Quality and Utilization Guide", Section 7: Energy
Efficiency, February 2007, www.leonardo-energy.org.
[3] Shrets, I.; Tolubinsky, V.; Kirakovsky, N.; Neduzhy, I.; and Sheludko, I. 1987. Heat
Engineering. Mir Publ., Moscow, Russia.
[4] Hammond, P. 1978. Electromagnetism for Engineers - An Introductory Course.
Pergamon, Oxford, London, UK.
[5] A. J. Mestel, ”On the flow in a channel induction furnace”, Journal of Fluid
Mechanics (1984), 147: 431-447 Cambridge University Press
[6] P. Dorland. J. D. Van Wyk and Fellow, "On the Influence of Coil Design and
Electromagnetic Configuration on the Efficiency of an Induction Melting Furnace",
IEEE Transactions on industry applications, vol. 36, no. 4, July/August 2000.
[7] Induction Heating System Topology Review, www.fairchildsemi.com/an/AN/AN-
9012.pdf , July 2000.
[8] D. A. Lazor, "Induction Related Considerations in Investment Casting", Modern
Investment Casting Technical Seminar March 27-29, 2001.
www.lectrothermprocesssystems.com/en/pdf/techdocs05.pdf
[9] Basics of Induction Heating " Induction Heating Guide"
www.inductoheat.co.uk/Downloads/lnduction_Heating_Guide.pdf
[10] J. Lee, S. K. Lim, K. Nam and D. Choi, "Design Method of an Optimal Induction
Heater Capacitance for Maximum Power Dissipation and Minimum Power Loss
Caused by ESR",
www.postech.ac.kr/ee/cmd/publications/designmethod.pdf
[11] K.C. Bala, "Design Analysis of an Electric Induction Furnace for Melting Aluminum
Scrap", Federal University of Technology Minna, Niger State, Nigeria, Oct. 2005,
www.journal.au.edu/au_techno/2005/oct05/vol9num2_article04.pdf
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www.inductotherm.com.
[13] A. K. Sawheny, A Course in Electrical Machine Design, J.C. Kapoor, 1981.
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[14] D. V. Riesen and K. Hameyer, "Coupled Electromagnetic, Structural-Dynamic, and
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42, no. 4, April 2006
[15] Lloyed H. Dixon, Jr. "Eddy Current Losses in Transformer Winding and Circuit
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[16] O.S. Fishman, "Power Supplies in Induction Melting systems", May 2001,
www.inductotherm.com.
[17] O.S. Fishman, "AC line distortion for static power converters used in induction
melting", September 2001, www.inductotherm.com.
[18] M. H. Rashid, Power Electronics circuits, devices and applications, Prentice Hall
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[19] B. K. Bose, Modern Power Electronics and AC Drivers, Prentice Hall PTR, 2001.
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[21] Cast iron, http://en.wikipedia.org/wiki/Cast_iron
[22] Metals - Specific Heat Capacities
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[23] Physics Lab: Specific and Latent Heat
http://phoenix.phys.clemson.edu/labs/223/spheat/index.html
[24] Iron, http://www.du.edu/~jcalvert/phys/iron.htm
[25] Resistivity of Iron
http://hypertextbook.com/facts/2004/JonathanRuditser.shtml
[26] Temperature coefficient of resistance
http://www.allaboutcircuits.com/vol_1/chpt_12/6.html
75
الرسالة باللغة العربيةملخص
بكفاءة تـسخين عاليـة حيث يتميز يستخدم التسخين الحثي استخداما واسع النطاق في الصناعات المعدنية
مما ساعد على إستخدام أفران الحث الكهربى لصهر المعادن و .نه غير ملوث لبيئة العمل كما إ ومعدل إنتاجية عالي
أفران الحث الكهربـي يوجد نوعان من و .وى الكهربية ذات التردد العالي القتطور مصادر في صناعة المسبوكات
. مستخدم في الصناعة، أفران حث بدون قلب وأفران حث قنويةال
حيـث تـم ) أفران حـث بـدون قلـب ( تهتم هذه الرسالة بتصميم أفرن الحث الكهربي من النوع األول
العناصـر المتطلبـات الميكانيكيـة تحدد .صة بفرن الحث الكهربي استعراض المتطلبات الكهربية والميكانيكية الخا
حـدد إلخ فـي حـين ت ... الهندسية الخاصة بالفرن مثل طول وقطر الفرن، ارتفاع المعدن، سمك العوازل والبطانة
. ومواصفات ملف الحث المطلوبة المطلوبة لتشغيل الفرن وصهر المعدن الكهربيةالمتطلبات الكهربية مقدار القدرة
تقديم نموذج لفرن الحث الكهربي، وتم استعراض مصدرين لتغذية الفـرن باسـتخدام فى هذه الرسالة تمو
حزمة فرن ومصدر التغذية باستخدام كما تم تصميم نموذج محاكاة لل .التوالى وعواكس رنين توازينين ال عواكس ر
ضا تم عمل مقارنة بين النتائج التي تـم أي .لقالمغنظام المسار و لنظام المسارالمفتوح وذلك MATLAB ـ برامج
عواكس رنين التـوازي وعـواكس وأخيرا تم عمل دراسة حول .الحصول عليها من المحاكاة وبين النتائج العملية
. وذلك بهدف المقارنة بينهمارنين التوالى
:وتتكون الرسالة من ستة أبواب
."مقدمة للرسالة" :األولالباب
يقدم هذا الباب مناقشة تفصيلية عن التسخين الحثي، أساسياته والعوامل التـي تـؤثر . "التسخين الحثي ":الثانيالباب
.كما تم تقديم فرن الحث الكهربي كتطبيق للتسخين الحثي وتم استعراض مكونات النظام. فيه
ي تؤثر في تصميم الفـرن في هذا الباب تتم مناقشة العوامل الت . "تصميم فرن حث كهربي بدون قلب ": الباب الثالث
تم أيضا تقديم كما .مثل تردد التشغيل، فوران المعدن، االرتفاع الهاللي للمعدن و عمق التيار المستحث داخل المعدن
. الفرن والحسابات الخاصة بذلكطريقة تصميم
ة الكهربيـة الخاصـة يقدم هذا الباب أنواع مصادر التغذي . "ي مصادر القوى في أنظمة الصهر الحث ":الرابعالباب
كأهم أنواع المصادر المستخدمة في عواكس رنين التوازي وعواكس رنين التوالى بأفران الحث، كما يناقش تفصيليا
.الصناعة
السابق تقديمه لتصميم فرن حث كهربـى بـدون تم تنفيذ التصميم في هذا الباب . "المحاكاة والنتائج " :الخامسالباب
تم عمل مقارنة بين النتائج التي تم الحصول عليها من المحاكاة وبـين النتـائج . ن الحديد قلب لصهر أربعة أطنان م
وأخيـرا تـم توالىرنين ال عواكس نظام زي أوال ثم مناقشة نتائج عواكس رنين التوا نظام تم مناقشة نتائج و .فعليةال
. الصناعةمقارنة بينهما وذلك من أجل معرفة أيهما أفضل كهربيا لالستخدام فيعمل
ما تم استنتاجه من هذه الدراسة وتـم تقـديم بعـض استعراضتم . " والعمل المستقبلي االستنتاجات": الباب السادس
. التوصيات واالقتراحات للعمل المستقبلي
ـةـــة اإلسكنـدريــعـامـج ـةـــة الهندسـآليـ
اإللكترونيات الصناعيةتطبيقات )تصميم ومحاآاة فرن حث آهربي بدون قلب(
رسالة علمية
مقدمة إلى الدراسات العليا بكلية الهندسة جامعة اإلسكندرية
استيفاء لمتطلبات الحصول على درجـة
رـيـ الماجست
في
ةـيـة الكهربـالهندس
مقدمة من
أحمد محمد الشرقاوي/ مهندس
2008