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


Prof. Dr.: Mohamed Yousry Gamal El-Deen ………………

Electrical Department


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.


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


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.


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].


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


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


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


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


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.


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


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)


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


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


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


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


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


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


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


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


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,


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


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


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


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


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)


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


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


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°


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


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


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)


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


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


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)


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


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


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


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


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 ⟩


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


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


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


47

item


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


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


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


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


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


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


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


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


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


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.


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


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


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


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


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)


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.


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


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


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


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.


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.


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)


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


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


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

[12] J. H. Mortimer "Batch Induction Melting the Science and Technology", Aug. 2003,

www.inductotherm.com.

[13] A. K. Sawheny, A Course in Electrical Machine Design, J.C. Kapoor, 1981.

References

74

[14] D. V. Riesen and K. Hameyer, "Coupled Electromagnetic, Structural-Dynamic, and

Acoustic Simulation of an Induction Furnace", IEEE Transaction on magnetics, vol.

42, no. 4, April 2006

[15] Lloyed H. Dixon, Jr. "Eddy Current Losses in Transformer Winding and Circuit

Wiring" http://focus.ti.com/lit/ml/slup197/slup197.pdf

[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

PTR, June 1994.

[19] B. K. Bose, Modern Power Electronics and AC Drivers, Prentice Hall PTR, 2001.

[20] F.P. Dawson, "A Comparison of Load Commutated Inverter Systems for Induction

Heating and Melting Applications", IEEE Transactions on power electronics, vol. 6,

no. 3, July 1991.

[21] Cast iron, http://en.wikipedia.org/wiki/Cast_iron

[22] Metals - Specific Heat Capacities

http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

[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

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The Thesis Industrial Electronics Applications (Design and Simulation of Coreless Induction Furnace)

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