Design and analysis of high frequency matrix converters for induction heating

Unlike other matrix converters, the matrix converters described in this thesis are the first direct converters to supply high frequency >150 kHz output current, mainly for induction heat

Summary

This thesis describes the development of novel high-frequency (>150 kHz) matrix converters for induction heating applications The primary goal has been to explore the possibility of making high performance direct converters, allowing more compact and reliable power converters to be realised, by removing the bulky energy storage components of the DC-link found in traditional approaches High input power quality, i.e unity input power factor and very low input total harmonic distortion (THD), and good efficiency are demanded

A single-phase matrix converter has been developed to firstly explore the possibility of performing high speed commutation of output current, without any DC-link between the input and the output A novel single-step voltage commutation strategy, implementing soft-switching condition over a wide power control range, has been developed and experimentally verified The high performance of the converter has been confirmed by comparison to a benchmark reference converter, which is a modified H-bridge converter with an unsmoothed DC-link A pulse density modulation scheme has also been developed and preliminarily verified, for use in the development of the three-phase to single-phase matrix converter

A novel topology of three-phase direct converter, in the form of a 3×2 matrix converter, featuring high input power quality, and soft-switching operation, has been proposed, along with a few novel modulation strategies A basic rectifying algorithm has been used to investigate the impact of unavoidable disconnection of one input phase (in a 3×2 matrix converter), for an interval of up to a few tens of switching cycles Following that, a constant output pulse density modulation (CPDM) method has been developed

and tested, showing improvements on the input current waveform, but further reduction

of THD is still required Three variable output pulse density modulation (VPDM) methods, utilising different pulse patterns, have finally been proposed, to create high input power quality and good efficiency, with results supported by measurements on an experimental laboratory prototype It is notable that this high performance has been achieved with a very simple controller, requiring no on-line calculations for the synthesis of three-phase input current system

Finally, some methods of improving converters’ efficiency, namely reducing on-state resistance of power devices, and application of synchronous rectification, have been investigated Since the on-state resistance of power devices has been reduced to a value that is not yet realistic in commercial devices, the investigation has therefore been carried out by simulations Switching patterns for both the single-phase and the three-phase to single-phase matrix converters have been modified to accommodate synchronous rectification action where appropriate, with supporting results from experiments on laboratory prototypes

Unlike other matrix converters, the matrix converters described in this thesis are the first direct converters to supply high frequency (>150 kHz) output current, mainly for induction heating applications, featuring the following advantages:

• Single-step voltage commutation, allowing high speed soft-switching, at low implementation cost

• Very high input quality, i.e unity power factor and very low input current THD

• Very good efficiencies (at least 92% at full power)

• PWM and PDM methods of power control, helping reduce EMC problems associated with frequency modulation methods

• Very simple control algorithm, independent of output frequency and requiring no online calculations

Published material based on the research presented in this thesis include:

N Nguyen-Quang, D.A Stone, C.M Bingham, & M.P Foster: ‘Single phase matrix

converter for radio frequency induction heating’, SPEEDAM 2006, Taormina, Italy

CD-ROM Proceedings

N Nguyen-Quang, D.A Stone, C.M Bingham, & M.P Foster: ‘Comparison of

single-phase matrix converter and H-bridge converter for radio frequency induction heating’,

EPE-2007, Aalborg, Denmark CD-ROM Proceedings

N Nguyen-Quang, D.A Stone, C.M Bingham, & M.P Foster: ‘A three-phase to

single-phase matrix converter for high-frequency induction heating’, accepted for

publication in EPE-2009, Barcelona, Spain

First, I would like to thank my supervisors, Dr David Stone and Dr Chris Bingham, for their invaluable guidance and support during the entire length of my PhD study I also thank Prof Geraint Jewell for acting as internal examiner, and Dr Suleiman Abu-Sharkh of the University of Southampton for acting as external examiner

I would also like to thank the Vietnamese government, in particular the “Vietnamese Overseas Scholarship Program”, for their financial support, without which my PhD study would be impossible

My thanks to all members of the Electrical Machines and Drives research group, where the work for this research was conducted This has been my second home thanks to your hospitality

My wife, Lien Cao-Bich, for her love, understanding and patience over the last 3 years Thank you for being a great companion

I would like to express my appreciation to my family and close friends In particular, I thank my mother, my father and my sister

To my mother

Table of Contents

Summary i

Acknowledgements iv

1 Introduction 1

1.1 Basic principles of induction heating 1

1.1.1 Excitation frequency vs heat penetration 4

1.1.2 Background to induction heating 6

1.2 Resonant inverters 11

1.2.1 Current-fed inverter 11

1.2.2 Voltage-source inverter 17

1.2.3 Alternative resonant load circuit 34

1.3 Methods used for analysing resonant-mode inverter systems 35

1.4 Power factor correcting rectifiers 40

1.5 Other converters 42

1.6 Proposed system 45

1.7 References 46

2 Benchmark reference converter and state-of-the-art matrix converter technologies

54

2.1 Introduction 54

2.2 Design of the reference system 56

2.2.1 Resonant output circuit 56

2.2.2 MOSFET-based H-bridge 64

2.2.3 Transistor gate sequencing 65

2.2.4 Gate drive module 67

2.3 Simulation and experimental results 68

2.4 State-of-the-art of matrix converter technology 74

2.4.1 Introduction 74

2.4.2 Background to matrix converter technology 75

2.4.3 Single-phase AC-AC converters 78

2.4.4 Three-phase to single-phase matrix converters 81

2.4.5 Three-phase to three-phase matrix converters 89

2.4.6 Practical bidirectional switch realisation 100

2.4.7 Commutation methods 102

2.4.8 Input filter design 107

2.4.9 Protection issues 109

2.4.10 Driving circuit designs 111

2.5 Summary 113

2.6 References 115

3 Single-phase matrix converter 123

3.1 Introduction 123

3.2 Fundamentals of high frequency single-phase matrix converter 124

3.2.1 Resonant output circuit (load) 124

3.2.2 Structure of the single-phase matrix converter 124

3.2.3 Switching control pattern and operating principle 125

3.3 Design of single-phase matrix converter 131

3.3.1 2x2 matrix converter design 131

3.3.2 Gate drive module design 132

3.3.3 Input filter design 134

3.4 Simulation and experimental results 135

3.5 Performance comparison of single-phase matrix converter and H-bridge converter 140

3.5.1 Topology comparison 140

3.5.2 Input quality comparison 142

3.5.3 Controllability comparison 144

3.5.4 Efficiency comparison 145

3.6 Pulse density modulation 148

3.7 Conclusions 151

3.8 References 153

4 Three-phase to single-phase matrix converter 154

4.1 Introduction 154

4.2 Basic principles of the three-phase to single-phase converter 156

4.3 Input rectifier algorithm 160

4.4 Constant output pulse density modulation 162

4.5 Variable output pulse density modulation 169

4.5.1 Interlaced pulse density modulation 172

4.5.2 Non-interlacing pulse density modulation 178

4.5.3 Hybrid pulse density modulation 181

4.5.4 Line frequency synchronisation and output current circulation 183

4.5.5 Performance evaluations 187

4.6 Conclusions and discussions 204

4.7 References 207

5 Performance improvement for matrix converters 209

5.1 Introduction 209

5.2 Influence of on-state resistance 209

5.3 Modified switching algorithms 211

5.4 Performance evaluation of matrix converters with new switching algorithms

214

5.5 Conclusions and discussions 219

5.6 References 222

6 Conclusions and Future Work 224

6.1 Conclusions 224

6.2 Future work 227

7 Appendices 230

7.1 Hardware schematics 230

7.2 FPGA configurations (VHDL code) 232

7.3 PIC and dsPIC programs (Basic and C code) 255

1 Introduction

The research and development of radio-frequency matrix converter technology, for use

in induction heating applications, is described This chapter introduces related technologies and the current state-of-the-art in the field A review of resonant inverters used in induction heating systems, and the analysis methods associated with those inverters, is also given

1.1 Basic principles of induction heating

The underlying principles of induction heating are based on the creation of an alternating electromagnetic field that is used to induce current in a load and in so doing heat the load (via the ‘skin effect’) The energy transfer mechanism is similar to

‘transformer action’, whereby energy is transferred from a primary winding to a secondary winding through induction In the case of induction heating systems, the primary is the heating coil, known as the ‘work-head’, and the secondary (which is effectively a short circuit) is the object to be heated up, termed the ‘work-piece’ The work-head and work-piece are therefore isolated, giving a non-contact heating method, which is very important for improving the product quality in metallurgy and semiconductor industries, for instance The method also provides localised heat treatment, allowing very accurate heat profiles to be realised

When designing transformers the coupling between the primary and secondary is usually good, however, the coupling between the heating coil and the load is normally poor as a consequence of the mechanical clearance needed for loading and heat isolation This means only a small fraction of the power from the work-head ultimately dissipates as heat in the load, and therefore, a loaded coil normally has a low power

factor The situation becomes worse in high frequency coils since the effect of the leakage inductance is more pronounced than in low frequency counterparts This also implies that the loaded work-head acts like an inductive load

In the induction heating industry, the quality factor, Q L, is usually used to denote the

effect of the poor coupling in work coils Q L is defined as in (1.1), where the coil has

the inductance of L (Henrys), and R L (Ohms) represents the sum of the coil and reflected

load resistances f s is the frequency of the electromagnetic field (which is usually the

switching frequency) In this definition, the coil inductance L and the total resistance R L

are in series The quality factor, in fact, describes the ratio between the reactive power and the active power of the coil

L

s L

R

L f

The magnetic coupling between the work-head and the work-piece depends on the magnetic properties of the material of the work-piece, with ferrous materials having

lower Q L than non-ferrous counterparts However, after heating above the Curie point,

at which point the ferrous material looses its ferromagnetic properties, Q L increases significantly, implying that much lower active power can be delivered to the load for a given VAr Table 1.1 shows some examples of quality factor for different materials and operating conditions [1.1]

Radio-frequency loaded work coils usually have Q values in the range 5-15 for ferrous

loads and between 10-25 for non-ferrous loads [1.2], implying that much more power is dissipated in the coil than into the load, which is a common case Therefore, coil losses

ultimately limit the Q However, coil loss is usually increased by the skin effect, which

increases the AC resistance of the coil By silver-plating the coil, or replacing the coil

with cooled Litz wire, the range of effective Q can sometimes be increased [1.1], [1.3]

Material VAr/W Steel below 730 0C 7 Steel above 730 0C 28

Table 1.1 Typical quality factor of common materials

The very poor power factor of the coil can be improved through the addition of a capacitor, which can be connected either in series or in parallel to the coil, resulting in either a series resonant tank, which increases the coil voltage, or a parallel resonant tank, which increases the coil current

With series configured tank circuits, the relatively large coil current has to flow through the power supply and the tank circuit, whereas only part of this current needs to be supplied to the tank circuit by the power supply in the case of parallel tank circuits This is because the parallel circuit allows a large amount of reactive power to circulate between the capacitor and the inductor Therefore, the required current from the inverter is only a fraction of the coil current, and this is the most important reason for using parallel tank circuits in induction heating

Parallel tank circuits, however, can not be readily used with voltage source inverters, as the high frequency impedance of the tank circuit tends to be low, and cause current spikes at the edges of the applied voltage waveform In contrast, series tank circuits are more suitable for voltage source inverters, as the inductance of the tank circuit will dominate at high frequency The series tank, however, usually requires a matching transformer due to its low impedance at resonance

The efficiency of the coil is also important when designing work pieces made of different materials For a tubular coil with a work piece inside it, the efficiency of the coil can be estimated from (1.2) [1.2], where ρc and µc are the resistivity and permeability of the coil, and ρw and µw are those of the work piece, respectively To provide an efficient solution, the work coil is always made of copper, the best practical conductor, and is normally water-cooled The efficiency is then typically around 50% for non-ferrous loads and for ferrous loads above their Curie point However, the efficiency can approach 100% for ferrous loads below the Curie point, because of the very high permeability and high resistivity of the material

w c w

c

µ µ

ρ ρ

η+

≈1

1

(1.2)

The coil also experiences skin effect, which usually increases its resistivity Therefore, the two methods described above for increasing the limit on the quality factor, also act

to improve the efficiency of the coil

1.1.1 Excitation frequency vs heat penetration

According to Lenz’s law, the induction of the current onto the surface of the work-piece due to the excitation field will create an opposing field, which reduces the magnetic field below the surface This effect, known as ‘skin effect’ causes an exponential decrease in current density with depth, as illustrated in Fig 1.1 The depth from the surface at which the magnitude of the current density is 1/e of its value at the surface

(where e is the base of natural logarithms) is called ‘depth of penetration’ or ‘skin

The depth of penetration depends on the resistivity and permeability of the material, and the frequency of the magnetic field, as shown in (1.3) [1.2]

For a given material whose resistivity and permeability are known, the applied excitation frequency can be used to control heat penetration Therefore, surface hardening, which creates hard and less fault-prone components, usually employs high frequency excitation, and is associated with shallow skin depth By contrast, through heating or ‘billet heating’, which requires the object to be uniformly heated up, generally uses relatively low frequency excitation

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Figure 1.1 Typical current density in induction heating applications

50 – 540 Hz Supply-frequency Melting, forging

500 Hz – 50 kHz Medium frequency (M.F.) Melting, forging, brazing, hardening

50 kHz – 10 MHz Radio frequency (R.F.) Welding, brazing, surface hardening

Table 1.2 Frequency bands for induction heating

Since frequency is the primary variable to control the skin depth (permeability being relatively constant), for induction heating, standard operating frequency bands have been defined, as shown in Table 1.2 [1.2]

1.1.2 Background to induction heating

Induction heating of objects has now become a relatively mature technology In 1927 [1.2], the first medium frequency melting furnaces were installed in Sheffield, using a motor-generator set to create the excitation field Radio transmitters with vacuum valves were subsequently modified to make valve-based generators for the first radio-frequency heating system Valve-based systems are still produced today [1.4] and the use of motor-generator based systems are still employed in a minority of systems

The use of motor-generator sets and valve-based generators do, however, have some disadvantages viz lower efficiencies, higher capital cost, fixed frequency of operation for motor-generator sets, high operating voltages for valve-based system, among others Consequently, solid-state inverters using junction transistors were subsequently favoured, but only at low power levels More successful were medium frequency solid-state systems based on thyristors utilising parallel tank circuits due to their low reactive circulating powers—consequently, current-fed inverters have become the most popular topology to date Nevertheless, thyristor power switching devices are now relatively slow compared to other power switch technologies, with practical limits of switching frequency of around 10 kHz (although some low power variants can switch at upto 50 kHz) Nevertheless, modern thyristors can have power ratings upto 18 MW per device

at 10 kHz [1.5] which is beyond the ratings of other fast switching technologies, and their use therefore remains prevalent

With the emergence of the IGBT, the limitations of medium frequency solid-state systems has been extended from its principle limit of 50 kHz to 150 kHz and beyond with power ratings per device of 4 MW at 50 kHz [1.6]

In the 1980s, a trend of developing MOSFET-based inverters to replace valve-based systems for radio frequency induction heating began to emerge [1.7] – [1.9]

‘Transitorized power supplies for induction heating’ [1.7] is one of the first attempts of making radio frequency solid-state inverters, in particular cycloconverters, voltage-fed inverters and current-fed inverters that used 100 – 150 kHz excitation and fed second-order resonant circuits—in this case the current-fed inverter provided the best performance for induction heating Specific outcomes of the study were that the voltage-fed inverter used ‘above resonance excitation of the load tank circuit’, enabling recovery problems associated with the parasitic diode of the MOSFET to be prevented The current-fed inverter always operates close to the resonant frequency of the load

Figure 1.2 Cycloconverter using MOSFETs

The ‘equivalent cycloconverter’ was realised but replacing the thyristors with MOSFETs—see Fig 1.2 Each transistor has a discrete fast-recovery blocking diode in series to provide a reverse blocking capability By monitoring which supply phases provide most positive or most negative voltages and switching the transistors in those phases in an antiphase manner at high frequency, a continuous high-frequency, single-phase current flows through the load The International Rectifier IRF610 device was used for the cycloconverter, and operating frequencies in excess of 100 kHz were achieved However, the cycloconverter requires additional control circuitry and more

complicated protection circuitry than the more common current- or voltage-fed inverter circuits Induced mains harmonics were also a significant problem even at the low power levels

Figure 1.3 Voltage-fed inverter using MOSFETs

A voltage-fed inverter, Fig 1.3, was also considered The parasitic diode of the MOSFETs cannot be used to carry reactive currents because its relatively slow reverse recovery time can cause ‘shoot-through’ conditions Therefore, the load needs to be excited above its resonant frequency to provide a lagging power-factor current The voltage-fed solution had the advantages of providing easy shut-down by switching off the MOSFETs in the bridge, and power control using frequency modulation However, the paper [1.7] reported problems in protecting the transistors against short-circuit fault conditions when the inverter operated with induction heating loads and in suffering excessive rate of rise of voltage when the load was driven away from resonance

Since frequency control is used to transfer power, the load is often excited away from its resonant frequency, and hence the switches have to turn off during high reactive current conditions, which are supported by parallel diodes—as soon as S1 begins turning off and the current through it is reduced, the load current begins to flow through D3 This will bring the voltage across S1 to VDC, less the conduction drop of diode D3, making the switching losses of S1 significant

S1

S2 S3

S4 D1

D2 D3

D4

V DC

Figure 1.4 Current-fed inverter using MOSFETs as output switches

The current-fed inverter proposed in [1.7] is shown in Fig 1.4 The inverter uses a variable current source, which is realised by employing a controlled rectifier and a smoothing inductor The inverter always operates around the resonant frequency of the load, and power control is obtained by varying the direct voltage supplied to the inverter circuit The author makes the point that this topology has a number of advantages, including a low component count, low switching losses and inherent short-circuit protection provided by the large smoothing inductor However, this topology uses the largest number of switching devices among the three systems, and having two switching systems is likely to increase any problems associated with EMC The inductor is necessary to supply a constant current into the inverter stage, thereby creating an effective square-wave current at the load From the perspective of the high-frequency current source, it will drive an effective low impedance with a parallel resonant circuit and high impedance with a series resonant circuit Therefore, a current-fed inverter may induce overvoltage ‘spikes’ when feeding a series resonant load, thereby making a parallel resonant tank circuit more suitable in this case Moreover, to prevent the inductor from becoming open-circuited, overlap periods have to be introduced into the switching sequence of the inverter stage: S1 and S2 on; S1, S2, S3, and S4 on; S3 and S4 on; S1, S2, S3, and S4 on The paper does discuss the presence of ‘ringing’ due to the parasitic lead inductance and the drain-to-source capacitance of the MOSFETs, and

S1

S3

S4

S2

emphasises the importance of a good component layout and routing to reduce the problem Many of the concepts pioneered in this paper remain in use, despite the practical problems encountered with early prototypes

In 2002, a state of the art review was conducted by H.I Sewell [1.1] In this work, the author identified the most commonly used inverters for industrial heating at the time A brief review of sales literature and academic publications has shown that the range of high frequency inverters has expanded in both frequency and power At frequencies up

to 800 kHz, MOSFET-based inverters from Inductoheat Banyard can deliver up to 3

MW [1.10], or 2500 kW with Lepel’s solution [1.11] IGBT-based inverters from Lepel can deliver up to 1200 kW at 30 kHz [1.11] Similarly, IGBT-based systems from RDO Induction can deliver up to 600 kW at up to 20 kHz or up to 60 kW at up to 150 kHz [1.12] Cheltenham Induction Heating offer a range of solid-state inverters that can transfer up to 120 kW in frequency range of 50 – 150 kHz [1.13] Solid-state induction welding units from Thermatool Europe can work from 100 to 800 kHz at power ratings

up to 1200 kW [1.14] Similar products, using solid-state technologies, are also available from Ajax Tocco Magnethermic [1.15], Inductelec [1.16], and Huettinger Electronic [1.4] These product ranges have been depicted as diamonds in Fig 1.5 to show current trends Also depicted in the figure are some systems reported in journal papers [1.17] – [1.21], marked as colour circles

In Fig 1.5, red is used to depict IGBT-based systems and blue for MOSFET-based systems Although in some cases the switch technology is not known (marked in black), the graph does suggest that the IGBTs are used in low frequency range and the MOSFETs are more suitable for higher frequency ranges

Lepel

Cheltenham Inductelec

Kifune et al

Bayindir et al Okuno et al

Mollov et al Ogiwara et al

Figure 1.5 Map of switch technology vs power and frequency

1.2 Resonant inverters

Having examined the relationship among switch technologies, power, and frequency, it

is reasonable to explore the topologies used for industrial heating Naturally, the inverter will create an AC output from a DC power supply, and the DC source can be a current source or a voltage source High power systems usually have to draw the power from the utility supply, which is an AC voltage source, so a current source can be realised by rectifying the voltage source feeding an appropriately large inductance In summary, most systems used in practice employ current-fed inverters and voltage-source inverters

1.2.1 Current-fed inverter

Current-fed circuits using thyristors remain the most common inverters used in medium-frequency induction heating applications [1.2], [1.22], [1.23], although MOSFET-based [1.7] systems are still popular and use the same basic circuit topology The high-power topology, as shown in Fig 1.4, uses a fully controlled rectifier to supply the current to the high-frequency heating inverter For low-power systems, a slightly different topology, as depicted in Fig 1.6, can be used

Figure 1.6 Low-power current-source topology

By assuming that the resonant ‘tank’ circuit, comprising the work-head inductor and the tank capacitor, behaves as a sinusoidal voltage source, and the supply to the bridge comprising the utility supply, the rectifier and the smoothing inductor, behaves as a DC current source, a basic operational understanding can be made Each switch element is

a unidirectional device, which will conduct current from top to bottom If a thyristor is used for the switching element, then it is inherently a unidirectional device, otherwise the switching element is generally made up of a transistor and a diode in series The operation of the circuit then follows in several intervals [1.7], as shown in Figs 1.7 – 1.10

Figure 1.7 Positive half-cycle power flow

Beginning with S1 and S2 in on-state, and S3 and S4 are in off-state; when the load voltage passes through zero, the current flow is as shown in Fig 1.7 Since the impact

of stray inductance L1 is small and the current is effectively constant, there is effectively no voltage across L1, and hence, the voltage across the current source is

S3

S4 S1

S2 L1

equal to the sinusoidal load voltage of the parallel tank Energy is transferred from the current source to the load circuit in this period, until S3 and S4 are switched on

At some point during the positive half-cycle of the load current, S3 and S4 are turned

on At this point, all switches are in the on-state, effectively shorting the output voltage

of the inverter Just after the switching event, there can be three possible current paths,

as shown in Fig 1.8 The current in the bottom loop will have the same magnitude as the source current, and there will be no currents flowing in the top loop, creating no currents going through both S3 and S4 Due to the stray inductance L1, the current in the top loop will increase whilst the current in the bottom loop will decrease at the same rate, making the currents through S1 and S2 fall to zero and the currents through S3 and S4 rise to the supply current

Figure 1.8 First inductor-commutating interval

When the currents through S1 and S2 reach zero, the switches become reverse-biased and conduct no current, despite the driving signals In reality, the thyristor or the in-series diode requires a small period to recover its reverse-blocking capability This time, termed ‘reverse recovery time’, can vary from 20 µs to 100 µs for modern thyristors [1.5], with longer periods belonging to larger devices During this recovery time, current spikes can be introduced into the load current In Fig 1.9, the flow of reverse recovery currents of S1 and S2 is illustrated in dark red

S1

S2

L1 S3

S4

Figure 1.9 Recovery time of the switch

Just prior to the load voltage changing polarity, S1 and S2 are switched off, and power

is returned to the supply until the load voltage changes polarity Power is then transferred to the tank circuit when the load voltage is in the negative half-cycle, as shown in Fig 1.10 At the end of this power-transfer interval, S1 and S2 are turned on and the load current will be inverted again, repeating the cycle

Figure 1.10 Second power-transferring interval after the safety margin

The current-source topology has its own relative merits The first advantage is the low reactive power flow between the power supply and the load, which means a better utilisation of the inverter, and an interesting solution for high power systems The nearly constant operating frequency is another advantage, since EMC problems are easier to ameliorate However, there are some significant disadvantages associated with this topology The most obvious problem is that the parasitic inductance of the connection between the inverter and the resonant tank undesirably affects the system impedance For a given current, the crossover time will be higher with longer connection cable length The situation becomes worse when the inverter operates at

L1 S3

S4 S1

S2

S1

S2

L1 S3

S4

higher frequencies, because the crossover time may take a large fraction of the shorter period This can place upper limits on the operating frequency of and the physical distance between the inverter and work-head Moreover, IGBTs and MOSFETs, which can have considerable parasitic capacitances across the power terminals, may result in increased switching losses, when they are switched on with a large voltage across them,

in a high frequency current-fed inverter

It has been shown that only amplitude modulation is suitable for power control in this current-source topology, and two input power conditioning circuits for low and high powers are as described below Both frequency modulation, which excites the tank away from its resonant frequency, and pulse-width modulation, which changes the phase shift between the load voltage and current, result in lower power factor In addition, because the average voltages at both ends of the supply inductor have to be equal, in steady-state, poor power factor may lead to excessive voltages on the switches Therefore, frequency modulation and pulse-width modulation are not applicable to the current-source topology

Both utility interfaces (Figs 1.4 and 1.6) have non-unity power factor, and the controlled rectifier may create significant distortion on the current waveform [1.23] In the low power interface (Fig 1.6), a buck converter is used to control the current through the DC link inductor, and a fixed six-pulse rectifier supplies the buck converter

thyristor-At higher power levels, the bulky DC link components make this choice uneconomic, and therefore, a six- or twelve-pulse thyristor-based variable rectifier is normally used

in high power systems (Fig 1.4) Significant harmonic distortion can be introduced into the mains when these power interfaces are used For a 5 kW power load and an ideal utility supply, the low power interface can have the input current as shown in Fig 1.11 using a SIMULINK model, with a relatively low DC link capacitor (100 µF) From a

practical perspective, the clamping effect due to the small mains line inductors and relatively large DC link smoothing capacitor can create a trapezoidal mains voltage and

a highly distorted supply current The power factor and the total harmonic distortion (THD) are also known to be worse when the ratio of the drawn current to short-circuit current of each phase is reduced [1.23] In the low-power case, it can be expected that poor power factors and large harmonic distortion exist due to the very small ratio of supply current to short-circuit current This can be improved by using additional line inductors to increase the ratio, but at the expense of more bulky magnetic components and less cost effective system

-50 0 50

Figure 1.11 Idealised mains input waveform for low power CSI

Significant mains distortion also exists in high power systems (Fig 1.4) The THD of the line current of an ideal utility supply, with an infinite DC link inductance, has been determined to be fixed at 31.08%, despite the switching angle of the rectifier The mains line inductance in practical systems may slightly reduce the THD of current in certain conditions, however, significant distortion of the supply voltage can occur due to commutation events, where two out of three phase voltages are shorted together to transfer the energy between the line inductances, creating line ‘notching’ For high power systems, this can cause problems to other equipment connecting to the same

utility supply, and standards recommended a minimum value for the line inductances between the rectifier and the common coupling point [1.23] Nevertheless, because large harmonic currents injected by the power interfaces to the utility supply may exceed the limits specified in standards, harmonic reduction techniques are still necessary, and many improved power quality converters, such as power factor correctors, have been proposed

In summary, the current source inverter has been used for most of the induction heating systems due to its simple and straightforward approach, however, it has detrimental effects on the utility supply, and low efficiency in high frequency systems

1.2.2 Voltage-source inverter

Voltage-source inverters were an emerging topology at the time of the publication of the review in [1.1] Historically, the performance of the voltage-source inverter was essentially ignored because of poor load regulation, slow turn-off time of the thyristors, and slow recovery of power diodes [1.24] However, with more modern switching devices such as MOSFETs and IGBTs, the disadvantages are now less critical, and the use of this topology has become a more attractive proposition

Figure 1.12 Voltage-source topology proposed in [1.7]

The proposed topology [1.7], is shown again in Fig 1.12 A filter network with small inductance and large DC link capacitor is usually used to reduce the mains noise and

D1

D2 D3

distortion, and to maintain a nearly constant voltage The inverter, connecting to the mains supply through an uncontrolled rectifier, feeds a series resonant tank formed by the work-head and the tank capacitor The resonant tank, which has low resonant impedance, is usually coupled to the inverter through a step-down transformer

The voltage-source topology in Fig 1.12 depicts no explicit power control method Power control can be obtained by using frequency modulation [1.7], [1.25] – [1.29] or phase-angle modulation [1.17], [1.30], [1.31], although others have been proposed such

as amplitude modulation [1.19], and pulse-density-modulation [1.32], [1.33]

Frequency modulation is the most straightforward control method for resonant circuits, and is described in many text books Therefore, it will be discussed first as a benchmark solution Using this control method, a switch will be turned on or off along with its counterpart in the adjacent leg, so that a square-wave voltage is applied to the resonant circuit For the particular case of operation at resonance, a simplified description of operation can be made using the assumption of sinusoidal current flows through the series resonant circuit, with a small lagging phase to the switching signals The description takes into account the parasitic capacitance, which is not negligible for large devices and directly affects the operating principle, but assumes ideal switching devices and diodes without voltage drops It can be shown that the functions of the load voltage in current source inverters and the load current in the voltage source inverters are interchangeable, therefore, the operation of these inverters can be very similar

Beginning at the point where the load current changes polarity and has a positive value, the state of inverter will be as shown in Fig 1.13, which is unchanged during the majority of the time that a positive current flows through the load circuit S1 and S2 are

in the on-state, and S3 and S4 are in the off-state During this period, the load receives

power from the supply through the DC link, and current flows from the supply to the load via the H-bridge

Figure 1.13 Positive power-transferring interval

Figure 1.14 First commutation interval

Part way through the positive half-cycle of the load current, S1 and S2 are switched off

As the inductive impedance of the load circuit tends to maintain the load current, C1 and C3 now support the current of S1, and C2 and C4 support the current of S2, as shown in Fig 1.14 The load current charges C1 and C2, whilst discharging C3 and C4, hence lowering the voltage at the node between S1 and S3, and raising that at the node

of S2 and S4 The charging/discharging progress is complete when C3 and C4 are fully discharged, and C1 and C2 are fully charged, (assuming C1-C4 have equal capacitances) In this interval, the load voltage gradually reduce from +VDC to –VDC, and there will be no power transferred from the supply to the load circuit

S1

S2 S3

S4 D1

D2 D3

D4 C1

C2 C3

C4

VDC

S3

S4 D1

D2 D3

D4 C1

C2 C3

C4 S1

S2 VDC

Figure 1.15 Diode conducting interval

As C3 is fully discharged, the voltage at the node between S1 and S3 reaches 0V, and D3 becomes forward-biased, carrying the load current and clamping the node voltage to 0V Similarly, D4 will carry the load current and clamp the voltage at the node between S2 and S4, to VDC when C2 is completely charged Therefore, the load current will flow into the DC link, as depicted in Fig 1.15, when the clamping effect is active It should be noted that power is returned to the DC link in this interval After a pre-determined dead time, S3 and S4 are switched on When using most types of switching devices, the diodes will still support the current since the switches are reversed-biased Some current, however, may flow through the MOSFETs at this stage if the devices’ gate-to-source voltage rises higher than the threshold voltage

The load current subsequently approaches zero and changes polarity, and S3 and S4 will carry the current as shown in Fig 1.16, as the diodes cannot support the reverse current, which is the forward current for the switches The load circuit now receives power from the DC link, with both its voltage and current of opposite polarity to the previous case This state remains until S3 and S4 are switched off, and the commutating process is repeated with the load current reversed D1 and D2 will then be forward-biased, realising the second power-returning phase in the cycle, until S1 and S2 are turned on, allowing the load current to begin the next cycle

S3

S4 D1

D2 D3

D4 C1

C2 C3

C4 S1

S2 VDC

Figure 1.16 Negative half-cycle power-transferring part

The input current of the resonant tank is highly dependent on excitation frequency, as can be seen in Fig 1.17, which shows an example Bode plot of the input current wrt

frequency In this example case, the resonant tank has a quality factor (Q T) of 5, and a resonant frequency of 150 kHz, and with amplitude of 100 V for the excitation voltage

100 110 120 130 140 150 160 170 180 190 200 100

200 300 400 500 600

-40 0 40 80

D2 D3

D4 C1

C2 C3

C4 S1

S2 VDC

If the voltage and the current are non-sinusoidal, then a Fourier series can be used to obtain a series of sinusoidal voltages and currents, and the total power can be calculated

by summing the harmonic powers (1.5), where V in(h) is the amplitude of the hth

-harmonic voltage, I in(h) is the amplitude of the hth-harmonic current, and φh represents

the phase angle between the hth order harmonic voltage and current

1

h

h h in h in

When operating close to the resonant frequency, a high QT series resonant circuit will filter out the harmonics of the input voltage, and the fundamental of the current can be assumed to flow It is therefore possible to have conditions where the power present due to current harmonics, is negligible In such cases, power can then be approximated

to the power provided by the product of the peak values of the fundamental voltage and fundamental current, and the displacement power factor (1.6)

The phase response shown in Fig 1.17 shows that the voltage will lag the current when operating below the resonant frequency, and leads the current when operating above the resonant frequency As an inductive load is expected when using the frequency modulation method, the operating frequency of the inverter needs to always be higher than the resonant frequency—this also limits the range of operating frequencies so that a monotonic characteristic of power versus frequency is obtained (Fig 1.18)

150 0 155 160 165 170 175 180 185 190 195 200 100

200 300 400 500 600

-50 0 50 100

Figure 1.18 Effect of power factor on power vs frequency

For systems employing pulse amplitude modulation [1.19], power transfer is controlled

by varying the amplitude of the DC link voltage, while frequency is fixed independently

to some ‘optimum set-point value’ via a PLL frequency-tracking scheme By forcing the operating frequency to be slightly above the resonant frequency, zero-voltage switching (ZVS) turn-on is realised In [1.19], a lossless snubber capacitor is used to implement ZVS turn-off, and to reduce the EMI noise However, no assessment of the amount of EMI noise reduction that can be achieved, is made Moreover, a small time-delay between the output current and voltage is maintained to ensure soft-switching commutation, and effects due to the reverse recovery of the switching devices (SITs) are overcome by connecting anti-parallel diodes across them, whilst the dead-time for

charging the snubbing capacitor together with the stray capacitance of the device is not taken into consideration in the study In addition, it is known that the additional snubber capacitors can create high surge currents in the switching devices if the charging time is not large enough, leading to more lossy operating conditions or even damage to the power switches

Frequency modulation also has its limitation Since the amplitude of the output voltage

is constant, the impedance of the resonant circuit determines the current and power For reasons given previously, a resonant circuit connected to a voltage source inverter normally operates at a frequency slightly higher than its resonant frequency Consequently, when the work-head becomes ‘loosely coupled’ electromagnetically (e.g when removing the work-piece), the resonant frequency will increase, and can become higher than the operating frequency of the system, thereby eliminating the ZVS conditions and causing the output current to increase to values that can ultimately destroy the power switches Therefore, most systems employ an additional control loop

to automatically increase the frequency in this event in order to reduce the current, thereby avoiding damage This does cause another problem, however As suggested by Fig 1.18: increasing the frequency will lower the current, but the power factor is also decreased, hence, causing further reductions of power As a consequence, well-matched coils are necessary to achieve reasonable power flow from the supply to the work-piece

The use of new work-heads can also be problematic when employing frequency modulation—it is difficult to ‘soft start’ the inverter and therefore switch failure can occur if the workhead resonant frequency is not the expected resonant frequencies or a capacitor fault occurs

Using a variable ratio transformer between the inverter and the resonant circuit can partially solve the impedance mismatch problem In this case, the normalized

impedance and power of the resonant load can be represented as functions of the normalized frequency, with different curves for different values of the quality factor (QT) The frequency range required to initiate a given change in transferred power then becomes a function of QT i.e a high QT has a high selectivity, i.e a smaller frequency range is needed for a higher QT circuit to initiate a given change in transferred power Changing the frequency over a wide range can also cause EMC problems, and therefore, alternative methods have been proposed One such method is the so-called PWM or phase shift control, which does not have corresponding switches turning off at the same time The method currently uses two different schemes In the first, the two legs have the same duty cycle but phase shifts are introduced, and a unity output power factor can

be achieved by making φ1 equal to zero [1.17], [1.30], [1.31] The second scheme, where corresponding switches are turned on synchronously, but are switched off asynchronously, has been introduced in [1.1] The relative merits of both schemes are now reviewed

When using the first scheme, depending on the load characteristics, the switching frequency and the phase shift, different operating modes are found: i) the four switches turn-on with ZVS, ii) the four switches turn-off with zero current (ZCS), and iii) both switches in one leg operate at ZVS, while those of the adjacent leg operate at ZCS A duty cycle of 50% is usually chosen for the simplicity Operating mode iii) will now be considered in more detail since it includes an analysis of the impact of the different switching conditions of the other two modes

Beginning with the instant at which the load current changes polarity, when S1 and S4 are in the on-state, as shown in Fig 1.19, as the load current is in its positive half-cycle and S2 is open, the current circulates through S1 and D4, effectively short-circuiting the load voltage This state remains until S4 is switched off (and S2 is complementally

switched on), and there is no power being transferred from the supply or to the load in this part of the cycle

Figure 1.19 First zero-voltage output interval

When S2 is switched on (and S4 is turned off), D4 becomes reverse-biased The load current quickly transfers from D4 to S2, along with some voltage spikes in the load voltage waveform due to the reverse recovery of D4 S4 is therefore turned off with zero current, but the switching on of S2 can be expected to be lossy with a high voltage across the switch and adequate current at the switching instant This form of commutation, termed zero current commutation, has been shown to be more effective than hard commutation, but worse than zero voltage commutation After the commutating interval, power is supplied to the load through S1 and S2, as shown in Fig 1.20 This state remains until S1 is switched off (and S3 is turned on) The series inductor in the load circuit forces D3 to support the load current, which now circulates through S2 and D3, making the load voltage fall to zero, and hence, no power is transferred to the load circuit in this phase S3 is switched on at the same time S1 is turned off, however, it does not support the current until it changes polarity

D1

D2 D4

D3

Figure 1.20 Positive half-cycle power-transferring part

After the output current changes polarity, the condition is as shown in Fig 1.21 The current now circulates through S3 and D2, and the commutation of D3 to S3 occurs at zero voltage on S3 This form of commutation, termed zero voltage commutation, has the advantage of eliminating problems associated with reverse recovery The output voltage remains at 0V until S4 is turned on, as shown in Fig 1.22

Figure 1.21 First zero-voltage output in negative half-cycle

The remaining operating states are similar to those of the positive half-cycle, and, indeed, the cycle are terminated by a diode recovery of D2 and zero voltage commutation of D1 to S1

Constant frequency operation is the main advantage of this method, along with unity power factor output if the two commutation events are symmetrical about the centre of the output current waveform The constant frequency operation also improves the tolerance of the inverter to mismatched loads Such benefits of these advantages, however, are reduced by the noise of the ZCS leg caused by the effects of parasitic inductance during the diode’s reverse recovery time The efficiency of the inverter is

S1

S3 D1

D2

D4

S4

also reduced because of switch turn-on at high voltage across the switches in the ZCS leg, particularly when attempting to achieve symmetrical switching for unity power factor, as the commutation will occur when a higher current flows through the diode, with higher reverse recovery charge to be dissipated

Figure 1.22 Negative half-cycle power-transferring part

In ZVS operating mode the output voltage leads the output current, and is obtained by increasing the phase shift between switching each leg or operating at frequencies above the resonant frequency By contrast, the output voltage in ZCS operating mode lags the output current, and this is achieved by reducing the phase shift between the legs or operating at frequencies below the resonant frequency

Recently, a modification to the control schemes has been made in order to improve the efficiency of the inverter [1.17] In this paper, an additional dead time has been introduced into the switching on time of the switches, meaning that a duty cycle of less than 50% is used The dead time and the phase shift enables the system to be operate at the resonant frequency, with one leg in zero-voltage zero-current switching turn-on mode and the other leg in zero-voltage zero-current switching turn-off mode This is shown to make quantitative improvements in efficiency, however, the problems associated with zero-current switching still remain

As previously discussed, an alternative method for PWM has been proposed in [1.1] In this scheme, the corresponding switches are turned on synchronously, but are switched

S3

S1 D1

off asynchronously The method makes use of snubbing capacitors, which are introduced to realise ZVS turn-off for both legs operating in ZVS turn-on, due to operating frequency being above resonance The full operating sequence of the modes

is shown in Figs 1.23-1.28

Figure 1.23 First power transfer phase

The output current, Iout, begins its positive half-cycle when S1 and S2 are turned on, as shown in Fig 1.23 A current flows from the DC link through S1 to the load circuit, and returns to the DC link via S2 S1 pulls the voltage at the node between S1 and S3,

VLC, to +VDC, the DC link voltage, and S2 clamps the voltage at the node between S2 and S4, VPWM, to 0V Therefore, the output voltage, Vout, is at +VDC, and power is transferred to the resonant tank during this period

At some point through the switching cycle, S2 (in the PWM leg) is turned off From this point onwards the current flowing from the resonant load is supported by C2 and C4, as depicted in Fig 1.24 This charges C2 and discharges C4, raising VPWM Since

VLC=VDC, the increase in VPWM causes a corresponding decrease in Vout Providing the capacitances of C2 and C4 are equal, charging of C2 and discharging of C4 are terminated when VPWM reaches +VDC, at which time D4 becomes forward biased and supports the current Since VPWM and VLC can be considered equal, Vout is zero The

S3

S4 D2

D2 D3

D4 C1

C2 C3

C4

LOAD S1

S2

VDC VLC

VPWM

load current circulates through S1, load circuit, and D4, and no power is transferred from the DC link to the load

Figure 1.24 PWM leg’s commutation

This condition remains until Iout approaches zero, when S1 switches off Current flowing to the resonant load circuit from the load commutated leg is now supported by C1 and C3 (Fig 1.25), and charges C1 and discharges C3, and thereby reducing VLCuntil the voltage at the node of S1 and S3 reaches zero At this time D3 becomes forward biased and clamps VLC to 0V Hence, Vout fall to –VDC, and is clamped It should be noted that in this state part of the power is transferred from the resonant load back to the power supply through D3 and D4

Figure 1.25 Positive load commutation

Also, D3 and D4 are carrying the output current This condition is maintained until the output current changes polarity, at which time S3 and S4 are switched on Since both

S3

S4 D2

D2 D3

D4 C1

C2 C3

C4

LOAD S1

S2

S3

S4 D2

D2 D3

D4 C1

C2 C3

C4

LOAD

S2 S1

switches are being effectively shorted out by their anti-parallel diodes and the output current is zero, turn-on losses from this event are essentially zero The output voltage is not affected either, and remains at –VDC The current then begins its negative half-cycle, and power is transferred to the load circuit for the negative half-cycle (Fig 1.26)

Figure 1.26 Second power transfer phase

Part way through the cycle, the PWM control switches off S4, as shown in Fig 1.27, making VPWM gradually fall to 0V, while C2 and C4 support the current When VPWM

reaches zero, D2 carries the current, clamping VPWM to 0V As S3 is still switched on, the load current circulates through S3, D2, and the load circuit, effectively short-circuiting the output voltage—there is therefore no power transferred to the load in this state

Figure 1.27 Negative PWM leg’s commutation

D2

D2 D3

D4 C1

C2 C3

D4 C1

C2 C3

Just prior to current reversal, S3 is switched off, and VLC rises to +VDC, forcing Vout to rise to +VDC C1 and C3 now support the current from the load circuit to the load commutated leg, as depicted in Fig 1.28 Again, part of the power is returned to the

DC link in this period, and the whole process repeats thereafter

Figure 1.28 Negative half-cycle load commutation

An AC voltage with no DC offsets can be created across the output terminals of the inverter if the switches in the PWM leg are turned on for the same lengths of time This allows a direct connection between the inverter and the load circuit (or the matching transformer) without a large DC blocking capacitor The even harmonics are also eliminated by this In practice, however, due to the imperfect matching of the components in the bridge, a small DC blocking capacitor is normally required

By combining this novel power control algorithm and a properly sized input filter, the H-bridge system proposed in [1.1] has been successful in supplying high frequency current to the load, whilst maintaining very high input power factor and very low input current total harmonic distortion

An alternative power control method is pulse-density modulation, utilising the dynamic response of the second-order work-head circuit [1.32], [1.33] In this control method, nearly unity power factor can be drawn from the utility, whilst power and maximum

S3

S4 D2

D2 D3

D4 C1

C2 C3

C4

LOAD

S2 S1