single phase to three phase converstion using two parallel rectifiers

SINGLE-PHASE TO THREE-PHASE DRIVE SYSTEM

USING TWO PAPALLEL SINGLE PHASE RECTIFIERS

A Main Project Report submitted in partial fulfilment of the Requirements for the award of the degree of

BACHELORE OF TECHNOLOGY

IN

ELECTRICAL & ELECTRONICS ENGINEERING

By

M.THRIVENI (09HT1A0225) B.RAJU (09HT1A0205) P.KARUNAKAR (09HT1A0235) B.NAGESWARA RAO (09HT1A0206) K.NAVEEN (09HT1A0221)

Under the guidance of

Mr.P.PURNA CHANDA RAO M.Tech

Assistant Professor

Department of Electrical & Electronics Engineering

Chalapathi Institute Of Technology(Approved by AICTE, Affiliated to JNTU Kakinada)

(2009-2013)

Department of Electrical & Electronics Engineering

Chalapathi Institute Of Technology(Approved by AICTE, Affiliated to JNTU Kakinada)

( 2009-2013)

CERTIFICATE

This is to certify that the project entitled “SINGLE -PHASE TO THREE-PHASEDRIVE

SYSTEM USING TWO PAPALLEL SINGLE PHASE RECTIFIERS” is a bonafide

Work done by M.THRIVENI (09HT1A0225), B.RAJU (09HT1A0205), P.KARUNAKAR

(09HT1A0235), B.NAGESWARA RAO (09HT1A0206), K.NAVEEN (09HT1A0221) in partial

Fulfillment of the Academic requirements for the award of the degree of Bachelor of

Technology in Electrical& Electronics Engineering, Submitted to the Department of

Electrical and Electronics Engineering, Chalapathi Institute of Technology, Mothadaka,

Guntur during the Period. This results embodied in the project report Have not been

Submitted to any other University or institute for the award of any degree.

Mr.P.Purna Chandra Rao M.Tech. Mr.N.Rajesh Babu M.Tech, MBA.

Project Guide, HeadoftheDepartment,

DepartmentofEEE, DepartmentofEEE,

Chalapathi institute of Technology. Chalapathi institute of Technology. .

Acknowledgment

We would like to express our heartfelt gratitude to my guide Mr. P.PURNA CHANDRA RAO,

Assistant Professor, Department of Electrical and Electronics Engineering, Chalapathi

Institute of Technology. He has given us tremendous support in both technical and moral front.

Without his support and encouragement, we would never have been able to complete the project

successfully.

We are grateful to Mr. N.RAJESH BABU, Head of the Department of Electrical

And Electronics Engineering, Chalapathi institute of Technology, for presenting us this

opportunity and for extending constant support and valuable guidance throughout the project.

Our profound thanks to Dr.C.Ravi Kanth, principal, chalapathi institute of

Technology, for his support.

We would also like to thank all our teaching staff members of EEE for giving us

Their valuable suggestions. Finally, we are thankful to one and all who contributed for the

Successful completion of our project work by

M.THRIVENI (09HT1A0225)

B.RAJU (09HT1A0205)

P.KARUNAKAR (09HT1A0235)

B.NAGESWARA RAO (09HT1A0206)

K.NAVEEN (09HTIA0221)

DECLARATION

We hereby declare that the project entitled “SINGLE PHASE TO THREE PHASE DRIVE

SYSTEM USING TWO PARALLEL SINGLE PHASE RECTIFIERS”, submitted in the partial

Fulfillment of the requirements for the award of Bachelor of Technology in Electrical & Electronics

Engineering, to Chalapathi Institute of Technology, Mothadaka, Guntur, affiliated to JNTU,

Kakinada is a authentic work and has not been submitted to any other university or institution for

Award of the degree by

M.THRIVENI (09HT1A0225)

B.RAJU (09HT1A0205)

P.KARUNAKAR (09HTA10235)

B.NAGESWARA RAO (09HT1A0206)

K.NAVEEN (09HT1A0221) .

ABSTRACT

Single-phase to three-phase ac–dc–ac conversion usually employs a full-bridge

topology. In these three phase induction motor is operated from single-phase supply by

using two parallel single-phase rectifiers The topology permits to reduce the rectifier

switch currents, the harmonic distortion at the input converter side, and presents

improvements on the fault tolerance characteristics and it is shown by reduction of

circulating current. . The system is composed of two parallel single-phase rectifiers, a

three-phase inverter, and an induction motor. The power continuity is a major issue

solved in this project and is achieved by using parallel converters. The fault in the

rectifier does not affect the power flow and if a fault in any rectifier is occurred the

entire power is fed through the other rectifier. The topology was simulated in

Matlab/simulink software and performance of induction motor by this topology was

studied.

1

CONTENTS

ABSTRACT i

List of Figures iv

List of Tables vi

ABSTRACT 1

LIST OF FIGURES 4

LIST OF TABLES 7

Chapter 1: INTRODUCTION 1

1.1 Introduction: 1

1.2 Motivation of Work: 2

1.3 Problem Definition: 2

1.4 Scope of the project: 2

1.5 Solution Technique: 2

1.6 Literature Overview: 2

Chapter 2:SINGLE PHASE A.C TO THREE PHASE A.C CONVERSION METHODS 8

2.1 Methods to Convert Single Phase to Three Phase Drive Systems 8

2.1.1 Rotary phase converter: 8

2.1.2 Static Phase Converter 9

2.1.3 Phase Perfect Digital Phase Converter: 9

2.2 Single-Phase to Three-Phase (1ø-3ø) Cycloconverters: 10

2.2.1 Integral Pulse Modulated (1ø-3ø) Cycloconverters: 11

2.2.2 Phase-Controlled (1ø-3ø) Cycloconverter: 11

2.3 Single-Phase-to-Three-Phase AC/DC/AC PWM Converter: 11

Chapter 3: CHARACTERISTICS OF INDUCTION MOTOR 13

3.1 Starting characteristics: 13

3.2 Running Characteristics: 14

3.3 Load characteristics: 15

3.3.1 Constant Torque, Variable Speed Loads: 15

3.3.2 Variable Torque, Variable Speed Loads: 16

3.3.3 Constant Power Loads: 16

3.3.4 Constant Power, Constant Torque Loads: 17

3.3.5 High Starting/Breakaway Torque followed by Constant Torque 17

3.4. Induction motor characteristics in the proposed system: 18

Chapter 4: CONTROL STRATEGIES OF CONVERTERS 20

4.1 Introduction: 20

4.2 Sinusoidal Pulse Width Modulation: 21

4.2.1 SPWM Spectra: 24

4.3 Space Vector PWM: 25

4.3.1 Principle of Space Vector PWM: 25

4.4. Vector Control technique: 33

4.5 control circuits adopted in the system: 34

4.5.1. Rectifier control circuit: 35

4.5.2. Inverter control circuit: 35

4.5.3. pi controller: 36

Chapter 5: DESIGN METHODOLOGY OF PROPOSED CONVERTER 37

5.1 Introduction: 37

5.2 Mathematical Modelling of the proposed system: 39

5.2.1.Different modes/loops in the proposed system: 39

5.3 PWM Strategy: 43

5.4 Control Strategy: 45

5.5 Harmonic Distortion: 46

5.6 Ratings of Switches: 49

5.7 DC-Link Capacitor Design: 50

5.8 Input Inductors: 51

5.9 Fault Compensation: 52

5.10 Losses and Efficiency: 54

5.11 Costs and Applications of Configuration: 56

5.12 pulse train of control circuits of rectifier and inverter switches: 56

Chapter 6: SIMULATION AND RESULT DISCUSSION 58

6.1 Simulation Results for 110V AC: 58

6.1.1 Simulation of Conventional Model: 58

6.1.2 Simulation of Proposed Model: 61

6.2 Simulation Results for 230V AC: 68

6.2.1 Simulation of Conventional Model: 68

6.2.2 Simulation of proposed Model: 70

Chapter 7: CONCLUSION AND FUTURE SCOPE 75

Conclusion: 75

Future Scope: 75

Chapter 8: BIBLIOGRAPHY 76

LIST OF FIGURES

Figure no. Description Page no.

Fig. 2.1: Block diagram for rotary phase converter 9

Fig 2.2: Block diagram of Phase Perfect Digital Phase Converter 10

Fig. 2.3(a): Single-phase-to-three-phase ac/dc/ac PWM converter 12

Fig.2.3(b): wave form of grid voltage & current 12

Fig. 3.1:Typical torque-speed curve of the three-phase induction motor

14

Fig. 3.2:Torque-speed curves of the motor with two different loads

15

Fig .3.3: Constant Torque, Variable Speed Loads 15

Fig. 3.4: Variable Torque, Variable Speed Loads 16

Fig. 3.5: Constant Power Loads 16

Fig. 3.6: Constant Power, Constant Torque Loads 17

Fig. 3.7:Relation between the Voltage and Torque versus Frequency

17

Fig. 3.8wave forms of three phase voltage, current, speed and torque

18

Fig. 4.1 Unipolar and bipolar modulation 22

Fig. 4.2: Simple Voltage Sourced Inverter 23

Fig. 4.3: Principal of Pulse Width Modulation 24

Fig. 4.4: SPWM Harmonic Spectra 25

Fig. 4.5: Three-phase voltage source PWM Inverter 25

Fig. 4.6: The eight inverter voltage vectors (V0 to V7) 27

Fig. 4.7:Locus comparison of maximum linear control voltage in Sine PWM and SVPWM

27

Fig. 4.8:The relationship of abc reference frame and stationary dq reference frame

28

Fig. 4.9: Basic switching vectors and sectors 29

Fig.4.10:Reference vector as a combination of adjacent vectors at sector 1

31

Fig. 4.11: Space vector PWM switching patterns at each sector 32

Fig. 4.12:Block diagram for vector control technique using direct torque and speed control

34

Fig. 4.13: Control circuit for rectifier 35

Fig. 4.14: Control circuit for inverter 36

Fig 4.15: Block diagram of pi controller 36

Fig. 5.1 Conventional single-phase to three phase drive system 37

Fig. 5.2(a) Proposed single-phase to three phase drive system 38

Fig. 5.2(b)Block diagram of proposed single-phase to three phase drive system model

38

Fig: 5.2.1a: Loop1 of the system model 39

Fig: 5.2.1(b): Loop2 of the system model 40

Fig: 5.2.1(c): Loop3 of the system model 40

Fig: 5.2.1(d): Loop4 of the system model 41

Fig. 5.3 Control Block Diagram for rectifier 45Fig. 5.4 WTHD of rectifier voltage (vab for proposed

configuration and vg for Standard configuration) as a function of μ

47

Fig. 5.5 Variables of rectifiers A and B. 48

Fig. 5.6 Currents ia , i’a , and io for double-carrier 49

Fig. 5.7(a)Flow of active power in Conventional ac–dc–ac single-phase to three phase converter

50

Fig. 5.7(b)Flow of active power in Proposed system with two rectifiers

50

Fig. 5.8: Inductor specification in terms of THD of ig and μ 52

Fig. 5.9(a):Proposed configuration highlighting devices of fault-tolerant system.

53

Fig.5.9 (b): Block diagram of the fault diagnosis system 53

Fig.5.10:Possibilities of configurations in terms of fault occurrence

54

Fig5.11(a): pulse trainee of rectifier control circuit 56

Fig.5.11(b): pulse trainee of inverter control circuit 57

Fig. 6.1: Simulink model of conventional system 58

Fig. 6.2: Wave forms of grid input voltage & current 58

Fig. 6.3: Wave form of DC-Link capacitor voltage 59

Fig. 6.4: Wave form of current i’a in rectifier A 59

Fig. 6.5: Wave form of output line voltage 60

Fig. 6.6: THD content at input current is 19.36% 60

Fig. 6.7: Simulink model of proposed system 61

Fig. 6.8: Simulink model of control circuit for rectifier 61

Fig. 6.9: Simulink model of control circuit for inverter 62

Fig. 6.10: Wave forms of grid input voltage & current 62

Fig. 6.11 : Wave form of DC-Link capacitor voltage 63

Fig. 6.12: Wave form of circulating current 63

Fig. 6.13: Wave forms of currents in rectifier A & B 64

Fig. 6.14: Wave forms of grid voltage & current in fault condition 64

Fig. 6.15: Wave forms currents in rectifier A & B in fault condition 65

Fig. 6.16: Wave forms currents in rectifier A in fault condition 65

Fig. 6.17: THD content at input current using SPWM Technique 66

Fig. 6.18 : THD content at input current using SVPWM Technique 66

Fig. 6.19: THD content at output voltage using SPWM Technique 67

Fig. 6.20 : THD content at output voltage using SVPWM Technique 67

Fig.6.21: Wave forms of grid input voltage & current 68

Fig. 6.22: Wave form of current in rectifier A 69


Fig. 6.24: Wave forms of currents in rectifier A & B 70

Fig. 6.25: Wave form of output line voltage 70

Fig. 6.26: Wave form of circulating current 71


Fig. 6.28 : THD content at input current using SVPWM Technique 72

Fig. 6.29: THD content at input current using SPWM technique 72

Fig. 6.30 : THD content at output voltage with SPWM technique 73

Fig. 6.31 : THD content at output voltage with SVPWM technique 73

LIST OF TABLES

Description Pg. No.Table 1: ratings of induction motor 19Table 2: Switching vectors, phase voltages and output line to line voltages 26Table 3: Efficiency of the Proposed System Normalized In Terms Conventional 55Table 4: Comparison of conventional and proposed systems for 110V supply 68Table 5: Comparison of conventional and proposed systems for 230V 74Table 6: Distribution of currents for different values of modulation index 74

Introduction

Chapter 1

INTRODUCTION

1.1 Introduction:

Many solutions have been proposed when the objective is to supply three-phase motors from single-phase ac mains. It is quite common to have only a single phase power grid in residential, commercial, manufacturing and mainly in rural areas, while the induction motor may require a three-phase power grid. The motor and power factor control and reduction of total harmonic distortion have been presented by using a single phase to three-phase converter topology, this is a two step conversion which involves single phase a.c to d.c by using a rectifier and then d.c to a.c by using three phase inverter reduced number of switching devices. The most desirable characteristics of ac to ac power converters are:

Sinusoidal input and output currents

Operation with nearly unity power factor for any load

Simple and compact power circuit

Generation of load voltage with arbitrary amplitude and frequency

A front end-rectifier followed by a pulse width modulated voltage source

inverter (VSI-PWM) has been well-established power converter configuration for many

industrial drives. The increasing costs on the utility usage, due to power quality

regulations and the need to improve the fault tolerance characteristics and VA capacity

of systems, have increased the interest in the development of power electronic

equipment with power factor quality capability. Electrical motors consume a large

amount of the available electrical energy and this energy tends to increase due to the

massive emerging applications of electrical motor drives, in appliances and in industrial

processes. Therefore, the improvement of the power factor of these low power drive

systems, usually in the range from fractional horsepower to one horsepower is of

particular interest. For these power ratings, the system configuration usually comprises

a single-phase to three-phase type of converter with additional circuitry for power factor

control and reduction of T.H.D. Single-phase to three-phase ac–dc–ac conversion

usually employs a full-bridge topology. This system composed of two parallel single-

phase rectifiers and a three-phase inverter and induction motor. The proposed system is

9

Introduction

conceived to operate where the single-phase utility grid is the unique option available.

Three such converter topologies, which use reduced number of switching devices, were

presented along with their power factor control scheme.

.

1.2 Motivation of Work:

In the present work a way to operate the motor and power factor control,

reduction of total harmonic distortion has been presented by using a single phase to

three-phase converter topology, which involves reduced number of switching devices.

The proposed schemes were shown to achieve unity power factor operation at the

supply side and high performance control of the motor drive system, etc. We will

analyze the performance of a single-phase a.c to three phase a.c circuit with emphasis

on the output harmonic content and utilization of input voltage. Parallel converters have

been used to improve the power capability, reliability, efficiency, and redundancy. Also

continuity of the power is obtained even though any one of the rectifier is failed.

1.3 Problem Definition:

Single phase to three phase ac-dc-ac conversion usually has the rectifier

switching currents, the harmonic distortion at the input converter side. Discontinuity of

the power is observed when a fault occurs across the rectifier.So these problems are

minimised in the given system by using parallel converter techniques.

1.4 Scope of the project:

As switching currents are more at the input side, parallel converters technique

has been used to reduce the switching currents. SVPWM technique has been used to

reduce the T.H.D content. If one of the rectifiers is failed, Continuity of the power is

observed by using parallel rectifiers.

1.5 Solution Technique:

parallel converter techniques has been employed for continuity of power for

sharing of current between two parallel rectifiers, so that switching currents are

reduced. PWM technique has been used to generate the gating pulses across the rectifier

switches. SVPWM technique is used to reduce the T.H.D content in the overall system.

10

Introduction

1.6 Literature Overview:

“High-Performance Speed-Sensorless Control of an Induction Motor Drive Using a

Minimalist Single-Phase PWM Converter” by Olorunfemi Ojo, Senior Member, IEEE,

Zhiqiao Wu, Student Member, IEEE, Gan Dong, Student Member, IEEE, and Sheetal

K. Asuri.

Summary:

Home appliances and comfort conditioners are yet to benefit from the recent

developments in power electronics because of cost constraints. In this paper, a speed-

sensor less induction motor drive system using converters with reduced device counts

(minimalist, sparse converters) and actuated from a single-phase system is proposed for

such low-cost applications. The analysis, control, dynamic, and steady-state

characteristics of the proposed drive are experimentally illustrated.

This paper has presented the methodology for the analysis and control of a high-

performance induction motor drive actuated by two controlled rectifier–inverter

systems with reduced count of switching devices. The general approach for determining

the modulation signals required for the carrier-based PWM pulse generation for this

class of minimalist converters has been set forth. The input supply voltage is a single

phase and the input current is controlled using a natural reference frame controller to

operate close to unity displacement power factor. The nature of the modulation signals,

the achievable motor dynamics, and waveforms are clearly layout in simulation results.

“Reduced Switch Count Multiple Three-Phase AC Machine Drive Systems” by

Cursino Brandão Jacobina, Senior Member, IEEE, Euzeli Cipriano dos Santos, Jr.,

Student Member, IEEE, Edison Roberto Cabral da Silva, Fellow, IEEE, Mauricio

Beltrão de Rossiter Correa, Member, IEEE, Antonio Marcus Nigeria Lima, Senior

Member, IEEE, and Talvanes Meneses Oliveira, Member, IEEE

Summary:

In this paper, two three-phase ac drive systems with reduced number of

components, named configurations and, are investigated. Configuration uses multiple

two-leg voltage source inverters in which all inverters share an extra-leg. Configuration

also employs multiple two-leg inverters but in this case the inverters share the midpoint

of a capacitor bank in the dc-link, instead. These configurations are compared to

configuration that employs multiple three-leg inverters. The main characteristics of the

11

Introduction

machine drive systems are presented together with selected experimental results that

demonstrate the feasibility of the proposed configurations.

Two components minimized multiple three-phase ac drive systems have been

examined in this paper. Configuration uses multiple two-leg converter topologies in

which all the inverters share an extra-leg. Configuration also uses multiple two-leg

converter topologies but, instead, they share the midpoint of the capacitor bank of the

dc-link. Configuration uses 1 legs and configuration uses 2 legs, while configuration

demands 3 legs, where is the number of drives. The overall performance of

configuration is superior to that of configuration because: 1) the lower THD; 2) the

voltage capability that can be split among the inverters; 3) the fact that the machine

voltages do not depend on the individual capacitor voltages; and 4) there is no ac

fundamental current flowing through the dc-link capacitors. Configurations and require

less power devices and consequently a less complex gating control circuitry.

“A Three-Phase Parallel Active Power Filter Operating With PCC Voltage

Compensation with Consideration for an Unbalanced Load” by Woo-Cheol Lee, Taeck-

Kie Lee, and Dong-Seok Hyun, Senior Member, IEEE

Summary:

The performance and dynamic characteristics of a three-phase parallel active

power filter (APF) with point of the common coupling (PCC) voltage compensation

with consideration for an unbalanced load is presented and analyzed in this paper. The

proposed scheme employs a pulse-width modulation (PWM) voltage-source inverter

and has two operation modes. First, it operates as a conventional active filter with

reactive power compensation when PCC voltage is within the 15% voltage drop range.

Second, it operates as a voltage compensator when PCC voltage is not within the 15%

voltage drop range. Both the APF and the voltage compensator compensate

asymmetries caused by nonlinear loads. Finally, the validity of this scheme is

investigated through the analysis of simulation and experimental results for a prototype

APF system rated at 10kVA.

So it can be conclude that three-phase parallel APF operating with PCC voltage

compensation with consideration for an unbalanced load, and compared functions of an

APF and a voltage compensator. The proposed scheme has two operation modes. First,

it operates as an APF with reactive power compensation when PCC voltage is within

the 15% voltage drop range. Second, when the PCC voltage is not within the 15%

voltage drop range, it operates as a voltage compensator. In order to improve APF

12

Introduction

performance, a dc voltage control loop was implemented with both the APF and the

voltage compensator. Both the APF and the voltage compensator compensate

asymmetries caused by nonlinear loads. This scheme will be used for critical industrial

equipment like PLCs, HID and adjustable speed drives, and it may fail in situations

where there are dramatic drops and harmonics in the PCC. To test the validity of the

proposed scheme, simulation and experimental results were analyzed.

“Control of Circulating Current in Two Parallel Three-Phase Boost Rectifiers” by

Zhihong Ye, Member, IEEE, Dushan Boroyevich, Member, IEEE, Jae-Young Choi,

Member, IEEE, and Fred C. Lee, Fellow, IEEE

Summary:

One unique feature in parallel three-phase converters is a potential zero-

sequence circulating current. To avoid the circulating current, most present technology

uses isolation approach, such as transformers or separate power supplies. This paper

proposes a parallel system where individual converters connect both ac and dc sides

directly without additional passive components to reduce size and cost of the overall

parallel system. In this case, the control of the circulating current becomes an important

objective in the converter design. This paper 1) develops an averaged model of the

parallel converters based on a phase-leg averaging technique; 2) a zero-sequence model

is then developed to predict the dynamics of the zero-sequence current; 3) based on the

zero-sequence model, this paper introduces a new control variable, which is associated

with space-vector modulation; 4) a strong zero-sequence current control loop is

designed to suppress the circulating current; 5) simulation and experimental results

validate the developed model and the proposed control scheme.

This work has developed an averaged model to predict zero sequence dynamics

in two parallel three-phase boost rectifiers. To control the zero-sequence current, a new

control variable associated with space-vector modulation was introduced. Since the

zero-sequence dynamic is a first-order system, a high bandwidth control loop was

designed to effectively suppress the circulating current. Both simulation and

experimental results validated the proposed control scheme. The implementation

requires only one additional current sensor. The control algorithm can be easily

programmed in a digital signal processor (DSP).This modelling approach and control

concept can be generalized for paralleling any two multi-phase converters, such as full

bridge rectifiers and inverters, three-phase three-leg rectifiers and inverters, and three-

13

Introduction

phase four-leg rectifiers and inverters. These converters cover most medium and high

power applications, such as motor drives, ac power supplies and dc power supplies.

“Study on Ideal Operation Status of Parallel Inverters” by Hui Cai, Rongxiang Zhao,

and Huan Yang, Student Member, IEEE

Summary:

In order to keep a parallel inverter system operating stably, it is important to

restrain the circulating current effectively. Based on the theoretical analysis, the

limitation of a conventional conclusion about ideal operation status of parallel inverters

is studied in detail. And then, the ideal operation status of the parallel inverter system is

well investigated in this paper. A new criterion about ideal operation status of parallel

inverters is concluded, i.e., there will be no circulating current among parallel inverters

only when their output voltages have the same frequency, phase, amplitude and are also

uniformly modulated. The concept of “uniform modulation” and the corresponding

conclusion are verified by simulation and experimental results.

The concept of “uniform modulation” for a parallel inverter system was

introduced. A new conclusion about the ideal operation status of a parallel inverter

system was concluded. Simulation and experimental results verified the theoretical

analysis result and the proposed conclusion. The new conclusion is more complete to

analyze the circulating current of a parallel inverter system. It also offers a new point of

view to restrain the circulating current of the parallel inverter system.

“Shunt Active-Power-Filter Topology Based on Parallel Interleaved Inverters.” by

Lucian Asiminoaei, Member, IEEE, Eddy Aeloiza, Student Member, IEEE, Prasad N.

Enjeti, Fellow, IEEE, and Frede Blaabjerg, Fellow, IEEE.

Summary:

In this paper, an interleaved active-power-filter concept with reduced size of

passive components is discussed. The topology is composed of two pulse width

modulation interleaved voltage-source inverters connected together on the ac line and

sharing the same dc-link capacitor. The advantages of the proposed approach are as

follows: 1) significant reduction in the linkage inductors’ size by decreasing the line-

current ripple due to the interleaving; 2) reduction of the switching stress in the dc-link

capacitor, due to the shared connection; and 3) more accurate compensation for high-

power applications, because the power sharing allows one to use a higher switching

frequency in each inverter. This paper analyzes the design of the passive components

and gives a practical and low-cost solution for the minimization of the circulation

14

Introduction

currents between the inverters, by using common-mode coils. Several simulation results

are discussed, and experimental results with a three-phase 10-kVA 400-V unit are

obtained to validate the theoretical analysis.

This paper discussed the advantages of two inverters connected in parallel and

sharing the same dc capacitor for reactive power and current-harmonic compensation.

Design specification analysis shows that the values of the passive components are

significantly reduced. The intrinsic modularity characteristic of the topology increases

the reliability and makes it suitable for high-power applications. Simulation results and

experiments validate the presented analysis. This paper concludes that the usage of

smaller line inductors and the replacement of the isolation transformer with common

mode coils gives lower costs and allows a faster response in tracking the harmonic-

current reference, which makes the topology very attractive for high-power industrial

APFs.

15

Introduction

Chapter 2

SINGLE PHASE A.C TO THREE PHASE A.C CONVERSION METHODS

2.1 Methods to Convert Single Phase to Three Phase Drive Systems:

A wide variety of commercial and industrial electrical equipment requires

three-phase power. Electric utilities do not install three-phase power as a matter of

course because it costs significantly more than single-phase installation. As an

alternative to utility installed three-phase, rotary phase converters, static phase

converters and phase converting variable frequency drives (VFD) have been used for

decades to generate three-phase power from a single-phase source. However these

technologies have serious limitations, which motivated Phase Technologies, LLC to

develop a new digital phase converter, Phase Perfect. This new patented technology

overcomes the limitations of earlier phase converters, and is an affordable alternative to

utility three-phase.

2.1.1 Rotary phase converter:

A rotary phase converter, abbreviated RPC, is an electrical machine that

produces three-phase electric power from single-phase electric power. This allows three

phase loads to run using generator or utility-supplied single-phase electric power. A

rotary phase converter may be built as a motor-generator set. These have the advantage

that in isolating the generated three-phase power from the single phase supply and

balancing the three-phase output. However, due to weight, cost, and efficiency

concerns, most RPCs are not built this way. Rotary Phase Converters Provide Reliable,

Balanced, and Efficient Three Phase Power.

All converters can be mainly categorized into two groups: one is cascade type

and another is unified type. In cascade type, the PWM converter for power factor

correction and the PWM inverter for speed control are connected in series with large

DC-Link capacitor and two static power converters are operated and controlled in

separate. In this type, specific number of switches, to compose the converter and

inverter, are required. Therefore, the required number of switches cannot be reduced

significantly. On the other hand, in the unified type, conventional concepts of PWM

converter and inverter are merged together and same converter handles the functions of

16

Introduction

PWM converter (power factor correction) and PWM inverter(motor control) at the same

time. As an added advantage, the input inductor, which is commonly used in the PWM

converter for power factor correction, can be eliminated and replaced by the existing

motor inductor. Therefore, this new concept can significantly reduce the number of

components, compared to any conventional cascade type topologies.

Fig. 2.1. block diagram for rotary phase converter

2.1.2 Static Phase Converter:

Static Phase Convertor allows three phase motors to operate on single phase

power Static Phase Converters operate by charging and discharging capacitors to

temporarily produce a 3rd phase of power for only a matter of seconds during start up

of electric motors, then it will drop out forcing the motor to continue to run on just 1

phase and only part of its windings. Due to their technology, Static Phase Converters do

not properly power any class of 3 phase machinery or equipment. They will not in any

way power 3 phase welders, 3 phase battery chargers, 3 phase lasers, or any type of

machinery with 3 phase circuitry. Static Phase Converters also will not start delta

wound 3 phase motors.

2.1.3 Phase Perfect Digital Phase Converter:

The Phase Perfect digital phase system is similar to static and rotary phase

converters in that two of the phase leads to the load come directly from the power line.

At that point the similarity ends. Power to generate the voltage for the third lead flows

17

Introduction

into the digital phase converter through an inductor and a set of semiconductor switches

which feed a DC (constant voltage) link capacitor. The switches on the input can

control the waveform of the input current and insure that it is sinusoidal, so as not to

create harmonic distortion on the power grid. The DC link capacitor is connected to a

second set of semiconductor switches which feed a second inductor and a filter

capacitor to smooth out the high-frequency pulses created by the switches.

The system is controlled by a small microcontroller, specifically a digital signal

processor (DSP) which can measure voltages and feed controlled pulses into the

switches, in addition to performing high-speed calculations. The DSP is constantly

monitoring the system voltages and current to insure that the input current is sinusoidal,

and the output voltage is also sinusoidal. The output voltage can be made equal in

magnitude to the input voltage to an accuracy that is primarily determined by the

measurement accuracy of the DSP. Typically, the line-line output voltages of Phase

Perfect are balanced to within 1-2%. As the load on the system changes, the DSP senses

any drop in the voltage and adjusts the pulses to the semiconductor switches to maintain

this accuracy from no load up to full load. Any motor load or any combination of

motors up to the maximum rating of the digital phase converter can be connected

without creating unbalanced voltages. This is the first product to apply modern

technology to the problem of phase conversion.

Fig 2.2. Block diagram of Phase Perfect Digital Phase Converter

2.2 Single-Phase to Three-Phase (1ø-3ø) Cycloconverters:

Recently, with the decrease in the size and the price of power electronics

switches, single-phase to three-phase cycloconverters started drawing more research

interest. Usually, an H bridge inverter produces a high frequency single-phase voltage

waveform, which is fed to the cycloconverter either through a high frequency

transformer or not. If a transformer is used, it isolates the inverter from the

cycloconverter. In addition to this, additional taps from the transformer can be used to

18

Introduction

power other converters producing a high frequency ac link. The single-phase high

frequency ac (HFAC) voltage can be either sinusoidal or trapezoidal. There might be

zero voltage intervals for control purposes or zero voltage commutation.

2.2.1 Integral Pulse Modulated (1ø-3ø) Cycloconverters:

The input to these cycloconverters is single-phase high frequency sinusoidal or

square waveforms with or without zero voltage gaps. Every half-cycle of the input

signal, the control for each phase decides if it needs a positive pulse or a negative pulse

using integral pulse modulation. For integral pulse modulation, the command signal and

the output phase voltage are integrated and the latter result is subtracted from the

former. For a positive difference, a negative pulse is required, and vice versa for the

negative difference. For the positive (negative) input half-cycle, if a positive pulse is

required, the upper (lower) switch is turned on; otherwise, the lower (upper) switch is

turned on.

Therefore, the three-phase output voltage consists of positive and negative half-

cycle pulses of the input voltage. Note that this converter can only work at output

frequencies which are multiples of the input frequency.

2.2.2 Phase-Controlled (1ø-3ø) Cycloconverter:

This cycloconverter converts the single-phase high frequency sinusoidal or square

wave voltage into three-phase voltages using the previously explained phase control

principles. The voltage command is compared to a saw tooth waveform to find the

firing instant of the switches. Depending on the polarity of the current and the input

voltage, the next switch to be turned on is determined. Compared to the previous one,

this converter has more complex control but it can work at any frequency.

2.3 Single-Phase-to-Three-Phase AC/DC/AC PWM Converter:

Single phase to three-phase pulse width-modulation (PWM) converters for low-

power three-phase induction motor drives, where a single- phase half-bridge PWM

rectifier and a two-leg inverter are used. The simplest circuit of an ac/dc/ac converter

topology converting from a single-phase supply to a three-phase variable-voltage

system is a single-phase full-bridge rectifier and a three-leg PWM inverter system. This

converter gives excellent performance such as sinusoidal control of source current,

unity power-factor control of the source side, constant dc voltage control, and

19

Introduction

bidirectional power flow. However, it requires ten active switching devices, so that it is

more expensive than other circuits.

Fig. 2.3(a). Single-phase-to-three-phase ac/dc/ac PWM converter

Fig.2.3 (b) wave form of grid voltage & current

20

Control Strategies of Converters

Chapter 3

CHARACTERISTICS OF INDUCTION MOTOR

Three-phase AC induction motors are widely used in industrial and commercial

applications. They are classified either as squirrel cage or wound-rotor motors. These

motors are self-starting and use no capacitor, start winding, centrifugal switch or other

starting device. Almost 90% of the three-phase AC Induction motors are of Squirrel-

cage type.

3.1 Starting characteristics:

Induction motors, at rest, appear just like a short circuited transformer and if

connected to the full supply voltage, draw a very high current known as the “Locked

Rotor Current.” They also produce torque which is known as the “Locked Rotor

Torque”. The Locked Rotor Torque (LRT) and the Locked Rotor Current (LRC) are a

function of the terminal voltage of the motor and the motor design. As the motor

accelerates, both the torque and the current will tend to alter with rotor speed if the

voltage is maintained constant. The starting current of a motor with a fixed voltage will

drop very slowly as the motor accelerates and will only begin to fall significantly when

the motor has reached at least 80% of the full speed. The actual curves for the induction

motors can vary considerably between designs but the general trend is for a high current

until the motor has almost reached full speed. The LRC of a motor can range from

500% of Full-Load Current (FLC) to as high as 1400% of FLC. Typically, good motors

fall in the range of 550% to 750% of FLC.

The starting torque of an induction motor starting with a fixed voltage will drop

a little to the minimum torque, known as the pull-up torque, as the motor accelerates

and then rises to a maximum torque, known as the breakdown or pull-out torque, at

almost full speed and then drop to zero at the synchronous speed. The curve of the start

torque against the rotor speed is dependent on the terminal voltage and the rotor design .

The LRT of an induction motor can vary from as low as 60% of FLT to as high as

350% of FLT. The pull-up torque can be as low as 40% of FLT and the breakdown

torque can be as high as 350% of FLT. Typically, LRTs for medium to large motors are

in the order of 120% of FLT to 280% of FLT. The PF of the motor at start is typically

21


0.1-0.25, rising to a maximum as the motor accelerates and then falling again as the

motor approaches full speed.

Fig. 3.1 Typical torque-speed curve of the three-phase induction motor

3.2 Running Characteristics:

Once the motor is up to speed, it operates at a low slip, at a speed determined by

the number of the stator poles. Typically, the full-load slip for the squirrel cage

induction motor is less than 5%. The actual full-load slip of a particular motor is

dependent on the motor design. The typical base speed of the four pole induction motor

varies between 1420 and 1480 RPM at 50 Hz, while the synchronous speed is 1500

RPM at 50 Hz. The current drawn by the induction motor has two components: reactive

component (magnetizing current) and active component (working current). The

magnetizing current is independent of the load but is dependent on the design of the

stator and the stator voltage. The actual magnetizing current of the induction motor can

vary, from as low as 20% of FLC for the large two pole machine, to as high as 60% for

the small eight pole machine.

The working current of the motor is directly proportional to the load. The

tendency for the large machines and high-speed machines is to exhibit a low

magnetizing current, while for the low-speed machines and small machines the

tendency is to exhibit a high magnetizing current. A typical medium sized four pole

machine has a magnetizing current of about 33% of FLC. A low magnetizing current

22


indicates a low iron loss, while a high magnetizing current indicates an increase in iron

loss and a resultant reduction in the operating efficiency.

3.3 Load characteristics:

In real applications, various kinds of loads exist with different torque-speed

curves. For example, Constant Torque, Variable Speed Load (screw compressors,

conveyors, feeders), Variable Torque, Variable Speed Load (fan, pump), Constant

Power Load (traction drives), Constant Power, Constant Torque Load (coiler drive) and

High Starting/Breakaway Torque followed by Constant Torque Load (extruders, screw

pumps). The motor load system is said to be stable when the developed motor torque is

equal to the load torque requirement. The motor will operate in a steady state at a fixed

speed. The response of the motor to any disturbance gives us an idea about the stability

of the motor load system. This concept helps us in quickly evaluating the selection of a

motor for driving a particular load.

Fig. 3.2 Torque-speed curves of the motor with two different loads

3.3.1 Constant Torque, Variable Speed Loads:

The torque required by this type of load is constant regardless of the speed. In

contrast, the power is linearly proportional to the speed. Equipment, such as screw

compressors, conveyors and feeders, has this type of characteristic.

23


Fig 3.3. Constant Torque, Variable Speed Loads

3.3.2 Variable Torque, Variable Speed Loads:

This is most commonly found in the industry and sometimes is known as a

quadratic torque load. The torque is the square of the speed, while the power is the cube

of the speed. This is the typical torque-speed characteristic of a fan or a pump.

Fig 3.4. Variable Torque, Variable Speed Loads

3.3.3 Constant Power Loads:

This type of load is rare but is sometimes found in the industry. The power

remains constant while the torque varies. The torque is inversely proportional to the

speed, which theoretically means infinite torque at zero speed and zero torque at infinite

speed. In practice, there is always a finite value to the breakaway torque required. This

type of load is characteristic of the traction drives, which require high torque at low

speeds for the initial acceleration and then a much reduced torque when at running

speed.

24


Fig 3.5. Constant Power Loads

3.3.4 Constant Power, Constant Torque Loads:

This is common in the paper industry. In this type of load, as speed increases,

the torque is constant with the power linearly increasing. When the torque starts to

decrease, the power then remains constant.

Fig 3.6 Constant Power, Constant Torque Loads

3.3.5 High Starting/Breakaway Torque followed by Constant Torque:

This type of load is characterized by very high torque at relatively low

frequencies. Typical applications include extruders and screw pumps.

25


Fig. 3.7. Relation between the Voltage and Torque versus Frequency

3.4. Induction motor characteristics in the proposed system:

Fig 3.8(a) line-line voltage(V)

The above figure shows line-line voltage of three phase induction motor of a given

input of 230V a.c to three phase inverter. It can be noticed that due to presence of

harmonic content there exists a distortion in the wave form.

Fig 3.8(b) Three phase currents (A)

The above figure shows three phase currents obtained from given input current of 23A.

Here in the induction motor the induced e.m.f in the rotor is very large, as a result a

very high starting current is seen.

Fig 3.8(c) Rotor speed of induction motor in rad/sec

The above figure shows rotor speed obtained as 120 rad/sec for applied voltage of 230

a.c, the reference speed set for this induction motor is 120 rad/sec, it can be clearly

observed that speed is maintained constant even though the input voltage is varied.

26


Fig 3.8(d) electromagnetic torque in N/m

The above figure shows electromagnetic in newton/metre, it can be observed that the

starting torque is very much high in the interval t=0 to t=0.1 and it has come to steady

state after t=0.1. The high starting torque is because it has to run high inertia load at

starting time.

Power 2 hp, 230vFrequency 50hzSpeed 1425rpm

Rotor Type Squirrel cage

Voltage(Line To Line)

230v

Stator Resistance(Rs)

0.64ohms

Stator Inductance(Lls)

0.21e-3h

Rotor Resistance(Rr)

0.26ohms

Rotor Inductance(Llr)

0.48e-3h

Mutual Inductance(Lm)

4e-3h

Inertia(J) 0.0226kg.m^2Reference Frame

Rotor

Table 1: Ratings of Induction Motor

The above table shows ratings of three phase induction motor for different

parameters.

27


Chapter 4

CONTROL STRATEGIES OF CONVERTERS

4.1 Introduction:

At present, voltage source converters are mostly used in electrical drives. These

converters utilize capacitors in the DC-link to store temporarily electrical energy.

Switching the power electronic devices allows the DC voltage to be modulated which

can result in a variable voltage and frequency waveform. The purpose of the modulator

is to generate the required switching signals for these switching devices on the basis of

user defined inputs. For this purpose, the voltage–time integral was introduced, which

in turn is tied to the average voltage per sample U(tk) that may be written as

(4.1)

where Ts is a given sample interval and u(t) represents the instantaneous voltage across

a single-phase of a load. The introduction of the variable Ts assumes the use of a fixed

sampling frequency which is normally judicially chosen higher than the fundamental

frequency range required to control electrical machines. The upper sampling frequency

limit is constrained by the need to limit the switching losses of the converter

semiconductor devices. The ability to control the converter devices in such a manner

that the load is provided with a user defined mean reference voltage per sample U∗(tk)

is instrumental to control current accurately. This statement can be made plausible by

considering the incremental flux linkage for one sample interval of a load in the form of

a coil with inductance L and resistance R which may be written as

(4.2)

The corresponding incremental change of load current (over a sample interval Ts) may

be written as in

(4.3)

28


the event that magnetic saturation effects may be ignored. This expression can, with the

aid of (4.3), be expressed as

(4.4)

which may be reduced to

(4.5)

when the time constant τ = L/R of the load is deemed to be relatively large compared to

Ts, as is normally the case for electrical machines. Central to the issue of controlling the

incremental current is therefore, according to (4.5), the ability of the modulator to

realize (within the constraint of this unit) the condition

(4.6)

for each sampling instance. Note that (4.6) simply states that the switching states of the

converter must be controlled by the modulator to ensure that the average voltage (per

sample) equals the user defined average reference value to ensure that the actual and

reference incremental current change (per sample interval) are equal.

How this may be achieved will be outlined in subsequent sections for various

converter topologies using an approach taken by Svensson. In effect, this approach

considers how the average voltage per sample U(tk) varies as function of the converter

switch on/off time within a sample interval. Once this relation is known for the

converter under consideration, the function in question is compared with the user

defined reference value to determine the converter switch state within each sample.

Initially, a single-phase half-bridge converter, will be considered followed by an

analysis of a single-phase full-bridge converter and three-phase converter.

4.2 Sinusoidal Pulse Width Modulation:

This is a method in which fixed dc input voltage is given to an inverter and the

output is a controlled ac voltage. This is done by adjusting the on and off periods of the

inverter components.

The advantages of PWM control are:

1. No additional components are required with this method.

29


2. Lower order harmonics are eliminated or minimised along with its output voltage

control. Hence, the filtering requirements are minimised since higher order harmonics

can be filtered easily.

If the half-cycle sine wave modulation, the triangular carrier only in a positive

or negative polarity range of changes, the resulting SPWM wave only in a polar Range,

called unipolar control mode. Figure 4.1(a) shows the unipolar and bipolar modulation

of PWM pulses. If the half-cycle sine wave modulation, triangular carrier in continuous

change between positive and negative polarity, the SPWM wave is between positive

and negative changes, known as bipolar control.

Fig. 4.1: Unipolar and bipolar modulation

The switches in the voltage source inverter (See Fig. 4.1(b)) can be turned on

and off as required. In the simplest approach, the top switch is turned on If turned on

and off only once in each cycle, a square wave waveform results. However, if turned on

several times in a cycle an improved harmonic profile may be achieved.

In the most straightforward implementation, generation of the desired output

voltage is achieved by comparing the desired reference waveform (modulating signal)

with a high-frequency triangular ‘carrier’ wave as depicted schematically in Fig.4.2.

Depending on whether the signal voltage is larger or smaller than the carrier waveform,

either the positive or negative dc bus voltage is applied at the output. Note that over the

period of one triangle wave, the average voltage applied to the load is proportional to

the amplitude of the signal (assumed constant) during this period. The resulting

chopped square waveform contains a replica of the desired waveform in its low

frequency components, with the higher frequency components being at frequencies of

an close to the carrier frequency.

30


Fig. 4.2: Simple Voltage Sourced Inverter

Notice that the root mean square value of the ac voltage waveform is still equal

to the dc bus voltage, and hence the total harmonic distortion is not affected by the

PWM process. The harmonic components are merely shifted into the higher frequency

range and are automatically filtered due to inductances in the ac system. When the

modulating signal is a sinusoid of amplitude Am, and the amplitude of the triangular

carrier is Ac, the ratio m=Am/Ac is known as the modulation index. Note that

controlling the modulation index therefor controls the amplitude of the applied output

voltage. With a sufficiently high carrier frequency (see Fig. 4.3 drawn for fc/fm = 21

and t = L/R = T/3; T = period of fundamental), the high frequency components do not

propagate significantly in the ac network (or load) due the presence of the inductive

elements. However, a higher carrier frequency does result in a larger number of

switching’s per cycle and hence in an increased power loss. Typically switching

frequencies in the 2-15 kHz range are considered adequate for power systems

applications. Also in three-phase systems it is advisable to use so that all three

waveforms are symmetric.

(4.7)

Note that the process works well for m<1. For m>1, there are periods of the

triangle wave in which there is no intersection of the carrier and the signal as in Fig.4.4.

However, a certain amount of this “over modulation” is often allowed in the interest of

obtaining a larger ac voltage magnitude even though the spectral content of the voltage

is rendered somewhat poorer.

31


Fig. 4.3: Principal of Pulse Width Modulation

Note that with an odd ratio for fc/fm, the waveform is anti-symmetric over a 360 degree

cycle. With an even number, there are harmonics of even order, but in particular also a

small dc component. Hence an even number is not recommended for single phase

inverters, particularly for small ratios of fc/fm.

4.2.1 SPWM Spectra:

Although the SPWM waveform has harmonics of several orders in the phase

voltage waveform, the dominant ones other than the fundamental are of order n and n±2

where n = fc/fm. This is evident for the spectrum for n=15 and m = 0.8 shown in

Fig.4.5. Note that if the other two phases are identically generated but 120o apart in

phase, the line-line voltage will not have any triple n harmonics. Hence it is advisable to

choose, as then the dominant harmonic will be eliminated. It is evident from Fig 4.5b,

that the dominant 15th harmonic in Fig. 4.5 is effectively eliminated in the line voltage.

Choosing a multiple of 3 is also convenient as then the same triangular waveform can

be used as the carrier in all three phases, leading to some simplification in hardware. It

is readily seen that as the where E is the dc bus voltage, that the rms value of the output

voltage signal is unaffected by the PWM process.. However, the problematic harmonics

32


are shifted to higher orders, thereby making filtering much easier. Often, the filtering is

carried out via the natural high-impedance characteristic of the load.

Fig. 4.4: SPWM Harmonic Spectra: n = 15, m =0.8

4.3 Space Vector PWM:

4.3.1 Principle of Space Vector PWM:

The circuit model of a typical three-phase voltage source PWM inverter is

shown in Fig. 4.9. S1 to S6 are the six power switches that shape the output, which are

controlled by the switching variables a, a′, b, b′, c and c′. When an upper transistor is

switched on, i.e., when a, b or c is 1, the corresponding lower transistor is switched off,

i.e., the corresponding a′, b′ or c′ is 0. Therefore, the on and off states of the upper

transistors S1, S3 and S5 can be used to determine the output voltage.

33


Fig. 4.5: Three-phase voltage source PWM Inverter

The relationship between the switching variable vector [a, b, c] t and the line-to-

line voltage vector [Vab Vbc Vca]t is given by (2.1) in the following:

(4.8)

Also, the relationship between the switching variable vector [a, b, c] t and the phase

voltage vector [Va Vb Vc]t can be expressed below.

(4.9)

there are eight possible combinations of on and off patterns for the three upper

power switches. The on and off states of the lower power devices are opposite to the

upper one and so are easily determined once the states of the upper power transistors

are determined. According to equations (4.8) and (4.9), the eight switching vectors,

output line to neutral voltage (phase voltage), and output line-to-line voltages in terms

of DC-link Vdc, are given in Table below which shows the eight inverter voltage vectors

(V0 to V7).

Table 2: Switching vectors, phase voltages and output line to line voltages

34


Fig. 4.6: The eight inverter voltage vectors (V0 to V7)

Space Vector PWM (SVPWM) refers to a special switching sequence of the

upper three power transistors of a three-phase power inverter. It has been shown to

generate less harmonic distortion in the output voltages and or currents applied to the

phases of an AC motor and to provide more efficient use of supply voltage compared

with sinusoidal modulation technique as shown in Fig. 4.11.

Fig. 4.7: Locus comparison of maximum linear control voltage in Sine PWM and SVPWM.

35


To implement the space vector PWM, the voltage equations in the abc reference

frame can be transformed into the stationary dq reference frame that consists of the

horizontal (d) and vertical (q) axes as depicted in below Figure.

Fig. 4.8: The relationship of abc reference frame and stationary dq reference frame.

From this figure, the relation between these two reference frames is below

fdq0 = Ksfabcwhere,

(4.10)

f denotes either a voltage or a current variable.

As described in above figure, the transformation is equivalent to an orthogonal

projection of [a, b, c]t onto the two-dimensional perpendicular to the vector [1, 1, 1]t

(the equivalent d-q plane) in a three-dimensional coordinate system. As a result, six

non-zero vectors and two zero vectors are possible. Six nonzero vectors (V1 - V6) shape

the axes of a hexagonal as depicted and feed electric power to the load.

The angle between any adjacent two non-zero vectors is 60 degrees.

Meanwhile, two zero vectors (V0 and V7) are at the origin and apply zero voltage to the

load. The eight vectors are called the basic space vectors and are denoted by V 0, V1, V2,

V3, V4, V5, V6, and V7. The same transformation can be applied to the desired output

voltage to get the desired reference voltage vector Vref in the d-q plane.

The objective of space vector PWM technique is to approximate the reference

voltage vector Vref using the eight switching patterns. One simple method of

36


approximation is to generate the average output of the inverter in a small period, T to

be the same as that of Vref in the same period.

Fig. 4.9: Basic switching vectors and sectors.

Therefore, space vector PWM can be implemented by the following steps:

Step 1. Determine Vd, Vq, Vref, and angle (α)

Step 2. Determine time duration T1, T2, T0

Step 3. Determine the switching time of each transistor (S1 to S6)

Step 1: Determine Vd, Vq, Vref, and angle (α):

From Fig. 4.14, the Vd, Vq, Vref, and angle (α) can be determined as follows:

(4.11)

(4.12)

37


(4.13)

where f = fundamental frequency

Step 2: Determine time duration T1, T2, T0:

From Fig. 4.15, the switching time duration can be calculated as follows:

Switching time duration at Sector 1

(4.14)

(4.15)

(4.16)

(4.17)

Switching time duration at any Sector

(4.18)

38


Fig. 4.10: Reference vector as a combination of adjacent vectors at sector 1.

Step 3: Determine the switching time of each transistor (S1 to S6):

(a) Sector 1. (b) Sector 2.

(c) Sector 3. (d) Sector 4.

39


(e) Sector 5. (f) Sector 6.

Fig. 4.11: Space vector PWM switching patterns at each sector.

Table 3: Switching Time Calculation at Each Sector

4.4. Vector Control technique:

This control is also known as the “field oriented control”, “flux oriented

control” or “indirect torque control”. Using field orientation (Clarke-Park

transformation), three-phase current vectors are converted to a two-dimensional rotating

reference frame (d-q) from a three-dimensional stationary reference frame. The “d”

component represents the flux producing component of the stator current and the “q”

component represents the torque producing component. These two decoupled

components can be independently controlled by passing though separate PI controllers.

The outputs of the PI controllers are transformed back to the three-dimensional

stationary reference plane using the inverse of the Clarke-Park transformation. The

corresponding switching pattern is pulse width modulated and implemented using the

SVM. This control simulates a separately exited DC motor model, which provides an

excellent torque-speed curve. The transformation from the stationary reference frame to

the rotating reference frame is done and controlled with reference to a specific flux

linkage space vector (stator flux linkage, rotor flux linkage or magnetizing flux

40


linkage). In general, there exists three possibilities for such selection and hence, three

different vector controls.

They are:

• Stator flux oriented control

• Rotor flux oriented control

• Magnetizing flux oriented control

The most challenging and ultimately, the limiting feature of the field orientation,

is the method whereby the flux angle is measured or estimated. Depending on the

method of measurement, the vector control is divided into two subcategories: direct and

indirect vector control. In direct vector control, the flux measurement is done by using

the flux sensing coils or the Hall devices. This adds to additional hardware cost and in

addition, measurement is not highly accurate. Therefore, this method is not a very good

control technique. The more common method is indirect vector control. In this method,

the flux angle is not measured directly, but is estimated from the equivalent circuit

model and from measurements of the rotor speed, the stator current and the voltage.

Fig. 4.12: block diagram for vector control technique using direct torque and speed control

4.5 control circuits adopted in the system:

Two control circuits has been used, one for rectifier circuit using pwm technique

and other for inverter using vector control technique, the details are as follows.

4.5.1. Rectifier control circuit:

41


The dc-link voltage vc is adjusted to its reference value v*c using the controller

Rc , which is a standard PI type controller. This controller provides the amplitude of the

reference grid current Ig . To control power factor and harmonics in the grid side, the

instantaneous reference current ig must be synchronized with voltage eg, as given in the

voltage oriented control (VOC) for three-phase system. This is obtained via blocks Ge-

Ig, based on a PLL scheme. The reference currents i*a and i*b are obtained by making

i∗a = i∗b = i∗g /2, which means that each rectifier receives half of the grid current.

The control of the rectifier currents is implemented using the controllers indicated by

blocks Ra and Rb . These controllers can be implemented using linear or nonlinear

techniques. In this paper, the current control law is the same as that used in the two

sequences synchronous controller described.

Fig. 4.13: control circuit for rectifier

4.5.2. Inverter control circuit:

In these control circuit speed reference has been taken from induction motor to

generate the gating pulses across the inverter switches. To implement vector control the

induction motor parameters must be known and values put into complex set of

mathematical equations developed from generalized machine theory. Here speed

controller generates a signal representing the demanded speed, and to drive a motor at

that speed also voltage signal is generated by using three phase sequence analyzer

where the magnitude of the voltage is generated, in order to generate pulses this two

42


phase transformation is changed to three phase transformation by using d-q axis of

trigonometric functions i.e., 2∏ sinωt (where ωt= 0, 145, 270 degrees) , thus three gating

pulses are generated.

Fig.4.14: control circuit for inverter

4.5.3. pi controller:

Pi controller consists of two components 1) kp which is proportional to the

error, it increases the loop gain of the sysytem 2) ki which is proportional to the integral

of the error, it increases the order of the system and reduces the steady state error.

Fig 4.15: block diagram of pi controller

In the simulink circuit KP & Ki values chosen based on trial and error method.

43

Design Methodology of Proposed Converter

Chapter 5

DESIGN METHODOLOGY OF PROPOSED CONVERTER

5.1 Introduction:

In this chapter the conventional and proposed system is design and analysed.

The circuit of conventional system ac-dc-ac is shown below in Fig. 5.1, which consists

of rectifier, a three phase inverter and induction motor. The conventional system

consists of total ten switches, a input inductor (Lg) and two capacitor banks.

Fig. 5.1: Conventional single-phase to three phase drive system

In the proposed system two parallel rectifiers, an inverter and induction motor

has been used. The system consists of total fourteen switches i.e., qa1, q’a1 , qa2 , and

q’a2 , and qb1, qb’1, qb2 and q’b2 of rectifier A & B, . The inverter is constituted of

switches qs1, q’s1, qs2, q’s2, qs3 and q’s3. The system is composed of grid, input

inductors (La , L’a ,Lb , and L’b ), capacitor bank at the dc link. The conduction state of

the switches is represented by variable sqa1 to sqs3, where sq = 1 indicates a closed

switch while sq = 0 an open one.

Four gating pulses has been given across to each two anti parallel switches in

rectifier circuit by using pwm technique and three pulses have generated by using

vector control across inverter where only one switch is on at upper leg lower leg at a

instant.

44

1ph ac

supply

Rectifier A

3PH VSI IM

Parallel converters

Control circuit

Rectifier B

Speed Ref

+

-

Vdc


Fig. 5.2(a): Proposed single-phase to three phase drive system

The below figure shows the block diagram of proposed system where single

phase a.c supply is converted to d.c by using a rectifier and by using a three phase

inverter d.c is converted to three phase a.c to operate a three phase induction motor and

also control circuits are designed in order to generate gating pulses across rectifier and

inverter switches.

Fig. 5.2(b): Block diagram of proposed single-phase to three phase drive system model

45


5.2 Mathematical Modelling of the proposed system:

From Fig. 2, the following equations can be derived for the front-end rectifier,

the below equations (5.1), (5.2), (5.3), (5.4), has been derived by applying kvl across

four loops in proposed circuit. Here resistance is also taken in to consideration in the

system.

5.2.1.Different modes/loops in the proposed system:

Here four different loops are considered for the designing of mathematical

modelling of the proposed system.

Fig: 5.2.1(a): loop1 of the system model

By applying the kirchoff voltage law in the above loop,

we get

(5.1)

Where Va10 , va20 are pole voltages across switches qa1 and qa2 respectively,

eg is the grid voltage ra, r’a, la, l’a are the resistances and inductances across input side,

Also ia, i’a are currents across rectifier A.

46


Fig: 5.2.1(b): loop2 of the system model

Similarly from the loop 2 we can get,

(5.2)

Where Vb10 , vb20 are pole voltages across switches qb1 and qb2 respectively,

eg is the grid voltage rb, r’b, lb, l’b are the resistances and inductances across input

side, ib and i’b are currents in rectifier B.

Fig: 5.2.1(c): loop3 of the system model

(5.3)

Where Va10 , Vb10 are pole voltages across switches qa1 and qb1 respectively,

ra, rb, la, lb are the resistances and inductances across input side, ia and ib are currents

in rectifier A and B respectively.

47


Fig: 5.2.1(d): loop4 of the system model

(5.4)

Where Va20 , Vb20 are pole voltages across switches qa2 and qb2 respectively

r’a, r’b, l’a, l’b are the resistances and inductances across input side, , ia and ib are

currents in rectifier A and B respectively.

Where p = d/dt and symbols like r and l represent the resistances and

inductances of the input inductors La, L’a, Lb, and L’b.

The grid current can be derived as,

(5.5)

The circulating current io can be defined from ia and i’a or ib and i’b , i.e.,

(5.6)

Introducing io and adding (5.3) and (5.4), relations (5.1)–(5.4) become

(5.7)

(5.8)

(5.9)

48


Where

(5.10)

(5.11)

(5.12)

Relations (5.7)–(5.9) and (5.5) constitute the front-end rectifier dynamic model.

Therefore, va (rectifier A), vb (rectifier B), and vo (rectifiers A and B) are used to

regulate currents ia, ib, and io, respectively. Reference currents i∗a and i∗b are chosen

equal to i∗g /2 and the reference circulating current i∗o is chosen equal to 0.

In order to both facilitate the control and share equally current,voltage, and

power between the rectifiers, the four inductors should be equal, i.e., r’g = ra = r’a = rb

= r’b and l’g = la =l’a = lb = l’b . In this case, the model (5.7)–(5.9) can be simplified to

the model given by

(5.13)

(5.14)

(5.15)

Additionally, the equations for ig , i’a , and i’b can be written as

(5.16)

(5.17)

(5.18)

In this ideal case (four identical inductors), the circulating current can be reduced to

zero imposing

(5.19)

When io = 0 (ia = i’a , ib = i’b ) the system model (5.7)–(5.9) is reduced to

49


(5.20)

(5.21)

Then, the model of the proposed system becomes similar to that of a system composed

of two conventional independent rectifiers

5.3 PWM Strategy:

The inverter can be commanded by using an adequate pulse width modulation

(PWM) strategy for three-phase voltage source inverter (VSI), so that it will not be

discussed here. In this section, the PWM strategy for the rectifier will be presented.

The rectifier pole voltages va10, va20, vb10, and vb20 depend on the

conduction states of the power switches, i.e.,

(5.22)

Where vc is the total dc-link voltage.

Considering that v∗a , v∗b , and v∗o denote the reference voltages determined

by the current controllers ,we found

(5.23)

(5.24)

(5.25)

The gating signals are directly calculated from the reference pole voltages

v∗a10, v∗a20, v∗b10, and v∗b20. However, (5.23)–(5.25) are not sufficient to

determine the four pole voltages uniquely from v∗a, v∗b and v∗o. Introducing an

auxiliary variable v∗x = v∗a20, that equation plus the three equations (5.23)–(5.25)

constitute a four independent equations system with four variables (v∗a10, v∗a20,

v∗b10, and v∗b20). Solving this system of equations, we obtain

(5.26)

(5.27)

(5.28)

50


(5.29)

From these equations, it can be seen that, besides v∗a, v∗b and v∗o, the pole

voltages depend on also of v∗x . The limit values of the variable v∗x can be calculated

by taking into account the maximum v∗c /2 and minimum −v∗c /2 value of the pole

voltages

(5.30)

(5.31)

Where v∗c is the reference dc-link voltages, v∗max = max ϑ and v∗min = min ϑ with

ϑ = {v∗a , 0, v∗a/2 + v∗b /2 − v∗o/2, v∗a/2 −v∗b /2 − v∗o/2}

Introducing a parameter μ (0 ≤ μ ≤ 1), the variable v∗x can be written as

(5.32)

When μ = 0, μ = 0.5, and μ = 1 the auxiliary variable v∗x has the following

values v∗x = v∗xmin, v∗x = v∗x have = (v∗xmin +v∗xmax)/2, and v∗x = v∗xmax,

respectively. When v∗x = v∗xmin or v∗x = v∗xmax a converter leg operates with

zero switching frequency.

Once v∗x is chosen, pole voltages v∗a10, v∗a20, v∗b10, and v∗b20are

defined from (5.26) to (5.29). The gating signals are obtained by comparing pole

voltages with one (vt1), two (vt1 and vt2) or more high frequency triangular carrier

signals. In the case of double-carrier approach, the phase shift of the two triangular

carrier signals (vt1 and vt2) is 180 ◦.

The parameter μ changes the place of the voltage pulses related to va and vb .

When v∗x = v∗xmin (μ = 0) or v∗x = v∗xmax(μ = 1) are selected, the pulses are

placed in the begin or in the end of the half period (Ts ) of the triangular carrier signal.

On the other hand, when v∗x =v∗x have the pulses are centred in the half period of the

carrier signal. The change of the position of the voltage pulses leads also to the change

in the distribution of the zero instantaneous voltages (i.e., va = 0 and vb = 0).With μ = 0

or μ = 1 the zero instantaneous voltages are placed at the beginning or at the end of the

switching period, respectively, while with μ = 0.5, they are distributed equally at the

beginning and at the end of the half period. This is similar to the distribution of the

51


zero-voltage vector in the three-phase inverter. Consequently, μ influences the

harmonic distortion of the voltages generated by the rectifier.

5.4 Control Strategy:

Fig. 5.3 presents the control block diagram of the system in Fig. 5.2,

highlighting the control of the rectifier. The rectifier circuit of the proposed system has

the same objectives of that in Fig. 5.1, i.e., to control the dc-link voltage and to

guarantee the grid power factor close to one. Additionally, the circulating current io in

the rectifier of the proposed system needs to be controlled. In this way, the dc-link

voltage vc is adjusted to its reference value vc using the controller Rc , which is a

standard PI type controller. This controller provides the amplitude of the reference grid

current Ig . To control power factor and harmonics in the grid side, the instantaneous

reference current ig must be synchronized with voltage eg , as given in the voltage

oriented control (VOC) for three-phase system. This is obtained via blocks Ge-Ig, based

on a PLL scheme. The reference currents i*a and i*b are obtained by making i∗a = i∗b

= i∗g /2, which means that each rectifier receives half of the grid current. The control

of the rectifier currents is implemented using the controllers indicated by blocks Ra and

Rb . These controllers can be implemented using linear or nonlinear techniques. In this

paper, the current control law is the same as that used in the two sequences synchronous

controller described.

Fig. 5.3: Control Block Diagram for rectifier

These current controllers define the input reference voltages v∗a and v∗b .The

homopolar current is measured (io ) and compared to its reference (i∗o = 0). The error

is the input of PI controller Ro , that determines the voltage v∗o . The calculation of

52


voltage v∗x is given from (5.30) to (5.32) as a function of μ, selected as shown in the

Section V. The motor there-phase voltages are supplied from the inverter (VSI). Block

VSI-Ctr indicates the inverter and its control. The control system is composed of the

PWM command and a torque/flux control strategy (e.g., field-oriented control or

volts/hertz control).

5.5 Harmonic Distortion:

The harmonic distortion of the converter voltages has been evaluated by using

the weighted THD (WTHD). It is computed by using

(5.33)

where a1 is the amplitude of the fundamental voltage, ai is the amplitude of ith

harmonic and p is the number of harmonics taken into consideration Fig. 4 shows the

WTHD of voltages generated by rectifiers [vab = (va + vb )/2 for the proposed

configuration and vg =vg10 − vg20 for the conventional one] at rated grid voltage as a

function of μ. Note that the parameter μ determines v∗x from (5.30) to (5.32). The

resultant voltage vab generated by rectifier is responsible to control ig, which means

that this voltage is used to regulate the harmonic distortion of the utility grid.

When the single-carrier PWM is used, the behaviour of WTHD of the proposed

system is similar to that of conventional one for all μ, as observed in Fig. 5.4. When the

double-carrier PWM is used with μ = 0.5, the WTHD is also the same for both

configurations. However, for the other values of μ the WTHD of the proposed system is

lower than that of the conventional one. The WTHD of the proposed topology (double-

carrier with μ = 0 or μ = 1) is close to 63% of that of the conventional topology (with μ

= 0.5). The study has also shown that it is possible to reduce the switching frequency of

the proposed system in 60% and still have the same WTHD of the standard

configuration.

53


Fig. 5.4: WTHD of rectifier voltage (vab for proposed configuration and vg forstandard configuration) as a function of μ.

The WTHD behaviour in Fig. 5.4 can be explained from Fig. 5.5. That figure

depicts the pole voltages (va10, va20, vb10, vb20) and their references (v∗a10, v∗a20,

v∗b10, v∗b20), the triangular carrier signals (vt1 , vt2 ), the resultant rectifier voltage

(vab ) and the circulating voltage (vo ). Fig. 5.5(a) and (c) shows these variables with

single-carrier (with μ = 1) and double-carrier (with μ =1), respectively. For the double-

carrier the voltage vab has smaller amplitude and better distribution along the half

switching period than that of single-carrier, which means a lower WTHD (as observed

in Fig. 5.4 for μ = 1). On the other hand, for μ = 0.5 the distribution of voltage vab

along the switching period is the same for both cases, i.e., single-carrier and double-

carrier have the same WTHD (as observed in Fig. 4 for μ = 0.5).

Besides the total harmonic distortion (THD) of the grid current ig , associated to

the WTHD of the voltage vab , the harmonic distortion analysis must also consider the

currents in the rectifiers. This is an important issue due to losses of the converter. The

harmonic distortion of the rectifier currents (ia , i’a , ib , and i’b ) with double-carrier is

higher than that of the grid current ig . When the parallel rectifier with double-carrier is

used, the THD of all these currents are reduced for μ = 0 orμ = 1 and increased for μ =

0.5. On the other hand, the THD of the circulating current is also smaller with μ = 0 or

μ = 1. Fig. 5.6 shows currents ia , i’a , and io for double-carrier with μ = 1 and μ = 0.5.

54


It can be seen that the mean values of the ripples of all currents are smaller when μ = 1

is selected.

In conclusion the optimal rectifier operation is obtained with double-carrier

making μ = 0 or μ = 1. A four-carrier approach may also be used. Compared with the

two-carrier strategy, the four-carrier strategy permits to reduce the harmonic distortion

of the grid current, but increases the rectifier losses.

Fig. 5.5: Variables of rectifiers A and B. (a) Single-carrier with μ = 1.

(b) Single-carrier with μ = 0.5. (c) Double-carrier with μ = 1.

(d) Double carrier with μ = 0.5.

55


Fig. 5.6: Currents ia , i_a , and io for double-carrier with μ = 1 and μ = 0.5.

5.6 Ratings of Switches:

Assuming same rms voltages at both grid and machine sides, a machine power

factor of 0.85 and neglecting the converter losses, currents of the rectifier switches

normalized in terms of currents of the inverter switches are 2.55 and 1.27 for the

conventional and the proposed single-phase to three-phase converter, respectively. Fig.

5.7(a) and (b) shows the flow of active power in the conventional and in the proposed

single-phase to three-phase converter, respectively. For balanced system (L’g =La = L’a

= Lb = L’b ), voltage vo is close to zero, so that the dc-link voltage is equal to that

required by the conventional system. Since the parallel connection scheme permits to

reduce the switch currents and preserve the dc-link voltage, the rating of each power

switch in the rectifier side is reduced.

56


Fig. 5.7(a): Flow of active power in Conventional ac–dc–ac single-phase to three phase converter

Fig. 5.7(b): Flow of active power in proposed system with two rectifiers

5.7 DC-Link Capacitor Design:

The dc-link capacitor design and calculation carried out in this section. The

voltage ripple over the dc capacitor is limited to an imposed maximum value of Δvmax.

some simplified assumptions are considered such that the integration time interval (t1,

t2) is half of the switching period Tsw and the dc current (Idc) is half of the peak value

of the nominal line current.

Then the minimum required dc capacitor is given by

57


Where idc and νdc are current and voltage of the dc capacitor, respectively, Tsw

is the switching period, and Δνdc is the voltage ripple.

1/2√ 2× 10 ×0.1 ×2230 × √ 2

C=4.7mF

5.8 Input Inductors:

The design of input inductors is carried out in this section.

Where Vdc is the voltage on the dc capacitor and Δi is the amplitude of the

cross-current developed during the interval t0, the Vdc obtained is 230V

LF= 2× 230×1/50

3(10+0.34+32)× √ 2

L= 5mH

The THD of the grid current as a function of μ for different values of ln [the

inductances of rectifiers A and B (l’g ) referred to that of the conventional configuration

(lg ), i.e., ln = l’g /lg ]. For ln > 0.4 (l’g > 0.4lg) the THD of the grid current of the

proposed topology is smaller than that of the conventional topology.

58


Fig. 5.8: Inductor specification in terms of THD of ig and μ.

5.9 Fault Compensation:

The proposed system presents redundancy of the rectifier converter, which can

be useful in fault-tolerant systems. The proposed system can provide compensation for

open-circuit and short-circuit failures occurring in the rectifier or inverter converter

devices.

The fault compensation is achieved by reconfiguring the power converter

topology with the help of isolating devices (fast active fuses—Fj , j = 1, . . . , 7) and

connecting devices (back-to-back connected SCRs—t1 , t2 , t3 ), as observed in Fig.

5.10(a). These devices are used to redefine the post-fault converter topology, which

allows continuous operation of the drive after isolation of the faulty power switches in

the converter. Fig. 5.10(b) presents the block diagram of the fault diagnosis system. In

this figure, the block fault identification system (FIS) detects and locates the faulty

switches, defining the leg to be isolated. This control system is based on the analysis of

the pole voltage error.

The fault detection and identification is carried out in four steps:

1) Measurement of pole voltages (vj0).

2) Computation of the voltage error εj0 by comparison of reference voltages and

measurements affected in Step 1).

3) Determination as to whether these errors correspond or not to a faulty condition; this

can be implemented by the hysteresis detector shown in Fig. 5.10(b).

4) Identification of the faulty switches by using ε’j0.

59


Fig. 5.9(a): Proposed configuration highlighting devices of fault-tolerant system.

Fig.5.9 (b): Block diagram of the fault diagnosis system.

This way, four possibilities of configurations have been considered in terms of faults

1) Pre-fault (“healthy”) operation.

2) Post-fault operation with fault at the rectifier B

3) Post-fault operation with fault at the rectifier A.

4) Post-fault operation with fault at the inverter.

When the fault occurrence is detected and identified by the control system, the

proposed system is reconfigured and becomes similar to that in Fig. 1. For instance, if a

fault in any switch of rectifier A has been detected by the control system, the whole

rectifier needs to be isolated.

60


Fig. 5.10: Possibilities of configurations in terms of fault occurrence. (a) Pre-fault system.

(b) Post-fault system with fault at the rectifier B. (c) Post-fault system with fault at the rectifier A. (d) Post-fault system with fault at the inverter.

This isolation procedure depends on the kind of fault detected. If an open-circuit

failure is detected, the control system will open all switches of the rectifier A. On the

other hand, if a short circuit is detected, the control system will turn on all switches

related to rectifier A, and in this case, the fuses will open, and consequently, the

rectifier will be isolated. Considering now a fault in one leg of inverter, in this case the

SCR related with this leg in turned on and the leg b1 is isolated, so that the leg b2 of

rectifier B will operate as the leg of inverter

5.10 Losses and Efficiency:

The evaluation of the rectifier losses is obtained through regression model

presented. The switch loss model includes:

1) IGBT and diode conduction losses

2) IGBT turn-on losses

3) IGBT turn-off losses and

4) Diode turn-off energy.

The loss evaluation takes into account just the rectifier circuit, since the inverter

side of converter is the same for the proposed and standard configurations. When the

61


rectifiers operate with a switching frequency equal to 5 kHz, the conduction and

switching losses of the proposed topology were 70% and 105%, respectively, of the

corresponding losses of the conventional topology. Consequently, in this case, the total

loss of the proposed topology was smaller than that of the conventional topology. The

increase of the switching frequency does not change the conduction losses of both

topologies, but increases their switching losses, especially for the proposed topology

that has a high number of switches. The efficiency of the topologies operating with a

switching frequency equal to 10 kHz and 5 kHz was evaluated by experimental

measurement with a 2 kW load. Table

Figure below shows the experimental results of the rectifier efficiency. Such

results are obtained for the proposed system (ηp) normalized in terms conventional one

(ηc), for three cases:

1) Both rectifiers operating at 10 kHz and L’g = Lg

2) Both rectifiers operating at 10 kHz and L’g = Lg /2 and

3) Both rectifiers operating at 5 kHz and L’g = Lg.

Three strategies are considered in terms of PWM control:

1) Single-carrier with μ = 0.5 (S-Ca μ = 0.5)

2) Double-carrier with μ = 0.5 (D-Ca μ = 0.5) and

3) Double carrier with μ = 0 (D-Ca μ = 0).

For case 1) the proposed configuration with double-carrier and μ = 0 have its

efficiency slightly smaller than that of the conventional one, but with the other PWM

strategies its efficiency is clearly inferior. In the other cases, the proposed configuration

with double-carrier and μ = 0 presents higher efficiency than the conventional one.

Table 3: Efficiency of the Proposed System Normalized In Terms Conventional One

5.11 Costs and Applications of Configuration:

62


The initial investment of the proposed system is higher than that of the standard

one, since the number of switches and devices such as fuses and triacs is highest. But,

considering the scenario when faults may occur, the drive operation needs to be stopped

for a non-programmed maintenance schedule. The cost of this schedule can be high and

this justifies the high initial investment inherent of fault-tolerant motor drive systems.

On the other hand, the initial investment can be justified if the THD or losses of the

conventional system is a critical factor. Furthermore, the cost of power switches has

decreased substantially. This permits to employ extra switches without increasing the

final price of converter dramatically The proposed system can be used in the same

applications as the conventional configuration (rural or remote application), especially

when the THD of the grid current, fault tolerance and efficiency of converter are critical

issues. In Brazil, it is quite common to have a single-phase distribution system and a

demand to supply a three-phase motor. A single-phase to three phase converter with

bidirectional flux in the rectifier circuit has been required in the distributed generation

system.

5.12 pulse train of control circuits of rectifier and inverter switches:

Fig 5.11(a) pulse trainee of rectifier control circuit

The above figure shows four generated pulse signals of qa1, qa2, qb1, qb2 for rectifier

switches.

63


Fig 5.11(b) pulse train for inverter switches

The above figure shows pulse train signals for inverter switches

64

Simulation and result discussion

Chapter 6

SIMULATION AND RESULT DISCUSSION

6.1 Simulation Results for 110V AC:

6.1.1 Simulation of Conventional Model:

Fig. 6.1: Simulink model of conventional system

The above figure shows the matlab/simulink model of the conventional system with

single rectifier and three phase inverter.

Fig. 6.2: Wave forms of grid input voltage & current

65


The above figure shows the input side grid voltage of 110 Volts and grid current of 10

Amps which are in phase, so that the power factor is close to unity.

Fig. 6.3: Wave form of DC-Link capacitor voltage

The above figure shows constant capacitor voltage of 230 V d.c across dc link

capacitors for a given input voltage of 110V a.c at the grid side, it can be seen that small

amount of dc link ripple component exists in the above waveform.

Fig. 6.4: Wave form of current in rectifier A

The above figure shows the input currents i'a of 4 Amps and along with their duty-

cycles which is pure sinusoidal.

66


Fig. 6.5: Wave form of output line voltage

The above figure shows the synthesized three-phase balanced line to line voltage of

125V obtained from input of 230V d.c to the three phase inverter. However, there still

exist some distortion and unbalance due to low speed at starting.

Fig. 6.6: THD content at input current is 19.36%

The above figure shows harmonic content of 19.35% at the input current side for the

conventional system.

67


6.1.2 Simulation of Proposed Model:

Fig. 6.7: Simulink model of proposed system

The above figure shows the matlab/simulink model of the two single phase rectifiers

connected in parallel which is controlled by a control strategy which helps in

controlling the DC link voltage, controls the circulating current io in the rectifier and

guarantee’s the grid power factor to be close to unity. The system is connected to a

three phase drive system with the help of an inverter.

Fig. 6.8: Simulink model of control circuit for rectifier

68


The above figure shows Matlab /simulink model of rectifier control circuit where

voltage Vc ic adjusted to its reference value V*c using pi controller.

Fig. 6.9: Simulink model of control circuit for inverter

The above figure shows Matlab /simulink model of inverter control circuit where speed

and torque is taken as reference from induction motor

Fig. 6.10: Wave forms of grid input voltage & current

The above figure shows the input side grid voltage of 110 Volts and grid current of

10 Amps which are in phase, so that the power factor is nearly to unity.

69



The above figure shows constant capacitor voltage of 230 Volts across dc link

capacitors obtained from 110V a.c supply, it can be seen that small amount of dc link

ripple component exists in the above waveform.

Fig. 6.12: Wave form of circulating current

The above figure shows circulating current which is close to zero, this current circulates

in the system itself and doesn’t goes to load, so these current made to zero.

70


Fig. 6.13: Wave forms of currents in rectifier A & B

The above figure shows the input currents of rectifier ia & ib of 4 Amps each and along

with their duty-cycles. It can be noticed that the currents are sinusoidal of equal

magnitude, this is due to modulation index(1/2) given in the control circuit for sharing

of equal currents from the total input current of 8A between two rectifiers.

6.1.1.1 Simulation results of Proposed Model when a fault is identified at rectifier B:

Fig. 6.14: Wave forms of grid voltage & current in fault condition

The above figure shows grid voltage and grid current which are in phase and also there

is a variation in waveforms due to failure of rectifier B

71


Fig. 6.15: Wave forms currents in rectifier A & B in fault condition

The above figure shows rectifier currents of rectifier ia & ib, it can be observed the

current ib is zero at interval 0.2, because of failure of rectifier B.

Fig. 6.16: Wave forms currents in rectifier A & B in fault condition

The above figure shows rectifier currents of rectifier ia & ib, it can be observed the

current ib is zero at interval 0.2,because of failure of rectifier B and then the fault is

isolated at interval 0.6. By using a clock signal the time period of fault is adjusted

intentionally by using circuit breaker.

72


Fig. 6.17: THD content at input current using SPWM Technique is 9.24%


proposed system by using SPWM Technique.

Fig. 6.18: THD content at input current using SVPWM Technique is 4.55%


proposed system by using SVPWM Technique.

73


Fig. 6.19: THD content at output voltage using SPWM Technique is 14.84%

The above figure shows harmonic content of 14.84% at the output voltage side for the

conventional system by using SPWM Technique.

Fig. 6.20: THD content at output voltage using SVPWM Technique is 12.90%



74


Parameters Conventional System

Proposed System

SPWM SVPWM

Input Current 7.831 Amps 5.518 Amps 5.35 Amps

Input Voltage 110 Volts 110 Volts 110 Volts

Power Factor 0.937 0.989 0.996Input Power 608.4 Watts 428.7 Watts 415.69 Watts

Total Harmonic Distortion

19.35% 9.24% 4.55%

Current through Switch

7.8Amps 6.8 Amps 6.3 Amps

Power Loss across switch

6.1 Watts 4.6 Watts 3.9 Watts

Output Voltage 121.24 Volts 121.24 Volts 121.24 VoltsOutput Current 4.023 Amps 3.28 Amps 3.3 AmpsOutput Power 487.76 Watts 398.22 Watts 400.54WattsEfficiency 80.17% 92.89% 96.25%

Table 4: Comparison of conventional and proposed systems

The above table shows comparison between conventional and proposed (with spwm

and svpwm) system, it can be clearly noticed that the total harmonic distortion is

reduced from 19.35% to 4.55% and improvement in power factor (0.937 t0 0.996) and

efficiency (80.17% to 96.25%).

6.2 Simulation Results for 230V AC:

6.2.1 Simulation of Conventional Model:

Fig.6.21: Wave forms of grid input voltage & current

75


The above figure shows the input side grid voltage of 230 Volts and grid current of

24 Amps which are in phase, so that the power factor is nearly unity.

Fig. 6.22: Wave form of current in rectifier A

The above figure shows the input current of rectifier ia of 22 Amps which is sinusoidal

and along with their duty-cycles.





76


6.2.2 Simulation of proposed Model:

Fig. 6.24: Wave forms of currents in rectifier A & B

The above figure shows the input currents of rectifier ia & ib of 13 Amps each and

along with their duty-cycles. It can be noticed that the currents are sinusoidal of

equal magnitude, this is due to modulation index(1/2) given in the control circuit for

sharing of equal currents from the total input current of 23A between two rectifiers

Fig. 6.25: Wave form of output line voltage

The above figure shows the synthesized three-phase balanced line to line voltage of

230V obtained from input of 440V d.c to the three phase inverter. However, there still

exist some distortion and unbalance due to low speed at starting.

77


Fig. 6.26: Wave form of circulating current

The above figure shows above shows circulating current which is close to zero, this

current circulates in the system itself and doesn’t goes to load, so these current is made

to zero.





78


Fig. 6.28: THD content at input current using SVPWM Technique of 4.02%

The above figure shows harmonic content of 4.02% at the input side for the proposed

system by using SVPWM Technique

Fig. 6.29: THD content at input current using SPWM technique of 8.12%

The above figure shows harmonic content of 8.12% at the input side for the proposed

system by using SPWM Technique.

79


Fig. 6.30: THD content at output voltage with SPWM technique of 15.34%



Fig. 6.31: THD content at output voltage with SVPWM technique of 10.26%


proposed system by using SVPWM Technique.

Parameters Conventional System Proposed System

SPWM SVPWM

80


Input Current 25.96 Amps 20.15 Amps 18.05 Amps

Input Voltage 230 Volts 230 Volts 230 Volts

Power Factor 0.937 0.989 0.996

Input Power 3226.6 Watts 2646.29 Watts 2390.23 Watts

Total Harmonic Distortion

19.32% 15.82% 4.55%

Current through Switches

12.98Amps 10.7 Amps 9 Amps

Power Loss across switches

16.84 Watts 11.45 Watts 8.1 Watts

Output Voltage 440 Volts 440 Volts 440 VoltsOutput Current 11.66 Amps 9.5 Amps 8.945 AmpsOutput Power 2794.37 Watts 2413.32 Watts 2260.90WattsEfficiency 86.67% 91.96% 94.6%

Table 5: Comparison of conventional and proposed systems

The above table shows comparison between conventional and proposed (with spwm

and svpwm) system, it can be clearly noticed that the total harmonic distortion is

reduced from 19.32% to 4.55% and improvement in power factor (0.937 to 0.996) and

efficiency (86.67% to 96.25%).

Table 6: Distribution of currents for different values of modulation index

Modulation index(µ)

Current of rectifier A(ia)

Current of rectifier B(ib)

0.2 18.4 Amps 4.6 Amps0.4 13.8 Amps 9.2 Amps0.5 11.5 Amps 11.5 Amps0.7 6.9 Amps 16.1 Amps0.9 2.3 Amps 20.7Amps

Table above shows sharing of input current (23Amps) between rectifier A and rectifier

B which are connected in parallel.

81


Chapter 7

CONCLUSION AND FUTURE SCOPE

Conclusion:

The system model and a suitable control strategy, including the pulse width

modulation technique (PWM), is developed. Parallel converters have been used to

improve the power capability, reliability, efficiency, and redundancy and other

advantage is parallel connection scheme permits to reduce the switching currents and

therefore rating of power in each switch of the rectifier side is reduced, hence continuity

of the power is observed. The system combines two parallel rectifiers without the use of

transformers. The complete comparison between the proposed and standard

configurations has been carried out in this project. The proposed topology permits to

reduce the total harmonic distortion and current and consequently to reduce the power

ratings of the power switches of the rectifier. Compared to the conventional topology,

the proposed system permits to reduce the rectifier switch currents, the THD of the grid

current and THD across output side and to increase the fault tolerance characteristics. In

addition, the losses of the proposed system is lower than that of the conventional

system.

Future Scope:

Parallel converter techniques can be employed to improve the performance of

active power filters uninterruptible power supplies (UPS), fault tolerance of doubly fed

induction generators, and three-phase drives.

To achieve even less %THD and to improve the dc bus utilisation advanced

inverter topologies (multilevel inverters, multi-cell inverters) with advanced modulation

and control techniques can be used. The speed control of three phase induction motor

can be done more precisely, % THD and dc bus utilisation can be improved if the

control strategy if the inverter is changed to DPWM (discontinuous pulse width

modulation) techniques.

82

Bibliography

Chapter 8

BIBLIOGRAPHY

[1] P. Enjeti and A. Rahman, “A new single phase to three phase converter with active

input current shaping for low cost AC motor drives,” IEEE Trans. Ind. Appl., vol.

29, no. 2, pp. 806–813, Jul./Aug. 1993.

[2] J. Itoh and K. Fujita, “Novel unity power factor circuits using zero-vector control

for single-phase input systems,” IEEE Trans. Power Electron., vol. 15, no. 1, pp.

36–43, Jan. 2000.

[3] B.K. Lee, B. Fahimi, and M. Ehsani, “Overviewof reduced parts converter

topologies for AC motor drives,” in Proc. IEEE PESC, 2001, pp. 2019– 2024.

[4] C. B. Jacobina, M. B. de R. Correa,A.M. N. Lima, and E. R. C. da Silva, “AC

motor drive systems with a reduced switch count converter,” IEEE Trans. Ind.

Appl., vol. 39, no. 5, pp. 1333–1342, Sep./Oct. 2003.

[5] R. Q. Machado, S. Buso, and J. A. Pomilio, “A line-interactive singlephase to

three-phase converter system,” IEEE Trans. Power Electron., vol. 21, no. 6, pp.

1628–1636, May 2006.

[6] O. Ojo, W. Zhiqiao, G. Dong, and S. Asuri, “High-performance speedsensorless

control of an induction motor drive using a minimalist singlephase PWM

converter,” IEEE Trans. Ind. Appl., vol. 41, no. 4, pp. 996– 1004, Jul./Aug. 2005.

[7] J. R. Rodr´ıguez, J. W. Dixon, J. R. Espinoza, J. Pontt, and P. Lezana,

“PWMregenerative rectifiers: State of the art,” IEEE Trans. Ind. Electron., vol. 52,

no. 1, pp. 5–22, Feb. 2005.

[8] M. N. Uddin, T. S. Radwan, and M. A. Rahman, “Fuzzy-logic controller-based

cost-effective four-switch three-phase inverter-fed IPM pp. 21–30, Jan./Feb.

2006.

[9] D.-C. Lee and Y.-S. Kim, “Control of single-phase-to-three-phase AC/DC/AC

PWM converters for induction motor drives,” IEEE Trans. Ind. Electron., vol. 54,

no. 2, pp. 797–804, Apr. 2007.`

83

single phase to three phase converstion using two parallel rectifiers

Documents