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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.TechAssistant Professor
Department of Electrical & Electronics Engineering
Chalapathi Institute Of Technology(Approved by AICTE, Affiliated to JNTU Kakinada)
(2009-2013)
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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)
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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) .
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ABSTRACT
Single-phase to three-phase acdcac conversion usually employs a full-bridge
topology. In these three phases 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
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CONTENTS
ABSTRACT i
List of Figures iv
List of Tables vi
ABSTRACT 1
LIST OF FIGURES 5
LIST OF TABLES 8
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: 3
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 (1-3) Cycloconverters: 10
2.2.1 Integral Pulse Modulated (1-3) Cycloconverters: 11
2.2.2 Phase-Controlled (1-3) 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: 16
3.3.5 High Starting/Breakaway Torque followed by Constant Torque 17
3.4. Induction motor characteristics in the proposed system: 17
Chapter 4: CONTROL STRATEGIES OF CONVERTERS 19
4.1 Introduction: 19
4.2 Sinusoidal Pulse Width Modulation: 21
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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
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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
motor14
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
Frequency17
Fig. 3.8wave forms of three phase voltage, current, speed and
torque18
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 SVPWM27
Fig. 4.8:The relationship of abc reference frame and stationary dq
reference frame28
Fig. 4.9: Basic switching vectors and sectors 29
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Fig.4.10:Reference vector as a combination of adjacent vectors at
sector 131
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 45
Fig. 5.4 WTHD of rectifier voltage (vab for proposed configuration
and vg for Standard configuration) as a function of 47
Fig. 5.5 Variables of rectifiers A and B. 48
Fig. 5.6 Currents ia , ia , and io fordouble-carrier 49
Fig. 5.7(a)Flow of active power in Conventional acdcac single-
phase to three phase converter50
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 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
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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 ia in rectifier A 59
Fig. 6.5: Wave form of output line voltage 60Fig. 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 67Fig.6.21: Wave forms of grid input voltage & current 68
Fig. 6.22: Wave form of current in rectifier A 69
Fig. 6.23: Wave form of DC-Link capacitor voltage 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. 6.27: Wave form of DC-Link capacitor voltage 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
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LIST OF TABLES
Description Pg. No.
Table 1: ratings of induction motor 19
Table 2: Switching vectors, phase voltages and output line to line voltages 26
Table 3: Efficiency of the Proposed System Normalized In Terms Conventional 55
Table 4: Comparison of conventional and proposed systems for 110V supply 68
Table 5: Comparison of conventional and proposed systems for 230V 74
Table 6: Distribution of currents for different values of modulation index 74
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Introduction
1
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 themassive 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 acdcac 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
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Introduction
3
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 rectifierinverter
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 Brando Jacobina, Senior Member, IEEE, Euzeli Cipriano dos Santos, Jr.,
Student Member, IEEE, Edison Roberto Cabral da Silva, Fellow, IEEE, Mauricio
Beltro 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
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Introduction
4
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
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Introduction
5
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-
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Introduction
6
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
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Introduction
7
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.
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1-3 AC Conversion Methods
8
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
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1-3 AC Conversion Methods
9
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
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1-3 AC Conversion Methods
10
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 (1-3) 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
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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 (1-3) 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 isrequired, 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(1-3) 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
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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
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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
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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
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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. 3.2Torque-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.
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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 aquadratic 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.
Fig 3.5. Constant Power Loads
3.3.4 Constant Power, Constant Torque Loads:
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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.
Fig. 3.7. Relation between the Voltage and Torque versus Frequency
3.4. Induction motor characteristics in the proposed system:
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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.
Fig 3.8(d) electromagnetic torque in N/m
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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, 230v
Frequency 50hz
Speed 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^2
Reference
Frame
Rotor
Table 1: Ratings of Induction Motor
The above table shows ratings of three phase induction motor for different
parameters.
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.
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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 voltagetime 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)
the event that magnetic saturation effects may be ignored. This expression can, with the
aid of (4.3), be expressed as
(4.4)
This may be reduced to
(4.5)
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When the time constant = 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 variousconverter 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.
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
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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.
Fig. 4.2: Simple Voltage Sourced Inverter
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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
switchings 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 m1, there are periods of thetriangle 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.
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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 n2
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 120 o 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
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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.
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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).
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Table 2: Switching vectors, phase voltages and output line to line voltages
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 togenerate 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.
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Fig. 4.7: Locus comparison of maximum linear control voltage in Sine PWM and SVPWM.
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 = Ksfabc
where,
(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.
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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 Vrefin 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
approximation is to generate the average output of the inverter in a small period, T to be
the same as that of Vrefin 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 ()
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 ():
From Fig. 4.14, the Vd, Vq, Vref, and angle () can be determined as follows:
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(4.11)
(4.12)
(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)
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(4.15)
(4.16)
(4.17)
Switching time duration at any Sector
(4.18)
Fig. 4.10: Reference vector as a combination of adjacent vectors at sector 1.
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Step 3: Determine the switching time of each transistor (S1 to S6):
(a) Sector 1. (b) Sector 2.
(c) Sector 3. (d) Sector 4.
(e) Sector 5. (f) Sector 6.
Fig. 4.11: Space vector PWM switching patterns at each sector.
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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
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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 .
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4.5.1. Rectifier control circuit:
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
ia = ib = ig /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
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where the magnitude of the voltage is generated, in order to generate pulses this two
phase transformation is changed to three phase transformation by using d-q axis of
trigonometric functions i.e., 2 sint (where t= 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 system 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.
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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, qa1 , qa2 , and
qa2 , and qb1, qb1, qb2 and qb2 of rectifier A & B, . The inverter is constituted of
switches qs1, qs1, qs2, qs2, qs3 and qs3. The system is composed of grid, input
inductors (La, La, Lb, and Lb), 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.
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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
1ph
ac
Rectifier
A
3PH
VSIIM
Parallel converters
Control
circuit
Rectifier
B
Speed Ref
Vdc
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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, ra, la, la are the resistances and inductances across input side,
Also ia, ia are currents across rectifier A.
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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, rb, lb, lb are the resistances and inductances across input
side, ib and ib are currents in rectifier B.
Fig: 5.2.1(c): loop3 of the system model
(5.3)
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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.
Fig: 5.2.1(d): loop4 of the system model
(5.4)
Where Va20, Vb20 are pole voltages across switches qa2 and qb2 respectively
ra, rb, la, lb 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, La, Lb, and Lb.
The grid current can be derived as,
(5.5)
The circulating current io can be defined from ia and ia or ib and ib , i.e.,
(5.6)
Introducing io and adding (5.3) and (5.4), relations (5.1)(5.4) become
(5.7)
(5.8)
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(5.9)
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 ia and ib are chosen
equal to ig /2 and the reference circulating current io 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., rg = ra = ra = rb
= rb and lg = la =la = lb = lb. 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 , ia , and ib can be written as
(5.16)
(5.17)
(5.18)
In this ideal case (four identical inductors), the circulating current can be reduced tozero imposing
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(5.19)
When Io = 0 (ia = ia, ib = ib) the system model (5.7)(5.9) is reduced to
(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 va, vb, and vo 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
va10, va20, vb10, and vb20. However, (5.23)(5.25) are not sufficient to determine
the four pole voltages uniquely from va, vb and vo. Introducing an auxiliary
variable vx = va20, that equation plus the three equations (5.23)(5.25) constitute a
four independent equations system with four variables (va10, va20, vb10, and
vb20). Solving this system of equations, we obtain
(5.26)
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(5.27)
(5.28)
(5.29)
From these equations, it can be seen that, besides va, vb and vo, the pole
voltages depend on also of vx. The limit values of the variable vx can be calculated
by taking into account the maximum vc /2 and minimum vc /2 value of the pole
voltages
(5.30)
(5.31)
Where vc is the reference dc-link voltages, vmax = max and vmin = min with
= {va , 0, va/2 + vb /2 vo/2, va/2 vb /2 vo/2}
Introducing a parameter (0 1), the variable vx can be written as
(5.32)
When = 0, = 0.5, and = 1 the auxiliary variable vx has the following
values vx = vxmin, vx = vx have = (vxmin +vxmax)/2, and vx = vxmax,
respectively. When vx = vxmin or vx = vxmax a converter leg operates with zero
switching frequency.
Once vx is chosen, pole voltages va10, va20, vb10, and vb20are 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 changes the place of the voltage pulses related to va and vb .
When vx = vxmin ( = 0) or vx = vxmax ( = 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 vx =vx 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
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distribution of the zero instantaneous voltages (i.e., va = 0 and vb = 0).With = 0 or
= 1 the zero instantaneous voltages are placed at the beginning or at the end of the
switching period, respectively, while with = 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
zero-voltage vector in the three-phase inverter. Consequently, 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 ia = ib
= ig /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
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These current controllers define the input reference voltages va and vb .The
homopolar current is measured (io ) and compared to its reference (io = 0). The error
is the input of PI controller Ro , that determines the voltage vo . The calculation of
voltage vx is given from (5.30) to (5.32) as a function of , 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 theWTHD 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 . Note that the parameter determines vx 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 , as observed in Fig. 5.4. When the
double-carrier PWM is used with = 0.5, the WTHD is also the same for both
configurations. However, for the other values of the WTHD of the proposed system is
lower than that of the conventional one. The WTHD of the proposed topology (double-
carrier with = 0 or = 1) is close to 63% of that of the conventional topology (with
= 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.
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Fig. 5.4: WTHD of rectifier voltage (vab for proposed configuration and vg for
standard configuration) as a function of.
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 (va10, va20,
vb10, vb20), 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 = 1) and double-carrier (with =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 = 1). On the other hand, for = 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 = 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 , ia , ib , and ib ) 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 = 0 or = 1 and increased for =
0.5. On the other hand, the THD of the circulating current is also smaller with = 0 or
= 1. Fig. 5.6 shows currents ia , ia , and io for double-carrier with = 1 and = 0.5.
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It can be seen that the mean values of the ripples of all currents are smaller when = 1
is selected.
In conclusion the optimal rectifier operation is obtained with double-carrier
making = 0 or = 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 = 1.
(b) Single-carrier with = 0.5.
(c) Double-carrier with = 1.
(d) Double carrier with = 0.5.
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Fig. 5.6: Currents ia , i_a , and io for double-carrier with = 1 and = 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 (Lg =La = La
= Lb = Lb ), 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.
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Fig. 5.7(a): Flow of active power in Conventional acdcac 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 ofvmax.
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
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Where idc anddc are current and voltage of the dc capacitor, respectively, Tsw
is the switching period, and dc is the voltage ripple.
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 i is the amplitude of the
cross-current developed during the interval t0, the Vdc obtained is 230V
LF=
L= 5mH
The THD of the grid current as a function of for different values of ln [the
inductances of rectifiers A and B (lg ) referred to that of the conventional configuration
(lg ), i.e., ln = lg /lg ]. For ln > 0.4 (lg > 0.4lg) the THD of the grid current of the
proposed topology is smaller than that of the conventional topology.
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Fig. 5.8: Inductor specification in terms of THD of ig and.
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 fusesFj , j = 1, . . . , 7) and
connecting devices (back-to-back connected SCRst1 , 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 j0 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).
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4) Identification of the faulty switches by using j0.
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.