a single-phase hybrid active power filter
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A SINGLE-PHASE HYBRID ACTIVE POWER FILTER
WITH PHOTOVOLTAIC APPLICATION
TAN PERNG CHENG
UNIVERSITI TEKNOLOGI MALAYSIA
iii
Special dedicated to my beloved mother and Chai Ling
iv
ACKNOWLEDGEMENT
I would like to take this opportunity to thank various people who have
provided much assistance and invaluable information to make this project a success.
First of all, I would like to take this opportunity to express my deepest gratitude to
my supervisor of this project, Associate Professor Dr. Zainal bin Salam for his
valuable guidance and generous encouragement throughout the project duration. His
patience in understanding my tasks and problems has brought light to the
development of this project.
I also wish to express my gratitude to the members of academic and technical
staff of Power Electronics and Drives Group, Department of Energy Conversion,
Faculty of Electrical Engineering, Universiti Teknologi Malaysia for the discussions
and technical assistances. Not forgetting my friends and the graduated seniors who
have encouraged and assisted me in needing times.
Last but not least, my utmost thanks go to my beloved mother and Chai Ling
for their unimaginable love, encouragement and support.
v
ABSTRACT
The past several years have seen a rapid increase of power electronics-based
loads connected to the distribution system. These types of loads draw nonsinusoidal
current from the mains, degrading the power quality by causing harmonic distortion.
This thesis proposes a single-phase hybrid active power filter with photovoltaic
application. The proposed topology interconnects a passive high-pass filter in
parallel with a shunt active power filter and a DC source that represents the
photovoltaic array. The uniqueness of the proposed topology is the fact that it
improves the harmonic filtering performance of a basic shunt active power filter, as
well as simultaneously supplies the power from the photovoltaic array to the load.
The compensation current reference for the proposed topology is obtained by using
the extension instantaneous reactive-power theorem. This theorem simplifies the
equations for the current reference estimation, thus leading to a more efficient
implementation in digital signal processor. To generate the compensation current
that follows the current reference, the fixed-band hysteresis current control method is
adopted. This work describes the design of circuit topology, control system, high-
pass filter and compensation current reference estimation. The system is verified by
simulation using MATLAB/Simulink simulation package. To validate the result, a
500 VA laboratory prototype is constructed. It is based on the dSPACE DS1104
digital signal processor. Experimental results show that the system effectively
reduces the total harmonic distortion of the source current from 130.2 % to 19.6 %.
Furthermore, it is demonstrated that the system can also supply active power to the
load.
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TABLE OF CONTENTS
CHAPTER TITLE PAGE
TITLE PAGE i
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES xii
LIST OF FIGURES xiii
LIST OF SYMBOLS xviii
LIST OF ABBREVIATIONS xxiii
LIST OF APPENDICES xxv
1 INTRODUCTION 1
1.1 Overview 1
1.2 Objective of Research 3
1.3 Methodology of Research 4
1.4 Thesis Organisation 5
2 LITERATURE REVIEW 7
2.1 Introduction 7
2.2 Electric Power Quality 7
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2.2.1 Fundamental of Harmonic Distortion 8
2.2.2 Harmonic Distortion Impacts on
Electric Power Quality 9
2.3 Harmonic Mitigation Approaches 10
2.3.1 Passive Filtering of Harmonic 11
2.3.2 Active Filtering of Harmonic 12
2.3.2.1 Shunt Active Power Filter 14
2.3.2.2 Series Active Power Filter 16
2.3.2.3 Hybrid Active Power Filter 18
2.4 Distribution Line Interactive Photovoltaic
Systems 19
2.4.1 Distribution Line Interactive
Photovoltaic Inverter 20
2.4.2 Photovoltaic Interactive Shunt
Active Power Filter 22
2.5 Reference Signal Estimation Techniques 23
2.5.1 Frequency Domain Approaches 24
2.5.1.1 Fourier Transform
Techniques 24
2.5.2 Time Domain Approaches 25
2.5.2.1 Instantaneous Reactive-
Power Theorem 26
2.5.2.2 Extension Instantaneous
Reactive-Power Theorem 27
2.5.2.3 Synchronous-Detection
Theorem 28
2.5.2.4 Synchronous-Reference-
Frame Theorem 29
2.5.2.5 Sine-Multiplication Theorem 29
2.6 Control Techniques for Active Power Filter 30
2.6.1 Linear Control Technique 30
2.6.2 Hysteresis Control Technique 32
2.7 Summary 33
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3 A SINGLE-PHASE HYBRID ACTIVE POWER
FILTER 35
3.1 Introduction 35
3.2 Operation Principle of the Proposed Hybrid
APF 36
3.3 The Proposed System Configuration 38
3.3.1 Proposed Overall System 38
3.3.2 Power Circuit 40
3.3.3 Interfacing Inductor 41
3.3.4 DC-Bus Capacitor 42
3.4 The Control System 43
3.4.1 Overall Control System 43
3.4.2 Compensation Current Reference
Estimation 45
3.4.3 DC-Bus Voltage Control 47
3.4.4 Digital Phase-Lock Loop 49
3.4.5 Digital Low-Pass Filter 51
3.5 Passive High-Pass Filter 53
3.6 Summary 57
4 SIMULATION OF THE PROPOSED HYBRID
ACTIVE POWER FILTER 58
4.1 Introduction 58
4.2 System Modelling via MATLAB/Simulink 59
4.2.1 Distribution Source 59
4.2.2 Nonlinear Load 60
4.2.3 Shunt Active Power Filter 61
4.2.4 Passive High-Pass Filter 63
4.2.5 Overall Control System 66
4.2.5.1 Reference Sinewave
Generator 67
4.2.5.2 Compensation Current
Reference Estimator 70
x
4.2.5.3 DC-Bus Voltage Controller
and PV Current Estimator 72
4.2.5.4 Fixed-Band Hysteresis
Current Controller 73
4.3 Basic Shunt Active Power Filter 74
4.4 Summary 75
5 HARDWARE IMPLEMENTATION OF THE
PROPOSED HYBRID ACTIVE POWER FILTER 76
5.1 Introduction 76
5.2 General Description of the Experimental
Set-Up 76
5.3 Experimental Prototype Construction 79
5.3.1 Nonlinear Load 80
5.3.2 Shunt Active Power Filter 81
5.3.2.1 Voltage Source Inverter 81
5.3.2.2 Interfacing Inductor 82
5.3.2.3 DC-Bus Capacitor 83
5.3.3 Gate-Driver Circuit 83
5.3.4 Passive High-Pass Filter 84
5.4 Analogue Signals Measurement 85
5.4.1 Hall-Effect Voltage Transducer 85
5.4.2 Hall-Effect Current Transducer 86
5.4.3 Analogue Prefilter 87
5.5 Controller Hardware and Software Tools 88
5.5.1 DS1104 DSP Controller Board 88
5.5.2 Software Tools 89
5.6 Control Software 91
5.6.1 Control Software Structure 91
5.6.2 Initialisation Routine 92
5.6.3 Service Routine 0 92
5.6.4 Interrupt Service Routine 1 93
5.7 Summary 96
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6 RESULTS AND ANALYSIS 97
6.1 Introduction 97
6.2 Results – Without Compensation 98
6.3 Reference Sinewave Generation 99
6.4 Compensation Current Reference Estimation 101
6.5 Results – Ideal Compensation 104
6.6 Results – Basic Shunt Active Power Filter
Compensation 107
6.7 Results – Proposed Hybrid Active Power
Filter Compensation 111
6.8 Photovoltaic Energy Handling Capability 115
6.9 Harmonic Distortion Analysis 116
6.10 Summary 121
7 CONCLUSIONS AND RECOMMENDATIONS
FOR FUTURE WORK 122
7.1 Conclusions 122
7.2 Recommendations for future work 123
REFERENCES 125
PUBLICATIONS 135
APPENDICES A – K 136 – 214
xii
LIST OF TABLES
TABLE NO. TITLE PAGE
5.1 Experimental prototype parameters 80 5.2 AC smoothing inductor specification 81 5.3 2.5 mH inductor specification 82 5.4 HPF inductor specification 85 5.5 Analogue prefilter specification 87 6.1 Calculated THD for the source current 121
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LIST OF FIGURES
FIGURE NO. TITLE PAGE
1.1 Current distortion caused by nonlinear resistor 1 2.1 Fourier series representation of a distorted waveform 8 2.2 Harmonic currents flowing through the system impedance result in harmonic voltages at the PCC 10 2.3 Common types of passive filters and their configurations 11 2.4 Generalised block diagram for APF 13 2.5 Subdivision of APF according to power circuit configurations and connections 14 2.6 Principle configuration of a VSI based shunt APF 15 2.7 Shunt APF harmonic filtering operation principle 16 2.8 Principle configuration of a VSI based series APF 17 2.9 Operation principle of series APF: (a) single-phase equivalent of series APF, (b) fundamental equivalent circuit, and (c) harmonic equivalent circuit 18 2.10 Hybrid APFs: (a) combination of shunt APF and shunt passive filter and (b) combination of series APF and shunt passive filter 19 2.11 Operation principle of a PV cell 20 2.12 Configuration of a distribution line interactive PV inverter system 21 2.13 Configuration of a PV interactive shunt APF system 22 2.14 Subdivision of reference signal estimation techniques 24
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2.15 Block diagram of linear control technique 31 2.16 Gating signal generation by linear controller 31 2.17 Block diagram of hysteresis control technique 32 2.18 Gating signal generation by hysteresis controller 33 3.1 Operation principle of the proposed hybrid APF
without PV power 36 3.2 Operation principle of the proposed hybrid APF
with PV power 37 3.3 System configuration of the proposed hybrid APF 39 3.4 Power circuit of the proposed hybrid APF 40 3.5 Switching ripple of the compensation current 41 3.6 Overall control system of the proposed hybrid APF 44 3.7 PI controller for DC-bus voltage control 48 3.8 A digital phase-lock loop model in z-domain 49 3.9 Block diagram of the digital low-pass filter for DC
components extraction 52 3.10 Graphical plot of HPF impedance transfer function
( )(sZ hp ) 55 3.11 Simplified model of the proposed hybrid APF 55 3.12 Graphical plot of source current to injected current
transfer function ( )(sH cds ) 56 4.1 Complete simulation model of the proposed hybrid APF connected to a DC source 59 4.2 Detail of “Distribution Source” block 60 4.3 Detail of “Nonlinear Load” block 61 4.4 Detail of “Shunt APF” block 62 4.5 Detail of “Passive HPF” block 63 4.6 Frequency response of the HPF impedance transfer function 65
xv
4.7 Frequency response of the source current to injected current transfer function 66 4.8 Detail of “Overall Control System” block 67 4.9 Detail of “Reference Sinewave Generator” block 68 4.10 Detail of “Phase Delay Compensation” block 68 4.11 Detail of “Compensation Current Reference Estimator” block 70 4.12 Detail of “DC-Bus Voltage Controller and PV Current Estimator” block 72 4.13 Detail of “Fixed-Band Hysteresis Current Controller” block 74 4.14 Complete simulation model of the basic shunt APF connected to a DC 74 5.1 Overall control block diagram of the experimental set-up 77 5.2 Actual overall experimental set-up 78 5.3 Actual experimental prototype. (1) interfacing inductor, (2) gate drivers, (3) VSI with DC-bus capacitor, (4) rectifier load, (5) DS1104 connector board, (6) smoothing inductor, (7) current and voltage transducers, (8) passive HPF 79 5.4 Schematic of experimental single-phase full-bridge VSI 82 5.5 DC-bus capacitor 83 5.6 Functional block diagram of gate driver circuit 84 5.7 Voltage signal measurement using LV25-P Hall-Effect voltage transducer 86 5.8 Current signal measurement using LA25-NP Hall-Effect current transducer 87 5.9 Analogue prefilter circuit 88 5.10 Block diagram of the DS1104 DSP controller board 89
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5.11 Graphical user interface of ControlDesk software 90 5.12 DS1104 control software structure 92 5.13 Initialisation routine flowchart 94 5.14 Service routine 0 flowchart 94 5.15 Interrupt service routine 1 flowchart 95 6.1 Simulation results – without compensation: source voltage and load current waveforms 98 6.2 Experimental results – without compensation:
source voltage and load current waveforms 99 6.3 Simulation results – PLL generated reference sinewave: source voltage and the generated reference sinewave waveforms 100 6.4 Experimental results – PLL generated reference sinewave: source voltage and the generated reference sinewave waveforms 100 6.5 Simulation results: load current and HPF current waveforms 101 6.6 Experimental results: load current and HPF current waveforms 102 6.7 Simulation results: estimated active load current, reactive load current, harmonic load current and reactive HPF current waveforms 103 6.8 Experimental results: estimated active load current, reactive load current, harmonic load current and reactive HPF current waveforms 104 6.9 Experimental prototype arrangement 105 6.10 Simulation results – ideal compensation condition: load current, compensation current, and source current waveforms 106 6.11 Experimental results – ideal compensation condition: load current, compensation current, and source current waveforms 107
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6.12 Simulation results – basic shunt APF compensation: source voltage, load current, compensation current and source current waveforms 108 6.13 Experimental results – basic shunt APF compensation: source voltage, load current, compensation current and source current waveforms 109 6.14 Simulation result – the relationship between the
compensation current reference and hysteresis band 110 6.15 Experimental result – the relationship between the
compensation current reference and hysteresis band 111 6.16 Simulation results – proposed topology compensation: source voltage, load current, HPF current, compensation current and source current waveforms 113 6.17 Experimental results – proposed topology compensation: source voltage, load current, HPF current, compensation current and source current waveforms 114 6.18 Simulation results – proposed hybrid APF with 250 W PV power generations: load current, compensation current and source current waveforms 115 6.19 Experimental results – proposed hybrid APF with 250 W PV power generations: load current, compensation current and source current waveforms 116 6.20 Spectrum of load current – without compensation: (a) simulation result and (b) experimental result 117 6.21 Spectrum of source current – with ideal compensation condition: (a) simulation result and (b) experimental result 118 6.22 Spectrum of source current – with basic shunt APF compensation: (a) simulation result and (b) experimental result 119 6.23 Spectrum of source current – with proposed topology compensation: (a) simulation result and (b) experimental result 120
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LIST OF SYMBOLS
a - Constant of )(1 zH
1LPFa , 2LPFa - Coefficients of )(zGLPF
A - Gain coefficient of )(sZ hp
c - Constant of )(2 zH
C - Capacitor
0C , 1C - Coefficients of z∆
dC - DC Smoothing capacitor
fC - DC-bus capacitor
hpC - High-pass filter capacitor
CfE - Energy in DC-bus capacitor
refCfE , - Reference energy in DC-bus capacitor
0f - Resonant frequency of passive high-pass filter
cf - Cut-off frequency of analogue prefilter
1cf - Cut-off frequency 1 of analogue prefilter
2cf - Cut-off frequency 2 of analogue prefilter
LPFf - Cut-off frequency of low-pass filter
rf - Parallel resonant frequency of low-pass filter
sf - Sampling frequency of discrete system
1sf - Sampling frequency 1 of the proposed scheme
2sf - Sampling frequency 2 of the proposed scheme
)(sGLPF - Transfer function of low-pass filter in s-domain
LPFG - Coefficient of )(zGLPF
xix
GD1 - Gate driver circuit 1
GD2 - Gate driver circuit 2
H - Hysteresis tolerance band of current controller
)(sH - Closed-loop transfer function of phase-lock loop in s-domain
)(zH - Closed-loop transfer function of phase-lock loop in z-domain
)(1 zH - Loop filter transfer function in z-domain
)(2 zH - Digitally-controlled oscillator transfer function in z-domain
)(sH cds - Transfer function of source current to injected current in
s-domain
maxH - Maximum crest of )(sH cds
CfI - Amplitude of DC-bus capacitor charging current
fi - Compensation current
ffi , - Compensation current fundamental component
hfi , - Compensation current harmonics components
reffi , - Compensation current reference signal
1,reffi - First component of compensation current reference signal
2,reffi - Second component of compensation current reference signal
hpi - High-pass filter current
hpI - rms value of high-pass filter current
phpi , - High-pass filter current active component
qhpi , - High-pass filter current reactive component
hysteresisi - Error of hysteresis current comparator
Li - Load current
LI - rms value of load current 'Li - Load current shifted by o90
fLi , - Load current fundamental component
hLi , - Load current harmonics component
qLi , - Load current reactive component
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noisei - Noise current
PVi - PV current
PVI - Amplitude of PV current
si - Source current
fsi , - Source current fundamental component
hsi , - Source current harmonics components
swi - Switching ripple of the compensation current
αi - α -axis of load current
βi - β -axis of load current
IK - Integration constant of PI controller
pK - Proportional constant of PI controller
L - Inductor
fL - APF interfacing inductor
hpL - High-pass filter inductor
sL - Source inductor
smoothL - AC smoothing inductor
hM - rms value of harmonic component h of the quantity M
p - Instantaneous active power
p - DC component of instantaneous active power
p~ - AC component of instantaneous active power
Lp - Instantaneous active load power
PVP - Active power of PV array/DC source
q - Instantaneous reactive power
Q - Quality factor of )(sZ hp
q - DC component of instantaneous reactive power
q~ - AC component of instantaneous reactive power
hpq - Instantaneous reactive HPF power
Lq - Instantaneous reactive load power
R - Resistor
xxi
BR - Bleed resistor
hpR - High-pass filter resistor
LR - Load resistor
0s , 1s - Poles of )(sH
nS - Rectifier load nominal complex power
)sin( tω - Reference sinewave
)90sin( o−ωt - 90˚ delayed reference sinewave
T - Period of source voltage
sT - Sampling period of discrete system
swT - Period of switching ripple
CfV - DC-bus voltage
fv - Compensation voltage
reffv , - Compensation voltage reference signal
sv - Source voltage
sV - rms value of source voltage
'sv - Source voltage shifted by o90
fsv , - Source voltage fundamental component
hsv , - Source voltage harmonics components
uv - Distribution voltage
αv - α -axis of source voltage
βv - β -axis of source voltage
ω - Damped frequency
0ω - Series resonant frequency of )(sZ hp
1ω - Parallel resonant frequency of )(sH cds
nω - Natural undamped frequency of low-pass filter
pω - Pole frequency of )(sZ hp
0z , 1z - Poles of )(zH
1−z - Unit delay
xxii
eqZ - Series APF equivalent impedance
fZ - Series APF impedance
)(sZ hp - High-pass filter impedance transfer function
sZ - Source impedance
)(sZ s - Source impedance transfer function
fsZ , - Source impedance fundamental component
hsZ , - Source impedance harmonics components
CfE∆ - Energy loss of DC-bus capacitor in one cycle
LI∆ - Peak rms value of reactive and harmonic load current
ppswI −∆ , - Peak-to-peak switching ripple
CfV∆ - Maximum/minimum DC-bus capacitor voltage
z∆ - Characteristic equation of )(zH
θ - Phase angle of load current
nθ - Phase angle of n-th load current component
)(zfdθ - Feedback signal of digital phase-lock loop
)(zinθ - Input signal of digital phase-lock loop
φ - Phase angle of source voltage
σ - Damping factor
0αβ - Orthogonal coordinates of stationary reference frame
ζ - Damping ratio
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LIST OF ABBREVIATIONS
AC - Alternating current
ADC - Analogue-to-digital converter
APF - Active power filter
ASD - Adjustable-speed motor drive
CPU - Central processing unit
DAC - Digital-to-analogue converter
DC - Direct current
DCO - Digitally-controlled oscillator
DSP - Digital signal processor
EMI - Electromagnetic interference
ESL - Equivalent series inductance
ESR - Equivalent series resistance
FFT - Fast Fourier Transform
HPF - High-pass filter
I/O - Input/output
IGBT - Insulated gate bipolar transistor
LPF - Low-pass filter
MOSFET - Power metal oxide-semiconductor field-effect transistor
p-q - Instantaneous reactive-power
PCC - Point of common coupling
PCI - Peripheral component interconnect
PI - Proportional-integral controller
PLL - Phase-lock loop
PQ - Power quality
PV - Photovoltaic
PWM - Pulse width modulation
xxiv
rms - Root-mean-square
RE - Renewable energy
RTI - Real-time interface
RTLib - Real-time library
RTW - Real-time workshop
THD - Total harmonic distortion
THD12.5 kHz - Total harmonic distortion calculated up to 12.5 kHz
VSI - Voltage source inverter
xxv
LIST OF APPENDICES
APPENDIX TITLE PAGE
A Derivation of minimum interfacing inductor ( min,fL ) 136 B Derivation of )(tpL , )(tqL and )(tqhp based on extension p-q theorem 139 C Proportional constant ( pK ) calculation using energy-balance principle 147 D Coefficients ( 1C and 0C ) derivation for the digital phase-lock loop 150 E )(sZ hp and )(sH cds derivation for the passive high-pass filter 153 F AC smoothing inductor ( smoothL ), interfacing inductor ( fL ) and HPF inductor ( hpL ) design 158 G Schematic of IGBT gate driver circuit 169 H Program listing for the DS1104 DSP controller board 171 I Conference paper presented at PECon 2004 195 J Conference paper presented at PEDS 2005 202 K Conference paper presented at PEMD 2006 209
CHAPTER 1
INTRODUCTION
1.1 Overview
The power quality (PQ) problems in power distribution systems are not new,
but only recently the effects of these problems have gained public awareness.
Advances in semiconductor device technology have fuelled a revolution in power
electronics over the past decade, and there are indications that this trend will
continue [1]. However these power equipments which include adjustable-speed
motor drives (ASDs), electronic power supplies, direct current (DC) motor drives,
battery chargers, electronic ballasts are responsible for the rise in related PQ
problems [2]-[4]. These nonlinear loads are constructed by nonlinear devices, in
which the current is not proportional to the applied voltage. A simple circuit as
shown in Figure 1.1 illustrates the concept of current distortion. In this case, a
sinusoidal voltage is applied to a simple nonlinear resistor in which the voltage and
current vary according to the curve shown. While the voltage is perfectly sinusoidal,
the resulting current is distorted.
Figure 1.1 Current distortion caused by nonlinear resistance
Nonlinear Resistor
V
I
i(t)
v(t)
2
Nonlinear loads appear to be prime sources of harmonic distortion in a power
distribution system. Harmonic currents produced by nonlinear loads are injected
back into power distribution systems through the point of common coupling (PCC).
These harmonic currents can interact adversely with a wide range of power system
equipment, most notably capacitors, transformers, and motors, causing additional
losses, overheating, and overloading [2]-[4].
There are set of conventional solutions to the harmonic distortion problems
which have existed for a long time. The passive filtering is the simplest conventional
solution to mitigate the harmonic distortion [5]-[7]. Although simple, these
conventional solutions that use passive elements do not always respond correctly to
the dynamics of the power distribution systems [8]. Over the years, these passive
filters have developed to high level of sophistication. Some even tuned to bypass
specific harmonic frequencies. However, the use of passive elements at high power
level makes the filter heavy and bulky. Moreover, the passive filters are known to
cause resonance, thus affecting the stability of the power distribution systems [9]. As
the regulatory requirements become more stringent, the passive filters might not be
able to meet future revisions of a particular Standard.
Remarkable progress in power electronics had spurred interest in active
power filter (APF) for harmonic distortion mitigation [10]-[15]. The basic principle
of APF is to utilise power electronics technologies to produce currents components
that cancel the harmonic currents from the nonlinear loads [10]. Previously, majority
of controllers developed for APF are based on analogue circuits [11], [12]. As a
result, the APF is inherently subjected to signal drift. Digital controller using digital
signal processor (DSP) or microprocessor is preferable, primarily due to its
flexibility and immunity to noise signals [13]-[15]. However it is known that using
digital methods, the high order harmonics are not filtered effectively. This is due to
the hardware limitation of sampling rate in real-time application [15]. Moreover, the
utilisation of fast switching transistors (i.e. IGBT) in APF application causes
switching frequency noise to appear in the compensated source current. This
switching frequency noise requires additional filtering to prevent interference with
other sensitive equipments.
3
The idea of hybrid APF has been proposed by several researchers [16]-[18].
In this scheme, a low cost passive high-pass filter (HPF) is used in addition to the
conventional APF. The harmonics filtering task is divided between the two filters.
The APF cancels the lower order harmonics, while the HPF filters the higher order
harmonics. The main objective of hybrid APF, therefore is to improve the filtering
performance of high-order harmonics while providing a cost-effective low order
harmonics mitigation.
Recently, there is an increasing concern about the environment. The need to
generate pollution-free energy has triggered considerable effort toward renewable
energy (RE). RE sources such as sunlight, wind, flowing water and biomass offer
the promise of clean and abundant energy [19]-[21]. They do not generate any
greenhouse gases and are inexhaustible [22]. Solar energy, in particular, is especially
attractive in a sunshine country like Malaysia. This energy is in DC form from
photovoltaic (PV) arrays. It is converted into a more convenient alternating current
(AC) power through an inverter system. Efforts have been made to combine the APF
with PV array [23]-[25]. However, it appears that no attempt has been made to
combine a hybrid APF with PV array.
1.2 Objective of Research
The objective of the research is two-fold: (1) to propose a new variation of
hybrid APF topology with PV application. (2) to propose a simple current reference
estimation method for the proposed topology.
To achieve the first objective, this research proposes a hybrid APF topology
for a single-phase system, connected to a DC source that represents the PV array.
The topology is unique because it effectively filters harmonic currents of low and
high frequencies to obtain sinusoidal source current. Furthermore, it simultaneously
supplies the power from the PV array to the load.
4
For the second objective, this research proposes the application of the
extension instantaneous reactive-power (p-q) theorem to estimate the compensation
current reference. Although the estimation of current reference based on extension
p-q theorem is not new [24]-[26], this approach has not yet being applied to a single-
phase hybrid APF system involving passive HPF, shunt APF and a PV array. Using
the extension p-q theorem, the resulting equations for the current reference is simpler
compared with the conventional p-q theorem presented in [27]. This will lead to
more efficient digital controller implementation using DSP.
1.3 Methodology of Research
In the elaboration of the research, a harmonic analysis of source current
distortion has been carried out. It has featured a nonlinear full-bridge diode rectifier
with DC smoothing capacitor and resistive load as a harmonic currents source. The
time domain simulation is performed using MATLAB/Simulink simulation package.
Afterwards, an extensive computer simulation involving the power circuit of the
shunt APF, passive HPF, a DC source that represents the PV array, current reference
estimation based on extension p-q theorem, phase-lock loop (PLL) circuit and fixed-
band hysteresis current controller is carried out.
Once satisfactory simulation results are obtained, the proposed topology is
tested in the laboratory with an experimental prototype. The prototype is designed to
compensate the distorted current produced by nonlinear load, as well as
simultaneously supplies the power from the PV array to the load. The proposed
algorithm and control system are implemented using a dSPACE DS1104 DSP
controller board.
Although the original work is intended to include the PV array, the
experimental set-up using PV array is not possible due to facility and time constraints.
However, the PV array can be adequately replaced with a DC source. This is
because the PV array is fundamentally a DC source that produces electricity in DC
form.
5
Finally, a harmonic analysis is carried out to validate the filtering
performance of the proposed hybrid APF in comparison to a basic shunt APF. The
experimental results are analyzed and compared with the results obtained from the
computer simulation.
1.4 Thesis Organisation
This thesis consists of this introductory chapter and six other chapters
arranged as follows:
Chapter 2 covers the literature review and a brief discussion of harmonic
distortion problems, conventional mitigation methods using passive filters and
improved mitigation methods using APF approaches. The efforts in combining the
PV array with the APF are discussed briefly. Different types of compensation
reference signal estimation techniques suitable for APF applications are reviewed. A
brief overview of the control strategies for APF is also provided in this chapter.
Chapter 3 presents the proposed hybrid APF topology. This chapter
elucidates the topology, operating principles and control of the proposed hybrid APF
and illustrates how this system can be used to supply the PV power to the load.
Emphasis is given to a discussion on the design consideration of the passive HPF.
Chapter 4 concerns the system level simulation using MATLAB/Simulink.
The computer simulation design is described in detail.
Chapter 5 describes the design and construction of the experimental
prototype to validate the proposed hybrid APF. Detailed description of each
hardware components is provided.
6
Chapter 6 provides the simulation and experimental results. Comparison
between the simulation and experimental results is discussed in detail. A harmonic
analysis is carried out to evaluate the filtering performance of the proposed hybrid
APF in comparison to a basic shunt APF.
Chapter 7 summarises the research undertaken and highlights the
contribution of this thesis. It offers recommendations for further research.
CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
This chapter reviews the development of active power filter (APF)
technologies. The discussion also includes a brief overview of harmonic distortion
problems and their impacts on electric power quality (PQ). The conventional
harmonic mitigation approaches using passive filters are presented first, followed by
the improved mitigation methods using APF techniques. The efforts in combining
the photovoltaic (PV) system with the APF are discussed briefly. In addition,
different types of reference signal estimation techniques are reviewed. Finally, an
overview on the APF control strategies is also provided.
2.2 Electric Power Quality
Power systems are designed to operate at frequencies of 50 or 60 Hz.
However, certain types of loads produce currents and voltages with frequencies that
are integer multiples of the 50 or 60 Hz fundamental frequency. These frequencies
components are a form of electrical pollution known as harmonic distortion.
Harmonic distortion has sparked research that has led to the present-day
understanding of PQ problems [2]-[4], [28]-[30]. In this section, the concept of
harmonic distortion is introduced and its impacts on electric PQ are discussed.
8
2.2.1 Fundamental of Harmonic Distortion
Due to the proliferation of nonlinear loads from power electronics converters,
one of the electric PQ issues that received much attention is the harmonic distortion.
These nonlinear loads control the flow of power by drawing currents only during
certain intervals of the 50/60 Hz period. Thus, the current drawn by the nonlinear
load is nonsinusoidal and appear chopped or flattened.
Figure 2.1 illustrates that any periodic, distorted waveform can be expressed
as a sum of pure sinusoids. The sum of sinusoids is referred to as a Fourier series,
named after the great mathematician who discovered the concept. The Fourier
analysis permits a periodic distorted waveform to be decomposed into an infinite
series containing DC component, fundamental component (50/60 Hz for power
systems) and its integer multiples called the harmonic components. The harmonic
number (h) usually specifies a harmonic component, which is the ratio of its
frequency to the fundamental frequency [4].
Figure 2.1 Fourier series representation of a distorted waveform
The total harmonic distortion (THD) is the most common measurement
indices of harmonic distortion [3], [4], [28], [31], [32]. THD applies to both current
and voltage and is defined as the root-mean-square (rms) value of harmonics divided
by the rms value of the fundamental, and then multiplied by 100% as shown in the
following equation:
50 Hz(h = 1)
150 Hz(h = 3)
+
+
+....
250 Hz(h = 5)
9
%1001
1
2max
×=∑>
M
MTHD
h
hh
, (2.1)
where hM is the rms value of harmonic component h of the quantity M .
THD of current varies from a few percent to more than 100%. THD of
voltage is usually less than 5%. Voltage THDs below 5% are widely considered to
be acceptable, while values above 10% are definitely unacceptable and will cause
problems for sensitive equipment and loads [4].
2.2.2 Harmonic Distortion Impacts on Electric Power Quality
For nearly all analyses, it is sufficient to treat nonlinear loads simply as
harmonic currents source [3], [4]. As Figure 2.2 shows, voltage distortion is the
result of distorted currents passing through the linear, series impedance of power
distribution system. Although the source bus is a pure sinusoid, there is a nonlinear
load that draws a distorted current. The harmonic currents passing through the
impedance of the system cause a voltage drop for each harmonic. This results in
harmonic voltages appearing at the PCC. The amount of voltage distortion depends
on the source impedance and the current.
Harmonics have a number of undesirable effects on electric PQ. These falls
into two basic categories: short-term and long-term. Short-term effects are usually
the most noticeable and are related to excessive voltage distortion. On the other hand,
long-term effects often go undetected and are usually related to increased resistive
losses or voltage stresses [28]. In addition, the harmonic currents produced by
nonlinear loads can interact adversely with a wide range of power system equipment,
most notably capacitors, transformers, and motors, causing additional losses,
overheating, and overloading. These harmonic currents can also cause interferences
with telecommunication lines and errors in metering devices [2]-[4], [30], [31].
10
Figure 2.2 Harmonic currents flowing through the system impedance result in
harmonic voltages at the PCC
Because of the adverse effects that harmonics have on electric PQ, certain
Standards have been developed to define a reasonable framework for harmonic
control [33]. The objective of such Standard is to propose steady-state harmonic
limits that are acceptable by both electric utilities and their customers.
2.3 Harmonic Mitigation Approaches
Harmonic distortion in power distribution systems can be suppressed through
three basic approaches [34] namely:
(1) Passive filter.
(2) Active power filter.
(3) Hybrid active power filter.
This section discusses general properties of various approaches for harmonic
distortion mitigation. The advantages, disadvantages, and limitations of these
approaches are also compiled in this section.
(Voltage Drop)+ _
PCC
Distorted Voltage
PureSinusoid Distorted Load
CurrentNonlinear
Load
11
2.3.1 Passive Filtering of Harmonic
Conventional solutions to the harmonic distortion problems have existed for a
long time. The passive filtering is the simplest conventional solution to mitigate the
harmonic distortion [4]-[8], [34]. Passive filters are inductance, capacitance, and
resistance elements configured and tuned to control harmonics. Figure 2.3 shows
common types of passive filters and their configurations.
Figure 2.3 Common types of passive filters and their configurations
The single-tuned “notch” filter is the most common and economical type of
passive filter [4], [5], [7]. The notch filter is connected in shunt with the power
distribution system and is series-tuned to present low impedance to a particular
harmonic current. Thus, harmonic currents are diverted from their normal flow path
through the filter.
Another popular type of passive filter is the high-pass filter (HPF) [4], [6]. A
HPF will allow a large percentage of all harmonics above its corner frequency to
pass through. HPF typically takes on one of the three forms, as shown in Figure 2.3.
The first-order, which is characterised by large power losses at fundamental
frequency, is rarely used. The second-order HPF is the simplest to apply while
providing good filtering action and reduced fundamental frequency losses [8]. The
filtering performance of the third-order HPF is superior to that of the second-order
HPF. However, it is found that the third-order HPF is not commonly used for low-
voltage or medium-voltage applications since the economic, complexity, and
reliability factors do not justify them [7].
Single-tuned 1st-orderHigh-pass
2nd-orderHigh-pass
3rd-orderHigh-pass
L
CR
CR L
C
R L
C
C
Load
Load
Load
Load
12
Although simple and least expensive, the passive filter inherits several
shortcomings. The filter components are very bulky because the harmonics that need
to be suppressed are usually of the low order [4], [8]. Furthermore the compensation
characteristics of these filters are influenced by the source impedance. As such, the
filter design is heavily dependent on the power system in which it is connected to [7].
The passive filter is also known to cause resonance, thus affecting the stability of the
power distribution systems [8], [9], [34].
Frequency variation of the power distribution system and tolerances in
components values affect the filtering characteristics. The size of the components
become impractical if the frequency variation is large [8], [9]. As the regulatory
requirements become more stringent, the passive filters might not be able to meet
future revisions of a particular Standard. This may required a retrofit of new filters.
2.3.2 Active Filtering of Harmonic
Remarkable progress in power electronics had spurred interest in APF for
harmonic distortion mitigation [1], [9], [10], [34], [35]. The basic principle of APF
is to utilise power electronics technologies to produce specific currents components
that cancel the harmonic currents components caused by the nonlinear load. Figure
2.4 shows the components of a typical APF system and their connections. The
information regarding the harmonic currents and other system variables are passed to
the compensation current/voltage reference signal estimator. The compensation
reference signal from the estimator drives the overall system controller. This in turn
provides the control for the gating signal generator. The output of the gating signal
generator controls the power circuit via a suitable interface. Finally, the power
circuit in the generalised block diagram can be connected in parallel, series or
parallel/series configurations depending on the interfacing inductor/transformer used.
13
Figure 2.4 Generalised block diagram for APF
APFs have a number of advantages over the passive filters. First of all, they
can suppress not only the supply current harmonics, but also the reactive currents.
Moreover, unlike passive filters, they do not cause harmful resonances with the
power distribution systems. Consequently, the APFs performances are independent
of the power distribution system properties [9], [34].
On the other hand, APFs have some drawbacks. Active filtering is a
relatively new technology, practically less than four decades old. There is still a
need for further research and development to make this technology well established.
An unfavourable but inseparable feature of APF is the necessity of fast switching of
high currents in the power circuit of the APF. This results in a high frequency noise
that may cause an electromagnetic interference (EMI) in the power distribution
systems [34].
APF can be connected in several power circuit configurations as illustrated in
the block diagram shown in Figure 2.5. In general, they are divided into three main
categories, namely shunt APF, series APF and hybrid APF.
supplyinterfacinginductor/
transformernonlinear Load
power circuit
interface
system variablesdetection
reference signalestimator
overall systemcontroller
gating signalsgenerator
switchingpattern
controleffort
referencesignal
compensatedvariables
14
Figure 2.5 Subdivision of APF according to power circuit configurations and
connections
2.3.2.1 Shunt Active Power Filter
This is most important configuration and widely used in active filtering
applications [1], [9]-[15], [35], [36]. A shunt APF consists of a controllable voltage
or current source. The voltage source inverter (VSI) based shunt APF is by far the
most common type used today, due to its well known topology and straight forward
installation procedure [11]-[15], [36].
Figure 2.6 shows the principle configuration of a VSI based shunt APF. It
consists of a DC-bus capacitor ( fC ), power electronic switches and an interfacing
inductors ( fL ). Shunt APF acts as a current source, compensating the harmonic
currents due to nonlinear loads. The operation of shunt APF is based on injection of
compensation current which is equivalent to the distorted current, thus eliminating
the original distorted current. This is achieved by “shaping” the compensation
current waveform ( fi ), using the VSI switches. The shape of compensation current
is obtained by measuring the load current ( Li ) and subtracting it from a sinusoidal
reference. The aim of shunt APF is to obtain a sinusoidal source current ( si ) using
the relationship: fLs iii −= .
Active Power Filter
series APF hybrid APFshunt APF
current-sourceinverter
voltage-sourceinverter
shunt APF+
series APF
series APF+
shunt PF
shunt APF+
shunt PF
APF in serieswith
shunt PF
Note:APF: Active power filter, PF: Passive filter
15
Figure 2.6 Principle configuration of a VSI based shunt APF
Suppose the nonlinear load current can be written as the sum of the
fundamental current component ( fLi , ) and the current harmonics ( hLi , ) according to
hLfLL iii ,, += (2.2)
then the injected compensation current by the shunt APF should be
hLf ii ,= (2.3)
the resulting source current is
fLfLs iiii ,=−= (2.4)
which only contains the fundamental component of the nonlinear load current and
thus free from harmonics. Figure 2.7 shows the ideal source current when the shunt
APF performs harmonic filtering of a diode rectifier. The injected shunt APF current
completely cancels the current harmonics from the nonlinear load, resulting in a
harmonic free source current.
From the nonlinear load current point of view, the shunt APF can be regarded
as a varying shunt impedance. The impedance is zero, or at least small, for the
harmonic frequencies and infinite in terms of the fundamental frequency. As a result,
reduction in the voltage distortion occurs because the harmonic currents flowing
+-
Cf
VSI
NonlinearLoad
Lf
is
if
AC Source iL
16
through the source impedance are reduced. Shunt APFs have the advantage of
carrying only the compensation current plus a small amount of active fundamental
current supplied to compensate for system losses [10], [35]. It can also contribute to
reactive power compensation. Moreover, it is also possible to connect several shunt
APFs in parallel to cater for higher currents, which makes this type of circuit suitable
for a wide range of power ratings [34].
Figure 2.7 Shunt APF harmonic filtering operation principle
2.3.2.2 Series Active Power Filter
The series APF is shown in Figure 2.8. It is connected in series with the
distribution line through a matching transformer [37]-[40]. VSI is used as the
controlled source, thus the principle configuration of series APF is similar to shunt
APF, except that the interfacing inductor of shunt APF is replaced with the
interfacing transformer.
The operation principle of series APF is based on isolation of the harmonics
in between the nonlinear load and the source. This is obtained by the injection of
harmonic voltages ( fv ) across the interfacing transformer. The injected harmonic
voltages are added/subtracted, to/from the source voltage to maintain a pure
sinusoidal voltage waveform across the nonlinear load. The series APF can be
thought of as a harmonic isolator as shown in Figure 2.9. It is controlled in such a
20 40 60 t [ms]
1
-1
0
1
-1
0
1
-1
0
i Li f
i s
17
way that it presents zero impedance for the fundamental component, but appears as a
resistor with high impedance for harmonic frequencies components. That is, no
current harmonics can flow from nonlinear load to source, and vice versa.
Figure 2.8 Principle configuration of a VSI based series APF
Figure 2.9 Operation principle of series APF: (a) single-phase equivalent of
series APF, (b) fundamental equivalent circuit, and (c) harmonic equivalent circuit
Series APFs are less common than their rival, i.e. the shunt APF [1], [10].
This is because they have to handle high load currents. The resulting high capacity
of load currents will increases their current rating considerably compared with shunt
APF, especially in the secondary side of the interfacing transformer. This will
increase the RI 2 losses [10]. However, the main advantage of series APFs over
shunt one is that they are ideal for voltage harmonics elimination [1]. It provides the
load with a pure sinusoidal waveform, which is important for voltage sensitive
devices (such as power system protection devices). With this feature, series APF is
suitable for improving the quality of the distribution source voltage.
(a) (b) (c)
Zs
vs
+
-
Zf
if
+-vf
is iL
Zs,f
vs,f
+
-
Zf
if,f
is,f iL,fZeq=0
Zs,h
vs,h
+
-
Zf
if,h
is,h iL,hZeq=∞
+-
Cf
VSI
NonlinearLoad
is vf
AC Source iL
18
2.3.2.3 Hybrid Active Power Filter
Previously, majority of the controllers developed for APF are based on
analogue circuits [9], [11], [12], [36]-[38]. As a result, the APF performance is
inherently subjected to signal drift [15]. Digital controllers using DSPs or
microcontrollers are preferable, primarily due to its flexibility and immunity to noise
[13]-[15], [39], [40]. However it is known that using digital methods, the high-order
harmonics are not filtered effectively. This is due to the hardware limitation of
sampling rate in real-time application [15]. Moreover, the utilisation of fast
switching transistors (i.e. IGBT) in APF application causes switching frequency
noise to appear in the compensated source current. This switching frequency noise
requires additional filtering to prevent interference with other sensitive equipment.
Technical limitations of conventional APFs mentioned above can be
overcome with hybrid APF configurations [16]-[18], [41]-[45]. They are typically
the combination of basic APFs and passive filters. Hybrid APFs, inheriting the
advantages of both passive filters and APFs, provide improved performance and
cost-effective solutions [42]. The idea behind this scheme is to simultaneously
reduce the switching noise and electromagnetic interference [34].
There are various hybrid APFs reported in literature [10], [41], [42], but the
two most prominent ones are shown in Figure 2.10. Figure 2.10 (a) is the system
configuration of the hybrid shunt APF. Both the shunt APF and passive filter are
connected in parallel with the nonlinear load [16]-[18]. The function of the hybrid
APF can thus divided into two parts: the low-order harmonics are cancelled by the
shunt APF, while the higher frequency harmonics are filtered by the passive HPF.
This topology lends itself to retrofit applications with the existing shunt APF.
Figure 2.10 (b) shows the system configuration of hybrid series APF, in
which the series APF is coupled to the distribution line by an interfacing transformer
[43]-[45]. The shunt passive filter consists of one or more single-tuned LC filters
and/or a HPF. The hybrid series APF is controlled to act as a harmonic isolator
between the source and nonlinear load by injection of a controlled harmonic voltage
source. It is controlled to offer zero impedance (short circuit) at the fundamental
19
frequency and high impedance (ideally open circuit) at all undesired harmonic
frequencies. This constrains all the nonlinear load current harmonics to flow into the
passive filter, decoupling the source and nonlinear load at all frequencies, except at
the fundamental.
Figure 2.10 Hybrid APFs: (a) combination of shunt APF and shunt passive filter
and (b) combination of series APF and shunt passive filter
2.4 Distribution Line Interactive Photovoltaic Systems
Recently, there is an increasing concern about the environment. The need to
generate pollution-free energy has triggered considerable effort toward renewable
energy (RE) system [19]-[22]. RE sources such as sunlight, wind, flowing water,
and biomass offer the promise of clean and abundant energy. Among the RE sources,
solar energy, is especially an attractive option in Malaysia, a country with abundant
supply of solar energy [22]. This useful energy is supplied in the form of DC power
from PV arrays bathed in sunlight and converted into more convenient AC power
through an inverter system [46].
Nonlinear LoadAC Source
Shunt PassiveFilterShunt APF
(a)
AC SourceNonlinear Load
Series APF Shunt PassiveFilter
(b)
20
Distribution line interactive PV inverters have been proposed [47]-[49]. They
merely provide real power from the PV array to the distribution line and fixed loads.
Efforts have been made to combine the shunt APF with PV system [23]-[25], [50],
[51]. The PV interactive shunt APF system can supply real power from the PV array
to loads, and support reactive and harmonic power simultaneously to utilise its
utmost installation capacity. This section reviews the distribution line interactive PV
inverter and the PV interactive shunt APF. A brief discussion on their operation
principles will be given.
2.4.1 Distribution Line Interactive Photovoltaic Inverter
PV technology was invented in the mid-20th century, using semiconductor
devices to convert sunlight into electric energy. This technology has many excellent
features: it causes little environmental burden, it is of a modular type technology that
can be easily expanded, and it is applicable almost everywhere [21], [22]. Figure
2.11 illustrates the operation principle of a PV cell. When the PV cell is exposed to
sunlight, electrical charges are generated and this can be conducted away by metal
contacts as DC electricity. Groups of PV cells are electrical configured into modules
and arrays, which can be used to power electrical loads. With the appropriate power
conversion equipment, PV systems can produce AC power compatible with any
conventional appliances, and interconnected to the distribution line.
Figure 2.11 Operation principle of a PV cell
Electrical Load
PhotovoltaicCell
Sun
(+)
(-)
DC CurrentFlow
21
Distribution line interactive PV systems are designed to operate in parallel
with the distribution line [47]-[49]. Figure 2.12 shows the configuration of a
distribution line interactive PV inverter system that comprises of a PV array, a DC-
bus capacitor, a smoothing inductor and an inverter. The primary component in
distribution line interactive PV systems is the inverter. The inverter converts the DC
power produced by the PV array into AC power consistent with the voltage of the
distribution system. A bi-directional interface is made between the PV system AC
output circuits and the distribution system, typically at the point of common coupling
(PCC). This allows the AC power produced by the PV system to supply the loads
and distribution line.
Figure 2.12 Configuration of a distribution line interactive PV inverter system
Generally, the distribution line interactive PV system extracts power from the
PV array, providing current to the distribution line. When the distribution power
sources need to provide the peak power to the load, the energy provided by PV array
can alleviate the burden of distribution power sources. At night and during no
sunlight periods, the power required by the loads is received from the distribution
line.
PCC
AC Source ElectricalLoad
+
-
Inverter
PV Array
22
2.4.2 Photovoltaic Interactive Shunt Active Power Filter
Distribution line interactive PV inverter discussed in previous sub-section
merely provides real power from the PV array to the distribution line and fixed loads.
However during no sunlight period, the operation of distribution line interactive PV
inverter is halted. Distinctly, its coefficient of utilisation is low. Recently,
researchers have spent efforts in developing PV interactive shunt APF systems [23]-
[25], [50], [51]. The PV interactive shunt APF can inject PV power into distribution
line. In addition, it can support reactive power compensation and filter harmonic
currents caused by nonlinear load.
Figure 2.13 illustrates the configuration of a PV interactive shunt APF system
which is similar to the standard distribution line interactive PV inverter system. This
scheme employs only one inverter to have the reactive power compensation,
harmonic currents mitigation, and real power supply functions.
Figure 2.13 Configuration of a PV interactive shunt APF system
In the day-time with intensive sunlight, the PV interactive shunt APF system
brings all its functions into operation. At night and during no sunlight periods, the
power required by the loads is received from the distribution system while the
inverter system only provides reactive power compensation and filter harmonic
PCC
AC Source
ElectricalLoad
+
-
Shunt APF
PV Array
NonlinearLoad
23
currents. Thus, the utilisation level of the PV interactive shunt APF system is higher
than the distribution line interactive PV inverter system.
Although the research in combining APF and PV array is not new, it appears
that no attempt has been made to combine a hybrid APF with PV array.
2.5 Reference Signal Estimation Techniques
As shown in Figure 2.4, the reference signal to be processed by the controller
is the key component that ensures the correct operation of APF. The reference signal
estimation is initiated through the detection of essential voltage/current signals to
gather accurate system variables information. The voltage variables to be sensed are
AC source voltage, DC-bus voltage of the APF, and voltage across interfacing
transformer. Typical current variables are load current, AC source current,
compensation current and DC-link current of the APF. Based on these system
variables feedbacks, reference signals estimation in terms of voltage/current levels
are estimated in frequency-domain or time-domain. Numerous publications, for
example [10], [35], [52]-[55] report on the theories related to detection and
measurement of the various system variables for reference signals estimation.
Figure 2.14 illustrates the considered reference signal estimation techniques.
These techniques cannot be considered to belong to the control loop since they
perform an independent task by providing the controller with the required reference
for further processing. This section presents the considered reference signal
estimation techniques, providing for each of them a short description of their basic
features.
24
Figure 2.14 Subdivision of reference signal estimation techniques
2.5.1 Frequency Domain Approaches
Reference signal estimation in frequency-domain is suitable for both single
and three phase systems. It is mainly derived from the principle of Fourier analysis
as follows.
2.5.1.1 Fourier Transform Techniques
In principle, Fourier Transform (either conventional or Fast Fourier
Transform (FFT)) is applied to the captured voltage/current signal. The harmonic
components of the captured voltage/current signal are first separated by eliminating
the fundamental component. Inverse Fourier Transform is then applied to estimate
the compensation reference signal in time domain [9], [10], [35], [52]-[55].
The main drawback of this technique is the accompanying time delay in
system variables sampling and computation of Fourier coefficients. This makes it
Reference SignalEstimation Techniques
FrequencyDomain
TimeDomain
Fourier Transform
p-q Theorem
Extension p-q Theorem
Synchronous-Detection Theorem
Synchronous-Reference-FrameTheorem
Sine-Multiplication Theorem
25
impractical for real-time application with dynamically varying loads. Therefore, this
technique is only suitable for slowly varying load conditions.
In order to make computation much faster, some modifications were
proposed and practiced in [56]. In this modified Fourier-series scheme, only the
fundamental component of current is calculated and this is used to separate the total
harmonic signal from the sampled load-current waveform.
2.5.2 Time Domain Approaches
Time-domain approaches are based on instantaneous estimation of reference
signal in the form of either voltage or current signal from distorted and harmonic-
polluted voltage and current signals. These approaches are applicable for both
single-phase and three-phase systems except for the synchronous-detection theorem
[59], [61] and synchronous-reference-frame theorem [13], [15], [17], [18], [40], [43],
[44], [50] which can only be adopted for three-phase systems.
2.5.2.1 Instantaneous Reactive-Power Theorem
The instantaneous reactive-power (p-q) theorem is proposed by Akagi et al.
[57]. This theorem is based on 0αβ transformation which transforms three-phase
voltages and currents into the 0αβ stationary reference frame [14], [45], [58]. From
this transformed quantities, the instantaneous active and reactive power of the
nonlinear load is calculated, which consists of a DC component and an AC
component. The AC component is extracted using HPF and taking inverse
transformation to obtain the compensation reference signals in terms of either
currents or voltages. This theorem is suitable only for a three-phase system and its
operation takes place under the assumption that the three-phase system voltage
26
waveforms are symmetrical and purely sinusoidal. If this technique is applied to
contaminated supplies, the resulting performance is proven to be poor [59].
In order to make the p-q theorem applicable for single-phase system, some
modifications in the original p-q theorem were proposed and implemented by
Dobrucky et al. [27]. The basics of extension p-q theorem for a single-phase system
are as follows:
Assume that the source voltage ( sv ) and load current ( Li ) of a single-phase system
are defined as
)sin(2)( tVtv ss ω= (2.5)
)sin(2)( θ+ω= tIti LL (2.6)
After complementing by fictitious imaginary phase (shifted by 90˚), the
complemented source voltage ( 'sv ) and load current ( '
Li ) are defined as
)90sin(2)(' o−ω= tVtv ss (2.7)
)90sin(2)(' o−θ+ω= tIti LL (2.8)
the αβ orthogonal co-ordinate system is obtained, whereby
)(tvv s=α and )(' tvv s=β (2.9)
)(tii L=α and )(' tii L=β (2.10)
Thus, the instantaneous active power of the load can be derived as
ppivivp ~+=⋅+⋅= ββαα (2.11)
27
The instantaneous reactive power of the load can be derived as
qqivivq ~+=⋅−⋅= αββα (2.12)
From the obtained instantaneous active and reactive power, the AC
components ( p~ and q~ ) are extracted using a HPF. The extracted AC components
are then used for compensation reference signal estimation.
2.5.2.2 Extension Instantaneous Reactive-Power Theorem
The conventional p-q theorem is revised and extended by Komatsu and
Kawabata [26] to make it applicable for three-phase unsymmetrical and distorted
voltage system. It differs from the conventional p-q theorem presented in [57]. In
extension p-q theorem, the source voltages are shifted by 90° for instantaneous
reactive power calculation [24]. Instead of the AC components in conventional p-q
theorem, the DC components are extracted using low-pass filters (LPFs) and taking
inverse transformation to obtain the compensation reference signals in terms of either
currents or voltages. The main advantage of this technique is that it is simpler to find
three-phase instantaneous reactive power than the conventional p-q theorem [26].
This technique is also suitable for single-phase APF systems [25], [60]. In
order to illustrate the difference between the extension p-q theorem with its former,
the basics of extension p-q theorem for single-phase system are presented in this sub-
section. Assume that the source voltage ( sv ) and load current ( Li ) of a single-phase
system are defined in equation (2.5) and (2.6) respectively.
The instantaneous active power of the load can be derived as
pptitvp Ls~)()( +=⋅= (2.13)
28
The instantaneous reactive power of the load can be derived as
qqtitvq Ls~)()(' +=⋅= (2.14)
where )(' tvs denotes the source voltage shifted by o90 .
The DC components ( qp and ) are extracted from the derived instantaneous
active and reactive power using LPFs. The extracted DC components are then used
for compensation reference signal estimation. It is clearly seen that the resulting
equations for the instantaneous active and reactive power of the load based on
extension p-q theorem are simpler compared with the p-q theorem [27] presented in
sub-section 2.5.2.1.
In this particular work, the extension p-q theorem is adopted for
compensation current reference estimation. Although the current reference
estimation based on the extension p-q theorem is not new [25], [60], this approach
has not yet been applied to a single-phase hybrid APF system involving passive HPF,
shunt APF and PV array.
2.5.2.3 Synchronous-Detection Theorem
Synchronous-detection theorem [59], [61] is very similar to p-q theorem. This
technique is suitable only for three-phase system and its operation relies on the fact
that the three-phase currents are balanced. It is based on the idea that the APF forces
the source current to be sinusoidal and in phase with the source voltage despite the
load variations. The average power is calculated and divided equally between the
three-phases. The reference signal is then synchronised relative to the source voltage
for each phase. Although this technique is easy to implement, it suffers from the fact
that it depends to a great extent on the harmonics in the source voltage [10].
29
2.5.2.4 Synchronous-Reference-Frame Theorem
This theorem relies on the Park’s Transformations to transform the three
phase system voltage and current variables into a synchronous rotating frame [13],
[15], [17], [18], [40], [43], [44], [50]. The active and reactive components of the
three-phase system are represented by the direct and quadrature components
respectively. In this theorem, the fundamental components are transformed into DC
quantities which can be separated easily through filtering.
This theorem is applicable only to three-phase system. The system is very
stable since the controller deals mainly with DC quantities. The computation is
instantaneous but incurs time delays in filtering the DC quantities [54].
2.5.2.5 Sine-Multiplication Theorem
This theorem is based on the process of multiplying the nonlinear load
current signal by a sine wave of fundamental frequency and integrating the result to
calculate the real fundamental component of the nonlinear load current [11], [12],
[36]. It is applicable for both single and three phase systems. The difference
between the instantaneous nonlinear load current and this fundamental component is
the command current for the APF. Although this technique eliminates the time delay
due to low/high-pass filtering, its performance is still slow (for more than one
complete mains cycle), due to integration and sampling [54]. This technique is
similar to the Fourier Technique. It is, however, differently implemented.
30
2.6 Control Techniques for Active Power Filter
The aim of APF control is to generate appropriate gating signals for the
switching transistors based on the estimated compensation reference signals. The
performance of an APF is affected significantly by the selection of control
techniques [62]. Therefore, the choice and implementation of the control technique
is very important for the achievement of a satisfactory APF performance.
A variety of control techniques, such as linear control [9], [11]-[13], [18],
[23]-[25], [36], [37], [40], digital deadbeat control [14], [15], [63]-[65], hysteresis
control [17], [26], [27], [57], [58], [60], etc., have been implemented for the APF
applications. Several publications [10], [52], [54], [55], [62] comprehensively report
the theories related to APF control techniques. This section briefly describes the
considered control techniques and their basic features.
2.6.1 Linear Control Technique
Linear control of an APF is accomplished by using a negative-feedback
system as shown in Figure 2.15. In this control scheme, the compensation current
( fi ) or voltage ( fv ) signal is compared with its estimated reference signal ( reffi , or
reffv , ) through the compensated error amplifier to produce the control signal. The
resulting control signal is then compared with a sawtooth signal through a pulse
width modulation (PWM) controller to generate the appropriate gating signals for the
switching transistors [9], [11]-[13], [18], [23]-[25], [36], [37], [40]. The frequency
of the repetitive sawtooth signal establishes the switching frequency. This frequency
is kept constant in linear control technique. As shown in Figure 2.16, the gating
signal is set high when the control signal has a higher numerical value than the
sawtooth signal and via versa.
31
Figure 2.15 Block diagram of linear control technique
Figure 2.16 Gating signal generation by linear controller
Generally, the Nyquist stability criterion and the Bode plots are used to
determine the appropriate compensation in the feedback loop for the desired steady-
state and transient responses. With analogue PWM circuit, the response is fast and
its implementation is simple [54]. Nevertheless, due to inherent problem of analogue
circuitry, the linear control technique has an unsatisfactory harmonic compensation
performance. This is mainly due to the limitation of the achievable bandwidth of the
compensated error amplifier [55], [62].
controlsignal
PWMcontroller
Active PowerFilter
gatingsignal
if,ref or vf,ref
+_
Compensatederror amplifier
if or vf
sawtoothsignal
sawtooth signalcontrol signal
0 t
gating signal
Ts( switching frequency fs =
1Ts
)
sawtoothsignal
controlsignal<
sawtoothsignal
controlsignal>
32
2.6.2 Hysteresis Control Technique
The control of APF can also be realised by the hysteresis control technique
[17], [26], [27], [57], [58], [60]. It imposes a bang-bang type instantaneous control
that forces the APF compensation current ( fi ) or voltage ( fv ) signal to follow its
estimated reference signal ( reffi , or reffv , ) within a certain tolerance band. This
control scheme is shown in a block diagram form in Figure 2.17. In this control
scheme, a signal deviation ( H ) is designed and imposed on reffi , or reffv , to form
the upper and lower limits of a hysteresis band. The fi or fv is then measured and
compared with reffi , or reffv , ; the resulting error is subjected to a hysteresis
controller to determine the gating signals when exceeds the upper or lower limits set
by (estimated reference signal + 2H ) or (estimated reference signal - 2
H ). As long
as the error is within the hysteresis band, no switching action is taken. Switching
occurs whenever the error hits the hysteresis band. The APF is therefore switched in
such a way that the peak-to-peak compensation current/voltage signal is limited to a
specified band determined by H as illustrated by Figure 2.18.
Figure 2.17 Block diagram of hysteresis control technique
In this particular work, a hysteresis current controller with a fixed H is
implemented. To obtain a compensation current ( fi ) with switching ripples as small
as possible, the value of H can be reduced. However, doing so results in higher
switching frequency. Thus, increases losses on the switching transistors.
error
Hysteresis bandcomparator
Active PowerFilter
gatingsignal
if,ref or vf,ref + _
if or vf
∑ error2
H+
2H−
33
The advantages of using the hysteresis current controller are its excellent
dynamic performance and controllability of the peak-to-peak current ripple within a
specified hysteresis band [54], [55], [62]. Furthermore, the implementation of this
control scheme is simple; this is evident from the controller structure shown in
Figure 2.17. However, this control scheme exhibits several unsatisfactory features.
The main drawback is that it produces uneven switching frequency. Consequently,
difficulties arise in designing the passive HPF. Furthermore, there is possibly
generation of unwanted resonances on the power distribution system [54], [62].
Besides, the irregular switching also affects the APF efficiency and reliability [55].
Figure 2.18 Gating signal generation by hysteresis controller
2.7 Summary
This chapter covers the development of APF technologies. A brief discussion
on the harmonic distortion problems and their impacts on electric PQ are given. The
conventional mitigation methods using passive filters are presented first, followed by
the improved mitigation methods using APFs. The efforts in combining the PV
system with the shunt APF are discussed briefly. This chapter also reviews different
types of reference signal estimation techniques which is an integral part of the APF.
Finally, an overview of the control strategies for APF is presented.
t
reference signal
actual signal
gating signal
( uneven frequency fs )
H
if or vfif or vf
if,ref or vf,ref
34
This review reveals that there is a significant interest in hybrid APF for PQ
improvement and RE source for electric power generation. This could be attributed
to the availability of suitable power-switching devices, high performance PV array
and fast computing devices (microcontroller and DSP) at affordable prices. It is
obvious that more work still needs to be done in integrating the hybrid APF with PV
array to achieve a multifunctional active filtering system.
CHAPTER 3
A SINGLE-PHASE HYBRID ACTIVE POWER FILTER
3.1 Introduction
It has been shown that one of the electric power quality (PQ) issues that
receive much attention is the harmonic distortion of the source current. The hybrid
APF has been demonstrated to be an effective solution for harmonic mitigation. On
the other hand, renewable energy (RE) sources, in particular solar energy has become
feasible due to enormous research and development work being conducted over the
years.
Considering these facts, a new variation of a single-phase hybrid APF
topology, connected to a PV array is proposed. This topology is unique because it
effectively filters harmonic currents less than 1 kHz and of higher frequencies.
Furthermore, it simultaneously supplies the power from the PV array to the load.
This work also proposes the application of the extension p-q theorem to estimate the
compensation current reference for this topology. The extension p-q theorem
simplifies the equations for the current reference. This will lead to a more efficient
implementation using DSP digital controller.
The proposed topology is presented in the following sections. It will
primarily focus on the operation principle, system configuration, overall control
system and passive HPF design.
36
3.2 Operation Principle of the Proposed Hybrid APF
The operation principle of the proposed hybrid APF is illustrated in Figure
3.1. It generates compensation current ( fi ) equal to the reactive load current ( qLi , ),
harmonic load current ( hLi , ) and reactive HPF current ( qhpi , ). This compensation
current is injected into the point of common coupling (PCC) through an interfacing
inductor. The compensated source current ( si ) is desired to be sinusoidal and in
phase with the source voltage ( sv ) to yield a maximum power factor.
Figure 3.1 Operation principle of the proposed hybrid APF without PV power
In the proposed scheme, the low-order harmonics are compensated using the
shunt APF, while the high-order harmonics are filtered by a passive high-pass filter
(HPF). Since the aim in using the HPF is to improve the filtering performance of
high-order harmonics, the HPF’s resonant frequency can be tuned to frequency
where the filtering performance of the shunt APF is impaired, i.e. over 1 kHz. In this
way, the size of the HPF can be kept small. It is envisaged that this configuration is
effective to improve the filtering performance of high-order harmonics.
Shunt APF
Nonlinear load
is
if
240 Vrms50Hz
vu 2:1iL
DC source
ihpPassiveHPF
vs PCC
iL = iL,p + iL,q + iL,his = iL,p
if = iL,q + iL,h + ihp,qihp = ihp,q
37
The size of interfacing inductor is a compromise between current control
dynamic response and switching ripple. The current control dynamic response can
be improved by using a small interfacing inductor. However, this would raise the
switching ripple in the basic shunt APF. In the proposed hybrid APF, the resulting
switching ripple is filtered by the HPF.
In day-time where intensive sunlight is available, the proposed hybrid APF
extracts power from the DC source that represents the PV array, providing additional
PV current ( PVi ) to the load. When the distribution source need to provide the peak
power to the load, the energy provided by the PV array can alleviate the burden of
distribution source as illustrated by Figure 3.2. At night and during no sunlight
periods, the power required by the load is delivered by the distribution source.
Figure 3.2 Operation principle of the proposed hybrid APF with PV power
Shunt APF
Nonlinear load
is
if
240 Vrms50Hz
vu 2:1iL
DC source
ihpPassiveHPF
vs PCC
iL = iL,p + iL,q + iL,his = iL,p - iPV
if = iL,q + iL,h + ihp,q + iPVihp = ihp,q
+
38
3.3 The Proposed System Configuration
In this section, the system configuration of the proposed single-phase hybrid
APF topology is presented. The power circuit, interfacing inductor, and DC-bus
capacitor are discussed in detail.
3.3.1 Proposed Overall System
Figure 3.3 shows the system configuration of the proposed single-phase
hybrid APF topology, connected in parallel with the nonlinear load. It consists of a
passive HPF, a single-phase shunt APF constructed using a full-bridge voltage
source inverter (VSI) and a DC source that represents PV array. Subscript s, L, f, and
hp refer to source, load, shunt APF and passive HPF. The shunt APF and the DC
source are connected back-to-back with a DC-bus capacitor ( fC ). The VSI used in
this topology is operated in current controlled mode (CCM) to make the
compensation current ( fi ) control possible. This VSI uses DC-bus capacitor as the
supply and switches at high-frequency to generate a compensation current that
follows the estimated current reference. Thus, the voltage across the DC-bus
capacitor ( CfV ) must kept to a value that is higher than the amplitude of the source
voltage ( sV⋅> 2 ).
The proposed hybrid APF is connected with the distribution line at the PCC
through an interfacing inductor ( fL ). This interfacing inductor provides isolation
from the distribution line. A large interfacing inductor is preferable because it results
in small switching ripple. However, the large interfacing inductor limits the dynamic
response of the compensation current. Therefore, there is a compromise involved in
sizing the interfacing inductor.
39
Figure 3.3 System configuration of the proposed hybrid APF
A second-order series resonant filter is selected as the passive HPF in the
proposed hybrid APF topology. It consists of a capacitor ( hpC ), an inductor ( hpL )
and an inductor bypass resistor ( hpR ). It acts like a sink for high frequency harmonic
components. The harmonic filtering function of the proposed hybrid APF can thus
divided into two parts: the low-order harmonics are cancelled by the shunt APF,
while the higher frequencies harmonics are filtered by the HPF.
The power distribution system of interest is 240 Vrms, 50 Hz sinusoidal AC
voltage. An isolation transformer with turn ratio of 2:1 is used to scale down the
distribution voltage ( uv ). The leakage inductor of the isolation transformer is
considered as the source inductor ( sL ). A full-bridge diode rectifier with DC
smoothing capacitor ( dC ), resistive load ( LR ) and AC smoothing inductor ( smoothL )
is selected as the nonlinear load. This type of load can be found in most power
electronics applications, i.e. switch-mode power supply, uninterruptible power
supply (UPS), AC motor drive and DC servo drive. It is used to convert the input
+
_
Cf
Shunt APF
Nonlinear load
Lf
is
if
Distributionvoltage
240 Vrms50Hz
vuvs
Sourcevoltage
2:1Ls
iL
Lsmooth
Cd RL
PV array
DC source
VCf
ihp
Passive HPF
PCC
S3
S4
S1
S2
Rhp
Lhp
Chp
40
AC to DC in an uncontrolled manner. It is well known that this nonlinear load draws
highly distorted current from the distribution source, thus a major source of harmonic
distortion [4].
3.3.2 Power Circuit
The power circuit used in the proposed hybrid APF is a full-bridge VSI as
shown in Figure 3.4. The VSI consists of four transistors, each connected to an anti-
parallel diode. The transistors are the insulated gate bipolar transistors (IGBTs).
They are selected due to their superior performance characteristics, i.e. low forward
voltage drop, fast switching times and high power handling capability.
Figure 3.4 Power circuit of the proposed hybrid APF
Gate drivers are needed to convert the gating signals to gate voltage that is
suitable to the IGBTs. The logic inverters ensure that each IGBTs on the same leg
complements each other. However, the finite switching times imply that during
current commutation, the IGBTs in one leg (S1 & S2 or S3 & S4) may conduct at the
switching instants. This will cause short circuit problem of the DC-bus capacitor
( fC ). Additional control logic in the gate drivers is needed to ensure the complete
turn on and turn off processes of the IGBTs in one bridge leg. This is referred to as
the blanking time, since both IGBTs have temporarily logic low gating signals.
+
_
VCf
S3
S4
S1
S2
Driver
Driver
Gating signal
Driver
Driver
Gating signal
Cf
41
3.3.3 Interfacing Inductor
The desired compensation current waveform is obtained by controlling the
switching of the IGBTs in the VSI. The switching ripple ( swi ) of the compensation
current is determined by the available driving voltage across the interfacing inductor,
the size of the interfacing inductor and switching frequency. In the proposed scheme,
the driving voltage is the DC-bus voltage ( CfV ). As shown in Figure 3.5, the bipolar
DC-bus voltage across the interfacing inductor determines the peak-to-peak
switching ripple ( ppswI −∆ , ).
Figure 3.5 Switching ripple of the compensation current
From Figure 3.5, the minimum interfacing inductor ( min,fL ) can be calculated
based on [66] as
max,,min, )(2 swppsw
Cff fI
VL
⋅∆⋅=
−
(3.1)
where max,swf maximum frequency of switching ripple and ppswI −∆ , is the peak-to-
peak switching ripple of compensation current. The detailed derivation of (3.1) is
presented in Appendix A.
swf
Cfppsw fL
VI
2, =∆ −
CfV
CfV−
swi
0 t
swsw f
T 1=
Driving voltage Switching ripple
42
3.3.4 DC-Bus Capacitor
The DC-bus capacitor ( fC ) is used as a temporally energy storage element in
the proposed hybrid APF as shown in Figure 3.3. During steady state condition, the
reactive and harmonic load currents will charge and discharge the DC-bus capacitor
during the source voltage period. The total reactive and harmonic load currents to be
compensated is the principle factor that causes the DC-bus capacitor voltage
fluctuation. To get a good compensation performance, serious voltage fluctuations
must be avoided. This can be achieved by proper sizing of the DC-bus capacitor.
The size determination of the DC-bus capacitor is based on the energy-
balance principle presented in [12]. Using this concept, the following equations can
be derived:
2221)()(
21 2
,2 TIVVVC LsrefCfCff ⋅∆⋅⋅=−∆ (3.2)
where CfV∆ is the maximum or minimum DC-bus voltage, refCfV , is the DC-bus
voltage reference, sV is the rms value of the source voltage, LI∆ is the peak rms
value of the reactive and harmonic load currents and T is the period of source
voltage. The size of DC-bus capacitor is determined by
2,
2 )()(22
refCfCf
Lsf VV
TIVC
−∆
⋅∆⋅≥ (3.3)
43
3.4 The Control System
The overall control system of the proposed single-phase hybrid APF is
described in this section. The compensation current reference estimation, DC-bus
voltage control, digital based phase-lock loop (PLL), and digital low-pass filter (LPF)
are discussed in detail.
3.4.1 Overall Control System
Figure 3.6 shows the overall control system for the proposed hybrid APF.
Subscript s, L, f, and hp refer to source, load, shunt APF and passive HPF. The task
of the control system is to produce appropriate gating signals for the switching
transistors (IGBTs). The control system consists of an instantaneous active/reactive
power calculator, three LPFs, a compensation current estimator, a proportional-
integral (PI) controller, a PLL and a hysteresis current controller.
Three current sensors and two voltage sensors are required for system
variables detection. The load current ( Li ), HPF current ( hpi ) and compensation
current ( fi ) are detected using Hall-Effect current sensors, while the source voltage
( sv ) and DC-bus voltage ( CfV ) are detected using Hall-Effect voltage sensors. The
digital based PLL is responsible to generate the reference sinewave ( )sin( tω and
)90sin( o−ωt ) with unity amplitude and synchronous with the source voltage.
The instantaneous active/reactive power calculator receives the load current,
source voltage and passive HPF current signals in real time. The instantaneous
active load power ( Lp ), instantaneous reactive load power ( Lq ) and the
instantaneous reactive HPF power ( hpq ) are calculated based on the extension p-q
theorem. Their DC components are filtered with three digital second-order
Butterworth LPFs. These DC components are then fed to the compensation current
reference estimator to obtain the reactive load current ( qLi , ), harmonic load current
44
( hLi , ) and reactive HPF current ( qhpi , ). The summation of these three current signals
will form the first component of the current reference signal ( 1,reffi ).
Figure 3.6 Overall control system of the proposed hybrid APF
The DC-bus voltage controller maintains the average voltage across the DC-
bus capacitor ( CfV ) constant against variations in distribution source. Under a loss
free situation, the hybrid APF does not need to draw any active power from the
distribution source. However, there will be losses in the resistance of interfacing
inductor, switches, etc., when the hybrid APF is generating the compensation current.
Unless these losses are regulated, the DC-bus voltage will drop steadily. Hence the
control of DC-bus voltage involves drawing an in phase sinusoidal charging current
( CfI ) from the distribution source.
The DC voltage across the DC-bus capacitor is detected and compared with
its reference voltage ( refCfV , ). The compared result is processed by a PI controller to
obtain the desired amplitude of the DC-bus capacitor charging current ( CfI ). This
charging current is then subtracted from the PV current ( PVI ). The resulting current
Hysteresiscurrent
controllerGatingsignals
pL, qL & qhpcalculator
iL
ihp
vs
-90o
PLL
LPFCompensationcurrent
estimator
if
VCf
VCf,ref
PIcontroller
ICf
PPVVCf,ref
DC-bus Voltage Controller
+
_
_
+
DSP Based Implementation
IPV
if,refiL,qiL,h
ihp,q
qhp
qL
_pL_
_ qhp
qL
pL
_
_
_ qhp
qL
pL+
+
+
~
~
~
switch
LPF
LPF
∑ ∑
+++
+
+
if,ref 2
if,ref 1
S1S2S3S4
sin( t-90o)ω
sin( t)ω
45
is then multiplied with the reference sinewave ( )sin( tω ) to form the second
component of current reference signal ( 2,reffi ). However, when a PV array is
connected to the DC-bus capacitor, the DC-bus voltage controller can be removed.
In order to generate the compensation current that follows the current
reference signal, the fixed-band hysteresis current control method is adopted. The
estimated compensation current reference signal ( reffi , ) and the actual compensation
current signal ( fi ) are fed to a fixed-band hysteresis current controller to generate
appropriate gating signals for the switching transistors.
3.4.2 Compensation Current Reference Estimation
Compensation current reference estimation for single-phase shunt APF based
on extension p-q theorem has been presented in [25]. In this work, the application of
the theorem is further extended to a single-phase hybrid APF connected to a PV
array. In the proposed topology, the extension p-q theorem is adopted for the
estimation of active, reactive and harmonic components of load current, and the
reactive component of HPF current.
For a single-phase distribution power system with nonlinear load, the load
current can be represented as,
∑∞
=
θ+ω=1
, )sin(2)(n
nnLL tnIti (3.4)
where nθ is the phase angle of the n-th load current component. Under normal
circumstances, the source voltage can be assumed to be a sinusoidal, i.e.,
)sin(2)( φ+ω= tVtv ss (3.5)
where φ is the phase angle of the source voltage.
46
The HPF current is assumed to contain only the reactive component as
)90sin(2)( o+ω= tIti hphp (3.6)
Therefore, the instantaneous active load power can be derived as
)()()( titvtp LsL ⋅=
LL pp ~+= (3.7)
The instantaneous reactive load power can be derived as follows
)()()( ' titvtq LsL ⋅=
LL qq ~+= (3.8)
The instantaneous reactive HPF power can thus be derived as
)()()( ' titvtq hpshp ⋅=
hphp qq ~+= (3.9)
where Lp , Lq and hpq represent the DC components; Lp~ , Lq~ and hpq~ denote the
AC components, and )(' tvs denotes the source voltage delayed by o90 . The detailed
derivation of )(tpL , )(tqL and )(tqhp based on extension p-q theorem is presented in
Appendix B.
By obtaining the DC components in (3.7), (3.8), and (3.9), the active load
current ( pLi , ), reactive load current ( qLi , ), harmonic load current ( hLi , ) and reactive
HPF current ( qhpi , ) can be readily estimated as follows:
47
)sin(2)(, tVpti
s
LpL ω⋅= (3.10)
)90sin(2)(,o−ω⋅= t
Vqti
s
LqL (3.11)
)()()()( ,,, titititi qLpLLhL −−= (3.12)
and
)90sin(2)(,o−ω⋅= t
Vq
tis
hpqhp (3.13)
Finally, the compensation current reference can be estimated as
)sin()sin(,
,,,, tV
PtIiiii
refCf
PVCfqhphLqLreff ω⋅+ω⋅−++= (3.14)
where PVP is the active power of PV array, CfI is the amplitude value of DC-bus
capacitor charging current and refCfV , is the DC-bus voltage reference.
3.4.3 DC-Bus Voltage Control
Under a loss free situation, the hybrid APF need not provide any active power
to cancel the reactive and harmonic currents from the load, and the reactive current
from the HPF. These currents show up as reactive power. Thus, it is indeed possible
to make the DC-bus capacitor delivers the reactive power demanded by the proposed
hybrid APF. As the reactive power comes from the DC-bus capacitor and this
reactive energy transfers between the load and the DC-bus capacitor (charging and
discharging of the DC-bus capacitor), the average DC-bus voltage can be maintained
at a prescribed value.
48
However, due to switching loss, capacitor leakage current, etc., the
distribution source must provide not only the active power required by the load but
also the additional power required by the VSI to maintain the DC-bus voltage
constant. Unless these losses are regulated, the DC-bus voltage will drop steadily.
A PI controller used to control the DC-bus voltage is shown in Figure 3.7. Its
transfer function can be represented as
sKKsH I
p +=)( (3.15)
where pK is the proportional constant that determines the dynamic response of the
DC-bus voltage control, and IK is the integration constant that determines its
settling time.
Figure 3.7 PI controller for DC-bus voltage control
It can be noted that if pK and IK are large, the DC-bus voltage regulation is
dominant, and the steady-state DC-bus voltage error is low. On the hand, if pK and
IK are small, the real power unbalance give little effect to the transient performance.
Therefore, the proper selection of pK and IK is essentially important to satisfy
above mentioned two control performances [23].
VCf
VCf,ref
voltagetransducer Kp + KI / s ICf
+
_ ∑
DC-bus actualvoltage
DC-bus voltagereference
capacitorcharging current
PI controller
49
As described in [12], the pK can be calculated using the energy-balance
principle. After pK is calculated, the IK can be determined empirically. Appendix
C presents the pK calculation using the energy-balance principle for the proposed
hybrid APF.
3.4.4 Digital Phase-Lock Loop
In order to generate the reference sinewave ( )sin( tω and )90sin( o−ωt ) with
unity amplitude and synchronised with the source voltage ( sv ), a digital PLL [67] is
realised. Figure 3.8 show a functional block diagram of a typical digital PLL model
in discrete time domain (z-domain). From this diagram, the digital PLL can be easily
recognised as a feedback control system. This system consists of a phase detector, a
loop filter and a digitally-controlled oscillator (DCO).
Figure 3.8 A digital phase-lock loop model in z-domain
The phase detector detects the phase difference between the input signal
( )(zinθ ) and the feedback signal ( )(zfdθ ). The compared result is sent to a loop
filter. Typically, the loop filter is a low-pass type. The output of loop filter is feed to
a DCO to generate the )(zfdθ . In order to generate )sin( tω with unity amplitude,
the )(zfdθ can be divided with the amplitude of the )(zinθ using a divider as
+
_ ∑input phase
signal
)(zinθ
phasedetector
Loop FilterH1(z)
1−z DCOH2(z)
)(zfdθfeedback phase signal
Divider
-90o
Digital PLL
sin( t-90o)ω
sin( t)ω
50
illustrated by Figure 3.8. On the other hand, the )90sin( o−ωt can be obtained by
delaying )sin( tω by 90°.
Since the system is described in discrete time-domain, the transfer functions
of each component are written in z-transform format as the following. Transfer
function of the loop filter is,
11)(1
−−
=z
azzH (3.16)
while the transfer function of a digitally-controlled oscillator (DCO) is given by
1)(2
−=
zczzH (3.17)
where a and c are constants of )(1 zH and )(2 zH respectively. The 1−z is a delay
unit. Usually it is a register or register array.
With the block diagram and the transfer functions of components in it, a
linear time invariant (LTI) model can be developed to represent the digital PLL with
a closed-loop transfer function derived as,
)1()2()( 2 czacz
caczzH−+−+
−= (3.18)
Based on the closed-loop transfer function in (3.18), one can easily recognise
that it is a second-order system. In control system theory, the transfer function of the
second-order system can be written in a general format as,
))(()()(
01 zzzzzNzH−−
= (3.19)
where 0z and 1z are two poles of the system in z-domain.
51
Based on the transfer function in (3.19), a characteristic equation of a discrete
time system is defined as,
01012
01 )())(()( zzzzzzzzzzz ++−=−−=∆ (3.20)
Defining 1C and 0C to be coefficients of the characteristics equation in (3.20),
)( 011 zzC +−=
010 zzC = (3.21)
Then, the characteristic equation can be re-written in a simplified format as,
012)( CzCzz ++=∆ (3.22)
As soon as 1C and 0C of the system are given, the poles of a second-order system
can be determined. Those two parameters are usually used to specify performance
requirements of a system. A detailed derivation of 1C and 0C is presented in
Appendix D.
3.4.5 Digital Low-Pass Filter
The compensation current estimation involves the use of DC components of
the calculated instantaneous active and reactive power as illustrated by (3.10), (3.11)
and (3.13). Consequently, LPFs are sufficient to extract the corresponding DC
components as shown in Figure 3.9. Each LPF consists of a second-order
Butterworth filter, with cut-off frequency ( LPFf ) equals to 5 Hz.
52
Figure 3.9 Block diagram of the digital low-pass filter for DC components
extraction
The transfer function of the second-order Butterworth LPF in s-domain is given by
22 21)(
LPFLPFLPF ss
sGω+ζω+
= (3.23)
where LPFLPF fπ=ω 2 is defined as natural undamped frequency and ζ is defined as
the damping ratio. Note that the second-order Butterworth LPF is characterised by
ζ =0.707 [69].
Under the bilinear transformation [68], the analogue LPF in (3.23) can be
transformed into digital LPF as follows:
1
1
11
22 21)(
−
−
+
−=
ω+ζω+=
zzsLPFLPF
LPF sszG 2
21
1
21
1)1(
−−
−
+++
=zaza
zG
LPFLPF
LPF (3.24)
where the filter coefficients LPFG , 1LPFa and 2LPFa are easily found to be:
2
2
21 LPFLPF
LPFLPFG
ω+ζω+ω
=
2
2
1 21)1(2
LPFLPF
LPFLPFa
ω+ζω+−ω
=
2
2
2 2121
LPFLPF
LPFLPFLPFa
ω+ζω+ω+ζω−
= (3.25)
LPF
qhp
qL
_pL_
_ qhp
qL
pL
_
_
_ qhp
qL
pL+
+
+
~
~
~LPF
LPF
53
Note that the LPFω in (3.25) is differed from the LPFω in (3.23) due to the fact of
digital implementation consideration [68]. The LPFω in (3.25) is given by
⎟⎟⎠
⎞⎜⎜⎝
⎛ π=ω
s
LPFLPF f
ftan (3.26)
where sf is the sampling frequency of the digital LPF. Therefore, the digital
second-order Butterworth LPF design is accomplished by the determination of sf
and LPFf .
3.5 Passive High-Pass Filter Design
The second-order damped series resonant type HPF topology is employed in
the proposed hybrid APF as shown in Figure 3.3. It consists of a capacitor ( hpC ), an
inductor ( hpL ) and an inductor bypass resistor ( hpR ). This filter will shunt a large
percentage of high frequency harmonic components at or above the resonant
frequency.
A generalised transfer function approach to harmonic filter design has been
presented in [7]. This approach is based on the Laplace transform and superposition
techniques. In this work, the generalised transfer function approach is adopted for
the HPF design. The HPF impedance transfer function can be derived in normalised
form as,
⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎟⎟
⎠
⎞⎜⎜⎝
⎛ω
+⎟⎟⎠
⎞⎜⎜⎝
⎛ω
⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛+
ω
= 11
1
)(0
2
0
sQ
s
ss
AsZ
p
hp (3.27)
54
In (3.27),
hpCA 1=
hphpCL1
0 =ω
hp
hpp L
R=ω
hp
hphp L
CRQ = (3.28)
where A is the gain coefficient, 0ω is the series resonant frequency, pω is the pole
frequency and Q is the quality factor. The detail of )(sZ hp derivation is presented in
Appendix E.
As illustrated by Figure 3.10, different transfer function characteristics are
possible depending on the value selected for the hpR . The tuning of this HPF is
accomplished by the determination of 0ω . The hpR is chosen based on the desired
high-pass response and the series resonant attenuation. Quality factors of
0.5 ≤≤ Q 2.0 are typical [5]. Higher Q factors allow more series resonant
attenuation and less high-pass. In contrast, lower Q factors provide less series
attenuation and greater high-pass response. Hence, a trade off between the series
resonant and high-pass response exists.
Figure 3.11 presents an equivalent circuit of the proposed hybrid APF for
harmonics, where hpZ is the equivalent impedance of HPF and sZ is the equivalent
distribution source impedance assumed to be a simple inductor ( sL ). In Figure 3.11,
the shunt APF is assumed to act as an ideal current source which produces the
55
compensation current that follows the compensation current reference, while the
nonlinear load is considered as a harmonic currents source. Since we are only
interested in the system performance with the harmonic components, the source
voltage can be neglected. This is because the source voltage is assumed to contain
only the fundamental frequency component.
Figure 3.10 Graphical plot of HPF impedance transfer function ( )(sZ hp )
Figure 3.11 Simplified model of the proposed hybrid APF
After the filter network is configured, a current divider transfer function can
be formulated. Referring to Figure 3.11, the source current to the injected current
transfer function ( )(sH cds ) can be derived as,
hphpLC1
hphpCR1
hpLωhpCω1
dBhp jZ )( ω
hpR
is,hPCC
iL,hif,h
LhpRhp
ChpLs
ZhpZs
ih
ihp,h
56
)()(
)( ,
sisi
sHh
hscds =
)()()(
sZsZsZ
shp
hp
+=
( ) 1)(
111
23
0
220
+⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅++⎟
⎟⎠
⎞⎜⎜⎝
⎛
+⎟⎟⎠
⎞⎜⎜⎝
⎛ω
+⎟⎟⎠
⎞⎜⎜⎝
⎛ω
=
sRL
sCLLsR
CLL
sQ
s
hp
hphphps
hp
hphps
(3.29)
Transfer function (3.29) is important because it can be used to assess the overall filter
performance. A detailed derivation of )(sH cds is presented in Appendix E.
A graphical plot of )(sH cds is shown in Figure 3.12, where it has one crest
( maxH ) due to the parallel resonance between hps LL + and hpC . In particular, this
parallel resonance is a problem, as it enlarges harmonics around the parallel resonant
frequency ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+π=
hphpsr CLL
f)(2
1 . This crest can be minimised by selecting the
value of Q factor close to 0.7 [6].
Figure 3.12 Graphical plot of source current to injected current transfer function
( )(sH cds )
hphpCR1
hphp LC1
hpsCL21
ω
s
hp
LRω
-20 dB/dec
1
Hmax
dBcds jH )( ω
)(1
hpshp LLC +
57
3.6 Summary
This chapter explains in detail the proposed single-phase hybrid APF
connected to a PV array. The overall topology is first highlighted to give an
overview of this work. Then, the operation of each main block is described. Next,
the overall control system is discussed in detail. Finally, the passive HPF design is
outlined.
The following statements summarise the discussions of the proposed
topology:
A new variation of a single-phase hybrid APF topology, connected to a DC
source that represents PV array is presented. The proposed topology is
unique because it effectively filters harmonic currents less than 1 kHz and of
higher frequencies. Furthermore, it simultaneously supplies the power from
the PV array to the load.
In this work, the application of the extension p-q theorem is further extended
to a single-phase hybrid APF for compensation current reference estimation.
This chapter offers the theoretical analysis on the proposed topology.
Computer aided simulations and laboratory experiments must be carried out to
validate the workability of the system.
CHAPTER 4
SIMULATION OF THE PROPOSED HYBRID
ACTIVE POWER FILTER
4.1 Introduction
Due to the complexity of modern power electronics system, computer
simulation has become an indispensable tool to analyse parts of circuits that is too
difficult or complex for hand calculation. This chapter is dedicated to the
MATLAB/Simulink simulation verification of the proposed single-phase hybrid
active power filter (APF). MATLAB/Simulink is an advanced software package for
modelling, simulating and analysing dynamic system [70].
To begin with, MATLAB/Simulink simulation models of the overall system
are developed. For simplicity, the DC source is used to represent the photovoltaic
(PV) array. The simulation mainly focuses on time-domain response analysis. The
simulation models are discussed part by part, starting with the modelling of
distribution source, nonlinear load, shunt APF and passive high-pass filter (HPF).
The development of the overall control system simulation model is outlined. In
addition, a basic shunt APF simulation model is also developed. It is to become the
benchmark comparison for the proposed hybrid APF.
59
4.2 System Modelling via MATLAB/Simulink
The complete simulation model of the proposed scheme, constructed using
the MATLAB/Simulink environment is depicted in Figure 4.1. It consists of
distribution source, nonlinear load, shunt APF, passive HPF, overall control system
and DC source. The fixed-step solver with single-tasking mode is selected so as to
be compatible with the targeted DS1104 digital signal processor (DSP) controller
board from dSPACE. The latter also operates at fixed-size signal sample rate. The
simulation fixed-step size is chosen to be 0.2 µ s. Generally, smaller simulation step
size increases the accuracy of the results but it also increases the simulation time.
Figure 4.1 Complete simulation model of the proposed hybrid APF connected to
a DC source
4.2.1 Distribution Source
The power distribution source considered in the simulations is a 240 Vrms, 50
Hz sinusoidal single-phase AC voltage source. This corresponds to the domestic
utility voltage in Malaysia. Figure 4.2 shows the detail of the “Distribution Source”
block. The distribution voltage ( uv ) is generated by the “AC Voltage Source”
60
blockset from “SimPowerSystems\Electrical Source” library. The isolation
transformer with turn ratio of 2:1 is constructed using the “Linear Transformer”
blockset from “SimPowerSystems\Elements” library. Note that the secondary
leakage inductor of the isolation transformer is considered as the source inductor
( sL ). A source resistor ( sR ) is connected in series to limit the inrush current. The
sL and sR are constructed using “Series RLC Branch” blockset. Their selected
values for the simulation model are given by
76.0=sL mH
4=sR Ω (4.1)
The current and voltage signals are sensed using “Current Measurement” and
“Voltage Measurement” blocksets from “SimPowerSystems\Measurements” library
respectively.
Figure 4.2 Detail of “Distribution Source” block
4.2.2 Nonlinear Load
Figure 4.3 shows the detail of the “Nonlinear Load” block. It consists of a
single-phase full-bridge diode rectifier with DC smoothing capacitor ( dC ), resistive
load ( LR ) and AC smoothing inductor ( smoothL ). The passive components values
selected for the simulation model are given by
61
15.1=smoothL mH
1000=dC µF
250=LR Ω (4.2)
The diode rectifier is constructed using the “Universal Bridge” blockset. The diodes
are configured as the power electronics devices in the “Universal Bridge” blockset.
Figure 4.3 Detail of “Nonlinear Load” block
4.2.3 Shunt Active Power Filter
The detail of “Shunt APF” block is illustrated in Figure 4.4. The shunt APF
consists of an interfacing inductor ( fL ), a voltage source inverter (VSI) and a DC-
bus capacitor ( fC ). The VSI is constructed using the “Universal Bridge” blockset.
The IGBTs with anti-parallel diodes are configured as the power electronics devices
in the “Universal Bridge” blockset.
The design expression described in Chapter 3 (Section 3.3.3) is used to
calculate the value of fL . The rated DC-bus voltage reference ( CfV ) used in the
simulation is set to 250 V, which is approximately one and a half times higher than
the amplitude of source voltage ( sV⋅2 ). The maximum switching frequency of the
switching ripple ( max,swf ) and peak-to-peak switching ripple ( ppswI −∆ , ) of the
62
compensation current is selected to be 12.5 kHz and 1.0 A respectively. Using (3.1)
the minimum value of fL can be calculated as
max,,min, )(2 swppsw
Cff fI
VL
⋅∆⋅=
−
10k5.12)0.1(2
250=
⋅⋅= mH (4.3)
Therefore, fL is chosen as 10 mH.
Figure 4.4 Detail of “Shunt APF” block
The DC-bus capacitor design procedure is described in Chapter 3 (Section
3.3.4). The DC-bus capacitor design parameters are given by
120=sV Vrms
6=∆ LI A
2=T ms
270=∆ CfV or 230 VDC (4.4)
63
where sV is the rms value of the source voltage, LI∆ is the peak rms value of the
reactive and harmonic load currents and T is the period of source voltage and CfV∆
is the maximum or minimum DC-bus voltage. Substituting (4.4) into (3.3), the size
of DC-bus capacitor can be calculated as
2,
2 )()(22
refCfCf
Lsf VV
TIVC
−∆
⋅∆⋅≥
22 )250()270(2
02.061202
−
⋅⋅⋅≥
07.979≥ µF (4.5)
Therefore, the selected value for fC is 990 µF.
4.2.4 Passive High-Pass Filter
The detail of “Passive HPF” block is presented in Figure 4.5. The passive
HPF consists of a capacitor ( hpC ), an inductor ( hpL ) and an inductor bypass resistor
( hpR ). These passive components are constructed using the “Parallel RLC Branch”
blockset.
Figure 4.5 Detail of “Passive HPF” block
64
The design procedure of the passive HPF is described in Chapter 3 (Section
3.5). The passive HPF is tuned to the resonant frequency of 1.28 kHz
( 28.12
10 =
π=
hphpCLf kHz). This resonant frequency value is chosen as the
filtering performance of the shunt APF is impaired above this frequency. The
calculated values of the HPF are
76.1=hpL mH
8.8=hpC µF (4.6)
The hpR is chosen based on the desired high-pass response and the series
resonant attenuation. Quality factors of 0.5 ≤≤ Q 2.0 are typical. In this work, the Q
factor is selected as 0.707, considering the required high-pass response over a wide
frequency band. From (3.28), the hpR can be derived as
hp
hphp C
LQR = (4.7)
Substituting (4.6) into (4.7), the value of hpR can be calculated as
=hpR 6
3
108.81076.1707.0 −
−
××
998.9= Ω (4.8)
Therefore, hpR is chosen as 10 Ω.
From (3.27), the frequency response of the HPF impedance transfer function
is illustrated in Figure 4.6. Examination of the HPF frequency response reveals that
the HPF acts as very low impedance above the resonant frequency ( 0f ) for which it
65
is tuned. As such, it effectively shunts most harmonic quantities above the resonant
frequency.
Figure 4.6 Frequency response of the HPF impedance transfer function
After the filter system is configured, the transfer function of source current to
injected current in (3.29) is used to assess the overall system performance. The
frequency response of the function )(sH cds is illustrated in Figure 4.7. There is a
crest due to the parallel resonance between hps LL + and hpC . In particular, this
parallel resonance is a problem, as it enlarges harmonics around the parallel resonant
frequency (hphps
r CLLf
)(21+π
= = 1.07 kHz). This crest can be minimised by
selecting the value of Q around 0.7. For the frequency response shown in Figure 4.7,
the )(sH cds can be evaluated at low and high frequencies. For low frequencies, it
has a 0 dB gain from 0 Hz to rf . At rf , the gain is determined by the selection of
Q . For high frequencies, the roll-off of the high frequency components above rf is
-20 dB per decade.
M
agni
tude
(dB
)
Frequency (Hz)
f0
66
Figure 4.7 Frequency response of the source current to injected current transfer
function
4.2.5 Overall Control System
The “Overall Control System” block of the proposed scheme is presented in
Figure 4.8. The task of the control system is to produce appropriate gating signals
for the switching transistors (IGBTs). It consists of four blocks namely “Reference
Sinewave Generator”, “Compensation Current Reference Estimator”, “DC-Bus
Voltage Controller and PV Current Estimator” and “Fixed-Band Hysteresis Current
Controller”.
For the targeted DSP implementation, analogue-to-digital converters (ADCs)
are needed to convert the detected system variables in analogue form into digital
form. The ADCs can be represented by the “Zero-Order Hold” (ZOH) blocksets
from “Simulink\Discrete” library, as illustrated by Figure 4.8. The sampling time of
ZOH1, ZOH2, ZOH3 and ZOH4 are chosen as 1sT = 100 µ s, while the sampling
time of ZOH5 is chosen as 2sT = 10 µ s. 2sT is desired to be small to fulfil the fast
processing speed requirement of the hysteresis current controller.
Mag
nitu
de (d
B)
Frequency (Hz)
fr
67
Figure 4.8 Detail of “Overall Control System” block
4.2.5.1 Reference Sinewave Generator
Figure 4.9 shows the detail of the “Reference Sinewave Generator” block. It
is responsible to generate the reference sinewave ( )sin( tω and )90sin( o−ωt ) with
unity amplitude and synchronous with the source voltage. Before the input phase
signal is processed by the “Digital Phase-Lock Loop” block, a “Discrete 2nd-Order
Low-Pass Filter” blockset from “SimPowerSystems\Discrete Control Blocks” library
is adopted to eliminate the high frequency noise. The cut-off frequency of the low-
pass filter is selected to be 100 Hz. There is a need for compensation of the inherent
phase delay in the low-pass filter due to the low cut-off frequency. The detail of the
“Phase Delay Compensation” block is presented in Figure 4.10. It is constructed
using the “Unit Delay” blocksets from the “Simulink\Discrete” library.
The “Digital Phase-Lock Loop” block is constructed using the “Discrete
Transfer Fcn” blockset. In order to generate )sin( tω with unity amplitude, the
68
output of “Digital Phase-Lock Loop” block is divided with the amplitude of the input
phase signal ( sV⋅2 ). The )90sin( o−ωt can be obtained by simply delaying
)sin( tω with 90˚. The “-90˚ degree” block is similar to the “Phase Delay
Compensation” block presented in Figure 4.10.
Figure 4.9 Detail of “Reference Sinewave Generator” block
Figure 4.10 Detail of “Phase Delay Compensation” block
The coefficients calculation procedures for the digital phase-lock loop (PLL)
are outlined in Chapter 3 (Section 3.4.4) and Appendix D. For the simulation model,
the digital PLL design parameters are given by
707.0=ζ
2002 ⋅π=ωn rad/s
100=sT µ s (4.9)
69
where ζ is the damping ratio, nω is the undamped frequency and sT is the sampling
period of the discrete system. Substituting (4.9) into (D.11), the characteristic
equation coefficients can be calculated as
snTeC ζω−= 2
0
)100)(2002)(707.0(2 µ⋅π−= e
=0.837203188
and
)1cos(2 21 ζ−ω−= ζω−
snT TeC sn
)707.01)100)(2002cos((2 2)100)(2002)(707.0( −µ⋅π−= µ⋅π−e
= -1.822754279 (4.10)
From the characteristic equation of (3.18) and (3.22), the constant c and constant a
of digital PLL can be calculated as
01 Cc −= =0.162796812
and
cCa 12 +
= =1.08875425 (4.11)
70
4.2.5.2 Compensation Current Reference Estimator
Figure 4.11 depicts the detail of the “Compensation Current Reference
Estimator” block. The source voltage, load current and HPF current signals are sent
through “Discrete 2nd-Order LPF” blocksets for noise filtering. These low-pass
filters (LPFs) are inserted to simulate the actual implementation, where signal filters
are necessary for good quality signal processing. The cut-off frequency of these low-
pass filters is selected to be 2 kHz. The filtered signals are used to estimate the
compensation current reference as discussed in Chapter 3 (Section 3.4.2). In Figure
4.11, the “Digital 2nd-Order Butterworth LPF” blocks are constructed using
“Discrete Transfer Fcn” blocksets.
Figure 4.11 Detail of “Compensation Current Reference Estimator” block
The design procedure for digital Butterworth LPF is outlined in Chapter 3
(Section 3.4.5). For the simulation model, the following design parameters are
selected as,
707.0=ζ
5=LPFf Hz
71
10=sf kHz (4.12)
where ζ is the damping ratio, LPFf is the cut-off frequency and sf is the sampling
frequency of the digital Butterworth LPF. Substituting (4.12) into (3.26), the natural
undamped frequency of the digital Butterworth LPF can be calculated as
⎟⎟⎠
⎞⎜⎜⎝
⎛ π=ω
s
LPFLPF f
ftan
⎟⎠⎞
⎜⎝⎛ ⋅π
=k105tan =1.570797619 310−× rad/s (4.13)
Substituting (4.12) and (4.13) into (3.25), the coefficients of digital Butterworth LPF
can be calculated as
2
2
21 LPFLPF
LPFLPFG
ω+ζω+ω
=
=2.46193087 610−×
2
2
1 21)1(2
LPFLPF
LPFLPFa
ω+ζω+−ω
=
= -1.995557792
and
2
2
2 2121
LPFLPF
LPFLPFLPFa
ω+ζω+ω+ζω−
=
=0.99556764 (4.14)
72
4.2.5.3 DC-Bus Voltage Controller and PV Current Estimator
The detail of the “DC-bus Voltage Controller and PV Current Estimator”
block is presented in Figure 4.12. The DC-bus voltage is first sent through a
“Discrete 2nd-Order LPF” blockset for noise filtering. The filtered signal is then
passed to a proportional-integral (PI) controller for DC-bus capacitor charging
current estimation. The proportional constant ( pK ) and integration constant ( IK )
blocks are constructed using the “Gain” blocksets from the “Simulink\Math
Operations” library. The integrator is constructed using “Discrete-Time Integrator”
blockset. It must be noted that when a DC source is connected to the DC-bus
capacitor, the PI controller can be removed by turning off “Switch (S5)” blockset.
Figure 4.12 Detail of “DC-Bus Voltage Controller and PV Current Estimator”
block
The PV current is obtained by dividing the available active PV power with
the DC-bus voltage reference. The resulting DC-bus capacitor charging current is
then subtracted from the PV current and multiplied with the reference sinewave to
form the second component of compensation current reference signal.
The design procedure of the PI controller is presented in Chapter 3 (Section
3.4.3) and Appendix C. The design parameters of the PI controller are:
73
990=fC µF
250, =refCfV VDC
120=sV Vrms
2=T ms (4.15)
Substituting (4.15) into (C.9), pK can be calculated as
s
refCffp VT
VCK
2
2 ,=
)120(202.0
)250)(990(2⋅⋅
µ=
=0.145840773 (4.16)
After pK is calculated, IK can be determined empirically. The value of IK is
chosen as 0.029 for the simulation model.
4.2.5.4 Fixed-Band Hysteresis Current Controller
Figure 4.13 illustrates the detail of “Fixed-Band Hysteresis Current
Controller” block. This current control technique imposes a bang-bang type
instantaneous control that forces the compensation current to follow its estimated
reference. The actual compensation current is subtracted from its estimated
reference. The resulting error is sent through a hysteresis controller to determine the
appropriate gating signals. In the simulation model, the hysteresis band ( H ) is
74
chosen as 1.0 A. The hysteresis controller is constructed using “Relay” blockset
from “Simulink\Discontinuities” library.
Figure 4.13 Detail of “Fixed-Band Hysteresis Current Controller” block
4.3 Basic Shunt Active Power Filter
Figure 4.14 illustrates a basic shunt APF simulation model constructed under
MATLAB/Simulink environment. It is used as a benchmark to investigate the
improvement in harmonic mitigation by the proposed hybrid APF. It consists of
distribution source, nonlinear load, shunt APF, overall control system and DC source.
Figure 4.14 Complete simulation model of the basic shunt APF connected to a DC
source
75
This simulation model for the basic shunt APF is similar to the model of the
proposed topology presented in Figure 4.1, except for the removal of “Passive HPF”
block. Therefore, the descriptions given in Section 4.2 are applicable for the basic
shunt APF. The basic shunt APF is configured to generate compensation current
equals to the reactive and harmonic load current.
4.4 Summary
The complete MATLAB/Simulink simulation model of the proposed hybrid
APF is presented. The models are discussed part by part, starting with the modelling
of distribution source, nonlinear load, shunt APF, passive high-pass filter (HPF) until
the development of the overall control system. Furthermore, a basic shunt APF
simulation model is developed as a benchmark. The simulation results will be
analysed and compared with the experimental results in Chapter 6.
CHAPTER 5
HARDWARE IMPLEMENTATION OF THE PROPOSED HYBRID
ACTIVE POWER FILTER
5.1 Introduction
In this chapter, the hardware implementation of a 500 VA experimental
prototype of the proposed hybrid active power filter (APF) is presented. The system
parameters used in the hardware implementation are the same used in simulation.
The general experimental set-up is presented first, followed by the descriptions on
prototype construction. Each component used in the prototype is discussed in
considerable detail. A section that describes the analogue signals measurement is
also provided. Finally, the overall control system implementation using DS1104
digital signal processor (DSP) controller board from dSPACE is presented.
5.2 General Description of the Experimental Set-Up
An overall block diagram of the experimental set-up is shown in Figure 5.1.
Figure 5.2 shows the actual overall experimental set-up. The experimental prototype
is supplied from a 240 Vrms, 50 Hz distribution source via a variable transformer and
a 2:1 turns ratio isolation transformer. The use of variable transformer allows the
system to be operated at lower than the rated voltage level, which is very useful
77
during the development stage. An isolation transformer is used mainly to provide
safety when using measuring equipments such as an oscilloscope.
The nonlinear load is constructed using a single-phase full-bridge diode
rectifier with DC smoothing capacitor and AC smoothing inductor. The nonlinear
load is applied in order to generate the load current to be compensated by the hybrid
APF. The diode rectifier load is purely resistive, i.e. a lamp ballast. The leakage
inductor of the isolation transformer is considered as the source inductor. The inrush
source current is limited by an additional resistor in series with the source voltage.
Figure 5.1 Overall block diagram of the experimental set-up
+
_
Shunt APF
Nonlinear Load
is
if
Distribution Source
240 Vrms(50Hz)
vsiL
VCfihp
PassiveHPF
PCC
Gating signals
VCf
iL
ihp
vs
if
VoltageTransducer
DS1104
GateDriver
CurrentTransducer
CurrentTransducer
CurrentTransducer
VoltageTransducer
4
PCIPC
VoltageSourceInverter
DCSource
Full-BridgeDiode
Rectifier
ACMains
IsolationTransformer
VariableTransformer
Power Ground
Digital Ground
Overall ControlSystem
AnaloguePrefilter
78
Figure 5.2 Actual overall experimental set-up
The proposed hybrid APF is connected in parallel with the nonlinear load
being compensated. It consists of a passive high-pass filter (HPF), a shunt APF
constructed using a full-bridge voltage source inverter (VSI), an interfacing inductor,
a DC-bus capacitor and a DC source. Note that the DC-bus capacitor is supplied by
a DC source with the desired constant DC voltage level. Due to time constraint, the
DC-bus voltage controller is not implemented experimentally.
The heart of the overall control system is the dSPACE DS1104 DSP
controller board. It is programmed to realise the compensation current reference
estimation and control algorithm. It is also used to generate the required gating
signals to the VSI. The DS1104 is linked to a personal computer (PC) through a PCI
slot interface. Programming with C code is done using the dedicated ControlDesk
Source Code Editor and Microtec PowerPC C Compiler and Linker. The executable
object files and libraries are generated and loaded onto the on-board global memory
for real-time execution.
DC Source Oscilloscope
Experimental Prototype
Computer Isolation Transformer
Variable Transformer
Resistive Load
Rectifier Bridge
79
The Hall-Effect current and voltage transducers are employed for the
analogue signals measurement. The measured signals are sampled using the DS1104
on-board analogue-to-digital converters (ADCs) and passed on to the DSP for further
processing.
5.3 Experimental Prototype Construction
This section explains the experimental prototype construction in steps,
describing each component used. Figure 5.3 shows the actual experimental
prototype. The prototype consists of interfacing inductor, gate drivers, VSI with DC-
bus capacitor, rectifier load, DS1104 connector board, smoothing inductor, current
and voltage transducers and passive HPF. The experimental prototype parameters
are shown in Table 5.1. The values and parameters of prototype components are the
same as those designed and simulated in Chapter 4.
Figure 5.3 Actual experimental prototype. (1) interfacing inductor, (2) gate
drivers, (3) VSI with DC-bus capacitor, (4) rectifier load, (5) DS1104 connector
board, (6) smoothing inductor, (7) current and voltage transducers, (8) passive HPF
1
2 3
4
5
6
7
8
1
2 3
4
5
6
7
8
80
Table 5.1 : Experimental prototype parameters
Parameters Symbol Value
Source voltage vs 120 Vrms (50 Hz)
Source inductor Ls 0.76 mH
Inrush current limiting resistor Rs 4 Ω
Rectifier Load Nominal Complex Power Sn 500 VA
Rectifier DC smoothing capacitor Cd 1000 µF
Rectifier AC smoothing inductor Lsmooth 1.15 mH
Load resistor RL 250 Ω
Hysteresis tolerance band H 1 A
Interfacing inductor Lf 10 mH
DC-bus capacitor Cf 990 µF
DC-bus voltage VCf 250 VDC
HPF resonant frequency f0 1.28 kHz
HPF inductor Lhp 1.76 mH
HPF capacitor Chp 8.8 µF
HPF inductor bypass resistor Rhp 10 Ω
5.3.1 Nonlinear Load
The nonlinear load used in the experimental prototype is a single-phase full-
bridge diode rectifier. The diode module consists of four diodes in a package. This
diode module is of the type SKB60/08 manufactured by Semikron, which is a 60 A,
800 Vrms device. The DC smoothing capacitor ( dC ) consists of a 1000 µF, 385 VDC
electrolytic capacitor (PEH200XJ4100M) manufactured by Evox Rifa. This
capacitor is a high performance long life electrolytic capacitor, which has low
equivalent series resistance (ESR) and low equivalent series inductance (ESL).
The AC smoothing inductor ( smoothL ) is wound on a 3C90 ferrite core
manufactured by Ferroxcube. The 3C90 is selected because it has low power losses
and high saturation flux density, which are vital for energy storage purpose [71].
81
Furthermore, it is able to operate at frequency as high as 200 kHz. The selected core
geometry is the E-E core type ETD59, which is suitable for high power application
and simple coil winding. The specification for smoothL is given in Table 5.2. The
detailed design procedure for smoothL is presented in Appendix F.
Table 5.2 : AC smoothing inductor specification
Core
material
Core
type
Number
of turns
N
(turns)
Saturation flux
density
Bsat
(G at 100 ˚C)
Effective
length
le
(mm)
Effective
area
Ae
(mm2)
Inductance
L
(mH)
3C90 ETD59 74 3400 139 368 1.15
5.3.2 Shunt Active Power Filter
The shunt APF consists of a voltage source inverter (VSI), an interfacing
inductor and a DC-bus capacitor. This subsection describes briefly on the shunt APF
construction.
5.3.2.1 Voltage Source Inverter
The experimental single-phase full-bridge VSI is made up of four units of
insulated gate bipolar transistors (IGBTs) as shown in Figure 5.4. The selected
IGBTs are of the type APT25GP120BDF1 manufactured by Advanced Power
Technology. Each unit has an IGBT device rated 1200 V and 33 A at 110 ˚C case
temperature. This IGBT combines the superior characteristics of bipolar junction
transistor and power metal oxide-semiconductor field-effect transistor (MOSFET).
Unlike it predecessor, the newer generation of IGBT can be switched without the use
of snubber components. The possibility of snubberless operation results in a much
simple design. As a result, it provides a lower cost alternative to a MOSFET.
82
Furthermore, the continuity of current during blanking time period is maintained by
the build-in anti-parallel diodes.
Figure 5.4 Schematic of experimental single-phase full-bridge VSI
5.3.2.2 Interfacing Inductor
The interfacing inductor ( fL ) consists of four inductors connected in series,
2.5 mH each to give a total inductance of 10 mH. The reason for not using a single
unit of a 10 mH inductor is because there is no suitable bobbin and ferrite core
available that meet the targeted design specifications. Each unit of the 2.5 mH
inductors is wound on 3C90 ferrite core manufactured by Ferroxcube. Its
specification is given in Table 5.3. The detailed design procedure of the 2.5 mH
inductor is presented in Appendix F.
Table 5.3 : 2.5 mH inductor specification
Core
material
Core
type
Number
of turns
N
(turns)
Saturation flux
density
Bsat
(G at 100 ˚C)
Effective
length
le
(mm)
Effective
area
Ae
(mm2)
Inductance
L
(mH)
3C90 ETD59 160 3400 139 368 2.5
+
_
VCf
S3
S4
S1
S2 G2
E2
G4
E4
G1
E1
G3
E3~
~
83
5.3.2.3 DC-Bus Capacitor
The DC-bus capacitor ( fC ) is constructed by arranging an array of capacitors
across the DC-bus rail, as shown in Figure 5.5. It consists of three electrolytic
capacitors connected in parallel, 330 µF, 400 VDC each to give a total capacitance of
990 µF. The electrolytic capacitors are of the type 2222-059-56331 manufactured
by BC Components. It is a high performance long life electrolytic capacitor, which
has low ESR and high ripple current capability. A bleed resistor (RB) is connected
across the capacitors to ensure that the high voltage is discharged when the shunt
APF is turned off.
Figure 5.5 DC-bus capacitor
5.3.3 Gate Driver Circuit
An IGBT is basically a voltage controlled device and exhibits MOSFET-like
capacitive gate-to-emitter characteristics. Therefore, low firing signals are sufficient
to turn the IGBT on and off. Figure 5.6 illustrates the functional block diagram of
the gate driver circuit. The two gating signals for the VSI are generated by the
DS1104 and latched out via two bits of high-speed input/output (I/O) ports. The gate
driver circuits (GD1 and GD2) interface between the gating signals and the IGBTs.
These circuits isolate and amplify the gating signals in order to turn on/off the IGBTs.
In this work, hard switching approach is applied for the VSI, therefore a blanking
time is needed for protection against shoot-through in the VSI leg. A blanking time
Cf1
330uF
Cf2
330uF
Cf3
330uF
RB
22 k (5W)
DC-Bus
+
_
84
of s 5.2 µ is provided internally by the gate driver circuit. The gate driver circuit is
from the design in [73] and its schematic is presented in Appendix G.
Figure 5.6 Functional block diagram of gate drive circuit
5.3.4 Passive High-Pass Filter
The HPF capacitor ( hpC ), inductor ( hpL ) and inductor bypass resistor ( hpR )
are designed according to the specification used in the simulation. The hpC consists
of four metallised polypropylene film capacitor connected in parallel, 2.2 µF each to
give a total capacitance of 8.8 µF. The selected capacitors are of the type 2222-468-
16225 manufactured by BC Components. The metallised polypropylene film
capacitor provides a fairly high capacitance per unit volume and high pulse durability,
thus making it suitable for filtering application.
The hpL is wound on a 3C90 ferrite core manufactured by Ferroxcube. The
specification for hpL is given in Table 5.4. The detail design procedure for hpL is
presented in Appendix F. The hpR with resistance value of 10 Ω is connected in
parallel with hpL . This resistor is made up of an aluminium clad wire wound resistor,
type HSC200-10R manufactured by Tyco Electronics. This resistor is suitable for
applications where high wattage dissipation in a small space is required.
S3
S4
S1
S2
DC-Bus (positive rail)
GD1 GD2
Gate drivecircuit
DS1104
GD1
GD2Gatingsignals
I/O 1
I/O 2
85
Table 5.4 : HPF inductor specification
Core
material
Core
type
Number
of turns
N
(turns)
Saturation flux
density
Bsat
(G at 100 ˚C)
Effective
length
le
(mm)
Effective
area
Ae
(mm2)
Inductance
L
(mH)
3C90 ETD59 113 3400 139 368 1.76
5.4 Analogue Signals Measurement
For the control system, it is necessary to measure the following five analogue
signals:
(1) DC-bus voltage, CfV
(2) Source voltage, sv
(3) Compensation current, fi
(4) Load current, Li
(5) HPF current, hpi
The measured signals are sampled using the DS1104 on-board ADCs and passed on
to the DSP for further processing. This section describes on the analogue signals
measurement using hall-effect voltage/current transducers. Finally, an analogue
prefilter for analogue input signal band-limiting is also presented.
5.4.1 Hall-Effect Voltage Transducer
For voltage signal measurement, a simple resistive voltage divider could be
used to obtain a scaled-down value of the voltage signal. Although this method is
simple, there are two potential drawbacks. The measurement of high voltage causes
the wire-wound resistor to heat up, deviating its resistance from its nominal value.
Secondly, there is no electrical isolation between high voltage ground and the digital
86
circuitry. Therefore, occurrence of spikes, noise etc. from the power distribution
system will be directly transmitted to the sensitive low-power circuits.
A preferable alternative is to use a Hall-Effect voltage transducer. The
particular device selected for this purpose is LV25-P, manufactured by LEM. It is an
instantaneous current output type with isolation capability of about 2.5 kVrms at 50
Hz. In this work, two Hall-Effect voltage transducers are required for CfV and sv
measurements. Figure 5.7 shows the circuitry to obtain an output proportional to
CfV or sv . Note that the earth from the LV25-P is connected to the digital ground.
Figure 5.7 Voltage signal measurement using LV25-P Hall-Effect voltage
transducer
5.4.2 Hall-Effect Current Transducer
Three current transducers are needed for fi , Li and hpi measurements. The
Hall-Effect current transducer type LA25-NP, manufactured by LEM is selected as
the current transducer. LA25-NP is an instantaneous current output type with
isolation capability of about 2.5 kVrms at 50 Hz. It provides five selectable current
measurement ranges (5/6/8/12/25 A). In this work, the current measurement range of
8 A is selected. Figure 5.8 shows the circuitry to obtain an output proportional to
fi , Li or hpi . Note that the earth from the LA25-NP is connected to the digital
ground.
LV25-P
+HT
-HT M
+
-1
2 3
4
5
-15V +15V
Digital ground
Proportional outputR1 22k(5W)
RM 200(0.5W)VCf or vs
+
87
Figure 5.8 Current signal measurement using LA25-NP Hall-Effect current
transducer
5.4.3 Analogue Prefilter
In order to sample a signal at a desired rate and satisfy the conditions of the
sampling theorem, the signal must be prefiltered by a low-pass analogue filter,
known as an anti-aliasing prefilter [68]. The output of the analogue prefilter will
then be band-limited and sampled properly at the desired sampling rate. In this work,
the VCf, vs, iL and ihp are sampled at 10 kHz sampling rate (fs1 = 10 kHz), while if is
sampled at 100 kHz sampling rate (fs2 = 100 kHz). Figure 5.9 shows the circuitry of
the analogue prefilter. It should be emphasized that the cut-off frequency
(212
1CCR
fcπ
= ) of the analogue prefilter must be taken to be half of the sampling
rate ( 521
11 ≅= sc ff kHz and 5021
22 ≅= sc ff kHz). The specification of the
analogue prefilter is given in Table 5.5.
Table 5.5 : Analogue prefilter specification
Cut-off frequency, fc R
(kΩ)
R3
(kΩ)
C1
(pF)
C2
(pF)
fc1 = 5 kHz 22 47 1000 2000
fc2 = 50 kHz 22 47 100 220
LA25-NP
1-5
6-10 M
+
-1
2 3
4
5
-15V +15V
Digital ground
Proportional output
RM 200(0.5W)if , iL or ihp
in
out
88
Figure 5.9 Analogue prefilter circuit
5.5 Controller Hardware and Software Tools
All the control algorithms, gating signals generation and protection of the
experimental prototype are performed by a DSP controller board, the DS1104 from
dSPACE [74]-[78]. This section presents the controller hardware and the software
tools for the overall control system implementation.
5.5.1 DS1104 DSP Controller Board
The DS1104 DSP controller board is used to develop, debug and execute the
control program. It is a standard board that can be plugged into a PCI slot of a PC.
The DS1104 is specially designed for the development of high-speed multivariable
digital controllers in various application fields. It is a complete real-time control
system based on a 603 PowerPC floating-point processor manufactured by Motorola,
running at 250 Mhz. For advanced I/O purposes, the controller board includes a
slave DSP subsystem based on the TMS320F240 DSP microcontroller manufactured
by Texas Instruments.
Figure 5.10 shows a block diagram that describes the main features of the
controller board. The rich selection of on-board peripherals such as ADCs, digital-
Analogueinput signal +
_
TL051 Analogueoutput signal
C2
C1
R1 R2
R3R = R1 = R2
89
to-analogue converters (DACs), bits I/O, Incremental Encoder Interface, Serial
Interface, Serial Peripheral Interface , User Interrupts, Encoder Interrupts, Slave DSP
interrupt, Timers Units make the interface task with gate driver circuit easier and
more reliable.
Figure 5.10 Block diagram of the DS1104 DSP controller board
5.5.2 Software Tools
Development tools from dSPACE’s Software is used to develop the control
program. It is an integrated system which is optimised to work with the DS1104
hardware. The main programming tools are a dedicated Source Code Editor,
Microtec PowerPC C Compiler and Linker. Other support tools include ControlDesk,
PCPCI Bus
PCI Interface
Interrupt Controller
Timers
Memory Controller
PowerPC 603e
32 MBSDRAM
8 MB FlashMemory
ADC4 Ch. 16-Bit4 Ch. 12-Bit
DAC8 Ch. 16-Bit
IncrementalEncoder
2 Ch.
Digital I/O20 Bit
Serial InterfaceRS232/RS485/
RS422
Dual PortRAM
TMS320F240DSP
PWM1 x 3-Phase4 x 1-Phase
4 CaptureInputs
SerialPeripheralInterface
Digital I/O14-Bit
24 Bit I/O Bus
DS1104
Slave DSP I/O Features
Master PPC I/O Features
90
Platform Manager, Experiment Manager, Real-Time Library (RTLib) and a real-time
platform known as Real-Time Interface (RTI). The ControlDesk, dSPACE’s well-
establish experiment software, provides all the functions to control and monitor the
DS1104 hardware. Figure 5.11 illustrates the graphical user interface of
ControlDesk software. It offers a variety of virtual instruments to build and
configure virtual instrument panels via instrumentation and provides functions to
perform parameter studies.
Figure 5.11 Graphical user interface of ControlDesk software
Basically, there are two approaches to create real-time applications to be
implemented on the DS1104: (1) Using RTI and (2) Handcoding. The dSPACE’s
RTI in conjunction with the Real-Time Workshop (RTW) from the MathWorks can
convert the developed Simulink model into real-time C code, i.e. the C code is
generated and implemented automatically on DS1104. Therefore, the user only need
to add the required dSPACE blocks into the developed Simulink model. This makes
the implementation process fast and simple. Although RTI approach is simple, it has
one shortcoming, in the sense that the system initialisation and I/O features are not
accessible [77].
91
An algorithm can also be handcoded manually using C language [79], then
the code is downloaded into the global memory of DS1104. All the tools required to
generate the object files are provided by the dSPACE’s software. By using the
handcoding approach, the system initialisation and I/O features are now accessible.
In this work, the handcoding approach is adopted.
5.6 Control Software
The main purpose of the software control is to generate the appropriate gating
signals to drive the switching transistors according to the estimated current reference.
This section explains the control algorithms implementation on the DS1104.
5.6.1 Control Software Structure
Figure 5.12 shows the structure of the control software for DS1104. At the
highest level, the control software consists of initialisation routine and run routines.
Upon completion of the necessary initialisation, the background service is started.
The background service is simply an infinite loop. At all time, the control processing
is done via one service routine (isr_srt0()) and one interrupt service routine
(isr_srt1()). Two timers are used, Timer 0 and Timer 1, with execution times chosen
to be 10 µs and 100 µs respectively. The control algorithms implemented during
Timer 1 are the reference sinewave generation, compensation current reference and
PV current estimation and system protection. The fixed-band hysteresis current
control algorithm is implemented during Timer 0. The host service routine
(host_service()) which is executed at every period of Timer 1 is responsible for the
data capture. The complete C code listings and program documentation can be found
in Appendix H.
92
Figure 5.12 DS1104 control software structure
5.6.2 Initialisation Routine
A flowchart describing the initialisation routine is given in Figure 5.13. After
start-up, initialisation of variables and various peripherals take place. Peripheral
initialisation involves the configuration of timer units, capture units, I/O bits, ADCs
and DACs, whose functions are software programmable. Each of the timers is
programmed to operate in the continuous down count mode. Timer 0 provides the
timebase for the isr_srt0(), while the isr_srt1()’s timebase is provided by Timer 1.
Timer 1 is also used to provide a central processing unit (CPU) interrupt at the fixed
rate. Thereafter, the infinite loop background service routine is called, and the
normal operation of the control begins.
5.6.3 Service Routine 0
Figure 5.14 shows a flowchart describing the service routine 0 (isr_srt0()).
The program reads the compensation current signal ( fi ) through the ADC channel 8.
Start
Initialisation Routine:- DSP Setup- Variables Initialisation- Peripheral Initilisation- Set Interrupts- Start Timers (Timer 0, Timer 1)- Start Background Service
Run Routines:
Background Service
Timer 0, isr_srt0():- Fixed-Band Hysteresis Current Control
Timer 1, isr_srt1():- Reference Sinewave Generation- Compensation Current Reference and PV Current Estimation- System Protection
host_service():- Data Capture
93
The sampled value is then subtracted from the compensation current reference signal
( reffi , ). The resulting error ( hysteresisi ) is subjected to a comparator to determine the
gating signals (bit I/O 5 and I/O 17) when exceeds/equals the predefined upper or
lower limits (0.5 or -0.5). As long as hysteresisi is within the limits, no switching action
is taken.
5.6.4 Interrupt Service Routine 1
A flowchart describing the interrupt service routine 1 (isr_srt1()) is given in
Figure 5.15. The program reads the DC-bus voltage ( CfV ), source voltage ( sv ), HPF
current ( hpi ) and load current ( Li ) signals from the ADC channel 2, 5, 6 and 7
respectively. The reference sinewave generator subroutine (phase_lock_loop()) is
first executed to generate the reference sinewave with unity amplitude and
synchronous with the source voltage. Then, the compensation current reference and
PV current estimator subroutine (extension_pq_theorem() and
compensation_current_ref()) is executed to obtain the current reference signal ( reffi , ).
A system protection subroutine (system_fault_protection()) is included to protect the
system from task overrun condition. When task overrun occurred, the system is
halted by sending a “low” enable signal (bit I/O 11 = 0) to the gate driver circuits.
The host service subroutine (host_service()) execution supports data capturing
feature of the ControlDesk software. Once all the executions are completed, the
interrupt is enabled to allow servicing of Timer 1 interrupt.
94
Figure 5.13 Initialisation routine flowchart
Figure 5.14 Service routine 0 flowchart
START
Initialise variables,peripherals
DSP setup
Set interrupts
Start Timer 0 and Timer 1
Background loop
isr_srt0(),isr_srt1()
STARTisr_srt0()
Read ADC8 for if
END
Start ADC8 conversionfor if
Sampling ends?No
Yes
Calculates ihysteresis = if - if,ref
ihysteresis=>0.5
Set bit I/O5, I/O17= ‘1’
Set bit I/O5, I/O17= ‘0’
ihysteresis=<-0.5
Yes
No
Yes
No
Remain bit I/O5, I/O17
95
Figure 5.15 Interrupt service routine 1 flowchart
START
isr_srt1()
Read ADC2,5,6,7 forVCf ,vs ,ihp ,iL
END
Sampling ends?No
Yes
Execute Reference Sinewave Generatorphase_lock_loop()
Start ADC2,5,6,7 conversionfor VCf ,vs ,ihp ,iL
Execute Compensation Current Referenceand PV Current Estimatorextension_pq_theorem(),
compensating_current_ref()
Execute System Protectionsystem_fault_protection()
Execute Host Servicehost_service()
Enable interrupt
System fault?
No
Set Enable Signal,bit I/O 11 to ‘1’
Yes
Set Enable Signal,bit I/O 11 to ‘0’
96
5.7 Summary
A 500 VA experimental prototype for the proposed hybrid APF is developed.
It consists of distribution source, nonlinear load, passive HPF, shunt APF and
dSPACE’s DS1104 DSP controller board. The major components used in the
prototype construction are discussed in detail. An overview of the DS1104 hardware
is given, followed by detail implementation of the control software. The flexibility
of the DS1104 enables easy implementation of the proposed control algorithms,
gating signals generation and system protection. The experimental results will be
analysed and compared with simulation results in Chapter 6.
CHAPTER 6
RESULTS AND ANALYSIS
6.1 Introduction
In Chapter 4, the MATLAB/Simulink simulation of the proposed hybrid APF
is discussed. This is followed by the description of the prototype construction. In
this chapter, the experimental results will be presented and analysed with reference to
the simulation work.
First, the performance of the distribution system without compensation is
given. Then, the result of “ideal compensation” will be presented. Under the ideal
case, the compensation current reference is calculated using the DS1104. However,
the proposed hybrid APF is not connected to the distribution system. We assume it
is modelled as an ideal current source. The aim of this exercise is to ensure the idea
that we propose (i.e. compensation current reference estimation using extension p-q
theorem) is workable without considering the effect of noise and the speed limitation
of the DS1104. Using this approach, we are able to validate effectiveness of the
proposed compensation scheme without having to worry about the external
influences.
Later in this chapter, we will show that the effect of noise changes the result
considerably. The speed limitation of DS1104 limits the controller sampling time,
which in turn degrades the performance of the hysteresis current controller. The
performance of the distribution system under the compensation of a basic shunt APF
98
and the proposed hybrid APF will be described. The discrepancies between the
simulation and experimental results are highlighted. The capability of the proposed
hybrid APF in handling the PV energy is evaluated. Finally, analysis on the Total
Harmonic Distortion (THD) for the proposed hybrid APF in comparison to a basic
shunt APF is carried out.
6.2 Results – Without Compensation
A single-phase full-bridge diode rectifier load is applied to the distribution
system in order to obtain the distorted load current. Figure 6.1 shows the simulated
source voltage and load current waveforms without any type of compensation. As
can be seen, the resulting load current is highly distorted. It deviates significantly
from a sinusoidal waveform. This distorted load current leads to distortion in the
source voltage waveform. This can be clearly observed by the existence of “flat-top”
at the peak of the source voltage waveform. The distortion in the source voltage
waveform is due to the presence of source inductor ( sL ) and source resistor ( sR ).
Figure 6.1 Simulation results – without compensation: source voltage and load
current waveforms
168 20 24 36Time, t [ms]
4 40
0
-300
-6-4-2
246
-200-100
0100200300
Load
Cur
rent
, iL [
A]
Sour
ce V
olta
ge, v
s [V
]
12 3228
99
The experimental source voltage and load current waveforms with similar
operating condition are shown in Figure 6.2. Measurements are done using the
Tektronix TDS 3054A 500 MHz four channel digital oscilloscope. It can be seen
that the experimental results are in close agreement with the simulation results shown
in Figure 6.1.
Figure 6.2 Experimental results – without compensation: source voltage and load
current waveforms
6.3 Reference Sinewave Generation
Figure 6.3 shows the simulated source voltage and the phase-lock loop (PLL)
generated reference sinewave ( )sin( tω and )90sin( o−ωt ) waveforms. Recall that
the PLL is used to generate the reference sinewave with unity amplitude and
synchronised with the source voltage ( sv ). From Figure 6.3, the obtained )sin( tω is
a pure sinusoidal waveform although the source voltage waveform is distorted.
Furthermore, the )sin( tω is synchronised with sv . A 90˚ shifted reference sinewave
signal ( )90sin( o−ωt ) is obtained by delaying )sin( tω by 90˚.
168 20 24 32Time, t [ms]
0 40
0
-300
-6-4-2
246
-200-100
0100200300
Load
Cur
rent
, iL [
A]
Sour
ce V
olta
ge, v
s [V
]
12 28 364
100
The experimental PLL generated waveforms are shown in Figure 6.4. Since
the data for the PLL generated reference sinewave are stored in the DS1104, they are
captured from the on-board digital-to-analogue converters (DACs). As can be
observed, the experimental results are in accordance with the results obtained from
the simulation.
Figure 6.3 Simulation results – PLL generated reference sinewave: source
voltage and the generated reference sinewave waveforms
Figure 6.4 Experimental results – PLL generated reference sinewave: source
voltage and the generated reference sinewave waveforms
0.0
-300
-1.5-1.0-0.5
0.51.01.5
-200-100
0100200300
Ref
eren
ce si
new
ave
Sour
ce V
olta
ge, v
s [V
]
Time, t [ms]168 20 24 364 4012 3228
sin(ωt) sin(ωt-90˚)
Time, t [ms]
0.0
-300
-1.5-1.0-0.5
0.51.01.5
-200-100
0100200300
Ref
eren
ce si
new
ave
Sour
ce V
olta
ge, v
s [V
]
168 20 24 320 4012 28 364
sin(ωt) sin(ωt-90˚)
101
6.4 Compensation Current Reference Estimation
In this section, we shall present the result for estimation of compensation
current reference using the extension p-q theorem. Figure 6.5 shows the simulated
load current and HPF current waveforms. As can be seen, both the current
waveforms are distorted. They deviate significantly from a sinusoidal waveform.
For the HPF current, the distortion is caused by the inflow of harmonic currents,
which are produced by the distorted source voltage [16].
Figure 6.5 Simulation results: load current and HPF current waveforms
These results are verified by experiment shown in Figure 6.6. However,
current spikes are observed in the experimental HPF current but not in the simulated
HPF current. The occurrences of these current spikes are probably due to the effect
of parasitic elements in the HPF.
0
-1.5-1.0-0.5
0.51.01.5
HPF
Cur
rent
, ihp
[A]
0
-3-2-1
123
Load
Cur
rent
, iL [
A]
Time, t [ms]168 20 24 364 4012 3228
102
Figure 6.6 Experimental results: load current and HPF current waveforms
By using extension p-q theorem presented in Section 3.4.2, the compensation
current reference can be decomposed into active, reactive and harmonic current
components. Referring to Figure 6.5, the various instantaneous components of the
load current are shown in Figure 6.7. It can be seen that the active load current ( pLi , )
is in phase with the source voltage ( sv ), while the reactive load current ( qLi , ) lags
pLi , by 90˚. The harmonic load current ( hLi , ) is obtained by subtracting pLi , and qLi ,
from the load current ( Li ):
)( ,,, qLpLLhL iiii +−= (6.1)
In addition, this figure also shows the reactive HPF ( qhpi , ) current waveform. It is in
phase with the HPF current ( hpi ).
Time, t [ms]168 20 24 320 4012 28 364
0
-1.5-1.0-0.5
0.51.01.5
HPF
Cur
rent
, ihp
[A]
0
-3-2-1
123
Load
Cur
rent
, iL [
A]
103
Figure 6.7 Simulation results: estimated active load current, reactive load current,
harmonic load current and reactive HPF current waveforms
The experimental results of the various instantaneous components of the load
current and HPF current are shown in Figure 6.8. These results are captured from the
DS1104 on-board DACs. As can be seen, the experimental results match very well
with the simulation results.
0
-0.6-0.4-0.2
0.20.40.6
0
-3-2-1
123
Har
mon
ic L
oad
Cur
rent
,i L,
h [A
]
0
-60-40-20
204060
Rea
ctiv
e Lo
ad C
urre
nt,
i L,q [
mA
]0
-1.5-1.0-0.5
0.51.01.5
Act
ive
Load
Cur
rent
,i L,
p [A
]R
eact
ive
HPF
Cur
rent
,i hp
,q [A
]
Time, t [ms]168 20 24 364 4012 3228
104
Figure 6.8 Experimental results: estimated active load current, reactive load
current, harmonic load current and reactive HPF current waveforms
6.5 Results – Ideal Compensation
In the previous section, we have obtained all the components of the
compensation current reference ( reffi , ). This section illustrates the effectiveness of
the estimated compensation current reference for harmonic mitigation under ideal
Time, t [ms]168 20 24 320 4012 28 364
0
-0.6-0.4-0.2
0.20.40.6
0
-3-2-1
123
Har
mon
ic L
oad
Cur
rent
,i L,
h [A
]
0
-60-40-20
204060
Rea
ctiv
e Lo
ad C
urre
nt,
i L,q [
mA
]0
-1.5-1.0-0.5
0.51.01.5
Act
ive
Load
Cur
rent
,i L,
p [A
]R
eact
ive
HPF
Cur
rent
,i hp
,q [A
]
105
compensation condition. The general arrangement of the experimental prototype
with ideal compensation condition is shown in Figure 6.9. In the ideal case, the
proposed hybrid APF is assumed to be an ideal current source. This ideal current
source is assumed to inject a compensation current ( fi ) which is equal to the
estimated compensation current reference ( reffi , ). The aim of this exercise is to
verify the correctness of compensation current reference calculation. This ensures
that the proposed idea is workable with the absence of unwanted noise. Therefore,
this exercise can be considered as a “controlled environment” type of experiment.
Figure 6.9 Experimental prototype arrangement
Applying Kirchhoff’s Current Law (KCL) at the point of common coupling
(PCC), we get
fLs iii −= (6.2)
where si is the source current after compensation, Li is the load current and fi is the
compensation current. The ideal current source is controlled to inject a
compensation current ( fi ) such that it cancels out the reactive and harmonic parts of
load current. In other words, reffi , is equivalent to the summation of qLi , and hLi , :
h,Lq,Lref,f iii += (6.3)
Nonlinear Load
is if
Distribution Source
240 Vrms(50Hz)
vs
iL
ProposedHybrid APF
PCC
Full-BridgeDiode
Rectifier
ACMains
Power Ground
106
Simulation based on (6.2) is carried out to verify the effectiveness of the reffi ,
under ideal compensation condition. Figure 6.10 shows the simulation results of this
analysis. Note that the source current ( si ) waveform is obtained mathematically by
subtracting fi from Li using (6.2). The resulting si appears to be a pure sinusoidal
waveform. This implies that si is perfectly free of harmonic distortion. The
simulation suggests that the proposed compensation scheme work very well.
Figure 6.10 Simulation results – ideal compensation condition: load current,
compensation current and source current waveforms
The simulation is proven by experiments as shown in Figure 6.11. These
results are captured from the DS1104 on-board DACs. As can be seen, the
experimental results match very closely with the simulation results shown in Figure
6.10. It can therefore be concluded that the application of extension p-q theorem to
estimate the compensation current reference for the proposed hybrid APF work very
well.
0
-1.5-1.0-0.5
0.51.01.5
Sour
ce C
urre
nt,
i s [A
]
0
-3-2-1
123
Com
pens
atio
n C
urre
nt,
i f [A
]
0
-3-2-1
123
Load
Cur
rent
,i L [
A]
Time, t [ms]168 20 24 364 4012 3228
107
Figure 6.11 Experimental results – ideal compensation condition: load current,
compensation current and source current waveforms
6.6 Results – Basic Shunt Active Power Filter Compensation
In Section 6.5, we have restricted our discussions on the compensation under
ideal condition, where we represent the proposed hybrid APF by an ideal current
source. This is to ensure that the estimated compensation current reference is
correctly calculated. However, in practice, the ideal current source is implemented
using a VSI along with an interfacing inductor ( fL ) and a DC-bus capacitor ( fC ).
The simulation results of the basic shunt APF are shown in Figure 6.12.
When the shunt APF is applied, the injected compensation current ( fi ) forces the
source current ( si ) to become a near sinusoidal waveform. It can be seen that the
source current waveform is in phase with the source voltage ( sv ) waveform,
resulting in unity power factor. Note that the source voltage, load current and source
current contain appreciable amount of high frequency harmonics. This is due to the
Time, t [ms]
0
-1.5-1.0-0.5
0.51.01.5
Sour
ce C
urre
nt,
i s [A
]
0
-3-2-1
123
Com
pens
atio
n C
urre
nt,
i f [A
]
0
-3-2-1
123
Load
Cur
rent
,i L [
A]
168 20 24 320 4012 28 364
108
unavoidable high frequency switching ripple of the compensation current and the
presence of source inductor ( sL ). When the high frequency switching ripple is
injected into the point of common coupling (PCC), it corrupts the source voltage,
load current and source current waveforms.
Figure 6.12 Simulation results – basic shunt APF compensation: source voltage,
load current, compensation current and source current waveforms
0
-3-2-1
123
Sour
ce C
urre
nt,
i s [A
]C
ompe
nsat
ion
Cur
rent
,i f [
A]
0
-6-4-2
246
Load
Cur
rent
,i L [
A]
0
-6-4-2
246
Sour
ce V
olta
ge,
v s [V
]
0
-300-200-100
100200300
Time, t [ms]168 20 24 364 4012 3228
109
The experimental results of the basic shunt APF compensation are shown in
Figure 6.13. The trend of the waveforms is consistent with the simulation. However,
from the results, it is observed that the switching ripple of the compensation current
is about 1.5 Apeak-to-peak even though the hysteresis band ( H ) is set to be 1.0 A. The
deviation in the magnitude of switching ripple is most probably due to the effect of
noise in the compensation current reference.
Figure 6.13 Experimental results – compensation with basic shunt APF: source
voltage, load current, compensation current and source current waveforms
Time, t [ms]
0
-3-2-1
123
Sour
ce C
urre
nt,
i s [A
]C
ompe
nsat
ion
Cur
rent
,i f [
A]
0
-6-4-2
246
Load
Cur
rent
,i L [
A]
0
-6-4-2
246
Sour
ce V
olta
ge,
v s [V
]
0
-300-200-100
100200300
168 20 24 320 4012 28 364
110
The ideal simulation result in Figure 6.14 illustrates the relationship between
the compensation current reference and the hysteresis band ( H ). In this case, the
compensation current reference is free of noise. The hysteresis band ( A 0.1=H )
can be simply imposed on the compensation current to form the upper ( A 5.0, +reffi )
and lower ( A 5.0, −reffi ) limits. Switches transition occurs whenever the
compensation current hits the upper or lower limit. As a result, the switching ripple
of compensation current can be maintained to be 1.0 Apeak-to-peak as shown in Figure
6.12.
Figure 6.14 Simulation result – The relationship between the compensation
current reference and hysteresis band
In the experimental work, noticeable noise currents ( noisei ) can be observed in
the compensation current reference as shown in Figure 6.15. The origin of this noise
could not be exactly detected. However, it probably due to radiated noise from high
frequency switching of power switches and inductors. In this case, the hysteresis
band ( A 0.1=H ) is imposed on the compensation current reference together with
0
-3
-2
-1
1
2
3
Com
pens
atio
n C
urre
nt R
efer
ence
,i f,r
ef [A
]
if,ref + 0.5A
H = 1.0 A
if,ref - 0.5A
Time, t [ms]168 20 24 364 4012 3228
111
noise currents to form the upper ( A 5.0|| max,, ++ noisereff ii ) and lower
( A 5.0|| min,, −− noisereff ii ) limits. As a result, a hysteresis band which is bigger than
1.0 A is formed, as shown in Figure 6.15. Consequently, the switching ripple of
compensation current will exceed the predefined hysteresis band. This fact, in our
view, is the main reason why the experimental results differ substantially from the
simulation.
Figure 6.15 Experimental result – The relationship between the compensation
current reference and hysteresis band
6.7 Results – Proposed Hybrid Active Power Filter Compensation
Section 6.6 clearly demonstrates that the harmonic distortion in the source
current is reduced significantly using the basic shunt APF. However, an appreciable
amount of switching ripple still remains in the source voltage, load current and
Time, t [ms]
0
-3
-2
-1
1
2
3
Com
pens
atio
n C
urre
nt R
efer
ence
,i f,r
ef [A
]
168 20 24 320 4012 28 364
if,ref + |inoise, max| + 0.5A
> 1.0 A
if,ref - |inoise, min| - 0.5A
inoise, max
inoise, min
112
source current waveforms. To reduce the switching ripple, a passive HPF is placed
in parallel with the shunt APF at the PCC. The HPF provides a path for the
switching ripple to flow.
Figure 6.16 shows the simulation results with the proposed hybrid APF.
When the hybrid APF is applied, the injected compensation current ( fi ) forces the
source current ( si ) to become a near sinusoidal waveform and in phase with the
source voltage waveform, resulting in unity power factor.
Comparing to the simulation result without HPF shown in Figure 6.12, the
switching ripple in the source current is greatly reduced. It can be concluded that the
HPF provides a path for the high frequency switching ripple to flow. This is evident
by the fact of that switching noise presence in the HPF current waveform. Hence,
the filtering performance of high frequency harmonics is improved by the proposed
topology.
Distortion is observed at the peak of source current waveform. This
distortion occurs when the current reference has a sharp ramp (i.e. at the peak of the
load current waveform). The compensation current tends to have a delay when
tracking sharp ramp in the current reference. This problem is probably due to the
insufficient sampling in the digitally implemented hysteresis current controller. The
finite sampling time of 10 µs for the hysteresis current controller may not be
sufficient to correct samples of the fast changing compensation current. As a result,
the effectiveness of the proposed compensation scheme is degraded and the
distortion occurs.
The simulation results are verified by that of experiments as shown in Figure
6.17. From the results, it is observed that the switching ripple of the compensation
current differs from the predefined hysteresis band ( H ). Again, the difference in
switching ripple is most probably due to the effect of noise currents in the
compensation current reference as previously described. The conformity of the
experimental results to the simulation results can be considered good, except for the
deviation in the switching ripple amplitude.
113
Figure 6.16 Simulation results – proposed topology compensation: source voltage,
load current, HPF current, compensation current and source current waveforms
0
-3-2-1
123
Sour
ce C
urre
nt,
i s [A
]C
ompe
nsat
ion
Cur
rent
,i f [
A]
0
-6-4-2
246
HPF
Cur
rent
,i hp
[A]
0
-1.5-1.0-0.5
0.51.01.5
Sour
ce V
olta
ge,
v s [V
]
0
-300-200-100
100200300
Load
Cur
rent
,i L [
A]
0
-6-4-2
246
Time, t [ms]168 20 24 364 4012 3228
114
Figure 6.17 Experimental results – proposed topology compensation: source
voltage, load current, HPF current, compensation current and source current
waveforms
Time, t [ms]
0
-3-2-1
123
Sour
ce C
urre
nt,
i s [A
]C
ompe
nsat
ion
Cur
rent
,i f [
A]
0
-6-4-2
246
Sour
ce V
olta
ge,
v s [V
]
0
-300-200-100
100200300
HPF
Cur
rent
,i hp
[A]
0
-1.5-1.0-0.5
0.51.01.5
Load
Cur
rent
,i L [
A]
0
-6-4-2
246
168 20 24 320 4012 28 364
115
6.8 Photovoltaic Energy Handling Capability
The harmonic mitigation feature of the proposed topology has been clearly
demonstrated in Section 6.7. This section presents the second feature of the
proposed topology, i.e. the PV energy handling capability. The overall experimental
setup is the same as the one used in Section 6.7. Therefore, the results obtained in
Section 6.7 can be treated as the results for the proposed topology with zero PV
power generation.
Figure 6.18 shows the simulated load current, compensation current and
source current waveforms with 250 W PV power being “injected” into the proposed
hybrid APF system. Compared to Figure 6.16, the amount of source current drawn
from the distribution source is reduced by 1.0 A. This implies that 250 W of PV
power is provided by the PV array. The remaining component of the source current
corresponds to the effect of digitally implemented hysteresis current controller as
previously described.
Figure 6.18 Simulation results – proposed hybrid APF with 250 W PV power
generations: load current, compensation current and source current waveforms
0
-3-2-1
123
Sour
ce C
urre
nt,
i s [A
]
0
-6-4-2
246
Com
pens
atio
n C
urre
nt,
i f [A
]
0
-6-4-2
246
Load
Cur
rent
,i L [
A]
Time, t [ms]168 20 24 364 4012 3228
116
These results demonstrate the PV power handling capability of the proposed
hybrid APF. It is further confirmed by the experimental results shown in Figure 6.19.
Figure 6.19 Experimental results – proposed hybrid APF with 250 W PV power
generations: load current, compensation current and source current waveforms
6.9 Harmonic Distortion Analysis
The total harmonic distortion (THD) is the most common indicator to
determine the quality of AC waveforms. Using the Fast Fourier Transform (FFT),
the harmonic spectrum of the source current under different compensation conditions
are presented. Then, the THD calculation is carried out for both of the simulation
and experimental results.
The spectrum of the source current without compensation is shown in Figure
6.20. From the spectra plot, it can be seen that the source current contains large
amount of harmonic current components of frequencies below 2 kHz. Note that the
values of the fundamental current components are equal in both simulation and
Time, t [ms]
0
-3-2-1
123
Sour
ce C
urre
nt,
i s [A
]
0
-6-4-2
246
Com
pens
atio
n C
urre
nt,
i f [A
]
0
-6-4-2
246
Load
Cur
rent
,i L [
A]
168 20 24 320 4012 28 364
117
experimental results. However, the harmonic components (i.e. 150 Hz, 250 Hz, 350
Hz, …, 2 kHz) of the experimental source current spectrum have bigger amplitude
than those obtained in the simulation. This is probably caused by the deviation of
components’ parameters between the simulation model and the experimental
prototype. However as can be observed, the trend is consistent.
Figure 6.20 Spectrum of load current – without compensation: (a) simulation
result and (b) experimental result
Figure 6.21 shows the spectrum of the source current with ideal
compensation condition. The waveform can be referred to Section 6.5. In
comparison to Figure 6.20, the source current is almost free of harmonics. The
source current is effectively compensated under ideal compensation condition. This
indicates that our proposed compensation scheme works very well without the
influence of external disturbances, such as noise.
Frequency, f [kHz]
0.6
00.20.4
0.81.01.2
2 6 8 124 10
(a)
0
Sour
ce C
urre
nt,
i s [A
]
(b)Frequency, f [kHz]
0.6
00.20.4
0.81.01.2
5.002.50 6.25 7.50 11.251.25 12.503.75 10.008.750
Sour
ce C
urre
nt,
i s [A
]
118
Figure 6.21 Spectrum of source current – with ideal compensation condition:
(a) simulation result and (b) experimental result
The spectrum of the source current with basic shunt APF compensation is
shown in Figure 6.22. The basic shunt APF successfully filters the harmonic current
components caused by the nonlinear load. Although the low frequency harmonic
components (i.e. less than 2 kHz) are filtered significantly, appreciable amount of
switching frequency harmonics still remain in the source current spectrum.
Furthermore, the introduction of blanking time probably causes the occurrence of the
odd multiple low order current harmonics (i.e. 150 Hz, 250 Hz and 350 Hz) in the
source current spectrum [66].
From Figure 6.22(a), the simulated switching frequency harmonics are
located around 7 kHz. However, the switching frequency harmonics obtained from
experiment are located around 3.5 kHz as indicated in Figure 6.22(b). The difference
can be attributed to the increase in hysteresis band size, due to the effect of noise as
explained earlier. The widening of hysteresis band results in lower switching
frequency.
Frequency, f [kHz]
0.6
00.20.4
0.81.01.2
2 6 8 124 10
(a)
0
Sour
ce C
urre
nt,
i s [A
]
(b)Frequency, f [kHz]
0.6
00.20.4
0.81.01.2
5.002.50 6.25 7.50 11.251.25 12.503.75 10.008.750
Sour
ce C
urre
nt,
i s [A
]
119
Figure 6.22 Spectrum of source current – with basic shunt APF compensation:
(a) simulation result and (b) experimental result
Figure 6.23 shows the spectrum of the source current with the proposed
hybrid APF compensation. In comparison to Figure 6.22, the source current
spectrum is almost free of switching frequency harmonic components. This implies
that the proposed hybrid APF compensates the distorted source current and
eliminates the switching frequency harmonics.
From the results shown in Figure 6.23, the source current spectrum still
contains odd multiple low order current harmonics (i.e. 150 Hz, 250 Hz and 350 Hz).
Again, these low order harmonic components are probably due to the effect of the
introduced blanking time.
Frequency, f [kHz]
0.6
00.20.4
0.81.01.2
2 6 8 124 10
(a)
0
Sour
ce C
urre
nt,
i s [A
]
(b)Frequency, f [kHz]
0.6
00.20.4
0.81.01.2
5.002.50 6.25 7.50 11.251.25 12.503.75 10.008.750
Sour
ce C
urre
nt,
i s [A
]
120
Figure 6.23 Spectrum of source current – with proposed topology compensation:
(a) simulation result and (b) experimental result
The THD calculated up to 12.5 kHz (THD12.5 kHz) for the source current
shown in Figure 6.20 to Figure 6.23 are tabulated in Table 6.1. It can be observed
that the THD12.5 kHz obtained from the experiments is in good agreement with the
simulation results. The source current THD12.5 kHz is reduced from 130.2 % to
% 5.36 with basic shunt APF. With the proposed hybrid APF, the source current
THD12.5 kHz is further reduced to 19.6 %. Thus, the harmonic filtering performance
of the proposed topology is superior compared to the basic shunt APF.
Note that the source current THD12.5 kHz is only 1.9 % under ideal
compensation condition, compared to 36.5 % with basic shunt APF and 19.6 % with
proposed hybrid APF. It can be concluded that the proposed compensation scheme
works very well in a “controlled environment”. However, its performance degraded
with noise and limitation in the digital implementation of hysteresis current
controller. In view of this, the compliance of the results obtained to the
recommended harmonics limit imposed by IEEE Standard 519 [33] is not scrutinised
further in this work.
Frequency, f [kHz]
0.6
00.20.4
0.81.01.2
2 6 8 124 10
(a)
0
Sour
ce C
urre
nt,
i s [A
]
(b)Frequency, f [kHz]
0.6
00.20.4
0.81.01.2
5.002.50 6.25 7.50 11.251.25 12.503.75 10.008.750
Sour
ce C
urre
nt,
i s [A
]
121
Table 6.1 : Calculated THD for the source current
Type of Compensation (Simulation result)
THD12.5 kHz [%]
(Experimental result) THD12.5 kHz
[%] Without compensation 106.8 130.2
Ideal compensation 1.8 1.9 Basic shunt APF 40.3 36.5 Proposed scheme 19.5 19.6
6.10 Summary
This chapter presents the results obtained from the simulations and
experiments. Several tests were conducted; their aims being to illustrate the
effectiveness of the proposed hybrid APF in harmonic mitigation. In addition, the
PV energy handling is also demonstrated. The differences between the experimental
results and simulation results are analysed and discussed. Finally, a detailed THD
analysis on source current spectrums is carried out to validate the harmonic filtering
performance of the proposed hybrid APF in comparison to a basic shunt APF.
The experimental results differ somewhat from the simulation. However, the
trends for both are quite agreeable. The discrepancies are probably due to the
following three reasons:
(1) The deviation in switching ripple is due to the effect of noise in the
compensation current reference.
(2) The introduced blanking time causes the occurrence of the odd
multiple low order current harmonics in the source current spectrums.
(3) Limitation in the digital implementation of fixed-band hysteresis
current controller degrades the harmonic filtering performance. The
sampling time (10 µs) for the hysteresis current controller may not be
effective enough to track the fast changing compensation current.
CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK
7.1 Conclusions
This thesis has presented the development of a new variation of a single-
phase hybrid APF topology, connected to a DC source that represents photovoltaic
(PV) array. Firstly, the previous research works and related literatures are reviewed
to give a better understanding of the related research area. This is followed by the
theoretical analysis and design of the proposed hybrid APF. Detailed description of
the proposed hybrid APF is provided to offer an overview of the operation principle
and its overall control system. Emphasis is given to the design of passive HPF and
compensation current reference estimation using extension p-q theorem.
Computer aided simulations are carried out using MATLAB/Simulink
simulation package. A 500 VA laboratory prototype is then constructed and tested to
realise the proposed hybrid APF. Results obtained from both the simulation and
experimental prototype are compared, analysed and verified with the theoretical
analysis. The harmonic filtering performance of the proposed hybrid APF is
validated by a detailed THD analysis. The analysed results conclude that the
proposed hybrid APF improves the harmonic filtering performance of the basic shunt
APF. Furthermore, it is capable in handling the PV energy.
123
This research work has led to two important contributions:
(1) A new variation of a single-phase hybrid APF topology for PV application is
proposed.
– It has been shown that the proposed topology effectively filters
harmonic currents less than 1 kHz and of higher frequencies.
Furthermore, the energy from the PV array is simultaneously supplied
to the load. This system configuration, to the best of the author’s
knowledge has not been proposed elsewhere.
(2) The application of extension p-q theorem is further extended to a single-phase
hybrid APF.
– Although the estimation of compensation current reference based on
extension p-q theorem is not new, this approach has not been
implemented to a single-phase hybrid APF system involving passive
HPF, shunt APF and a PV array. Using the extension p-q theorem,
the resulting equations for the current reference is simple. This will
lead to more efficient implementation in digital controller using DSP.
7.2 Recommendations for Future Work
Three recommendations for future work are described as follows:
(1) Replacement of current controller.
– It has been shown that the harmonic filtering performance of the
proposed hybrid APF is significantly affected by the selection of
current control approach. Although the hysteresis current control
approach is simplest to implement, it has been proven to be the major
cause in the degradation of the harmonic filtering performance.
124
Therefore, improvement in harmonic filtering performance can be
expected by incorporating a suitable current controller, for example:
proportional-integral (PI) controller, deadbeat controller and sliding
mode controller.
(2) Implementation of DC-bus voltage controller.
– Due to time constraint, the DC-bus voltage controller is not
implemented in this work. The proposed hybrid APF is supplied by a
DC source instead of the DC-bus capacitor. However, this approach
may not be valid if the amplitude of the source voltage is increased.
This implies that a DC source with higher output voltage level is
required, making the system unpractical. Therefore, the DC-bus
voltage controller is needed to avoid the use of additional DC source.
(3) Utilisation of maximum power point tracker.
– The energy from the sunlight can be converted to electric energy by
means of a PV array. A maximum power point tracker as reported in
[23] can be used to extract the maximum available PV energy from
the PV array. By the utilisation of maximum power point tracker, a
PV array can be used to replace the DC source in the proposed hybrid
APF.
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PUBLICATIONS
1. Tan, P. C. and Salam, Z. A New Single-Phase Two-Wire Hybrid Active
Power Filter Using Extension p-q Theorem for Photovoltaic Application.
Proceedings of the National Power and Energy Conference (PECon).
November 29-30, 2004. Malaysia, Kuala Lumpur: IEEE. 2004. 126-131.
2. Tan, P. C., Salam, Z. and Jusoh, A. A Single-Phase Hybrid Active Power
Filter Using Extension p-q Theorem for Photovoltaic Application.
Proceedings of the International Conference on Power Electronics and Drive
Systems (PEDS). November 28 – December 1, 2005. Malaysia, Kuala
Lumpur: IEEE. 2005. 1250-1255.
3. Tan, P. C., Jusoh, A. and Salam, Z. A Single-Phase Hybrid Active Power
Filter Connected to a Photovoltaic Array. Proceedings of the International
Conference on Power Electronics, Machines and Drives (PEMD). April 4-6,
2006. Ireland, Dublin: IEE. 2006. 85-89.
4. Tan, P. C., Jusoh, A. and Salam, Z. Some Design Considerations of a Single-
Phase Hybrid Active Power Filter. Proceedings of the 1st International
National Power and Energy Conference (PECon). November 28-29, 2006.
Malaysia, Putra Jaya: IEEE. 2006. in press.
APPENDIX A
DERIVATION OF MINIMUM INTERFACING INDUCTOR ( min,fL )
In practice, a controllable voltage source ( tv ) is applied to the interfacing
inductor ( fL ) terminal to establish the compensation current ( fi ) as illustrated by
Figure A.1.
Figure A.1 Equivalent circuit of shunt active power filter
Therefore, fi in the interfacing inductor is determined by tv , the source
voltage ( sv ), the interfacing inductor resistor ( fR ) and the interfacing inductor, as
given by
dtdi
LiRvv ffffst ++= (A.1)
vt
ifLf Rf
vs
137
The terminal voltage and the compensation current can be expressed in terms of their
DC and the switching ripple components as
)()( tvVtv swtt +=
)()( tiIti swff += (A.2)
where )(tvsw and )(tisw are the ripple components in tv and fi , respectively. From
(A.1) and (A.2)
dttdiLtiIRvtvV sw
fswffsswt)()]([)( +++=+ (A.3)
where
fft IRV = (A.4)
and
dttdiLtiRvtv sw
fswfssw)()()( ++= (A.5)
We know that the ripple current is high frequency component and primarily
determined by the interfacing inductor ( sL ). Therefore, sv and fR are assumed to
have negligible effects. From (A.5),
dttdiLtv sw
fsw)()( ≅ (A.6)
Figure A.2 shows the voltage ripple )(tvsw and the resulting ripple current )(tisw
using (A.6). Assumed that the voltage ripple )(tvsw is represented by the bipolar
DC-bus voltage ( CfV or CfV− ).
138
Figure A.2 Switching ripple of the compensation current
From these waveforms, the peak-to-peak switching ripple can be calculated
as
f
swsw
Ltv
dttdi )()(=
∫=∆ −2
0, )(1 swT
swf
ppsw dttvL
I
f
swCfppsw L
TVI
2, =∆ −
swf
Cfppsw fL
VI
2, =∆ − (A.7)
From (A.7), the minimum interfacing inductor ( min,fL ) can be derived as
max,,min, )(2 swppsw
Cff fI
VL
⋅∆⋅=
−
(A.8)
where max,swf maximum frequency of switching ripple and ppswI −∆ , is the peak-to-
peak switching ripple of compensation current.
swf
Cfppsw fL
VI
2, =∆ −
CfV
CfV−
swi
0 t
swsw f
T 1=
Driving voltage (vt) Switching ripple
APPENDIX B
DERIVATION OF )(tpL , )(tqL AND )(tqhp BASED ON
EXTENSION P-Q THEOREM
From (3.4), the load current is
∑∞
=
θ+ω=1
, )sin(2)(n
nnLL tnIti (B.1)
From (3.5), the source voltage is
)sin(2)( φ+ω= tVtv ss (B.2)
From (3.6), the HPF current is
)90sin(2)( °+ω= tIti hphp (B.3)
B1. Derivation of )(tpL
The instantaneous active load power can be derived as
)()()( titvtp LsL ⋅=
140
⎥⎦
⎤⎢⎣
⎡θ+ω+θ+ω⋅φ+ω= ∑
∞
=2,11, )sin(2)sin(2)sin(2
nnnLLs tnItItV
∑∞
=
θ+ωφ+ω+θ+ω⋅φ+ω=2
,11, )sin()sin(2)sin()sin(2n
nnLsLs tntIVtItV (B.4)
DC component AC component
Solve for the DC component of (B.4),
)sin()sin(2 11, θ+ωφ+ω ttIV Ls
)]sin()cos()cos()[sin()]sin()cos()cos()[sin(2 111, θω+θω⋅φω+φω= ttttIV Ls
)sin()cos()cos()sin()cos()cos()(sin2 112
1, θφωω+θφω= tttIV Ls
)sin()sin()(cos)cos()sin()cos()sin( 12
1 θφω+θφωω+ ttt
)sin()sin()(cos)cos()cos()(sin2 12
12
1, θφω+θφω= ttIV Ls
)]sin()cos()cos())[sin(cos()sin( 11 θφ+θφωω+ tt
)sin()sin()(cos)cos()cos()(sin2 12
12
1, θφω+θφω= ttIV Ls
)sin()cos()sin( 1θ+φωω+ tt
)sin()sin()(cos2)cos()cos()(sin2 12
12
1, θφω+θφω= ttIV Ls
)sin()cos()sin(2 1θ+φωω+ tt
)sin()cos()sin(2)](sin)()[sincos()cos( 122
11, θ+φωω+ω+ωθφ= ttttIV Ls
)](cos)()[cossin()sin( 221 tt ω+ωθφ+
141
)sin()cos()sin(2)](sin)(cos1)[cos()cos( 122
11, θ+φωω+ω+ω−θφ= ttttIV Ls
)](cos)(sin1)[sin()sin( 221 tt ω+ω−θφ+
))](sin)((cos1)[cos()cos( 2211, ttIV Ls ω−ω−θφ=
)sin()cos()sin(2 1θ+φωω+ tt ))](sin)((cos1)[sin()sin( 221 tt ω−ω+θφ+
)]sin()2sin()2cos(1)[cos()cos( 111, θ+φω+ω−θφ= ttIV Ls
)]2cos(1)[sin()sin( 1 tω+θφ+
)cos()cos()2cos()cos()cos( 111, θφω−θφ= tIV Ls
)]sin()cos()cos())[sin(2sin( 11 θφ+θφω+ t
)sin()sin()2cos()sin()sin( 11 θφω+θφ+ t
)cos()cos()2cos()sin()sin()cos()cos( 1111, θφω−θφ+θφ= tIV Ls
)sin()cos()2sin()cos()sin()2cos( 11 θφω+θφω+ tt
)sin()cos()2sin( 1θφω+ t
)cos()cos()2[cos()sin()sin()cos()cos( 1111, θφω−θφ+θφ= tIV Ls
)sin()cos()2sin()cos()sin()2cos( 11 θφω−θφω− tt
)]sin()cos()2sin( 1θφω− t
))sin()sin()cos())(cos(2[cos()cos( 1111, θφ−θφω−θ−φ= tIV Ls
))sin()cos()cos())(sin(2sin( 11 θφ+θφω− t
)]sin()2sin()cos()2[cos()cos( 1111, θ+φω−θ+φω−θ−φ= ttIV Ls
)2cos()cos( 111, θ+φ+ω−θ−φ= tIV Ls (B.5)
142
Therefore, the instantaneous active load power can be written as
)(tpL )2cos()cos( 11,11, θ+φ+ω−θ−φ= tIVIV LsLs
∑∞
=
θ+ωφ+ω+2
, )sin()sin(2n
nnLs tntIV
LL pp ~+= (B.6)
where
Lp )2cos()cos( 11,11, θ+φ+ω−θ−φ= tIVIV LsLs (B.7)
and
Lp~ ∑∞
=
θ+ωφ+ω=2
, )sin()sin(2n
nnLs tntIV (B.8)
Notation Lp represents the DC component and Lp~ denotes the AC component of
instantaneous active load power.
B2. Derivation of )(tqL
The instantaneous reactive load power can be obtained by multiplying the load
current with a 90°-shifted source voltage ( )(' tvs ) as follows:
)()()( ' titvtq LsL ⋅=
⎥⎦
⎤⎢⎣
⎡θ+ω+θ+ω⋅−φ+ω= ∑
∞
=2,11, )sin(2)sin(2)90sin(2
nnnLLs tnItItV o
143
⎥⎦
⎤⎢⎣
⎡θ+ω+θ+ω⋅φ+ω−= ∑
∞
=2,11, )sin(2)sin(2)cos(2
nnnLLs tnItItV
∑∞
=
θ+ωφ+ω+θ+ω⋅φ+ω−=2
,11, )sin()sin(2)sin()cos(2n
nnLsLs tntIVtItV (B.9)
DC component AC component
Solve for the DC component of (B.9),
)sin()cos(2 11, θ+ωφ+ω− ttIV Ls
)]sin()cos()cos()[sin()]sin()sin()cos()[cos(2 111, θω+θω⋅φω−φω−= ttttIV Ls
)sin()cos()(cos)cos()cos()cos()sin(2 12
11, θφω+θφωω−= tttIV Ls
)sin()sin()(sin)cos()sin()cos()sin( 12
1 θφω−θφωω− ttt
)sin()sin()(sin)cos()cos()(cos2 12
12
1, θφω−θφω−= ttIV Ls
)]sin()sin()cos())[cos(cos()sin( 11 θφ−θφωω+ tt
)sin()sin()(sin)cos()cos()(cos2 12
12
1, θφω−θφω−= ttIV Ls
)cos()cos()sin( 1θ+φωω+ tt
)cos()sin()(sin2)sin()cos()(cos2 12
12
1, θφω+θφω−= ttIV Ls
)cos()cos()sin(2 1θ+φωω− tt
)cos()cos()sin(2)](cos)()[cossin()cos( 122
11, θ+φωω−ω+ωθφ−= ttttIV Ls
)](sin)()[sincos()sin( 221 tt ω+ωθφ+
144
)](sin)(cos1)[sin()cos( 2211, ttIV Ls ω−ω+θφ−=
)](cos)(sin1)[cos()sin()cos()cos()sin(2 2211 tttt ω−ω+θφ+θ+φωω−
)]cos()cos()sin(2)]2cos(1)[sin()cos( 111, θ+φωω−ω+θφ−= tttIV Ls
)]2cos(1)[cos()sin( 1 tω−θφ+
)cos()sin()2cos()sin()cos()2cos()sin()cos( 1111, θφω−θφω−θφ−= ttIV Ls
)cos()sin()cos()cos()sin(2 11 θφ+θ+φωω− tt
)sin()cos()cos()sin( 111, θφ−θφ= Ls IV
)cos()2sin()]sin()cos()cos())[sin(2cos( 111 θ+φω−θφ+θφω− tt
)cos()2sin()sin()2cos()sin( 1111, θ+φω−θ−φω−θ−φ= ttIV Ls
)]sin()2cos()cos()2[sin()sin( 1111, θ−φω+θ+φω−θ−φ= ttIV Ls
)2sin()sin( 111, θ+φ+ω−θ−φ= tIV Ls (B.10)
Therefore, the instantaneous reactive load power can be written as
)(tqL )2sin()sin( 11,11, θ+φ+ω−θ−φ= tIVIV LsLs
∑∞
=
θ+ωφ+ω−2
, )sin()sin(2n
nnLs tntIV
LL qq ~+= (B.11)
where
Lq )2sin()sin( 11,11, θ+φ+ω−θ−φ= tIVIV LsLs (B.12)
145
and
Lq~ ∑∞
=
θ+ωφ+ω−=2
, )sin()sin(2n
nnLs tntIV (B.13)
Notation Lq represents the DC component and Lq~ denotes the AC component of
instantaneous reactive load power.
B3. Derivation of )(tqhp
The instantaneous reactive HPF power can be obtained by multiplying the HPF
current with a 90°-shifted source voltage ( )(' tvs ) as follows:
)()()( ' titvtq hpshp ⋅=
[ ])90sin(2)90sin(2 °+ω⋅−φ+ω= tItV hpso
[ ])90sin(2)cos(2 °+ω⋅φ+ω−= tItV hps
)90sin()cos(2 o+ω⋅φ+ω−= tItV hps (B.14)
DC component
It can be observed that the DC component of (B.14) is similar to the DC
component of (B.9). Therefore, the derivation of (B.10) is applicable for (B.14) by
simply replace the 1θ in (B.10) with 90°. Solve for the DC component of (B.14),
146
)90sin()cos(2 o+ωφ+ω− ttIV hps
)2sin()sin( 11 θ+φ+ω−θ−φ= tIV hps
)902sin()90sin( oo +φ+ω−−φ= tIV hps
)2cos()cos( φ+ω−φ−= tIV hps (B.15)
Therefore, the instantaneous reactive HPF power can be written as
)(tqhp )2cos()cos( φ+ω−φ−= tIV hps
hphp qq ~+= (B.16)
where
hpq )2cos()cos( φ+ω−φ−= tIV hps (B.17)
and
hpq~ = 0 (B.18)
Notation hpq represents the DC component and hpq~ denotes the AC component of
instantaneous reactive HPF power.
APPENDIX C
PROPORTIONAL CONSTANT (KP) CALCULATION USING
ENERGY-BALANCE PRINCIPLE
The proportional constant ( pK ) calculation using the energy-balance
principle is proposed by Hsu, C. Y. [12]. In this work, the energy-balance principle
is adopted for pK calculation. After pK is calculated, the integration constant ( IK )
can be determined using empirical method. The pK calculation based energy-
balance principle for the proposed hybrid APF is described as in the following.
If the reference voltage across the DC-bus capacitor is refCfV , , then the reference
energy in the capacitor will be
2,, 2
1refCffrefCf VCE = (C.1)
while the instantaneous energy in the capacitor is
)(21)( 2 tvCtE CffCf = (C.2)
Therefore, the energy loss of the capacitor in one cycle is
)()( , tEEtE CfrefCfCf −=∆
148
)(2
22, tvV
CCfrefCf
f −=
)()(2 ,, tvVtvV
CCfrefCfCfrefCf
f −+= (C.3)
Assume that the variation in DC-bus voltage within one cycle is moderate, the term
)( , tvV CfrefCf + can be approximated as
refCfCfrefCf VtvV ,, 2)( ≈+ (C.4)
)()( ,, tvVVCtE CfrefCfrefCffCf −=∆ (C.5)
Since this energy loss must be supplied by the distribution source, the peak value of
the DC-bus capacitor charging current ( CfI ) can be estimated as follows:
Cf
T
Cfs EdttItV ∆=ωω∫0
)sin()sin(2 (C.6)
Therefore
Cfs
Cf EVT
I ∆=22 (C.7)
Substituting (C.5) into (C.7) gives
)(22
,, tvVVCVT
I CfrefCfrefCffs
Cf −=
)(2
2,
, tvVVT
VCCfrefCf
s
refCff −=
149
)( , tvVK CfrefCfp −= (C.8)
where the proportional constant ( pK ) is given by
s
refCffp VT
VCK
2
2 ,= (C.9)
APPENDIX D
COEFFICIENTS ( 1C AND 0C ) DERIVATION FOR THE DIGITAL
PHASE-LOCK LOOP
From (3.16), the loop filter transfer function is
11)(1
−−
=z
azzH (D.1)
From (3.17), the DCO transfer function is
1)(2
−=
zczzH (D.2)
The derivation of digital PLL closed-loop transfer function is given by
1
1
)(2)(11)(2)(1)( −
−
⋅⋅+⋅⋅
=zzHzH
zzHzHzH
1
1
1111
111
−
−
−⋅
−−
+
⋅−
⋅−−
=z
zcz
zaz
zzcz
zaz
)()12( 2 caczzzcacz
−++−−
=
151
)1()2(2 czaczcacz
−+−+−
= (D.3)
Based on the closed-loop transfer function in (D.3), one can easily tell that is
a second-order system. In control system theory, the transfer function of the second-
order system can often be written in a general format as
))(()()(
01 zzzzzNzH−−
= (D.4)
where 0z and 1z are two poles of the system in z-domain.
Based on transfer function in (D.4), a characteristic equation of a discrete
time system is defined as
01012
01 )())(()( zzzzzzzzzzz ++−=−−=∆ (D.5)
Defining 1C and 0C to be coefficients of the characteristics equation in (D.5)
)( 011 zzC +−=
010 zzC = (D.6)
Then, the characteristic equation can be re-written in a simplified format as
012)( CzCzz ++=∆ (D.7)
Normally the output responses of a discrete-time control system are also
functions of continuous-time variable t. Therefore, the goal is to map the z-domain
second-order system model in (D.3) to meet the performance requirements specified
by damping ratio ( ζ ) and undamped frequency ( nω ) in corresponding s-domain
second-order model given by
152
22
2
2)(
nn
n
sssH
ω+ζω+ω
= (D.8)
By solving the roots of the characteristics equation in (D.8), two poles ( 0s and 1s ) of
the system can be derived as
ω+σ−=ζ−ω+ζω−= jjs nn2
0 1
ω−σ−=ζ−ω−ζω−= jjs nn2
1 1 (D.9)
where σ is defined as the damping factor and ω is defined as damped frequency.
By definition of discrete-time transformation [68], two poles of this system in
z-domain can be mapped from the poles in s-domain in the following way
)1(0
20 ζ−ω+ζω−== snsns TjTTs eez
)1(1
21 ζ−ω−ζω−== snsns TjTTs eez (D.10)
where sT is the sampling period of the discrete system. Substitutes 0z and 1z in
(D.10) into (D.6), coefficients 0C and 1C of the characteristic equation (D.7) can be
derived in a format that is described by parameter ζ and nω as
snTeC ζω−= 2
0
)1cos(2 21 ζ−ω−= ζω−
snT TeC sn (D.11)
Now, a characteristic equation coefficients ( 0C and 1C ) are derived by mapping the
poles in a continuous-time domain system.
APPENDIX E
)(sZhp AND )(sH cds DERIVATION FOR THE PASSIVE HIGH-PASS
FILTER
E.1 Derivation of HPF Impedance Transfer Function ( )(sZhp )
Figure E.1 shows the layout of the second-order damped series resonant type
high-pass filter (HPF). It consists of a capacitor ( hpC ), an inductor ( hpL ) and an
inductor bypass resistor ( hpR ).
Figure E.1 Layout of the second-order damped series resonant type HPF
Using a little algebra, the HPF impedance transfer function in (3.27) can be derived
as following:
)//(1)( hphphp
hp RsLsC
sZ +=
sLhpRhp
sChp
1
Zhp
154
⎟⎟⎠
⎞⎜⎜⎝
⎛
+
⋅+=
hphp
hphp
hp RsLRsL
sC1
hphp
hphp
hp RsLRsL
sC ++=
1
)()( 2
hphphp
hphphphphp
RsLsCRLCsRsL
+
++=
)1(
2
+
++=
hp
hphphp
hphphphphp
LR
sRsC
RsLRLCs
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
++⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
=
1
11
2
hp
hphphp
hp
hp
hphp
hp
LR
sRsC
LR
s
LC
sR
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
+⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
⋅
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+
= 11
11
1
12
hphphp
hphphphp
hp
hp
hp
LC
s
LC
RLC
s
LR
ss
C
⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎟⎟
⎠
⎞⎜⎜⎝
⎛ω
+⎟⎟⎠
⎞⎜⎜⎝
⎛ω
⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛+
ω
= 11
1 0
2
0
sQ
s
ss
A
p
(E.1)
155
where
hpCA 1=
hphpCL1
0 =ω
hp
hpp L
R=ω
hp
hphp L
CRQ = (E.2)
In (E.1), A is the gain coefficient, 0ω is the series resonant frequency, pω is the
pole frequency and Q is the quality factor.
E.2 Derivation of Source Current to Injected Current Transfer Function
( )(sH cds )
From (3.29), the source current to injected current transfer function is
)()(
)( ,
sisi
sHh
hscds =
)()()(
sZsZsZ
shp
hp
+= (E.3)
In (E.3), the HPF impedance transfer function ( )(sZ hp ) and source impedance
transfer function ( )(sZ s ) are given by
156
⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎟⎟
⎠
⎞⎜⎜⎝
⎛ω
+⎟⎟⎠
⎞⎜⎜⎝
⎛ω
⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛+
ω
= 11
1
)(0
2
0
sQ
s
ss
AsZ
p
hp
ss sLsZ =)( (E.4)
Substituting (E.4) into (E.3),
shphphphp
hphphphphp
hphphphp
hphphphphp
cds
sLRsCLCs
RsLRLCs
RsCLCsRsLRLCs
sH
+⎟⎟⎠
⎞⎜⎜⎝
⎛
+
++
⎟⎟⎠
⎞⎜⎜⎝
⎛
+
++
=
2
2
2
2
)(
⎟⎟⎠
⎞⎜⎜⎝
⎛
+
++++
⎟⎟⎠
⎞⎜⎜⎝
⎛
+
++
=
hphphphp
hphphphpshphphphphp
hphphphp
hphphphphp
RsCLCsRsCLCssLRsLRLCs
RsCLCsRsLRLCs
2
22
2
2
)()(
⎟⎟⎠
⎞⎜⎜⎝
⎛
+
++++
⎟⎟⎠
⎞⎜⎜⎝
⎛
+
++
=
hphphphp
hphpshphpshphphphphp
hphphphp
hphphphphp
RsCLCsRCLsLCLsRsLRLCs
RsCLCsRsLRLCs
2
232
2
2
)()(
))(23
2
hphphpshphphphps
hphphphphp
RsLLLRCsLCLsRsLRLCs
++++
++=
⎟⎟⎠
⎞⎜⎜⎝
⎛++++
++=
1)(23
2
hp
hphpshp
hp
hphpshp
hphphphphp
RL
sLLCsR
LCLsR
RsLRLCs
157
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
++⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+
+
+⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
=
1
)(1
11
11
2
3
2
hp
hp
hpshphp
hphps
hphphp
hphphphp
LR
s
LLC
sR
LCLs
LC
s
LC
RLC
s
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛+
ω+⎟⎟
⎠
⎞⎜⎜⎝
⎛ω
+
+⎟⎟⎠
⎞⎜⎜⎝
⎛ω
+⎟⎟⎠
⎞⎜⎜⎝
⎛ω
=
1
11
2
1
3
0
2
0
php
hphps ssR
LCLs
sQ
s
(E.5)
In (E.5),
hphpCL1
0 =ω
)(1
1hpshp LLC +
=ω
hp
hpp L
R=ω
hp
hphp L
CRQ = (E.6)
where 0ω is the series resonant frequency, 1ω is the parallel resonant frequency, pω
is the pole frequency and Q is the quality factor.
APPENDIX F
AC SMOOTHING INDUCTOR (Lsmooth), INTERFACING INDUCTOR (Lf)
AND HPF INDUCTOR (Lhp) DESIGN
Inductor is an indispensable part of most power electronic converters.
However, they are not commercially available in a wide range of properties but are
usually designed and constructed for the particular application. In this situation, the
design procedures for the inductors [72] used in this work are presented as a general
design guideline. A more complete appreciation of their capabilities and limitations
can only be gained through experience and experimentation.
F.1 General Design Procedure for Inductor
Step 1 Assemble design variables
The design variables consist of the following parameters:
(1) Inductance value, L (H)
(2) Rated DC current, IDC (A)
(3) Rated rms current, Irms (A)
(4) Operating frequency, f (Hz)
These values are found via the design calculations for the specific power electronic
converter circuit in which the inductor is to be used.
159
Step 2 Specification of winding parameters
In this work, the conductor windings of inductor is made from copper
because of it high conductivity. Round wire or Litz wire can be chosen as the type of
winding conductor. Selection of the conductor type will depend on the operating
frequency and the important of eddy current loss in the winding. After the conductor
type is selected, the allowable current density can now be estimated (e.g. 300 circular
mils/A). The wire area is chosen on the basic of a safe current density. The total
circular mil area of the wire (A) is then calculated as
)300(rmsIA = circular mils (F.1)
From the wire table in Figure F.1, the wire having the closest circular mil area to the
calculated value will be selected. And from the wire table, the diameter of the
selected wire is D. The wire area per turn (At) can then be calculated by assuming
wire area per turn is 2D rather than 42Dπ .
Step 3 Choose core material, shape and size
The core material, shape and size are chosen next. The choice of material
will be influenced by the operating frequency. Variety of core material like magnetic
steels, powdered iron cores, amorphous metallic glasses and ferrite cores can be
considered. In this work, the ferrite material 3C90 manufactured by Ferroxcube is
chosen as the core material because it is able to operate at frequency as high as 200
kHz. The choice of core shape, that is E-core, U-core, toroid and so forth, will
depend on cost, availability, and ease of making the windings on the chosen core
shape. The selected core shape is the E-E core type which is suitable for high power
application and easy coil winding.
The core size is related to the product of the core winding area (Ac) and the
effective area (Ae) of its magnetic path. For any inductor, the voltage across it may
be defined either in terms of the rate of change of current in it or the rate of change of
flux in its core. Or
160
810)()( −φ== dtdNdtdiLE (F.2)
from which
88 10)(10)( −− =φ= didBNAdtdNL e (F.3)
where E is in volts, L is in henrys for N in turns, Ae in square centimetres, dB in gauss,
and di in amperes. Now, dB = Bmax for di = Imax. Then
max
8max 10)(
NBLIAe
+
= (F.4)
But the core winding area (Ae) must be chosen to accommodate the required number
of turns at the specified safe-current density and the fraction of the total core winding
area usable. Thus, assume only 75% of the core winding area Ac is usable and
assume N turns of wire, whose area per turns is At. Then
ct ANA 75.0=
or
75.0t
cNAA = (F.5)
with Ac and At in square centimetres. Multiplying (F.4) and (F.5)
)75.0(10)(
max
8max
NBNALI
AA tce
+
=
max
8max 10)(33.1
BALI t
+
= (F.6)
161
In (F.6), as soon as the wire area is specified (on the basic of safe operating
current density), all terms on the right-hand side are specified and the product AeAc is
fixed. A core with the required product is then selected from the vendor’s datasheet.
Once this core is selected, Ae is determined from the datasheet and from (F.4), N is
calculated, since all other parameters in it are already fixed.
Step 4 Specification of the air gap length
The design of a gapped core is to avoid core saturation under conditions of a
DC current. The DC current produces magnetic bias close to the top of the hysteresis
loop and prevents it from being able to sustain a voltage when the AC voltage is in
such a direction as to move it further up the loop toward saturation. This can be
clearly seen in Figure F.2. Before the air gap is introduced, a given DC current, IDC,
forces the operating point in H to
lNIH DCπ
=4.0 (F.7)
where H is in oersteds for N in turns, l (magnetic path length) in centimetres. If this
value of H set operating point at P1, then the quiescent operating point in B is B1.
Any AC voltage applied to the inductor can only produce a B in the positive half
cycle of twice (Bsaturation – B1) before the core saturates. If the voltage
Saturation is avoided by introducing an air gap in series in the magnetic path.
The effect of this is to flatten out the hysteresis loop as shown in Figure F.2. The
same DC current sets the operating point in B, further down from saturation to a
point like P2. Now, in the positive half cycle, the Bsaturation – B2 can be sustained
across the inductor before it saturates.
The fundamental relation in magnetic circuits is Ampere’s law:
NIdlH π=∫ 4.0 (F.8)
162
This states the line integration around a closed loop of length l of the dot product of
the field intensity H and element of length dl is equal to 0.4πNI, where NI is the
ampere turns enclosed by the loop. When an air gap is introduced in the length path,
the field intensity is constant and parallel across the air gap. Thus
NIlHlHdlH aaii π=+=∫ 4.0 (F.9)
where Hi is the core field intensity and Ha is the air gap field intensity. If the air gap
is narrow and there is no bulging of fringing of magnetic flux as it across the air gap,
then the flux density in the core, Bi, is equal to that in air, Ba. Then, Hi = Bi / µi
where µi is the average core permeability and Ha = Ba / µa = Bi, since Ba = Bi and
permeability of air, µa is unity. Then
NIlBlB aiiii π=+µ 4.0
or
aii
i
aiii ll
NIll
NIBµ+µπ
=+µπ
=4.04.0 (F.10)
(F.10) states that for a given NI product, the flux density in the core with an air gap
of length la is smaller than with no air gap in the ratio aii
i
lllµ+
.
In (F.10), the maximum flux density in core, Bi, will occur at maximum I in
the inductor. This maximum I is the maximum at the top of the current ramp. In
(F.9), Bi will be set to prevent the core from rising on the slow knee of its hysteresis
loop at maximum temperature. Thus, as soon as the number of turns N and core
length li are chosen, (F.10) permits selecting air gap length.
163
Figu
re F
.1
Mag
netic
wire
tabl
e (C
ourte
sy B
elde
n C
orp.
)
164
Figure F.2 Typical relationship between magnetic flux density and field strength
F.2 AC Smoothing Inductor (Lsmooth) Design
Step 1 Assemble design variables
The design variables consist of the following parameters:
Inductance value, L = 1.15 mH
Rated DC current, IDC = 0 A
Rated rms current, Irms = 5 A
Operating frequency, f = 100 kHz
Step 2 Specification of winding parameters
The round wire made from copper is chosen as the winding conductor. The
wire area is chosen on the basic of a safe current density. As a first guess, a current
density of 300 circular mils/A is chosen. The total circular mil area of the wire (A) is
then calculated as
)300(rmsIA =
B (Flux density)
H (Field strength)
B
Hysteresis loop ofgapless core
Flattened hysteresisloop of gapped core
P1
P2
B1
B2
Bsaturation
-BsaturationBias in oersteds
165
1500)300(5 == circular mils (F.11)
From the wire table in Figure F.1, the wire having the closest circular mil area to this
is No. 18 wire (1620 circular mils). And from the wire table, the diameter of this
wire is 0.043 in/0.11 cm. In this work, the copper wire with diameter (D) of 0.125
cm is selected due to the availability. Assuming wire area per turn is 2D rather than
42Dπ , the wire area per turn (At) can be calculated as
2DAt =
01563.0)125.0( 2 == cm2 (F.12)
Step 3 Choose core material, shape and size
The selected core material and shape are as following:
Core material : 3C90 (ferrite)
Core shape : E-E core
In (F.6), take 3000max =B G, which is safely below saturation for ferrite
material 3C90 ( 3400=saturationB G). The required ce AA product for the core is
)75.0(10)(33.1
max
8max
BALIAA t
ce
+
=
3000
10)01563.0)(520)(1015.1(33.1 83 +− ⋅+×=
633.5= cm4 (F.13)
Looking through a ferrite core vendor’s catalogue [71], a ferrite core Ferroxcube type
ETD59 is found to have the required ce AA product. Its eA is quoted as 3.68 cm2; its
166
cA is 3.66 cm2. This gives an ce AA product of 13.4688 cm4, which is big enough for
ease of making the windings.
The number of required turns is calculated from (F.4):
max
8max 10)(
BALIN
e
+
=
646.73)3000)(68.3(
)10)(07.7)(1015.1( 83
=×
=+−
74≅ turns (F.14)
The ETD59 bobbin has cA of 3.66 cm2. The area per turn of wire is then
0495.07466.3 = cm2, and its diameter is 222.00495.0 = cm. This calculated
value of diameter is bigger than the diameter of the selected copper wire ( 125.0=D
cm). The ETD59 bobbin can thus handle the required 74 turns of copper wire with
125.0=D cm at the specified current density of 300 circular mils/A.
Step 4 Specification of the air gap length
Now, the air gap length ( al ) must be specified from (F.10). In that equation,
iµ is the permeability of the core material. The chosen Ferroxcube 3C90 material
has a iµ of 2300 [71]. Then for a maxB of 3000 G, 707.0max =I A, and 74=N
turns, from (F.10),
i
iaii B
NIll µπ=µ+
4.0
)3000()2300)(07.7)(74(4.0 π
= 043.504= cm (F.15)
167
Since the ETD59 bobbin has a mean path length il of 13.9 cm, from (F.15),
043.504=µ+ aii ll
Thus,
2131.02300
9.13043.504=
−=al cm (F.16)
The ferrite core comes in two halves. Thus, if a spacer is located between the two
halves, the air gap is actually twice the spacer thickness. Since this spacer is in series
with four “legs” of the ferrite core, the spacer thickness must then be
05328.042131.0 = cm. This completes the design of the AC smoothing inductor.
F.3 Interfacing Inductor (Lf) Design
The interfacing inductor (Lf) consists of four inductors connected in series,
2.5 mH each, to give a total inductance of 10 mH. The reason for not using one 10
mH inductor as in the simulation is because there is no suitable bobbin and ferrite
core available that meet the targeted design specifications. This section will describe
the design of the 2.5 mH inductor.
The design variables consist of the following parameters:
Inductance value, L = 2.5 mH
Rated DC current, IDC = 0 A
Rated rms current, Irms = 5 A
Operating frequency, f = 100 kHz
The design parameters of the 2.5 mH inductor can be readily calculated following the
calculation example given by (F.11) – (F.16). Table F.1 shows the specification of
the 2.5 mH inductor.
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Table F.1 : 2.5 mH inductor specification
Core
material
Core
type
Number
of turns
N
(turns)
Saturation flux
density
Bsat
(G at 100 ˚C)
Wire
type
Air gap
length
la
(cm)
Inductance
L
(mH)
3C90 ETD59 160 3400 No. 18 0.468 2.5
F.4 High-Pass Filter Inductor (Lhp) Design
The HPF inductor ( hpL ) consists of a 1.76 mH inductor. This section will
describe the design of Lhp.
The design variables consist of the following parameters:
Inductance value, L = 1.76 mH
Rated DC current, IDC = 0 A
Rated rms current, Irms = 5 A
Operating frequency, f = 100 kHz
The design parameters of hpL can be readily calculated following the calculation
example given by (F.11) – (F.16). Table F.2 shows the specification of hpL .
Table F.2 : hpL specification
Core
material
Core
type
Number
of turns
N
(turns)
Saturation flux
density
Bsat
(G at 100 ˚C)
Wire
type
Air gap
length
la
(cm)
Inductance
L
(mH)
3C90 ETD59 113 3400 No. 18 0.329 1.76
APPENDIX G
SCHEMATIC OF IGBT GATE DRIVER CIRCUIT
G.1 Opto-Coupler Circuit
Figure G.1 Schematic of opto-couple
G.2 Gate Logic and Blanking Time Circuit
Figure G.2 Schematic of gate logic and blanking time
R15
10RUpper Leg
R14270R
R13270R
VCC3
OUT1
C140.1uF
Lower leg
VCC
C150.1uF
OUT2
Jout
CON4
1234
U10
HCPL 3150
1234 5
678
N/CANODKOTODN/C VEE
VoVo
VCC
VEE2
VCC
U9
HCPL 3150
1234 5
678
N/CANODKOTODN/C VEE
VoVo
VCC
VEE3
R16
10R
VCC2
JP2
4 Header 1234
Upper Leg
R10
270R
R8
10k
D9
D1N4148
U7B
74ACT08
4
56
R9
20k
VCC
R7
10k
U7A
74ACT08
1
23
C10
0.01uF
U8A
74ACT14
1 2
input1
R12
270R
U8B
74ACT14
3 4
U8E
74ACT14
11 10
JP1
2 Header12
en1
R610K
C130.001uF
R510K
C11
0.01uFC12
0.001uF
VCC
Vin+12V
Lower leg
D10
D1N4148
R11
20k
170
G.3 Isolated Push-Pull DC-DC Power Supply Circuit
Figu
re G
.3
Isol
ated
pus
h-pu
ll D
C-D
C p
ower
supp
ly
APPENDIX H
PROGRAM LISTING FOR THE DS1104 DSP CONTROLLER BOARD
H.1 DS1104 Source Code Listing
/************************************************************************** TITLE : SINGLE-PHASE HYBRID ACTIVE POWER FILTER Writer : Tan Perng Cheng Power Electronics and Drives Group, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Malaysia. Date of Creation : 1st. August 2004 Last Update : 1st. November 2005 DESCRIPTION : This program generates the gating signals to the single-phase hybrid APF to compensate the reactive and harmonic currents generated by a nonlinear load. In addition, a DC source power handling function is added in this program to illustrate the DC source power handling capability of the proposed scheme. This program is dedicated to run on DS1104 DSP controller board. **************************************************************************/ /************************************************************************** Include Files - Brtenv.h is the header file for DS1104 **************************************************************************/ #include <Brtenv.h> /* DS1104 header file */ #include <stdlib.h> /* declares calloc */ #include <io1104.h> /* I/O header file */ #include <stdio.h> #include <math.h>
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/************************************************************************** Timer 0 and Timer 1 Period Setting **************************************************************************/ #define ST0 10.0e-6 /* Timer 0 = 10e-6 s */ #define ST1 100.0e-6 /* Timer 1 = 100e-6 s */ /************************************************************************** Variables for ControlDesk's Instruments **************************************************************************/ Float64 exec_time0, exec_time1; /* Execution time */ Float64 pi = 3.14159265358979; /* Define value of pi */ int n1, n2; /* Counter */ UInt32 mask_set = 0; volatile int iselect = 0; Float64 iref_out; /* DAC output signal select */ /* System Fault Protection */ int enable1 = 1; /* Overrun & DSP error */ volatile int enable2 = 0; /* User control */ int enable3 = 0; /* Main fault detection */ int enable4 = 0; /* DC-bus capacitor voltage fault */ /* ADC Input Signals */ Float64 vsource_adc1; /* ADC Ch.5: source voltage */ Float64 iload_adc1; /* ADC Ch.7: load current */ Float64 ihpf_adc1; /* ADC Ch.6: HPF current */ Float64 vcap_adc; /* ADC Ch.2: DC-bus voltage */ Float64 icomp_adc; /* ADC Ch.8: Actual comp. current */ /* Conditioned ADC Input Signals */ Float64 vsource_adc; /* Conditioned ADC Ch.5 */ Float64 iload_adc; /* Conditioned ADC Ch.7 */ Float64 ihpf_adc; /* Conditioned ADC Ch.6 */ /* DC Source Current */ Float64 ipv_ref = 0.000; volatile Float64 ipv = 0.000; /* Hysteresis Current Controller */ Float64 i_hysteresis; /* Compensation Current References */ Float64 ip_load; Float64 iq_load; Float64 ihpw_load; Float64 iq_hpf; Float64 ic_load; Float64 is_compensated; Float64 ic_ref; Float64 ic_ref1; Float64 ic_ref2;
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Float64 sine_ref_syn; Float64 sine_ref_90deg; /************************************************************************** Parameters of routine compensating_current_ref() **************************************************************************/ /*------------------------------------------------------------------------- Parameters for subroutine delay8() -------------------------------------------------------------------------*/ Float64 *w8; int D8 = 50; /*------------------------------------------------------------------------- Parameters of subroutine delay9() -------------------------------------------------------------------------*/ Float64 *w9; int D9 = 43; /*------------------------------------------------------------------------- Parameters of subroutine delay10() -------------------------------------------------------------------------*/ Float64 *w10; int D10 = 99; /************************************************************************** Parameters of routine extension_pq_theorem() **************************************************************************/ Float64 vsource_adc_90deg; Float64 Pload; Float64 Pload_dc; Float64 Qload; Float64 Qload_dc; Float64 Qhpf; Float64 Qhpf_dc; /*------------------------------------------------------------------------- Parameters of subroutine delay4() -------------------------------------------------------------------------*/ Float64 *w4; int D4 = 50; /*------------------------------------------------------------------------- Parameters of subroutine fir5() -------------------------------------------------------------------------*/ Float64 *a5, *b5, *w5; int M5,L5;
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/*------------------------------------------------------------------------- Parameters of subroutine fir6() -------------------------------------------------------------------------*/ Float64 *a6, *b6, *w6; int M6,L6; /*------------------------------------------------------------------------- Parameters of subroutine fir7() -------------------------------------------------------------------------*/ Float64 *a7, *b7, *w7; int M7,L7; /*------------------------------------------------------------------------- Parameters of subroutine fir11() -------------------------------------------------------------------------*/ Float64 *a11, *b11, *w11; int M11,L11; /*------------------------------------------------------------------------- Parameters of subroutine fir12() -------------------------------------------------------------------------*/ Float64 *a12, *b12, *w12; int M12,L12; /*------------------------------------------------------------------------- Parameters of subroutine fir13() -------------------------------------------------------------------------*/ Float64 *a13, *b13, *w13; int M13,L13; /************************************************************************** Parameters of routine phase_lock_loop() **************************************************************************/ Float64 y1_a; Float64 y1_b; Float64 y1_c; Float64 y1_d; Float64 y1_e; Float64 vs_rms; Float64 vs_rms1; Float64 vpll; Float64 sine_ref; /*------------------------------------------------------------------------- Parameters of subroutine integ1() -------------------------------------------------------------------------*/ Float64 *w2, y1_c1, y1_c2;
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/*------------------------------------------------------------------------- Parameters of subroutine fir1() -------------------------------------------------------------------------*/ Float64 *a1, *b1, *w1; int M1,L1; /*------------------------------------------------------------------------- Parameters of subroutine pll() -------------------------------------------------------------------------*/ Float64 *a3, *b3, *w3; int M3,L3; /************************************************************************** Subroutine listing for routine compensating_current_ref() **************************************************************************/ /*------------------------------------------------------------------------- Subroutine delay8() - 90 degree phase shifting -------------------------------------------------------------------------*/ Float64 delay8(x) Float64 x; int i; Float64 z8; z8 = w8[D8]; w8[0] = x; for (i = D8; i>=1; i--) w8[i] = w8[i-1]; return z8; /*------------------------------------------------------------------------- Subroutine delay9() - source voltage synchronisation -------------------------------------------------------------------------*/ Float64 delay9(x) Float64 x; int i; Float64 z9; z9 = w9[D9]; w9[0] = x;
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for (i = D9; i>=1; i--) w9[i] = w9[i-1]; return z9; /*------------------------------------------------------------------------- Subroutine delay10() - phase delay compensation -------------------------------------------------------------------------*/ Float64 delay10(x) Float64 x; int i; Float64 z10; z10 = w10[D10]; w10[0] = x; for (i = D10; i>=1; i--) w10[i] = w10[i-1]; return z10; /************************************************************************** Subroutine listing for routine extension_pq_theorem() **************************************************************************/ /*------------------------------------------------------------------------- Subroutine delay4() - delay vsource_adc with 90 degree -------------------------------------------------------------------------*/ Float64 delay4(x) Float64 x; int i; Float64 z; z = w4[D4]; w4[0] = x; for (i = D4; i>=1; i--) w4[i] = w4[i-1];
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return z; /*------------------------------------------------------------------------- Subroutine fir5() - 2nd-order LPF, fc = 5 Hz, G = 0.5 -------------------------------------------------------------------------*/ Float64 fir5(x) Float64 x; int i, K; Float64 y = 0; M5 = 2; /* M-th degree numerator */ L5 = 2; /* L-th degree numerator */ K = (L5 <= M5) ? M5 : L5; /* K = max(M,L) */ w5[0] = x; /* Current input sample */ a5[0] = 1.0; /* Filter coefficients */ a5[1] = -1.995551847; a5[2] = 0.995561717; b5[0] = 2.467776264e-6; b5[1] = 2 * 2.467776264e-6; b5[2] = 2.467776264e-6; for (i=1; i<=M5; i++) w5[0] -= a5[i] * w5[i]; /* Input adder */ for (i=0; i<=L5; i++) y += b5[i] * w5[i]; /* Output adder */ for (i=K; i>=1; i--) w5[i] = w5[i-1]; /* Reverse-order updating */ return y; /* current output sample */
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/*------------------------------------------------------------------------- Subroutine fir6() - 2nd-order LPF, fc = 5 Hz, G = 0.5 -------------------------------------------------------------------------*/ Float64 fir6(x) Float64 x; int i, K; Float64 y = 0; M6 = 2; /* M-th degree numerator */ L6 = 2; /* L-th degree numerator */ K = (L6 <= M6) ? M6 : L6; /* K = max(M,L) */ w6[0] = x; /* Current input sample */ a6[0] = 1.0; /* Filter coefficients */ a6[1] = -1.995551847; a6[2] = 0.995561717; b6[0] = 2.467776264e-6; b6[1] = 2 * 2.467776264e-6; b6[2] = 2.467776264e-6; for (i=1; i<=M6; i++) w6[0] -= a6[i] * w6[i]; /* Input adder */ for (i=0; i<=L6; i++) y += b6[i] * w6[i]; /* Output adder */ for (i=K; i>=1; i--) w6[i] = w6[i-1]; /* Reverse-order updating */ return y; /* Current output sample */
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/*------------------------------------------------------------------------- Subroutine fir7() - 2nd-order LPF, fc = 5 Hz, G = 0.5 -------------------------------------------------------------------------*/ Float64 fir7(x) Float64 x; int i, K; Float64 y = 0; M7 = 2; /* M-th degree numerator */ L7 = 2; /* L-th degree numerator */ K = (L7 <= M7) ? M7 : L7; /* K = max(M,L) */ w7[0] = x; /* Current input sample */ a7[0] = 1.0; /* Filter coefficients */ a7[1] = -1.995551847; a7[2] = 0.995561717; b7[0] = 2.467776264e-6; b7[1] = 2 * 2.467776264e-6; b7[2] = 2.467776264e-6; for (i=1; i<=M7; i++) w7[0] -= a7[i] * w7[i]; /* Input adder */ for (i=0; i<=L7; i++) y += b7[i] * w7[i]; /* Output adder */ for (i=K; i>=1; i--) w7[i] = w7[i-1]; /* Reverse-order updating */ return y; /* Current output sample */
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/*------------------------------------------------------------------------- Subroutine fir11() - 2nd-order LPF, fc = 2 kHz, G = 0.5 -------------------------------------------------------------------------*/ Float64 fir11(x) Float64 x; int i, K; Float64 y = 0; M11 = 2; /* M-th degree numerator */ L11 = 2; /* L-th degree numerator */ K = (L11 <= M11) ? M11 : L11; /* K = max(M,L) */ w11[0] = x; /* Current input sample */ a11[0] = 1.0; /* Filter coefficients */ a11[1] = -0.368188532; a11[2] = 0.1956396086; b11[0] = 0.2068627691; b11[1] = 2 * 0.2068627691; b11[2] = 0.2068627691; for (i=1; i<=M11; i++) w11[0] -= a11[i] * w11[i]; /* Input adder */ for (i=0; i<=L11; i++) y += b11[i] * w11[i]; /* Output adder */ for (i=K; i>=1; i--) w11[i] = w11[i-1]; /* Reverse-order updating */ return y; /* Current output sample */
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/*------------------------------------------------------------------------- Subroutine fir12() - 2nd-order LPF, fc = 2 kHz, G = 0.5 -------------------------------------------------------------------------*/ Float64 fir12(x) Float64 x; int i, K; Float64 y = 0; M12 = 2; /* M-th degree numerator */ L12 = 2; /* L-th degree numerator */ K = (L12 <= M12) ? M12 : L12; /* K = max(M,L) */ w12[0] = x; /* Current input sample */ a12[0] = 1.0; /* Filter coefficients */ a12[1] = -0.368188532; a12[2] = 0.1956396086; b12[0] = 0.2068627691; b12[1] = 2 * 0.2068627691; b12[2] = 0.2068627691; for (i=1; i<=M12; i++) w12[0] -= a12[i] * w12[i]; /* Input adder */ for (i=0; i<=L12; i++) y += b12[i] * w12[i]; /* Output adder */ for (i=K; i>=1; i--) w12[i] = w12[i-1]; /* Reverse-order updating */ return y; /* Current output sample */
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/*------------------------------------------------------------------------- Subroutine fir13() - 2nd-order LPF, fc = 2 kHz, G = 0.5 -------------------------------------------------------------------------*/ Float64 fir13(x) Float64 x; int i, K; Float64 y = 0; M13 = 2; /* M-th degree numerator */ L13 = 2; /* L-th degree numerator */ K = (L13 <= M13) ? M13 : L13; /* K = max(M,L) */ w13[0] = x; /* Current input sample */ a13[0] = 1.0; /* Filter coefficients */ a13[1] = -0.368188532; a13[2] = 0.1956396086; b13[0] = 0.2068627691; b13[1] = 2 * 0.2068627691; b13[2] = 0.2068627691; for (i=1; i<=M13; i++) w13[0] -= a13[i] * w13[i]; /* Input adder */ for (i=0; i<=L13; i++) y += b13[i] * w13[i]; /* Output adder */ for (i=K; i>=1; i--) w13[i] = w13[i-1]; /* Reverse-order updating */ return y; /* Current output sample */ /************************************************************************** Subroutine listing for routine phase_lock_loop() **************************************************************************/ /*------------------------------------------------------------------------- Subroutine reset_integ1() - avoid saturation of integral, integ1() -------------------------------------------------------------------------*/
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reset_integ1() n2++; if(n2 == 200) w2[0] = 0; /* Reset integ1() */ y1_c1 = y1_c; n2 = 0; else if(n2 == 100) y1_c2 = y1_c; /*------------------------------------------------------------------------- Subroutine integ1() - integrate with Euler -------------------------------------------------------------------------*/ Float64 integ1(x) Float64 x; w2[0] = w2[0] + x * ST1; /* Integrate with Euler */ return w2[0]; /*------------------------------------------------------------------------- Subroutine fir1() - 2nd-order LPF, fc = 100 Hz, G = 0.5 -------------------------------------------------------------------------*/ Float64 fir1(x) Float64 x; int i, K; Float64 y = 0; M1 = 2; /* M-th degree numerator */ L1 = 2; /* L-th degree numerator */ K = (L1 <= M1) ? M1 : L1; /* K = max(M,L) */ w1[0] = x; /* Current input sample */ a1[0] = 1.0; /* Filter coefficient */ a1[1] = -1.91109177; a1[2] = 0.914879321; b1[0] = 9.46887707e-4; /* Filter coefficient */ b1[1] = 2 * 9.46887707e-4; b1[2] = 9.46887707e-4;
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for (i=1; i<=M1; i++) w1[0] -= a1[i] * w1[i]; /* Input adder */ for (i=0; i<=L1; i++) y += b1[i] * w1[i]; /* Output adder */ for (i=K; i>=1; i--) w1[i] = w1[i-1]; /* Reverse-order updating */ return y; /* Current output sample */ /*------------------------------------------------------------------------- Subroutine pll() - reference sinewave signal generation -------------------------------------------------------------------------*/ Float64 pll(x) Float64 x; int i, K; double y = 0; M3 = 2; /* M-th degree numerator */ L3 = 2; /* L-th degree numerator */ K = (L3 <= M3) ? M3 : L3; /* K = max(M,L) */ w3[0] = x; /* Current input sample */ a3[0] = 1.0; /* Filter coefficient */ a3[1] = -1.822754277; a3[2] = 0.837203188; b3[0] = 0.0; /* Filter coefficient */ b3[1] = 0.177245723; b3[2] = -0.162796812; for (i=1; i<=M3; i++) w3[0] -= a3[i] * w3[i]; /* Input adder */ for (i=0; i<=L3; i++)
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y += b3[i] * w3[i]; /* Output adder */ for (i=K; i>=1; i--) w3[i] = w3[i-1]; /* reverse-order updating */ return y; /* Current output sample */ /************************************************************************** Routine phase_lock_loop() **************************************************************************/ phase_lock_loop() vsource_adc1 = 450.4896276 * ds1104_adc_read_ch(5); /* Read current ADC5 input of vsource */ y1_a = 1.414093802 * fir1(vsource_adc1); /* Using fir1() */ vpll = pll(y1_a); /* Using pll() */ y1_b = 50 * pow(y1_a, 2); y1_c = integ1(y1_b); /* Using integ1() */ reset_integ1(); /* Using reset_integ1() */ y1_d = y1_c1 - y1_c2; y1_e = fabs(y1_d); vs_rms1 = 1.414213562 * sqrt(y1_e); if (vs_rms1 <= 20) vs_rms = 20; /* Set initial source voltage level */ enable3 = 0; /* Mains fault protection */ else vs_rms = vs_rms1; enable3 = 1; /* Mains fault protection */ ds1104_adc_mux(2);
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vcap_adc = 450.4896276 * ds1104_adc_read_ch(2); /* Read current ADC2 input of DC-bus voltage */ if (vcap_adc >= 200) /* DC-bus voltage must be bigger than 200V */ enable4 = 1; /* DC-bus voltage fault protection */ else enable4 = 0; /* DC-bus voltage fault protection */ sine_ref = 0.663349917 * vpll / vs_rms; /* Generates reference sinewave */ sine_ref_syn = -1 * delay9(sine_ref); /* Synchronise sine_ref with source voltage */ /************************************************************************** Routine extension_pq_theorem() **************************************************************************/ extension_pq_theorem() vsource_adc = fir11(vsource_adc1); iload_adc1 = 7.817275402 * ds1104_adc_read_ch(7); /* Read current ADC7 input of iload */ iload_adc = fir12(iload_adc1); ihpf_adc1 = 7.817275402 * ds1104_adc_read_ch(6); /* Read current ADC6 input of ihpf */ ihpf_adc = fir13(ihpf_adc1); vsource_adc_90deg = delay4(vsource_adc); /* 90-degree phase shift of vsource_adc */ Pload = vsource_adc * iload_adc; /* Instantaneous active load power*/ Qload = vsource_adc_90deg * iload_adc; /* Instantaneous reactive load power*/ Qhpf = vsource_adc_90deg * ihpf_adc; /* Instantaneous reactive HPF power*/
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Pload_dc = fir5(Pload); /* Using fir5() */ Qload_dc = fir6(Qload); /* Using fir6() */ Qhpf_dc = fir7(Qhpf); /* Using fir7() */ /************************************************************************** Routine compensating_current_ref() **************************************************************************/ compensating_current_ref() sine_ref_90deg = delay8(sine_ref_syn); /* 90-degree phase shift of sine_ref */ ip_load = 1.414213562 * Pload_dc / vs_rms * sine_ref_syn; /* Active component of load current */ iq_load = 1.414213562 * Qload_dc / vs_rms * sine_ref_90deg; /* Reactive component of load current */ ihpw_load = iload_adc - iq_load - ip_load; /* Harmonic component of load current */ ic_load = iq_load + ihpw_load; /* Load's compensation current reference */ iq_hpf = 1.414213562 * Qhpf_dc / vs_rms * sine_ref_90deg; /* Reactive component of HPF current */ ipv_ref = ipv * sine_ref_syn; /* Active component of DC source current */ ic_ref2 = ic_load + iq_hpf + ipv_ref; /* Compensation current + DC source current */ ic_ref1 = -1 * delay10(ic_ref2); /* Phase delay compensation */ if(ic_ref1 >= 7.0) ic_ref = 7.0; /* Over current protection, upper limit = 7.0 A */ else if(ic_ref1 <= -7.0) ic_ref = -7.0; /* Over current protection, lower limit = -7.0 A */ else ic_ref = ic_ref1;
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is_compensated = iload_adc + ihpf_adc - ic_ref; /* Calculated compensated source current (ideal case) */ if (iselect == 0) iref_out = sine_ref_syn; else if (iselect == 1) iref_out = ip_load; else if (iselect == 2) iref_out = iq_load; else if (iselect == 3) iref_out = ihpw_load; else if (iselect == 4) iref_out = iq_hpf; else if (iselect == 5) iref_out = ic_load; else if (iselect == 6) iref_out = ic_ref; ds1104_dac_write(5, iref_out / 10); /* DAC5 output signal selection */ ds1104_dac_strobe(); /* Activate the previously written DAC values synchronously */ /************************************************************************** Routine system_fault_protection() **************************************************************************/ system_fault_protection() if (enable1 == 1 && enable2 == 1 && enable3 == 1 && enable4 == 1) ds1104_bit_io_set(DS1104_DIO11); /* Sets I/O port 11 to '1' */ else ds1104_bit_io_clear(DS1104_DIO11); /* Sets I/O port 11 to '0' */
189
/************************************************************************** Routine error_hook_function() - is activated when an error message is generated **************************************************************************/ int error_hook_function(msg_submodule_type sm, msg_no_type no) enable1 = 0; /* Enable signal 1 is 0 when error occurs */ return(1); /* Display the error message */ /************************************************************************** Interrupt service routine 0, isr_srt0() - Hysteresis current controller **************************************************************************/ isr_srt0() RTLIB_TIC_START(); /* Start execution time 0 measurement */ ds1104_adc_start(DS1104_ADC5); /* Start 12-bit's ADC */ icomp_adc = 7.817275402 * ds1104_adc_read_ch(8); /* Read current ADC8 input of icomp */ i_hysteresis = icomp_adc - ic_ref; if (i_hysteresis >= 0.5) mask_set = 0x00000; ds1104_bit_io_clear(0x20020); /* Sets I/O 5 and I/O 17 to '0' */ else if (i_hysteresis <= -0.5) mask_set = 0x20020; ds1104_bit_io_set(0x20020); /* Sets I/O 5 and I/O 17 to '1' */ else ds1104_bit_io_set(mask_set); /* Remain I/O 5 and I/O 17 */ exec_time0 = RTLIB_TIC_READ(); /* Read the execution time 0 */
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/************************************************************************** Interrupt service routine 1, isr_srt1() - Reference sinewave generation - Compensation Current Reference and DC source Current estimation **************************************************************************/ isr_srt1() ts_timestamp_type ts; /* Time stamping function */ ds1104_begin_isr_timer1(); /* Overload check */ RTLIB_TIC_START(); /* Start execution time 1 measurement */ ds1104_adc_start(DS1104_ADC1|DS1104_ADC2|DS1104_ADC3|DS1104_ADC4); /* Start Mux ADC & 12-bit's ADC simultaneously */ phase_lock_loop(); /* Using phase_lock_loop() */ extension_pq_theorem(); /* Using extension_pq_theorem() */ compensating_current_ref(); /* Using compensating_current_ref() */ system_fault_protection(); /* Using system_fault_protection() */ ts_timestamp_read(&ts); /* Read time stamp */ host_service(1, &ts); /* Data acquisition service using time stamping */ exec_time1 = RTLIB_TIC_READ(); /* Read the execution time 1 */ ds1104_end_isr_timer1(); /* Overload check */ /************************************************************************** Main Program **************************************************************************/ void main() /* Variables Initialisation */ n1 = 0; n2 = 0; Pload = 1; Qload = 1; Qhpf = 1; /* Initialise arrays of fir1() */ a1 = (Float64 *)calloc(3, sizeof(Float64));
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b1 = (Float64 *)calloc(3, sizeof(Float64)); w1 = (Float64 *)calloc(3, sizeof(Float64)); /* Initialise arrays of integ1() */ w2 = (Float64 *)calloc(1, sizeof(Float64)); /* Initialise arrays of pll() */ a3 = (Float64 *)calloc(3, sizeof(Float64)); b3 = (Float64 *)calloc(3, sizeof(Float64)); w3 = (Float64 *)calloc(3, sizeof(Float64)); /* Initialise arrays of delay4() */ w4 = (Float64 *)calloc(51, sizeof(Float64)); /* Initialise arrays of fir5() */ a5 = (Float64 *)calloc(3, sizeof(Float64)); b5 = (Float64 *)calloc(3, sizeof(Float64)); w5 = (Float64 *)calloc(3, sizeof(Float64)); /* Initialise arrays of fir6() */ a6 = (Float64 *)calloc(3, sizeof(Float64)); b6 = (Float64 *)calloc(3, sizeof(Float64)); w6 = (Float64 *)calloc(3, sizeof(Float64)); /* Initialise arrays of fir7() */ a7 = (Float64 *)calloc(3, sizeof(Float64)); b7 = (Float64 *)calloc(3, sizeof(Float64)); w7 = (Float64 *)calloc(3, sizeof(Float64)); /* Initialise arrays of delay8() */ w8 = (Float64 *)calloc(51, sizeof(Float64)); /* Initialise arrays of delay9() */ w9 = (Float64 *)calloc(44, sizeof(Float64)); /* Initialise arrays of delay10() */ w10 = (Float64 *)calloc(100, sizeof(Float64)); /* Initialise arrays of fir11() */ a11 = (Float64 *)calloc(3, sizeof(Float64)); b11 = (Float64 *)calloc(3, sizeof(Float64)); w11 = (Float64 *)calloc(3, sizeof(Float64)); /* Initialise arrays of fir12() */ a12 = (Float64 *)calloc(3, sizeof(Float64)); b12 = (Float64 *)calloc(3, sizeof(Float64)); w12 = (Float64 *)calloc(3, sizeof(Float64)); /* Initialise arrays of fir13() */ a13 = (Float64 *)calloc(3, sizeof(Float64)); b13 = (Float64 *)calloc(3, sizeof(Float64));
192
w13 = (Float64 *)calloc(3, sizeof(Float64)); /* DS1104 and RTLib1104 initialization */ init(); /* Announce the hook function to the message module */ msg_error_hook_set(error_hook_function); /* Sets bits I/O 5, I/O 11 and I/O 17 to output */ ds1104_bit_io_init(DS1104_DIO5_OUT|DS1104_DIO11_OUT|DS1104_DIO17_OUT); /* Sets the bits I/O 5, I/O 11 and I/O 17 to '0' */ ds1104_bit_io_clear(DS1104_DIO5|DS1104_DIO11|DS1104_DIO17); /* Initialize DAC in latched mode */ ds1104_dac_init(DS1104_DACMODE_LATCHED); /* Start timer0 with service routine isr_srt0() */ ds1104_start_isr_timer0(ST0, isr_srt0); /* Start timer1 with interrupt service routine isr_srt1() */ ds1104_start_isr_timer1(ST1, isr_srt1); /* Message generation */ msg_info_set(MSG_SM_USER, 0, "System Started."); /* Background service */ while(1) RTLIB_BACKGROUND_SERVICE();
H.2 Variable Description File (TRC File) for ControlDesk’s Instrument
_floating_point_type(64,IEEE) _integer_type(32) -- signals available for ControlDesk -- -- signal name type address group "Model Root in ""DS1104.c"""
193
group "Execution Time 0" exec_time0 type: flt (64,IEEE) alias: "Execution Time 0" flags: READONLY endgroup group "Execution Time 1" exec_time1 type: flt (64,IEEE) alias: "Execution Time 1" flags: READONLY endgroup group "Signals of Phase-Lock Loop" vsource_adc flt vs_rms flt sine_ref flt y1_a flt endgroup group "Signals of Extension P-Q Theorem" iload_adc flt ihpf_adc flt Pload flt Pload_dc flt Qload flt Qload_dc flt Qhpf flt Qhpf_dc flt endgroup group "Signals of Compensation Current Reference" sine_ref_syn flt sine_ref_90deg flt ip_load flt iq_load flt
194
ihpw_load flt iq_hpf flt ic_load flt ic_ref flt is_compensated flt endgroup group "Signals of Hysteresis Current Controller" icomp_adc flt i_hysteresis flt enable1 int enable2 int enable3 int enable4 int endgroup group "Signals of DC-Bus Voltage Regulation" vcap_adc flt endgroup group "Signals of DC Source Current" ipv flt ipv_ref flt endgroup group "Current Signal at DACH5" iselect int endgroup endgroup
196
Abstract--This paper presents a new single-phase two-wire
hybrid active power filter configuration that interconnects a passive high-pass filter in parallel with an active power filter and a photovoltaic system. The proposed configuration can improves the filtering performance of the conventional active power filter, as well as simultaneously supply the power from the photovoltaic arrays to the load and utility. Furthermore, the derivation of compensation current reference is simplified with the utilization of extension p-q theorem. This paper will describe the proposed hybrid active power filter with photovoltaic system. It will primarily focus on the power circuit, control system and the compensation current reference derivation. The proposed system effectively filters harmonics under 1 kHz but also higher frequency to achieve wideband harmonics compensation. The THD of source current is reduced from 76.83 % to 3.21 %. The simulation results that verify the theoretical predictions of the proposed configuration will be presented.
Index Terms--Extension p-q theorem, hybrid active power filter, photovoltaic, power electronics, wideband harmonic compensation.
I. INTRODUCTION HE pass several decades have seen a rapid increase of power electronics-based loads connected to the utility
system. However, the proliferation of these non-linear loads has raised concern with regard to the resulting harmonic distortion levels of the supply current on the power system. Passive filter is the traditional method of harmonic filtering. It is well known that the application of passive filters creates new system resonances that are dependent on the specific system conditions [1]. Although this solution is simple, it has brings rise to several shortcomings. Furthermore, since the harmonics that to be eliminated is of low order, large filter components are required.
Active power filters (APFs) were developed to mitigate problem of passive filters. The advantages of APFs are widely recognized and are discussed extensively in [2]-[5]. However, the major part of the controller developed in the conventional
This project was supported by the Intensification of Research in Priority Areas (IRPA) grant from the Ministry of Science, Technology and the Environment, Malaysia (MOSTE).
The authors are with the Department of Energy Conversion, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor Bahru, Malaysia.
(email: perngcheng@ieee.org, zainals@fke.utm.my)
APF consists of analog circuits. As a result, the conventional APF is subjected to fine adjustment and signal drift inherent in analog circuit [2], [3]. A digital controller using a digital signal processor (DSP) or a microprocessor is preferable to an analog controller in terms of flexible implementation of the APF [4], [5]. The drawbacks of digital implementation are that the high order harmonics are not filtered effectively and the switching ripples remain in the source current. This is due to the time and phase delay in the digital controller and measurement of signals sampling. Hybrid APFs were developed, where a passive filter is connected parallel to a conventional APF [6], [7]. The hybrid APF configuration is effective in improving the damping performance of high-order harmonics.
Recently, there is an increasing concern about the environment pollution. The need to generate pollution-free energy has trigger intensive considerable effort toward alternative source of energy. Solar energy, in particular, is a promising option. Some researcher had spent their effort in developing the combined system of an APF and a photovoltaic (PV) system [8], [9]. However, the existing hybrid APF configurations are not yet utilized for the PV application.
The p-q theorem was adopted for current reference derivation in the hybrid APF system [10]. Definition and study of the extension p-q theorem has been proposed [11], [12]. This fresh definition is simpler and clearer for the current commands derivation compared with the p-q theorem presented in [13]. However, the extension p-q theorem is not yet being applied in the hybrid APF system.
In this paper, we proposed a new single-phase two-wire hybrid APF configuration that interconnects a hybrid APF with a photovoltaic system. The extension p-q theorem is utilized to create the compensation current reference derivation. Furthermore, the derivation of compensation current reference is simplified with the utilization of extension p-q theorem. The proposed configuration can improves the filtering performance of the conventional APF, as well as simultaneously supply the power from the PV arrays to the load and utility.
This paper will describe the proposed hybrid APF with PV system. It will primarily focus on the power circuit, control system and compensation current reference derivation. Finally, the simulation results that verify the theoretical
A New Single-Phase Two-Wire Hybrid Active Power Filter Using Extension p-q
Theorem for Photovoltaic Application P. C. Tan, Student Member, IEEE, and Z. Salam, Member, IEEE
T
197predictions of the proposed configuration will be presented.
II. PROPOSED SYSTEM CONFIGURATION AND PRINCIPLE OF OPERATION
Fig. 1 presents the power circuit of the proposed hybrid APF with PV system in parallel with a nonlinear load that is supplied by source voltage from the point of common coupling (PCC). The proposed hybrid APV consists of a passive high-pass filter (HPF), a shunt APF constructed by a single-phase full-bridge voltage source inverter (VSI) connected to a DC-bus capacitor; and PV arrays in parallel with the DC-bus capacitor. In the proposed scheme, the low-order harmonics are compensated using the shunt APF, while the high-order harmonics are filtered with the passive HPF. This configuration is effective to improve the filtering performance of the high-order harmonics.
The VSI is operating in the current-controlled mode (CCM) with the utilization of fixed-band hysteresis current controller. Furthermore, the proposed hybrid APF with PV system is connected with the utility line at the PCC through a series inductor allowing the reactive power control. Subscripts u, s, PCC, L, f, and hp refer to utility, source, PCC, load, APF, and HPF variables respectively.
Fig. 1. Configuration of the proposed hybrid APF with PV system.
Fig. 2 shows the block diagram of the proposed control
system for the hybrid APF. The source current is desired to be sinusoidal to yield a maximum power factor. In this work, the extension p-q theorem is introduced to derive the compensation current reference.
Fig. 2. Overall system configuration and control block diagram.
In order to generate the compensation current that follows the current reference, the fixed-band hysteresis current control method is adopted. The proposed scheme is controlled to inject the reactive and harmonic current of the nonlinear load and the reactive current of the HPF. Furthermore, a current must be drawn form the utility source to maintain the voltage across the DC-bus capacitor to a preset value that is higher than the amplitude of the source voltage. A proportional-integral (PI) controller is implemented for the DC-bus capacitor voltage control. Under the normal operation, the PV system will provide active power to the load and the utility. Under poor PV power generation condition, the utility source supplies the active power to the load directly.
A. Derivation of Compensation Current Reference Compensation current reference derivation for the single-
phase two-wire APF based on extension p-q theorem has been presented in [8]. In this work, the application of the theorem is further extended for current reference derivation in a single-phase two-wire hybrid APF with PV system. For the proposed scheme, the extension p-q theorem is adopted for the derivation of harmonics, active and reactive components of nonlinear load current and the reactive component of passive HPF current.
For a single-phase two-wire system with nonlinear load, the load current can be represented as
( ) ( )∑∞
=
θ+ω=1
, sin2n
nnLL tnIti (1)
Under normal circumstances, the voltage at PCC can be assumed to be a sinusoidal, i.e.,
( ) ( )φ+ω= tVtv PCCPCC sin2 (2) The HPF current can be represented as
( ) ( )o90sin2 , +ω= tIti nhphp (3)
Therefore, the instantaneous active power of nonlinear load can be calculated as
( ) ( ) ( )titvtp LPCCL ⋅= ( ) ( )11,11, 2coscos θ+φ+ω−θ−φ= tIVIV LPCCLPCC
( ) ( )∑∞
=
φ+ωθ+ω+2
, sinsin2n
nnLPCC ttnIV
LL pp ~+= (4) The instantaneous reactive power of nonlinear load can be written as follows:
( ) ( ) ( )titvtq LPCCL ⋅= ' ( ) ( )11,11, 2sinsin θ+φ+ω−θ−φ= tIVIV LPCCLPCC
( ) ( )∑∞
=
φ+ωθ+ω−2
, sinsin2n
nnLPCC ttnIV
LL qq ~+= (5) The instantaneous reactive power of HPF can be calculated as
198
( ) ( ) ( )titvtq hpPCChp ⋅= '
( ) ( )oo 902sin90sin 1,1, +φ+ω−−φ= tIVIV hpPCChpPCC
hphp qq ~+= (6)
where Lp , Lq and hpp represent the constant part, Lp~ , Lq~
and hpp~ denote the variant component, and ( )tvPCC' denotes
the PCC voltage shifted by o90 . By obtaining the constant part in (4), (5) and (6), the
harmonics ( pLi , ), active ( qLi , ) and reactive ( hLi , )
components of nonlinear load current and the reactive ( qhpi , )
component of the passive HPF current can be readily calculated as follows:
( ) ( )tuV
ptiPCC
LpL 2, = (7)
( ) ( )o902, −= tuV
qtiPCC
LqL (8)
( ) ( ) ( ) ( )titititi qLpLLhL ,,, −−= (9)
and
( ) ( )o902, −= tuVq
tiPCC
hpqhp (10)
where ( )tu is a unit vector in phase with the PCC voltage. Finally, the compensation current reference can be
expressed as
( ) ( )tuV
PtuIiiiirefCf
PVCfqhphLqLf ⋅+⋅−++=
,,,,
* (11)
where PVP is the active power of PV arrays, CfI is the DC-
bus capacitor charging current, and refCfV , is DC-bus capacitor voltage reference.
B. Fixed-Band Hysteresis Current Controller In order to generate the compensation current that follows
the compensation current reference, the fixed-band hysteresis current control method is adopted. Fig. 3 is the simplified equivalent circuit of the main power circuit, where 1S and 2S are two switches, and sV is the source voltage. For a case of
sinusoidal reference current *fi as shown in Fig. 4, the actual
compensation current fi , is compared with the fixed
hysteresis band around the reference current, 1S and 2S should be controlled by the following rules,
(1) When the compensation current sample fi tries to go
beyond the upper hysteresis band, 1S is turned off and 2S is turned on. Assuming PCCCf VV > , then fi
decreases linearly. (2) When the compensation current sample fi tries to go
beyond the upper hysteresis band, 1S is turned on and 2S is turned off, then fi increases linearly.
By this way, fi is driven to follow the current reference *fi
within a fixed hysteresis band. The switching frequency depends on how fast the current changes from the upper limit to the lower limit and vice versa. Therefore, the switching frequency does not remain constant but varies with respect to the current waveform.
Fig. 3. Simplified equivalent circuit of main power circuit.
Fig. 4. Principle of the fixed-band hysteresis current control.
C. Design of Passive High-Pass Filter The passive HPF consists of a capacitor hpC , an inductor
hpL and a resistor hpR . Fig. 5 presents an equivalent circuit
of HPF for harmonics, where hpZ is the equivalent impedance
of HPF and sZ is the equivalent source impedance. In Fig. 5, the nonlinear load is considered as a harmonics current source. Since we are only interested in the system performance with the harmonic components, we can neglect the source voltage. This is because the source voltage is assumed to contain only the fundamental frequency current component.
199Fig. 5. Equivalent circuit of HPF for harmonics.
A transfer function approach to passive HPF design has been presented in [14]. The filter impedance transfer function
( )sH hp can be expressed as
( )⎥⎥
⎦
⎤
⎢⎢
⎣
⎡+⎟⎟
⎠
⎞⎜⎜⎝
⎛ω
+⎟⎟⎠
⎞⎜⎜⎝
⎛ω
⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛+
ω
= 11
1
2
oo
p
hps
Qs
ss
AsH (12)
In (12),
CA 1
= , hphp
o CL1
=ω , hp
hpp L
R=ω ,
hp
hphp L
CRQ =
where A is gain coefficient, oω is series resonant frequency,
pω is pole frequency, and Q is HPF quality factor.
For the simulation purpose, the leakage impedance of the transformer is regarded as the source impedance, sL = 0.573mH (2.5 percent, 2 kVA base). The passive HPF is tuned
to the resonant frequency of 1 kHz ( of =hphpCLπ2
1 =1
kHz). This resonant frequency value is chosen as the filtering performance of the APF is impaired above this frequency. The design parameters of the HPF are
hpL = 1.15 mH
hpC = 22 µ F
hpR = 5 Ω
The quality factors of 0.5 ≤≤ Q 2.0 are typical. Higher Q factors allow more series resonant attenuation and less high-pass. By contrast, lower Q factors provide less series resonant attenuation and greater high-pass response. Hence, the proper selection of Q is essentially required to satisfy the series resonant and high-pass response performances. In this work, the Q factor was selected as 0.69, considering the required high-pass response over a wide frequency band.
The transfer function ( )sHcs from the source current hsi ,
to the nonlinear load current hLi , can be expressed as
( ) ( )( )
( )( ) ( )sZsZ
sZsisi
sHhps
hp
hL
hscs +
==,
, (13)
Depending on the value selected for the resistor hpR , many
different transfer function characteristics are possible. The resistor hpR is chosen based on the desired high-pass
response and the series resonant attenuation. A bode magnitude plot of ( )sHcs is shown in Fig. 6 where it has one crest due to the parallel resonance between hps LL + and hpC
at 817.5 Hz ( 5.817=rf Hz). In particular, the parallel resonance is a problem, as it enlarge harmonics around 817.5 Hz. This crest can be minimized by selecting the value of Q
factor close to 0.7. In Fig. 6, the filtering performance of high-order harmonics above 1 kHz is improved with HPF.
Fig. 6. Bode magnitude diagram of the transfer function ( )sHcs from the source current to the nonlinear load current.
III. SIMULATION RESULTS The proposed hybrid APF was simulated using MATLAB
Simulink program. The system parameters are shown in Table I. In the simulation, a diode rectifier with a DC-link capacitor
dC and a smoothing inductor smoothL was used as a harmonic producing nonlinear load. The simulated source voltage and current waveforms without compensation for load resistance
LR of 125 Ω are shown in Fig. 7.
TABLE I MATLAB SIMULINK SIMULATION PARAMETERS
Utility Voltage Vu = 240 Vrms (50 Hz) Source Inductance Ls = 0.573 mH Rectifier DC-link Capacitor Cd = 1000 µF Rectifier Smoothing Inductor Lsmooth = 5 mH Rectifier Load Nominal Power Pn = 1 kVA Maximum Switching Frequency fsw,max = 20 kHz Hysteresis Current Control Band H = 0.4 Apeak-to-peak
Sampling Time Ts = 50 µs APF Inductor Lf = 12.5 mH APF DC-bus Capacitor Cf = 1000 µF DC-bus Capacitor Voltage Reference VCf,ref = 200 Vdc
HPF Inductor Lhp = 1.15 mH HPF Capacitor Chp = 22 µF HPF Resistor Rhp = 5 Ω Fig. 8 presents simulation results with shunt APF. As can
be seen, the source voltage and current consists a large amount of high-order harmonics. The simulation results with proposed scheme are shown in Fig. 9. Now, the high-order harmonics are filtered from the source voltage and current. Table II presents the harmonics content of the source current without compensation, with shunt APF and with the proposed scheme respectively. It can be observed that the total harmonic distortion (THD20 kHz) of source current is reduced from 76.83 % to 4.39 % with shunt APF. With proposed scheme, THD20 kHz of source current is further reduced from 76.83 % to 3.21 %. The proposed system effectively filters harmonics under 1 kHz but also higher frequency to achieve wideband harmonics compensation.
200
(a)
(b)
Fig. 7. Simulated results without harmonic compensation, (a) source voltage and (b) source current waveforms.
(a)
(b)
Fig. 8. Simulated results with shunt APF. (a) source voltage and (b) source current waveforms.
Fig. 10 shows the proposed system performance when the load resistance changes stepwise from 250 Ω to 125 Ω at time t = 0.6 s. The simulation results show that the proposed system is able to keep the source current sinusoidal under this transient condition.
During normal operation, as 300 W of PV arrays power is processed by the hybrid APF at time t = 0.6 s, the corresponding simulated source voltage and current waveforms are presented in Fig. 11. The simulation results show that the source current remains sinusoidal waveform and
the PV arrays power is successfully provided to the load and utility.
(a)
(b)
Fig. 9. Simulated results with proposed scheme. (a) source voltage and (b) source current waveforms.
(a)
(b)
Fig. 10. Simulated results with the proposed scheme in a case of step load change. (a) source voltage and (b) source current.
201TABLE II
HARMONIC CURRENT COMPONENTS
Load Basic APF Proposed Scheme n iL(n) / iL(1)
[%] is(n) / is(1)
[%] is(n) / is(1)
[%] 5 39.95 1.60 1.63 7 13.40 1.55 0.07
11 6.31 1.26 0.61 13 3.51 0.91 0.69 17 2.21 0.55 0.79 19 1.88 0.48 0.68 23 1.19 0.22 0.43 25 1.14 0.14 0.32 29 0.82 0.22 0.06 31 0.70 0.26 0.03 35 0.57 0.11 0.15 37 0.47 0.02 0.15
THD2 kHz 76.83 3.58 3.19 THD20 kHz 4.39 3.21
(a)
(b)
Fig. 11. Simulated results for the proposed scheme with 300 W active power generation from PV arrays. (a) source voltage and (b) source current.
IV. CONCLUSION A new single-phase two-wire hybrid APF configuration
that interconnects the hybrid APF with the PV system is presented. The proposed scheme combines the APF with the passive filter to improve the filtering performance of high-order harmonics. Furthermore, the proposed scheme can deal with PV power. The derivation of compensation current reference is simpler and clearer with the utilization of extension p-q theorem. The simulation results show the effectiveness of the proposed scheme for wideband harmonics compensation and PV power handling capability.
V. REFERENCES [1] D. Sutanto, M. Bou-rabee, K. S. Tam, and C. S. Chang, "Harmonic
filters for industrial power systems," in Proc. IEE International Conf. on
Advances in Power System Control, Operation and Management, vol. 2, pp. 594-598, Nov. 1991.
[2] H. L. Jou, J. C. Wu, and H. Y. Chu, "New single-phase active power filter," in Proc. IEE Electronic Power Application, vol. 141, no. 3, pp. 129-134, May 1994.
[3] C. Y. Hsu, and H. –Y. Wu, "A new single-phase active power with reduced energy storage capacitor," in Proc. IEE Electronic Power Applications, vol. 143, no. 1, pp. 23-28, Jan. 1996.
[4] S. G. Jeong and M. H. Woo, "DSP-based active power filter with predictive current control," IEEE Trans. Ind. Electron., vol. 44, pp. 329-336, June 1997.
[5] S. Buso, L. Malesani, P. Mattavelli, and R. Veronese, "Design and fully digital control of parallel active power filters for thyristor rectifiers to comply with IEC-1000-3-2 standards," IEEE Trans. Ind. Applicat., vol. 34, pp. 508-517, May/June 1998.
[6] M. Routimo, M. Salo, and H. Tuusa, "A novel control method for wideband harmonic compensation," in Proc. IEEE PEDS’03 Conf., vol. 1, Nov. 2003, pp. 799-804.
[7] S. Fukuda and T. Endoh, "Control method for a combined active power filter system employing a current source converter and a high pass filter," IEEE Trans. Ind. Applicat., vol. 31, no. 3, pp. 590-597, May-June 1995.
[8] T. –F. Wu, C. –L. Shen, C. H. Chang, and J. –Y. Chiu, "A 1 φ 3W grid-connection PV power inverter with partial active power filter," in Proc. IEEE PESC’02, vol. 3, June 2002, pp. 1512-1517.
[9] S. Kim, G. Yoo, and J. Song, "A bifunctional utility connected photovoltaic system with power factor correction and U.P.S. facilify," in Proc. of Photovoltaic Specialist Conf., May 1996, pp. 1363-1368.
[10] C. Lijun and A. V. Jouanne, "A comparison and assessment of hybrid filter topologies and control algorithms," in Proc. IEEE PESC’01, vol. 2, June 2001, pp. 565-570.
[11] Y. Komatsu and T. Kawabata, "Characteristics of three phase active power filter using extension pq theory," in Proc. of the IEEE Ind. Electron. Conf., vol. 2, July 1997, pp. 302-307.
[12] Y. Komatsu and T. Kawabata, "A control method of active power filter in unsymmetrical voltage system," in Proc. IEEE PEDS’97 Conf., vol. 2, May 1997, pp. 839-843.
[13] H. Akagi, Y. Kanazawa, and A. Nabae, "Instantaneous reactive power compensators comprising switching devices without energy storage components," IEEE Trans. Ind. Applicat., vol. IA-20, no. 3, pp. 625-630, May/June 1984.
[14] J. K. Phipps, "A Transfer function approach to harmonic filter design," IEEE Ind. Applicat. Mag., vol. 3, pp. 68-82, Mar./Apr. 1997.
Perng-Cheng Tan was born in Johor, Malaysia in 1980. He received the B.Sc. degree in electrical engineering from Universiti Technologi Malaysia (UTM), Johor, Malaysia, in 2003. He is currently pursuing the M.E.E. degree at the Department of Energy Conversion, Faculty of Electrical Engineering, UTM, Malaysia.
His research interests are the areas of active power filters, power electronics, and renewable energy.
Zainal Salam was born in Seremban, Malaysia in 1963. He received his secondary education from Victoria Institution, Kuala Lumpur. He obtained his B.Sc., M.E.E. and Ph.D. from the University of California, UTM and University of Birmingham, UK, in 1985, 1989 and 1997, respectively.
He has been a lecturer at UTM for 18 years and is currently the Head Department of Energy Conversion Department. He has been working in several researches and consulting works with SIRIM
and GBT on battery powered converters. His research interests include all areas of power electronics. Currently, he
is involved in several IRPA projects in the area of renewable energy, power electronics and machine control. His hobby is traveling.
203
A Single-Phase Hybrid Active Power Filter using Extension p-q Theorem for Photovoltaic Application
P. C. Tan, Student Member, IEEE, and Z. Salam, Member, IEEE and A. Jusoh Power Electronics and Drives Group, Department of Energy Conversion, Faculty of Electrical Engineering,
Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor Bahru, Malaysia.
perngcheng@ieee.org, zainals@fke.utm.my, awang@fke.utm.my
Abstract—This paper presents a single-phase two-wire hybrid active power filter that is used in conjunction with photovoltaic system. The uniqueness of proposed scheme is the fact that it improves the filtering performance of the conventional active power filter, as well as simultaneously supplies the power from the photovoltaic array to the load and distribution system. The current commands derivation is based on the extension instantaneous-reactive power theorem. The proposed scheme is described in detail. It will primarily focus on the power circuit, the compensation current reference derivation, and the passive high-pass filter design. Experimental results obtained from a laboratory system that verifies the viability and effectiveness of the proposed scheme are presented.
Keywords-extension p-q theorem; hybrid active power filter; photovoltaic; power electronics
I. INTRODUCTION Due to the proliferation of nonlinear and switching loads
from power electronics converters, there is an increasing concern to control and reduce the harmonics current in distribution power lines [1]. These types of loads draw nonsinusoidal currents from the mains, causing power quality (PQ) problems.
The passive filtering is the simplest solution to mitigate the harmonics problem. Although simple, the passive filter is large, heavy and bulky [2], [3]. The passive filter is known to cause resonance, thus affecting the stability of the power systems. As the regulatory requirements become more stringent, the passive filter might not meet future revisions of a particular Standard.
Remarkable progress in power electronics had spurred interest in active power filter (APF) for harmonics mitigation. The basic principle of APF is to utilize power electronics technologies to produce harmonics current components that cancel the harmonics current components from the nonlinear loads. Previously, majority of the controllers developed for APF are based on analog circuits [4], [5]. As a result, the APF is inherently subjected to signal drift. Digital controller using digital signal processor (DSP) or microprocessor is preferable, primarily due to its flexibility and immunity to noise [6], [7]. However it is known that using digital methods, the high order harmonics are not filtered effectively and the switching ripples remain in the source current. This is due to the time and phase delay in digital controller.
The idea of hybrid APF has been proposed by several researchers [8]-[10]. In this scheme, a passive filter is used in addition to a conventional APF. The main purpose of the passive filter is to improve the damping performance of high-order harmonics.
Recently, there is an increasing concern about the environment pollution. The need to generate pollution-free energy has triggers considerable effort toward renewable source of energy [11]. Solar energy, in particular, is a promising option. Efforts have been made to combine the APF with photovoltaic (PV) system [12]-[14]. However, it appears that no attempt has been made to combine a hybrid APF with PV system.
In this paper, a new variation of a hybrid APF is developed. We propose a hybrid APF topology for a single-phase two-wire system, connected to a PV array. The proposed topology is unique because it effectively filters harmonics current less than 1 kHz and of higher frequency. Furthermore, it simultaneously supplies the power from the PV array to the load and the distribution. The main contribution of this work is the application of the extension instantaneous-reactive power (p-q) theorem to derive the compensation current reference for this topology. Although the derivation of current reference based on extension p-q theorem is not new [13]-[15], this approach has not yet being applied to a single-phase two-wire hybrid APF system involving passive high-pass filter (HPF), APF and PV array. Using the extension p-q theorem, the resulting equations for the reference current of single-phase two-wire system is simpler compared with the p-q theorem presented in [16].
This paper will describe the proposed hybrid APF with PV system. It will primarily focus on the power circuit, the compensation current reference derivation, and the passive HPF design. Finally, the experimental results that verify the theoretical predictions of the proposed configuration will be presented.
II. PRINCIPLE OF OPERATION Fig. 1 presents the proposed hybrid APF with PV system
block diagram, connected in parallel with a nonlinear load. It consists of a passive HPF, a single-phase APF constructed using a full-bridge voltage source inverter (VSI) and PV array.
This project was supported by the Intensification of Research in Priority Areas (IRPA) grant from the Ministry of Science, Technology and Innovation (MOSTI), Malaysia.
204The VSI and the PV array are connected in parallel with the DC-bus capacitor. In the proposed scheme, the low-order harmonics are compensated using the shunt APF, while the high-order harmonics are filtered by the passive HPF. It is envisaged that this configuration is effective to improve the filtering performance of high-order harmonics, thus achieving wideband harmonic compensation.
The VSI is operated in the current-controlled mode (CCM). Furthermore, the proposed hybrid APF with PV system is connected with the distribution line at the point of common coupling (PCC) through a filter inductor, allowing the reactive power control. Fig. 2 shows the control system for the proposed hybrid APF with PV system. The compensated source current is desired to be sinusoidal to yield a maximum power factor (PF). The extension p-q theorem is introduced to derive the compensation current reference.
Figure 1. Configuration of the proposed hybrid APF with PV system.
Figure 2. Overall system configuration and control block diagram.
In order to generate the compensation current that follows the current reference, the fixed-band hysteresis current control method is adopted. The aim is to inject the reactive and harmonics currents of the nonlinear load and the reactive current of the passive HPF. Furthermore, a current must be drawn from the distribution source to maintain the voltage across the DC-bus capacitor to a value that is higher than the amplitude of the source voltage. A proportional-integral (PI) controller is implemented for the DC-bus capacitor voltage control. Under the normal operation, the PV array will provide active power to the load and the distribution. However, under no PV power generation condition, the distribution source supplies the active power to the load directly.
A. Derivation of Compensation Current Reference Compensation current reference derivation for the single-
phase two-wire APF based on extension p-q theorem has been presented in [14]. In this work, the application of the theorem is further extended to a single-phase two-wire hybrid APF with PV system. The compensation current reference derivation for the proposed scheme is presented in [17]. The extension p-q theorem is adopted for the derivation of active, reactive and harmonics components of nonlinear load current and the reactive component of passive HPF current.
For a single-phase two-wire system with nonlinear load, the load current can be represented as
( ) ( )∑ θ+ω=∞
=1, sin2
nnnLL tnIti . (1)
Under normal circumstances, the voltage at PCC can be assumed to be a sinusoidal, i.e.,
( ) ( )φ+ω= tVtv PCCPCC sin2 . (2)
The HPF current can be represented as
( ) ( )o90sin2 , +ω= tIti nhphp . (3)
Therefore, the instantaneous active power of nonlinear load can be calculated as
( ) ( ) ( )titvtp LPCCL ⋅=
LL pp ~+= . (4)
The instantaneous reactive power of nonlinear load can be written as follows
( ) ( ) ( )titvtq LPCCL ⋅= '
LL qq ~+= . (5)
Figure 2
Figure 1
205The instantaneous reactive power of HPF can be calculated as
( ) ( ) ( )titvtq hpPCChp ⋅= '
hphp qq ~+= , (6)
where Lp , Lq and hpp represent the constant part, Lp~ , Lq~
and hpp~ denote the variant component, and ( )tvPCC' denotes
the PCC voltage shifted by o90 .
By obtaining the constant part in (4), (5) and (6), the active ( pLi , ), reactive ( qLi , ) and harmonics ( hLi , ) components of
nonlinear load current and the reactive ( qhpi , ) component of the passive HPF current can be readily calculated as follows:
( ) ( )tuV
pti
PCC
LpL 2, = , (7)
( ) ( )o902, −= tuV
qtiPCC
LqL , (8)
( ) ( ) ( ) ( )titititi qLpLLhL ,,, −−= , (9)
and
( ) ( )o902, −= tuV
qti
PCC
hpqhp , (10)
where ( )tu is a unit vector in phase with the PCC voltage.
Finally, the compensation current reference can be expressed as
( ) ( )tuV
PtuIiiii
refCf
PVCfqhphLqLf ⋅+⋅−++=
,,,,
* , (11)
where PVP is the active power of PV array, CfI is the DC-bus capacitor charging current, and refCfV , is DC-bus capacitor voltage reference.
B. Design of Passive High-Pass Filter The second-order damped series resonant type HPF
topology is adopted in the proposed hybrid APF with PV system. The HPF consists of a capacitor hpC , inductor hpL
and an inductor bypass resistor hpR . Fig. 3 presents an equivalent circuit of the proposed hybrid APF system for harmonics, where hpZ is the equivalent impedance of HPF
and sZ is the equivalent source impedance assumed to be a simple inductor. In Fig. 3, the shunt APF is assumed to act as an ideal current source which produces the compensation current that follows the current reference, while the nonlinear load is considered as a harmonics current source.
Since we are only interested in the system performance with the harmonics components, we can neglect the source voltage. This is because the source voltage is assumed to contain only the fundamental frequency component.
A generalized transfer function approach to harmonic filter design has been presented in [18]. This method is based on the Laplace transform and superposition. In this work, the transfer function approach to harmonic filter design is adopted for the passive HPF design. The HPF impedance transfer function
( )sH hp can be derived in normalized form as
( ) ( )⎥⎥
⎦
⎤
⎢⎢
⎣
⎡+⎟⎟
⎠
⎞⎜⎜⎝
⎛ω
+⎟⎟⎠
⎞⎜⎜⎝
⎛ω
⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛+
ω
== 11
1
2
oo
p
hphps
Qs
ss
AsZsH . (12)
In (12),
hpCA 1= ,
hphpo
CL1
=ω , hp
hpp L
R=ω ,
hp
hphp L
CRQ = ,
where A is the gain coefficient, oω is the series resonant frequency, pω is the pole frequency, and Q is the quality factor.
The passive HPF is tuned to the resonant frequency of 1.28
kHz (hphp
oCL
fπ
=2
1 = 1.28 kHz). This resonant frequency
value is chosen as the filtering performance of the APF is impaired above this frequency.
Depending on the value selected for the inductor bypass resistor hpR , many different transfer function characteristics
are possible. The inductor bypass resistor hpR is chosen based on the desired high-pass response and the series resonant attenuation. The quality factors of 0.5 ≤≤ Q 2.0 are typical.
Figure 3. Simplified model of the hybrid filter.
Figure 3
206Higher Q factors allow more series resonant attenuation and less high-pass. By contrast, lower Q factors provide less series resonant attenuation and greater high-pass response. Hence, the proper selection of Q is essentially required to satisfy the series resonant and high-pass response performances. In this work, the Q factor was selected as 0.69, considering the required high-pass response over a wide frequency band.
After the hybrid APF with PV system is configured and ( )sZ hp is known, the distribution system current to injected
current transfer function ( )sH cds can be derived for the hybrid APF with PV system connected to the PCC as
( ) ( )( )
( )( ) ( )sZsZ
sZsisi
sHshp
hp
h
hscds +
== , . (13)
Transfer function (13) is important because it can be used to assess the overall system performance.
A bode magnitude plot of ( )sH cds is shown in Fig. 4 where it has one crest due to the parallel resonance between
hps LL + and hpC . In particular, the parallel resonance is a problem, as it enlarges harmonics around the parallel resonant
frequency (hphps
rCLL
f)(2
1+π
= = 1.07 kHz). This crest
can be minimized by selecting the value of Q factor close to 0.7. For the plot shown in Fig. 4, the distribution system current to injected current transfer function ( )sH cds can be evaluated at low and high frequencies. For low frequencies, it has a 0 dB gain from 0 Hz to the parallel resonant frequency
rf . At rf the gain is determined by the selection of Q . For high frequencies, the roll-off of the high frequency components above the parallel resonant frequency rf is -20 dB per decade. Hence, the harmonics filtering is divided between the two filters: the low-order harmonics are compensated using the shunt APF, while the high-order harmonics are filtered by the passive HPF.
Figure 4. Bode magnitude diagram of the transfer function ( )sHcds for the proposed hybrid APF system.
III. EXPERIMENTAL RESULTS The proposed hybrid APF system was tested in the
laboratory with a low-power experimental prototype. The system parameters are shown in Table I. For the experimental system, the leakage impedance of the transformer is assumed to be the source impedance, sL = 0.76 mH. The passive HPF is tuned to the resonant frequency of 1.28 kHz. The design parameters of the HPF are: hpL = 1.76 mH, hpC = 8.8 µ F
and hpR = 10 Ω . A diode rectifier with a DC-link capacitor
dC and a smoothing inductor smoothL was used as the load. The control system was implemented using a dSPACE DS1104 DSP board.
The source current waveform and its harmonics spectra without compensation are shown in Fig. 5. As can be seen, the source current is highly distorted. Fig. 6 presents the source current waveform with basic shunt APF. From the spectra, it can be observed that for the basic APF the source current contains appreciable amount of high-order harmonics. The harmonics are effectively filtered by the proposed scheme, as depicted by Fig. 7. The total harmonic distortion calculated up to 10 kHz (THD10 kHz) is reduced from 130 % to 36 % using the basic shunt APF. With the proposed scheme, the THD10 kHz is further reduced to 19 %.
Fig. 8 shows the performance of the proposed hybrid APF with a PV array during normal operation. Fig. 8(a) shows the load current and compensated source current waveforms with no active power generation from PV array. The active power is provided by the distribution line directly. Fig. 8(b) shows the load current and compensated source current waveforms with 350 W active power generation from PV array. The experimental results obtained show that the generated PV power is provided to the load and distribution through the proposed hybrid APF system.
TABLE I. EXPERIMENTAL SYSTEM PARAMETERS
Distribution Voltage Vu = 240 Vrms (50 Hz) Source Inductance Ls = 0.76 mH Rectifier DC-link Capacitor Cd = 1000 µF Rectifier Smoothing Inductor Lsmooth = 1.15 mH Maximum Switching Frequency fsw,max = 10 kHz Hysteresis Current Control Band H = 1.0 Apeak-to-peak
APF Inductor Lf = 10.0 mH APF DC-bus Capacitor Cf = 1000 µF DC-bus Capacitor Voltage Reference VCf,ref = 250 Vdc
HPF Inductor Lhp = 1.76 mH HPF Capacitor Chp = 8.8 µF HPF Resistor Rhp = 10 Ω Load Resistor RL = 250 Ω
Figure 4
207
Load Resistance, LR = 250 Ω
(a) Scales: source current 2A/div, time 4ms/div.
(a)
Load Resistance, LR = 250 Ω
(a) Scales: source current 2A/div, time 4ms/div.
(b)
Load Resistance, LR = 250 Ω
(a) Scales: source current 2A/div, time 4ms/div.
(a)
Load Resistance, LR = 250 Ω
(a) Scales: load current 4A/div, source current 4A/div, time 4ms/div.
(b)
Load Resistance, LR = 250 Ω
(b) Scales: spectra 100mA/div, frequency 1.25kHz/div.
(b)
Load Resistance, LR = 250 Ω
(b) Scales: spectra 200mA/div, frequency 1.25kHz/div.
(b)
Load Resistance, LR = 250 Ω
(b) Scales: spectra 200mA/div, frequency 1.25kHz/div.
(b)
Load Resistance, LR = 250 Ω
(b) Scales: load current 4A/div, source current 4A/div, time 4ms/div.
(b)
Figure 8(b)
Figure 7(b)
Figure 6(b)
Figure 5(b)
Figure 8(a)
Figure 7(a)
Figure 6(a)
Figure 5(a)
Figure 5. Experimental results without compensation, (a) source current waveform and (b) source current spectra.
Figure 6. Experimental results with basic shunt APF, (a) source current waveform and (b) source current spectra.
Figure 7. Experimental results with proposed scheme, (a) source current waveform and (b) source current spectra.
Figure 8. Experimental results with proposed APF with PV system, (a) load and source current waveforms with no PV power generation and (b) load and source current waveforms with 350 W PV power generation.
Fundamental
is Fundamental
is Fundamental
iL
is
iL
is
is
208IV. CONCLUSION
A single-phase two-wire hybrid APF that interconnects to the PV system is presented. The proposed scheme combines the APF with a passive filter to improve the filtering performance of high-order harmonics. The derivation of compensation current reference is simpler with the utilization of extension p-q theorem. The experimental results show the effectiveness of the proposed scheme for wideband harmonics compensation and PV power handling capability.
REFERENCES [1] H. Akagi, “New trends in active filters for power conditioning,” IEEE
Trans. on Industry Applications, vol. 32, no. 6, pp. 1312-1322, Nov.-Dec. 1996.
[2] D. Sutanto, M. Bou-rabee, K. S. Tam, and C. S. Chang, “Harmonic filters for industrial power systems,” in Proc. IEE International Conference on Advances in Power System Control, Operation and Management, APSCOM, 1991, Hong Kong, vol. 2, pp. 594-598.
[3] J. C. Das, “Passive filters – potentialities and limitations,” IEEE Trans. on Industry Applications, vol. 40, no.1, pp. 232-241, Jan.-Feb. 2004.
[4] H. L. Jou, J. C. Wu, and H. Y. Chu, “New single-phase active power filter,” in Proc. IEE Electric Power Applications, vol. 141, no. 3, pp. 129-134, May 1994.
[5] C. Y. Hsu, and H. –Y. Wu, “A new single-phase active power filter with reduced energy-storage capacity,” in Proc. IEE Electric Power Applications, vol. 143, no. 1, pp. 25-30, Jan. 1996.
[6] S. G. Jeong and M. H. Woo, “DSP-based active power filter with predictive current control,” IEEE Trans. on Industrial Electronics, vol. 44, no. 3, pp. 329-336, June 1997.
[7] S. Buso, L. Malesani, P. Mattavelli, and R. Veronese, “Design and fully digital control of parallel active power filters for thyristor rectifiers to comply with IEC-1000-3-2 standards,” IEEE Trans. on Industry Applications, vol. 34, no. 3, pp. 508-517, May-June 1998.
[8] S. Fukuda and T. Endoh, “Control method for a combined active filter system employing a current source converter and a high pass filter,”
IEEE Trans. on Industry Applications, vol. 31, no. 3, pp. 590-597, May-June 1995.
[9] S. Khositkasame and S. Sangwongwanich, “Design of harmonic current detector and stability analysis of a hybrid parallel active filter,” in Proc. Power Conversion Conference, PCC, 1997, Nagaoka, Japan, vol. 1, pp. 181-186.
[10] M. Routimo, M. Salo, and H. Tuusa, “A novel control method for wideband harmonic compensation,” in Proc. IEEE International Conference on Power Electronics and Drive Systems, PEDS, 2003, Singapore, vol. 1, pp. 799-804.
[11] S. R. Bull, “Renewable energy today and tomorrow,” in Proc. of the IEEE, vol. 89, no. 8, pp. 1216-1226, Aug. 2001.
[12] S. Kim, G. Yoo, and J. Song, “A bifunctional utility connected photovoltaic system with power factor correction and U.P.S. facility,” in Proc. IEEE Photovoltaic Specialist Conference, 1996, Washington, USA, pp. 1363-1368.
[13] Y. Komatsu, “Application of the extension pq theory to a mains-coupled photovoltaic system,” in Proc. Power Conversion Conference, PCC, 2002, Osaka, Japan, vol. 2, pp. 816-821.
[14] T. –F. Wu, C. –L. Shen, C. H. Chang, and J. –Y. Chiu, “1/spl phi/ 3W grid-connection PV power inverter with partial active power filter,” IEEE Trans. on Aerospace and Electronic Systems, vol. 39, no. 2, pp. 635-646, April 2003.
[15] Y. Komatsu and T. Kawabata, “Characteristics of three phase active power filter using extension pq theory,” in Proc. IEEE International Symposium on Industrial Electronics, ISIE, 1997, Guimaraes, Portugal, vol. 2, pp. 302-307.
[16] B. Dobrucky, H. Kim, V. Racek, M. Roch, and M. Pokorny, “Single-phase power active filter and compensator using instantaneous reactive power method,” in Proc. Power Conversion Conference, PCC, 2002, Osaka, Japan, vol. 1, pp. 167-171.
[17] P. C. Tan and Z. Salam, “A new single-phase two-wire hybrid active power filter using extension p-q theorem for photovoltaic application,” in Proc. National Power and Energy Conference, PECon, 2004, Malaysia, pp. 126-131.
[18] J. K. Phipps, “A transfer function approach to harmonic filter design,” IEEE Industry Applications Magazine, vol. 3, no. 2, pp. 68-82, Mar.-Apr. 1997.
APPENDIX K
CONFERENCE PAPER PRESENTED AT PEMD 2006
210
A Single-Phase Hybrid Active Power Filter Connected to a Photovoltaic Array
P.C. Tan, A. Jusoh, Z. Salam*
*Power Electronics and Drives Group, Department of Energy Conversion, Faculty of Electrical Engineering,
Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor Bahru, Malaysia.
philip.pctan@gmail.com, awang@fke.utm.my, zainals@fke.utm.my
Keywords: extension p-q theorem; hybrid active power filter; passive high-pass filter; photovoltaic; power electronics.
Abstract
Due to the proliferation of nonlinear and switching loads from power electronics converters, there is an increasing concern to control and reduce the harmonic currents in distribution power lines. These types of loads draw nonsinusoidal currents from the mains, causing harmonic distortion. One of the methods to reduce the problem is by using the power electronics approach. This paper presents a single-phase hybrid active power filter connected to a photovoltaic array. The uniqueness of the proposed scheme is the fact that it improves the filtering performance of the conventional shunt active power filter, as well as simultaneously supplies the power from the photovoltaic array to the load. The compensation current reference estimation is based on the extension instantaneous reactive-power theorem. Experimental results obtained from a laboratory system that verifies the viability and effectiveness of the proposed scheme are presented.
1 Introduction
Remarkable progress in power electronics had spurred interest in active power filter (APF) for harmonic distortion mitigation [1,3,5,7,8,9]. Digital controller using digital signal processor (DSP) or microprocessor is preferable for APF application, primarily due to its flexibility and immunity to noise signals [1,3,8]. However, it is known that for digital methods, the high order harmonics are not filtered effectively. This is due to the hardware limitation of sampling rate in real-time application. Moreover, the utilisation of fast switching transistors in APF application causes switching frequency noise appears in the compensated source current [4]. This switching frequency noise required additional filtering to prevent interference with other sensitive equipment. The idea of hybrid APF has been proposed by several researchers [6,11,14]. In this scheme, a low cost passive high-pass filter (HPF) is used in addition to the conventional APF. The harmonic filtering task is divided between the two filters. The APF cancels the lower order harmonics, while the HPF
filters the remaining harmonics. The main purpose of this scheme is to improve the damping performance of high-order harmonics and provide a cost-effective harmonic mitigation approach [14]. Recently, there is an increasing concern about the environment. The need to generate pollution-free energy has triggers considerable effort toward renewable energy [2]. Renewable energy such as sunlight, wind, flowing water and biomass offer the promise of clean and abundant energy. Solar energy, in particular, is especially an attractive option because it does not generate any greenhouse gases and it is inexhaustible. Efforts have been made to combine the APF with photovoltaic (PV) array [10,12,16]. However, it appears that no attempt has been made to combine a hybrid APF with PV array. In this paper, a new variation of a hybrid APF is developed. We propose a hybrid APF topology for a single-phase system, connected to a PV array. The proposed topology is unique because it effectively filters harmonic currents less than 1 kHz and of higher frequency. Furthermore, it simultaneously supplies the power from the PV array to the load and the distribution source. The main contribution of this work is the application of the extension instantaneous reactive-power (p-q) theorem to estimate the compensation current reference for this topology. Although the compensation current reference estimation based on extension p-q theorem is not new [12,13,16], this approach has not yet being applied to a single-phase hybrid APF system involving passive HPF, shunt APF and PV array.
2 Proposed system configuration
Figure 1 shows the configuration of the proposed single-phase hybrid APF topology, connected in parallel with the nonlinear load being compensated. It consists of a passive HPF, a single-phase shunt APF constructed using a full-bridge voltage source inverter (VSI) and a PV array. Subscript s, L, f and hp refer to source, load, shunt APF and passive HPF. The shunt APF and the PV array are connected back-to-back with a DC-bus capacitor (Cf). The proposed hybrid APF is connected with the distribution line at the point of common coupling (PCC) through an interfacing inductor (Lf).
211
Figure 1: Configuration of the proposed hybrid APF
connected to a PV array. A second-order series resonant filter is selected as the passive HPF in the proposed hybrid APF topology. It consists of a capacitor (Chp), an inductor (Lhp) and an inductor bypass resistor (Rhp). It acts like a sink for high-frequency harmonic components. The power distribution system of interest is in the form of a 240 Vrms, 50 Hz sinusoidal AC voltage (vu) provided by the distribution source. An isolation transformer with turn ratio of 2:1 is used to scale down the distribution voltage. The leakage inductor of the isolation transformer is considered as the source inductor (Ls).
3 Operation principle
As illustrated by Figure 2, the operation principle of the proposed hybrid APF is that it generates compensation current (if) equal and opposite in polarity to the reactive load current (iL,q), harmonic load current (iL,h) and reactive HPF current (ihp,q). This compensation current is injected into the PCC through an interfacing inductor. The compensated source current (is) is desired to be sinusoidal and in phase with the source voltage (vs) to yield a maximum power factor.
Figure 2: Operation principle of the proposed hybrid APF. In the proposed scheme, the low-order harmonics are compensated using the shunt APF, while the high-order harmonics and switching ripple (isw) are filtered by a passive
HPF. Since the aim in using the HPF is to improve the filtering performance of high-order harmonics, the HPF can be tuned to frequency where the filtering performance of the shunt APF is impaired, i.e. close to 1 kHz. It is envisaged that this configuration is effective to improve the filtering performance of high-order harmonics. The passive HPF design for the proposed scheme is presented in [15]. In the day-time with intensive sunlight, the proposed hybrid APF extracts power from the PV array, providing additional PV current (iPV) to the load and distribution source. When the distribution source need to provide the peak power to the load, the energy provided by PV array can alleviate the burden of distribution source as illustrated in Figure 2. At night and during no sunlight periods, the power required by the load is delivered by the distribution source directly.
4 The overall control system
Figure 3 shows the overall control system for the proposed scheme. The task of the control system is to produce appropriate gating signals for the switching transistors. It can be found that the control system consists of an instantaneous active/reactive power calculator (pL, qL & qhp calculator), three low-pass filter (LPF), a compensation current estimator, a propotional-integral (PI) controller, a phase-lock loop (PLL) and a fixed-band hysteresis current controller.
Figure 3: Overall control system of the proposed hybrid APF. The instantaneous active/reactive power calculator receives the load current (iL), source voltage (vs) and HPF current (ihp) signals in real time. The instantaneous active load power (pL), instantaneous reactive load power (qL) and the instantaneous reactive HPF power (qhp) are calculated based on the extension p-q theorem. Their DC components are filtered with three second-order Butterworth low-pass filters (LPFs). These DC components are then fed to the compensation current estimator to obtain the reactive load current (iL,q), harmonic load current (iL,h) and reactive HPF current (ihp,q). The summation of these three current signals will form the first component of the current reference signal (if,ref 1).
+
_
Cf
Shunt APF
Nonlinear load
Lf
is
if
Distributionvoltage
240 Vrms50Hz
vu vs
Sourcevoltage
2:1 Ls
iL
Lsmooth
Cd RL
PV array
VCf
ihp
PassiveHPF
PCC
S3
S4
S1
S2
Rhp
LhpChp
Hysteresiscurrent
controllerGatingsignals
pL, qL & qhpcalculator
iLihpvs
-90o
PLL
LPFCompensationcurrent
estimator
if
VCf
VCf,ref
PI controllerICf
PPVVCf,ref
DC-bus VoltageController
+
_
_+
DSP Based Implementation
IPV
if,refiL,q
iL,hihp,q
∑ ∑
+++
+
+
if,ref 2
if,ref 1
S1S2S3S4
LPFLPF
cos( t)
sin( t)ω
ω
_pLpL+ ~
qL_
qL+ ~
qhp_
qhp+ ~ qhp
qL
_pL__
Shunt APF
Nonlinear loadis
if
240 Vrms50Hz
vu 2:1iL
PV Array
ihpPassiveHPF
vs PCC
iL = iL,p + iL,q + iL,his = iL,p + ihp,p - iPV
if = iL,q + iL,h + ihp,q + isw + iPVihp = ihp,p + ihp,q + isw
+
212
The DC-bus voltage controller maintains the average voltage across the DC-bus capacitor (VCf) constant against variations in distribution source. The DC voltage across the DC-bus capacitor is detected and compared with its reference voltage (VCf,ref). The compared result is processed by a PI controller to obtain the desired amplitude of the DC-bus capacitor charging current (ICf). This charging current is then subtracted from the PV current (IPV). The resulting current is then multiplied with the reference sinewave (sin(ωt)) to form second component of current reference signal (if,ref 2). In order to generate the compensation current (if) that follows the current reference signal (if,ref), the fixed-band hysteresis current control method is adopted.
4.1 Compensation current reference estimation
Compensation current reference estimation for the single-phase APF based on extension p-q theorem has been presented in [16]. In this work, the application of the theorem is further extended to a single-phase hybrid APF connected to a PV array. For a single-phase system with nonlinear load, the load current can be represented as
∑∞
=
θ+ω=1
, )sin(2)(n
nnLL tnIti . (1)
Under normal circumstances, the source voltage can be assumed to be a sinusoidal, i.e.,
)sin(2)( φ+ω= tVtv ss . (2) The HPF current can be represented as
)90sin(2)( °+ω= tIti hphp . (3) Therefore, the instantaneous active load power can be calculated as
)()()( titvtp LsL ⋅= LL pp ~+= . (4)
The instantaneous reactive load power can be written as
)()()( ' titvtq LsL ⋅= LL qq ~+= . (5)
The instantaneous reactive HPF power can be calculated as
)()()( ' titvtq hpshp ⋅= hphp qq ~+= . (6)
where Lp , Lq and hpp represent the constant part, Lp~ , Lq~
and hpp~ denote the variant component, and )(' tvs denotes the source voltage shifted by 90˚.
By obtaining the constant part in Equation (4), (5) and (6), the active (iL,p), reactive (iL,q) and harmonics (iL,h) components of load current and the reactive (ihp,q) component of the passive HPF current can be readily calculated as follows:
)(2)(, tuVpti
s
LpL = , (7)
)90(2)(,o−= tu
Vqti
s
LqL , (8)
)()()()( ,,, titititi qLpLLhL −−= , (9)
and
)90(2)(,o−= tu
Vq
tis
hpqhp , (10)
where u(t) is a unit vector in phase with the source voltage. Finally, the compensation current reference can be expressed as
)()(,
,,,, tuV
PtuIiiiirefCf
PVCfqhphLqLreff ⋅+⋅−++= ,(11)
where PPV is the active power of PV array, ICf is the DC-bus capacitor charging current, and VCf,ref is DC-bus capacitor voltage reference.
5 Experimental results
The proposed hybrid APF connected to a PV array was tested in the laboratory with a low-power experimental prototype as shown in Figure 4. The VSI was built using 1200 V, 25 A IGBTs. The control system was implemented using a dSPACE DS1104 DSP board. For the experimental system, the leakage impedance of the transformer is assumed to be the source impedance (Ls = 0.76 mH). The passive HPF is tuned to the resonant frequency of 1.28 kHz. The design parameters of the HPF are: Lhp = 1.76 mH, Chp = 8.8 µF and Rhp = 10 Ω. A full-bridge diode rectifier with DC smoothing capacitor (Cd), resistive load (RL) and AC smoothing inductor (Lsmooth) was used as the nonlinear load. Other prototype parameters are shown in Table 1.
Distribution Voltage Vu = 240 Vrms (50 Hz)
Rectifier DC-link Capacitor Cd = 1000 µF
Rectifier Smoothing Inductor Lsmooth = 1.15 mH
Maximum Switching Frequency fsw,max = 10 kHz
Hysteresis Current Control Band H = 1.0 Apeak-to-peak
APF Inductor Lf = 10.0 mH
APF DC-bus Capacitor Cf = 990 µF
DC-bus Capacitor Voltage Reference VCf,ref = 250 Vdc
Load Resistor RL = 250 Ω
Table 1: Experimental prototype parameters.
213
Figure 4: Prototype. (1) interfacing inductor, (2) drivers, (3)
IGBT bridge with DC-bus capacitor, (4) rectifier load, (5) DSP connector board, (6) smoothing inductor, (7) current and voltage transducers, (8) passive high-pass filter.
The source current waveform and its harmonics spectra without compensation are shown in Figure 5. As can be seen, the source current is highly distorted. Figure 6 presents the source current waveform with basic shunt APF. From the spectra, it can be observed that for the basic APF the source current contains appreciable amount of high-order harmonics. The harmonics are effectively filtered by the proposed scheme, as depicted by Figure 7. The total harmonic distortion calculated up to 10 kHz (THD10 kHz) is reduced from 130 % to 36 % using the basic shunt APF. With the proposed scheme, the THD10 kHz is further reduced to 19 %.
(a) Scales: source current 2 A/div, time 4 ms/div
(b) Scales: spectra 200 mA/div, frequency 1.25 kHz/div
Figure 5: Experimental results without compensation,
(a)source current waveform and (b)source current spectra.
(a) Scales: source current 1 A/div, time 4 ms/div
(b) Scales: spectra 200 mA/div, frequency 1.25 kHz/div
Figure 6: Experimental results with basic APF, (a)source
current waveform and (b)source current spectra.
(a) Scales: source current 1 A/div, time 4 ms/div
(b) Scales: spectra 200 mA/div, frequency 1.25 kHz/div
Figure 7: Experimental results with proposed scheme,
(a)source current waveform and (b)source current spectra. Figure 8 illustrates the PV power handling capability of the proposed hybrid APF. Figure 8(a) shows the load current and compensated source current waveforms with no active power generation from PV array. The active power is provided by the distribution source directly. Figure 8(b) shows the load current and compensated source current waveforms with 250W active power generation from PV array. The experimental results obtained show that the generated PV power is provided to the load through the proposed hybrid APF system to alleviate the burden of distribution source.
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(a) Scales: load current 2 A/div, source current 2 A/div, time 4 ms/div
(b) Scales: load current 2 A/div, source current 2 A/div, time 4 ms/div
Figure 8: Experimental results with proposed scheme, (a)load
and source current with no PV power and (b)load and source current with 250W PV power.
6 Conclusion
A single-phase hybrid APF connected to a PV array is presented. The proposed scheme combines the APF with a passive filter to improve the filtering performance of high-order harmonics. The compensation current reference estimation is simpler with the utilisation of extension p-q theorem. The experimental results show the effectiveness of the proposed scheme for wideband harmonics compensation and PV power handling capability.
Acknowledgements
This project was supported by the Intensification of Research in Priority Areas (IRPA) grant from the Ministry of Science, Technology and Innovation (MOSTI), Malaysia.
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