19 analysis and simulation of a three phase shunt active power filter with pq theory control t
TRANSCRIPT
Department of Electrical and Computer Engineering
Analysis and Simulation of a Three
Phase Shunt Active Power Filter with
PQ Theory Control Technique
By
Matthew Jonathan Lee
(12623114)
A thesis submitted for the degree of
Bachelor of Engineering in Electrical Engineering
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
TITLE: Analysis and simulation of a three-phase shunt active power filter with PQ theory control technique
AUTHOR: LEE, Matthew Jonathan FAMILY NAME: Lee GIVEN NAME: Matthew
DATE 3rd November 2006 SUPERVISOR Dr. Mohammad A.S Masoum
DEGREE Bachelor of Engineering OPTION Electrical Engineering
ABSTRACT
This project investigates the analysis and simulation of a shunt active power filter. The shunt active power filter provides current harmonic compensation for a nonlinear load on a single bus network. Current harmonic compensation is achieved by implementation of a PQ theory controller, which monitors the load current and injects equal amplitude and opposite phase compensation currents to neutralise load current harmonics. This ensures the source current remains fundamental. The project simulated results showed that a shunt active power filter is suited for use in current harmonic compensation on any bus on a power system network.
INDEXING TERMS Active Filter, PQ theory
GOOD AVERAGE POOR
TECHNICAL REPORT
REPORT
EXAMINER CO-EXAMINER
Synopsis This project investigates the analysis and simulation of a shunt active power filter.
The shunt active power filter provides current harmonic compensation for a
nonlinear load on a single bus network. Current harmonic compensation is achieved
by implementation of a PQ theory controller, which monitors the load current and
injects equal amplitude and opposite phase compensation currents to neutralise load
current harmonics. This ensures the source current remains fundamental. The project
simulated results showed that a shunt active power filter is suited for use in current
harmonic compensation on any bus on a power system network.
3rd November 2006
Matthew Lee
7 Scott Road
WANNEROO WA 6065
Professor Syed Islam
Head of Department
Department of Electrical and Computer Engineering
Curtin University of Technology
Kent St
BENTLEY WA 6102
Dear Professor Syed Islam,
I, Matthew Lee, hereby submit this thesis entitled “Analysis and Simulation of a
Three Phase Shunt Active filter using PQ Theory Control Technique” as partial
fulfillment for the degree of Bachelor of Engineering (Electrical Engineering).
This thesis is entirely my own work outside of where acknowledgement is given.
Yours sincerely,
Matthew Lee
12623114
Acknowledgements I would like to acknowledge and thank Dr Mohammad A.S Masoum for his role as
project supervisor. Dr Masoum provided much guidance, assistance and technical
information throughout this project. Though the project did not always go to plan, Dr
Masoum was always able to suggest alternative methods for various parts of the
project, and contributed greatly to the success of both the thesis and project
presentation.
I would also like to acknowledge Mr Rob Thornton of EnergySafety for his countless
hours spent providing technical information and suggestions for improvement
throughout this project.
I would also like to acknowledge Mr. Douglas Bonsu for giving up many of his
evenings to ensure a working simulation.
I would also like to acknowledge Miss Miriam Hamilton for her many hours spent
formatting my thesis and ensuring it met the strict guidelines.
i
Table of Contents Acknowledgements................................................................................................................................ i
Table of Contents ................................................................................................................................. ii
List of Figures...................................................................................................................................... vi
List of Tables ....................................................................................................................................... ix
CHAPTER 1 ......................................................................................................................................... 1
1.0 INTRODUCTION.......................................................................................................................... 1 1.1 The need for harmonic compensation.......................................................................................................... 1 1.2 Objective and aims ...................................................................................................................................... 2 1.3 Overview of project ..................................................................................................................................... 3
CHAPTER 2 ......................................................................................................................................... 5
2.0 THEORY OF HARMONICS FILTERS...................................................................................... 5 2.1 What are harmonic filters?.......................................................................................................................... 5 2.2 Types of harmonic filters involved in harmonic compensation ................................................................... 5 2.3 Classification of harmonic filters by system configuration ......................................................................... 7 2.4 Classification of harmonic filters by operating principle............................................................................ 7 2.5 Advantages/Disadvantages of each filter for application choice .............................................................. 11
CHAPTER 3 ....................................................................................................................................... 12
3.0 ACTIVE FILTERS RECOMMENDED STRATEGY.............................................................. 12 3.1 Introduction ............................................................................................................................................... 12 3.2 Classification of active filters .................................................................................................................... 12 3.3 Classification according to power rating and speed of response in compensated system......................... 13
3.3.1 Low power applications ................................................................................................... 14 3.3.1.1 Single-phase systems .......................................................................................... 14 3.3.1.2 Three-phase systems ........................................................................................... 15
3.3.2 Medium power applications............................................................................................. 15 3.3.3 High power applications .................................................................................................. 16
3.4 Classification according to power circuit, configurations and connections ............................................. 17 3.4.1 Shunt active filters ........................................................................................................... 17 3.4.2 Series active filters........................................................................................................... 18 3.4.3 Other combinations.......................................................................................................... 19
3.4.3.1 Combination of both shunt and series active filters ............................................ 19 3.4.3.2 Combination of series active and shunt passive filters ....................................... 20 3.4.3.3 Combination of shunt active and passive filters ................................................. 21 3.4.3.4 Active filter in series with shunt passive filters .................................................. 22
3.5 Classification according to compensated variable.................................................................................... 23
ii
3.5.1 Reactive power compensation ......................................................................................... 23 3.5.2 Harmonic compensation .................................................................................................. 24
3.5.2.1 Compensation of voltage harmonics................................................................... 24 3.5.2.2 Compensation of current harmonics ................................................................... 24
3.5.3 Balancing of three phase systems .................................................................................... 25 3.5.3.1 Balancing of mains voltage in three phase systems ............................................ 25 3.5.3.2 Balancing of mains current in three phase systems............................................. 25
3.5.4 Multiple compensation..................................................................................................... 26 3.5.4.1 Harmonic current with reactive power compensation......................................... 26 3.5.4.2 Harmonic voltages with reactive power compensation....................................... 26 3.5.4.3 Harmonic current and voltages ........................................................................... 26 3.5.4.4 Harmonic current and voltages with reactive power compensation.................... 27
3.6 Classification based upon control technique............................................................................................. 28 3.6.1 Open loop systems ........................................................................................................... 28 3.6.2 Closed loop systems......................................................................................................... 28
3.6.2.1 Constant capacitor voltage technique.................................................................. 29 3.6.2.2 Constant inductor current technique ................................................................... 29 3.6.2.3 Optimisation technique ....................................................................................... 29 3.6.2.4 Linear voltage control technique......................................................................... 30 3.6.2.5 Other techniques ................................................................................................. 30
3.7 Active filters harmonic detection and extraction ....................................................................................... 31 3.7.1 Types of harmonic detection strategies............................................................................ 31
3.7.1.1 Load current sensing........................................................................................... 31 3.7.1.2 Source current sensing ........................................................................................ 32 3.7.1.3 Point of Common Coupling (PCC) voltage sensing ........................................... 32
3.8 Classification based upon current/voltage reference estimation technique .............................................. 34 3.8.1 Current/voltage reference synthesis (continuous time-domain)....................................... 34
3.8.1.1 High pass filter method....................................................................................... 34 3.8.1.2 Low pass filter method........................................................................................ 35
3.8.2 Current/voltage reference calculation (discrete time or frequency domain) .................... 35 3.8.2.1 Time domain approaches .................................................................................... 35
3.8.2.1.1 Instantaneous reactive power algorithm ............................................... 36 3.8.2.1.2 Synchronous detection algorithm ......................................................... 37 3.8.2.1.3 Constant active power algorithm .......................................................... 37 3.8.2.1.4 Constant power factor algorithm .......................................................... 37 3.8.2.1.5 Fictitious power compensation algorithm............................................. 37 3.8.2.1.6 Synchronous frame based algorithm..................................................... 38 3.8.2.1.7 Synchronous flux detection algorithm.................................................. 38
3.8.2.2 Frequency domain approaches............................................................................ 38 3.8.2.2.1 Conventional Fourier and FFT algorithms ........................................... 39 3.8.2.2.2 Sine multiplication technique ............................................................... 39 3.8.2.2.3 Modified Fourier series techniques....................................................... 39
3.8.2.3 Other algorithms ................................................................................................. 40
CHAPTER 4 ....................................................................................................................................... 41
4.0 SHUNT ACTIVE FILTER WITH PQ CONTROLLER.......................................................... 41 4.1 Introduction ............................................................................................................................................... 41 4.2 Summary of active filter operation ............................................................................................................ 41
iii
4.3 Critical component operation.................................................................................................................... 42 4.3.1 DC voltage regulator........................................................................................................ 42 4.3.2 Active Filter Controller.................................................................................................... 44
4.3.2.1 Positive-sequence voltage detector ..................................................................... 44 4.3.2.2 The PQ Theory.................................................................................................... 47
4.3.3 Dynamic hysteresis band PWM controller....................................................................... 50 4.3.4 Other components ............................................................................................................ 53
CHAPTER 5 ....................................................................................................................................... 54
5.0 TWO BUS NETWORK MODEL SIMULATION .................................................................... 54 5.1 Introduction ............................................................................................................................................... 54 5.2 Simulation Component Comparison.......................................................................................................... 54
5.2.1 DC voltage regulator........................................................................................................ 55 5.2.2 Active Filter Controller.................................................................................................... 56
5.2.2.1 Positive Sequence Voltage Detector ................................................................... 56 5.2.2.1.1 Phase Locked Loop (PLL) and Sine Generator Model......................... 56
5.2.2.2 PQ Theory model................................................................................................ 59 5.2.2.3 Dynamic hysteresis PWM current converter model ........................................... 65
5.2.3 Inverter Injection.............................................................................................................. 66 5.2.4 System Modeling ............................................................................................................. 68
CHAPTER 6 ....................................................................................................................................... 69
6.0 MODEL VERIFICATION – CASE STUDIES ......................................................................... 69 6.1 Introduction ............................................................................................................................................... 69 6.2 Verification Procedure – six pulse thyristor converter.............................................................................. 69
6.2.1 Harmonic load modeling.................................................................................................. 69 6.2.2 Compensation results ....................................................................................................... 70 6.2.3 Source Waveforms........................................................................................................... 71
6.3 Verification Procedure – Three phase diode rectifier ............................................................................... 73 6.3.1 Harmonic load modeling.................................................................................................. 73 6.3.2 Compensation Results...................................................................................................... 74 6.3.3 Source Waveforms........................................................................................................... 75
6.4 Discussion.................................................................................................................................................. 76
CHAPTER 7 ....................................................................................................................................... 78
7.0 CONCLUSION............................................................................................................................. 78 7.1 Discussion.................................................................................................................................................. 78 7.2 Future Implications ................................................................................................................................... 79
CHAPTER 8 ....................................................................................................................................... 80
8.0 BIBLIOGRAPHY ........................................................................................................................ 80
APPENDICES .................................................................................................................................... 81 Appendix A – Gantt Chart ............................................................................................................................... 82
iv
Appendix B – Filter combinations ................................................................................................................... 84 Appendix C – Summary and Comparison of Filters ........................................................................................ 87 Appendix D – Shunt Active Filter System ........................................................................................................ 89 Appendix E – PQ Theory Controller ............................................................................................................... 90 Appendix F – DC Voltage Regulator MATLAB Code ..................................................................................... 91 Appendix G – Dynamic Hysteresis PWM Current Controller MATLAB Code................................................ 92
v
List of Figures
Figure 3.1 Generalized block diagram for active power filters [2] ..................................................... 13 Figure 3.2 Subdivisions of active filters according to speed response and power rating [2] .............. 14 Figure 3.3 Subdivision of power system filters according to power circuit configurations
and connections [2]............................................................................................................. 17 Figure 3.4 Shunt active filter used alone [4] ....................................................................................... 18 Figure 3.5 Shunt active filter network configuration [2] ..................................................................... 18 Figure 3.6 Series active filter configuration [2] .................................................................................. 19 Figure 3.7 Series active filter used alone [4]....................................................................................... 19 Figure 3.8 Combination of shunt and series active filters [2] ............................................................. 20 Figure 3.9 Series active and shunt filter combination [2] ................................................................... 20 Figure 3.10 Shunt active and shunt passive filter combination [2] ..................................................... 21 Figure 3.11 Active filter in series with shunt passive filter combination [2] ....................................... 22 Figure 3.12 Subdivision according to compensated variables [2]....................................................... 23 Figure 3.13 Classification of active power filters according to control techniques [2] ...................... 28 Figure 3.14 Load current sensing compensation schematic [7] .......................................................... 32 Figure 3.15 Source current sensing compensation schematic [7] ....................................................... 32 Figure 3.16 PCC voltage sensing compensation schematic [7]........................................................... 33 Figure 3.17 Subdivision according to current/voltage estimation techniques [2] ............................... 34 Figure 3.18 Calculations for the constant instantaneous supply power control strategy [8] .............. 36 Figure 4.1 DC voltage regulator schematic[6].................................................................................... 43 Figure 4.2 Block diagram of the fundamental positive sequence voltage detector [6] ........................ 47 Figure 4.3 Power components of the p-q theory in alpha-beta-0 coordinates [10]............................. 49 Figure 4.4 PQ theory control [6]......................................................................................................... 50 Figure 4.5 Hysteresis controller [6] .................................................................................................... 51 Figure 4.6 Hysteresis band PWM control [11].................................................................................... 52 Figure 5.1 Simulated DC voltage regulator circuit ............................................................................. 55 Figure 5.2 DC voltage regulator limit function ................................................................................... 55 Figure 5.3 Positive voltage sequence detector model .......................................................................... 56 Figure 5.4 PLL and sine generator ...................................................................................................... 57 Figure 5.5 Synchronising PLL circuit [12].......................................................................................... 57 Figure 5.6 Waveforms of Iα, Iβ and load current distortion ................................................................. 58 Figure 5.7 Total PQ theory model ....................................................................................................... 59 Figure 5.8 Power calculation............................................................................................................... 60 Figure 5.9 Clarke transformation ........................................................................................................ 60 Figure 5.10 Vα, Vβ to PQ controller ..................................................................................................... 60 Figure 5.11 Input harmonic load current............................................................................................. 61 Figure 5.12 Power waveform............................................................................................................... 61
vi
Figure 5.13 α-β current reference calculations ................................................................................... 62 Figure 5.14 Reference alpha-beta current ........................................................................................... 62 Figure 5.15 Alpha-Beta-0 to phase current compensation .................................................................. 63 Figure 5.16 Three phase compensation current................................................................................... 63 Figure 5.17 IEEE transaction paper comparisons – compensation currents [6] ................................ 64 Figure 5.18 Top stage view.................................................................................................................. 65 Figure 5.19 Hysteresis control model .................................................................................................. 66 Figure 5.20 Shunt inverter ................................................................................................................... 67 Figure 5.21 Shunt system ..................................................................................................................... 68 Figure 6.1 Three phase 6 pulse current source converter .................................................................. 69 Figure 6.2 Output current waveform ................................................................................................... 70 Figure 6.3 THD before active filter...................................................................................................... 70 Figure 6.4 THD reduction after active filter ........................................................................................ 71 Figure 6.5 Source current waveforms before compensation................................................................ 72 Figure 6.6 Source current waveforms after compensation .................................................................. 72 Figure 6.7 Single phase diode rectifier ................................................................................................ 73 Figure 6.8 Single phase diode rectifier output voltage and current..................................................... 73 Figure 6.9 Uncompensated THD system.............................................................................................. 74 Figure 6.10 Compensated THD system................................................................................................ 74 Figure 6.11 Uncompensated phase source current.............................................................................. 75 Figure 6.12 Diode rectifier compensated waveform............................................................................ 75 Figure 6.13 Computed source and current waveforms [6] .................................................................. 76 Figure A.1 Gantt chart ......................................................................................................................... 82 Figure A.2 Gantt chart (continued)...................................................................................................... 83 Figure B.1 Basic parallel-passive filter for current-source nonlinear loads. ...................................... 84 Figure B.2 Basic series-passive filter for voltage-source nonlinear loads. ......................................... 84 Figure B.3 Basic parallel-active filter for current-source nonlinear loads. ........................................ 84 Figure B.4 Basic series-active filter for voltage-source nonlinear loads............................................. 84 Figure B.5 Parallel combination of parallel-active and parallel-passive filters for current-
source nonlinear loads. ....................................................................................................... 84 Figure B.6 Series combination of series-active and series-passive filters for voltage-source
nonlinear loads.................................................................................................................... 84 Figure B.7 Hybrid of series-active and parallel-passive filters for current-source nonlinear
loads .................................................................................................................................... 84 Figure B.8 Hybrid of parallel-active and series-passive filters for voltage-source nonlinear
loads .................................................................................................................................... 84 Figure B.9 Series combination of parallel-passive and parallel-active filters for current-
source nonlinear loads ........................................................................................................ 84 Figure B.10 Parallel combination of series-passive and series-active filters for voltage-
source nonlinear loads. ....................................................................................................... 85 Figure B.11 Combined system of series-active and parallel-active filters for current-source
nonlinear loads.................................................................................................................... 85
vii
Figure B.12 Combined system of series-active and parallel-active filters for voltage-source nonlinear loads.................................................................................................................... 85
Figure B.13 Combined system of series-passive and parallel-passive filters for current-source nonlinear loads. ....................................................................................................... 85
Figure B.14 Combined system of parallel-passive and series-passive filters for voltage-source nonlinear loads. ....................................................................................................... 85
Figure B.15 Circuit I to reduce fundamental voltage of parallel-active filter. .................................... 85 Figure B.16 Circuit I to reduce fundamental current of series-active filter......................................... 85 Figure B.17 Circuit II to reduce fundamental voltage of parallel-active filter. ................................... 85 Figure B.18 Circuit II to reduce fundamental current of series-active filter. ...................................... 85 Figure B.19 Circuit III to reduce fundamental voltage of parallel-active filter................................... 86 Figure B.20 Circuit III to reduce fundamental current of series-active filter. ..................................... 86 Figure B.21 Circuit IV to reduce fundamental voltage of parallel-active filter. .................................. 86 Figure B.22 Circuit IV to reduce fundamental current of series-active filter. ..................................... 86 Figure D.1 Shunt active filter system ................................................................................................... 89 Figure E.1 PQ theory controller .......................................................................................................... 90
viii
List of Tables Table 4.1 Variation conditions for the capacitor voltage Vc1 and Vc2................................................. 42 Table C.1A Comparison of filters ........................................................................................................ 87 Table C.1A (continued) Comparison of filters ..................................................................................... 88
ix
CHAPTER 1 1.0 INTRODUCTION
1.1 The need for harmonic compensation
The implementation of Active Filters in this modern electronic age has become an
increasingly essential element to the power network. With advancements in
technology since the early eighties and significant trends of power electronic devices
among consumers and industry, utilities are continually pressured in providing a
quality and reliable supply. Power electronic devices such as computers, printers,
faxes, fluorescent lighting and most other office equipment all create harmonics.
These types of devices are commonly classified collectively as ‘nonlinear loads’.
Nonlinear loads create harmonics by drawing current in abrupt short pulses rather
than in a smooth sinusoidal manner.
In Australia, generators are designed to operate at the fundamental frequency of 50
Hz. Harmonics of frequencies above this value that are created at the load end must be
supplied from the generator. The major issues associated with the supply of
harmonics to nonlinear loads are severe overheating and insulation damage. Increased
operating temperatures of generators and transformers degrade the insulation material
of its windings. If this heating were continued to the point at which the insulation
fails, a flashover may occur should it be combined with leakage current from its
conductors. This would permanently damage the device and result in loss of
generation causing widespread blackouts.
1
One solution to this foreseeable problem is to install active filters for each nonlinear
load in the power system network. Although presently very uneconomical, the
installation of active filters proves indispensable for solving power quality problems
in distribution networks such as harmonic current compensation, reactive current
compensation, voltage sag compensation, voltage flicker compensation and negative
phase sequence current compensation. Ultimately, this would ensure a polluted free
system with increased reliability and quality.
1.2 Objective and aims
The objective of this project is to thoroughly analyse and simulate a shunt active
power filter. In doing so, the accuracy of current compensation for current harmonics
found at a nonlinear load, for the PQ theory control technique is supported and also
substantiates the reliability and effectiveness of this model for integration into a
power system network. The model is implemented across a two bus network
including generation to the application of the nonlinear load.
The aim of the system simulation is to verify the active filters effectiveness for a
variety of different nonlinear load cases. These are a six pulse thyristor current
converter and a three phase diode bridge rectifier with RL load. In each scenario, total
harmonic distortion measurements are undertaken along with a variety of waveforms
and the results are justified accordingly.
One of the most important features of the shunt active filter system proposed is its
versatility over a variety of different conditions. The application of the positive
2
sequence voltage detector from within the active filter controller is the key component
of the system. The positive sequence voltage detector gives incredible versatility to
the application of the active filter, because it can be installed and compensate for load
current harmonics even when the input voltage is highly distorted and unbalanced.
When filters alike do not contain this feature and is installed with a distorted voltage
input, the outcome is a low efficient current harmonic compensator with poor
accuracy of compensation current determination.
1.3 Overview of project
Chapter 2 introduces the concept of harmonic filtering and the key approaches
undertaken in compensation. It gives an overview of the different types of harmonic
filters and their advantages and disadvantages in application.
Chapter 3 promotes the concept of active filters as a recommended strategy in
providing accurate harmonic compensation. Active filters are classified according to
power rating, speed of response, power circuit, the compensated variable, the control
technique and the current/voltage reference determination.
Chapter 4 describes the shunt three phase active filter model configuration. The
reasoning behind major key components of the model are thoroughly argued
discussed.
3
Chapter 5 implements the simulation of the shunt three phase active filter
configuration discussed in chapter 4. Each aspect is thoroughly discussed and is
compared to the IEEE transaction paper for verification.
Chapter 6 provides the model verification of the shunt active filter in the form of two
case study scenarios. Each case study is investigated and an output of the results are
justified.
Chapter 7 concluded the thesis and provides suggestions for future scope of work.
(See Appendix A for project plan)
4
CHAPTER 2
2.0 THEORY OF HARMONICS FILTERS
2.1 What are harmonic filters?
Harmonic filters are used to eliminate the harmonic distortion caused by nonlinear
loads. Specifically, harmonic filters are designed to attenuate or in some filters
eliminate the potentially dangerous effects of harmonic currents active within the
power distribution system. Filters can be designed to trap these currents and, through
the use of a series of capacitors, coils, and resistors, shunt them to ground. A filter
may contain several of these elements, each designed to compensate a particular
frequency or an array of frequencies.
2.2 Types of harmonic filters involved in harmonic compensation
Filters are often the most common solution that is used to mitigate harmonics from a
power system. Unlike other solutions, filters offer a simpler inexpensive alternative
with high benefits. There are three different types of filters each offering their own
unique solution to reduce and eliminate harmonics. These harmonic filters are
broadly classified into passive, active and hybrid structures. The choice of filter used
is dependent upon the nature of the problem and the economic cost associated with
implementation.
A passive filter is composed of only passive elements such as inductors, capacitors
and resistors thus not requiring any operational amplifiers. Passive filters are
inexpensive compared with most other mitigating devices. Its structure may be either
of the series or parallel type. The structure chosen for implementation depends on the
type of harmonic source present. Internally, they cause the harmonic current to
5
resonate at its frequency. Through this approach, the harmonic currents are
attenuated in the LC circuits tuned to the harmonic orders requiring filtering. This
prevents the severe harmonic currents traveling upstream to the power source
causing increased widespread problems.
An active filter is implemented when orders of harmonic currents are varying. One
case evident of demanding varying harmonics from the power system are variable
speed drives. Its structure may be either of the series of parallel type. The structure
chosen for implementation depends on the type of harmonic sources present in the
power system and the effects that different filter solutions would cause to the overall
system performance. Active filters use active components such as IGBT-transistors
to inject negative harmonics into the network effectively replacing a portion of the
distorted current wave coming from the load. This is achieved by producing
harmonic components of equal amplitude but opposite phase shift, which cancel the
harmonic components of the non-linear loads.
Hybrid filters combine an active filter and a passive filter. Its structure may be either
of the series or parallel type. The passive filter carries out basic filtering (5th order,
for example) and the active filter, through precise control, covers higher harmonics.
6
2.3 Classification of harmonic filters by system configuration
There are many filter configurations which can be designed to eliminate troublesome
harmonic orders or to suppress them. The characterization of nonlinear loads and
their effects on the power system has lead to the derivation of 22 filter configurations
as shown in figures B.1 through to B.22. Figures B.1, B.3, B.5, B.7, B.9, B.15, B.17,
B.19 and B.21 are recognised configurations and figures B.2, B.4 and B.11 are
unfamiliar. Figures B.6, B.8, B.10, B.12, B.13, B.14, B.16, B.18, B.20 and B.22 are
novel and newly presented by [1]. Figures B.1, B.3, B.5, B.7, B.9, B.11, B.13, B.15,
B.17, B.19 and B.21 are dual to figures B.2, B.4, B.6, B.8, B.10, B.12, B.14, B.16,
B.18, B.20 and B.22 respectively. The filter configurations are in either parallel or
series however, the components used to achieve this are the same. This is due to the
two types of harmonic sources namely, current type and voltage type sources. It is
evident that other combinations based on these 22 basic configurations are possible.
For example, figures B.9 and B.10 can be modified using the dominant harmonic
active filter technique [1].
2.4 Classification of harmonic filters by operating principle
The configuration shown in figure B.1 is that of a parallel passive filter (PPF). The
PPF contains resonant LC tuned components corresponding to a particular harmonic
frequency. The filter is designed to provide a high impedance block at the load or
harmonic current source. This high impedance path effectively blocks currents of the
tuned harmonic order, thus acting as a harmonic current sink. The ultimate circuit of
the PPF is a capacitor. The configuration shown in figure B.2 is that of a series
passive filter (SPF). Unlike the PPF, the SPF acts like a current harmonic dam
providing high impedance blocks to the harmonic voltages of a specific order which
is tuned by the resonant LC components. In Figure B.2 , three resonant passive
7
filters are connected in series of which each LC component is tuned for the
respective 5th, 7th and 11th harmonic orders. The three resonant circuits provide a high
impedance path specifically designed to block the 5th, 7th and 11th harmonic orders
respectively. The ultimate circuit of the SPF is an inductor [1].
Figure B.3 shows the basic configuration of a parallel active filter (PAF). This filter
injects and supplies to the nonlinear load, harmonic currents of the same amplitude
but opposite phase shift. This effectively is designed to cancel the load harmonic
current. Thus, this filter acts like a harmonic current source. Figure B.4 shows the
basic configuration of a series active filter (SAF). Unlike the configuration in figure
B.3, this filter is connected in series and injects and supplies to the nonlinear voltage
source, harmonic voltage of the same amplitude but of opposite phase. This filter acts
like a harmonic voltage source to block harmonic current flow. The inverter used for
the PAF and SAF can be either a voltage source or current source inverter. In figures,
B.3-B.4, a voltage source inverter was used and this is evident by the energy storing
capacitor connected [1].
A parallel and series combination of a PAF and PPF is shown in figures B.5 and B.6,
respectively. The parallel combination is compatible for current source nonlinear
loads and the series combination is well-matched with voltage source nonlinear loads
as discussed previously. Due to the limited switching frequency and rating of the
active inverter, the PAF is better suited for the compensation of low order harmonics
such as the 5th and 7th. The PPF on the other hand is better equipped and compact to
handle the upper order harmonics such as the 11th. The combination of the two filters
provides excellent role sharing and be used in applications where a number of lower
and upper harmonics are present [1].
8
Figure B.7 shows a hybrid system of a small SAF and a PPF for current-source
nonlinear loads. The small SAF is used to eliminate the PPF’s problems, such as
resonance and influence of the source impedance, and enhance compensation
performance. The PPF sinks the load-harmonic current. Figure B.8 and B.7 are dual
circuits, where the hybrid system of a PAF and a SPF is designed for voltage-source
nonlinear loads. Contrary to figure B.7, the SPF in figure B.8 blocks harmonic
current and the PAF can be used to enhance the SPF’s performance and eliminate the
SPF’s resonance [1].
Figure B.9 shows a unique configuration whereby the rating of the PAF can be
reduced. This figure shows the series combination of a PPF and PAF. The PAF as
usual, injects harmonic current to the load to cancel out the load harmonics. In
addition, the PAF also provides fundamental current. This reduces the size of the VA
rating of the PAF and still provides excellent performance, as does a PAF. Figure
B.10 is the dual circuit of figure B.9 and shows a parallel combination of a SPF and
SAF. Similarly, the VA rating of the SAF can be reduced by letting fundamental
current through the SPF [1].
Figure B.11 shows a perfect model for true filter elimination for current source
nonlinear loads. This configuration includes all active components and therefore is
designed to eliminate all harmonic content rather than simply providing attenuation.
The PAF as usual, supplies harmonic current to the nonlinear load of equal amplitude
but opposite phase to cancel the load harmonic current. The SAF also blocks any
harmonic current from flowing through the line. In providing total elimination of
9
harmonic current, this configuration also ensures a pure sinusoidal and constant
voltage to the load. Figure B.12 is the dual circuit of figure B.11. This configuration
is ideal for voltage type harmonic loads. This system blocks harmonic current and
provides a pure sinusoidal voltage to all loads connected. Figure B.13 and B.14 show
the respective combination of passive filters for harmonic current-source loads and
harmonic voltage-source loads [1].
Active filters are expensive and have difficulties with high power application,
although their performance is superior. It is desirable to reduce active filters required
rating. Figures B.15 through B.22 shows examples of how to reduce fundamental
voltage across the PAF and fundamental current through the SAF. For example, in
figure B.15 the C and L form a voltage divider to reduce fundamental voltage across
the PAF. The fundamental voltage across the PAF is determined by impedance ratio
of C and L. Figure B.16 shows the dual circuit of figure B.15, where C and L form a
current divider to reduce fundamental current of the SAF. In figure B.17, an LC
parallel circuit resonating at the fundamental frequency is used to increase the
impedance ratio and reduce the fundamental voltage further. On the contrary, figure
B.18 uses an LC series resonating at the line frequency, thus further reducing the
SAF’s fundamental current. In figures B.19 and B.21, fundamental voltages across
the PAF can be reduced to zero by controlling the PAF’s injected fundamental
current. Similarly, in figures B.20 and B.22, fundamental current through the SAF
can be reduced to zero by controlling the SAF’s produced fundamental voltage [1].
10
2.5 Advantages/Disadvantages of each filter for application choice
Shunt passive filters have been widely used because of their low cost and low loss.
This is because the components are common but also because no active elements are
required. The performances of the filters are very sensitive to the power system
impedance and series or parallel resonance with the power system impedance may
occur. Also, the effective compensation with the variation of the voltage can not be
carried out with passive filters.
The performance of parallel active power filters (APF) does not depend on the power
system impedance, and dynamic compensation of harmonic and reactive power can
be achieved. Unfortunately, the VA rating of the power electronic converter in APF
becomes very large because it must withstand the line-frequency utility voltage.
Associated with the large VA converter rating are high cost, high electro-magnetic
interference and high power losses.
Appendix C summarises the main features of all configurations in terms of control
schemes, circuit designs and application considerations.
11
CHAPTER 3
3.0 ACTIVE FILTERS RECOMMENDED STRATEGY
3.1 Introduction
Active Filters are commonly used for providing harmonic compensation to a system
by controlling current harmonics in supply networks at the low to medium voltage
distribution level or for reactive power or voltage control at high voltage distribution
level [2]. These functions may be combined in a single circuit to achieve the various
functions mentioned above or in separate active filters which can attack each aspect
individually. The block diagram presented in section 3.2 shows the basic sequence of
operation for the active filter. This diagram shows various sections of the filter each
responding to its own classification.
3.2 Classification of active filters
The block diagram shown in figure 3.1 represents the key components of a typical
active power filter along with their interconnections. The reference signal estimator
monitors the harmonic current from the nonlinear load along with information about
other system variables. The reference signal from the current estimator, as well as
other signals, drives the overall system controller. This in turn provides the control
for the PWM switching pattern generator. The output of the PWM pattern generator
controls the power circuit through a suitable interface. The power circuit in the
generalized block diagram can be connected in parallel, series or parallel/series
configurations, depending on the transformer used [2].
12
Figure 3.1 Generalized block diagram for active power filters [2]
Active power filters according to [2] can be classified based on the following criteria:
1. Power rating and speed of response required in compensated systems;
2. Power-circuit configuration and connections;
3. System parameters to be compensated;
4. Control techniques employed; and
5. Technique used for estimating the reference current/voltage.
3.3 Classification according to power rating and speed of response in compensated
system
The block diagram shown in figure 3.2 shows the classification based on this
criterion. The size of nonlinear loads play a major role in deciding the way different
control methods are implemented. The filter required for compensation must be
practical for the load and this decision affects the speed of response. In general a
reciprocal relationship exists between the cost of a particular system to the required
speed of response [2].
13
Figure 3.2 Subdivisions of active filters according to speed response and power rating [2]
3.3.1 Low power applications
Low power applications govern applications with a power rating below 100kVA.
Applications of these sizes are generally associated with residential areas,
commercial buildings, hospitals and for a wide range of medium sized factory loads
and motor drive systems. Active filters chosen for this power range employ
sophisticated techniques catering with high pulse number PWM voltage or current
source inverters. The response time for smaller applications is relatively much faster
than other sizes ranging from ten microseconds to ten milliseconds. This type
comprises the following two categories [2].
3.3.1.1 Single-phase systems
Low power rating loads generally require single phase active filters [3]. They are
generally most employed in commercial buildings with a large number of computers.
This application means that current harmonics can be treated at the point of common
coupling (PCC). It is often economical and practical to install single phase active
filters on distribution based sites of reduced size capacity than a larger rated filter
installed upstream. This is due to the large number of the single-phase loads within
14
one building and the harmful consequences associated with the presence of large
amounts of harmonic in the neutral line. This allows for more selective compensation
as the operating conditions vary. Due to the load capacity drawn from residential
loads, it is rare for a high concentration of harmonics, and thus the impacts on the
neutral lines are not significant. Residential customers tend not invest in purchasing
active filters because there are no compulsory harmonic regulations however, the
main advantage of such an installation are that operating frequencies can be
increased moving to improved performance since only low ratings are employed [2].
3.3.1.2 Three-phase systems
The installation of three-phase filters is used for three-phase applications. Different
filter configurations can be tested and installed based upon whether the loads are
balanced or unbalanced. At levels below 100kVA, a three phase filter can be
reconfigured to compensate for three individual single phases in one unit or for a
single three-phase supply. When nonlinear loads are balanced, meaning all three
phased impedances are equal, a single three-phase-inverter configuration is
employed [4]. This choice of inverter is used when the objective is to eliminate as
many current harmonics as possible, assuming that the magnitudes and respective
phase angles in each phase are the same. In the situation when nonlinear loads are
unbalanced, or supply voltages are unsymmetrical, three single phase inverter
circuits are used [2].
3.3.2 Medium power applications
Power systems ranging between 100kVA to 10MVA fit the class of a medium power
application. Due to the fact that phase unbalances are reduced on this sized system,
the major objective is to eliminate current harmonics. In general, capacitive and
15
inductive static compensators, line-commutated thyristor converters, synchronous
condensers and cascaded multilevel-inverter VAR compensators, are often more
economic as reactive power compensation using active filters often is not viable.
This is due to the high voltage as well as problems with isolation and series/parallel
connection of switches. The speed of response expected in this range is of the order
of tens of milliseconds. [2]
3.3.3 High power applications
At high power ratings, the use of active filters becomes very uneconomical. This is
because of the lack of high switching frequency power devices that can control the
current flow. Thus, this is a major disadvantage for such systems. In addition, even
the latest advances in semiconductor technology still fall short as extra high voltages
of a few hundred kilovolts cannot be tolerated. The series-parallel combination is
possible however; implementation is difficult and also cost-ineffective. Harmonic
pollution upstream affecting high power ranges above 10MVA is not such a problem
compared against low power systems. The implementation of single and three phase
filters downstream at the low voltage system provides suitable compensation such
that significant harmonic pollution upstream is minimal. The static-VAR
compensation is then the major concern and is usually compensated for by using
traditional static power conditioners/filters as well as several sets of synchronous
condensers connected in parallel and cascaded multilevel-inverter VAR
compensators. The required response time for such cases is in the range of tens of
seconds, which is sufficient for contactors and circuit breakers to operate after taking
the optimal-switching decision. Power fluctuations in the range of a few seconds are,
on the other hand, treated by the generating stations' ancillary devices. [2]
16
3.4 Classification according to power circuit, configurations and connections
The choice of power circuit chosen for the active filter greatly influences its
efficiency and accuracy in providing true compensation. It is therefore important that
the correct circuit configuration is chosen. Figure 3.3 classes’ three major types of
filter structures along with the relevant power circuit.
Figure 3.3 Subdivision of power system filters according to power circuit configurations and
connections [2]
3.4.1 Shunt active filters
Shunt active filters are by far the most widely accept and dominant filter of choice in
most industrial processes. Figures 3.4-3.5 show the system configuration of the shunt
design. The active filter is connected in parallel at the PCC and is fed from the main
power circuit. The objective of the shunt active filter is to supply opposing harmonic
current to the nonlinear load effectively resulting in a net harmonic current. This
means that the supply signals remain purely fundamental. Shunt filters also have the
additional benefit of contributing to reactive power compensation and balancing of
three-phase currents. Since the active filter is connected in parallel to the PCC, only
the compensation current plus a small amount of active fundamental current is
carried in the unit. For an increased range of power ratings, several shunt active
filters can be combined together to withstand higher currents. This configuration
consists of four distinct categories of circuit, namely inverter configurations,
17
switched-capacitor circuits, lattice-structured filters and voltage-regulator-type
filters[2].
Figure 3.4 Shunt active filter used alone [4]
Figure 3.5 Shunt active filter network configuration [2]
3.4.2 Series active filters
The objective of the series active filter is to maintain a pure sinusoidal voltage
waveform across the load. This is achieved by producing a PWM voltage waveform
which is added or subtracted against the supply voltage waveform. The choice of
power circuit used in most cases is the voltage-fed PWM inverter without a current
minor loop. The active filter acts as a voltage source and thus it is often a preferred
solution of harmonic producing loads such as large capacity diode rectifiers with
capacitive loads. In general, series active filters are less commonly used against the
shunt design. Unlike the shunt filter which carries mainly compensation current, the
series circuit has to handle high load currents. This causes an increased rating of the
filter suitable to carry the increased current. Series filters offer the main advantage
over the shunt configuration of achieving ac voltage regulation by eliminating
18
voltage-waveform harmonics. This means the load contains a pure sinusoidal
waveform [2].
Figure 3.6 Series active filter configuration [2]
Figure 3.7 Series active filter used alone [4]
3.4.3 Other combinations
In some cases, the combinations of shunt and series active filters provide a greater
effectiveness in eliminating harmonic pollution from the system.
3.4.3.1 Combination of both shunt and series active filters
The diagram shown in figure 3.8 shows the combination of both parallel and series
active filters. This system combines both the benefits of the shunt and series and is
often used to achieve the demanding power system requirements. The control of
active filters can be complex. A combination of the two provides an even greater
complexity. The higher cost involved in a more complex design has shown a reduced
demand for the combined structure. As a result of the increased cost and complexity,
this combination has received less attention than other configurations. Flexible AC
19
transmission systems, commonly abbreviated as FACTS regularly make use of the
arrangement [2].
Figure 3.8 Combination of shunt and series active filters [2]
3.4.3.2 Combination of series active and shunt passive filters
The combination of the active parallel and active series filters in 3.4.3.1 was seen to
be very complex in control yielding a high cost. One method of reducing these
problems was to replace the parallel active filter with a passive structure. The series
active filter, which constitutes high impedance for high-frequency harmonics, is
accompanied by a parallel passive filter to provide a path for the harmonic currents
of the load. This combination, represented by figure 3.9, permits an improvement
over the characteristics of plain series active filters and the extension of their
capabilities to include current- harmonic reduction and voltage- harmonic
elimination. Passive filters are often easier and simple to implement and do not
require any control circuit. This, this deserves to be most beneficial. [2]
Figure 3.9 Series active and shunt filter combination [2]
20
3.4.3.3 Combination of shunt active and passive filters
As mentioned in 3.4.1, shunt active filters are best suitable to compensate for lower
order harmonics thus only requiring low power rating which serves most economical.
This configuration makes use of a passive filter which serves to compensate for the
high order load current harmonics. This combination, represented by figure 3.10
presents this important configuration. Combinations such as this can be designed to
compensate for higher powers without excessive costs for high-power switching. The
major disadvantage of this configuration is the fact that passive filters can only be
tuned for a specific predefined harmonic and thus cannot be easily changed for loads
which have varying harmonics. [2]
Figure 3.10 Shunt active and shunt passive filter combination [2]
21
3.4.3.4 Active filter in series with shunt passive filters
The combination of an active filter in series with a shunt passive filter is considered a
significant design configuration for medium and high voltage applications. The
passive filter is designed to reduce the voltage stress applied to the switches in the
active filter. This design is in its infancy of development however, further research is
still needed to assess the effectiveness of the configuration. [2]
Figure 3.11 Active filter in series with shunt passive filter combination [2]
22
3.5 Classification according to compensated variable
Active filters are designed to provide suitable compensation for a particular variable
or a multiple of sorts in cases of combination structures. Figure 3.12 shows the
variety of compensated variable that active filters can provide for.
Figure 3.12 Subdivision according to compensated variables [2]
3.5.1 Reactive power compensation
The shunt active filter does provide reactive power compensation however; they
rarely treat the problem of power-factor correction on its own owing to the fact that
other quasidynamic, cheaper and slower-in-response reactive-power compensators
are available in the market. When this technique is applied, lower power applications
are more suited since the currents needed for reactive-power compensation are of the
same order of magnitude as the rated current of the load. It would be a waste of
sophisticated equipment to tackle them without the use of other power factor-
correction devices, such as thyristor-controlled reactors and capacitors; especially in
single-phase systems, where in certain specific applications the requirement is for
accurate compensation without harmonics generation [2].
23
3.5.2 Harmonic compensation
Within the system, active filters can be used to provide suitable harmonic
compensation for voltage harmonics and current harmonics. These harmonic are the
most important variable requiring compensation.
3.5.2.1 Compensation of voltage harmonics
In general, the concern for compensating voltage harmonics is not high due to the
fact that power supplies usually have low impedance [5]. Generally, at the point of
common coupling, ridged standards are implemented to ensure a correct level of total
harmonic distortion (THD) and voltage regulation is maintained. The problem of
compensating for voltage harmonics is to ensure the supply to be purely sinusoidal.
This is important for harmonic voltage sensitive devices such as power system
protection devices and superconducting magnetic energy storage. Voltage harmonics
are related to current harmonics by the impedance of the line. Although
compensation of voltage harmonics helps to provide a reduction in current
harmonics, this however, does not negate the necessity to current harmonic
compensation [2].
3.5.2.2 Compensation of current harmonics
Current harmonic compensation strategies are exceptionally important as mentioned
by [4]. From 3.5.2.1, current harmonics are greatly reduced by the compensation of
voltage harmonics at the consumer’s point of common coupling. The reduction in
current harmonics is not only important for reasons such as device heating and
reduction in life of devices but also in design of power system equipment. One of the
major design criteria covers the magnitude of the current and its waveform. This is to
reduce cable and feeder losses. Since the root mean square (RMS) of the load current
24
incorporates the sum of squares of individual harmonics, true current harmonic
compensation will aid system designers for better approached power rating
equipment [2].
3.5.3 Balancing of three phase systems
In most low and medium voltage distribution systems, it is frequent to find situations
where the currents and voltages in the three phases are not balanced and are not
evenly distributed by 120 degrees.
3.5.3.1 Balancing of mains voltage in three phase systems
Voltage imbalance is a situation where each phase voltage is unequal in magnitude
and is not displaced by 120 degrees. This is a direct result of current imbalances and
the severity of the system imbalances is governed by the magnitude of the supply
impedance. The solution to this problem is to add or subtract the corresponding
amount of instantaneous voltage to force it to follow the reference sinusoidal
waveform. On high voltage systems, the supply impedance does not impact severely
on system performance and thus the problem of mains voltage unbalances are
primarily related to low rating systems. [2]
3.5.3.2 Balancing of mains current in three phase systems
In low power applications such as compensating for residential loads, the magnitude
of currents supplied to the grid depends entirely upon the level of imbalance in the
system. In most cases, the compensator would be forced to supply rated current [4].
This places a limitation on the power handling capability.
25
3.5.4 Multiple compensation
To target a variety of variables requiring compensation, often it is usual to combine
different combinations to improve the effectiveness of the filter. The following are
the most frequently used combinations.
3.5.4.1 Harmonic current with reactive power compensation
One very common filter design makes use of combining aspects of reactive power
compensation together with harmonic current elimination. This ensures the supply
current remains purely fundamental free from distributing harmonics whilst making
certain the current is in phase with the supply voltage [6]. This approach is very cost
effective because only one device is used for all aspects rather than including
multiple circuits for each individual objective. The active filter used here however,
suffers from poor power switching limits and thus can only serve as a compensator
for low powered applications [2].
3.5.4.2 Harmonic voltages with reactive power compensation
This combination, however rare, takes place in certain configurations for controlling
the voltage harmonics, which would normally affect indirectly (using suitable
feedback) the reactive-power compensation. This compensation system is only
suitable for low-power applications [2].
3.5.4.3 Harmonic current and voltages
To compensate for both current and voltage system harmonics, a shunt and series
active filter configuration must be used respectively. Integrating this filter serves to
eliminate load harmonics whilst ensuring the supply remains fundamental. This type
of design contains very complex control algorithms and is normally used only for
26
very sensitive devices such as power-system-protection equipment and
superconducting magnetic-energy storage systems [2].
3.5.4.4 Harmonic current and voltages with reactive power
compensation
This filter design incorporates all three compensating variables into one unit. It
controls all harmonics and reactive power within the system. This is achieved by
implementing of a parallel/series active filter combination. The control for this
design is very complex and difficult to maintain and thus is not often employed [2].
27
3.6 Classification based upon control technique
Figure 3.13 presents the basic control structure for active power system filters. The
two main techniques are open look control and closed loop control.
Figure 3.13 Classification of active power filters according to control techniques [2]
3.6.1 Open loop systems
Open-loop systems sense the load current and the harmonics it contains. They inject
a fixed amount of power in the form of current (mainly reactive) into the system,
which may compensate for most of the harmonics and/or reactive power available.
Since there is no feedback loop on this system, there is no reference to check the
performance and accuracy of the filter. This is a traditional technique and in present
day is not often used [2].
3.6.2 Closed loop systems
Closed loop control systems incorporate a feedback loop providing greater accuracy
of current injection for harmonic compensation as well as reactive power reduction
well over the open loop design. This feature enables true sensing of the required
variables under consideration. Almost all new techniques in use are of this type.
28
3.6.2.1 Constant capacitor voltage technique
In this technique, the DC link contains a capacitor and once charged, this capacitor
voltage is the voltage source which controls the current waveform by PWM
techniques. The voltage across the terminals of the capacitor often fluctuates due to
the fact that energy is either supplied or expelled. To regulate and maintain terminal
voltage levels, a reference voltage is chosen. The difference between the actual
capacitor voltage and the predefined reference voltage determines the active
component of power required to compensate for losses in the filter. This error
difference is added to the current-controller error signal to determine the overall
system error to be processed by the current controller. This technique is widely
accepted and is very popular [2].
3.6.2.2 Constant inductor current technique
The control replaces the use of the capacitor in the DC link with an inductor. The
system operates much the same as mentioned in 3.6.2.1 however; the capacitor
voltage is replaced with the inductor current. This is achieved in two ways: (i)
current pulse-width modulation where like in 3.6.2.1, the PWM provides the required
pulses to represent the average current signal and (ii) current pulse amplitude
modulation which is a new control method provides the active filter with a basis for
amplitude modulation rather than solely the width [2].
3.6.2.3 Optimisation technique
The optimization procedure for switched-capacitor and lattice-filter circuits is the
same. The rate of rise of the current and the amplitude depend mainly on the size of
the capacitors and the initial voltages on them. These factors are functions of the
switching patterns, and they provide considerable flexibility in shaping the waveform
of the current drawn by the filter. The key to controlling these filter configurations is
29
to determine the appropriate switching function for the switches. The main task of
the system controller is to minimise a predetermined number of individual load-
current harmonics, in addition minimising either the THD or the fundamental
component of the filter current. However, this is not performed instantaneously. A
time delay exists between the detection of a change in the harmonic current and the
application of the new set of switching angles obtained from the optimisation
procedure. This system is mainly suitable for constant or slowly varying loads [2].
3.6.2.4 Linear voltage control technique
Series active filters incorporating the additional benefit of voltage regulation can be
controlled using the linear voltage control technique. Through regularly charging and
discharging the capacitor through linear control, the capacitor voltage can be
regulated. The reference capacitor voltage can be determined based upon the
harmonic reference. The charge in the supply loop of the circuit and thus switching
frequency can be controlled by the regular variations of the capacitor voltage in
contrast to the abrupt changes in inverter voltage waveforms. This technique ensures
that the supply side receives no abrupt variation of voltage and this reduces the
amount of high-frequency harmonics injected into the supply due to the presence of
the PWM inverter [2].
3.6.2.5 Other techniques
Other control techniques exist that simply provide small changes to the
aforementioned techniques, providing simply newer or better performance over their
predecessors. These techniques may include the use of state of the art adaptive,
predictive and sliding-mode controllers, which are normally difficult to implement
without the use of Digital Signal Processing (DSP). These techniques can be
implemented in either the time domain or the frequency domain [2].
30
3.7 Active filters harmonic detection and extraction
A shunt active filter acts as a controllable harmonic current source. In principle,
harmonic compensation is achieved when the current source is commanded to inject
harmonic currents of the same magnitude but opposite phase to the load harmonic
currents. Before the inverter can subtly inject opposing harmonic currents into the
power system, appropriate harmonic detection strategies must be implemented to
efficiently sense and determine the harmonic current from the nonlinear load.
3.7.1 Types of harmonic detection strategies
There are 3 different types of harmonic detection strategies used to determine the
current reference for the active filter. These are [4],
1. Measuring the load harmonic current to be compensated and using this as a
reference command;
2. Measuring source harmonic current and controlling the filter to minimise it;
and
3. Measuring harmonic voltage at the active filter point of common coupling
(PCC) and controlling the filter to minimise the voltage distortion.
3.7.1.1 Load current sensing
This method involves measurement of the load current and subsequent extraction of
its harmonic content using a high pass filter scheme. The harmonic components, so
extracted, are adjusted for polarity and used as reference commands for the current
controller. This is explained with the help of equation 3.1 and figure 3.14. Denoting
the harmonic components of the load current by , the describing equation for this
strategy is
lhi
31
* ( ) ( )c lhi t i t= (3.1)
Figure 3.14 Load current sensing compensation schematic [7]
3.7.1.2 Source current sensing
In this strategy, the source current is measured and its harmonic component
extracted. This is scaled by a suitable controller, generally of the proportional type.
The output of the proportional controller is provided as a reference to the current
controller. This is schematically represented in figure 3.15 and analytically expressed
by equation 3.2. Denoting the harmonic components of the source current by shi , the
describing equation for this strategy is
* ( ) ( )c sh si t K i t= − × h (3.2)
Figure 3.15 Source current sensing compensation schematic [7]
3.7.1.3 Point of Common Coupling (PCC) voltage sensing
This method requires measurement of the harmonic component of the Point of
Common Coupling (PCC) voltage, e(t). The harmonic component is then used to
generate the current reference, after passing it through a proportional controller.
Schematically, it is represented in figure 3.16 and analytically expressed by equation
32
3.3. Denoting the harmonic components of the PCC voltage by , the describing
equation for this strategy is
he
* ( ) ( )c vh hi t K e t= × (3.3)
Figure 3.16 PCC voltage sensing compensation schematic [7]
Load current sensing and supply current sensing are suitable for shunt active filters
installed in the vicinity of one or more harmonic producing loads by individual high-
powered consumers. PCC voltage sensing is suitable for shunt active filters, which
will be installed on distribution systems by utilities. Supply current detection is the
most basic harmonic detection method for series active filters acting as a voltage
source [4].
33
3.8 Classification based upon current/voltage reference estimation technique
There are numerous techniques each sub classified in figure 3.17 which propose
methods to calculate and determine the appropriate compensating reference current
used for the active filter to pass to the PWM inverter.
Active power-system filters
Current/voltageReference calculation
Instant reactive power
Current/voltage reference synthesis
Highpass-filter method
Lowpass-filter method
Time domain
Frequency domain
Other algorithms
Synchronous detection
Constant active power
Constant (utility) power factor
Fictitious power consumption
Synchronous frame
Synchronous flux detection
Conventional Fourier and FFT
Sine-multiplication technique
Modified-Fourier-series technique
Figure 3.17 Subdivision according to current/voltage estimation techniques [2]
3.8.1 Current/voltage reference synthesis (continuous time-domain)
In this method, an analogue signal filter is applied at the supply side to determine the
current harmonics from the supply. This technique is very simple and easy to
implement however introduces major amounts of magnitude and phase errors [2].
3.8.1.1 High pass filter method
This method uses a high pass filter to pass high ordered frequencies effectively
removing low order components in the load current signal. The filtered frequencies
constitute the reference portion. This technique however, is susceptible to noise as
this is undesired [2].
34
3.8.1.2 Low pass filter method
This method is favored in terms of reference synthesis because unlike the high pass
filter method, the effects of noise in the filtered portion are suppressed. The desired
reference value is the harmonic component found in the load current. This is
determined by subtracting the low order frequency component found from
implementing a low pass filter from the total load current. This presents the harmonic
portion from the load current waveform. This technique however, introduces large
magnitude and phase errors [2].
3.8.2 Current/voltage reference calculation (discrete time or frequency
domain)
The techniques mentioned in 3.7.1 have many disadvantages to their use namely,
phase and magnitude errors as well as the effects of noise. The calculation of
harmonics therefore provides the most appropriate alternative. Two major techniques
are classified in either time domain or frequency domain [2].
3.8.2.1 Time domain approaches
The following seven subdivisions of time-domain approaches are mainly used for
three-phase systems except for the fictitious-power-compensation technique which
can be adopted for single- or three-phase systems. The time-domain methods are
mainly used to gain more speed or fewer calculations compared to the frequency-
domain methods [2].
35
3.8.2.1.1 Instantaneous reactive power algorithm
Instantaneous power theory determines the harmonic distortion from the
instantaneous power calculation in a three-phase system, which is the multiplication
of the instantaneous values of the currents and voltages [8].
.v v ipv v iqα β α
β α β
⎛ ⎞ ⎛⎛ ⎞= ⎜ ⎟ ⎜⎜ ⎟ −⎝ ⎠ ⎝ ⎠ ⎝
⎞⎟⎠
(3.4)
The values of the instantaneous power p and q, which are the real and respective
imaginary powers, contain dc and ac components depending on the existing active,
reactive and distorted powers in the system. The dc components of p and q represent
the active and reactive powers and must be removed with high-pass filters to retain
only the ac signals. The ac components converted by an inverse transformation
matrix to the abc-frame represent the harmonic distortion, which is given as the
reference for the current controller. These processes are depicted in figure 3.18.
Figure 3.18 Calculations for the constant instantaneous supply power control strategy [8]
This operation takes place only under the assumption that the three-phase system is
balanced and that the voltage waveforms are purely sinusoidal. If, on the other hand,
this technique is applied to contaminated supplies, the resulting performance is
proven to be poor [2, 8].
36
3.8.2.1.2 Synchronous detection algorithm
This technique relies in the fact that the three phase currents are balanced. The
average power is calculated and divided equally between the three phases. The signal
is then synchronised relative to the mains voltage for each phase. This technique,
however easy to implement, suffers from the fact that it depends to a great extent on
the harmonics in the voltage signal. [2]
3.8.2.1.3 Constant active power algorithm
The instantaneous and average powers of the load are calculated. The active power
component of the system is controlled to keep the instantaneous real power constant,
while maintaining the imaginary power to zero. This technique performs fairly well
under ordinary conditions. However, the performance deteriorates when the supply is
contaminated. [2, 9]
3.8.2.1.4 Constant power factor algorithm
This technique forces the instantaneous current signal to track the voltage-reference
waveform. This implies that the power factor is fixed to unity and the system would
only be suitable for the combined system of VAR and current-harmonic
compensation. [2]
3.8.2.1.5 Fictitious power compensation algorithm
The system controller is designed to minimise the undesired component of power. In
this aspect, it is similar to the instantaneous-reactive-power algorithm but with a
different definition of power. This approach is suitable for both single and three
phase systems. However it involves a large amount of computation.[2]
37
3.8.2.1.6 Synchronous frame based algorithm
This algorithm relies on Park transformations to transform the three phase system
from a stationary reference frame into synchronously rotating direct, quadrature and
zero-sequence components. These can easily be analysed since the fundamental-
frequency component is transformed into DC quantities [34]. The active and reactive
components of the system are represented by the direct and quadrature components,
respectively. The high-order harmonics still remain in the signal; however they are
modulated at different frequencies. These are the undesired components to be
eliminated from the system and they represent the reference harmonic current. 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.
This method is applicable only to three-phase systems.[2]
3.8.2.1.7 Synchronous flux detection algorithm
This technique applies Park transformations to transfer the system into
synchronously rotating direct, quadrature and zero-sequence frames of reference.
However, it applies the transformation on the flux linkage of the filter inductance,
which is then controlled using the output voltages and currents in separate integral
loops. The presence of these integral loops incorporates time delays, which depend
on the frequency response of the special feed forward and feedback integrators.[2]
3.8.2.2 Frequency domain approaches
The frequency-domain methods are mainly identified with Fourier analysis,
rearranged in such a manner that this provides the result as fast as possible with a
reduced number of calculations, to allow a real-time implementation in DSP’s. Once
the Fourier transform is taken, the APF converter-switching function is computed to
produce the distortion canceling output. With this strategy the inverter switching
38
frequency must be more than twice the highest compensating harmonic frequency.
This strategy has a poorer dynamic response and it not as widely used. [2]
3.8.2.2.1 Conventional Fourier and FFT algorithms
Using the Fast Fourier Transform (FFT), the harmonic current can be reconstructed
by eliminating the fundamental component from the transformed current signal and
then the inverse transform is applied to obtain a time-domain signal. The main
disadvantage of this system is the accompanying time delay. This technique needs to
take samples of one complete cycle (or an integral number of cycles) to generate the
Fourier coefficients and it is therefore suitable for slowly varying load conditions.[2]
3.8.2.2.2 Sine multiplication technique
This method relies on the process of multiplying the current signal by a sine wave of
the fundamental frequency and integrating the result. This results in a loss of all the
high-order harmonics using a simple low-pass filter. The performance is still slow
(more than one complete mains cycle). This technique is similar to the Fourier
techniques presented above; it is, however, differently implemented.[2]
3.8.2.2.3 Modified Fourier series techniques
The principle behind this technique is that only the fundamental component of
current is calculated and this is used to separate the total harmonic signal from the
sampled load-current waveform. The practical implementation of this technique
relies on modifying the main Fourier series equations to generate a recursive formula
with a sliding window. This technique is adapted to use two different circular arrays
to store the components of the sine and cosine coefficients computed every sampling
sub cycle. The newly computed values of the desired coefficient are stored in place
of the old ones and the overall sums of the sine and cosine coefficients are updated
39
continuously. The computation time is much less than that of other techniques used
for single-phase applications. This technique is equally suitable for single- or three-
phase systems. [2]
3.8.2.3 Other algorithms
There are numerous optimization and estimation techniques, and all the utilities and
libraries for estimation can be used to perform this task. However some new methods
arise, such as the neural network and adaptive-estimation techniques which are fairly
accurate and have, of course, much better response. Unfortunately, presently
available control hardware is not suitable for implementation of these techniques.[2]
40
CHAPTER 4
4.0 SHUNT ACTIVE FILTER WITH PQ CONTROLLER
4.1 Introduction
The objective of shunt active filters is ultimately the same, the primary goal being to
compensate for current harmonics in the power system. A variety of active filters
also extend upon this initial goal to include reactive power compensation and as an
outcome of this power factor correction. The model shown in appendix D is a
simplified schematic of a three phase shunt active power filter implementation to a
power system network. This active filter model subtly compensates for current
harmonics and reduces of the total harmonic distortion.
4.2 Summary of active filter operation
Current source nonlinear loads such as a six-pulse thyristor converter require
harmonics from the generator. Although the demand for current harmonics may only
be of a few orders above the fundamental, the generator upstream is compelled to
supply this current. This causes the generator to operate at frequencies above the
nominal 50Hz or 60Hz and in doing so, also creates a negative phase-sequence
component which is undesirable.
A shunt active filter is considered a current source because it injects non-sinusoidal
current through the parallel branch of the network in order to compensate for the
current harmonic demand of the nonlinear load. The role of the active filter controller
is to sense and monitor the load current and to appropriately determine the correct
41
reference harmonic current for the inverter. Once the correct reference harmonic
content is determined; this reference current is fed through a suitable current
controller which then is sent to the inverter for injection into the network. Appendix
D shows the model of the three phase four wire shunt active power filter using a
conventional three leg converter.
4.3 Critical component operation
4.3.1 DC voltage regulator
The dc voltage regulator is designed to automatically maintain a constant voltage
level. It supervises the dc capacitor voltages and provides two control signals, Ploss
and ε . The capacitor voltages of C1 and C2 vary by certain conditions caused by the
shape of the current reference and the hysteresis bandwidth. If the current references
are assumed to be composed from zero-sequence components, the line currents will
return through the neutral wire. For a split capacitor inverter topology as shown in
figure D.1, the currents can flow in both directions through the switches and
capacitors. Therefore, variations in the capacitor voltages can also be caused by a
zero-sequence current reference as shown in Table 4.1 [6].
0 fkfk
dii and
dt> 0< Increase the voltage in C1
0 fkfk
dii and
dt< 0< Decrease the voltage in C1
0 fkfk
dii and
dt< 0> Increase the voltage in C2
0 fkfk
dii and
dt> 0> Decrease the voltage in C2
Table 4.1 Variation conditions for the capacitor voltage Vc1 and Vc2
42
Figure 4.1 DC voltage regulator schematic[6]
The inputs to the dc voltage regulator are the two capacitor voltages and an internal
fixed reference voltage. The capacitor voltage difference from the reference input is
filtered using a lower pass filter with a cutoff frequency at 20 Hz to render it
insensitive to the fundamental frequency voltage variations which appear when the
active filter compensates the fundamental zero sequence current of the load. The
voltage is then amplified using a proportional-integral (PI) controller which outputs
signal Ploss. Ploss aims to compensate for losses in the PWM converter which tends to
discharge the dc capacitors and thus neutralise the dc bus voltage variations. This
gives rise to a negative feedback loop.
The second output from the dc voltage regulator is the dynamic offset level. This
offset level is dynamic because it changes accordingly as to ensure that the difference
in dc capacitor voltages 2 1(Vc Vc )− stays within an acceptable tolerance limit. The
capacitor voltage difference is filtered and then sent along with the reference voltage
to a limiting function which is used to determine the appropriate limits.
43
The limit function must adhere to the following limits:
1 0.05
0.05 0.050.05
1 0.05
ref
ref refref
ref
V V
V V V VV
V V
ε
ε
ε
⎧ = − ⇔ Δ < −⎪
Δ⎪ = ⇔ − ≤ Δ ≤⎨⎪⎪ = ⇔ Δ >⎩
(4.1)
4.3.2 Active Filter Controller
4.3.2.1 Positive-sequence voltage detector
The active filter controller suitably determines reference currents by integration of an
appropriate control theory. This model incorporates the PQ theory. The input to the
controller monitors the load current waveform and the source voltage waveform and
calculates power based upon these parameters. Since the shunt active filter is
designed predominantly for current harmonic mitigation, the harmonics present in
the power waveform can be assumed to be attributed solely by the current harmonics
demanded by the nonlinear load. If one assumes that the voltage waveform is
perfectly sinusoidal and free from all harmonics then this condition becomes true. If
the three phase voltage input to the controller is unbalanced or high distorted, then
the reference currents calculated would not completely filter the current harmonics
demanded by the nonlinear load. This situation gives rise for the need of a positive
sequence voltage detector.
The positive sequence voltage detector shown in figure 4.2 derives the positive
sequence fundamental signal from a three phase voltage signal carried by the power
line. The PLL control circuit tracks the positive sequence voltage at the fundamental
frequency of highly distorted and unbalanced three phase signals. The synchronizing
circuit determines accurately the fundamental frequency of the system voltage and
44
phase angle of the measured signals which may be unbalanced and contain
harmonics.
The fundamental frequency is used as input to a sine wave generator that produces
three auxiliary signals namely ( ) to be used as ‘fundamental positive
sequence currents’ along the detector [6]. These currents together with the line
voltages are then inputs to a Clarke
' , ' , 'a b ci i i
0α β− − transformation algorithm and power
calculation. Equation 4.2 shows the transformation matrix which converts the phase
voltages and phase currents into the appropriate reference frame. Equation 4.3
determines the power values composed from the fundamental positive sequence
voltage and auxiliary currents.
The α β− voltage reference box of figure 4.2 calculates the alpha and beta reference
voltages given by equation 4.4. Finally, the a-b-c instantaneous values of the
fundamental positive sequence voltage are determined by the 0α β− − inverse
transformation box, without errors in the amplitude or phase angle as shown in
equation 4.5. The voltages calculated from equation 8 are now considered as input to
the main control circuit.
Thus the purpose of the positive sequence voltage detector is justified as the active
filter controller compensates the load current as if it were connected directly to a
perfectly balanced sinusoidal voltage source, irrelevant if the source is in fact
unbalanced or highly distorted [6]:
45
0
0
1 1 12 2 2
2 1 11 .3 2 2
3 302 2
1 1 12 2 2
2 1 11 .3 2 2
3 302 2
a
b
c
a
b
c
v vv vv v
i ii ii i
α
β
α
β
⎛ ⎞⎜ ⎟
⎛ ⎞ ⎜ ⎟ ⎛ ⎞− −⎜ ⎟ ⎜ ⎟ ⎜ ⎟=⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ −⎜ ⎟⎜ ⎟⎝ ⎠
⎛ ⎞⎜ ⎟
⎛ ⎞ ⎜ ⎟ ⎛ ⎞− −⎜ ⎟ ⎜ ⎟ ⎜ ⎟=⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ −⎜ ⎟⎜ ⎟⎝ ⎠
(4.2)
0 0 0 00 .0
p v ip v vq v v
α β α
0
iiβ α β
⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟ = ⎜ ⎟⎜ ⎟
⎜ ⎟ ⎜ ⎟−⎝ ⎠ ⎝ ⎠
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
(4.3)
2 2
' ' ' '1 . .' ' '' ' '
v i i pv i ii i q
α α β
β β αα β
⎛ ⎞⎛ ⎞ ⎛ ⎞= ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟−+⎝ ⎠ ⎝ ⎠ ⎝ ⎠
(4.4)
1 0'
'2 1 3' .'3 2 2
'1 3
2 2
a
b
c
vv
vv
v
α
β
⎛ ⎞⎜ ⎟⎜ ⎟⎛ ⎞
⎛ ⎞−⎜ ⎟ ⎜ ⎟= ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎜ ⎟ ⎜ ⎟⎝ ⎠ −⎜ ⎟−⎜ ⎟
⎝ ⎠
(4.5)
46
Figure 4.2 Block diagram of the fundamental positive sequence voltage detector [6]
4.3.2.2 The PQ Theory
The p-q theory formally known as “The Generalized Theory of the Instantaneous
Reactive Power in Three-Phase Circuit” was first developed by H. Akagi in 1983.
[10] It is based in instantaneous values in three phase power systems with or without
neutral wire, and is valid for steady state or transitory operations, as well as for
generic voltage and current waveforms. The p-q theory consists of an algebraic
transformation known as a Clarke transformation of the three phase input voltages
and the load harmonic currents in the a-b-c coordinates to the 0α β− − reference
frame followed by the calculation of the real and reactive instantaneous power
components.
From equation (4.3), equation (4.6) shows how expanding the matrices give the
algebraic formula for determining the instantaneous zero sequence power,
instantaneous real power and the instantaneous imaginary power [10].
0 0 0p v ip v i v iq v i v i
α α β β
α β β α
= ×
= × + ×
= × − ×
(4.6)
Figure 4.3 shows a diagram of the interactions of each of the power components
within the power system and how each relates to one another.
47
0p is the average value of the instantaneous zero sequence power. This corresponds
to the power which is transferred from the power supply to the load through the zero
sequence components of voltage and current.
~
0p corresponds to the alternating power of the instantaneous zero sequence power.
This relates to the exchanged power between the power supply and the load through
the zero sequence components of voltage and current. The zero sequence power only
exists in three phase systems with neutral wire.
p is the mean value of the instantaneous real power. This corresponds to the energy
per unit time unity which is transferred from the power supply to the load.
~p is alternating value of the instantaneous real power. This corresponds to power
which is exchanged between the power supply to the load.
q is the instantaneous imaginary power. This corresponds to the power that is
exchanged between the phases of the load. This component is not constructive to the
system and is accountable for the undesirable current which circulate between the
system phases. The reactive power does not transfer power from the supply to the
load nor does it exchange power.
48
Figure 4.3 Power components of the p-q theory in alpha-beta-0 coordinates [10]
From figure 4.3, the only component of the power obtained through the p-q theory
that is desirable and constructive is the average real power and the average zero
sequence power. This is because power is transferred from the supply to the load.
The other components of power are less desirable and this can be compensated by
the shunt active filter. [10]
The control diagram for the shunt active filter controller is shown in figure 4.4. An
important component to note is the high pass filter with cut off frequency of 50Hz.
This filter receives the instantaneous real power from equation 4.3 and filters all
frequencies of power greater than the fundamental. The output waveform is thus the
harmonic power which is recognized as containing only current harmonics. This is
justified as once can assume a perfectly sinusoidal voltage source by virtue of the
integrated positive sequence voltage detector.
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−Δ+−
⎟⎟⎠
⎞⎜⎜⎝
⎛ −
+=⎟⎟
⎠
⎞⎜⎜⎝
⎛
qpp
vvvv
vvii
c
c~
22 ..1**
αβ
βα
βαβ
α (4.7)
49
0
0
1 1 02
*2 1 1 3* .3 2 22* *
1 1 32 22
ca
cb
cc c
i ii ii i
α
β
⎛ ⎞⎜ ⎟⎜ ⎟ ⎛ ⎞−⎛ ⎞ ⎜ ⎟− ⎜ ⎟⎜ ⎟ = ⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎜ ⎟− −⎜ ⎟⎜ ⎟⎝ ⎠
(4.8)
*
The harmonic power output from the high pass filter together with the reactive power
is used in equation 4.7 to determine the alpha and beta references of the currents.
These currents are then inputs to equation 4.8 where the instantaneous current
references to the PWM current control are determined.
Figure 4.4 PQ theory control [6]
4.3.3 Dynamic hysteresis band PWM controller
Current control is implemented through feedback modulation of a dynamic hysteresis
band PWM controller. The shunt line current tracks the reference current within a
hysteresis band. By comparing the reference currents calculated by the controller
with the measured values of compensation currents, the command signals for the
inverter semiconductor switches can be produced.
50
Figure 4.6 illustrates the principle of the dynamic hysteresis current controller
technique. If the shunt line current exceeds the maximum limit of the hysteresis
band, the upper switch of the inverter arm is turned off and the lower switch is turned
on. As a result, the current starts to decay. If the current crosses the minimum limit of
the hysteresis band, the lower switch of the inverter arm is turned off and the upper
switch is turned on. As a result, the current gets back into the hysteresis band. Hence,
the shunt line current is forced to track the reference current with the hysteresis band.
ε
fai
fbifci
*cai*cbi*cci
1S
2S
3S
4S
5S
6S
Figure 4.5 Hysteresis controller [6]
The signal ε actuates as a dynamic offset level that is added to both hysteresis band
limits in the PWM current control as shown in figure 4.5. The maximum and
minimum limits are determined by equation 4.9 [6].
*
*
*
Upper hysteresis band limit = (1 )
Lower hysteresis band limit = (1 )
( , , ) s the instantaneous current reference & is a fixed semi-bandwidth of the hysteresis control
ck
ck
ck
i
i
where i k a b c i
ε
ε
⎧ + Δ +⎪⎨
−Δ −⎪⎩
=
[4.9]
51
Thus, the signal ε shifts the hysteresis band to change the switching times such that
1 2
2 1
00
C C
C C
rises V and lowers Vrises V and lowers V
εε> ⇒⎧
⎨ < ⇒⎩ [4.10]
Figure 4.6 Hysteresis band PWM control [11]
52
4.3.4 Other components
Appendix D shows an inductive filter and RC high pass filter placed at the inverter
output. The inductive filter is designed to limit the ripple of the compensation
currents whilst the RC high pass filter is set in the active filter output to filter the
inverter commutation frequencies.
Low power active filters are installed close to each problematic load, avoiding the
circulation of current harmonics, reactive currents and neutral currents through the
utility power lines. This solution reduces the power lines losses and voltage drops,
and avoids voltage distortions at the load terminals.
53
CHAPTER 5
5.0 TWO BUS NETWORK MODEL SIMULATION
5.1 Introduction
Simulation is a powerful way to reduce development time and ensure the proper
fulfillment of critical steps. In this project, simulations were performed, which
allowed the study of its behavior under different operation conditions, and permitted
the tuning of some controller parameters together with the optimization of the active
filter component values. Matlab/Simulink and the Power System Blockset were used
as simulation tools in this development, as it offered an integrated environment
between designing control algorithms and the electrical network models.
5.2 Simulation Component Comparison
Each component of the shunt active filter controller was simulated and tested. Major
simulated block models together with accompanying waveforms were compared
against those found in the key IEEE transaction paper [6].
54
5.2.1 DC voltage regulator The block model for the dc voltage regulator is shown in figure 5.1.
Figure 5.1 Simulated DC voltage regulator circuit
The reference voltage is equal to 600V. Vdc1 and Vdc2 are ‘from tags’ that monitor the
capacitor voltage value and are inputs to the dc voltage regulator. The limit function
obeys equation 4.1 and is shown in figure 5.2 along with the MATLAB code for the
function which is shown in Appendix F.
Figure 5.2 DC voltage regulator limit function
The parameter values for the PI control such as the proportional gain (Kp) and
integral gain (Ki) were achieved through a trial and error approach until the system
maintained stability. These values were Kp = 0.0.1 and Ki = 50.
55
5.2.2 Active Filter Controller
5.2.2.1 Positive Sequence Voltage Detector
The block model for the positive sequence voltage detector is shown in figure 5.3.
The input is a three phase unbalanced or high distorted voltage and the output gives a
purely sinusoidal voltage, free from harmonics which is used as the input to the p-q
controller.
Figure 5.3 Positive voltage sequence detector model
5.2.2.1.1 Phase Locked Loop (PLL) and Sine Generator Model
The PLL block model combined with the sine generator model is shown in figure
5.4. The input is unbalanced or highly distorted three phase voltages and the output is
three phase auxiliary currents used as ‘fundamental positive sequence signals’ along
the detector. The normalized inputs for the PI controller ( ) ip
KG s Ks
⎡ ⎤= +⎢ ⎥⎣ ⎦are Kp =
0.98, Ki = 80.
56
Figure 5.4 PLL and sine generator
The PLL and sine generator model shown in figure 5.4 can be verified by figure 5.5
taken from [12].
∑
X
Xsin( )tω sin( / 2)tω π−
sin( / 2 2 / 3)tω π π− −
sin( / 2 2 / 3)tω π π− +sin( 2 / 3)tω π+
1s
abV
cbV
( )ai tω
( )ci tω
3P φ ω
1ai
1bi
1ci
tω
Figure 5.5 Synchronising PLL circuit [12]
Since the current harmonic nonlinear load used for this simulation are balanced and
thus demands current harmonics only, the voltage will remain sinusoidal. To test and
verify that the model is correct, three phase load distorted current waveforms are
used at the input as a substitute.
57
Figure 5.6 Waveforms of Iα, Iβ and load current distortion
Figure 5.6 shows the three phase distorted nonlinear load input to the positive
sequence detector. The output shows Iα and Iβ perfectly sinusoidal. Thus the
positive sequence voltage detector had been modeled and is shown through
waveforms that the model is functioning as desired.
58
5.2.2.2 PQ Theory model
Appendix E shows the complete PQ theory circuit schematic found in the IEEE
transaction paper [6]. The total simulated model of the PQ theory is shown in figure
5.7.
Figure 5.7 Total PQ theory model
The inputs to the PQ controller are the measured load currents from the nonlinear
load and the α β− voltage reference from the positive sequence voltage detector.
The outputs are the three phase reference currents to be sent to the inverter for
injection. A closer analysis of the power calculation block diagram is shown in figure
5.8. The three phase harmonic load currents are converted into the α β− current
reference using equation 4.2 and is modeled by figure 5.9. Figure 5.8 used equation
4.3 to define the instantaneous, imaginary and zero sequence power.
59
Figure 5.8 Power calculation
Figure 5.9 Clarke transformation
The waveforms showed in figures 5.10 and 5.11 represent the input voltage and load
current respectively to the PQ controller.
Figure 5.10 Vα, Vβ to PQ controller
60
Figure 5.11 Input harmonic load current
The waveform of the instantaneous power shown in figure 5.12 comprises of current
harmonics. This is because of the implementation of the positive sequence voltage
detector creating a perfectly harmonic free sinusoidal voltage.
Figure 5.12 Power waveform
61
The inverse power transformation block model shown in figure 5.13 gives the
α β− current reference calculations.
Figure 5.13 α-β current reference calculations
Using the single second order high pass filter, the waveform from the inverse power
transformation is shown in figure 5.14.
Figure 5.14 Reference alpha-beta current
The inverse current reference transformation block model shown in figure 5.15 gives
the phase current reference calculations.
62
Figure 5.15 Alpha-Beta-0 to phase current compensation
The waveform from the inverse current transformation is shown in figure 5.16. These
three phase currents are then sent to the filter for injection through the shunt branch
to the neutralise the load harmonic current.
Figure 5.16 Three phase compensation current
63
The IEEE transaction paper of [4] shows a subtle difference between the three phase
compensation currents. This can be attributed to differences in the parameter values
between some components of the controller and system network which were
assumed given these were not present in the paper.
Figure 5.17 IEEE transaction paper comparisons – compensation currents [6]
64
5.2.2.3 Dynamic hysteresis PWM current converter model
The top stage level of the dynamic hysteresis current PWM converter is shown in
figure 5.18. The inputs are the reference currents from the PQ controller, the
dynamic offset level, the bandwidth and the shunt line current. The outputs are
switching signals used to control the inverter switches.
Figure 5.18 Top stage view
Within each of the three hysteresis control blocks, a series of functions are set in
order to appropriately control each switch of the inverter. Equation 4.9 is modeled
and the calculated process behind each hysteresis control block together with the
embedded MATLAB function code is hown in figure 5.19 and Appendix G
respectively.
s
65
Figure 5.19 Hysteresis control model
5.2.3 Inverter Injection
igure 5.20 shows the inverter portion of the active filter responsible for injecting the
comp allel branch to supplement the current harmonic load
F
ensation current in the par
demanded from by the source. Vdc1 and Vdc2 are two dc capacitors used to provide
the necessary voltage to power the inverter. This voltage is regulated by the dc
voltage regulator. The shunt inverter receives signals sent from the dynamic
hysteresis PWM current controller and outputs three phase compensation currents.
66
Figure 5.20 Shunt inverter
67
5.2.4 System Modeling Figure 5.21 shows the shunt system connected into the existing power system
network. The connected lines before the active filter are from the generator and the
connected line after the filter connects to the nonlinear load. The system consists of
the shunt inverter along with series commutation inductance of 2.5 millihenries. A
tuned high pass filter is also connected to filter the inverter commutation frequencies.
The high pass filter RC parameters are 1 ohm and 30 microfarads.
Figure 5.21 Shunt system
68
CHAPTER 6
6.0 MODEL VERIFICATION – CASE STUDIES
6.1 Introduction
A three phase six pulse current source converter and a three phase diode rectifier are
used independently to verify the functionality of the active filter in its ability to
compensate for current harmonics.
6.2 Verification Procedure – six pulse thyristor converter
6.2.1 Harmonic load modeling Figure 6.1 shows the three phase six pulse current source converter used to model the
current harmonic nonlinear load. The thyristor converter receives switching signals
from the synchronized six pulse generator and outputs a controlled dc waveform due
to the alpha angle set by the generator. Values for the α angle = 30 degrees, R = 25.5
ohms and the output current is 8.12A.
Figure 6.1 Three phase 6 pulse current source converter
69
The output current from the thyristor converter is shown in figure 6.2.
Figure 6.2 Output current waveform
6.2.2 Compensation results Figure 6.3 shows the effect of current harmonics due to the nonlinear load to the
power system network. Since a balanced nonlinear load is connected across three
phases, the total harmonic distortion (THD) over the entire system will be the same
across a particular phase. Without the shunt active filter connected, the THD due to
the three phase thyristor converter is 32.65%.
Figure 6.3 THD before active filter
70
Figure 6.4 THD reduction after active filter
Figure 6.4 shows the shunt system connected into the power system network. With
the shunt active filter connected, the THD due to the three phase thyristor converter
is 2.234%. This value shows a 30.416% compensation of the active filter compared
to the THD found in figure 6.3. Thus, the filter is compensating as desired.
6.2.3 Source Waveforms Figures 6.5 and 6.6 show the three phase source current waveform before
compensation and after compensation respectively.
71
Figure 6.5 Source current waveforms before compensation
Figure 6.6 Source current waveforms after compensation
72
6.3 Verification Procedure – Three phase diode rectifier
6.3.1 Harmonic load modeling Figure 6.7 shows the harmonic load model of the diode rectifier with an RL load.
The connection of the diode presents a balanced load as the rectifier was connected
across all three phases to ground. The commutation inductance = 3 mH, Rdc =20
ohms and Ldc = 300 mH.
Figure 6.7 Single phase diode rectifier
Figure 6.8 shows the diode rectifier output voltage and current
Figure 6.8 Single phase diode rectifier output voltage and current
73
6.3.2 Compensation Results
Figure 6.9 shows the uncompensated power system network with the three phase
diode rectifier as load. The THD of the system is 21.52%. Figure 6.10 shows the
power system when the shunt active filter was implemented. The THD was brought
down to 2.106%.
Figure 6.9 Uncompensated THD system
Figure 6.10 Compensated THD system
74
6.3.3 Source Waveforms Figures 6.11 and 6.12 showed the uncompensated and compensated source current
waveform for the diode rectifier.
Figure 6.11 Uncompensated phase source current
Figure 6.12 Diode rectifier compensated waveform
75
6.4 Discussion
The waveform shown in figures 6.13 is the IEEE paper waveform of the source
current found in [6]. The configuration of the system model from the paper included
a diode bridge connected at t = 30ms from b-phase and neutral, two controlled
(thyristor) bridges connected after t = 40ms across all phases and a-phase and neutral
respectively. For simplicity, and to avoid increased complications due to unbalanced
loads; this project incorporated the two loads used in the case studies for separate
testing. Thus, figures 6.6 and 6.7 concur with the sinusoidal relationship of figure
6.13.
Figure 6.13 Computed source and current waveforms [6]
From sections 6.2.2 and 6.3.2, the THD was reduced to 2.234% and 2.106%
respectively. The active filter does not totally filter all harmonics, such as reducing
the THD to 0% for several reasons.
An inverter is a power electronics device which uses several switches at appropriate
times to shape the output waveforms as desired. This short abrupt switching, self
generates internal harmonics and partially contributes to the small THD.
76
Another source of harmonics comes from efficiency issues from the positive
sequence voltage detector which could have propagated throughout the system. If
this is true, harmonics from the input voltage source would contribute to inaccurate
compensation and this could also partially contribute to the small THD.
77
CHAPTER 7
7.0 CONCLUSION
7.1 Discussion
This project investigated the analysis and simulation of a shunt active power filter.
The project simulated results showed that the shunt active power filter model
proposed was suited for use in current harmonic compensation on any single bus on a
power system network. One of the areas of strength for this project includes the
implementation of a positive sequence voltage detector. This allows the filter to
become more versatile as it can be installed in areas of high voltage distortion or
unbalanced input signals. The filter, given these input conditions has the ability to
extract the positive sequence component of the input voltage as it compensates for
current harmonics. Thus, the filter acts as if it was connected to a perfectly sinusoidal
input.
Another major strength of this shunt active power filter is the results achieved under
the two case study scenarios. For each of the given nonlinear loads, the active filter
reduced the total harmonic distortion to below 5%. The strength is the fact that the
internal harmonics generated by the inverter remained minimal. This is a definite
advantage and adds to the positive outcome to the overall success of the
compensation.
Areas of weakness in this project include the efficiency of the major high pass filter,
which is responsible for filtering the harmonic component from the real power
78
waveform. In addition, the hysteresis band PWM current controller proves a likely
source of errors due to the complexity.
7.2 Future Implications
For future research, once might consider designing a higher order high pass filter for
within the controller. This filter is responsible for filtering out the harmonic
component of the real power. As all filters are not ideal, and thus lack in their ability
to filter every component as required, an element of error is introduced in the
calculation of the reference currents and thus compensation currents. This error is
such that the compensation currents will not exactly match the load harmonic
currents and thus harmonic currents will remain in the system. Although the total
harmonic distortion will be reduced, designing a filter of a higher order will prove
valuable in increasing the filters accuracy and thus efficiency.
The determination of the PI controller values is also another area of interest for
future consideration. These values relate to the compensation of the DC voltage
regulator maintaining a regulated voltage across the two capacitors such that it will
provide voltage to power the inverter. In general the determination of these values is
very cumbersome and for this project a trial and error approach was sustained. These
values are accurate to the extent of observing output waveforms from the controller
and adjusting the parameters accordingly to achieve a plateau curve at time increases.
79
CHAPTER 8
8.0 BIBLIOGRAPHY
[1] F. Z. Peng, "Harmonic sources and filtering approaches," Industry
Applications Magazine, IEEE, vol. 7, pp. 18-25, 2001. [2] M. El-Habrouk, M. K. Darwish, and P. Mehta, "Active power filters: a
review," Electric Power Applications, IEE Proceedings-, vol. 147, pp. 403-413, 2000.
[3] C. Y. Hsu and H. Y. Wu, "A new single-phase active power filter with reduced energy-storage capacity," Electric Power Applications, IEE Proceedings-, vol. 143, pp. 25-30, 1996.
[4] H. Akagi, "New trends in active filters for power conditioning," Industry Applications, IEEE Transactions on, vol. 32, pp. 1312-1322, 1996.
[5] V. B. Bhavaraju and P. Enjeti, "A fast active power filter to correct line voltage sags," Industrial Electronics, IEEE Transactions on, vol. 41, pp. 333-338, 1994.
[6] M. Aredes, J. Hafner, and K. Heumann, "Three-phase four-wire shunt active filter control strategies," Power Electronics, IEEE Transactions on, vol. 12, pp. 311-318, 1997.
[7] P. S. Sensarma, K. R. Padiyar, and V. Ramanarayanan, "A comparative study of harmonic filtering strategies for a shunt active filter," 2000, pp. 2509-2516 vol.4.
[8] J. Afonso, C. Couto, and J. Martins, "Active Filters with Control Based on the p-q Theory," IEEE Industrial Electronics Society Newsletter, vol. 47, pp. 5-10, September 2000.
[9] A. Cavallini and G. C. Montanari, "Compensation strategies for shunt active-filter control," Power Electronics, IEEE Transactions on, vol. 9, pp. 587-593, 1994.
[10] J. Afonso, H. Silva, and J. Martins, "Active Filters for Power Quality Improvement," IEEE Power Technology, pp. 10-13, September 2001.
[11] MathWorks, "Simulink - Model-Based and System-Based Design Modelling, Simulation, Implementation," 5 ed, 2002.
[12] L. F. C. Monteiro, M. Aredes, and J. A. Moor Neto, "A control strategy for unified power quality conditioner," 2003, pp. 391-396 vol. 1.
[13] J. Technologies, "Guide to Harmonics with AC variable Frequency Drives." vol. 2006 Illinois, 2006.
80
APPENDICES
81
Appendix A – Gantt Chart
Figure A.1 Gantt chart
82
Figure A.2 Gantt chart (continued)
83
Appendix B – Filter combinations
Figure B.1 Basic parallel-passive filter for current-source nonlinear loads.
Figure B.2 Basic series-passive filter for voltage-source nonlinear loads.
Figure B.3 Basic parallel-active filter for current-source nonlinear loads.
Figure B.4 Basic series-active filter for voltage-source nonlinear loads.
Figure B.5 Parallel combination of parallel-active and parallel-passive filters for current-source nonlinear loads.
Figure B.6 Series combination of series-active and series-passive filters for voltage-source nonlinear loads.
Figure B.7 Hybrid of series-active and parallel-passive filters for current-source nonlinear loads
Figure B.8 Hybrid of parallel-active and series-passive filters for voltage-source nonlinear loads
Figure B.9 Series combination of parallel-passive and parallel-active filters for current-source nonlinear loads
84
Figure B.10 Parallel combination of series-passive and series-active filters for voltage-source nonlinear loads.
Figure B.11 Combined system of series-active and parallel-active filters for current-source nonlinear loads.
Figure B.12 Combined system of series-active and parallel-active filters for voltage-source nonlinear loads
Figure B.13 Combined system of series-passive and parallel-passive filters for current-source nonlinear loads.
Figure B.14 Combined system of parallel-passive and series-passive filters for voltage-source nonlinear loads.
Figure B.15 Circuit I to reduce fundamental voltage of parallel-active filter.
Figure B.16 Circuit I to reduce fundamental current of series-active filter.
Figure B.17 Circuit II to reduce fundamental voltage of parallel-active filter.
Figure B.18 Circuit II to reduce fundamental current of series-active filter.
85
Figure B.19 Circuit III to reduce fundamental voltage of parallel-active filter.
Figure B.20 Circuit III to reduce fundamental current of series-active filter.
Figure B.21 Circuit IV to reduce fundamental voltage of parallel-active filter.
Figure B.22 Circuit IV to reduce fundamental current of series-active filter.
86
Appendix C – Summary and Comparison of Filters
Fig.
Operating principle/ Suited nonlinear
loads
Circuit design and control scheme
Features, performance, and
consideration
VA rating/system cost
A.1
Harmonic sink/CSNL Low-impedance circuit or series-resonant circuit
Resonance with and influenced by the source impedance
Var+harmonic current i.e. V*(IVAR+ILh) /cheapest
A.2 Harmonic dam / VSNL
High-impedance circuit or parallel resonance circuit
No resonance whit and no bad influence by the source
Fundamental+harmonic voltage /i.e.I*(Vdf +Vlh) Cheapest
A.3 Current source/ CSNL PAF injects current so that Ic =Ilh
Ideal performance to CSNL
V*Ilh / expensive
A.4 Voltage source /VSNL
SAF produces voltage Vc= -VLh
Ideal performance to VSNL
I*VLh / expensive
A.5 Current source+ harmonic sink / CSNL
PAF: low-order harmonic compensation and resonance damping; PPF: high-order harmonic compensation
Good performance, compensation role sharing, dynamic var compensation possible
PAF:V*ILh(5,7)
PPF:V*(Ivar+ILh(11,13,..))/faily expensive
A.6 Voltage source+ harmonic dam / VSNL
SAF: low-order harmonic compensation and damping; SPF: high-order harmonic compensation
Good performance, compensation role sharing, dynamic voltage regulation possible
SAF:I*VLh(5,7) PPF:I*(Vdf+VLh(11,13,..))/fairly expensive
A.7 SAF: harmonic isolation FPF: harmonic compensation / CSNL
SAF: blocking harmonic current PPF: low-impedance circuit
Ideal performance, dynamic voltage regulation possible
SAF: I*ILh ZF,minimize VA rating, PPF: V*(IVar+ILh) /minimized system cost
A.8 PAF: harmonic isolation SPF: harmonic blocking /VSNL
PAF: eliminate upstream and adjacent harmonics so that no harmonics appear at the terminal voltage VT SPF: high impedance circuit
Ideal performance, dynamic VAR compensation possible by PAF
PAF:V*Ih(upstream+adjacent) , SPF:I*(Vf+VLh) / minimized system cost
A.9 PAF: enhancing PPF and resonance damping PPF: harmonic compensation/CSNL
PAF: is controlled so that load-harmonic current is absorbed completely by the PPF PPF: low-impedance circuit
Ideal performance to CSNL, source harmonic voltage will appear at the terminal VT
PAF:(IVar+ILh)*ILh ZF , minimized VA, PPF: V*(Ivar+Ilh)/ minimized system cost
A.10
SAF: enhancing SPF SAF: harmonic blocking/ VSNL
SAF: helping to block harmonic current, Vc= -Vlh
SPF:high- impedance circuit
Ideal performance to VSNL/no harmonic resonance
SAF: VLhVLh/ZD, minimized VA SPF:I*(Vf+VLh) / minimized system cost
A.11 SAF: harmonic isolation PAF: harmonic compensation / CSNL
SAF: harmonic isolation, source harmonic compensation, and voltage regulation, PAF:load-harmonic compen.
Ideal performance to CSNL, dynamic voltage regulation and var compensation possible
SAF: I*VSh , PAF: V*(Ivar+ILh)/ most expensive
A.12 SAF: harmonic compen. PAF: harmonic shunting / VSNL
SAF: load-harmonic compensation, PAF: shunt to upstream and adjacent harmonics
Ideal performance to , dynamic var compensation possible
SAF: I*VLh , PAF: V*Ih(upstream/adjacent) /most expensive
Table C.2A Comparison of filters
87
A.13 SPF: harmonic
isolation PPF: harmonic compensation / CSNL
SPF: for harmonic isolation and source harmonic compensation; PPF: for load-harmonic compensation
Better performance than PPF alone, VT becomes sinusoidal even when VSh exists
SPF I*VSh , PAF: V*(Ivar+ILh)/ cheap
A.14 SPF: harmonic compen. PPF: harmonic shunting/ VSNL
SPF: load-harmonic compensation; PPF: provides shunt to adjacent harmonic loads
Make the terminal voltage VT more sinusoidal when source and adjacent harmonic exist
SPF: I*VLh , PPF: V*Ih(upstream/adjacent) / cheap
A.15 A.17 A.19 A.21
Use LC circuits to reduce fundamental voltage applied on PAF / CSNL
Fundamental voltage of the PAF can be reduced to XL /(XC+XL) in Fig.A.15, to XL/(XP+XL) in Fig.A.17, and to zero in Fig. A.19 and A.21. On the other hand, harmonic current injected by the PAF will cause harmonic drop over XC or XP.
An optimum design is desirable to minimize the total VA rating of PAF and total system cost. Dynamic var compensation not possible.
Fig.A.15:(VXL /(XC+XL)+ILhXC)*ILh Fig.A.17:(VXL /(XP+XL)+ILhXP)*ILh Fig. A.19:ILhXP*(ILh+V/XP) Fig. A.21:ILhXC*(ILh+V/XC)
A.16 A.18 A.20 A.22
Use LC circuit to reduce fundamental current flowing through SAF/ VSNL
Fundamental current of the SAF can be reduced to XL
/(XC+XL) in Fig.A.16, to XL/(XC+XL) in Fig.A.18, and to zero in Fig. A.20 and A.22. On the other hand, harmonic voltage produced by the SAF will cause harmonic current over XC or XP.
An optimum design is desirable to minimize the total VA rating of SAF and total system cost. Dynamic voltage regulation not possible.
Fig.A.16:(IXL /(XC+XL)+VLh /XL)*VLh Fig.A.18:(VXL /(XS+XL)+VLh /
XS)*ILh Fig. A.20:VLh / XS*(VLh+IXS) Fig. A.22:VLh /XL*(VLh+IXL)
Table C.3A (continued) Comparison of filters
88
Appendix D – Shunt Active Filter System
Figure D.1 Shunt active filter system
89
Appendix E – PQ Theory Controller
Figure E.1 PQ theory controller
90
Appendix F – DC Voltage Regulator MATLAB Code
function y = fcn(Vc, Vref, e) % This block supports an embeddable subset of the MATLAB language. % See the help menu for details. if Vc< (-0.05 * Vref) y=-1; elseif Vc > (0.05 * Vref) y=1; else y=e; end
91
Appendix G – Dynamic Hysteresis PWM Current Controller MATLAB Code
function y = fcn(ifr, IrMax, IrMin, u3) % This block supports an embeddable subset of the MATLAB language. % See the help menu for details. if ifr >= IrMax y=1; elseif ifr <= IrMin y=0; else y=u3; end
92