thai nguyen university university of technology
TRANSCRIPT
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THAI NGUYEN UNIVERSITY
UNIVERSITY OF TECHNOLOGY
STUDY ON CONTROLLER DESIGN FOR
THE ACTIVE FILTER
Speciality: Automation and Control Engineering
Code: 9520216
ABSTRACT OF DOCTORAL DISSERTATION IN ENGINEERING
THAI NGUYEN – 2021
2
Research project completed at
University of Technology – Thai Nguyen University
Scientific supervisor 1: Assoc. Prof. Nguyen Duy Cuong, Dr.
Scientific supervisor 2: Prof. Horst Puta, D.Sc.
Opponent 1:………………………………………………....
Opponent 2:………………………………………………....
Opponent 3:……………………………………………........
The dissertation will be reported in front of the Dissertation Exam Council
at University level hold at :………………………………………………..
on the...day of...... 2021 at ....
The dissertation can be found at:
- The Library at University of Technology -Thai Nguyen University
- Leaning Resource Center of Thai Nguyen University
- Viet Nam National Library
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FOREWORDS
1. Necessaries of the research project
Electric power transmission systems is responsible for providing
energy for power consumption loads. It depends on the nature of
households of the electricity consumption, characteristics of the load are
also very different. Industrial loads include motors controlled by high
frequency switching frequency converters, high frequency furnaces,
saturation engines; Commercial electrical loads in high buildings are
saturation transformers, LEDs, computers, computing systems that store
data, etc. All of these types of devices are collectively known as non-
linear devices because they cause harmonics in the grid and can generate
problems with power system quality.
To evaluate the influence of harmonics, total harmonic distortion
(THD) factor is used, according to IEEE Std 519, THD of the current in
the system should be less than 5%.
Thus, the study on control of active filters to reduce harmonics
generated by non-linear loads is an urgent issue in order to improve the
power grid quality. Therefore, Ph.D. student chooses the research
project "Study on controller design for the active filter" to contribute to
reduction of harmonics and improvement of the power quality.
2. The objectives of missions of the research project
Overall objective: To analyze harmonics caused by non-linear loads
and study on controller design for the active filter to reduce harmonics
and improve power quality.
To achieve this objective, the research project sets out the following
main tasks:
- To analyze harmonics caused by non-linear loads with a 3-phase
4-wire transmission system.
- To perform classic controllers for active filters and to suggest
improvement of controller quality.
- To design the controller for the active filter by classic and modern
controllers
3. Research subject and scope of the dissertation
- Study subject
Model of Shunt active filter to generate compensatory currents on
the grid with non-linear working loads working, in order to bring the
grid current back to sinusoid with permissible THD [%]
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- Research scope
+ Studying on the mathematical basis for the active filter and
calculating the optimal parameters for the active filter;
+ Selecting and developing details of controller structures for active
filters. Designing advanced controllers for the active filters by using
modern control methods.
4. Research Methods
To achieve the objectives of the research project, research methods
in the dissertation are used as follows:
- Research on the theoretical aspect:
It is to analyze and synthesize mathematical basic knowledge of 3-
phase 4-wire transmission system with nonlinear load. It is to evaluate
studies published on articles, journals, and references on the controller
for the active filter. It is to study on the modern controller and apply the
classic and modern controller for the active filter.
- Study on experiment aspect by simulation:
+ Using Matlab-Simulink simulation tool for verifying theoretical
assumptions and algorithms proposed from the dissertation;
+ Verifying the research results by the experiment close to the
actual conditions, ie. experiments conducted to assess the controller
quality of the controller (when conditions allow).
5. New scientific findings, scientific and practical significance of the
dissertation - Specific contributions of the dissertation are as follows
+ It is to successfully use p, q instantaneous power theory applied
in calculating the applied current according to the measured current and
voltage, converting to the two-phase (α-β) and three-phase (a, b, c)
reference frame to generate impulses for IGBTs;
+ It is to design adaptive hysteresis current controller (HCC) based
on the fuzzy adjustment mechanism on the basis of mathematical model
built according to p,q instantaneous power theory;
+ It is to successfully apply genetic algorithm (GA) to optimize
parameters for the active filter, including PI controller.
-Scientific significance of the dissertation:
+ Advanced control methods and optimal algorithms in the
disertation are used to improve the efficiency of classic and modern
controllers (HCC, PID) applied for the controller of the active power
filter;
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+ It is to partly contribute to controller research for an active filter
that reduces harmonics and improves power quality.
- Practical significance of the dissertation
+ The dissertation contributes to improve the harmonic filtering
quality of active filters, reduce harmonic harms on the grid, increase the
lifespan of devices and increase the accuracy of the measuring
equipment, etc.;
- The research results of the dissertation are references for students in
major of control and automation, graduate students and Ph.D. students
who are interested in researching the design of predictive controllers for
nonlinear systems; problems in the controller design process for the
active filter.
6. Overall structure of the disertation
The disertation contents are presented in 4 chapters, the introduction
and conclusion are arranged as follows:
Chapter 1. Overview of the research issue
This chapter presents an overview of harmonics and the harmonic
effects on the grid; the active power filter with problems in the active
filter design process. There are statistics and analysis of solutions
proposed domestically and internationally on active filter power design.
Chapter 2. Mathematics basis of active power filters
Chapter 2 gives the structure of Shunt active power filter and
operation of the filter. From then, the filter parameters are calculated and
p,q instantaneous power theory is applied to calculate the input offset
current for the active filter controller.
Chapter 3. Controller design for active power filter
On the mathematical basis outlined in Chapter 2, this chapter’s
controllers are built for the active power filter. It includes as follows:
- It is to apply a fuzzy controller to adjust parameters of
Hysteresis current controller (HCC) to improve the controller quality
and reduce switching frequency IGBT;
- It is to optimize parameters for the active filter using a PI
controller by the genetic algorithm (GA);
Chapter 4. Simulation results on matlab - simulink – Plecs
It is on the theoretical basis and simulation results of the controller
operation applied for the active power filter that is proposed and
demonstrated in Chapter 2, Chapter 3. In this chapter, the dissertation
builds a positive power filter model with a nonlinear load that is a 3-
6
phase AC - AC converter and verifies the correctness of the proposed
theory by simulation on Matlab –Simulink.
CHAPTER 1. OVERVIEW OF THE RESEARCH ISSUE
1.1 Harmonics in the power grid and harmonic filtering solutions
1.1.1 Harmonics in the power grid
a. Harmonics
Harmonics are high-order harmonic waves whose frequency is a
multiple of the fundamental wave frequency. In the power grid, the basic
wave of the power supply is a sinusoidal wave with a frequency of 50
Hz, the waves with a frequency of 150 Hz and 250 Hz are the third order
and fifth order harmonics, respectively.
Harmonics can be independently calculated or combined with
different harmonics for a generalized form. Harmonic amplitude is a key
interested component, because it has a main effect on the system.
An important parameter to evaluate the effect of harmonics is the
coefficient of total harmonic distortion):
2
1
1
n
n
X
THDX
(1.5)
In the world, some standards such as IEEE 519-2014, IEC 1000-4-
3 on limit of high order harmonic wave composition on the grid are
given for each type of load specified THD <5%, specifically for the
digital load THD <3%.
b. Causes of harmonic generation
Causes of harmonic generation due to non-linear loads such as
industrial loads: Power electronics devices, arc furnaces, welding
machines, electronic starter, closing circuit of large power transformers,
etc. Civil loads: Gas discharge lamp, television, copier, computer,
microwave, etc.
c. Harmonic harms
Harmonics can cause cables to overheat and damage insulation.
The motor can also overheat or cause noise and fluctuations in the rotor
torque leading to mechanical resonance and vibration. Capacitors
overheat that leads to dielectric damage in most cases. Display devices
using electricity and lights may flicker, protective devices able to
disconnect power, error computers (data network) and measuring
equipment giving incorrect results.
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1.2 Active power filter and issues in active power filter design
1.2.1 Overview of active power filter
Active Power filter (APF) is filter using power electronic molecules
to filter out the high-order harmonics on the electrical system by
generating harmonics that are normal and reverse phase with those
generated in the circuit. The active filter aims to reduce current
harmonics and compensate for reactive power.
Figure 1. Operation principle of the active filter
Load
In Figure 1.10, it shows that total harmonics generated by the source I
source and harmonics generated by the active filter is zero. However, the
active filter should to be controlled according to signals of source
waveforms and load waveform and reflected in the current feedback
because these waves are always changing. Thanks to the active filter, the
voltage quality also improves and the power loss in the grid is reduced.
1.2.2 Issues in the active filter design
a. Active filter structure
b. Calculation to determine harmonic compensation current.
c. Calculation of the inverter parameters
d. Controller structure construction.
The controller plays a central role in the active filter, performing
control of power circuit (IGBT, MOSFET, etc.) to generate harmonic
compensation current in accordance with calculation for the necessary
harmonic compensation current. This controller can be designed on the
basis of controllers of PID, Fuzzy, Noron, etc. The quality of the active
filter depends mainly on the design of this controller. The quality of the
active filter mainly depends on the design of this controller.
Nonlinear load
Active filter
AC source
Source
Source wave
Grid harmonics
Filter harmonics
Total wave
Load
w
a
s
t
o
a
n
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y
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b
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The research project focused on building the controller for the active
filter, performing simulations, verifying factually and comparing with
the results of the published research works.
1.3 Domestic and foreign studies and research orientation of the
research project.
1.3.1 Domestic studies.
Currently passive filters are often used to filter harmonics in Vietnam.
The study on active filters to filter harmonics and compensate for reactive
power is quite new. There are not many research works published.
1.3.2 Foreign studies.
In foreign countries, many authors are interested in harmonic
filtering and reactive power compensation to increase power quality. In
which, it provided a method to calculate the harmonic current and
control structure for the APF with different controllers. In this section,
the author focused on analyzing articles that mentioned building
controllers for active filters.
1.4 The research orientation of the dissertation
On the basis of analysis of results published in domestic and
international research works, articles, the dissertation will step by step
solve the following issues:
- It is to select shunt harmonic filtering method and to build the structure
for Shunt Active Filter;
- It is to apply modern controllers to improve efficiency for the active
power filter.
- It is to use genetic algorithm (GA) optimization to adjust parameters
for the active filter and classic controller.
1.5 Conclusion of chapter 1
In chapter 1, an overview on the harmonics on the grid, the causes
and harms of the harmonics, together with criteria for assessing
harmonic influences on the grid are presented. On the basis of harmonic
filtering solutions, the dissertation focuses on active filtering solutions
and give main directions for the active filter design.
It is to analyse the domestic and international publications on
controller design for the active filter. On that basis, the research
direction of the dissertation is given.
CHAPTER 2. MATHEMATICS BASIS OF
THE ACTIVE POWER FILTER
2.1 The structure of shunt active power filter
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In chapter 1, three basic constructs of active power filter are outlined:
Shunt APF, Series APF and Hybrid APF. After comparative evaluation,
the structure of Shunt APF is oriented to use in the dissertation.
Shunt Active Power Filter (SAPF) is a three-phase voltage source
inverter used to stabilize the power system efficiency by generating
reference currents for IGBT bridge circuit to reduce or suppress high-
order harmonics and compensate for reactive power.
Figure 2-1: Basic structure of Shunt Active Power Filter
Where + iS is the current of the power source
+ iC is the current of the active filter
+ iL is the load current.
The gain is given as: S C Li i i (2.1)
Shunt Active Power Filter (SAPF) grid loss can be reduced by
enhancing the power factor and suppressing high-order harmonic
components. Besides, SAPF also reduces voltage decrease on
transmission lines without using booster transformers. SAPF will
increase the transmission capacity of rated power (active power) of
transformer stations , so SAPF can reduce the operating time in case of
overload [23].
As shown in Figure 2.1, we can analyze iL load current component
to the sum of the basic current and high order parallel harmonic current:
S C L C F Hi i i i i i (2.2)
Where + iF is the fundamental frequency current
+ iH is the sum of high order parallel harmonic current
Hence let the current of source sin be: S Fi i , the gain is given as:
0C H C Hi i i i (2.3)
Thus, the operation of the active power filter ensures that the iC
current has a current vector with the same magnitude of the total
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harmonic current vector but reversed phase. In order to do this function,
the active power filter ensures to perform two following issues:
-It is on the basis of the current signal (iL), the voltage (V) measured
from the load on the system to calculate the total harmonic
compensation current ( *
C Hi i ).
-The current controller performs closed-loop feedback control to
perform IGBT on / off control that emits iC current to the grid such that *
C Ci i . The contents of controller design are analyzed in details in
chapter 3 of the dissertation.
2.2 Finding the reference current based on p,q instantaneous
reactive power theory
On p,q theoretical basis, the reference current is calculated
according to the measured current and voltage, then converted to a
reference frame (α, β) using the Clarke conversion method, from then
the switching current is used to generate IGBT impulses after estimating
a three-phase reference current using the Clarke inverse transform.
Details of this method are discussed in the dissertation [8].
Figure 2.2 shows that the block diagram of the section on the
reference current calculation is based on p-q theory. Figure 2.2 shows
detailed conversion matrix of the section on the reference current
calculation. This section will be explained in detail by mathematical
equations and transformations.
Figure 2-2: The structure diagram of the reference current based on
p-q theory
Where, p and q are the real and reactive powers consumed by the
harmonic components. DC voltage regulator is used to adapt the voltage
across the capacitor of the reverse flow circuit following a
predetermined value of voltage. The deviation of the desired current
across the capacitor and its variable value is taken into account in the
harmonic power calculation.
Co. system abc converted to α , β
Co. system abc converted to α , β
[Ty
pe a
quo
te
fro
m
the
doc
um
ent
or
the
su
mm
ary
of
an
inte
p.q instanneous
power
calculation
Calculation of
the current
placed on
coordinate
system α, β
Coordinate system α , β
converted to
coordinate
system abc
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2.2.1 Application of the instantaneous power in calculating harmonic
compensation currents Instantaneous power theory is applied to the process of calculation
and design of active power filters effectively on the basis of the
following advantages:
- Instantaneous power theory is applies to a 3-phase system.
- The theory allows to apply with balanced and unbalanced 3-phase
systems with or without harmonics at both voltage and current.
- Instantaneous computation allows a fast response speed with the
system.
- Simple calculation is on the basis of the coordinate system
conversions
Figure 2-3: Power compensation components p , q , 0p and 0p under
coordinates a-b-c
As the above analytical expressions and display on Figure 2.6, p is
the only element that load needed to receive, while other components
will be exchanged through SAPF. 0p is the component provided from
power source to load, it will exchange with SAPF to transmit to the load
without depending on the operation of SAPF.
The above analysis shows that SAPF only needs to compensate
components and these components are exchanged instantaneously
between SAPF and load. The reactive power component q is
compensated through SAPF without depending on the capacity of the
capacitor C. Thus, the active filter capacity needs to compensate:
AF
AF
p p
q q
(2.32)
And the current should offset:
*
2 2*
1c
c
v vi p
v v qv vi
(2.33)
Power
source
Load
Active filter
12
However, since the voltage across the capacitor is not stable, to
ensure the voltage across the capacitor remained constant, the power
source needs to provide a power losep to keep the constant voltage across
the capacitor. Therefore, the formula for calculating the necessary
current compensation in the system αβ when combining both harmonic
filter function and reactive power compensation is given as:
*
2 2*
1c lose
c
v vi p p
v vv v qi
(2.34)
From this formula, the current compensation in the coordinate
system abc is given as
*
*
*
*
*
1 0
2 1 3
3 2 2
1 1
2 2
ca
c
cb
c
cc
ii
ii
i
(2.35)
This reverse transformation aimed to find three-phase current
applied to IGBTs inverters, from that, hysteresis current controller
(HCC) can be used in combination with PWM pulse generator to
activate valve pairs of IGBTs to adjust the current compensation able to
be generated by the inverters
Figure 2-4: Overview of conversion matrix for the process of finding a
reference currents according to p-q theory using Clarke transform
2.3 Conclusion of Chapter 2
On the basis of the diversity of the active power filter structure,
chapter 2 selected the structure of shunt active power filter and analyzed
the operation of the active filter of this type. From then, the filter
parameters are calculated and p, q instantaneous power theory are applied
to calculate the input offset current, which can be used for the control
loop circuit, in addition to the active filter controllers such as (2.34) and
3-phase
voltage
source
Load
current
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(2.35). The research results of Chapter 2 will be the mathematical basis
for the active filter control methods which will be presented in Chapter 3.
CHAPTER 3.
CONTROLLER DESIGN FOR ACTIVE POWER FILTER
3.1 Controller structure of active power filter
The controller structure of a three-phase shunt active-power filter
(SAPF) is shown in Figure 3.1.
Figure 3-1: General structure of shunt three-phase active power
filtration system
Firstly, offset power current is calculated based on the voltage and
load current through reference compensation current calculator. Then
Hysteresis current controller (HCC) is applied to the current controller,
the output signal of the controller is a switching logic pulses to excite
the valve pairs of IGBTs. The amplitude and output signal form of a
three-phase inverter using IGBTs are automatically adjusted by change
of switching frequency of the IGBTs how to let the desired
compensation current follow the reference compensation current.
3.2 Hysteresis current controller (HCC) designed based on
mathematical model developed according to p-q instantaneous
power theory.
Reference
Compensation Curent
Calculator (RCCC)
Current controller
Nonlinear load
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Figure 3-2: Structure of a three-phase active power filter using
hysteresis current controller (HCC) for electric current
Hysteresis current controller (HCC) [10] is the simplest and most
commonly used method with high stability, rapid response and
adaptability to changing load conditions. However, the biggest
disadvantage of this method is that the switching frequency of IGBTs
depends on the properties of the load. The switching frequency of
IGBTs is determined by the difference between the reference current and
the real current with the permitted thresholds (HB +) and (HB-). Thus,
the actual current is adjusted how to adhere to the reference current in a
hysteresis band given in advance. The deviation function is calculated
according to the equation (3.12).
, ,i r i f ie i i (3.12)
Where,
ie : deviation of phase current i,
r : symbol for reference current,
f : symbol for the output current of the active power filter,
I : symbol for A, B, C means phase A, B, C.
With the input current, it is the current errors between the input current
and the output current of the filter, the structure of hysteresis current
controller (HCC) combined with the open pulse generator IGBTs is
showed in Figure 3.4.
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Figure 3-3: The structure and principles of hysteresis current controller
(HCC)
The switching operation principle is established by the following law
If the current error is lower than the lower bound (HB-), the
switching state will be high (SSon).
1i one HB SS (3.13)
If the current error is greater than the upper bound (HB+), the
switching state will be low (SSoff).
0i offe HB SS (3.14)
If the current error is in the range from the lower bound (HB-) to
the upper bound (HB +), the switching state will remain the same as the
previous state (SSremain).
( _ )i remainHB e HB SS SS pre state (3.15)
The operation of hysteresis current controller describes the energy
exchange between the active filter and the system load as shown in
Figure 3.5 below:
Figure 3-4: Hysteresis current controller PWM curent
The widths of the upper and lower bands in hysteresis current
controller directly affect the controller quality. On the theoretical basis,
the smaller this hysteresis band width is, the smaller the error between
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given value and control value is. However, in practice this hysteresis
band width cannot be zero, it depends on the switching frequency of the
IGBT inverter. Each IGBO inverter has the maximum switching
frequency. According to the manufacturer, the greater the switching
frequency is, the higher the power loss and the smaller device life are..
3.2.1 Adaptive hysteresis current controller (HACK) based on fuzzy
regulation adjustment mechanism designed based on math model built
according to p-q instantaneous power theory
For the hysteresis current controller (HCC), the adhesion quality of
the compensated current depends on the hysteresis bands (HB +) and
(HB-). If the hysteresis band HOB (band from low threshold to high
threshold) increases, the switching frequency of Gibbets (fuss)
decreases, however, TH.D. increase. Otherwise, if hysteresis band is
small, TH.D. will decrease but the switching frequency of Gibbets will
increase very high. Therefore, the author proposes an adaptive hysteresis
current controller using a fuzzy adjustment mechanism. It is to apply
fuzzy controller for adaptive adjustment of hysteresis band value in a
hysteresis current controller.
Figure 3-5: The structure of adaptive HCC using fuzzy adjustment mechanism
It is the structure diagram of adaptive HCC controller using fuzzy
controller to adjust hysteresis band value. On structure diagram of this
controller, hysteresis band (HB) value of hysteresis current controller
will not be fixed but will be changed. The value of HB will be adjusted
by the fuzzy controller on the basis of the given current deviation signal
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and the reflected current together with the differential of the current
differential value.
Figure 3-6: The hysteresis current controller is based on a fuzzy
adjustment mechanism
In this case the fuzzy controller minimizes the current error by
adapting the hysteresis band to the input of current error and the rate of
change of that error.
If then (3.21)
If then (3.22)
Where, is current error; is upper bound; lower bound;
is background value; is automatically calculated value by the fuzzy
controller
The input fuzzy is characterized by linguistic variables such as: NB
- strong negative, NS - medium negative, Z - Zero, PS - medium
positive, PB - strong positive for the input ((ei(t) , dei(t)/dt), and output
( ). The membership functions are selected as shown below.
NB NS Z PS PB
0
1
-0.5 -0.25 0 0.50.25
µei
ei(t)
NB NS Z PS PB
0
1
-0.1 -0.05 0 0.10.05
µ∆I
NB NS Z PS PB
0
1
-5 -2.5 0 52.5dei(t)/dt
µdei(t)/dt
∆I
Figure 3 -7: Membership function between input and output
The input number is 2 and the number of membership functions is 5, so
we have the composition rule table of 25 rules given in Table 3.2.
Table 3-1 Fuzzy Rule
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dei(t)/dt
ei(t)
NB NS Z PS PB
NB NB NB NS NS Z
NS NS NS NS Z PS
Z NS NS Z PS PB
PS NS Z Z PS PB
PB Z PS PS PS PB
3.3 The active power filter design based on PI controller
The structure of a typical active power filter is shown in Figure
3.11. In which , PI controller is used. The active power filter control
outlined consists of two loop circuits: the outer circuit is used to
determine the offset set current icref based on the load current iL, this
compensated current is the set amount for the inner loop circuit or the
desired current that the inverter must create to put on the grid for the
purpose of compensation for harmonics and reactive power; the inner
loop circuit is responsible for generating compensation current iC how to
stick to the current icref that needs to be compensated by adjusting a full
three-phase bridge inverter of the voltage source.
Assuming that the current passing through the nonlinear load is
distorted due to the harmonic iL, the active power filter will measure the
current iL and calculate to put on the grid of compensated current iC how
to let the the current passing pass through the power source iS = iL + iC is
always a sinusoid. This means that the harmonic sources of the
generated load will be fully compensated by iC.
VSI
IGBT
abc
αβ
abc
αβ
Vαβ ilαβ
ila,b,c Va,b,c
LPF
p qabc
αβ PIUdk
Calculator
p,q
Calculator
irα ,irβ PI
ira,b,c
q
p
p
ifa,b,c
ifa,b,c
La,b,c
irα,β
p0 p
V*dc
Vdc
T1,…,6
Va,b,c
C
Vdc VSI
IGBT
Logic
Operators
NonLinear
Load
Figure 3-8: The active filter control structure using PI controller
19
PI controller for voltage Vđc has control structure as shown in
Figure 3.12.
KpC
KiC
V*dc evdc
1
s
Vdc
p0
Figure 3-9: PI controller structure for Vdc
The power P0 to maintain a constant voltage across the capacitor
(Vdc) is calculated as follows:
0
1pC iC vdcp K K e
s
(3.24)
PI controller performs to control compensated current harmonic
compensated current for the active power filter shown in Figure 3.13.
ira,b,c
ifa,b,c
ei
T1
T2
T3
T4T5
T6
1
sKi
Kp
TWC
Udk,i
Logic
Operators
Figure 3-10: PI controller controls the harmonic compensation current
The 3-phase control signal is calculated by the following formula:
, , ,
1dk a dk b dk c p i iU U U K K e
s
(3.25)
PI controller is designed to combine with triangle wave carrier
(TWC) signal to realize switching pulse width change in IGBT.
The triangular wave carrier has a normalized amplitude of 1 and a
frequency of 50 kHz, so the control signal at the output of harmonic
compensated controller is also normalized in band 0 - 1.
The 3-phase control signal will combine a pulse logic switcher to
generate 6 opened and closed pulses for IGBT inverter as illustrated in
Figure 3.14.
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Udk,iTWC
T1
T4
T
Q
Q
Figure 3-11: Impact Uđk on signals opened and closed IGBT
Thus, to design the active filter on the basis of PI controller, it is
necessary to build the accuracy mathematical model of the system. The
calculation of parameters for 2 PI controllers and some other parameters
(Lf, Cdc, V*dc) is complicated.
3.3.1 Using genetic algorithm (GA) for optimization of parameters a
three-phase shunt active power filter
As stated above, some parameters of SAPF system need to be
optimized to store the minimum value of total harmonic distortion.
These parameters include inductor Lf, DC link capacitor V*dc, KpC, KiC
of DC link DC voltage compensator and Kp, Ki of PI current controller.
GA working principle to optimize parameters of SAPF [11] is
illustrated through the diagram displayed in Figure 3.16 following the
steps below:
Step 1: It is to initialize parameters of genetic algorithm such as
population size (N), number of generations (G), probability of
hybridization (Pc), probability of mutation (Pm). It is randomly initialize
a population of N individuals, each with a set of 7 optimized variables
( Lf, Cdc, V*dc, KpC, KiC, Kp, Ki). The range of values of variables is Lf =
[0.7, 1.5] mH, Cdc =[0.5, 5] mF, V*dc = [600, 1200] V, KpC =[50, 1000],
KiC =[50, 1000], Kp =[50, 1000], Ki =[50, 1000].
Step 2: It is to calculate the adaptive value of each individual in the
population. Here, THD value is selected as the target function:
(3.5)
Step 3: It is to check the stop condition of the algorithm. The stop
condition here is when THD is less than a given value or the algorithm
reaches number of G generation. If the condition is satisfied then stop
and return the best individual along with the target function value,
otherwise continue to step 4.
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Step 4: It is to perform calculations of GA such as selection,
optimization, mutation to create new populations. The algorithm is then
repeated from step 2 until a stop condition is reached.
The suitable parameters for GA are as follows: - Maximum number of generations G = 40, population size N = 40, individuals are represented by real numbers.
Selection is done according to the tournament method
- It is to select homogeneous mutation with probability Pm = 0.08
- Select a cross dispersal hybrid with probability Pc = 0.8. 3.4. Conclusion of chapter 3
On the mathematical basis outlined in Chapter 2, Chapter 3 has
built up controllers for the active power filter. It Includes
determination of current applied by p,q instantaneous power theory,
application of this result to design external circuit controllers for a
active power filter, helping to improve controller quality and reduce
IGBT switching frequency as well as THD value. It is to design
modern controller (HCC applied by fuzzy modifier) and optimize
parameters for the positive filter as well as PI controller for the current
loop (inner loop), contributing to improve the efficiency of the active
power filter.
CHAPTER 4. SIMULATION RESULTS ON MATLAB -
SIMULINK
4.1. Overview diagram of the three-phase active power filter system
according to the p-q instantaneous power theory built on MATLAB/SIMULINK
Figure 4-1: Model of a three-phase shunt active filter based on p-q
instantaneous power theory performed on Matlab - Simulink software
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Table 4-1 Parameters of the simulation system on matlab
Parameters of the system
Power source Non-linear load Shunt APF
Diode bridge with
Resistor (
4.1.1. Simulation results in use of the active filter with the method of
Hysteresis current controller
Figure 4-2: The current of phase A influenced by the harmonic source
(bridge rectifier) in the absence of the filter
Throught THD analysis of phase electric current without an active
filter, the total harmonic distortion of the system is 29.97%
Figure 4-3: The electric current waveform and THD of the current of
phase A in the absence of the filter
Thus, we can see that when there is not the filter to impact, the
distorted current of phase A is without sinusoid. Spectral analysis
showed that THD is 29.97%.
Simulation with hysteresis band HB = ± 0.5
Compensated harmonic current is generated by the inverter with
HCC controller (HB = ± 0.5). The signal spectrum of the current of
phase A are analyzed when using an active filter with a HCC controller
(HB = ± 0.5)
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Figure 4-4: The electric current waveform and THD of the current of
phase A in the presence of the filter and hysteresis band of HCC (+/- 0.5)
After using an active filter controlled by HCC controller with a fixed
hysteresis band ( ), THD is 10.21% and the switching frequency
( ) is about 30 kHz.
Simulation with hysteresis band HB = 0
Signal spectrum of the current of phase A are analyzed when using an
active filter with a HCC controller (HB = 0)
Figure 4-5: The electric current waveform and THD of the current of
phase A in the presence of the filter and hysteresis band of HCC (0)
After using an active filter controlled by HCC controller with a fixed
hysteresis band (0), THD is 1.93% and the switching frequency ( ) is
about 500 kHz.
4.1.2. Simulation results when using the active filter with the method
of Hysteresis current controller to modify parameters by fuzzy
Compensation current is generated after HCC controller adjusting
parameters by fuzzy.
The signal spectrum of the current of phase A are analyzed when
using a HCC controller with parameters modified by fuzzy controller
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Figure 4-6: The electric current waveform and THD of the current of
phase A in the presence of the filter and hysteresis band of HCC adapted
by the fuzzy modifier
The simulation results can be summarized by us as the following table:
Table 4-2 Comparison of results the active filter with adaptive HCC
and HCC controllers
THD and IGBT switching frequency ( )
HB = ( ) HB = 0 Adaptive HB
by fuzzy
The simulation results demonstrate that when the system is filtered
by shunt active filter with hysteresis band of HCC controller adapted by
the fuzzy modifier, THD results of the system is the smallest (1.54 %),
and 60 kHz is the acceptable frequency.
4.2. Overview diagram of the three-phase active power filter system
according to the p-q instantaneous power theory built on MATLAB/SIMULINK
Figure 4-7: Model of a three-phase shunt active filter based on p-q
instantaneous power theory performed on Matlab - Simulink software
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Table 4-3: Parameters of the simulation system on matlab
Parameters of the system
Power source Non-linear load Shunt APF
Diode bridge with
Resistor (
4.3. The simulation results from the proposal in using genetic
algorithm (GA) to optimize parameters of the active filter with
the proportional - integral controller structure
4.3.1 Input data
Target function: the total harmonic distortion (THD) in unit of
percentage (%)
Population size = 40.
Number of parameters selected for modifying = 7 including (Lf,
Cdc, V*dc, KpC, KiC, Kp, Ki).
Number of seeded times of the genetic algorithm (GA) =40.
4.3.2 Results
Parameters after running GA:
The best value of THD = 0.0148 (1.48%)
Optimal parameters of SAPF: Lf =2.05mH; Cdc =4.9mF; V*dc
=875; KpC =30; KiC = 40; Kp = 0.5; Ki =5.
Figure 4-8: A 3-phase current after applying the active filter
Figure 4-9: Analysis of FFT of the current signal
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4.3.3 Comments
- PI controller is a classic controller, so PhD. student wants to
exploit to be able to understand and clearly analyze operation of the
active filter. It is to simulate the active filter on Matlab / Simulink from
which it is possible to design advanced controllers applied into active
filters.
- Use of genetic algorithm (GA) is proposed to optimize the active
filter’s parameters. Simulation is performed to find the optimal
parameter for the active filter using a PI controller.
- The simulation results shows that when the system does not use
the active filter, value of THD is 29.97% and after using the active filter
designed on the basis of fuzzy adaptive HCC, the value of THD is 1.54
% and PI controller with optimal parameters by genetic algorithm (GA),
the value of THD is 1.48%.
4.4 Conclusion of chapter 4
Research results of HCC controller of adaptive fuzzy modifier
applied into the power filter shows that when there are effects of the
active filter, the current signal on the grid has a sinusoidal form with
fundamental frequency and a value of THD of 1.54%. This THD value
is smaller than the allowable standard value (5%).
Active filter controller uses a PI controller, which is a classic
controller. The simulation results of this method can be to refer to the
design of advanced controllers applied to active filters.
The simulation results showed that when the system did not use the
active filter, THD = 29.97% and after using the active filter designed on
the basis of a PI controller with optimized parameters by the Genetic
algorithm (GA), THD = 1.48%.
CONCLUSIONS AND RECOMMENDATIONS
1. Conclusions:
The controllers built in this dissertation for the active power filter
were firstly based on the platform of classic controllers (PI) to analyze
in detail problems in the design of the active power filter. From then, it
is used as the basis of application for modern controllers such as fuzzy
logic, neurons and optimal genetic algorithms (GA) to adjust parameters
for active filters and classic controllers, etc. to improve the working
efficiency for the active power filter and reduce THD index [%].
27
With my own efforts, I also try my best to achieve some initially
new contributions as follows:
1. It is to build a solid mathematical basis to serve as a basis for
designing suitable controllers for active filters such as proposing the
method of p, q instantaneous power to calculate the current value set i,
i, ia, ib, ic, for control design.
2. It is to design adaptive hysteresis current controller (HCC) based
on the fuzzy adjustment mechanism based on mathematical model built
according to p,q instantaneous power theory;
3. Genetic algorithm (GA) is applied to optimize parameters for the
active filter, PI controller and predictive controls; Thanks to GA, the PI
controller achieves THD = 1.48% as very high switching frequency
causing power loss.
The requested objectives of research of the dissertation are fully
met. There are many prospects for application in practice.
2. Recommendations
The contents of the dissertation have some new contributions to the
active filter controller. However, it is only to address very narrow issues
on active filter controller for the load in industrial field in general
speaking. Study on active filter controller continues to attract the
attention of specialized scientists and PhD. students with the following
issues: active filters designed to be suitable for asymmetric nonlinear
loads causing a large value of THD []; Both harmonic filtering and
combination of cos compensation for the grid, etc.
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LIST OF SCIENTIFIC WORKS PUBLISHED
1. “Harmonic Elimination based on Fuzzy Logic in combination with
Hysteresis Control Algorithm”, IEEE International Conference on
Systems Science and Engineering 2017;
2. “Design of Dynamic-Static Var Compensation based on
Microcontroller for Improving Power Factor”, IEEE International
Conference on Systems Science and Engineering 2017;
3. Optimizing Parameters of The Shunt Active Power Filter Using
Genetic Algorithm, The 9th International Conference, KSE 2017,
Hue, Vietnam, October 19-21, 2017;
4. "Design of shunt active power filter based on the classical PID
controller for eliminating harmonics", Journal of Military Science &
Technology, ISSN 1859 – 1043 – Special issue No. 08 - 2018, 179-
188.
5. “Study of genetic algorithm application to optimize parameter of a
three phase shunt active power filter”, TNU Journal of Science and
Technology, ISSN 1859 – 2171, 2734 – 9098, số 05/2021