1

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-

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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

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8

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

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ary

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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

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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

13

(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

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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