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International Electrical Engineering Journal (IEEJ)

Vol. 7 (2016) No.5, pp. 2266-2278

ISSN 2078-2365

http://www.ieejournal.com/

2266 Halawa et. al., Power Quality Improvement Using a Shunt Active Power Filter Based on the Hysteresis Current Controller

Abstract— one of the main power quality concerns currently is

the existence of harmonics. Shunt active power filters are

widely applied in power distribution grids to mitigate current

harmonics and compensate the reactive power. In this paper

the instantaneous reactive power theory is used to detect

reference compensation current for the controller of the shunt

active filter and a hysteresis current controller is used to

synthesize it precisely. Hysteresis current controller is one of

the simplest current control methods and the most popular one

for active power filter applications, but it suffers from an

uneven switching frequency, to overcome this disadvantage a

novel fuzzy hysteresis current controller is being used. The

proposed controller is characterized by simplicity as a result of

reducing the size of calculations that makes it acting faster and

doesn’t rely on the load parameters. The system was modeled

and simulated using MATLAB/SIMULINK. The results of

simulation are presented and discussed they show the

effectiveness of the proposed fuzzy hysteresis controller in

improving the PWM performance and thus improve the shunt

active power filter performance.

Index Terms— Shunt Active Power Filters, p-q theory,

Hysteresis Band Current Controller, Fuzzy Logic, Harmonic

Distortion

I. INTRODUCTION

Ideally an electricity supply should fixedly show a perfectly

sinusoidal voltage signal at every customer location. However,

for a number of reasons, utilities often find it difficult to

maintain such desirable condition [1.2]. For example the

widespread use of nonlinear devices likes (microprocessor,

variable speed drives, uninterrupted power supplies and

electronic lighting) which have become used on a large scale.

These modern power electronic devices draw a significant

amount of harmonics from the electrical grid; these non

sinusoidal currents interact with the impedance of the power

distribution lines creating voltage distortion at the point of

common coupling (PCC) that can affect both the distribution

system equipment and the user loads connected to it. As a

result, the utilities obliged to reduce the total harmonic

distortion (THD) at the point of common coupling below 5%

as given in the IEEE 519-1992 harmonic standard. This can

be achieved through the use of the harmonic filters whether

passive or active filters [3-5]. The passive filtering is the

simplest classical solution to mitigate the harmonic distortion,

these filters consisting of R, L and C elements connected in

various configurations. Although simple, these filters have

many defects such as fixed compensation, bulky size and

resonance so these filters may not be able to achieve the

desired performance thus we need to use dynamic and

adjustable devices to mitigate the power quality problems

such as active power filters [6,7]. Active power filters are

considered the most ideal solutions to the many of power

quality problems such as harmonics, reactive power, regulate

terminal voltage, flicker and improve voltage balance in three

phase systems. Shunt active power filter is the most important

configuration and widely used in active power line

conditioners applications. It automatically adapts to changes

in the grid and load fluctuations, can compensate for several

harmonic orders and eliminating the risk of resonance

between the filter and the grid impedance [8-14].

II. SHUNT ACTIVE POWER FILTER

Shunt active power filter based on voltage source converter

(VSC) is an effective solution to current harmonics, reactive

power and current unbalance. The basic principle of this filter

is to use power electronics technologies to generate particular

currents components that can cancel the current harmonic

components from non linear load [15-17].

The performance of the shunt active filter depends on the

reference compensating current detection algorithm and the

current control technique used to drive the gating pulses of the

active power filter switches to generate compensating current

that should be injected into the power system to mitigate the

current harmonics and compensate the reactive power

[18-22].

The compensation characteristics of the shunt APF are shown

in Fig. 1

Power Quality Improvement Using a

Shunt Active Power Filter Based on the

Hysteresis Current Controller

Mohamed Halawa1, Belal Abou-Zalam2, Abdel-Azem Sobaih3

1,2,3Industrial Electronics and Control Engineering Department, Faculty of Electronic Engineering, Menoufia University, Egypt

M7alawa @gmail.com



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ISSN 2078-2365



Fig.1 Basic configuration of a shunt active filter

III. INSTANTANEOUS REACTIVE POWER THEORY

Estimation of reference compensating current can be done

through two main approaches, time domain and frequency

domain approach. A time domain method uses the

conventional concepts of circuit analysis and algebraic

transformations that require less calculation, thus simplifying

the control function, in the opposite the frequency domain

methods require a large amount of calculations and a lot of

memory [23]

Reactive power theory is the most commonly used time

domain methods where it is very efficient and flexible in

designing controllers for active power filters. It’s based on a

set of instantaneous powers defined in the time domain, thus

allowing the controller of the active filters to operate in real

time. The following steps are used to calculate current

harmonic components of the load current that are used as a

reference signal for the shunt active power filter controller

[24-26].

Step 1: transform the three phase load currents and phase

voltages from the a-b-c coordinates to 0 coordinates

by:

1 11

2 2 2

3 3 30

2 2

a

b

c

ii

ii

i

(1)

1 11

2 2 2

3 3 30

2 2

a

b

c

vv

vv

v

(2)

Step 2: calculate the values of the instantaneous real and

imaginary powers by:

p v i v i (3)

q v i v i (4)

Step 3: for this step, as shown in Fig. 2. The high pass filter is

used to extract the oscillating components of real power.

P P

Fig.2 The high pass filter used to extract the ac component of p

Step 4: The compensated currents produced by the shunt APF

in coordinates are;

*

2 2*

1

-

c

c

i v v p

v v qv vi

(5)

Step 5: these currents are transformed from coordinates

to the a-b-c coordinates that are used as a reference signal for

active power filter controller:

*

*

*

*

*

1 0

2 1 3

3 2 2

1 3

2 2

ca

c

cb

c

cc

ii

ii

i

(6)

IV. HYSTERESIS CURRENT CONTROL

Current controller is the most critical part for the shunt

active power filter performance that drawn more attention

from industry and researchers [27]. It force power circuit of

the shunt active filter to synthesize the compensating current

precisely by drive the gating pulses of the active power filter

switches [28].

There are various current control methods such as PI

control, sinusoidal PWM and hysteresis control. Hysteresis

current controller has proven to be the most suitable for all the

application of current controlled voltage source converters in

shunt active power filters [29-33]. It derives the switching

signals of the active power filter switches by comparing the

current error signal with a constant hysteresis band as shown

in Fig. 3

HPF



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Fig. 3 a constant hysteresis band current control loop

The current controller is designed to the three phases and

the switching logic for each phase is developed as follows

[5,23,34-36].

If the error current exceeds the upper 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 error current crosses the lower limit of the band ,

the lower switch is turned off and the upper switch is turned

on. As a result, the current gets back into the hysteresis band.

The main problem when applying the conventional

hysteresis band current controller is its uneven switching

frequency and that leads to audio noises, high switching losses,

injection of high frequency ripple current to the system and

difficulty in designing suitable filters to remove these high

frequency components. To avoid these unsatisfactory features

adaptive hysteresis band has been recommended in the

literature [37-44] to control the modulation frequency.

Fig. 4 PWM current and voltage waves with hysteresis band current control

Fig. 4. Shows current and voltage waves of the PWM-voltage

source inverter for phase a. The behavior of the switching

can be divided into two components over one switching

period, as follows:

1) During the switching period (t1):

The current ramps from lower hysteresis band –HB to the

upper hysteresis band +HB and the inverter side voltage

is 0.5 dcv

1(0.5 - ( )) a

dc s

div v t

dt L

(7)

2) During the switching period (t2):

The currents ramps from upper hysteresis band +HB to the

lower hysteresis band -HB and the inverter side voltage is -0.5

vdc

-1

(0.5 ( ))adc s

div v t

dt L (8)

From the geometry of Figure 4, we can write

*

1 1 2a adi dit t HB

dt dt

(9)

*

2 2 2a adi dit t HB

dt dt

(10)

1 2

1s

sw

t t Tf

(11)

Where t1 and t2 are the respective switching intervals, and

swf is the modulation frequency Adding (9) and (10) and

substituting (11), we can write:

*

1 2

10a a a

sw

di di dit t

dt dt f dt

(12)

Subtracting (10) from (9), we get *

1 2 1 24 ( )a a adi di diHB t t t t

dt dt dt

(13)

Substituting (8) in (13)

*

1 2 1 24 ( ) ( )a adi diHB t t t t

dt dt

(14)

Substituting (8) in (12) and simplifying *

1 2( )

a

sw a

di dtt t

f di dt (15)

Substituting (15) in (14), gives

2

2

0.125 ( )4[ (1 ( ))]dc s

sw dc

v v tLHB S

f L v L (16)

Where fsw is the switching frequency; 0.5 vdc is half of the

total bus voltage; L is the output load inductor; vs(t) is the

supply voltage; S is the slope of reference current and HB is

the hysteresis band.

The adaptive HB should be derived instantaneously during



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each sample time to keep the switching frequency remains

nearly constant, this can be achieved with the help of fuzzy

logic controller as stated In literature [20,23,45,46]. which S

and vs(t) are taken as input variables to the fuzzy controller

and the HB is the output. But if the reference current is

assumed to be smooth, the following equations can be written

in the switching intervals t1 and t2:

1

0.5 - ( )2 dc sv v tHB

t L (17)

2

- 0.5 - ( )-2 dc sv v tHB

t L (18)

Combining (17) and (18) and solving for the switching period

T gives:

2 2

2

(0.25 ( ))

dc

dc s

LHBvT

v v t

(19)

2 2(0.25 ( ))

2

dc ssw

dc

v v tf

LHBv

(20)

For a fixed hysteresis band current controller the

parameters of equation (02) are constant except for the supply

voltage that changes over each fundamental cycle causing

uneven switching frequency for the voltage source converter,

ttherefore, if HB can be varied in response to vs (t) a constant

switching frequency can be achieved [47,48]. In next section

fuzzy logic based adaptive hysteresis current controller will

help to fix the switching frequency.

V. THE PROPOSED FUZZY LOGIC FOR

HYSTERESIS CURRENT CONTROLLER

The fuzzy logic controller is one of the advantageous

control methods for systems facing difficulties in obtaining

mathematical models or having performance restrictions with

traditional linear control methods. In a fuzzy logic controller,

the control signal is determined from the assessment of a set

of linguistic rules (if-then rules), these rules are obtained from

our understanding of the process to be controlled. To design

fuzzy controller, variables that can represent the dynamic

performance of the system to be controlled must be taken as

the inputs to the controller [49]. Subsequently the supply

voltage vS(t) and its derivative ∆ vS(t) are chosen as inputs to

the fuzzy controller, and the hysteresis band (HB) is taken as

the output as shown in Fig. 5

Fig.5 The proposed fuzzy hysteresis band current controller

VI. SIMULATION RESULTS

This section introduce the details of simulations that have

been implemented using MATLAB/SIMULINK, to shows

the performance of the proposed shunt active power filter to

mitigate the current harmonics and compensate reactive

power in the distribution grid. Test system that was used to

carry out the analysis consists of a three-phase diode bridge

rectifier with RL load Connected to three-phase three wire

distribution system and shunt active power filter connected to

the system by an inductor L. The control strategy of the shunt

active filter based on p-q theory to generate the reference

compensation current, hysteresis band current controller to

drive the gating signals of the shunt active filter switches and

PI controller to regulate the voltage of dc side capacitor of the

shunt active filter. The values of the circuit components used

in the simulation are given in Table I. The system

performance was analyzed without the shunt active filter and

Fig. 6 gives the details of source voltage, source current, load

current, harmonic spectrum of the supply current, real and

reactive power supplied by the source to the load. It is seen

that line current is distorted due to nonlinear load and the total

harmonic distortion (THD) of the supply current is 24.44%,

this current distortion resulting from the dominance of 5th, 7th,

11th and 13th harmonic spectral components. Real and reactive

power supplied from the source to the load have constant

values and a superposition of oscillating components, These

oscillating components are related to the presence of

harmonics.



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Table I System parameters

Parameter Specification

Supply Phase to Phase Voltage 400 V

Grid Frequency 50 Hz

Supply Line Parameters Rs=0.01Ω & Ls=1ϻH

Load R=13Ω & L=100mH

Rectifier Side Inductance 1mH

Filter Coupling Inductance 4mH

Filter Capacitance 2mF

Reference DC Voltage 700V

Fixed Hysteresis Band Limit 0.7 A

Proportional gain KP 0.89

Integral gain KI 197

Sampling Time 5e-6

(a)

(b)

(c)

(d)

(e) .

(f)

Fig.6. Simulation results without SAPF (a) source voltage (b) supply current

(c) load current (d) harmonic spectrum of the line current (e) load real power

(f) load reactive power



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A. PERFORMANCE OF FIXED HYSTERESIS

BAND CURRENT CONTROLLER BASED

SAPF

The system performance was analyzed and the resulting

waveforms source voltage, source current, load current,

reference current, filter current, tracking shunt active filter for

phase (a), supply current, harmonic spectrum of the supply

current, real and reactive power supplied by the source to the

load are shown in Fig. 7(a)-(i) respectively. As shows the

shunt active power filter (SAPF) shows a good filtering

process which leads to compensate harmonic components

from the source current, as it is clear from Table II and

harmonic spectrum analysis of the supply current, THD of the

source current has decreased from 24.44% to 2.63% that is

less than 5% which is in compliance with IEEE 519-1992

standard for harmonics under non linear loads. As well shows

the undesired portions of the real and reactive power of the

load that related to the presence of harmonics have been

compensated by the SAPF and the source supplies only

fundamental real power and zero reactive power to the load.

In spite of that when applying the conventional hysteresis

band current controller the Shunt APF operates in uneven

switching frequency as it is shown in Fig. 8. This uneven

switching frequency Leads to audio noises, high switching

losses, injection of high frequency ripple current to the system

and makes the design of suitable filters to remove these high

frequency components is difficult, difficulty in determining

convenient switching device and calculate its switching

losses. To avoid these unsatisfactory features, adaptive

hysteresis band current controller with the changeable

hysteresis band will be used based on the fuzzy logic.

(a)

(b)

(c)

(d)

(e)



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ISSN 2078-2365



(f)

(g)

(h)

(i)

Fig.7. Simulation results of shunt active filter based fixed HCC (a) source

voltage (b) load current (c) reference current (d) filter current (e) supply

current (f) tracking shunt active filter for phase (a), (g) ) harmonic spectrum

of the supply current (h) real power supplied by the source to the load. (i)

reactive supplied by the source to the load.

(a)

(b)

Fig. 8 (a) switching patterns of S1 (b) FFT analysis of the source current in

high frequency range.

Table II Total harmonic distortion of source and load current

THD% Phase a Phase b Phase c

Source current 2.58 2.61 2.70

Load Current 24.44 24.34 24.55

B. PERFORMANCE OF TRADITIONAL FUZZY

HYSTERESIS BAND CURRENT

CONTROLLER BASED SAPF

In literature[23][45][46][20] Five linguistic variables are

set to the inputs and output of the controller as NL (Negative

Large), NM (Negative Medium), ZE (Zero), PM (Positive

Medium), PL (Positive Large) for inputs and PVS (Positive

Very Small), PS (Positive small), PM (Positive Medium), PL

(Positive Large), PVL (Positive Very Large) for output,

triangular membership functions have been used for input

and output variables and 25 linguistic rules. The system

performance was analyzed and the resulting waveforms

source voltage, source current, load current, reference

current, filter current, tracking shunt active filter for phase (a),

supply current, harmonic spectrum of the supply current, real

and reactive power supplied by the source to the load are



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shown in Fig. 9(a)-(i) respectively. The THD of the supply

current has decreased from 24.44% to 3.03% as it is clear

from Table III and harmonic spectrum of the compensated

source current and we can see that the reactive power drawn

by the load becomes zero and the source supplies only

fundamental real power to the load, this means that all the

undesirable current components of the load are being

eliminated. As shown in Fig.10. The switching frequency

becomes nearly constant and the switching ripple components

of the source current has been concentrated to a narrow range

around (10 KHz to 13 KHz)

(a)

(b)

(c)

(d)

(e)

(f)

(g)



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(h)

(i)

Fig.9. Simulation results of traditional fuzzy HCC (a) source voltage (b) load

current (c) reference current (d) filter current (e) supply current (f) tracking

shunt active filter for phase (a), (g) ) harmonic spectrum of the supply current

(h) real power supplied by the source to the load. (i) reactive supplied by the

source to the load.

Table III Total harmonic distortion of source and load currents



Load Current 24.44 24.34 24.55

(a)

(b)



C. PERFORMANCE OF PROPOSED FUZZY

HYSTERESIS BAND CURRENT

CONTROLLER BASED SAPF

Three linguistic variables are set to the inputs and output of

the controller as NL (Negative Large), ZE (Zero), PL

(Positive Large) for inputs and PS (Positive small), PM

(Positive Medium), PL (Positive Large) for output, triangular

membership functions as shown in Fig. 11, have been used for

input and output variables because of its simplicity, the fuzzy

rules are given in Table IV. Fig. 12 (a)-(e) highlights the

performance of proposed fuzzy hysteresis current controller,

gives the details of source voltage, source current, load

current, reference current, filter current, tracking shunt active

filter for phase (a), supply current, harmonic spectrum of the

supply current, real and reactive power supplied by the source

to the load. The THD of the supply current has decreased

from 24.44% to 2.66% as it is clear from Table V and

harmonic spectrum of the compensated source current and the

undesired portions of the real and reactive powers of the load

that related to the presence of harmonics have been

compensated by the SAPF and the source supplies only

fundamental real power and zero reactive power to the load. It

is seen from Fig. 13, that the switching frequency becomes

nearly constant and the switching ripple components of the

source current has been concentrated to a narrow range

around (15 KHz), this means that the proposed fuzzy

hysteresis band current controller has worked properly and

the modulation frequency of the shunt active power filter is

held in 15 KHz, Hence select the appropriate filter to mitigate

the ripple components in the filter current, determine

convenient switching device and calculate switching losses

has become easier.

Table IV Fuzzy inference rule

Vs (t)

PL Z NL



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∆ Vs (t)

PL PS PS PS

Z PM PL PM

NL PS PS PS

(a)

(b)

(c)

Fig. 11 Membership functions of the input variables and output variable

(a) Source voltage (b) rate of change of source voltage (c) hysteresis

band

(a)

(b)

(c)

(d)

(e)



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(f)

(g)

(h)

(i)

Fig.10. simulation results of proposed fuzzy HCC (a) source voltage (b) load

current (c) reference current (d) filter current (e) supply current (f) tracking

shunt active filter for phase (a), (g) ) harmonic spectrum of the supply current

(h) real power supplied by the source to the load. (i) reactive supplied by the

source to the load.

Table V Total harmonic distortion of source and load currents



Load Current 24.44 24.34 24.55

(a)

(b)



VII. RESULTS AND ANALYSIS

The results obtained from the simulation is given in table

VII .It shows that the three current controllers, fixed HCC,

Traditional fuzzy HCC and Proposed fuzzy HCC have been

found to meet the IEEE 519-1992 standard for harmonics

under nonlinear loads where THD is less than 5% at the point

of common coupling, with the following observations:

The proposed fuzzy HCC gets better compensation

than traditional fuzzy HCC.

The modulation frequency is held nearly fixed with

Traditional fuzzy HCC and got constant more

and more using the proposed fuzzy HCC contrary

to fixed HCC.

The proposed fuzzy HCC acts faster than

traditional Fuzzy HCC as a result of the use of

simplified calculations (9 rules instead of 25

rules)



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The proposed fuzzy HCC forces the compensating

current to track the reference compensation

current more accurately.

The proposed fuzzy HCC characterized by

removing reliance on variable parameters like

reference current that is detected from load

parameters and uses only fixed parameters like

supply voltage that does not change in a real

system.

Table VII Summary of total harmonic distortion of source current and

switching frequency for each current controller

Current Control

Technique

THD % Switching Frequency

(KHz) Without Filter 24.44

FHCC 2.63 10:18

Traditional fuzzy HCC 3.03 10:13

Proposed fuzzy HCC 2.66 15

VIII. CONCLUSION

Shunt active power filter is the most effective solution to

mitigate the current harmonics and compensate the reactive

power. In this paper a novel current control strategy based on

fuzzy logic for shunt APF was introduced to improve the

current controller technique that is the backbone of the shunt

active power filter operation. The simulation results have

verified the effectiveness of this new technique to fix the

modulation frequency of the shunt active power filter

compared to the conventional current controller where the

modulation frequency changing over a wide range causing

many of undesirable effects.

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