power quality improvement using a f our l eg s apf b ased on … energy and power...

Power Quality Improvement Using a Four Leg SAPF

Based on Phase Locked Loop with Multi Variable

Filter under Unbalanced Source Voltages and Loads

Ali Chebabhi

ICEPS Laboratory

Department of Electrical

Engineering

University of Sidi Bel-Abbes

Algeria

[email protected]

Mohammed K. Fellah

ICEPS Laboratory

Department of Electrical

Engineering

University of Sidi Bel-Abbes

Algeria

[email protected]

Abdelhalim Kessal

Faculty of Science and

Technology

University of Bordj Bou

Arreridj

Algeria

[email protected]

Mohamed F. Benkhoris

IREENA Laboratory

University of Nantes at Saint

Nazaire

France

Mohamed-

Fouad.Benkhoris@univ-

nantes.fr

Abstract—Harmonics, zero-sequence current, switching losses,

switching frequency, and reactive power compensation are

significant power quality problems. In this paper a four leg shunt

active power filter with fixed switching frequency is proposed

which consists of a four leg inverter controlled by three

dimensional space vector modulation (3D-SVM). Four leg

inverter is tuned at the zero-sequence current accumulated in the

neutral wire. At this four leg inverter controlled by three

dimensional space vector modulation is low switching losses of

inverter switches. Consequently four leg shunt active power filter

compensates for zero-sequence and other harmonics, and

reactive power under unbalanced source voltage and single-phase

loads. A new modified instantaneous real, imaginary and zero-

sequence powers pq0 theory with phase locked loop (PLL) based

on Multi variable filter (MVF) in the αβo axes is presented for

reference current extraction and estimates good source voltages

without harmonics under unbalanced source voltage and single-

phase loads.

Keywords—Four-leg shunt active power filters; 3D-SVM; pq0

theory; Zero-sequence current; PLL; MVF; STF; Harmonic

currents compensation; Reactive power compensation.

I. INTRODUCTION

Harmonics power electronics controlled and domestic

equipment are increasingly using more single-phase loads

connected with power electronic circuits having a non-linear

behavior, such as single-phase rectifiers, variable speed, and

other electrical equipment. They give in the four wire

electrical networks rise to a harmonics and zero-sequence

current causing harmful effects of source and line voltage and

current quality, losses in all components connected to the

system and extreme neutral wire currents, etc. [1-3]

Several researches around the world are observing,

studying, to model the harmonics in order to better understand

them and be intelligent to propose extra effective solutions to

shun the manifestation of pollution and limit their swell. For

power quality improvement in four wire electrical networks,

harmonics produced by non-linear single-phase loads and

reactive power necessities should be compensated by the

compensator. Four leg shunt active power filter have been

used to injecting into the four wire electrical networks

harmonic currents and zero-sequence current of same

amplitude and opposite phase as those of absorbed by the non-

linear single-phase loads [4], and to compensate the

requirements reactive power [5]. Their main advantage is

small volume, high efficiency, without resonance, injecting all

harmonic currents, and give a dynamic and flexible solution to

reduce harmonics and reactive power compensation [3], thus

keeping the source currents approximately sinusoidal and still

in phase with the corresponding voltage and the power factor

is almost unitary.

The instantaneous powers method (pq0) presented and

student in [6] is valid only if the source and line voltages are

non- distorted (sinusoidal and balanced). It is generally not the

case in practice [8]. To formulate this method universal for all

unbalanced and distorted of source and line voltages, we use

the system phase-locked loop (PLL) for detecting and

determine the source voltages phase angle, frequency and

amplitude.

In recent years, many PLL structures have been developed

and presented in the literature [9-11]. The main objective of

this work is to obtain a universal method for reference current

extraction and estimate a good source and line voltage without

harmonics under unbalanced source voltages and single-phase

loads.

In this study, we use a modified instantaneous real,

imaginary and zero-sequence powers pq0 theory with PLL

based on a new type of extraction component filter called

multi variable filter (MVF) or Self Tuning Filter (STF). Its

basic principle is based on the extraction of the fundamental

component of the source and line voltages, directly according

to the αβo-axes [12-14]. also for the increasing performances

in term of low switching losses, fixed switching frequency of

inverter switches and THD, the three dimensional space vector

modulation (3D-SVM) technique represented and detail

student as [3], [15-16], and [19] is used for generating the

switching signals.

This paper presents a comparison study of two methods for

extracted and generate the reference currents used for a four-

leg shunt active power filter control. These methods are:

conventional pq0 theory, and modified pq0 theory with PLL

based on MVF.

International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015

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II. PQ0 THEORY

The real, imaginary and zero-sequence instant powers

(pq0) theory has been applied successfully in controllers of

active power line conditioners [6], [17], [19].

The real power pl, the imaginary power ql and the zero-

sequence power pl0 are expressed by the following matrix:

v v 0p il ll l

q v v 0 il l l l

p 0 0 v il0 l0 l0

(1)

Component of real power can be expressed as the sum of a

DC component and an AC component: [17]

p p pl l l

(2)

Whenlp is DC component and

lp is AC component.

Eq (3), we can deduce the corresponding current

components: *

f l0 l l0 l

*

f l0 l l0 l2 2

l0 l l 2 2

f 0 l l l0

pi v v v v 01

i v v v v 0 qv ( v v )

i 0 0 ( v v ) p

(3)

l123v

l123il oi

p

qFPB

*

f 123i

dcp

(2.39)

Equation

l 0i (2.42)

Equation

*

f oi

p

p

p

q

l0i

l̂v l̂v

l̂v l̂v

abco PLL

l123v̂

*

abcoabc

o

*

Fig.3. Blok diagram of the pq0 theory with PLL

III. CONVENTIONAL PHASE LOCKED LOOP (PLL)

Fig. 2 represents detailed synoptic of used conventional

PLL. This method detects the parameters max( ,V ) of

fundamental source voltages components who has given by

the following equation: [9-10]

1

2

3

2

3

2

3

s

s max

s

ˆsin( )v

ˆv V sin( )

vˆsin( )

(4)

With, ̂ the angular position estimate of the vector of three-

phase source voltages.

Fig 2 Blok diagram of the conventional PLL

After the transformation of Eq (4) in the synchronous

reference frame (dq axes), one obtains:

ˆ ˆcos( ) sin( )

ˆ ˆsin( ) cos( )

sd s

sq s

v v

v v

(5)

3

32

sd maxv .V sin t cos( ) cos t sin( )

(6)

3

32

sd maxˆv .V sin( ) (7)

By supposing that ˆ( ) is very small, then the preceding

expression can be expressed by:

max

33 )

2ˆ(sdv V

(8)

The transfer function of PI regulator is defined by:

i

p

kH k

s (9)

The position angular is given by:

ˆs

(10)

From where, one finds the transfer function of the system:

2

33

2

33

2

p i max

p i max

k s k . .V

ˆs k s k . .V

(12)

The gains kp and ki, are given by:

2

max max

(2 ) 21 2 2 2

3 3 3 3

c c

i p

f fk and k

V V

(13)

In order to obtain a good compromise between the

stability and the dynamic response, one chooses 0.707 .

IV. MULTI-VARIABLE FILTER (MVF)

The schema of the Multi-Variable Filter is illustrated in

Fig. 3. [12] and [14] In the stationary reference, the expression of the basic

components is given by:

ks X s X s X s

s s

kX s X s X s

s sX s

X

(14)

With: K=210.

1

s

1

s

k

k

c

c

lv

lv

lv

lv

Fig. 3. A Multi-variable Filter

V. IMPROVED PHASE LOCKED LOOP (PLLMVF)

Fig. 4. Blok diagram of the improved PLL with MVF or PLLMVF


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VI. ANALYZE OF THE TWO PLL PERFORMANCES

Different performances of a PLL for an unbalanced three-

phase source voltages and with frequency (f = 50 Hz).

A. The conventional PLL

The unbalanced three-phase source voltages are given by

the following system:

s1

s2 max

s3

sin( t )v 2v V (1 )sin( t )

3v2

(1 )sin( t )3

(15)

With: γ, λ is the constants which allow unbalanced three-phase

system.

Fig. 5. Simulation results of conventional PLL

Figs. 5 illustrates the simulation results of the

conventional PLL for an unbalanced of the source voltages

due to a decrease in the amplitude of phase 2, while putting (γ

= -0.27, λ = -0.45).

The position angular oscillates indeed with a pulsation of

(2w) about its reference, which generate the deformations of

the outputs of PLL. The THD of the two signals sine, cosine

and for the outputs of PLL is 5.65%.

B. The improved PLLMVF

Fig. 6. Simulation results of the improved PLLMVF

The PLLFMV is carried out on an unbalanced source and

line voltages due to a decrease in the amplitude of phases 2

and 3, contrary to the results found with the conventional PLL,

the position angular is non-oscillating and periodically linear.

The αβ voltages are well filtered, and we obtain the balanced

unit sinusoids and very good qualities at the outputs of

PLLFMV.

VII. SIMULATION OF THE FOUR LEG SHUNT ACTIVE POWER

FILTRE

The work objective is to compare study of two different

source voltages estimated and the reference currents extracted

uses a three phase four-wire four-leg shunt active power filter

(SAPF). The techniques that are considered for comparative

study are: pq0 theory associated with conventional PLL due to

a new pq0 theory associated with PLL based on Multi-variable

Filter called PLLMVF. This is carried out by numerical

simulation under unbalanced source voltage and single-phase

loads. The performance of the proposed techniques is

evaluated through Sim Power Systems and S-Function of

MATLAB fig. 5. System parameters are given in Table I.

TABLE I. SYSTEM PARAMETERS FOR SIMULATION AND LOAD

SPECIFICATIONS

Parameter Value

Capacitance of the capacitor Cdc 5 mF

DC bus voltage Vdc 800 V

Coupling impedance Rf ,Lf 0.1 mΩ, 0.1 mH

The source voltage and frequency 220 V, 50Hz

Source impedance Rs ,Ls 1 mΩ, 1 mH

Line impedance Rl ,Ll 1 mΩ, 1 mH

Load impedance Rch ,Lch 5Ω, 10 mH

Unbalanced Load R ,L 5Ω, 10 mH

Nominal switching frequency fsn =14 kHz

Fig. 7. Schematic block diagram of a control of four four-leg shunt active

power filter based on improved PLLMVF

A. Simulation of SAPF with balanced source voltages

Figs. 8 and 10 shows the performance of four-leg SAPF

based on pq0 theory associated with the two types of PLL

(conventional and improved PLL) under balanced source

voltage and unbalanced single phase nonlinear loads. The

performance indices are as source currents, loads currents,

harmonic and three reference currents, source current and

corresponding voltage of the first phase, neutral wire current,

and DC bus voltage. After examination of this dynamic

performance, it is concluded that four-leg SAPF source

currents waveform is sinusoidal and in phase with the


3

corresponding voltage using the two types of PLL (the power

factor is unitary), the monitoring of the compensator harmonic

and the reference currents if123 and if123ref is constructed with

zero error for the two types of PLL, The neutral current is

successfully reduced with the two types of PLL.

1. The conventional PLL

Fig. 8. Performance of the four leg SAPF under balanced source voltages based on conventional PLL, before and after unbalanced loads

(i) (ii)

Fig. 9. Spectrum of source current of first phase under balanced source voltages based on conventional PLL: (i) before unbalanced loads, (ii) after

unbalanced loads

2. The improved PLLMVF

Fig. 10. Performance of the four leg SAPF under balanced source voltages

based on improved PLLMVF, before and after unbalanced loads

(i) (ii)

Fig. 11. Spectrum of source current of first phase under balanced source

voltages based on improved PLLMVF: (i) before unbalanced loads, (ii) after unbalanced loads

The harmonics spectra of phase „1‟ source current (is1)

under balanced source voltage before and after unbalanced

loads with the two types of PLL are shown in Figs. 9 and 10 (I

and ii) respectively. The THD of phase „1‟ source current (is1)

with the conventional PLL is observed as 1.29% and 2.03%

before and after unbalanced loads respectively and with the

improved PLLMVF is observed as 1.22% and 1.94% before and

after unbalanced loads respectively, and it satisfies guidelines

of IEEE-519 standard. It is concluding that four-leg SAPF

based on pq0 theory with two types of PLL is competent to

achieve the functions of unbalanced loads and harmonics

suppression under balanced source voltage.

Detailed summary of four-leg SAPF performances under

balanced source voltage before and after unbalanced loads

with the two types of PLL are shown in Table II.

TABLE II. %THD OF SOURCE CURRENTS COMPARISON OF THE TWO

TYPES OF PLL UNDER BALANCED SOURCE VOLTAGES

Conventional PLL Improved PLLMVF Balanced

Loads Unbalanced

Loads Balanced

Loads Unbalanced

Loads Source current THD 1.29% 2.03% 1.22% 1. 94%

B. Simulation of SAPF with unbalanced source voltages

For this case, the unbalanced and distorted 3-phase mains

voltages are as below:

s1

s2

s3

220 2

160 2

v sin( t )2

v sin( t )3

2v sin( t )120 2

3

(16)

The four leg SAPF with unbalanced source voltages is

tested with the two types of PLL under balanced and

unbalanced single phase nonlinear loads, and the results are

presented in following sub sections.

Figs. 12 and 13 shows the unbalanced source voltage,

estimated source voltages, source currents, harmonic and three

reference currents, source current and corresponding voltage

of the first phase, and the neutral wire current simulation

results of four-leg SAPF performance based on pq0 theory

associated with the two types of PLL (conventional and

improved PLL) under unbalanced source voltages and single

phase nonlinear loads. It is observed that four-leg SAPF using

the conventional PLL the source currents and estimated source


4

voltages are deformers, however the performance of four-leg

SAPF using proposed improved PLLMVF, the source currents

are become sinusoidal and the estimated source voltages are

restored to the balanced set of sinusoidal voltages before and

after unbalanced loads.

1. The Conventional PLL

Fig. 12. Performance of the four leg SAPF under unbalanced source voltages

based on conventional PLL, before and after unbalanced loads

2. THE IMPROVED PLLMVF

Fig. 13. Performance of the four leg SAPF under unbalanced source voltages based on improved PLLMVF, before and after unbalanced loads

The harmonics spectra of source currents under

unbalanced source voltage before and after unbalanced loads

with the two types of PLL are shown in Figs. 14 to 17 (i, ii and

iii). A comparison of this harmonics spectra are presented in

Table III. The THD of the three phase source currents before

unbalanced loads using the conventional PLL are 7.9%, 8.31%

and 8.57% Figs. 14 (i, ii and iii) which reduces to 2668%,

2672% and 266% respectively using proposed improved

PLLMVF Figs. 16 (i, ii and iii), and after unbalanced loads are

8.56%, 9.02% and 9.10% using the conventional PLL Figs. 15

(i, ii and iii), which reduces to 2.93%, 2.96% and 2.92% using

proposed improved PLLMVF Figs. 17 (i, ii and iii).

These results show reasonable performance of the four-leg

SAPF based on pq0 theory with the improved PLLMVF.

(i) (ii) (iii)

Fig. 14. Spectrum of source currents under unbalanced source voltages with conventional PLL before unbalanced loads

(i) (ii) (iii)

Fig. 15. Spectrum of source currents under unbalanced source voltages with conventional PLL after unbalanced loads

(i) (ii) (iii)

Fig. 16. Spectrum of source currents under unbalanced source voltages with improved PLLFMV before unbalanced loads


5

(i) (ii) (iii)

Fig. 17. Spectrum of source currents under unbalanced source voltages with improved PLLFMV after unbalanced loads

TABLE III. %THD OF SOURCE CURRENTS COMPARISON OF THE TWO TYPES OF PLL UNDER UNBALANCED SOURCE VOLTAGES

Conventional PLL Improved PLLMVF

Balanced Loads unbalanced Loads Balanced Loads unbalanced Loads

THD of source currents %

is1 769% 8.56% 2668% 2693%

is2 8631% 9.02% 2672% 2696%

is3 8657% 9.10% 266% 2692%

VIII. CONCLUSION

A new modified instantaneous real, imaginary and zero-

sequence powers pq0 theory with a phase locked loop (PLL)

based on Multi variable filter (MVF) in the αβo axes control

algorithm with a Three Dimensional Space Vector Modulation

has been used in four leg inverter based shunt active power

filter for power quality improvement under unbalanced source

voltage and single-phase loads. The use of phase locked loop

based on Multi variable filter has an acceptable performance

of a four leg shunt active power filter which has been

approved by simulation results. Because it absolutely restored

to the balanced set of sinusoidal the source currents and

voltages under unbalanced source voltage and single-phase

loads, it has been establish as a successful solution to power

quality problems. For source current harmonics and zero-

sequence current, a four leg shunt active power filter with

proposed controller has been used which has eliminated the

source current harmonics and zero-sequence current under

unbalanced source voltage and single-phase loads. The Three

Dimensional Space Vector Modulation for four leg inverter

controller has also established its success in switching losses

reduced and switching frequency fixed. The simulation results

have confirmed the main advantages of proposed modified

instantaneous real, imaginary and zero-sequence powers pq0

theory with a phase locked loop based on Multi variable filter.

ACKNOWLEDGMENTS

The authors like to thank the ICEPS Laboratory (Djillali

Liabes University of Sidi Bel-Abbes) and the Algerian general

direction of research DGRDT for their financial support.

REFERENCES

[1] A. Chebabhi, M-K fellah, N. Rouabah, Dj. Khodja «Commande d'un filtre actif shunt par la technique de contrôle directe de puissance basée sur le flux virtuel» CGE'07, 7ème Conférence sur le Génie Electrique. EMP, Bordj El Bahri, Alger, Algérie, 12-13 Avril 2011; 04/2011.

[2] S-H.Hosseini, T. Nouri, M. Sabahi “Power Quality Enhancement Using a New Hybrid Active Power Filter Under Non-Ideal Source and Load Conditions » 2009 IEEE.

[3] A. Chebabhi, M-K Fellah, A. Kessal, M-F Benkhoris « Comparative Study of reference currents and DC bus voltage Control for Three Phase Four Wire Four Leg shunt active power filter to Compensate Harmonics and Reactive Power with 3D SVM» ISA Transactions, http://dx.doi.org/10.1016/j.isatra.2015.01.011i.

[4] S. R. Arya, B. Singh “Power quality improvement under nonideal AC mains indistribution system” Electric Power Systems Research vol:106, pp: 86–94, 2014.

[5] P. Kanjiya, V. Khadkikar, H-H. Zeineldin “Optimal Control of Shunt Active Power Filter to Meet IEEE Std. 519 Current Harmonic Constraints Under Nonideal Supply Condition” IEEE Transactions on industrial electronics, vol. 62, no. 2, february 2015.

[6] Â. Araújo, J.G. Pinto, B. Exposto, C. Couto, J.L. Afonso “Implementation and Comparison of Different Switching Techniques for Shunt Active Power Filters” IEEE 2014.

[7] K. Bhattacharjee, “Harmonic mitigation by SRF theory based active power filter using adaptive hysteresis control “ Conference Power and Energy Systems: Towards Sustainable Energy , 13-15 March, pp: 1- 6, 2014.

[8] M. Hosseinpour, M. Mohamadian, A.Y. Varjani “RDFT based Control of a 3-phase 4-leg Shunt Active Power Filter under Unbalanced Load and Non-ideal Mains Voltage Conditions” 2014, IEEE The 22nd Iranian Conference on Electrical Engineering (ICEE 2014).

[9] S. Karvekar, D. Patil “Comparison of Reference Current Generation for Shunt Active Power Filter Using Goertzel Algorithm And Enhanced PLL” IEEE, International Conference on Circuit, Power and Computing Technologies [ICCPCT], 2014.

[10] H. K. Yada, M.S.R Murthy “A New Topology and Control Strategy for Extraction of Reference Current using Single Phase SOGI-PLL for Three-Phase Four-Wire Shunt Active Power Filter” IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), 2014.

[11] B. Singh, S. R. Arya “Back-Propagation Control Algorithm for Power Quality Improvement using SHAPF” IEEE transactions on industrial electronics, january 2014.

[12] H. Kouara, A. Chaghi « Three phase four wire shunt active power filter based fuzzy logic dc‐bus voltage control” Acta Technica Corviniensis-Bulletin of Engineering, Tome V, 2012.

[13] A. Benaissa, B. Rabhi, A. Moussi, M. F. Benkhoris, J.C. Le Claire “Fuzzy logic controller for five-level shunt active power filter under distorted voltage conditions” IEEE, 38th Annual Conference on Industrial Electronics Society, IECON 2012, pp: 4973–4978, 25-28 Oct. 2012.

[14] B. Singh, S. K. Dube, S. R. Arya “An improved control algorithm of DSTATCOM for power quality improvement” Electric Power and Energy Systems, vol:64, pp: 493–504, 2015.

[15] A. Chebabhi, M-K Fellah, M-F Benkhoris «Control of the Three Phase four-wire four-leg SAPF Using 3D-SVM Based on the Two Methods of Reference Signals Generating CV and SRF in the dqo-axes» Journal of Electrical Engineering, vol:1 no:1, pp:32-39, 03/2015.

[16] A. Chebabhi, M-K Fellah, M-F Benkhoris «Application of PQR theory for control of a 3-phase 4-wire 4-legs shunt active power filter in the αβο-axes using 3d-svm technique» Leonardo Journal of Sciences (LJS), Issue 26 (January-June), 2015 (14), pp: 17-28.

[17] H. Ouadi, A. A. Chihab, F. Giri “Adaptive nonlinear control of three-phase shunt active power filters with magnetic saturation” Electric Power and Energy Systems, vol:69, pp: 104–115, 2015.

[18] A. Chebabhi, M-K Fellah, M-F Benkhoris, A. Kessal «Fuzzy logic controllers and Three Dimensional Space Vector Modulation technique in the αβo axes for three-phase four-wire four-leg shunt active power filter »The 2nd International Conference on Power Electronics and their Applications (ICPEA 2015),, University of Djelfa, Algeria; 03/2015.


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power quality improvement using a f our l eg s apf b ased on … energy and power...

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