Research Article ModifiedPWMTechniqueforHarmonicReductiondownloads.hindawi.com/archive/2012/917897.pdf · rations, control strategies, and applications of active filters are offered

International Scholarly Research NetworkISRN ElectronicsVolume 2012, Article ID 917897, 8 pagesdoi:10.5402/2012/917897

Research Article

Modified PWM Technique for Harmonic Reduction

Alireza Hoseinpour1 and Reza Ghazi2

1 Sistan & Baluchestan Regional Electrical Company (SBREC), Zahedan 9817917765, Iran2 Ferdowsi University of Mashad, Mashad 9177948974, Iran

Correspondence should be addressed to Alireza Hoseinpour, ali reza [email protected]

Received 12 March 2012; Accepted 8 April 2012

Academic Editors: H. A. Alzaher, A. R. Seidel, and E. Tlelo-Cuautle

Copyright © 2012 A. Hoseinpour and R. Ghazi. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

This paper presents a Shunt Active Filter (SAF) based on the Variable Index Pulse Width Modulation approach. In the proposedmethod of Pulse Width Modulation (PWM), the triangular wave is derived by integration of the reference signals. This methodintroduces two basic advantages; the first one is that the triangular signal contains the information of the signal to be obtained inoutput and the second advantage is that its amplitude is varied in proportion to the amplitude of the reference signal. Therefore,in this PWM method, the modulation index is varied according to the variation of the reference signal, so it is termed as VariableIndex Pulse Width Modulation. In order to demonstrate the validity of the proposed method, the obtained simulation results arecompared with results of the Space Vector Modulation (SVM) approach. Furthermore, it is shown that in the case of nonsinusoidalvoltages, the SAF with the proposed control strategy can provide the filtering action. This method is quite easy to implement andrequires lower circuitry. The results show that the proposed method can satisfy the IEEE-519 standard regarding the reduction ofharmonics.

1. Introduction

Nonlinear loads such as adjustable speed drives, powersupplies for various electronic equipments are the originof both current and voltage harmonics production in thedistribution system leading to the power quality problem. Inresponse to the power quality problem, IEEE 519 and IEC EN61000-3 standards specify regulations governing harmoniccompliance. Numerous active filters are introduced as effec-tive means to meet the harmonic standards beside the passivefilters that have been proposed [1–4]. The SAF has become amature technology in recent years. The operation principle ofan active filter is based on PWM or SVM three-phase inverterto generate nonsinusoidal currents to meet harmonic currentrequirement of the nonlinear load. Many various configu-rations, control strategies, and applications of active filtersare offered in the literature [5–7]. The SAF performs thefiltering action by injecting harmonic components whichcancel those from the load, thereby the line current becomesfree of harmonics [8]. In filter design and its application, themethods for extraction of the harmonics from line currentand determination of the filter reference current play an

important and crucial role. Indeed, accuracy and speed ofthe SAF response are related to this point [9–11]. Timedomain and frequency domain are two well-known methodsfor generation of reference current [12–15]. Time domainmethods are based on measurements and transformation ofthree-phase quantities such as d-q or p-q transformation,whereas the frequency methods are based on the FastFourier Transformation (FFT). The main advantage of timedomain methods is their fast response. On the other side,frequency domain methods can provide accurate individualand multiple harmonic detection of load current. Timedomain methods, such as, instantaneous reactive powerdepend on source voltage harmonic. This fact is proved withmathematical equations. With regard to the compensationobjectives, the control strategy and the method for extractingthe nonactive load currents references are determined [8–15]. The purpose of this paper is to compensate the harmoniccurrent using the frequency domain method of compensa-tion in which all harmonic current components are targetedand eliminated. In this paper a novel PWM technique withthe property of variable index based on the integral ofreference current is suggested and applied on a SAF. To

2 ISRN Electronics

Identificationbox

AC

VIP

WM

Dri

ver

Tria

ngu

lar

wav

ege

ner

ator

abc

g

s1

s3

s2

Figure 1: Configuration of SAF.

demonstrate its performance and superiority the obtainedresults are compared with [16] in which the SVM techniquebased on Hysteresis Current Controller (HCC) is used. Thepaper is organized as follows. Section 2 defines the config-uration and control system of SAF. The proposed modifiedPWM technique is introduced in Section 3. Section 4 isdevoted to the application of SAF on a sample circuit witha nonlinear load considering sinusoidal and nonsinusoidalsources. The simulation results are presented in this section,and the necessary comparison has been made to validateits superiority and performance. Conclusions are given inSection 5.

2. Shunt Active Filter

The SAF configuration is shown in Figure 1 which consists ofidentification, modulation, and inverter sections.

The reference signal is generated in the identificationsection. This signal defines the current that should beproduced by the three-phase inverter of SAF. There are twomethods for generating the reference signal: time domainand frequency domain. The time domain methods, suchas, d-q transformation (or synchronous rotating refer-ence frame), p-q transformation (or instantaneous reactivepower), and symmetrical components transformation arebased on measurements and transformation of the three-phase quantities.

The main advantage of the time domain methods overthe frequency domain methods which are based on theFast Fourier Transformation (FFT) is their fast responses.However, the frequency domain methods provide accurateindividual and multiple harmonic load currents detection[10]. Time domain methods, such as, instantaneous reactivepower method depend on the source voltage harmonics. Thismatter is proved using the mathematical equations. In thistheory voltages and currents are measured in abc frame, thenare transformed into orthogonal frame as follows.

⎡⎢⎣vαvβvo

⎤⎥⎦ =

√23

⎡⎢⎢⎢⎢⎢⎣

1 −0.5 −0.5

0−√3

2

√3

21√2

1√2

1√2

⎤⎥⎥⎥⎥⎥⎦

⎡⎢⎣vavbvc

⎤⎥⎦,

⎡⎢⎣iαiβio

⎤⎥⎦ =

√23

⎡⎢⎢⎢⎢⎢⎣

1 −0.5 −0.5

0−√3

2

√3

21√2

1√2

1√2

⎤⎥⎥⎥⎥⎥⎦

⎡⎢⎣iaibic

⎤⎥⎦. (1)

In new frame the powers are calculated by

⎡⎢⎣PqPo

⎤⎥⎦ =

⎡⎢⎣vα vβ 0−vβ vα 0

0 0 vo

⎤⎥⎦

⎡⎢⎣iαiβi0

⎤⎥⎦. (2)

These powers comprise dc and ac components. If theaim is to compensate the line current harmonics, the com-pensator should generate the ac terms. Therefore, the cur-rents of SAF are obtained which can be converted into abcframe.

⎡⎢⎣i∗αi∗βi∗0

⎤⎥⎦ =

⎡⎢⎣vα vβ 0−vβ vα 0

0 0 vo

⎤⎥⎦−1⎡⎢⎣−Pac

−qac

−Poac

⎤⎥⎦, (3)

⎡⎢⎣i∗ai∗bi∗c

⎤⎥⎦ =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

√23

⎡⎢⎢⎢⎢⎢⎣

1 −0.5 −0.5

0−√3

2

√3

21√2

1√2

1√2

⎤⎥⎥⎥⎥⎥⎦

⎫⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎭

−1

⎡⎢⎣i∗αi∗βi∗0

⎤⎥⎦. (4)

Although this approach provides a good response whenthe source is sinusoidal, but it does not for nonsinusoidalsources. Generally, the voltage and current in nonsinusoidalsources contain harmonics given by

va =∞∑

n=1

√2Vn sin

(nωt + ψn

),

vb =∞∑

n=1

√2Vn sin

(nωt + 120 + ψn

),

vc =∞∑

n=1

√2Vn sin

(nωt − 120 + ψn

),

ISRN Electronics 3

ia =∞∑

n=1

√2In sin

(nωt − φn

),

ib =∞∑

n=1

√2In sin

(nωt − φn + 120

),

ic =∞∑

n=1

√2In sin

(nωt − φn − 120

).

(5)

These voltages and currents are transformed into orthogonalframe which can be expressed as positive, negative, and zerosequences by (6)

vα =√

3∞∑

n=1

V+n sin

(nωt + ψ+

n

)+V−

n sin(nωt + ψ−n

),

vβ =√

3∞∑

n=1

−V+n cos

(nωt + ψ+

n

)+V−

n cos(nωt + ψ−n

),

vo =√

6∞∑

n=1

Von sin

(nωt + ψ0

n

),

iα =√

3∞∑

n=1

(I+n sin

(nωt − φ+

n

)+ I−n sin

(nωt − φ−n

)),

iβ =√

3∞∑

n=1

(−I+n cos

(nωt − φ+

n

)+ I−n cos

(nωt − φ−n

)),

io =√

3∞∑

n=1

(Ion sin

(nωt − φ0

n

)).

(6)

The power components are obtained from (6), and (3) as

P = 3∞∑

i=1

∞∑

j=1

{V+j I

+i cos

((i− j

)ωt + φ+

i − ψ+j

)

+V−j I−i cos

((i− j

)ωt + φ−i − ψ−j

)

−V+j I−i cos

((i + j

)ωt + φ−i + ψ+

j

)

−V−j I

+i cos

((i + j

)ωt + φ+

i + ψ−j)}

,

q = 3∞∑

i=1

∞∑

j=1

{−V+

j I+i sin

((i− j

)ωt + φ+

i − ψ+j

)

+V−j I−i sin

((i− j

)ωt + φ−i − ψ−j

)

+V+j I−i sin

((i + j

)ωt + φ−i + ψ+

j

)

−V−j I

+i sin

((i + j

)ωt + φ+

i + ψ−j)}

,

Po = 3∞∑

i=1

∞∑

j=1

Voj Ioj

{cos((i− j

)ωt + φoi − ψoj

)

− cos((i + j

)ωt + φoi + ψoj

)}.

(7)

The dc terms are extracted from (7) and given by (8)

Pdc = 3∞∑

n=1

V+n I

+n cos

(φ+n − ψ+

n

)+V−

n I−n cos

(φ−n − ψ−n

),

qdc = 3∞∑

n=1

−V+n I

+n sin

(φ+n − ψ+

n

)+V−

n I−n cos

(φ−n − ψ−n

),

podc = 3∞∑

n=1

VonI

on cos

(φon − ψon

).

(8)

It can be seen from (8) that harmonics components arealso available in the dc power term; it means that com-pensation of the ac terms is not sufficient to reduce harmo-nics. Therefore, instantaneous reactive power theory is notsuitable where source is non sinusoidal. The method used inthis paper is a frequency domain approach based on BandReject Filter (BRF). In this approach, the line current signalis passed through a BRF having a center frequency equalto power system fundamental frequency. The output signalcontains all harmonics except the fundamental harmonic, soit can be a suitable reference signal for compensation. More-over, the BRF method does not require any voltage sensor,in contrast to the instantaneous reactive power method inwhich three voltage sensors are needed, so it can be more eco-nomical.

In the next section a new method of modulation is des-cribed and compared with the previous method.

3. Variable Index Pulse Width Modulation

In all previously developed SAFs in which the PWM tech-niques are used, the reference signal is compared with thetriangular signal. Such triangular signals have no informa-tion. However, in the proposed method the triangular signalis derived from the integral of reference signal so it will bean intelligent signal and has the following advantages. Theobtained triangular signal contains the information relatedto the output signal and also its amplitude will vary in pro-portion to the amplitude of the reference signal. In fact, themodulation index changes regarding the amplitude of thereference signal, hence it is termed (VIPWM). The procedureof this type of modulation for phase a (leg q1&q4) in Figure 2is described as follows.

For generation of a triangular signal we need an integra-tor with reset capability. According to Figure 3, in the positivehalf cycle at first, the integral of the reference current isperformed, then the output of the integrator which is the tri-angular wave, compared with the reference current. So longas the reference current is greater than the integrator output,transistor q1 is on and transistor q4 is off. When these twosignals are equal, the integrator becomes reset and as long asthe integrator output is zero, q1 is off and q4 is on. When out-put begins to increase q1 starts to conduct and q4 ceases. Thisprocess is continued up to the end of the positive half cycle.

However, during the negative half cycle, as long as theintegrator output is greater than the reference signal, q4

conducts and q1 does not. When two signals are equal, the

4 ISRN Electronics

abc

q1

q4

q3

q6

q5

q2

Figure 2: The structure of three-phase inverter.

+

−

Reference

Integrator

Reset

s1

s4

Figure 3: Configuration of circuitry for transistor driving.

integrator becomes reset and as long as the integrator outputis zero q1 is on and q4 is off. When the integrator outputdecreases from zero T4 begins to conduct and T1 ceases.

The sine wave, triangular wave and the required signalfor driving the transistor q1 corresponding to PWM with aConstant Index Pulse Width Modulation (CIPWM) thatm =0.9 are shown in Figure 4. The similar plots for VIPWM areshown in Figure 5.

4. Simulation Result

To show the ability of the SAF under the proposed controlstrategy, two cases have been simulated. In the first case, theload is nonlinear and the source is sinusoidal, while in thesecond case the source is non sinusoidal.

4.1. Sinusoidal Source. To evaluate the performance of theVIPWM technique it is applied on a three-phase SAF usingMATLAB Simulink and PSIM software. To demonstrate itsability in reducing the harmonic components from linecurrent, a bridge rectifier with an RL circuit is considered asa nonlinear load. The line current without SAF is shown inFigure 6(a). The line current frequency spectra can be calcu-lated using the following equations in which the amplitudeof the peak current considered to be equal to (±Ia), that is,the small variations in peak are neglected. So we have

i1(t) = a0 +∞∑

n=1

[an cos(nωt) + bn sin(nωt)],

a0 = Idc = 12π

2π∫

0

i1(t)d(ωt) = 0,

an(t) = 1π

∫ 2π

0il(t) cos(nωt)d(ωt)

= 1π

[∫ 5π/6

π/6Ia cos(nωt)d(ωt)

−∫ 11π/6

7π/6Ia cos(nωt)d(ωt)

]= 0,

bn(t) = 1π

∫ 2π

0il(t) sin(nωt)d(ωt)

= 1π

[∫ 5π/6

π/6Ia cos(nωt)d(ωt)

−∫ 11π/6

7π/6Ia cos(nωt)d(ωt)

]=⇒

bn(t) =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

0 if n = 2k,

0 if n = 3k,4Ianπ

sin(nπ

3

)otherwise.

(9)

According to (9) the amplitude of 2nd and 3rd harmonicsand their multiples are zero but there exist other harmonics.The line current frequency spectra are shown in Figure 6(b).It is clear from this figure that the total harmonic distortion(THD) is equal to 28.56% which is very high, so according toIEEE 519 standard to it should be reduced.

To do so, a SAF with the proposed control system isemployed. The compensator desirable current and its har-monic spectra are shown in Figures 7(a) and 7(b), respect-ively. The line current and its harmonic spectra after com-pensation by CIPWM are shown in Figures 8(a) and 8(b),respectively. The line current and its harmonic spectra com-pensated by VIPWM are also shown in Figures 9(a) and 9(b),respectively. It can be seen from these figures that the THDof CIPWM is 8.06% and that of VIPWM is 4.02%. So inthis respect the VIPWM is superior to CIPWM. To show theability of the proposed method, a comparison is made withresult of [16], where the SVM-based HCC is used and theobtained THD is equal to 5.32% which still does not satisfythe IEEE519 standard, while the proposed method of thepresent paper does. Furthermore, its implementation is easyand requires lower costs and circuitry.

4.2. Nonsinusoidal Source. In most of research works foundin the literature which are dealing with the problem of activefiltering, the source is considered to be pure sinusoidal,whereas due to the wide speared nonlinear loads in modernelectric systems, this assumption is no longer valid. It isshown that the proposed method of PWM has the abilityto tackle the problem of nonsinusoidal voltage. For thispurpose a triangular source voltage is applied on the testsystem. This input voltage and its frequency spectra areshown in Figures 10(a) and 10(b), respectively. Accordingto the frequency spectra the THD of this signal is equalto 12.12%. The line current and its frequency spectra arealso shown in Figures 11(a) and 11(b). The THD of linecurrent before compensation is 28.31%. The line current

ISRN Electronics 5

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016−100−80−60−40−20

020406080

100

Time (s)

Am

plit

ude

(a)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (s)

(b)

Figure 4: Modulation with constant index (m = 0.9). (a) Sine wave and triangular wave. (b) Logic signal for driving transistor T1.

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

−100

0

100

Time (s)

Am

plit

ude

−50

50

(a)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (s)

(b)

Figure 5: Modulation with variable index. (a) Sine wave and triangular wave. (b) Logic signal for driving transistor T1.

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3−200

−150

−100

−50

0

50

100

150

200

Time (s)

Lin

e cu

rren

t

(a)

0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

160

Harmonic order

Mag

nit

ude

Fundamental (60 Hz) = 163.4, THD = 28.56%

(b)

Figure 6: Line current without SAF for nonlinear load. (a) Original current waveform. (b) Current frequency spectra.

−80

−60

−40

−20

0

20

40

60

80

Lin

e cu

rren

t

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3

Time (s)

(a)

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16

Harmonic order

Mag

nit

ude

(b)

Figure 7: Desired current to be provided by SAF. (a) Original current waveform. (b) Current frequency spectra.

6 ISRN Electronics

0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2−200

−150

−100

−50

0

50

100

150

200

Time (s)

Lin

e cu

rren

t

IaIbIc

(a)

0

50

100

150


0 2 4 6 8 10 12 14 16

Harmonic order

Mag

nit

ude

(b)

Figure 8: Line current with SAF operated by CIPWM method. (a) Original current waveform. (b) Current frequency spectra.

−200

−150

−100

−50

0

50

100

150

200

Lin

e cu

rren

t

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3

Time (s)

(a)

0

20

40

60

80

100

120

140

160


Mag

nit

ude

0 2 4 6 8 10 12 14 16

Harmonic order

(b)

Figure 9: Line current with SAF operated by VIPWM method. (a) Original current waveform. (b) Current frequency spectra.

−150

−100

−50

0

50

100

150

Inpu

t vo

ltag

e

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3

Time (s)

(a)

0

10

20

30

40

50

60

70

80

90Fundamental (60 Hz) = 89.15, THD = 12.12%

Mag

nit

ude

0 2 4 6 8 10 12 14 16

Harmonic order

(b)

Figure 10: Input voltage without SAF. (a) Voltage waveform. (b) Frequency spectra.

and its frequency spectra after compensation with CIPWMand VIPWM are shown in Figures 12(a) and 12(b) andFigures 13(a) and 13(b), respectively. In the first system theTHD is 8.28% whereas THD of the compensated line currentwith VIPWM is equal to 4.14%. It is clear from these obser-vations that the THD is greatly reduced. Hence, the SAF canproperly work for both cases, but the second one is preferred.

Hence, the proposed SAF can properly operate in bothcases.

5. Conclusion

In this paper, the ability and the performance of shunt activefilters (SAFs) are improved by proposing a new type of PWM

ISRN Electronics 7

−150

−100

−50

0

50

100

150

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3

Time (s)

Lin

e cu

rren

t

(a)

0 5 10 15 20 250

20

40

60

80

100

120

140

160

Harmonic order


Mag

nit

ude

(b)

Figure 11: Line current without SAF for nonlinear load. (a) Original current waveform. (b) Current frequency spectra.

0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2−200

−100

0

100

200

Time (s)

Lin

e cu

rren

t

(a)

0

50

100

150


0 2 4 6 8 10 12 14 16

Harmonic order

Mag

nit

ude

(b)

Figure 12: Line current with SAF operated by CIPWM method (a) Original current waveform. (b) Current frequency spectra.

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3

Time (s)

−200

−150

−100

−50

0

50

100

150

200

Lin

e cu

rren

t

(a)

0 2 4 6 8 10 12 14 16

Harmonic order

0

20

40

60

80

100

120

140

160

Mag

nit

ude


(b)

Figure 13: Line current with SAF operated by VIPWM method (a) Original current waveform. (b) Current frequency spectra.

technique. In our proposed PWM method, the modulationindex varies according to the variations of the referencesignals, so it is termed as Variable Index Pulse Width Modula-tion (VIPWM) technique. The simulation results show thatthe SAF under this PWM technique can greatly removethe harmonic components from line current to satisfy therequirement of IEEE standard. The obtained results alsoshow that this technique can do the filtering action in the

case of nonsinusoidal voltage source. This method is easy toimplement with lower cost and circuitry.

Appendix

In nonlinear load: R = 1Ω, L = 0.3 mH. The magnitude ofsinusoidal and nonsinusoidal source is 110 V and their fre-quency is 60 Hz.

8 ISRN Electronics

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Research Article ModifiedPWMTechniqueforHarmonicReductiondownloads.hindawi.com/archive/2012/917897.pdf · rations, control strategies, and applications of active filters are offered