009-062

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Abstract— AC/DC controlled and uncontrolled converters are

widely used in many industrial applications. The large harmonic

input currents generated of such converters are well-known problems

that can lead to voltage distortion and increased losses in distribution

system. In order to solve the converter generated harmonic problems

a number of techniques proposed by many authors, one of these isthe current injection method, which is considered in this paper.

The principle of this method is to modify the input current waveform

by injecting every harmonic components of the rectified current, with

an opposite phase, to the AC side of the converter. The current

injection circuit is used for harmonic reduction of the controlled and

uncontrolled single-phase bridge rectifier. Analytical study of current

injection technique shows a drastic minimization of 3rd , 5th, 7th ,

9th,…. harmonic components of the input current, with total

harmonic distortion (THD) of the input current reduced from 48% to

~10% and power factor improved nearly to unity. Applying the

technique of current injection approximately sinusoidal waveform of

the input current are obtained, when the injection current effective

values nearly equal to DC load current for first current configuration

or equal to 0.666 of the DC load for circuit configuration. Simulation

of the controlled and uncontrolled single-phase bridge rectifier

current injection circuit presented by (Matlab Simulink). The

obtained result showed reduction in the total harmonic distortion and

the power factor closed to unity for many values of the firing angle (

α ). In addition the results showed good consistency between the

theoretical analysis and simulation results.

Keywords— Current Injection, CC(controlled converter)

Harmonic Reduction, Single Phase Converter.

I. I NTRODUCTION

HE control of electric power with power electronic

devices has become very important over the last years.

Whole new classes of motors have been enabled by power electronics, and the future offers the possibility of more

effective control of the electric power grid using power

electronics [1]. Power systems are designed to operate at

fundamental frequencies. However, certain types of non-linear

loads produce currents and voltages with frequencies that are

integer multiples of the fundamental frequency. These higher

frequencies are a form of electrical pollution known as power

system harmonics [2].

Ideally, voltage and current waveforms are perfect

sinusoids. However, because of the increased popularity of

electronic and other non-linear loads, these waveforms quite

often become distorted. This deviation from a perfect sine

wave can be represented by harmonics sinusoidal components

having a frequency that is an integral multiple of the

fundamental frequency Fig. 1. Thus, a pure voltage or current

sine wave has no distortion and no harmonics, and a non-

sinusoidal wave has distortion and harmonics. To quantify the

distortion, the term total harmonic distortion (THD) is used

[2]. The term is the ratio of the harmonic components of

voltage (or current) to the voltage (or current) of the

fundamental alone:

1

2

2

100%V

THDV

n

nnV ∑

∞=

=

×=

1

2

2

100% I

THDI

n

nn I ∑

∞=

=

×=

…..(1)

Where: nn I V , r.m.s value of nth harmonic component

n nth harmonic component

V1,I1 r.m.s value of fundamental components [6].

The characteristic harmonics are based on the number of

rectifiers (pulse number) used in a circuit and can bedetermined by the following equation:

n = (k x p) ±1

Where: k = an integer (1, 2, 3, 4, 5 …)

p = number of pulses of rectifier [3].

Fig.1Distorted waveform composed 3rd harmonic and fundamental

W. M. Lawrance proposed a method of reducing harmonic

currents on the AC supply side of a three phase diode rectifier.

The process consists of modifying the secondary current

waveform by injecting a third harmonic current into the

neutral point of the converter transformer. The third harmonic

current is automatically generated using LC passive filters.

Hussein I. Zainal Salar A. Kadir Hilmi F. Ameen

Electrical Engineering Department, Engineering College, Salahaddin University

Erbil, IRAQ

Contact Author email:[email protected]

New Design Circuit Harmonic Reduction of

Single Phase Converter by Current Injecting

Method

T

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2

1

2

1

2

s

ss

I

I I THDI

−=

The limitation of this method is the additional power losses by

the resistors present in the passive network [4].

S. kim, P. Enjeti proposed a new approach to improve power

factor and reduce current harmonics of a three-phase diode

rectifier using the technique of the line injection.The proposed

approach is passive and consists of a novel interconnection of

a star-delta transformer between the AC and DC sides of the

diode rectifier. A circulating third harmonic current is

automatically generated, and injected to the AC side lines of the rectifier. The resulting input current is near sinusoidal in

shape with a significant reduction in supply current harmonics.

The disadvantage of this approach is the additional cost of the

star-delta transformer which is rated about 43% of the rectifier

output power [5].

X.Dai, Y.Xu, D.He Proposed a novel solution to the problem

of harmonic pollution caused by an AC/DC single-phase

bridge rectifier by adding an additional passive resonant net

between the AC and DC sides of the rectifier. The passive

resonant network, which consists of an inductance and three

capacitances, will generate a second harmonic current and this

current injected to the AC supply line of the rectifier.Simulation results show that the total harmonic distortion

THD of the supply current can be reduced from 50% to 10%

[6]. J. Carlos and A.H. Samra discussed a novel approach of

zigzag transformer connected between AC and DC sides of

UCC. They showed by simulation using Electro-Magnetic

Transient Program, that the generated circulating current

drastically reduces the supply current harmonics. No practical

results are presented [7]. P. Pejovic and Z. Janda analyzed the

diode rectifier applying passive current injection networks

proposed in [4] and [5]. The result of their analysis showed

that the minimum THD of the input current is obtained when

the phase displacement between the third harmonic voltage

and current equal to zero, and the amplitude of the current

injected to each phase of the rectifier equal to one half of the

load current [8]. P. Pejovic and Z. Janda proposed a low

harmonic three phase diode rectifier that applies near optimal

current injectionthree resistors and three nondissipative filters.

The injection network consists of thirteen elements [9]. P.

Bozovic and P. Pejovic proposed a novel passive current

injection for three phase full bridge Thyristor rectifier. The

rectifier utilizes current injection network consists of a

transformer with the turn ratio 1:1, an inductor, two capacitors

and one pair of antiparallel connected thyristors. The result

show that obtained the minimizing input current THD, while

preserving high efficiency of the rectifier [10]. Basil. M. Sand Hussein.I.Z proposed a new concept and a novel passive

resonant network, which is connected between the AC and DC

sides of the Three-phase rectifier, analyses and simulated by

PSPICE program. The result show that the shape of line

current becomes nearly sinusoidal and the THD of the AC

supply current can be reduced from 32% to 5% [11]. The aim

of this Paper is to reduce current harmonics and improve

power factor of input current in a single-phase controlled and

uncontrolled rectifier based on harmonic current injection

technique in order to get input current waveform near to

sinusoidal waveform. For this purpose the current injection

circuit have been used and proposed. Therefore the broad

objectives of this paper ; Analyzing the current injection

technique for single-phase CC rectifier in order to minimize

harmonic distortion and improve power factor of the input

current, mathematical analysis of the passive current injection

network in order to get the equations of elements to design

current injection network and simulating the circuitconfiguration of CC rectifier with and without current

injection, using (Matlab Simulink) program, and comparing

the waveforms results. The circuit arrangement of a single-

phase full converter is shown in Fig. 2 with a highly inductive

load. During the positive half-cycle, thyristor and are

forward biased; and when these two thyristor are fired

simultaneously at , the load is connected to the input supply

through and . During the negative half-cycle, thyristor and

are forward biased; and firing of thyristors and will apply

the supply voltage across thyristor and as reverse blocking

voltage [20].

Fig.2 single phase bridge converter

II-Harmonic Analysis of the Input Current

The input current of a controlled-bridge rectifier is a square

waveform when the load is high inductive load. In addition,

the input current is shifted by the firing angle with respect

to the input voltage , as shown in Fig.3

The Fourier Series analysis of input current waveform in

Fig. 3

)(5sin254.0)(3sin424.0)sin(273.1[ α ω α ω α ω α −+−+−= t t t I i d s

...])(9sin141.0)(7sin181.0 +−+−+ α α t t ….(2)

It is clear from Eq. 2 that the harmonic orders of input

current are only the odd harmonics such as 3,5,7,9.

The r.m.s value of the fundamental component current is

α α

d

d

s I I

I 9.02

273.11 ==

……(3)

The total harmonic distortion (THD) of the input current is

given by ……(4)

By substituting Eq.2 in to Eq.4, the THDI equal to 48.43% [12];

Fig. 3 Waveform of input current and voltage of the single-phase

controlled rectifier with high inductive load.

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The harmonic series of the waveform given in Fig. 2.3(b) is:

)(7sin181.0)(5sin254.0)(3sin424.0[ α ω α ω α ω α −+−+−−= t t t I i d inj

.......)(9sin141.0 +−+ α ω t ……..(5)

Where iinj is all harmonic components of the ideal injection

current. If the harmonic current components given by Eq.5

are injected to the input current of the converter (adding the

two waveform given in Fig.4(a) and Fig.4(b), then the

waveform in Fig.4(c) is obtained. This waveform has a

fundamental frequency only, which is the first term of Eq. 2.

This means that by injecting a current which has a waveform

given in Fig. 4(b) to the input current of the converter, all the

harmonic components of the input current are eliminated.

When injecting any current waveform to the AC side of the

converter, there will be switching affect on this waveform.

The ideal harmonic current waveform after switching is shown

in Fig.4(b).

Fig. 4 Principle of current injection technique(a) Input current without harmonic current injection

(b) Ideal current waveform of all harmonic components of (a) with

opposite phase (c) Ideal current waveform after injection

(fundamental component)

Fig.5 shows a single phase thyristor bridge converter with a passive current injection network. The passive current

injection network is connected between the AC and DC sides

of the thyristor bridge converter.

The passive current injection network consists of current

injection network, and current injection device. The current

injection network consists of adjusting coil element, and this

coil is used to adjust the magnitude and phase of the second

harmonic current. The current injection device is applied to

divide current in three equal parts, and each parts can be

realized as current injection capacitors (C j ) in series with

current injection inductors (L j ). The current injection device

used for power factor correction and the reactance of the

current injection capacitors must be equal to the reactance

current injection inductors at second harmonic frequency.

Fig.(5) Thyristor bridge converter with passive current

injection circuit.

Fig.6 Current direction of thyristor bridge converter with current

injection(a) (T1,T2) conducting.(b) (T3, T4 ) conducting

Fig.6 shows that the input current after current injection equal

to (3

2 2i I d +α

) .The current of the thyristors (T1,T3 ) equal to

(2

i I d

+α

) but the current of the thyristors (T2,T4 ) equal to

(3

2i I d +α

), the current passing in thyristors (T1,T3 ) is

greater than the current passing in thyristors (T2,T4 ), therefore

the converter is unbalanced.

The positive peak value of must coincide with the positive

pulse center of the input current before harmonic current

injection. Therefore from Fig. 2.6(b) the second harmonic

current is to be given in the following equation

)2

22sin()(2cos2

π α ω α ω +−−=−−= t I t I i mm

…(6)

Where Im is the max. value of second harmonic current.

Since the converter operation is divided into two periods, in

each period a pair of thyristors are conducting. Therefore theconverter input current after current injection can be expressed

as:

'

si

+−

+

=

)3

2(

3

2

2

2

i I

i I

d

d

α

α

+≤≤+

+≤≤

α π ω α π

α π ω α

2t

t

….(7)

Where '

siis the input current after harmonic current

reduction. Defining the injecting factor as:

α

ρ d

m

I

I = ….(8)

Where α d I is the DC load current. The injection currentduring a complete period can be expressed as:

inji'

−∗∗

−∗∗−

==

)(2cos3

2

)(2cos3

2

3

22

α ω ρ

α ω ρ

α

α

t I

t I

i

d

d

+≤≤+

+≤≤

α π ω α π

α π ω α

2t

t

……(9)

The injection current inji' in Fig. 7(c) during a complete

period α π ω α +≤≤ 2t can be obtained by the switching

function (SF ). Then the harmonic components of the injection

current can be expressed by Fourier series as follow:

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2'

3

2iSF i inj ×=

….(10)

Substituting SF ,Eq.6 and Eq. 8 in to Eq.10, then the

injection current becomes as follow:

*'

α ρ d inj I i =

)(5sin202.0)(3sin508.0)sin(283.0 α ω α ω α ω −−−−− t t t

)11.......()(9sin098.0)(7sin132.0 −−−−− α ω α ω t t

The input current after harmonic current reduction

can be obtained by adding Eq. 2 and Eq.11 as:

si ' = *α d I

)(3sin)508.0424.0()sin()283.0273.1( α ω ρ α ω ρ −−+−+ t t

)(7sin)132.0181.0()(5sin)202.0254.0( α ω ρ α ω ρ −−+−−+ t t

)12.......()(9sin)098.0141.0( −−−+ α ω t

Eq.12 shows that the harmonic component amplitudes of

input current depend on the injection factor ρ which is

dependant on the max. value of second harmonic current( m I )

and load current ( α d I ). Fig. 7(d) shows the waveform of the

input current after harmonic current reduction at 1= ρ .

Fig.7 a- Switching function or input current without currentinjection b- Second harmonic current c- The injection

current after switching d- Input current with current injection.

III.OPTIMUM I NJECTION FACTOR FOR CIRCUIT

It is clear from Eq.12 that each harmonic component of the

input current can be attenuated to zero by an appropriate

selection of injecting factor. By substituting harmonic

component current from Eq. 12 in to Eq.4, and considering the

harmonic order up to 17th, therefore the total harmonic

distortion THD for input current

( ))13.....(34.06691.0347.0

273.1283.0

1 2+−

+= ρ ρ

ρ THD

Differentiating Eq.13 with respect to shows that THD has

a minimum value at . Fig.8 shows the THD versus the

injection factor . The minimum THD (10%) can be obtained

when is nearly equal to 1. This is called optimum.

Therefore the optimum minimization of input current

distortion is obtained when and Eq.12 is reduced to:

si' = α d I )(5sin052.0)(3sin084.0)sin(556.1 α ω α ω α ω −+−+− t t t

)14)....((9sin042.0)(7sin048.0 α ω α ω −+−+ t t

It is clear from Eq.14 that the fundamental component of input

current is increased from (α d I 273.1 ) to (

α d I 556.1 ) and

Significant reduction in input current harmonics compared

with Eq. 2.

Fig.8 THD% variation with injection factor ρ for uncontrolled

converter .

The of single phase converter can be represented as the

product of a distortion factor and displacement factor. The

distortion factor is the ratio of the r.m.s of the fundamental

component to the total r.m.s of input current. The

displacement factor is the cosine of the input displacement

angle which is the angular displacement between the

fundamental component of the ac input current and the supply

voltage. The fundamental component is either in phase or lags

behind the voltage by an angle which depends upon the firing

angle [22].

PF = distortion factor × displacement factor

)15.....(cos 11 θ ×=

Is

IsPF

1 Is is the r.m.s value of the fundamental component of

input current , Is is the total r.m.s value of the input current

and 1θ is the angle between the fundamental component of theinput current and the supply voltage.

V-Design Circuit

The capacitor & inductor injection value as a function of for

PF compensation and with harmonic current injection can be

expressed as:

)16....(sin556.1 α α d

m

j I

V X =

Simplifying the above equation at resonance LjCj X X =

at

(α=0).

m

do

fV

I C

π

α α

16

sincos556.19 ×=

α π 2sin556.192

0d

m

I f V L

×= ……..(17)

The value of passive current injection network elements for

different firing angle which connected between the AC and

DC sides of the thyristor bridge converter based on the

equations that have been derived to select the elements value

of passive current injection network, where the thyristor

bridge converter is supplied by single-phase voltage

source,(100V) peak, 50 Hz, and high inductive load(1H ).

Maximum converter load current is assumed 5A. Therefore

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the converter output current at firing angle is α α cos5=d I .

From Eq. 16 and Eq. 17 the capacitance and inductance values

for optimum current injection and PF compensation for

different firing angle can be calculated. Table I gives the

capacitance and inductance values (theoretical, simulation) at

different values of the firing angle.

Table I The injection capacitance and inductance value at

different value of firing angle.

The adjusting inductance value in table.II gives the coil

element inductance (theoretical, simulation) at different values

of the firing angle.

Table II. Adjusting inductance at different values of firing angle

IV. SIMULATION RESUILTS

Table. III. gives simulation results of the PF and THD for

different firing angles.Firing

angle

Without current injection With current injection

PF THD% PF THD%

0 0.91 48 0.99 9.6

15 0.88 47.3 0.98 11.7

30 0.8 46.6 0.96 12.8

45 0.65 45.6 0.95 13.6

60 0.46 43.8 0.85 17.6

It is noticed for Table. III

i- The THD of input current are significantly reduced after

current injection. ii-The PF is significantly improved iii-The

THD of input current are slightly increased as firing angle

increased. Figs. 9(a), 9(b), 9(c), and 9(d) show the simulated

voltage and input current without and with interconnection of

current injection network for firing angle 0 and 45o

respectively. Figs. 10(a), 10(b), 10(c), and 10(d) show the

harmonic spectrum for input current without and with

interconnection of current injection network for firing angle 0

and 45o

respectively.

Fig.9 a- Input voltage and current without injection (α =0)

b- Input voltage and current with injection (α =0)

c-Input voltage and current without injection (α =450)

d- Input voltage and current with injection (α =450)

α Theoretical Simulation

jC

j L

jC

j L

0 f µ 0

mH 0 f µ 15

mH 169

15 f µ 69

mH 36 f µ 69

mH 36

30 f µ 5.77

mH 7.32 f µ 5.77

mH 7.32

45 f µ 139

mH 18 f µ 139

mH 18

60 f µ 38

mH 66 f µ 38

mH 66

Firing angle 0 15 30 4

5

60

( f L )

Theoretical

mH 6

mH 8

mH 12

m16

mH 24

( f

L )

Simulation

mH 6

mH 10

mH 14

m18

mH 26

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Fig.10 a-Harmonic spectrum for input current without

injection (α =0), b-Harmonic spectrum for input current with

injection (α =0), c-Harmonic spectrum for input current

without injection (α =450

), d-Harmonic spectrum for input

current with injection (α =450).

Table IV. Harmonic order for current injection and without

current injection.

VI.CONCLUSION

In this paper using the current injection technique to reduce

harmonic distortion of the input current in single-phase CC,

and it’s simulated by computer using (Matlab Simulink).The

shape of the input current is almost sinusoidal. The Simulation

and theoretical analysis of input current after harmonic current

injection show that the total harmonic distortion (THD) is

reduced from (48.8%) to (10%) for zero firing angle but the

total harmonic distortion increased when the firing angle

increased. The injection circuit is simple and very cheap. The

passive current injection network is lossless.

R EFERENCES

[1] Timothy L. Skvarenina, “The Power Electronics Handbook”, Industrial

Electronics Series, Published in 2002 by CRS Press LLC.

[2] Prof. Mack Grady, “Understanding Power System Harmonics”,

University of Texas at Austin, June 2005, www.ece.utexas.edu/~grady.

[3] SQUARE D, Product Data Bulletion, “Power System Harmonics

Causes and Effects of Variable Frequency Drives Related to the IEEE

519-1992 Standard”, Bulleti No.8803PD9402, Raleigh, No, USA,

August 1994.

[4] W. B. Lawrance and W. Mielezarski, “Harmonic Current Reduction in

a Three-Phase Diode Bridge Rectifier”, IEEE Trans. Industrial

Electronics, Vol. 39, No. 6, PP. 571-576, Dec. 1992.[5] S. kim, P. Enjeti. P. Packebush and I.J. Pital, “A New

Approach to Improve Power Factor and Reduce

Harmonic in Three-phase Diode Rectifier Type Utility

Interface”, IEEE Trans. On Industry Applications, Vol.

30, No. 6, PP. 1557-1564, November/December 1994.[6] X.Dai. ,Y.Xu. and D.He, “Novel Passive Rectifier with Low THD

Based on Harmonics Injection and Counteracting Principle”, IEE Tran.

On Power Elect. Power Appl., Vol. 145, No. 4, July 1998.

[7] Jana Carlos and Abdul H. Samra, “A New Technique to Reduce Line

Current Harmonics Generated by a Three phase Bridge Rectifier”,

IEEE, PP.345-359, 1998.

[8] P.Pejovic and Z.Janda, “An Analysis of Three-Phase Low Harmonic

Rectifiers Applying the Third-Harmonic Current Injection”, IEEE

Trans. On Power Electronics, Vol. 14, No. 3, PP. 397-407, May 1999.

[9] P.Pejovic and Z.Janda, “Low- Harmonic Three-Phase Rectifier Applying Current Injection”, IEEE Proc.-Electric Power Appl., Vol.

146, No. 5, PP. 545-551, September 1999.

[10] P.Bozovic and P.Pejovic, “A Novel Three-Phase Full Bridge Thyristor

Rectifier based On the Controlled Third Harmonic Current Injection”,

IEEE Bologna Power Tech Conference, June 23-26, 2003, Bologna,

Italy.

[11] Basil M. Saied and Hussein I.Zynal, “Minimizing Current Distortion of

a Three-Phase Bridge Rectifier based On Line Injection Technique”,

IEEE Trans. On Power Electronics, Vol. 26, No. 6, November 2006.

[12] Muhammad H. Rashid, “Power Electronics Circuit,

Devices, and Applications”, Third Edition, New Delhi

(Prentice-Hall of India Private limited), 2004.

Harmonic

order

Without Current

Injection

With current

injection

3rd 42.3% 8.6%

5th 25.4% 4.4%

7th 18% 3.8%

9th 14% 6.2%

11th 11.5% 3.2%

13th

9.7% 5.6%PF 0.91 0.99

THD 48% 9.6%

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