# A Modified Harmonics Reduction Technique for a Three-Phase Controlled Converter

**ABSTRACT** Three-phase controlled converters have many applications especially in adjustable speed drives and renewable energy. A three-phase controlled converter is a good option in these applications due to its low cost, simplicity, and maintainability with respect to other solutions like a full-bridge insulated gate bipolar transistor converter or a Vienna rectifier. Line current harmonics in this converter is very high; therefore, a harmonics reduction technique is needed to remedy the problem. In this paper, an improved injection current technique is introduced to reduce line current harmonics. The optimal amplitude and phase angle of the injection current for different loads and firing angles have been mathematically determined. Simulation for this technique has been performed by using the PSIM simulation program. An experimental prototype has been built to verify the mathematical and simulation results. The simulation and experimental results show a sensitive variation in the total harmonic distortion of the line current for the amplitude and angle of injection current variations. The simulation and experimental results prove the superiority of this technique in mitigating the requirements for harmonics standards.

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- International Review on Modeling and Simulations (I.RE.MO.S.). 04/2011; 4(4):525-532.
- SourceAvailable from: Ali M. Eltamaly
- SourceAvailable from: Ali M. Eltamaly
##### Conference Paper: A novel harmonic reduction technique for controlled converter by third harmonic current injection

Harmonics and Quality of Power (ICHQP), 2012 IEEE 15th International Conference on; 01/2012

Page 1

1190IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 3, MARCH 2008

A Modified Harmonics Reduction Technique

for a Three-Phase Controlled Converter

Ali M. Eltamaly

Abstract—Three-phase controlled converters have many appli-

cationsespeciallyinadjustablespeeddrives andrenewableenergy.

A three-phase controlled converter is a good option in these ap-

plications due to its low cost, simplicity, and maintainability with

respect to other solutions like a full-bridge insulated gate bipolar

transistor converter or a Vienna rectifier. Line current harmonics

in this converter is very high; therefore, a harmonics reduction

technique is needed to remedy the problem. In this paper, an

improved injection current technique is introduced to reduce line

current harmonics. The optimal amplitude and phase angle of

the injection current for different loads and firing angles have

been mathematically determined. Simulation for this technique

has been performed by using the PSIM simulation program. An

experimental prototype has been built to verify the mathematical

and simulation results. The simulation and experimental results

show a sensitive variation in the total harmonic distortion of

the line current for the amplitude and angle of injection current

variations. The simulation and experimental results prove the

superiority of this technique in mitigating the requirements for

harmonics standards.

Index Terms—Harmonics, third harmonic injection, three-

phase controlled converter.

I. INTRODUCTION

I

tifier in interfacing adjustable speed drives (ASD) [1]–[4] and

renewable energy in electric utilities [5], [6]. The three-phase

controlled converter has a simple construction and control, low

cost, and low acoustic noise compared with other solutions like

full-bridge insulated gate bipolar transistor line side inverters

or Vienna rectifiers. The line current of a controlled converter

and its fast Fourier transform (FFT) components are shown

in Fig. 1. It is clear from this waveform that this converter

generates high harmonics in the line currents which distort the

voltage at the point of common coupling in the power system. A

lot of efforts have been performed to reduce harmonic contents

in the utility line currents of controlled converters [7]–[27].

Passive filters have been used in many researches with different

configurations [7], [8], but this technique suffers from bulky,

heavy filter elements and sometimes causes resonance prob-

lems. Active filters have been used in many researches and it

seems to be an interesting option, but this technique suffers

from complexity and high cost [9], [10]. Hybrid solutions

N MODERN power electronics converters, a three-phase

controlled converter is commonly used especially as a rec-

Manuscript received November 23, 2006; revised September 10, 2007.

The author is with the Department of Electrical Engineering, College of

Engineering, King Saud University, Riyadh 11421, Saudi Arabia (e-mail:

eltamaly@ksu.edu.sa).

Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2007.908542

Fig. 1.

harmonic reduction means.

Supply current and its FFT of controlled converter without any

using active filters and passive filters are used in high-power

applications to improve passive filter performance [11]. An

increasing number of pulses [12]–[15] reduces the harmonic

contents in a line current. However, this technique is heavy,

has high cost, complex construction, needs to be large in size,

and it is not readily available from the manufacturer [14]. Early

work in third harmonics injection techniques have been used in

[6], [8], [27]. Some other literatures use switches in the main

path of power flow which increase the switching losses and

reduce the system reliability [5]. Injection of third harmonic

current to line currents can be achieved by using LC branches

tuned around the third harmonic frequency [27]. However, this

scheme suffers from bulky construction, resonant problems,

and the current in the injection branch is very sensitive to the

deviation of the L and C values. Most three-phase line current

harmonics reduction techniques are summarized in [28], [29].

Injection of the third harmonic to a line current using a zigzag

transformer has been shown in many researches [5], [17]–[27].

These researches and the ideas shown in this research show the

superiority of this technique in reducing the harmonic contents

oflinecurrentsandincreasingthepowerfactorofthecontrolled

or uncontrolled converters.

II. PROPOSED APPROACH

Fig. 2 shows the topology of the proposed approach to reduce

harmonics generated by a line commutated SCR inverter used

0278-0046/$25.00 © 2008 IEEE

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ELTAMALY: MODIFIED HARMONICS REDUCTION TECHNIQUE OF THREE-PHASE CONTROLLED CONVERTER1191

Fig. 2. Proposed approach.

in ASD. This approach contains a zigzag transformer that gives

high impedance for the fundamental frequency component and

very low impedance for the injection current. A single-phase

transformer is connected between the dc-link mid-point “o” and

the zigzag transformer neutral “n.” The secondary of single-

phase transformer is connected to a rectifier boost converter

stage feeding the dc link. The injected current If can be

regulated by operating a single switch. The duty ratio of the

boost converter can be varied to control the injection current

depending on the dc link voltage.

The main goal of this paper is to obtain the optimal rms value

and phase angle of the injection current to get the minimum

total harmonic distortion (THD) of the supply current. Previous

results indicate that the best rms value of the third harmonic

current is equal to the average value of the dc link current [13],

[14]. However, it is not the only condition required. The angle

of injection current also plays a very important role in the THD

of the line current. Therefore, it is important to determine the

relation between the angle of injection current ψ and the firing

angle α.

For firing angle α = 20◦(as an example), Fig. 3(a) shows

the utility line current with respect to the voltage of phase

“a”. Fig. 3(b) shows the third harmonic injection current with

respect to phase a voltage. It is clear from this waveform that

the injection current leads the phase a voltage by 120◦, which

agrees with the analysis and waveforms in the upcoming sec-

tions. Fig. 3(c) shows the line current with the third harmonic

current along with the phase voltage a. This figure reveals that

the angle between Ifand Iamust be 180◦with respect to the

third harmonic frequency. Fig. 3(d) shows the voltage between

point “d” and “n” Vdn, the voltage between point “f” and “n”

Vfnand the voltage between “o” and “n” Vonalong with phase

“a” voltage. The third harmonic components of the voltages

Vdn, Vfnand Vonhave been used to inject the third harmonic

back to the utility line current to reduce the harmonic content.

Therefore, a careful analysis of these voltages is required to

get the optimum value of injection current and its angle ψ. It

is convenient to employ the Fourier series in the analysis of

Fig. 3.

(a) Voltage and current of phase a. (b) Voltage of phase a and reinjection

current. (c) Voltage, current of phase a and reinjection current. (d) The voltages

Vdn, Von, and Vfn.

Various voltages and currents of the proposed approach at α = 20◦.

the distorted waveforms. In general, a nonsinusoidal waveform

f(wt) can be expressed as follows:

f(ωt) = a0+

∞

?

n=1

(ancos(nωt) + bnsin(nωt))

where a0, an, and bnare Fourier coefficients.

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1192IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 3, MARCH 2008

By applying Fourier equations to the waveforms of Vdn, the

third harmonic component is obtained as follows:

a3=3

π

5π

6+α

?

π

6+α

Vmsinωt ∗ cos3ωtdωt

=3√3Vm

8π

5π

6+α

?

π

6+α

[2sin(2α) − sin(4α)]

(1)

b3=3

π

Vmsinωt ∗ sin3ωtdωt

=3√3Vm

8π

[cos(4α) − 2cos(2α)].

(2)

From (1) and (2), Vdn3and its angle can be obtained as in (3)

and (4)

?

where

Vm

peak value of phase voltage;

VLL

rms value of line to line supply voltage;

Vdn3

rms value of third harmonic of the voltage between

points d and n.

And angle of Vdn3is

Vdn3=

1

√2∗

a2

3+ b2

3=3VLL

8π

?

1 + 8sin2α

(3)

tan−1

?a3

b3

?

= tan−1

?2sin(2α) − sin(4α)

cos(4α) − 2cos(2α)

?

.

(4)

In the same way, Vfn3can be obtained as follows:

a3=3

π

11π

6+α

?

7π

6+α

Vmsinωt ∗ cos3ωtdωt

=3√3Vm

8π

115π

?

7π

6+α

[2sin(2α) − sin(4α)]

6+α

Vmsinωt ∗ sin3ωtdωt

(5)

b3=3

π

=3√3Vm

8π

[cos(4α) − 2cos(2α)].

(6)

From (5) and (6), Vfn3and its angle are obtained as in (7)

and (8)

?

Vfn3 is the rms value of the third harmonic of the voltage

between points f and n and the angle of Vfn3is

?a3

Von3=Vdn3+ Vfn3

2

Vfn3=

1

√2∗

a2

3+ b2

3=3VLL

8π

?

1 + 8sin2α.

(7)

tan−1

b3

?

= tan−1

?2sin(2α) − sin(4α)

.

cos(4α) − 2cos(2α)

?

(8)

(9)

Then,

Von3=3VLL

8π

?

1 + 8sin2α

(10)

and angle of Von3, is

θ = tan−1

?a3

=Von3

b3

?

= tan−1

?2sin(2α) − sin(4α)

∠(θ − ψ)

cos(4α) − 2cos(2α)

?

(11)

If=Von3∠θ

Z∠ψZ

(12)

where,Von3isthermsvalueofthethirdharmonicofthevoltage

between points o and n, and, θ is the angle of Von3, and, ψ is

the angle between Von3and If.

As shown in Fig. 3, the voltage Vais taken as a reference

value, so the phase angle of the fundamental and third harmonic

components of phase a current are −α and −3α, respectively.

As explained in [25] and as is clear from Fig. 3, the optimum

phase difference between phase a current and injection current

is 180◦, then

(θ − ψopt) − (−3α) = 180 ⇒ ψopt= θ + 3α − 180.

From (13) and Fig. 3, the phase difference between each vector

for various firing angles α = 20◦and 40◦(as an example) is

shown in Fig. 5. From (10) the relation between Von3and the

firing angle α is shown in Fig. 4. In the same way, from (13)

the relation between the angle of Von3and the angle between

If, and ψ along with the firing angle α is shown in Fig. 5.

(13)

III. DESIGN EXAMPLE

Experimental and simulation verification for this technique

has been carried out. The prototype model is used in the

simulation and in the experiment. A dc link is connected with a

three-phase pulsewidth modulation (PWM) inverter and 1-kW

squirrel cage induction motor. For the controlled rectifier, the

values of Von3 vary between Von3(α = 0) = 0.1194 p.u. to

Von3(α = 90◦) = 0.358 p.u. At full load, the dc current Io=

0.6224 p.u. The base voltage and current are 220 V and 3.3 A,

respectively.

The simulation results in the next section reveals that the

minimum THD occurs almost at If/Io= 1.25, so at full load;

If= 0.8 p.u. The rated third harmonic current passing through

the zigzag transformer is If/3 = 0.2667 p.u. The value of If

is controlled depending on the value of the dc link current for

minimum THD. The third harmonic injection current can be

controlled by controlling the duty ratio of the boost converter. A

current sensor is used to measure the actual dc link current and

the third harmonic injection current. The error signal between

these two currents is used to control the duty ratio of the boost

converter. 10 kHz switching frequency of the boost converter is

used in simulation and in the practical prototype. The schematic

of the controlled circuit of the boost converter is shown

in Fig. 6.

Design of Single-Phase Transformer

The rated primary voltage of a single-phase transformer in

the third harmonic injection pass is Von3(α = 90) = 0.358 p.u.

Page 4

ELTAMALY: MODIFIED HARMONICS REDUCTION TECHNIQUE OF THREE-PHASE CONTROLLED CONVERTER1193

Fig. 4.

(b) α = 40◦.

Phase difference between each component for (a) α = 20◦and

Fig. 5.Variation of Von3, θ, ψoptwith α at VLL= 220 V.

Fig. 6.Schematic of the control circuit of the boost converter.

Also, the rated primary current of this transformer is If=

0.8 p.u. Therefore, the rated kilovoltampere of this transformer

is 0.8 ∗ 0.358 = 0.286 p.u.

The turns ratio of the step-up single-phase must handle the

minimum value as well as the maximum value of Von3. The

minimum value of Von3is at α = 0, which is Von3(α = 0) =

0.1194 p.u. Then, the corresponding value of V?

on3is

V?

on3(α = 0) = 0.1194/n

p.u.(14)

The output dc voltage of the single-phase diode rectifier,

Vbiis

√2 ∗ V?

The minimum value of Von3corresponds to the maximum

value of the duty ratio of the boost converter. Assume the

Vbi= 2 ∗

on/π.

(15)

maximum allowable value of the duty ratio is 0.8. Then, the

output voltage of the boost converter, Vbois

Vbo= Vbi/(1 − D).

(16)

Substitute the value of Vbifrom (15) into (16) and D = 0.8,

the following equation can be obtained

?

= 10 ∗

The output voltage from the boost converter must equal the

dc link voltage. The dc link voltage is kept constant at 1.25 p.u.

by controlling the firing angle of the controlled converter and

the modulation index of the PWM inverter. Thus, by equating

(17) with 2.2 p.u., the following equation can be obtained:

√2 ∗ V?

Then

on3(α = 0) = 2.2 ∗ π/(10√2)p.u.

Byequating thevalues of V?

equation can be obtained:

0.1194/n = 2.2 ∗ π/(10√2).

Then, the turns ratio of the single-phase transformer is

n = 10√2 ∗ 0.1194/(2.2 ∗ π) = 0.24.

Vbo(D = 0.8) =2 ∗

√2 ∗ V?

√2 ∗ V?

on/π

?

/π.

/(1 − 0.8)

?

on

?

(17)

10 ∗

on3/π = 2.2 p.u.

V?

(18)

on3in(14) and (18),the following

(19)

IV. SIMULATION AND EXPERIMENTAL RESULTS

The simulation of the proposed technique has been per-

formed using the PSIM computer program [30]. The same

values of the components used in the simulation program have

been used in the experimental prototype to compare these

results.

Fig. 7 shows the simulation and experimental results of the

relation between THD and the value of If/Io for different

values of firing angle α. This figure reveals that the optimal

value of If/Iois about 1.25 for the best THD. Also, it is clear

that the best THD is linearly proportional to the firing angle

α. This figure shows the importance of the third harmonic

injection technique especially for high values of firing angle α.

Fig. 8 shows the simulation and experimental results of the

relation between THD and the angle of Ifwith respect to Von,

ψ at If/Io= 1.25 for different values of firing angle α. It is

clear that the best THD occurs around ψopt, which is obtained

from (13). The value of ψoptincreases as the firing angle α

increases. There is an interesting contrast between the results

shown in Figs. 5 and 8 in the optimum value of the injection

current for different values of α.

The simulation and experimental waveforms are shown for

α = 20◦and 40◦as an example.

A. Simulation and Experimental Results at α = 20◦

Fig. 9 shows the waveforms of voltage Vdfand Vab. Fig. 10

shows the supply current waveform and its FFT components

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1194IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 3, MARCH 2008

Fig. 7.

firing angle, α.

Relation between THD and the value of If/Iofor different values of

Fig. 8.

the angle of Ifwith respect to Von at If/Io= 1.25 for different values of

firing angle, α.

Simulation and experimental results of the relation between THD and

Fig. 9.Waveforms of voltage Vdfand Vab.

with respect to phase a voltage without injection of the third

harmonic current. It is clear from this figure that the supply cur-

rent has very high THD mostly of fifth and seventh harmonics.

Fig. 11 shows the voltage of Vdn, and Vfn. It is shown in the top

of the experimental result waveform that the frequency of this

voltage is 180◦, which is the third harmonic voltage, and the

Fig. 10.

phase a voltage without injection of third harmonic current. (a) Experimental

result. (b) FFT components of Ia.

Supply current waveform and its FFT components with respect to

Fig. 11.Voltage of Vdn, and Vfn.

value of rms voltage is 39.9, which can be obtained from (10)

at α = 20◦. Fig. 12 shows the supply current waveform and

its FFT components with respect to the phase a voltage with

optimum amplitude and angle of the third harmonic current

injection. It is clear from this figure that the supply current

comes very near to the sine-wave with 5% THD.

Fig. 13 shows the supply current waveform Ia and the

optimum value and angle of injection of the third harmonic

current with respect to the phase a voltage. It is clear from

these waveforms that the value of the angle between Ifand Va

is about 120◦and the angle between Iaand Ifis 180◦which

agree with the vector diagram shown in Fig. 4(a).

Page 6

ELTAMALY: MODIFIED HARMONICS REDUCTION TECHNIQUE OF THREE-PHASE CONTROLLED CONVERTER 1195

Fig. 12.

phase a voltage at optimum third harmonic current injection. (a) Simulation

result. (b) Experimental result. (c) FFT components of Ia.

Supply current waveform and its FFT components with respect to

B. Simulation and Experimental Results at α = 40◦

Fig. 14 shows the waveforms of voltage Vdfand Vab. Fig. 15

shows the supply current waveform and its FFT components

along with phase a voltage without injection of the third har-

monic current. It is clear from this figure that the supply current

has very high THD mostly of fifth and seventh harmonics. It is

clear that this THD is higher than the one with α = 40◦.

Fig. 16 shows the voltage of Vdn and Vfn and their FFT

components with respect to phase a voltage. It is clear from

this figure that these voltages have triplex harmonics and the

third harmonic is the most dominant. It is also clear that both

voltages Vdn, and Vfnhave the same harmonics.

Fig. 13.

injection third harmonic current with respect to phase a voltage. (a) Simulation

result for Vaand If. (b) Experimental result for Vaand If. (c) Experimental

result for Iaand If.

Supply current waveform Ia and optimum value and angle of

Fig. 14. Waveforms of voltage Vdfand Vab.

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1196IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 3, MARCH 2008

Fig. 15.

a voltage without injection of third harmonic current. (a) Experimental result.

(b) FFT components of Ia.

Supply current waveform and its FFT components along with phase

Fig. 16.

phase a voltage. (a) Experimental result. (b) FFT components of Vdnand Vdn.

Voltage of Vdn, and Vfnand their FFT components with respect to

Fig. 17.

value and angle of injection third harmonic current. (a) Experimental result.

(b) FFT components of Ia.

Supply current waveform and its FFT components with optimum

Fig. 18.

injection third harmonic current with respect to phase a voltage. (a) Simulation

result. (b) Experimental result.

Supply current waveform Ia and optimum value and angle of

Page 8

ELTAMALY: MODIFIED HARMONICS REDUCTION TECHNIQUE OF THREE-PHASE CONTROLLED CONVERTER1197

Fig. 17 shows the supply current waveform and its FFT

components with optimum value and angle of injection of the

thirdharmoniccurrent.Itisclearfromthisfigurethatthesupply

current comes very near to the sine-wave with 6% THD.

Fig. 18 shows the supply current waveform Iaand optimum

value and angle of the third harmonic injection current with

respect to phase a voltage. It is clear from these waveforms that

the angle between Ifand Vais about 60◦, which agree with the

vector diagram in Fig. 4(b).

V. CONCLUSION

The third harmonics injection technique plays a significant

role in reducing the THD of the utility line current of three-

phase controlled converters. The optimal amplitude and phase

angle of the injection current changes with the firing angle.

In this paper, a detailed analysis for determining the relation

between the optimal amplitude and phase angle of the injection

current along with the firing angle has been carried out. The

THD of line current is highly affected by the amplitude of

the third harmonic injection current as well as its phase angle

with the supply voltage. The optimum amplitude and angle of

the third harmonic current have been determined by a detailed

mathematicalanalysisofthesystem.TheTHDoftheutilityline

current from the simulation and experimental results proves the

mathematical results for this technique. The THD of the utility

line current with optimal harmonic injection current is lower

than the limits of harmonics standards.

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Ali M. Eltamaly was born in Eldakahlia, Egypt, on

June 28, 1969. He received the B.S. (with distinction

and honor degree), M.Sc., and Ph.D. degrees from

Elminia University, Elminia, Egypt, in 1992, 1996,

and 2000, respectively.

He joined the Electrical Engineering Department,

Texas A&M University, College Station, as a visitor

from 1997 to 2000. He was a member of the Faculty

of the College of Engineering, Elminia University,

from 1993 to 2005. He moved to Elmansoura Uni-

versity, Elmansoura, Egypt, in June 2005. He is

currently a member of the College of Engineering of King Saud University,

Riyadh, Saudi Arabia, since October 2005. His research interests are in the

area of power electronics, motor drives and renewable energy, where he

cosupervised a number of M.Sc. and Ph.D. thesis and published about 30

papers, two books, and number of technical projects.

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