IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.57,NO.7,JULY 2010 2307

Symmetrical Hybrid Multilevel DC–AC Converters

With Reduced Number of Insulated DC Supplies

Domingo A.Ruiz-Caballero,Reynaldo M.Ramos-Astudillo,Samir Ahmad Mussa,Member,IEEE,and

Marcelo Lobo Heldwein,Member,IEEE

Abstract—Novel symmetric hybrid multilevel topologies are in-

troduced for both single- and three-phase medium-voltage high-

power systems.The topology conception is presented in detail,

where a three-level switching cell with low component count,and

its modulation pattern give the origin of the proposed converters.

Voltage sharing and low output-voltage distortion are achieved.

The theoretical frequency spectra are derived.Switching devices

are separated into high- and low-frequency devices,generating

hybrid converters.Five-level three-phase topologies are generated

fromonly three insulated dc sources,while the number of semicon-

ductors is the same as for the cascaded H bridge.Both simulation

and experimental results are provided showing the validity of the

analysis.

Index Terms—DC–AC converters,hybrid inverters,modula-

tion,symmetrical multilevel converters.

I.I

NTRODUCTION

H

IGH-POWER three-phase medium-voltage (MV) appli-

cations have been steadily growing in numbers and ap-

plications.Power electronics research in this ﬁeld has been

following the same trend and ﬁnding solutions in ﬁelds such

as serial connection of switches,multilevel topologies,mod-

ulation techniques,cooling,and converter reliability,among

others.In this context,multilevel topologies rise as consistent

and widespread solutions to the problem [1],[2].Various

multilevel topologies have been proposed [3]–[8] in order to

improve performance,adapt to requirements,and avoid propri-

etary technologies.

Multilevel converters have been introduced in the 1970s

and 1980s [9]–[11] giving impulse to high-power conver-

sion through multilevel inverters suitable to MV applications.

Such converters are able to synthesize high-quality voltage

waveforms while allowing semiconductors with lower voltage

ratings to be employed.However,technical and economical

barriers,such as the cost of drivers and protection,the need

for stabilizing dc supply voltages,circuit layout,and packaging

cause the number of levels to be limited.Most applications

have the number of levels given by the semiconductor voltage

ratings.

Manuscript received March 13,2009;revised August 24,2009;accepted

October 20,2009.Date of publication November 20,2009;date of current

version June 11,2010.

D.Ruiz-Caballero and R.Ramos-Astudillo are with the Department of Elec-

trical Engineering,Pontiﬁcia Universidad Catolica de Valparaiso,Valparaiso

2241,Chile (e-mail:domingo@pucv.cl).

M.L.Heldwein and S.A.Mussa are with the Power Electronics Institute

(INEP),Federal University of Santa Catarina (UFSC),Florianópolis 88040-

970,Brazil (e-mail:heldwein@inep.ufsc.br;samir@inep.ufsc.br).

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.2009.2036636

Several multilevel topologies have been proposed in the

literature [3]–[32].Classifying the multilevel converters ac-

cording to the type of voltage synthesis leads to basically

three types of converters,namely:1) diode-clamped convert-

ers [10],[11],[25],[26];2) capacitor-clamped converters

[4],[25],[26];and 3) cascaded converters with insulated

dc sources [3],[6],[9],[12],[15]–[20],[23],[33],[34],

which are further subdivided into hybrids/nonhybrids and

symmetrical/asymmetrical.Hybrid converters are converters

that present semiconductor switching at different frequen-

cies.Symmetrical converters are converters with symmetric dc

sources.

An example of asymmetrical hybrid topology is given in

[17].The converter is based on a binary conﬁguration being

capable of synthesizing (2

N+1

−1) voltage levels at the load

terminals,where N is the number of insulated dc sources.

The converter is built with a cascade of H-bridge converters

where some of the converters switch at a lower frequency

and are supplied with higher voltages.High-quality voltage

waveforms result from this strategy.Another inventive ap-

proach is presented in [13],where semiconductors employing

different technologies (gate turn-off (GTOs) and insulated-gate

bipolar transistors) switch at different frequencies,but the low-

frequency devices still switch at frequencies higher than the

fundamental.

This paper presents a novel symmetrical hybrid-converter

concept in its single- and three-phase versions.The topologies

are based on a low switch count three-level pulsewidth mod-

ulation (PWM) switching cell connected to a low-frequency

switched bridge.Thus,high modularity is achieved.Compared

with an H-bridge cascaded multilevel converter,the number

of overall insulated dc sources is reduced in the proposed

converter,while the number of semiconductors is kept the same.

Thus,the proposed concept appears as a useful and suitable

solution for MV applications where input-side insulation is re-

quired along with high efﬁciency and modularity.Furthermore,

by reducing the number of insulated dc supplies,the number

of cables connecting the input transformer terminals to the

rectifying bridges is reduced.

This paper is organized as follows.The derivation of the

ﬁve-level switching cell is presented in Section II.The single-

and three-phase versions of the proposed concept,along with

proper modulation strategies,are explained,respectively,in

Sections III and IV.The theoretical analysis of the load voltages

employing the proposed modulation is performed in Section V.

Finally,experimental results are presented,and conclusions are

given.

0278-0046/$26.00 ©2010 IEEE

2308 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.57,NO.7,JULY 2010

Fig.1.Three-level buck-type dc–dc converter (a) topology [21] and

(b) modulation signals and voltage v

xy

.

Fig.2.(a) Three-level buck-type dc–dc converter switching cell as a basis

for the derivation of a (b) bidirectional three-level dc–dc switching cell and an

example of an achievable (c) three-level load voltage v

xy

.

II.B

IDIRECTIONAL

M

ULTILEVEL

C

ELL

D

ERIVATION

Fig.1(a) shows the three-level buck-type dc–dc converter

[21] which is able to generate three voltage levels at the termi-

nals of the output ﬁlter.The voltage v

xy

is illustrated in Fig.1(b)

for the given modulation pattern.In addition to the discussed

characteristics,the converter is able to generate a voltage v

xy

with double that of the switching frequency and,thus,reduce

ﬁlter passive components L

o

and C

o

.This converter employs

semiconductors rated for half of the dc-link voltage and,with

a proper modulation strategy,allows the balancing of the dc-

link voltages by symmetrically charging and discharging the

dc-link capacitors.This converter is the basis for the proposed

multilevel converter as seen in the following.

The switching cell of the three-level buck-type dc–dc con-

verter shown is redrawn in Fig.2(a).It is seen that this cell

is only able to process unidirectional load currents.In order

to provide bidirectional current capability,switches S

1

and S

4

must employ antiparallel diodes D

2

and D

3

and antiparallel

switches.With this,the converter shown in Fig.2(b) is able

to handle bidirectional load currents,and a positive three-level

load voltage v

xy

[cf.Fig.2(c)] can be generated.

Fig.3.(a) Proposed single-phase ﬁve-level symmetrical hybrid dc–ac con-

verter and (b) its possible load-voltage v

AN

levels according to the switched

semiconductors.

III.S

INGLE

-P

HASE

S

YMMETRICAL

H

YBRID

M

ULTILEVEL

C

ONVERTER

Considering the three-level switching cell shown in Fig.2(b),

it is possible to turn it into a dc–ac converter by properly

switching the connection of the load terminals.This can be

implemented with the conﬁguration shown in Fig.3(a),where

switches S

5

to S

8

are connected as a full-bridge inverter that is

responsible for switching the load terminals according to the

gate signals.Fig.3(b) shows the possible load voltage v

AN

levels for the speciﬁed switching conditions.It is seen that

the pairs S

5

/S

8

and S

6

/S

7

are turned on complementarily in

order to generate,respectively,negative and positive voltages.

The three-level dc–dc converter switches S

1

to S

4

are switched

according to a proper modulation pattern in order to generate a

desired load voltage.

Therefore,the converter shown in Fig.3(a) is a ﬁve-level

single-phase inverter where switches S

1

to S

4

operate at high

frequency and are rated for half of the dc-link voltage E.

Switches S

5

to S

8

are rated for the full dc-link voltage 2E.

On the other hand,switches S

5

to S

8

can be implemented

with low-frequency devices such as GTOs,integrated gate-

commutated thyristors,and others,since they switch a single

time per load-voltage period under zero voltage.Based on

this strategy,the proposed converter is a symmetric (equal

dc sources) hybrid (multiple carrier frequencies) multilevel

converter.Furthermore,the number of levels can be increased

by cascading multiple single-phase converters.This can be

achieved with other topologies as well.

As shown in [14] and [24],the total number of level across

the load terminals N

AB

for the proposed topology is given by

N

AB

= 2N +1 (1)

where N is the total number of dc sources.

RUIZ-CABALLERO et al.:HYBRID MULTILEVEL DC–AC CONVERTERS WITH REDUCED NUMBER OF DC SUPPLIES 2309

Fig.4.Modulation strategy.(a) Carriers and modulating signal.(b) Gate

pulses.(c) Modulation logic.

A.Single-Phase Modulation Strategy

The high-frequency switches S

1

to S

4

are driven by PWM

signals obtained through sinusoidal unipolar PWM (S-PWM),

where the gate signals are generated by the comparison of

the modulating signal v

M

with triangular carriers v

t1

and v

t2

,

displaced 180

◦

fromeach other,as shown in Fig.4(a).The gate

signals for the low-frequency switches S

5

to S

8

are obtained

from the direct comparison of the modulating signal v

M

with

zero.As an example,the gate pulses are shown in Fig.4(b),

and the PMW generation logic is shown in Fig.4(c).With

this modulation scheme,the ﬁrst observed harmonic at the load

terminals appears at twice the switching frequency.

IV.T

HREE

-P

HASE

S

YMMETRICAL

H

YBRID

M

ULTILEVEL

C

ONVERTER

The three-phase version of the proposed converter is formed

by connecting the single-phase modules in a Y -conﬁguration

supplying a three-phase load through terminals A,B,and C,as

shown in the three-phase symmetric hybrid ﬁve-level converter

of Fig.6(a).It is observed that two common terminals exist,

one N for the load that is Y connected in the drawing and

another O that connects the three inverter legs and serves as

a reference for the modulation scheme.The converter presents

the same number of semiconductors as a symmetric cascaded

H-bridge ﬁve-level converter while reducing the minimum re-

quired number of insulated dc sources from six to three.For

the hybrid topology,the power processed in the three insulated

supplies is larger,and two balanced series-connected sources

are necessary for each dc supply.

Five voltage levels can be generated per converter leg,

namely,−2E,−E,zero,+E,and +2E,as seen in Table I.

Thus,as for a cascaded H-bridge,125 space vectors (cf.Fig.5)

can be generated by the three-phase system.Furthermore,as

the voltage levels −E,zero,and +E can be generated with

different switching states,extra redundancy is achieved,and a

total of 343 vectors are available.The achievable redundancy

is important for optimizing modulation schemes and can be

TABLE I

S

WITCHING

S

TATES AND

R

ESPECTIVE

V

OLTAGE

L

EVELS

PER

C

ONVERTER

L

EG

Fig.5.Space-vector diagram for the proposed three-phase symmetrical hy-

brid ﬁve-level dc–ac converter.Voltage levels −2E,−E,zero,+E,and +2E

are,respectively,represented by −2,−1,0,1,and 2.

employed in order to balance the dc-link voltages if the dc

sources are not separately regulated.

Different solutions are foreseen to produce the necessary

insulated dc sources from a three-phase MV distribution grid.

Bidirectional-rectiﬁer approaches such as the ones discussed

in [20] and [35] can be employed.However,bidirectional

solutions typically present higher costs and are not employed

in commercial products at this moment [36].In this con-

text,unidirectional front ends arise as economical attractive

solutions,and three alternatives are shown in Fig.6.The

ﬁrst solution [cf.Fig.6(b)] presents an insulation transformer

where all secondaries are constructed with voltages in phase

and,thus,lead to a six-pulse-type rectiﬁer where the input

current total harmonic distortions (THDs) typically range from

18% to 40%.Therefore,the six-pulse solution is typically not

able to meet grid regulations such as the IEEE-519,the ER

G5/4,or the IEC 61000 series.Fig.6(c) shows a unidirec-

tional rectiﬁer that is able to generate three insulated supplies

with a transformer with secondaries displaced by ±20

◦

.This

leads to an 18-pulse rectiﬁer where the harmonic distortion

is much lower than the ﬁrst alternative.Circuit simulations

2310 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.57,NO.7,JULY 2010

Fig.6.Proposed (a) three-phase symmetrical hybrid ﬁve-level dc–ac converter and three different unidirectional front-end possibilities;(b) 6-pulse uncontrolled

rectiﬁer;(c) 18-pulse uncontrolled rectiﬁer with secondaries displaced by ±20

◦

;and (d) 36-pulse uncontrolled rectiﬁer with secondaries displaced by ±10

◦

.

of the complete multilevel converter employing the 18-pulse

rectiﬁer [cf.Fig.6(c)],output-voltage ripple of ΔV

o

≤ 4%,

input voltages presenting unbalances of ±3%,input inductors

L

in,p.u.

∼

=

5%,and leakage inductances of around L

σ,p.u.

∼

=

0.2% show that the input current THD approaches 10.5%,and

the highest single harmonic is typically the ﬁfth,with 9.9%

of the fundamental.Thus,compliance with international grid

codes depends on the relation between short-circuit currents

and the rated converter current or on the inclusion of tuned

and/or active ﬁlters.Both 6-pulse and 18-pulse front ends do

not guarantee the balance of the partial dc voltage.Thus,if

these schemes are applied,sensoring and active control through

the converter’s modulation should be implemented.A 36-pulse

unidirectional passive rectiﬁer is shown in Fig.6(d),where the

secondaries of the insulation transformer are displaced by 10

◦

.

Every two secondaries are connected in series after the diode

bridges so that the balance of the partial dc-supply voltages

is guaranteed.Furthermore,simulations of this system [cf.

Fig.6(d)] supplying the multilevel converter and employing the

same parameters as with the 18-pulse simulations lead to input

current THDs of around 3.71% and a higher single harmonic

with 1.62%of the fundamental at the third harmonic.Based on

the simulation results,the 36-pulse solution is able to meet the

most stringent grid codes for MV networks.

A.Three-Phase Modulation Strategy

The modulation strategy is based on the single-phase mod-

ulation strategy (cf.Section III-A) and employs three sinu-

soidal modulating signals v

Mj

,with j = A,B,C,displaced

120

◦

from each other,which are compared with two triangular

carriers v

t1

and v

t2

with a displacement of 180

◦

.

TABLE II

S

PECIFICATIONS FOR THE

N

UMERICAL

S

IMULATION OF THE

S

INGLE

-P

HASE

F

IVE

-L

EVEL

C

ONVERTER

B.Three-Phase Simulation Results

This section presents the simulation results from the three-

phase ﬁve-level converter.The simulation speciﬁcations are

given in Table II.

Fig.7 shows the load voltages obtained in the simulation.

The ﬁve-level phase voltage v

AO

is seen in Fig.7(a),while

the line voltage v

AB

presents nine levels [cf.Fig.7(b)].The

ﬁrst-harmonic component for the three-phase version continues

appearing at twice the switching frequency.The phase voltage

v

AN

at the load presents ﬁfteen levels for this modulation index

even though the ﬁve-level converter enables seventeen voltage

levels.

V.S

PECTRAL

A

NALYSIS OF THE

O

UTPUT

V

OLTAGES

In order to analytically deﬁne the output-voltage spectra and

associated THD values,this section shows the derivation of the

expressions for the three-phase converters.

RUIZ-CABALLERO et al.:HYBRID MULTILEVEL DC–AC CONVERTERS WITH REDUCED NUMBER OF DC SUPPLIES 2311

Fig.7.Simulated output voltages:(a) Phase-voltage v

AO

waveform.

(b) Frequency spectrumof the phase voltage.(c) Line-voltage v

AB

waveform.

(d) Spectrumof the line voltage.

A.Three-Phase Output-Voltage Analysis

The phase voltage v

AO

for the three-phase converter is

deﬁned as

v

AO

(t) = 2EMsin(ω

1

t) +

∞

n=2

∞

v=1

4E

nπ

J

v

(nπ M)

× [sin(v ω

1

t +nω

s

t) +sin(v ω

1

t −nω

s

t)] (2)

where n = 2,4,6,...,v = 1,3,5,...,ω

1

= 2πf

o

,ω

s

= 2πf

s

,

and J

v

(·) is the Bessel function of the ﬁfth order.

The output line-to-line voltage for the ﬁve-level converter

employing the proposed modulation strategy is given by

v

AB

(t) =2

√

3EMsin

ω

1

t −

π

6

+

∞

n=2

∞

v=1

4E

nπ

J

v

(nπ M)

× [N

P

sin(v ω

1

t +nω

s

t +α

P

)

+N

N

sin(v ω

1

t −nω

s

t +α

N

)] (3)

with n = 2,4,6,...,v = 1,3,5,...,γ = 2π/3,and

N

P

=

2{1 −cos [γ(v +n)]} (4)

N

N

=

2{1 −cos [γ(v −n)]} (5)

TABLE III

O

UTPUT

-V

OLTAGE

H

ARMONIC

C

OMPONENTS AND

F

REQUENCIES

Fig.8.Variation of the peak value of the harmonic components of the

(a) phase voltage and (b) output line-to-line voltage in dependence of the

modulation index.

α

P

= tan

−1

−cot

γ

2

(v +n)

(6)

α

N

= tan

−1

−cot

γ

2

(v −n)

.(7)

The peak value of the harmonic components of the output volt-

age and their respective frequencies are expressed in Table III

and shown in Fig.8,in dependence of the modulation index

M.Both phase- [cf.Fig.8(a)] and line- [cf.Fig.8(b)]voltage

components are given.The harmonic components are obtained

fromthe variation of h = nm

f

±v.

Plotting (2) and (3) leads to the waveforms shown in Fig.9

for a modulation index M = 0.94.From the analysis of the

output voltages,it is observed that both phase and line volt-

ages present harmonic components at the same frequencies.

However,the amplitude and phase of these harmonics have

distinct values.Unlike the single-phase converter load voltage,

the three-phase version presents sidebands that are not symmet-

ric with respect to the center frequency.Thus,two amplitude

functions A

ph/lin,n,v

and B

ph/lin,n,v

are required to properly

deﬁne the sideband amplitudes.

2312 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.57,NO.7,JULY 2010

Fig.9.Voltages obtained from (2) and (3) normalized with respect to half of

the dc-link voltage E for M = 0.94.

Fig.10.Implemented three-phase symmetrical hybrid ﬁve-level converter

prototype.

B.Experimental Results

A low-power three-phase prototype of the proposed con-

verter (cf.Fig.10) has been built in order to validate the theoret-

ical analysis.The input dc voltage is set to E = 100 V,while

the output power is 400 W.The load fundamental frequency

is f

o

= 50 Hz and the switching frequency f

s

= 1500 Hz.An

output ﬁlter with parameters L

o

= 8 mH and C

o

= 8 μF per

phase has been placed at the terminals of the Y -connected load.

The input insulated dc sources have been generated from a

220-V/60-Hz-fed three-phase transformer supplying three in-

sulated secondaries connected to single-phase rectiﬁers and

smoothing capacitors.

The modulation strategy based on the S-PWM described

in Section IV-A is adopted.The practical implementation

of the modulation algorithm is performed in a DSP,model

TMS320F2812,where the gate signals are generated in an

open-loop scheme.The modulation employs the DSP’s event

manager (EVA and EVB) and a few I/O pins.The high-

frequency PWMpulses are produced by the DSP’s PWMmod-

ules,while the low-frequency signals are software generated by

comparing the modulating signals to zero.The sinusoidal refer-

ences are computed internally through a routine that calculates

50-Hz rectiﬁed sinusoidal signals.A zero-crossing detector is

Fig.11.Experimental waveforms:input dc voltage 2E,phase voltage v

AO

,

load phase-voltage fundamental component v

AN,(1)

,and phase current i

A

.

Fig.12.Voltages across the switches S

A1

,S

A3

,S

A5

,and S

A7

.

virtually implemented in order to compare the polarity of the

sinusoidal references.

Fig.11 shows the acquired waveforms for the three-phase

converter prototype.It is observed that the phase-voltage v

AO

precisely follows the theoretical waveform while presenting

a high-quality sinusoidal fundamental component v

AN,(1)

at

50 Hz.The load phase current i

A

,which is ﬁltered,follows the

fundamental voltage shape.The dc voltage across one of the

inputs shows the expected 120-Hz ripple and presents a mean

value around 2E

∼

=

200 V.

The voltages across the switches can be observed in Fig.12,

where the high-frequency switches S

A1

and S

A3

present a

maximum voltage around half the value of the dc source

(V

SA1,max

∼

=

V

A3,max

∼

=

100 V).It is observed that the low-

frequency switches withstand the full dc-link voltage (

∼

=

200 V)

and conduct a single time per fundamental period.

The phase and line voltages are shown in Fig.13(a),

from where the frequency spectra is computed and shown in

Fig.13(b).A comparison of the experimentally obtained spec-

tra and the theoretical ones shows good agreement and,thus,

validates the performed analysis.In order to illustrate the three-

phase operation of the built system,Fig.14 shows the three out-

put line-to-line voltages V

AB

,V

BC

,and V

CA

.The nine levels

RUIZ-CABALLERO et al.:HYBRID MULTILEVEL DC–AC CONVERTERS WITH REDUCED NUMBER OF DC SUPPLIES 2313

Fig.13.Experimental voltage (a) waveforms V

AO

and V

AB

,and (b) fre-

quency spectra for V

AO

and V

AB

.

Fig.14.Three-phase systemline-to-line voltages V

AB

,V

BC

,and V

CA

.

are clearly seen at the line voltages,and the overall system is

able to deliver high-quality voltages to a three-phase load.

VI.C

ONCLUSION

Anovel symmetrical hybrid multilevel dc–ac converter based

on a three-level switching cell has been proposed along with

suitable modulation strategies for single- and three-phase sys-

tems.Both single- and three-phase systems are characterized

by high- and low-frequency switches,which do not require

clamping diodes nor capacitors.The switching cells are fed

by insulated dc supplies of equal value.The ﬁve-level version

of the converter has been thoroughly analyzed.It presents

only three insulated supplies and appears as an alternative to

symmetric cascaded H-bridge converters or to the asymmetric

hybrid topologies.

From the achieved results and analysis,it is observed that

the system is able to supply high-quality alternating voltages

to a three-phase system.This is achieved with a modulation

strategy based on the S-PWM patterns.With this,the low-

frequency switches withstand the full dc-link voltage,while the

fast-switching semiconductors block only half of it.

The single-phase system presents ﬁve levels at the load

voltage,while the three-phase one allows ﬁfteen levels at the

phase voltages and nine levels at the line voltages,both with

low-harmonic distortion.Based on the theoretical computation

of the output voltages,it is observed that the high-frequency

spectral components are displaced to the even multiples of the

high-frequency carriers,meaning that the ﬁrst harmonic to be

ﬁltered lies on double that of the switching frequency.This

characteristic has been validated through experimental results.

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Domingo A.Ruiz-Caballero was born in Santi-

ago,Chile,in 1963.He received the B.S.degree

in electrical engineering fromPontiﬁcia Universidad

Catolica de Valparaiso,Valparaiso,Chile,in 1989,

and the M.Eng.and Dr.Eng.degrees from Power

Electronics Institute (INEP),Federal University of

Santa Catarina,Florianópolis,Brazil,in 1992 and

1999,respectively.

Since 2000,he has been with the Department

of Electrical Engineering,Pontiﬁcal Catholic Uni-

versity of Valparaiso,where he is currently an

Associate Professor.His ﬁelds of interest include high-frequency switching

converters,power quality,multilevel inverters,and soft-switching techniques.

Dr.Ruiz-Caballero is currently a member of the Brazilian Power Electronics

Society (SOBRAEP).

Reynaldo M.Ramos-Astudillo was born in Taltal,

Chile,in 1972.He received the B.S.degree in

electrical engineering and the M.Eng.degree from

Pontiﬁcia Universidad Catolica de Valparaiso,

Valparaiso,Chile,in 2003 and 2009,respectively.

Since 2003,he has been with the Department

of Electrical Engineering,Pontiﬁcal Catholic Uni-

versity of Valparaiso.His ﬁelds of interest include

high-frequency switching converters,power quality,

multilevel inverters,and soft-switching techniques.

Samir Ahmad Mussa (M’06) was born in

Jaguari-RS,Brazil,in 1964.He received the B.S.

degree in electrical engineering from the Federal

University of Santa Maria,Santa Maria,Brazil,in

1988,and a second degree in mathematics/physics.

He received the M.Eng.and Ph.D.degrees in elec-

trical engineering from the Federal University of

Santa Catarina (UFSC),Florianópolis,Brazil,in

1994 and 2003,respectively.

He is currently an Adjunct Professor with

the Power Electronics Institute (INEP-UFSC),

Florianópolis.His research interests include digital control applied to power

electronics,power-factor-correction techniques and DSP/FPGA applications.

Dr.Mussa is currently a member of the Brazilian Power Electronics Society

(SOBRAEP).

Marcelo Lobo Heldwein (S’99–M’08) received

the B.S.and M.S.degrees in electrical engineer-

ing from the Federal University of Santa Catarina,

Florianópolis,Brazil,in 1997 and 1999,respectively,

and the Dr.Sc.degree from the Swiss Federal In-

stitute of Technology (ETH),Zurich,Switzerland,

in 2007.

From 1999 to 2001,he was a Research Assistant

with the Power Electronics Institute,Federal Uni-

versity of Santa Catarina,where he worked as a

Postdocoral Fellow from 2008 to 2010.From 2001

to 2003,he was an Electrical Design Engineer with Emerson Energy Systems,

in Brazil and in Sweden.He is currently an Adjunct Professor at the Electrical

Engineering Department,Federal University of Santa Catarina.His research

interests include power factor correction techniques,static power converters

and electromagnetic compatibility.

Dr.Heldwein is currently a member of the Brazilian Power Electronics

Society (SOBRAEP).

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