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.RuizCaballero,Reynaldo M.RamosAstudillo,Samir Ahmad Mussa,Member,IEEE,and
Marcelo Lobo Heldwein,Member,IEEE
Abstract—Novel symmetric hybrid multilevel topologies are in
troduced for both single and threephase mediumvoltage high
power systems.The topology conception is presented in detail,
where a threelevel switching cell with low component count,and
its modulation pattern give the origin of the proposed converters.
Voltage sharing and low outputvoltage distortion are achieved.
The theoretical frequency spectra are derived.Switching devices
are separated into high and lowfrequency devices,generating
hybrid converters.Fivelevel threephase 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
IGHPOWER threephase mediumvoltage (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 highpower conver
sion through multilevel inverters suitable to MV applications.
Such converters are able to synthesize highquality 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.RuizCaballero and R.RamosAstudillo are with the Department of Elec
trical Engineering,Pontiﬁcia Universidad Catolica de Valparaiso,Valparaiso
2241,Chile (email: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 (email: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) diodeclamped convert
ers [10],[11],[25],[26];2) capacitorclamped 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 Hbridge converters
where some of the converters switch at a lower frequency
and are supplied with higher voltages.Highquality voltage
waveforms result from this strategy.Another inventive ap
proach is presented in [13],where semiconductors employing
different technologies (gate turnoff (GTOs) and insulatedgate
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 hybridconverter
concept in its single and threephase versions.The topologies
are based on a low switch count threelevel pulsewidth mod
ulation (PWM) switching cell connected to a lowfrequency
switched bridge.Thus,high modularity is achieved.Compared
with an Hbridge 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 inputside 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
ﬁvelevel switching cell is presented in Section II.The single
and threephase 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.
02780046/$26.00 ©2010 IEEE
2308 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.57,NO.7,JULY 2010
Fig.1.Threelevel bucktype dc–dc converter (a) topology [21] and
(b) modulation signals and voltage v
xy
.
Fig.2.(a) Threelevel bucktype dc–dc converter switching cell as a basis
for the derivation of a (b) bidirectional threelevel dc–dc switching cell and an
example of an achievable (c) threelevel load voltage v
xy
.
II.B
IDIRECTIONAL
M
ULTILEVEL
C
ELL
D
ERIVATION
Fig.1(a) shows the threelevel bucktype 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 dclink voltage and,with
a proper modulation strategy,allows the balancing of the dc
link voltages by symmetrically charging and discharging the
dclink capacitors.This converter is the basis for the proposed
multilevel converter as seen in the following.
The switching cell of the threelevel bucktype 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 threelevel
load voltage v
xy
[cf.Fig.2(c)] can be generated.
Fig.3.(a) Proposed singlephase ﬁvelevel symmetrical hybrid dc–ac con
verter and (b) its possible loadvoltage v
AN
levels according to the switched
semiconductors.
III.S
INGLE
P
HASE
S
YMMETRICAL
H
YBRID
M
ULTILEVEL
C
ONVERTER
Considering the threelevel 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 fullbridge 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 threelevel 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 ﬁvelevel
singlephase inverter where switches S
1
to S
4
operate at high
frequency and are rated for half of the dclink voltage E.
Switches S
5
to S
8
are rated for the full dclink voltage 2E.
On the other hand,switches S
5
to S
8
can be implemented
with lowfrequency devices such as GTOs,integrated gate
commutated thyristors,and others,since they switch a single
time per loadvoltage 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 singlephase 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.
RUIZCABALLERO 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.SinglePhase Modulation Strategy
The highfrequency switches S
1
to S
4
are driven by PWM
signals obtained through sinusoidal unipolar PWM (SPWM),
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 lowfrequency 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 threephase version of the proposed converter is formed
by connecting the singlephase modules in a Y conﬁguration
supplying a threephase load through terminals A,B,and C,as
shown in the threephase symmetric hybrid ﬁvelevel 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
Hbridge ﬁvelevel 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 seriesconnected 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 Hbridge,125 space vectors (cf.Fig.5)
can be generated by the threephase 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.Spacevector diagram for the proposed threephase symmetrical hy
brid ﬁvelevel 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 dclink voltages if the dc
sources are not separately regulated.
Different solutions are foreseen to produce the necessary
insulated dc sources from a threephase MV distribution grid.
Bidirectionalrectiﬁer 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 sixpulsetype rectiﬁer where the input
current total harmonic distortions (THDs) typically range from
18% to 40%.Therefore,the sixpulse solution is typically not
able to meet grid regulations such as the IEEE519,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 18pulse 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) threephase symmetrical hybrid ﬁvelevel dc–ac converter and three different unidirectional frontend possibilities;(b) 6pulse uncontrolled
rectiﬁer;(c) 18pulse uncontrolled rectiﬁer with secondaries displaced by ±20
◦
;and (d) 36pulse uncontrolled rectiﬁer with secondaries displaced by ±10
◦
.
of the complete multilevel converter employing the 18pulse
rectiﬁer [cf.Fig.6(c)],outputvoltage 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 shortcircuit currents
and the rated converter current or on the inclusion of tuned
and/or active ﬁlters.Both 6pulse and 18pulse 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 36pulse
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 dcsupply voltages
is guaranteed.Furthermore,simulations of this system [cf.
Fig.6(d)] supplying the multilevel converter and employing the
same parameters as with the 18pulse 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 36pulse solution is able to meet the
most stringent grid codes for MV networks.
A.ThreePhase Modulation Strategy
The modulation strategy is based on the singlephase mod
ulation strategy (cf.Section IIIA) 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.ThreePhase Simulation Results
This section presents the simulation results from the three
phase ﬁvelevel converter.The simulation speciﬁcations are
given in Table II.
Fig.7 shows the load voltages obtained in the simulation.
The ﬁvelevel phase voltage v
AO
is seen in Fig.7(a),while
the line voltage v
AB
presents nine levels [cf.Fig.7(b)].The
ﬁrstharmonic component for the threephase 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 ﬁvelevel converter enables seventeen voltage
levels.
V.S
PECTRAL
A
NALYSIS OF THE
O
UTPUT
V
OLTAGES
In order to analytically deﬁne the outputvoltage spectra and
associated THD values,this section shows the derivation of the
expressions for the threephase converters.
RUIZCABALLERO et al.:HYBRID MULTILEVEL DC–AC CONVERTERS WITH REDUCED NUMBER OF DC SUPPLIES 2311
Fig.7.Simulated output voltages:(a) Phasevoltage v
AO
waveform.
(b) Frequency spectrumof the phase voltage.(c) Linevoltage v
AB
waveform.
(d) Spectrumof the line voltage.
A.ThreePhase OutputVoltage Analysis
The phase voltage v
AO
for the threephase 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 linetoline voltage for the ﬁvelevel 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 linetoline 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 singlephase converter load voltage,
the threephase 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 dclink voltage E for M = 0.94.
Fig.10.Implemented threephase symmetrical hybrid ﬁvelevel converter
prototype.
B.Experimental Results
A lowpower threephase 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
220V/60Hzfed threephase transformer supplying three in
sulated secondaries connected to singlephase rectiﬁers and
smoothing capacitors.
The modulation strategy based on the SPWM described
in Section IVA is adopted.The practical implementation
of the modulation algorithm is performed in a DSP,model
TMS320F2812,where the gate signals are generated in an
openloop 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 lowfrequency signals are software generated by
comparing the modulating signals to zero.The sinusoidal refer
ences are computed internally through a routine that calculates
50Hz rectiﬁed sinusoidal signals.A zerocrossing detector is
Fig.11.Experimental waveforms:input dc voltage 2E,phase voltage v
AO
,
load phasevoltage 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 threephase
converter prototype.It is observed that the phasevoltage v
AO
precisely follows the theoretical waveform while presenting
a highquality 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 120Hz ripple and presents a mean
value around 2E
∼
=
200 V.
The voltages across the switches can be observed in Fig.12,
where the highfrequency 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 dclink 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 linetoline voltages V
AB
,V
BC
,and V
CA
.The nine levels
RUIZCABALLERO 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.Threephase systemlinetoline voltages V
AB
,V
BC
,and V
CA
.
are clearly seen at the line voltages,and the overall system is
able to deliver highquality voltages to a threephase load.
VI.C
ONCLUSION
Anovel symmetrical hybrid multilevel dc–ac converter based
on a threelevel switching cell has been proposed along with
suitable modulation strategies for single and threephase sys
tems.Both single and threephase systems are characterized
by high and lowfrequency switches,which do not require
clamping diodes nor capacitors.The switching cells are fed
by insulated dc supplies of equal value.The ﬁvelevel version
of the converter has been thoroughly analyzed.It presents
only three insulated supplies and appears as an alternative to
symmetric cascaded Hbridge converters or to the asymmetric
hybrid topologies.
From the achieved results and analysis,it is observed that
the system is able to supply highquality alternating voltages
to a threephase system.This is achieved with a modulation
strategy based on the SPWM patterns.With this,the low
frequency switches withstand the full dclink voltage,while the
fastswitching semiconductors block only half of it.
The singlephase system presents ﬁve levels at the load
voltage,while the threephase one allows ﬁfteen levels at the
phase voltages and nine levels at the line voltages,both with
lowharmonic distortion.Based on the theoretical computation
of the output voltages,it is observed that the highfrequency
spectral components are displaced to the even multiples of the
highfrequency 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.
R
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Domingo A.RuizCaballero 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 highfrequency switching
converters,power quality,multilevel inverters,and softswitching techniques.
Dr.RuizCaballero is currently a member of the Brazilian Power Electronics
Society (SOBRAEP).
Reynaldo M.RamosAstudillo 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
highfrequency switching converters,power quality,
multilevel inverters,and softswitching techniques.
Samir Ahmad Mussa (M’06) was born in
JaguariRS,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 (INEPUFSC),
Florianópolis.His research interests include digital control applied to power
electronics,powerfactorcorrection 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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