Symmetrical Hybrid Multilevel DC–AC Converters With Reduced ...

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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

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

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

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.
R
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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).