A Grid-Connected Photovoltaic System with a
Maximum Power Point Tracker using Passivity-Based
Control applied in a Boost Converter
A. F. Cupertino, J. T. de Resende, H. A. Pereira
S. I. Seleme Júnior
Gerência de Especialistas em Sistemas Elétricos de Potência
Universidade Federal de Viçosa
Viçosa, Brasil
allan.cupertino@yahoo.com.br, resende@ufv.br,
heverton.pereira@ufv.br
Programa de Pós-Graduação em Engenharia Elétrica
Universidade Federal de Minas Gerais
Belo Horizonte, Brasil
seleme@cpdee.ufmg.br
I.
INTRODUCTION
The interest in renewable energy has been driven by a
combination of fuel price spikes, climate change concerns,
public awareness, and advancements in renewable energy
technologies [1]. In this context, the solar photovoltaic (PV)
energy has gained prominence for its low environmental
impact, long operating time and silent operation.
source such as shown in Figure 3. Furthermore, variations in
the incident solar irradiance and temperature have a great
impact on the generated power as illustrated in Figure 4.
In application of PV-arrays connected to the grid, the
voltage generated level should be as steady as possible due its
interaction with an existent system. If it does not occur, a
protection system can be activated in order to disconnect it
from the grid [3].
69.7
Instaled Power (GWp)
Abstract—The power generated by a solar photovoltaic panel is
strongly dependent on climate conditions. For this reason, a gridconnected system needs a good response for variations in the
solar irradiance and temperature. A non-linear control technique
which has a good rejection of disturbances is the passivity-based
control. This work presents the application of the passivity-based
control in a maximum power tracker boost converter for a gridconnected photovoltaic system. The fast response of the control
allows a better use of the photovoltaic array energy, increasing
the efficiency of the system, and ensuring stability for all
operation range.
A significant growth in the installed power on solar
photovoltaic systems has occurred. In 2011 its value was of
69.68 GWp, a growth of 76 % with respect to the previous
year, as shown in Figure 1. More than 95% of this power is
generated by grid-connected systems [2].
Photovoltaic solar energy is a source that is subject to
seasonal weather conditions. The behavior of the photovoltaic
panel is something between a current source and a voltage
The authors would like to thank to CNPQ, FAPEMIG and CAPES for
their assistance and financial support.
2.3
2.8
4.0
5.4
7.0
9.5
15.7
2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Year
Figure 1. Growth of the global PV installed power [2].
Moderate
Forecast (GWp)
The European Photovoltaic Industry Association (EPIA)
made a forecast for the installed power of solar photovoltaic
energy considering two scenarios, as shown in Figure 2. The
first scenario (Moderate) assumes rather pessimistic market
behavior with no major reinforcement of existing support
mechanisms, or strong decrease/limitation of existing schemes.
The second scenario (Policy-Driven) assumes the continuation
or introduction of adequate support mechanisms, accompanied
by a strong political will consider PV as a major power source
in the coming years.
39.5
22.9
Policy-Driven
300
200
100
0
2012
2013
2014
Year
2015
2016
Figure 2. Forecast until 2016 for solar photovoltaic installed power [2].
There are, basically, two topologies for PV grid-connected
systems, as shown in Figure 5 and described below:
Figure 3. Characteristics curves of a solar photovoltaic panel.
•
Topology 1: The photovoltaic panels are connected
directly to the DC bus of the PWM inverter [5], [7],
[8];
•
Topology 2: The photovoltaic panels are connected in
a DC chopper and after to the DC bus with one PWM
inverter [4], [6], [9].
The first topology needs more solar panels connected in
series and is more sensitive to significant variations in the
incident irradiance. Besides, the MPPT algorithm is
implemented in the control of the inverter. The second
topology can be used for a small number of solar panels and
allows a better control of the power.
For the control of the DC chopper, some works use
proportional-integral-derivate (PID) controllers [9]. Many of
these systems are non-minimum phase, making it difficult to
design PID controllers. Furthermore, the use of traditional
approaches in the frequency domain considers a linearization
around the operation point. All these factors degrade the
performance of the controller for large variations in reference
values [10].
(a)
Some works propose nonlinear control techniques to
improve the responses during disturbances [11]. In this
context, the passivity-based control (PBC) has presented good
results [12], [13], [14].
The control by passivity applied to the dynamic system is
based on energy functions. This technique derives a control
law allowing the plant to store less energy than it absorbs [15].
The design of PBC consists in modifying the system energy
adding damping through the dissipative structure. This
approach is valid for a wide range of operation and large signal
stability is assured [16], [17].
(b)
Figure 4. Effect of incident irradiance (a) and temperature (b) in I x V curves
of a solar panel.
There are in the literature several studies about the
performance of grid-connected photovoltaic systems. Most of
their aims are:
•
Control the active and reactive power injected in the
grid [4], [5];
•
Reduce the current harmonic distortion [5];
•
Make the maximum power point tracking (MPPT) of
the solar system [4], [5], [6].
The application of passivity-based control in DC converters
was studied in different works: Using energy functions,
Sanders proposed control laws for the PBC [18]. Furthermore,
[17] added in the work of Sanders an integral action in order to
eliminate the steady state errors. Finally, Sira-Ramirez
proposed works [19], [20], in which the converters were
modeled as Euler-Lagrange (EL) systems to which the PBC
concepts were applied.
In this context, the present work shows simulation results of
a grid-connected photovoltaic system with a maximum power
point tracker (MPPT). A DC boost converter working as
MPPT and a PWM inverter connect the system to the grid, as
shown in Figure 6. The control of the boost converter is made
by PBC. This technique allows obtaining a fast dynamic
response and good rejection of disturbances.
(a)
(b)
Figure 5. Topologies of grid-connected solar photovoltaic systems: (a) Topology 1 and (b) Topology 2.
Figure 6. Simulated grid-connected photovoltaic system.
II.
METHODOLOGY
A. Solar panel modeling
The electrical circuit model of the solar panel used in this
work is shown in Figure 7. The resistances represent the
voltage drop and losses for both the current going to the load
( ) and the reverse leakage current of the diode ( ),
respectively. is a DC current source. In Table I, some
parameters reported by solar panels manufacturers are given.
The variable is calculated as:
∆"#
TABLE I.
MAIN PARAMETERS OF A SOLAR PANEL
Parameter
Symbol
Maximum Power (W)
Maximum Power Voltage (V)
Maximum power current (A)
Short circuit current (A)
Temperature coefficient of (A/K)
Open circuit voltage (V)
Temperature coefficient of (V/K)
The equation of the current in the solar panel is:
$
$%&'
(1)
(2)
Where is the current in the nominal conditions,
calculated by:
Figure 7. Model of a solar photovoltaic panel.
1 (3)
∆" " "( (T is the solar panel temperature and T* is the
nominal solar panel temperature); $ e $%&' are the values of
incident solar irradiance and the reference irradiance (W/m²),
respectively. The variable / is the temperature coefficient of
the short circuit current (A/K).
The reverse leakage current in the diode, I is:
∆"
23 45 ∆6#
7
1
8
1
(4)
is the nominal short-circuit current, is the nominal
open circuit voltage and is the coefficient of the open circuit
voltage (V/K). The variable 9is the ideality constant of the
diode, contained in the range1 : 9 : 1.5. Finally, = is
calculated by:
= >"
(5)
Where > the Boltzmann’s constant, " is the temperature of
the panel (K) and is the electron charge.
An algorithm for adjusting and is proposed in [21].
The method is based on the fact that there exists only one pair
? , A for which the maximum power calculated by the I-V
model B is equal to the maximum experimental power
from the datasheet
. Using B in equation
(1), one has [21]:
#
C
BD BD 1E (6)
Figure 9. Boost converter model.
The interactive process is shown in Figure 8. The initial
values of and are [21]:
F
BG 0
BG PW
E ; J RXY U and K RKZ U.
K[
0
0
The variables KZ and K[ represent the inductor current and
capacitor voltage, respectively. The symbol Q represents the
duty cycle.
PJ C
(7)
The desired values for the average inductor current and
average capacitor voltage are respectively the panel current and
voltage on maximum power point. The vector of averaged
dynamic error is defined by:
K M]O KZ` M]O
K̃ M]O
K̃ M]O ^ Z
_ ^ Z
_
K̃[ M]O
K[ M]O K[` M]O
As KM]O K̃ M]O K` M]O withK` M]O aKZ` M]O
the desired state, it can be obtained that:
IJ K̃L MNJ J OK̃ PJ M1 QOJ aIJ KL` MNJ J OK` b
B. Boost converter modeling and control
For the modeling of the Boost converter it will be assumed
that the control strategy of the inverter guarantees that the DC
bus voltage is approximately constant. According to [22] it is
possible to linearize the I x V curve of the solar panel around
the maximum power point. Thus, the solar panel can be
modeled as a voltage source in series with a resistance. For this
reason, the dynamics of the converter can be modeled as in
Figure 9. The Euler-Lagrange model of this converter is given
as:
0
0
S 0
0 1
U ;NJ R
U ;J C0 1W E ;
0 T
1 0
Where:
IJ R
K[` M]Ob6
(10)
The design of the PBC consists in modifying the system
energy by adding damping through the dissipative structure
[16]. This modification is accomplished through the addition,
in closed loop, of a dissipative term that emulates a resistor
connected in series with the inductor, denoted byZ . This
strategy is denominated indirect control, or series control. The
addition of the dissipative term is:
Figure 8. Algorithm of the method used to adjust the I x V model [21].
IJ KL MNJ J OK PJ M1 QOJ
(9)
(8)
ZX R
Z
0
Z
X` C 0
0
U
0
0
1W E
(11)
and the new dissipative structure is given as:
(12)
Given a desired J` MJ ZX O, it is possible to verify
the following change in the dynamic averaged error equation:
IJ K̃L MNJ J` OK̃ PJ M1 QOJ aIJ KL` MNJ J OK` ZX K̃b
(13)
The energy adjustment of the system is obtained doing:
PJ M1 QOJ aIJ KL` MNJ J OK` ZX K̃ b 0
In this circumstance, the error equation will be:
(14)
IJ K̃L MNJ J OK̃ 0
(15)
1
c` K̃ 6 IJ K̃ e 0; ∀K g 0
2
(16)
cL` M]O : K̃ 6 J` K̃ : hc` M]O i 0M∀K g 0O
(17)
PJ M1 QOJ aIJ KL` MNJ J OK` ZX K̃b
(18)
The desired energy in terms of the error can be modeled
byc` :
c` is a Lyapunov function candidate for (15). The time
derivative of (16) along the paths (15) results in:
Where h is strictly positive and constant. The condition
(17) is ensured for (15), and satisfied if:
P K[`
KZ`
m
k KL[` T
l
aK Z MKZ KZ` O SKLZ` b
kQ 1 [`
j
XY
axis current. Therefore, it is possible to obtain an independent
control law for the two axes.
A synchronism technique is necessary to connect the
system to the grid, made by a Phase Locked Loop (PLL)
circuit. This structure estimates the grid voltage angle for the
control of the inverter. In this work a Synchronous Reference
Frame – PLL (SRF-PLL) was used, shown in Figure 10. The
PI control is adjusted in order to obtain a fast response and
good filtering.
A LCL filter was used to reduce the harmonics generated
by IGBT’s switching. Its topology is shown in Figure 11. The
design of this component is presented in [23]. The modulation
strategy used was the sinusoidal pulse-width modulation
(SPWM).
Accomplishing some algebraic manipulations, the result is:
Figure 10. SRF-PLL blocks diagram.
(19)
The equations in (19) are the expressions of the control
law. To avoid the influence of parasite elements, reference [17]
proposed an integral action, as:
=
Q(= Q n MK[ K[` Oo]
(20)
Equation (20) gives the duty cycle of the converter for the
control of the input voltage. The variables Z and are
parameters of the controller.
C. PWM inverter modeling
For the inverter modeling, a balanced three-phase system is
assumed, and only the positive sequence control is considered.
The expressions of the active and reactive power injected to the
grid are:
3
` ` r r #
2
p
3
s r ` ` r #
2
(21)
Where M` , r O are the direct and quadrature components of
the grid voltage. M` , r O are the direct and quadrature
components of the current injected by the inverter.
Using the grid voltage angle as orientation, results in
r 0. Thus, the active power is defined only by the direct
axis current and the reactive power is defined by the quadrature
Figure 11. LCL filter structure.
In order to write the dynamic equations of the system, it
will be assumed that in the fundamental frequencyω* , the
LCL filter can be approximated for a L filter whose inductance
is the sum of the inductances LZ andLv . The dynamics of the
grid side can be written as:
wx ∙ zx S ∙
ozx
{x
o]
(22)
{x is the
Where {vx is the vector of inverter output voltage, V
vector of grid voltage, xı is the vector of filter current, S S S1 and  1. Extracting the components o and € of
(22), results in:
w` ∙ ` S ∙
wr ∙ r S ∙
o`
‚( ∙ S ∙ r `
o]
or
‚( ∙ S ∙ ` r
o]
(23)
(24)
The terms ‚( ∙ S ∙ r ` and ‚( ∙ S ∙ ` are
compensated by a feed-forward action. By applying the
Laplace transform to the compensated system, the transfer
function of the inverter is given as:
$ MƒO w` MƒO wr MƒO
1
` MƒO
r MƒO ƒS Where the inputs are the voltages
outputs are the currents ` and r .
The DC bus dynamics is given as:
T
oXY
X= `
o]
(25)
w` and wr and the
(26)
The application of the Laplace transform to (26) results in:
ƒTXY X= MƒO ` MƒO
(27)
The term X= is a disturbance in the control (see Fig. 6).
It is assumed in this work that the DC bus loop is sufficiently
fast, as to eliminate the perturbation term. For this reason, the
DC bus transfer function will be:
$` MƒO XY MƒO
1
` MƒO
ƒT
(28)
Where the input is the current ` MƒO and the output, the dc
bus voltage, XY .
The control loops of the inverter are shown in Figure 12 .
Externally, there is the reactive power loop that controls the
power factor and the loop to regulate the DC bus voltage. The
current control loops use proportional controllers and the
external loops use proportional-integral controllers. The
controller gains were adjusted by the poles allocation method.
The parameters of the solar panel (model SM 48KSM,
manufactured by Kyocera) are shown in Table II. The value of
the resistances was calculated by the adjust algorithm, and the
obtained values was:
†
0.1558Ω
115.0317Ω
The parameters of the boost converter, of the inverter and
of the LCL filter are shown in Table III.
TABLE II.
ELECTRICAL PERFORMANCE OF SM 48KSM UNDER
STANDARD TEST CONDITIONS(*STC)
Parameter
Value
48‹
18.6
2.59Ž
22.1
2.89Ž
0.070/
1.66Ž/
*STC: Irradiance1000‹/[ , AM1.5 spectrum, module temperature 25 °C.
TABLE III.
PARAMETERS OF THE CONVERTER AND INVERTER
Boost Converter
(
2,9>‹
X
20>cK
S
15c
T
330Q
0.2 mF
TXY
D. Simulation
It was simulated in Matlab/Simulink®, version 7.10.0, a
photovoltaic system of 4.8 kWp. The solar array consists of
100 panels, in a connection of 20 panels in series and 5 blocks
in parallel.

SZ
S'
T'
`
Inverter
10 kHz
7.5 mH
20 µH
13 µF
2.5 Ω
In a real system, it is necessary to inform the value of the
voltage and current in the maximum power point using a given
algorithm. This algorithm is not presented here. For the
simulations, the values of voltage and current in the maximum
power point were supposed to be known. The objective here is
only the fast dynamic response of the passivity based control. It
must be observed that the speed of the algorithm of MPPT
tends to degrade the response of the PBC controller, because of
the time to stabilize the reference.
III.
Figure 12. Control loops of the inverter.
(29)
RESULTS
The variation of solar irradiance is shown in Figure 13.
This change represents the shadow made by a cloud, for
example. The three phase injected current is shown in Figure
14. It can be observed that the inverter’s control regulate the
amplitude of the current in function of the generated power.
Besides, as shown by Figure 15, the amplitude of the
harmonics is in accordance to the IEEE Recommended
Practice for Utility Interface of Photovoltaic (PV) Systems
(IEEE Std 929-2000). This fact shows the appropriate design
of the LCL filter.
Figure 16 shows the variables of solar panel (voltage and
current) and the DC bus voltage. The passivity based control
allows the solar panel to work in the maximum power point.
Thus, the fast dynamic response of the control improves the
400
PV voltage (V)
efficiency of the generation. Figure 17 (b) shows the active and
reactive power. The active power injected in the grid is very
close to the generated value. The difference is due to the
internal losses in the system. The reactive power oscillates
around zero giving a power factor close to one.
300
200
100
0
0
0.2
0.4
1100
0.6
0.8
1
0.6
0.8
1
0.6
0.8
1
time (s)
15
PV current (A)
1000
Irradiance (W/m²)
900
800
10
0
-5
0
0.2
0.4
time (s)
700
520
DC bus (V)
600
500
400
0
0.1
0.2
0.3
0.4
0.5
time (s)
0.6
0.7
0.8
0.9
510
500
490
1
0
0.2
0.4
time (s)
Figure 13. Solar irradiance on solar photovoltaic panels.
Figure 16. Voltage and current of the solar panel and DC bus voltage.
20
5
1000 W/m²
4
800 W/m²
10
Power (kW)
15
three phase currents (A)
5
500 W/m²
3
2
5
1
0
0
0
generated
injected
0.2
0.4
0.6
0.8
1
0.6
0.8
1
time (s)
-5
200
-15
-20
0
0.1
0.2
0.3
0.4
0.5
time (s)
0.6
0.7
0.8
0.9
1
Figure 14. Three phase injected currents.
current in phase A (A)
100
0
-100
-200
0
20
0.2
0.4
time (s)
Figure 17. Generated and injected power.
10
0
IV.
-10
-20
0.07
0.08
0.09
0.1
0.11
0.12
time (s)
0.13
0.14
0.15
0.16
0.08 ← fundamental: 17.15 A - THD = 0.07%
0.06
0.04
0.02
0
0
50
100
150
harmonic order
200
250
Figure 15. Current harmonic spectrum in phase A.
CONCLUSIONS
The analysis and study of the insertion of solar photovoltaic
panels in power networks is important in order to increase the
market competitiveness of this source.
0.1
Mag (% of fundamental)
Reactive Power (VAr)
-10
300
The presented results show that the PBC applied to the
converter allows the panel to work in the maximum power
point with fast dynamic response, improving the efficiency of
the grid-connected system. Besides, the control of the inverter
connects the system to the grid with high efficiency and with
low harmonic distortion.
ACKNOWLEDGMENT
The authors would like to thank to CNPQ, FAPEMIG and
CAPES for their assistance and financial support.
Adaptive Passivity-Based Control of Average DC-to-DC Power
Converters Models. International Journal of Adaptative Control and
Signal Processing, v. 12, p. 63-80, 1998.
[20]
SIRA-RAMÍREZ, H.; NIETO, M. D. D. A Lagrangian Approach to
Average Modeling of Pulsewidth-Modulation Controlled DC-to- DC
Power Converters. IEEE Transactions on Circuits and Systems-I:
Fundamental Theory and Applications, v. 43, p. 427-430, Maio 1996.
[21]
VILLALVA, M. G.; GAZOLI, J. R.; FILHO, E. R. Comprehensive
Approach to Modeling and Simulation of Photovoltaic Arrays. IEEE
Transactions on Power Electronics, v. 24, n. 1, p. 1198-1208, Maio
2009.
REFERENCES
[1]
NACWA. Renewable Energy Resources: Banking On Biosolids, 2010.
[2]
EPIA. Global Market Outlook for Photovoltaics until 2016. 1ª. ed.:
EPIA, v. I, 2012.
[3]
MASTERS, G. M. Renewable and Efficient Electric Power Systems.
New Jersey: Wiley Interscience, 2004.
[22]
[4]
LO, Y.-K.; LEE, T.-P.; WU, K.-H. Grid-Connected Photovoltaic
System With Power Factor Correction. IEEE Transactions on
Industrial Electronics, v. 55, n. 5, p. 2224-2227, May 2008.
VILLALVA, M. G.; RUPPERT FILHO, E. Dynamic analysis of the
input-controlled buck-converter fed by a photovoltaic array. Controle
& Automação, v. 19, 2008.
[23]
[5]
MEZA, C. et al. Lyapunov-Based Control Scheme for Single-Phase
Grid-Connected PV Central Inverters. IEEE Trasactions on Control
Systems Technology, v. 20, n. 2, p. 520-529, March 2012.
LISERRE, M.; BLAABJERG, L.; HANSEN, S. Design and control of
an LCL-filter based three-phase active rectifier. IEEE Transactions on
Industry Applications, v. 41, n. 5, p. 1281-1291, September 2001.
[6]
WAI, R.-J.; WANG, W.-H. Grid-Connected Photovoltaic Generation
System. IEEE Transactions on Circuits and Systems, v. 55, n. 3, p.
953-964, April 2008.
[7]
MASTROMAURO, R. A. et al. A Single-Phase Voltage-Controlled
Grid-Connected Photovoltaic System With Power Quality Conditioner
Functionality. IEEE Transactions on Industrial Electronics, v. 56, n.
11, p. 4436-4444, November 2009.
[8]
ZHANG, et al. Three-Phase Grid-Connected Photovoltaic System with
SVPWM Current Controller. IPEMC, p. 2161-2164, 2009.
[9]
ANTUNES, F.; TORRES, A. M. A three-phase grid-connected PV
system. 26th IECON , v. 1, p. 723 - 728, 2000.
[10]
SIRA-RAMIREZ, H.; ORTEGA, R. Passivity-Based Controllers for
the Stabilization of DC-to-DC Power Converters. 34th Conference on
Decision & Control, New Orleans, p. 3471-3476, December 1995.
[11]
BECHERIF, M.; PAIRE, D.; MIRAOUI, A. Energy management of
solar panel and battery system with passive control. International
Conference on Clean Electrical Power, p. 14-19, Maio 2007.
[12]
BECHERIF, M.; AYAD, M. Y.; ABOUBOU, A. Hybridization of
Solar Panel and Batteries for Street Lighting by Passity Based Control.
IEEE International Energy Conference, Al Manamah, p. 664-669,
2010.
[13]
BECHERIF, M.; AYAD, M. Y.; HISSEL, D. Modelling and control
study of two hybrid structures for street lighting. IEEE International
Symposium on Industrial Electronics, Gdansk, p. 2215-2221, Junho
2011.
[14]
MU, K.; MA, X.; ZHU, D. A New Nonlinear Control Strategy for
Three-Phase Photovoltaic Grid-Connected Inverter. International
Conference on Eletronic & Mechanical Engineering and Information
Technology, Harbin, p. 4611-4614, 2011.
[15]
ORTEGA, R. et al. Passivity based Control of Euler Lagrange
Systems: Mechanical, Electrical and Electromechanical Applications.
[S.l.]: Springer-Verlag, 1998.
[16]
JELTSEMA, D.; SCHERPEN, J. M. A. Tuning of Passivity-Preserving
Controllers for Switched Mode Power Converters. IEEE Transactions
on Automatic Control, v. 49, p. 1333-1334, Agosto 2004.
[17]
LEYVA, R. et al. Passivity-based integral control of a boost converter
for large-signal stability. IEE Proceedings. Control Theory and
Applications, v. 153, p. 139-146, Março 2006.
[18]
SANDERS, S. R.; VERGHESE, G. C. Lyapunov-Based Control for
Switched Power Converters. IEEE Transactions on Power Electronics,
v. 7, p. 17-24, Janeiro 1992.
[19]
SIRA-RAMÍREZ, H.; ORTEGA, R.; GARCÍA-ESTEBAN, M.
BIOGRAPHIES
Allan Fagner Cupertino was born in Visconde do
Rio Branco, Brazil. He is student of Electrical
Engineering at Federal University of Viçosa, Viçosa,
Brazil. Currently is integrant of GESEP, where
develop works about power electronics applied in
renewable energy systems. His research interests
include solar photovoltaic, wind energy, control
applied on power electronics and grid integration of
dispersed generation.
José Tarcísio de Resende received M.S. degrees in
electrical engineering from the Federal University of
Itajubá (UNIFEI), Itajubá, Brazil, in 1994, and P.H.
degree in electrical engineering from the Federal
University of Uberlândia (UFU), in 1999. He is
currently Professor at Federal University of Viçosa,
Brazil. His research interests include modeling of
electric machines, power systems and renewable
energy.
Seleme Isaac Seleme Jr. received the B.S. degree in
electrical engineering from the Escola Politecnica
(USP), Sao Paulo, Brazil, in 1977, the M.S. degree in
electrical engineering from the Federal University of
Santa Catarina, Florianópolis, Brazil, in 1985, and the
Ph.D. degree in control and automation from the
Institut National Polytechnique de Grenoble
(INPG),Grenoble, France, in 1994. He spent a
sabbatical leave with the Power Electronics Group,
University of California, Berkeley, in 2002. He is currently an Associate
Professor with the Department of Electronic Engineering, Federal University
of Minas Gerais, Belo Horizonte, Brazil. His research interests are electrical
drives, control applied to power electrics and electromechanic systems.
Heverton Augusto Pereira was born in São Miguel
do Anta, Brazil, in 1984. He received the B.S. degree
in electrical engineering from the Federal University
of Viçosa (UFV),Viçosa, Brazil, in 2007, the M.S.
degree in electrical engineering from the
Universidade Estadual de Campinas (UNICAMP),
Campinas, Brazil, in 2009, and currently is Ph.D.
student from the Federal University of Minas Gerais
(UFMG), Belo Horizonte, Brazil. He is currently an
Assistant Professor with the Department of Electric Engineering, Federal
University of Viçosa, Brazil. His research interests are wind power, solar
energy and power quality.