1. CONTROL DESIGN OF CONVERTERS FOR WIND ENERGY CONVERSION
SYSTEMS APPLIED TO BATTERY CHARGING
Herminio M. de Oliveira Filho, René P. T. Bascopé,
Luiz H. S. C. Barreto, Fernado L. M. Antunes and Demercil S. Oliveira Jr.
Federal University of Ceará – UFC, Group of Energy Processing and Control - GPEC
PO Box 6001, P. Code 60455-760, Tel.: +55(85) 33669586
herminio@dee.ufc.br, demercil@dee.ufc.br
Abstract – This paper presents a control design for a (400 W – 5 kW) associated with battery chargers are very
small size wind generation system for battery charging useful [3].
applications. A boost converter is used to regulate the The directed connection of a three-phase rectifier to
battery bank voltage, in order to implement a MPPT and batteries is a common practice adopted by some
limit the maximum current through the battery. The manufacturers [4]. Although there is simplicity and
system overview and modeling are presented including robustness, several problems associated with this solution
characteristics of wind turbine, generator, power result [3], such as the reduction of batteries useful life and
converter, control system, and supervisory system. increase of power losses. A dc/dc converter can be inserted
Simulations of the system are performed using between the rectifier output and the battery to change the
MATLAB/SIMULINK software for the case of battery apparent DC bus impedance seen by the generator [5] and
bank voltage regulation. improved efficiency can be obtained with the implementation
of maximum power point tracking algorithms (MPPT).
Keywords – Battery chargers, boost converters, control Within this context, this paper presents a system which
methods, wind generation, maximum power point employs a boost converter in cascade with the rectifier to
tracking. regulate the battery bank voltage, in order to implement a
MPPT algorithm and reduce the machine rotation in front of
I. INTRODUCTION high current levels through the battery. The system model,
control method, and supervisory system strategy are
Wind energy is a renewable energy source that does not investigated. Simulations results regarding the regulation of
pollute and is present everywhere. This kind of energy has the battery bank voltage are also presented.
become popular in electric power generation since 1970’s.
Within this period the world faced the Oil Crisis, which
caused an emphatic investment in wind systems to try to
reduce the employ of petroleum, which is used in power
stations.
The installed wind capacity in the world has increased
more than 30% per year over the last decade [1]. The current
surge in wind energy development is driven by multiple
forces in favor of wind power including its tremendous
environmental, social, and economic benefits, technological
maturity, the deregulation of electricity markets throughout
the world, public support, and government incentives [2].
A wind generation system can be used basically in three Fig. 1. Proposed topology.
distinct applications: isolated systems, hybrid systems and
grid connected systems. Basic characteristics of the systems II. PROPOSED TOPOLOGY
include power and energy system storage capability.
Generally, small size isolated systems demand energy The proposed system (Figure 1) is composed of a wind
storage by the use of batteries or in the form of gravitational turbine directly connected to a permanent magnet
potential energy in order to store the water pumped in synchronous generator (PMSG) rated at 40 V/1000 W in
reservoir raised for posterior use. More specifically, for cascade with a battery charger which supplies four batteries
electric generation in isolated systems, small wind turbines rated at 12 V/50 Ah.

2. The battery charger operates to obtain maximum power ρ ⋅θ g = ω g (5)
transferred to the batteries and can also limit the current and Where:
voltage levels of the battery bank. It is composed by a three-
phase full-bridge diode rectifier in cascade with a boost
g - angle that defines the mechanical position of the
converter. The duty cycle of converter is changed in
rotor [rad].
accordance with control system, which receives a reference
signal of supervisory system. ρ ⋅θ r = P ⋅ ω g (6)
III. SYSTEM MODELING Where:
r - angle that defines the electrical position of the
A. Wind Turbine Model rotor [rad].
Equation (1) is used in the implementation of wind turbine P - Pole pairs number.
model [6]. It describes the performance of power coefficient
(Rate between extracted mechanical power and available The electric model of the PMSG in steady-state operation
wind power) for different wind velocities and axis turbine. is described by (7):
¥ ¢
C5 Va Ea Ra 0 0 Ia La M ab M ac Ia
£
C2
C p = C1 ⋅ − C3 ⋅ β − C4 ⋅ e λi + C6 ⋅ λ (1) Vb = Eb − 0 I b − M ba ⋅
d (7)
£
Rb 0
Lb M bc
Ib
λi
¤ ¡
dt
Vc Ec 0 0 Rc Ic M ca M cb Lc Ic
Where:
Where:
Cp - power coefficient;
Cn - aerodynamic parameters (C1 to C6) of the turbine;
¦ Va, Vb, Vc - phase voltages [V];
- pitch angle [rad];
§ Ra, Rb, Rc - phase winding resistances [ ];
- tip speed [m/s];
§ La, Lb, Lc - phase winding self-inductances [H];
i - parameter given in (2).
Mab, Mac, Mbc - phase winding mutual inductances [H].
1 1 0.035 The values considered in the simulation are 0.5 Ω/phase
= − 3 (2)
λi λ + 0.08 ⋅ β β + 1 (resistance), 3.35 mH (self-inductance), and 3.06 mH
(mutual inductance) [3].
In the simulations tests, the following constants mentioned
in (1) are considered: C1 = 0.5176, C2 = 116, C3 = 0.40, C4 = IV. CONTROL METHOD
5, C5 = 21, C6 = 0.0068. These values are given for a three-
bladed wind turbine, with similar aerodynamic
characteristics to the turbine used in the system. The value of A. Power Stage Design
¦
chosen for simulation is 0º, as maximum Cp is obtained in Although this paper shows only simulations of proposed
this condition [3]. system, the design of the power stage is necessary to obtain
the transfer functions of the system plants. The system was
B. Generator Model then designed in accordance with [8].
The machine used in the simulation is a PMSG rated 1000 Preliminary specifications are:
W, 1000 rpm, 7 pole pairs, and axial flux. With many • output power: Po = 1000 W;
advantages over other kinds of generators, PMSGs are • switching frequency: fs = 50 kHz;
usually used in small wind turbine systems [7]. The dynamic • inductor current ripple: IL = 2%;
model of machine is obtained in [6], described by (3) to (6). • output voltage ripple: Vb = 0.25%;
Ea ⋅ I a + Eb ⋅ I b + Ec ⋅ I c • input voltage ripple: Vi = 2%.
Te =
(3) The values obtained for the filter elements are:
ωg
• inductance: L = 662 H;
Where: • output capacitance: Co = 4400 F;
- electrical torque [N.m];
Te • input capacitance: Ci = 6600 F.
Ia, Ib, Ic - phase currents [A]; Switches and diodes are also considered ideal to simplify
Ea, Eb, Ec - induced electromotive force [V]; the analysis.
¨
g - mechanical speed of the generator [rad/s].
B. Control System Design
J ⋅ ρ ⋅ ϖ g = Tm − Te − B ⋅ ϖ g (4) The control system was designed according to [8], and is
Where: composed by three proportional-integrator (PI) filter
J - inertia moment [km.m2]; controllers. Since this type of controller presents small
©
- differential operator. bandwidth, the speed response is slow. Thus they are
Tm - mechanical torque [N.m]; supposed to present high gain at low frequencies and
B - coefficient of viscous friction. improve the steady state precision.

3. Fig. 2. Control Design.
The transfer functions of controlled plants were obtained I L (s) Vo
applying the ac model for small signals of the PWM switch GI L _ d ( s) = = (8)
[9]. d (s) s ⋅ L
The block diagram of the implemented control system is The Bode diagram for open-loop transfer function without
shown in Figure 2. The internal controller CiL(s) regulates the compensation OLNi (s) and the compensator Ci(s) is shown in
average inductor current IL. This is compared with a current Figure 3. The compensator was designed to obtain an open-
reference provided by an intermediate controller, which closed transfer function with compensation OLCi(s) with
regulates the input voltage or dc bus voltage Vi. The input crossover frequency of 5 kHz, slope of -20 dB/decade across
voltage reference is provided by the external controller that zero magnitude, and phase margin equal to 55º. Figure 4
regulates the battery bank voltage. This signal is compared represents OLCi(s), which is given by the product between
with a voltage reference one provided by the supervisory OLNi(s) and Ci (s).
system.
1) Average Inductor Current Control - The transfer
function of the plant in (8) is obtained considering only the
duty cycle d(s) and inductor current perturbations IL(s). The
remaining magnitudes are considered time invariant. The
inductor resistance is neglected to simplify the analysis.
Fig. 4. Bode diagram for OLCi(s).
2) Input Voltage Control - The transfer function of the
plant in (9) is obtained considering only inductor current IL(s)
and input voltage Vi (s) perturbations. The other magnitudes
are considered time invariant. The input capacitance
resistance RCi is considered in this plant because it affects the
dc bus voltage ripple.
Fig. 3. Bode diagram for OLNi(s) and Ci(s).
Vi (s ) s + 1 RCi ⋅ Ci
GVi _ I L ( s ) = =-RCi ⋅ (9)
The plant for the aforementioned control system is formed I L ( s) s
by (8) and PWM modulator, whose transfer function is Fm(s).

4. dB/decade across zero magnitude, and phase margin equal to
84º. The input voltage controller is slower than the average
current one to minimize the inductor current ripple. Figure 6
shows OLCVe(s), which is obtained from the product between
OLNVe(s) and CVe(s).
3) Output Voltage Control - The transfer function of the
plant in (10) is obtained considering only input voltage Vi(s)
and output voltage Vo(s) perturbations. The other magnitudes
are considered time invariant. The battery bank model is
formed by capacitance C2 in series with resistance Rb. It is
very important because it causes the battery bank voltage
ripple. Inductor, output capacitance and switch resistances
are ignored to simplify the analysis. The battery bank
capacitance model is obtained in (11).
The closed-loop transfer function with compensation
CLTFVe(s) obtained for (8) has 18 poles. To simplify the
analysis of the control system, it was approximated for a first
order transfer function observing the unit step response for
CLTFVe(s). The obtained result is given in (12). Therefore,
the plant for this control system is constituted by (10) and
(12).
Rb DL s + 1 RbC2
GVo _Ve ( s )= ⋅ 2 2
(10)
LC2 Rb DL DL
Fig. 5. Bode diagram for OLNve(s) and CVe(s). s +s +
3 2
s+
LC1 LC1C2
Where:
DL - complementary duty cycle.
3600 ⋅ Cap
C2 = (11)
N ⋅Vb
Cap - battery capacity;
N - number of batteries.
200
CLTFVi ( s ) = (12)
s + 200
Fig. 6. Bode diagram for OLCve(s).
The plant analyzed for this control project is formed by
(9) and closed-loop transfer function with compensation
CLTFi(s) obtained for (8).
The Bode diagram for open-loop transfer function without
compensation OLNVe(s) and compensator CVe(s) designed is
presented in Figure 5. The compensator was designed to
provide an open-closed transfer function with compensation
OLCi(s) with crossover frequency of 400 Hz, slope of -20 Fig. 7. Bode diagram for OLNvo(s).

5. The Bode diagram for open-loop transfer function without V. SUPERVISORY SYSTEM
compensation OLNVo(s) and compensator CVo(s) is shown in
Figure 7. The compensator was designed to obtain an open- The supervisory system flow chart is shown in Figure 9. It
closed transfer function with compensation OLCVo(s) with gives the set point for the control system and is composed of
crossover frequency of 0.1 Hz, slope of -20 dB/decade across three functions: battery current regulation, output voltage
zero magnitude, and phase margin equal to 90º. The voltage regulation and MPPT algorithm.
controller is the slowest one. Slow response is necessary to The first and second functions have priority because they
reduce inductor current and input voltage ripple. Moreover, it are necessary to avoid reduction on battery useful life due to
reduces noise. Figure 8 shows the Bode plot for OLCvo(s). overvoltage and overcurrent, respectively. They regulate the
converter through the operation of the wind turbine out of its
maximum power point. The limit for battery current is 20%
of battery capacity and the limit for output voltage is voltage
recommended by the battery manufactor.
The third function consists in regulating the converter to
operate the wind generator at maximum power point using a
MMPT algorithm.
VI. SIMULATED SYSTEM
The simulations have the objective to evaluate and
validate the proposed system model. This paper will only be
concerned with battery voltage regulation, as simulations are
performed using MATLAB/SIMULINK.
The simulated circuit is shown in Figure 10. The average
current model for boost converter was used to simplify the
analysis and reduce simulation time. The output voltage
reference was chosen to regulate battery voltage bank around
the floating point, defined as 53.7 V. Wind speed was varied
from 6 to 11 m/s in 100 seconds.
The simulated waveforms are given in Figure 11. It is
observed that power coefficient practically assumes its
maximum value, but mechanical speed is low. This fact
occurred because wind turbine is out of maximum power
point due to fixed reference signal of the controller. The
wind turbine speed is decreased and large part of generated
Fig. 8. Bode diagram for OLCvo(s) power is waste in the generator internal resistance.
The battery voltage regulation can be seen in Figure 12.
Voltage ripple assumes values between 53.7 and 54.4 V,
corresponding to a variation of 0.7 V. Figure 12 also shows
that input voltage ripple is very small, but inductor current
one is greater due to the response of the input voltage
controller, as one can see in their respective reference
signals.
VII. CONCLUSIONS
This paper has presented an alternative for control design
of boost converter for small size wind generator systems
applied to battery charging. The system was designed and
studied via simulated results. One has verified that control
system performance is satisfactory for battery bank voltage
regulation. It was possible to break the turbine without the
use of external resistances or converters.
Although simulations have demonstrated good results, it
will be harder to implement the complete system due to high
complexity of the plant.
Future perspectives for additional studies include
simulating the complete supervisory system and the
Fig. 9. Flow chart for supervisory system. development of an experimental prototype.

6. Fig. 10. Schematic of the simulated circuit.
Velocity (m/s)
10
ACKNOWLEDGEMENT
Wind
5
The authors acknowledge the members of Group of
0 10 20 30 40 50 60 70 80 90 100 Energy Processing and Control (GPEC) for the friendship
Speed (rad/sec)
100
Mechanical
and overall support.
50
0
0 10 20 30 40 50 60 70 80 90 100
REFERENCES
Coefficient
0.4 [1] P. Gipe, “Soaring to new heights: the word energy market”,
Power
0.2 Renewable Energy World, vol. 5, no. 4, pp. 33-47,
0 10 20 30 40 50 60 70 80 90 100
September/October 2003.
[2] Q. Wang, L. Chang, “An Intelligent Maximum Power
Power (W)
Generated
2000
Extraction Algorithm for Inverter-Based Variable Speed Wind
1000 Turbine Systems”, IEEE Transactions on Power Electronics,
0
0 10 20 30 40 50 60 70 80 90 100
vol. 19, no. 5, September 2004.
[3] I. R. Machado, H. M. Oliveira F., L. H. S. C. Barreto, D. S.
Power (W)
500
DC Bus
Oliveira Jr., “Wind Generation System for Charging
Batteries”, in Proc. of Brazilian Power Electronics
0
0 10 20 30 40 50 60 70 80 90 100
Conference, COBEP, pp. 371-376, October 2007.
Time (sec) [4] www.enersud.com.br, access in 12/04/2008, 11:20 AM.
[5] T. Tafticht, K. Agbossou, A. Chériti, M. L. Doumbia, “Output
Fig. 11. Simulation results.
Maximization of a Permanent Magnet Synchronous Generator
Based Stand-Alone Wind Turbine, IEEE ISIE, pp. 2412-2416,
50 July 2006.
Current (A)
[6] S. Heier, Grid Integration of Wind Energy Conversion
Inductor
Systems, John Wiley Sons, 1st Edition, West Sussex,
0 England, 1998.
0 20 40 60 80 100
15 [7] Z. Guo, L. Chang, “FEM Study of Permanent Magnet
Voltage (V)
Synchronous Generators for Small Wind Turbines” Canadian
Input
10
Conference on Electrical and Computer Engineering, pp. 641-
5
0 20 40 60 80 100
644, May 2005.
54.5 [8] R. W. Erickson, D. Maksimovic, Fundamentals of Power
Voltage (V)
Electronics, Kluwer Academic Publishers, 2nd Edition, New
Battery
54
York, USA, 2004.
53.5
0 20 40 60 80 100
[9] V. Vorpérian, “Simplified Analysis of PWM Converters Using
1.195 the Model of the PWM Switch Part I: Continuous Conduction
Reference
Voltage
Mode”, IEEE Transactions on Aerospace and Electronics
Input
1.19
Systems, vol. 26, no. 3, pp. 490-496, May 2003.
1.185
0 20 40 60 80 100
10 BIOGRAPHIES
Reference
Inductor
Current
5
Herminio Miguel de Oliveira Filho was born in Taguatinga, Distrito
0 Federal, Brazil, on 1983. He received the B.Sc. degree in Electrical
0 20 40 60 80 100
Time (sec) Engineering from the Federal University of Ceará, Brazil, in 2007.
Currently, he is an engineer and M.Sc. student with the Group of Energy
Fig. 12. Simulation results.

7. Processing and Control in the Federal University of Ceará. His interest areas the IEEE Power Electronics Society and Industrial Application Society and
include control applications, switching power supplies, and renewable the Brazilian Power Electronics Society (SOBRAEP).
energy applications. Fernando Luiz Marcelo Antunes, Ph.D. B.Sc. degree in Electrical
René Pastor Torrico Bascopé, Dr. was born in Cochabamba, Bolivia, on Engineering from Federal University of Ceará, Brazil, in 1978, B.Sc. degree
1967. He received the BSc from San Simón University of Cochabamba, in Business and Administration from Estate University of Ceará, Brazil,
Bolivia, in 1992, and its MSc and Dr. degrees from the Federal University of MSc. degree from the University of São Paulo, Brazil, in 1980 and PhD
Santa Catarina, Brazil, in 1994 and 2000, respectively. During 1995 and degree Loughborough University of Technology, United Kingdom (UK) in
1996, he was Research Engineer in the Power Electronics Institute of 1991. He is a lecturer at Federal University of Ceará, Brazil, teaching Power
Federal University of Santa Catarina. From March 2001 to May 2003, he has Electronics and Electric Machines at graduate and undergraduate levels. He
been an Assistant Professor at the Univali – University of Itajaí, Brazil. coordinates the Energy Processing and Control Group of the UFC where
Currently, he is Professor of the Federal University of Ceará. His main research projects are carried out with financial support of research
research interests include power supplies, power factor correction development agencies and public and private companies. He is member of
techniques, UPS systems, and renewable energy applications. the SOBRAEP, SBA and IEEE.
Prof. Luiz Henrique Silva Colado Barreto, Dr. He received the B.Sc. Prof. Demercil de Souza Oliveira Júnior, Dr. has B.Sc. (1999) and M.Sc.
degree in Electrical Engineering from Universidade Federal de Mato Grosso, degrees (2001) in Electrical Engineering from Federal University of
Brazil, in 1997 and the M.Sc. and Ph.D. degrees from the Universidade Uberlândia, Brazil, and Dr. degree (2004) from Federal University of Santa
Federal de Uberlândia, Brazil, in 1999 and 2003 respectively. Since June Catarina, Brazil. His fields of interest include power electronics, soft-
2003, he has been with the Electrical Engineering Department, Universidade switching, wind energy systems, DC/DC converters, etc. At the moment he
Federal do Ceará, Brazil, where he is a Professor of Electrical Engineering. is Professor and Researcher in Federal University of Ceará, Brazil, and is
His research interest areas include high-frequency power conversion, reviewer from IEEE Transactions on Industrial Electronics and IEEE
modeling and control of converters, power factor correction circuits, new Transactions on Power Electronics.
converters topologies, UPS system and fuel cell. Dr. Barreto is member of