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This technique is compared with the traditional linear PIstrategy. The topology of isolated photovoltaic system ispresented inFig. 2.

Fig. 2 Battery charger topology.

II.

MODELING OF THE SYSTEM

A.

Maximum Power Point Tracker (MPPT)

The MPPT is an algorithm that maintains the photovoltaicpanel delivering maximum power to the system at variouslevels of solar radiation. It was used the incrementalconductance algorithm. The incremental conductancealgorithm is considered better than other techniques based onthe principle of perturbation and observation, because it has afaster response to changes in solar radiation.

The operating principle of the algorithm is the incremental

calculation of the derivative of the curve of power once thisvalue is zero at the maximum power point [11].Fig. 3 showsthe algorithm.

Fig. 3 Incremental conductance algorithm [8].

B. Solar panel modeling

The electrical model of the solar panel used in this work isshown in Fig. 4 and is presented in details by [12]. The

resistances represent the voltage drop and losses for both thecurrent flowing through the load () and the reverse leakagecurrent of the diode (), respectively. is a controlled DCcurrent source. In Table I the parameters of a solar panelSM48KSM, manufactured by Kyocera are presented.

Fig. 4 Photovoltaic panel model.

TABLE I. MAIN PARAMETERS OF A SOLAR PANEL.

Parameter Symbol Value

Maximum Power () 48Maximum Power Voltage () 18.6Maximum Power Current () 2.59

Open Vircuit Voltage () 22.1Short Circuit Current () 2.89

Temperature Coefficient of ( ) -0.07Temperature Coefficient of ( ) 0.00166

C.

Boost converter modeling and PI control

The modeling of the boost converter assumes that the

battery voltage is constant. This is a good approximationbecause the battery voltage variation during the chargingprocess is very small. Besides, the curve of the solarpanel is linearized around the maximum power point, like isshown in Fig. 5 [8]. In this situation, the solar panel can bemodeled as a voltage source in series with a resistance. Thus,the battery charger equivalent circuit is shown inFig. 6.

Fig. 5 I x V curve of the solar panel SM48KSM and its linearization around

the maximum power point.

Fig. 6 Battery charger equivalent circuit.

0 5 10 15 20 250

0.5

1

1.5

2

2.5

3

3.5

Voltage (V)

Current(A)

I x V curve

Linearization

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And the new dissipative structure is given as:

(13)Given a desired , it is possible to verify

the following change in the dynamic averaged error equation(14):

(14)The energy adjustment of the system is obtained doing:

(15)In this circumstance, the error dynamic equation is: (16)The desired energy in terms of the error can be modeled

by: (17)

is a Lyapunov function candidate for (16). The time

derivative of(17) along the paths(16) results in: (18)Where is strictly positive and constant. The condition

(18) is ensured for(16),and satisfied if: (19)Doing the matrix products of(19),the result is:

{

(20)

The equations(20) contains the expressions of the controllaw. To avoid the influence of parasite elements, reference[16] proposed an integral action, as:

(21)Equation(21) gives the duty cycle of the converter for the

control of the input voltage. The variables and areparameters of the controller. Where and .E.

Simulation

It was simulated inMatlab/Simulinka photovoltaic systemof 48

. The solar array consists in a single panel model SM

48KSM whose parameters are shown in TABLE I. Theparameters of the boost converter applied in photovoltaicsystem are showed inTABLE II.Finally the parameters of thebatteries used in the simulation are showed inTABLE III.

The algorithm of incremental conductance (MPPT) uses asampling frequency of 10 and a step voltage of 1 . Itis necessary calculate the maximum power point current of thepanel for the PBC technique. As this algorithm is onlyobtained maximum output voltage of the panel, this value isobtained using(22). (22)

Where is the maximum power point current of thepanel, is the output power of the panel while is thevoltage calculated by the algorithm.

TABLE II. PARAMETERS OF THE CONVERTER.

Boost Converter

Inductor 8.0 Capacitor in Panel

1.5

Capacitor in Battery 15 Output Voltage 36 Frequency Switching 20Inductor Resistance 0.1 Capacitor Resistance 0.05

Diode Voltage 0.8 IGBT Voltage 1.0

TABLE III. PARAMETERS OF THE BATTERY.

Battery (Nickel-Metal-Hydride)

Nominal Voltage 36 Nominal Capacity 60

Initial Stage of Charge 20 %

Maximum Capacity 64.61

Fully Charged Voltage 42.4 Nominal Discharge Current 12Internal Resistance 0.006 TheFig. 8 shows the solar radiation profile used to test and

compare the performance of the two control techniques. Thisprofile consists in ramp variations and will impact in themaximum power point voltage of the panel.

In order to analyze the impact of parameters uncertain inthe system response, variations of in the inductanceand in the resistance of the inductor are simulated.

Fig. 8 Solar radiation profile.

III. RESULTS

A.

Performance during solar radiation variation

TheFig. 9 shows the electrical variables of the solar panel

for both PI and PBC technique. The panel voltage and current

follows the maximum power at all levels of radiation.

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800

900

1000

1100

Time (s)

Solarirradiance(W/m2)

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During solar radiation variations, the transient response of

each controller is different. As can be seen in Fig. 10, the

PBC technique follows the maximum power point voltage

with a smaller current overshoot and is faster than PI

technique.The battery current ripple reduces when the PBC technique

is used, like is shown inFig. 11.This fact can be justified bythe duty cycle calculated for each technique. In the sameoperation point there is a larger oscillation in the duty cyclecalculated by the PI technique. In this case, the PBC controlhas the advantages of improving the battery current and areduction of the switch stress.

Fig. 9 Electrical parameters of the photovoltaic panel for PI and PBCtechniques.

Fig. 10 Details in the voltage and current response for PI and PBC

techniques.

.

Fig. 11 Battery current and duty cycle of converter for PI and PBCtechniques.

B.Performance during parameter variation

Variations in internal resistance and inductance of the

inductor influence in the dynamic of both control techniques,

like shown in Fig. 12 and Fig. 13. However, in the PI

technique there is an increase in the response time, which

does not happen in the PBC technique.The behavior of the current in the battery is presented in

Fig. 14 andFig. 15.Variations in the inductor did not impactin the current dynamic response. It can be observed that theinductance has an impact in the current ripple. On the otherhand, the increase of the resistance impacts in the efficiency ofthe converter, reducing the average current in the battery.

Fig. 12 Voltage response of the PI and PBC techniques during variations in

the inductance.

IV.

CONCLUSION

This work presented a battery charger supplied by a 48photovoltaic panel connected to a boost converter. Theincremental conductance algorithm was used to find themaximum power from the panel. It was proposed the PBCtechnique and this was compared with the traditional PItechnique.

The PBC control had a faster response in the maximumpower point tracker and a smaller ripple in the duty cycle.Both components lifetime and charger process are improvedusing this technique. Besides, the PBC strategy was morestable during parameters variation than PI technique.

0 2 4 6 8 10 1210

15

20

25

Time (s)

Voltage(V)

PI

PBC

0 2 4 6 8 10 120

1

2

3

Time (s)

Current(A)

PI

PBC

0 2 4 6 8 10 120

10

20

30

40

50

Time (s)

Power(W)

PI

PBC

3.5 4 4.5 5 5.5 6 6.51

1.5

2

2.5

3

Time (s)

Current(A)

PI

PBC

3.5 4 4.5 5 5.5 6 6.515

16

17

18

19

20

Time (s)

Voltage(V)

PI

PBC

0 2 4 6 8 10 12

0

50

100

Time (s)

DutyCycle(%

)

PI

PBC

0 2 4 6 8 10 120

0.5

1

Time (s)Currentinthebatteries(A)

PI

PBC

3.5 4 4.5 5 5.5 6 6.5

16.5

17

17.5

Time (s)

Voltage

(V)

L L +20% L -20%

3.5 4 4.5 5 5.5 6 6.517.2

17.4

17.6

17.8

Time (s)

Voltage

(V)

PBC

L L +20% L -20%

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Fig. 13 Voltage response for PI and PBC techniques during variations in theresistance.

Fig. 14 Battery current response for PI and PBC techniques during

variations in the inductance.

Fig. 15 Battery current response for PI and PBC techniques during

variations in the resistance.

REFERENCES

[1] EUROPEAN PHOTOVOLTAIC INDUSTRY ASSOCIATION.Global Market Outlook for Photovoltaics 2013-2017. EuropeanPhotovoltaic Industry Association. [S.l.], p. 60. 2012.

[2] CASTRO, R. M. G. Energias Renovveis e Produo

Descentralizada. Universidade Tcnica de Lisboa. Lisboa. 2002.

[3] ENSLIN, J. H. R.; WOLF, M. S.; SNYMAN, D. B. Integratedphotovoltaic maximum power point tracking converter. IEEETransactions on Industrial Electronics, 44, 1997. 769-773.

[4] IEA. Management of Storage Batteries used in Stand-AlonePhotovoltaic Power Systems - Report_IEA_PVPS_T3-10:2002.International Energy Agency (IEA). [S.l.]. 2002.

[5] SOUSA, J. M. N. D. Sistema bidirecional de carga de bateriaspara o FEUP VEC. Universidade do Porto. Porto, p. 111. 2013.

[6] LINDEN, D.; REDDY, T. B. Handbook of Batteries. 3. ed.[S.l.]: McGraw- Hill, 2002.

[7] AMBROSIO, R. C.; TICIANELLI, E. A. Baterias de nquel-

hidreto metlico, uma alternativa para as baterias de nquel-cdmio. Scielo, 2001. ISSN ISSN 0100-4042. Disponivel em:

. Acesso em: 28 jan.2014.

[8] VILLALVA, M. G.; SIQUEIRA, T. G. D.; FILHO, E. R.Voltage regulation of photovoltaic arrays: small-signal analysisand control design. IET Transactions on Power Electronics, v. 3,

p. 869-880, 2010.

[9] BECHERIF, M.; AYAD, M. Y.; ABOUBOU, A. Hybridizationof Solar Panel and Batteries for Street Lighting by Passity BasedControl. IEEE International Energy Conference, Al Manamah,

p. 664-669, 2010.

[10] MU, K.; MA, X.; ZHU, D. A New Nonlinear Control Strategyfor Three-Phase Photovoltaic Grid-Connected Inverter.International Conference on Eletronic & Mechanical

Engineering and Information Technology, Harbin, p. 4611-4614,2011.

[11] ALMEIDA, P. M. D. Modelagem e Controle de Conversores

Estticos Fonte de Tenso utilizados em Sistemas de GeraoFotovoltaicos Conectados Rede Eltrica de Distribuio.UFJF. Juiz de Fora, p. 190. 2011. (Master thesis).

[12] VILLALVA, M. G.; GAZOLI, J. R.; FILHO, E. R.Comprehensive Approach to Modeling and Simulation ofPhotovoltaic Arrays. IEEE Transactions on Power Electronics,

v. 24, n. 1, p. 1198-1208, March 2009.

[13] ERICKSON, R. W.; MAKSIMOVIC, D. Fundamentals ofPower Eletronics. 2. ed. New York: Klumer AcademicPublishers, 2004.

[14] CUPERTINO, A. F. et al. A Grid Connected Photovoltaic

System with a Maximum Power Point Tracker using PassivityBased Control applied in a Boost Converter. UFV. Fortaleza, p.8. 2012.

[15] 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,August 2004.

[16] LEYVA, R. et al. Passivity-based integral control of a boost

converter for large-signal stability. IEE Proceedings. ControlTheory and Applications, v. 153, p. 139-146, March 2006.

3.5 4 4.5 5 5.5 6 6.5

16.5

17

17.5

Time (s)

Voltage(V)

PI

RL RL +20% RL -20%

3.5 4 4.5 5 5.5 6 6.517.2

17.4

17.6

17.8

Time (s)

Voltage(V)

PBC

RL RL +20% RL -20%

3.5 4 4.5 5 5.5 6 6.50.4

0.6

0.8

1

Time (s)

Current(A)

PI

L +20% L L -20%

3.5 4 4.5 5 5.5 6 6.5

0.5

0.6

0.7

0.8

0.9

Time (s)

Current(A)

PBC

L +20% L L -20%

3.5 4 4.5 5 5.5 6 6.50.4

0.6

0.8

1

Time (s)

Current(A)

PI

RL -20% RL RL +20%

3.5 4 4.5 5 5.5 6 6.5

0.5

0.6

0.7

0.8

0.9

Time (s)

Current(A

)

PBC

RL -20% RL RL +20%

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BIOGRAPHIES

Valentim Ernandes Neto was born in Aimors,Brazil. He is student of Electrical Engineering at

Federal University of Viosa (UFV), Viosa, Brazil,since 2012. Currently is integrant of GESEP, where

develop works about power electronics applied in

renewable energy systems. His research interests

include photovoltaic energy and control applied inpower converters.

Filipe Perez was born in Uberaba-MG, 1990. He isstudent of Electrical Engineering at FederalUniversity of Viosa (UFV), Viosa, Brazil, since

2008. Currently is integrant of GESEP, where

develop works in the area of power systems andrenewable sources, especially solar energy. Currently

working with control converters for photovoltaic

panels. His research interests include power systems,automation and control.

Andr Gomes Trres received the B.S. degree, theM.S. and the Ph.D. degree in electrical engineeringfrom the Federal University of Minas Gerais

(UFMG), Belo Horizonte, Brazil, in 1998, 2000 and

2004 respectively. Since 2005 he has been with the

Department of Electric Engineering, UFV, Brazil. His

research interests include power electronics, electrical

drives and process automation.

Allan Fagner Cupertino received the B.S. degree inelectrical engineering from the Federal University ofViosa (UFV), Viosa, Brazil, in 2013. He is

integrant of GESEP, where developed works about

power electronics applied in renewable energysystems. Currently he is Master student from Federal

University of Minas Gerais (UFMG), Belo Horizonte,Brazil. His research interests include solar

photovoltaic, wind energy, control applied in power

electronics and grid integration of dispersed generation systems.

Heverton Augusto Pereirareceived the B.S. degreein electrical engineering from the Federal University

of Viosa (UFV), Viosa, Brazil, in 2007, the M.S.

degree in electrical engineering from the StateUniversity of Campinas (UNICAMP), Campinas,

Brazil, in 2009. Currently he is Ph.D. student from

the Federal University of Minas Gerais (UFMG),

Belo Horizonte, Brazil. Since 2009 he has been with

the Department of Electric Engineering, UFV, Brazil.

His research interests are wind power, solar energy and power quality.