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MPPT controller for a photovoltaic power systembased on fuzzy logic

GARRAOUI RadhiaNational Engineering school of Gabes ,Tunisia

Photovoltaic, Wind and Geothermal Systems Research Gabes, Tunisia

radhiagarraoui@gmail.com

SBITA LassaadNational Engineering school of Gabes, Tunisia

Photovoltaic, Wind and Geothermal Systems Research Gabes, Tunisia

lassaad.sbita@enig.rnu.tn

Mouna BEN HAMEDNational Engineering school of Gabes, Tunisia

Photovoltaic, Wind and Geothermal Systems Research Gabes, Tunisia

mouna.benhamed@enig.rnu.tn

Abstract— this paper proposes a maximum power point tracking algorithm based on fuzzy logic control for photovoltaic systems, According to the nonlinear characteristic of photovoltaic array[1], it’s necessary to find a solution to track the maximum power of the PV system in order to improve its efficiency. The fuzzy logic controller presented in this work provide fast response and good performance against the climatic and load change and uses directly the DC/DC converter duty cycle as a control parameter.Simulation results show that the proposed algorithm can effectively improve the efficiency of photovoltaic array output.Index Terms— photovoltaic system; MPPT Fuzzy Control.

I. INTRODUCTION

According to the advent of energy crisis and the increasingly serious environmental pollution. It is essential to use renewable energies which are characterized by their negligible pollution level as an example we find wind, hydraulic and solar energy which have been greatly developedand it becomes the focus of attention [2]. The solar photovoltaic energy has been widely utilized in many applications and the maximum power point tracking (MPPT) control becomes an important topic for PV systems, Unfortunately, the maximum power produced by the PV array changes with solar radiation and cell temperature so in this paper, we develop a fuzzy robust MPPT method for solar PV systems that occur a high level of performance. A new test of robustness is presented to be sure of the performance of the new controller. This method is applicable for any kind of load connected to the PV array.

NomenclatureG: Global insulation (W /m²). :alpha the control signal

Gn: Reference insulation (W /m2). Iscr: short circuit current (A).

Iph: Light-generated current (A). Ki: Short circuit current temperature

coefficient (A/°K).

I: output current (A). T: Cell junction temperature (°C).

V: output voltage (V). Tref: Reference cell temperature (°C).

A: ideality factor. Kb: Boltzmann constant (1.38e-23).

Irr: saturation current (A) at Tref. Eg: Band gap energy (eV).

Id: PV saturation current (A). q: charge of an electron.

II. THE CHARACTERISTIC OF A PV ARRAY

In order to investigate the reliability of MPPT using fuzzy logic algorithm, a photovoltaic power system with a boost converter is presented in Fig.1, A boost converter can be used to increase the voltage magnitude its output voltage can be calculated from (1)

(1 )

VinVout

Where Vin is the input voltage (output voltage of PV array),Vout is the output voltage and is the duty ratio of controllable switch SW

Fig. 1. The photovoltaic system.various modeling of solar cells has been proposed in the literature [3]. There is a proposition of an equivalent circuit model of a PV cell presented in Fig.2, which is composed of a light generator source, diode, a parallel resistor expressing a leakage current, and a series resistor describing an internal resistance to the current flow. The equivalent model of a PV cell is using the mathematical expression Eq. 2, Eq. 3 and Eq.4, where parallel resistor Rsh is neglected because of its large resistance and the series resistor Rs is neglected due to its very small resistance in order to simplify the simulation. Eq. (1) describes the output current of the cell:

SSD'13 1569682157

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2013 10th International Multi-Conference on Systems, Signals & Devices (SSD) Hammamet, Tunisia, March 18-21, 2013

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- exp( ) -1qV

I I Iph d k TAbThe equation of PV current as a function of temperature and irradiation can be written as

( )ph scr i rn

GI I k T TG

The well known saturation current equation is given by:3

1 1exp( )gd rr

r b r

qETI IT k A T T

Fig. 2. Model of a PV cell.The PV characteristic curve is presented in Fig.3 under

different illumination. Fig. 4 shows the I–V curves for the array at different temperature levels. The open circuit voltage and the power increase with the solar irradiation; however with high temperature it seems to be the inverse. The PV generator’s power is decreasing with important value of temperature.

0 5 10 15 200

1

2

3

4

V(V)

I(A)

1000w/m²

800w/m²

600w/m²

400w/m²

200w/m²

Fig. 3. The I-V characteristics under different irradiations and T=25°C.

0 5 10 15 200

1

2

3

4

V(V)

I(A)

25°C

45°C

75°C

65°C

Fig. 4. The I-V characteristics under different temperatures and G=1000W/m².

III. BOOST CONVERTER MODELFor a PV system connected to a resistive load there is a

necessity to insert a boost type converter [4] and [5] presented

in Fig.5 that will use a certain controller in order to maintain the maximum power, the system is written in two sets of state equation that are depending on the position of switch SW, if it is in position (1), SW=0, the differential equation is:

1(1)

1( )(1)

I V VoutLVoutVout C RLoad

I

If the switch SW is in position (2), SW=1, the differential equation is expressed as:

1(2)

1(2)

I

VoutRLoad

VdtL

Vout C

Fig. 5. Model of a boost converter.

0 1 .

The dynamic equation of the system can be described by:V VV out outI

L L LVI IoutVout C C R Cload

IV. FUZZY LOGIC MPPT CONTROLLERFrom the perspective of engineering, we can assume that in

situations where traditional methods of modeling from physical observations prove unsatisfactory, subjective science, especially fuzzy logic can make a lot of services. When knowledge about how to solve a problem, drive a large system, make an adjustment ... etc. are available. This implies that weknow define rigorous methods of knowledge representation. In practice, the resolution of a specific problem may use the joint use of objective methods traditional and subjective. Fuzzylogic provides a formal framework, which did not exist before. To implement these methods in a rigorous way, this part is devoted to the presentation of the fundamentals of fuzzy logic, and their uses to represent the reasoning based on linguistic expressions. The fuzzy theory allows the modeling and rigorous treatment of imprecise information, uncertain and

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subjective. It allows to approximate nonlinear functions. It is a theory perfectly suited to the optimization problem, which has to be addressed in this draft paper .It has indeed, to make a highly nonlinear function P and sensors that can be infinitesimal precision. The study in this work based on the real-time observation of the criteria entered. In each of these approaches, a converter is used after inference and criteria canbuild an alpha value, which is the duty cycle of the converter, this value leads to the determination of the value sought for each moment. The principle of fuzzy logic based on the fuzzification, which is a transformation of a digital value in degrees of fuzzy membership by evaluating a membership function. Blur MPPT controller is composed of:

basis rules, which contains definitions of terms used in the control and rules characterizing the target of the command and describing the conduct of the expert;logic decision that transforms using fuzzy reasoning techniques part fuzzy inference after fuzzification, a new fuzzy part;fuzzification interface which transforms the measured input of fuzzy;defuzzification interface to the output, which determines a specific action from the descriptions of the fuzzy output variables. This can be seen in Fig. 6below, which shows a block diagram of the fuzzy logic controller. Each of the main components has been discussed.

Fig. 6. The FLC controller.

In case of fuzzy MPPT the law control is based on the error dE)). Therefore, the activation of all

In simple cases, this variation of the order is obtained by a simple reading of a decision table defined offline. The form of this control law is given by:

.1 1k dDk k k

Where KD is the gain associated with the control signal. TheEq. 9, Eq. 10 and Eq. 11 presented respectively the error E, the variation of the error dE and d as follows:

( ) ( 1)( )

( ) ( 1)

P k P kPV PVE KV k V kPV PV

( ) ( 1)dE E K E K

The sign of the difference E (K) shows the position of the operating point at time k. Indeed, if for example E (K) has a positive sign then it is located on the left side of the operating point maximum, this is clearly explained in Fig. 7. The entrance dE expresses the moving direction of the point of operation MPP. The method of defuzzification is the centroid method represented by equation Eq. 11.

( )1

( )1

nj jjd n

jj On the other hand, the error E and error change dE are

normalized as follows: .

.

X K EE EX K dEdE dE

(12)

Where KE and KdE are the scale factors (standardization). We vary these factors until we have a proper transient control. In fact, it is they which will determine the performance of the MPPT controller.

V. OVERALL STRUCTURE OF FUZZY OPTIMIZATION

In this Fuzzy controller, the range of interest of each input variable and the output variable is divided into five classes which are denoted as follows:

NB: negative big,NS: negative for smallZO: for about zero,PS: positive smallPB: positive for large

The fuzzy rules used to determine the controller output signal as a function of the input signals. They connect the output to the input signals by linguistic terms which take into account the experience and know-how acquired by a human operator. Simply translating remarks sense. For example, it is quite clear that, if the error is strongly negative and its variation is also the control signal must be approximately zero, but if the error is approximately zero and its variation as it will be the same order.

Now, if the error is approximately zero, but its variation is strongly negative, the positive control signal is small, or if the error is strongly negative but the variation is approximately zero. The control signal will be strongly positive. These considerations lead to the adoption of a decision table anti-diagonal, summarizing the rules chosen, it is Table. 1

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Table. 1. Anti-diagonal decision table.

CE

E

NB NS ZO PS PB

NB ZO ZO PB PB PBNS ZO ZO PS PS PSZO PS ZO ZO ZO NSPS NS NS ZO ZO ZOPB NB NB ZO ZO ZO

VI. SIMULATION RESULTS

We consider the simultaneous variation of climatic condition mentioned in Fig. 8 and Fig. 9, there are three different areas: A is the area where the temperature is constant and the irradiation is variable, B seems to be the inverse then the temperature is thevariable condition here and finally area C where we consider asimultaneous change of the temperature and irradiation, the target is to test the robustness of the fuzzy MPPT controller.

We note the following answers provided by the fuzzyMPPT controller on the voltage, which was set at Fig. 10, and on current presented at Fig. 11, it provides a fast and efficient response against trade lighting in area A. And the photovoltaic system has responded correctly. This affects the power which in turn tends to optimal values for each illumination according to the results presented in Fig. 12. The MPPT controller based on fuzzy logic resisted with success the abrupt change of illumination, This is clear if we examine the nature of the generated control signal, while observing the simulation result in Fig. 13 ,the influence of the good nature of command is clear at the output current Iout of Fig. 14. This is confirmed also by the plot of the error response in Fig.15. It has a very small value around zero. Fig. 16. gives a clear idea about the controller’s parameters. Considering now the area B, the power P displayed at Fig.12, decreases with increasing temperature. And it is the same for the voltage V shown at Fig. 10. For the current I which the simulation result is shown in Fig. 11, we note that itincreases slightly due to the temperature rise. Again the fuzzyMPPT controller ensures a good response to the temperature change, by observing the load current response and the signal control alpha we ensure easily the effective response of the fuzzy controller. The new test of robustness is given by area C then we consider a simultaneous change of irradiation and temperature after examining the power response at Fig. 12. We ensure that is providing rapid and stable response. MPPT controller based on fuzzy logic show low sensitivity against the fluctuation of the load as shown in Fig.17, according to the responses on power, control signal, load current and the error variation presented respectively in Fig. 18, Fig. 19 ,Fig. 20 and Fig.21.

0 5 10 15 200

20

40

60

80

V(V)

P(W

)

dP/dV<0dP/dV>0

dP/dV=0

Fig.7. Slope of PV curve characteristics at different points.

0 0.5 1 1.5 2 2.5 3 3.5295

300

305

310

315

320

Time(s)

Tem

pera

ture

(Kel

vin)

A B C

Fig. 8. Temperature variation.

0 0.5 1 1.5 2 2.5 3 3.5200

400

600

800

1000

Time(s)

Irra

diat

ion(

W/m

²)

C A B

Fig. 9. Irradiation variation.

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0 0.5 1 1.5 2 2.5 3 3.50

5

10

15

20

Time(s)

V(V

),V

opt(

V)

V(V)Vopt(V)

A C B

Fig. 10. The PV voltage.

0 0.5 1 1.5 2 2.5 3 3.50

1

2

3

4

Time(s)

I(A

)

I(A)Iopt(A) A

C

B

Fig. 11. The PV current.

0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

Time(s)

P(W

)

P(W)Popt(W)

A B C

Fig. 12. The PV power.

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

Time(s)

alph

a

alpha

alpha opt

A B C

Fig. 13. The control signal.

0 0.5 1 1.5 2 2.5 3 3.50

0.5

1

1.5

Time(s)

Iout

(A)

Iout(A)

Iout(A)

A B C

Fig. 14. The load current.

0 0.5 1 1.5 2 2.5 3 3.5-100

-50

0

50

100

Time(S)

E,dE

0 0.1 0.2-15-10

-505

1.26 1.28 1.3 1.32-0.02-0.01

00.01

EdE

Fig. 15. The error and the error variation.

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Fig. 16. The surface.

0 0.5 1 1.5 2 2.520

40

60

80

100

Time(s)

RLoa

d

Fig. 17. The load current.

0 0.5 1 1.5 2 2.50

20

40

60

80

Time(s)

P(W

),Pop

t(W)

1.5 1.52 1.54 1.56

50

60

P(W)Popt(W)

Fig. 18. The Power.

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

Time(s)

alph

a,al

pha

opt

1.5 1.55

0.7

0.75

alphaalpha opt

0.5 0.60.5

0.6

0.7

Fig. 19. The control signal.

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

Time(s)

Iout

(A),I

outo

pt(A

)

Iout(A)Ioutopt(A)

Fig. 20. The load current.

0 0.5 1 1.5 2 2.5-80

-60

-40

-20

0

20

Time(s)

E,dE

EdE0.3 0.35 0.4

-0.04-0.02

00.02

EdE

Fig. 21. The error and the error variation.

VII. CONCLUSIONThis paper presents an algorithm of the photovoltaic array

maximum power point tracking which is based on fuzzy logic. It directly sees the duty cycle of the boost converter as control variables and makes the output power value of photovoltaic array to be close to the theoretical maximum value. The simulation results show that: in the case of illumination, temperature and load change quickly, it also can quickly find a new maximum power point, and has a higher power output efficiency. So, it seems to be a new and robust solution for the PV array.

REFERENCES

[1] T. Shimizu, O. Hashimoto, and G. Kimura, “A novel high-performanceUtility-interactive photovoltaic inverter system,” IEEE Trans. Power Electron., vol. 18, no. 2, pp. 704–711, Mar. 2003.[2] [Mohan Kolhe. Techno-Economic Optimum Sizing of a Stand-Alone Solar Photovoltaic System IEEE Transactions Energy Conversion,VOL. 24, NO. 2, pp. 511-519, JUNE 2009.[3] M. G Villalva, J. R. Gazoli, and E. R. Filho, “Comprehensive approachto modeling and simulation of photovoltaic arrays,” IEEE Trans. PowerElectron., vol. 24, no. 5, pp. 1198–1208, May 2009.[4] H. De Battista, R.J. Mantz ; ‘’Variable structure control of aphotovoltaicenergy converter’’ IEE Proc. Control Theor. Appl., 149 (2002), pp. 303–310[5] BEN HAMED M., SBITA L., FLAH A., ABID A. and GARRAOUI R.,"A real time implementation of an improved MPPT controller for photovoltaic systems ", Renewable Energy and Vehicular Technology (REVET), 2012 First International Conference on, Hammamet, Tunisia, pp. 173 – 178, March 2012.

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