Pv Mppt Fuzzy Logic

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2013, Article ID 762946, 10 pageshttp://dx.doi.org/10.1155/2013/762946

Research ArticlePhotovoltaic System Modeling with Fuzzy Logic BasedMaximum Power Point Tracking Algorithm

Hasan Mahamudul, Mekhilef Saad, and Metselaar Ibrahim Henk

Faculty of Engineering, University of Malaya, 50670 Kuala Lumpur, Malaysia

Correspondence should be addressed to Hasan Mahamudul; hasan [email protected]

Received 15 April 2013; Accepted 15 June 2013

Academic Editor: Jun-Ho Yum

Copyright © 2013 Hasan Mahamudul et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

This paper represents a novel modeling technique of PV module with a fuzzy logic based MPPT algorithm and boost converterin Simulink environment. The prime contributions of this work are simplification of PV modeling technique and implementationof fuzzy based MPPT system to track maximum power efficiently. The main highlighted points of this paper are to demonstratethe precise control of the duty cycle with respect to various atmospheric conditions, illustration of PV characteristic curves, andoperation analysis of the converter. The proposed system has been applied for three different PVmodules SOLKAR 36W, BPMSX60W, and KC85T 87W. Finally the resultant data has been compared with the theoretical prediction and company specified valueto ensure the validity of the system.

1. Introduction

At present, efficient generation of green energy is the primechallenge for the researcher of this field.With the explosion ofworld population and rapid industrialization, energy demandis increasing drastically. But the natural sources of energylike coal, oil, and natural gas are limited. As a result, theonly way to overcome the challenge is the development ofrenewable and inexhaustible energy. Among the renewablesources, solar energy is the pioneer. The features such asnontoxic, harmless, inexhaustible, and carbon dioxide emis-sion free conversion have made this topic very interesting.But the energy conversion efficiency of solar system has notreached a satisfactory level yet, so the researches in this fieldcontinue. The recent trends on which research concentratesmost are fabrication of effective PV cell, modification ofcell arrangement and array configuration, implementationof maximum power point tracking algorithm, and so forth.Among the aforementioned, technology application ofMPPTtechnique is the most popular because it improves the PVefficiency significantly. But the initial installment cost of aPV system with MPPT technique is very high. So, it is veryimportant to carry out a reliable simulation before going forpractical implementation [1–10].

Accuratemodeling of the PVmodule is the first step of thesimulation process. Though a number of publications havealready described different types of PVmodeling techniques.But these works were very complicated and time consuming.In addition, MATLAB coding based simulator were usedby most of the authors for illustrating 𝐼-𝑉 and 𝑃-𝑉 curves[11, 12].The problemwith these simulators is that they cannotbe used for different modules simultaneously. Herewith thereexists some possibility of data manipulation. The proposedtechnique can be used to illustrate the characteristic curvesof any specific model instantly.

Different types of MPPT algorithm such as hill climbing,voltage feedback, current feedback, perturb and observation,incremental conductance, fuzzy logic, and neural networkhave been discussed. Among them, hill climbing and voltagefeedback are quite easy to implement, but these algorithmsare not efficient in tracking the maximum power withsudden variation in environmental condition. The conven-tional (P&O) and incremental conductance aremore popularbecause they show a better performance with environmentalconditions, and implementation is also easy. But they possessan extra 𝑃-𝐼 control loop which makes the tracking processof these two algorithms slow. ANN based algorithms showimpressive improvement in efficiency, but the selection of

2 International Journal of Photoenergy

the number of neurons and settings of hidden layers for ANNis a hard task, and implementation of this algorithm is quitedifficult [13–19].

Therefore, for this work a fuzzy logic based MPPTalgorithm has been used. Some good works based on fuzzylogic has already existed. But in most of the works an extragain block has been added with the fuzzy system for tuningthe output [20, 21]. In this algorithm the gain block has beenremoved, and duty cycle has been calculated directly usingseven rules based fuzzy system. The developed algorithmis able to track the maximum power with a convenientspeed, and it shows a very dynamic response with suddenvariations in environmental conditions. At the same time,the implementation of this algorithm is also possible withavailable components at a lower cost.

Selection of an appropriate converter is another impor-tant issue when implementing a PV-MPPT system. Recentwork has shown that various types of converters have beenused for different applications [22, 23]. In this work a boosttopology has been selected with an intention to use thesystem for high voltage applications. Finally the developedPV module and MPPT technique has been connected withthe boost converter to analyze the performance of the system.

The sequential work flow of this paper is as follows,in Section 2 the modeling process of PV module has beendescribed with the necessary mathematical equations. InSections 3 and 4 implementation of theMPPT algorithm andboost converter have been discussed in detail. In Section 5 allthe necessary results and discussions are given to check thefeasibility of the system. A brief conclusion has been addedto finalize the work.

2. Modeling of PV Module inSimulink Platform

The PV module is a combination of solar cells which isbasically a photoactive semiconductor P-N junction diode.The PV cell absorbs solar energy and converts it into elec-tricity. Different configurations of PV cell can be used toillustrate the 𝑉-𝐼 curves such as single diode model, twodiode model, and 𝑅

𝑠-𝑅𝑝model. But among them due to

degree of accuracy and simplicity single diode model hasbeen used in a number of previous works. For this reason, thesingle diode configuration of PV module has been selectedfor this work. Figure 1 represents the circuit configuration ofa PV cell [24, 25].

2.1. Necessary Mathematical Equations Related to PV Mod-eling. The 𝑉-𝐼 curves of a PV module can be expressedusing some nonlinear exponential mathematical equations.These equations are mostly related to diode characteristics.A comprehensive discussion of PV characteristics has beengiven in [26, 27].

For the PV output current, 𝐼pv, one has

𝐼pv = 𝑁𝑝 ∗ 𝐼ph − 𝑁𝑝 ∗ 𝐼𝑜

× [exp{𝑞 ∗(𝑉pv + 𝐼pv ∗ 𝑅𝑠)

𝑁𝑠𝐴𝐾𝑇

} − 1] .

(1)

Ideal PV cell

Dio

de

Io Rp

Rs

Iph

Figure 1: Circuit configuration of single diode PV cell.

For the PV saturation current,

𝐼𝑜= 𝐼rs[

𝑇

𝑇𝑟

]

3

exp[𝑞 ∗𝐸𝑔

𝐴𝑘{1/𝑇𝑟− 1/𝑇}

] . (2)

For the PV reverse saturation current, 𝐼rs, one has

𝐼rs =𝐼scr

[exp (𝑞𝑉oc/𝑁𝑠𝑘𝐴𝑇) − 1]. (3)

For the PV photo current, 𝐼ph, one has

𝐼ph = [𝐼scr + 𝐾𝑖 (𝑇 − 𝑇𝑟)] ∗𝑆

1000. (4)

For simplification of the notation, a constant has beenintroduced as 𝐶

𝑜;

𝐶𝑜= 𝑁𝑠𝑘𝐴𝑇. (5)

2.2. Complete Simulink Implementation of the PV Module.For this modeling technique, four matlab function blockshave been used. Each block contains the mathematical equa-tions for 𝐼ph, 𝐼pv, 𝐼𝑜, and 𝐶𝑜. In this modeling process𝑁

𝑠,𝑁𝑝,

𝑇, 𝑆, and 𝑉in have been used as main input parameters, while𝑃pv, 𝐼pv, and 𝑉pv were taken as output parameters. Figures 2and 3 represent the internal and external configuration of themodeling technique clearly.

Figure 2 represents the view of internal mathematicaloperation of the PV module.

Figure 3 is the external configuration of PV module forthe simulation of characteristic curves.

These two figures clearly explain the modeling techniqueof the PV module. Only and changing the parameters fromthe input ports according to the company specified value,characteristic curves for different modules can be obtainedby using this model.

The developed prototype has been applied to simu-late the characteristics curves of PV modules. The (STC)

International Journal of Photoenergy 3

1

2

3

4

5

273

AddMatlab

function

Matlab function

Matlab function

Matlab function

Product

Add Product

SubProduct

Sub1

2

3

Product

GainProduct

Divide

0.1

T

Np

Ns

S

Constant(Q)

Mat

hfu

nctio

n

For Io

For Co

Vin

Constant(1)

For Iph

For Irs

(eu)

Vpv

Ipv

Ppv

Figure 2: Internal mathematical functional block diagram of PV module.

25

1

36

Temperature

Variable irradiations

Number of parallel cell

Number of series cell

PV m

odul

eT

Np

Ns

S

Vin

Vin

P-V scope

V-I scopeVpv

Ipv

Ppv

Vpv display

Ipv display

Ppv display

Figure 3: External Simulink window view of the PV module.

specifications of the modules have been given in Table 3.Finally, Figures 4 and 5 represent the characteristics curvesfor SOLKAR 36W, Figures 6 and 7 represent for BP MSX60W, Figures 8 and 9 represent for KC85T 87W PVmodule.

3. Implementation of Fuzzy Logic BasedMPPT Algorithm

In this algorithm, PV input current and voltage have beentaken as input, and duty cycle has been calculated as output.


1

2.5

0.5

V-I plot

1000W/m2

500W/m2

100W/m2

V (V)

I(A

)

5 10 15 20

Figure 4: Characteristics curve for SOLKAR 36W module. 𝑉-𝐼curves of SOLKAR 36W at different radiations.

10

20

40

P(W

)

1000W/m2

500W/m2

100W/m2

V (V)5 10 15 20

P-V plot

Figure 5: Characteristics curve for SOLKAR 36W module. 𝑃-𝑉curves of SOLKAR 36W at different radiations.

2

3.5

1

V-I plot

1000W/m2

500W/m2

100W/m2

V (V)

I(A

)

5 10 15 20

Figure 6: Characteristics curve for BP MSX 60W module. 𝑉-𝐼curves of BP MSX 60W for different radiations.

10

30

60

20

40

P(W

)

1000W/m2

500W/m2

100W/m2

V (V)5 10 15 20

P-V plot

Figure 7: Characteristics curve for BP MSX 60W module. 𝑃-𝑉curves of BP MSX 60W for different radiations.

3

5

1

V-I plot

1000W/m2

500W/m2

100W/m2

V (V)

I(A

)

5 10 15 20

Figure 8: Characteristics curve for Kyocera KC85T 87W module.𝑉-𝐼 curves of KC85T 87W at different radiations.

20

70

90

50

80

P(W

)

1000W/m2

500W/m2

100W/m2

V (V)5 10 15 20

P-V plot

Figure 9: Characteristics curve for Kyocera KC85T 87W module.𝑃-𝑉 curves of KC85T 87W at different radiations.


Initialize with PV

input current and voltage

Calculation of error and

change of error signal

Set up of membership function for

fuzzy variables

Setting of fuzzy rules

Calculation of duty

cycle

Figure 10: Flow chart of the fuzzy logic algorithm.

1

2

1

Fuzzy logic controller

Subsystem forgeneration of error (E)

and change oferror (CE) d

Vpv

Ipv

Figure 11: The external block view of the fuzzy logic algorithm.

181NM ZENS PM PBPSNB

0

1

0.5

0 0.60.30.3

Plot points

Membership function plot for (E)

−0.6

Input variable “error”

Figure 12: Graphical view of the membership function for errorsignal.

The flow chart of Figure 10 represents the basic concept of thealgorithm.

The equations associated with the calculation of errorand change of error signal have been listed below [20, 21] asfollows:

𝐸(𝐾) =Δ𝐼

Δ𝑉+𝐼

𝑉=Δ𝑃

Δ𝑉=Δ𝑃

Δ𝐼,

CE (𝐾) = 𝐸 (𝐾) − 𝐸 (𝐾 − 1) ,

Δ𝐼 = 𝐼 (𝐾) − 𝐼 (𝐾 − 1) ,

Δ𝑉 = 𝑉 (𝐾) − 𝑉 (𝐾 − 1) ,

Δ𝑃 = 𝑃 (𝐾) − 𝑃 (𝐾 − 1) .

(6)

3.1. Simulink Block View of the Fuzzy MPPT. Figure 11 showsthe block view of the fuzzy logic algorithm in Simulinkwindow.

3.2. Membership Functions and Rule Settings of Fuzzy MPPTAlgorithm

3.2.1. Membership Function. For this work, triangular shapedmembership function has been chosen. The range of thesignal has been selected by checking the oscillation of eachsignal. Figures 12, 13, and 14 represent the graphical view of

181

0

0.5

1NB NM NS ZE PS PM PB

60 3

Plot points

Membership function plot for (CE)

Input variable “error change”−6 −3

Figure 13: Graphical view of the membership function for changeof error signal.

181

0

1

0.5

0.1 0.7

NB NM NS ZE PS PM PB

0.4

Plot points

Output variable “duty cycle”

Membership function plot of (d)

Figure 14: Graphical view of the membership function for dutycycle.

the membership function for error, change of error, and dutycycle of the fuzzy logic controller.

3.2.2. Rule Settings of Fuzzy MPPT. For the rule settingsof fuzzy logic MPPT, different number of subset has beenused. But for this work, seven subset based forty-nine ruleshave been used. The tuning of forty nine rules is quite timeconsuming, but it represents better accuracy and dynamicresponse. The fuzzy rules are included in Table 1.

3.2.3. Surface View of the Fuzzy Functions. Figure 15 illus-trates the surface view of the fuzzy input and output func-tions. From this figure the variation of duty cycle with respect


Table 1: The forty-nine fuzzy rules of the fuzzy system.

𝐸CE

NB NM NS ZE PS PM PBNB ZE ZE ZE NB NB NB NBNM ZE ZE ZE NM NM NM NMNS NS ZE ZE NS NS NS NSZE NM NS ZE ZE ZE PS PMPS PM PS PS PS ZE ZE ZEPM PM PM PM ZE ZE ZE ZEPB PB PB PB ZE ZE ZE ZE

0.7

0.6

0.5

0.4

0.3

0.2

5 0 −5 0.2 0.4 0.6 0.8

Error

Dut

y cy

cle

Error change

Figure 15: Surface view of fuzzy input versus output functions.

to the error (𝐸) and change of error (CE) is observed clearly.This also verifies the proper operation of fuzzy controller.

4. Operation and Design of a Boost Converter

Figure 16 shows the basic circuit configuration of a boostconverter, where 𝑉

𝑔is the dc input voltage, 𝐿 is the boost

inductor, 𝑆 is the controlled switch, 𝐷 is a diode, 𝐶 is a filtercapacitor, and 𝑅 is the load resistance. Boost converter worksin two states. When the switch 𝑆 is open, current in the boostinductor increases linearly, and the diode𝐷 is off at that time.When the switch 𝑆 is closed, the energy stored in the inductoris released through the diode to the output 𝑅𝐶 circuit. Thedetails of boost converter has been described in [28, 29].

The main equation associated with duty cycle and input-output voltage of boost converter is given below as follows:

𝑀 =𝑉𝑜

𝑉𝑔

=1

1 − 𝐷. (7)

The rest of the necessary equations related to the design-ing are listed below as follows:

inductor ripple current (peak to peak), Δ𝐼𝐿= (𝑉𝑔∗

𝐷)/(𝑓𝑠∗ 𝐿);

capacitor ripple voltage (peak to peak), Δ𝑉𝑐= (𝐼𝑜∗

𝐷)/(𝑓𝑠∗ 𝐶);

critical value of inductor necessary for the continuousconducting mode, 𝐿

𝑏= (1 − 𝐷

2

)𝐷𝑅/2𝑓𝑠;

L

IL

+

+

−

−Vg S

VL

C

DVo

R

Figure 16: Circuit diagram of boost converter.

minimum value of the filter capacitance that results inthe voltage ripple, 𝐶min = 𝐷/2𝑓𝑠𝑅;

current ripple factor, CRF = Δ𝐼𝐿/𝐼𝐿;

voltage ripple factor, VRF = Δ𝑉𝑜/𝑉𝑜.

The values of the components obtained from the equationsare associated with the practical implementation of the con-verter. Such as, for continuous current operation of circuit,the value of inductor 𝐿 > 𝐿

𝑏, and to limit the output voltage

ripple the condition 𝐶 > 𝐶min should be satisfied. Besides,Δ𝐼𝐿and Δ𝑉

𝑐are related to CRF and VRF. The value of these

two terms should not exceed 30% and 5%, respectively.The specifications of the necessary components selected

for this work are listed below.

(1) Boost inductor = 290 𝜇H(2) Input filter capacitor = 250 𝜇F(3) MOSFET IRS045(4) Resistive load = 35Ω (SOLKAR), 22Ω (BPMSX), and

13Ω (KC85T).(5) Output filter capacitor = 330 𝜇F(6) Switching frequency = 10 kHz.

5. Simulation Results and Discussion

The complete setup of the system for data collection, whichincludes PV module, boost converter, fuzzy based MPPT,and DC load, has been given below. Figure 17 represents thecomplete view of the system.

In Table 2 resultant data obtained from the proposedsystem for various irradiations are tabulated. From the tableit is clear that at S.T.C (25∘C and 1000W/m2) the obtainedmaximum power 𝑃max = 37.02W for SOLKAR 36W, 𝑃max =57.45W for BP MSX 60W, and 𝑃max = 86.52Wfor KC85T87W. At the same time company specified maximum powerof these threemodule are 37.04W, 58W for 87W, respectively.The negligible deviation between the obtained and specifiedvalues ensures validity of the developed PV module.

Figures 18 and 19 represent the response of the duty cyclewith respect to the variation in irradiation level. At 𝑡 = 0.05irradiation is 𝑆 = 400W/m2 and duty cycle 𝐷 = 0.1; from𝑡 = 0.05 to 𝑡 = 0.15 the level of irradiation is constant at 𝑆 =1000W/m2, for this period value Duty cycle 𝐷 = 0.7 is also


PWM generator

Variable irradiations

Temperature

Number of

Number of

series cells

parallel cells

Fuzzy based Mppt algorithm

Current measurement Current measurementDiode

Voltagemeasure

Output current display

Output voltage display

Output power display

Duty cycle scope

PV m

odul

e

Duty cycleInput current

Input voltage

G

T

Ti

Np

Np

Ns Ns

S

S

D

−

−

V

+ +i−+

−

+

V

250𝜇

f

330

𝜇f

Output current, voltage,and power scope3

5Ω

290𝜇H

Figure 17: Complete system implementation in Simulink for data analysis.

Table 2: The resultant output voltage, current, and power at different irradiation for standard test temp (25∘C) for the selected three PVmodules.

Irradiation at25∘C temp.

SOLKAR-36 W PV module BP MSX-60 W PV module KYOCERA KC85T-87 W PV moduleMaximumcurrent(𝐼max)

Maximumvoltage(𝑉max)

Maximumpower(𝑃max)

Maximumcurrent(𝐼max)



Maximumcurrent(𝐼max)



1000W/m2 1.029 36 37.02 1.739 33.04 57.45 2.527 34.238 86.52800W/m2 0.932 32.6 30.4 1.48 28.11 41.6 2.111 27.44 57.92500W/m2 0.624 21.85 13.64 0.9399 17.86 16.79 1.348 17.53 23.63300W/m2 0.3754 13.14 4.93 0.5642 10.72 6.048 0.8017 10.42 8.532

0.2Time (s)

0.05 0.15

400 400 W/m2

1000 1000 W/m2

700

Variable irradiation

S(W

/m2)

Figure 18: Variable irradiation with respect to time to observe thevariation in duty cycle.

constant. After that irradiation goes down to 𝑆 = 400W/m2and duty cycle again goes down to𝐷 = 0.1 at 𝑡 =∼ 0.15, whichdemonstrates the dynamic performance of the system.

Figure 20 represents the curve for variable irradiation,and Figure 21 to Figure 23 represent the voltage, current, and

0.1

1

0.5

0.20.160.06

Variation induty cycle

Time (s)

Dut

y cy

cle (d

)

Figure 19: Variation in duty cycle with respect to irradiations.

power tracking curves for the three PVmodules. In Figure 21for SOLKAR 36W it has been shown that, at 𝑡 = 0.06 s,irradiation 𝑆 = 500W/m2, and obtained power𝑃= 13W, thenirradiation goes from 𝑆 = 500W/m2 to 𝑆 = 1000W/m2 and itcontinues until 𝑡 = 0.15 s; from the tracking curve it is shownthat power for this period is 𝑃 = 36W; again at 𝑡 = 0.15 s,


Table 3: Standard test condition (STC) specification of the PV modules.

Parameter SOLKAR 36W BP MSX 60W KC85T 87WMaximum rated power (𝑃max) 37.08W 58W 87WMaximum voltage (𝑉mp) 16.56V 17.1 V 17.4VMaximum current (𝐼mp) 2.25A 3.5 A 5.02AOpen-circuit voltage (𝑉oc) 21.24V 21.1 V 21.7 VShort-circuit current (𝐼scr) 2.55 A 3.8 A 5.34A

0.20.150.05Time (s)

Variable irradiation

S(W

/m2)

1000 W/m2

800 W/m2

400

1000

700

Figure 20: Variable irradiation with respect to time to observe thetracking capability.

Time (s)

Time (s)

Time (s)

40

30

20

0.5

1

1.5

15

25

40

0.20.10.05 0.15

0.20.10.05 0.15

0.20.10.05 0.15

SOLKAR 36 W

SOLKAR 36 W

SOLKAR 36 W

P(W

)I

(A)

V(V

)

≅ 37W

Figure 21: Power, voltage, and current tracking of SOLKAR 36W.

BP MSX 60W

BP MSX 60W

BP MSX 60W

P(W

)

0.5

1

2

≅ 58W

Time (s)

Time (s)

Time (s)

60

40

30

15

25

40

0.20.10.05 0.15

0.20.10.05 0.15

0.20.10.05 0.15

I(A

)V

(V)

Figure 22: Tracking of maximum power, voltage, and current withrespect to different irradiations for BP MSX 60W.

radiation goes down to 𝑆 = 800W/m2 and power also goesdown to 𝑃 = 30W.

Figures 22 and 23 show the similar results for BP MSX60W and KC85T 87W. These values coincide with theobtained result of Table 2. So, the equality between the graphsand table also ensures the validity of the proposed system.

6. Conclusion

A versatile and efficient modeling technique of PV modulewith a fuzzy logic basedMPPT system has been implementedin this paper.Themain objectives of this paper were to reducethe complexity of PV modeling and to implement the fuzzytechnique in a simple way to control the duty cycle directly.The proposed modeling technique and MPPT algorithm hasbeen applied for three specified PV modules with a boostconverter. The data obtained from the prototype were foundto be very close to the theoretical prediction. The graphical


Time (s)

Time (s)

Time (s)

90

50

30

1

2

3

15

25

40

0.20.10.05 0.15

0.20.10.05 0.15

0.20.10.05 0.15

P(W

)

KC85T 87W

KC85T 87W

KC85T 87W

I(A

)V

(V)

≅ 87W

Figure 23: Tracking of maximum power, voltage, and current withrespect to different irradiations for KC85T 87W.

representation with respect to various environmental con-ditions demonstrates the tracking capability and dynamicresponse of the system with precise control of the duty cycle.So, it can be concluded that application of this system willenhance the PV system efficiency with a significant reductionin system cost. Not only that, this model can also be usedas a fundamental stage for a grid connected PV plant, solarpumping system, and smart grid PV interconnection system.

Nomenclature

𝑉pv: The output voltage of the PV module (V)𝑇𝑟: The reference temperature = 298K

𝐼ph: The light generated current in a PVmodule (A)

𝐴 = 𝐵: Ideality factor = 1.6𝑞: Electron charge = 1.6 × 10−19 C𝐼scr: The PV module short-circuit current at

25∘C and 1000W/m2𝐾𝑖: The short-circuit current temperature

coefficient𝐸𝑔: The band gap for silicon = 1.1 eV

𝐾V: The open-circuit voltage temperaturecoefficient

𝐼pv: The output current of the PV module (A)𝑇: The module operating temperature in

Kelvin

𝐼𝑜: The PV module saturation current (A)

𝑘: Boltzman constant = 1.3805 × 10−23 J/K𝑅𝑠: The series resistance of the PV module

𝑆: The PV module illumination (W/m2)𝑁𝑠: The number of cells connected in series

𝑁𝑝: The number of cells connected in parallel

𝑉oc: The open circuit voltage.

Acknowledgments

The authors would like to acknowledge the financial supportfrom the High Impact Research Grant (HIRG) scheme(UM-MoHE) project no.: UM.C/HIR/MOHE/ENG/24) andproject no.: (UM.C/HIR/MOHE/ENG/21) to carry out thisresearch.

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