 Open Access
 Total Downloads : 331
 Authors : Taoufik Laagoubi, Mostafa Bouzi, Mohamed Benchagra
 Paper ID : IJERTV4IS110184
 Volume & Issue : Volume 04, Issue 11 (November 2015)
 Published (First Online): 19112015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Analysis and Comparaison of MPPT Nonlinear Controllers for PV System using Buck Converter
T. Laagoubi, M. Bouzi Univ. Hassan 1,
FacultÃ© des Sciences et Techniques, Laboratoire IMMII,
Settat, Morocco
M. Benchagra Univ. Hassan 1,
Ecole Nationale des Sciences AppliquÃ©es, Laboratoire LISERT, Khouribga, Morocco
Abstract This paper describes a maximum power point tracking (MPPT) approach in photovoltaic system based on sliding mode control (SMC) and fuzzy logic control (FLC). Due

Photovoltaic cell

PV ARRAY
to the nonlinear output characteristic, fuzzy control and Sliding Mode Control are introduced to realize MPPT. The simulation is carried out based on proposed algorithm. Compared with the conventional duty cycle of perturb and observe (P&O) control method, they can track de maximum power point quickly and accurately. For simulation, a simulation model in Simulink/Matlab of a solar cell has been presented. A buck converter has been used to control the solar cell output voltage. The MPPT control the duty cycle of the buck converter.
Keywords MPPT; Solar Energy; Photovoltaic; PV; DCDC Converters; buck converter; Nonlinear Control; perturb and Observe; Fuzzy Logic Control; Sliding Mode Control Introduction

INTRODUCTION
Solar energy is the conversion of the energy from the sun to usable electricity. The most common source of solar energy utilizes photovoltaic cells to convert sunlight into electricity. Photovoltaic utilize a semiconductor to absorb the radiation from the sun, when the semiconductor absorbs this radiation it emits electrons, which are the origin of electricity.
Photovoltaic cell is the most basic of a PV modules. Solar cell consist of a PN junction fabricated in a layer semiconductor. The currentvoltage ( ) and power voltage ( ) outputs characteristics of solar cell is similar to that of a diode[1][3]. Under sun, photons with energy greater than the bandgap energy of the semiconductor are absorbed and great an electronhole pair and create a current proportional to the irradiation.
The performance of a photovoltaic cell is usually presented by its () curve and () which is produced for several irradiation levels and several cell temperature levels.
The variation of current versus voltage curve is shown in Fig.1 under various irradiation levels (200, 500 and 800W/mÂ²). For each irradiation, the maximum power point (MPP) is such that the area defined by is maximum.
1
MPP – 800W/mÂ²
Normalized current
0.8
Solar energy has extraordinary advantages when compared with other source. The field of photovoltaic (PV) solar energy has experienced a remarkable growth for past two decades. However, Maximum Power Point Tracking (MPPT) control is an essential part of a PV system to extract maximum power from the PV [1][3].
0.6
0.4
0.2
0
MPP – 500W/mÂ²
MPP – 200W/mÂ²
In recent years, a large number of techniques has been developed and implemented for tracking the Maximum Power Point (MPP) [4][6].
Fuzzy and sliding mode controls is two nonlinear robust MPPT approach. In this work we propose a comparison between the two controllers and Perturb and Observe (P&O) MPPT method and we will take an interest in the transitional regime.
In the second paragraph, we present a photovoltaic cell with different curve of voltage output, current output and power output for various climatic conditions.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized voltage
Fig. 1. Variation of normalized current vs voltage curve of PV array
The variation of power versus voltage curve is shown in Fig.2 for various irradiation levels (200, 500 and 800W/mÂ²).
The output power has a maximum at a output voltage .
When the irradiation increases the maximum power increases.
1
0.8
MPP – 800W/mÂ² MPP – 500W/mÂ²
Where
V = kbT
t
e
Normalized power
0.6
0.4
0.2
0
MPP – 200W/mÂ²
: output current of solar cell (A)
: photocurrent current passing PN junction (A)
0 : reverse saturation current of PV (A)
: output voltage of solar cell (V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized voltage
Fig. 2. Variation of normalized power vs voltage curve of PV array
The variation of current versus voltage curve under various temperature of solar cell(253545Â°C) is shown in Fig.3. The maximum power decreases as the temperature increases.
1
Normalized Current
0.8
45Â°C
: number of cells
: diode quality
: series resistance ()
: shunt resistance ()
: electron charge (C)
: Boltzmanns constant (. 1 )
: temperature of solar cell (K)
: thermal voltage (V)
0.6
0.4
0.2
0
35Â°C
25Â°C
We have used Matlab/simulink to implement the model of the solar PV panel.
The equivalent circuit of equation (1) is presented schematically in Fig.5 with a DC voltage generator which models the photocurrent, a diode which models the
0 0.2 0.4 0.6 0.8 1
Normalized voltage
Fig. 3. Variation of normalized current vs voltage curve of PV array
The variation of power versus voltage curve is shown in Fig.4 for various solar cell temperature. The maximum power decreases when solar cell temperature increases.
semiconductor and two resistors which models the escape currents.
0.8
0.7
Normalised power
0.6
0.5
0.4
0.3
25Â°C
45Â°C
35Â°C
Where
Fig. 5. Simulink model of the solar PV model
0.2
0.1
0
0 0.2 0.4 0.6 0.8 1
Normalised voltage
Fig. 4. Variation of normalized power vs voltage curve of PV array
We can observe that low solar irradiance and high cell temperature will reduce the power conversion capability.



Simulink model of the solar PV model
The above characteristics can be deduced from a mathematical model.
The general mathematical expression for the illuminated () curve for a solar panel is given by the following one exponential equation [1]
: diode current
: shunt resistance
: series resistance
The key specification of PV module are shown in Table I.
At temperature 
25 
Â°C 

Open circuit voltage 
21.6 
V 

Short circuit current 
1.31 
A 

Voltage, maximum power 
17.0 
V 

Current, maximum power 
1.18 
A 

Maximum power 
20.0 
W 
TABLE I. PV MODULE PARAMETERS
I = i I [exp ( Vpv+IpvRs) 1] Vpv+IpvRs
pv pv 0
NsVt
Rsh
To properly use a PV module, it must operate in its maximum power point MPP. Next paragraph describe how tracking the maximum power point.

MAXIMUM POWER POINT TRACKING
The goal of the MPPT is to find the maximum power

DCDC CONVERTERS MODELING
The MPPT algorithm, control the duty cycle of a buck converter[14]. Fig.8. shows a buck converter model in Simulink.
k
under different operating conditions, i.e. the different g m
temperature and irradiation values. C E
Fig.6. shows the variation of normalized power versus normalized voltage curve under different irradiation (200, 400, 600, 800, 1000W.mÂ²) and the maximum power point curve.
L
1
0.9
0.8
Normalized power
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Maximum Power Point
Fig. 8. Buck converter Simulink model
The buck converter can be written in two sets of state equation depends on the duty cycle equations (8) and (9)
The buck converter operate in two state. If the IGBT is on or off, if it is on, the diode is blocked so the buck converter Simulink model is equivalent to the circuit shown in Fig.9.
1 L
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized voltage
Fig. 6. Maximum power point
01
The problem considered by MPPT techniques is to automatically find the corresponding duty cycle for voltage
or current at which a PV array should operate to obtain the maximum power point output under a given irradiation and temperature [1][3].
Fig.7. shows MPPT system where is PV voltage, is
Fig. 9. Buck converter equivalent circuit when IGBT is on.
The system can be written in two equations :
dV01 = iL1 V01
dt C
CRL
PV current, is the load voltage, is the load current and
is a duty cycle.
L
o a d
DCDC
Converter
And
diL1 = Vpv V01
dt L L
PV Panel
If the IGBT is off, the diode is conducting so the buck converter Simulink model is equivalent to the circuit shown in Fig.10.
MPPT
Algorithm
2 L
PWM
02
Fig. 7. MPPT system
The MPPT system contains five elements which are the PV load, DCDC converter, load, the Pulse width Modulation (PWM) and the MPPT algorithm.
Fig. 10. Buck converter equivalent circuit when IGBT is of.
The system can be written in to two equation :
The following paragraph describing the DCDC buck converter.
dV02 =
dt
iL2
C
V02 CRL
And
diL1 = V01
( 1) : previous output power
( 1) : previous output voltage
dt L
The buck converter can be written in two sets of state equation depends on the duty cycle :
( 1) : previous error
( 1) : previous change error
Table II shows the rule table of fuzzy controller,
And
dV0 = iL VL
dt C CRL
where all the entries of matrix are fuzzy sets of error E, change of error CE and duty cycle D [9].
E\CE
NB
NS
ZE
PS
PB
NB
ZE
ZE
NB
NB
NB
NS
ZE
ZE
NS
NS
NS
ZE
NS
ZE
ZE
ZE
PS
PS
PS
PS
PS
ZE
ZE
PB
PB
PB
PB
ZE
ZE
TABLE II. FUZZY RULE BASE TABLE
diL = Vpv D V0
dt L L
If the IGBT is on = 1, and if it is of = 1

MPPT ALGORITHMS
This paragraph describing three MPPT algorithms which are the Fuzzy logic , sliding mode and perturb and observe controls.

Fuzzy logic control
Fuzzy logic controller have the advantage to working with imprecise inputs, not needing an accurate mathematical model, and handling nonlinearity[7][10].
Fuzzy logic controller generally consists of three stages: fuzzification, rules base table lookup, and defuzzification. During fuzzification, numerical input variables are converted into linguistic based on membership function similar to Fig.11. In this case five fuzzy levels are used : NB (Negative Big), NS (Negative Small), ZE(Zero), PS (Positive Small) and PB (Positive Big).
NB NS ZE PS PB
If, for example, the operating point is far to the left to the maximum power point (MPP) that is E is PB and CE is ZE, then we need to largely increase the duty cycle, that D should be PB to reach the MPP.
To explain the steps to follow to determine how the fuzzy logic controller operate, we take an example of an operating point. Which the membership of error and changing error is shown in Fig.12. and Fig.13.
NB NS ZE PS PB
1
0.6
0.4
0
b a 0 a b
PS.
Fig. 12. Membership function for error E
We read, the error E is sixty percent ZE and forty percent
Fig. 11. Membership function for inputs and output of fuzzy controller
The inputs to a MPPT fuzzy logic controller are usually an error and a change error .
1
0.8
NB NS ZE PS PB
E(n) = P(n)P(n1)
V(n)V(n1)
0.2
CE(n) = E(n) E(n 1)
Where
() : actual output power
() : actual output voltage
() : actual error
() : actual change error
0
Fig. 13. Membership function for changing error CE
In this example changing error is 80% NS and 20% NB. From fuzzy rules base table, we have :
is 60% ZE and is 80% NS, is 60% ZE
is 60% ZE and is 20% NB, is 20% NS
is 40% PS and is 80% NS, is 40% PS
is 40% PS and is 20% NB, is 20% PS In result,
is 60% ZE, 20% NS and 40% PS
Then the membership function for duty cycle is shown
In Simulink we use the bloc shown in Fig.16.[10]
E CE
I V
Fuzzy logic controller
Fig. 16. Simulink bloc for fuzzy logic controller

Sliding mode control
in Fig.14.
1
0.6
0.4
0.2
NB NS ZE PS PB
Fig. 14. Membership function for duty cycle D
The advantage of sliding mode controller are various and important : high precision, good stability, simplicity, invariance, robustness [11],[13], [14].
A typical sliding mode control has two modes of operation. One is called the approaching mode, where the system state converges to a predefined manifold named sliding function in finite time. The other mode is called the sliding mode, where the system state is confined on the sliding
surface and is driven to the origin. In this study, we introduce the concept of the approaching control approach. By selecting
The last stage of fuzzy logic controller is the
defuzzification that converts the fuzzy duty cycle into numerical duty cycle proportional to the black area in fig.14.
The algorithm of the fuzzy logic controller is as follows. The actual voltage and current of PV array can be measured continuously and the power can be deduced by calculation,
the sliding surface as = 0, it is guaranteed that the system
state will hit the surface produce maximum power output persistently [11],[13].
The expression of sliding surface is :
pv
then, the error and changing error can be calculated and
Ppv = I2 Rpv = I
(2R
+ I Rpv
) = 0
<>converted into linguistic variables based on membership function, so, the linguistic duty cycle can be converted into
Ipv
Ipv pv
pv pv Ipv
numerical variables based on fuzzy rules then, the duty cycle can be converted by defuzzification. Fig.15. shows the fuzzy logic controller algorithm.
Where
PV.
=
is the equivalent load connect to the
Start
The nontrivial solution of Eq (11) is :
Set ,
2Rpv + I
Rpv = 0
pv
Ipv
() = ; () =
The sliding surface is defined as :
= 2Rpv
Rpv
+ I
PV Ipv
Fuzzification
Calculate E(n), CE()
The buck converter can be written in two sets of state equation depends on the duty cycle D : (7) and (8). Which can be combined into one set of state equation to represent the dynamic of system :
Rules
= (1 D)X 1 + DX 2
Defuzzification
Based on the observation of duty cycle versus operation region as depicted, the duty cycle output control can be chosen as :
Output
= { + > 0
( 1) = ; ( 1) =
< 0
Equivalent control is determined by condition
dipv
Return
Fig. 15. Algorithm for fuzzy logic controller
= [
]
= 0
dt
The equivalent control is derived :
[ TFig.18. shows the P&O algorithm [15].
Start
D =
dX] f(X) = VPV
[eq T VL dX] g(X)
Finally The control is given by :
1 + 1
= { + 0 + 1 0 + 0
where k is a positive constant
Set out
Measure ,
= ++
=
The duty cycle of sliding mode controller is determined by the operating point. As the operating point is to the left of maximum power point (MPP), the sliding surface is negative so the duty cycle decrease. The same the duty cycle increase if the operating point is in the right of MPP.Fig.17.
1
MPP
>
Yes
=
No
Normalised power
0.8
0.6
0.4
0.2
0
0
<0 <0
D decrease D increase
High duty cycle Low duty cycle
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalised voltage
Fig. 17. Duty cycle versus operation region
Fig. 18. Algorithm for P&O controller


SIMULATION RESULTS
The MPPT simulation results present the response of a PV array with different MPPT approach : fuzzy logic, sliding mode and P&O controllers.
Fig.19 shows the power response obtained using Fuzzy logic(FL) and Sliding mode(SM) controllers based MPPT and Perturb & Observe algorithm. From the above results it seems that the PV power which is controlled by the proposed SM

Perturb and observe (P&O) control
There have been extensive applications of the P&O MPPT algorithm in various types of PV system. This is because P&O algorithm has a simple control structure and few measured parameters are required for the power tracking. Moreover, it has an advantage of not relying on the PV module characteristics in the MPPT process and so can be easily applied to any PV panel. The name of algorithm itself reveals that it operates by periodically perturbing the control variable and comparing the instantaneous PV output power after
Controller is more stable than FL and P&O MPPT techniques. The power curve obtained with SM is smoother when compared to FL and P&O algorithms. Fig.20 shows the output voltage of buck converter using Fuzzy Logic, SM, FL and P&O Controllers.
20
15
perturbation with that before. The outcome of the PV power comparison together with the PV voltage condition determines the direction of the next perturbation that should be used.
The simplicity of perturb and observe method make it the most commonly used MPPT algorithm in commercial PV
10
Power
Fuzzy logic
5
Sliding mode
0
P&O
products. It is easy to implement.
This is essentially a trial and error method. The PV controller increase the reference for the inverter output power by a small amount, and then detect the actual output power. If the output power is indeed increased, it will increase again until the output starts to decrease, at which the controller decreases the reference avoid collapse of the PV output due to the highly nonlinear PV characteristic [4],[5],[12].
0 0.05 0.1 0.15 0.2 0.25
Time
Fig. 19. Power output under step changing irradiation for P&O, Fuzzy and Sliding mode MPPT methods
10 REFERENCES
8
Voltage
6 Fuzzy logic P&O 4
Sliding mode
2
0
0 0.05 0.1 0.15 0.2 0.25
Time
Fig. 20. Voltage output under step changing irradiation for P&O, Fuzzy and Sliding mode MPPT methods


CONCLUSIONS
In this paper, three method for MPPT (Fuzzy logic, Sliding mode and P&O). Three of them have been applied to an energy conversion chain by DCDC buck converter. We compared the simulation results obtained by subjecting the system to the same controlled environmental conditions.
It is concluded that the overall model in Simulink/Matlab is satisfactory for simulation purposes.
Even if, in transitional regime, the sliding mode present a delay due to the calculation step, it respond quickly.
All this algorithm converge to desirable output. Sliding mode controller exhibits fast dynamic performance and stable response, response of fuzzy logic controller is fast and stable than P&O controller but is slow and not as stable as sliding mode controller.
The response of sliding mode controller is better than fuzzy logic and Perturb and observe controllers, but it requires too many calculation and system equations. In contrast, the fuzzy logic controllers is easy to introduce, it does not require the system equations. Both of them is fast than P&O controllers.

C. Protogeropoulos, B. J. Brinkworth, R. H. Marshall, B. M. Cross: Evaluation of two theoretical models in simulating the performance of amorphous silicon solar cells, In: 10th European Photovoltaic Solar Energy Conference, 812 April 1991 Lisbon, Portugal.

VandanaKhanna, Bijoy Kishore Das, Dinesh Bisht: Matlab/Simelectronics Models Based Study of Solar Cells. In: International Journal of Renewable Energy Research Vandana Khanna and al., Vol.3, No.1, 2013

Wail REZGUI, Leila Hayet MOUSS & Mohamed Djamel MOUSS: Modeling of a photovoltaic field in Malfunctioning. In: Control, Decision and Information Technologies (CoDIT), 2013 International Conference.

Trishan Esram, Patrick L. Chapman, Comparaison of photovoltaic array maximum power point tracking techniques. In: IEEE Transactions on Energy Conversion, Vol. 22, No. 2, June 2007.

Ali Nasr Allah Ali, Mohamed H. Saied, M. Z. Mostafa, T. M. Abdel Moneim: A Survey of Maximum PPT techniques of PV Systems. In: 2012 IEEE Energytech.

C. Liu, B. Wu and R. Cheung: Advanced Algorithm for MPPT Control of Photovoltaic Systems, In: Canadian Solar Buildings Conference Montreal, August 2024, 2004

GARRAOUI Radhia, Mouna BEN HAMED, SBITA Lassaad: MPPT Controller for a Photovoltaic Power System Based on Fuzzy Logic, In: 2013 10th International MultiConference on Systems, Signals & Devices (SSD) Hammamet, Tunisia, March 1821, 2013.

Lixia Sun, Zhengdandan, Fengling Han: Study on MPPT Approach in Photovoltaic System Based on Fuzzy Control In: Industrial Electronics and Applications (ICIEA), 2013 8th IEEE Conference.

C.Y. Won, D.H. Kim, S.C. Kim, W.S. Kim, and H.S. Kim A new maximum power point tracker of photovoltaic Arrays Using Fuzzy Controller, In: Proc. 25th Annu. IEEE Power Electron. Spec. Conf., 1994, pp. 396403.

M.S. KHIREDDINE, M.T. MAKHLOUFI, Y. ABDESSEMED, A. BOUTARFA: Tracking power photovoltaic system with a fuzzy logic control strategy, In: Computer Science and Information Technology (CSIT), 2014 6th International Conference.

ChenChi Chu, ChiehLi Chen: Robust maximum power point tracking method for photovoltaic cells : A sliding mode control approach, In: Solar Energy 83 (2009) 13701378.

D. Rekioua , A.Y.Achour, T. Rekioua: Tracking power photovoltaic system with sliding mode control strategy, In: Energy Procedia 36 – 219 230, 2013

Samer Alsadi, Basim Alsayid: Maximum power point tracking simulation for photovoltaic systems using perturb and observe algorithm, In: International Journal of Engineering and Innovative Technology (IJEIT), Volume 2, Issue 6, ISSN: 22773754, 2012.

SiewChong Tan, Y. M. Lai, Martin K. H. Cheung, and Chi K. Tse: On the Practical Design of a Sliding Mode Voltage Controlled Buck Converter, In: IEEE Transactions on Power Electronics, Vol. 20, No. 2, March 2005.

JoeAir Jiang, TsongLiang Huang, YingTung Hsiao and ChiaHong Chen: Maximum Power Tracking for Photovoltaic Power Systems, In: Tamkang Journal of Science and Engineering, Vol. 8, No 2, pp. 147_153 (2005).