Fuzzy Logic Neuron

Energy Procedia 12 (2011) 538 – 546

1876-6102 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of University of Electronic Science and Technology of China (UESTC).doi:10.1016/j.egypro.2011.10.073

Available online at www.sciencedirect.com

Energy Procedia

Energy Procedia 00 (2011) 000-000

www.elsevier.com/locate/procedia

ICSGCE 2011: 27–30 September 2011, Chengdu, China

Maximum Power Point Tracking of Photovoltaic Generation Based on the Type 2 Fuzzy Logic Control Method

Amir Gheibi*, S.M.A.Mohammadi, M.maghfoori

The Electrical Engineering Department, Shahid Bahonar University of Kerman, Iran.

Abstract

According to a nonlinear current-voltage characteristic Photovoltaic for exploitation of this optimization we need to track maximum output instantly. The aim of this paper is to search maximum power point (MPP) Based on the Type2 Fuzzy logic controller (T2FLC) which is a novel method in maximum power point tracking (MPPT). Solar cells’ MPP varies with solar insolation and ambient temperature. With the improved efficiencies of power electronics converters, it is now possible to operate photovoltaic (PV) power systems at its MPP in order to improve the overall system efficiency. This paper presents a T2FLC method for tracking MPP in photovoltaic power systems and the control system is established simultaneously. The results of simulation show that the T2FLC significantly improves the robustness of controller’s PV during the tracking phase as compared to a conventional type1 fuzzy logic control (T1FLC) in present of noise in photovoltaic power systems. This noise maybe insert to system when voltage and current are measured. We show that the results obtained with T2FLC are better than the ones obtained with the T1FLC method.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of ICSGCE 2011

Keywords: Boost converter; MPPT; Photovoltaic; Solar cell; Type2 FLC

1. Introduction

Solar energy, as an emerged green energy resource with characteristics of copiousness, cleanness, environmental protection and no territorial restrictions and so on, is widely used. The Photovoltaic (PV) arrays produce electric power directly from sun light. Due to their initial high costs, solar cells have not yet been an attractive alternative for electricity users who are able to buy cheaper electrical energy from the utility grid. PV gives the well-known nonlinear relationship between the current and voltage of the PV

* Corresponding author. Tel.: +986613228124.E-mail address: [email protected].

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of University of Electronic Science and Technology of China (UESTC).

Amir Gheibi et al. / Energy Procedia 12 (2011) 538 – 546 5392 Amir Gheibi et al. / Energy Procedia 00 (2011) 000-000

cells; it can be observed that there is a unique point, under given illumination, at which the cell produces maximum power, That’s why it’s be called MPP. This point occurs when the rate of change of the power with respect to the voltage is equal to zero. Because the output characteristic of the solar cells varies with the environments, conversion efficiency of the solar cells is relatively low; getting some benefits from the converted energy by solar cells as much as possible becomes a key issue in the solar energy utilization. The Boost converters are widely used in PV generation as an interface between the PV panel and the load, allowing the follow-up of the MPP. Based on concept, a kind of maximum power point tracking (MPPT) technology is suggested. Many MPPT techniques have been proposed, they can be categorized as: The methods based on a algorithm for example perturbation and observation (P&O)methods [15]-[18]

and IC that measured cell characteristics ( current, voltage, power) are employed along with an online search algorithm to compute the corresponding MPP independent of insolation, temperature . Intelligent controlling methods [1]-[6]-[13]-[14]. Consist of fuzzy logic control (FLC) and Adaptive

fuzzy logic control (AFLC) and Artificial neural network (ANN). Computational method [16]-[21].Characteristics of solar cells is modeled using mathematical

equations or numerical approximations. The model most be valid under different insolations, temperature, and degradation conditions.

The model which we considered in this paper is based on type2 fuzzy logic control (T2FLC). The concept of a type2 fuzzy set was introduced by Zadeh [11]. This controller considers uncertainty of the model which is characterized by membership functions (MFs) that are they fuzzy. FLCs are usually constructed using type1 fuzzy sets. Such FLCs have been applied to many areas, especially for the control of complex nonlinear systems that are difficult to model analytically. Despite their popularity, research has shown that type1 FLCs may have difficulties in modeling and minimizing the effect of uncertainties. The quantification of the degree of uncertainty in a system depends on the type of uncertainty one is trying to measure and on the particular measure selected for that type of uncertainty.

2. The Characteristic of a PV

The relationship between output voltage and current of the solar cell at same light intensity and temperature as depicted in Fig.1. It can be observed that under a certain light intensity and temperature there is a unique point located at the knee of the I-V curve, at which the MPP can be generated from the PV. Boost converter is used to have MPP of PV. This controller placed between PV and load. But MPP varies with changing temperature and sun light intensity. Fig.1 shows these variations.

0 5 10 15 20 250

10

20

30

40

50

60

Voltage (V)

P o

w e

r (W

)

1000 W/m2

800 W/m2

600 W/m2

T =25oC

0 5 10 15 20 250

10

20

30

40

50

60

Voltage (V)

P o

w e

r (W

)

60 oC

40 oC

25 oC

S =1000 W/m2

(a) (b)

Fig.1. Variations of MPP with changing: (a) isolation (b) temperature

540 Amir Gheibi et al. / Energy Procedia 12 (2011) 538 – 546Amir Gheibi et al. / Energy Procedia 00 (2011) 000-000 3

3. Type1 Fuzzy Logic Controller

This controller has been applied to photovoltaic systems in many papers since now [4]-[10]. Type1 fuzzy logic controller is made of fuzzification, knowledge and inference unit, defuzzification and the membership function of the inputs and output are indicated in Fig. 2. The fuzzy control requires that variable used in describing the control rules has to be expressed in terms of fuzzy set notations with linguistic labels. The rule base that associates the fuzzy output to the fuzzy inputs is derived by understanding the system behavior.

After the rules have been evaluated, the last step to complete the fuzzy control algorithm is to calculate the crisp output of the fuzzy control with the process of defuzzification. The implementation of the fuzzy controller in terms of type1 and type2 fuzzy sets has two input variables; the error ( )e t and the error

variation )(te∆ , given by:

( )( )

( )

p te t

v t

∆=∆

, ( ) ( ) ( 1)e t e t e t∆ = − − (1)

Fig.2. Structure of a type1 FLC

4. Type2 fuzzy logic controller

A T2FLC composed of four basic elements (Fig.3): the type1 fuzzyfier, the fuzzy rule-base, the inference engine, and the type1 defuzzyfier. The fuzzy rule-base is a collection of rules, which are combined in the inference engine, to produce a fuzzy output. Table1 shows these rule bases with Lower Standard Deviation (LSD) and Upper Standard Deviation (USD) which are one of important characteristics of T2FLC[19]-[20],which these shows in Fig. 4. The type1 fuzzyfier maps the crisp input into type1 fuzzy sets, which are subsequently used as inputs to the inference engine, whereas the type1 defuzzyfier maps the type1 fuzzy sets produced by the inference engine into crisp numbers.

A T1FLCs are unable to handle rule uncertainties directly, because they use type1 fuzzy sets that are certain. On the other hand, T2FLCs are very useful in circumstances where it is difficult to determine an exact, and measurement uncertainties [8]. It is known that type2 fuzzy set let us to model and to minimize the effects of uncertainties in rule base FLC. Unfortunately, type2 fuzzy sets are more difficult to use and understand than type1 fuzzy sets; hence, their use is not widespread yet.A T2FLC A

~ , is characterized by the membership function:

Knowledge baseRule base

Fuzzification Decision making

Defuzzification

)(te

)(te∆

Crisp inputs

Crisp output

)(tu


( ) ( )( ) [ ]{ }( )

( ) ( ) [ ]

, , , , 0,1

0 , 1

, / , 0,1x

xA

A

xAx X u J

A x u x u x X u J

x u

A x u x u J

µ

µ

µ∈ ∈

= ∀ ∈ ∀ ∈ ⊆

≤ ≤

= ⊆∫ ∫

%

%

%

%

%

(2)

Fig. 3. Structure of a type2 FLC

Hence, a type2 membership grade can be any subset in [0, 1], the primary membership, and corresponding to each primary membership, there is a secondary membership (which can also be in [0, 1]) that defines the possibilities for the primary membership.

This uncertainty is represented by a region called footprint of uncertainty (FOU) which can be described in terms of an upper membership function (UMF) and a lower membership function (LMF) as shown in Fig. 4.

-20 -15 -10 -5 0 5 10 15 200

0.2

0.4

0.6

0.8

1

e(t) and de(t)

M e

m b

e r

s h

i p

f u

n c

t i o

n v

a l

u e

UMF

LMF

N e g a t i v e P o s i t i v eZ e r o

(a)

Fuzzification

Defuzzification

( )e t

)(te∆

Crisp inputs

)(tu

Rule Base

Inference

Fuzzyinput sets

Fuzzyoutput

sets

Type-reducedSet (Type1)

Type-reducer

Crisp output


-20 -15 -10 -5 0 5 10 15 200

0.2

0.4

0.6

0.8

1

u(t)

M e

m b

e r

s h

i p

f u

n c

t i

o n

v

a l

u e

P PG

Z

NNG

(b)Fig.4. membership function: (a) inputs (b) output

4.1. Fuzzification and the Rules

The fuzzifier maps a crisp point ( )1 1 2,..., ....T

p Px x x X X X X= ∈ × × × ≡ into a type2 fuzzy set XA% in

X. As a type2 singleton fuzzifier in a singleton fuzzification with the input fuzzy set having only asingle point on nonzero membership is used, we have:

~

'

'1 11 0Ax

X XX X

µ ∀ == ∀ ≠ (3)

The structure of rules in a T1FLC and a T2FLC is the same. However, in the latter the antecedents and the consequents will be represented by T2FLCs. Suppose a T2FLC has p inputs 1 2, ,......, px x x an output

y, and a multiple input single output (MISO). It is assumed that there are M rules and the lth rule in the type2 FLC can be written as follows:

MlGisythenFisxIFFisxIFR llpp

ll ,...2,1~~

....~

: 11 = (4)

4.2. B. Inference

In T2FLC, the inference engine combines rules and gives a mapping from input T2FLCs to output T2FLCs. It is necessary to compute the join (unions), the meet ∏ (intersections), and the extended

sup-star composition (sup-star compositions) of type2 relations. If~ ~ ~

1 ......l l lPF F A× × = , Eq. (4) can be re-

written as:

~ ~ ~ ~ ~

1: ...... , 1,....,l l l l l lPR F F G A G l M× × → = → = (5)

lR Rule is described by the membership function ( ) ( )1, ,...., ,l l pR Rx y x x yµ µ= where:

( ) ( ) ( ) ( )~ ~ ~ ~1, ,l l l l l

i

PiiR

A G F G

x y x y x yµ µ µ µ=→

= = ∏ ∏ (6)


In general, the p-dimensional input to lR is given by the type2 fuzzy set XA% whose membership

function is:

( ) ( )~ ~1iX

Pii

A XX xµ µ== ∏ (7)

where iX

~ (i=1; . . . ; p) are the labels of the fuzzy sets describing the inputs. Each rule lR determines a

type2 fuzzy set lX

l RAB ~~ = such that:

( ) ( )

( ) ( )

~~

~ , , 1,....,

ll

x

l

x

A oRB

x X RA

y y

X X y y Y l M

µ µ

µ µ∈

= =

∀ ∈ = ∏C

(8)

This equation is the input / output relationship between the T2FSLC that activates one rule in the inference engine and the T2FLC at the output of that engine as described in Fig. 3. In the FLC we used interval T2FLCs and meet under product t-norm, so the result of the input and antecedent operations,

which are contained in the firing set, ( )~1 'l

i

Pii

F

firingSet xµ== ∏ , is an interval T1FLC set :

( ) ( ) ( )' ' , ' ,ll ll lF x f x f x f f = ≡

(9)

where:

( ) ( ) ( )( ) ( ) ( )

~ ~1

~ ~1

' '1

' '1

' *.....*

' *.....*

l l

P

l l

P

lPF F

l

F F P

f x x x

f x x x

µ µ

µ µ

=

= (10)

Note * is the product operation.

4.3. Type-reducer and defuzzification

The type-reducer generates a T1FLC output which is then converted into a crisp output through the defuzzifier. This T1FLC is also an interval set. For the case of our FLC we used center of sets (cos) type reduction, cosY which is given by:

∫ ∫ ∫ ∑∑

∫∈ ∈ ∈

=

=

=

=

∈

==

],[ ],[ ],[ 1

1

],[

cos

111 111

/1........

],[

rlMMMM

rMl

Myyy fff fff

Mi

i

i

Mi

i

ii

yyy

rl

f

yf

yyY (11)

This interval set is determined by its two end points, ly and ry , which correspond to the centroid of

the type2 interval consequent set iG~ expressed as:

1 1

1...... 1/ [ , ]i

N Ny y

Ni ii iil rG

J J i

yC y y

θ θ

θθ=

∈ ∈

= =∑∫ ∫% (12)

Before the computation of cos ( )Y X , we must evaluate (12) , and its two end points, ly and ry . Let the

values of if and iy that are associated with ly are denoted by lif and l

iy , respectively, and the values of

if and iy that are associated with ry are denoted by irf and i

ry , respectively, then from (11), we have:


1

1

M i il li

l M ili

f yy

f=

=

= ∑∑

(13)

1

1

M i ir ri

r M iri

f yy

f=

=

= ∑∑

(14)

From the type-reducer we obtain an interval set )(cos XY , to defuzzify it we use the average of ly

and ry , so the defuzzified output of an interval singleton T2FLS is:

( )2

l ry yy X

+= (15)

Table.1 shows the characteristics of the inputs and output of the T2FLC system with three parameters for tuning (the mean of the inputs' and outputs' membership function (MF)).

Table 1: Characteristics of the Inputs and Output of the T2 Flc

Variable Term Center Lower Standard Deviation Upper Standard Deviation

Input e

Negative Zero

Positive

-Me 0

Me

3.25 5.24

Input delta-eNegative

ZeroPositive

-Mde 0

Mde

3.25 5.24

Output

NGNZP

PG

-Mo-Mo/2

0Mo/2Mo

1.6233 4.6233

In this experiment, the lower and upper standard deviations are fixed.

5. Simulation

By receiving controlling signal from controller, Boost converter kept voltage at a value which has maximum power (Fig. 5). Assume an expected noise is imported to system. Equation (15) shows this noise:

2

2

signal

noise

PsSNR

Pη= =∑∑

(16)

Because most signals have a very wide dynamic range, SNRis usually expressed in terms of the logarithmic decibel scale,

SNR (db):

10( ) 10log signal

noise

PSNR db

P

=

(17)


Usually this noise is imported to system when voltage and current are measured. Noise is applied to system is shown in Fig. 5. We have been exerted noise in T1FLC [7] and have been comparedperformance of T1FLC and T2FLC which was simulated in MATLAB with different SNR is shown on table 2.

Fig. 5. Structure of photovoltaic array with applied noise

Table (2) indicates for a constant value of SNR T2FLC has less error than T1FLC because it coverts more uncertainty. The above applications have demonstrated that T2FLC is better at modeling uncertainties than T1FLC.

Table 2: Compare Between Rates of Error Type1and Type2

∫ )(te

SNR(db) Type1 Type2 34 2.1171 0.1608 44 2.0939 0.1553 54 2.0689 0.1364

Fig. 6 shows MPPT with noise in PV panel.

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

60

Time (s)

P o

w e

r (W

)

0 2 4 6 8 10 12 14 16 18 20

0

10

20

30

40

50

60

Time (s)

P o

w e

r (W

)

(a) (b)Fig. 6. Comparing MPPT with noise in (a)T1FLC (b)T2FLC

6. Conclusion

In this paper we applied T2FLC on photovoltaic panel. We observed it is proper for performance in noisy environments just like these environments. Noise importation is unavoidable .so using controller which is could decrease noise effect is very important. By considering the results of simulation which were achieved in this paper it is noticeable; T2FLC has better operation than FLCT1 whenever noise was present. On the other hand because of its complicating and time consuming calculation T2FLC is slower than T1FLC.


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Fuzzy Logic Neuron