Hopfield Neural Network Optimized Fuzzy Logic Controller for Maximum Power Point Tracking in a Photovoltaic System

Research Article

Hopfield Neural Network Optimized Fuzzy Logic Controller forMaximum Power Point Tracking in a Photovoltaic System

Subiyanto, Azah Mohamed, and Hussain Shareef

Department of Electrical, Electronic, and Systems Engineering, National University of Malaysia, Bangi, 43600 Selangor, Malaysia

Correspondence should be addressed to Subiyanto, biyantote [email protected]

Copyright © 2012 Subiyanto et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper presents a Hopfield neural network (HNN) optimized fuzzy logic controller (FLC) for maximum power point trackingin photovoltaic (PV) systems. In the proposed method, HNN is utilized to automatically tune the FLC membership functionsinstead of adopting the trial-and-error approach. As in any fuzzy system, initial tuning parameters are extracted from expertknowledge using an improved model of a PV module under varying solar radiation, temperature, and load conditions. Thelinguistic variables for FLC are derived from, traditional perturbation and observation method. Simulation results showed that theproposed optimized FLC provides fast and accurate tracking of the PV maximum power point under varying operating conditionscompared to that of the manually tuned FLC using trial and error.

1. Introduction

Because of the demand for electric energy and environmentalissues such as pollution and the effects of global warming,renewable energy sources are considered as an option forgenerating clean energy technologies [1]. Among them, thephotovoltaic (PV) energy from solar radiation has receivedgreat attention, as it appears to be one of the most promisingrenewable energy sources in the world [2]. PV systems havebeen developed to supply clean energy for fulfilling theenergy demand required by the modern society. However, thewidespread use of PV systems poses several challenges suchas increasing the efficiency of energy conversion, ensuringthe reliability of power electronic converters, and meetingthe requirements for grid connection [3]. One step toovercome the problem of low energy conversion efficiencyof PV modules and to get the maximum possible poweris to extract maximum power from the PV system atevery instant of time. To achieve this, it is mandatory tooperate the PV systems close to its maximum power point(MPP). Maximum power point tracking (MPPT) system isan electronic system that plays a vital role in operating thePV modules in a manner that it produces it is maximumpower according to the situation [4]. Many MPPT controlstrategies have been elaborated in the literature, starting with

simple techniques such as voltage and current feedback-based MPPT to more improved power-based MPPT such asthe perturbation and observation (P&O) technique and theincremental conductance technique [5].

Recently, fuzzy logic has been applied for tracking theMPP of PV systems in [6–9] because it has the advantagesof being robust, design simplicity, and minimal requirementfor accurate mathematical model. It is found that fuzzy logic-based P&O and hill climbing MPPT methods perform batterdue to optimized perturbation. However, the fuzzy methodsdepend on careful selection of parameter, definition of mem-bership function, and the fuzzy rules table. Developing fuzzymethod also involves expert knowledge and experimentationin selecting parameters and membership functions. For thisreason, adaptive fuzzy logic control [10] and parameteroptimization techniques such as genetic algorithm [11] andparticle swam optimization [12, 13] have been introduced toovercome the problem in MPPT algorithms.

A number of studies on MPPT have concentrated onthe application of artificial neural network (ANN) [14, 15].In most of these ANN-based methods, large number offield data considering atmospheric conditions are requiredto train the ANN. Moreover, the main problem of ANN-based methods are that it is system dependent and cannot be

4.5

4

3.5

3

2.5

2

1.5

1

0.5

0

Cu

rren

t(A

)

0 20 40 60 80

Voltage (V)

Cell temperature 20◦C1000 W/m2

800 W/m2

600 W/m2

400 W/m2

200 W/m2

(Reference data for 200 watt model)

(a) Effect of irradiation

4.5

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Cu

rren

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Voltage (V)

75◦C50◦C

25◦C

A -1.5, 1000 W/m2M

0◦C

(Reference data for 200 watt model)

(b) Effect of temperature

Figure 1: V-I Characteristic of a typical PV module.

PV arrayDC-DC

converter

Load orother

devices

MPPTcontrolleralgorithm

PW

M

Vpv

Ipv

Figure 2: MPPT controller in a PV system.

Fuzzy rules

InferenceFuzzificationΔDk

Defu zificationzΔPk

pv ΔDk+1ref

Figure 3: Components of a fuzzy logic controller.

implemented for PV arrays with different characteristics. Ina related work, a voltage-based MPPT using ANN has beendeveloped in which an optimal instantaneous voltage factorwas determined from a trained ANN [16]. The inputs of theANN consist of temperature module and solar irradiation.

The combined use of fuzzy logic and ANN to trackmaximum power point in PV systems can be found in[17, 18]. In this method, ANN is trained offline usingexperimental data to define a reference voltage, which is thevoltage at the maximum power point according to the PVarray characteristic. The reference voltage is then comparedto the instantaneous array voltage to generate a signal error.The signal error and change of the error are considered asthe FLC inputs. The FLC generates a duty cycle value for thepulse width modulation (PWM) generator. The PWM is then

I1

I2

Ii

In

w21

N1

N2

Ni

Nn

wi1

wn1

wn2

wni

w2i

w2n

wi2

w1n

w1i

w12

...

...

Figure 4: Discrete Hopfield neural network.

0

1g(λu)

Figure 5: Curve of a sigmoid function.

SP1

SP2SP3

SP4

SP5

SP6

SP7

−10x1 x2 x3

x4

x5 x6 x7

1

ΔPkpv

μΔPk pv

Figure 6: Membership functions coding for ΔPkpv.

SD1SD2

SD3SD4

SD5

SD6

SD7SD8

SD9

z1 z2 z3 z4 z5 z6 z7 z8 z9

μΔDk re

f

ΔDkref

Figure 7: Membership functions coding for ΔDkref.

applied to the switching of the boost converter connected toa PV array. A drawback of this method is that it needs muchdata for offline training.

In this paper, a new variant of intelligent technique isproposed and used together with fuzzy logic-based MPPTcontroller in a PV system. Here, the fuzzy logic MPPTcontroller is integrated with the Hopfield neural network(HNN) to optimize the membership function of the fuzzysystem. The HNN has been applied to various fields sinceHopfield proposed the model [19, 20]. In optimizationproblems, the HNN has a well-demonstrated capability offinding solutions to complex tasks. HNN has been appliedto solve optimization problems based on convergence of theenergy function and coefficients weighting [21–23].1

2. Maximum Power Point Tracking and FuzzyLogic

PV is not a constant DC energy source but has variation ofoutput power, which depends strongly on the current drawnby the load. Besides, PV characteristic also changes withtemperature and irradiation variation [4]. Thus, the outputvoltage (V) of PV varies with the current (I). Figure 1 shows2the characteristic of a 200 W Sanyo PV module [24]. Themodule can be used as a single system or it can be connectedto other similar modules to increase the voltage and current.In multimodule systems, PV modules are wired in series andparallel to form a PV array. From Figure 1, it can be seenthat the PV module voltage varies from 0 V until the opencircuit voltage (Voc) of the module. Similarly, the currentvaries from 0 A until the short circuit current (Isc) of the

module. The Voc and Isc of a PV module also depend ontemperature and solar irradiation.

For any PV system, the output power is increased bytracking the maximum power point (MPP) of the system.To achieve this, an MPPT controller is required to track theoptimum power of the PV system and it is usually connectedto a boost converter located between the PV panel and load asshown in Figure 2 [6–8]. Many different control techniquessuch as the P&O and fuzzy logic are used in the MPPTcontroller.

The main components of a fuzzy logic controller (FLC)are fuzzification, fuzzy rules inference, and defuzzification asshown in Figure 3. The input variables to the FLC are thechange in power of PV (ΔPk

pv) array and direction of changein duty cycle (ΔDk) of boost converter whereas the output ofthe FLC is the change of the duty cycle that must be applied tocontrol boost converter (ΔDk+1

ref ). The formulation for ΔPkpv

and ΔDk can be expressed as follows:

Pkpv = Vk

pv · Ikpv,

ΔPkpv = Pk

pv − Pk−1pv ,

ΔDk = Dk −Dk−1,

(1)

where, Pkpv: PV array output power at kth iteration, Vk

pv: PVarray output voltage at kth iteration, Ikpv: PV array outputcurrent at kth iteration, Dk: measured duty cycle to controlswitch of DC-DC converter at kth iteration, Dk+1

ref : duty cyclethat must be applied to control switch of DC-DC converterat (k + 1)th iteration, Δ: a small change.

The universe of discourse for the first input variable(ΔPk

pv) is assigned in terms of its linguistic variable by usingseven fuzzy subsets which are denoted by negative large(NL), negative medium (NM), negative small (NS), zero (Z),positive small (PS), positive medium (PM), and positive large(PL). The universe of discourse for the second input variable(ΔDk) defines the changes in direction of duty cycle whichis classified into three fuzzy sets, namely, negative (N), zero(Z), and positive (P). The output variable (ΔDk

ref) is assignedin terms of its linguistic variable by using nine fuzzy subsetswhich are denoted by negative double large (NLL), negativelarge (NL), negative medium (NM), negative small (NS),zero (Z), positive small (PS), positive medium (PM), positivelarge (PL), and positive double large (PLL). Then, the fuzzyrules are generated as shown in Table 1 with ΔPk

pv and ΔDk

as inputs while ΔDkref as the output. This table is also known

as fuzzy associative matrix (FAM). The fuzzy inference of theFLC is based on Mamdani’s method, which is associated withthe max-min composition. The defuzzification technique isbased on the centroid method, which is used to compute thecrisp output, ΔDk

ref. 3

43. Design of Optimized FLC with HNN

The proposed design is to develop optimal membership 5function of the FLC especially for MPPT in PV systemsapplication. The HNN representation and the integration ofHNN and FLC is described in the following subsections.

+

−

PV arrayDC-DC

converter

HFLC

Initial D

et Dk

Pulse

generator

Driver

Load

ΔDk Delay

Delay

Delay

×

?s

ΔPkpv

Vpv

IpvDk+1

ref

ΔDk+1ref

Pkpv

Gained PWM

PWM

Figure 8: Physical implementation of PV MPPT system using HFLC.

Load

Continuous

MPPT Controller

+ +

+

+

+

+

+

+

+

+

+

− −

−

−

−

Temperature

25

25

Temperature 1

Subsystem 5

Out 1

Out 1

Out 1

Out 1

Out 1

Out 1

Subsystem 4

Subsystem 3

Subsystem 2

Subsystem 1

Subsystem

Step 5

Step 3

Step 2

Step 1

PV 6

I feedback

Insolation PV module (I)

Temperature

I feedback

Insolation PV module (I)

Temperature

I feedback

Insolation PV module (I)

Temperature

I feedback

Insolation PV module (I)

Temperature

I feedback

Insolation PV module (I)

Temperature

I feedback

Insolation PV module (I)

Temperature

PV 5

PV 4

PV 3

PV 2

PV 1

Measurement PV Measurement boost

Irradiation 1

Irradiation

1000

1000

IGBT

g

m

C

E

I L

FcnDiode 1

Add 1

Add

VVI array

I array

(Vin)

Iout

PWM

PWM

(u(1) + u(2))/2iis

Vout

powerGUI

I pv 1

I pv 2

I pv 3

I pv 4

I pv 5

I pv 6

Vpv

Vpv

Vpv

IpvIpv

Ipv

Vpv

Ipv

Vpv

Ipv

Vpv

Ipv

Vpv

Ipv

Figure 9: MATLAB simulation model of a PV MPPT controller.

Table 1: Fuzzy rules for the proposed FLC.

Input-1 (ΔPkpv)

NL NM NS ZE PS PM PL

Input-2 (ΔDk)

N PLL PL PM PS NM NL NLL

ZE NL NM NS ZE PS PM PL

P NLL NL NM NS PM PL PLL

0 10 20 30 40 50 60 70 800

0.5

1

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4

4.5

Voltage (V)

Cu

rren

t(A

)

Temperature = 20◦CG = 1000 W/m2

G = 800 W/m2

G = 600 W/m2

G = 400 W/m2

G = 200 W/m2

Figure 10: Effects of solar radiation at constant temperature on thePV module.

0 10 20 30 40 50 60 70 800

0.5

1

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Voltage (V)

Cu

rren

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T = 75◦C

T = 50◦CT = 25◦C

T = 0◦C

Irradiation = 1000 W/m2

Figure 11: Effects of temperature at constant solar radiation on thePV module.

3.1. Hopfield Neural Network Representation. The HNNnetwork is useful for associative memory and optimizationin a symmetrical structure. The basic structure of the HNNis shown in Figure 4 [25].

The HNN uses a two-state threshold “neuron” that fol-lows a stochastic algorithm where each neuron, or processingelement, Ni has two states with values either 0 or 1. Theinputs of each neuron come from two sources; externalinputs, Ii, and inputs from other neurons, N j . The total inputto neuron Ni is given by

in−Ni =∑i /= j

Ii + o−Njwji, (2)

0 50 100 150 2000

200

400

600

800

1000

1200

MPP by HFLCTheoretical MPP

PV array voltage (V)

PV

arra

ypo

wer

(W) G = 1000 W/m2

G = 800 W/m2

G = 600 W/m2

G = 400 W/m2

G = 200 W/m2

Figure 12: Performance of the HFLC-based MPPT under variousirradiation at constant temperature T = 25◦C.

0 50 100 150 2000

200

400

600

800

1000

1200

MPP by HFLCTheoretical MPP

PV array voltage (V)

PV

arra

ypo

wer

(W)

T = 75◦CT = 50◦CT = 25◦CT = 0◦C

Figure 13: Performance of the HFLC based MPPT under varioustemperatures at constant irradiation G = 1000 W/m2.

where in−Ni: total input to neuron i, wji: synaptic intercon-nection strength from neuron Ni to neuron Nj , Ii: externalinput to neuron Ni, o−Nj : output of neuron Nj .

Each neuron samples its input at random times. Itchanges the value of its output or leaves it fixed accordingto a threshold rule with thresholds θi:

o−Ni =⎧⎨⎩

1, if in−Ni ≥ θi,

0, if in−Ni < θi.(3)

0.95 1 1.05 1.1 1.15 1.2 1.25800

850

900

950

1000

1050

Time (s)

Sola

rir

radi

atio

n(W

/m2)

Solar irradiation

Figure 14: Slow change of irradiation from 1000 W/m2 to900 W/m2.

0.95 1 1.05 1.1 1.15 1.2 1.251060

1080

1100

1120

1140

1160

1180

1200

Time (s)

PV

arra

ypo

wer

(W)

MPPT by HFLC

MPPT by FLC

MPPT by P and O

Figure 15: PV output power under slow irradiation change from1000 W/m2 to 900 W/m2.

Then the energy function of the HNN is defined as

E = −12

∑i /= j

∑j

o−Ni · o−Nj ·wij −∑i

Ii · o−Ni +∑i

θi · o−Ni.

(4)

The change in E due to the changing state of neuron Ni byΔo−Ni is given by

ΔE = −⎡⎣∑

j

o−Nj ·wij + Ii − θi

⎤⎦Δo−Ni, (5)

where Δo−Ni is the change in the output of neuron Ni.The continuous and deterministic model of the HNN is

based on continuous variables and responses but retains all

0.99 1 1.01 1.02 1.03 1.04900

920

940

960

980

1000

1020

Time (s)

Solar irradiation

Sola

rir

radi

atio

n(W

/m2)

Figure 16: Drastic change in irradiation from 1000 W/m2 to950 W/m2.

0.99 1 1.01 1.02 1.03 1.04800

850

900

950

1000

1050

1100

1150

1200

1250

1300

Time (s)

PV

arra

ypo

wer

(W)

MPPT by P and OMPPT by FLCMPPT by HFLC

Figure 17: PV output power under drastic irradiation change from1000 W/m2 to 950 W/m2.

of the significant behaviors of the original model describedabove. The output variable o−Ni for neuron Ni has values inthe range of 0 ≤ o Ni ≤ 1 and the input-output function isa continuous and monotonically increasing function of theinput in−Ni to neuron Ni.

The dynamics of the neurons is defined as [18]

duidt

= −uiτ

+∑j

wi j · o−Nj + Ii, (6)

where τ: a constant, ui: input of HNN.

1 1.05 1.1 1.15 1.2 1.25 1.320

25

30

35

40

45

50

55

Time (s)

Temperature

Tem

pera

ture

(◦C

)

Figure 18: Slow change of temperatures from 25◦C to 50◦C.

1 1.05 1.1 1.15 1.2 1.25 1.31130

1140

1150

1160

1170

1180

1190

1200

1210

Time (s)

PV

arra

yp

ower

(W)

MPPT by FLC

MPPT by HFLC

MPPT by P and O

Figure 19: PV output power under slow temperature change from25◦C to 50◦C.

A typical output of neuron Ni is a sigmoid function asshown in Figure 5. Mathematically it is given by

o−Ni = g(λui) = 11 + e−λui

, (7)

where λ is the gain that determines the shape of the sigmoidfunction.

The energy function of the continuous HNN is similarlydefined as [19]

E = −⎡⎣1

2

n∑i=1

n∑j=1

wijo−Ni · o−Nj +n∑i=1

Iio−Ni

⎤⎦, (8)

0.998 1 1.002 1.004 1.006 1.008 1.01 1.012 1.01424

25

26

27

28

29

30

31

Time (s)

Temperature

Tem

pera

ture

(◦C

)

Figure 20: Drastic temperature changes from 25◦C to 30◦C.

0.998 1 1.002 1.004 1.006 1.008 1.01 1.012 1.0141185

1190

1195

1200

1205

Time (s)

PV

arra

yp

ower

(W)

1 1.005 1.011187.5

1188

1188.5

1189

1189.5Enlarged section

P and OFLCHFLC

Figure 21: PV output power under sudden temperature changefrom 25◦C to 30◦C.

and it is change in energy is given by

ΔE = −⎡⎣∑

j

o−Nj ·wij + Ii

⎤⎦Δo−Ni. (9)

dE/dt is always less than zero because g is a monotonicallyincreasing function. Therefore, the network solution movesin the same direction as the decrease in energy. The solutionseeks out a minimum of E and comes to a stop at stabilitypoint.

0.99 0.995 1 1.005 1.01 1.015 1.02 1.025900

950

1000

1050

Time (s)

Solar irradiation part I

Solar irradiation part II

Sola

rir

radi

atio

n(W

/m2)

Figure 22: Partial shading of solar irradiation change.

0.99 0.995 1 1.005 1.01 1.015 1.02 1.0251110

1120

1130

1140

1150

1160

1170

1180

1190

1200

1210

Time (s)

PV

arra

ypo

wer

(W)

MPPT by HFLCMPPT by FLCMPPT by P and O

Figure 23: PV output power under partial shading with of solarirradiation change 1000 W/m2 to 950 W/m2.

3.2. Integrating HNN and FLC. Despite using expert knowl-edge in the formulation of the inference rules and themembership functions of FLC, there are still some defectssuch as center of fuzzification and range of the fuzzification.To improve these defects, the proposed FLC uses HNN tofind the optimal membership functions which is achieved byconsidering the following steps.

(1) Defining neuron for the HNN. In the design of theproposed optimal FLC, two inputs, ΔPk

pv and direction ΔDk,

and one output, ΔDkref, are used as described before. For

0.25 0.3 0.35 0.4 0.45 0.5

400

500

600

700

800

900

1000

1100

1200

Time (s)

Solar irradiation part ISolar irradiation part II

Sola

rir

radi

atio

n(W

/m2)

Figure 24: Partial change of solar irradiation 400 W/m2to1000 W/m2.

0.25 0.3 0.35 0.4 0.45 0.5250

300

350

400

450

500

550

600

Time (s)

PV

arra

ypo

wer

(W)

MPPT by P and OMPPT by FLCMPPT by HFLC

Figure 25: PV output power under partial change of irradiation400 W/m2 to 1000 W/m2.

simplicity, the design is only based on membership functionsof ΔPk

pv and ΔDkref. ΔP

kpv is described with seven membership

functions, as illustrated in Figure 6, and ΔDkref is described

with nine membership functions, as illustrated in Figure 7.In Figure 6, the centers of ΔPk

pv membership function arex1, x2, x3, x4, x5, x6, and x7 while in Figure 7, the centers ofΔDk

ref membership function are z1, z2, z3, z4, z5, z6, z7, z8, andz9. Based on the number of centers of ΔPk

pv and ΔDkref, the

proposed HNN consists of 16 neurons with variables given

0 50 100 150 2000

100

200

300

400

500

600

700

800

PV array voltage (V)

PV

arra

ypo

wer

(W)

PV array characteristicMPP by HFLC

MPP by FLCMPP by P and O

Figure 26: MPP under partial shading 200 W/m2 and 1000 W/m2.

0 50 100 150 2000

100

200

300

400

500

600

700

800

PV array voltage (V)

PV

arra

yp

ower

(W)

PV array characteristicMPP by HFLC

MPP by FLCMPP by P and O

Figure 27: MPP under partial shading 400 W/m2 and 1000 W/m2.

as x1 = −SP1; x2 = −SP2; x3 = −SP3; x4 = SP4; x5 = SP5; x6 =SP6; x7 = SP7; z1 = −SD1; z2 = −SD2; z3 = −SD3; z4 = −SD4;z5 = SD5; z6 = SD6; z7 = SD7; z8 = SD8; z9 = SD9. SP1–SP7 areoutput value of neurons N1–N7(o N1–o N7) while SD1–SD9

are output values of neurons N8–N16(o N8–o N16).

0 50 100 150 2000

100

200

300

400

500

600

700

800

PV array voltage (V)

PV

arra

ypo

wer

(W)

PV array characteristicMPP by HFLC

MPP by FLCMPP by P and O

900

Figure 28: MPP under partial shading 600 W/m2 and 1000 W/m2.

0 50 100 150 2000

PV array voltage (V)

PV array characteristicMPP by HFLC

MPP by FLCMPP by P and O

200

400

600

800

1000

1200

PV

arra

yp

ower

(W)

Figure 29: MPP under partial shading 800 W/m2 and 1000 W/m2.

When comparing the values of neurons in Figures 6 and7, the following constraints should be satisfied.

SP4 = 0,

SP1 = SPmax left ,

SP7 = SPmax right,

0 ≤ SP3 ≤ SP2 ≤ SP1,

0 ≤ SP6 ≤ SP5 ≤ SP7,

SD5 = 0,

SD1 = SDmax left,

SD9 = SDmax right,

0 ≤ SD4 ≤ SD3 ≤ SD2 ≤ SD1,

0 ≤ SD6 ≤ SD7 ≤ SD8 ≤ SD9.

(10)

(2) Defining objective function for the optimization problem.The goal of MPPT is to achieve ΔPk

pv = 0 and ΔDkref = 0.

Therefore, the quadratic criterion to be minimized is

E = E1 + E2 = 12A(ΔPk

pv

)2+

12B(ΔDk

ref

)2, (11)

where, E: energy function to be minimized, A,B: constants.From (11), the first part of E, which is E1 =

(1/2)A(ΔPkpv)2 only depends on the universe of ΔPk

pv whichis in the first input of FLC. The ΔPk

pv is defined bydefuzzification of the universe of ΔPk

pv using a centroidfunction as:

ΔPkpv =

∑7i=1 μ

(ΔPk

pv

)ixi

∑7i=1 μ

(ΔPk

pv

)i

, (12)

where μ(ΔPkpv)

iis a membership value of xi.

E1 depends only on neurons Ni (i = 1, 2, 3, 4, 5, 6, 7).Knowing that the left side of ΔPk

pv in the membershipfunction of the first input is μ(ΔPk

pv)i /= 0 for x1, x2, x3, then,

ΔPkpv can be rewritten as

ΔPkpv =

∑3i=1 μ

(ΔPk

pv

)ixi

∑7i=1 μ

(ΔPk

pv

)i

. (13)

Then, the first half of energy function E1 can be rewritten asE1a:

E1a = 12A

⎡⎢⎣∑3

i=1 μ(ΔPk

pv

)ixi

∑7i=1 μ

(ΔPk

pv

)i

⎤⎥⎦

2

,

E1a = 12

A∑7

i=1

∑7j μ(ΔPk

pv

)iμ(ΔPk

pv

)j

×⎛⎝

3∑i=1

3∑j=1

μ(ΔPk

pv

)iμ(ΔPk

pv

)j(−o−N)i (−o−N) j

⎞⎠

E1a = 12

⎡⎢⎣

3∑i=1

3∑j

⎡⎢⎣

Aμ(ΔPk

pv

)iμ(ΔPk

pv

)j∑7

i=1

∑7j μ(ΔPk

pv

)iμ(ΔPk

pv

)j

⎤⎥⎦o−Ni · o−Nj

⎤⎥⎦.

(14)

Considering that the right side and center of ΔPkpv in the

membership function of the first input of FLC is μ(ΔPkpv)

i=

0 for x1, x2, x3, hence ΔPkpv can be rewritten as:

ΔPkpv =

∑7i=4 μ

(ΔPk

pv

)ixi

∑7i=4 μ

(ΔPk

pv

)i

. (15)

Similarly, the second half of energy function E1 is rewrittenas E1b:

E1b= 12

⎡⎢⎣

7∑i=5

7∑j=5

⎡⎢⎣

Aμ(ΔPk

pv

)iμ(ΔPk

pv

)j∑7

i=1

∑7j=1 μ

(ΔPk

pv

)iμ(ΔPk

pv

)j

⎤⎥⎦o−Ni · o−Nj

⎤⎥⎦.

(16)

Since the first part of E1 is the summation of left side (E1a)and right side (E1b) of the ΔPk

pv membership function, E1 canbe expressed as:

E1 = 12A(ΔPk

pv

)2 = E1a + E1b,

E1= 12

⎡⎢⎣

7∑i=4

7∑j=4

⎡⎢⎣

Aμ(ΔPk

pv

)iμ(ΔPk

pv

)j∑7

i=1

∑7j=1 μ

(ΔPk

pv

)iμ(ΔPk

pv

)j

⎤⎥⎦o−Ni · o−Nj

⎤⎥⎦,

(17)

where o N = 0 for i = 4, j = 4.The second part, E2 = (1/2)B(ΔDk

ref)2 is related to

the output of FLC and depends only on neurons Ni (i =8, 9, 10, 11, 12, 13, 14, 15, 16). The ΔDk

ref can be defined bydefuzzification by using the centroid method and is writtenas:

ΔDkref =

∑9k=1 μ

(ΔDk

ref

)mzm

∑9k=1 μ

(ΔDk

ref

)m

. (18)

Similar to the equations shown in obtaining E1,E2 can beexpressed as

E2 = 12

⎡⎢⎣

9∑m=1

9∑n=1

⎡⎢⎣

Bμ(ΔDk

ref

)mμ(ΔDk

ref

)n∑9

m=1

∑9n=1 μ

(ΔDk

ref

)mμ(ΔDk

ref

)n

⎤⎥⎦zmzn

⎤⎥⎦,

E2 = 12

⎡⎢⎣

16∑i=8

16∑j=8

⎡⎢⎣

Bμ(ΔDk

pv

)iμ(ΔDk

pv

)j∑16

i=8

∑16j=8 μ

(ΔDk

pv

)iμ(ΔDk

pv

)j

⎤⎥⎦o−Ni · o−Nj

⎤⎥⎦,

(19)

where N = 0 for i = 12, j = 12 and μ(ΔDkref) is the

membership value of zn.Finally, the total energy function E is expressed as

E = E1 + E2,

E= 12

⎡⎢⎣

7∑i=1

7∑j=1

⎡⎢⎣

Aμ(ΔPk

pv

)iμ(ΔPk

pv

)j∑7

i=1

∑7j=1 μ

(ΔPk

pv

)iμ(ΔPk

pv

)j

⎤⎥⎦o−Ni · o−Nj

⎤⎥⎦

+12

⎡⎢⎣

16∑i=8

16∑j=8

⎡⎢⎣

Bμ(ΔDk

ref

)iμ(ΔDk

ref

)j∑16

i=8

∑16j=8 μ

(ΔDk

ref

)iμ(ΔDk

ref

)j

⎤⎥⎦o−Ni · o−Nj

⎤⎥⎦.

(20)

where N = 0 for i = 4, 12; j = 4, 12.By comparing (8) with (20), the weight matrix of neurons

Ni to N j in the HNN is derived and given as:

wij =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

w11 w12 w13 . . . 0

w21 w22

w31 w32

...

0 0 0 wnn

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

, (21)

where,

wij = −Aμ(ΔPk

pv

)iμ(ΔPk

pv

)j∑7

i=1

∑7j=1 μ

(ΔPk

pv

)iμ(ΔPk

pv

)j

,

for i and j = 1, 2, 3, 4, 5, 6, 7,

wij = −Bμ(ΔDk

ref

)iφμ(ΔDk

ref

)j∑16

i=8

∑16j=8 μ

(ΔDk

ref

)iμ(Δk

ref

)j

,

for i, j = 8, 9, 10, 11, 12, 13, 14, 15, 16,

wij = 0, for other.

(22)

(3) Design for Physical Implementation. The physical imple-mentation of MPPT for PV systems using Hopfield opti-mized FLC (HFLC) is described in terms of a block diagramas shown in Figure 8.

As shown in Figure 8, the system consists of PV array,DC-DC converter, load, and control system. The controlsystem consist of voltage and current measurement system,controlled pulse with modulation (PWM) generator withHFLC, and a switching driver circuit to gain the PWM. Atthe initial step (k = 0), the control system generates squarewave signals with a small duty cycle (D), of value 10%. Inthe next step (k = 1), the value of D is increased by ΔDk

refthat is defined by HFLC as discussed in the previous section.The value of D is always updated by the increment ΔDk

ref. Thevalue of ΔDk

ref tends to change in either positive or negativedirection as |ΔDk

ref| decline towards zero.

4. Simulation Results

The performance of the proposed HFLC under differ-ent operating conditions is validated using the MAT-LAB/Simulink software. In the PV model shown in Figure 9,there are two groups of PV arrays connected in parallel.Every group consists of 3 PV modules connected in series.The PV module parameters are obtained from the SanyoHIP-200BA3 PV technical datasheet [24]. In the simulations,first the characteristics of the PV module are validated andthen the performance of the HFLC under various conditionsis evaluated to investigate the effectiveness of the HFLCmethod. 6

7

84.1. Validation of PV Module Simulation. Figures 10 and 11show the results of the I-V characteristics of the simulatedPV module as a function of irradiation and temperature,respectively. It can be observed from the above figures thatthe I-V curves of the simulated PV module are quite similarto the I-V curves of the Sanyo HIP-200BA3 PV moduleprovided by the Sanyo manufacturer in Figure 1. Therefore, itis quite reasonable to use the PV module model to verify theperformance of the proposed HFLC-based MPPT controllerunder simulation environment.

4.2. Performance of MPPT by Using HFLC. Figures 12 and 13show the performance of the HFLC in finding the maximumpower point (MPP) of the PV system shown in Figure 9under varying irradiations and temperatures, respectively.From the figures, the MPP obtained from HFLC is comparedwith the theoretical MPP. The results of the MPP clearly showthat both MPPs are very close to each other.

To further demonstrate the performance of the HFLCMPPT controller, simulations were performed under thefollowing test conditions.

(i) Constant temperature at 25◦C and changing the solarradiation slowly and drastically.

(ii) Constant solar radiation at 1000 W/m2 and changingthe temperature slowly and drastically.

(iii) Constant temperature at 25◦C and considering par-tial shading and change in solar radiation.

The MPPT controller was also tested using the conven-tional FLC and the P&O MPPT methods.

4.2.1. Effect of Changing the Solar Radiation. To analyze theeffect of solar radiation, simulations were carried out undervarious solar irradiations but at constant temperature of25◦C. Figure 14 shows the change in solar irradiation from1000 W/m2 to 900 W/m2. Figure 15 shows the PV outputpower when subjected to the changing solar irradiations.From Figure 15, it can be seen that the HFLC, and FLC-basedMPPT gives greater PV output powers than the P&O-basedMPPT.

Figure 16 shows the sudden change in solar irradiationfrom 1000 W/m2 to 950 W/m2 while Figure 17 shows theresponse of the MPPT controller in terms of PV outputpower when subjected to a sudden change in solar irradia-tion. From the figures, it is noted that the PV output power isgreatest for MPPT controlled by HFLC compared to that ofFLC and P&O methods. Furthermore, MPPT controlled byHFLC gives a fast response to reach the new MPP after solarirradiation changes.

4.2.2. Effect of Change in Temperature. This simulation iscarried out to illustrate the performance of the MPPTmethods under constant solar irradiation of 1000 W/m2andchanges in temperature. Figures 18 and 20 depict the slowand sudden changes in temperature, respectively. Figures19 and 21 show the corresponding PV output powersduring slow and sudden changes in temperature, respectively.From Figure 19, it can be noted that for slow temperaturechanges, the MPPT controlled by HFLC and FLC giveshigher PV output power than the P&O method especiallyat the transient state. While in the case of drastic changein temperature, the MPPT controlled by HFLC achievethe highest PV output at the transient state as shown inFigure 21.

4.2.3. Effect of Partial Shaded Solar Irradiation. Simulation isalso performed to illustrate the effectiveness of the MPPT ofPV systems under some partial shading case. In this case,it is assumed that a half of the PV array receives constantsolar irradiation of 1000 W/m2 and the other half withshading solar irradiation which changes from 1000 W/m2

to 950 W/m2. This condition is depicted in Figure 22. Thepower harvested from the PV array for this case is shown inFigure 23. From Figure 23, it can be seen that performanceof MPPT controlled by HFLC is the best among the othercompared methods.

Another case describes a situation of solar irradiationchanging from 400 W/m2 to 1000 W/m2, to a half of the PVarray while the other half receiving constant 400 W/m2 undershading as shown in Figure 24. The PV output power for thiscase is shown in Figure 25. From the figure, it can be notedthat the FLC and P&O failed to track the MPP correctly.However, the proposed HFLC MPPT method successfullyfinds the MPP around 590 W as shown in Figure 25.

Figures 26, 27, 28, and 29 show the characteristic curvesof voltage versus power (V-P) of the modeled PV array undervarious partial shading conditions described in Table 2.

From Figures 26 and 27, it can be seen that the HFLCmethod is accurate in finding the MPP (590 W) while

Table 2: Various partial shaded solar irradiation.

No.Solar irradiation (W/m2)

Part I Part II

(1) 1000 200

(2) 1000 400

(3) 1000 600

(4) 1000 800

the conventional FLC and P&O methods failed to do so.Generally, the conventional FLC and P&O methods just findlocal maximum power point. However, for case as depicted inFigures 28 and 29, all of the MPPT methods correctly trackedthe MPP.

5. Conclusion

A new Hopfield optimized FLC for MPPT of PV systemis proposed in which improvement is made by applyingHNN to find the optimal width of each fuzzificationinput and output of the FLC. A complete PV system withHFLC MPPT controller was modeled and implementedin Matlab/Simulink to simulate various irradiation andtemperature conditions so as to verify the performance ofthe proposed MPPT method. Simulation results show thatthe proposed HFLC MPPT method is robust and accuratecompared to the other conventional MPPT methods. TheHFLC MPPT method successfully tracks the global max-imum power point of a PV module even under partialshading.

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