 Open Access
 Total Downloads : 253
 Authors : N. Bhupesh Kumar, Dr. K. Vijaya Kumar Reddy
 Paper ID : IJERTV2IS110271
 Volume & Issue : Volume 02, Issue 11 (November 2013)
 Published (First Online): 06112013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Advanced Fuzzy Logic Controller for Tracking the Maximum Power Point of PV Arrays
Advanced Fuzzy Logic Controller for Tracking the Maximum Power Point of PV Arrays

N. Bhupesh Kumar, Sr. Assistant Professor, Department of EEE, Sir C R Reddy College of Engineering, Eluru

Dr. K. Vijaya Kumar Reddy, Professor, Department of ME,JNTUH, Hyderabad
Abstract With the increasing fossil fuel deficit, global warming
There is a unique point on the curve, called the maximum
and damage to the ecosystem the studies on photovoltaic
power point (MPP), at which the array operates with
generation are increasing extensively as it is an inexhaustible and
maximum efficiency and produces maximum output power.
broadly available energy resource. However, the output power
As it is well known, the MPP of a PV power generation
induced in the photovoltaic modules depends on solar radiation and temperature of the solar cells. Therefore, to maximize the
system depends on array temperature, solar insolation, shading conditions, and PV cells aging, so it is necessary to constantly
efficiency of the renewable energy system, it is necessary to track
track the MPP of the solar array. A switchmode power
the maximum power point of the PV array. This paper presents a maximum power point tracker using fuzzy set theory to improve
converter, called a maximum power point tracker (MPPT), can be used to maintain the PV arrays operating point at the
energy conversion efficiency. An advanced fuzzy controller is
MPP. The MPPT does this by controlling the PV arrays
proposed, by using a fuzzy cognitive network, which is in close
voltage or current independently of those of the load. If
cooperation with the presented fuzzy controller. This new method gives a very good maximum power operation of any PV array under different climatic conditions such as changing insolation and temperature. The simulation studies show the effectiveness of the proposed algorithm.
properly controlled by an MPPT algorithm, the MPPT can locate and track the MPP of the PV array. However, the location of the MPP in the IV plane is not known a priori. It must be located, either through model calculations or by a search algorithm. Fig. 2 shows a family of PV IV curves

INTRODUCTION
under increasing irradiance, but at constant temperature.
With the increasing fossil fuel deficit, global warming
Needless to say there is a change in the array voltage at which
and damage to the ecosystem, renewable energy sources
the MPP occurs. For years, research has focused on various
(solar, wind, tidal, and geothermal, etc.) are attracting more
MPP control algorithms to draw the maximum power of the solar array. These techniques include lookup table methods,
attention as alternative energy sources. Among the
using neural networks [1], [2], perturbation and observation
renewable energy sources solar photovoltaic (PV) energy has
(P&O) methods [3][6], and computational methods [7]. For
been widely utilized in smallsized applications. It is also the
example, Hiyama et al. [1] presented a neural network
most promising candidate for research and development for largescale uses as the fabrication of less costly photovoltaic
application to the identification of the optimal operating point of PV modules and designed a PItype controller for realtime
devices becomes a reality.
maximum power tracking. Optimal operating voltages are
Photovoltaic system as a number of applications such as
identified through the proposed neural network by using the
water pumping, domestic and street lighting, electric
opencircuit voltages measured from monitoring cells and
vehicles, hybrid systems, military and space applications,
optimal operating currents are calculated from the measured
refrigeration and vaccine storage, power plants, etc., all in either standalone or gridconnected configurations. A PV array is by nature a nonlinear power source, which under
shortcircuit currents
constant
uniform
irradiance
has a
currentvoltage
(IV)
characteristic like that shown in Fig. 1.
Figure 2: PV array (I V) characteristics at various insolation levels
The output of the neural network goes through the PI
Figure 1: PV array (I V) and PV characteristics
controller
to the
voltage
control
loop
of the
inverter to
change
the
terminal
voltage of
the
PV system
to the
Moreover, during the operation
of the PV array the FCN
identified optimal one.
weights are continuously updated
based on data from
the
Fuzzybased MPPT
technique [8],
[9] is one of theencountered operating conditions. The performance of the
computational methods, which have
demonstrated fine
method is tested using climatic data for a specific PV system
performances under different environmental operating conditions.
of the market, which reaches its MPP with great accuracy for various operational conditions, such as changing insolation
The fuzzy controller introduced in [8] uses dP/dI and its
and temperature and seasonal variations.
variations
(dP/dI), as the
inputs and
computes MPPT
Organization of the paper is as follows. In Section II,
converter duty cycle. The fuzzy tracker of [9] considers
mathematical relations between the essential variables of a
variation of duty cycle, but replaces dP/dI by the variation of
PV system are presented. These relations are necessary for
panel power. An online search algorithm that does not
simulating its operation under different insolation and
require the measurement of temperature and solar irradiation
temperature levels. In Section III, an MPPT method, which
level is proposed in reference [10]. Other researchers
is based on a fuzzy controller methodology, is analysed.
analysed and coared the various MPPT techniques [7], [11],
Section IV makes a brief introduction in FCMs and presents
[12]. Besides that, in [11] a simple DSPbased MPPTthe graph of the proposed FCN, which will be used in close
algorithm is proposed, while in [12] a combination of the
cooperation with the fuzzy controller, in order to track the
modified constant voltage control and the incremental
MPP of a PV system. Simulated experimental results, based
conductance method is introduced, showing good efficiency
on climatic data of one year and on the operation of a typical
(especially in lower insolation intensity). Finally, in [13],
PV array of the market are given in Section V. Finally,
[14] efforts have been made to model the dynamic behaviour of a PV system in order to study its interaction with the pertinent MPPT system, while in [15], MPPT assessment and testing methods were presented in order to identify the accuracy, error and efficiency of the MPPTs.This paper presents an advanced fuzzy logic controller, which uses fuzzy sets theory [8] in close cooperation with fuzzy cognitive networks (FCNs). FCNs [16], [17] constitute
Section VI concludes the work.

SIMULATION OF THE PV SYSTEM
an extension
of the
well
known
fuzzy
cognitive
maps
(FCMs) [18], so that they are able to operate in continuous interaction with the physical system they represent, while at the same time they keep track of the various operationalFigure 3 : Equivalent circuit of a solar cell
equilibrium points met by the system. FCNs can model
Using the equivalent circuit of a solar cell (Fig. 3) and
dynamical complex systems that change with time following
the pertinent equations [11] the nonlinear (IV)
nonlinear laws. They use a symbolic representation for the
characteristics of a solar array are extracted, neglecting the
description and modelling of the system. In order to
series resistance
illustrate different aspects in the behaviour of the system, an
I I I exp[qV / kTA) 1] Vi
(1)
FCN is consisted of nodes with each node representing a
i ph rs i R
characteristic of the system, including possible control sh
actions. These nodes interact with each other showing the dynamics of the system under study. Moreover, the FCN has the ability of continuous interaction with the physical system
Where Ii is the PV array output current (A); Vi is the PV array output voltage (V); q is the charge of an electron; k is Boltzmanns constant in J/K; A is the pn junction ideality
it represents, sending control actions and receiving feedback
factor; T is the cell temperature (K); and Irs is the cell
from the system. The FCN integrates the accumulated
reverse saturation current. The factor A in (1) determines the
experience and knowledge on the operation of the system, as
cell deviation from the ideal pn junction characteristics.
a result of the method by which it is constructed, i.e., using human experts who know the operation of system and its
The ideal value ranges between 1 and 5, according to [11] and to the commercially available software package for PV
behaviour, but most significantly, it can adapt this
systems PVSYST V3.1 (see Table I).
knowledge based on the feedback from the physical system or by using appropriate training data.
The photocurrent Iph depends on the solar radiation and the cell temperature as stated in the following:
The
nodes
of the
FCN represent essential
operational S
(Voltage,
Current,
Insolation,
Temperature)
and
control
I ph I scr Ki T Tr
(2)
(Current)
variables
of the
PV system.
The
node
100
interconnection weights are determined using data, which are
Where
Iscr
is the
PV array
short
circuit
current at
constructed so that they cover the operation of a PV system under a wide range of different climatic conditions. Once the
reference
temperature
and
radiation
(A);
ki is
the
short
FCN
is trained it
can be
mounted
on any PV
system.
circuit current temperature coefficient (A/K) and S is the solar radiation (mW/cm2).

MPPT BY FUZZY LOGIC CONTROLLER [8]
TABLE 1
The
objective
of the
controller
is to
track
and
Factor A Dependence on PV Technology
Technology A
extract maximum power from the PV arrays for a given solar insolation level. The maximum power corresponding to the optimum operating point is determined for a different solar
Simono
1.2
insolation level. Normally a dc dc converter is utilized
Sipoly aSi:H
aSi:H tandem aSi:H triple CdTe
CIS
1.3
1.8
3.3
5
1.5
1.5
between the input source and the load for the purpose of MPPT.

Fuzzification
In [8], the authors focused on single inputsingle
AsGa 1.3
output plant, in which control is determined on the basis of satisfaction of two criteria relating to two input variables of
The reverse saturation current Irs varies with temperature,
the presented controller, namely error (E) and
change of
according to the following:
error (CE), at a sampling instant k.
The variable E and CE are expressed as follows:
T 3
1.115 1
1
P (k ) P (k 1)
Irs Irr T exp k1 A T
T
(3)
Ek pv pv
(7)
r
r
I pv (k ) I pv (k 1)
Where Tr is the cell reference temperature, Irr is the
CE(k)
= E(k)
– E(l1)
(8)
reverse saturation current at Tr, k is the Boltzmanns
constant in eV/K and the band gap energy of
the
Where Ppv(k) and Ipv(k) are the power and current of the
semiconductor used in the cell is equal to 1.115.
PV array, respectively. Therefore, E(k) is zero at the
Finally, the next equation was used in the computer
maximum power point of a PV array. In Fig. 4(a), the fuzzy
simulations to obtain the open circuit voltage of the PV array Equations
set of input E(k) is presented, while in Fig. 4(b), the fuzzy set of input CE(k) is shown. Finally, Fig. 4(c) shows the
AkT I ph I rs
respective fuzzy set of the output dD, which represents the
Voc q
ln
I rs
(4)
change of the on/off duty ratio of the switch S of a stepup boost converter similar to the one shown in Fig. 5.
From (2) to (4), we get
I k T T s 3
scr i
r
100
Tr
1.115 1
1
I rr
exp
1
(5)
exp
Vocq / AkT 1
T
k A Tr
T
and from (1)
Rsh
Voc
(6)

I rs exp qVoc / kTA 1
The
required
data
for
identifying
the
maximum
operating point at any insolation level and temperature are the following:

ki ;

Open circuit voltage Voc (for initial conditions Tr = 25 C, S = 100 mW/cm2);

Short circuit current Iscr (for initial conditions Tr = 25 C, S = 100 mW/cm2);

Maximum power voltage Vmp (for initial conditions Tr =25 C, S = 100 mW/cm2);

Maximum power point current Imp(for initial conditions Tr = 25 C, S = 100 mW/cm2);
Figure. 5. Stepup boost converter for MPPT.
Table – II
Figure. 4. Membership function for (a) input E(k); (b) input CE(k); (c) output dD.


Inference Method
Table II shows the rule table of the fuzzy controller where all the entries of the matrix are fuzzy sets of error E(k) change of error CE(k), and change of duty ratio dD to the boost converter. In the case of fuzzy control, the control rule must be designed in order that input variable E(k) has to always be zero.
As an example control rule in Table II: IF E is PB AND CE is ZO THEN dD is PB
FUZZY RULE TABLE
Figure. 6. Sample versus power of PV array using P&O method. At point A, the P&O method reaches the MPP for first time after iteration (27)
Figure. 7. Sample versus power of PV array, using fuzzy controller method. At point B, the fuzzy controllers method reaches MPP after iteration (24).
As a fuzzy inference method, Mamdanis method is
So far the fuzzy controller is performing better
used with maxmin operation fuzzy combination law. For the
compared to the classic P&O one by adjusting appropriately
defuzzification the centre of area (COA) and the max
the voltage of the dcdc converter, in order to reach the MPP
criterion method (MCM) is used [19].
of a PV array, faster and with no fluctuation. Some
The characteristics of the simulated dcdc boost
disadvantages of the fuzzy controllers method are
converter ae given in the Appendix A.
eliminated using FCN. As it is well known, the MPP of a PV
The fuzzy controller method is used as MPPT instead of
array varies according to temperature and/or insolation
the simple P&O method [20], because by doing so there is a
variations; thus, the fuzzy controller starts its search for this
reduction not only in the time required to track the MPP but
new MPP, by using as starting point the previous MPP
also in the fluctuation of power, as it is clearly presented in Figs. 6 and 7.
(corresponding to the previous temperature and insolation levels). This devolvement demands a considerable number
of iterations, especially if this new MPP is located far away from the previous one, which means that the wasted energy
influences other nodes and in which degree. The weight of the interconnection between node Ci and node Cj denoted by
is significant.

faster
devolvement
from
one
MPP to
Wij,
could be
positive
(Wij
>0)
for
positive
causality or
another is ensured with the use of an FCN, just like the
negative
(Wij
<0)
for
negative
causality or
there is no
proposed one presented in the next section. It will be shown in the following results that FCN, in close cooperation with the presented fuzzy controller, will become a robust MPPT
relationship between node Ci , and node Cj , thus Wij = 0.
The causal knowledge of the dynamic behaviour of the
method, in order to minimize the wasted energy.
system is
stored
in the
structure
of the
map
and in
the
interconnections
that
summarize
the
correlation
between


FCN APPROACH FOR THE PHOTOVOLTAIC PROJECT
This section presents an FCN designed to represent the operation of a photovoltaic system. Our aim is to use the
cause and effect. The value of each node is influenced by the values of the connected nodes with the corresponding causal weights and by its previous value. So, the value Aj for each node Cj is calculated by the following rule [21]:
FCNs, which are extensions
of FCMs, for estimating the
N
s s1
s1
maximum power point of the photovoltaic system.
Aj
f Ai
i1,i j
Wij Aj
(9)

FCMs
FCMs
approach is a hybrid
modelling methodology,
where
Asj , is the value of node Cj at step s,
Asi 1 is the value of node Ci , at step s 1,
exploiting characteristics of both fuzzy logic and neural
Asj1 is the value of node Cj at step s 1, and
networks theories, and it may play an important role in the
Wij is the weight of the interconnection between
development of intelligent manufacturing systems. The
nodes Ci and Cj Â·
utilization of existing knowledge and experience on the
f is a squashing function: f = 1/[1 + ecx ].
operation of complex systems is the core of this modelling approach.
The graphical illustration of an FCM is a signed directed graph with feedback, consisting of nodes and weighted inter connections. Nodes of the graph stand for the nodes that are used to describe the behaviour of the system and they are
By using c = 1, we convert the nodes values in the range [0,1].
To account for the existence of steady nodes, (9) has to be slightly modified so that it does not provide with erroneous results. Steady value nodes are the nodes that influence the remaining graph but they are not influenced by any other
connected by signed and weighted arcs representing the
node of the graph. In this case, nodes values are now
causal relationships that exist among nodes (Fig. 8).
computed through equations [16]
s,FCM
N s1,FCM
s1,FCM
Aj
f Ai
i1,i j
Wij Aj
(10)
And for the steadystate nodes the correction equation is
A
A
s,FCM
j
system
A
A
j
(11)
where Asystemj is the nodes value, derived from the physical system.

Cognitive Graph for the PV Project
The
graph shown in
Fig. 9
represents a photovoltaic
Figure. 8. Simple fuzzy cognitive map
Each node represents a characteristic of the system. In general it stands for states, variables, events, actions, goals, values, trends of the system, which is modelled as an FCM
system, for a MPPT use. The graph have six nodes, where nodes C1, C2, and C6 are steady value nodes and nodes C3, C4, C5 could be control nodes. In this approach, node C4 is the control node whose value is used to regulate the current of the system. The regulation of the current of the system means that a different power is now the output power of the
[18]. Each node is characterized by a number Aj , whichphotovoltaic.
Control
nodes
are
the
nodes
the
values of
represents its value and it results from the transformation of the real value of the systems variable, for which this node
which will be used to the real system as control actions. Node C4 is used to calculate the optimum current needed to
stands, in the interval [0, 1]. It must be mentioned that all the
regulate
the
output
power
of the
photovoltaic
in the
values
in the
graph
are
fuzzy,
and
so weights
of the
maximum point. The nodes of the graph are related to the
interconnections
belong
to the
interval
[1,1].
With
the
following physical quantities of the photovoltaic system.
graphical
representation of
the
behavioral
model
of the
system,
it becomes
clear
which
node
of the
system
Figure. 9 FCN Designed for the photovoltaic project
Node C1 represents the irradiation with range in the interval [0, 1], 0 is the minimum point of the irradiation
For example the value of weight W63 is allowed to be updated when the weights that affect node C3 (W13, W43, and W53) are going to take values larger from the absolute value 1. In this situation, weight is activated and its value is no longer set to zero. By using equilibrium node C6 and the weights connecting this node with nodes C3, C4, and C5, we manage to regulate the values of nodes C3, C4, and C5, by always keeping values of the graph weights below absolute value 1.

FCN Approach for the Photovoltaic Project
FCN [16], [17], constitute an extension of FCMs. Unlike FCMs, which rely only on the use of the initially acquired experts knowledge about the operation of the system and which is represented by the weights values of the map, FCNs may use these values only as a starting point or may not use them at all. The operation of FCNs is tightly connected with
(usually 0
mW/cm2)
and
one
is the
maximum
point,
the operation of the physical system providing control values
corresponding to 100 mW/cm2.
and taking feedback from the system. Moreover, during its initial training or its subsequent interaction with the physical
Node C2 represents the temperature that also must be in
system,
the
FCN
keeps
track of
its
previous
equilibrium
the
interval
[0,1].
Zero is
the
minimum
point
of the
points by means of a collection of fuzzy ifthen rules. Using
temperature
(usually 30
C)
and
one
is the
maximum
these characteristics, the FCN becomes a dynamic control
point, usualy 70C. system. In this paper we use the FCN in close cooperation
with a
fuzzy MPPT controller
and
with
a PV system as
Node
C3 represents
the
optimum
voltage
of the
shown in
Fig.
10.
The
FCN
is first
offline
trained by
photovoltaic system for the climatologic data obtained at the specific point of time, which also must be in the interval [0, 1], 0 is the minimum point of the voltage (usually 0 V) and one is the maximum point Vmax, where Vmax is calculated, according to (4) by setting
T = Tmin and S = Smax.
appropriately constructed data and then it is connected to any PV system to get feedback and send control values to regulate its output. Once the FCN is trained its knowledge can be updated and the FCN acts as an adaptive controller of the PV system.

Initial
OffLine
Training of
the
FCN:
The
offline
Node
C4 represents
the
optimum
current of
the
training is being performed in an incremental manner. This
photovoltaic system for the climatologic data obtained at the means that for each training data vector that contains PV
specific point of time, which also must be in the interval [0,
value
variables
corresponding to
different
operation
1]. Here 0 is the minimum point of the current (usually 0 A) and 1 is the maximum point Imax, where Imax is calculated, according to(2) by setting T = Tmax and S = Smax.
Node C5 expresses the optimum output power of the
conditions, the FCN weights are updated to comply with the data vector. Moreover, this new acquired knowledge is been stored in a fuzzyrule data base. We can divide the training into two cooperating stages.
photovoltaic system for the climatologic data obtained at 2) Stage 1Weight Updating Using New Data: This
the specific point of time, which also must be in the interval
stage
is concerned
with
the
method
of updating
the
[0, 1]. Here 0 is the minimum point of the power (usually 0interconnections
weights
of FCN
taking
into
account
W) and 1 is the maximum point Wmax, where Wmax is a
training
data.
Since
the
training is
being
performed
characteristic given from PV operational data under Tmin and Smax.
incrementally, during stage 1, only one data vector is used. The FCN converges to its new weights values after a number
of iterations. In each training iteration the FCN uses the
Node C6 is an artificial design node, the value of which is used to regulate the equilibrium point in the nodes C3, C4,
updated weights to reach new equilibrium node values by means of (10) and (11). These values are compared to the
and C5. The value of C6 is steady and equals 1. The weights
given
training
values
and
the
error
is given
for
the
new
W63, W64, and W65, respectively, are originally set to 0 and are allowed to change only, when one or more weights affecting nodes 3, 4, and 5 exceed the value of absolute 1.
updating iteration.
Rij
in
i1
Wij
Wij
if Wij
0 and
Rij 0if Wij 0
(14)
where constant value is used to drive values Rij in the range [0, 1]. In most practical situations, = 0.1.

Stage 2Storage of the New Knowledge in a Fuzzy Rule
Database:
The
procedure
described
in the
previous
stage
modifies our knowledge about the system by continuously modifying the weight interconnections and consequently, the node values. After the weight updating is taking place, the FCN reaches a new equilibrium point using (10) and (11). Since a new training vector might produce different weights and different equilibrium point we have to keep track of the current knowledge (weights and equilibrium points) to be used after the training phase. We do that by producing fuzzy ifthen rules, according to the following procedure [17].
Suppose, for example, that the FCN after being trained by a data vector converges to the following weight matrix:
W=
and concludes to an equilibrium point, which is
A = [A1 A2
A3 A4
A5 A6].
Suppose also that for a new training data vector, it concludes to a new equilibrium point
B = [B1 B2
B3 B4
B5 B6]
Figure10: simplified flowchart of the proposed method
With weight matrix
W=
W=
K=
The
offline
training
and
the
subsequent
operation
are
The
fuzzy
rule
database,
which is
obtained
using
the
described bellow.
information
from
the
two
previous
equilibrium
points, is
The weight updating is used by the following extended delta rule [16]
depicted in Figures. 11 and 12 and is resolved as follows:
j
j
p Asystem
N
1
A system W A system
There are two rules related to the above two different equilibrium situations
1 e
A system A FCN
i 1,i j i
(12)
ij j
Rule 1
j j and node 4 is mf1 and node 5 is mf1 and node 6 is mf1
W k W k 1 R ap(1 p)A FCN
(13)
ij ij ij i
where p is the error, k is the number of iteration, a is the
w23 is mf1 and w24 is mf1 and w25 is mf1 and w34 is mf1
learning rate (usually a = 0.1) and Rij is a calibration
and w35 is mf1 and w43 is mf1 and w45 is mf1 and w53 is
variable, which prevents the FCN node and weight values
mf1 and w54 is mf1 and w63 is mf1 and w64 is mf1 and
from being driven in their saturation point. Rij can be
w65 is mf1
computed by the following [16]:
Rule 2
Figure. 11. Lefthand side (if part).
The
number
and
shape
of the
fuzzy
membership
functions of
the
variables of
both
sides
of the
rules
are
gradually modified as new desired equilibrium points appear to the system during its training. To add a new triangular membership function in the fuzzy description of a variable, the new value of the variable must differ from one already
encountered
value
more
than a
specified
threshold.
The
threshold
comes
usually as
a compromise
between
the
maximum number of allowable rules and the detail in fuzzy representation of each variable.
Figure. 12. Righthand side (then part).
Once
the
new
knowledge
has
been
stored
using
the
above procedure we run again stage 1 using a new training vector. The procedure stops after all data vectors have been
If there is a change in the values of temperature and
presented.

Control of a PV System Using the Trained FCN and the Fuzzy Controller:
Once the FCN is offline trained, it can be connected to
insolation before the fuzzy controller drives the duty ratio of the switch S to the proper value corresponding to the MPP then the FCN interferes to the procedure and sends a new proper value for MPP voltage for the new insolation and
the PV system according to Fig. 10. The FCN receives
temperature
feedback from the fuzzy controller and from the PV array also. Once the error E(k) of the fuzzy controller is set to zero, it means that the duty ratio of the switch S of the boost converter is set to the proper value, so that the PV array is in



RESULTS
It is quite evident that irradiation and temperature play
its maximum power point. This new maimum power point
the most significant role on the maximum power that is
gives a new equilibrium point to the FCN. The new
drawn from a PV module. In order to measure these two
equilibrium point is used to train further the FCN.
quantities a pyranometer and a thermocouple is often used, although the output from these two measuring devices is not
always
the
most
adequate
information
to identify
the
the calculated by only the fuzzy controller method [8]. It is
operating point yielding the maximum power, which is of course a drawback of this methodology. The short circuit
clearly depicted that by using the FCN + fuzzy controller MPPT system, we have a significant energy gain. Actually,
current
from
the
PV array
gives
the
most
adequate
the combined method needs only five iterations, in order to
information of the effective insolation and temperature using (1)(6).
reach the new MPP, while the fuzzy controller method alone needs 12 iterations, in order to reach the same MPP. Each
We construct
training
data
for
the
FCN
using
the
iteration
corresponds
to one
second,
following
the
same
following
procedure: We
use
some
typical
climatic
data.
sampling procedure with [8].
These data are chosen to be Irradiation (Snode 1). We select
values
in the
range
0100
mW/cm2
using a
step
of 5
mW/cm2. Temperature (Tnode 2). We select values in the range 30 C70 C, using a step of 5 C.
By using all the possible combinations of these data and
by using
the
simulation
of the
photovoltaic
array, we
calculate the values of the optimum voltage (node 3), current (node 4), and output power (node 5) from (1) to (4). Using these node values for nodes 15, we update the weights of the FCN according to stage 1 of the training procedure and
Figure. 13. Sample versus power of PVarray. (A) Theoretical, (B) proposed method, and (C) fuzzy controller
for
the
equilibrium
point
derived
for
any
possible
combination, we store the knowledge according to stage 2.
The possible combinations of the climatic data are 441 and the FCN creates 21 triangular fuzzy numbers for nodes 1 and 2, 24 for node 3, 48 for node 4, 43 for node 5, 5 for node
6. Also,
287
fuzzy ifthen
rules
are created
to store
the
knowledge. The number of rules appears to be large because they account for all possible combinations of climatic data, even for those which are unlikely ever to occur. This number could be significantly reduced if we exclude this kind of combinations.
When we connect the FCN system to the PV array, if the
Figure. 14. Sample versus power of PVarray. (A) Theoretical, (B) proposed method, and (C) fuzzy controller
In Fig. 14, a similar comparison among the performance
error E(k) is zero, fuzzy MPPT controller sends the values of
of the three methods but in different temperature and
nodes 1 and 2 to the training part of the algorithm and
insolation conditions than those of Fig. 13 is given. We can
through the fuzzy rule database, the system decides, which
see that the new MPP was exactly the point that the FCN
weights values are appropriate to express the values of nodes
instantly returned to the dcdc converter for the new
3, 4, and 5. Executing (10) and (11) and by using the weights derived above, we calculate the new equilibrium point which expresses the values of the optimum current, voltage and output power of the PV array for the climatic data obtained at the specific time instant. In the next step the FCN sends the values of the control nodes to the dcdc boost converter, thus determining the optimum current, which corresponds to the maximum output power for the climatic data obtained at the specific time instant.
In order to evaluate the effectiveness of the proposed
insolation and temperature levels. That is why the proposed method (B) does not need to use the fuzzy controller, in order to reach the MPP. In this case by using the proposed method we reach the MPP after only one iteration, while by using only the fuzzy controller the system reached the MPP after 18 iterations.
algorithm,
we used
the
trained
FCN
for
controlling
the
operation of the BP270L PV array. The parameters of the PV array are given in Appendix B, where a sample of the weight
matrix
and
the
corresponding
equilibrium
points
is also
given. Fig. 13 presents a comparison between (A) the
Figure. 15. Sample versus power of PVarray. (A) Theoretical, (B) proposed
theoretical (computed by (1)(4)) MPP, (B) the calculated by the proposed FCN and fuzzy controller method and (C)
method (offline trained FCN), (C) fuzzy controller, and (D) proposed method (only online trained FCN).
Fig. 15 demonstrates the reason why it is better to use

Based
on these
parameters
the
training
data
are
offline training. As we can see the system is in an MPP,
produced
using
the
various
combinations
of the
corresponding to a specific insolation and temperature level. climatic data and (1)(4).
The
next
MPP,
corresponding
to another
insolation
and

The FCN is being offline trained using the above data
temperature level, is a point with which the FCN has already been trained offline. Using, as feedback from the PV array, the values of current, voltage and sort circuit current and by using (1)(4) the control system calculates the insolation and the temperature corresponding to the feedback values. The so computed insolation and temperature values are in this
and according to the procedure described in Section IV.

Once the FCN is offline trained, it is left to operate with the specific PV array in close cooperation with the fuzzy controller.


It is evident that this procedure can be applied to any
case values with which FCN has already been trained off PV array of the market.
line.
Thus,
the
proposed
method
returns
the
optimum
control law instantly to the dcdc converter, as it is shown in Fig. 15 (plot B). If there was no offline training, then the values of insolation and temperature, corresponding to the

CONCLUSION
A novel method for maximum power point tracking was presented in this paper. The method combines a fuzzy MPPT
new
MPP,
would
not be
values
for
insolation
and
with
an appropriately
designed
FCN
to speedup
the
temperature, with which the FCN has already been trained. procedure of reaching the accurate maximum power point of
In this case the FCN returns initially an MPP value, which is
a photovoltaic
array
under
changing
environmental
far
away
from
the
actual
one.
Therefore,
the
proposed
conditions. The method presents very good results, i.e., only
method
will
need a
number of
steps
before
reaching the
0.78% error in energy production when compared with the
actual
MPP
(plot
D).
It has
to be
mentioned
that
this
theoretical expected production of a commercially available
phenomenon
appears
mainly
in the
beginning of
the
photovoltaic array, simulated n climatic data of a whole
operation of the method, when the FCN is totally untrained. year. The methodology can be applied on any photovoltaic
After
a sufficient
time of
operation
the
FCN
gains
array of the market. Due to the existence of the FCN the
experience and therefore it acts as if it was initially offline trained
method could track and adapt to any physical variations of the photovoltaic array through time. Therefore, the method is
guaranteed
to present
its
very
good
performance
TABLE III
COMPARISON OF VARIOUS MPPT METHODS
independently of these variations.
APPENDIX A
The dcdc boost converter has been simulated, according to characteristics described below:
Array: BP270L PV array;
MPPT Method 
kWh(Px) 
Error (%) (PAPx)/PA 
A. Theoretical Total energy within year 2002 
PA = 70.389 

B. Offline trained FCN+ Fuzzy Controller 
PB=70.38745 
0.78 
C. Fuzzy Controller 
PC = 65.96857 
6.28 
D. Only online trained FCN + Fuzzy Controller 
PD = 68.995 
1.98 
MPPT Method 
kWh(Px) 
Error (%) (PAPx)/PA 
A. Theoretical Total energy within year 2002 
PA = 70.389 

B. Offline trained FCN+ Fuzzy Controller 
PB=70.38745 
0.78 
C. Fuzzy Controller 
PC = 65.96857 
6.28 
D. Only online trained FCN + Fuzzy Controller 
PD = 68.995 
1.98 

dcdc converter input voltage (Vi): 13.724.7 V;

dcdc converter output voltage (Vo): 48 V;

Switching frequency (f s): 33 kHz.
Finally, in order to estimate the energy gain of the new method (FCN + fuzzy controller MPPT) in comparison to
Below are shown the basic equations necessary for the dcdc boost converter design [22]
the method which uses fuzzy controller only we performed the following experiment. Using data from the year 2002 we ran both methods to give us the maximum power points and
Vo
Vi
1
1 D
t
, I i I o
1
1 D
1
calculated
the
energy
acquired
from
the
PV array.
Both
where
D on
and T
methods are compared to the optimal one [theoretical MPP values, computed by using (1) – (4) and the results are shown in Table III. It can be observed that the proposed method
T f s
APPENDIX B
PV system data:
(both
cases

and D)
outperforms
method C
(fuzzy

ki
= 2.8 mA/ C;
controller only). Actually, when the offline trained FCN is used the proposed method provides with only a 0.78% less energy production than the optimal (theoretical) case.
ii) iii) iv)
Open circuit voltage Voc = 21.4 V; Short circuit current Iscr = 4.48 A; Maximum power voltage Vmp = 17.1 V;
A typical
real
life
application
of the
proposed

Maximum power current Imp = 4.15 A.
methodology would require the following steps. Based on the node description presented in Section IV and

Once a specific PV array is selected its parameters, as by using the PV system data given by the manufacturer we


those
indicated
in Appendix B,
are
entered
to the
can see, as an example, an equilibrium point with weight
controller. matrix
W =
And A vector is A = [0.247
0.5762
0.6288
0.2179
0.1837
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The A vector means that
[18]
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S = 24.7mW/cm2, W = 16.048W.
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