Download fig. 2. the output characteristics of photovoltaic cells

CONTROL METHOD OF PHOTOVOLTAIC
MAXIMUM POWER POINT TRACKING BASED
ON FUZZY THEORY
1
Priyank Srivastava, 2Saumitra Mishra, 3Pankaj Gupta
1Assistant
Professor, EN Dept, SMS Technical Campus, Lucknow, India
2Sr. Lecturer, EC Dept, SRMCEM, Lucknow, India
3Assistant Professor, EN Dept, SMS Technical Campus, Lucknow, India
due to other factors such as PV module temperature and load
conditions. In order to maximize the power derived from the
PV module it is important to operate the module at its optimal
power point. To achieve this, a controller called a Maximum
Power Point Tracker is required.
The feedback control of maximum power point tracking is
usually based on power as a variable, which play the role of
the photovoltaic cell internal resistance and external load
impedance matching. The fuzzy control is a typical intelligent
control method, its most important feature is the experience
and knowledge of the experts used to control the language
rules, it does not rely on the precise mathematical model of
controlled object and be able to overcome the nonlinear
effects. In the photovoltaic power generation system, we
usually via a DC / DC or DC / AC connected photovoltaic
arrays and load, adjust the PWM duty cycle to achieve optimal
matching of the damping, so that maximum output power can
be achieved. Fuzzy control can automatically adjust the duty
cycle based on the magnitude of the power change, quick to
perceive the external environment changes, in the case that
does not interfere with the normal work of the system, find the
maximum power point. Thus, the adaptive duty cycle
disturbances MPPT method based on fuzzy logic control is
proposed.
Abstract— There is a large energy demand due to
industrial development and population growth specially in
India. The main challenge in replacing conventional
energy sources with newer and more environmentally
friendly alternatives, such as solar and wind energy, is how
to capture the maximum energy and deliver the maximum
power at a minimum cost for a given load. The output
power of Photovoltaic cells or solar panels has nonlinear
characteristics and these are affected by temperature, light
intensity and load. In order to improve photoelectric
conversion efficiency, maximum power point tracking
(MPPT) is required. According to the mechanism and
control methods of Maximum Power Point Tracking
(MPPT), a new modified adaptive duty cycle perturbation
MPPT control method which is based on fuzzy theory is
presented. The experimental results show the proposed
system can track the MPP with better performance
characteristics.
Index Terms— Buck-Boost Converter, Fuzzy Logic
Controller (FLC), Maximum Power Point Tracking
(MPPT), Photovoltaic (PV)
Introduction
Among various renewable and sustainable energy sources,
solar energy provides the opportunity to generate power
without emitting any greenhouse gas. The photovoltaic (PV)
system technologies have increasing roles in electric power
technologies, providing more secure power sources and
pollution-free electric supplies. Photovoltaic power generation
system can directly convert solar energy into electrical energy.
The current - voltage output of photovoltaic battery is
nonlinear, coupled with changes in the sunshine, temperature
and other factors, the output power is constantly changing.
The PV array can supply the maximum power to the load at a
particular operating point which is generally called as
maximum power point (MPP), at which the entire PV system
operates with maximum efficiency and produces its maximum
power. Currently, PV modules have very low efficiencies with
only about 12 − 29% efficiency in their ability to convert
sunlight to electrical power. Gallium Arsenide solar cells have
a high efficiency of 29%, while Silicon solar cells have an
efficiency of about 12-14%. The efficiency can drop further
Photovoltaic Cell Characteristics
A PV module is composed of individual solar cells
connected in series and parallel and mounted on a single
panel. The goal is to calculate the power output from a PV
module based on an analytical model that defines the
current-voltage relationships based on the electrical
characteristics of the module.
Photovoltaic Cell Mathematical Model and the Output
Characteristics. According to the electronic theory, the
equivalent mathematical model of the photovoltaic cells is:
I = Isc – I0[ exp[ (V + IRS)/AKT ] - 1] – [(V + IRS)/RSH] (1)
Where IPV = [Ipvr + KI( T-298)]S/100
(2)
1
(3)
FIG.1. EQUIVALENT CIRCUIT OF A SOLAR CELL
Power-Voltage characteristics
Where I and V is respectively the battery output current
and port voltage; IPV is the photocurrent; I0 is the battery
internal equivalent diode PN junction reverse saturation
current; q is the charge of an electron; A is diode PN
junction ideality factor; K is the Boltzmann constant, 1. 38
×10-23 J / K ; T is the operating temperature of photovoltaic
cells; Rs is the battery's series resistance; T r is the absolute
temperature, 273K; Ior is the diode saturation drain current
under Tr; Eco is the width of silicon; S is the light intensity,
W / m2; Ipvr is the short-circuit current under the conditions
of 298 K and of 1000 W/ m2 ; KI is short-circuit current
temperature coefficient under the conditions of I scr.
Affected by environmental factors such as light,
temperature, the output characteristics of photovoltaic cells
has the obvious nonlinear. Based on the above model can
make the IV and PV curves of photovoltaic cells are as
shown in Figure1.
FIG. 2. THE OUTPUT CHARACTERISTICS OF PHOTOVOLTAIC
CELLS
Basic Principles of Fuzzy Control
Fuzzy Logic
Fuzzy Logic is a branch of Artificial Intelligence. It owes its
origin to Lofti Zadeh, a professor at the University of
California, Berkley, who developed fuzzy set theory in 1965.
The basic concept underlying fuzzy logic is that of a linguistic
variable, that is, a variable whose values are words rather than
numbers (such as small and large). Fuzzy logic uses fuzzy sets
to relate classes of objects with unclearly defined boundaries
in which membership is a matter of degree[20].
Fuzzy Sets and Membership Functions
A fuzzy set is an extension of a crisp set where an element can
only belong to a set (full membership) or not belong at all (no
membership). Fuzzy sets allow partial membership which
means that an element may partially belong to more than one
set. A fuzzy set A is characterized by a membership function
µA that assigns to each object in a given class a grade of
membership to the set. The grade of membership ranges from
0 (no membership) to 1 (full membership) written as,
µA :U  [0,1]
which means that the fuzzy set A belongs to the universal set
U (called the universe of discourse) defined in a specific
problem. A membership function defines how each point in
the input space is mapped to a degree of membership[20].
Fuzzy Rules and Inferencing
The use of fuzzy sets allows the characterization of the system
behavior through fuzzy rules between linguistic variables. A
fuzzy rule is a conditional statement Ri based on expert
knowledge expressed in the form:
Ri: IF x is small THEN y is large
Current-Voltage characteristics
2
where x and y are fuzzy variables and small and large are
labels of the fuzzy sets.
If there are n rules, the rule set is represented by the union of
these rules i.e.,
R = R1 else R2 else ….. Rn .
A fuzzy controller is based on a collection R, of control rules.
The execution of these rules is governed by the compositional
rule of inference.
Fuzzy Controller Structure
The general structure of a fuzzy logic controller is presented in
Figure and comprises of four principal components:
• Fuzzification interface: - It converts input data into suitable
linguistic values using a membership function.
• Knowledge base: - Consists of a database with the necessary
linguistic definitions and the control rule set.
• Inference engine: - It simulates a human decision making
process in order to infer the fuzzy control action from the
knowledge of the control rules and the linguistic variable
definitions.
• Defuzzification interface: - Converts an inferred fuzzy
controller output into a non-fuzzy control action.
Fig. 4: Current-voltage characteristic of a PV module
Fig. 5: Power-voltage characteristic of a PV module
Figure 3 Basic configuration of fuzzy logic controller[20]
Fig 6: Photovoltaic MPPT system
PRINCIPLE OF MAXIMUM POWER POINT
TRACKING CONTROL
The photovoltaic module operation depends strongly on the load
characteristics, (Fig. 4 and 5) to which it is connected [14,]. Indeed,
for a load, with an internal resistance R i , the optimal adaptation
occurs only at one particular operating point, called Maximum Power
Point (MPP) and noted in our case P max .
Thus, when a direct connection is carried out between the source and
the load, (Fig. 4), the output of the PV module is seldom maximum
and the operating point is not optimal.
To overcome this problem, it is necessary to add an adaptation
device, MPPT controller with a DC-DC converter, between the
source and the load, (Fig. 6), [14]. Furthermore the characteristics of
a PV system vary with temperature and insolation, (Fig. 7
and 8) [6, 7]. So, the MPPT controller is also required to track the
new modified maximum power point in its corresponding curve
whenever temperature and/or insolation variation occurs[14].
Fig. 7: Influence of the solar radiation for constant temperature
3
• Any sensor data that provides some indication of a system's
actions and reactions is sufficient. This allows the sensors to
be inexpensive and imprecise thus keeping the overall system
cost and complexity low.
• Its rule-based operation enables any reasonable number of
inputs to be processed and numerous outputs generated. The
control system can be broken into smaller units that use
several smaller fuzzy logic controllers distributed on the
system, each with more limited responsibilities.[20]
MODELING AND SIMULINK RESULTS
Buck-boost converter modelling
The model of a buck-boost converter is shown in Figure 6.4 .
It consists of four basic components; Switching device
(MOSFET), diode, inductor, and capacitor. These components
are not ideal and some of the non-idealities are considered
when modeling. The inductor is modeled as an ideal inductor
in series with a resistance L R. The capacitor is modeled as an
ideal capacitor in series with a resistance C R. L R and C R
are used to model the power losses in the inductor and
capacitor respectively.
Step-up and Step-down of voltages depends upon the values
of Duty cycle D
Fig. 8: Influence of the temperature of junction for constant
insolation
Application of Fuzzy Logic in MPPT Control
If the value of duty cycle is less than 0.5 then step down
occurs and above 0.5 step up occurs
–For D = 1/2, the output voltage is the same as the input
voltage.
–For D = 2/3, the output voltage is double the input voltage,
–For D = 1/3, the output voltage is half the input voltage
Fig. 9. Flowchart of the algorithm steps
Fuzzy logic control relies on basic physical properties of the
system, and it potentially able to extend control capability
even to those operating conditions where linear control
techniques fail, i.e., large signal dynamics and large parameter
variations. As fuzzy logic control is based on heuristic rules,
application of nonlinear control laws to overcome the
nonlinear nature of dc-dc converters is easy. Fuzzy logic
offers several unique features that make it a particularly good
choice for these types of control problems because:
• It is inherently robust as it does not require precise, noisefree inputs. The output control is a smooth control function
despite a wide range of input variations.
• It can be easily modified to improve system performance by
generating appropriate governing rules.
Fig.10 Model simulation of BUCK-BOOST COVERTER in
MATLAB/SIMULINK
4
Result analysis for buck-boost
40
300
35
250
30
200
OUTPUT VOLTAGE
OUTPUT VOLTAGE
25
20
15
150
100
10
50
5
0
0
-5
0
1
2
3
4
5
TIME
6
7
8
9
10
-50
0
1
2
3
4
5
TIME
6
7
8
9
10
Fig. 11.Output of buck-boost converter when input voltage is
100V and duty cycle is 0.2
Fig.12 Output of buck-boost converter when input voltage is
100V and duty cycle is 0.7
MPPT Fuzzy Logic Controller MODELLING &
RESULT
Fuzzy Logic (FL) is one of the most popular control methods
which is known by its multi-rule-based variable’s
consideration . This method provides faster results compared
to other Artificial Intelligent control methods such as Genetic
Algorithm and Neural Networks. Being fast and robust are the
main reasons of choosing FL for MPPT in the current study.
To implement the FL in a problem, different steps of this
algorithm must be taken which are as follows.
Fig.13 Modeling of fuzzy logic controller
value of . The max-min method was applied to extract the 
from the triangle type membership function.
Fuzzification
The input defined in Equations
F(t) =
𝛥𝑃(𝑡)
𝛥𝑉(𝑡)
=
𝑃(𝑡)−𝑃(𝑡−1)
𝑉(𝑡)−𝑉(𝑡−1)
and ΔF(t) = F(t) − F(t − 1)
need to be fuzzified by some membership functions. For each
input value, the respective membership function returns a
Inference Diagram
A rule base must be applied to the obtained membership
function according to Mamdani. The rule table is designed and
shown in Table1.
5
ΔF(t)
F(t)
NB
NB
NM
NS
ZE
PS
PM
PB
ZE
ZE
ZE
NB
NB
NB
NB
NM
NS
ZE
PS
PM
PB
ZE
ZE
NS
PS
PM
PB
ZE
ZE
ZE
PS
PM
PB
ZE
ZE
ZE
PS
PM
PB
NM
NS
ZE
PS
PM
PB
NM
NS
ZE
ZE
ZE
ZE
NM
NS
ZE
ZE
ZE
ZE
NM
NS
PS
ZE
ZE
ZE
The 3D input-output surface is also obtained by using
MATLAB FL Inference.
Table 1: control rules of fuzzy logic controller
Now modeling of MPPT fuzzy controller for its each
membership function inputs and outputs are shown in the
following figures.
Fig.15. Surface waveform of the FLC
Defuzzification
For the Defuzzification, the centroid method is applied to
return a proper value for the duty cycle variation (ΔD). The
difuzzified output value of the FLC must be added to a
reference value of duty cycle which is considered equal to 0.5
for the current study. The result is the optimum value of D can
be sent to the buck-boost converter as a control signal
Thus variations in duty cycle have been implemented with the
help of fuzzy logic controller for various input combinations
under different conditions of variations.
(a)
CONCLUSION
On the whole, it is concluded that the overall objective of
formulating and implementing a fuzzy logic controller for
maximum power point tracker of a photovoltaic power system
has been met. All membership functions of Fuzzy logic
controller were modeled in MATLAB.
Surface Waveform for Fuzzy controller was plotted and seen.
Fuzzy rules were implemented for more smooth operation.
Rule viewer fuzzy controller results were achieved for duty
cycle adjustment i.e. fuzzy controller output.
Current-Voltage characteristics curves for photovoltaic are
successfully plotted and seen. Also Power-Voltage
characteristics curve are successfully plotted and seen.
Buck-boost converter was found to be the most suitable
topology among Buck, Boost and Buck-Boost converter for
MPP tracking. Buck-Boost converter is successfully modeled.
Its step-up and step-down operations are successfully achieved
and results are shown.
Although there is a large amount of work that can and should
still be done, the work in this paper has created a solid
foundation to allow that work to continue.
(b)
(c)
Fig. 14 Membership function of (a) input F, (b) input ΔF and
(c) output ΔD
6
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