Performance Analysis of Solar Photovoltaic System

with Fuzzy Based Variable Step Size MPPT

Algorithm Using Matlab /Simulink
Sarika E.P Josephkutti Jacob Dr Sheik Mohammed S
Research Scholar, Division of EEE Head of Division, EEE Assistant Professor, EEE
Cochin University College of Engineering Cochin University College of Engineering T.K.M College of Engineering
Alappuzha, India Alappuzha, India Kollam, India
sarikaep@cusat.ac.in josephkutti@yahoo.com sheikmsulthan@gmail.com

Shiny Paul
Associate Professor, EEE
Cochin University College of Engineering
Alappuzha, India
shinypaul@yahoo.com

Abstract— In the recent decades, Photovoltaic (PV) power amongst renewables has increased to 31.1% at the end of
generation has become one of the primary power source due to 2017-18 from just 3.8% at the end 2011-2012.
the advantages such as less maintenance and environmental
benefits. Moreover, the generation source is ultimately free and
abundant. However, the major barriers related to PV power
generation are low power conversion efficiency, high cost of PV
modules and nonlinearity in output power. Because of low
power conversion efficiency, PV systems should work always at
its Maximum Power Point (MPP). A power conditioning unit
with Maximum Power Point Tracking (MPPT) technique is
employed in the PV systems to harvest maximum power. The
main function of MPPT is to detect the MPP for the given
conditions and operate the system at that point. In this paper
Fuzzy Logic Controller (FLC) based variable step size MPPT
for a standalone solar PV system is presented. Solar PV system
with Fuzzy based MPPT controller is built in Matlab
/Simulink. The performance of proposed variable step size
fuzzy MPPT algorithm is studied for different input conditions Fig.1.Year wise solar and wind capacity addition data [1]
and analyzed in terms of performance parameters such as
tracking speed, steady state oscillations, response under Maximum Power Point Tracking is a technique employed in
variations in irradiance and temparature, average output SPV systems to harvest maximum available power from the
power and output power ripple. The results are compared with PV module. The main challenge in Solar PV system is to
Variable Step Size Incremental Conductance (VSS InC) MPPT track maximum power under all environmental conditions.
algorithm and conventional InC based PV system. According to maximum power transfer theorem, to transfer
maximum power from source to load, the value of load
resistance should be equal to source resistance ie the value
Keywords— Solar Photovoltaic (SPV), Maximum Power
of load resistance should be optimized in such a way to
Point Tracking (MPPT), Fuzzy Logic Control (FLC), Variable
match with the source resistance. But, this optimal
Step Size Incremental Conductance (VSS InC), Simulation,
MATLAB/Simulink.
resistance value changes with change in environmental
conditions. Therefore, it is not practically possible to change
I. INTRODUCTION the value of load resistance corresponding to every change
in environmental conditions. MPPT controller is designed
Photovoltaic energy is one of the most promising energy
such that it changes the converter’s operating point so that
source since it is pollution free and abundantly available. As
load resistance and source are made equal under all
on 31 March 2018 solar installations in India has crossed 20
environmental conditions. Many algorithms have been
GW and the total grid connected solar installations has
introduced to track MPP at varying environmental
reached 20.6 GW whereas the rooftop capacity crossed the 1
conditions. When compared to other methods Perturb and
GW. The total installed solar capacity added during 2017-18
observe (P&O) [2, 3] and Incremental Conductance
is around 10GW, which is almost double that of the algorithm (InC) [4, 5] are widely used due to their simplicity
previous year. Solar installation during the last year is more and easiness in implementation. Other simple MPPT
than 5 times the wind capacity installed during the same techniques introduced are Open Circuit Voltage [5], Short
year. The year wise solar and wind capacity addition data as Circuit Current method [5]. The intelligent technique based
provided by Ministry of New and Renewable Energy MPPT algorithms such as fuzzy MPPT [6, 7], Artificial
(MNRE) is given below [1]. The contribution of SPV Neural Network [6] and a combination of Neuro Fuzzy [8]

978-1-5386-0576-9/18/$31.00 ©2018 IEEE

are also proposed. These MPPT techniques differ from each different semiconductor materials such as monocrystalline
other in terms of input parameters, tracking speed and silicon, polycrystalline silicon, amorphous silicon and
accuracy. copper‐indium selenide.PV cells convert solar energy into
Fig.2 shows the functional block diagram of a standalone electricity. This conversion occurs when the PV cells are
solar PV system. DC-DC converter interconnects PV exposed to light which causes electrons to drift and this
module and load. The MPPT controller receives the inputs produces an electric current. The amount of current depends
and adjusts the duty cycle to harvest maximum power from on the cell size as well as the irradiation level.
the solar PV module under all environmental conditions. Fig.4 presents the equivalent circuit of a PV cell which
The output of the DC-DC converter can be used to power consists of a photocurrent source (Ipv), Diode (D), a parallel
the DC load directly or AC loads by employing an inverter. resistor (Rp) and a series resistor (Rse).
In a grid connected system, the output of inverter is directly
connected to the grid.

Fig.4. Equivalent Circuit of a PV Cell

Photocurrent ( ) generated by the PV cell is given as

= ( −
) (1)
Fig.2. A Typical PV System with MPPT Controller Output current ( ) is expressed as,
II. THEORETICAL BACKGROUND = − − (2)

A. Performance of Solar Photovoltaic Cell The diode current ( ) equation is

Irradiance and temperature are the most important q (3)
parameters that describe the operating conditions of the PV I d = I {exp( + IRse ) * V − 1}
s ( nkTC N S )
cell. The Standard Test Conditions (STC) of SPV cell is
Irradiation (G) of 1000W/m2 and temperature (T) of 250C. Isc is the short-circuit current at 25°C and =1000W/m2
PV modules are tested under these conditions during (STC), Tc and Tr are the cell temparature and reference
manufacturing. But these conditions vary at the PV temperature of the cell respectively. Is is the saturation
installation site. Fig.3. shows the effect of change in current of the diode, k is the Boltzmann constant [1.38x10 -
23
irradiance and temperature in the power generation of PV J/K], the electron charge is denoted by q [1.60x10-19C],
modules. and n is the diode ideality factor and depends on the
technology used [9, 10].
C. MPPT Techniques

1) Conventional Incremental Conductance(InC) MPPT

The conventional Inc MPPT uses change in PV power

( ) , change in PV voltage (Δ ) and change in PV
current ( ) to compute the MPP [11].The following
Fig.3. Effect of irradiance and temperature in the output power of the PV equations are based on InC MPPT.
module
( )
From Fig 3, it is clear that the peak power changes = = (4)
correspondingly to the variations in irradiance and
temperature. Module voltage Vpv is almost constant and
module current Ipv is directly proportional to irradiation level At MPP, equation (4) will be equal to zero. That is
and hence PV power increases as irradiation level increases. =- (5)
But module voltage Vpv is inversely proportional and
module current Ipv is almost constant as temperature
changes. Therefore PV power decreases as temperature level In this equation - represents the instantaneous
increases. MPPT algorithms are intended to control the PV conductance and is the incremental conductance. InC
system and extract maximum power under varying
environmental conditions. MPPT works based on the following conditions.
B. Solar PV Cell Electrical Modelling
, =0 (6)
PV module consists of silicon based PV cells connected in , 0 (7)
series and parallel, depending on the voltage or current
requirements. PV cells are available commercially in , 0 (8)
 3) Fuzzy Logic Controller (FLC)
Fig 5 shows the flow chart of Inc algorithm [11].
Fuzzy controller consists of an input stage (Fuzzification), a
processing stage (Inference and Rule base), and an output
stage (Defuzzification).The diagrammatic representation of
FLC is given in Fig.7.

Fig.7. Block diagram of Fuzzy Logic Controller.

Fig.5. Incremental Conductance MPPT Flowchart.
Fuzzy sets are the input variables in a fuzzy control system
Based on (6), (7) & (8), the algorithm continuously tracks are mapped by a set of Membership Functions (MF). The
the PV output parameters and it adjusts the duty cycle (D) of process of converting the crisp input values into the
the converter either by increasing or decreasing the membership functions is called fuzzification and obtaining
perturbation ( D) until reaches the MPP. The draw backs of crisp input values from the membership functions of the
the conventional InC MPPT algorithm are that it oscillates given fuzzy sets is called defuzzification. Logic rules in the
around the MPP once it reaches there and it shows slower form of If-Then statements are used in the processing stage.
response in varying weather conditions. The step size for Among the different defuzzification techniques, centroid
conventional InC is a fixed value ( D = 0.01) and this is one method is most commonly used.
of the reasons for its slower response. These draw backs are The centroid method is defined as
overcome by the variable step size InC. ( ( ) )
( )
(9)
2) Variable Step Size InC (VSS InC) MPPT Algorithm where, x is the output and μ is the membership function of x.
Thus FLC receives the input(s), process then by applying
rules and generate the output(s). In our case FLC is used as
In this algorithm is compared with an error and MPPT controller to generate duty cycle value based on the
depending on the value of error corresponding step value is change in PV module outputs.
given. If the operating point is close to the MPP a small step D. DC-DC Converter
value (dDsmall ) is given and if the operating point is far
away from the MPP, the algorithm gives large step value
(dDbig) [12]. VSS InC MPPT is designed with duty cycle Boost converter is widely used for PV application because
values dDbig =0.025 and dDsmall= 0.005 and the performance of its simple design, high conversion efficiency and reduced
of PV system with VSS InC MPPT is analysed by voltage stress. Boost converter circuit is shown in Fig.8.
simulation. Fig.6 illustrates the flow chart of VSS InC
MPPT.

Fig.8.Boost Converter Circuit.

The converter circuit consists of Inductor (L), Diode (D),

Capacitor (C), load resistor (RL), the control switch (S). For
this converter, output voltage(V ) will be greater than the
input voltage (V ). The output voltage of converter depends
on the duty cycle of the control switch and can be controlled
by varying the ON time of the switch. Thus, for a duty cycle
D, the average output voltage can be calculated as below.
= (10)
Fig.6. Variable Step Size Incremental Conductance MPPT Flowchart.
 Boost Converter circuit is mathematically modelled the output of the fuzzy system is change in duty cycle
using the equations below [9]. dD[14]. The input variables of the fuzzy system are
expressed as
(a)During the ON period of switch(Ton): = ( ) −( ) (19)
= ( ) −( ) (20)
(on) = (11) The fuzzy output of system is given by
= − (21)
(on) = − (12)
The rules of the fuzzy MPPT controller are given in Table
(b)During the OFF period of switch (Toff):
II.
(off) = − (13)
I (off) = −I (14) TABLE II: FUZZY RULES
= (15) dP
NB NS Z PS PB
dI
= (16)
NB NB NS NS PS PB
In an ideal circuit the input and output power of the NS NB NS NS PS PB
converter will be same ie. = or =
Z NB NS Z PS PB
The inductor and capacitor value of the boost converter
can be calculated as below [13]. PS PB PS PS NS NB
PB PB PS PS NS NB
(c) Selection of Inductor
To develop an optimized fuzzy MPPT controller, 5 MFs are
The inductor value of the Boost converter can be
selected for each of the input. The MFs of the inputs are
calculated from
defined as Negative Big (NB), Negative Small (NS), Zero
L = (17) (Z), Positive Small (PS) and Positive Big (PB). Since the
number of MFs is selected as 5, 25 rules have been
where is the switching frequency and is the input developed. For eg: if dP is NB and dI is NB , will be PB
current ripple. Current Ripple Factor (CRF) is the ratio means the operating point is far away from MPP and fuzzy
between input current ripple and output current and is controller generates a very large dutycycle. Similarly when
normally taken as 0.3. the operating point is near to MPP, it generates a very small
duty cycle. Membership functions for the input and output
(d) Selection of Capacitor variables of fuzzy MPPT are shown in Fig. 9(a), 9(b) and
The capacitor value of the Boost converter is expressed as 9(c) respectively.
C = (18)
where is the ripple in output voltage and is normally
taken as 5% of output voltage. Solarex MSX60 PV module
has Vmp=17.IV, Imp=3.5A and the maximum power Pm=60W
[12] is used as source in this study. Therefore, a 60W boost
converter is designed and modelled using the above
equations. The component details are presented in Table I.

TABLE I. BOOST CONVERTER SPECIFICATIONS

Fig.9(a). Membership Function of Input variable 1(dP)

Description Value
Input Voltage 17V
Output Voltage 30V
Output Current 2A
Switching Frequency 10KHz
Input Capacitance 100µF
Fig 9(b). Membership Function of Input variable 2(dI)
Output Capacitance 60µF
Inductor 700µH
Resistor 15Ω

III. DEVELOPMENT OF FUZZY BASED VARIABLE

STEP SIZE MPPT
The inputs of the fuzzy system are the change in PV output Fig 9(c). Membership Function of output variable (dD)
power dP and the change in PV output current dI whereas
 The surface view of fuzzy rules is shown in Fig 10. B) Constant Temperature and Varying Irradiation
In this case, the temperature of the module is kept constant
(T=250C) and the irradiation is varied. The varying
irradiation pattern used for the simulation is shown in
Fig.12. Fig.13 (a) and Fig.13 (b) shows the output power
and duty ratio respectively for the conventional InC, VSS
InC and the proposed Fuzzy based VSS MPPT based system
under this condition. The proposed MPPT shows faster
response whenever the changes occur in the environmental
conditions, lesser oscillations around MPP and also the duty
cycle given by the controller is more accurate comparing to
Fig.10.Surface view of Fuzzy rules the other controller.

IV. SIMULATION RESULTS AND DISCUSSION

The MATLAB based simulation model of the PV system is
operated under three different conditions, i) Standard Test
Condition ii) Constant temperature and varying irradiation
and iii) Constant irradiation and varying temperature. The
system is simulated with Conventional InC MPPT, VSS InC
MPPT and fuzzy based VSS MPPT. Fig.12.Varying Temparature Pattern

A) Standard Test Conditions (STC)

Fig. 11(a) and 11(b) shows output power and duty ratio
respectively for the VSS InC and the proposed Fuzzy based
VSS MPPT based system under STC. The maximum output
power of MSX60 PV under STC is 60W. The output power
obtained by simulating PV system model with VSS Fuzzy Fig.13. (a) Module Output Power for constant Temperature and varying
Irradiation
MPPT is 59.94W. The output power matches well with the
manufacturer’s data sheet specifications. This shows that the
duty cycle given by the proposed system is accurate. From
Fig. 11(a), it can be seen that the conventional InC MPPT
controller takes 0.165s to reach the MPP whereas VSS InC
MPPT controller takes 0.07s to reach the same point. But
both the conventional and VSS InC oscillates around the
MPP after reaching the MPP. But the proposed Fuzzy
Fig.13. (b) Duty cycle for constant temperature and varying irradiation
MPPT takes only 0.05s to reach MPP which shows a faster
response and the method also possess lesser oscillations C) Constant Irradiation and Varying Temperature
around the MPP when compared to the other method.
In this case, the irradiation of the module is kept constant (G
= 1000W/m2) and the temperature is varied. The varying
temperature pattern used for the simulation is shown in
Fig.14. Fig.15 (a) and Fig.15 (b) shows the output power
and duty ratio respectively for the conventional InC, VSS
InC and the proposed Fuzzy MPPT based system under
these conditions. The results obtained with the proposed
controller under this condition well matches with the desired
values. This means that more accurate duty cycle is
generated by proposed fuzzy based VSS MPPT when
compared to the other one.
Fig.11(a) Module Output Power under Standard Test Conditions

Fig.14.Varying Temparature Pattern

Fig.11 (b) Dutycycle under Standard Test Conditions
TABLE III. POWER OUTPUT & RIPPLE OF CONVENTIONAL InC,
VSS InC AND VSS FUZZY UNDER VARYING TEMPARATURE

Temperature-25oC
Parameters Irradiation (W/m2)
800 900 1000 1100 700
InC 47.02 53.12 59.21 65.21 39.43
Pavg (W) VSS InC 47.24 53.65 59.94 65.81 39.98
VSS Fuzzy 48.24 54.95 60.02 66.8 40.78
Ripple InC 0.88 1.03 0.90 0.33 0.74
VSS InC 0.30 0.64 0.46 0.33 0.02
(%) Fig.16. (b) Output power ripple under constant irradiation and varying
VSS Fuzzy 0.27 0.02 0.03 0.04 0.01
temparature.

Table III & IV provides information about the average

power output and percentage ripple of InC and Fuzzy based
system for constant irradiation-varying temperature and
varying temperature –constant irradiation conditions.

TABLE IV: POWER OUTPUT & RIPPLE OF CONVENTIONAL InC,

VSS InC AND VSS FUZZY UNDER VARYING IRRADIATION

Irradiation-1000W/m2
Parameters Temperature ( oC )
20 25 35 50 40
Fig.15. (a) Power for varying temperature and constant irradiation InC 62.12 59.81 53.21 45.02 51.81
Pavg
VSS InC 62.97 60.09 54.06 46.07 52.01
(W)
VSS Fuzzy 63.91 60.45 54.87 46.98 52.25
InC 2.31 1.98 1.51 1.42 1.31
Ripple
VSS InC 1.95 0.47 0.39 0.27 0.14
(%)
VSS Fuzzy 0.03 0.07 0.07 0.01 0.03

Analyzing the above data it is evident that VSS Fuzzy

based MPPT system possess more average output power and
negligible output power ripple when compared to InC based
Fig.15. (b) Duty cycle for varying temperature and constant irradiation system. Thus, the overall efficiency of Fuzzy based solar PV
system will be comparatively high.
After analysing the above graphs, it is clear that Fuzzy
based MPPT method is having fast response over varying V. CONCLUSION
environmental conditions towards MPP than InC based In this paper, a standalone solar PV system with Fuzzy
system. Moreover, the oscillations around the MPP is based VSS MPPT controller for fast changing
smaller in the case of Fuzzy based system when compared environmental conditions is presented. Performance of the
to conventional InC and VSS InC based system. Oscillations proposed MPPT controller is analyzed in terms of
in duty cycle will reflect on output power and finally the performance parameters such as tracking speed, steady state
efficiency of the whole system is affected. Fig.16 (a) and oscillations, average output power and output power ripple
Fig. 16(b) shows the output power ripple in InC and Fuzzy under fast changing environmental conditions. The results
based system under 25oC, 1000 W/m2 and 1000W/m2,35oC are compared with conventional InC and VSS InC MPPT.
conditions respectively. The results obtained shows that the proposed MPPT
controller is having faster response than conventional one
under fast changing environmental conditions. The duty
cycle generated by this proposed MPPT is more accurate,
shows lesser oscillations around MPP and has more average
output power and less output power ripple than the other
MPPT techniques.
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