Fill Factor Based Maximum Power Point Tracking
(MPPT) for Standalone Solar PV System
4th International Conference on Advances in Energy Research
Indian Institute of Technology Bombay (IITB)
Sir Padampat Singhania University, Udaipur
A fill factor based new approach for maximization of efficiency of solar PV
system is investigated using modified MPPT technique.
On the I-V characteristic curve of solar PV module, fill factor is one of the most
important parameter for determining and tracking the maximum power points
(MPPs) throughout the day.
In the proposed technique, the area under the I-V curve is to be optimized .for
a fill factor value of 1.
The fill factor having a value 1 represents the maximum possible efficiency of
a solar PV module yields .
The present technique may be considered as the modified version of the
constant voltage method for MPPT.
Apart from the mathematical description of the proposed technique, the
simulated curves of I-V and P-V characteristics (with MPP) of solar PV module
The proposed MPPT technique has many features over the existing MPPTs like
reduced sensor requirement, direct determination of MPP, reduced tracking
time, maximized efficiency and cost effectiveness.
• In recent times, the overwhelming consumption of fossil fuels for various
energy needs has reflected a big danger to our environment.
• Electricity generation from fossil fuels (like coal, gas and other petroleum
products) in various thermal power plants across the world is the most
hazardous sector for our environmentally safe society.
• Different greenhouse gases (GHGs) like CO2, CO, SO2, NOx and other
pollutants are the uncontrolled byproducts from these thermal power
plants. These GHGs pollute the environment at a very severe level and
causes many dangerous and fatal diseases in humans, animals and plants in
our society. The massive production of these poisonous gases not only leads
to many health problems but it also contributes to the biggest climate
change challenge called global warming.
• Global warming is the biggest challenge and a frontier to work upon for a
sustainable and ecologically balanced society. Due to global warming, the
various environment related problems like flood and drought may arise in
different part of the world.
• Apart from all these ecological problems, one more factual point is
important that the fossil fuels will not be available for a long time.
• Fossil fuels are depleting day by day due to their uncontrolled and extensive
consumption in power plants, automobile and other energy applications.
• Due to all these facts, the solar energy has drawn attention of energy
professionals for electrical power generation for many years. The efficiency of
solar power generating system using photovoltaic (PV) technology is the most
important parameter in utilizing the solar PV systems.
• The efficiency represents the maximum power output from solar PV power
system. The maximum power output can be achieved by an electronic tracking
of maximum power points (MPPs) on the characteristic curve of solar PV
• The MPPs can be tracked by a power electronic circuitry called maximum
power point tracker (MPPT).
• In a MPPT, a DC-DC converter is used to adjust the output voltage from PV
module to the load in such a way that it indicates the maximum possible
power on the characteristic curve.
• The operation of DC-DC converter is carried out by its electronic switch (usually
MOSFET). The switching is controlled by means of a control algorithm.
• Many MPPTs have been discussed and developed till date. Here Perturb and
Observe (P&O) and Incremental Conductance method are discussed and a new
fill factor based MPPT technique has been proposed for maximized efficiency
of solar PV system.
STANDALONE SOLAR PV SYSTEM
• A complete standalone solar PV system comprises of the
following components, solar PV module(s), maximum power
point tracker (MPPT), electrical load, charge controller,
battery, inverter (for ac loads). Figure 1 represents a typical
solar PV power system.
Fig 1 Typical Standalone Solar Photovoltaic (SPV) System
PV MODULE CHARACTERIZATION
Electrical circuit and Characteristic equations of solar cell
The characteristics of PV module are the basic requirement
for tracking the maximum power points (MPPs) using any
MPPT technique. For characterizing the solar PV module, it is
required to model the characteristic equation from an
electrical equivalent of solar cell (module) as in following
Fig 2 Electrical Equivalent model of solar PV cell
The current produced by the solar cell is given by:
I = IL − ID − ISH
I = output current (amperes)
IL = photo generated current (amperes)
ID = diode current (amperes)
ISH = shunt current (amperes).
The current through these elements is governed by the
voltage across them:
Vj = V + IRS
Vj = voltage across both diode and resistor RSH (volts)
V = voltage across the output terminals (volts)
I = output current (amperes)
RS = series resistance (Ω).
I-V and P-V characteristic curves of solar PV module
I-V and P-V characteristics of solar PV module are the basic requirement for
tracking of MPP by using any of the MPPT technique or algorithm. Therefore the
following characteristic curves are simulated in the MATLAB environment. The
maximum power point (MPP) is also indicated on both of the curves.
Fig. 3 I-V and P-V Characteristic Curves
SOME EXISTING MPPT TECHNIQUES
Several MPPT techniques (algorithms) have been
developed in past years varying in terms of
implementation complexity and tracking speed and
stability of MPP. No MPPT provides an optimized
efficiency of solar PV system at any instant of time. In
the following section, some existing MPPT techniques
have been briefly discussed.
• Perturb and Observe (P&O) based MPPT
This is the mostly used and a primary algorithm which is quite
simple to implement. In this method, the voltage is perturbed
(changed) and output power is measured for various
perturbation stages. Subsequently output is compared with
the previous values and the voltage is perturbed accordingly
to ensure the point of maximum power. Perturb and Observe
method has been used by most of the researchers to develop
its new variants like voltage based P&O and Duty cycle based
P&O. Perturb and observe based MPPT does not depend on
PV array , tracking efficiency is good but with unstable
operating points, implementation is simple, sensing
parameters are voltage and current. The P&O technique can
be represented by the following figure.
• Incremental Conductance based MPPT
The incremental conductance method is based upon the fact
that the power would be maximum with the condition that
its differential with respect to voltage equals to zero. On the
P-V characteristic curve, the differential of power with
respect to voltage is zero, positive or negative on the peak of
the curve (i.e. at MPP), on the left to MPP and on the right to
MPP respectively. The following description of this method
gives the mechanism of operation. The maximum power
point yields the following situation
At MPP, dP/dV = 0
Solving the above equation, the following situation persist for
MPP and other two point,
dP/dV = -I/V at MPP,
dP/dV > -I/V on LHS, dP/dV <
-I/V on RHS The operation of Incremental conductance
method can be represented as in the following figure
• Constant Voltage Ratio based MPPT
Constant Voltage Ratio based method is one of the cheapest method for
MPPT implementation. It does not require any sensor to sense the
voltage or current. It works on the principle that for a given
characteristic curve, the ratio of maximum power voltage to the open
circuit voltage is constant and that will be less than 1. The greater value
of this constant indicates the greater efficiency of the PV system at a
given instant of time. After calculating the values of Vmp and Voc, the
operating point is forced to be at the calculated value of this constant.
The precise value of the constant is the primary requirement of this
MPPT technique. The biggest advantage of this technique is that it does
not require any voltage or current sensor.
Proposed Fill Factor based MPPT
• The is also concerned with the constant voltage method. The
proposed technique is also a data based technique so the
available or calculated data for the various parameters like
VOC, ISC,, VMP and IMP are required.
• In the case of constant voltage method, the ratio of two
voltages (VMP and VOC ) is calculated which is constant. In the
case of fill factor based technique, the ratio of two powers (P MP
and PTH ) is calculated and the operating point is forced to
operate at MPP.
• Mathematically we can state that the maximum possible area
(product of voltage and current) formed by the intersection of
horizontal line (voltage) extended to the I-V curve and vertical line
(current) extended to the I-V curve.
• The maximum power point is always present at the point of
intersection of these extended lines from voltage axis (voltage
at maximum power-Vmp) and current axis (current at maximum
• This MPPT represents the maximum output power (Po (max) = Vmp x
Imp) extracted from the solar PV system to the electrical load.
The rectangle formed by these two line represents the fill
factor of the solar PV cell.
• The optimization of this parameter i.e. fill factor in turn
ensures the higher efficiency of the overall solar PV system.
• The proposed methodology based upon fill factor
maximization may be considered as the modified version of
the constant voltage method based MPPT technique. The fill
factor based mechanism has been illustrated in the following
Fig. 5 Fill factor representation of proposed MPPT technique
• Mathematical Description of Fill Factor
The fill factor may be defined as ratio of theoretical power to the
maximum power which can be mathematically represented as
Fill Factor (FF) = VMP.IMP/ VOC.ISC = P
VOC= open circuit voltage
ISC= short circuit current
VMP= Voltage at the point of maximum power
IMP= Current at the point of maximum power
The optimized Value of fill factor leads to the more squareness of the
I-V characteristic curve of solar PV module. Consequently it causes
to the maximized efficiency of solar PV power generating system.
The maximum theoretical FF from a solar cell can be determined by
differentiating the power from a solar cell with respect to voltage and finding
where this is equal to zero.
The above equation only relates Voc to Vmp, and other equations are required
to find Imp and FF. Therefore the expression for Fill Factor (FF) can be
determined empirically as:
This whole expression is the function of open circuit voltage (V OC). It means
that the optimized value of this function will yield to ensure the extraction of
maximum power from solar PV system to the load at any instant of time
throughout the day. The above mathematical description of fill factor reflects
that at the point of maximum power (at dP/dv = 0), the fill factor will be
having a maximized efficiency of solar PV system.
Proposed Maximum Power Angle Determination Based Maximum Power
Point Tracking (MPPT) for Maximizing the Efficiency of Solar PV System
•In the proposed MPPT method, the maximum power point (MPP) is tracked
using the geometrical and mathematical analysis of the I-V characteristic
curve of the solar PV module.
•In this method, the angle made from the intersection point of open circuit
voltage (VOC) and short circuit current (ISC) with respect to the voltage (V) axis to
the point of maximum power (MPP) is determined using the known
parameters of the solar PV module. The MPP angle determination for the
following characteristic curves is analyzed as follows.
•The point of theoretical power (PTH) is the intersection point of VOC and ISC.
Therefore a hypotenuse is drawn from the point P TH to the point of origin. Then
the angle made by this hypotenuse and the voltage (V) axis is 45 0 (as evident
from the figure). It also reflects that the angle made by this hypotenuse and
current (I) axis is also 450. Now it is needed to determine the angle made by
the line (joining PTH and ISC) and the line (joining PTH and MPP).
The following calculation steps are used for determining the MPP angle for the
given characteristic curves.
The corresponding value of voltage at MPP (VMP) = 17 volts
The corresponding value of current at MPP (IMP) = 3.5 A
The corresponding value of voltage at VOC = 21 volts
The corresponding value of current at ISC = 3.8 A
It is also clear (from the figure) that AB = 3.8-3.5= 0.30 A and BC = 3.5-3.05= 0.45
where AB = distance between MPP and ISC – PTH line and
BC = distance between MPP and hypotenuse (line joining P TH to origin)
Therefore the maximum power point angle will be
00 < ΘMPP (MPP angle) < 22.50
In right-angled triangle ∆ ABPTH,
BPTH2 = AB2 + APTH2
or BPTH = √AB2 + APTH2
AB = 0.30
APTH= 21-17 = 4
Therefore BPTH = √0.302 + 42 = √16.09 = 4.011234
Now the ΘMPP (MPP angle) can be easily determined as the following formula
Cos ΘMPP = APTH / BPTH
or ΘMPP = Cos-1(APTH / BPTH) = Cos-1(4 /4.011234) = Cos-1(0.9972) = 4.28860
ΘMPP = 4.28860
• This is the approximate value of MPP angle for the given characteristic
• The generalized formula for determining the MPP angle has been derived
ΘMPP = Cos-1(APTH / BPTH)
• In this method, the operating point is forced to reach to MPP using
proposed MPP angle determination methodology.
• The following illustrations show the mechanism for the proposed MPPT
control method based on MPP angle determination.
• For tracking the MPP using this formula, the information about the
characteristic parameters are to be known.
Mechanism of maximum power point (MPP) angle technique for MPPT
The effect of fill factor on the design of an improved control
algorithm for a MPPT of standalone solar PV power generating
system is investigated. The empirically derived expression of fill
factor is proved to be a potent basis for a modified MPPT which
ensures the maximum possible efficiency of the solar PV system.
It has been also observed that the proposed MPPT technique is
having an empirical relationship with constant voltage method
for MPPT. The fill factor based technique is a form of data based
method. Due to its data based approach, the external circuitry
like voltage and current sensors are not needed for MPPT
implementation. Apart from fill factor based MPPT a new MPP
angle based approach has been also discussed. This proposed
technique eliminates the requirement of sensors therefore the
cost of the system decreases. The proposed methodology is
proved to be an economically sustained alternative to the
existing MPPT techniques.