1. Modeling of Maximum Power Point Tracking
Algorithm for Photovoltaic Systems
Ioan Viorel Banu, Marcel Istrate
“Gheorghe Asachi” Technical University of Iasi
Faculty of Electrical Engineering
Iasi, Romania
ibanu@ee.tuiasi.ro, mistrate@ee.tuiasi.ro
Abstract—This paper presents a modeling method of photovoltaic
(PV) systems and an implementation of the incremental
conductance for maximum power point tracking (MPPT)
algorithm. The method is used to study the influence of rapidly
changing irradiance level concerning performance of
photovoltaic systems. A simple circuit model of the dc/dc buck
converter connected to the photovoltaic systems is used to easily
simulate the incremental conductance MPPT method. The model
has been implemented in MATLAB / Simulink. The simulation
results are presented and analyzed to validate that the proposed
simulation model is effective for MPPT control of the
photovoltaic systems at rapidly changing irradiation condition.
Keywords—modeling; photovoltaic systems; maximum power
point tracking; incremental conductance; buck converter
I. INTRODUCTION
The photovoltaic (PV) domain provide one of the most
efficient ways of producing energy, with real perspectives in
the future, considering the actual situation of the classical
power resources around the world. It becomes a real problem
the fact that we have insufficient supplies of this kind of power
resources for insuring the world's needs.
Usually, when a PV module is directly connected to a load,
the operating point is rarely at the maximum power point or
MPP [1]. The principle of maximum power point tracking
(MPPT) is to place a convertor between the load and the PV
array, as shown in Fig. 1 [1-4], to regulate the array output
voltage (or current) so that the maximum available power is
extracted [5]. A power converter is necessary to adjust the
energy flow from the PV array to the load [1]. In the method
described in [2], the power converter is controlled using the PV
array output power [3]. Voltage and current sensing allow
measuring the power. If the value of power is available can be
decided if go up or down on the power curve [1].
The PV array is an unregulated dc power source, which has
to be properly conditioned in order to interface it to the grid.
The dc/dc converter is present at the PV array output for MPPT
purposes, i.e. for extracting the maximum available power for a
given insolation level [5]. The step-down dc/dc converter (buck
converter) is used as a dc transformer which can match the PV
array optimum load by changing its switching duty ratio (D)
[6]. In general, the operation of an ideal buck converter [6-9] is
described by (1).
Figure 1. Block diagram of a PV array connected to the load [1].
D=II=VV outininout , (1)
where inV and inI are the voltage and current at the PV array
side (i.e. the input of the buck converter), and outV and outI
are the voltage and current at the load side (i.e. the output of
the buck converter).
Multiple well-known direct control algorithms are used to
perform the maximum power point tracking (MPPT) [1]. There
are at least 19 distinct methods of MPPT control algorithms
with different variations on implementation and performance
[9]. One of the MPPT algorithms that are well known is the
incremental conductance algorithm.
The incremental conductance algorithm is based on the
differentiation of the PV array power versus voltage curve as in
(2) [1, 9].
dV
dI
V+I=
dV
dI
V+
dV
dV
I=
dV
d(VI)
=
dV
dP
(2)
The MPP will be found when [1, 9]:
dV
dI
V
I
0=
dV
dI
V+I0=
dV
dP
=−⇒⇒ , (3)
where I/V represent the instantaneous conductance of PV
array and dI/dV is the incremental conductance (instantaneous

2. change in conductance). The comparison of those two
quantities tells us on which side of the MPP we are currently
operating [1].
The analysis of the derivative, presented in (4), can
determine whether the PV array is operating at MPP or far
from it, as is shown in Fig. 2 [9, 10].
⎪
⎩
⎪
⎨
⎧
><
==
<>
MPP
MPP
MPP
VVfor0,dP/dV
VVfor0,dP/dV
VVfor0,dP/dV
(4)
Figure 2. Sign of the dP/dV at different positions on the P-V characteristic
curve of a PV array [10, 11].
The principle of this algorithm [1, 9, 11, 12] is described in
Flow chart presented in Fig. 3, where the triangle represent
decision making [1].
Figure 3. Flow chart of the incremental conductance algorithm.
II. SIMULINK MODEL OF PV SYSTEM WITH MPPT
The model shown in Fig. 4 represents a PV solar panel
connected to resistive load through a dc/dc buck converter with
MPPT controller.
Figure 4. Model of a PV solar panel connected to a load.
In Fig. 5 is shown the model of PV panel as a constant dc
source created using the Lookup Table block from Simulink®
as in [1, 13]. The model has two inputs an irradiance inputs
coming from port 1 and respectively a voltage input that is
coming as a feedback from the system and the output of the
block is calculated the current. This model generated current
and received voltage back from the circuit. The PV panel has
36 photovoltaic solar cells connected in series. The parameters
of a single solar cell of PV panel model are listed in Table I.
Figure 5. Block diagram of a PV panel connected to the load.
TABLE I. THE PARAMETERS OF A SINGLE SOLAR CELL
Table
Head
The Parameters of a Single Solar Cell
Parameter Value
1. Short-circuit current ( )A 34.7Isc =
2. Open-circuit voltage ( )V 6.0Voc =
3. Quality factor N = 1.39989
4. Series resistance ( )Ω 00415132.0Rs =
5.
First order temperature coefficient for
( )1/KIph
TIPH1 = 0.0008
6. Temperature exponent for sI TXIS1 = 3.3842
7. Temperature exponent for sR TRS1 = 0
8. Parameter extraction temperature ( )C° TMEAS = 25
9. Fixed circuit temperature ( )C° TFIXED = 25

3. Fig. 6 shows a Simulink®
diagram of a buck converter in
that can be seen its components parameters [1]. For the
implementation of buck converter is used
SimPowerSystems™, where can be built any custom structure.
The buck converter has a voltage input from the PV solar panel
and a reference command input from MPPT controller which
command the power MOSFET transistor. At the output of the
buck converter is connected a resistive load of 2 ohms.
Figure 6. Diagram of a buck converter [1].
When the MOSFET is switched on, the current from the PV
array can only flow through the inductor into the parallel RC
combination of the capacitor C and of the resistive load R,
where the capacitor voltage increases. When the MOSFET is
off, current must remain flowing in the inductor, so the
inductor current is now supplied by the capacitor through the
diode, causing the capacitor to discharge. The extent to which
the capacitor charges or discharges depends upon the duty
cycle of the MOSFET. If the MOSFET is on continuously, the
capacitor will charge to the array voltage. If the MOSFET is
not on at all, the capacitor will not charge at all [8].
In Fig. 7 is implemented the MPPT controller using the
Stateflow®
from Simulink®
library. Stateflow®
chart is a very
powerful tool that graphically allows to do state machines and
logical event based controllers and can be created states and
transitions. All of these transitions are based on decision based
on measurement of system. It used a 100 kHz pulse-width
modulation (PWM) driver for dynamics of the buck converter.
The MPPT controller makes a step size in the duty cycle of the
MOSFET [1].
The MPPT controller is realized using incremental
conductance algorithm as in [1]. The graphics interface is
shown in Fig. 8 in that can be visualized when the program
running how is making the decision and how the system is
moving from one state to another [1].
Figure 7. Block diagram of the MPPT controller [1].
Figure 8. Stateflow®
chart implementation of the incremental conductance
algorithm [1].
III. RESULTS AND DISCUSSIONS
The model shown in Fig. 4 was simulated using
MATLAB®
/ Simulink®
. The results obtained have been shown
in Table II.
Fig. 9 presents how the irradiance that falls on PV solar
panel is changing. The voltage and the current vary depending
on irradiance. The curve of variable irradiance is plotted using
a signal builder, where the irradiance is not very realistic,
because this are instantaneous changing irradiance, what will
be equivalent to do very fast cloud moving for example [14],
what allowing to the sun changing instantaneous which is not
happen, but allow to give an idea of measure of how fast the
controller responds [1].
In Fig. 10 is shown the V-P characteristics curve of the PV
Solar Panel for different level of irradiance at temperature of
25°C.
Figure 9. Variation of irradiance used in simulation.

4. Figure 10. V-P characteristics for different irradiance levels.
The simulation was run with the MPPT controller using the
incremental conductance algorithm. Fig. 11 presents the
voltage, current and power coming out of the PV solar panel
which is the magenta lines and the cyan lines which are the
output of the buck converter. The voltage at the input of PV
panel is stabilized at 17 V. As the irradiance is changing, the
MPPT controller makes the power coming out of the PV array
to be kept at maximum [1]. The PV solar panel generate 93.1
W maxim power and the power obtained at the output of buck
converter was found to be around 87 W for a solar irradiation
level of 2
W/m800 (Fig. 11). The incremental conductance
method has an efficiency of 93%. This suggests that the MPPT
controller is doing a pretty good job.
Figure 11. The simulation results of the PV system with MPPT controller.
The simulation was then run without the MPPT controller,
under the same irradiance level. It was seen that when we do
not use an MPPT algorithm, the power obtained at the load
side, for a solar irradiation value of 2
W/m800 , was around
68.6 W (Fig. 12). It must be noted that the PV solar panel
generated 93.1 W maxim power (Fig. 10) for this irradiance
level. Therefore, the output power is smaller.
Figure 12. The simulation results of the PV system without MPPT controller.
From Table II result that the MPPT controller increasing
the efficiency of the PV system as a whole. The loss of power
from the available 93.1 W generated by the PV solar panel to
87 W at the output of buck converter can be explained by
losses in coupling circuit (diode and capacitor), losses in the
PWM circuit and the inductive and capacitive losses in the
buck converter circuit. Therefore, it was seen that using the
incremental conductance MPPT method increased the
efficiency of the photovoltaic system, for a solar irradiation
value of 2
W/m800 , by approximately 26 % from an output
power of 68.6 W to an obtained output power of 87 W.
TABLE II. POWER AS A FUNCTION OF IRRADIANCE MODIFICATION
Irradiance
(W/m²)
Power depending on irradiance (W)
Maximum
power
from V-P
curves
With MPPT Without MPPT
Output of
PV panel
Output of
buck
converter
Output of
PV panel
Output of
buck
converter
400 45. 2 45.2 41 19.5 17.2
600 69.5 69.5 64 42.3 38.7
800 93.1 93.1 87 73.3 68.6
1000 116.9 116.9 110 110 104.1
1200 140.6 140.6 134 140.6 134
The efficiency results for the incremental conductance
algorithm and the case of directly connecting of PV array to the
load are presented in Table III.
TABLE III. EFFICIENCY OF THE MPPT ALGORITHM
Table
Head
Efficiency of the MPPT algorithm (%)
With MPPT Without MPPT
1. 0.93 0.7
Legend:
─Output of PV solar panel;
─Output of the buck converter.
Legend:
─Output of PV solar panel;
─Output of the buck converter.

5. In Table IV are presented the efficiency increase of the PV
systems by using MPPT controller with incremental
conductance algorithm against case without MPPT controller.
TABLE IV. EFFICIENCY INCREASE OF PV SYSTEM
Table
Head
Efficiency increase of PV system
Irradiance (W/m²) Efficiency of PV System (%)
1. 400 138
2. 600 65
3. 800 26.82
4. 1000 5.66
5. 1200 0
Fig. 13 shows the step change response [15] of the MPPT
controller under fast changing irradiance level. As can be seen
from Fig 13 a), for a step size of duty cycle )( dΔ of 0.003
samples, the recovery step is 0.004 samples under increase step
of irradiance of 2
W/m200 and for decrease step of irradiance
from 2
W/m1200 to 2
W/m600 the response of buck converter
are 0.008 samples. As shown in figure 13 b), for a step size of
duty cycle of 0.008 samples and the same irradiance step
conditions stated above, the step change response is 0.002 and
0.004 respectively.
Irradiance step between 800 2
W/m and 1000 2
W/m
Irradiance step between 1000 2
W/m and 1200 2
W/m
Irradiance step between 1200 2
W/m and 600 2
W/m
Irradiance step between 600 2
W/m and 400 2
W/m
Legend: ─Output of PV solar panel; ─Output of the buck converter.
a) b)
Figure 13. Step change response of power, for the two cases of step size for
duty cycle change )( dΔ : a) 003.0=Δd samples, b) 008.0=Δd samples
IV. CONCLUSIONS
This paper discussed the implementation of a maximum
power point tracking algorithm for a photovoltaic system that
is used to evaluate the performance of the incremental
conductance method under rapidly changing irradiance level.
The algorithm was tested against fast change in irradiance (step
change in irradiance).
The simulation model includes the PV solar panel, the
dc/dc buck converter and the MPPT controller. The modeling
and simulation was done in MATLAB®
/ Simulink®
. This
simulation model enabled the analysis of the performance of
PV systems. The simulation results were presented and
analyzed to validate that the incremental conductance
algorithm is effective at rapidly changing irradiance level. This
model provides a good evaluation of performance of MPPT
control for the PV systems.
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