2. 1. Introduction
Renewable energy sources play an important role in electric
power generation [1]. Various renewable sources such as solar
energy, wind energy, geothermal, are harnessed for electric power
generation. Solar energy is a good alternative for electric power
generation due to its availability and cleanliness [2–4]. Solar
energy is directly converted into electricity by solar photovoltaic
(PV) module. PV modules have maximum power points (MPP)
corresponding to the surrounding condition such as solar irradi-
ance, temperature of the PV modules, cell area and load. In order
for the PV module to deliver its maximum power, several max-
imum power point tracking (MPPT) methods [5–9] were proposed
in both stand-alone and grid-connected PV systems.
In stand-alone systems, MPPT algorithms are usually imple-
mented on DC–DC converters, battery banks are required to store
surplus energy [10]. In grid-connected systems, the energy pro-
duced by the PV array can be transferred to the grid via a DC–DC
converter which is used as an MPPT controller and an inverter
which converts the DC bus voltage to the AC grid voltage.
However, this can be achieved using only a specific DC–AC inverter
[11–13].
MPPT methods can be classified into indirect and direct
methods [6]. The indirect methods, such as open-circuit and
short-circuit methods [14–16], require a prior knowledge of the
PV array characteristics, or are based on mathematical relation-
ships which does not meet all meteorological conditions. There-
fore, they cannot precisely track the MPP of PV array at any
irradiance and cell temperature. In addition, according to Femia
et al. [17], using temperature and irradiance as sensed parameters
is not advised, because their measurement requires expensive
devices that have to be placed throughout the PV array, in order to
get the values of such variables for each panel or group of them,
thus making the measurement very expensive, especially for large
PV plants.
On the other hand, direct methods work under any meteor-
ological condition. The most used direct methods are [6]: Pertur-
bation and Observation (P&O) [18–20], Incremental Conductance
(IncCond) [21–24], and Fuzzy Logic (FL) based MPPT method [25–
28]. Commercial products typically use perturbative MPPT meth-
ods, determining, instant by instant, the voltage value at which the
PV module delivers its maximum power. P&O and IncCond
methods usually control the reference signal of a DC–DC converter
that matches the PV module voltage with that of the DC bus or
works as a battery charger [13,17]. The main advantages of these
two methods are that they are compatible with any PV generator,
they require no information about the PV generator, and they are
simple to implement on a digital controller [29]. In addition, it is
possible to integrate these methods into commercial inverters
[30–33]. Furthermore, the MPPT methods can be classified into
conventional and intelligent methods. As shown in Table 1,
intelligent techniques (i.e. fuzzy logic (FL) and artificial neural
networks (ANN) based MPPT methods) are more efficient, they
have fast response, but they are more complex compared to the
conventional techniques that are generally simple, cheap and less
efficient.
Although there are multiple MPPT techniques that are men-
tioned in literature, this paper provides a survey on the well-
known techniques used in the PV systems, i.e. the P&O method,
the IncCond method and the FL based MPPT method.
2. Photovoltaic generator characteristics
Solar cells consist of a p–n junction fabricated in a thin layer of
semiconductor [34]. They are like p–n diodes, their characteristics
are also similar. A solar cell equivalent electrical circuit can be
represented by a single-diode model as shown in Fig. 1a, where R
represents the effective load of the cell. The relationship between
the cell terminal current and voltage is the following [35–37]:
I ¼ Iph Io exp
V þI RS
a Vth
1
V þI RS
RP
ð1Þ
where I and V are the output current and output voltage of the
photovoltaic cell, respectively, Io is the diode’s reverse saturation
current, a is the diode ideality factor, RS and RP is the series and
parallel resistance, respectively. Vth is the thermal voltage of the
cell, which is expressed as,
Vth ¼
kb T
q
ð2Þ
where q is the electron charge (1602 1019
C), T is the junction
temperature in Kelvin (K), and kb is the Boltzmann constant
(1380 1023
J/K). Iph is the generated photocurrent; it depends
mainly on the radiation and cell’s temperature, which is expressed
as,
Iph ¼ Isc_STC þKi T TSTC
ð Þ
G
GSTC
ð3Þ
where Isc_STC (in Ampere, A) is the short-circuit current at standard
test conditions (STC), TSTC (25 1C) is the cell temperature at STC, G
(in watts per square meters, W/m2
) is the irradiation on the cell
surface, GSTC (1000 W/m2
) is the irradiation at STC, and Ki is the
short circuit current coefficient, usually provided by the cell
manufacturer. In addition, the saturation current Io is influenced
by the temperature according to the following equation [37,38],
Io ¼
Isc_STC þKi T TSTC
ð Þ
exp Voc_STC þKv T TSTC
ð Þ
=a Vth
1
ð4Þ
Table 1
Major characteristics of MPPT methods.
MPPT method Sensed
parameters
PV array
dependent?
Direct or
indirect?
Analog or
digital?
Efficiency Response/
speed
Cost Complexity
implementation
Conventional
methods
PO Voltage,
current
No Direct Both Low Varies Low Low
IncCond Voltage,
current
No Direct Digital Medium Varies Low Medium
Open-circuit voltage
method
Voltage Yes Indirect Both Low Medium Low Low
Short-circuit current
method
Current Yes Indirect Both Medium Medium Low Medium
Intelligent
methods
Fuzzy logic Voltage,
current
Yes Direct Digital Height Fast Height Medium
Neural networks Varies Yes Indirect Digital Height Fast Height Height
B. Bendib et al. / Renewable and Sustainable Energy Reviews 45 (2015) 637–648
638
3. where Voc_STC(in Volt, V) is the open circuit voltage at STC; Kv is the
open circuit voltage coefficient, these values are available on the
datasheet provided by module’s manufacturer.
2.1. Series/parallel grouping
The output power from a single PV cell is relatively small. To
produce the required voltage and power, PV cells are connected in
series and parallel. They are grouped into modules. Modules are
combined to form panels. These panels are connected together to
build up the entire PV array. Then, any desired current–voltage (I–
V) and power–voltage (P–V) characteristic could be generated [38].
Therefore, the I–V characteristic equation of a PV array (arranged
in NP parallel and NS series solar cell) can be expressed as,
I ¼ Np Iph Np
Io exp
V þI Ns=Np
RS
Ns a Vth
1
V þI Ns=Np
RS
Ns=Np
RP
ð5Þ
where connecting cells in series will increase the output voltage
and connecting them in parallel will increase the output current.
Fig. 1b shows the I–V and P–V characteristic of the PV module at a
fixed cell temperature T and at a certain solar radiation, G. In this
figure (I–V curve), there are three remarkable points:
The short circuit point (0, Isc), (i.e. the point where the I–V curve
meets the voltage axis). Where Isc is the short circuit current
that can be drawn by connecting the positive and negative
terminals of PV module. It is the greatest generated current
value when the voltage is zero (V¼0).
The open circuit point (Voc, 0), (i.e. the point where the I–V
curve meets the current axis). Where Voc is the open circuit
voltage of PV module. It reflects the voltage of the module in
the night. In this case, no current is generated (I¼0).
The maximum power point, MPP (Vmpp, Impp): at this point, the
PV module is said to operate at maximum efficiency and
produces its maximum output power (Pmax) given by:
Pmax ¼ Vmpp Impp ð6Þ
where Impp and Vmpp are the optimal operating current and
voltage of PV module, respectively. When a PV module is
directly connected to a load, the operating point will be at
the intersection of the I–V curve of the PV module and the load
curve. Most of the time, this operating point does not meet the
maximum power point (MPP) of PV module. Furthermore, as
the maximum power point depends on solar radiation and cell
temperature, which vary randomly, the MPP position is con-
tinuously changing [39]. Therefore, it is very important to
ensure that the module operates at maximum efficiency
because the main problem with PV energy generation systems
is low efficiency [40]. In order to overcome this problem,
specific circuits, called maximum power point trackers (MPPT),
are used [39].
Typically, the MPPT is achieved by interposing a DC–DC con-
verter between the PV array and the load, thus, from the voltage
and/or current measurements, the MPPT algorithm generates the
optimal duty ratio (D) in order to maintain the electrical quantities
(V, I, and P) at values corresponding to the maximum power point.
2.2. Effect of solar radiation and cell temperature
The I–V characteristics of a PV cell strongly depend on solar
radiation and temperature [41–43]. Fig. 2a shows that the output
current I of a PV module is widely influenced by the variation in
solar irradiance G, whereas the output voltage V stays almost
constant. In the other hand, for a changing temperature one can
see that the voltage varies widely while the current remains
almost unchanged (Fig. 2b).
Fig. 3a and b shows how the dependency of output current (I)
and output voltage (V) on solar irradiance and cell temperature
translate into a dependency of the output power (P) on the same
two parameters. Fig. 3a confirms the expected behavior of a device
that converts solar energy into electricity: the output power of a
PV generator is largely reduced for a decreasing irradiance.
Furthermore, Fig. 3b shows that the output power decreases by
an increase in cell temperature. This can be explained by the
dependency of the open circuit voltage (Voc) on the cell tempera-
ture as follows [44]
Voc ¼ Voc;STC þKv T TSTC
ð Þ ð7Þ
3. MPPT control algorithms
Many methods for maximum power point tracking had been
proposed [6,45–47]. Two algorithms are often used to achieve the
MPPT namely: the perturbation and observation (PO) and the
incremental conductance (IncCond) methods. Recently, these two
methods have been implemented on a commercial MPPT inverter.
On the other hand fuzzy logic has received much attention from a
number of researchers in the area of power electronics. Fuzzy logic
control is somewhat easy to implement, because it does not need
exact mathematical model of the plant.
Fig. 1. (a) Solar cell circuit model; (b) I–V and P–V characteristics of a PV module.
B. Bendib et al. / Renewable and Sustainable Energy Reviews 45 (2015) 637–648 639
4. 3.1. PO method
The PO method is widely used in commercial products and is
the basis of the largest part of the most sophisticated algorithms
presented in the literature [17]. It is widely employed in practice,
due to its low-cost, simplicity and ease of implementation
[19,40,48]. The PO algorithm operates periodically by perturbing
the operating voltage point (V) and observing the power variation
in order to deduct the direction of change to give to the voltage
reference Vref [49]. Thus, if the operating voltage V of the PV array
is perturbed in a given direction and if the power drawn from the
PV array increases, this means that the operating point has moved
toward the MPP and, therefore, the operating voltage must be
further perturbed in the same direction. Otherwise, if the power
drawn from the PV array decreases, the operating point has moved
away from the MPP and, therefore, the direction of the operating
voltage perturbation must be reversed [19]. Fig. 4a shows a flow
chart of the PO algorithm. With this algorithm the operating
voltage V is perturbed at every MPPT cycle. As soon as the MPP is
reached, V will oscillate around the ideal operating voltage Vmpp.
This causes a power loss which depends on the step width of the
perturbation, CP [19]. The major disadvantages of the PO
technique are occasional deviation from the maximum operating
point in case of rapidly changing atmospheric conditions, such as
broken clouds. Furthermore, an appropriate perturbation size is
important to ensure good performance in both dynamic and
steady-state response [9].
Several improvements of the PO algorithm have been pro-
posed in order to reduce the number of oscillations around the
MPP in steady state, but they slow down the algorithm to
changing atmospheric conditions and decrease the algorithm
efficiency during cloudy days [17]. This drawback can be shown
in Fig. 4b, where the PO MPPT operating point path for an
irradiance variation from 500 W/m2
to 1000 W/m2
is reported. The
example shows two different behaviors in the output power (P)
versus voltage (V) plane. The continuous line in Fig. 4b shows the
operating point trajectory under slowly changing irradiance,
whereas the dotted line shows the failure of PO controller to
track the MPP when a rapid increase in irradiance occurs.
The rapid increase in irradiance can be characterized by the
increase in power twice in the last two cycles of the PO algorithm
or by the direction of perturbation which remains the same for the
last two steps. A solution to this problem is to add a new condition
in the PO MPPT algorithm [50,51]. Therefore, the algorithm must
Fig. 2. I–V characteristics of a PV array: (a) for various values of irradiance G at a temperature of 25 1C; (b) for various values of cell temperature T at an irradiance
of 1000 W/m2
.
Fig. 3. P–V characteristics of a PV array: (a) for various values of irradiance G at a temperature of 25 1C; (b) for various values of temperature T at an irradiance of 1000 W/m2
.
B. Bendib et al. / Renewable and Sustainable Energy Reviews 45 (2015) 637–648
640
5. take into account the variations of power (ΔP) and voltage (ΔV) at
consecutive time intervals (k1) and (k). The improved PO
algorithm then uses four variables (i.e. ΔV(k1), ΔP(k1), ΔV
(k) and ΔP(k)), which gives 16 possible cases as shown in Table 2.
If the increase in power is caused by the perturbation and not by
increase of the irradiance, the improved PO algorithm causes a
decrease in power for one cycle (wrong direction of perturbation),
but takes again in the correct direction in the next cycle [51].
3.2. IncCond method
The incremental conductance (IncCond) method is based on
the fact that the slope of the PV array power versus voltage (P–V)
curve is zero at the MPP. It was proposed to improve the tracking
accuracy and dynamic performance under rapidly varying condi-
tions [22–24]. The output voltage and current from the PV array
are monitored upon which the MPPT controller relies to calculate
the conductance and incremental conductance, and to make its
decision (to increase or decrease duty ratio output). The output
power of PV array can be expressed as: P¼V I. Then, the
derivative of product yields:
dP
dV
¼
d V I
ð Þ
dV
¼ IþV
dI
dV
)
1
V
dP
dV
¼
I
V
þ
dI
dV
ð8Þ
where P, V and I are the PV array output power, voltage and
current, respectively. The purpose of this algorithm is to find the
voltage operating point at which the PV array instantaneous
conductance (I/V) is equal to the incremental conductance (dI/
dV). As shown in Fig. 5a, the slope of the PV array power curve is
zero at the MPP, increasing on the left of the MPP and decreasing
on the right-hand side of the MPP. This is expressed by the
following equations:
dP
dV
¼ 0 if
dI
dV
¼
I
V
; at MPP
ð Þ ð9Þ
dP
dV
40 if
dI
dV
4 I=V; left of MPP
ð Þ ð10Þ
dP
dV
o0 if
dI
dV
o
I
V
; right of MPP
ð Þ ð11Þ
The flowchart of the IncCond algorithm is shown in Fig. 5b. In
this method, two sensors are employed to measure the array’s
operating voltage V and current I. The incremental changes dV and
dI can be calculated digitally by sampling the PV array output
current I and voltage V at consecutive time intervals (k1) and (k)
as follows [52]:
dVðkÞ ¼ VðkÞVðk1Þ ð12Þ
dIðkÞ ¼ IðkÞIðk1Þ ð13Þ
As shown in Fig. 5b, Vref is the reference voltage at which the PV
array is forced to operate. At the MPP, Vref equals to Vmpp. Once the
MPP is reached, the operation of the PV array is maintained at this
point unless a change in dI is noticed, indicating a change in
meteorological conditions and the MPP. The algorithm decrements
or increments Vref using a constant adjustment step width (Ca) to
track the new MPP [7]. IncCond algorithm can actually calculate
Fig. 4. (a) Flow chart of the PO MPPT algorithm (CP is the perturbation step width); (b) path of MPP with the PO algorithm under slowly (dotted line) and rapidly
(continued line) changing irradiance.
Table 2
Truth table for the Improved PO algorithm [47].
ΔV(k1) ΔP(k1) ΔV(k) ΔP(k) ΔV(kþ1)
þ
þ þ
þ
þ þ þ
þ þ
þ þ þ
þ þ
þ þ þ
þ þ
þ þ
þ þ
þ þ þ
þ þ þ
þ þ þ þ
þ þ þ
þ þ þ þ
B. Bendib et al. / Renewable and Sustainable Energy Reviews 45 (2015) 637–648 641
6. the direction in which to perturb the operating point to reach the
MPP. Thus, under rapid increasing radiation levels, it should not
have in the wrong direction, as PO can. In [53], a comprehensive
comparison between PO and the IncCond method is made; it
shows that the efficiency of experimental results is up to 95%. In
[54], the efficiency was observed to be as much as 98.2%, but it is
doubtful of the IncCond method reliability issues due to the noise
of components [55].
Because of measurement’s errors and the quantification, the
condition (I/V¼ dI/dV) is rarely achieved, therefore under stable
environmental conditions, the system oscillates around the MPP.
Furthermore, it is very difficult to adjust V to the exact Vmpp when
using a constant adjustment step width (Ca). An attempt has been
made to solve this problem by taking variable step size [24]. But, it
requires complex and costly control circuits [9]. A solution to this
problem would be to add a small marginal error (ε) to the
maximum power condition (I/VþdI/dV¼0) such that the MPP is
presumed to be found if [53,56]
dI
dV
þ
I
V
rε ð14Þ
The value of this marginal error (ε) determines the sensitivity
of the system. This error is selected with respect to the swap
between steady-state oscillations and risk of fluctuating at a
similar operating point [55].
3.3. Fuzzy MPPT controller
There are three stages in this control algorithm, namely
fuzzification, inference method and defuzzification.
3.3.1. Fuzzification
The fuzzification makes it possible to transform real variables
into fuzzy variables. The actual voltage and current of PV array can
Fig. 5. (a) IncCond method principle, (b) flow chart of the IncCond MPPT algorithm (Ca is the adjustment step width)
Input variable E
Membership
functions
µ
(E)
Input variable CE
Membership
functions
µ
(CE)
Output variable D
Membership
functions
µ
(
D)
Fig. 6. Membership functions for: (a) input variable E, (b) input variable CE, (c) output variable ΔD.
B. Bendib et al. / Renewable and Sustainable Energy Reviews 45 (2015) 637–648
642
7. be measured continuously and the power can be calculated [25].
The input variables of proposed controller are an error (E) and a
change in error (CE). At a sampling instant k, these variables are
expressed as follows [25,57]:
EðkÞ ¼
PðkÞPðk1Þ
IðkÞIðk1Þ
ð15Þ
CEðkÞ ¼ EðkÞEðk1Þ ð16Þ
where P(k) and I(k) are the power and current of the PV array,
respectively. The change in duty ratio (ΔD) of a DC–DC converter is
used as an output of the proposed controller. These input and
output variables, i.e. E, CE and ΔD are expressed in terms of
linguistic variables or labels such as PB (positive big), PS (positive
small), Z0 (zero), NS (negative small), NB (negative big) using basic
fuzzy subsets. Fig. 6 shows the membership functions of five basic
fuzzy subsets for input and output variables. The input E(k) shows
if the operating point at the instant k is located on the left or on
the right of the MPP on the P–I characteristic, while the input CE(k)
expresses the displacement direction of this point. Therefore, the
control is done by changing the duty ratio (ΔD) according to the
slope E(k) in order to bring back the operation point on the
maximum point where the slope is zero.
3.3.2. Inference method
Table 3 shows the rule table of a fuzzy controller, where all
the entries of the matrix are fuzzy sets of error (E), change of
error (CE) and change of duty ratio (ΔD) to the converter. The fuzzy
rules shown in Table 3 are employed for controlling the DC–DC
converter such as the maximum power of the PV generator is
reached. As an example, the rule in Table 3: IF E is PB AND CE is Z0
THEN ΔD is PB. This implies that “if operating point is distant from
maximum power point towards left hand side and the change
of slope in P–I characteristic is about zero, increase duty ratio
largely“.
Fuzzy control usually uses one of the following methods: Max–
Min, Max–Prod, Somme–Prod inference method. In this paper, the
inference method of Mamdani [58], which is the Max–Min fuzzy
combination, is used.
3.3.3. Defuzzification
It was seen that the inference method provides a function for
the resulting membership variable; it thus acts of fuzzy informa-
tion. Given that DC–DC converter requires a precise control signal
D at its entry, it is necessary to transform this fuzzy information
into deterministic information, this transformation is called defuz-
zification. The most used methods for defuzzification are the
center of area (COA), Mean of Maxima (MOM), and Max Criterion
Method (MCM).
In this paper, the defuzzification is performed using the COA of
final combined fuzzy set. The final combined fuzzy set is defined
by the union of all rule output fuzzy sets using the maximum
aggregation method [58,59]. Thus, the change of duty ratio ΔD is
determined by the COA method as follows:
ΔDðkÞ ¼
Pn
j ¼ 1 μ ΔDjðkÞ
ΔDjðkÞ
Pn
j ¼ 1 μ ΔDjðkÞ
ð17Þ
The output of fuzzy logic controller is the change of duty ratio
ΔD(k), which is converted to the duty ratio D(k) by
DðkÞ ¼ Dðk1ÞþΔDðkÞ ð18Þ
4. Simulation results
As shown in Fig. 7a, the PV system under study consists of a PV
generator, a DC–DC buck converter with an MPPT controller
connected to a 12-V storage battery. The system is simulated using
Matlab/Simulink environment as shown in Fig. 7b.
Simulink enables the division of a simulated system into a
number of subsystems. These subsystems can be modeled and
tested separately and then interconnected to form the whole
system. This makes it possible to build physical subsystems
models such as the photovoltaic generator, the DC–DC converter
[60], the batteries [61], and the MPPT control block as independent
units and check their proper operation. Finally these subsystems
can be combined to form a whole MPPT-controlled PV system as
shown in Fig. 7b. MPPT techniques and converter types can be
combined and their operation can be simulated on PV panels and a
battery pack of any desired size under an unlimited variety of
operating conditions. The PV module, Solarex MSX60, was chosen
Table 3
Rule base of the fuzzy controller.
E CE
NB NS ZO PS PB
NB ZO ZO NB NB NB
NS ZO ZO NS NS NS
ZO NS ZO ZO ZO PS
PS PS PS PS ZO ZO
PB PB PB PB ZO ZO
Fig. 7. (a) MPPT-controlled block diagram of the PV system, (b) Simulink implementation of the PV system.
B. Bendib et al. / Renewable and Sustainable Energy Reviews 45 (2015) 637–648 643
8. for simulation. This module consists of 36 series polycrystalline
cells, and provides 60 W maximum power and 17.1 V optimal
voltage at nominal conditions as shown in Table 4 [62].
4.1. Stable environmental conditions
Fig. 8a shows the PV array power (P) and operating voltage (V),
the battery voltage (Vb), and the duty-cycle ratio (D) of a PO-
controlled power supply using a buck converter under given
values of cell temperature (T¼45 1C) and solar irradiance
(G¼1000 W/m2
). In this case, a 10-Hz sampling frequency is used
for the MPPT algorithm. Initially, the duty-cycle ratio was set to
D¼0.7. Within 20 s the battery voltage Vb increases rapidly to
reach 12.28 V. After, despite further voltage increase, the PO
controller manages to adjust the duty ratio D very quickly such
that a stable output power is achieved. After this point the output
power does not vary any further since the PV generator operates
under stable conditions.
Fig. 8b shows detailed results of Fig. 8a. It shows clearly the
continuous oscillation of the operating point around the optimal
Table 4
Electrical characteristics data of (MSX60) PV module [63].
Electrical characteristics Symbols Values
Open-circuit voltage Voc 21.1 V
Short-circuit current Isc 3.8 A
Optimum operating voltage Vmpp 17.1 V
Optimum operating current Impp 3.5 A
Maximum power at STC Pmpp 60 W
Current temperature coefficient of Isc Ki (0.06570.015) %/1C
Voltage temperature coefficient of Voc Kv (80710) mV/1C
Fig. 8. (a) Simulation of the PO method, using a buck converter under stable conditions. (b) Detailed signals of the PO MPPT simulation at a frequency of 10 Hz.
Fig. 9. (a) Comparison of various signals MPPT for the power, the voltage, and the control variable D with a buck converter at a frequency of 100 Hz; (b) comparison of
different detailed signals MPPT at a frequency of 100 Hz.
B. Bendib et al. / Renewable and Sustainable Energy Reviews 45 (2015) 637–648
644
9. power point (MPP). This is a result of the continuous perturbation
of the operating voltage (V) in order to find the MPP. A step-by-
step comparison of the control signal (D) in the bottom curve
(Fig. 8b) with the power signal (P) in the up curve shows how the
control signal changes its stepping direction whenever a decrease
in power is detected. This continuous oscillation is fundamental to
the PO technique. Furthermore, it can be observed that the
power signal (P) alternates between two different minimums. This
is due to the two different slopes in the power–voltage (P–V)
characteristic.
Fig. 9a shows, in a comparative way, the simulation results (at a
sampling frequency of 100 Hz) between fuzzy and conventional
MPPT. It can be seen how the fuzzy MPPT controller reduced the
response time of photovoltaic system. It is clearly observed that
the system without MPPT has a great loss of energy.
In this paper tracking efficiency was used to evaluate the
tracking performance for different MPPT methods. The tracking
efficiency is defined as [63],
ηMPPT ¼
R t2
t1
Pdt
R t2
t1
Pmaxdt
ð19Þ
where t1 is the start-up time of the system and t2 is the close-
down time of the system, P is the array output power, and Pmax is
the theoretical maximum array power. The tracking efficiency
obtained from the previous curves (Fig. 9a) is shown as a
comparison of the various MPPT techniques as shown in Table 5.
The efficiency with fuzzy MPPT controller is above 99% under
stable conditions, whereas the efficiency of other conventional
MPPT methods varied between 96% and 97%. However, the direct
method (without MPPT) has a considerable loss of energy and the
efficiency is almost 66% (Table 5).
Fig. 9b shows detailed results of Fig. 9a. We can see continuous
oscillation of operation point for the conventional techniques; this
is due to the continuous perturbation of the operating voltage in
order to reach the MPP. Meanwhile, this phenomenon of oscilla-
tion is not observed in the fuzzy method, where the signals
representing the power (P), the voltage (V) and the duty ratio
(D) remain almost constant. This results in a power losses
reduction.
4.2. Slow increase in radiation
A slow increase in radiation from 800 W/m2
to 1000 W/m2
over a time period of 5 s was simulated; meanwhile the cell
temperature was kept constant at 45 1C. Observation of the output
power curves of the various MPPT techniques led to the graph
shown in Fig. 10a. It can be noticed through Fig. 10a, that the
output power of the improved PO technique increases slowly and
with a smaller oscillation than the power of the other MPPT
methods. This is caused by the intended reaction of the improved
PO to an increase in radiation. In fact, the small amplitude
oscillations of the fuzzy MPPT technique during the period of
increasing radiation are only a repeated deviation of the operating
point in both directions of the MPP and the MPPT is fast enough to
always find its way back to the MPP.
4.3. Rapid increase in radiation
A rapid increase in irradiance from 1000 W/m2
to 1500 W/m2
within a time period of 2.5 s was simulated. The cell temperature
was kept at a constant value of 45 1C. Under these operating
conditions, the improved PO MPPT method becomes more
efficient (Fig. 10b). Fig. 10b shows how the output power of the
improved PO MPPT increases linearly during the increase of
irradiance, whereas the other conventional MPPT techniques
experience a considerable deviation from the MPP. It can be seen
Table 5
Tracking efficiency and response time comparison for different MPPT techniques
under stable conditions.
Algorithm Tracking efficiency, ηMPPT(%) Response time (s)
Fuzzy logic 99.22 0.80
PO 96.98 2.95
Improved PO 96.07 2.93
IncCond 97.00 2.97
Improved IncCond 96.95 3.00
Without MPPT 66.15 420
Fig. 10. Power output signals of the various MPPT techniques (a): under slowly increase in radiation (b): under rapidly increasing radiation levels.
B. Bendib et al. / Renewable and Sustainable Energy Reviews 45 (2015) 637–648 645
10. that the fuzzy MPPT, in this case, is the fastest with the least
oscillation around the MPP.
The tracking efficiency of each technique in the rapid variation
of irradiance is presented in Table 6. As can be seen, the efficiency
varied between 95% and 99%, but the fuzzy method is the most
efficient and converges quickly to the MPP.
4.4. Slow increase in temperature
In this case, a slow increase in temperature from 45 1C to 50 1C
over a time period of 5 s was simulated, whereas the irradiance
was kept constant at 1000 W/m2
. Simulation results are shown in
Fig. 11a. It can be observed that, all MPPT controllers track the MPP
with insignificant oscillations.
4.5. Rapid increase in temperature
Although the temperature during a day does not change
quickly, a rapid variation of temperature is used here to evaluate
the performance of the studied MPPT techniques. In this case, a
rapid increase in cell temperature from 45 1C to 60 1C over a time
period of 2.5 s was simulated, whereas the irradiance was kept
constant at 1000 W/m2
. Simulation results are shown in Fig. 11b.
As shown by the figure, the fuzzy MPPT method is superior to
the other methods in tracking the MPP of the system. The available
power is about 53 W while the cell temperature is 45 1C. However,
when the cell temperature increases from 45 1C to 60 1C the
developed fuzzy controller tracks rapidly the new MPP (48 W)
with negligible oscillations. However, the other MPPT techniques
have some deviation from the MPP during this increase of
temperature.
The tracking efficiency of each technique during slow and rapid
variation of temperature is presented in Table 7. As can be seen,
the efficiency varies between 95% and 96% for conventional
techniques. In this case, the fuzzy MPPT technique is the most
efficient with 99%, whereas the direct method (without MPPT) is
the least efficient with 69%.
5. Conclusion
In order to improve the performance of photovoltaic (PV)
systems, various conventional and intelligent maximum power
Fig. 11. Power output signals of the various MPPT techniques (a): under slowly increase in temperature (b): under rapidly increasing temperature.
Table 7
Tracking efficiency comparison for different MPPT techniques under slow and rapid variation of temperature.
Algorithm Tracking efficiency, ηMPPT (%)
Slow increase in temperature Rapid increase in temperature
Fuzzy logic 99.22 99.21
PO 96.76 96.64
Improved PO 95.85 95.69
IncCond 96.78 96.66
Improved IncCond 96.78 96.67
Without MPPT 66.99 68.92
Table 6
Tracking efficiency comparison for different MPPT techniques under slow and rapid
variation of irradiance.
Algorithm Tracking efficiency, ηMPPT(%)
Slow increase in irradiance Rapid increase in irradiance
Fuzzy logic 99.14 99.01
PO 96.77 96.64
Improved PO 96.13 95.69
IncCond 96.75 96.66
Improved IncCond 96.76 96.67
Without MPPT 59.64 68.93
B. Bendib et al. / Renewable and Sustainable Energy Reviews 45 (2015) 637–648
646
11. point tracking (MPPT) methods were used. This paper provides a
study on the most MPPT techniques used in the PV systems, i.e. the
perturbation and observation (PO) method, the incremental
conductance (IncCond) method and the fuzzy logic (FL) based
MPPT method.
Within the context of this paper, numerical simulations (using
Simulink/Matlab) were carried out for PV systems containing
conventional and intellligent fuzzy MPPT controllers, under vary-
ing climatic conditions. The obtained simulation results are very
promising and prove in general that the fuzzy MPPT controller
performances, in terms of stability, precision and speed in the
tracking of the MPP are much better than those of the conven-
tional MPPT methods (PO and IncCond).
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648
![1. Introduction
Renewable energy sources play an important role in electric
power generation [1]. Various renewable sources such as solar
energy, wind energy, geothermal, are harnessed for electric power
generation. Solar energy is a good alternative for electric power
generation due to its availability and cleanliness [2–4]. Solar
energy is directly converted into electricity by solar photovoltaic
(PV) module. PV modules have maximum power points (MPP)
corresponding to the surrounding condition such as solar irradi-
ance, temperature of the PV modules, cell area and load. In order
for the PV module to deliver its maximum power, several max-
imum power point tracking (MPPT) methods [5–9] were proposed
in both stand-alone and grid-connected PV systems.
In stand-alone systems, MPPT algorithms are usually imple-
mented on DC–DC converters, battery banks are required to store
surplus energy [10]. In grid-connected systems, the energy pro-
duced by the PV array can be transferred to the grid via a DC–DC
converter which is used as an MPPT controller and an inverter
which converts the DC bus voltage to the AC grid voltage.
However, this can be achieved using only a specific DC–AC inverter
[11–13].
MPPT methods can be classified into indirect and direct
methods [6]. The indirect methods, such as open-circuit and
short-circuit methods [14–16], require a prior knowledge of the
PV array characteristics, or are based on mathematical relation-
ships which does not meet all meteorological conditions. There-
fore, they cannot precisely track the MPP of PV array at any
irradiance and cell temperature. In addition, according to Femia
et al. [17], using temperature and irradiance as sensed parameters
is not advised, because their measurement requires expensive
devices that have to be placed throughout the PV array, in order to
get the values of such variables for each panel or group of them,
thus making the measurement very expensive, especially for large
PV plants.
On the other hand, direct methods work under any meteor-
ological condition. The most used direct methods are [6]: Pertur-
bation and Observation (P&O) [18–20], Incremental Conductance
(IncCond) [21–24], and Fuzzy Logic (FL) based MPPT method [25–
28]. Commercial products typically use perturbative MPPT meth-
ods, determining, instant by instant, the voltage value at which the
PV module delivers its maximum power. P&O and IncCond
methods usually control the reference signal of a DC–DC converter
that matches the PV module voltage with that of the DC bus or
works as a battery charger [13,17]. The main advantages of these
two methods are that they are compatible with any PV generator,
they require no information about the PV generator, and they are
simple to implement on a digital controller [29]. In addition, it is
possible to integrate these methods into commercial inverters
[30–33]. Furthermore, the MPPT methods can be classified into
conventional and intelligent methods. As shown in Table 1,
intelligent techniques (i.e. fuzzy logic (FL) and artificial neural
networks (ANN) based MPPT methods) are more efficient, they
have fast response, but they are more complex compared to the
conventional techniques that are generally simple, cheap and less
efficient.
Although there are multiple MPPT techniques that are men-
tioned in literature, this paper provides a survey on the well-
known techniques used in the PV systems, i.e. the P&O method,
the IncCond method and the FL based MPPT method.
2. Photovoltaic generator characteristics
Solar cells consist of a p–n junction fabricated in a thin layer of
semiconductor [34]. They are like p–n diodes, their characteristics
are also similar. A solar cell equivalent electrical circuit can be
represented by a single-diode model as shown in Fig. 1a, where R
represents the effective load of the cell. The relationship between
the cell terminal current and voltage is the following [35–37]:
I ¼ Iph Io exp
V þI RS
a Vth
1
V þI RS
RP
ð1Þ
where I and V are the output current and output voltage of the
photovoltaic cell, respectively, Io is the diode’s reverse saturation
current, a is the diode ideality factor, RS and RP is the series and
parallel resistance, respectively. Vth is the thermal voltage of the
cell, which is expressed as,
Vth ¼
kb T
q
ð2Þ
where q is the electron charge (1602 1019
C), T is the junction
temperature in Kelvin (K), and kb is the Boltzmann constant
(1380 1023
J/K). Iph is the generated photocurrent; it depends
mainly on the radiation and cell’s temperature, which is expressed
as,
Iph ¼ Isc_STC þKi T TSTC
ð Þ
G
GSTC
ð3Þ
where Isc_STC (in Ampere, A) is the short-circuit current at standard
test conditions (STC), TSTC (25 1C) is the cell temperature at STC, G
(in watts per square meters, W/m2
) is the irradiation on the cell
surface, GSTC (1000 W/m2
) is the irradiation at STC, and Ki is the
short circuit current coefficient, usually provided by the cell
manufacturer. In addition, the saturation current Io is influenced
by the temperature according to the following equation [37,38],
Io ¼
Isc_STC þKi T TSTC
ð Þ
exp Voc_STC þKv T TSTC
ð Þ
=a Vth
1
ð4Þ
Table 1
Major characteristics of MPPT methods.
MPPT method Sensed
parameters
PV array
dependent?
Direct or
indirect?
Analog or
digital?
Efficiency Response/
speed
Cost Complexity
implementation
Conventional
methods
PO Voltage,
current
No Direct Both Low Varies Low Low
IncCond Voltage,
current
No Direct Digital Medium Varies Low Medium
Open-circuit voltage
method
Voltage Yes Indirect Both Low Medium Low Low
Short-circuit current
method
Current Yes Indirect Both Medium Medium Low Medium
Intelligent
methods
Fuzzy logic Voltage,
current
Yes Direct Digital Height Fast Height Medium
Neural networks Varies Yes Indirect Digital Height Fast Height Height
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