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2013 International Conference on Circuits, Power and Computing Technologies [ICCPCT-2013]
A New Adaptive P&O MPPT Algorithm Based on FSCC Method for Photovoltaic System
Sathish Kumar Kollimalla Student Member, IEEE
Department of Electrical Engineering, Indian Institute of Technology
Madras, Chennai, India. [email protected]
Abstract-Maximum power point tracking (MPPT) techniques are used in photovoltaic (PV) systems to extract maximum power from the PV module. There are number of techniques available in literature. In this paper, an adaptive P&O MPPT algorithm is proposed using conventional perturb and observe (P&O) and fractional short circuit current (FSCC) methods. P&O method is widely used because of its low-cost and ease of implementation. The P&O method oscillates close to maximum power point (MPP) , when atmospheric conditions are constant or slowly varying. However, when irradiance and temperature are changing rapidly, this method fails to track MPP with rapid speed. In order to consider rapidly varying atmospheric conditions an adaptive control algorithm is proposed, by measuring the short circuit current at different irradiance levels and temperatures. In this proposed method current perturbation is considered instead of voltage perturbation. The proposed method has faster dynamics and improved stability compared to the conventional P&O method. The effectiveness of proposed MPPT algorithm is verified using digital simulations.
Index Terms-PV module; maximum power point tracking
(MPPT); perturb and observe (P&O) method; fractional short
circuit current (FSCC) method; adaptive control.
I. INTRODUCT ION
Non-conventional energy sources are expected to play an
important role in meeting the world's power demand, due to
their independence from availability of limited power sources
and their less impact on the environment. Solar power gener
ation is currently considered as one of the most useful renew
able energy sources as it is pollution free, maintenance free,
fast technological progress and continuous cost reduction. The
fundamental element in solar power generation system is the
solar cell or photovoltaic (PV) cell that converts sunlight into
direct current (DC) electricity. A photovoltaic (PV) module is
an interconnected collection of cells combined as one item.
Multiple modules can be wired together either in parallel or
in series or in both to form an array. In general, the larger
the area of a module or array, the more electricity that it can
produce.
The main hindrance to solar energy going widespread is
the cost of installing solar modules. The biggest disadvantage
of solar energy production revolve around the fact that power
generation is not constant throughout the day, it is always
changing with weather conditions, i.e., irradiation and temper
ature. Furthermore, the efficiency of solar energy conversion
to electrical energy is very low which is only in the range of
9-17% [1], especially under low irradiation states, this means
Mahesh Kumar Mishra Senior Member, IEEE
Department of Electrical Engineering, Indian Institute of Technology
Madras, Chennai, India.
that a fairly vast amount of surface area is required to produce
a lot of electricity. Therefore, maximum power point tracking
(MPPT) is an essential part of the photovoltaic system to
ensure that power converter circuits operate at the maximum
power point of the solar array. Various MPPT algorithms have
been developed [2] - [3]. These algorithms are differ from
each other in terms of number of sensors used, complexity
in algorithm and cost to implement the algorithm. The main
objective of all these MPPT algorithms is to achieve fast
and accurate tracking performance and minimize oscillations
due to varying weather conditions. Each algorithm can be
categorized based on the type of the control variable it uses: a)
voltage, b) current, or c) duty cycle. Among different MPPT
methods, much focus has been on perturb and observe (P&O)
[4] - [5] and hill climbing (HC) [6] - [7] methods. The P&O
method involves a perturbation in the operating voltage of solar
array and hill climbing involves a perturbation in the duty ratio
of power converter.
In P&O method the voltage is being increased or decreased
with fixed step size in the direction of reaching the maximum
power point (MPP). The process is repeated periodically until
the MPP is reached. At steady state, the operating point
oscillates around the MPP giving rise to the wastage of some
amount of available energy. These oscillations can be mini
mized by reducing the fixed step size, but it takes relatively
more time to reach MPP. The solution to this conflicting
situation is to have a variable step size as suggested in [8] - [9].
Although, the implementation of these methods are simple,
but it is not very accurate and rapid, since the effects of
temperature and irradiation are not taken into consideration.
Several methods are proposed to address these issues by
considering adaptive perturbation [10] - [11].
Another method is fractional open circuit voltage (or frac
tional short circuit current) based algorithm, the MPP voltage
V MP P (or MPP current IMP p) with respect to the open
circuit voltage Vac (or short circuit current Iso) [12] -
[14] is monitored. Since this method approximates a constant
ratio, its accuracy cannot be guaranteed under varying weather
conditions.
To overcome the above mentioned drawbacks, several meth
ods have been proposed using artificial intelligence (AI) based
algorithms such as neural network (NN) [15] and fuzzy logic
controller (FLC) [16]. But these methods also have drawbacks
like, they require large data storage and extensive compu
tation. For instance, NN requires large amount of data for
978-1-4673-4922-2113/$31.00 ©20 13 IEEE 406
2013 International Conference on Circuits, Power and Computing Technologies [ICCPCT-2013]
training which is the major constraint. Similarly, FLC requires
extensive computation to deal with a) fuzzification b) rule
base storage c) inference mechanism and d) defuzzification
operations. Furthermore, low cost hardware processors cannot
be used for these applications because the MPP continuously
changes with atmospheric conditions in real time.
In this paper, an adaptive P&O algorithm is designed in
order to overcome the drawbacks in the conventional P&O
method. In this proposed method, current perturbation is
considered to speed up the tracking performance. The current
perturbation can be realized by using sliding mode controller
(SMC) as discussed in [17]. In order to handle the rapidly
varying atmospheric conditions an adaptive control algorithm
is used.
This paper is organized as follows. In Section IT, modeling
of PV module and array is discussed. The proposed adaptive
P&O MPPT algorithm is designed and analyzed in Section Ill.
Simulation study is reported in Section IV. Finally, conclusions
are summarized in Section V.
11. MODELLING OF PV MODULE
The photovoltaic (PV) cell is basically a p-n junction
fabricated in a thin wafer of semiconductor. The solar energy
is directly converted to electricity through photovoltaic effect.
PV cell exhibits a nonlinear P-V and I-V characteristics
which vary with cell temperature (T) and solar irradiance
(S). Different equivalent circuit models of PV cell has been
discussed in literature [18]-[20].
A. PV Cell Model
The equivalent circuit of the general model of PV cell,
which consists of a photo current source, a parallel resistor
representing a leakage current, a diode, and a series resistor
describing an internal resistance to the current flow. This is
shown in Fig. 1.
Rs Ipv �
s 1 � ! Irs Rsh Vpv Iph I
Fig. 1. Equivalent circuit of PV cell
The nonlinear voltage-current characteristic equation of a
PV cell is given as [21], ( q(Vpv+Jc�vRs) ) Vpv + IpvRs I h - I e Akl - 1 - (1) p rs
Rsh where, Ipv and Vpv are terminal current and voltage of
PV cell respectively, Irs is diode reverse saturation cur
rent, q ( = 1.609 x 1O-19C) is an electron charge, k ( = 1.38 X 10-23 J / K) is a Boltzmann's constant and other pa
rameters can be obtained from specifications given in [22].
B. PV Module Model
s
� Ns
Fig. 2. Equivalent circuit of PV module
NSR N S p
1 r
PV cells are connected in series-parallel configuration in
order to produce enough power, because the power production
from a typical PV cell is less than 2 W. The equivalent circuit
of PV module is shown in Fig. 2. The nonlinear voltage-current
characteristic equation of PV module is given as [21],
(2)
Rsh where, N p is number of cells connected in parallel and N s is number of cells connected in series as shown in Fig. 2.
C. Solution for Nonlinear Equation
The model is processed in a MATLAB script file and the
output voltage or current is evaluated in terms of the irradiance
and cell temperature. Newton Raphson (NR) method is used
to solve the nonlinear equations as given [23],
f(xn) Xn+l = Xn -
f'(xn) (3)
where, Xn is the value of x at nth instant, l' is the derivative
of f w.r.t. x and f can be derived from (2) as given,
f(x) = Ipv - Nplph + NpVpv/�s + IpvRs
sh ( q(Vpv/NS+fpvRs/Np) ) +Nplrs e AkT - 1
(4)
where, x can be either Ipv or Vpv' In this paper, Vpv is
considered as x.
D. Characteristics of PV Array
The PV module considered for simulation is Solarex
MSX60 [23]. A PV array is formed by connecting 6 modules
in series and 6 modules in parallel. The specifications of PV
array at Standard Temperature Condition (STC) is given in
Table I.
The impact of temperature and irradiance on the I-V and
P-V characteristics are shown in Fig. 3. As the temperature
is increased, the output voltage decreases drastically whereas
the output current increases marginally; henceforth there is a
net reduction in output power. As the irradiance is increased,
the output current increases significantly, as a result of which
407
2013 International Conference on Circuits, Power and Computing Technologies [ICCPCT-2013]
TABLE 1 SPECIFICATIONS OF PV ARRAY AT STC (S = 1000 W/m2, T = 25°C)
Parameters Symbol Value Maximum Power PMPP 2160 W Voltage at Maximum Power VMPP 102.6 V Current at Maximum Power IMPP 21 A Open Circuit Voltage Vac 126.6 V Short Circuit Current Isc 22.8 A
-- Power -- Current S=500W/m2
10 1000 � $ ... ;: Q) Q) � � 5 0 500 �
80 Voltage (V) 120 (a)
-- Power -- Current T= lODe
1500 � 1000 i> � 500
o 50 100 Voltage (V) 150 (b)
Fig. 3. Simulated I-V and P-V characteristics of PV array, (a) at constant solar irradiance 500 W / m 2 (b) at constant temperature 10° C
the output power also increases. Therefore, from Fig. 3 it can
be concluded that the PV array output current is significantly
affected by irradiation level, whereas the PV array output
voltage is affected by temperature.
Ill. MPPT ALGORITHM
The objective of MPPT algorithm is to automatically track
the current (IMP p ) and voltage (V MP p ) of PV array at which
maximum output power (PMPP) is obtained under a specific
irradiance and temperature. In this paper, an adaptive P&O
MPPT algorithm is proposed using conventional P&O and
fractional short circuit current (FSCC) methods. These two
methods are explained briefly.
A. Perturb and Observe Method
Conventional P&O method involves a perturbation in the
operating voltage b. V of the PV array as shown in Table 11. The performance of P&O method is heavily dependent on the
trade off between the tracking speed and the oscillations that
occurs around the MPP.
B. Fractional Short-Circuit Current (FSCC) Method
The output current of PV array is almost constant in the
voltage region of 0 to V MP P under varying atmospheric
Perturbation Positive Positive Negative Negative
TABLE II SUMMARY OF P & 0 METHOD
Change in Power Next Perturbation Positive Positive Negative Negative Positive Negative Negative Positive
conditions as shown in Fig. 3, and IMPP is approximately
linearly related to the short circuit current Ise as given in [2]
(5)
where, ksc is a proportionality constant, and it lies in between
0.78 and 0.92.
The short circuit current Ise is measured by shorting the PV
array periodically. It requires an additional switch. Measuring
Ise during operation is complicated. During this period the
output power is reduced. Since (5) is an approximation, the
PV array will never perfectly match the MPP.
C. Adaptive P&O MPPT Algorithm
i-Adaptive control-I L ___ al.1l�!!'� ___ :
Fig. 4. Flowchart of the proposed MPPT algorithm
This algorithm incorporates two major modifications to
conventional P&O method:
1) Considering current perturbation instead of voltage per
turbation to speed up the tracking performance as ex
plained using flowchart Fig. 4.
2) Moving the operating point to left hand side of MPP to
handle the sudden changes in weather conditions.
In Fig. 4, Ipv( k), Vpv( k) and Ppv( k) are output current,
voltage and power of PV array at kth iteration respectively
and b.I is current perturbation size. The generalized equation
is derived for the proposed MPPT algorithm as given,
Ipv( k + 2) = Ipv( k + 1) + sign(Ipv( k + 1) - Ipv( k)) (6)
*sign(Ppv( k + 1) - Ppv( k)) * b.I.
408
2013 International Conference on Circuits, Power and Computing Technologies [ICCPCT-2013]
where, the function sign(.) gives either + 1 or -1 depending
on positive or negative value inside the function respectively.
The idea behind considering current perturbation is ex
plained as follows. At a given temperature and irradiance, the
output current of PV array in the voltage region of 0 to V MP P i.e. left hand side (LHS) of MPP is almost constant as shown
in Fig. 3. On the other hand the current is drastically changing
in the right hand side (RHS). Therefore, when the operating
point lies in the left hand side of MPP, then even for relatively
smaller perturbation in current compared to voltage makes the
PV system to reach MPP faster with reduced oscillations. If
the operating point lies in the right hand side of MPP and
operating current Ipv( k) is less than [IMPP - (Ise -IMPP )], then current perturbation gives slower response. To avoid this
situation an adaptive control algorithm is proposed.
Adaptive control algorithm always tries to keep the operat
ing point in the left hand side of MPP. Once MPP is reached
then VMPP & IMPP oscillates around MPP depending on
perturbation size. Let assume that, initially PV array is op
erating at point A as shown in Fig. 3(a) and Fig. 3(b). The
operating point A corresponds to MPP indicated by E. If there
is a sudden increase in temperature or irradiance, then the
operating point changes from A to B i.e., left hand side (LHS)
of new MPP denoted by F as shown in Fig. 3(a) and Fig.
3(b) respectively. The MPPT algorithm directs the PV array to
change the operating point from B to C. The operating point C
corresponds to new MPP as indicated by F. If there is a sudden
decrease in temperature or irradiance, then the operating point
changes from C to D i.e., right hand side (RHS) of new MPP
denoted by E as shown in Fig. 3(a) and Fig. 3(b) respectively.
Therefore, whenever there is a change in temperature or
irradiance then the operating point (Vpv, Ipv) is to be shifted
to (O,Ise) i.e., left hand side of MPP. This can be done
by obtaining the short circuit current. Different methods are
available for obtaining the short circuit current as mentioned
in fractional short-circuit current method. The short circuit
current Ise is measured by shorting the PV array periodically.
Once the short circuit current Ise is measured, then the new
operating point on LHS of MPP is calculated as explained in
fractional short circuit method [2]. In (5), ksc varies between
0.78 and 0.92 depending on weather conditions. In order
to avoid the operating point on RHS of MPP, consider the
maximum value of ksc. Therefore, the new operating point is
given as
Ipv( k) = 0.92 Ise . (7)
IV. SIMULAT ION ST UDIES
The proposed MPPT algorithm is verified for sudden
changes in weather conditions through digital simulations
using MATLAB. In the following section, MPPT algorithm
has been studied for different conditions of irradiation and
temperatures. The specifications of PV array are given in Table
I. The perturbation considered for current and voltage are
6.1 = 0.06A and 6.V = 1.25 V.
A. Sudden increase in irradiance
In this simulation the PV array is simulated for sudden
increase in irradiance from 400 Wjm2 to 800 Wjm2 at 50th
- Proposed MPPT - - PV Curve - Conventional MPPT
2000 .------�-----r-:=_.......__--_, � � 1000 g:.
0 0 50 Ca) 100 Voltage CV) 150
;�F:;.�.6�.... .• . •.. HHS.H:::�.= ... .
.. . . . ......
.
. . o · · · · · · · · · 8.4� · · · · · · · · · · · · · · · · : · · · · · · · · · · · · · · · · · . · · · · · . . . . . . . . . . . . . _IOL----'-----'------'---..I...----' o 20 40 (b) 60 Iterations 100
Cc) 60 Iterations 100 � :::: � . . . . . . . . . . . . . . �.. •. 197j� .. . .. . .
� 10009r�
.··
�i19J ..
.•. .
..
...
.. . . . . . . . .
� _T 93� . _ o o 20 40 Cd) 60 Iterations 100
Fig. 5. Simulation results of sudden increase in irradiance from 400 W / m 2 to 800 W/m2
iteration, assuming constant temperature of 100G. Fig. 5(a)
shows tracking of MPP for conventional and proposed MPPT.
Figs. 5(b )-( d) shows the simulation results of current, voltage
and powers of PV array against number of iterations to reach
the MPP. For conventional MPPT the operating point starts
from point A and reaches the maximum power point B as
shown in Fig. 5(a), at 50th iteration the operating point follows
the path B-C-D-C-E to reach the new maximum power point
E as irradiance is increased. For proposed MPPT the operating
point starts from F and reaches the maximum power point B, at
50th iteration the operating point follows the path B-E to reach
the new maximum power point E as irradiance is increased.
Figs. 5(b )-( d) shows that, the number of iterations to reach
MPP is less for proposed MPPT. The graphs are zoomed in
the intervals of (20 - 40) and (70 - 90) iterations to observe
the oscillations and perturbations. It is also observed that, for
proposed MPPT the oscillations around MPP are minimized
when compared to conventional MPPT.
B. Sudden decrease in irradiance
In this simulation the PV array is simulated for sudden
decrease in irradiance from 800 Wjm2 to 400 Wjm2 at 50th
iteration, assuming constant temperature of 100G. Fig. 6(a)
shows tracking of MPP for conventional and proposed MPPT.
Figs. 6(b)-(d) shows the simulation results of current, voltage
and powers of PV array against number of iterations to reach
the MPP. Here B and D are maximum power points. Fig.
6 shows that proposed MPPT tracks the MPP faster and
minimizes the oscillations.
409
2013 International Conference on Circuits, Power and Computing Technologies [ICCPCT-2013]
- Proposed MPPT - - PV Curve - Conventional MPPT
2000 ,---------�-----r-:;;;_,,3I....._--___, � � 1000 &
$
! u
0 0 50 (a) 100 Voltage (V) 150
10 �16.& · ..
. ..
. ..
. = .
. : ...... � .. .. ���J7'�� . . . . . . . . . ".".".
·.' 8 .65� . . . . •• . . . . . . . . ' . . .
-1� L..._ ... _ .. _ ... _ ... _ ........... _ ... _ ... _ ... _ .. _ ... _ . . .
.J... .•.. _ .. _ ... _ ... _ ... _ ... _:'-8_04_5 __ ·--....1..·. _. _._ ... _ .. ---, . .
o 20 40 (b) 60 Iterations 100
r:r L--_ .. ..
. .
_:::...I...-.�_ . . . • . _' --L.-. �--• • _-_----'-:--._::�_=----'-. · ._ ...
.
_ ... .
----' ... . .
o 20 40 (c) 60 Iterations 100
i ::!k LL-_·····_:::---'-lmYb_:_ · _···· ·····...l._··_ ·····_·� ·----'i'--: _:iid_ ·· ·--,-· .•• _ .• ..
... _ .
. .
__' ..... o 20 40 (d) 60 Iterations 100
Fig. 6. Simulation results of sudden decrease in irradiance from 800 W/m2 to 400 W/m2
C. Sudden increase in temperature
� 1000
i> 500 � "'"
- Proposed MPPT - - PV Curve - Conventional MPPT
40 (a) 80 Voltage (V) 120
I :: �tt�%@------,------· · · �
. . . . . . . ----,----:::iM!f1----'---------.. . . . . . . .
o 20 40 (b) 60 Iterations 100
r�L..-t- ·· ···- :--L-�-· · -··· · ·····----'.· .• _ ..... _< _ ••••• -'----!_:�_. ---,--.. ... _ .. _ ..... ----' .... o 20 40 (c) 60 Iterations 100
1500 �
i 1� LL-�L_ •••• · _��:---'-.ymr_·.····· _···.·····_·· •• ·...l._ · ••••• _ ••••• ·_ ••• ----'i'--:4_�_· .. --'-. _ .... _ ..••• ----' ••••• o 20 40 (d) 60 Iterations 100
increase in temperature from 40°C to 80°C at 50th iteration,
assuming constant irradiance of 500 W/m2. Fig. 7(a) shows
tracking of MPP for conventional and proposed MPPT. Figs.
7(b)-(d) shows the simulation results of current, voltage and
powers of PV array against number of iterations to reach
the MPP. For conventional MPPT the operating point starts
from point A and reaches the maximum power point B as
shown in Fig. 7(a), at 50th iteration the operating point
follows the path B-C-D to reach the new MPP as temperature
is increased. For proposed MPPT the operating point starts
from E and reaches the maximum power point B, at 50th
iteration the operating point follows the path B-D to reach the
new maximum power point D as temperature is increased.
It is observed that proposed MPPT tracks MPP faster and
minimizes the oscillations.
D. Sudden decrease in temperature
In this simulation the PV array is simulated for sudden
decrease in temperature from 80°C to 40°C at 50th iteration,
assuming constant irradiance of 500 W/m2. Fig. 8(a) shows
tracking of MPP for conventional and proposed MPPT. Figs.
8(b)-(d) shows the simulation results of current, voltage and
powers of PV array against number of iterations to reach
the MPP. Here B and C are maximum power points. Fig. 8
shows that proposed MPPT algorithm tracks the maximum
power point faster than conventional P&O MPPT algorithm,
and minimizes the oscillations.
� 1000
1 500
- Proposed MPPT - - PV Curve - Conventional MPPT
40 (a) 80 Voltage (V) 120
:: tt:� ···· l:� o . o 20 40 60 iteratIOns 100 (b)
r�L-E_-:�....L.. _·_'-----·....L..: _�_�_'___----' o 20 40 ( C) 60 Iterations 100
f� LL-ff_·····_ ::---'-rvvE_ ·· ._ .• . _ .. ...l._i _····· ·_·· .. ----' ...• _:�_�_ ..... --'-•.•.• _ ... .. _ . . . . . __' •..•. o 20 40 (d) 60 Iterations 100
Fig. 7. Simulation results of sudden increase in temperature from 400e to Fig. 8. Simulation results of sudden decrease in temperature from 800e to
�e �e
In this simulation the PV array is simulated for sudden From the above simulations, it is clear that the proposed
410
2013 International Conference on Circuits, Power and Computing Technologies [ICCPCT-2013]
MPPT algorithm effectively reduces the sustained oscillations
and tracks the MPP faster, irrespective of increase or decrease
of irradiance and temperatures.
V. ACKNOWLEDGEMENT
This work is supported by the Ministry of Science and Tech
nology, DST, India (Project No.: DSTffM/SERII2klO/47). The
authors would like to thank the Ministry of Science and
Technology, DST, India.
VI. CONCLUSION
In this paper, an adaptive P&O MPPT algorithm is proposed
using conventional P&O and fractional short circuit current
(FSCC) methods. In order to speed up the tracking perfor
mance, current perturbation is used in the conventional P&O
instead of voltage perturbation. In order to consider the sudden
changes in irradiance and temperature, the operating point is
shifted to left hand side of the MPP in PV curve by measuring
the short circuit current. Results presented in the paper clearly
demonstrate that, the proposed algorithm has faster dynamics
and improved stability compared to the conventional P&O
algorithm. The steady state and transient states of the proposed
MPPT algorithm is successfully demonstrated using digital
simulations.
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