close

Вход

Log in using OpenID

embedDownload
Int. J. Advance. Soft Comput. Appl., Vol. 6, No.2, July 2014
ISSN 2074-8523; Copyright © SCRG Publication, 2014
An Intelligent Differential Evolution based
Maximum Power Point Tracking (MPPT)
Technique for Partially Shaded Photo Voltaic
(PV) Array
Sridhar Ramasamy1,*, Jeevananthan .S2 and S.S.Dash1 Thamizh Selvan1
1
EEE Department SRM University, Tamil Nadu, India
sridharmanly@gmail.com
2
EEE Department Pondicherry Engineering College Pondicherry, India.
Abstract
The main aim of this study is to amend the maximum power point
tracking (MPPT) for the photo voltaic (PV) array when it suffers from
partially shaded conditions. When a photo voltaic panel is shaded for a
fraction of time, the power output reduces invariably. During partially
shaded conditions the power-voltage curves exhibit multiple maxima
which makes the conventional MPPT techniques (perturb and observe,
incremental conductance etc.) to get trapped in the local maxima. This
paper proposes a Differential Evolution (DE) curdled algorithm to track
the global maximum power point thereby increasing the performance of
PV array and acquiring a better maxima point. The proposed algorithm is
realized in MATLAB/Simulink environment. The credibility of the
algorithm is ensured by comparing the results of DE algorithm with its
well entrenched counterparts Particle Swarm Optimisation (PSO) MPPT
technique and Ant Colony Algorithm (ACO). Also this study proves that
the suggested technique would prevail over the most prominent Perturb
and Observe (P&O) MPPT when the PV array is under shading
conditions.
Keywords: Differential Evolution Algorithm (DEA); Maximum Power Point
Tracking (MPPT); Photovoltaic (PV) array; Partially Shaded Conditions (PSC).
Insolation
2
R. Sridhar et.al
.
1
Introduction
Photovoltaic (PV) power generators convert the energy of solar radiation directly
to electrical energy [1]. With a spurt in the use of non-conventional energy
sources, PV installations are being increasingly employed in several applications
[2]. However, a major challenge in using a PV source is to tackle the situations
like unstable atmospheric conditions and rapidly fluctuating shadow [3]. The
performance of a photovoltaic (PV) array strongly depends on the operating
environmental conditions, such as temperature, solar insolation, shading and array
configuration. Often the PV arrays get shadowed (almost in all applications,
except the satellite power systems) completely or partially by the passing clouds,
buildings, poles, trees etc. Maximum Power Point Tracking Technique (MPPT) is
a mundane and established algorithm, which is being employed in every
renewable energy systems. Many research papers have been archived with various
schemes over past decades for the MPPT in PV system without considering the
partial shading [4]-[7]. The power-voltage characteristic curve of PV array under
partially shaded condition has multiple local maxima and causes the mere failure
of conventional MPPT or reduces its effectiveness due to their inability to
discriminate between the local and global peak [8]. A stage has been reached,
where MPPT algorithms with inherent property of tracking at shadings are
indispensable. Undoubtedly, a host of algorithm to tackle the shading has been
reported. A large number of papers on minimizing the shading losses have been
evidenced. The fundamental concept of loss reduction is reconfiguring the
hardware connection of photovoltaic modules so that all series modules are
provided with a uniform irradiation level [9]. But at times the reconfiguration
technique becomes cumbersome when shading pattern changes very rapidly and
therefore the research on global search algorithm proliferated and many research
papers addressing it have been archived [10].
The numerical analysis highlights the effect of bypass diodes. A MATLABbased modeling and simulation scheme has been developed for the suitable study
of the I–V and P–V characteristics of a PV array under a non-uniform insolation
due to partial shading. The mathematical model of partially shaded array helped a
lot in developing and evaluating new MPPT techniques for partially shaded
conditions [11-12]. PSO has its strong hold on MPPT arena as researchers have
well explored the nuances of the algorithm and making it more compatible and
efficient by adjusting convergence speed, improving search techniques etc [1316].A very recent research article on cuckoo search aided MPPT authenticates the
fervent interest prevailing in the research arena on this subject [17]. Ant Colony
algorithm(ACO),the one which is more conducive for travelling salesmen
problem had also its hand in contributing towards maximum power extraction in
shaded PV array [18] .Differential Evolution algorithm is the next prominent
3
An Intelligent Differential Evolution
global search algorithm to PSO, renders it contribution to make MPPT a
intelligent one[19-20].A neoteric research article by Kok Soon Tey[21] elaborates
the DE aided MPPT for a partially shaded PV array. This contemporary work
uses PSIM software to study the effects of partially shading and claims that the
suggested technique has an edge over improved perturb and observe [22] and
direct search algorithm [23].
The proposed work in this paper has its own distinctive methodology in
implementing DE for partially shaded PV array .Most of the papers including [21]
follow a single stage control in which the duty cycle is directly fetched as output
from the DE controller whereas the work proposed here in this paper has a double
stage control to increase the reliability. The target vectors initialized are the
voltage values and not the duty cycle .DE MPPT controller gives a reference
voltage at which the peak power exists. This reference voltage is tuned through a
PI controller and appropriate duty cycle is generated through pulse width
modulation (PWM).Also the detail on the fitness or objective function by which
the DE algorithm works is given in this paper whereas in most of the research
article pertaining to global MPP tracking does not have detail on that. Moreover
the DE MPPT results are compared not only with conventional P&O technique
but also with advanced techniques like PSO and ACO.
From the literature survey, it may be concluded that, it is very important to
study the P-V characteristics of PV array with the effects of shading, also a
suitable probabilistic, stochastic optimization technique which will prevail over
conventional algorithms in obtaining the global optima is crucially need. The first
objective of this paper is to present a MATLAB-based modeling and simulation
scheme suitable for studying the I–V and P–V characteristics of a PV array under
the partial shading and section 2 presents this clearly. Secondly, it proposes a
Differential Evolution (DE) based modified MPPT scheme to successfully track
the maximum power point under shading condition and the versatility of the DE
MPPT is checked by comparing its performance with PSO , ACO and Perturb and
Observe algorithm, section 3 and 4 witness it .
2
PV Array Modeling
A solar cell is the fundamental component in a solar module. Since the net output
voltage of a Solar cell is very low, they are connected in parallel or series or both
ways, to meet practical demands. To mathematically model PV array ,the
fundamental equations are derived from the equivalent circuit of the solar cell
shown in Fig 1.
4
R. Sridhar et.al
Fig. 1. Equivalent circuit of the practical PV cell
The simplest equivalent circuit of a solar cell is a current source in parallel with a
diode. Say I, be the current flowing out of the parallel circuit comprising a current
source and diode and it is given by the equation (1)
I = I pv − I d
(1)
Fig. 2. I-V Characteristic curve of a cell
To simulate the characteristics of the PV panel a detailed mathematical modeling
of the same should be done. In this paper, a model of moderate complexity is
used. The net current of the cell is the difference of the photocurrent, IPV and the
normal diode current Id:
 q ( V + IR S )

I = I pv − I 0  e nKT − 1
(2)




The model includes the temperature dependence of photocurrent Ipv and saturation
current of the diode Io.
I pv = I pv (T1 ) + K 0 (T − T1 )
(3)
Photon generated current:
I pv (T1 ) = I SC (T1 , nom )
G
Gnom
Increase in Isc for unit increase in temperature:
(4)
5
An Intelligent Differential Evolution
K0 =
I SC (T2 ) − I SC (T1 )
(T 2 − T1 )
(5)
Diode Saturation Current at a given temperature
3
n
qV0 (T1 )
1 1 
nk  - 
 T T1 
T
I 0 =I 0 (T1 )×   e
 T1 
Diode Saturation Current at standard temperature
I SC (T1 )
I 0 (T1 )=
 qVoc(T1 ) 
-1 
e
nkT1


(6)
(7)
From equations 4 & 6 it can be inferred that the short circuit current of a PV panel
depends upon the irradiation and the open circuit voltage depends upon the
temperature. This vital relation can be represented graphically by Fig 3.As the
temperature increases the open circuit voltage decreases and also the peak power
increases for corresponding increase in insolation
Fig. 3. Different P-V curves under various insolation & temperature.
From the characteristic curves the inferences made are (i) Power of the module
has a single maximum point for each irradiation level; (ii) Peak power of the
module changes with change in temperature; (iii) Peak of the module changes
with the change in irradiation levels; (iv) There is a definite need to track the peak
power in order to maximize the utilizations of the solar module.
6
R. Sridhar et.al
Fig.4. Simulink model of I-V& P-V characteristics
2.1
Effects of the PV Array under Partially Shaded Conditions
When the solar irradiance on a PV array is uniform, only one MPP will exist on
the P-V curve of PV array. However, when the irradiance is not uniform (partially
shaded) because of many reasons like shadow, sand particles over the panel etc,
multiple maximum power points (multiple local maxima) can be witnessed.
Fig. 5. Simulink model of I-V& P-V characteristics of Partially Shaded PV array
Partial shading of even one cell on a solar panel will reduce its power output.
Because all cells are connected in a series string, the weakest cell will bring the
others down to its reduced power level. When the panel is partially shaded there is
possibility of existence of multi peaks. In a simulation environment, multi peak
curves can be witnessed when the panels are exposed to heterogeneous irradiation
7
An Intelligent Differential Evolution
and temperature levels .Fig 5 shows three shaded panels which are realized in
MATLAB environment through a graphical user interface (GUI) tool and the
figure clearly depicts that in a PV array when the individual panels are at partial
shaded condition (PS1 ,PS2 PS3 ) ,the resultant curve (PS1 + PS2 + PS3) exhibit
multi power peaks .A typical 3-D diagram having multi peaks is shown in Figure
6.
Fig. 6. Three dimensional representation of P-V curve
3
DE Aided MPPT –The Proposed Approach
A block diagram of the proposed system is shown in fig 7. A boost-type dc-dc
converter is used to interface the PV module to the load. The MPPT controller is
employed to track the maximum power point of the PV array. For A uniformly
illuminated condition the P&O MPPT algorithm is good enough to find out the
MPP of the PV module and produces the respective duty cycle for the dc-dc boost
converter. But in partially shaded condition since the conventional P&O MPPT
algorithm fails by tracking only the local MPP of the PV module, differential
evolution algorithm is used to find out the global MPP of PV module[21]. The
inputs to the DE controller will be the irradiation (G) and temperature (T) of the
cell. A duty cycle relevant to the peak power is calculated and that duty cycle is
fed to the dc-dc converter .The DE algorithm perform its search based on the
fitness or objective function[24] .The objective functional equation of DE mppt is
so cautiously framed by involving all the four relatively dependent parameters
namely Voltage(V), Current(I), Irradiation(G), Temperature(T).
The functional fitness equation of the PV array formed by three individual panels
are given by the equation (8)
fit = I ∗ PVfunc(I 1 , Suns1 , T1 ) + i 2 PVfunc(I 2 , Suns2 , T2 ) + i3 ∗ PVfunc(I 3 , Suns3 , T3 )
(8)
Here suffixes 1,2, 3 refers to panel 1 , panel 2, panel 3.
8
R. Sridhar et.al
Fig. 7.Proposed Approach
Step 1: Assume,
No. of particles = 5
Scaling Factor F= 0.7
Crossover CR= 0.6
Iter_max =100 err_min = 0.04V
Step 2: Initialize each of the particles with any random voltage V1 volt
Step 3: Calculate the fitness values of all the particles.
Step 4: Select the individual Xi with maximum fitness which is the target vector.
Step 5: Select three more individuals namely Xr1, Xr2, and Xr3 by random
Step 6: Create the trial vector
ViG+1 = Xa,G + F*(Xb,g – Xcg)
Step 7: Create a random vector with values between 0 and 1
Step 8: Compare the values of random vector with crossover constant
Xi’’ = Vig+1 if rand(i) <=CR
Xi’’ = Xi if rand(i) > CR
Step 9: Calculate the fitness of the resultant vector
Step 10: If the fitness of the resultant vector is greater than the fitness of the target
vector, then the resultant vector is selected for the next iteration. Else the target
vector is selected for the next generation.
Step 11: Repeat the steps 5 to 10 for the remaining 4 particles
Step 12: Repeat the steps 3 to 11 till the end criteria is met
Step 13: Output the voltage corresponding to the maximum power
4
Results and Discussions
The table 1 shows the electrical parameters of PV system which is taken for the
study. A PV array of 3 panels are taken for consideration and the three panels are
9
An Intelligent Differential Evolution
not uniformly exposed to sun’s irradiation and as a result the cumulative power
curve will exhibit a multi peak embedded curve as shown in Fig.8. The simple
observation on Fig.8 reveals that there occur global maxima at 82.2 Watts and two
local maxima at 64 Watts and 40 watts.
Table 1: Parameter Specifications of WS-140 (WSBYW03101693)
Solar panel at Standard test condition (STC)
Parameters
Maximum Power
(Pmax)
Voltage at Pmax (Vmpp)
Values
140 watts
Current at Pmax (Impp)
8.24 amps
Open circuit voltage
(Voc)
Short circuit current
(Isc)
Temperature
coefficient of Isc (KI)
Temperature
coefficient of Voc (KV)
NOCT
21 volts
17 volts
8.89 amps
(0.065 ± 0.015)%/
o
C
-(80 ± 10)mV/ oC
(47 ± 2) oC
Fig. 8. PV curve of a shaded array
10
R. Sridhar et.al
Fig.9. Convergence of DE MPPT (Figure (a) shows the initial distribution
chromosomes
(b) Convergence around MPP (c) convergence in MPP
Fig.9. shows the convergence of differential evolution aided MPPT .It has 3 panes
where pane(a) shows the random distribution of chromosomes over the search
space. One can asses five chromosomes that are distributed randomly. Pane (b)
shows the convergence of chromosomes around the maximum power point say
approximately around 82W.The final convergence at maximum power point is
shown in pane (c).Though the algorithm is made to run for 100 iterations ,the
convergence of DE is so versatile that the maximum power is tracked within 15
odd iterations irrespective of any change in temperature or irradiation. Table 2
shows the tabulation between voltage and Power values (G best) and (G fit) with
respect to 15 odd iterations.
The power output and the operating voltage waveforms are shown in figure 10.
Also the experiment is carried out at three different instants (timings) and the
results are shown in 3-D graph(refer figure 11). The inference is that within 10
iterations the DE algorithm swiftly converges though its initial search starts with
random initialization. The comparison table presenting various other MPPT
techniques are shown in table 3.
11
An Intelligent Differential Evolution
Figure 10 Simulation output of DE MPPT for the shaded array
Table.2 Simulation output of DE MPPT
Iteration
Voltage
Power Output
1
9.4219
79.0708
2
9.4287
79.0708
3
8.8354
81.6079
4
8.3776
82.0499
5
8.4188
82.0535
6
8.4188
82.0535
7
8.4164
82.0535
8
8.4137
82.0536
9
8.4133
82.0536
10
8.4133
82.0536
12
R. Sridhar et.al
Fig.11 Convergence graphs at 3 instants (runs)
5
Comparative Results of MPPT Techniques
5.1
Perturb & Observe MPPT
The Perturb and Observe (P and O) mppt logic is to adjust the operating voltage
of the panel until the maximum power from it is achieved. During this operation
the terminal voltage is continuously perturbed and power is measured. In a
stipulated direction if power increases for a change in operating voltage then it is
understood the search is moving forward towards MPP. If the power decreases,
then the operating point would have crossed peak power point and the direction
should be reversed. This perturbation is done by controlling the duty cycle
( δ).But when multiple peaks occur. Perturb and observe technique when
employed to a partially shaded PV array, there is every possibility of this
algorithm to get stuck with local maxima instead of tracing the global one .Table 4
presents that, for a given shading pattern the perturb and observe technique gets
stuck with the local maxima of 38 Watts .
5.2
Particle Swarm Optimisation
In PSO algorithm, the particles position is changed based on the Pbest particles in
the neighbourhood as well as Gbest achieved by all the particles. The new particle
position is given by the equation
xik +1 = xik + Φ ik +1
(9)
where xik is the particle position and Φi is the step size. The velocity is given by
13
An Intelligent Differential Evolution
{
}
{
}
Φik +1 = ωΦ ik + c1r1 Pbesti − xik + c2 r2 Gbesti − xik
(10)
The PSO algorithm is the most prominent MPPT technique among all the global
search algorithm .Among all other global search algorithm , PSO is the most
reliable among research community as many papers have been archived for PSO
MPPT .The PSO MPPT is advantageous than any other technique in convergence
, versatility and reliability . But at the same time , the proposed DE algorithm has
a slender edge over the PSO in Power output value .The power tracked by DE
algorithm is slightly more compared to the power obtained by PSO for the same
shading pattern ,Table 3 witnesses the same .
5.3
Ant Colony Algorithm
Ant colony algorithm came into existence by mimicking the social behavior of
ants. When ants search their food it would follow a shortest path between their
nest and food. They have an inherent capacity to emit a chemical called
pheromone which drags response within members of the same species .When
ants wander for search of food it would emit pheromone trail on their way. The
search may be random initially. Ants may also follow the same path while
returning to the nest as it would trace the pheromone trail. Therefore the
pheromone trail becomes even thicker and rigid and will be the shortest path. If
the pheromone path is not the shortest then it would evaporate and vanish off its
own.
Tij = ρTij (t − 1) + ∆Tij ;
t = 1,2,3...T
(11)
where
Tij - Revised concentration of pheromone
∆Tij - Change in Pheromone concentration
ρ - Pheromone concentration rate (0-1)
The pheromone rate ‘ ρ ’ plays a crucial role as absurd values.
Concentration rate would wrongly direct the convergence to happen at local
maximum.
Pheromone concentration ∆Tij is given by
 R / fitness k Iij is chosen by ant k
∆Tij = 
0 otherwise
(12)
ACO MPPT has dragged less attention in the MPPT research arena but for a
research initiative [18].This research article claims to have superior characteristics
than PSO for the shading pattern . The complexity of realizing the ACO MPPT as
hardware still remain unsolved where as the DE algorithm has a clear advantage
over its ACO counterpart .The convergence of ACO is slow compared to DE
.Table.3 shows the comparative analysis of all three the MPPT techniques
discussed in this section with that of DE MPPT .
14
R. Sridhar et.al
Table 3. Comparative results of MPPT Techniques
Shading Pattern
Scheme
Panel 1
45*C ,0.8Suns
Without MPPT
12.05 W
NA
With P&O
MPPT
38.0 W
0.02s
DE MPPT
Controller
81.79W
2.276s
PSO MPPT
Controller
81.37 W
1.8 sec
ANT MPPT
Controller
81.367
2.2 sec
Panel 2
25, 0.6
Panel 3
45,.72
6
Power
delivered
Time taken to
reach MPP
Conclusion
The photovoltaic (PV) industry is grooming into a most reliable energy market
among other renewable sources .Research in improving its conversion efficiency
is in rigor that the cost of PV system will come down relatively .Maximum power
tracking technique which is a indispensable embodiment in a photovoltaic power
system which is used to enhance the power conversion efficiency. .DE based mppt
algorithm is proposed here for a partially shaded PV array where conventional
mppt algorithms tend to fail .The results validate the versatility of the proposed
technique and assures that DE algorithm has a clear edge over its counterpart
techniques like PSO AND ACO either in convergence technique or maximum
power extraction .For a given shading pattern DE mppt is capable of extracting
82.5 Watts where as a conventional perturb and observe mppt technique will get
stuck with a local maxima of 42 Watts. The work suggested can be extended for
multiple PV arrays with a multi dimensional search by DE algorithm.
7
Future Work
To enhance the power extraction capability, the power conditioning units may be
placed for each PV shaded panel in an array .But when multiple power
conditioning units are used, a uni-dimensional DE will not be sufficient and the
total power extraction capability will be poor. Therefore a multi-dimensional DE
should be implemented.
.
15
An Intelligent Differential Evolution
References
[1] Antonio Luque and Steven Hegedus, “Handbook of Photovoltaic Science and
Engineering”, John Wiley & Sons Ltd.(2003).
[2] R. Messenger and J. Ventre, Photovoltaic Systems Engineering, 2nd ed.,
Boca Raton, FL: CRC Press, (2004)
[3] Lijun Gao, Roger A. Dougal, Shengyi Liu, and Albena P. Iotova, “ParallelConnected Solar PV System to Address Partial and Rapidly Fluctuating
Shadow Conditions”, IEEE Transactions on Industrial Electronics, Vol.56,
No.5,( 2009) pp.1548- 1556.
[4] E. Koutroulis, K. Kalaitzakis, and N. C. Voulgaris, “Development of a
Microcontroller-based photovoltaic maximum power point tracking control
System,” IEEE Trans. Power Electron, Vol.16, No.1, ( 2001), pp.46–54.
[5] W. Xiao, N. Ozog, and W. G. Dunford, “Topology study of
Photovoltaic interface for maximum power point tracking,” IEEE Trans. Ind.
Electron.,Vol.54, No.3,( 2007), pp.1696–1704.
[6] Fangrui Liu, Shanxu Duan, Bangyin Liu, Yong Kang, “A variable step size
INC MPPT method for PV Systems”, IEEE Trans. Ind. Electron, Vol.55,
No.7, (2008) pp. 2622-2628.
[7] N. Femia, G. Petrone, G. Spagnuolon, and M. Vitelli, “Optimization of
Perturb and observe maximum power point tracking method,” IEEE Trans.
Power Electron. Vol.20, No.4(2005), pp.963–973.
[8] K. Hussein, I. Muta, T. Hoshino, and M. Osakada, “Maximum photovoltaic
Power tracking: An algorithm for rapidly changing atmospheric conditions,”
Proc. Inst. Elect. Eng.—Gener. Transm. Distrib., Vol.142,No.1,( 1995), pp.
59–64.
[9] Y.-J. Wang P.-C. Hsu, “Analytical Modelling of partial shading and different
Orientation of photovoltaic modules”, IET Renew. Power Generation,
Vol. 4, No. 3,( 2010), pp. 272–282.
[10] Y.L. Liu, H. Zhou,“MPPT Control Method of PV System Based on
PSO,”,Vol. 36, (2010), pp. 265-267.
[11] Zainal Salam, Jubaer Ahmed, Benny S. Merugu “The application of soft
Computing methods for MPPT of PV system: A technological and status
Review “, Applied Energy”, Vol.107 (2013), pp.135–148.
[12] Hiren Patel and Vivek Agarwal, “MATLAB-Based Modelling to Study the
Effects of Partial Shading on PV Array Characteristics”, IEEE Transactions
On Energy Conversion, Vol. 23, No. 1,(2008), pp. 302-310.
[13] KashifIshaque, Zainal Salam, Hamed Taheri and Amir Shamsudin,
“Maximum Power Point Tracking for PV System under Partial Shading
Condition via Particle Swarm Optimization”, Proceedings of IEEE
International Applied Power Electronics Colloquium (IAPEC),( 2011),
pp.5-9.
[14] Liu Y. H., Huang S. C., Huang J. W., Liang W.C., “A partial swarm
16
R. Sridhar et.al
optimization based maximumpower point tracking algorithm for PV systems
operating under partially shaded conditions”, IEEE Transactions on Energy
Conversation, Vol. 27, No. 4. (2012),pp.1027-1035.
[15] Phimmasone V., Endo T., Kondo Y., Miyatake M., “Improvement of
maximum power point tracker for photovoltaic generators with partial
swarm optimization technique by adding repulsive force among agents”,
Proceedings of International conference on Electrical Machines and
Systems,(2009), pp 1-6.
[16] Kornelakis A, “Multi-objective partial swarm optimization for the
optimal design of photovoltaic grid-connected system”, Solar Energy 84
(2010), pp.2022-2033.
[17] Jubaer Ahmed and Zainal Salam, “A Maximum Power Point Tracking
(MPPT) for PV system using Cuckoo Search with partial shading
Capability”, Applied Energy, Vol.119,( 2014),pp.118–130.
[18] Lian Lianjiang, Douglas L. Maskell, jagdish c. patra, “A novel ant colony
Optimization-based maximum power point tracking for photovoltaic
systems under partially shaded conditions”,Energy and Buildings,
Vol.58,(2013), pp 227-236.
[19] Kashifishaque, Zainal Salam, “An Improved modeling method to determine
the model parameters of photovoltaic modules using differential
evolution (DE)”, Solar energy,Vol.85,(2011), pp 2349-2359.
[20] Sheraz M., Abido M. A., An efficient MPPT controller using differential
Evolution and neural network, IEEE International Conference on Power and
Energy, (2012), pp.378-383.
[21] Kok Soon Tey, Saad Mekhilef, Hong-Tzer Yang, andMing-Kai Chuang ,”
A Differential Evolution Based MPPT Method for Photovoltaic
Modules under Partial Shading Conditions”, International Journal of Photo
energy,Vol.2014 (2014).pp.1-10.
[22] E. Koutroulis and F. Blaabjerg, “A new technique for tracking
the global maximum power point of PV arrays operating under
Partial-shading conditions,” IEEE Journal of Photovoltaics, Vol.
2, No.2,( 2012), pp. 184–190.
[23] T. L. Nguyen and K.-S. Low, “A global maximum power point
Tracking scheme employing DIRECT search algorithm for photovoltaic
Systems,” IEEE Transactions on Industrial Electronics,
Vol. 57, No. 10,(2010) pp. 3456–3467.
[24] Swagatam Das and Ponnuthurai Nagaratnam Suganthan,” Differential
Evolution: A Survey of the State-of-the-Art,” IEEE Transactions of
Evolutionary Computing. Vol.15,No.1,( 2011),pp 4-31.
1/--pages
Пожаловаться на содержимое документа