Photovoltaic Panels Extraction under Evolutionally Algorithms: A Comparative Study Energy and...
Transcript of Photovoltaic Panels Extraction under Evolutionally Algorithms: A Comparative Study Energy and...
Photovoltaic Panels Extraction under Evolutionally Algorithms:
A Comparative Study
I. Benouareth*1, K. Khelil
2 and I. Abadlia
3
*1,2Unv. Souk Ahras, Fac. Sci & Tec. LEER, Lab. Souk Ahras, Algeria.
3Unv. Badji Mokhtar Annaba, Fac. engineering. LASA Lab. Annaba, Box 12, 23000, Algeria.
Email: [email protected]
Abstract –The center of the intention of this paper is the
extraction of photovoltaic panel’s parameters, using
Evolutionally Algorithms (EAs). PV panels are
optimized via genetic algorithm and particle swarm
optimization techniques at different atmospheric
conditions and various parameters whereas panels of
constructor are prepared in ideal conditions. So, the
object of the present optimization is too accurate
extraction of PV panel parameters in different
conditions via objective function. A comparative study
between proposed optimization methods and a real
modal panel of constructor is realized and results are
obtained by MATLAB.
Keywords – Photovoltaic Panels, Extraction,
Evolutionally Algorithms, Genetic Algorithms,
Particle Swarm Optimization, Objective function
I. INTRODUCTION
Renewable energy sources are getting more
attention in recent years as alternative means of
generating electricity in various parts of the world.
Various motivations are promoting serious
contribution of environmental pleasant (friendly)
energy sources in mass electricity production in many
countries. Some of these reasons are: environmental
concerns due to greenhouse effect, possible reduction
and price increase of conventional energy primary
resource.
Solar energy is one of the most promising emission
free resources that are currently being used all over
the world to (contribute) supply the rising demands of
electric power. Solar photovoltaic is the fastest
growing power-generation technology in the world
with an annual average increase of 60% between
2004-2009 [1]. The traditional extraction methods
were based on direct approaches on the use of I-V
curve features such as axis intercepts and the
gradients at selected points, to determine some cell
parameters. However, accuracy of these techniques
was limited due to nonlinearity of measured I-V data,
multi variable and multi modal problem which have
many local optimal [1] and [2]. The recent developed
algorithms are based on nature motivated ideas, such
as ant a colony optimization, evolutionary algorithms,
and a particle swarm optimization etc. [3].
Most of these algorithms are meta-heuristic and
they may be applied to a large variety of problems. In
a similar context, Artificial Bee Colony (ABC)
algorithm was initially proposed by Karaboga in 2005
as a technical report for numerical optimization
problem [4]. Artificial Bee Colony Algorithm (ABC)
is nature-inspired meta-heuristic, which imitates the
foraging behavior of bees.
Furthermore, the best EA method is validated with
six PV modules of different types (multicrystalline,
mono-crystalline, and thin-film) from various
manufacturers. Finally a table is proposed to compare
the performance of each method; although the table
may not be appropriated for benchmarking. It can be
used as a guideline to indicate the best EA method to
extract the parameters of a one diode PV cell model.
II. MATHEMATICAL MODEL OF PV PANEL
Despite the fact that the diffusion and
recombination currents are linearly independent, it is
possible to combine them together under the
introduction of a nonphysical diode ideality factor n.
The use of this single diode model, to describe the
static I-V characteristic, has recently been considered
widely, it has also been used successfully to fit
experimental data. The single diode model equivalent
circuit is shown in Fig. 1 [5].
Fig. 1: Equivalent circuit of a single diode model.
In this model, Eq. (1) is reduced to the following
equation
𝐼 = 𝐼𝑝ℎ − 𝐼𝑜 [𝑒𝑥𝑝 (𝑉 + 𝐼𝑅𝑠
𝑛𝑉𝑇
) − 1] −𝑉 + 𝐼𝑅𝑠
𝑅𝑠ℎ
(1)
The photovoltaic panel comprising 𝑁𝑆cells in
series, assume that all cells are identical and are
exposed to the same temperature and a uniform
illumination𝐼𝑝𝑎𝑛𝑛𝑒𝑎𝑢 = 𝐼𝑐𝑒𝑙𝑙𝑢𝑙𝑒and𝑉𝑝𝑎𝑛𝑛𝑒𝑎𝑢 = 𝑁𝑆. 𝑉𝑐𝑒𝑙𝑙𝑢𝑙𝑒
In this work, we use the three photovoltaic panels are
[6]: MSX PV-60, MSX-64 and KyoceraKG200GT.
Under standard test conditions (air mass 1.5, cell
temperature = 25°𝐶 and irradiation = 1000𝑊/𝑚2
are given in Table I where IPV is the current generated
by the incidence of light; Io is the reverse saturation
currents of diode. The Io term is introduced to
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compensate (for) the recombination loss in the
depletion region as described in Chih-Tang et al.
(1957). Other variables are defined as follows: VT is
equivalent to (Ns*k *T/q) which are the thermal
voltages of the PV module having Ns cells connected
in series, q is the electron charge (1.60217646.10-19
C), k is the Boltzmann constant (1.3806503. 10-23
J/K)
and T is the temperature of the P_N junction in
Kelvin
Table I: Electrical characteristics in STC
KG200GT MSX-64 MSX-60
maximum power
(𝑃𝑚𝑎𝑥) 200W 64W 60W
Peak voltage
(𝑉𝑚𝑝) 26.312V 17.5V 17.1V
Peak current
(𝐼𝑚𝑝) 7.61A 3.66A 3.5A
Short-circuit current
(𝐼𝑆𝐶) 8.21A 4.0A 3.8A
Open circuit voltage
(𝑉𝑂𝐶) 32.9V 21.3V 21.1V
Temperature Coefficient
of 𝑉𝑂𝐶 (−𝟖𝟎 ± 𝟏𝟎)𝒎𝑽/°𝑪
Temperature Coefficient
of 𝐼𝑆𝐶 (𝟎. 𝟎𝟎𝟔𝟓 ± 𝟎. 𝟎𝟏𝟓)%/°𝑪
Temperature Coefficient
of 𝑃𝑚𝑎𝑥 −(𝟎. 𝟓 ± 𝟎. 𝟎𝟓)%/°𝑪
cells Number 36
III. BRIEF OVERVIEW OF EVOLUTIONALLY
ALGORITHMS
A) Genetic algorithm
The genetic algorithm (GA) is based on the theory
of biological evolution (Holland, 1975). Fig. 2 shows
the flow chart of GA. The common operators used in
GAs are described as follows [7-9]:
Selection
This procedure selects the chromosomes that
contribute in the reproduction process to give birth to
the next generation. Only the best chromosomes are
considered for the next generation. The selection
process can be realized by various techniques,
including the elitist model, the ranking model, the
roulette wheel procedure (Haupt and Haupt, 2004),
etc.
Mutation
It introduces changes in some genes (parameters)
of a chromosome in a population. This procedure is
performed by GAs to explore new solutions. Random
mutations modify a small percentage of the
population except for the best chromosomes. A
mutation rate between 1% and 20% often obtain
better results. If the mutation rate is above 20%, many
good parameters can be mutated, and causing a pause
the algorithm. Note that the new value of each
parameter should be in the [𝑋𝐼𝐿,𝑋𝐼𝐻] corresponding
interval. Consequently, after paring, mutated
parameters are engaged to ensure that the parameters
space is explored in new regions.
Crossover
This process uses two selected chromosomes from
a current generation (parents) and crosses them with
some probability to obtain two individuals for the new
generation. There are several types of crossover, but
the simplest method is arbitrarily to choose one or
more parameters in the chromosome of each parent, to
mark as crossover points. Then, the criteria between
these points are merely swapped between the two
parents. Although GA has been used extensively in
many applications, numerous computational
difficulties, namely premature convergence, low
speed, and degradation for highly interactive fitness
function are reported (Zwe-Lee, 2004; Ji et al., 2006).
Fig. 2: Flow chart of GA.
B) Particle swarm optimization
Particle swarm optimization (PSO) is a stochastic
population-based search method, modeled after the
behavior of bird flocks (Eberhart and Kennedy, 1995;
Kennedy and Eberhart, 1995) [10-12].
A PSO algorithm maintains a swarm of individuals
called particles where each ones represents a
candidate solution.
Particles follow a simple behavior: emulate the
success of neighboring particles, and achieve their
own achievement. The position of a particle is
therefore influenced by the best particle in a
neighborhood.
The velocity is calculated by:
International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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𝒗𝒊(𝒕 + 𝟏) = 𝝎 𝒗𝒊(𝒕) + 𝒄𝟏𝒓𝟏[𝒙𝒑𝒊(𝒕) − 𝒙𝒊(𝒕)]+ 𝒄𝟐𝒓𝟐[𝒈(𝒕) − 𝒙𝒊(𝒕)] (2)
Where 𝑾 is the inertia weight, 𝑪𝟏 and 𝑪𝟐 are the Well
as the best solution found by the particle. Particle
position, xi, are adjusted using: 𝒙𝒊 (𝒕) = 𝒙𝒊 (𝒕 − 𝟏) + 𝒗𝒊 (𝒕) (3) Where the velocity component, vi, represents the step
size. Acceleration coefficients, r1, r2 Є U (0, 1), (yi) it
is the own best position of particle i, and 𝒊 is the
neighborhood best position of particle i. The inertia
weight w plays an important role in balancing the
global research and local research. A large w
facilitates a global research while a small inertia
weight facilitates a local research. It can be a positive
constant or a positive decreasing linear function of
iteration index j. In (Ye et al., 2009), the inertia
weight was used from the following falling linear
function:
𝑾(𝒋) = (𝒘𝒎𝒂𝒙 − 𝒘𝒎𝒊𝒏)𝒋
𝑮𝒎𝒂𝒙 (4)
Where𝒘𝒎𝒂𝒙 and 𝒘𝒎𝒊𝒏 are the final weight and the
initial weight, respectively, and 𝐺𝑚𝑎𝑥 is the maximum
iteration number
The velocity is further updated by following law
(5)
Where𝑉𝑚𝑎𝑥 is a constant that it is set to clamp the
unnecessary wandering of particles. The choice of
𝑉𝑚𝑎𝑥 usually is equivalent to the maximum acceptable
departure of any particle in that dimension (Shi and
Eberhart, 1998). Fig. 3 depicts the flow chart of the
PSO. Due to excessive roaming of particles, high
convergence time and great number of iterations are
experienced (Ye et al., 2009).Furthermore, penalizing
unnecessary movement of particles can affect the
convergence performance. For instance, in a PSO
based PV cell parameters extraction (Ye et al., 2009),
the authors have used a common approach to penalize
the velocity of the particles with a factor𝑉𝑚𝑎𝑥. The
global exploration ability of a PSO strongly depends
on this factor. If 𝑉𝑚𝑎𝑥 is too large, particles may
reveal good and satisfactory solutions. Otherwise a
small value of 𝑉𝑚𝑎𝑥 will end the particles to go
beyond locally good solutions. Hence, the choice of
𝑉𝑚𝑎𝑥may not be consistent for different types of PV
modules.
Fig. 3: Flow chart of PSO.
IV. EXTRACTING MODEL PARAMETERS AND
PROBLEM FORMULATION
Evolutionary algorithms provide an efficient and
improved optimization for non-convex problems.
Generally, the cost functions used in the estimation of
electrical model parameters are not convex.
Therefore, evolutionary algorithms are expected to
offer better performance than conventional
optimization techniques. In our work, we adopted the
genetic algorithm (GA) and particle swarm
Optimization (PSO) and differential evolution (DE)
for this type of estimation problem. The objective
function used in the algorithm is to solve the
(𝟏)equation to determine the five parameters in
question. These parameters will be used to predict the
values given by the manufacturer, ie the short-circuit
current 𝐼𝑠𝑐 the open circuit voltage𝑉𝑜𝑐 , the maximum
power 𝑃𝑚𝑎𝑥thevoltage at the maximum power𝑉𝑚𝑝and
current of maximum power𝐼𝑚𝑝. Thus the optimization
problem is minimized the cost function is the sum of
quadratic errors
𝑱 = (𝑰𝒔𝒄 − 𝒔𝒄)𝟐+ (𝑽𝒐𝒄 − 𝒐𝒄)
𝟐+ (𝑷𝒎𝒂𝒙 − 𝒎𝒂𝒙)
𝟐
+ (𝑽𝒎𝒑 − 𝒎𝒑)𝟐+ (𝑰𝒎𝒑 − 𝒎𝒑)
𝟐 (6)
Isc, Voc, Pmax, Vmp, ImpWhere the predicted values
of short circuit are current, open circuit voltage,
maximum power, maximum power voltage and
current at maximum power respectively.
A. Performance of the genetic algorithm (GA) and
particle swarm (PSO)
Using the data in Table I from the data sheet
provided by the manufacturer of photovoltaic panels
in question, 𝑃𝑚𝑎𝑥 , 𝑉𝑚𝑝 , 𝐼𝑚𝑝 , 𝐼𝑆𝐶 , 𝑉𝑂𝐶 namely the five
values, the five parameters 𝐼𝑝ℎ , 𝐼𝑜 , 𝑅𝑠, 𝑅𝑠ℎ, 𝑛 forming
chromosome are estimated. The tables II and III
present the parameters of algorithm GA and PSO
respectively.
TABLE II: PARAMETERS OF THE GENETIC ALGORITHM.
Parameter’s Value’s
Population size 100
variables Number 5
Maximum generations 100
Selection stochastic
Crossover dispersed
crossing Probability 0.8
Mutation Gaussian
Elite Count Data 20
TABLE III: PARAMETERS OF THE PSO.
Parameter’s Value’s
Population size 100
Variables Number 5
Maximum generations 100
C1 2
C2 2
W 0.3
B. Optimization Steps
1. Initial population
A random initial population chromosome is
International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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generated. Each chromosome is a string in the
following form𝐼𝑝ℎ 𝐼𝑜 𝑅𝑠 𝑅𝑠ℎ 𝑛. Thus, in
our optimization, the initial population is a real
valued (matrix) environment. Following a
research of the literature related to the field of
modeling, intervals of five parameters are chosen
as follows:
𝐼𝑠𝑐 − 1 ≤ 𝐼𝑝ℎ ≤ 𝐼𝑠𝑐 + 1
10−8 ≤ 𝐼𝑜 ≤ 10−7
0.05 ≤ 𝑅𝑠 ≤ 2
100 ≤ 𝑅𝑠ℎ ≤ 1000
1 ≤ 𝑛 ≤ 1.5
2. Solve the nonlinear equation:
𝐼 = 𝐼𝑝ℎ − 𝐼𝑜 [𝑒𝑥𝑝 (𝑉 + 𝐼𝑅𝑠
𝑛𝑉𝑇) − 1] −
𝑉 + 𝐼𝑅𝑠
𝑅𝑠ℎ
Each chromosome is replaced in the equation
above. The equation is solved using the Newton
Raphson method for solving non-linear equations to
determine the characteristics I (V) and P (V) of the
module.
3. Calculation of parameters
From I-V and P-V characteristics determined in
step 3: the Values of Pmax, Vmp, Impare extracted
from the power vector P=V*I the values Isc, Vocare
calculated by interpolation.
𝒔𝒄, 𝒐𝒄, 𝒎𝒂𝒙, 𝒎𝒑, 𝒎𝒑
4. Evaluation of the objective function:
Evaluate the cost (or fitness) of each chromosome
in the population. The objective function (or cost)
assigns each individual (chromosome) of the
population a numerical value reflecting its quality as a
potential solution. The cost defines the capacity of the
individual (chromosome) to survive and produce
offspring. In our case, the objective function is the
quadratic error given by equation
V. VALIDATION AND RESULTS OF
SIMULATION
In order to validate our model, all
photovoltaic panels are measured (See Table I for the
characteristics). The method, based on the
optimization is to extract the five parameters of the
model 𝐼𝑝ℎ 𝐼𝑜 𝑅𝑠 𝑅𝑠ℎ 𝑛 minimizing the square
error (EQ) 𝑃𝑚𝑎𝑥 , 𝑉𝑚𝑝 , 𝐼𝑚𝑝, 𝐼𝑆𝐶 , 𝑉𝑂𝐶 between the
values given by the manufacturer and the values
Isc, Voc, Pmax, Vmp, Imp estimated. To check the
accuracy, the fidelity and to obtain better solutions,
algorithms are executed toward 100 times and all five
parameters. Giving the value of the smallest square
error is considered to be the most optimal solution to
the problem. The results are shown in
Table.IVandTable.Vfor the different panels.
TABLEIV.VALUES OF FIVE PARAMETERS ESTIMATED BY THE GA
TABLE V VALUES OF FIVE PARAMETERS ESTIMATED BY THE PSO
Using the estimated values shown (in the tables
shown) in Table IV and Table V, the five parameters
𝑃𝑚𝑎𝑥 , 𝑉𝑚𝑝 , 𝐼𝑚𝑝 , 𝐼𝑆𝐶 , 𝑉𝑂𝐶 are calculated and compared
with those given by the manufacturers as illustrated
by Table VI, Table VI,and Table VI for photovoltaic
panels. The quadratic error (6) is calculated to
appreciate better the combination of our values with
those provided by the manufacturer itself.
Table VI Comparison of five parameters given by the
manufacturer of MSX-60 with those extracted from the
model proposed by (GA) and (PSO) MSX-60
Manufactu
rer
GA PSO
Maximum
power𝑷𝒎𝒂𝒙 [𝑾] 60 60.076 60.0288
Peak voltage 𝑽𝒎𝒑 [𝑽] 17.1 16.792 17.0667
Peak current (𝑰𝒎𝒑) [𝑨] 3.5 3.5775 3.5173
𝑆ℎ𝑜𝑟𝑡_𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑐𝑢𝑟𝑟𝑒𝑛𝑡𝑰𝑺𝑪 [𝑨] 3.8 3.9520 3.8000
Open circuit
voltage 𝑽𝑶𝑪[𝑽] 21.1 21.326 21.0826
square error 0.0705 0.0012
Table VII Comparison of five parameters given by the
manufacturer of MSX-64 with those extracted from the
model proposed by (GA) and (PSO) MSX-64
manufactu
rer
GA PSO
Maximum power𝑃𝑚𝑎𝑥 [𝑊] 64 64.110 64.034
Peak voltage 𝑉𝑚𝑝 [𝑉] 17.5 17.336 17.462
Peak current (𝐼𝑚𝑝) [𝐴] 3.66 3.6980 3.6670
𝑆ℎ𝑜𝑟𝑡_𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑐𝑢𝑟𝑟𝑒𝑛𝑡𝐼𝑆𝐶 [𝐴] 4 3.9983 3.9972
Open circuit voltage 𝑉𝑂𝐶[𝑉] 21.3 21.283 21.271
square error 0.0406 0.0035
Parameters KG200GT MSX-60 MSX-64
Photocurrent
𝑰𝒑𝒉[A] 8.2986 3.8039 4.0029
saturation current
𝑰𝒐[A] 2.374×10_8 4.998x10−8 9.379x10−8
𝑹𝒔[Ω]
series resistance 0.21072 0.2220 0.1356
parallel resistance
𝑹𝒑[Ω] 123.2693 365.8308 221.4217
𝒏
Ideality factor 1.2078 1.2759 1.3139
Parameters KG200GT MSX-60 MSX-64
Photocurrent
𝑰𝒑𝒉 [A] 8.2220 3.8203 4.0013
saturation current
𝑰𝒐[A] 3.110×10_8 5.93x10−8 5.604x10−8
𝑹𝒔[Ω]
series resistance 0.2709 0.2221 0.1578
parallel resistance
𝑹𝒑[Ω] 741.5098 376.6715 223.7207
𝒏
Ideality factor 1.2241 1.2716 1.2762
International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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Table VIII Comparison of five parameters given by the
manufacturer of KyoceraKG200GTwith those extracted from the
model proposed by (GA) and (PSO)
KG200GT
manufacturer GA PSO
Maximum
power𝑃𝑚𝑎𝑥 [𝑊] 200 199.92 200.06
Peak voltage 𝑉𝑚𝑝 [𝑉] 26.312 26.593 26.231
Peak current (𝐼𝑚𝑝) [𝐴] 7.61 7.4802 7.6268
𝑆ℎ𝑜𝑟𝑡_𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑐𝑢𝑟𝑟𝑒𝑛𝑡𝐼𝑆𝐶 [𝐴] 8.21 8.1956 8.2070
Open circuit
voltage 𝑉𝑂𝐶[𝑉] 32.9 32.844 32.890
square error 0.2724 0.0087
Based on the proposed model and its five
parameters identified by the optimization algorithms
characteristics IV, curves are plotted and compared
with the curves given in the data sheets of the
manufacturer of photovoltaic modules. Fig. 4, Fig. 5
and Fig.6 illustrate the IV characteristics given by the
manufacturer and the model proposed for both
photovoltaic panels considered. From these figures, it
is easy to notice that the characteristics obtained from
optimized model are nearly identical to those given by
the manufacturer.
Fig. 4: characteristics I-V of the MSX 60 module by the
manufacturer.
Fig. 5: characteristics I-V of the MSX 64 module by GA
Fig. 6: characteristics I-V of the MSX 60 module by PSO
Through modeling it is possible to predict the
behavior of the module, and consequently the
photovoltaic panels, taking into account the changes
in environmental parameters such as temperature and
sunshine. To illustrate this advantage, we have drawn,
for the MSX-60 module, PV characteristics (Fig. 7)
for different temperatures and IV characteristics for
different radiation (Fig.8).
Fig. 7: characteristics P-V of the MSX 60 module by GA and PSO
respectively for different temperatures
Fig. 8: characteristics I-V of the MSX 60 module by GA and PS
respectively for different irradiations
To compare the two techniques used to optimize we
can only focus on the characteristics of P (V) and I
(V). Thus, we adopted four criteria, namely the
accuracy of the solution, consistency, speed
convergence of the algorithm, and the number
parameters of control.
Accuracy of the solution
Fig.9, Fig.10 and Fig.11 illustrate the relative
errors between the estimated values and those given
by the manufacturer for PV modules MSX60, MSX64
and KG200GT respectively from the figures. The two
methods have fairly low relative errors. However the
PSO algorithm is more accurate than the GA
algorithm.
Consistency of solution
Fig.12EvenFig.16present the estimated values of
𝐼𝑝ℎ 𝐼𝑜 𝑅𝑠 𝑅𝑠ℎ 𝑛 versus 100 executions for
MSX60 module. Then (then) the Fig.17 shows the
value of the cost function based on 100 runs of the
algorithm. When we observe the figure, we find that
the solution obtained by the GA algorithm (and) is
(very random) unsystematic while the PSO algorithm
provides the best stability. To appreciate better the
difference between the three algorithms, the relative
standard deviation of the various methods is
calculated as illustrated by the table VIII. The results
of this Table confirm the superiority of the PSO
algorithm in terms of the consistency of the solution.
0 5 10 15 20 250
1
2
3
4
5
6
modèle : MSX64 Irradiation = 1000 W/m2
Tension [V]
Cou
rant
[A]
T = 0°C
T = 25°C
T = 50°C
T = 75°C
0 5 10 15 20 250
1
2
3
4
5
6
modèle : MSX64 Irradiation = 1000 W/m2
Tension [V]
Cou
rant
[A]
T = 0°C
T = 25°C
T = 50°C
T = 75°C
0 5 10 15 20 250
10
20
30
40
50
60
70
80
90
modèle : MSX60 Irradiation = 1000 W/m2
Tension [V]
Pu
issa
nce
[W
]
T = 0°C
T = 25°C
T = 50°C
T = 75°C
0 5 10 15 20 250
10
20
30
40
50
60
70
80
90
modèle : MSX60 Irradiation = 1000 W/m2
Tension [V]
Pu
issa
nce
[W
]
T = 0°C
T = 25°C
T = 50°C
T = 75°C
0 5 10 15 20 250
1
2
3
4
5
6
modèle : MSX60 Température de cellule = 25°C
Tension [V]
Co
ura
nt [A
] G = 1000W/m2
G = 800W/m2
G = 600W/m2
G = 400W/m2
G = 200W/m2
0 5 10 15 20 250
1
2
3
4
5
6
modèle : MSX60 Température de cellule = 25°C
Tension [V]
Co
ura
nt [A
] G = 1000W/m2
G = 800W/m2
G = 600W/m2
G = 400W/m2
G = 200W/m2
International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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Fig.9: Relative error of the
Isc, Voc, Pmax, Vmp, Imprespectively of MSX-60.
Fig. 10: Relative error of the
Isc, Voc, Pmax, Vmp, Imp respectively of MSX-60
Fig. 11: Relative error of the
Isc, Voc, Pmax, Vmp, Imp respectively of MSX-60
Fig. 12: performance Convergence of Iph with PSO and GA
Fig.13: performance Convergence of Io with PSO and GA
Fig. 14: performance Convergence of Rs with PSO and GA
Fig. 15: performance Convergence of RP with PSO and GA
Fig. 16: performance Convergence of n with PSO and GA
Fig. 17: performance Convergence of the fitness with PSO and GA
Table VIII Comparison of five parameters given by the
Method
Parameters
GA PSO
Iph 0,28202% 0,00967%
Io 5,42e--14% 2,29e--14%
Rs 5,0271% 0,6009%
RP 40,8950% 18,1420%
N 0,5502% 0,1337%
Fitness (cost) 0.1624% 0,0043%
Speed of convergence
Figure 18 shows the convergence of the three
algorithms. According to the figure, it is clear that the
PSO slowly converges virtually to the GA algorithm
giving better solution.
International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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Fig. 18: Speed of convergence
Number of control parameters
Four evolutionary methods have less Observation.
Controller’s parameters ease the tuning effort and
facilitate the formulation of the optimization problem.
- In GA: crossover rate, mutation factor, number of
Childs in elite strategy and migration factor
- In PSO: W is the inertia weight C1 and C2 are the
acceleration coefficients,
VI. CONCLUSION
In this paper, the extractions of parameters of three
PV modules are performed. We even compare the two
techniques, used in estimating parameterized PV
panels comparative, discover from the exact view
point uniformity of solution convergence of the
algorithm. The number of control parameters show
that the method PSO is relatively more efficient. The
relevant simulation results have been given by
Programming using MATLAB.
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International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015
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