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Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Renewable and Sustainable Energy Reviews
journal homepage: www.elsevier.com/locate/rser
Metaheuristic algorithms for PV parameter identification: A comprehensive
review with an application to threshold setting for fault detection in PV
systems
Dhanup S. Pillai, N. Rajasekar
⁎
Solar Energy Research Cell (SERC), School of Electrical Engineering (SELECT), VIT University, Vellore, India
A R T I C L E I N F O
A B S T R A C T
Keywords:
Parameter extraction
Fault detection
PV
Metaheuristic algorithms
Optimization techniques
Precise model parameters being the prerequisite for realizing accurate PV models, parameter identification
techniques have gained immense interest over the years among the researchers specializing in PV systems. The
application of various promising metaheuristic algorithms to optimize the model parameters have lightened up
the scope of further enhancements in this field. Ever since, numerous metaheuristic algorithms have deployed for
this purpose. With handful of techniques available in this regard, this paper takes up an initiative to review the
existing metaheuristic algorithms based parameter extraction techniques with an emphasis on their compatibility, accuracy, convergence speed, range of parameters set and their validating environment. Based on the
analysis conducted, accurate models available for 17 different industrial solar cells/modules are identified.
Inspired by this review, an unidentified gateway between parameter extraction and fault detection in PV systems
have been identified; and has further extended this review to differentiate some models that can help the researchers to achieve accurate, efficient and rapid fault detection. This review is a valuable gathering of statistics
from the various researches carried out in PV parameter extraction which can assist enhanced researches for
fault detection in PV systems as well.
1. Introduction
Over the decades, efforts have been made to efficiently harness the
abundant renewable energy resources like Sun, Wind, Tides, and
Geothermal Heat to meet the extended energy needs of the mankind.
The contained humungous energy capability and copious availability
irrespective of global locations makes solar energy the foremost among
all resources. However, this unmatched energy resource in real time,
encounters difficulties in the form of PV non-linearity, low PV panel
efficiency and unavailability of standard models for PV performance
assessment. Moreover, constraints in real time data acquisition add to
its complexity. Besides, recent power quality issues due to the penetration of large roof top PV power plants in low voltage distribution
systems necessitates critical simulation tool. Further, the prediction of
PV panel performance is vital in design, optimization, and simulation
analysis of PV systems. Therefore, the need for simulation modeling of
real PV power plants remains indispensable in both academic and industrial point of view. Unfortunately, till date, no exact model for PV
characteristic prediction has been made available. Moreover, the existing single and double diode model prediction is vulnerable to the
model parameter variations; especially under the context of low irradiance. Further, poor model prediction sometimes lead to erroneous
Abbreviations: ABCO, Artificial Bee Colony Optimization; AE, Absolute Error; AGA, Adaptive Genetic Algorithm; APSO, Particle Swarm Optimization with Adaptive Inertia Weight
Control; BBO-M, Bio-Geography Based Optimization with Mutation Strategies; BMO, Bird Mating Optimization; CPSO, Chaos Particle Swarm Optimization; DD, Double Diode; DEIM,
Differential Evolution with Integral Mutation; GGHS, Grouping Based Global Harmony Search; HS, Harmony Search; IADE, Improved Adaptive Differential Evolution; IBCPSO, PSO with
Inverse Barrier Constraints; IP, Interior Point; JADE, Adaptive Differential Evolution; LS, Least Square; MPP, Maximum Power Point; N.A, Not Applicable; NMS, Nelder-Mead Algorithm;
NR, Newton-Raphson; P-DE, Penalty Based Differential Evolution; PSA, Parallel Swarm algorithm; PV, Photovoltaic; RMSE, Root Mean Squared Error; SBMO, Simplified Bird Mating
Optimization; SIV, Suitability Index Variable; STLBO, Simplified Teaching Learning Based Optimization; TVIWAC-PSO, Particle Swarm Optimization with Time Varying Inertia Weight
and Acceleration Coefficients; ABSO, Artificial Bee Swarm Optimization; AIS, Artificial Immune System; ANN, Artificial Neural Network; BBO, Bio-Geography Based Optimization; BFA,
Bacterial Foraging Algorithm; BPFPA, Bee Pollinated Flower Pollination Algorithm; CPU, Central Processing Unit; DE, Differential Evolution; GA, Genetic Algorithm; GPU, Graphical
Processing unit; HSI, Habitat Suitability Index; IAE, Individual Absolute Error; IGHS, Innovative Global Harmony Search; IPSO, Improved Particle Swarm Optimization; LM, LevenbergMarquardt; MPCOA, Mutative-Scale Parallel Chaos Optimization; MSE, Mean Squared Error; N.E, Not Extracting; NOCT, Nominal Operating Cell Temperature; N.S, Not Specified; PS,
Pattern Search; PSO, Particle Swarm Optimization; R-JADE, Repaired Adaptive Differential Evolution; SA, Simulated Annealing; SD, Single Diode; STC, Standard Test Conditions; TLBO,
Teaching Learning Based Optimization; VC-PSO, Particle Swarm Optimization with Velocity Clamping
⁎
Correspondence to: School of Electrical Engineering, VIT University, Vellore, Tamil Nadu 632014, India.
E-mail addresses: [email protected] (D.S. Pillai), [email protected] (N. Rajasekar).
http://dx.doi.org/10.1016/j.rser.2017.10.107
Received 23 January 2017; Received in revised form 19 August 2017; Accepted 28 October 2017
1364-0321/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Pillai, D.S., Renewable and Sustainable Energy Reviews (2017), http://dx.doi.org/10.1016/j.rser.2017.10.107
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Nomenclature
V
VMP
VPV
W
W .L
Wmin
XB
XW
BP
C1
CG
D
F
fmin
Gb
Id
IMP
IPV
ISC
K
Ki
KV
mcf
Me
NP
PAR
Pb
PMi
q
ri
rm
RP
RPO
Tbest
TF
Tnew
Vd
VOC
VT
We
Wmax
Ws
Xe
Z
Greek symbols
α
λS
σ0
γ
ε2
L (λ )
β
σG
μS
ε
μm
Cross over rate
Immigration rate
Standard deviation of initial generation
Scaling factor for FPA
Switching operator in DEIM
Levy factor
Mutation rate
Standard deviation of current generation
Emigration rate
Switching factor
Mutation probability
English symbols
a
Diode ideality factor
Bandwidth of generation
BW
C2
Social coefficient
Cr
Cross over rate
E
Energy state
fmax
Maximum fitness value
G
Irradiance (W/m2)
HM
Harmony memory
Reverse saturation current (A)
I0
Photon current (A)
IPh
IPVn
Photon current (A)
Random index
j
Iteration index
k
k max
Maximum number of iterations
M
Number of mutant vectors
Md
Classic Mutation
mu
Mutation variable
NS
Number of cells in series
parent 1, 2 Current solutions in GA
Pm
Mutation rate
PMP
Power at maximum power point (W)
r
Random number between 0 and 1
Rank of the Vector
Ri
RS
Series resistance (Ω)
RSO
Reciprocal of the slope at open circuit point (Ω)
T
Temperature (K)
Temperature control parameter
TC
Told
Old teacher
Velocity of particle
Voltage at maximum power point (V)
Output PV voltage (V)
Inertia weight
Worst learner
Final inertia weight
Best vector
Worst vector
Base point
Cognitive coefficient
Current generation
Search space
Scaling factor
Minimum fitness value
Global best solution
Diode current (A)
Current at maximum power point (A)
Output PV current (A)
Short circuit current (A)
Boltzmann constant (J/K)
Temperature coefficient of short circuit current (A/K)
Temperature coefficient at open circuit voltage (V/K)
Mutation control factor
Electromagnetism based mutation
Population size
Pitch adjusting rate
Current best solution
Probability of selection
Charge of one electron (C)
Random number between 0 and 1
Random number between 0 and 1
Shunt resistance (Ω)
Reciprocal of the slope at short circuit point (Ω)
Best teacher
Teaching factor
New teacher
Diode voltage (V)
Open circuit voltage (V)
Thermal voltage (V)
End weight in TVIWAC-PSO
Initial inertia weight
Start weight in TVIWAC-PSO
Elite vector
Chaotic variable
parameters since the data varies and are not available in the datasheet
provided by the manufacturers either. Making the scenario even worse,
these parameters are to be processed from the minimal data provided in
the datasheet. Therefore, to build an accurate and reliable PV model,
precise model parameters are mandatory. The scope for an authentic
parameter extraction technique further widens and transforms into an
optimization problem since most of the parameter extraction techniques are carried out using optimization techniques. Many optimization
techniques have been deployed to handle the multimodal parameter
optimization problem. Inspired by the significance of PV cell modeling
techniques, even reviews were made available based on the analysis of
different optimization techniques [11–14]. In [11], a survey has been
conducted on the various analytical methods and different soft computing techniques available for PV parameter extraction. A review on
various analytical methods in terms of number of parameters extracted
and the effect of each parameter on model characteristics is discussed in
[12]. Comparative analysis of specific six different bio inspired
triggering of protection circuits under normal operating conditions as
well. Hence, the subject of PV parameter estimation assumes surmount
importance even in the context of PV fault detection due to the fact that
most of the fault prediction is based on the estimated I-V curves.
Overall, the requirement of accurate PV model is always on high demand.
Researches on PV panel model prediction remains as an agile field
due to: 1) Non-linear PV characteristics and 2) its colossal dependency
on insolation level and panel temperature. Among many models that
exist, the noteworthy PV models to be mentioned are 1) Single Diode
(SD) model and 2) Double Diode (DD) model [1–3]. Apart from these,
the other models detailed in literature are three diode model [4], single
diode model with parasitic capacitor [5], improved two diode model
[6,7], reverse two diode model, generalized three diode model [8],
diffusion based model [9] and multi diode model [10]. However, model
accuracy varies based on the estimated model parameters. Unfortunately, it is hardly possible to set global values for these
2
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
2.2. Double diode PV model
metaheuristic techniques and its scopes for improvement are elaborated
in [13]. While in [14], the author has outlined a detailed review on the
accuracy of the metaheuristic algorithms and its hybrid variants used
for parameter identification. However, none of these researches have
produced an assessment of metaheuristic algorithms based on their
error evaluation and its application towards PV fault diagnostics.
Moreover, a critical performance evaluation over a wide range of metaheuristic algorithms used for parameter extraction problem has not
been studied either. On the other hand, for rapid detection and mitigation of faults, various fault detection techniques often compare the
real time entities with the threshold ones. Undoubtedly, accuracy of the
threshold limits set by the PV model decides the reliability of a fault
detection technique. Hence, there exists a colossal dependency of PV
parameter extraction for PV fault diagnosis. With handful of literature
available, the paper aims to provide an authentic document that reviews the various parameter extraction techniques. Further, this review
is extended to differentiate some PV models that can guide researchers/
PV manufacturers to achieve accurate, efficient and rapid fault detection. All available previous literatures lack this effort. The subsections
provide details regarding: 1) PV modeling, 2) different PV parameter
extraction techniques and its applicability towards parameter identification, 3) fault detection in PV systems and its application towards
parameter identification.
The sole difference between DD model and SD model is the presence
of an additional diode, ‘D2’ as depicted in Fig. 3. The presence of second
diode imparts a better accuracy to the model especially at low irradiance levels when compared to the SD model. The diode D2 is in cooperated in the model to represent the recombination losses occurring
in the depletion layer during low irradiance levels.
Here the output current, Ipv is given by [1–3] as;
Ipv = Ipvn − Id1 − Id2 −
Vpv + Ipv Rs
Rp
(5)
The diode currents Id1 and Id2 are given as
Id1 = IO1 ⎡exp ⎛
⎢
⎝
⎣
q (Vpv + Ipv RS ) ⎞
Id2 = IO2 ⎡exp ⎛
⎢
⎝
⎣
q (Vpv + Ipv RS ) ⎞
⎜
⎜
a1 NS Vt
a2 NS Vt
⎟
⎠
⎟
⎠
− 1⎤
⎥
⎦
(6)
− 1⎤
⎥
⎦
(7)
Hence, for a PV cell (NS = 1), the output current equation can be derived as:
q (Vpv + Ipv RS ) ⎞
⎧
Ipv = Ipvn − IO1 ⎡exp ⎛
− 1⎤
⎢
⎥
⎨
a1 Vt
⎝
⎠
⎣
⎦
⎩
⎜
2. PV modeling
− IO2 ⎡exp ⎛
⎢
⎝
⎣
⎜
The two basic PV modeling techniques convenient to represent a PV
module are SD modeling and DD modeling. Sometimes, the ideal PV
models presented in [15,16] are also used for the theoretical understanding of PV concepts. Most methods in literature prefer the SD model
due to its simplicity and lesser number of parameters. However, the
lack of accuracy of SD model makes the DD model preferable for certain
applications where precise I-V and P-V characteristics are required. At
the same time, the DD model has the disadvantage of high computational burden due to more number of model parameters. The steps involved in realizing a PV model for a PV cell is depicted in Fig. 1.
− Id −
(1)
From literature [1–3], the diode current can be expressed as,
Id = { I0 [exp (Vd/ aVT )] − 1}
(2)
Now VT is given by the equation
Vt =
NS KT
q
⎜
(3)
Embedding (1)–(3), the current equation for a single PV cell (NS =
1) can be obtained as
Ipv = Ipvn − Io ⎧exp ⎛
⎨
⎝
⎩
⎜
q (Vpv + Ipv Rs ) ⎞
aKT
Vpv + Rs Ipv
− 1⎫ −
⎬
Rp
⎠
⎭
⎟
(8)
PV model plays an inevitable role in simulation analysis, design
optimization and fault diagnosis of any PV system. Further, the ability
of the PV model to replicate accurate I-V characteristics under all insolation and temperature profiles is of extreme significance. However,
the accurate I-V curve emulation entirely depends on the precision of
the unknown model parameters deermined. Moreover, these values are
neither readily available in manufacturer datasheet nor it can be found
using simple calculations. In addition, the presence of noise in the extracted synthetic data adds to the difficulty. With manufacturers only
providing experimental I-V curve for Standard Test Conditions
(1000 W/m2 and 25 °C), the process of identifying model parameters
utilizing a suitable strategy becomes extremely indispensable. This high
potential research area is commonly referred as “PV parameter identification problem”. Here, the term parameter identification refers to the
process of finding out the unknown model parameters indicated in Eqs.
(4) and (8). The complete cycle of parameter extraction process and the
commonly identified parameters along with the manufacturer data is
illustrated in Fig. 4 and Table 1 respectively.
As mentioned earlier, estimating PV model parameters is a strenuous and difficult assignment due to: 1) Minimal amount of data
available, 2) Ample number of unknowns and 3) Complex mathematical
VPV + Ipv Rs
Rp
Vpv + Ipv RS ⎞
⎫
− 1⎤ − ⎛
⎥⎬
RP
⎠
⎠
⎦⎭ ⎝
⎟
a2 Vt
3. PV parameter extraction
The SD model of a solar PV cell is shown in Fig. 2. It comprises of an
illuminated current source, ‘IPVn ’ or ‘IPh ’, diode, ‘D’ that represents the
optical and recombination losses at the surface of the semiconductor,
series resistance, ‘RS ’ and shunt resistance, ‘RP ’ that account for the
leakage losses.
From figure, by node analysis,
n
q (Vpv + Ipv RS ) ⎞
From (8) it is clear that the DD model has seven unknown parameters namely IPVn , I01, I02 , RS , RP , a1 and a2 . As explained above each
parameter is highly dependent to Irradiation levels and temperature
[17].
2.1. Single diode PV model
Ipv = IPV
⎟
⎟
(4)
From (4), SD model has five unknown parameters; IPVn , I0 , RS , RP
and a .
Fig. 1. PV modeling.
3
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
+
I pv
Rs
Ipvn
(Iph)
Rp
Vpv
D
Id
Mathematical
Equations
Analytical Method
Objective
Function
[ Error ]
PV Model
-
Extracted
Parameters to
Model
Metaheuristic
Optimization
Fig. 2. Single diode model.
I pv
Rs
+
Fig. 5. Steps for parameter identification.
I d2
I d1
Rp
D1
I pvn
(I ph )
Objective
Function
[ MPP ]
superior to analytical methods. At the same time, it should be emphasized that analytical methods are handy if there are only a few unknown
parameters. Sometimes, to reduce the computational burden, merging
an analytical method with a metaheuristic algorithm proved to be advantageous. Similarly, combining two optimization algorithms have
also led to improvement in accuracy. Thus the solutions to the broad PV
parameter extraction problem can be categorized into three: 1) Analytical methods, 2) Metaheuristic optimization and 3) Hybrid methods.
The steps involved in solving parameter identification problem can be
illustrated using Fig. 5. To handle the voluminous data's of the methods
involved, this paper focuses on briefing the different metaheuristic algorithms and its hybrid versions; while only a short description about
the analytical methods is added for the basic understanding.
V pv
D2
Fig. 3. Double diode model.
Data from
Manufacturer
Sheet
Parameter
Identification
Method
3.1. Analytical approach for PV parameter extraction
Model
Parameters
Analytical methods rely on deriving necessary mathematical equations in order to realize PV characteristics. In a mathematical sense, for
solving an equation with ‘n’ number of unknowns, at least ‘n’ equations
are necessary. For instance, identifying SD model and DD model parameters require at least five and seven equations accordingly. The idea
behind formulating these equations can be explained with the help of a
single diode ‘RS ’ model. Further, the same can be extended to conventional SD and DD models as well. A single diode ‘RS ’ model is a
simplified form of conventional SD model where the parameter ‘RP ’ in
the SD model tends to infinity. Hence, the current through the parallel
RP branch in the current Eqs. (1) and (4) are eliminated for this model.
The modified output current equation now reduces to;
Initialization
Fig. 4. Cycle of parameter extraction.
Table 1
Model parameters and its availability.
Parameters
Manufacturer Data Sheet
PV Model Parameters
VOC
IPVn (Iph)
ISC
I01
IMP
I02
VMP
a1
PMP
a2
Ki
RS
Kv
RP
Ipv = Ipvn − Io ⎧exp ⎜⎛
⎨
⎝
⎩
computations. Hence, over the decades, to resolve the problem of
parameter identification, researchers have made use of several approaches. Initially, analytical methods were used to extract model
parameters by utilizing a series of interdependent mathematical equations to co-relate between different model parameters [18–40]. Most of
them use: 1) short-circuit current, 2) open-circuit voltage and 3) maximum power point voltage and current along with the manufacturer
data to derive suitable equations. However, solving these equations
mathematically consumes monumental time and effort. On the other
hand, introduction of metaheuristic algorithms brought a radical
change in the way researchers approached the PV model parameter
estimation problem. These metaheuristic algorithms transformed the
difficult model parameter identification problem to a simple non-linear
constrained optimization problem. The colossal benefits of using metaheuristic algorithms are: 1) Superior accuracy, 2) Flexibility to adopt.
The additional advantage of these methods in case of parameter identification is its capability to match the actual curve with minimal error
via curve fitting technique. This approach made the method extremely
q (Vpv + Ipv Rs ) ⎞
⎟
aKT
⎠
− 1⎫
⎬
⎭
(9)
There are four unknown parameters in a single diode ‘RS ’ model is;
‘IPVn ’, ‘I0 ’, ‘RS ’ and ‘a ’. To solve for these unknown parameters at least
four equations are necessary.
From the maximum power point in the I-V curve,
Ipv = IMP, Vpv = VMP,
IMP = Ipvn − Io ⎧exp ⎛
⎨
⎝
⎩
q (VMP + IMP Rs ) ⎞
− 1⎫
⎬
aKT
⎠
⎭
(10)
With the help of the short-circuit point; Ipv = ISC , Vpv = 0
qR I
ISC = Ipvn − Io ⎧exp ⎛ S SC ⎞ − 1⎫
⎬
⎨
aKT ⎠
⎝
⎭
⎩
(11)
From the open circuit point in the I-V curve; Ipv = 0, Vpv = VOC ;
0 = Ipvn − Io ⎧exp ⎜⎛
⎨
⎝
⎩
q (VOC + Ipv Rs ) ⎞
aKT
⎟
⎠
− 1⎫
⎬
⎭
Combining (10) and (11), (13) and (14) can be derived as
4
(12)
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
ISC
IO =
exp
3.2. Metaheuristic algorithms for PV parameter Identification
( ) − exp (
qVOC
aKT
qRS ISC
aKT
(
( )
)
(13)
qRS ISC
aKT
)
(
⎡
− 1⎤ ⎤
ISC ⎡exp
⎣
⎦ ⎥
IPVn = ISC ⎢1 +
qV
qR
OC
S ISC ⎥
⎢
exp aKT − exp aKT
⎢
⎥
⎣
⎦
)
Metaheuristic algorithms, in last few decades, have gained immense
momentum for solving complex multi objective optimization problems
in various engineering disciplines [41–44]. The enormous capability in
finding potential solutions provoked its importance towards PV parameter identification problem. The evolution of metaheuristic algorithms started with Genetic Algorithm (GA) followed by Differential
Evolution (DE) and Particle Swarm Optimization (PSO). Inspired by
these basic algorithms, several new and hybrid metaheuristic algorithms were developed in recent years [45–81]. Some prominent objective functions utilized by various metaheuristic algorithms for PV
parameter optimization are: 1) Root Mean Squared Error (RMSE)
[48,51–57,60,62–71,73,74], 2) Mean Squared Error (MSE) [45,59,72],
3) Absolute Error (A.E) [46,58,75,76] and 4) Derivative at maximum
power point (MPP) [60,67]. In this section, basic theory of every metaheuristic algorithm and its improved variants are outlined for fundamental understanding. Further, the performance of each algorithm is
reviewed based on: 1) Type of approach, 2) Compatibility towards
parameter identification, 3) Accuracy, 4) Convergence speed and 5)
Range of parameters set. In literature, as shown in Table 2, it can be
observed that each algorithm has used numerous solar cells/modules to
validate their results. However, for brevity, the ranges set and the
identified parameters are shown only for either one of the cells/modules used by each algorithm and the inferences discussed are identical
for other cells/modules as well. Moreover, a detailed analysis based on
all the cells/modules used for parameter identification is presented in
Section 4. The validating conditions of each method have also been
taken into account for a better evaluation on the performance various
algorithms.
(14)
At MPP, the derivative of the output power with respect to the
voltage must be zero. Hence, at the maximum power point;
d (VMP IMP )
dP
dI
=
= VMP
+ IMP = 0
dV
dV
dV
i. e.
(15)
dI
−IMP
=
dV
VMP
(16)
Combining (16) and the derivative of (9) with respect to Vpv,
−IMP
=
VMP
qIO
aKT
qIO
aKT
exp ⎡
⎣
exp ⎡
⎣
q (VMP + RS IMP )
⎤
aKT
⎦
q (VMP + RS IMP )
⎤
aKT
⎦
−1
(17)
Thus, by analytical approach, the parameter extraction of a single
diode ‘RS ’ model can be executed by solving the four Eqs. (12)–(14) and
(17) [30–32]. It is noteworthy to mention that, instead of Eq. (17),
either one of the two slope equations derived at the open circuit point
or the short circuit point in the I-V curve can also be used to extract the
model parameters [33]. The same procedure can be adopted for SD and
DD models except that it requires some additional equations to extract
the parameters. For instance, for the conventional SD model, both the
slope equations (RSO , RPO ) are used along with the equations at the
open circuit, short circuit and maximum power points [19–21,34–40].
While, to extract the model parameters for a DD model, an additional
equation is derived using the assumption that the sum of the ideality
factors of the two diodes D1 and D2 is 3 [23–27]. For a detailed study on
analytical methods readers can refer to [14]. To conclude, the following
disadvantages limit the adaptability of analytical methods towards
parameter identification problem.
3.2.1. Genetic algorithm (GA)
GA is a bio-inspired population-based algorithm which replicates
the phenomenon of ‘survival of the fittest’ [82]. The formulation of
objective function involves expressing the decision variables that are
encoded as chromosomes. An iteration based control strategy is followed to improve the quality of each chromosome (solution). Based on
the fitness value of an off spring, the quality of the solutions is evaluated and off springs for further iterations is chosen. Several works on
GA for the non-linear optimization of PV parameter estimation problem
is presented in [83,84]. GA follows three main steps; selection, crossover and mutation
➣
➣
➣
➣
Involved complex mathematical expressions and computations.
Monumental time consumption in solving the equations.
Convergence is not always guaranteed.
Assumptions made for simplification significantly affect the accuracy of the parameters extracted.
➣ Difficult to apply for improved PV models as the mathematical
formulations will be highly complex.
1. Selection: Initially, solutions are randomly generated and the fitness
of each solution is evaluated. After selection, only fitter chromosomes are selected for the next generation.
Table 2
Cells/modules used for parameter identification.
Refs.
Tested cells/Modules
[46]
[47]
[48,51,60,63,65,66,68,73–75,77]
[49]
[51,59,64,72,75]
[52]
[53]
[55]
[56]
[61]
[67]
[70]
[71]
[73]
[79]
[80]
Sanyo HIT215, KC200 GT and ST40 PV Modules
KC 200GT, ST40 and E20/333 PV Modules
57 mm dia RTC France Solar Cell
SM 55 PV Module, Thin film ST40 PV Module, S75 Solar Module
57 mm dia RTC France Solar Cell, Photo watt PWP201 PV Module
SL80CE Solar Cell, Photo watt PWP201 PV Module
S75, SM55, S115, SQ150 PC, ST36 and ST40 PV Modules
57 mm dia RTC France Solar Cell, KC200GT and PWP201 PV Modules
5 W CuInSe2 Solar Cell, 50 W mono-Si and 50 W multi-Si PV Modules
Kyocera KD210GH-2PU, Shell SP-70, Shell SQ-85 and ST-40 Thin Film PV Modules
S36, SM55 and ST40 PV Modules
57 mm dia RTC France Solar Cell, Photo watt PWP201, S75, SM40, SM55, KC200 GT and ST40 PV Modules.
57 mm dia RTC France Solar Cell, KC200GT, SM55 and ST-40 Thin Film PV Modules
Kyocera KC120 PV Module
OST 80 Solar Cell, SM55 PV Module
S36 PV Module, SP 70 PV Module, SM55 PV Module, KC200 GT PV Module
5
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
the diversity factor of the algorithm. In AGA + LS method, the typical
LS operator initially performs a local search at the start point and is
used to adjust the population to enhance the performance of GA. A
detailed analysis on AGA + LS method proposed in [48] gives the
following inferences: 1) The initial setting of parameters are based on
the short circuit and open circuit points in the IV curve to eliminate the
trial run, 2) In validation, AGA + LS method outperformed the
conventional Newton method and conductance method, 3) No
validations were done in the context of varying irradiation and
temperature levels and 4) Even though the accuracy was slightly
improved, AGA + LS have slow convergence characteristics. A
critical comparison of all these methods is presented in Table 3 while
the results obtained via optimization are consolidated in Table 4.
2. Crossover: Generates the off springs for the upcoming generation as
α . parent 1 + (1 − α ) . parent 2 ⎫
offspring = ⎧
⎨
⎩ (1 − α ) . parent 1 + α . parent 2 ⎬
⎭
(18)
3. Mutation: Helps to achieve better off springs which the crossover
operation might have missed. A user defined mutation rate, β is used
for mutation operation.
offspring = ± β . offspring + offspring
(19)
For a better understanding, the flowchart of GA method is also
presented in Fig. 6.
3.2.2. Differential evolution (DE)
Rather than GA, DE treats solutions as real numbers called particles
and hence, no encoding is required [86]. The algorithm is formulated
by having four operations namely initialization, mutation, crossover
and selection.
3.2.1.1. Hybrid and adaptive versions of GA. To further enhance the
performance of conventional GA, several hybrid and adaptive variants
of GA were also proposed in literature [46–48]. To reduce the
computational burden of GA, Newton Raphson technique was used to
extract two model parameters in a hybrid strategy (GA + NR) proposed
in [46]. In another hybrid approach, GA was used along with an interior
point method to determine the MPP of a given I-V curve which has been
formulated as a sub problem of the parameter identification problem to
match the NOCT and STC MPP data of the manufacturer data sheet
[47]. Adaptive genetic algorithm (AGA) is an adaptive variant of GA
with an improved selection routine and an adaptive control of crossover
and mutation factors. In [48], AGA was merged with the Least Square
algorithm (AGA + LS) to build a hybrid strategy for parameter
identification as well.
1. Initialization: A target vector representing the solutions is randomly
set. i.e. for the ith particle,
Xi CG : i → {1, 2, 3........ NP }
(20)
2. Mutation: Two vectors are randomly selected and their weighted
difference is utilized to mutate the ith vector.
Mi, CG = Xi, CG + F . (Xr 2, CG − Xr 3, CG )
(21)
Where ‘Mi, CG’ is the resultant vector, ‘Xr2, CG’ and ‘Xr3, CG’ are two
vectors randomly selected from the current generation i.e. r1, r2 are
in the range {1,2,3……NP}.
3. Crossover: Generates trial vectors using the resultant mutated vectors for the next generation by a non-uniform operation.
3.2.1.2. Application towards PV parameter extraction. Compared to the
analytical methods, when GA is applied for parameter identification;
the mutation phase efficiently explores new dimensions in the search
space to search for potential solutions while the cross over operation
intends to improve the diversity among the population. In the proposed
work in [45], crossover operation has been applied to all chromosomes
and a mutation rate of 4% was utilized to extract the SD model
parameters of a 50 W solar panel. The comparison was made with Pasan
CT 801 software model and found that the parameter values estimated
by GA for the solar cell possess significant error particularly for the
values of ‘I0’ and ‘Rp’. However, validations on different irradiance and
temperature levels were not assessed. In GA + NR hybrid strategy
employed in [46], GA was used to extract three parameters, ‘RS’, ‘RP’
and ‘a’ whereas ‘Iph’ and ‘I0’ were extracted analytically using NR
method. NR is an effective iterative technique, when initialized to solve
for only less number of parameters. Hence, GA + NR hybrid parameter
identification reduces the computational burden of GA. In validation,
the hybrid version outperformed the ANN model and the conventional
analytical ‘RS’ model in terms of accuracy. The algorithm was validated
using both MATLAB tool box and MATLAB coding. The results of the
former were used for comparisons. Interestingly, the method is one of
the very few which have considered the shading effects on a PV panel
and has successfully validated KC200GT PV module under partial
shading conditions. In [47], a multi objective based optimization [85]
considering the standard and nominal operating cell temperature
(NOCT) conditions of a PV was carried out to extract the model
parameters of an SD model using GA + IP hybrid strategy. The IP
method in contrast with other optimization techniques can traverse a
set of internal points inside the boundaries to reach the global best
solution This undoubtedly has increased the accuracy particularly for
the nominal operating conditions of a PV. Furthermore, in validation,
the method has outperformed the conventional NR method and PSO
with barrier constraints in terms of accuracy. However, poor
convergence persists even though the modifications have improved
Mi . CG , if ri ≤ Cr or j = rni ⎫
UJ i, CG = ⎧
⎨
⎭
⎩ Xi, CG , if ri > Cr or j ≠ rni ⎬
(22)
4. Selection: Regardless of the fitness value, parent vectors emerges to
the next generation while the trial vectors are selected according to
their fitness values as,
Start
YES
Reinitialization
Condition
satisfied ??
Initialization
Generate the first population of
the chromosomes
Evaluate the populations
fitness
Next iteration
reinitialization
NO
NO
All
chromosomes
finished
Perform selection and
produce the parents
YES
Perform cross over and generate
off springs
Output the offspring
End
Mutate the chromosomes according
to mutation rate
Fig. 6. Flowchart for GA method.
6
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
vector. The binomial crossover operation in R-JADE can be
mathematically represented as
Table 3
GA and its variants used for parameter identification.
Method
utilization of search space due to mutation and crossover
• Better
operations.
in exploration but poor in exploitation.
• Good
computational burden.
• High
technique converges fast when number of unknowns is low.
• NR
computational burden.
• Low
depends on the parameters optimized by GA.
• Accuracy
objective based optimization.
• Multi
in real-time operating conditions.
• Accurate
convergence.
• Slow
stage selection routine using tournament and roulette• Two
wheel selection.
local search.
• Improved
tuning of control parameters.
• Adaptive
• Slow convergence.
GA
GA + NR
GA + IP
AGA + LS
Xi . CG + 1
Uji, CG = bij Mi, CG + (1 − bij ). Xi, CG
Specific comments
Ui . CG, if f (Ui .(CG + 1) ) ≥ f (Xi . CG ) ⎫
=⎧
⎨
⎭
⎩ x i . CG , if f (Ui .(CG + 1) ) < f (Xi . CG ) ⎬
(24)
In addition, a ranking based mutation was also proposed to ensure
that high quality vectors are selected for the mutation process.
R 2
PMi = ⎛ i ⎞
⎝M⎠
(25)
Similarly in [52], an improved adaptive DE (IADE) method was
proposed; which is an extended adaptation of conventional DE method
in which the choice of scaling factor (F) and crossover rate (Cr) is wisely
done by utilizing the memory of the particles. The control parameter ‘A’
used in this method links the current and previous fitness values of a
particle and ‘A’ is defined as
A=
fitness. best (i)
fitness. best (i − 1)
(26)
In penalty based differential evolution (P-DE) presented in [53],
boundary limits are checked when a mutant parameter is selected as the
trial vector. A new penalty function was introduced in the control
structure to make sure that all the trial vectors lie within the specified
range. Any control variable violating the solution space during particle
update will be replaced by the penalty based function to lie within the
constraints defined as follows;
(23)
For a better understanding, the flowchart for DE method is depicted
in Fig. 7. Related works on DE based optimization are presented in
[87,88].
Ui (CG) − r (x iH − x iL), Ui (CG) > XiH ⎫
Ui (CG) = ⎧
U
⎨
⎭
⎩ i (CG) + r (XiH − XiL ), Ui (CG) < XiL ⎬
3.2.2.1. Hybrid and adaptive versions of DE. In a vision to achieve an
enhanced trade-off between exploration and exploitation capability;
researchers have applied many adaptive variants of DE and its
improved versions for PV parameter identification. Among them,
adaptive differential evolution (JADE) is an improved variant which
employ adaptive mutation and crossover rates rather than using user
defined ones [50]. To further improve JADE method; repaired adaptive
differential evolution (R-JADE) was proposed in [51]. This method
introduced an automatic repairing technique for crossover rate which
improves the randomness in control variable. The repaired crossover
rate is obtained by using a binary string, ‘bij ’ generated for each target
(27)
where ‘Ui (CG) ’ is the recombined vector, ‘ XiH ’ and ‘ XiL ’ are the upper and
lower bounds of ‘ Xi ’ respectively and ‘r’ is a random number in the
range {0, 1}.
DEIM is a hybrid version of DE proposed in [54,55] which uses
hybrid mutation operation per iteration. The type of mutation to be
used depends on the current standard deviation (σ) of the vectors and
can be expressed as;
M , if σ G < ε2 σ 0||⎫
M=⎧ e
⎨
M
otherwise ⎬
⎭
⎩ d,
(28)
Table 4
Parameter identification using GA and its variants.
Method
GA [45]
AGA + NR
[46]
GA + IP [47]
GA + LS [48]
Approach
Metaheuristic
Hybrid
Hybrid
Hybrid
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
Cell/Module
0.01–1.2
0.331
N. S
99,050
N. S
0.136
N. S
1.0196
N. S
12,170
–
–
–
–
50 W panel (Make N.S)
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
KC200GT PV Module
0.01–1.2
0.331
50–1000
883.925
N. E
N-R Method
1–2
1.106
N. E
N-R Method
–
–
–
–
RS (Ω)
0.01–1.2
0.29
RP (Ω)
50–1000
480.496
Iph (A)
N. E
N-R Method
a1
1–2
1.112
I01 (µA)
N. S
0.00423
a2
1–2
1.377
I02 (µA)
N. S
0.0091
PV Model
SD
Range Set
Extracted
Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
0.001–1
0.214
50–1100
1060.66
N. E
A.M
1–2
1.348
N. E
A.M
–
–
–
–
PV Model
SD
Range Set
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
W.R.T Slope at
Voc
0.0364
W.R.T Slope at
Isc
52.7293
1–5% of Isc
0.5–2
0–10% of Isc
–
–
0.7607
1.4804
0.3198
–
–
PV Model
SD
Range Set
Extracted
Parameters
PV Model
SD
Range Set
Extracted
Parameters
DD
Range Set
Extracted
Parameters
Extracted
Parameters
N.S: Not Specified, N.E: Not Extracting, A.M: Analytical Method W.R.T: With Respect To.
7
KC200 GT PV Module
57 mm RTC France Solar
Cell
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Fig. 7. Flowchart for differential evolution.
Re -initialization
Start
NO
DE Initialization
Re -
Any improvement
in the fitness of trial
vectors compare to
target vectors??
initialization
Condition
satisfied ??
YES
Select the target vectors and perform
YES
DE operation
NO
Update target vectors
Mutation to obtain the
mutant vector
NO
Is objective
function
Crossover to obtain the
obtained ??
YES
trial vector
Display the best target vector
Calculate objective
funcion
stop
Next iteration
Multi crystalline S75 PV module was carried out in [53]. In agreement
to the control strategies adopted, the method has shown good accuracy
and a satisfactory convergence. The validations presented in this work
shows good agreement with the experimental values especially under
varying irradiation levels. Moreover, it outperforms GA, SA, DE and
PSO algorithms as well. In a more critical perspective, the extracted
values of ‘RS’ and ‘RP’ were found to be unsound at particularly low
irradiance profiles. Unlike all other DE variants, DEIM does not perform
of a local search. Instead, the two mutation steps incorporated per
iteration improves the search ability and reduces the number of
assessments required to reach the optimum solution. Furthermore,
DEIM uses a sigmoid logistic function which can significantly
improve the convergence speed. The application is discussed in
[54,55] where the hybrid DEIM technique was used to extract the
model parameters of SD and DD models. In the validations presented,
the method has outperformed all conventional DE methods in terms of
accuracy and convergence speed. The algorithm was also tested to
analyze its performance under different irradiance levels and the results
obtained were in good agreement with the experimental curves.
However, in SD model, the range of ‘RP’ is chosen so high compared
to the extracted parameter value. Furthermore, in the DD model, the
extracted parameters ‘a1’ and ‘a2’ shows the same value which may
induce false emulation under varying irradiation levels. Some key
points on the peculiarity of each DE variant is illustrated in Table 5 and
Table 6 represents the results obtained for each DE variant when
applied for parameter extraction.
3.2.2.2. Application towards PV parameter extraction. Unlike GA, DE
primarily utilizes the mutation operation rather than the cross-over
operation as an initial search. The mutation operation is based on the
weighted difference of two vectors which can substantially improve the
search space. Hence, the recombination phase will be more effective to
achieve feasible parameters. Authors in [49] employed the DE based
optimization technique to extract the SD model parameters of three
different solar cells/modules. In this work, three industrial PV modules
were considered for validation. The proposed method extracted
different parameter values for ‘a’, ‘Rs’ and ‘Rp’ at different
temperature and irradiance levels with a mutation and crossover rate
of 0.4. The ideality factor was found decreasing with increase in
temperature. Furthermore, the method outperformed ABC, ABSO, AIS
and ANN based SD models in validation. The application of R-JADE
algorithm towards PV parameter extraction (both SD and DD model) for
a 57 mm dia RTC France PV cell is presented in [51]. The proposed
ranking based mutation ensures that the best vectors are selected for
mutation operation while the cross-over repairing technique based on
the average number of components taken from the mutant gives an
improved exploitation. The method shows improved RMSE but suffers
from poor convergence speed. However, in validation, R-JADE has
outperformed ABC, ABSO, AIS and conventional DE algorithms. The
advantage of IADE when applied for parameter extraction is that the
memory based adaptive control makes sure that the search space is
better exploited while updating the particles. Hence, the resultant
vectors are expected to be potentially more feasible solutions. The
application of IADE for PV parameter extraction is presented in [52]
where the model parameters for an 80 W PV module were estimated.
The experimental validations were done for both the PV cell and the PV
module. As shown in Table 6, IADE extracted different parameters for
different irradiance levels. At several instances, parameter values
obtained for ‘RS’, ‘RP’ and ‘a’ were erroneous with respect to the
change in irradiation levels. However, in the validations presented,
IADE outperforms GA, PSO and SA. When P-DE is used to optimize
model parameters, the effect of penalty function is that it ensures that
all particles reach the global optimum by continuously shifting the
violated parameters towards the feasible region. However, the
increased search space in penalty based DE method can reduce the
convergence speed and hence a large mutation factor is usually used to
account for it. The application of P-DE for the parameter extraction of a
3.2.3. Particle Swarm Optimization Algorithm (PSO)
PSO is a bio inspired algorithm evolved from the bird flocking
phenomenon [89–91]. The method defines a solution space where the
target vectors are treated as particles. These particles move along the
solution space with a velocity, ‘V’ to reach the optimal position. PSO
method has three phases, initialization, exploration and evaluation.
■ Initialization: Defines the population size and starts from a random
particle.
■ Exploration: The current position of the particles, ‘Xi’ updates as they
move along the search space with velocity, ‘Vi’. During the evaluation process, the current best position of the particle, ‘Pbi’ and the
global best position ‘Gb’ are recorded. The position of each particle is
8
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Pbi = Xik ,
Gb = Pbi ,
Table 5
DE and its variants used for parameter identification.
Method
if f (x ik ) ≥ f (Pi )
if f (Pbi ) ≥ f (Gb)
(31)
Specific comments
operation is used for initial exploration.
• Mutation
recombination phase compared to GA.
• Effective
fitness evaluation for parent vectors.
• No
mutation and crossover operations.
• Adaptive
diversity among populations.
• Better
crossover rate repairing.
• Automatic
for vectors.
• Ranking
selection of mutant vector.
• Probabilistic
based cross over and mutation phases.
• Memory
diversity
• Improved
premature convergence.
• No
trial vectors.
• Penalizes
exploitation.
• Better
mutation operations.
• Hybrid
initial local search.
• No
• Good convergence speed.
DE
JADE
R-JADE
IADE
P-DE
DEIM
The continuous evaluation of the global best solution makes PSO
best suited for parameter extraction and maximum power point
tracking applications [92–98]. For a better understanding of the algorithm, a flowchart is presented in Fig. 8.
3.2.3.1. Hybrid and adaptive versions of PSO. Inspired by the flexibility
and adaptability of PSO towards any difficult optimization problem,
researchers have proposed many variants of PSO to solve PV model
parameter identification problem. In [56], an adaptive PSO (APSO)
based on linearly decreasing inertia weight function is proposed. The
linearly decreasing inertia weight function used in APSO method is
given by;
W (t ) = Wmax − (Wmax − Wmin ) k / k max
updated using the following strategy;
Xik + 1 = Xik + Vik + 1
(29)
Vik + 1 = W . Vik + [r1 C1 (Pbi − Xik )] + [r2 C2 (Gb − Xik )]
(30)
(32)
Alternatively in [57], the authors proposed an improved PSO (IPSO)
using dynamic inertia weight function to control the velocity of the
particle. The modified inertia weight function used in IPSO is;
(33)
W ′ = Wu−k
where Xik + 1 represents the updated position of the ith particle, Xik is
the current position of the ith particle, Vik + 1 is the updated velocity
and Vik is the current velocity.
■ Evaluation: The fitness value of the particles is evaluated in this
phase to update the recorded data for ‘Pbi ’ and ‘Gb ’.
where ‘W ′’ is the user defined inertia weight in the range {0, 1}, ‘u’ uses
a value between 1.001 and 1.005 and ‘K’ is the iteration number. PSO
with velocity clamping (VC-PSO) is a finely tuned version of APSO
which employs a velocity clamping function to update the particles
[58]. The velocity update in VC-PSO for the jth particle is defined as;
Table 6
Parameter identification using DE and its variants.
Method
DE [49]
R-JADE [51]
IADE [52]
P-DE [53]
DEIM [54,55]
Approach
Analytical
Metaheuristic
Metaheuristic
Metaheuristic
Hybrid
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
Cell/Module
0.1–1
Varies with
G&T
100–3000
Varies with
G&T
N. E
N. E
1–2
Varies with
G&T
N. E
N. E
–
–
–
–
Multi Crystalline S 75
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
57 mm dia RTC
France Solar Cell
0–0.5
0.03638
0–100
53.7185
0–1
0.76078
1–2
1.4812
0–1
0.32302
–
–
–
–
RS (Ω)
0–0.5
0.03674
RP (Ω)
0–100
54.4854
Iph (A)
0–1
0.76078
a1
1–2
1.451
I01 (µA)
0–1
0.22597
a2
1–2
2
I02 (µA)
0–1
0.7494
PV Model
SD
Range Set
Extracted
Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
0–2
Varies with
G&T
50–5000
Varies with
G&T
0–5
Varies with
G&T
0–10
Varies with
G&T
0–1
Varies with
G&T
–
–
–
–
PV Model
DD
Range Set
Extracted
Parameters
RS (Ω)
RP (Ω)
Iph (A)
a1
I01 (µA)
a2
I02 (µA)
0–1
Varies with
G
50–1000
Varies with G
0–7.6
Varies with
G
0.5–4
Varies with
G
0–1
Varies with G
0.5–4
Varies
with G
0–1
Varies
with G
PV Model
SD
Range Set
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
0.1–2
100–5000
1–8
1–2
–
–
Extracted
Parameters
DD
Range Set
Extracted
Parameters
0.5533
115.211
4.4412
1.376
1E− 12 to 1E
−5
1.01
–
–
RS (Ω)
N. S
0.59
RP (Ω)
N. S
541.368
Iph (A)
N. S
3.5556
a1
N. S
1.3971
I01 (µA)
N. S
4.33
a2
N. S
1.3971
I02 (µA)
N. S
4.67
PV Model
SD
Range Set
Extracted
Parameters
PV Model
SD
Range Set
Extracted
Parameters
DD
Range Set
Extracted
Parameters
G: Irradiance, T: Temperature, N.S: Not Specified, N.E: Not Extracting.
9
SL80 CE
Multi Crystalline S 75
KC120 PV Module
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Fig. 8. Flowchart for PSO algorithm.
Vj,
if Vj < Vmax ⎫
Vj + 1 = ⎧
Vmax . j,
otherwise ⎬
⎨
⎩
⎭
accuracy. The authors identified that the accuracy is highly dependent
on the initial setting of parameter values for ‘RS’ and ‘RP’ since it
directly affects ‘a2’ and ‘I02’. Hence, a global approach was used to set
the initial ranges for these parameters and is expressed Table 8.
However, the extracted parameter values show significant error with
respect to the theoretical concepts of a PV. The compatibility of IPSO
towards parameter extraction is that the dynamic inertia weight
function reduces the velocity accordingly to make use of the positions
that a conventional PSO might have missed to achieve a better curve fit.
In the validations presented in [57], IPSO outperformed the
conventional GA algorithm. However, a close examination on the
results presented in Table 8 indicates that the parameter ‘Iph’ was
extracted out of the range selected. Furthermore, the convergence
characteristics were not analyzed. At the same time, high values of
velocity can sometimes tempt the particles to move away from their
solution ranges in PSO and APSO. Hence, to compensate this draw back;
velocity clamping approach was proposed in [58] for achieving an
efficient trade-off between the local search and the global search ability
of the algorithm [101,102]. A review on the performance of VC-PSO
based parameter identification gives the following observations: 1) The
extracted value for a1 is > 1 and a2 is > 2; which are not in fit with
theoretical concepts, 2) In optimization, assuming value for one
parameter can affect the quality of other parameters as well, 3)
Wrongly extracted value for parameter ‘RP’ might be affecting a1 and
a2 since the value of ‘RP’ has a direct effect on the ideality factor [56]
and 4) A three-diode model was proposed for PV modeling and the
model parameters were extracted to show its superiority when
compared with the conventional SD and DD models. While, in CPSO,
when there is stagnation in solutions; a chaotic search is performed to
produce ‘D’ neighboring points around the stagnated particle to update
its position and thereby eliminating the local minima. After critically
reviewing the CPSO technique in [59], following observations have
been made: 1) The global search performance and the local
convergence of conventional PSO are improved by embedding a
chaotic search, 2) It does not require any trial runs to set the initial
ranges of the PV parameters and instead, a mathematical formulation
indicated in Table 8 has been used, 3) In validation, the method
outperformed [103–106]; viz. the conventional Newton method, fivepoint method and the conductance method. However, control
(34)
where ‘Vmax . j ’ is the maximum allowable velocity, ‘Vj ’ is the current
velocity of the jth particle and ‘Vj+1’ is the new velocity. By introducing
a chaotic based principle [99], a new chaos particle swarm optimization
(CPSO) was proposed in [59]. Apart from conventional and adaptive
versions; PSO with time varying inertia weight and acceleration coefficients (TVIWAC-PSO) proposed in [60]. TVIWAC-PSO adaptively
controls both inertia weight and acceleration coefficients in the conventional PSO. The control of these parameters can be expressed as;
For inertia weight control,
W = We +
k max − k
(We − Ws )
k max − 1
(35)
For acceleration coefficient control,
C1n = C1e +
k max − k
(C1e − C1s )
k max − 1
(36)
C2n = C2e +
k max − k
(C2e − C2s )
k max − 1
(37)
where ‘C1n’ and ‘C2n’ are the updated values of C1 and C2 respectively,
‘C1s’, ‘C2s’, ‘C1e’ and ‘C2e’ represents the start values and end values of C1
and C2 respectively. For optimal solution, ‘C1’ tends to vary from 2.5 to
0.5 and ‘C2’ varies from 0.5 to 2.5. In a hybrid PSO version proposed in
[61], PSO with inverse barrier constraints (IBCPSO) was merged with
an analytical method for optimization. Compared to other PSO
methods, IBCPSO used an Inverse Barrier Constraints (IBC) based objective function to optimize model parameters.
3.2.3.2. Application towards PV parameter extraction. Improper selection
of control parameters in conventional PSO can make the algorithm to
get trapped at a local optimum [100]. To attenuate the aforementioned
drawback, adaptive selection of inertia weight was found beneficial in
[56]. In this regard, a better global search during the initial runs and an
efficient local search during the final runs were achieved. Hence, when
used for parameter identification APSO safeguards the best solutions
until the end. The experimental results of the proposed work indicated
the superiority of the DD model with respect to the SD model in terms of
10
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
parameters play a crucial rule in any PSO variant and hence, finding
optimal control parameters using trial runs is computationally very
expensive [107–109]. Hence, in TVIWAC-PSO, all the three control
parameters are adaptively controlled throughout the iterations.
Furthermore, it facilitates better exploitation and faster convergence.
From the proposed research work in [60], it is evident that time varying
values of inertia weight and acceleration coefficients enhanced both the
convergence speed and the accuracy of the algorithm compared to all
other PSO versions. Furthermore, in validation, TVIWAC-PSO
outperformed ABSO, SA and PSO based methods. However, the
performance of the algorithm in varying irradiation and temperature
levels were not assessed. Rather than conducting field tests to
determine the ranges of the initial parameters; IBCPSO incorporates
these constraints in the objective function itself. This will heavily
penalize the objective function when solutions reach near to their
boundaries. Due to this heavily constrained objective function
evaluation, [61] adopted an analytical method along with IBCPSO to
extract two parameters of a SD model. The consolidated data is
illustrated in Table 8 and the following inferences on the method are
likely to be suggested: 1) A new objective function based on the barrier
constant, irradiance and temperature was proposed, 2) In validation,
IBCPSO outperformed all the conventional direct methods used for
parameter extraction, 3) The change in series resistance with respect to
diode ideality factor was monitored and 4) Time varying model
parameters were suggested to account for the time varying
temperature levels. A critical comparison of all the PSO variants are
presented in Table 7 and the parameters identification results are
illustrated in Table 8. Readers can also refer [110–112] where reviews
on metaheuristic algorithms are presented with an application to
maximum power point tracking.
3.2.5.2. Application towards PV parameter extraction. In ABCO, to
further improve a stagnated solution, scout bees are used perform
random searches. This exploration significantly improves the quality of
the solutions when used for parameter identification. In the validations
presented in [63], ABC outperformed HS, PSO, GA and BFA in terms of
accuracy as well as convergence speed. However, all comparisons were
made for same irradiance levels. Inspired by the effectiveness of ABCO,
the authors in this research suggested harmony search algorithms as an
effective alternative to solve parameter identification problem. On the
other hand, in ABC + NMS hybrid technique, a three-stage strategy is
used to reach the optimal solution: 1) ABC is used for initial
exploration, 2) NMS is used to perform exploitation and 3) Adaptive
NMS is used for a fine search to reach the global best. In [64], ABC +
NMS algorithm was used to extract both the SD and DD model
parameters. In validation, ABC + NMS strategy outperformed ABSO,
STLBO and R-JADE algorithms. Furthermore, the method was
successfully validated in varying environmental conditions for a PWP
201 PV module. However, the method suffers from slow convergence
and there are a number of control parameters to be manually tuned.
The consolidated data is illustrated in Table 10.
3.2.6. Artificial Bee Swarm Algorithm Optimization (ABSO)
ABSO is a similar algorithm to PSO but it follows the bee algorithm
approach [118]. Similar to ABCO, bees having low quality food sources
(solutions) are treated as scout bees which explore the search space.
However, a notable procedure followed in ABSO is that among the
onlooker bees; some bees are selected as elite bees [65]. Elite bees
encourage the onlooker bees to find the best solution obtained so far.
Using the tournament selection approach, each onlooker bee selects an
elite bee to update their position as follows;
j
Xnew
= X j + Wb rb (Xbj − X j ) + We re (Xej − X j )
3.2.4. Mutative Scale Parallel Chaos Optimization Algorithm (MPCOA)
Unlike swarm optimization, [113,114] proposed a population based
pure chaotic optimization technique (COA) with multiple chaotic
mapping on each decision variable. MPCOA is an improved version of
COA which utilizes the cross over and merging operations between two
randomly selected parallel variables along with a mutative scale search
space to achieve a wider search space for the particles [62].
(38)
‘Xe’ is the elite bee, ‘Xb’ is the best achievement by onlooker bee and
‘rb’ and ‘re’ are random numbers in the range {0, 1}. ‘Wb ’, ‘We ’ are control
parameters which are linearly decreasing functions defined as
3.2.4.1. Application towards PV parameter extraction. Since PV
parameters are to be very precise, MPCOA utilizes two additional
strategies: 1) The solutions obtained by chaotic search are further
updated using recombination and merging operations, 2) When parallel
solutions are gathered, a mutative scale search space is used to exploit
the exact solution. MPCOA based PV model realized in [62] was
validated in different irradiation levels for two different PV modules.
In the validations carried out, the method outperformed GA, CPSO,
ABSO, PS, SA and HS techniques; both in terms of accuracy and
convergence speed. The results obtained are consolidated in Table 9.
Regardless of its computational burden, it is worth to mention that
MPCOA has shown prodigious capability in handling the parameter
identification problem.
Wb = Wb , max − (Wb max − Wb min ) k / k max
(39)
We = We , max − (We max − We min ) k / k max
(40)
3.2.6.1. Application towards PV parameter extraction. In ABSO, to
balance between local and global search; the control parameters, ‘Wb ’
and ‘We ’ are adaptively tuned during the runs. Further, the elite strategy
adopted in ABSO improves the quality of potential solutions through
Table 7
PSO and its variants used for parameter identification.
Method
PSO
APSO
3.2.5. Artificial Bee Colony Optimization (ABCO)
ABCO algorithm has been evolved from the food search behavior of
honey bees [115]. In ABCO, three types of bees continuously search for
food and their food sources are treated as the solutions [116,117].
Among the bees, scout bees explore the search space while employed
bees and onlooker bees perform exploitation.
IPSO
VC-PSO
CPSO
TVIWAC-PSO
3.2.5.1. Hybrid variant of ABCO. In [64], Nelder-Mead algorithm
(NMS) was fused with ABCO to further enhance the performance of
the algorithm. In the proposed hybrid strategy (ABC + NMS), ABC was
used to perform the initial global search while the NMS algorithm
performs the local search during the final runs.
IBCPSO
11
Specific comments
exploration and exploitation.
• Good
memory requirement.
• Large
depends upon user defined values for control
• Performance
parameters.
control of inertia weight function
• Adaptive
best solutions until the end.
• Preserves
dynamic inertia weight function.
• Uses
exploitation of search space.
• Improved
control of velocity of particles.
• Optimal
decreasing inertia weight.
• Linearly
chaotic search.
• Embedded
exploitation.
• Excellent
complex.
• Computationally
control of all control variables.
• Adaptive
tradeoff between exploration and exploitation.
• Enhanced
convergence speed.
• Good
function based on barrier constraints.
• Objective
initial ranges to be set.
• No
• High computational burden.
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Table 8
Parameter identification using PSO and its variants.
Method
APSO [56]
IPSO [57]
VCPSO [58]
CPSO [59]
TVIWACPSO [60]
IBCPSO [61]
Approach
Metaheuristic
Metaheuristic
Metaheuristic
Metaheuristic
Metaheuristic
Hybrid
PV Model
DD
Range Set
Extracted
Parameters
RS (Ω)
RP (Ω)
Iph (A)
a1
I01 (µA)
a2
I02 (µA)
Cell/Module
± 70% of Slope at Isc
0.02386
± 70% of Slope at Voc
4.04
N. S
4.21
1–5
1.74
0–1
121
1–5
4.78
0–1
0.0005
50 W Multi-Silicon
Module. Make N. S
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
N.S
0–0.05
0.02334
10–500
100.13
1.5–1.6
1.6928
1–5
1.6961
0–100
56.3
–
–
–
–
PV Model
DD
Range Set
Extracted
Parameters
RS (Ω)
RP (Ω)
Iph (A)
a1
I01 (µA)
a2
I02 (µA)
N. S
0.01515
N. S
33.704
Isc
Isc
N. S
1.233
N. S
0.0084
N. S
2.57
N. S
15.29
PV Model
SD
Range Set
Extracted
Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
w.r.t Slope at Isc
0.0354
w.r.t Slope at Voc
59.012
1–5% of Isc
0.7607
0.5–2
1.5033
0–10% of Isc
0.4
–
–
–
–
PV Model
SD
Range Set
Extracted
Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
N. A
0.03638
N. A
53.6894
N. A
0.76078
N. A
1.4811
N. A
0.32267
–
–
–
–
PV Model
SD
Range Set
Extracted
Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
IBC
Varies with G & T
IBC
Varies with G & T
N. E
A.M
IBC
Varies
with G & T
N. E
A.M
–
–
–
–
PV Model
SD
Range Set
Extracted
Parameters
N.S
57 mm RTC France
Solar Cell
57 mm RTC France
Solar Cell
KD210 GH-2PU
G: Irradiance, T: Temperature, N.S: Not Specified, N.E: Not Extracting, N.A: Not Applicable, w.r.t: with respect to.
Also, it is important to note that the value of I and E is usually
chosen as 1. The value of ‘λ’ decides whether to modify SIV or not while
‘µ’ decides which solution should migrate. A good solution indicates
that high HSI islands have large number of species while a low HSI
island with small number of species indicates a poor solution.
better exploitation. In the research work proposed in [65], a similar
objective function to that of ABCO was employed to extract both the SD
and DD model parameters; and the results are illustrated in Table 11.
Compared to ABCO, ABSO shows a better performance in the DD model
but lacked rapid convergence. In the validations presented, ABSO
outperforms PSO, GA, PS, HS, CPSO and SA. However, the
validations were based on only for one irradiance level. Furthermore,
the optimal performance of ABSO depends on the user defined control
parameter ‘ne’ (number of elite bees).
3.2.7.1. Adaptive variant of BBO. To overcome the disadvantages of the
conventional BBO algorithm [120], hybrid mutation and hybrid
migration is proposed in BBO-M [66]. Hybrid migration in this
method replicates the mutation phase in DE algorithm. Furthermore,
a chaotic search is also introduced in BBO-M. In an essence; BBO-M
integrates new advantages into the conventional BBO keeping its
advantages intact.
3.2.7. Biogeography Based Optimization (BBO)
BBO method works on the theory of island Bio-Geography [119].
Each Island is considered to have a habitat suitability index (HSI) and
each variable in the island is called as suitability index variable (SIV). In
BBO method, immigration with an immigration rate, ‘λ’ and emigration
with an emigration rate, ‘µ’ are the two fundamental phases of the algorithm. The immigration and emigration of the Sth individual can be
mathematically represented as
s
λs = I ⎛1 − ⎞
n⎠
⎝
(41)
s
μs = E ⎛ ⎞
⎝n⎠
(42)
3.2.7.2. Application towards PV parameter extraction. When used for
parameter identification, the hybrid migration replicating the mutation
phase of DE provides diversity among the generations and makes the
algorithm robust. Furthermore, the chaotic variable is used to find the
optimal solution once the solution reaches close to the optimal value.
The parameter identification using BBO-M proposed in [66] has been
reviewed and the following inferences are made: 1) BBO-M is
computationally expensive since the number of parameters to be
controlled through the runs is high, 2) In model parameter extraction,
Table 9
Parameter identification using MPCOA.
Ref.
[62]
Approach
Numerical
PV Model
SD
√
Range Set
Extracted Parameters
DD
√
Range Set
Extracted Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
Cell/Module
0–0.5
0.03635
RS (Ω)
0–0.5
0.03635
0–100
54.6328
RP (Ω)
0–100
54.2531
0–1
0.76073
Iph (A)
0–1
0.76078
1–2
1.48168
a1
1–2
1.47844
0–1
0.32655
I01 (µA)
0–1
0.31259
–
–
a2
1–2
1.78459
–
–
I02 (µA)
0–1
0.04528
57 mm dia RTC France Solar Cell
12
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Table 10
Parameter identification using ABC and its hybrid variant.
Method
ABCO [63]
Approach
Metaheuristic
ABC + NMS [64]
Hybrid
PV Model
SD
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
PV Model
SD
Range Set
Extracted Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
0–0.5
0.0364
RS (Ω)
0–0.5
0.0364
0–100
53.6433
RP (Ω)
0–100
53.7804
0–1
0.7608
Iph (A)
0–1
0.7608
1–2
1.4817
a1
1–2
1.4495
0–1
0.3251
I01 (µA)
0–1
0.0407
–
–
a2
1–2
1.4885
–
–
I02 (µA)
0–1
0.2874
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
0–2
1.20127
0–2000
981.982
0–2
1.03051
1–2
48.643
0–50
3.48226
–
–
–
–
Cell/Module
57 mm RTC France Solar Cell
PWP 201 PV Module
Table 11
Parameter identification using ABSO.
Method
ABSO [65]
Approach
Metaheuristic
PV Model
SD
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0(µA)
–
–
Cell/Module
0–0.5
0.03659
RS(Ω)
0–5
0.03657
0–100
52.2903
RP (Ω)
0–100
54.6219
0–1
0.7608
Iph (A)
0–1
0.76078
1–2
1.47583
a1
1–2
1.46512
0–1
0.30623
I01 (µA)
0–1
0.26713
–
–
a2
1–2
1.98152
–
–
I02 (µA)
0–1
0.38191
57 mm dia RTC France Solar Cell
method showed good accuracy particularly in low irradiance profiles.
Furthermore, it outperformed AIS and GA methods in terms of accuracy
and convergence speed. It is noteworthy that the parameters extracted
using BFA will be helpful in characterization of partially shaded PV
modules. However, the model parameters; ‘RS’ and ‘a’ obtained for an
irradiation of G = 200 W/m2 were erroneous.
BBO-M dominates PSO, BBO, ABSO, HS, PS, DE and SA algorithms in
terms of accuracy, 3) ABSO is poor in convergence and 4) Validations
were not done in varying irradiation and temperature profiles. Table 12
indicates the resultant parameters obtained via optimization.
3.2.8. Bacterial Foraging Algorithm (BFA)
BFA is an evolutionary algorithm evolved from the food search
behavior of Escherichia coli bacteria (E-coli) [121]. BFA optimization is
performed with the help of four processes; chemotaxis, swarming, reproduction and elimination-dispersion [67]. In chemotaxis phase, E-coli
swim or tumble towards a food source while in swarming, all bacteria
follows the bacterium which is at the optimum path with the help of a
suitable communication strategy. In reproduction phase; the healthier
bacteria split into two according to their fitness function in such a way
that the swarm size remains constant. In elimination-dispersion step; to
reduce the likelihood of bacteria converging to local optima, some
bacteria get eliminated and some get dispersed according to a predefined elimination-dispersion probability.
3.2.9. Bird Mating Optimization Algorithm (BMO)
BMO deals with a society of four different types of birds; polyandrous, monogamous, polygynous, and promiscuous [68]. To search
for potential solutions in the search space, BMO uses several mating
strategies: 1) Among many, monogamous birds select one elite female
bird using a roulette wheel probability to produce a brood, 2) Polygynous birds mate with more than one female bird to produce a brood
having multiple combinations of female genes and 3) The polyandrous
birds adopt a probabilistic approach to select an elite male bird to
generate their brood. Furthermore, the worst birds in the society are
replaced by promiscuous birds which are more feasible solutions. The
initial generation of promiscuous birds is generated using a chaotic
sequence and is updated as the algorithm proceeds.
3.2.8.1. Application towards PV parameter extraction. In BFA, to
efficiently explore the search space from all dimensions, swimming
movement explores directional search spaces and the tumble movement
explores random spaces. The reproduction and elimination phases
provide an excellent exploitation with less computational effort as
well. In addition, BFA does not require any initial guess on the
parameters to be extracted. BFA based parameter identification
proposed in [67] has been reviewed and the obtained results are
illustrated in Table 13. As illustrated in the reviewed data, BFA
extracted different parameters for different environmental conditions.
‘IPh’ and ‘Id’ were mathematically calculated whereas the extracted
parameters are ‘RS’, ‘RP’ and ‘a’ . The validations were done for constant
irradiance, varying temperature and vice versa. In validations, the
3.2.9.1. Simplified BMO variant. Compared to BMO, simplified BMO
(SBMO) proposed in [69] has the following peculiarities: 1) SBMO has
an improved breeding concept similar to the reproduction in
[122–124], 2) A ranking based strategy is adopted to classify the
birds in the society. In SBMO birds are classified into three groups
according to their fitness value as;
Type I: Female birds (N1).
N
N1 = round ⎛ ⎞
⎝ 10 ⎠
(43)
Type II: Male birds mate with one female bird (N2).
Table 12
Parameter identification using BBO-M.
Method
BBO-M [66]
Approach
Metaheuristic
PV Model
SD
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
RS(Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
Cell/Module
0–0.5
0.03642
RS(Ω)
0–0.5
0.03664
0–100
53.3623
RP(Ω)
0–100
55.0494
0–1
0.76078
Iph (A)
0–1
0.76083
1–2
1.47984
a1
1–2
2
0–1E-6
0.31874
I01 (µA)
0–1E-6
0.59115
–
–
a2
1–2
1.45798
–
–
I02 (µA)
0–1E-6
0.24523
57 mm dia RTC France Solar Cell
13
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Table 13
Parameter identification using BFA.
Method
BFA [67]
Approach
Metaheuristic
PV Model
SD
Range Set
Extracted Parameters
RS (Ω)
RP(Ω)
Iph (A)
a
I0(µA)
Cell/Module
0–2
Varies with G & T
50–500
Varies with G & T
N. E
A.M
1–2
Varies with G & T
N. E
A.M
SM55
N.E: Not Extracting, G: Irradiance, T: Temperature, A.M: Analytical Method.
7
⎞
N2 = round N ⎛
⎝ 10 ⎠
GGHS and IGHS algorithms. The consolidated results of [68,69] is
presented in Table 14.
(44)
Type III: Male birds mate with two female birds (N3)
3.2.10. Flower Pollination Algorithm (FPA)
FPA is a nature inspired algorithm that resembles the pollination
process of flowers [125]. Two types of pollination processes are used in
FPA method to search for new solutions [70]: 1) Biotic pollination accomplished using insects; 2) Abiotic pollination, where wind acts as the
pollinator. Cross-pollination/biotic pollination takes place between
different species of different plants; accompanied by levy flights, bees,
birds and bats as pollinators represents the global search of the algorithm which can be mathematically represented as;
(45)
N3 = N − N1 − N2
where ‘N” is the total number birds in the society set by the user.
3.2.9.2. Application towards PV parameter extraction. The probability
based selection approach and elite strategy proposed in BMO ensure
that the best birds are selected for mating and hence, the broods will be
more feasible solutions. At the same time mutation control factor (mcf)
maintains diversity among the population and avoids premature
convergence. Since chaotic sequence can discover potential solutions
in the untested regions of search space; BMO easily escapes from the
local optima. On the other hand, in SBMO; type II and type III birds
move randomly towards the elite birds from all dimensions of the
search space for a better exploration while type I birds are high quality
solutions which exploit the search space by self-breeding. The prime
advantage of SBMO is that it is more user-friendly as it doesn't need real
time control of any parameters after initialization. In [68] the SD model
parameters for a 57 mm dia RTC France commercial solar cell were
extracted using BMO algorithm. A critical review of BMO based
parameter identification gives the following observations: 1) The
algorithm with its enhanced ability to search for global optimum via
various sleeking patterns has outperformed CPSO, GA, PS, SA, HS,
GGHS, IGHS and ABSO techniques in terms of accuracy, 2) In
validation, the algorithm has also proved successful in tracking the
MPP co-ordinates accurately, 3) BMO has excellent convergence
characteristics and 4) The accuracy of model parameters in varying
irradiation and temperature levels were not assessed. In SBMO based
parameter identification proposed in [69], the value of ideality factor,
‘a’ was found varying in the range of 1.99–2 with respect to a
corresponding change in irradiation levels from 1000 W/m2 to
200 W/m2. Sticking to the basic concepts of PV, this can induce false
emulation particularly in varying irradiation levels. The initial range set
for parameter ‘RP’ was too low for a configuration of 160 PV cells
connected in series. Hence, he extracted value of ‘RP’ was in the range of
5–10 Ω which is very low. This might have affected the optimization of
parameter ‘a ’ as well. However, in validation, SBMO outperformed PSO,
x it + 1 = x it + γ L (λ )(gbest − x it )
(46)
‘ x it + 1’
‘ x it ’
is the resultant pollen and
represents the current pollen.
With wind as pollinator, self-pollination/abiotic pollination between
different species of the same plant represents the local search of the
algorithm.
x it + 1 = x it + ε (xkt − x tj )
‘ xkt ’,
(47)
‘ x tj ’
represent pollens of the same species. The ε (epsilon) is of
uniform distribution ε∈{0, 1}.
3.2.10.1. Hybrid version of FPA. Improving the pollen exploitation
capability, a new Bee Pollinated Flower Pollination Algorithm
(BPFPA) was proposed recently in literature by fusing the bee colony
properties to the basic FPA [71]. Compared to FPA, a simplex method
making use of the discard solution operator used in the ABC algorithm
was incorporated in the basic FPA to build the BPFPA structure.
3.2.10.2. Application towards PV parameter extraction. Rather than
using computationally expensive specific strategies, FPA uses a
probability switch function to switch between global pollination and
local pollination between the runs. The balance between exploration
and exploitation is effectively laid by the utilization of global
pollination during initial runs and local pollination during final runs.
Hence the computational burden of FPA is very low. In the application
discussed in [70], 1) FPA outperformed ABCO, ABSO, AIS, P-DE, BBO
and SBMO in terms of accuracy and convergence time, 2) Initial range
of the parameters was selected globally for all the modules used, 3) FPA
Table 14
Parameter Identification using BMO and SBMO.
Method
BMO [68]
SBMO [69]
Approach
Metaheuristic
Metaheuristic
PV Model
SD
Range Set
Extracted
Parameters
DD
Range Set
Extracted
Parameters
PV Model
SD
Range Set
Extracted
Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
0–0.5
0.03636
0–100
53.8716
0–1
0.76077
1–2
1.4817
0–1
0.32479
–
–
–
–
RS (Ω)
0–0.5
0.03682
RP (Ω)
0–100
55.8081
Iph (A)
0–1
0.76078
a1
1–2
1.4453
I01 (µA)
0–1
0.2111
a2
1–2
2
I02 (µA)
0–1
0.8769
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
0–0.5
Varies with
G&T
0–100
Varies with
G&T
0–1
Varies with
G&T
1–2
Varies with
G&T
0–1
Varies with
G&T
–
–
–
–
G: Irradiance, T: Temperature.
14
Cell/Module
57 mm RTC France Solar
Cell
Amorphous Silicon PV
module
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
minimum is high. SA was applied for parameter identification
problem in [72]. In the proposed work, the validations were done
based on an assumption that irradiation has no effect on the cell
parameters which eventually is wrong. Further in validations
presented, SA outperformed the conventional microcomputer based
parameter extraction technique [128] and Pattern Search (PS)
algorithm in terms of accuracy in an SD model. However, the
performance of SA can be significantly improved if the control
parameter ‘T’ is adaptively controlled. In LM + SA algorithm, SA
based control of damping factor enhances the search ability of LM
algorithm to achieve a global solution by improving the search routine
during every Iteration [129]. When LM + SA algorithm was used for
parameter identification in [73], SA based damping control increased
the accuracy of all the model parameters extracted. In the validations
presented, LM + SA algorithm outperformed GA, SA, PS, DE, CPSO,
ABSO, GGHS and Newton methods. The results of parameter
identification using SA and its hybrid variant are illustrated in Table 16.
performed better in all conditions of temperature and irradiance with
low RMSE error, 4) FPA has only two control parameters to be tuned in
real time and 5) The probability switch function needs optimal control
for satisfactory performance. On the other hand, the ABC discard
operator employed in BPFPA generates diversity among the bee
population to strengthen the pollens for a better exploration. This
strategy further strengthens the exploitation process in FPA to achieve
more accurate solutions. In BPFPA based parameter identification
presented in [71], the model parameters, ‘IPh’ and ‘I0’ were calculated
mathematically while ‘RS’, ‘RP’ and ‘a’ were extracted. In this research,
the innovation of incorporating discard pollen strategy in BPFPA has
remarkably increased the quality of extracted parameters. In validation,
BPFPA outperformed PSO, GA, FPA, ABSO, HS, PS, SA and CPSO based
parameter identification techniques. It is worth to mention that the
method has shown terrific promise towards parameter extraction and
can be considered as one of the most reliable extraction techniques.
Furthermore, BPFPA shows good convergence characteristics as well.
The extracted parameters are elucidated in Table 15.
3.2.12. Harmony Search Algorithm (HS)
HS algorithm replicates the adjustment of pitch in musical instruments for achieving a pleasing harmony. In HS, a harmony memory
(HM) is used to store a set of randomly generated harmony vectors. For
updating each variable, either one of the following three rules is utilized: 1) Update by a value in the memory, 2) Update by choosing a
value closer to HM, 3) Update using a random value. Through successive iterations, the worst harmonies in the memory are updated with
better harmonies generated, yielding an optimal solution.
3.2.11. Simulated Annealing Algorithm (SA)
Inspired by the process of production of crystals using annealing, SA
algorithm was proposed in [126,127]. SA algorithm has two main
processes: 1) Change over between states and 2) Control of temperature
to obtain the lowest energy state. SA method starts at an initial solid
state, ‘Xi’ with an energy level, ‘E i’. The next state ‘X2’ with an energy
level ‘E2’ will be accepted only if the following equation is satisfied.
(48)
E1 − E2 ≤ 0
If E1 − E2 > 0 , the state is accepted according to the probability
function given by
E −E
⎛ 1 2⎞
P (E , TC ) = e⎝ KB TC ⎠
3.2.12.1. Other variants of HS algorithm. Grouping based global
harmony search (GGHS) is an improved variant of HS which wisely
uses the harmonies in the harmony memory. In GGHS, HM is classified
into groups based on their fitness quality and the improvisation is done
using the following rules: 1) Select the interesting group using
tournament selection, 2) Using roulette wheel selection, select an
elite harmony from the interesting group to improvise the current
harmony. Another adaptive variant; innovative global harmony search
(IGHS) uses predefined high quality elite harmonies for improvisation.
The high quality elite harmonies are selected from HM using a roulette
wheel approach to update the current harmony. The conventional HS
and all its improved versions were used for parameter identification in
[74].
(49)
The control parameter, ‘TC ’ is controlled during the whole search of
the algorithm until the lowest energy state is obtained.
3.2.11.1. Hybrid variant of SA. In [73], a hybrid strategy (LM + SA)
was proposed where SA algorithm was used to control the damping
factor of Levenberg-Marquardt (LM) algorithm. LM algorithm has the
complimentary features of two methods: 1) The steepest descent and 2)
Gauss-Newton method. The switching between the two methods is
ensured by its damping factor that has to be controlled during each
iteration step. In LM + SA algorithm, SA optimization is used to
optimize the value of damping factor in each iteration step.
3.2.12.2. Application towards PV parameter extraction. In HS, using the
pre-defined and range specific harmonies in HM to update current
solutions provide randomness in exploration of the search space. The
two control parameters; pitch adjustment rate (PAR) and band width of
generations (B.W) balances between exploration and exploitation
capabilities of the algorithm [130,131]. After reviewing HS based
3.2.11.2. Application towards PV parameter extraction. In SA algorithm,
even if there is randomness while exploring new solutions, the accuracy
is low since the memory of the solutions is not used for updating the
crystals. Hence, probability of solutions to get trapped at local
Table 15
Parameter identification using FPA and BPFPA.
Method
FPA [70]
BPFPA [71]
Approach
Metaheuristic
Hybrid
PV Model
SD
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
PV Model
SD
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
Cell/Module
0–1
0.03655
RS (Ω)
0–1
0.03633
0–5000
52.8771
RP (Ω)
0–5000
52.3475
0–2
0.76079
Iph (A)
0–2
0.7608
1–4
1.47707
a1
1–4
1.47477
0–1
0.31068
I01 (µA)
0–1
0.30009
–
–
a2
1–4
2
–
–
I02 (µA)
0–1
0.16616
57 mm dia RTC France Solar Cell
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
57 mm dia RTC France Solar Cell
0–2
0.0366
RS (Ω)
0–2
0.0364
50–900
57.7151
RP (Ω)
50–900
59.624
N.E
A.M
Iph (A)
N.E
A.M
0.5–2
1.4774
a1
0.1–2
1.4793
N.E
A.M
I01 (µA)
N.E
A.M
–
–
a2
1.2–4
2
–
–
I02 (µA)
N.E
A.M
N.E: Not Extracting, A.M: Analytical Method.
15
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Table 16
Parameter identification using SA and its hybrid variant.
Method
SA [72]
LM + SA [73]
Approach
Metaheuristic
Hybrid
PV Model
SD
√
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
PV Model
SD
Range Set
Extracted Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
Cell/Module
N. A
0.0313
RS (Ω)
N. A
0.0345
N. A
64.1026
RP (Ω)
N. A
43.1034
N. A
0.7617
Iph (A)
N. A
0.7623
N. A
1.6
a1
N. A
1.5172
N. A
0.998
I01 (µA)
N. A
0.4767
–
–
a2
N. A
2
–
–
I02 (µA)
N. A
0.01
KC200GT PV Module
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
57 mm RTC France Solar Cell
N. S
0.03463
N. S
53.3264
N. S
0.76078
N. S
0.31849
N. S
1.47976
–
–
–
–
N.A: Not Applicable, N.S: Not Specified.
routine steps: 1) Exploratory search and 2) Pattern move. Exploratory
search starts at an arbitrary random point called base point (BP) and
with BP as center, the initial search generates a mesh of 2n points by
spanning 2n coordinate directions. In pattern move, the base point is
updated to a new point in the current direction by harnessing the
memory of the last two BPs and is expressed as;
parameter identification carried out in [74], the following inferences
are likely to be presented: 1) The parameter setting of all HS based
algorithms are based on an initial trial, 2) In validations, HS
outperformed PSO, SA, PS and GA algorithms in terms of accuracy, 3)
HS is poor in convergence and 4) Performance of HS in varying
irradiation and temperature levels were not assessed. Since accuracy
is the uncompromised feature of any parameter extraction technique,
GGHS adopts tournament selection to select the best group for updating
the harmony while roulette wheel selection is adopted to enhance the
probability of selecting a quality harmony from HM. When used for
parameter extraction, with the same range of parameters as HS used,
GGHS extracted quality model parameters especially for ‘Rp’ and ‘a’. In
further validations, GGHS outperformed PSO, SA, PS and GA algorithms
as well. However, similar to HS, GGHS shows slow convergence
characteristics. On the other hand, compared to HS and GGHS, since
the predefined harmonies are of high quality, the improvisation process
in IGHS provides better solutions. While reviewing IGHS based
parameter identification, following observations were made: 1) For
DD model, the value of a2 is less than a1 which is not a theoretical fit, 2)
IGHS is outperformed by GGHS in terms of accuracy in the SD model, 3)
For a DD model IGHS extracted accurate parameters when compared
with HS, GGHS, GA, PSO, SA and PS methods. The consolidated
parameter identification data obtained for HS algorithm and its
improved versions is shown in Table 17.
k+
k
k
k−1
XBp
= XBp
+ [XBp
− XBp
]
(50)
If this move deemed successful, i.e. the objective function has imk+
’ and if
proved, the next exploratory search starts from the new BP, ‘ XBp
the pattern move is unsuccessful, then the exploratory search again
k
’.
starts from the old BP, ‘ XBp
3.2.13.1. Application towards PV parameter extraction. Incase of
parameter identification, the unique advantages of PS algorithm are:
1) it is insensitive to the initial starting point and 2) it uses its own
search history to determine the search direction for forthcoming
iterations. The exploratory search in PS searches for all possible
solutions in a wider dimension around the starting base point.
However, PS algorithm is weak in exploiting best solutions. Refs.
[75,76] used PS algorithm to extract the PV parameters and the
refined data is presented in Table 18. In the proposed work: 1) A new
objective function based on the IAE (Individual absolute Error) was
used for optimization, 2) In IAE analysis, PS outperformed the
conventional Newton method and GA, 3) Based on IAEs obtained for
DD and SD models, the authors commented that SD model is quite
sufficient for PV analysis, 4) The value of a1 > a2 in DD parameters is
unusual with respect to the theoretical concepts and 5) The
3.2.13. Pattern Search algorithm (PS)
Pattern Search is a metaheuristic algorithm which does not require
any derivative data for optimization [132]. The method includes two
Table 17
Parameter identification using HS and its variants.
Method
HS [74]
GGHS [74]
IGHS [74]
Approach
Metaheuristic
Metaheuristic
Metaheuristic
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
Cell/Module
0–0.5
0.03663
RS(Ω)
0–0.5
0.03545
0–100
53.5946
RP (Ω)
0–100
46.827
0–1
0.7607
Iph (A)
0–1
0.76176
1–2
1.47538
a1
1–2
1.49439
0–1
0.30495
I01 (µA)
0–1
0.12545
–
–
a2
1–2
1.49989
–
–
I02 (µA)
0–1
0.2547
57 mm dia RTC France Solar Cell
PV Model
SD
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
57 mm dia RTC France Solar Cell
0–0.5
0.03631
RS (Ω)
0–0.5
0.03562
0–100
53.0647
RP (Ω)
0–100
62.7899
0–1
0.76092
Iph (A)
0–1
0.76056
1–2
1.48217
a1
1–2
1.49638
0–1
0.3262
I01 (µA)
0–1
0.37014
–
–
a2
1–2
1.92998
–
–
I02 (µA)
0–1
0.13504
PV Model
SD
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
0–0.5
0.03613
RS(Ω)
0–0.5
0.0369
0–100
53.2845
RP (Ω)
0–100
56.8368
0–1
0.76077
Iph (A)
0–1
0.76079
1–2
1.4874
a1
1–2
1.92126
0–1
0.34351
I01 (µA)
0–1
0.9731
–
–
a2
1–2
1.42814
–
–
I02 (µA)
0–1
0.16791
PV Model
SD
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
16
57 mm dia RTC France Solar Cell
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Table 18
Parameter identification using PS.
Method
PS [75,76]
Approach
Metaheuristic
PV Model
SD
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
Cell/Module
N. S
0.0313
RS (Ω)
N. S
0.032
N. S
64.1026
RP (Ω)
N. S
81.3008
N. S
0.7617
Iph (A)
N. S
0.7602
N. S
1.6
a1
N. S
1.6
N. S
0.998
I01 (µA)
N. S
0.9889
–
–
a2
N. S
1.192
–
–
I02 (µA)
N. S
0.0001
57 mm dia RTC France Solar Cell
N.S: Not Specified.
Table 19
Parameter identification using STLBO.
Method
STLBO [77]
Approach
Metaheuristic
PV Model
SD
Range Set
Extracted Parameters
DD
Range Set
Extracted Parameters
RS (Ω)
RP (Ω)
Iph (A)
a
I0 (µA)
–
–
Cell/Module
0–0.5
0.03638
RS (Ω)
0–0.5
0.03674
0–100
53.7187
RP (Ω)
0–100
55.492
0–1
0.76078
Iph (A)
0–1
0.76078
1–2
1.48114
a1
1–2
1.4505
0–1
0.32302
Id0 (µA)
0–1
0.22566
–
–
a2
1–2
0.75217
–
–
Id0 (µA)
0–1
2
57 mm dia RTC France Solar Cell
Table 20
Analysis of 57 mm dia RTC France solar cell.
Sl. no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
SD Model
Sl. no.
Algorithm
RMSE
BPFPA
FPA
MPCOA
STLBO
R-JADE
TVIWAC PSO
BMO
ABC + NMS
ABC
BBO-M
LM + SA
PSA
IADE
GGHS
ABSO
IGHS
HS
SA
CPSO
AGA + LS
PS
7.27E
7.84E
9.45E
9.86E
9.86E
9.86E
9.86E
9.86E
9.86E
9.86E
9.86E
9.87E
9.89E
9.91E
9.91E
9.93E
9.95E
1.70E
2.65E
2.75E
2.86E
Convergence
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
04
04
04
04
04
04
04
04
04
04
04
04
04
04
04
04
04
03
01
01
01
Fast
Fast
Fast
N. S
Slow
Fast
Fast
Slow
Fast
Slow
Fast
Fast
N. S
Slow
Slow
Slow
Slow
N. S
N. S
Slow
N. S
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
–
–
–
–
–
–
DD Model
Algorithm
RMSE
BPFPA
FPA
MPCOA
STLBO
R-JADE
ABC + NMS
BMO
BB0-M
ABSO
ABC
IGHS
GGHS
HS
SA
PS
–
–
–
–
–
–
7.23E
7.73E
9.22E
9.82E
9.82E
9.82E
9.83E
9.83E
9.83E
9.86E
9.86E
1.07E
1.26E
N. S
N. S
–
–
–
–
–
–
Convergence
−
−
−
−
−
−
−
−
−
−
−
−
−
04
04
04
04
04
04
04
04
04
04
04
03
03
Fast
Fast
Fast
N. S
Slow
Slow
Fast
Slow
Slow
Fast
Slow
Slow
Slow
N. S
N. S
–
–
–
–
–
–
N. S: Not Specified.
in the population and is given by (52).
environmental factors were not considered for validating the model.
N . S, if f (N . S ) < f (W . L) ⎫
W. L = ⎧
⎬
⎨
W
⎭
⎩ . L, else
3.2.14. Teaching Learning Based Optimization (TLBO)
TLBO replicates the teaching learning process between teachers and
learners. TLBO has two main phases; 1) Teaching phase: The quality of
the teacher is improved with the help of a user defined teaching factor,
‘TF’ such that the quality of learners also increases; 2) Learning phase:
The learners try to improve their own quality by the interacting with
randomly selected learners.
3.2.14.2. Application towards PV parameter extraction. When TLBO is
used for parameter identification; the randomness in the teaching
factor, ‘TF’ significantly affects the accuracy of the extracted
parameters; while in the case of STLBO, the redefined teacher phase
performs a local search to find the near optimum with the help of a
mutation variable. Furthermore, introduction of chaotic variable
enriches the mutation operation with a good random uniformity. The
reduction in number of function evaluations (FES) reduces the FES cost
of the algorithm and increases the convergence speed as well [133].
Parameters estimated and ranges selected by STLBO method for
extracting PV parameters are illustrated in Table 19. A critical review
on STLBO based parameter identification [77] gives the following
observations: 1) The enhanced search capability of STLBO has
3.2.14.1. Simplified version. In simplified TLBO (STLBO) proposed in
[77]; teaching phase has an improved concept while the learning phase
is similar to that of TLBO. The best teacher obtained in TLBO is further
improved in STLBO using a local search operation.
Tnew + mu, if rm < μ ⎫
(Tnew )* = ⎧
otherwise ⎬
⎨
⎭
⎩Tnew,
(52)
(51)
In addition, an elite strategy is also used to update the worst learner
17
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Table 21
Accurate models for different PV cells/modules.
Sl. no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Cell/Module
Accurate model
57 mm dia RTC France Solar cell
Photo watt PWP-201 Solar Module
Polycrystalline S36 Solar Module
Shell SP70 Solar Module
Shell SM55 PV Module
Kyocera KC200GT PV Module
Kyocera KC210 PV Module
Thin Film ST40 PV Module
Polycrystalline S75 PV Module
Sanyo HIT15 PV Module
SL80CE PV Module
Multi crystalline S115 PV Module
Thin Film ST36 PV Module
Mono crystalline SQ150PC PV Module
Sun power E20/333 Mono crystalline PV Module
Shell SM40 Mono crystalline PV Module
Shell SQ85 Mono crystalline PV Module
DD
RMSE/AE
Convergence
SD
RMSE/AE
Convergence
BPFPA based
N. A
BPFPA based
AIS based
BPFPA based
BPFPA based
DEIM based
BPFPA based
FPA based
N. A
N. A
P-DE based
P-DE based
P-DE based
N. A
FPA based
N. A
7.23E − 04
–
5.87 E − 04
N. S
4.58E − 04
2.20E − 04
0.0606 (AE)
3.65E − 04
2.34890E − 03
–
–
N. S
N. S
N. S
–
2.21152E − 03
–
Fast
–
Fast
Fast
Fast
Fast
Fast
Fast
Fast
–
–
Fast
Fast
Fast
–
Fast
–
BPFPA based
FPA based
BFA based
IBCPSO based
FPA based
FPA based
N. A
FPA based
DE based
GA + NR based
IADE based
N. A
N. A
MPCOA based
GA + IP based
FPA based
IBCPSO based
7.270E − 04
2.05467E − 03
N. S
N. S
1.5020E − 04
9.9985E − 04
–
8.50040E − 04
N. S
0.01608 (AE)
1.15000E − 02
–
–
2.60000E − 02
2.60000E − 02
2.00000E − 03
N. S
Fast
Fast
Fast
Slow
Fast
Fast
–
Fast
N. S
Fast
N. S
–
–
Fast
N. S
Fast
Slow
N.S: Not specified, N.A: Not Available.
Parameter
Extraction
Single/double
diode model
Prediction of I-V
and P-Vcurves
V& I sensors
Real time
Values/ Curves
obtained from [135]. In validation, ANN outperformed the conventional direct extraction technique. The authors in [82] employed AIS to
predict the DD model parameters of four different PV modules. The
parameter ‘IPh’ for all the modules was computed using a direct analytical method. In the validations presented, AIS outperformed conventional PSO and GA. However, all validations are corresponding to
STC only. When PSA was used for parameter identification in [81], for
the same work load of PSO, the method improved the convergence time
significantly even for a very large swarm size. However the complexity
of the system and requirement of additional components limits its use
for parameter identification.
Setting Threshold
values /curves
Fault detection
Comparison
PV array
Fig. 9. Fault detection in PV systems.
succeeded in extracting highly accurate model parameters for both SD
and DD models, 2) The algorithm outperformed ABSO, HS, PS, SA,
GGHS, CPSO, IADE and TLBO in terms of accuracy and 3) The
algorithm was validated only for standard test conditions.
4. Overall review on accuracy and convergence speed of
metaheuristic algorithms based parameter identification for
various PV cells/modules
3.3. Other techniques for parameter identification
This section analyzes the performance of each metaheuristic algorithm deployed for parameter extraction. The analysis of accuracy and
convergence speed has been done based on how low the objective
function value is and how many iterations an algorithm takes to reach
the lowest fitness value respectively. In this work, those algorithms
which can rapidly converge to the best fitness value with in 400
iterations are treated to be fast while others are considered to be slow.
Furthermore, a comparative evaluation on the accuracy of each method
is carried out to identify the best PV model available for each cell/
module specified with a viewpoint to set benchmarks for further research advancements. Seventeen different PV cells/modules mentioned
in Table 3 are considered in this regard. In literature, 57 mm dia RTC
France solar cell was found to be the most commonly used solar cell for
parameter identification. The detailed analysis conducted on the various models realized by different metaheuristic algorithms and their
hybrid versions for 57 mm dia RTC France solar cell is illustrated in
Table 20. From Table 20, it is evident that, out of the 21 metaheuristic
algorithms, 15 metaheuristic techniques have extracted the DD model
parameters for RTC France solar cell whereas all the techniques extracted the SD model parameters. The analysis clearly confirms: 1)
BPFPA based model surpasses all the other models in terms of accuracy
and convergence speed; both in SD and DD models, 2) The RMSE error
values are significantly low for the BPFPA and FPA based models when
compared to the MPCOA model; which is the third lowest in terms of
RMSE, 3) In the case of DD model, BPFPA, FPA, MPCOA, STLBO, RJADE and TVIWAC PSO methods extracted fairly accurate parameters
and are found reliable to work with and 4) Out of the six, R-JADE is
In literature, Artificial Neural Networks (ANN) which resembles the
nervous system of human beings [79]; Artificial Immune System (AIS)
which is inspired by the defense mechanism of the human body against
pathogens [80] and Parallel Swarm Algorithm (PSA) which utilizes the
computational power of a central processing unit (CPU) and a graphical
processing unit (GPU) [81] were also used for parameter identification.
It should be appreciated that all these methods have taken up a novel
initiative to solve the parameter identification problem; but all these
methods are still unproven and unclear. However, a very brief review
on these methods is also presented in this section. Artificial Neural
Network is a computational model which replicates the biological
neural network. Once the network is trained with accurate data, ANN
can predict the output corresponding to the input data. On the other
hand AIS employ a multipoint cross over and mutation strategy for
attaining a global maximum solution. Inspired by [134], PSA incorporates a CPU and GPU based parallel computing system with the
conventional PSO for fitness value evaluation.
3.3.1. Application towards PV parameter extraction
The accuracy of ANN completely relies on its initial training and
getting accurate data for training is in fact a very difficult task.
Furthermore, as the number of training test increases, the error also
exceeds. This limits the use of ANN for PV parameter identification. In
[79], a trained ANN was used to extract the model parameters of an SD
model. The training sets and the validating data for the network were
18
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
Table 22
Validating environment of various realized models for different cells/modules.
(a)
Kyocera KC200GT PV Module
DD Model
SD Model
Algorithm
Validating Environment
Algorithm
Validating Environment
BPFPA
MPCOA
GA + NR
AIS
Varying temperature and Irradiation Levels
Varying Irradiation Levels
Varying temperature and Irradiation Levels
Standard Test Conditions
FPA
MPCOA
GA + NR
GA + P
Varying
Varying
Varying
Varying
temperature and Irradiation Levels
Irradiation Levels
temperature and Irradiation Levels
temperature and Irradiation Levels
(b)
RTC France Solar Cell
DD Model
SD Model
Algorithm
Validating Environment
Algorithm
Validating Environment
All algorithms
Standard Test Conditions
All algorithms
Standard Test Conditions
(c)
Shell SM55 PV Module
DD Model
SD Model
Algorithm
Validating Environment
Algorithm
Validating Environment
BPFPA
FPA
P-DE
AIS
Varying temperature and Irradiation Levels
Varying temperature and Irradiation Levels
Varying Irradiation Levels
Standard Test Conditions
FPA
BFA
DE
Varying temperature and Irradiation Levels
Varying temperature and Irradiation Levels
Varying temperature and Irradiation Levels
(d)
Thin Film ST40 PV Module
DD Model
SD Model
Algorithm
Validating Environment
Algorithm
Validating Environment
BPFPA
FPA
P-DE
–
–
Varying temperature and Irradiation Levels
Varying temperature and Irradiation Levels
Varying Irradiation Levels
–
–
FPA
GA + NR
GA + IP
BFA
DE
Varying
Varying
Varying
Varying
Varying
temperature and Irradiation
Irradiation Levels
temperature and Irradiation
temperature and Irradiation
temperature and Irradiation
Levels
Levels
Levels
Levels
bound to cause catastrophic failures in PV arrays and are the prime
underlying cause for panel degradation as well. Even though many
protection devices are available, faults occurring at low irradiance levels may remain even undetected in the PV system. With immense investment on land to acquire the huge area required for the installation
of PV systems, even a small reduction of power due to a fault cannot be
tolerated. Indeed, instant detection of faults and its mitigation is highly
demanded irrespective of its type and location. In this regard, accurate
PV models are extremely useful to predict the faulty electrical characteristics of a PV array in prior and will guide the user to rapidly detect
the fault. Usually fault detection is performed by employing either one
of the following techniques [136–156]:
poor in convergence speed. The analysis is same in the case with SD
model as well.
Apart from RTC France solar cell, similar analysis as performed in
Table 20 has been carried out for all other PV cells/modules specified in
Table 2 to identify the accurate PV model available for each cell/
module. However, for brevity, each case is not shown. Further, an
overall consolidated analysis for all 17 PV cells/modules is exhibited in
Table 21. For the analysis presented in Table 21, it is worth to mention
that, while comparing an RMSE error evaluation method with an AE
based technique, the RMSE method is usually considered to be better
because RMSE is probably the most accurately interpreted statistic
available for curve fitting. For uniformity, the analyzed data for RMSE
and AE given in Table 21 are all taken for the standard test conditions.
Furthermore, while analyzing some models as specified in [47], the
absolute error for both STC and NOCT were available. In those cases,
the overall AE was assumed to be the average of the two.
○ Comparison of real time outputs with threshold values.
○ Analyzing real time I-V and P-V curves with threshold curves.
○ By defining new parameters depending on irradiation and temperature [152].
○ Detecting change in MPPT voltage [153].
○ Using satellite image or infrared thermography [154,155].
5. Application of parameter extraction to fault detection in PV
systems
Among the various fault detection techniques proposed over the
years, the first two techniques are most commonly adopted; for which
an accurate PV model is indispensable to emulate the PV
Inspired by the review on various PV models; an unidentified
gateway of interest between parameter extraction and fault detection in
PV systems has been noticed. Uninterrupted and unnoticed faults are
19
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
–
–
–
N. A
FPA Based Model
N. A
Yes
Yes
FPA Based Model
IBCPSO Based Model
BPFPA Based Model
–
–
–
–
–
N. A
–
–
GA + NR Based Model
–
N. A
N. A
–
–
BPFPA Based Model
N. A
–
AIS Based Model
–
–
DEIM Based Model
–
–
N. A
N. A
–
–
–
N. A
N. A
N. A
BPFPA Based Model
N. A
BPFPA Based Model
BPFPA Based Model
N. A
BPFPA Based Model
FPA Based Model
N. A
N. A
P-DE Based Model
P-DE Based Model
P-DE Based Model
N. A
No
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
No
Yes
No
No
Yes
Yes
N. A
ABC-NMS Based Model
BFA Based Model
IBC-PSO Based Model
FPA Based Model
FPA Based Model
N. A
FPA Based Model
DE Based Model
N. A
IADE Based Model
N. A
N. A
MPCOA Based Model
GA + IP Based Model
SD Model
DD Model
SD Model
DD Model
SD Model
This paper has reviewed handful of parameter extraction techniques
using metaheuristic algorithms with an emphasis on its compatibility,
approach, range of parameters set, accuracy and convergence speed.
Some key inferences on the performance of each algorithm when applied for parameter identification problem were discussed. Among all
the algorithms used for parameter identification, BPFPA was found to
be the superior in terms of accuracy and convergence speed.
Furthermore, 17 different cells/modules used for parameter identification were analyzed and the accurate model available for each cell/
module was identified. A brief review regarding the analytical methods
for parameter extraction was also presented. Above all, the application
of parameter extraction towards threshold setting for fault detection in
PV systems has been explained in detail and the models capable for
predicting accurate thresholds were identified for each cell/module.
After reviewing metaheuristic algorithms and its hybrid variants employed so far for parameter identification, the following points are
likely to be suggested.
16
17
N.A: Not Available.
Yes
No
No
No
Yes
No
Yes
Yes
No
Yes
Yes
No
No
Yes
Yes
Yes
No
57 mm dia RTC France Solar cell
Photo watt PWP-201 Solar Module
Polycrystalline S36 Solar Module
Shell SP70 Solar Module
Shell SM55 PV Module
Kyocera KC200GT PV Module
Kyocera KC210 PV Module
Thin Film ST40 PV Module
Polycrystalline S75 PV Module
Sanyo HIT15 PV Module
SL80CE PV Module
Multi crystalline S115 PV Module
Thin Film ST36 PV Module
Mono crystalline SQ150PC PV Module
Sun power E20/333 Mono crystalline PV
Module
Shell SM40 Mono crystalline PV Module
Shell SQ85 Mono crystalline PV Module
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
DD Model
Solar Cell/Module
Whether accurate model is available for Threshold Setting in Fault
Detection Systems?
characteristics. This scheme of detecting PV fault is depicted in Fig. 9.
In literature, PSO based parameter identification and fault detection by
analyzing the change in the parameters extracted is illustrated in [136].
A similar approach using LS based parameter identification is proposed
in [150]. IV curves were simulated to set the thresholds for detecting
the fault in [138,140,142,143,148]. Authors in [144,147] trained ANN
with model predicted threshold curves to identify the fault; while in
[137,139,141,145,156] faults are detected by comparing real time
output power with the threshold values. Similar approaches are followed in [146,149,151] to detect the fault. From the survey, it is evident that all these fault detection techniques need threshold values
predicted by a suitable PV model to detect the fault. Moreover, a PV
model selected for predicting these threshold limits must be capable to
accurately emulate the PV characteristics in all temperature and irradiation profiles. In addition to the environmental effect on a PV, partial
shading is a very common and intense issue which can drastically
change the electrical characteristics of a PV. Hence, a PV model which
is tested only for STC might not be sensitive enough to accurately
emulate the PV characteristics in real-time operating conditions. Using
these models for fault detection can cause erroneous detection of faults
due to the wrongly set threshold limits. Hence, identifying PV models
which are efficient to set accurate threshold limits for fault detection
under all working environments is of massive importance. This indeed
necessitates that, while selecting a PV model for the fault detection of a
particular cell/module, extreme care must be given to identify the
model that has been validated for all environmental conditions. Hence,
an attempt has been made in this paper to identify those models
available for 17 different solar cells/modules; which will guide researchers/manufacturers to set accurate thresholds for achieving rapid
fault detection. As shown in Table 22, for each PV cell/module, the
testing conditions of their respective models have been evaluated. A
careful examination on Table 22 indicates that no PV models realized
for RTC France solar cell was validated for varying irradiation and
temperature levels. Hence, for fault detection of an RTC France solar
cell, no reliable models are available. However, among all the models
used for the particular cell, FPA based model possesses the highest
accuracy. The same analysis presented in Table 22 has been conducted
for all the cells/modules used for parameter extraction. Furthermore, an
overall consolidated analysis is presented in Table 23 where the most
accurate model available for each solar cell/module; which can help PV
manufacturers/researchers to achieve rapid fault detection is identified.
6. Summary
Sl. n
Table 23
Models available for threshold setting for fault detection in PV systems.
If Yes, Name of the Model
If No, the most accurate model available for Fault Detection
D.S. Pillai, N. Rajasekar
➣ Algorithms can perform better if accurate range for each unknown
parameter is initialized. Most algorithms rely on a trial run to determine the range to be set. Indeed, this is not reliable as the noise
levels may substantially affect the trial run. Hence, a global concept
20
Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx
D.S. Pillai, N. Rajasekar
➣
➣
➣
➣
➣
➣
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or a mathematical formulation with the help of the data available in
the data sheet must be proposed; which will remarkably help the
algorithms to perform better irrespective of the type of PV cells or
modules they use.
Even though accurate parameters can be identified for standard test
conditions, those parameters may not be accurate enough in nominal operating conditions. Considering the fact that STC conditions
are globally not available, for an opinion about the accuracy and
performance of the algorithm, the realized models must be tested for
all operating conditions.
Even though DD model is slightly sophisticated with higher number
of unknown parameters when compared to SD model, it can efficiently predict the I-V and P-V characteristics in varying irradiance
and temperature levels. Hence for environment sensitive applications, particularly for fault detection in PV systems, DD model must
be used.
When parameter extraction techniques are used to define thresholds
for fault detection in PV systems, apart from the accuracy of the
technique, the convergence speed must also be considered for
achieving rapid fault detection. In this regard, the computational
speed of the algorithm has high dependency on the number of fitness evaluations in each iteration step. Hence when used for applications like fault deduction and maximum power point tracking
which demands high speed computation, care should be given to
select an accurate algorithm with less number of fitness evaluations.
Considering the promise that metaheuristic algorithms has shown,
the parameter identification can be extended to much improved PV
models other than the conventional SD and DD models such that the
models realized can be applied to highly sensitive applications too.
Application of new and improved metaheuristic algorithms like Prey
Predator algorithm, Radial Movement optimization, Grey Wolf, Fire
Fly optimization algorithm etc. for parameter identification, is expected to further enhance the quality of the model parameters extracted.
As a future work, an assessment on the performance of each parameter identification technique with respect to various irradiance
and temperature profiles is suggested.
Acknowledgments
The authors would like to thank the Management, VIT University,
Vellore, India for providing the support to carry out research work. This
work is carried out at Solar Energy Research Cell (SERC), School of
Electrical Engineering, VIT University, Vellore. Further, the authors
also would like to thank the reviewers for their valuable comments and
recommendations to improve the quality of the paper.
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