Literature Review

R E V I E W A R T I C L E

Review on parameter estimation techniques of solar photovoltaic systems

Radhakrishnan Venkateswari1 | Natarajan Rajasekar2

1VIT University, Vellore, India 2Solar Energy Research Cell, School of Electrical Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India

Correspondence Natarajan Rajasekar, Solar Energy Research Cell, School of Electrical Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu 632 014, India. Email: [email protected]

Summary

Beyond meeting power demand, switching to solar energy especially solar

photovoltaic (PV) offers many advantages like modularity, minimal mainte-

nance, pollution free, and zero noise. Yet, its cell modeling is critical in design,

simulation analysis, evaluation, and control of solar PV system; most impor-

tantly to tap its maximum potential. However, precise PV cell modeling is

complicated by PV nonlinearity, presence of large unknown model parameter,

and absence of a unique method. Since number of model parameters involved

is directly related to model accuracy, and efficiency; determination of its values

assume high priority. Besides, application of meta-heuristic algorithms via

numerical extraction is popular as it suits for any PV cell/module types and

operating conditions. However, existence of many algorithms have drawn

attention toward assessment of each method based on its merits, demerits,

suitability/ability to parameter estimation problem, and complexity involved.

Hence, few authors reviewed the subject of PV model parameter estimation.

But existing reviews focused on comparative analysis of analytical and meta-

heuristic approaches, analysis of models, and application of meta-heuristic

methods for model parameter extraction. Thus, lack a comprehensive analysis

on methods based on different objective function, assessment on

List of Symbols and Abbreviations: ABC, artificial bee colony; ABSO, artificial bee swarm optimization; ADEA, adaptive differential evolution algorithm; AIS, artificial immune system; BBO, biogeography based optimization; BFA, bacteria foraging algorithm; BMO, bird mating optimization; CBSA, backtracking search algorithm with competitive learning; CGBO, chaotic-GBO; COA, coyote optimization algorithm; CPSO, chaotic particle swarm optimization; CSA, crow search algorithm; CSO, cat swarm optimization; CSO, cuckoo search optimization; CWOA, chaotic whale optimization algorithm evolution; DDM, double diode model; DET, differential evolution technique; DPDE, directional permutation differential evolution algorithm; EJaya, enhanced Jaya; ELPSO, enhanced leader particle swarm optimization; EO, equilibrium optimizer; EO-Jaya, elite opposition-based Jaya; ER-WCA, evaporation rate based water cycle algorithm; FF, firefly; FPA, flower pollination algorithm; FPSO, flexible particle swarm optimization; GA, genetic algorithm; GCPSO, guaranteed convergence particle swarm optimization; GGHS, grouping-based global harmony search; GOBL, generalized opposition-based learning; GWO, grey wolf optimization; GWOCSA, grey wolf optimization and cuckoo search algorithm; HFAPS, hybrid firefly and pattern search; HSA, harmony search algorithm; IADE, improved adaptive DE; ICA, imperialist competitive algorithm; ICSO, improved cuckoo search optimization algorithm; IGHS, innovative global harmony search; IJaya, improved Jaya; ILSA, improved learning search optimization algorithm; ImSMA, improved version slime mould algorithm; ISCA, improvement sine cosine algorithm; ITLBO, improved teaching-learning-based optimization; MPSO, mutant particle swarm optimization; MPSO, mutant PSO with adaptive mutation strategy; NMSOLMFO, Nelder-Mead Moth Flame; ORcr-IJADE, onlooker-ranking-based mutation operator-improved adaptive differential; PGJaya, performance-guided Jaya; PS, pattern search; PSO, particle swarm optimization; PSOGWO, particle swarm optimization and grey wolf optimization; Rcr-IJADE, repaired adaptive differential evolution; RLWOA, refraction-learning-based whale optimization algorithm; RMSE, root mean square error; SA, simulated annealing; SDM, single diode model; SEDE, self-adaptive ensemble-based differential evolution; SFO, sunflower optimizer; SFS, stochastic fractal search; SMA, slime mould algorithm; SSA, salp swarm algorithm; TGA, tree growth algorithm; TLBO, teaching learning based optimization; TVACPSO, time-varying acceleration coefficients particle swarm optimization; WDO, wind-driven optimization; WOA, whale optimization algorithm.

Received: 8 February 2021 Revised: 5 August 2021 Accepted: 9 September 2021

DOI: 10.1002/2050-7038.13113

Int Trans Electr Energ Syst. 2021;31:e13113. wileyonlinelibrary.com/journal/etep © 2021 John Wiley & Sons Ltd. 1 of 72

https://doi.org/10.1002/2050-7038.13113

environmental conditions, and cumulative analysis on selective set of algo-

rithm based on efficiency. Therefore, this work reviews optimization algo-

rithms presented for parameter estimation focusing on (a) objective function

used, (b) modeling type, (c) algorithm employed for parameter extraction, and

(d) PV technology. Further, provides a comprehensive assessment on various

modules types used for validation, comparisons made with methods, advan-

tages and disadvantages associated with each method with respect to parame-

ter estimation platform, critical analysis on each method at STC, and varying

irradiance conditions. In addition, a critical evaluation on specific set of algo-

rithm based on objective function values is also carried out. Thus explores and

display the characteristics of various techniques related to PV cell modeling

and serve to be a single reference for researchers working in the field of PV

parameter estimation.

K E Y W O R D S

meta-heuristics methods, parameter estimation, PV cell modeling, solar PV

1 | INTRODUCTION

Preserving the last residues of the fossil fuel created thrust toward utilization of abundantly available renewable energy sources.1 Increased penetration and its continuous influence in the power sector is phenomenal and the most promising in creation of secure and sustainable energy.2 Among many renewable energy resources, solar photovoltaic (PV) made prodigious contribution toward sustainable power generation.3 This energy resource remains at an unprecedented height by generating 480 GW of power supplying 2.8% of the world's electrical demand approximately by the end of the year 2020.4

Albeit solar energy is abundant, and leads the way in forefront5; its growth is obstructed by factors such as partial shading,6 intermittent nature,7 high initial cost,8 and expensive storage requirement.9 Thus, precise modeling becomes obligatory and inevitable to predict the PV system performance before implementation.10 Moreover, the prophecy of PV panel working characteristics is pivotal in the design, simulation analysis, evaluation, and control of solar PV system.11

Further, modeling helps in understanding the working principle and operating characteristics of a solar PV system under various atmospheric conditions.12

However, limited by virtue of inherent data unavailability13; PV cell modeling approaches so far applied analytical,14 iterative,15 and meta-heuristic methods16 to model PV panel characteristics. Wherein, all the methods intend to rebuild the PV characteristics by identifying the missing unknown parameters.17 Modeling using analytical method is complex and lack efficiency as it involves additional equations.18,19 Likewise, iterative technique is bound to considerable computational complexity; since mathematical procedure for “n” iterative times are executed until the desired output is attained.20 Meanwhile, application of meta-heuristic algorithms via numerical extraction is popular as it suits for any PV cell/module types and operating conditions.21

Eventually, variety of meta-heuristic based parameter extraction techniques have been investigated so far.22 How- ever, existence of many algorithms have drawn attention toward assessment of each method based on its merits, demerits, suitability/ability to parameter estimation problem, and complexity involved. Hence, few authors reviewed the subject of PV model parameter estimation. For instance, in Reference 23 review on various meta-heuristic algo- rithms involved in identifying the parameters of single and double diode model (SDM and DDM) is expounded. A detailed comparative study between analytical and meta-heuristic approaches is presented.24 A synergetic review work on stochastic algorithms employed for evaluating one and two diode model parameters of PV and fault detection of a PV system is explained.25 However, the reviews mentioned has one or more of the following limitations, (a) Only works related to one and two diode model is discussed, (b) limited discussions are made concerning objective function values and the identified parameters, and (c) number of works considered for analysis is minimal and details pertinent to the suitability analysis of the optimization method for various PV module selected is found missing.26 Therefore,

2 of 72 VENKATESWARI AND RAJASEKAR

understanding the importance of parameter estimation techniques in PV cell efficiency enhancement, a detailed review on parameter estimation techniques is proposed in this article. The significant contributions made in this review article can be summarized as:

1. This work reviews optimization methods to a greater extent such that a collection of nearly 29 algorithms with its variants published till date has been studied.

2. Brief discussion on each algorithm highlighting its merits and demerits is presented and a detailed comparison table on recent published works is portrayed.

3. The review consolidates the different objective function used with emphasis on root mean square error (RMSE) objective function. Further, the best-suited algorithm for every case study is presented.

4. This article expounds a detailed survey on (a) modeling types, (b) algorithm employed for parameter extraction, (c) PV technology, and (d) type of panel used for research work.

5. Six case studies based on manufacturing technology and modeling at STC and various atmospheric conditions have been discussed.

6. To facilitate decision making for PV researchers involved in the Parameter estimation works, a discussion on PV materials, modeling, performance metrics, various algorithms, and its results have been analyzed and presented.

This review article is structured as follows: Section 1 presents an introduction. Followed by the introduction, an over- view of the solar cell and its I-V and P-V characteristics is expounded in Section 2. Section 3 presents a detailed descrip- tion of the modeling of solar PV. Section 4 provides information about the methods involved in parameter evaluation of solar PV and a detailed discussion on above-mentioned algorithms is provided in Section 5. To evaluate the results and effectiveness of each algorithm, comparative result analysis is performed in Section 6. Finally, in Section 7 conclusion and future work is presented.

2 | SOLAR PV AND ITS CHARACTERISTICS

The basic building block of a PV module is its solar cell; capable of generating electrical power in mow is connected in serial/parallel to form a module.27 For high power applications, these modules are further interconnected to form a PV array.28 The pictorial transformation of solar PV cell to a PV array is represented in Figure 1.

The major limitation of PV based power generation is its limited availability and dependency on factors such solar insolation, temperature, tilt angle, and the materials used.30 The primary being insolation and temperature greatly influences the amount of current generated and output voltage. For instance, irradiation controls the short circuit cur- rent delivered by the panel31; while temperature defines the open-circuit voltage.29 To imply its significance typical solar PV panel of Kotak 80 W V-I characteristics at different insolation and temperature is shown in Figure 2. From the

FIGURE 1 Formation of photovoltaic (PV) cell, module, and an array29

VENKATESWARI AND RAJASEKAR 3 of 72

characteristics curves, it is understood both these nature controlled parameters influence largely on PV performance. Hence, should be accounted during PV modeling.

2.1 | Solar cell materials on its performance

Having understood the importance of solar cells, rigorous research on its efficiency improvement led to the develop- ment of three tangible PV types.32 However, the generations they belong are defined based on the materials used.33 In each generation substantial improvement that fundamentally makes the solar cell compact, highly efficient,34 and com- mercially viable35 are introduced. The materials that correspond to first,36 second,37 and third21 generation solar cells are silicon,38 Cd Te,39 and nanocrystals organic40 polymer materials, respectively.41 The solar cell material classification based on manufacturing technology is depicted in Figure 3.

It is noteworthy to mention that more than 90% of present solar cells are silicon-based first-generation type with efficiency of 29%43; wherein the conversion efficiency of Single-crystalline PV panel is 14% to 17.5%43 and of poly- crystalline solar cell vary between 12% and 14%.43 Polycrystalline solar cells are economical, stronger compared to monocrystalline type. On the other hand, the thin-film cells are equally good and popular use CIGS and Cd Te material holding a higher efficiency of approximately 9% to 12%.43

Amorphous silicon type solar cell exhibit 40 times absorption capacity than monocrystalline cell and also does not require high temperature for its manufacturing. Nonetheless, its efficiency is 5% to 7% still poorer than polycrystalline type.43 Similarly, the contribution of a third-generation solar cell comprising DSSC, nano, polymer, and perovskite in PV growth is steadily increasing.44 These third-generation solar cells show increased efficiency at a reduced cost. Even

FIGURE 2 I-V curves of solar photovoltaic (PV) panel under varying irradiance at constant temperature and vice versa

Silicon based

Thin films cells

Multi layer cells

Organic, polymer, nano materials, perovskite, DSSCs

Mono-crystalline poly-crystalline

Copper Indium Gallium Selenide (CIGS) cell, Cadmium Telluride (CdTe)Cell, Amorphous silicon

PV growth

FIGURE 3 Generations of photovoltaic (PV) growth42

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though the DSSC is economical, the sunlight absorption capability of this type of cell is feeble45; while the complexity in mass production of nano cells is elevated.25 Only perovskite-type solar cell among the third generation is promis- ing.46 The efficiency chart of various solar cell materials types is illustrated in Figure 4.

2.2 | Modeling methods of solar PV

Generally, a solar PV cell is modeled using electrical equivalent circuit that ideally comprises of diode, resistors, and a current source. Because of the nonlinearity present, several PV cell modelling methods have evolved in recent past. The major classification of PV cell models are one diode,47 two diode,48 and three diode model.49 The number of diodes pre- sent in the model determines the I-V curve prediction accuracy.

Conventionally, ideal single diode that consists of a diode in parallel to the current source is used.50 This ideal equivalent circuit is later modified with introduction of series resistor (RS)

51 and shunt resistance (RP) to take into account the losses that occur due to the metallic junction and carrier recombination, respectively.52 The model with resistors RS, RP included is called SDM.

53 Due to its simplicity, accuracy, and reliability, SDM are commonly used in practice for modeling and simulation purpose.54 For certain cases, the performance of a SDM is found to be satisfactory, even after neglecting recombination losses existing in the diode.55 However, for accurate curve reproduction, inclusion of recombination losses is helpful hence lead to the development of DDMs.4 Further, inclusion of another diode improved its modeling performance and accuracy even at low irradiance conditions but at the cost of increased com- plexity.56 Similarly, evolution of modeling leads to the development of three diode model as well to enhance accuracy.57

The equivalent circuit model, its design equations and the particulars of unknown parameters are showed in Table 1 (Figure 5). The table also indicates that as the number of diodes increases, the model parameters to be estimated also increases thereby increasing the complexity.59

3 | PV MODULE PARAMETER ESTIMATION

Apart from model selection, another important step that improves the cell modeling of solar PV is its unknown parame- ter estimation. In the process of PV modeling, accurate estimation of every unknown parameter is equally important. For better understanding, the various process involved in PV modeling and its parameter estimation methods is shown in Figure 6. One of the simplest methods to determine unknown parameters of solar PV is by applying specific operat- ing conditions, and solve using trial and hit process. Undoubtedly, this technique produces the lowest efficiency as the predicted values vary largely.

Two commonly followed procedure in unknown parameter determination is (a) analytical60 and (b) meta-heuristic optimization61 methods. In the case of an analytical method, a nonlinear solar PV characteristic is attained by applying different operating condition together with available manufacturer datasheet values.62 While meta-heuristic method fol- lows curve fit procedure to predict the IV curve63; wherein every data point on the IV curve predicted is matched with the actual values.

FIGURE 4 Efficiency of various photovoltaic (PV) materials43

VENKATESWARI AND RAJASEKAR 5 of 72

T A B L E

1 M o d el in g m et h o d s o f so la r p h o to vo lt ai c

S .

n o .

S in g le

d io d e m o d el

(S D M )

D o u b le

d io d e m o d el

(D D M )

T ri p le

d io d e m o d el

(T D M )

1 SD

M is co m p o se d o f a d io d e an

d tw

o re si st o rs

co n n ec te d

in se ri es

an d p ar al le l to

th e d io d e to

co m p en

sa te

th e

lo ss es

5 8

D D M

h as

co m p o se d tw

o d io d e an

d tw

o re si st o rs

co n n ec te d in

se ri es

an d p ar al le l to

th e d io d e to

co m p en

sa te

th e lo ss es

5 4

T D M

is co m p o se d o f th re e d io d e an

d tw

o re si st o rs

co n n ec te d in

se ri es

an d p ar al le l to

th e d io d e to

co m p en

sa te

th e lo ss es .5 6

2

(a )

(b )

(c )

3 I P

V ¼ I p

h � I o � I s h

I P V ¼ I p

h � I P

V ex p

V P V þR

sI P V

n V

t

h i �

1 h

i I P

V ¼ I p

h � I o

1 � I o

2 � I s h

I P V ¼ I p

h � I o

1 ex p

q V

P V þR

sI P V

½ �

n 1 V

t

h i �

1 h

i �I

o 2 ex p

q V

P V þR

sI P V

½ �

n 2 V

t

h i �

1 h

i � V

P V þR

sI P V

R sh

h i

I P V ¼ I L � I o

1 � I o

2 � I o

3 � I s h

I P V ¼ I p

h � I o

1 ex p

q V

P V þR

sI P V

½ �

n 1 V

t

h i �

1 h

i �I

o 2 ex p

q V

P V þR

s I P

V ½

� n 2 V

t

h i �

1 h

i �I

o 3 ex p

q V

P V þR

s I P

V ½

� n 3 V

t

h i �

1 h

i � V

P V þR

s I P

V R sh

h i

N ot e: I o ,I

o 1 ,I

o 2 ,I

o 3 , re ve rs e sa tu ra ti o n cu rr en

ts ; I p

h , p h as e cu rr en

t; I P

V an

d V

P V , P V cu rr en

t an

d vo lt ag e; R s an

d R sh , se ri es

an d sh u t re si st an

ce ; n , id ea li ty

fa ct o r; V

t, th er m al

vo lt ag e; q , el ec tr o n ch

ar ge .

6 of 72 VENKATESWARI AND RAJASEKAR

Apart from model selection, another important step that improves the cell modeling of solar PV is its unknown parameter estimation.64 In the process of PV modeling, accurate estimation of every unknown parameter is equally important.65 For better understanding, the various process involved in PV modeling and its parameter estimation methods is shown in Figure 6. One of the simplest methods to determine unknown parameters of solar PV is by apply- ing specific operating conditions, and solve using trial and hit process. Undoubtedly, this technique produces the lowest efficiency as the predicted values vary largely.36 Two commonly followed procedure in unknown parameter determina- tion is (a) analytical and (b) meta-heuristic optimization methods. In the case of an analytical method, a nonlinear solar PV characteristic is attained by applying different operating condition together with available manufacturer datasheet values. While meta-heuristic method follows curve fit procedure to predict the IV curve; wherein every data point on the IV curve predicted is matched with the actual values.

For both the cases, to model PV cell, maker's specific data like (a) current at maximum power (Imp), (b) Voltage at maximum power (Vmp), (c) Short circuit current (Isc), and (d) Open circuit voltage (Voc) are necessary. Besides, the other values required for modeling an efficient PV solar model are (a) Diode saturation current (Io), (b) PV current (Ipv), (c) diode ideality factor (A), (d) series resistance (Rs), and (e) parallel resistance (RP).

66 Undoubtedly these data are unknown and also unavailable in the manufacturer's spec sheet. Thus, for obtaining an exact I-V curve through soft- ware simulation requires information about these unknown parameters.58 Further, to lessen the computation burden

FIGURE 5 Modeling of solar photovoltaic (PV).23 (A) Equivalent circuit of single diode model (SDM),58 (B) equivalent circuit of double diode model (DDM),54 and (C) equivalent circuit of triple diode model (TDM)56

FIGURE 6 Process involved in photovoltaic modeling and its parameter estimation

VENKATESWARI AND RAJASEKAR 7 of 72

and to enhance the performance, the meta-heuristic algorithms are employed.46 Even these methods can be combined with analytical techniques for superior performance.

3.1 | Meta-heuristic method-based solar PV parameter estimation

Existence of several unknown parameters, difficulty in mathematical formulation, involvement of large number of mathematical equations, and use of operating conditions such as Voc, Isc, Vmpp, and Impp restricts the use of analytical methods for PV modelling.59 Further, solving such equations is complex, consumes quality time, and requires more attempts to find accurate result.65

Hence, as an alternative to overcome the shortcomings of an analytical method, meta-heuristic optimization methods are used for accurate PV parameter extraction.19 Moreover, it is observed that the obtained result matches well with the actual characteristics curve of solar PV with minimal error.24 Further, any dynamic variation either in insola- tion and temperature can also be reproduced.35 Hence, meta-heuristic algorithms are desirable in PV cell modeling compared to analytical methods.23 Generally, they are categorized into (a) evolution based, (b) nature-based, (c) human-based, and (d) bio-inspired techniques. Categorization of the different method is illustrated in Figure 7.

3.2 | Performance metrics—an overview

Performance metrics defined play an integral role in a method success since it decides the overall quality of the predic- tion.70 The various metrics defined so far for optimization techniques are Root Mean Square Error (RMSE),71 Mean Square Error (MSE),72 Mean Bias Error (MBE),73 Absolute Error (AE),74 Individual Absolute Error (IAE),75 Relative Error (RE),76 and Sum of Squared Error (SSE).77 Among all, RMSE is widely used as objective function to determine the efficiency of a method.78 Various other functions used to measure the quality of meta-heuristic methods output are listed in Table 2.

4 | VARIOUS META-HEURISTIC METHODS FOR PV PARAMETER ESTIMATION

As highlighted in the previous discussion, meta-heuristic methods are the most preferred choice for PV parameter esti- mation. Numerous methods were applied for improved PV characteristics prediction. Among many the most prominent 29 parameter estimation algorithms covering evolutionary-based DE, GA algorithms, Nature-inspired based PS, SA, WDO, ERWCA, FPA, Bio-inspired based PSO, BFA, ABC, CSO, FF, CS, GWO, BMO, CSA, WOA, SSA, Elephant water search, Shark Smell, and human-based HS, ICA, SA, Jaya, AIS, BBO algorithms are selected and analyzed further. An intensive comparative analysis based on the efficiency of all meta-heuristic algorithms to find the best meta-heuristic algorithm (MA) in estimating the parameters of the PV panel is performed.

This efficiency analysis on each algorithm is performed by considering the RMSE factor; wherein the algorithm with the lowest RMSE value is considered as more effective in parameter assessment of solar PV.79 In all the cases, the parameters and RMSE values obtained by all the algorithms at STC is alone considered.80 The technology utilized for the manufacturing of solar is also given due importance and considered as one of the main factors in this investigation. The commonly used technologies were monocrystalline81 based SM55, SW245, SP190, STM6-40/36, 1STH-235-WH, SQ85, HIT-215, S75, thin film80 based 752 GaAs, ST50, and polycrystalline82 based KS20T, kC200GT, RTC France, S36, SP70, ST36, RSM50, SM255, PWP201, Sharp ND-R250A5, SX3200N, KD210GH-2PU, and ST40 were also considered during the analysis. The various optimization algorithms involved in estimating the parameters are explained as follows:

4.1 | Pattern search algorithm

Pattern search (PS) algorithm developed by Hooke and Jeeves in the year of 1961 is a numerical based MA employed for solving the optimization problems.82 The two main steps involved in this algorithm are (a) exploratory search and

8 of 72 VENKATESWARI AND RAJASEKAR

(b) PS. In case of exploratory search, the initial search starts by considering “n” random point termed as Base Point (BP) and proceeds further search by forming a mesh with “2n” points covering “2n” coordinate directions. Meanwhile, it also monitors the solution at each search step.83 In PS, if the search process is progressive; the BP is replaced by the new value in the same direction by considering the previous BP.83 The process is mathematically expressed as

XkBp ¼ XkBp þ XkBp �Xk�1Bp h i

ð1Þ

If the current move is successful, then the perturbation is done with the new “XBp+k,” and if the move is a failure, then the pattern exploration proceeds with old “XBp

k.”

Wind optimization algorithm (WOA)

Evaporation rate based water Cycle algorithm (ERWCA)

Simulated annealing (SA)

Pattern search (PS)

Flower pollination algorithm (FPA)

Piece-wise approximation

Special transformation

theory

Particle swarm optimization (PSO)

Bacterial foraging optimization (BFO)

Artificial bee colony (ABC)

Cat swarm optimization (CSO)

Cuckoo algorithm (CA)

Whale optimization algorithm (WOA)

Crow search algorithm (CSA)

Salp swarm algorithm (SSA)

Grey wolf optimization (GWO)

Bird mating optimization (BMO)

Differential evolution (DE)

Genetic algorithm (GA)

Artificial i mmune system (AIS)

Harmony search (HS)

Imperialistic competitive algorithm (ICA)

Teaching learning based optimization (TLBO)

Biogeography based optimization (BBO)

Newton- raphson

Least square

Gauss seidal

A n

al yt

ic al

m et

h od

s

M e tah

eu r istic

M eth

od s

M etah

eu ristic

m eth

od s

Evo lutio n based

Nature based

Human based

Bio - Ins pire d

JAYA algorithm

Brain storming algorithm

Gravitational search algorithm

Artificial bee swarm optimization

Fire fly (FF)

Shark smell optimization(SSO)

Elephant swarm water search algorithm

FIGURE 7 Various algorithms in identifying the parameters of solar photovoltaic18,23-25,51,67-69

VENKATESWARI AND RAJASEKAR 9 of 72

4.2 | Simulated annealing algorithm

It is a probabilistic search technique that adopts the metallurgical annealing process involved in producing high quality defect-less steel.84 The two main steps involved in the heat treatment process are (a) increasing the temperature near to the melting point and (b) process of cooling. Simulated Annealing (SA) methods treat the cost function and control parameter for the optimization as the energy state and temperature of the metal. Since, the rate of cooling is the decid- ing factor in obtaining the optimal solution that is, lesser the cooling rate, lesser the acceptance of the worst solution (solution with poor fitness).85 The basic equation involved in SA algorithm is

Tnew ¼ s * Told ð2Þ

where “Told” and “Tnew” are old and new temperature, “s” is the cooling rate.

4.3 | Genetic algorithm

Genetic algorithm (GA) optimization proposed by John Holland in the year 1970is a nature-enthused optimization technique inspired by the biological evolution of humans.86 The keystone steps involved in this algorithm are selection, crossover, and mutation. Thus through the process of reproduction new individuals randomly selected from existing population are allowed in creation of healthy succeeding generation. The steps involved in GA are illustrated in Figure 8.87

TABLE 2 Tabulation of performance metrics

S. no. Performance metrics Formulae

1. Root Mean Square Error (RMSE)

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPN i¼0

Iest,j�Im,j

� �2 N

vuut 2. Absolute Error

AE ¼ PN i¼0

Iest,j �Im,j ����

���� 3. Relative Error RE ¼ Im,j�Iest,jIest,j 4. Mean Absolute Error

MAE ¼ PN i¼0

Im,j�Iest,j N

5. Normalized Mean Absolute Error (NMAE) NMAE ¼ PN

i¼0 Im,j�Iest,j=Iest,j

N

6. Mean Bias Error (MBE) MBE ¼ Im,j�Iest,jN 7. Individual Absolute Error (IAE), IAE ¼ Imeasured �Iestimatedj j

Note: Im,j, measured experimental current of jth pair of IV data; Iest,j, estimated current of PV; Imeasured&Iestimated, experimentally measured and estimated current; N, number of data points in I-V characteristics.

FIGURE 8 Steps involved in genetic algorithm86

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4.4 | Differential evolution algorithm

Differential evolution (DE) algorithm is proposed by David. E. Goldberg in 1989. It derives evolutionary process in find- ing optimal solution for a given problem.88 It follows four main steps such as initialization, mutation, crossover, and selection in finding the optimal solution for a nonlinear optimization problem and is shown in Figure 9.90 Further workflow diagram of DE is shown in Figure 10.

4.4.1 | Adaptive differential evolution algorithm

Optimal parameter setting in DE is difficult; hence to overcome this drawback an adaptive DE algorithm (ADEA) is introduced.92 In ADEA, the constraints like population, mutation, and crossover rates are efficiently controlled by the parameters successfully.93 The population diversity decides the convergence rate and to deliver optimum result flag (Fu), the parameter is included.

94

Fu ¼ 1 if αkj ≥ ML 0 otherwise

( ) ð3Þ

Mutation factor adaptation is given as

Fi ¼ randSi PkF2,0:1 � �

ð4Þ

Cross over rate adaptation is given as,

RCi ¼ randni PkRC2,0:1 � �

ð5Þ

4.5 | Particle swarm optimization

A nature-inspired technique developed by Dr. Eberhart and Dr. Kennedy in 1995 based on the flocking and schooling nature of the birds and fish.95 It is a known fact that the group members always take the lead of anyone among them in the population which is closer to a food source (optimal solution).96 In the same way, each member in particle swarm optimization (PSO) representing a potential solution for an optimization problem takes the lead of one best element closer to the optimal solution.97 The nature of particles in a swarm in finding the food source is incorporated in this

FIGURE 9 Steps involved in differential evolution89

VENKATESWARI AND RAJASEKAR 11 of 72

algorithm to extract SDM and DDM parameters.98 The particle position and velocity can be obtained by utilizing the following equations

Zi t þ1ð Þ ¼ Zi tð ÞþVi t þ1ð Þ Vi tð Þ ¼ Vi t þ1ð Þþa1r1 Ibest tð Þ�Zi t �1ð Þð Þþa2r2 gbest tð Þ�Zi t �1ð Þð Þ

� ð6Þ

where “i” is the particle position at time instant “t,” “v” corresponds velocity “a1” and “a2” is the acceleration coeffi- cient, “r1” and “r2” random vectors. The workflow process involved in PSO is illustrated in Figure 11.

4.6 | Artificial immune system

Artificial immune system (AIS) incorporate human intelligence in solving real-time problem.99 Immune network theory devel- oped by Jerne in 1974 identified that a group of B cells are responsible for working of the entire immune system.100 This algorithm is developed based on special features of immune system including learning and memory in solving complex problems.101

FIGURE 10 Differential evolution algorithm91

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4.7 | Harmony search algorithm

The harmony search algorithm (HAS) is based on the concept of musical harmony, a process in which all the instruments sounds are synchronized making it pleasant to hear.102 In this context, various instruments

FIGURE 11 Particle swarm optimization (PSO)98 algorithm

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producing sound are considered as the population and the outcome pleasant music with harmony is consid- ered as the global optimum solution. A musician always finds the best harmony by comparing with audio aes- thetic quality (fitness function).103 Similarly, for any real-time problem best-optimized solution needs to be found by considering the available objectives and limitations. The steps followed for finding the optimized solution are.104

Step 1: Provide the inputs required for the optimization problem such as harmony memory size (HMS), number of swarms, equality and inequality constraints, number of iterations, harmony memory considering rate (HMCR), pitch adjusting rate (PAR), and maximum and minimum value of bandwidth.

Step 2: Make ready or initialize the selected harmony memory. Step 3: Update the harmony memory with the best fitness function by replacing the worst fitness function. Step 4: Check if the optimal solution is achieved for the given problem else repeat the above process until the best

solution with a minimum value of an objective function is achieved.

4.8 | Bacteria foraging algorithm

Bacteria foraging algorithm (BFA) is a bio-inspired technique developed by Kevin. M. Passino.105 Bacterium living nature is designed as an optimization technique and is employed for extracting the bounds of SDM and DDM models.106 The foraging approach of the bacteria undergoes four main stages (a) chemotaxis, (b) swarming, (c) reproduction, and (d) removal and dispersal.107 The movement of the bacterium is represen- ted in Figure 12.

4.9 | Artificial bee colony algorithm

Artificial bee colony (ABC) algorithm is a MA developed by using the decision-making nature of honey bees. ABC proved its versatility in attaining accuracy,109 obtaining minimal fitness function.110 The ABC is composed of three dis- tinct sets of bees and they are: (a) employed, (b) onlooker, and (c) scouts. Each group of bees has a distinct objective in the parameter estimation process.111 The employer bees are employed to gather data related to the food source and its exact location such as its distance and direction from the hive. The onlooker's bees are responsible for choosing the best food source. These characteristics are deployed in estimating the parameters of a solar module. The workflow process in ABSO is illustrated in Figure 13.

4.10 | Artificial bee swarm optimization algorithm

The artificial bee swarm optimization (ABSO) algorithm incorporates the concept of PSO and ABC algorithm to aug- ment the performance in parameter estimation of solar PV.112 Similar to the ABC algorithm, the employee bees, scout,

FIGURE 12 Movement of a bacterium108

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and onlooker bees are employed for finding the optimal solution. The only difference to the previous ABC procedure is, in ABSO a fewer number of onlooker bees are as treated as elite bees in tracking the best food source.113 The workflow process in ABSO is illustrated in Figure 14.

4.11 | Imperialist competitive algorithm

In 2007, Gargari developed imperialist competitive algorithm (ICA) inspired by the concepts of imperialistic competi- tion procedures. It is classified as two groups: the initial one named as imperialists and colonies. Generally, the colonies in the initial population share imperialists based on the powers.115 Through the process of imperialistic competition, the more powerful empire tends to increases power and less powerful tends to crumble. This algorithm aims in building a powerful empire.116 The procedure followed in ICA is incorporated in estimating the parameters of solar PV. The flow chart for ICA is depicted in Figure 15.

4.12 | Cat swarm optimization

Cat swarm optimization (CSO) is a nature-inspired algorithm that imitates the behavior of a group of cats. The living nature of the cats are observed and is incorporated in finding the best solution for an optimization problem.117 Nor- mally the cats will be operating in two modes while finding its target namely: (a) seeking mode and (b) tracking mode. In seeking mode, the cat changes its position from the original state to next at a very low speed by cautiously observing

FIGURE 13 Artificial bee swarm optimization (ABSO) algorithm114

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the surrounding environment. Whereas, in tracking mode, the cat moves very fast in the process of searching and reaching its target.118

Initially, the number of cats and the search space of N-dimension is determined. It should be noted that each cat has its own and distinct movement, position, and velocity during the search process. Then, this process of tracking is continued until the best solution has arrived. Here, the Movement of each cat and its position is considered as a solu- tion for an optimization problem. Similarly, the positions of all the cats are observed and the cat with the best fitness (position) value for the given objective function is considered as an optimal solution. The flow chart for CSO is depicted in Figure 16.

4.13 | Biogeography based optimization

Biogeography based optimization (BBO) a MA proposed for solving multi-objective optimization problems. BBO algo- rithm was developed after getting inspired by observing nature's way of organizing and allocating the geographical

FIGURE 14 Artificial bee swarm optimization (ABSO) algorithm114

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region for all the living species like plants and animals in various locations of the earth. The concept of species arrival and its exit from an island is mathematically modeled and incorporated in this algorithm to find the optimal solu- tion.119 Every island has its Habitat Suitability Index (HSI) that defines whether the island is suitable for habituation. Similarly, each variable in the island has an individual suitability index variable (SIV). The island with high HIS is con- sidered as the optimal solution. The HIS is always varying because the variables always tend to move from an island with high HSI value toward the island with low HIS. The rate immigration (μs) and emigration (λs) of an “s

th” variable to and from an island and of an island is mathematically expressed as follows120:

λs ¼ 1� s n

μs ¼ E

s n

9>= >; ð7Þ

FIGURE 15 Imperialist competitive algorithm116

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where “E” and “I” are the highest immigration and emigration rate of a variable exists in an island and always takes a value of 1. “s” and “n” are the number of possible species and solutions. Further, the “λ” defines the SIV of a variable while the “μs” chooses the solution to be migrated in the process.

4.14 | FireFly algorithm

FireFly (FF) algorithm proposed by Yang is a bio-inspired algorithm that works using illumination intensity of fireflies following a random search in acquiring the optimal solution.121 Each FF has the capability of creating flashlight by a

FIGURE 16 Cat swarm optimization algorithm118

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biochemical reaction that in turn induce bioluminescence in the dark. Thereby, the work process is carried out by con- sidering the brightness of the fireflies as an objective function.122 It is because the location of the FF is altered based on the light intensity of individual fireflies in a series of steps. The procedural stages followed in the FF method is explained below:

1. Force of attraction depends on the brightness irrespective of their sex 2. In the nonappearance of flies with higher illumination, the flies may unsystematically. 3. Defining the brightness of a fly is based on its objective function.78

4.15 | Cuckoo search optimization algorithm

Cuckoo search is a bio-inspired algorithm proposed using the parasitic breeding concept of cuckoo birds.123 The cleverness of cuckoo in multiplying its procreation opportunity is applied in finding the optimal solution for the optimization problems.124One of the promising method in extracting the parameters at a higher accuracy rate espe- cially under various operating constraints.125 CSA incorporating Lévy walk allows it to explore the search space effectively and also making it as an efficient method.125 Even though effective in exploration, and finding global optima, the number tuning parameters is four which leads to a tedious tuning process. Further, random nature of levy walk may lead the method to out of bound parameter limits that totally reduces the accuracy of the obtained solutions.126

4.16 | Wind driven optimization

Wind-driven optimization (WDO), newly developed nature enthused optimization technique established by Zikri Bayraktar for electromagnetic application. It is a technique depending on atmospheric motion utilized for multi- dimensional problems. The idea is based on the movement of air particles from high to low-pressure area to balance the air pressure and the same is utilized in evaluating the solar PV parameters.127 The workflow process of WDO is illustrated on Figure 17.

4.17 | Flower pollination algorithm

Flower pollination algorithm (FPA) is a population-based nature-inspired algorithm developed by Xin-She Yang for solving the optimization problems. The logic behind the flower pollination process is incorporated in devel- oping this algorithm. Naturally, pollination is the process of transferring the pollen from one to another plant for reproduction and pollinators such as birds, insects, honeybees, wind, and so on128 perform it. The pollination process may occur between the same species or between different species of plants. If the pollination occurs between same species of plants, then it is called self or biotic pollination else it is called cross or abiotic pollina- tion. Irrespective of the type, the pollination is a vital factor in process of optimization of plants species in terms of both number and fitness value.129 The main steps involved in developing the FPA is explained in a flow chart as shown in Figure 18:

4.18 | Teaching learning based optimization

The teaching-learning based optimization (TLBO) algorithm uses the teaching and learning capability of a teacher and student in a study hall environment. The teaching-learning process is a continuous repetitive procedure of transferring knowledge between the teacher and students. The proposed algorithm is composed of two phases namely teaching and learning phase.130 In the teaching phase, the students acquire knowledge from the teacher whereas, in the case of a stu- dent's phase, the students learn and gain knowledge by interacting with other students.131 The workflow process of TLBO algorithm is illustrated in Figure 19.

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4.19 | Grey wolf optimization

The concept behind the grey wolf optimization (GWO) algorithm is originated from the living and hunting nature of the grey wolfs. The social hierarchical order and the hunting mechanism are the two factors taken into account for developing the mathematical model for the GWO algorithm. The pecking order of the grey wolfs is mathematically modeled to find the best solution for an optimization problem. Based on the tropic levels of the food chain, the grey wolfs are categorized into four groups132: alpha, beta, delta, and omega. The alpha type grey wolfs occupies the topmost position in the food chain.

FIGURE 17 Wind-driven optimization (WDO) algorithm127

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The beta group takes the next position and receives orders from the alplha group grey wolf and completes the task. The omega group GW takes the lowest position and acts as a scapegoat. Another factor considered is the hunting nature of the wolf and it is explained as follows: (a) initially, the grey wolfs concentrates on finding the target, (b) Then, it sur- rounds the target, (c) and finally, it hunts the target.133 The workflow process of GWO is illustrated in Figure 20 authors in Reference 136 utilized GWO to extract the parameters of solar PV.

4.20 | Bird mating optimization

Bird mating optimization (BMO) is a bio-inspired algorithm proposed using the parasitic breeding approach concept of birds. The cleverness of birds in multiplying its reproduction opportunity is applied in finding the optimal solution for the optimization problems. In general, the birds are classified into four categories based on the nature of mating namely: (a). polyandrous, (b) monogamous, (c), polygynous, and (d) promiscuous.134

The birds come under monogamous always select one best female bird by following a roulette wheel probability for reproduction while in case of polygynous, the birds perform a random mating with a greater number of female birds to produce a greater number of offspring with the best fitness. The polyandrous is the female birds where it will have a

FIGURE 18 Flower pollination algorithm128,129

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relationship with more number of male birds. Promiscuous birds are the offspring that replaces the birds with poor fit- ness by using the chaotic sequence mating pattern.

Each gene of the new brood is given using135:

Brood ¼ Birdþ w*r* favouritebird�birdð Þð Þ ð8Þ

where “r” is a random number ranges between [0, 1] and “w” is the inertia weight. The author in [171] used BMO in identifying the parameters that are used for modeling the single diode solar PV.

FIGURE 19 Teaching-learning-based optimization (TLBO) algorithm131

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4.21 | Crow search algorithm

The crows are the most intelligent birds with the largest brain in relative to its body size. It sharply remembers the faces like unfriendly member approaches.137 Based on the intelligence of crow, the crow search algorithm (CSA) is developed and this new optimization technique aims at finding an optimal solution from available solutions.138 The calculation proce- dure involved in this population-based algorithm is simple and easier to implement for various applications. It considers the specific position of “N” crow present in a general hunt space along with the position of each crow's memory.

4.22 | Whale optimization algorithm

The foraging nature of the whale is incorporated in finding a solution for optimization problems. To find the potential solution in a search space, the whale optimization algorithm (WOA) uses the prey searching strategy of whale and it is explained as follows: initially, the whale surrounds the food source.139

FIGURE 20 Grey wolf optimization algorithm134,135

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Then it uses a bubble net attacking method for the exploitation of the food source. Further, the exploration is con- tinued in the wider search space if the obtained solution is not a global solution.140 The foraging nature and hunting technique of whale is in depicted in Figure 21. The bubble-net hunting technique of whale141 is shown in Figure 22.

4.23 | Salp swarm algorithm

Salp swarm algorithm (SSA) is a population-based intelligent algorithm proposed by Mirjalili et al to solve multi- objective problems. Salp is a kind of water animal belongs to Salpidae family. SSA is based on the swarming behavior of slaps and their social interaction.142 In the process of finding the solution for an optimization problem, all the slaps are combined to form a salp chain as shown Figure 23.

The salp chains are mathematically divided into two groups consisting of a head salp and follower slaps. The leader salp is always positioned at the starting of the chain and leads all the follower in the process of tracking food source. During the process of search, the position of salp is defined in a d-dimensional search space, where “d” is the number of variables for a given problem. The food source “F” is the swarm's target. The food searching nature of salp is designed as an algorithm and employed to evaluate the parameters of solar PV.

4.24 | Evaporation rate based water cycle algorithm

The authors in Reference 143 developed the evaporation rate based water cycle algorithm (ER-WCA) to evaluate the parameters used for modeling the SDMs and DDMs. The ERWCA is the extension of the WCA where the evaporation rate is incorporated for avoiding the premature convergence and better exploration in finding the solution with the best fitness value. ER-WCA, an improved version of watercycle algorithm (WCA) developed in 2012 incorporates nature of water flow and evaporation rate of the streams and rivers that ultimately enhance the exploration and exploitation

FIGURE 21 Foraging nature of the whale

FIGURE 22 Bubble net hunting technique of whale141

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rate.144 The concept of water reaching sea using its variance is employed solving the real-time problems and delivers significant performance compared to GA, ACO, ABC, and so on.144

4.25 | Jaya algorithm

Jaya is a MA that is used for solving the constrained problems without using the hyper parameters. Jaya algorithm is flexible since requires only two parameters for its operation namely population size and the number of generation. Hence, the complexity in tuning the parameters is less.145 Albeit improper tuning of these two parameters increases the computational burden and leads to premature convergence.145

4.26 | Coyote optimization algorithm

Inspired by the living nature of the canis latran class, the coyote optimization algorithm (COA) was developed. This algorithm is similar to GWO, but COA uses the social behavior of the coyotes, rather than using its hunting nature. The analogy behind this concept is: each coyote in the population is considered a potential solution, and their behavior is considered as a cost. Dur- ing optimization, it also considers the factors like environmental conditions, cultural difference among their groups, birth and death rate.76 A complete summary of the works done by various authors on various algorithm is provided in the Table 3.

4.27 | Other algorithms

The authors in Reference 179 used evolution shuffled complex algorithm enhanced by opposition-based learning strat- egy (ESCE-OBL) to estimate the solar modules parameters to overcome the premature convergence problem of the con- ventional shuffled complex evolution algorithm (SCE), The optimal performance of ESCE-OBL method is found after implementing it to R.T.C France and Photowatt-PWP201with minimized RMSE of 9.86E � 04 and 0.02425. To enhance the performance of the PV module, the authors in Reference 180 combined simplified swarm optimization (SSO) and Nelder-Mead simplex (NMS) algorithms. The developed algorithm is employed for both SDM and DDM and its robust- ness is analyzed by comparing it with the hybrid ABC and Nelder-Mead simplex (EHA-NMS) algorithm in terms of RMSE. The best RMSE obtained by SSO and (EHA-NMS) for SDM and DDM are 0.000986, 0.000986, and 0.0009824848518, 0.0009824848518, respectively. The results show that SSSO has a better ability to producing the lowest RMSE and also a more suitable technique for parameter extraction.

An author in Reference 181 proposed modified simplified swarm optimization (MSSO) technique in this study for evaluating the parameters of SDM and DDM of the solar PV. MSSO is the improved version of SSO that overcomes the

FIGURE 23 Salp chain formation in the process of food search142

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TABLE 3 Review on various research works based on meta-heuristic algorithms

References Remarks

Pattern search algorithm 84 Implemented a pattern search for PV parameter optimization in case of SDM and DDM. The developed method conquers

the premature convergence and achieves least RMSE results of 1.18e � 2. Simulated annealing 146 It is important to note that, SA method itself suffer from premature convergence problem, therefore integrated with PSO

method for better performance. This hybrid particle swarm optimization and simulated annealing combination (HPSOSA) reach RMSE of 7.7301e � 4 and 15.18e � 4 value for single and double diode model based parameters extraction, respectively.

37 Incorporated metallurgical annealing process for determining the parameters involved in single and double diode modeling of a solar module. To check the efficacy of the developed model, it is tested for two commercial silicon and polycrystalline solar cells subjected to insolation and temperature of 1000 w/m2 and 35�C and arrived minimum RMSE of 0.0017 and 0.0026, respectively.

Genetic algorithm 147 Genetic algorithm is applied for three distinct PV modules such as mono-crystalline (HIT-215), multi-crystalline

(KC200GT), and thin-film (ST40) to determine its usefulness in parameter estimation for SDM and DDM. The effects of temperature and insolation on the PV performance are also studied. Minimal difference between the simulated value and the manufacturer's datasheet values is found having absolute error value of 0.016615, 0.0152, and 0.0094 for mono, thin film, and multicrystaline based panels, respectively.

148 Used three well-recognized meta heuristic algorithms like GA, PSO, and DE to evaluate the parameter extraction of dye- sensitized solar cells (DSSC). The author attempted to find a suitable algorithm for the given DSSCs with enhanced accuracy. After employing the above-mentioned algorithms, the RMSEs arrived via GA, PSO, and DE were 2.6965 � 10�6, 3.1539 � 10�6, and 2.6957 � 10�6. Furthermore, the efficiency of accurate parameter determination for the PV modules using evolutionary algorithms is also studied by adding a random noise. The results show PSO a better convergence speed, noise-resistant, and usefulness in parameter extraction.

Differential evolution algorithm 91 Differential evolution (DE) algorithm for extracting the “RS, RP, a” parameters of SDM is carried out in Reference 91. The

obtained results were compared with the RS model and parameters are identified for commercial solar cells such as S75, ST40, and SM55.

92 To improve DE performance, an improved adaptive DE (IADE) for PV parameter extraction of SDM is proposed. IADE is the extension of the DE algorithm and automatically updates the two control parameters used in conventional DE. The PSO method with capability of locating global optimum is combined with binary constraints to form a new algorithm for enhanced performance. The parameters attained were compared with other algorithms and it is proved to be effective in the estimation of parameters of solar module

93 Rcr-IJADE is developed by incorporating crossover rate repairing technique and ranking-based mutation in the conventional JADE algorithm and implemented for SDM and DDM. Performance analysis is done by comparing the proposed algorithm with other algorithms and the results prove that Rcr-IJADE is an unfailing method in parameter extraction. The RMSE obtained for SDM with Newton, CPSO, SA, PS, and Rcr-IJADE are 0.7805, 3.5E � 3, 2.7E � 3, 1.18E � 2, and 2.425E � 3. The RMSE obtained for DDM for PS, ABSO, SA, IGHS, and Rcr-IJADE are 1.518e � 2, 9.8635E � 04, 1.664e � 2, 9.8344E � 04, and 9.8248E � 04, respectively. From the result analysis, the Rcr-IJADE provided the ultimate performance in terms of RMSE and parameter extraction.

94 The Rcr-IJADE is modified by incorporating an onlooker-ranking-based mutation operator (O(β)R). This modification enhances the searching capabilities by not getting trapped into the local minima. The performance of ORcr-IJADE is authenticated by comparing RMSE value with various algorithms like TLBO, Newton, Rcr-IJADE, CPSO, PS, SA method. In case of SDM, the RMSE obtained from TLBO, Newton, Rcr-IJADE, CPSO, PS, SA, and proposed ORcr- IJADE are 6.567087E � 03, 6.313257E � 03, 2.425074886073E � 03, 4.212772E � 03, 4.507511E � 03, 4.169322E � 03, and 2.425074886071E � 03. While for DDM, the RMSE obtained from GGHS, PS, SA, HS, IGHS, ABSO, BMO, BFA, ABC-DE, ABC, Rcr-IJADE and ORcr-IJADE are 1.068370E � 03, 1.517666E � 02, 1.664353E � 02, 1.259652E � 03, 9.865724E � 04, 9.857451E � 04, 9.826615E � 04, 2.982676E � 01, 4.852788E � 03, 1.114580E � 03, 9.824859E � 04, and 9.824858E � 04.; wherein the ORcr-IJADE delivered superior performance in extraction of solar PV parameters.

149 Presented adaptive differential evolution technique (DET) for parameter extraction of SDM and DDM. To measure the precision of the developed method, the outcome was validated with experimental data under various working constraints. The attained outcomes with DET showed good consistency compared to CPSO, GA, HAS, and ABSO.

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TABLE 3 (Continued)

References Remarks

The RMSE obtained for SDM from CPSO, GA, HAS, ABSO, and DET are 0.0015, 0.0191, 9.950e � 4, 9.9124e � 4, and 9.3e � 4. Whereas, the RMSE obtained for DDM from PS, HSA, ABSO, SA, and DET are 0.015482, 0.001264, 0.000983, 0.017035, and 0.000924. Moreover, the developed algorithm is tested for mono and poly-crystalline PV modules. The proposed method showed more accurate results compared with the other techniques.

Particle swarm optimization 126 Developed mutant particle swarm optimization (MPSO) to minimize the objective function (RMSE) to extract the

parameters of both single (IL, IS, RS, RP, n) and double (IL, IS1, IS1, RS, RP, n1, n2) diode PV module. MPSO is applied for three distinct PV modules of mono-crystalline (SM55), multi-crystalline KC200GT, thin-film ST40 under varying irradiance and temperatures. Further, the performance of MPSO is validated by comparing with other optimization algorithms.

150 Proposed flexible particle swarm optimization (FPSO) technique to estimate the parameters of both SDM and DDM PV modules. An elimination phase is incorporated in conventional PSO so that the particles with poor fitness functions are removed during the start from the search space thereby the burden in finding the optimal parameters is minimized and the fitness function (RMSE) is enhanced. The results of DDM are compared with other optimization techniques PSO, BMO method for SM55, KY200GT, and SM255 PV modules. The FPSO method achieved RMSE of 0.016743 compared to PSO and BMO.

151 Proposed time-varying acceleration coefficients particle swarm optimization (TVACPSO) to evaluate the parameters of single and double diode models. In TVACPSO, the two deciding parameters personal and social acceleration coefficients are improved. To improve exploration during the starting of the searching phase the personal coefficient is increased. Further, exploitation is done by reducing the social acceleration value. It is also found that application of the above step made TVACPSO to show superior performance for SDM and DDM with low RMSE value of 7.7301EE � 4 and 7.4365EE � 4 for single and double diode model. This value is relatively lower compared to other meta-heuristic techniques such as CPSO, ICA, TLBO, GWO, WCA, and PS having a RMSE of 1.0372E � 3, 7.7487E � 4, 9.5145E � 4, 9.4655E � 4, 2.0502E � 3, and 9.7000E � 3, respectively.

152 Presented an enhanced leader PSO (ELPSO) to estimate the parameters of single and double diode PV module. In the process of finding the optimal solution, a five consecutive mutation operators are added to the head of the swarm. If the mutated leader provides optimal value for the fitness function, then the iteration proceed with the enhanced mutated leader direction toward the optimal solution. wherein the RMSE value obtained by CPSO, BSA, ABC, GA, PS, and proposed ELPSO for SDM 7.7301E � 4, 1.4436E � 3, 8.8636E � 4, 4.1020E � 3, 2.0502E � 3, 7.7301E � 4, and 7.4444E � 4; wherein for DDM are 0.00110851, 8.0824E � 4 5.91958E � 3 8.1646E � 3, and 7.4240E � 4, respectively.

153 The authors used guaranteed convergence particle swarm optimization (GCPSO) to find the parameters of SDM and DDM. In GCPSO, the velocity of the particle is modified in such way that the best solution not only considers its velocity, but also the velocities of other particles present in the swarm. The main reason for making this modification is to enhance the process of exploring the best solution in a multidimensional search space. This method overcomes the premature convergence limitation of the conventional PSO and ensuring the convergence to the minimum fitness function

154 To improve the capability of PV module, author in Reference 154 used PSO incorporating binary constraints for PV parameter extraction. The PSO method is capable of locating global optimum with binary constraints. Further, the results attained via the proposed method were compared with other algorithms and it is proved to be effective in the estimation of parameters of a solar module.

155 Another author in Reference 155 used a different combination of PSO and LS method to evaluate SDM parameters. The developed algorithms were implemented to poly-crystalline and monocrystalline solar module and results were validated by comparing with the manufacturer's datasheet values. It is found that the proposed method is effective in parameter extraction with an error value between measured and predicted solar cell parameters is not exceeding 8%.

Artificial immune system (AIS) 156 Presented artificial immune system (AIS) algorithm for unknown PV parameters identification for DDM model. To

authenticate the results of AIS, many conventional algorithms such as GA and PSO are compared. The developed method is tested on various PV panel make such as S36, SP70, SM55, KC200GT, and is found better in extracting the PV parameter extraction at higher computational speed and less convergence error.

(Continues)

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TABLE 3 (Continued)

References Remarks

Harmony search 157 Incorporated grouping-based global harmony search (GGHS) and innovative global harmony search (IGHS) for

estimating the parameters of SDM and DDM. Both the combination of achieve improved performance than conventional HS algorithm in terms of both exploration and exploitation of the optimal solution. The outcome of GGHS and IGHS are compared with many conventional algorithms. The RMSE attained for SDM by HS, GGHS, IGHS, SA, and PS are 9.9510e � 4, 9.9097e � 4, 9.9306e � 4, 0.01900, and 0.01494, respectively. While, the RMSE attained for DDM by HS, GGHS, IGHS, SA, and PS are 0.00126, 0.00107, 9.8635e � 4, 0.01664, and 0.01518, respectively. From the analysis, it is evident that the developed models hold good results in the estimation of PV parameters.

Bacterial foraging 108 Proposed BFA for evaluating the parameters such as RS, RP, a of SDM. To assess the performance of BFA, the outcome is

confirmed with GA, AIS. Furthermore, the developed algorithm was implemented in commercial solar cells such as S36, ST40, and SM55 to verify its working characteristics.

74 Used meta-heuristic algorithms such as particle swarm optimization (PSO), bacterial foraging (BF), and PSO-guided BF to evaluate the parameter extraction of LDK C1D2-140P solar PV module. The author compared the outcome of the proposed algorithm with other algorithms at various operating conditions and found that PSO-guided BF delivered a better convergence speed, and precision.

Artificial bee colony 158 Presented chaotic improved artificial bee colony (CIABC) in evaluating the parameters of single and double diode model.

Authors introduced the concept of chaotic maps for exploring and exploiting the best solution. For performance validation, the parameters arrived via CIABC method for SDM and DDM are compared with many other algorithms like STLBO, GOTLBO, ABC, IGHS, ABSO, SA, CSO, and MABC. The RMSE obtained for SDM by STLBO, GOTLBO, ABC, IGHS, ABSO, SA, CSO, MABC, and developed CIABC are 9.8602e � 4, 9.87442e � 4, 9.862e � 4, 9.9306e � 4, 9.9124e � 4, 0.0013 9.8602e � 4, 9.861e � 4, and 9.8602e � 4. Wherein, the RMSE obtained for SDM by STLBO, GOTLBO, ABC, IGHS, ABSO, SA, CSO, MABC, and developed CIABC are 9.8248e � 4, 9.83177e � 4, 9.861e � 4, 9.8635e � 4, 9.8344e � 4, 0.01664, 9.8252e � 4,9.8276e � 4, and 9.8262e � 4. From the analysis, it is found that the proposed method is reliable in estimating the solar PV parameters.

113 An author in Reference 113 modified ABC algorithm for parameter identification of single and double diode model; wherein the search for the optimal solution is performed by scout and employee bees. The RMSE values attained through other algorithms such as GA, CPSO, PS, SA, IGHS, ABSO, GGHS, ABC, and modified ABC are 0.01908, 0.00139, 0.01494, 0.01900, 9.930e � 4, 9.912e � 4, 9.909e � 4, 9.862e � 4, and 9.861e � 4.similarly, For a double diode model the RMSE values attained through other algorithms like HS, PS, SA, IGHS, ABSO, GGHS, ABC, and developed MABC were 0.00126, 0.01518, 0.01664, 9.8635e � 4, 9.8344e � 4, 0.00107, 9.861e � 4, and 9.8276e � 4. From the RMSE analysis, it is evident that the proposed algorithm ABC performs better by producing the least value for the objective function, hence, it is best suited for parameter extraction of solar PV.

Artificial bee swarm optimization 114 Proposed artificial bee swarm optimization (ABSO) to find the unknown parameters of single and double diode model of

solar PV. The decision-making strategy of the honey bees during the food search process is incorporated in parameter estimation. To state the usefulness of the ABSO algorithms, it is compared with various algorithms. The RMSE obtained by a single diode model by CPSO, GA, PS, SA, HS, and ABSO were 9.9124e � 4, 0.00139, 0.01908, 0.01494, 0.01900, and 9.9510e � 4. While the RMSE arrived via for double diode model, PS, SA, HS, and ABSO were 0.01518, 0.01664, 0.00126, and 9.8344e � 4. It is evident from the results that among all the algorithms, the ABSO has the highest efficiency and least RMSE.

Imperialist competitive algorithm 159 Implemented an imperialist competitive algorithm (ICA) to model the SDM and DDM of a solar cell. The imperialistic

concept in building a powerful empire with best solutions is incorporated in finding the parameters of the PV module. The MAE obtained from ICA and other algorithms like PS, ADE, SA, HSA, ABO, CPSO, BMO, and MBA were 5.66478e � 4 and 0.0022, 6.8091e � 04, 0.0022, 6.89346e � 4, 6.82615e � 4, 0.005067, 6.80808e � 4, and 0.0012, respectively for single diode model. For double diode model, the RMSE obtained for ICA and PS, ADE, SA, HSA, ABO, BMO, and MBA were 5.26589e � 4 and 0.0019, 6.8113e � 04, 0.0014, 6.66808e � 4, 6.73e � 4, 6.64115e � 4, and 0.0013. Based on the investigation, the author has concluded that ICA is a potential technique for PV cell/module identification.

28 of 72 VENKATESWARI AND RAJASEKAR

TABLE 3 (Continued)

References Remarks

Cat swarm optimization 160 Used CSO algorithm to find out the 5 and 7 parameters of single and double diode PV module. Owing to its high

flexibility and high convergence rate, the CSO produced prominent results in extracting parameters. Further, the performance of the developed algorithm is validated by comparing it with other algorithms like PSO, GA, SA, PS, Newton, HS, GGHS, IGHS, DE, LMSA, and ABSO. The RMSE obtained from CSO and other algorithms like PSO, GA, SA, PS, Newton, HS, GGHS, IGHS, DE, LMSA, and ABSO were 9.8602e � 4 and 0.00139, 0.01908, 0.01900, 0.01494, 9.6964e � 3, 9.9510e � 4, 9.9097e � 4, 9.9306e � 4, 2.3423e � 3, 9.8640e � 4, 9.9124e � 4, respectively for single diode model. For double diode model, the RMSE obtained for CSO and PSO, GA, SA, PS, HS, GGHS, IGHS, and ABSO were 9.8252e � 4 and 0.0166, 0.3604, 0.01664, 0.01518, 0.00126, 0.00107, and 9.8635e � 4. The developed algorithm offered a better outcome compared to conventional techniques.

Biogeography-based optimization algorithm 161 Proposed Biogeography-Based Optimization algorithm with Mutant strategy (BBO-M) for extracting the parameters of

SDM and DDM of solar PV. The mutant approach incorporating chaos theory enhances the exploration and exploitation capability of the developed algorithm. To state, the usefulness of BBO-M, comparative analysis with other algorithms like BBO, DE, ABSO, PS, SA, HS is performed primarily w.r.t RMSE. The RMSEs of BBO, DE, IADE, ABSO, CPSO, GA, PS, SA, HS, and the proposed BBO-M were 0.00238, 0.00100, 9.8900e � 4, 9.9124e � 4, 0.00139, 0.01908, 0.01494, 0.01900, 9.9510e � 4, and 9.8634e � 4 for SDM. Similarly, in case of DDM, DE, ABSO, PS, SA, HS, and the proposed BBO-M were 0.0016, 0.0010, 9.8344e � 4, 0.01518, 0.01664, 0.00126, and 9.8272e � 4. Results show that the proposed BBO-M algorithm is efficient in parameter identification of PV modules.

Firefly 162 The authors in Reference 162 used Hybrid Firefly And Pattern Search (HFAPS) to evaluate the parameters of SDM and

DDM. In this work, the firefly and pattern search technique are combined to yield better results in parameter extraction. The balance between exploration and exploitation is maintained. Initially, the firefly algorithm is employed for exploring a large search area, later; the pattern search algorithm is implemented for the solution population that was already obtained using firefly algorithm. To find the effectiveness of the proposed algorithm in parameter estimation, it is applied for three distinct PV modules of KC200GT, SX3200N, and 1STH-235-WH under varying irradiance and temperatures.

Cuckoo search optimization 163 Authors evaluated the parameters of a single diode model of a solar module. The performance validation for the

parameters attained via CS technique for SDM was compared with other many algorithms such as CPSO, GA and PS. The RMSE obtained for SDM by CPSO, GA, PS, and developed CS are 0.0014, 0.0191, 0.0149, and 0.0010.

Wind driven optimization 164 An authors in Reference 164 implemented a WDO algorithm identifying the values of DDM parameter. The author

related the results with commercial cells shell SP140-PC, KS20GT, SW245, and SP190 panel along with BPFPA, and CWOA method at various operating conditions. It is found that WDO showed a better result in terms of convergence speed, accuracy.

Flower pollination algorithm 165 The authors in Reference 165 used Flower Pollination Algorithm to extract the parameter of SDM and DDM of the PV

array. To find the effectiveness of proposed FPA, a comparative analysis is performed in terms of RMSE with other algorithms like FPA, Newton, LMSA, MPCOA, CS, ABSO, ABC, and PS. The RMSEs obtained for SD model with FPA, Newton, LMSA, MPCOA, CS, ABSO, ABC, PS, and the proposed FPA are 09.6964e � 03, 9.8640e � 04, 9.4457e � 04, 0.00109, .9124e � 4, 9.8262e � 4, 1.4936e � 02, and 7.7301e � 04, respectively. Similarly, the RMSEs attained for DDM by FPA, MPCOA, ABSO, HS, SA, and the proposed FPA are 9.2163e � 4, 9.8344e � 4, 0.00126, 0.01664, and 7.8425e � 04. Results show that the proposed algorithm is efficient in parameter identification of PV modules. But the conventional FPA suffers from premature convergence and complex to implement.

81 To overcome the above-mentioned issues in Reference 165, author combined ABC and FPA to find parameters of solar cell module. The inclusion of discard pollen operator feature in conventional FPA enhanced the quality of the parameter estimation process by eliminating the pollens exhibiting poor characteristics. The performance of the developed hybrid Bee Pollinator FPA (BPFPA) is further enriched with elite based mutation strategy. Further for results validation, the parameters attained using BPFPA method is compared with various promising algorithms like GA, PS, HS, FPA, and ABSO. Among all analyzed algorithms, the proposed BPFPA showed optimal performance by producing minimized RMSE value of 7.27E � 4, compared to 7.730E � 4, 9.91E � 4, 0.00139, 0.01494, 0.01900, 0.01908

(Continues)

VENKATESWARI AND RAJASEKAR 29 of 72

TABLE 3 (Continued)

References Remarks

values for FPA ABSO, CPSO, PS, SA, and GA, respectively for single diode model. Whereas for the double diode model, the RMSE attained via BPFA is 7.23E � 4 while it was 7.84E � 4, 9.83E � 4, 0.00126, 0.0158, 0.016 for FPA, ABSO, HS, PS, and SA. This comparison result demonstrates the superiority of the BPFO algorithm in parameter estimation.

166 Used Modified flower algorithm (MFA) to evaluate the parameters of SDM and DDM of solar PV. To estimate the accomplishment of the MFA, the acquired outcome was compared with other methods; wherein the RMSEs of SA, GE, WA, FA, LSA, and the MFA were 0.062, 0.0842, 0.0186, 0.0556, and 0.0181 for DDM. Furthermore, for the single diode PV module model, the RMSEs for SA, GE, WA, FA, LSA, and MFA were 0.064, 0.046, 0.022, 0.0224, and 0.02. The outcome specifies that developed MFA can be used as a precise and robust instrument to ascertain the parameters of various solar cell models.

167 Proposed Flower Pollination Algorithm (FPA) with the Nelder–Mead (NM) simplex method and the Generalized Opposition-Based Learning (GOBL) mechanism to evaluate the SDM and DDM parameters of a solar cell. Initially, the FPA is used in exploring the entire search space. Then NM is applied to the solution obtained from FPA for better exploitation. Finally, GOBL helps the algorithm in arriving optimal solution thereby not getting trapped at the local optima. The versatility of the developed algorithm is proved by comparing it with various algorithm and employing it to various PV modules

Teaching-learning-based optimization 168 Authors used Improved Teaching-Learning-Based Optimization (ITLBO) to evaluate the parameters of SDM and DDM of

solar PV. The RMSEs of the obtained results with IJaya, MLBSA, TLBO, SATLBO, LETLBO, GOTLBO, TLABC and the ITLBO were 9.8293E � 04, 9.8249E � 04, 1.0069E � 03, 9.8280E � 04, 9.8571E � 04, 9.9544E � 04, 9.8415E � 04, and 9.8248E � 04 for DD model. Moreover, for the single diode PV module model, the RMSEs for IJaya, MLBSA, TLBO, SATLBO, LETLBO, GOTLBO, TLABC, and ITLBO were 9.8603E � 04, 9.8602E � 04, 9.8733E � 04, 9.8602E � 04, 9.8603E � 04, 9.8658E � 04, 9.8602E � 04, and 9.8602E � 04. It indicates ITLBO is best suited to identify the parameters of solar cell models.

169 Authors developed TLBO method to estimate the parameters of a single diode model of the PV module. The developed algorithms were implemented to poly-crystalline and monocrystalline solar module and results were validated by comparing with the manufacturer's datasheet values.

170 Authors considered and combined the excellent feature of exploration capability of ABC and exploitation capacity of TLBO to propose a new algorithm called TLABC for effective parameter extraction of the PV cell. The outcome of TLABC was compared with TLBO, NIWTLBO, LETLBO, GOTLBO, ABC, GABC, MABC, and GBABC. The RMSEs of the obtained results TLBO, NIWTLBO, LETLBO, GOTLBO, ABC, GABC, MABC, GBABC, and TLABC were 9.87332E � 04, 9.86025E � 04, 9.86034E � 04, 9.86578E�04, 9.88148E � 04, 9.96438E � 04, 9.88080E � 04, 9.88006E � 04, and 9.86022E�04, respectively for SD model. Moreover, for the double diode PV module model, the RMSEs for TLBO, NIWTLBO, LETLBO, GOTLBO, ABC, GABC, MABC, GBABC, and TLABC were 1.00692E � 03, 9.84618E � 04, 9.85712E � 04, 9.85437E � 04, 9.89560E � 04, 9.88625E � 04, 9.92030E � 04, 9.90699E � 04, and 9.84145E � 04, respectively. From the analysis, it can be observed the proposed TLABC algorithm provides the lowest RMSE thereby providing superior performance in PV parameter extraction.

Grey wolf optimization 171 Implemented the developed algorithm in RTC France commercial solar cell and also compared the obtained results with

various conventional algorithms such as CPSO, GA, PS, SA, and HS. From the detailed analysis, it is ascertained that the proposed algorithm outperforms the other algorithms in terms of convergence speed, accuracy and also in finding the MPP coordinates accurately.

Crow search algorithm 172 Presented a CSA for unknown parameters identification of the single and double diode model of solar PV. To validate the

performance of CSA, it is compared with many conventional algorithms such as Shuffled Frog Leaping Algorithm (SFLA), GA. From the investigation, it is found that the proposed method is reliable in estimating the solar PV parameters.

Whale optimization algorithm 173 The authors presented an opposition-based learning strategy incorporated WOA for modeling the single, double and

triple diode solar PV. The proposed algorithm removes the premature convergence issue existing in the conventional methods and also exhibits a high convergence. Further for performance validation, the parameters arrived via the CWOA method for SDM, DDM and TDM were compared with other many algorithms. The RMSE obtained for SDM by HS, GGHS, IGHS, ABSO, CWOA, ABC, and CSO and developed WOA were 9.8602e � 4,9.9510e � 4, 9.9097e � 4,

30 of 72 VENKATESWARI AND RAJASEKAR

TABLE 3 (Continued)

References Remarks

9.9306 e � 4, 9.9124e � 4, 9.8602e � 4 9.862e � 4 and 9.8602e � 4. Similarly, RMSEs obtained for DDM by IGHS, ABSO, CSO, ABC, CWOA, and WOA were 9.8635e � 4, 9.8344e � 4, 9.8252e � 4, 9.861e � 4, 9.8272e � 4, and 9.8251e � 4, respectively; whereas for triple diode model, RMSEs attained by ABC, teaching-learning based optimization (STBLO) and modified WOA, were 9.8466e � 4, 9.8253e � 4, 9.8249e � 4, respectively. From the analysis, it is found that the proposed WOA outperforms the other algorithms in producing a minimized error.

174 Authors proposed WOA for parameter identification for single, double and triple diode model of solar PV. The author incorporated the living nature of whales in parameter estimation and for minimizing the objective function. The RMSE obtained for single, double, and triple diode model were 1.93E � 08, 2.75E � 08, and 9.8488E � 8. The proposed WOA yielded better results in obtaining the least objective function.

90 For a better exploration and exploitation of the PV module parameters, the authors in Reference 90, proposed a hybrid DE/WOA method. The DE which is capable of locating global optimum and WOA which is good in not getting trapped at local optima is combined to form a new algorithm for enhanced parameter extraction of a solar module. Further, for performance validation, the parameters arrived via DE/WOA method for SDM and DDM were compared with other algorithms and it is proved to be effective in the estimation of parameters of the solar module.

175 The authors used Chaotic Whale Optimization Algorithm (CWOA), an extension of the, the proposed algorithm incorporates the Singer chaotic map strategy in the initialization stage to increase the convergence speed and eliminates the premature convergence. Further for performance validation, the parameters arrived via CWOA method for SDM and DDM are compared with other algorithms like BMO, STBLO, HH, GGHS, IGHS, DE, LMSA, SA, CPSO, Rcr-IJADE, GOTLBO, CSO, BFA, ABSO, PS, Newton, and ABC. The proposed algorithm proved to be effective in the estimation of parameters of a solar module.

Salp swarm algorithm 176 Authors proposed SSA for extracting the parameters of DDM (IL, IS1, IS1, RS, RP, n1, n2) of solar PV. The swarming nature

of the salp is incorporated in devising the SSA algorithm. The results of the developed algorithm have reasonable MSE with a minimum value of 4.8405e � 03 and 3.6935e � 04 for a G = 366 W/m2, T = 18�C, and G = 810.2 W/m2, T = 22.74�C. The superior performance of the original SSA was validated by comparing it with other prominent algorithms like ALO, GSA, and WOA.

ER-WCA 177 ER-WCA is implemented using four basic steps namely, initialization, water movement from streams to rivers or sea,

raining and evaporation cycle, and its evaporation rate.177 To validate the developed algorithm, the SDM and DDM parameters calculated using ERWCA produced minimum RMSE values of 2.3558e � 3 while it is 2.3564e � 3, 2.4e � 3, 2.7e � 3, 3.5e � 3, for NM-MPSO, IADESA, and CPSO, respectively for single diode model. Similarly, for double diode model RMSE produced by ERWCA was 9.824849003 while it was 9.825e � 4, 9.83177e � 4, 9.8276e � 4, 9.8252e � 4, 9.8272e � 4, and 9.861e � 4, respectively for NM-MPSO, GOTLBO, MABC, CSO, BBO-M, and ABC. Based on the presented detailed investigation of the RMSE values obtained, it is found that ER-ERWCA is an efficient algorithm for extracting the parameters of a solar PV cell/module.

Jaya algorithm 178 Authors used elite opposition-based Jaya (EO-Jaya) technique to find the parameters of SDM and DDM. The

conventional Jaya algorithm is combined with Elite Opposition-based Learning mechanism where the solutions are allowed to move in the opposite direction in the given search space. The reason behind modifications is to find the optimal result with the finest fitness value. The results obtained from the proposed EO-Jaya technique were compared with the other well-known meta-heuristic algorithms. The RMSEs of EO-Jaya MABC, GOTLBO, ABSO, and ABC were 9.8603, 9.8610, 9.8744, 9.9124, and 9.8620, respectively for SDM and 9.8262 9.8276, 9.8318, 9.8344, and 9.8610 for DDM. The EO-Jaya based algorithm exhibited the best result and thereby it can be efficiently utilized for parameter extraction of the solar PV

145 Authors proposed a performance-guided Jaya (PGJaya) for extracting the parameters of SDM and DDM of the solar PV. In this algorithm, the individual performance of each solution among the entire population is considered. For better exploring, self-adaptive chaotic perturbation mechanism is incorporated in the developed methodology. To investigate the usefulness of the developed approach, comparative studies with other algorithms are performed. Further, the evaluation for the quality of identified parameters is performed by employing the PGJaya algorithm for three distinct PV modules of Mono-crystalline (SM55), Multi-crystalline KC200GT, Thin-film ST40 under varying irradiance and temperatures. Based on the detailed analysis, it is found that the performance of PGJaya technique is superior in obtaining minimized RMSE.

(Continues)

VENKATESWARI AND RAJASEKAR 31 of 72

main drawback of the traditional SSO. Because in SSO, the new solution obtained replaces the previous solution irrespective of the new solution is best or worst which ultimately lead to a less efficient result. The MSSO which is enhanced version replaces the UM of SSO by a random variable at each generation. Hence, the updating of the solution is performed only if the current solution is better than the older one. Furthermore, the performance of MSSO is com- pared with the reported results of different techniques such as SSO, ABC, SBMO, and PERC particularly based on objec- tive function (RMSE). For a SDM, the RMSEs attained from SSO, ABC, SBMO, ABSO, HS, PSO, GA, and MSSO were9.8640E � 04, 9.8619E � 04, 9.8610E � 04, 9.9124E � 04, 9.9510E � 04, 1.3900E � 03, 1.8704E � 02, and 9.8607E � 04. Similarly, for a DDM, the RMSEs attained from SSO, ABC, SBMO, ABSO, HS, PSO, GA, and MSSO were 9.9129E � 04, 9.8387E � 04, 9.8485E � 04, 9.8344E � 04, 1.2600E � 03, 1.6600E � 02, 3.6040E – 01, and 9.8281E � 04. By comparing the accuracy, convergence speed and RMSE ability of the other techniques, MSSO shows the highest accuracy in estimating the PV parameters. An author in Reference 148 used three well-recognized MAs such as GA, PSO, and DE to evaluate the parameter extraction of dye-sensitized solar cells (DSCs). The author has attempted to compare and find a suitable algorithm for the given DSSCs with enhanced accuracy. After employing the above- mentioned algorithms, the RMSEs arrived via GA, PSO, and DE were 2.6965 � 10 � 6, 3.1539 � 10 � 6, and 2.6957 � 10 � 6. Furthermore, the efficiency of obtaining accurate parameter for the PV modules the evolutionary algo- rithms was tested by adding a random noise and it is found that PSO showed a better result in terms of convergence speed, noise-resistant and effective in parameter extraction with less error. An author in Reference 182 used a fast and accurate hybrid method to calculate the parameters of a DDM of a solar cell. In this work, initially, the values of Io2, Rp, Io1, and IPV are calculated analytically concerning a1, a2, and Rs. Having the obtained a1, a2, and Rs value as reference, the Ipv value can be computed. Then the DE method is employed for better tuning and to find the optimum values a1, a2, and Rs. Furthermore, the developed method is applied to various solar panels such as SP75, SM110-24, RSM50, S25, ST36, ST20, and it is found better in extracting the PV parameter extraction at higher computational speed. An author in Reference 183 implemented modified elephant swarm water search algorithm for extracting SDM and DDM parame- ters of a PV module. The effectiveness of the proposed method was tested considering various performance metrics including accuracy, speed, and success rate in extracting the PV parameters. An author in Reference 184 proposed Gravitational Search Algorithm (GSA) in this study for evaluating the parameters of SDM and DDM of the solar PV by linearly decreasing the gravitational constant. The results were compared with GA, EA, Newton algorithm, and GSA with exponentially decreasing gravitational constant. An author in Reference 185 employed an improved brainstorming algorithm for extracting the single and double diode parameters of solar PV. The RMSE obtained for SDM and DDM were 1.0442E � 11 and 2.3748E � 05 and is found to be minimal when compared to various prominent algorithms.

Authors in Reference 186 proposed backtracking search algorithm incorporating Competitive-learning technique (CBSA) for evaluating parameters of SDM and DDM based PV modules. Application of this competitive technique enhances the global search capability by splitting the entire population into two and initializing the searching process. The RMSE obtained by the proposed method for SDM and DDM were 2.425075E � 03and 9.824849E � 04 and the results were compared with various methods such as BSA, IBSA, ABSA, IADE, MLBSA, ABSO, BBO-M, GGHS, IGHS, SATLBO, NM-MPSO, IJaya, GOTLBO, MABC, IWOA, and CWOA. Authors in Reference 187 estimated the parameters of SDM, DDM, and triple diode model (TDM) based PV modules utilizing the branch and bound algorithm. RMSE and MAE parameters were considered to check the effectiveness of the proposed and compared with ISCA, ABSO, PS, GOFPANM, and IBEXOPT techniques. UPLO and LOUP values in calculating the bounds required objective function enhanced its estimating capability with faster convergence. Proposed coyote optimization algorithm (COA),57 improved differential evolutionary algorithm (IDEA),188 and tree growth algorithm (TGA)189 was proposed to evaluate the param- eters of SDM, DDM, and TDMs and considered RMSE as a efficiency-defining factor. The COA compared its results with ABC, STBLO, OBWOA and the RMSE attained with SDM, DDM, and TDM in COA method were 7.7547 � 10 � 4, 7.64801 � 10 � 4, and 7.59756 � 10 � 4, respectively; wherein the TGA algorithm produced 9.280171173 � 10 � 04,

TABLE 3 (Continued)

References Remarks

Coyote optimization algorithm 57 The authors in Reference 57 utilized COA for determining the parameters used for triple diode modeling of solar PV.

Further for validation purpose, the author has implemented the developed algorithm in commercial solar PV such as KC200GT and MSX-60.

32 of 72 VENKATESWARI AND RAJASEKAR

8.4825747 � 10 � 4, and 8.3197747 � 10 � 4 for SDM, DDM, and TDM models of LSM PV modules. In case of IDEA, scaling factor is modified to improve the performance of conventional DE technique and obtained zero error at thee important points including short-circuit, open-circuit, and MPP regions. When surveyed, including the recently devel- oped improved cuckoo search optimization algorithm,190 improved learning search optimization algorithm,191 meta- phor less algorithm (Rao-2 (R-II), and Rao-3 (R-III))192 slime mould algorithm,193,194 TSO,195 refraction-learning-based WOA,196 directional permutation differential evolution,197 stochastic fractal search,198 chaotic-GBO,199 Improved ver- sion slime mould,200 chaoticJaya,201 Improved FPA,202 and EJaya203 estimated the parameters of PV modules. Few algo- rithms above mentioned attempted evaluate the parameters of either SDM, DDM, or TDM; wherein few algorithms estimated for SDM and DDM and a few for all the three models. Majority of algorithms considered RMSE as objective function to evaluate the performance of the developed method. The complete details of the algorithms and its pros and cons are given in Tables 4 and 5.

5 | META-ANALYSIS IN PV PARAMETER ESTIMATION RESEARCH

This section deals with the statistical analysis on outcomes of multiple scientific research studies related to PV parame- ter estimation. The analysis includes discussion on different PV cell modeling, its impact on various PV cell manufacturing technology and MAs developed to date to define the PV cell parameters. The following consolidates works on PV parameter research hence attempts to improve PV cell performance prediction via modeling as a solitary objective. An outline of the analysis is pictorially represented in Figure 24.

5.1 | Analysis based on manufacturing technology and modeling

According to literature, the affordable and highly competent PV cell materials have been progressed over three genera- tions by crossing the various stages of unceasing development from one to another generation. Among three generations,40 the first-generation PV cells used single silicon crystal for its making thus delivering moderate efficiency at a reasonably higher cost.41 Unceasing study on cost lessening and efficacy enhancement provided a way for the growth of thin-film technology, which is economical with improved cell effectiveness.42 Further, the second-generation PV cells have the following merits such as higher flexibility, easy handling, and lesser current loss. The highly efficient dye-sensitized solar cells (DSSCs), polymer cells, nano-crystals materials, and nano-porous materials fall under third- generation PV technology.52

Analysis of PV cell modeling techniques reveals that the single, double, and triple diode modeling was developed and used in designing a PV cell. Among them, one diode model is very commonly used because of its merit of deliver- ing moderate efficiency. The two diode and three diode models are capable of producing higher efficiency at reasonably higher computational burden compared to the previous type. Further, this investigation on the parameter estimation scrutinized several types of research considering only SDM or DDM model or the both, widely applied in all PV panel technology and commonly used panel make. Among the based works carried out so far 29 algorithms from 52 research articles are reviewed. The composition of SDM and DDM contribution to cell modeling is listed below:

1. 19.23% works were carried out with only SDM model 2. 11.54% works were carried out with only DDM model 3. 69.23% researches were conducted for both SDM and DDM 4. 55% used monocrystalline based SM55 panel make and 45% used other types of monocrystalline based panels. 5. 58% used thin-film based ST40 panel make and 42% used other types of Thin-film solar panels. 6. Among polycrystalline based solar PV, 30% works were carried out with KC200GT type and 24% with RTC France

and rest 46% with other polycrystalline based panels.

5.2 | Analysis based on RMSE of algorithms developed

Stronger the analysis, more accurate the solution obtained for any optimization problem. This section elucidates critical analysis on the efficiency of performance of all 27 algorithms considered to find the best MA involved in the parameter

VENKATESWARI AND RAJASEKAR 33 of 72

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th in -f il m

H IT -2 15 , K C 20 0G

T ,

ST 40

B et te r ex p lo ra ti o n an

d ex p lo it at io n is

at ta in ed

[9 1]

D E

M an

u fa ct u re r

sh ee t d at a

SD M

A E

R S m o d el

re su lt s

M o n o -c ry st al li n e,

th in -f il m

SM 55 , S7 5,

ST 40

P re m at u re

co n ve rg en

ce is el im

in at ed

[9 2]

IA D E

E xp er im

en ta l

d at a

SD M ,

D D M

IA E , R M SE

A B SO

, C P SO

, H SA

, SA

, P S,

O IS , an

d D A B

M o n o -c ry st al li n e

an d m u lt i-

cr ys ta ll in e

SM 55 , K C 20 0G

T E xt en

si o n o f th e D E al go ri th m

th at

au to m at ic al ly

u p d at es

th e tw

o co n tr o l p ar am

et er s u se d in

co n ve n ti o n al

D E

[9 3]

R cr -I JA

D E

E xp er im

en ta l

d at a

SD M ,

D D M

IA E

P S,

IG H S,

A B SO

M u lt i- cr ys ta ll in e

P W P 20 1,

R T C

F ra n ce

In co rp o ra te d cr o ss o ve r ra te

re p ai ri n g

te ch

n iq u e an

d ra n k in g- b as ed

m u ta ti o n in

th e co n ve n ti o n al

JA D E

al go ri th m

to en

h an

ce p er fo rm

an ce

in p ar am

et er

ex tr ac ti o n

[9 4]

O R cr -I JA

D E

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

D E , P SO

, A B C b as ed

al go ri th m s

M o n o -c ry st al li n e,

th in -f il m , an

d m u lt i-

cr ys ta ll in e

SP 70 , SQ

85 , ST

40 ,

P W P 20 1,

R T C

F ra n ce

M o d if ie d R cr -I JA

D E b y in co rp o ra ti n g

an o n lo o k er -r an

k in g- b as ed

m u ta ti o n o p er at o r (O

(β )R ). an

d

th er eb y en

h an

ce s th e se ar ch

in g

ca p ab il it ie s b y n o t ge tt in g tr ap

p ed

in to

th e lo ca l m in im

a

[1 49 ]

D E T

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

C P SO

, G A , H A S,

A B SO

M o n o -c ry st al li n e

SM 55 , R T C F ra n ce

O u tc o m es

w it h D E T sh o w ed

go o d

co n si st en

cy co m p ar ed

to C P SO

, G A ,

H A S,

A B SO

.

[1 26 ]

M P SO

ex p er im

en ta l

d at a

SD M ,

D D M

R M SE

C P SO

, A B SO

, P S,

SA , D E T ,

M P C O , T V A C P SO

, F P A ,

G O F P A N M

M o n o -c ry st al li n e,

m u lt i-

cr ys ta ll in e, an

d th in -f il m

SM 55 , K C 20 0G

T ,

ST 40

C o n ve rg en

ce sp ee d is ap

p re ci ab ly

h ig h

[1 52 ]

E L P SO

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

C P SO

, B SA

, A B C , G A , P S,

N ew

to n

M o n o -c ry st al li n e

an d m u lt i-

cr ys ta ll in e

SM 55 , K C 20 0G

T In

E L P SO

, fo r ea ch

it er at io n in

th e

p ro ce ss

o f fi n d in g th e o p ti m al

so lu ti o n , fi ve

co n se cu ti ve

m u ta ti o n

34 of 72 VENKATESWARI AND RAJASEKAR

T A B L E

4 (C o n ti n u ed )

R ef er en

ce s

A lg o ri th

m u se d

D a ta

u se d

M o d el in g

O b je ct iv e

fu n ct io n

C o m p a re d m et h o d s

T y p es

o f

p a n el

u se d

P V m o d u le s u se d

R em

a rk

s

o p er at o rs

ar e ad

d ed

to th e h ea d o f

th e sw

ar m

to in cr ea se

it s

p er fo rm

an ce

[1 50 ]

F P SO

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

P SO

, B M O

M o n o -c ry st al li n e

an d m u lt i-

cr ys ta ll in e

SM 55 , K C 20 0G

T E li m in at io n p h as e is in co rp o ra te d in

co n ve n ti o n al

P SO

so th at

th e

p ar ti cl es

w it h p o o r fi tn es s fu n ct io n s

ar e re m o ve d d u ri n g th e st ar t fr o m

th e se ar ch

sp ac e

[1 51 ]

T V A C P SO

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

C P SO

, IC

A , T L B O , G W O ,

W C A , P S

M o n o -c ry st al li n e

an d m u lt i-

cr ys ta ll in e

SM 55 , K C 20 0G

T P re m at u re

co n ve rg en

ce is su e ex is ti n g

in th e tr ad

it io n al

P SO

is el im

in at ed

[1 52 ]

G C P SO

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

, IA

E ,

M A E , A E

G C P SO

,T V A C P SO

, P P SO

, A B C -D

E P o ly cr ys ta ll in e

N D -R 25 0A

5, R T C

F ra n ce

T h e ve lo ci ty

o f th e p ar ti cl e is m o d if ie d

in su ch

w ay

th at

th e b es t so lu ti o n

n o t o n ly

co n si d er s it s ve lo ci ty

b u t

al so

th e ve lo ci ti es

o f o th er

p ar ti cl es

p re se n t in

th e sw

ar m

[1 56 ]

A IS

E xp er im

en ta l

d at a

SD M ,

D D M

M SE

, A E

G A , P SO

M o n o -c ry st al li n e

an d m u lt i-

cr ys ta ll in e

SP 70 , SM

55 ,

K C 20 0G

T , S3 6

P V p ar am

et er

ex tr ac ti o n is d o n e at

h ig h er

co m p u ta ti o n al

sp ee d an

d le ss

co n ve rg en

ce er ro r

[1 57 ]

G G H S & IG

H S

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

N A

N A

N A

O ve rc o m es

th e p re m at u re

co n ve rg en

ce

[1 08 ]

B F A

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

G A , A IS

M o n o -c ry st al li n e,

m u lt i-

cr ys ta ll in e, an

d th in -f il m

SM 55 , S3 6,

ST 40 ,

P er fe ct

b al an

ce b et w ee n th e

ex p lo ra ti o n an

d ex p lo it at io n st ag e

[7 4]

P SO

& B F A

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

P SO

, B F A

M u lt i- cr ys ta ll in e

L D K C 1D

2- 14 0P

B et te r co n ve rg en

ce sp ee d at

va ri o u s

o p er at in g co n d it io n s co n si d er ed

[1 58 ]

C IA

B C

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

ST L B O , G O T L B O , A B C , IG

H S,

A B SO

, SA

, C SO

an d M A B C

M u lt i- cr ys ta ll in e

ST M 6- 12 0/ 36

In tr o d u ce d th e co n ce p t o f ch

ao ti c

m ap

s fo r ex p lo ri n g an

d ex p lo it in g

th e b es t so lu ti o n

[1 13 ]

M A B C

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

H S,

P S,

SA , IG

H S,

A B SO

,

C G H S,

A B C

N A

N A

A B C p er fo rm

s b et te r b y p ro d u ci n g th e

le as t va lu e fo r th e o b je ct iv e fu n ct io n

[1 14 ]

A B SO

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

C P SO

, G A , P S,

SA , an

d H S

C o m m er ci al

ce ll

R .T .C .F

ra n ce

D ec is io n -m

ak in g st ra te gy

o f th e h o n ey

b ee s d u ri n g th e fo o d se ar ch

p ro ce ss

is in co rp o ra te d in

p ar am

et er

es ti m at io n

[1 59 ]

IC A

E xp er im

en ta l

d at a

SD M ,

D D M

M A E

P S,

A D E , H S,

A B C , M B A ,

B M O

M o n o -c ry st al li n e,

th in -f il m , an

d

m u lt i-

cr ys ta ll in e

SQ 15 0- P C , ST

40 ,

K C 20 0G

T , R .T .C

F ra n ce

A rt ic le

co n cl u d es

th at

IC A is a

p o te n ti al

te ch

n iq u e fo r P V ce ll /

m o d u le

id en

ti fi ca ti o n

(C o n ti n u es )

VENKATESWARI AND RAJASEKAR 35 of 72

T A B L E

4 (C o n ti n u ed )

R ef er en

ce s

A lg o ri th

m u se d

D a ta

u se d

M o d el in g

O b je ct iv e

fu n ct io n

C o m p a re d m et h o d s

T y p es

o f

p a n el

u se d

P V m o d u le s u se d

R em

a rk

s

[1 60 ]

C SO

(C at )

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

P SO

, G A , SA

, P S,

N ew

to n

N A

N A

O w in g to

it s h ig h fl ex ib il it y an

d h ig h

co n ve rg en

ce ra te , th e C SO

p ro d u ce d

p ro m in en

t re su lt s in

ex tr ac ti n g

p ar am

et er s

[1 61 ]

B B O -M

E xp er im

en ta l

d at a

SD M ,

D D M

M ea n E rr o r

B B O -M

, B B O , D E ,G

H S,

P SO

-w , G A

C o m m er ci al

ce ll

R T C F ra n ce

M u ta n t ap

p ro ac h in co rp o ra ti n g ch

ao s

th eo ry

en h an

ce s th e ex p lo ra ti o n

an d ex p lo it at io n ca p ab il it y o f th e

d ev el o p ed

al go ri th m

[1 62 ]

H F A P S

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

G A , P SO

, SA

, P S,

E L P SO

, B P F P A , H S,

B F A , G G H S,

SS O , IG

H S,

A B C , A B SO

, G O T L B O ,,M

SS O , B M O

M o n o -c ry st al li n e

an d m u lt i-

cr ys ta ll in e

ST M 6- 40 /3 6,

P h o to w at t- P W P

20 , K C 20 0G

T ,

R T C F ra n ce

B al an

ce b et w ee n ex p lo ri n g an

d ex p lo it in g is m ai n ta in ed

b y

im p le m en

ti n g b o th

th e al go ri th m s

fo r p ar am

et er

ex tr ac ti o n

[1 63 ]

C SO

E xp er im

en ta l

d at a

SD M

R M SE

C P SO

,1 4 G A ,1 3 an

d P S

M u lt i- cr ys ta ll in e

K C 20 0G

T , R T C

F ra n ce

O ve rc o m es

th e p re m at u re

co n ve rg en

ce

[1 64 ]

W D O

E xp er im

en ta l

d at a

D D M

IA E

N o t va il ab le

M on

o- cr ys ta ll in e,

th in -f il m ,a n d

m u lt i- cr ys ta ll in e

SP 14 0- P C , K S2 0G

T ,

SW 24 5 an

d SP

19 0

W D O sh o w ed

a b et te r re su lt in

te rm

s

o f co n ve rg en

ce sp ee d , ac cu ra cy

at va ri o u s o p er at in g co n d it io n s

[1 65 ]

F P A

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

N ew

to n , L M SA

, M P C O A , C S,

A B SO

, A B C , P S

M u lt i- cr ys ta ll in e

P W P 20 1,

R T C

F ra n ce

C o n ve n ti o n al

F P A su ff er s fr o m

p re m at u re

co n ve rg en

ce an

d co m p le x to

im p le m en

t

[8 1]

B P F P A

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

G A , P S,

H S,

F P A , an

d A B SO

N A

N A

In cl u si o n o f d is ca rd

p o ll en

O p er at o r

fe at u re s in

co n ve n ti o n al

F P A

el im

in at ed

q u an

ti ty

o f th e p o ll en

s ex h ib it in g p o o r ch

ar ac te ri st ic s

[1 66 ]

M F A

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

L SA

, SA

M u lt ic ry st al li n e

K yo se ra , Sa n yo

M F A ca n b e u se d as

a p re ci se

an d

ro b u st in st ru m en

t to

as ce rt ai n th e

p ar am

et er s o f va ri o u s so la r ce ll

m o d el s

[1 68 ]

IT L B O

E xp er im

en ta l

d at a

SD M ,

D D M

A E

IJ ay a, M L B SA

, T L B O ,

SA T L B O , L E T L B O ,

G O T L B O , an

d T L A B C

M o n o -c ry st al li n e

an d m u lt i-

cr ys ta ll in e

ST M 6- 40 /3 6,

P h o to w at t-

P W P 20 1

P ro p os ed

al go ri th m

re m ov es

th e

p re m at u re

co n ve rg en ce

is su e ex is ti n g

in th e co n ve n ti on

al m et h od

s an

d al so

ex h ib it s a h ig h co n ve rg en

ce

[1 69 ]

T L B O

E xp er im

en ta l

d at a

SD M ,

D D M

R el at iv e

E rr o r

T L B O w it h n o is e

M o n o cr ys ta ll in e

an d

p o ly cr ys ta ll in e

N A

P ro p o se d m et h o d w as

te st ed

co n si d er in g va ri o u s p er fo rm

an ce

m et ri cs

in cl u d in g ac cu ra cy , sp ee d ,

an d su cc es s ra te

[1 70 ]

T L A B C

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

T L B O , A B C

M u lt i- cr ys ta ll in e

P h o to

w at t- P W P 20 1,

R T C F ra n ce

C om

bi n ed

th e ex ce ll en t fe at u re

of

ex pl or at io n ca p ab il it y of

A B C an d

ex pl oi ta ti on

ca pa ci ty of

T L B O to

pr op os ed

36 of 72 VENKATESWARI AND RAJASEKAR

T A B L E

4 (C o n ti n u ed )

R ef er en

ce s

A lg o ri th

m u se d

D a ta

u se d

M o d el in g

O b je ct iv e

fu n ct io n

C o m p a re d m et h o d s

T y p es

o f

p a n el

u se d

P V m o d u le s u se d

R em

a rk

s

[1 71 ]

B M O

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

B M O , P S,

SA , H S,

G G H S,

IG H S,

A B SO

C o m m er ci al

ce ll

R T C F ra n ce

P ro p o se d al go ri th m

o u tp er fo rm

s th e

o th er

al go ri th m s in

te rm

s o f

co n ve rg en

ce sp ee d , ac cu ra cy

an d

al so

in fi n d in g th e M P P co o rd in at es

ac cu ra te ly

[1 72 ]

C SA

E xp er im

en ta l

d at a

SD M ,

D D M

P o w er

er ro r

G A

M u lt i- cr ys ta ll in e

K yo ce ra

K C 20 0G

T C o m p ar ed

re su lt s w it h sh u ff le d fr o g

le ap

in g al go ri th m

(S F L A ) an

d G A

[1 73 ]

C W O A

E xp er im

en ta l

d at a

SD M ,

D D M ,

an d

T D M

R M SE

B M O , ST

B L O , P S,

H S,

G G H S,

IG H S,

A B SO

, SA

, C SO

M o n o -c ry st al li n e

an d m u lt i-

cr ys ta ll in e

ST M 6- 40 /3 6,

ST M 6- 12 0/ 36

T h e p ro p o se d al go ri th m

re m o ve s th e

p re m at u re

co n ve rg en

ce is su e

ex is ti n g in

th e co n ve n ti o n al

m et h o d s an

d al so

ex h ib it s a h ig h

co n ve rg en

ce

[1 74 ]

W O A

E xp er im

en ta l

d at a

SD M ,

D D M ,

an d

T D M

ab so lu te

cu rr en

t

er ro r

G A

M u lt i- cr ys ta ll in e

K yo ce ra

K C 20 0G

T In co rp o ra te d th e li vi n g n at u re

o f

w h al es

in p ar am

et er

es ti m at io n an

d

fo r m in im

iz in g th e o b je ct iv e

fu n ct io n

[9 0]

H yb ri d D E /W

O A

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

N A

N A

N A

D E lo ca te s gl o b al

o p ti m u m

an d W O A

h el p s in

n o t ge tt in g tr ap

p ed

at lo ca l

o p ti m a

[1 75 ]

C W O A

E xp er im

en ta l

d at a

SD M ,

D D M ,

an d

T D M

R M SE

B M O , ST

B L O , P S,

H S,

G G H S,

IG H S,

A B SO

, SA

, an

d C SO

M o n o -c ry st al li n e

an d m u lt i-

cr ys ta ll in e

ST M 6- 40 /3 6,

ST M 6- 12 0/ 36

In co rp o ra te s th e si n ge r ch

ao ti c m ap

st ra te gy

in th e in it ia li za ti o n st ag e to

in cr ea se

th e co n ve rg en

ce sp ee d an

d el im

in at es

th e p re m at u re

co n ve rg en

ce

[1 76 ]

SS A

E xp er im

en ta l

d at a

D D M

M SE

, A E

A L O , G SA

, an

d W O A

N A

N A

D ev el o p ed

al go ri th m

h av e re as o n ab le

M SE

w it h a m in im

u m

va lu e o f

4. 84 05 E �

03 an

d 3. 69 35 E �

04 fo r

a G =

36 6 W /m

2 , T =

18 � C

an d

G =

81 0. 2 W /m

2 , T =

22 .7 4� C .

[1 43 ]

E R W C A

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

SD M : N M -M

P SO

, IA

D E SA

, C P SO

D D M : N M -M

P SO

, G O T L B O ,

M A B C , C SO

, B B O -M

, an

d

A B C

M u lt i- cr ys ta ll in e

P W P -2 01 , R T C

F ra n ce

E xt en

si o n o f th e W C A w h er e th e

ev ap

o ra ti o n ra te

is in co rp o ra te d fo r

av o id in g th e p re m at u re

co n ve rg en

ce an

d b et te r ex p lo ra ti o n in

fi n d in g th e

so lu ti o n w it h th e b es t fi tn es s va lu e

[1 78 ]

E O -J ay a

E xp er im

en ta l

D at a

SD M ,

D D M

R M SE

E O -J ay a M A B C , G O T L B O ,

A B SO

, an

d A B C

C o m m er ci al

ce ll

R T C F ra n ce

C o n ve n ti o n al

Ja ya

al go ri th m

is co m b in ed

w it h E li te

o p p o si ti o n -

b as ed

le ar n in g m ec h an

is m

w h er e

th e so lu ti o n s ar e al lo w ed

to m o ve

in th e o p p o si te

d ir ec ti o n in

th e gi ve n

se ar ch

sp ac e

(C o n ti n u es )

VENKATESWARI AND RAJASEKAR 37 of 72

T A B L E

4 (C o n ti n u ed )

R ef er en

ce s

A lg o ri th

m u se d

D a ta

u se d

M o d el in g

O b je ct iv e

fu n ct io n

C o m p a re d m et h o d s

T y p es

o f

p a n el

u se d

P V m o d u le s u se d

R em

a rk

s

[1 45 ]

P G Ja ya

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

IJ ay a, Ja ya , G O T L B O , T L A B C ,

C L P SO

, an

d D E /B B O

M o n o -c ry st al li n e,

m u lt i-

cr ys ta ll in e, an

d th in -f il m

SM 55 , K C 20 0G

T ,

ST 40

F o r b et te r ex p lo ri n g, se lf -a d ap

ti ve

ch ao ti c p er tu rb at io n m ec h an

is m

is in co rp o ra te d in

th e d ev el o p ed

m et h o d o lo gy

[7 6]

C O A

E xp er im

en ta l

d at a

T D M

R M SE

N A

M u lt i- cr ys ta ll in e

K C 20 0G

T an

d M SX

- 60

T h e p ro p o se d al go ri th m

re m o ve s th e

p re m at u re

co n ve rg en

ce is su e

ex is ti n g in

th e co n ve n ti o n al

m et h o d s an

d al so

ex h ib it s a h ig h

co n ve rg en

ce

[1 79 ]

E SC

E -O

B L

E xp er im

en ta l

d at a

T D M

R M SE

G O F P A N M , R cr -I JA

D E , an

d SC

E M u lt i- cr ys ta ll in e

-P W P 20 1,

R .T .C

F ra n ce

T o o ve rc o m e th e p re m at u re

co n ve rg en

ce p ro b le m

o f th e

co n ve n ti o n al

sh u ff le d co m p le x

ev o lu ti o n al go ri th m

(S C E ), O B L

st ra te gy

is in co rp o ra te d in

th e

p ro p o se d m et h o d

[1 80 ]

SS SO

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

h yb ri d A B C an

d N el d er -M

ea d

si m p le x (E H A -N

M S)

N A

N A

C o m b in at io n o f si m p li fi ed

sw ar m

o p ti m iz at io n (S SO

) an

d N el d er -

M ea d si m p le x (N

M S)

al go ri th m s

[1 81 ]

M SS O

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

SS O , A B C , SB

M O , A B SO

, H S,

P SO

, an

d G A

N A

N A

Im p ro ve d ve rs io n o f SS O th at

o ve rc o m es

th e m ai n d ra w b ac k o f

th e tr ad

it io n al

SS O

[1 83 ]

M E SW

SA E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

N o t av ai la b le

N A

N A

p ro p o se d m et h o d w as

te st ed

co n si d er in g va ri o u s p er fo rm

an ce

m et ri cs

in cl u d in g ac cu ra cy , sp ee d ,

an d su cc es s ra te

[1 84 ]

G SA

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

G A , E A , an

d N ew

to n

al go ri th m

N A

N A

L in ea r d ec re as e in

th e gr av it at io n al

co n st an

t is in co rp o ra te d fo r

p ar am

et er

ex tr ac ti o n

[1 85 ]

IB SA

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

N o t av ai la b le

N A

N A

P re co n ve rg en

ce is el im

in at ed .

[1 86 ]

C B SA

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

B SA

, IB SA

, A B SA

, IA

D E ,

M L B SA

, A B SO

, B B O -M

, G G H S,

IG H S,

SA T L B O , N M -

M P SO

, IJ ay a, G O T L B O ,

M A B C , IW

O A , an

d C W O A

P o ly cr ys ta ll li n e

N A

A p p li ca ti o n o f th is co m p et it iv e

te ch

n iq u e en

h an

ce s th e gl o b al

se ar ch

ca p ab il it y b y sp li tt in g th e

en ti re

p o p u la ti o n in to

tw o an

d

in it ia li zi n g th e se ar ch

in g p ro ce ss

[1 87 ]

B ra n ch

an d b o u n d

al go ri th m

E xp er im

en ta l

d at a

SD M ,

D D M ,

an d

T D M

R M SE

, M A E

IS C A , A B SO

, P S,

G O F P A N M ,

an d IB E X O P T

C o m m er ci al

ce ll

R T C F ra n ce

U P L O an

d L O U P va lu es

in ca lc u la ti n g

th e b o u n d s re q u ir ed

o b je ct iv e

fu n ct io n en

h an

ce d it s es ti m at in g

ca p ab il it y w it h fa st er

co n ve rg en

ce

38 of 72 VENKATESWARI AND RAJASEKAR

T A B L E

4 (C o n ti n u ed )

R ef er en

ce s

A lg o ri th

m u se d

D a ta

u se d

M o d el in g

O b je ct iv e

fu n ct io n

C o m p a re d m et h o d s

T y p es

o f

p a n el

u se d

P V m o d u le s u se d

R em

a rk

s

[5 7]

C O A

E xp er im

en ta l

d at a

SD M ,

D D M ,

an d

T D M

R M SE

, M A E

A B C , ST

B L O , an

d O B W O A

M o n o -c ry st al li n e,

m u lt i-

cr ys ta ll in e, an

d th in -f il m

SM 55 , ST

40 ,

K C 20 0G

T ,

P W P 20 1, , R T C

F ra n ce ,

B et te r ex p lo ra ti o n an

d ex p lo it at io n is

at ta in ed

[1 88 ]

ID E A

E xp er im

en ta l

d at a

SD M ,

D D M ,

an d

T D M

Su m m at io n

o f er ro r

va lu es

G W O , SS A , P SO

, an

d G A

P o ly cr ys ta ll in e

T P 28 5,

A SM

- 7- P E R C -3 65

Sc al in g fa ct o r is m o d if ie d to

im p ro ve

th e p er fo rm

an ce

o f co n ve n ti o n al

D E

te ch

n iq u e an

d o b ta in ed

ze ro

er ro r

at th ee

im p o rt an

t p o in ts in cl u d in g

sh o rt -c ir cu it , o p en

-c ir cu it , an

d M P P

re gi o n s

[1 89 ]

T re e gr o w th

al go ri th m

(T G A )

E xp er im

en ta l

d at a

SD M ,

D D M ,

an d

T D M

R M SE

A B SO

, P SO

, G A , A B C , SB

M O ,

SS O , an

d M SS O

P o ly cr ys ta ll in e

L SM

20 A p p li ed

fo r SD

M , D D M , an

d T D M

m o d el s. A m o n g al l th e m o d el s, th e

p er fo rm

an ce

o f T G A is d es ir ab le

w it h h ig h co n ve rg en

ce ra te

[1 90 ]

IC SO

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

P S,

SA , G O F P A N M , IJ ay a, an

d T L A B C

M u lt i- cr ys ta ll in e

P W P 20 1

A d ap

ti ve

st ep

si ze

co n ce p t is fo ll o w ed

to im

p ro ve

th e co n ve rg en

ce ra te

o f

IC SO

; w h er ei n fi xe d st ep

si ze

is fo ll o w ed

in C SO

[1 91 ]

IL SA

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

, A E ,

R E

ST L B O , T L A B C , IJ ay a,

G O T L B O , C L P SO

, D E /B B O ,

an d B L P SO

M o n o -c ry st al li n e,

m u lt i-

cr ys ta ll in e, an

d th in -f il m

SM 55 , K C 20 0G

T ,

ST 40

Se lf -a d ap

ti ve

w ei gh

ti n g an

d p er tu rb at io n co n ce p t d u ri n g

it er at iv e p ro ce ss

im p ro vi se

th e

p er fo rm

an ce

an d el im

in at es

p re m at u re

co n ve rg en

ce

[1 92 ]

M et ap

h o r le ss

al go ri th m

(R ao -2

(R -I I) , an

d R ao -3

(R -I II ))

E xp er im

en ta l

d at a

SD M ,

D D M ,

an d

T D M

R M SE

P SO

, C S,

A B C , an

d T L O

P o ly cr ys ta ll in e

P W P 20 1,

R T C

F ra n ce

T u n in g o f co n tr o l p ar am

et er s is n o t

re q u ir ed , ac cu ra cy

ra te

an d

co n ve rg en

ce sp ee d is h ig h co m p ar ed

to co m p ar ed

m et h o d s

[1 93 ]

SM A

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

IJ A Y A , E R W C A , an

d N M SO

L M F O

P o ly cr ys ta ll in e

P h o to w at t P W P 20 1

L SM

20 M at h em

at ic al

m o d el

in co rp o ra ti n g

ad ap

ti ve

w ei gh

ts to

o b ta in

n eg at iv e

an d p o si ti ve

fe ed b ac k o f th e

p ro p ag at io n w av e d u ri n g fo o d

se ar ch

in g p ro ce ss

in cr ea se s th e

ex p lo ra ti o n an

d ex p lo it at io n ab il it y

o f th e al go ri th m

[1 94 ]

SM A (K

U M A R )

E xp er im

en ta l

d at a

SD M ,

D D M ,

an d

T D M

R M SE

A B C , C S,

P SO

, T L O , an

d R A O

P o ly cr ys ta ll in e

P W M 20 1,

R T C

F ra n ce

M at h em

at ic al

m o d el

in co rp o ra ti n g

ad ap

ti ve

w ei gh

ts to

o b ta in

n eg at iv e

an d p o si ti ve

fe ed b ac k o f th e

p ro p ag at io n w av e d u ri n g fo o d

se ar ch

in g p ro ce ss

in cr ea se s th e

ex p lo ra ti o n an

d ex p lo it at io n ab il it y

o f th e al go ri th m

(C o n ti n u es )

VENKATESWARI AND RAJASEKAR 39 of 72

T A B L E

4 (C o n ti n u ed )

R ef er en

ce s

A lg o ri th

m u se d

D a ta

u se d

M o d el in g

O b je ct iv e

fu n ct io n

C o m p a re d m et h o d s

T y p es

o f

p a n el

u se d

P V m o d u le s u se d

R em

a rk

s

[1 95 ]

T SO

E xp er im

en ta l

d at a

T D M

Su m m at io n

o f

ab so lu te

er ro rs

W O A , G W O , SF

O P o ly cr ys ta ll in e

K C -2 00 -G

T , M SX

-6 0,

C S6 K 28 0M

B et te r ex p lo ra ti o n an

d ex p lo it at io n is

at ta in ed

[1 96 ]

R L W O A

E xp er im

en ta l

d at a

SD M

R M SE

B SA

, L B SA

, G O T L B O , D E -

B B O , L E T L B O , C L P SO

,

B L P SO

, an

d W O A

N A

N A

In co rp o ra te d re fr ac ti o n -l ea rn in g- b as ed

te ch

n iq u e an

d n o n li n ea r co n ve rs io n

in co n ve n ti o n al

W O A to

n o t ge tt in g

tr ap

p ed

lo ca l p ea k an

d en

h an

ci n g

gl o b al

se ar ch

ca p ab il it y

[1 97 ]

D P D E

E xp er im

en ta l

d at a

SD M ,

D D M ,

an d

T D M

R M SE

D E b as ed

al go ri th m s, IJ A Y A ,

M L B SA

, C L P SO

, G W O , an

d W D O

M o n o cr ys ta ll in e

an d

p o ly cr ys ta ll in e

ST M 6- 40 /3 6,

P h o to w at t-

P W P 20 1,

ST P 6- 12 0/ 36

P ro p o se d al go ri th m

u se s d ir ec ti o n

re la te d in fo rm

at io n o f th e

d if fe re n ti al

ve ct o r to

n o t ge t tr ap

p ed

in lo ca l m ax im

a w it h en

h an

ce d

gl o b al

se ar ch

in g ca p ab il it y

[1 98 ]

SF S

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

IJ ay a, H S,

G A , IM

F O , p SF

S, B B O -M

, an

d N M SO

L M F O

P o ly cr ys ta ll in e

ST P 6 12 0/ 36

B et te r ex p lo ra ti o n an

d ex p lo it at io n is

at ta in ed

[1 99 ]

C G B O

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

G B O , M P A , E O , IM

O , W O A ,

P SO

, an

d IP SO

T h in

fi lm

, p o ly cr ys ta ll in e,

an d

m o n o cr ys ta ll in e

T C Si , P V M 75 2

G aA

sc el l,

P W P 20 1,

k C 20 0G

T , SM

55

F in e- tu n in g ra n d o m

m o ve m en

ts el im

in at es

p re m at u re

co n ve rg en

ce an

d en

h an

ce s th e ex p lo ra ti o n

ca p ab il it y. Im

p le m en

ti n g ch

ao ti c

b eh

av io r an

d tu n in g th e d ir ec ti o n o f

m o ve m en

t in cr ea se s th e

co n ve rg en

ce ra te

[2 00 ]

Im SM

A E xp er im

en ta l

d at a

SD M

R M SE

V ar io u s 19

p ro m in en

t al go ri th m s

P o ly cr ys ta ll in e

ST P 6- 12 0/ 36 , R T C

F ra n ce

Im p le m en

te d L am

b er t W -f u n ct io n in

M at h em

at ic al

m o d el

h av in g

ad ap

ti ve

w ei gh

ts to

o b ta in

n eg at iv e

an d p o si ti ve

fe ed b ac k o f th e

p ro p ag at io n w av e d u ri n g fo o d

se ar ch

in g p ro ce ss

th at

in cr ea se s th e

ex p lo ra ti o n an

d ex p lo it at io n ab il it y

o f th e al go ri th m

[2 01 ]

C Ja ya

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

Ja ya , P SO

, an

d G A

P o ly cr ys ta ll in e

an d

m o n o cr ys ta ll in e

ST P 6- 12 0/ 36

P V ,

ST M 6- 40 /3 6,

R T C

F ra n ce

Se lf -a d ap

ti ve

w ei gh

t co n ce p t is

in cl u d ed

in co n ve n ti o n al

Ja ya

al go ri th m

to av o id

ge tt in g tr ap

p ed

in lo ca l m ax im

a an

d en

h an

ci n g th e

co n ve rg en

ce ra te .T

h re e co n ce p ts

su ch

as Si n e, lo gi st ic s an

d te n t m ap

ar e in cl u d ed

to at ta in

th e gl o b al

so lu ti o n

40 of 72 VENKATESWARI AND RAJASEKAR

T A B L E

4 (C o n ti n u ed )

R ef er en

ce s

A lg o ri th

m u se d

D a ta

u se d

M o d el in g

O b je ct iv e

fu n ct io n

C o m p a re d m et h o d s

T y p es

o f

p a n el

u se d

P V m o d u le s u se d

R em

a rk

s

[2 02 ]

Im p ro ve d F P A

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

V ar io u s 15

es ta b li sh ed

al go ri th m s

P o ly cr ys ta ll in e

P W P -2 01 , R T C

F ra n ce

D yn

am ic sw

it ch

p ro b ab il it y

es ta b li sh es

b al an

ce b et w ee n

ex p lo ra ti o n an

d ex p lo it at io n

p ro ce ss . D yn

am ic sw

it ch

p ro b ab il it y

el im

in at es

th e p re m at u re

co n ve rg en

ce is su es

[2 03 ]

E Ja ya

E xp er im

en ta l

d at a

SD M ,

D D M

R M SE

E Ja ya , Ja ya , IJ ay a, P G Ja ya ,

IT L B O , G O T L B O , M L B SA

, T L A B C , A G D E , T A P SO

, an

d SM

A E S

P o ly cr ys ta ll in e

an d

m o n o cr ys ta ll in e

P W P -2 01 ,

ST P 6- 12 0/ 36 ,

ST M 6- 40 /3 6

O p p o si ti o n -b as ed

le ar n in g m ec h an

is m

is in cl u d ed

in co n ve n ti o n al

Ja ya

al go ri th m

to av o id

ge tt in g tr ap

p ed

in lo ca l m ax im

a an

d en

h an

ci n g th e

co n ve rg en

ce ra te

[2 04 ]

G W O

E xp er im

en ta l

d at a

SD M

R M SE

,

M B E , SD

(A & W )

P SO

M o n o -c ry st al li n e,

m u lt i-

cr ys ta ll in e, an

d th in -f il m

SM 55 , K C 20 0G

T ,

ST 40

E xp lo ra ti o n an

d ex p lo it at io n ca p ac it y

o f G W O is u ti li ze d to

at ta in

b et te r

co n ve rg en

ce

[1 25 ]

P SO

G W O

E xp er im

en ta l

d at a

SD M

R M SE

G W O , G W O C S

M o n o -c ry st al li n e

an d m u lt i-

cr ys ta ll in e

SQ 85 , K C 20 0G

T L o ca l M in im

a an

d p re m at u re

co n ve rg en

ce is el im

in at ed

[2 05 ]

G W O C SA

E xp er im

en ta l

d at a

T D M

R M SE

P SO

, M V O , SC

A , C SA

, an

d G W O

M u lt i- cr ys ta ll in e

K C 20 0G

T P re m at u re

co n ve rg en

ce is su e is

el im

in at ed

VENKATESWARI AND RAJASEKAR 41 of 72

TABLE 5 Pros and cons of various algorithms

Algorithm Pros Cons

GA GA adopts three simple steps to find the minima in the case of nonconvex optimization125

GA involve wide search to choose chromosomes from an initial population that makes it computationally complex with lesser accuracy.126 It exhibits Low speed convergence because it requires enormous calculation. Further, the computation time of GA is higher.81 Its inability in local search results in being trapped in local minima.114

PS The local search capability of PS method is moderately higher162

Significant drawback of PS is it exhibits premature convergence if the selected pattern is wrong.162

SA Number of parameters to be tuned is lesser compared other algorithms125

Highly depends on its initial parameters, including cooling schedule, matching temperature and relative trade-off between those two factors. Designing cooling scheme is a complex procedure and requires high computation during its iterations.126

PSO PSO is easy to implement since only few parameters to adjust and its computations are faster compared to GA81,143

Major shortcomings of the PSO algorithm is it encounters premature convergence, requires high computation effort, produce low quality solutions in case of multimodal problems126 and if it is getting trapped in local minima.125

ABC Absence of a local search in the iterative process makes it more efficient. Further, the usage of three different operators helps in avoiding local optima in case of complex problems.158 Further, the involvement of various groups of bees with different patterns to explore the search space enhances its flexibility and achieves better balance between exploration and exploitation stage114

Premature convergence,90 random position selection for scout bees decreases its effectiveness.143

DE Most popular algorithm having more merits including fewer control parameters, simplicity, easy to program and high convergence at high speed160

The faster convergence has the higher the probability of premature convergence. The population size required for DE to work on a given problem is high that results in increasing computational burden.150

CAT Significant merits include flexibility, higher convergence and producing highly consistent results.160

CSO is slightly more complex compared to PSO method.160

Jaya Jaya algorithm is flexible since requires only two parameters for its operation namely population size and the number of generation. Hence, the complexity in tuning the parameters is less145

Improper tuning of these two parameters increases the computational burden and leads to premature convergence.145

FF FF algorithm converges to a global optimum at a faster rate and at higher accuracy than conventional algorithm.81

Delivers poor performance at exploitation step and its parameter tunings is complex.81

WOA Lesser number of parameters to be fine-tuned, simple in structure, less computational effort, and convergence speed is high174

Its adaptive parameter tuning depends on the random distribution and similar to other conventional algorithms, it suffers from premature convergence in case of multimodal search spaces.174

FPA Its convergence rate is essentially exponential. Delivers good performance with respect to convergence and obtaining an accurate curve fit165

Irrespective of the methods effectiveness in attaining accurate curve fit, FPA failed to check the pollens continuously resulting in generating poor fitness solutions; it leads to delayed convergence.81

ABSO Yields better convergence compared to conventional ABC ABSO delivers poor performance during repeated succession. Further, the brood mechanism followed in BM increases the procedural complexity and in implementation.

42 of 72 VENKATESWARI AND RAJASEKAR

estimation of solar PV. One of the factors that decide the efficiency of any algorithm is its objective function. For this reason, the RMSE objective function is considered as the deciding factor in defining the efficiency of each algorithm.

An algorithm is considered to be more efficient only if it has the lowest RMSE value. Hence, to arrive at a firm con- clusion, a comparative analysis of the effectiveness of all MAs is performed by considering the predefined RMSE factor. In all the cases, the parameters and RMSE calculations performed by all the algorithms are obtained at STC conditions.

In this study, 29 PV parameter estimation algorithms including evolutionary-based DE, GA algorithms, Nature-inspired based PS, SA, WDO, ERWCA, FPA meta-heuristic techniques, Bio-inspired based PSO, BFA, ABC, CSO, FF, CS, GWO, BMO, CSA, WOA, SSA, and human real-life based HS, ICA, SA, Jaya, AIS, and BBO are considered for analysis. Further- more, the commonly used PV panels of three different types; monocrystalline based SM55, SW245, SP190, STM6-40/36, 1STH-235-WH, SQ85, HIT-215, S75, Thin film based 752 GaAs, ST50 and polycrystalline based KS20T, kC200GT, RTC France, S36, SP70, ST36, RSM50, SM255, PWP201, Sharp ND-R250A5, SX3200N, KD210GH-2PU, ST40 PV modules are studied. For easy understanding, the performance comparison of algorithms is done separately concerning PV model and technology utilized. The cases considered for analysis are SDM-mono, SDM-thin-film, SDM-polycrystalline and DDM- mono, DDM-thin film, and DDM-polycrystalline are represented in Tables 6-11, respectively.

5.3 | Case study of the estimated parameter at STC

Six different cases at STC with two different modeling and three types of PV material types are considered for analysis. Every combination is extremely studied to know its suitability. The various cases are explained as follows.

TABLE 5 (Continued)

Algorithm Pros Cons

TLBO TLBO method requires only on algorithmic parameter namely population size. Hence complexity related to tuning of parameter is lesser131

It suffers from various shortcomings including lesser accuracy and reliability, particularly in case of double diode model.143

SSA SSA exhibits merits such as simple in structure, requires less computational effort with acceptable efficiency176

Convergence rate is lesser compared to other algorithms.176

BBO BBO algorithms are successful and favors local exploitation process125

It requires a relatively larger population that in turn reduces its computational speed.143

HS HS method is a highly promising method since it follows a simple concept and it is easy to implement. HS method produced better results compared to SA160

HS method tree parameters including pitch adjusting rate, bandwidth and harmony memory. It requires a large memory that may indirectly increases computational time.160 HS method fails to show its versatility in terms of local exploration and numerical computation.90

BMO SSA exhibits merits such as simple in structure, requires less computational effort with acceptable efficiency90

Even though BMO technique seems to be simple, the complexity increases if perceptive, various species are used.90

BFA Use of elimination step in BFA avoids premature convergence and improves solution space

Computational burden is high in case of bacterial foraging algorithm

Cuckoo One of the promising methods in extracting the parameters at a higher accuracy rate especially under various operating constraints.125 CSA incorporating Lévy walk allows it to explore the search space effectively and also making it as a efficient method125

Even though effective in exploration, and finding global optima, the number tuning parameters is four which leads to a tedious tuning process. Further, random nature of levy walk may lead the method to out of bound parameter limits that totally reduces the accuracy of the obtained solutions.126

AIS BBO algorithms are successful in favors local exploitation process125

Number of steps involved in AIS were four and they are clonal selection, immune memory, affinity maturation, and receptor. Hence, implementation of this method is complex and requires more time for computation. Moreover the error value obtained is higher which makes it less suitable for parameter extraction.156

VENKATESWARI AND RAJASEKAR 43 of 72

Case I. SDM with monocrystalline technology.

Case (I) summarizes the results obtained for monocrystalline type PV parameter extraction based on SDM. The fit- ness function calculated at STC by various meta-heuristic parameters extraction algorithms is provided in Table 6. Con- cerning every panel, the techniques are ranked in Table 6. The information in the table explains that FPA with SM55 panel approach to parameter estimation yields the lesser RMSE value of 0.00015024 is attained. In addition to that, the FPA estimates the parameter values with a minimum convergence time and high accuracy even at low irradiance and partial shading conditions. Whereas, the CWOA technique using 1STH-235-WH panel records the second-lowest RMSE of 9.86E � 4 when compared to other MA parameter extraction methods.

Finally, the MPSO algorithm using the SM55 panel is comparatively good to the other above-mentioned algorithm and considered as the third best algorithm with an RMSE value of 1.03E � 03. The results of the RMSE attained using various algorithms is shown in Figure 25A-C.

Case II. SDM with thin film technology.

The Case II performs a comparative analysis to identify the best algorithm that estimates the parameters of thin-film technology-based SDM of solar PV. By considering the RMSE factor, the MPSO, Jaya, and FPA of ST40 panel occupy the first three best positions with the RMSE values of 5.63979E � 04, 7.34E � 04, and 8.5E � 04, respectively and it is shown in Figure 26 and Table 7. The reason behind the PSO technique in obtaining better RMSE is using the mutant strategy during the exploration stage, where swarms are divided into more groups so that the entire search space is explored in finding the best solution.

Case III. SDM with polycrystalline technology.

The performance of various mentioned parameter estimation algorithm for polycrystalline based SDM-PV panel is compared concerning RMSE. The calculated modeling parameters with RMSE values by the MAs are given in Table 8. From the observation, among all RMSE results produced by various algorithms, the IADE of KC200GT solar PV make produced lesser RMSE value of 4.38E � 11. Besides producing minimal RMSE, the exploration rate and convergence speed are high in case of IADE based estimation techniques. Then WOA using KC200GT panel produced a low RMSE

FIGURE 24 Meta-analysis on photovoltaic (PV) technology

44 of 72 VENKATESWARI AND RAJASEKAR

T A B L E

6 R es u lt an

al ys is fo r m o n o cr ys ta ll in e te ch

n o lo gy -b as ed

SD M

o f a P V p an

el u si n g R M SE

u n d er

ST C

T y p e o f p a n el

A lg o ri th

m

P a ra m et er s

R S

R P

I S I L

n R M S E

R a n k

SM 55

F P A 1 6 5

0. 33 90 05

45 1. 22 05

1. 36 E �

07 3. 45 02 05

1. 37 80 97

1. 50 E �

04 1

M P SO

1 2 6

0. 33 01 28 8

48 0. 83 06

1. 67 E �

07 3. 45 01 84 1

1. 39 18 87 2

1. 03 E �

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1 4 5

0. 32 90 84 97

48 4. 36 21 04

1. 70 E �

07 3. 45 00 90 71

1. 39 59 08 94

1. 15 E �

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1 6 7

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45 5. 66 37 30 8

1. 22 E �

09 3. 40 35 39 18

1. 08 02 75 62

1. 46 E �

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10 4. 92

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1 5 0

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02 1

VENKATESWARI AND RAJASEKAR 45 of 72

value of 1.93E � 08. Finally, again the ERWCA method of SX3200N PV panel type produced an RMSE of 5.159179E � 4 which is lesser than all optimization algorithms except the ELPSO. The performance of various methods are illustrated in Figure 25D-I.

Case IV. DDM with monocrystalline technology.

The Case IV summarizes the results obtained for monocrystalline technology-based DDM of a PV panel. The modeling parameters and fitness function calculated at STC by various meta-heuristic parameters extraction algorithms are tabulated in Table 9. From the comparative analysis, it is observed that BPFPA with SM55 panel approach to parameter estimation yields lesser RMSE value of 4.58E � 4. The concept of division among the swarms was used in BPFPA to explore the entire search space and finding the optimal solution. The main advantages of BPFPA are more flexible and it maintains a proper balance between the exploration and exploitation in the process of finding the global solution. Whereas, the FPA technique using the same panel of SM55 stands second by providing an RMSE value of 0.00052542. Finally, the CWOA algorithm using STM6-40/36 panel occupies the third position with an RMSE value of 9.8272E � 4 when compared to other MA parameter extraction methods. The RMSE obtained by various methods are illustrated in Figure 27A-C

Case V. DDM with thin-film technology.

The Case V performs a comparative analysis to identify the best algorithm that estimates the parameters of thin-film technology-based DDM solar PV. The calculated modeling parameters with RMSE values are given in Table 10.

By considering the RMSE factor as shown in Figure 27, when compared to other optimization algorithms, the ELPSO of 752 GaAs produces an RMSE value of 2.75E � 08. Wherein the BPFA, MPSO, and FPA of ST40 panel make occupies the first three best positions with the RMSE values of 3.65E � 4, 5.94090E � 4, and 0.00099148, respectively.

Case VI. DDM with polycrystalline technology.

The performance of various mentioned parameter estimation algorithm for polycrystalline based DDM -PV panel is compared for RMSE. The calculated modeling parameters with RMSE values by the MAs are given in Table 11. From the observation, among all RMSE results produced by various algorithms, the GCPSO of RTC France solar PV make produced lesser RMSE value of 9.83E � 10; wherein, in GCPSO Scale factor which defines the search space area to be explored for finding the best solution is used as controlling factor in defining the velocity of the global best particle. The concept of modifying the velocity equation makes the GCPSO provide better performance in parameter estimation. The WOA method of KC200GT PV panel type produced a comparatively better RMSE of 2.7E � 8 which is lesser than all optimization algorithms with less convergence time. Finally, the BPFA of KC200GT PV make method produced a low RMSE value of 7.7301E � 4, it is still comparatively higher than the previous method. The RMSE obtained by various methods is illustrated in Figure 28D-F.

TABLE 7 Result analysis for thin-film technology-based SDM of a PV panel using RMSE under STC

Type of panel Algorithm

Parameters

RankRS RP IS IL n RMSE

ST40 MPSO126 1.1148351 356.134233 1.50E � 06 2.67588871 1.4963375 5.64E � 04 1 PGJaya145 1.11305759 358.244278 1.53E � 06 2.67575018 1.50055956 7.34E � 04 2 FPA165 1.122786 356.2676 1.41E � 06 2.675131 1.493337 8.50E � 04 3 GOFPANM167 1.2902707 223.4199276 8.25E � 08 2.70190621 1.25470413 1.88E � 03 4 GA87 1.149 860.75 NA NA 1.558 9.40E � 03 5

752 GaAs ELPSO152 0.159052 14.429507 0 0.115016 1.76859 2.54E � 02 1 Thin film BBO-M161 0.03642 53.36227 3.19E � 07 0.76078 1.47984 9.86E � 04 1

SBMO135 0.10472 5.13413 4.01E � 08 1.0729 1.9998 7.19E � 03 2

46 of 72 VENKATESWARI AND RAJASEKAR

T A B L E

8 R es u lt an

al ys is o n p o ly cr ys ta ll in e te ch

n o lo gy

b as ed

SD M

o f a P V p an

el u si n g R M SE

u n d er

ST C

N a m e o f p a n el

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m

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R a n k

R S

R P

I S I L

n R M S E

k C 20 0G

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0. 28 15

42 4. 22

8. 56 E �

08 8. 28

1. 29

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1 2 6

0. 34 48 50 8

75 3. 21 48 3

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09 8. 21 70 82 1

1. 07 27 49 6

1. 43 E �

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(C o n ti n u es )

VENKATESWARI AND RAJASEKAR 47 of 72

T A B L E

8 (C o n ti n u ed )

N a m e o f p a n el

A lg o ri th

m

P a ra m et er s

R a n k

R S

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48 of 72 VENKATESWARI AND RAJASEKAR

T A B L E

9 R es u lt an

al ys is fo r m o n o cr ys ta ll in e te ch

n o lo gy -b as ed

D D M

o f a P V p an

el b as ed

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m

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R a n k

R S

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I S 1

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2 9. 82 48 49 E �

04 2

VENKATESWARI AND RAJASEKAR 49 of 72

T A B L E

1 0

R es u lt an

al ys is fo r th in -f il m

te ch

n o lo gy -b as ed

D D M

o f a P V p an

el b as ed

o n R M SE

u n d er

ST C

T y p e o f p a n el

A lg o ri th

m

P a ra m et er s

R a n k R S

R S

R P

I S 1

I S 2

I L n 1

n 2

R M S E

ST 40

B P F P A 8 1

1. 10 2

33 2. 54

1. 60 E �

08 1. 56 E �

08 1. 49 5

3. 25 6

3. 65 E �

04 1

M P SO

1 2 6

1. 12 03 50 8

37 4. 22 61 24

1. 32 E �

06 7. 21 E �

05 2. 67 53 63 66

1. 48 33 15 16

4 5. 94 09 E �

4 2

F P A 1 6 5

1. 12 16 74

33 2. 99 76

1. 20 E �

06 6. 23 E �

05 2. 67 80 46

1. 47 73 28

3. 72 40 13

9. 91 E �

04 3

IC A 1 1 6

1. 50 80 53

37 7 65 3. 42 7

2. 65 E �

08 1. 58 E �

12 2. 68

1. 96 84 83

1. 28 84 81

8. 30 E �

03 4

G O F P A N M

1 6 7

1. 31 87 88 2

21 7. 16 29 08 3

1. 39 E �

07 1. 16 E �

09 2. 70 36 28 5

1. 33 60 21 88

1. 04 96 77 57

1. 87 E �

02 5

75 2 G aA

s E L P SO

1 5 2

0. 5

10 0

1. 77 50 00 e �

10 1. 00 E �

12 0. 10 31 92

2 1. 57 10 52

2. 08 E �

03 1

50 of 72 VENKATESWARI AND RAJASEKAR

T A B L E

1 1

R es u lt an

al ys is fo r p o ly cr ys ta ll in e te ch

n o lo gy -b as ed

D D M

o f a P V p an

el b as ed

o n R M SE

u n d er

ST C

T y p e o f p a n el

A lg o ri th

m

P a ra m et er s

R a n k

R S

R P

I S 1

I S 2

I L n 1

n 2

R M S E

K C 20 0G

T W O A 1 7 4

0. 27 45

29 1. 4

1. 92 E �

08 3. 73 E �

10 8. 14 6

1. 20 1

1. 10 7

2. 75 E �

08 1

B P F P A 8 1

0. 33 9

40 0. 12

6. 38 E �

09 2. 57 E �

07 1. 80 2

2. 98

2. 20 E �

04 2

IC A 1 1 6

0. 00 38

10 8. 78 44

1. 43 E �

07 2. 64 E �

09 8. 21

1. 32 74

1. 08 51

5. 26 E �

04 3

M P SO

1 2 6

0. 34 40 62 17

76 3. 73 71 99

2. 20 E �

09 9. 76 E �

07 8. 21 68 75 57

1. 07 42 31 45

3. 84 79 03 72 9

1. 15 E �

03 4

M F A 1 6 6

0. 17 69

39 6. 91 4

2. 91 E �

05 5. 85 E �

06 4. 72 97

57 .9 18 6

11 1. 97

1. 81 E �

02 5

D E T 1 4 9

0. 34

16 0. 64

4. 25 E �

10 4. 28 E �

10 6. 93 4

1. 04

1. 36

2. 10 E �

02 6

W IN

D 1 6 4

4. 40 E �

01 11 48 .6

1. 39 E �

06 1. 33 E �

06 4. 69 94

1. 96 18

1. 36 09

1. 26 E �

01 7

F IR

E W O R K S3

6 0. 30 3

34 3. 1

1. 11 E �

08 1. 11 E �

08 8. 21

1 1. 2

N A

N A

C ro w

[1 83 ]

0. 3

33 4

1. 73 E �8

5. 75 E �

10 8. 21

1. 35

1. 3

N A

N A

G A 8 7

0. 29

48 0. 49 6

4. 23 E �

09 9. 15 E �

09 1. 11 2

1. 37 7

N A

N A

A IS

1 5 6

0. 30 3

34 3. 1

1. 11 E �

08 1. 87 E �

10 N A

1. 2

1 N A

N A

R .T .C

F ra n ce

G C P SO

1 5 3

0. 03 67 5

55 .5 29 6

2. 25 E �

07 7. 55 E �

07 0. 76 07 8

1. 45 05 4

1. 99 99 8

9. 83 E �

10 1

IC A 1 1 6

0. 02 94

50 6. 56 E �

07 1. 58 E �

10 0. 76 05

1. 59 7

1 5. 27 E �

04 2

E L P SO

1 5 2

0. 03 75 51

55 .9 20 47 1

1E �

00 6

9. 91 68 24 E �

8 0. 76 08 29 57

1. 83 57 67

1. 38 60 91

7. 42 40 E �

4 3

T V A C P SO

1 5 1

0. 03 79 73

56 .5 49 60 5

4. 05 E �

08 9. 27 E �

07 0. 76 08 09

1. 32 71 6

1. 73 53 15

7. 44 E �

04 4

P A T T E R N & F F 1 6 2

0. 03 67 40 4

55 .4 85 5

2. 26 E �

07 7. 49 E �

07 0. 76 07 81

1. 45 10 1

2 9. 83 E �

04 5

T L B O 1 6 9

0. 03 67

55 .4 85 4

2. 26 E �

07 7. 49 E �

07 0. 76 08

1. 45 1

2 9. 83 E �

04 5

B C H S1

2 4

0. 03 67 4

55 .4 85 44

7. 49 E �

07 2. 26 E �

07 0. 76 07 8

2 1. 45 10 2

9. 82 5E

� 04

6

E SC

E -O

B L 1 7 9

0. 03 67 4

55 .4 85 44

2. 26 E �

07 7. 49 E �

07 0. 76 07 81

1. 45 10 17

2 9. 83 E �

04 7

B M O 1 7 1

0. 03 68 2

55 .8 08 1

2. 11 E �

07 8. 77 E �

07 0. 76 07 8

1. 44 53 3

1. 99 99 7

9. 83 E �

04 8

P G Ja ya

1 4 5

0. 03 68

55 .8 13 5

0. 21 03 1

8. 85 E �

07 0. 76 08

1. 44 5

2 9. 83 E �

04 8

M o d if ie d A B C 1 1 3

0. 03 67 12 15

54 .7 55 00 94

6. 31 E �

07 2. 41 E �

07 0. 76 07 82 1

2. 00 00 05 38

1. 45 68 57 3

9. 83 E �

04 8

SA T L B O 1 3 0

0. 03 66 3

55 .1 17

2. 51 E �

07 5. 45 E �

07 0. 76 07 8

1. 45 98 2

1. 99 94 1

9. 83 E �

04 8

M SS O 1 8 1

0. 03 66 88

55 .7 14 66 2

2. 35 E �

07 0. 67 15 93 -6

0. 76 07 48

1. 45 42 55

1. 99 53 05

9. 83 E �

04 8

IM P .S

H U F F (I SC

E )2 3

0. 03 67 40 4

55 .4 85 44 09

2. 26 E �

07 7. 49 E �

07 0. 76 07 81 08

1. 45 10 16 7

2 9. 83 E �

04 8

G O T L B O 1 3 1

0. 03 67 83

56 .0 75 30 4

8. 00 E �

07 2. 20 E �

07 0. 76 07 52

1. 99 99 73

1. 44 89 74

9. 83 E �

04 8

A B C 1 1 4

0. 03 65 7

54 .6 21 9

2. 67 E �

07 3. 82 E �

07 0. 76 07 8

1. 46 51 2

1. 98 15 2

9. 83 E �

04 8

T L A B C 1 7 0

0. 03 66 7

54 .6 67 97

4. 24 E �

07 2. 40 E �

07 0. 76 08 1

1. 90 75

1. 45 67 1

9. 84 E �

04 9

A B C 21

1 4

0. 0. 64

53 .7 80 4

4. 07 E �

08 2. 87 E �

07 0. 76 08

1. 44 95

1. 48 85

9. 86 E �

04 10

H S

0. 03 54 5

46 .8 26 96

1. 25 E �

07 2. 55 E �

07 0. 76 17 6

1. 49 43 9

1. 49 98 9

1. 26 E �

03 11

(C o n ti n u es )

VENKATESWARI AND RAJASEKAR 51 of 72

T A B L E

1 1

(C o n ti n u ed )

T y p e o f p a n el

A lg o ri th

m

P a ra m et er s

R a n k

R S

R P

I S 1

I S 2

I L n 1

n 2

R M S E

G SA

2 0 7

0. 03 39 16

81 .6 87 84 9

5. 66 E �

07 6. 89 E �

08 0. 76 03 4

1 53 8 56 3

1. 93 11 73

1. 31 E �

03 12

M E SW

SA 1 8 3

0. 03 64 87

54 .3 78 84

0. 26 77 64

2. 87 E �

01 76 0 77 9

2 1. 47 18 53

2. 80 E �

03 13

SA 1 4 6

0. 03 45

0. 02 32

4. 77 E �

07 1. 00 E �

08 0. 76 23

1. 51 72

2 N A

N A

O B W O A 1 4 1

0. 03 67 1

55 .3 99

2. 30 E �

07 6. 20 E �

07 0. 76 07 6

1. 49 15 4

2 9. 82 51

N A

P W P 20 1

IJ ay a1

7 4

0. 03 76

77 .8 51 9

5. 04 E �

09 7. 51 E �

07 0. 76 01

1. 21 86

1. 62 47

9. 83 E �

04 1

T V A C P SO

1 5 1

1. 23 56 32

82 1. 65 28 07

2. 64 E �

06 1. 00 E �

12 1. 03 14 34

47 .5 55 95 8

10 0

2. 05 E �

03 2

G C P SO

7 7

1. 23 92 88 4

74 4. 71 53 98 5

2. 51 E �

06 1. 00 E �

06 1. 03 23 82 33

1. 31 73 04 65

1. 31 69 39 92

2. 05 E �

03 2

M E SW

SA 1 8 3

1. 20 50 25

85 5. 54 01

3. 31 E �

06 7. 80 E �

03 1. 03 17 46

48 .4 80 34

50 6. 86 E �

02 3

ST M 6- 12 0/ 36

C h ao ti c A B C 1 4

0. 03 67 28

55 .3 78 26 1

2. 28 E �

07 6. 48 E �

07 7. 61 E �

07 1. 45 16 23

1. 98 83 43

9. 83 E �

04 1

K C 12 0- 1

SH U F F SC

E 1 7 9

3. 03 E �

01 53 .0 04 3

2. 80 E �

01 4. 16 E �

01 8. 17 56

31 .7 42 5

78 .4 27 4

3. 87 E �

01 1

Sh ar p N D -R 25 0A

5 G C P SO

7 7

0. 59 18 70 53

49 99 .9 96

2. 16 E �

05 7. 80 E �

01 9. 14 48 65 39

1. 20 65 79 13

1. 20 65 78 91

7. 70 E �

03 1

SX 32 00 N

E R W C A 1 4 3

0. 03 67 41 8

55 .4 85 8

2. 26 E �

07 7. 51 E �

07 0. 76 07 81

1. 45 09 3

2 9. 82 E �

04 1

S3 6

B P F P A 8 1

0. 02 58

45 8. 36

1. 60 E �

08 1. 15 E �

08 1. 15

3. 13

5. 87 E �

04 1

A IS

1 5 6

0. 67 8

20 0

4. 85 E �

09 9. 33 E �

11 N A

1. 2

1 N A

N A

S7 5

F P A 1 6 5

0. 38 03 97 1

79 0. 31 88

7. 89 E �

10 3. 35 E �

09 8. 22 26 43

1. 03 06 93

2. 34 92 79

2. 35 E �

03 1

G O F P A N M

1 6 7

0. 25 96 80 45

37 3. 62 17 88 7

1. 01 E �

07 2. 42 E �

08 4. 69 67 00 96

3. 56 81 24 87

1. 22 19 80 08

2. 53 E �

02 2

SP 70

F IR

E W O R K S3

6 0. 50 24 44

26 4. 90 71

1. 87 E �

10 1. 87 E �

10 4. 7

1 1. 2

N A

N A

A IS

1 5 6

0. 50 2

26 4. 9

1. 01 E �

08 1. 87 E �

10 N A

1. 2

1 N A

N A

p o ly

R SM

50 H Y B R ID

D E 1 8 2

0. 55 1

11 43 .2 89

5. 37 E �

10 8. 79 E �

06 3. 10 2

1. 06 1

2. 02 7

N A

N A

p o ly

ST 36

H Y B R ID

D E 1 8 2

1. 25 4

10 44 .6 76

5. 44 E �

07 8. 40 E �

05 2. 68 4

1. 66 5

2. 06 2

N A

P O L Y

O R cr -I JA

D E 9 4

0. 03 67 4

55 .4 85 43 8

2. 26 E �

07 7. 49 E �

07 0. 76 07 81

1. 45 10 17

2 9. 82 E �

04 1

R cr -I JA

D E 9 3

0. 03 67 4

55 .4 85 44 3

2. 26 E �

07 7. 49 E �

07 0. 76 07 81

55 .4 85 44 3

2 9. 82 E �

04 1

C at

1 6 0

0. 03 67 37

55 .3 81 3

2. 30 E �

07 7. 30 E �

07 0. 76 07 8

1. 45 15 1

1. 99 76 9

9. 83 E �

04 2

B B O -M

1 6 1

0. 03 66 4

55 .0 49 4

5. 91 E �

07 2. 45 E �

07 0. 76 08 3

2 1. 45 79 8

9. 83 E �

04 2

P S1

6 2

0. 03 2

0. 01 23

9. 89 E �

07 1. 00 E �

10 0. 76 02

1. 6

1. 19 2

2. 86 E �

01 4

P S1

6 2

0. 03 2

G sh

= 0. 01 23

9. 89 E �

07 1. 00 E �

10 0. 76 02

1. 6

1. 19 2

N A

-

52 of 72 VENKATESWARI AND RAJASEKAR

FIGURE 25 Analysis on single diode model (SDM) with mono and polycrystalline technology based on root mean square error (RMSE)

FIGURE 26 Analysis on single diode model (SDM) with thin-film technology based on root mean square error (RMSE)

VENKATESWARI AND RAJASEKAR 53 of 72

5.4 | Case study of the estimated parameter at varying irradiance conditions

The analysis under varying irradiance conditions (200, 400, 600, and 800 W/m2) delivers valuable insights into the cur- rent state of deployment, types of parameter estimation techniques existing and their Performance. The analysis is based on a range of RMSE to extract the parameters of both SDM and DDM of solar PV. Further, this study attempts to provide a detailed analysis of PV parameters estimated grounded on up-to-date and reliable statistics. Further, these reports aid to inform the current debate about parameter estimation techniques and assist researchers to make deci- sions on employing an appropriate technique.

Case I. SDM with monocrystalline technology under varying irradiance conditions.

This section examines the RMSE values of various parameter estimation algorithms for monocrystalline based SDM. The RMSE values attained by various techniques are provided in Table 12. By considering the RMSE factor, the

FIGURE 27 Result analysis for thin-film technology based double diode model of a photovoltaic (PV) panel based on root mean square error (RMSE)

FIGURE 28 Analysis on double diode model (DDM) with mono and polycrystalline technology based on root mean square error (RMSE)

54 of 72 VENKATESWARI AND RAJASEKAR

MPSO for 200 and 600 W/m2, FPA for 400, 800 W/m2 of SM55 panel occupies the first positions with the RMSE values of 3.20E � 04, 6.20E � 05, 7.40E � 04, and 3.14E � 04, respectively and it is shown in Figure 29A-D.

Case II. DDM with monocrystalline technology under varying irradiance conditions.

The performance of various mentioned parameter estimation algorithm for monocrystalline based DDM-PV panel is compared concerning RMSE. The considered modeling parameters with RMSE values by the various algorithms are specified in Table 13. From the observation, among all RMSE results produced by various algorithms, the MPSO pro- duced lesser RMSE value of 3.32E � 04 for an irradiance value of 200 W/m2. The BPFPA method of SM55 PV panel type produced a comparatively better RMSE of 1.26E � 4 at 400 W/m2 which is lesser than all optimization algorithms with less convergence time. Again, the BPFPA method of SM55 PV panel type produced minimum RMSE of 3.65E � 4 and 1.58E � 4 under 600 and 800 W/m2, respectively as shown in Figure 29E-H.

TABLE 12 Result analysis for monocrystalline technology-based SDM of a PV panel based on RMSE under various irradiance conditions

Type of panel Algorithm

Irradiance (W/m2)

Parameters

RS RP Is IL n RMSE

SM55 MPSO126 200 0.286589 448.2175 1.46E � 01 0.69151 1.378814 3.20E � 04 PGJaya145 200 0.28642 448.2315 1.47E � 01 0.691509 1.380719 3.21E � 04 FPA 200 0.33908 461.0258 1.40E � 01 0.689899 1.378876 5.72E � 04 GOFPANM167 200 0.658795 288.0549 2.29E � 03 0.694073 1.105302 2.51E � 03 DE149 200 0.3 271.8618 NA NA 1.4079 NA

BFOA74 200 0.63 1.79 NA NA 1.34 NA

MPSO126 400 0.395169 427.3221 1.04E � 01 1.382833 1.350951 7.05E � 04 PGJaya145 400 0.39655 427.1129 1.01E � 01 1.382842 1.352057 7.08E � 04 FPA165 400 0.338997 454.0656 1.38E � 01 1.38005 1.378208 6.20E � 05 GOFPANM167 400 0.270183 1056.327 8.55E � 02 1.358516 1.349415 6.05E � 03 DE149 400 0.3127 457.0585 NA NA 1.3752 NA

BFOA62 400 0.42 2.76 NA NA 1.43 NA

MPSO126 600 0.332954 447.9632 1.51E � 01 2.070961 1.382984 7.40E � 04 PGJaya145 600 0.330379 450.3085 1.56E � 01 2.070889 1.387702 8.24E � 04 FPA165 600 0.339027 435.3609 1.38E � 01 2.070495 1.378755 9.09E � 04 GOFPANM167 600 0.440091 471.5596 8.95E � 02 2.047539 1.189313 1.12E � 01 DE149 600 0.3127 421.6824 NA NA 1.397 NA

BFOA62 600 0.74 1.14 NA NA 1.1 NA

MPSO126 800 0.339101 458.113 1.41E � 01 2.760435 1.377407 5.89E � 04 PGJaya145 800 0.33762 459.8227 1.44E � 01 2.760383 1.381102 8.24E � 04 FPA165 800 0.339019 451.4057 1.37E � 01 2.76 1.377859 3.14E � 04 GOFPANM167 800 0.658795 288.0549 2.3E � 03 0.694073 1.105302 2.51E � 03 DE149 800 0.3191 318.8889 NA NA 1.397 NA

BFOA62 800 0.37 1.1 NA NA 1.34 NA

1STH235WH HYBRID(FF + PS)162

200 0.538067 388.6414 4.50E � 05 1.736608 54.91253 1.94E � 02 600 0.377745 764.5885 1.50E � 04 5.147846 64.11109 1.95E � 02

VENKATESWARI AND RAJASEKAR 55 of 72

FIGURE 29 Result analysis for monocrystalline technology-based single diode model (SDM) and double diode model (DDM) of a photovoltaic (PV) panel based on root mean square error (RMSE) under various irradiance conditions

56 of 72 VENKATESWARI AND RAJASEKAR

T A B L E

1 3

R es u lt an

al ys is fo r m o n o cr ys ta ll in e te ch

n o lo gy -b as ed

D D M

o f a P V p an

el b as ed

o n R M SE

u n d er

va ri o u s ir ra d ia n ce

co n d it io n s

T y p e o f p a n el

A lg o ri th

m G (W

/m 2 )

P a ra m et er s

R S

R P

I S 1

I S 2

R S

n 1

n 2

R M S E

SM 55

M P SO

1 2 6

20 0

0. 38 11 85 7

45 1. 37 36 7

3. 54 E �

02 0. 42 51 21 4

0. 69 15 99 6

1. 27 83 70 7

1. 67 75 83 8

3. 32 E �

04

B P F P A 8 1

20 0

0. 35 69

44 0. 56

2. 56 E �

08 5. 99 E �

08 N A

1. 45 4

2. 85 4

6. 85 E �

04

F P A 1 6 5

20 0

0. 33 90 00 7

44 3. 46 34

1. 40 E �

01 1. 42 E �

01 0. 69 05 77 1

1. 37 81 75

3. 45 68 5

4. 09 E �

04

G O F P A N M

1 6 7

20 0

0. 70 76 71 3

28 2. 75 42 7

0. 00 12 22 9

1. 39 E �

03 0. 69 46 00 7

1. 34 85 00 7

1. 07 83 86 9

2. 50 E �

03

M P SO

1 2 6

40 0

0. 37 29 56 4

43 4. 54 00 4

0. 11 81 08 6

2. 29 E �

01 1. 38 26 19 4

1. 36 33 44 2

2. 42 28 87 4

7. 32 E �

04

B P F P A 8 1

40 0

0. 36 6

41 8. 36

1. 99 E �

08 4. 56 E �

08 N A

1. 45 4

2. 85 4

1. 26 E �

04

F P A 1 6 5

40 0

0. 33 86 84 3

45 1. 18 3

0. 13 92 18 9

1. 22 E �

01 1. 38 06 96

1. 37 79 24

2. 29 72 63

6. 09 E �

04

G O F P A N M

1 6 7

40 0

0. 32 74 72 3

11 84 .5 34 7

0. 95 71 37 1

8. 7E

� 03

1. 35 81 63 4

1. 78 07 35 5

1. 20 03 31 5

5. 97 E �

03

M P SO

1 2 6

60 0

0. 33 35 43 1

44 7. 69 84 6

0. 14 93 06 8

5. 91 E �

02 2. 07 09 64 2

1. 38 22 65 1

3. 12 67 74 3

7. 40 E �

04

B P F P A 8 1

60 0

0. 35 33

42 0. 66 5

1. 36 E �

08 5. 57 E �

08 N A

1. 25 63

2. 69 42

3. 65 E �

04

F P A 1 6 5

60 0

0. 33 80 30 5

48 0. 16 78

0. 14 72 42 3

0. 15 30 21

2. 06 89 47

1. 38 24 51

2. 83 41 06

5. 35 E �

04

G O F P A N M

1 6 7

60 0

0. 48 94 58 2

50 3. 42 77 9

0. 00 01 69 3

1. 25 E �

01 2. 04 70 18 9

1. 00 08 90 7

1. 48 80 63

1. 12 E �

02

M P SO

1 2 6

80 0

0. 33 99 00 8

45 7. 64 49 6

0. 13 81 62 6

3. 24 E �

01 2. 76 04 59 5

1. 37 59 88 4

2. 97 92 39 2

5. 91 E �

04

B P F P A 8 1

80 0

0. 42 5

41 5. 35 2

1. 41 E �

08 6. 60 E �

07 N A

1. 29 E + 00

2. 97 E + 00

1. 58 E �

04

F P A 1 6 5

80 0

0. 33 88 29

46 9. 33 6

0. 14 25 45 2

6. 76 E �

01 2. 75 93 54

1. 37 97 19

3. 14 59 1

4. 10 E �

04

G O F P A N M

1 6 7

80 0

0. 53 09 54 4

39 3. 95 46 4

0. 00 01 57 7

1. 22 E �

03 2. 72 79 35 8

1. 00 73 19 7

1. 13 26 68

2. 50 E �

02

VENKATESWARI AND RAJASEKAR 57 of 72

Case III. SDM with thin-film technology under varying irradiance conditions.

The Case IV reviews the outcomes gained for thin-film technology-based SDM of a PV panel. The modeling parame- ters and fitness function estimated at various irradiance by various meta-heuristic parameters extraction algorithms are tabulated in Table 14. By considering the RMSE factor, the MPSO at 200, 400 W/m2 and FPA at, 600, 800 W/m2

occupies the first best positions with the RMSE values of 4.68E � 03, 5.62E � 04, 5.62E � 04, and 4.55E � 04, respec- tively and it is shown in Figure 30A-D.

Case IV. DDM with thin-film technology under varying irradiance conditions.

This section examines the RMSE values of various parameter estimation algorithms for DDM based thin-film solar PV. The RMSE values achieved by numerous techniques are provided in Table 15. By considering the RMSE factor, the FPA at 200 W/m2, BPFPA at 400 W/m2, MPSO at, 600 W/m2, and again BPFPA at 800 W/m2 occupies the first best positions with the RMSE values of 3.70E� 4, 2.53e � 4, 5.85E � 4, and 5.59E � 4, respectively and it is shown in Figure 30E-H.

TABLE 14 Result analysis for thin-film technology-based SDM of a PV panel based on RMSE under various irradiance conditions

Algorithm Irradiance (W/m2) G (W/m2)

Parameters

RS RP Is IL N RMSE

SM55 MPSO126 200 1.13247 347.9391 1.60 0.53294 1.508484 4.68E � 03 PGJaya145 200 1.185761 344.9813 1.43E 0.533138 1.497513 4.78E � 04 FPA165 200 1.105976 346.0733 1.508465 0.532235 1.508465 8.71E � 04 GOFPANM167 200 2 343.3746 1 0.546297 1.43716 7.68E � 03 DE149 200 1.0187 384.6959 NA NA 1.6297 NA

BFOA62 200 0.91 2.34 NA NA 1.73 NA

MPSO126 400 1.091071 360.6319 1.759776 1.067647 1.516792 5.62E � 04 PGJaya145 400 1.080524 362.538 1.85E + 00 1.067543 1.524492 6.31E � 04 FPA165 400 1.102002 362.0731 1.723246 1.066905 1.517492 6.21E � 04 GOFPANM167 400 1.320864 310.228 1 1.083355 1.451668 7.87E � 03 DE149 400 1.0027 309.5164 NA NA 1.6547 NA

BFOA62 400 0.99 1.25 NA NA 1.81 NA

MPSO126 600 1.115301 346.989 1.42E + 08 1.604855 1.492018 5.85E � 04 PGJaya145 600 1.112591 347.7152 1.44E + 00 1.604808 1.495841 6.74E � 04 FPA165 600 1.120239 344.7073 1.487202 1.604418 1.487202 5.41E � 04 GOFPANM167 600 1.205567 264.742 1 1.622439 1.455639 1.25E � 02 DE149 600 1.0027 299.2976 NA NA 1.6496 NA

BFOA62 600 0.84 0.702 NA NA 1.83 NA

MPSO126 800 1.127075 332.0005 1.14E + 00 2.138076 1.4694 5.92E � 04 PGJaya145 800 1.124563 333.623 1.17E + 00 2.137955 1.473957 6.74E � 04 FPA165 800 1.141579 328.0618 1.023342 2.137686 1.461888 4.55E � 04 GOFPANM167 800 2 343.3746 1 0.546297 1.43716 7.68E � 03 DE149 800 1.01 370.9784 NA NA 1.6496 NA

BFOA62 800 0.77 2.29 NA NA 1.28 NA

58 of 72 VENKATESWARI AND RAJASEKAR

FIGURE 30 Result analysis for thin-film technology-based single diode model and double diode model of a photovoltaic (PV) panel based on root mean square error (RMSE) under various irradiance conditions

VENKATESWARI AND RAJASEKAR 59 of 72

T A B L E

1 5

R es u lt an

al ys is fo r th in -f il m

te ch

n o lo gy -b as ed

D D M

o f a P V p an

el b as ed

o n R M SE

u n d er

va ri o u s ir ra d ia n ce

co n d it io n s

A lg o ri th

m Ir ra d ia n ce

(W /m

2 )

G (W

/m 2 )

P a ra m et er s

R S

R P

I S 1

I S 2

R S

n 1

n 2

R M S E

ST 40

M P SO

1 2 6

20 0

1. 14 65 23 4

34 9. 57 84 8

5. 72 61 98 6

1. 50 69 31 5

0. 53 28 80 8

1. 50 17 34 9

3. 40 48 56 1

4. 65 E �

04

B P F P A 8 1

20 0

1. 11 5

32 2. 58

1. 40 E �

09 1. 59 E �

07 N A

1. 44 8

3. 35 2

5. 25 E �

04

F P A 9 8

20 0

1. 14 07 72

31 4. 23 27

1. 29 E +

00 1. 50 E +

00 0. 53 28 49 2

1. 48 47 85

3. 10 12 58

3. 70 E �

04

G O F P A N M

1 6 7

20 0

1. 82 47 21

37 7. 09 04 1

1 1

0. 54 46 51 6

1. 51 66 5

1. 51 66 49 9

6. 92 E �

03

M P SO

1 2 6

40 0

1. 09 28 54 6

36 3. 44 61 1

1. 72 72 18 9

11 .1 32 18 1

1. 06 75 61 9

1. 51 44 08 4

4 5. 64 E �

04

B P F P A 8 1

40 0

1. 12 9

33 6. 52

1. 56 E �

08 1. 59 E �

08 N A

1. 48 7

3. 50 2

2. 53 E �

04

F P A 9 8

40 0

1. 14 79 78

32 2. 02 61

8. 12 E �

01 74 .7 19

1. 07 11 09

1. 43 84 19

3. 67 85 99

3. 83 E �

04

G O F P A N M

1 6 7

40 0

1. 21 38 01 8

34 6. 57 12 9

9. 99 E �

01 0. 99 93 37 5

1. 08 11 23 7

1. 52 59 09 6

1. 52 37 47 5

6. 92 E �

03

M P SO

1 2 6

60 0

1. 11 76 72 8

35 0. 54 71 1

1. 35 89 45 4

19 .1 61 67 3

1. 60 47 66 1

1. 48 7. 67 96

4 5. 85 E �

04

B P F P A 8 1

60 0

1. 12 5

32 9. 56

1. 15 E �

08 1. 47 E �

08 N A

1. 40 2

3. 44 5

7. 85 E �

04

F P A 9 8

60 0

1. 12 31 32

33 9. 45 45

1. 19 69

47 .3 83 19

1. 60 61 46

1. 47 78 7

3. 06 53 3

9. 29 E �

04

G O F P A N M

1 6 7

60 0

1. 13 60 30 4

30 3. 59 47 5

1 1

1. 61 89 92 2

1. 52 94 01 2

1. 52 93 78

1. 11 E �

02

M P SO

1 2 6

80 0

1. 13 02 56 3

34 0. 00 62 1

1. 05 97 53

37 .4 30 99

2. 13 78 14 8

1. 46 24 76 1

4 6. 06 E �

04

B P F P A 8 1

80 0

1. 19 6

34 4. 56

1. 50 E �

08 1. 49 E �

08 N A

1. 42 5

3. 48 5

5. 59 E �

04

F P A 9 8

80 0

1. 13 88 31

31 3. 83 27

1. 03 50 84

1. 12 56 82

2. 14 35 22

1. 46 22 71

3. 30 52 67

7. 65 E �

04

G O F P A N M

1 6 7

80 0

1. 04 73 41 1

22 0. 67 17 4

9. 99 E �

01 0. 99 99 98 9

2. 16 33 60 9

1. 53 16 74

1. 53 17 40 5

1. 33 E �

02

60 of 72 VENKATESWARI AND RAJASEKAR

Case V. SDM with polycrystalline technology under varying irradiance conditions.

The performance of various mentioned parameter estimation algorithm for polycrystalline based SDM-PV panel is compared for RMSE. The calculated modeling parameters with RMSE values by the MAs are given in Table 16 and Figure 31A-D, respectively. From the observation, among all RMSE results produced by various algorithms, the ER- WCA of KC200GT solar PV make produced lesser RMSE at 200, 400, and 600 W/m2 with the value of 1.51E � 4, 3.28E � 5, 7.68E � 4 and FPA at 800 W/m2 with RMSE value of 0.000735, respectively.

Case VI. DDM with polycrystalline technology under varying irradiance conditions.

The performance of various mentioned parameter estimation algorithm for polycrystalline based DDM -PV panel is compared to RMSE. The calculated modeling parameters with RMSE values by the MAs are given in Table 17 and Figure 31E-H. From the observation, among all RMSE results produced by various algorithms, the BPFPA of KC200GT solar PV make produced lesser RMSE at 200, 400, 600, and 800 W/m2 with the value of 3.12E � 4, 2.14E � 5, 3.14E � 4, and 4.14E � 4, respectively.

TABLE 16 Result analysis for polycrystalline technology-based SDM of a PV panel using RMSE under various irradiance conditions

Algorithm Irradiance (W/m2) Type of panel

SDM-POLY

RS RP Is IL n RMSE

SM55 MPSO126 200 0.379742 690.6491 5.30E � 04 1.646148 1.002619 1.14E � 03 ERWCA143 200 0.319368 868.3201 8.69E � 10 1.645074 1.072741 1.51E � 04 PGJaya145 200 0.378951 697.7378 5.37E � 04 1.645905 1.004631 1.42E � 03 FF-PS162 200 0.272048 1161.4 4.44E � 02 8.177455 69.80604 4.43E � 02 FPA165 200 0.378527 718.6799 1.010337 1.642036 1.010337 9.33E � 04

MPSO126 400 0.355314 748.8205 1.44E � 03 3.287905 1.051893 1.39E � 03 ERWCA143 400

PGJaya145 400 35 044 054 762.7355 1.61E � 03 3.287691 1.058725 1.44E � 03 FF-PS162 400

FPA165 400 0.355436 742.3341 1.46E � 03 3.283832 1.05386 9.62E � 04

MPSO126 600 0.337818 739.969 3.80E � 03 4.934361 1.102202 1.28E � 03 ERWCA143 600 0.321917 292.0804 9.25E � 10 4.934781 1.075513 7.68E � 04 PGJaya145 600 0.335764 762.6261 4.12E � 03 4.933921 1.107392 1.34E � 03 FF-PS162 600 0.132137 359.1577 3.15E � 01 4.93922 78.3876 4.09E � 02 FPA165 600 0.338722 727.3864 1.103524 4.92998 1.103524 1.00E � 03

MPSO126 800 0.35642 737.2757 9.89E � 04 6.571658 1.035554 1.46E � 03 ERWCA143 800

PGJaya145 800 0.356858 764.3966 9.83E � 04 6.570779 1.036721 1.34E � 03 FF-PS162 800

FPA165 800 0.358294 757.5718 9.81E � 04 6.565279 1.03665 7.35E � 04 SX3200N ERWCA143 200 0.296319 3159.954 3.83E � 08 1.785744 1.059864 3.28E � 05

FF-PS162 200 0.337609 2000 2.79E � 02 1.781057 52.08052 9.98E � 03 ERWCA143 400 0.295242 1123.254 4.08E � 08 5.356718 1.063468 5.10E + 02 FF-PS162 400 0.287199 333.8148 5.46E � 02 5.372796 54.02059 2.37E � 02

VENKATESWARI AND RAJASEKAR 61 of 72

FIGURE 31 Result analysis for polycrystalline technology-based single diode model (SDM) and double diode model (DDM) of a photovoltaic (PV) panel based on root mean square error (RMSE) under various irradiance conditions

62 of 72 VENKATESWARI AND RAJASEKAR

T A B L E

1 7

R es u lt an

al ys is fo r p o ly cr ys ta ll in e te ch

n o lo gy -b as ed

D D M

o f a P V p an

el u si n g R M SE

u n d er

va ri o u s ir ra d ia n ce

co n d it io n s

A lg o ri th

m Ir ra d ia n ce

(W /m

2 )

T y p e o f p a n el

P a ra m et er s

R S

R P

I S 1

I S 2

I L n 1

n 2

R M S E

K C 20 0G

T M P SO

1 2 6

20 0

0. 37 90 08 3

70 1. 12 43 77

5. 12 E �

04 2. 95 20 71 7

1. 64 00 00 2

1. 00 11 07 9

3. 22 35 94 69

1. 41 E �

03

B P F P A 8 1

20 0

0. 28 7

38 7. 36

8. 53 E �

09 3. 97 E �

07 N A

1. 96 6

2. 74 1

3. 12 E �

04

F P A 1 6 5

20 0

0. 40 76 64

76 1. 55 69

7. 74 E �

04 6. 20 E �

03 1. 65 16 33

1. 01 69 06

2. 49 55 9

8. 57 E �

04

M P SO

1 2 6

40 0

0. 35 58 08 3

75 2. 82 64 34

1. 41 E �

03 2. 48 45 24 8

3. 28 78 56 1

1. 05 10 60 3

3. 99 99 99 87

1. 39 E �

03

B P F P A 8 1

40 0

0. 32

39 6. 47

4. 58 E �

09 2. 87 E �

07 N A

1. 75 3

2. 98 2

2. 47 E �

04

F P A 1 6 5

40 0

0. 40 09

79 0. 12 16

7. 53 E �

04 1. 36 E �

03 3. 29 54 72

1. 02 05 57

2. 68 77 89

1. 87 E �

03

M P SO

1 2 6

60 0

0. 33 77 17 2

74 0. 79 35 39

3. 81 E �

03 1. 1E

� 01

4. 93 43 49

1. 10 17 93 1

4 1. 28 E �

03

B P F P A 8 1

60 0

31 4

37 4. 51

4. 92 E �

09 4. 77 E �

07 N A

1. 76 9

2. 66 3

3. 48 E �

04

F P A 1 6 5

60 0

0. 39 59 01

76 9. 56 41

7. 57 E �

04 1. 77 E �

03 4. 93 90 89

1. 02 42 32

2. 75 23 19

2. 14 E �

03

M P SO

1 2 6

80 0

0. 35 69 43 1

7 72 1 22 2 73 7

9. 24 E �

04 3. 08 E �

01 6. 57 08 85 6

1. 03 25 94

2. 13 64 45 8

1. 45 E �

03

B P F P A 8 1

80 0

0. 34 1

38 9. 77

4. 52 E �

06 3. 87 E �

07 N A

1. 74 1

2. 65 5

4. 12 E �

04

F P A 1 6 5

80 0

0. 38 27 71

79 1. 04 1

8. 17 E �

04 1. 17 E �

03 6. 57 79 32

1. 02 84 72

2. 61 58 32

2. 22 E �

03

S7 5

G O F P A N M

20 0

0. 26 35 22

41 1. 69 35 6

0. 13 03 62 08

2. 5E

� 01

0. 94 41 12 2

2. 70 81 25 5

1. 23 41 11 9

1. 59 E �

03

40 0

0. 26 43 44

35 0. 08 34 7

0. 60 47 24 91

6. 4E

� 03

1. 88 42 21 8

4 1. 14 05 87

9. 34 E �

03

60 0

0. 39 31 93

29 8. 04 90 7

0. 00 00 72 29

6. 05 E �

04 2. 82 98 77 3

1. 00 02 80 7

1. 03 47 55 1

2. 33 E �

02

80 0

0. 35 17 81

42 5. 94 34 9

0. 61 56 08 83

3. 27 E �

03 3. 75 64 21

3. 93 97 24 7

1. 10 66 75 1

2. 23 E �

01

VENKATESWARI AND RAJASEKAR 63 of 72

5.5 | Summary of analysis

1. Considering the modeling and manufacturing technology, the algorithms that produced highly efficient results based on the RMSE results at STC, were listed below i. FPA of SDM and SSA of DDM for monocrystalline technology holds the first position in delivering mini-

mum RMSE. ii. PSO of SDM and BPFPA of DDM for thin-film technology holds the first position in delivering minimum RMSE. iii. IADE of SDM and GCPSO of DDM for polycrystalline technology holds the first position in delivering minimum RMSE.

2. Further, the conventional Parameter estimations algorithms like PSO, FPA to overcome its limitations; instead com- bining of two or more algorithms. For an example, initially authors used PSO algorithm to extract the parameters of solar PV; wherein, the authors in Reference 152 proposed ELPSO, a modified version/variant of PSO by incorporat- ing five-mutation operator to leader of the swarm to overcome the pre convergence problem existing in the conven- tional PSO algorithm. 1. Similarly, based on PV technology and modeling, the algorithms that produced best results at various irradiance

conditions including 200, 400, and 600 W/m2 are listed as follows. 2. For SDM- monocrystalline case, the PSO at 200 and 600 W/m2 irradiances and FPA at 400 and 800 W/m2 deliver

the least RMSE when compared to methods compared. 3. For DDM- monocrystalline case, the PSO at 200 W/m2 and BPFPA at 400, 600, and 800 W/m2 produced the low-

est RMSE values. 4. For SDM- thin-film technology, the PSO at 200 and 400 W/m2 irradiances and FPA at 600 and 800 W/m2 deliver

the least RMSE. 5. For DDM- thin-film technology, the FPA at 200 W/m2, BFPA at 600 and 800 W/m2 and PSO at 600 W/m2 offered

the minimum RMSE values 6. For SDM- polycrystalline technology, the ERWCA at 200, 400, and 600 W/m2 irradiances and FPA at and 800 W/

m2 delivers the least RMSE 7. For DDM-polycrystalline technology, the BPFPA at 200, 400, 600, and 800 W/m2 delivers the least RMSE.

6 | CONCLUSION

This review article based on PV parameters estimation since its influence on PV growth is significant. In this article, a col- lection of nearly 29 algorithms with their variants published to date have been reviewed; a brief discussion on each algo- rithm was carried out and presented. This article expounds to explore and exploit the working concept of various researches considering key factors such as (a) type of modeling, (b) algorithm employed for parameter extraction, (c) material of panel, (d) PV technology, (e) type of panel used for research work, and (f) performance metrics in analyzing the efficiency of every algorithm. Further Case study on estimated PV parameter at STC and varying irradiance conditions comprising 12 different cases considering formerly mentioned factors in research work have been extensively studied to know the suitability of every algorithm; further supporting graphs, illustrations, data tables have been included in the man- uscript to enhance the researchers understanding. Finally, the algorithm that delivered the best outcome considering envi- ronmental conditions is discussed. Further, the usefulness of every algorithm is determined by considering the RMSE value. All the algorithms are equally good, still there exist a very little difference in their efficiency when RMSE factor is considered. Among the 29 algorithms reviewed, the performance of FPA and its variants, ERWCA, BPFP, PSO, and its vari- ants shows better performance in parameter estimation The least RMSE values concerning monocrystalline, Thin film and polycrystalline produced by FPA, BPFPA, and ERWCA were 1.50E � 04, 2.53E � 04, and 1.51E � 04, respectively. This review useful for ambitious researchers working on solar PV for understanding its basics and logic. For further betterment of MA in parameter estimation, some suggestions are provided in the following section.

7 | FUTURE WORK

In this review, an in-depth analysis of widely used MAs for parameter estimation was performed. Still, some points required to enhance the performance of the algorithms utilized for parameter estimation are endorsed in this section for the future purpose. The suggestions are given as follows:

64 of 72 VENKATESWARI AND RAJASEKAR

1. It is recommended to utilize the combination of analytical and MA for extracting the parameters of solar PV 2. It could be much appreciable and useful if more experimentation in parameter estimation is performed with three

diode models 3. Very few works were carried out with Thin-Film based commercial solar cells. Hence it is recommended to make

more attempts of researches using thin-film based solar modules 4. An attempt can be made with other commercial solar PV except for monocrystalline based SM55, thin-film based

ST40, and polycrystalline based RTC France and KC200GT. 5. It is recommended to explore more meta-heuristic-based algorithms to extract the parameters of solar PV 6. In all the research work based every MA, the influence of all the objective functions is not taken in to account. It

would be better if all the objective functions are considered for determining the efficiency

ACKNOWLEDGMENT This work has been carried out in Solar Energy Research cell (SERC), School of Electrical Engineering (SELECT), Vellore Institute of Technology (VIT), Vellore. Hereby authors would like to thank VIT management for their support.

CONFLICT OF INTEREST Authors declare there are no conflicts of interest.

PEER REVIEW The peer review history for this article is available at https://publons.com/publon/10.1002/2050-7038.13113.

DATA AVAILABILITY STATEMENT The data that support the findings of this study are available from the corresponding author upon reasonable request.

ORCID Natarajan Rajasekar https://orcid.org/0000-0001-6489-1736

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How to cite this article: Venkateswari R, Rajasekar N. Review on parameter estimation techniques of solar photovoltaic systems. Int Trans Electr Energ Syst. 2021;31(11):e13113. doi:10.1002/2050-7038.13113

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