Parameter Extraction of Solar Photovoltaic Cell and Module Models with Metaheuristic Algorithms: A Review
Abstract
:1. Introduction
 The mathematical models of current commonly used SDM, DDM, TDM, and PV modules are explained;
 The characteristics of each metaheuristic method and their enhancements and applications are outlined;
 The statistical results of RMSE, TNFES, SIAE and algorithmic settings of selected metaheuristics are summarized and compared;
 The output characteristics of the PV system are discussed for the dynamic temperature, irradiance, and partial shading, and the variation in parameters and RMSE are analyzed;
 Existing challenges and possible future work focuses are analyzed and provided.
2. PV Models and Problem Formulations
2.1. PV Models
2.1.1. SDM
2.1.2. DDM
2.1.3. TDM
2.1.4. PV Module
2.1.5. PV Model Review
2.2. Problem Formulations
2.3. Indicators Summary
 Friedman test (FT), Wilcoxon rank sum test (WRT), and Wilcoxon signed rank test (WST): they broaden evaluation scales from statistical perspectives;
 In addition, a few works in the literature also use evaluation indicators such as the sum of squares of power, current, and voltage errors (ERR) [61].
3. Methods and Results
3.1. GAs
3.2. DEs
3.3. PSOs
3.4. ABCs
3.5. GWOs
3.6. JAYAs
3.7. TLBOs
3.8. WOAs
3.9. Hybrids
3.10. Others
4. Whole Analysis and Research Prospects
4.1. Data Analysis
 The STD of RMSE reflects the results’ robustness, MIN RMSE means the results’ accuracy, and other RMSEs denote the range and sharpness of the fluctuations in the results. The SDM, DDM and PhotowattPWP201 models of DEDIWPSO had the MIN RMSE (7.730062 × 10^{−4}, 7.182306 × 10^{−4}, and 2.03992 × 10^{−3}), mean RMSE (7.730062 × 10^{−4}, 7.187462 × 10^{−4}, and 2.03992 × 10^{−3}), MAX RMSE (7.730062 × 10^{−4}, 7.3181 × 10^{−4}, and 2.03992 × 10^{−3}) and STD (5.18668 × 10^{−15}, 2.486129 × 10^{−6}, and 2.995389 × 10^{−15}). It is followed by IGSK with MIN RMSE (9.8602188 × 10^{−4}, 9.8248485 × 10^{−4}, and 2.4250749 × 10^{−3}), mean RMSE (9.8602188 × 10^{−4}, 9.8272774 × 10^{−4}, and 2.4250749 × 10^{−3}), MAX MRSE (9.8602188 × 10^{−4}, 9.8602188 × 10^{−4}, and 2.4250749 × 10^{−3}) and STD (3.5821018 × 10^{−17}, 8.9578942 × 10^{−7}, and 2.9226647 × 10^{−17}). Then, EOTLBO, OLBGWO, CSOOJAYA, RLDE, ABCTRR, IWOA, TLBOBSA, HSOA, and SOS followed.
 Figure 4 shows the combined FT ranking for the SDM, DDM, and PhotowattPWP201. It combines the absolute accuracy of the methods in a wide range of cases. GSK ranks first, followed by MCSWOA, IWOA, GCPSO, QILDE, DE/WOA, DMTLBO, HSOA, MLJAYA, SOS, TLABC, PSOST, ABCTRR, IGWO, HDE, TLBOBSA, ISNMWOA, and DPDE. GSK, as a new method achieving the highest accuracy, demonstrates the need to explore the performance of new schemes in this issue. It is worth noting that the rankings of the same methods in different PV models may differ, which indicates that different PV models have varied preferences for algorithms.
 TNFES is related to the computational resources consumed, with a lower TNFES representing a lower computational burden. For the SDM and module, ABCTRR had the fewest TNFES (1000) while other methods basically used a TNFES of 50,000. For the DDM, ABCTRR had the fewest TNFES (5000), while most of the rest consumed a TNFES of 50,000.
4.2. Analysis of Temperature and Irradiance Influences
4.2.1. Uniform Irradiance and Temperature
4.2.2. Partial Shade Conditions
4.3. Analysis of Modified Diode Models’ Works
4.4. Analysis of Dynamic Models’ Works
4.5. Whole Analysis
 The promotion of GA has been rare in recent years, and accuracy is supposed to be enhanced.
 DE’s convergence rate and PSO’s accuracy could improve.
 ABC is weakly exploited and significant in parameter settings.
 GWO and WOA have few parameters and struggle with multidimensional issues.
 JAYA and TLBO’s promotions are flawed in accuracy.
 Hybrid approaches may complicate the implementation and introduce additional parameters.
 New approaches are not sufficiently balanced for specific issues. For example, GSK, SDO, TGA, and SOS are underexploited, and HHO and FPOA are underexplored.
 TNFES is a sign of computational resources, yet its value is almost pitched at 50,000. Reducing TNFES without compromising accuracy is imperative.
 More diodes in the cell model may increase the extraction accuracy. Recently, a four diode model was proposed [47] and the results showed good fitting effect. However, more diodes also indicate more parameters that need to be extracted and solutions are also more intractable. Hence, selecting a suitable PV model for an algorithm is challenging.
 Some of the literature used too few PV cases to demonstrate metaheuristics’ generalizability.
 Metaheuristics’ effectiveness is devoid of practical engineering applications.
 More and exact measured data means more accurate extraction results, but obtaining sufficient highprecision measurements is challenging and costly.
 In engineering, running time is pivotal. Hence, cutting running times is a challenge.
 Multiple matrices are imperative to signal the competitiveness of metaheuristic results, yet some of the literature adopted few matrices for comparison.
4.6. Research Prospects
 Exploration techniques such as chaotic mapping and secondorder oscillation mechanisms can be considered to incorporate into GA. They are envisaged to augment accuracy and robustness.
 DE might be combined with exploitationbased metaheuristics, such as the Search Backtracking Algorithm, or with search mechanisms that accelerate the convergence. PSO demands more diversityraising search mechanisms such as trust region reflection, taboo search, and fitness distance balance. Additionally, studies on adapting their parameters are welltried.
 ABC considers introducing neighborhood search and adaptive mechanisms to speed up the convergence.
 For GWO and WOA, adaptive operators could be inserted to improve applicability in the face of highdimensional issues.
 JAYA and TLBO could borrow the explorationtype mechanisms in CSOOJAYA, MTLBO, and EBLSHADE to improve the overall performance.
 Hybrid methods can identify contributing components through component analysis and remove unimportant components to alleviate implementation redundancy.
 New methods can adopt adaptive learning, neighborhood search, chaotic mapping, and algorithmic blending techniques to enhance their behavior.
 For the parameter extraction, diminishing computational resources’ consumption is at stake. Reducing TNFES while maintaining the same accuracy by introducing different techniques, i.e., local search and reinforcement learning, is a direction worthy of further research.
 Some methods are feasible for lowdimensional issues, and some deliver better performance for highdimensional issues. Meanwhile, the selection of MSDM, MDDM, MTDM, and FDM with 6, 8, 10, and 11 unknown parameters to be included in the cell model is a future research direction for further performance improvement. Hence, it would be interesting to pick the right algorithm improvement to render PV models with desirable accuracy.
 For the issue of too few employed cases, more cases are considered in future research to reveal the methods’ generalizability. Examples include cases at different temperatures and irradiances and cases in partial shade.
 The realtime extraction of PV models’ parameters at different operating conditions is highly suggested. It is excellent work to accurately model the dynamics of photovoltaics for practical engineering problems.
 Faced with the problem of little measured data, inserting deep learning techniques such as neural networks to eliminate erroneous data and expand the amount of data for metaheuristic methods is an effective way to facilitate the extraction accuracy.
 The graphical processing unit (GPU) allows different solutions to be updated simultaneously to raise the efficiency. Thus, metaheuristic methods’ speed improvements can be geared toward direct runtime reductions through GPUlike devices.
 More performance evaluation indicators can demonstrate metaheuristic methods’ overall effectiveness more comprehensively. Therefore, introducing more multifaceted indicators is necessary to enhance persuasiveness.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Method  Main Contributors  Case  Algorithmic Parameter  Indicator  TNFES  Run 

GA [63]  Harrag et al., CCNS Laboratory, Department of Electronics, Faculty of Technology, Ferhat Abbas University  30XLS  NP = 100, CP = 0.5, MP = 0.02  SE  10,000   
34XLS  
AGA [64]  Kumari et al., School of Electrical Engineering, VIT University    C1 = 0.01, C2 = 0.001       
GNN [65]  Wang et al., Zhengzhou University of Aeronautics  SDM  NP = 30  RMSE  9000  80 
DDM  NP = 50  RMSE  15,000  80 
Method  Main Contributors  Case  Algorithmic Parameter  Indicator  TNFES  Run 

IADE [68]  Jiang et al., School of Computer Engineering, Nanyang Technological University  SDM  Iteration = 8000, a = ln2, b = 0.5  RMSE    30 
PhotowattPWP201  30  
SL80CE36M    
LSHADE [61]  Biswas et al., School of Electrical and Electronic Engineering, Nanyang Technological University  Kyocera KC200GT  NP = 50, F = rand (0.1, 0.5), CR = rand (0.1, 0.5)  ERR  50,000  30 
Shell SQ85  
Shell ST40  
DE3P [23]  Chin et al., Centre of Electrical Energy Systems, School of Electrical Engineering, Universiti Teknologi Malaysia  SDM  NP = 50, F = 0.7, CR = 0.8  RMSE SIAE MIAE  2500  35 
PhotowattPWP201  
STM640/36  
STP6120/36  
EJADE [69]  Li et al., School of Computer Engineering, Hubei University of Arts and Science  SDM  NP_{max} = 50, NP_{min} = 4  RMSE  10,000  30 
DDM  20,000  
PhotowattPWP201  10,000  
STM640/36  15,000  
STP6120/36  15,000  
QILDE [70]  Xiong et al., Guizhou Key Laboratory of Intelligent Technology in Power System, College of Electrical Engineering, Guizhou University  SDM  F = rand (0.1, 1), CR = rand (0, 1)  RMSE FT  10,000  50 
DDM  20,000  50  
PhotowattPWP201  10,000  50  
STM640/36  30,000  50  
STP6120/36  30,000  50  
Sharp NDR250A5  30,000  50  
EBLSHADE [71]  Song et al., School of Computer Science and Technology, Shandong Technology and Business University  SDM  NP = 50, H = 100, w1 = 0.2, w2 = 0.6, pmin = 0.05, pmax = 0.2  RMSE IAE  4000  30 
DDM  10,000  30  
PhotowattPWP201  5000  30  
STM640/36  10,000  30  
STP6120/36  15,000  30  
DEDCF [72]  Parida et al., Department of Electrical Engineering, ITER, Siksha O Anusandhan  SDM  NP = 10D, F = rand (0.1, 0.9), CR = rand (0, 1)  RMSE MIAE  10,000  50 
DDM  14,000  50  
PhotowattPWP201  10,000  50  
DPDE [73]  Gao et al., Faculty of Engineering, University of Toyama  SDM  NP = 18D, H = 5, p = 0.11  RMSE SIAE WRT FT  50,000  30 
DDM  
TDM  
PhotowattPWP201  
STM640/36  
STP6120/36  
RLDE [41]  Hu et al., School of Computer Science, China University of Geosciences  SDM  NP = 30, f = −0.1 or 0 or 0.1, CR = 0.9  RMSE  30,000  30 
DDM  
PhotowattPWP201  
STM640/36  
STP6120/36  
HDE [74]  Wang et al., School of Software, Yunnan University  SDM  NP = 30, p = 0.1  RMSE WRT FT  50,000  30 
DDM  
TDM  
PhotowattPWP201  
STM640/36  
STP6120/36  
MSDE [75]  Kharchouf et al., University Abdelmalek Essadi, FSTT  SDM  NP = 10D, F = 0.7, CR = 0.8  RMSE  10,000  30 
DDM  14,000  
PhotowattPWP201  10,000  
STM640/36  10,000  
FADE [76]  Dang et al., Institute for Electrical Power and Integrated Energy of Shaanxi Province, Xi’an University of Technology  PhotowattPWP201  NP = 25, uF^{init} = 0.7, CR^{init} = 0.5  RMSE SIAE  75,000  30 
STM640/36  
STP6120/36 
Method  Case  SIAE  MIN RMSE  Mean RMSE  MAX RMSE  STD of RMSE  Rank 

IADE [68]  SDM    9.8900 × 10^{−4}        N/A 
PhotowattPWP201    2.4000 × 10^{−3}        
SL80CE36M    1.15 × 10^{−2}        
DE3P [23]  SDM  0.0172  8.1291 × 10^{−4}        N/A 
PhotowattPWP201  0.0505  2.422747 × 10^{−3}        
STM640/36  0.0210  1.774 × 10^{−3}        
STP6120/36  0.2091  1.4091 × 10^{−2}        
EJADE [69]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  5.13 × 10^{−17}  4.333 
DDM    9.8248 × 10^{−4}  9.8363 × 10^{−4}  9.8602 × 10^{−4}  1.36 × 10^{−6}  
PhotowattPWP201    2.4251 × 10^{−3}  2.4251 × 10^{−3}  2.4251 × 10^{−3}  3.27 × 10^{−17}  
STM640/36    1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.7298 × 10^{−3}  5.94 × 10^{−18}  
STP6120/36    1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.6601 × 10^{−2}  2.33 × 10^{−17}  
QILDE [70]  SDM  0.01770381  9.8602 × 10^{−4}  9.8603 × 10^{−4}  9.8616 × 10^{−4}  2.7839 × 10^{−8}  4.333 
DDM  0.01731807  9.8248 × 10^{−4}  9.8480 × 10^{−4}  9.8968 × 10^{−4}  1.5868 × 10^{−6}  
PhotowattPWP201  0.04178701  2.4251 × 10^{−3}  2.4257 × 10^{−3}  2.4370 × 10^{−3}  2.2436 × 10^{−6}  
STM640/36  0.02177419  1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.1295 × 10^{−17}  
STP6120/36  0.27797426  1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.6601 × 10^{−2}  2.8518 × 10^{−14}  
Sharp NDR250A5  0.21759981  1.1183 × 10^{−2}  1.1183 × 10^{−2}  1.1183 × 10^{−2}  5.1647 × 10^{−10}  
EBLSHADE [71]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}    1.9169 × 10^{−15}  5.833 
DDM    9.8295 × 10^{−4}  9.8574 × 10^{−4}    1.2825 × 10^{−6}  
PhotowattPWP201    2.4251 × 10^{−3}  2.4251 × 10^{−3}    2.8821 × 10^{−17}  
STM640/36    1.7298 × 10^{−3}  1.7298 × 10^{−3}    6.40591 × 10^{−14}  
STP6120/36    1.6601 × 10^{−2}  1.6601 × 10^{−2}    8.0544 × 10^{−16}  
DEDCF [72]  SDM    7.730062 × 10^{−4}        2 
DDM    7.419648 × 10^{−4}        
PhotowattPWP201    2.05296 × 10^{−3}        
DPDE [73]  SDM  0.02153  9.86021877891470 × 10^{−4}  9.86021877891542 × 10^{−4}  9.86021877891588 × 10^{−4}  2.57114481592195 × 10^{−17}  5.333 
DDM  0.021276  9.82484827161920 × 10^{−4}  9.82549779378988 × 10^{−4}  9.83081420487992 × 10^{−4}  1.51333797156833 × 10^{−7}  
TDM  0.021275  9.82484851785319 × 10^{−4}  9.83096769943567 × 10^{−4}  9.86188097663681 × 10^{−4}  1.02284590208062 × 10^{−6}  
PhotowattPWP201  0.048924  2.42507486809506 × 10^{−3}  2.42507486809511 × 10^{−3}  2.42507486809514 × 10^{−3}  1.82238517018742 × 10^{−17}  
STM640/36  0.021903  1.72981370994065 × 10^{−3}  1.72981370994068 × 10^{−3}  1.72981370994070 × 10^{−3}  1.09732017119964 × 10^{−17}  
STP6120/36  0.317128  1.66006031250851 × 10^{−2}  1.66006031250854 × 10^{−2}  1.66006031250855 × 10^{−2}  7.66886076234863 × 10^{−17}  
RLDE [41]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  3.4834 × 10^{−17}  4.333 
DDM    9.8248 × 10^{−4}  9.8695 × 10^{−4}  9.8457 × 10^{−4}  1.7498 × 10^{−6}  
PhotowattPWP201    2.4251 × 10^{−3}  2.4251 × 10^{−3}  2.4251 × 10^{−3}  6.3084 × 10^{−17}  
STM640/36    1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.5784 × 10^{−17}  
STP6120/36    1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.9764 × 10^{−16}  
HDE [74]  SDM  0.021527  9.86021877891313 × 10^{−4}  9.86021877891456 × 10^{−4}  9.86021877891534 × 10^{−4}  4.56994495305984 × 10^{−17}  4.667 
DDM  0.021275  9.82484851785123 × 10^{−4}  9.84154478759700 × 10^{−4}  9.86021877891565 × 10^{−4}  1.67264373173134 × 10^{−6}  
TDM  0.021275  9.82484851785213 × 10^{−4}  9.82852008467139 × 10^{−4}  9.88358683960422 × 10^{−4}  1.08111146060101 × 10^{−6}  
PhotowattPWP201  0.048924  2.42507486809496 × 10^{−4}  2.42507486809504 × 10^{−4}  2.42507486809510 × 10^{−3}  3.15406568173825 × 10^{−17}  
STM640/36  0.021903  1.72981370994065 × 10^{−3}  1.72981370994068 × 10^{−3}  1.72981370994070 × 10^{−3}  7.89430228096153 × 10^{−18}  
STP6120/36  0.31713  1.66006031250847 × 10^{−2}  1.66006031250851 × 10^{−2}  1.66006031250855 × 10^{−2}  1.86128634500124 × 10^{−16}  
MSDE [75]  SDM    7.7692 × 10^{−4}        1.333 
DDM    7.63 × 10^{−4}        
PhotowattPWP201    1.7298 × 10^{−3}        
STM640/36    2.0529 × 10^{−3}        
FADE [76]  PhotowattPWP201  0.0489237  2.42507 × 10^{−3}  2.42507 × 10^{−3}  2.42507 × 10^{−3}    N/A 
STM640/36  0.0219033  1.72981 × 10^{−3}  1.72981 × 10^{−3}  1.72981 × 10^{−3}    
STP6120/36  0.3171278  1.66006 × 10^{−2}  1.66006 × 10^{−2}  1.66006 × 10^{−2}   
Method  Main Contributors  Case  Algorithmic Parameter  Indicator  TNFES  Run 

PSO [79]  Ben et al., Laboratory of Electronics, Signal Processing and Physical Modeling, Faculty of Sciences of Agadir Ibn Zohr University  SDM  NP = 50, Iteration = 1000, w = 0.4, c_{1} = c_{2} = 2  RMSE IAE     
PSOAEM [80]  Ni et al., Institute of Equipment Supervision and Inspection; Suzhou Nuclear Power Research Institute    NP = 50    10,000   
MPSO [81]  Merchaoui et al., Electrical Department, National Engineering School of Monastir, University of Monastir  SDM  NP = 60, Iteration = 2000, w = 0.4, c_{1} = c_{2} = 2  RMSE IAE     
DDM  
PhotowattPWP201  
IFRI25060  
GCPSO [82]  Nunes et al., Department of Electromechanical Engineering, University of Beira Interior  SDM  NP = 20D, Iteration = 10,000, w = 0.55, c_{1} = 1, c_{2} = 2  RMSE SIAE    100 
DDM  
PhotowattPWP201  
Sharp NDR250A5  
ELPSO [83]  Rezaee et al., Department of Electrical Engineering, LashteneshaZibakenar Branch, Islamic Azad University  SDM  NP = 991, c_{1} = 1, c_{2} = 2  RMSE IAE  101,000  30 
DDM  NP = 1489, c_{1} = 1, c_{2} = 2  151,500  
STM640/36  NP = 991, c_{1} = 1, c_{2} = 2  101,000  
SAIWPSO [84]  Kiani et al., Department of Electrical Engineering, University of Engineering and Technology, Taxila  SDM  NP = 100, Iteration = 10,000,  RMSE    100 
DDM  
DEDIWPSO [85]  Kiani et al., Department of Electrical Engineering, University of Engineering and Technology, Taxila  SDM  NP = 100, Iteration = 10,000, w^{init} = 0.8  RMSE IAE    30 
DDM  
PhotowattPWP201  
JKM330P72  
PPSO [86]  Gao et al., Department of Electrical and Computer Engineering, National University of Singapore  SDM  DDM: NP = 6400, Others: NP = 3200, w = 0.5, c_{1} = 2.5, c_{2} = 1.6  RMSE  640,000  30 
DDM  2,560,000  
PhotowattPWP201  640,000  
PSOST [87]  Kiani et al., Department of Electrical Engineering, University of Engineering and Technology, Taxila  SDM  NP = 100, Iteration = 10,000,  RMSE SIAE    30 
DDM  
PhotowattPWP201  
JKM330P72  
PSOCS [88]  Fan et al., College of Electrical and Electronic Engineering, Wenzhou University  SDM  NP = 30  RMSE  20,000  30 
DDM  
PhotowattPWP201  
SM55    
KC200GT  
ST40 
Method  Case  SIAE  MIN RMSE  Mean RMSE  MAX RMSE  STD of RMSE  Rank 

MPSO [81]  SDM    7.7301 × 10^{−4}        4 
DDM    7.4444 × 10^{−4}        
PhotowattPWP201    2.0530 × 10^{−3}        
IFRI25060    7.5589 × 10^{−3}        
GCPSO [82]  SDM  0.01763274  7.730063 × 10^{−4}  7.730063 × 10^{−4}  7.730065 × 10^{−4}  4.055839W11  2.667 
DDM  0.01637239  7.182745 × 10^{−4}  7.301380 × 10^{−4}  7.417141 × 10^{−4}  5.371802 × 10^{−6}  
PhotowattPWP201  0.04400032  2.046535 × 10^{−3}  2.046535 × 10^{−3}  2.046536 × 10^{−3}  1.105194 × 10^{−10}  
Sharp NDR250A5  0.21867809  7.697717 × 10^{−3}  7.697717 × 10^{−3}  7.697719 × 10^{−3}  2.395516 × 10^{−10}  
ELPSO [83]  SDM    7.7301 × 10^{−4}  7.7314 × 10^{−4}  7.7455 × 10^{−4}  3.4508 × 10^{−7}  N/A 
DDM    7.4240 × 10^{−4}  7.5904 × 10^{−4}  7.9208 × 10^{−4}  9.4291 × 10^{−6}  
STM640/36    2.1803 × 10^{−3}  2.2503 × 10^{−3}  3.7160 × 10^{−3}  2.9211 × 10^{−4}  
SAIWPSO [84]  SDM    7.73006 × 10^{−4}  7.73006 × 10^{−4}  7.73006 × 10^{−4}  5.49562 × 10^{−15}  N/A 
DDM    7.41937 × 10^{−4}  7.42261 × 10^{−4}  7.54275 × 10^{−4}  1.41853 × 10^{−6}  
DEDIWPSO [85]  SDM    7.730062 × 10^{−4}  7.730062 × 10^{−4}  7.730062 × 10^{−4}  5.18668 × 10^{−15}  1.5 
DDM    7.182306 × 10^{−4}  7.187462 × 10^{−4}  7.318100 × 10^{−4}  2.486129 × 10^{−6}  
PhotowattPWP201    2.03992 × 10^{−3}  2.03992 × 10^{−3}  2.03992 × 10^{−3}  2.995389 × 10^{−15}  
JKM330P72    4.3113 × 10^{−2}  4.3113 × 10^{−2}  4.3113 × 10^{−2}    
PPSO [86]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  7.0798 × 10^{−13}  5.167 
DDM    9.8248 × 10^{−4}  9.8323 × 10^{−4}  9.8602 × 10^{−4}  1.3436 × 10^{−6}  
PhotowattPWP201    2.4250 × 10^{−3}  2.4250 × 10^{−3}  2.4250 × 10^{−3}  2.8947 × 10^{−13}  
PSOST [87]  SDM  0.0214710  7.73006 × 10^{−4}  7.73006 × 10^{−4}  7.73006 × 10^{−4}  5.18622 × 10^{−15}  1.833 
DDM  0.0212734  7.183701 × 10^{−4}  7.187382 × 10^{−4}  7.218291 × 10^{−4}  1.318531 × 10^{−6}  
PhotowattPWP201  0.055499  2.03992 × 10^{−3}  2.03992 × 10^{−3}  2.03992 × 10^{−3}  2.91529 × 10^{−15}  
JKM330P72    4.3114 × 10^{−2}  4.3114 × 10^{−2}  4.3114 × 10^{−2}  6.2983 × 10^{−17}  
PSOCS [88]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8603 × 10^{−4}  1.7459 × 10^{−9}  5.833 
DDM    9.8297 × 10^{−4}  1.0286 × 10^{−3}  1.4133 × 10^{−4}  9.9217 × 10^{−5}  
PhotowattPWP201    2.4251 × 10^{−3}  2.4252 × 10^{−3}  2.4282 × 10^{−3}  5.9113 × 10^{−7}  
SM55    3.8067 × 10^{−3}        
KC200GT    2.5402 × 10^{−2}        
ST40    7.3431 × 10^{−4}       
Method  Main Contributors  Case  Algorithmic Parameter  Indicator  TNFES  Run 

TLABC [91]  Chen et al., School of Electrical and Information Engineering, Jiangsu University  SDM  NP = 50, limit = 200, scale factor F = rand (0, 1)  RMSE SIAE  50,000  30 
DDM  
PhotowattPWP201  
ABCTRR [92]  Wu et al., College of Physics and Information Engineering, Fuzhou University  SDM  NP = 10, limit = 10  RMSE SIAE  1000  1000 
DDM  NP = 10, limit = 20  5000  
PhotowattPWP201  NP = 10, limit = 10  1000  
IABC [93]  Xu et al., College of Mathematics and Physics, Inner Mongolia University for Nationalities  SDM  NP = 50, limit = 50  RMSE IAE  50,000   
DDM  
ABCLs [94]  Tefek et al., Department of Computer Engineering, Osmaniye Korkut Ata University  SDM  NP = 100, limit = 250  RMSE IAE  50,000  30 
DDM  NP = 100, limit = 500  
PhotowattPWP201  NP = 100, limit = 250  
Bestsofar ABC [95]  Garoudja et al., Centre de Développement des Technologies Avancées, CDTA  SDM  NP = 150, limit = 750  RMSE  35,000   
LG395N2W  
FDB TLABC [96]  Duman et al., Electrical Engineering, Engineering and Natural Sciences Faculty, Bandirma Onyedi Eylul University  SDM  NP = 50, limit = 200, scale factor F = rand (0, 1)  RMSE SIAE MIAE  50,000  51 
DDM  70,000  51  
PhotowattPWP201  50,000  51  
STM640/36  50,000    
STP6120/36  50,000   
Method  Case  SIAE  MIN RMSE  Mean RMSE  MAX RMSE  STD of RMSE  Rank 

TLABC [92]  SDM  0.02152738  9.86022 × 10^{−4}  9.98523 × 10^{−4}  1.03970 × 10^{−3}  1.86022 × 10^{−5}  3.667 
DDM  0.00135397  9.84145 × 10^{−4}  1.05553 × 10^{−3}  1.05553 × 10^{−3}  1.55034 × 10^{−4}  
PhotowattPWP201  0.04880919  2.42507 × 10^{−3}  2.42647 × 10^{−3}  2.44584 × 10^{−3}  3.99568 × 10^{−6}  
ABCTRR [92]  SDM  0.02152687  9.860219 × 10^{−4}  9.860219 × 10^{−4}  9.860219 × 10^{−4}  6.15 × 10^{−17}  3 
DDM  0.02127522  9.824849 × 10^{−4}  9.825556 × 10^{−4}  9.860219 × 10^{−4}  4.95 × 10^{−7}  
PhotowattPWP201  0.04892367  2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.425075 × 10^{−3}  9.68 × 10^{−17}  
IABC [93]  SDM    9.8602 × 10^{−4}        N/A 
DDM    9.8248 × 10^{−4}        
ABCLs [94]  SDM    9.8602 × 10^{−4}        2 
DDM    9.8257 × 10^{−4}        
PhotowattPWP201    2.4251 × 10^{−4}        
Bestsofar ABC [95]  SDM    0.027        N/A 
LG395N2W    0.013        
FDB TLABC [96]  SDM  0.017633  7.7301 × 10^{−4}        1.333 
DDM  0.017001  7.4194 × 10^{−4}        
PhotowattPWP201    2.054 × 10^{−3}        
STM640/36    1.7319 × 10^{−3}        
STP6120/36    1.4251 × 10^{−2}       
Method  Main Contributors  Case  Algorithmic Parameter  Indicator  TNFES  Run 

GWO [98]  Vinod et al., Department of Electrical Engineering, Speciality of Optmization in Engineering, National Institute of Technology, Silchar, India  SDM  NP = 50  RMSE, IAE  50,000   
MGGWO [99]  AlShabi et al., Mechanical and Nuclear Engineering Department, University of Sharjah, Sharjah, UAE  SDM  NP = 20  RMSE, MIAE  1,000,000   
OLBGWO [100]  Xavier et al., Bule Hora University  SDM  NP = 30, Orthogonal experiment levels: 3, Orthogonal experiment factors: 4  RMSE SIAE WRT  30,000  30 
DDM  
PhotowattPWP201  
ST40  
KC200GT  
IGWO [101]  Yesilbudak, Department of Electrical and Electronics Engineering, Faculty of Engineering and Architecture, Nevsehir Haci Bektas V eli University  SDM  NP = 15  RMSE IAE  25,000  50 
DDM  
TDM  
PhotowattPWP201  
IGWO [102]  Ramadan et al., Department of Electrical Engineering, Faculty of Engineering, Aswan University  TDM  NP = 1000, Iteration = 5000, r1 = rand, r2 = rand  RMSE    30 
PhotowattPWP201 
Method  Case  SIAE  MIN RMSE  Mean RMSE  MAX RMSE  STD of RMSE  Rank 

GWO [98]  SDM    9.94378 × 10^{−4}        N/A 
MGGWO [99]  SDM    4 × 10^{−4}        N/A 
OLBGWO [100]  SDM    9.86 × 10^{−4}  9.86 × 10^{−4}  9.86 × 10^{−4}  1.4 × 10^{−8}  1.333 
DDM    9.83 × 10^{−4}  9.85 × 10^{−4}  9.86 × 10^{−4}  1.78 × 10^{−6}  
PhotowattPWP201    2.4 × 10^{−3}  2.4 × 10^{−3}  2.4 × 10^{−3}  2.4284 × 10^{−9}  
ST40    9.5666 × 10^{−4}        
KC200GT    2.48 × 10^{−2}        
IGWO [101]  SDM  0.02152728  9.8602 × 10^{−4}        1.667 
DDM  0.02127500  9.824852 × 10^{−4}        
TDM  0.02128348  9.8251 × 10^{−4}        
PhotowattPWP201  0.04892353  2.425075 × 10^{−3}        
IGWO [102]  TDM    9.8331 × 10^{−4}  9.84 × 10^{−4}  9.85 × 10^{−4}  6.60404 × 10^{−7}  N/A 
PhotowattPWP201    2.4276291 × 10^{−3}  2.432 × 10^{−3}  2.438 × 10^{−3}  5.26003 × 10^{−6} 
Method  Main Contributors  Case  Algorithmic Parameter  Indicator  TNFES  Run 

IJAYA [104]  Yu et al., School of Electrical Engineering, Zhengzhou University  SDM  NP = 20  RMSE IAE  50,000  30 
DDM  
PhotowattPWP201  
EOJaya [105]  Wang et al., Department of Systems Engineering and Engineering Management, City University of Hong Kong  SDM  NP = 150  RMSE  1,500,000  50 
DDM  
JayaNM [106]  Luo et al., School of Computer and Communication Engineering, University of Science and Technology Beijing (USTB)  SDM  NP = 150  RMSE  1,500,000   
PGJAYA [107]  Yu et al., School of Electrical Engineering, Zhengzhou University  SDM  NP = 20  RMSE  50,000  30 
DDM  
PhotowattPWP201  
MJA [108]  Luu et al., Faculty of Electronics Technology, Industrial University of Ho Chi Minh City  SDM  NP^{init} = 10D, NP^{min} = D, r = rand (−0.5, 0.5),  RMSE    30 
DDM  
LCJAYA [109]  Jian et al., School of Optical Electrical and Computer Engineering, University of Shanghai for Science and Technology  SDM  NP = 20  RMSE  50,000  30 
DDM  
PhotowattPWP201  
CLJAYA [110]  Zhang et al., School of Electrical and Information Engineering, Tianjin University  SDM  NP = 20  RMSE MIAE  20,000   
DDM  50,000  
PhotowattPWP201  30,000  
EJAYA [111]  Yang et al., School of Computer Science, China University of Geosciences  SDM  NP = 30, rate Ra = 0.3  RMSE WST  30,000  30 
DDM  
PhotowattPWP201  
STM640/36  
STP6120/36  
CJAYA [112]  Premkumar et al., Department of Electrical and Electronics Engineering, GMR Institute of Technology  SDM  NP = 30  RMSE IAE WST  50,000  30 
DDM  NP = 50  
STM640/36  NP = 80  
STP6120/36  NP = 80  
MLJAYA [113]  Saadaoui et al., Laboratory of Materials and Renewable Energies, Faculty of Science, Ibn Zohr University  SDM  NP = 30, F = 3randn  RMSE SIAE    30 
DDM  
PhotowattPWP201  
CSOOJAYA [114]  Jian et al., School of Optical Electrical and Computer Engineering, University of Shanghai for Science and Technology  SDM  NP = 20  RMSE IAE  50,000  30 
DDM  
PhotowattPWP201 
Method  Case  SIAE  MIN RMSE  Mean RMSE  MAX RMSE  STD of RMSE  Rank 

IJAYA [104]  SDM    9.8603 × 10^{−4}  9.9204 × 10^{−4}  1.0622 × 10^{−3}  1.4033 × 10^{−5}  6.5 
DDM    9.8293 × 10^{−4}  1.0269 × 10^{−3}  1.4055 × 10^{−3}  9.8325 × 10^{−5}  
PhotowattPWP201    2.4251 × 10^{−3}  2.4289 × 10^{−3}  2.4393 × 10^{−3}  3.7755 × 10^{−6}  
EOJaya [105]  SDM    9.8603 × 10^{−4}        N/A 
DDM    9.8262 × 10^{−4}        
JayaNM [106]  SDM    9.8602 × 10^{−4}        N/A 
PGJAYA [107]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  1.4485 × 10^{−9}  3.833 
DDM    9.8263 × 10^{−4}  9.8582 × 10^{−4}  9.9499 × 10^{−4}  2.5375 × 10^{−6}  
PhotowattPWP201    2.425075 × 10^{−3}  2.425144 × 10^{−3}  2.426764 × 10^{−3}  3.071420 × 10^{−7}  
MJA [108]  SDM    9.860218 × 10^{−4}  9.860218 × 10^{−4}  9.860218 × 10^{−4}  1.99 × 10^{−17}  N/A 
DDM    9.824848 × 10^{−4}  9.8260 × 10^{−4}  9.860218 × 10^{−4}  6.46 × 10^{−7}  
LCJAYA [109]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  5.6997 × 10^{−16}  3.5 
DDM    9.8250 × 10^{−4}  9.8308 × 10^{−4}  9.8602 × 10^{−4}  1.3118 × 10^{−6}  
PhotowattPWP201    2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.415229 × 10^{−16}  
CLJAYA [110]  SDM    9.8602 × 10^{−4}        3.167 
DDM    9.8249 × 10^{−4}        
PhotowattPWP201    2.425075 × 10^{−3}        
EJAYA [111]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  6.80 × 10^{−17}  3.5 
DDM    9.8248 × 10^{−4}  9.8448 × 10^{−4}  9.8602 × 10^{−4}  1.51 × 10^{−6}  
PhotowattPWP201    2.4251 × 10^{−3}  2.4251 × 10^{−3}  2.4251 × 10^{−4}  6.39 × 10^{−17}  
STM640/36    1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.47 × 10^{−17}  
STP6120/36    1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.6601 × 10^{−2}  2.68 × 10^{−16}  
CJAYA [112]  SDM    9.8625 × 10^{−4}  9.8878 × 10^{−4}  9.8991 × 10^{−4}  4.5584 × 10^{−8}  N/A 
DDM    1.0145 × 10^{−3}  1.01458 × 10^{−3}  1.0365 × 10^{−3}  7.5514 × 10^{−5}  
STM640/36    1.7242 × 10^{−3}  1.7289 × 10^{−3}  1.7845 × 10^{−3}  1.4751 × 10^{−7}  
STP6120/36    1.6285 × 10^{−2}  1.6299 × 10^{−2}  1.6302 × 10^{−2}  3.2565 × 10^{−7}  
MLJAYA [113]  SDM  0.01781248  9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}    3.667 
DDM  0.0176  9.8294 × 10^{−4}  1.0618 × 10^{−3}  1.42102 × 10^{−3}    
PhotowattPWP201  0.04686375  2.4250748 × 10^{−3}  2.44395 × 10^{−3}  2.49419 × 10^{−3}    
CSOOJAYA [114]  SDM    9.860219 × 10^{−4}  9.860219 × 10^{−4}  9.860219 × 10^{−4}  4.717305 × 10^{−17}  3.833 
DDM    9.824849 × 10^{−4}  9.824849 × 10^{−4}  9.824849 × 10^{−4}  5.576332 × 10^{−17}  
PhotowattPWP201    2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.699858 × 10^{−17} 
Method  Main Contributors  Case  Algorithmic Parameter  Indicator  TNFES  Run 

GOTLBO [116]  Chen et al., School of Electrical and Information Engineering, Jiangsu University  SDM  NP = 20, SDM: Jr = 0.1, DDM: Jr = 0  RMSE  10,000  30 
DDM  20,000  
SATLBO [117]  Yu et al., Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology  SDM  NP = 40  RMSE  50,000  30 
DDM  
PhotowattPWP201  
ETLBO [118]  Ramadan et al., Department of Electrical Engineering, Faculty of Engineering, Aswan University  SDM  NP = 200, Iteration = 5000,  RMSE IAE     
DDM  
STM640/36  
STP6120/36  
EOTLBO [21]  Xiong et al., Guizhou Key Laboratory of Intelligent Technology in Power System, College of Electrical Engineering, Guizhou University  SDM  NP = 50  RMSE WRT FT  20,000  50 
DDM  
PhotowattPWP201  
Sharp NDR250A5  
MTLBO [119]  AbdelBasset et al., Faculty of Computers and Informatics, Zagazig University  SDM  NP = 50  RMSE  50,000  30 
DDM  
PhotowattPWP201  
STM640/36  
STP6120/36  
DMTLBO [120]  Li et al., Guizhou Key Laboratory of Intelligent Technology in Power System, College of Electrical Engineering, Guizhou University  SDM  NP = 50  RMSE SIAE  50,000  30 
DDM  
PhotowattPWP201  
STM640/36  
STP6120/36 
Method  Case  SIAE  MIN RMSE  Mean RMSE  MAX RMSE  STD of RMSE  Rank 

GOTLBO [116]  SDM    9.87442 × 10^{−4}  1.33488 × 10^{−3}  1.98244 × 10^{−3}  2.99407 × 10^{−4}  N/A 
DDM    9.83177 × 10^{−4}  1.24360 × 10^{−3}  1.78774 × 10^{−3}  2.09115 × 10^{−4}  
SATLBO [117]  SDM    9.86022 × 10^{−4}  9.87795 × 10^{−4}  9.94939 × 10^{−6}  2.30015 × 10^{−6}  3.667 
DDM    9.828037 × 10^{−4}  9.981111 × 10^{−4}  1.047045 × 10^{−3}  1.951533 × 10^{−5}  
PhotowattPWP201    2.425075 × 10^{−3}  2.425428 × 10^{−3}  2.429130 × 10^{−3}  7.410517 × 10^{−7}  
ETLBO [118]  SDM    9.86022 × 10^{−4}        N/A 
DDM    9.8241 × 10^{−4}        
STM640/36    1.7759 × 10^{−3}        
STP6120/36    1.6172 × 10^{−2}        
EOTLBO [21]  SDM    9.86021878 × 10^{−4}  9.86021878 × 10^{−4}  9.86021878 × 10^{−4}  4.12665088 × 10^{−17}  1.667 
DDM    9.82484852 × 10^{−4}  9.84733697 × 10^{−4}  9.89424104 × 10^{−4}  1.69176118 × 10^{−6}  
PhotowattPWP201    2.42507487 × 10^{−3}  2.42507487 × 10^{−3}  2.42507487 × 10^{−3}  3.61995116 × 10^{−17}  
Sharp NDR250A5    1.11833356 × 10^{−2}  1.11839904 × 10^{−2}  1.12154997 × 10^{−2}  4.54767027 × 10^{−6}  
MTLBO [119]  SDM    9.860219 × 10^{−4}  9.860219 × 10^{−4}  9.860219 × 10^{−4}  1.9292748 × 10^{−17}  2.667 
DDM    9.824849 × 10^{−4}  9.824855 × 10^{−4}  9.825026 × 10^{−4}  3.3000000 × 10^{−9}  
PhotowattPWP201    2.4250749 × 10^{−3}  2.4250749 × 10^{−3}  2.4250749 × 10^{−3}  1.3070107 × 10^{−17}  
STM640/36    1.7298137 × 10^{−3}  1.7298137 × 10^{−3}  1.7298137 × 10^{−3}  5.9363718 × 10^{−18}  
STP6120/36    1.66006031 × 10^{−2}  1.66006031 × 10^{−2}  1.66006031 × 10^{−2}  8.0041380 × 10^{−17}  
DMTLBO [120]  SDM  0.0178  9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  2.07 × 10^{−17}  2 
DDM  0.0176  9.8248 × 10^{−4}  9.8406 × 10^{−4}  9.8638 × 10^{−4}  1.53 × 10^{−6}  
PhotowattPWP201  0.0411  2.4251 × 10^{−3}  2.4251 × 10^{−3}  2.4251 × 10^{−3}  2.15 × 10^{−17}  
STM640/36  0.0215  1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.7298 × 10^{−3}  5.74 × 10^{−14}  
STP6120/36  0.2741  1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.6601 × 10^{−2}  4.55 × 10^{−10} 
Method  Main Contributors  Case  Algorithmic Parameter  Indicator  TNFES  Run 

WOA [124]  Elazab et al., Electrical Power and Machines Department, Faculty of Engineering, Ain Shams University  KC200GT  NP = 30, Iteration = 500,    15,000   
IWOA [123]  Xiong et al., Guizhou Key Laboratory of Intelligent Technology in Power System, College of Electrical Engineering, Guizhou University  SDM  NP = 50, Iteration = 2000,  RMSE SIAE WRT, FT    50 
DDM  
PhotowattPWP201  
MCSWOA [18]  Xiong et al., Guizhou Key Laboratory of Intelligent Technology in Power System, College of Electrical Engineering, Guizhou University  SDM  NP = 50  RMSE SIAE FT  50,000  50 
DDM  
PhotowattPWP201  
STM640/36  
STP6120/36  
Sharp NDR250A5  
SWOA [125]  Pourmousa et al., Department of Electrical Engineering, Iran University of Science and Technology  SDM  NP = 30, Iteration = 5000,  RMSE IAE    30 
DDM  
TDM  
PhotowattPWP201  
ISNMWOA [126]  Peng et al., Department of Computer Science and Artificial Intelligence, Wenzhou University  SDM  NP = 30  RMSE SIAE  20,000   
DDM  
TDM  
PhotowattPWP201 
Method  Case  SIAE  MIN RMSE  Mean RMSE  MAX RMSE  STD of RMSE  Rank 

IWOA [123]  SDM  0.01770338  9.860219 × 10^{−4}  9.860219 × 10^{−4}  9.860219 × 10^{−4}  5.12 × 10^{−16}  2.667 
DDM  0.01735511  9.824849 × 10^{−4}  9.826140 × 10^{−4}  9.860219 × 10^{−4}  9.86 × 10^{−5}  
PhotowattPWP201  0.04176116  2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.90 × 10^{−17}  
MCSWOA [18]  SDM  0.01770381  9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  4.8373 × 10^{−10}  3.167 
DDM  0.01730633  9.8250 × 10^{−4}  1.0078 × 10^{−3}  1.1903 × 10^{−3}  3.7264 × 10^{−5}  
PhotowattPWP201  0.04178694  2.4251 × 10^{−3}  2.4252 × 10^{−3}  2.4270 × 10^{−3}  3.2927 × 10^{−7}  
STM640/36  0.02177346  1.7298 × 10^{−3}  1.7311 × 10^{−3}  1.7364 × 10^{−3}  1.0774 × 10^{−6}  
STP6120/36  0.27780418  1.6601 × 10^{−2}  1.6632 × 10^{−2}  1.6741 × 10^{−2}  2.6486 × 10^{−5}  
Sharp NDR250A5  0.21759970  1.1183 × 10^{−2}  1.1187 × 10^{−2}  1.1244 × 10^{−2}  9.1358 × 10^{−6}  
SWOA [125]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}    2 
DDM    9.8249 × 10^{−4}  9.8250 × 10^{−4}  9.8251 × 10^{−4}    
TDM    9.8033 × 10^{−4}  9.8051 × 10^{−4}  9.8154 × 10^{−4}    
PhotowattPWP201    2.4250 × 10^{−3}  2.4250 × 10^{−3}  2.4250 × 10^{−3}    
ISNMWOA [126]  SDM  0.021527008  9.8602 × 10^{−4}        2.167 
DDM  0.021275213  9.8248 × 10^{−4}        
TDM  0.021275347  9.8248 × 10^{−4}        
PhotowattPWP201  0.048923833  2.4251 × 10^{−3}       
Method  Main Contributors  Case  Algorithmic Parameter  Indicator  TNFES  Run 

DE/WOA [127]  Xiong et al., Guizhou Key Laboratory of Intelligent Technology in Power System, College of Electrical Engineering, Guizhou University  SDM  NP = 40, F = rand (0.1, 1), CR = rand (0, 1)  RMSE MIAE  50,000  50 
DDM  
PhotowattPWP201  
GWOCS [128]  Long et al., Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics  SDM  NP = 30  RMSE IAE FT  50,000  30 
DDM  
PhotowattPWP201  
STM640/36  
PSOGWO [129]  Rezk et al., College of Engineering at Wadi Addawaser, Prince Sattam Bin Abdulaziz University  PhotowattPWP201  Iteration = 1200  RMSE MIAE     
STE4/100  Iteration = 6000  
FSM  Iteration = 2000  
ATLDE [130]  Li et al., School of Computer Science, China University of Geosciences  SDM  NP = 50, F = rand, CR = 0.9  RMSE SIAE WRT  30,000  30 
DDM  
STM640/36  
STP6120/36  
HHODE [131]  Ndi et al., Technology and Applied Sciences Laboratory, University of Douala  SDM  Iteration = 3000  RMSE    20 
DDM  
HAJAYADE [132]  Yu et al., School of Management Science and Engineering, Nanjing University of Information Science and Technology  SDM  NP = 20, CR = 0.5  RMSE WST  50,000  30 
DDM  
PhotowattPWP201  
STM640/36  
STP6120/36  
EHGWOSCA [133]  Devarapalli et al., Department of EEE, Lendi Institute of Engineering and Technology  SDM  Iteration = 500  ERR    30 
DDM  
Shell S75  
Shell CS6K280M  
Shell ST40  
HPSODOX [47]  Singh et al., Electrical and Instrumentation Engineering Department, Thapar Institute of Engineering and Technology  SDM    RMSE FT     
DDM  
TDM  
FDM  
TLBOBSA [134]  Weng et al., Department of Computer Science and Artificial Intelligence, Wenzhou University  SDM  NP = 30  RMSE SIAE  20,000  30 
DDM  
TDM  
PhotowattPWP201 
Method  Case  SIAE  MIN RMSE  Mean RMSE  MAX RMSE  STD of RMSE  Rank 

DE/WOA [127]  SDM  0.01770392  9.860219 × 10^{−4}  9.860219 × 10^{−4}  9.860219 × 10^{−4}  3.545178 × 10^{−17}  2.333 
DDM  0.01731808  9.824849 × 10^{−4}  9.829703 × 10^{−4}  9.860377 × 10^{−4}  9.152178 × 10^{−7}  
PhotowattPWP201  0.04178725  2.425075 × 10^{−3}  2.425092 × 10^{−3}  2.425442 × 10^{−3}  6.270718 × 10^{−8}  
GWOCS [128]  SDM    9.8607 × 10^{−4}  9.8874 × 10^{−4}  9.9095 × 10^{−4}  2.4696 × 10^{−6}  3.5 
DDM    9.8334 × 10^{−4}  9.9411 × 10^{−4}  1.0017 × 10^{−3}  9.5937 × 10^{−6}  
PhotowattPWP201    2.4251 × 10^{−3}  2.4261 × 10^{−3}  2.4275 × 10^{−3}  1.1967 × 10^{−6}  
STM640/36    1.7337 × 10^{−3}  1.7457 × 10^{−3}  1.7528 × 10^{−3}  1.0447 × 10^{−5}  
PSOGWO [129]  PhotowattPWP201  0.06292  3.06 × 10^{−3}        N/A 
STE4/100  0.00384  3.0574 × 10^{−4}        
FSM  0.16023  9.14 × 10^{−3}        
ATLDE [130]  SDM  0.0177  9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  2.44 × 10^{−17}  N/A 
DDM  0.0173  9.8218 × 10^{−4}  9.8372 × 10^{−4}  9.8603 × 10^{−4}  1.37 × 10^{−6}  
STM640/36  0.0218  1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.7298 × 10^{−3}  8.22 × 10^{−18}  
STP6120/36  0.2780  1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.02 × 10^{−16}  
HHODE [131]  SDM    1.4664 × 10^{−3}        N/A 
DDM    1.5978 × 10^{−3}        
HAJAYADE [132]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  0  2.833 
DDM    9.8294 × 10^{−4}  9.8641 × 10^{−4}  9.96 × 10^{−4}  2.8534 × 10^{−6}  
PhotowattPWP201    2.4251 × 10^{−3}  2.4251 × 10^{−3}  2.4251 × 10^{−3}  3.2215 × 10^{−15}  
STM640/36    1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.7298 × 10^{−3}  3.6569 × 10^{−16}  
STP6120/36    1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.6606 × 10^{−2}  9.2421 × 10^{−7}  
HPSODOX [47]  SDM    6.4923 × 10^{−9}        N/A 
DDM    6.5120 × 10^{−9}        
TDM    6.5424 × 10^{−9}        
FDM    6.5656 × 10^{−9}        
TLBOBSA [134]  SDM  0.021526887  9.86902 × 10^{−4}  9.8602 × 10^{−4}  9.8603 × 10^{−4}  5.64965 × 10^{−10}  1.667 
DDM  0.021312577  9.8155 × 10^{−4}  1.1334 × 10^{−3}  2.2181 × 10^{−3}  3.0012 × 10^{−4}  
TDM  0.021263898  9.82553 × 10^{−4}  1.2081 × 10^{−3}  3.0608 × 10^{−3}  4.9433 × 10^{−4}  
PhotowattPWP201  0.048923676  2.42507 × 10^{−3}  2.42535 × 10^{−3}  2.43167 × 10^{−3}  1.21238 × 10^{−6} 
Method  Main Contributors  Case  Algorithmic Parameter  Indicator  TNFES  Run 

WHHO [135]  Naeijian et al., Department of Electrical Engineering, Babol Noshirvani University of Technology  SDM  NP = 30, Iteration = 5000,  RMSE IAE    30 
DDM  
TDM  
PhotowattPWP201  
GSK [4]  Xiong et al., Guizhou Key Laboratory of Intelligent Technology in Power System, College of Electrical Engineering, Guizhou University  SDM  NP = 30, k_{r} = 0.9, k_{f} = 0.5, K = 10, p = 0.1  RMSE SIAE FT  30,000  30 
DDM  50,000  
PhotowattPWP201  30,000  
STM640/36  30,000  
STP6120/36  30,000  
IGSK [136]  Sallam et al., The Faculty of Computers and Information, Zagazig University  SDM  NP^{init} = 25, k_{r} = 0.9, k_{f} = 0.5, K = 10, p = 0.1  RMSE WST  10,000  30 
DDM  20,000  
PhotowattPWP201  10,000  
STM640/36  15,000  
STP6120/36  15,000  
SDO [137]  Xiong et al., Guizhou Key Laboratory of Intelligent Technology in Power System, College of Electrical Engineering, Guizhou University  SDM  NP = 20  RMSE SIAE WRT FT  50,000  50 
DDM  
PVM 752 GaAs  
STM640/36  
STP6120/36  
TGA [138]  Diab et al., Electrical Engineering Department, Faculty of Engineering, Minia University  SDM  NP = 500, Iteration = 500,  RMSE     
DDM  
TDM  
PVM 752 GaAs  
PhotowattPWP201  
STE 20/100  
SSA [139]  Abbassi et al., University of Kairouan, Institute of Applied Sciences and Technology of Kasserine (ISSATKas)  TITAN1250  NP = 30, Iteration = 100,  RMSE IAE    30 
TSA [140]  Sharma et al., Research and Development Department, University of Petroleum and Energy Studies  PhotowattPWP201  NP = 30  RMSE, SIAE, FT  50,000  30 
CGO [142]  Ramadan et al., Department of Electrical Engineering, Faculty of Engineering, Aswan University  TDM  Iteration = 1000  RMSE IAE    15 
PhotowattPWP201  
HSOA [143]  Long et al., Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics  SDM  NP = 30, f_{cmax} = 2, f_{cmin} = 0, F = 0.5  RMSE SIAE FT  50,000  20 
DDM  
PhotowattPWP201  
RUN [144]  Shaban et al., Faculty of Computers and Information, Minia University  SDM  NP = 30, Iteration = 1000, a = 20, b = 12  RMSE IAE FT    30 
DDM  
TDM  
FPOA [145]  Chellaswamy et al., Department of ECE, Lords Institute of Engineering and Technology  Sample2, Sample5  β = 1.45, S_{p} = 0.85  MIAE     
CTSA [141]  Gupta et al., Electrical and Instrumentation Engineering Department, Thapar Institute of Engineering and Technology  DDM  NP = 50, Iteration = 1000  RMSE SIAE     
TDM  
SOS [146]  Xiong et al., Guizhou Key Laboratory of Intelligent Technology in Power System, College of Electrical Engineering, Guizhou University  SDM  NP = 50  RMSE SIAE WRT  50,000  50 
DDM  
PhotowattPWP201 
Method  Case  SIAE  MIN RMSE  Mean RMSE  MAX RMSE  STD of RMSE  Rank 

WHHO [135]  SDM    9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}    2.667 
DDM    9.82487 × 10^{−4}  9.8249 × 10^{−4}  9.8250 × 10^{−4}    
TDM    9.80751 × 10^{−4}  9.8085 × 10^{−4}  9.8149 × 10^{−4}    
PhotowattPWP201    2.4250 × 10^{−3}  2.4250 × 10^{−3}  2.4250 × 10^{−3}    
GSK [4]  SDM  0.0174  9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  2.18 × 10^{−17}  3 
DDM  0.0175  9.8248 × 10^{−4}  9.8280 × 10^{−4}  9.8602 × 10^{−4}  8.72 × 10^{−7}  
PhotowattPWP201  0.0411  2.4251 × 10^{−3}  2.4251 × 10^{−3}  2.4251 × 10^{−3}  1.04 × 10^{−9}  
STM640/36  0.0218  1.7298 × 10^{−3}  1.7298 × 10^{−3}  1.7298 × 10^{−3}  6.25 × 10^{−18}  
STP6120/36  0.2829  1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.6601 × 10^{−2}  1.44 × 10^{−16}  
IGSK [136]  SDM    9.8602188 × 10^{−4}  9.8602188 × 10^{−4}  9.8602188 × 10^{−4}  3.5821018 × 10^{−17}  3.33 
DDM    9.8248485 × 10^{−4}  9.8272774 × 10^{−4}  9.8602188 × 10^{−4}  8.9578942 × 10^{−7}  
PhotowattPWP201    2.4250749 × 10^{−3}  2.4250749 × 10^{−3}  2.4250749 × 10^{−3}  2.9226647 × 10^{−17}  
STM640/36    1.7298137 × 10^{−3}  1.7298137 × 10^{−3}  1.7298137 × 10^{−3}  7.0155794 × 10^{−18}  
STP6120/36    1.6600603 × 10^{−2}  1.6600603 × 10^{−2}  1.6600603 × 10^{−2}  1.7069489 × 10^{−16}  
SDO [137]  SDM  0.01770381  9.8602 × 10^{−4}  9.8603 × 10^{−4}  9.8616 × 10^{−4}  2.5141 × 10^{−8}  N/A 
DDM  0.01730620  9.8250 × 10^{−4}  9.8822 × 10^{−4}  1.0271 × 10^{−3}  8.8518 × 10^{−6}  
PVM 752 GaAs  0.00593491  2.3487 × 10^{−4}  3.1727 × 10^{−4}  3.7700 × 10^{−4}  2.7687 × 10^{−5}  
STM640/36  0.02177419  1.7298 × 10^{−3}  1.7703 × 10^{−3}  1.9500 × 10^{−3}  4.5108 × 10^{−5}  
STP6120/36  0.27797428  1.6601 × 10^{−2}  1.6683 × 10^{−2}  1.6866 × 10^{−2}  7.1751 × 10^{−5}  
TGA [138]  SDM    9.750530454421328 × 10^{−4}        2.667 
DDM    8.488244232381 × 10^{−4}        
TDM    8.251052783901371 × 10^{−4}        
PVM 752 GaAs    9.037521972258222 × 10^{−4}        
PhotowattPWP201    3.819491771269 × 10^{−3}        
STE 20/100    9.28071173 × 10^{−4}        
SSA [139]  TITAN1250(366)    2.9681 × 10−04        N/A 
TITAN1250(810.2)    1.5777 × 10−06        
TSA [140]  PhotowattPWP201  0.0594  5.06 × 10^{−4}  1.45 × 10^{−3}  2.34 × 10^{−2}  1.25 × 10^{−3}  N/A 
CGO [142]  TDM    9.82 × 10^{−4}  9.82 × 10^{−4}  9.82 × 10^{−4}  1.24841 × 10^{−9}  N/A 
PhotowattPWP201    2.425075 × 10^{−3}  2.425092 × 10^{−3}  2.4251 × 10^{−3}  1.44688 × 10^{−8}  
HSOA [143]  SDM  0.0177065  9.8602 × 10^{−4}  1.0479 × 10^{−3}  1.1683 × 10^{−3}  5.3832 × 10^{−5}  4 
DDM  0.017402  9.8376 × 10^{−4}  1.1175 × 10^{−3}  1.7642 × 10^{−3}  1.9107 × 10^{−4}  
PhotowattPWP201  0.041788  2.4251 × 10^{−3}  2.4251 × 10^{−3}  2.4253 × 10^{−3}  4.1556 × 10^{−8}  
RUN [144]  SDM    9.86242 × 10^{−4}  1.479894 × 10^{−3}  2.444572 × 10^{−3}  4.30699 × 10^{−4}  N/A 
DDM    9.87168 × 10^{−4}  1.481762 × 10^{−3}  2.947571 × 10^{−3}  5.14117 × 10^{−4}  
TDM    9.89133 × 10^{−4}  1.581238 × 10^{−3}  6.239595 × 10^{−3}  1.078762 × 10^{−3}  
CTSA [141]  DDM  0.2621  1.0239 × 10^{−8}  2.1185 × 10^{−8}  9.6017 × 10^{−8}  3.9865 × 10^{−8}  N/A 
TDM  0.0075  1.0036 × 10^{−6}  3.4906 × 10^{−6}  9.4766 × 10^{−6}  2.7057 × 10^{−6}  
SOS [146]  SDM  0.0181  9.8609 × 10^{−4}  1.0245 × 10^{−3}  1.1982 × 10^{−3}  5.2184 × 10^{−5}  5.333 
DDM  0.0182  9.8518 × 10^{−4}  1.0627 × 10^{−3}  1.3498 × 10^{−3}  9.6141 × 10^{−5}  
PhotowattPWP201  0.0421  2.4251 × 10^{−3}  2.4361 × 10^{−3}  2.5103 × 10^{−3}  1.7503 × 10^{−5} 
Method  Case  MIN RMSE  Mean RMSE  MAX RMSE  STD of RMSE  Rank 

ABCTRR [92]  SDM  9.860219 × 10^{−4}  9.860219 × 10^{−4}  9.860219 × 10^{−4}  6.15 × 10^{−17}  5.958 
DDM  9.824849 × 10^{−4}  9.825556 × 10^{−4}  9.860219 × 10^{−4}  4.95 × 10^{−7}  
PhotowattPWP201  2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.425075 × 10^{−3}  9.68 × 10^{−17}  
RLDE [41]  SDM  9.8602 × 10^{−4}  9.8602 × 10^{−4}  9.8602 × 10^{−4}  3.4834 × 10^{−17}  5.125 
DDM  9.8248 × 10^{−4}  9.8695 × 10^{−4}  9.8457 × 10^{−4}  1.7498 × 10^{−6}  
PhotowattPWP201  2.4251 × 10^{−3}  2.4251 × 10^{−3}  2.4251 × 10^{−3}  6.3084 × 10^{−17}  
OLBGWO [100]  SDM  9.86 × 10^{−4}  9.86 × 10^{−4}  9.86 × 10^{−4}  1.4 × 10^{−8}  4.583 
DDM  9.83 × 10^{−4}  9.85 × 10^{−4}  9.86 × 10^{−4}  1.78 × 10^{−6}  
PhotowattPWP201  2.4 × 10^{−3}  2.4 × 10^{−3}  2.4 × 10^{−3}  2.4284 × 10^{−9}  
CSOOJAYA [114]  SDM  9.860219 × 10^{−4}  9.860219 × 10^{−4}  9.860219 × 10^{−4}  4.717305 × 10^{−17}  4.917 
DDM  9.824849 × 10^{−4}  9.824849 × 10^{−4}  9.824849 × 10^{−4}  5.576332 × 10^{−17}  
PhotowattPWP201  2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.699858 × 10^{−17}  
DEDIWPSO [85]  SDM  7.730062 × 10^{−4}  7.730062 × 10^{−4}  7.730062 × 10^{−4}  5.18668 × 10^{−15}  2.5 
DDM  7.182306 × 10^{−4}  7.187462 × 10^{−4}  7.318100 × 10^{−4}  2.486129 × 10^{−6}  
PhotowattPWP201  2.03992 × 10^{−3}  2.03992 × 10^{−3}  2.03992 × 10^{−3}  2.995389 × 10^{−15}  
EOTLBO [21]  SDM  9.86021878 × 10^{−4}  9.86021878 × 10^{−4}  9.86021878 × 10^{−4}  4.12665088 × 10^{−17}  4.5 
DDM  9.82484852 × 10^{−4}  9.84733697 × 10^{−4}  9.89424104 × 10^{−4}  1.69176118 × 10^{−6}  
PhotowattPWP201  2.42507487 × 10^{−3}  2.42507487 × 10^{−3}  2.42507487 × 10^{−3}  3.61995116 × 10^{−17}  
IWOA [123]  SDM  9.860219 × 10^{−4}  9.860219 × 10^{−4}  9.860219 × 10^{−4}  5.12 × 10^{−16}  6.375 
DDM  9.824849 × 10^{−4}  9.826140 × 10^{−4}  9.860219 × 10^{−4}  9.86 × 10^{−5}  
PhotowattPWP201  2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.425075 × 10^{−3}  2.90 × 10^{−17}  
TLBOBSA [134]  SDM  9.86902 × 10^{−4}  9.8602 × 10^{−4}  9.8603 × 10^{−4}  5.64965 × 10^{−10}  8.292 
DDM  9.8155 × 10^{−4}  1.1334 × 10^{−3}  2.2181 × 10^{−3}  3.0012 × 10^{−4}  
PhotowattPWP201  2.42507 × 10^{−3}  2.42535 × 10^{−3}  2.43167 × 10^{−3}  1.21238 × 10^{−6}  
IGSK [136]  SDM  9.8602188 × 10^{−4}  9.8602188 × 10^{−4}  9.8602188 × 10^{−4}  3.5821018 × 10^{−17}  4.333 
DDM  9.8248485 × 10^{−4}  9.8272774 × 10^{−4}  9.8602188 × 10^{−4}  8.9578942 × 10^{−7}  
PhotowattPWP201  2.4250749 × 10^{−3}  2.4250749 × 10^{−3}  2.4250749 × 10^{−3}  2.9226647 × 10^{−17}  
HSOA [143]  SDM  9.8602 × 10^{−4}  1.0479 × 10^{−3}  1.1683 × 10^{−3}  5.3832 × 10^{−5}  9.333 
DDM  9.8376 × 10^{−4}  1.1175 × 10^{−3}  1.7642 × 10^{−3}  1.9107 × 10^{−4}  
PhotowattPWP201  2.4251 × 10^{−3}  2.4251 × 10^{−3}  2.4253 × 10^{−3}  4.1556 × 10^{−8}  
SOS [146]  SDM  9.8609 × 10^{−4}  1.0245 × 10^{−3}  1.1982 × 10^{−3}  5.2184 × 10^{−5}  10.083 
DDM  9.8518 × 10^{−4}  1.0627 × 10^{−3}  1.3498 × 10^{−3}  9.6141 × 10^{−5}  
PhotowattPWP201  2.4251 × 10^{−3}  2.4361 × 10^{−3}  2.5103 × 10^{−3}  1.7503 × 10^{−5} 
Radiation /W/m^{2}  Temperature /°C  I_{ph}/A  I_{ssd}/μA  n  R_{s}/Ω  R_{sh}/Ω  RMSE 

Variable  Fixed  
1000  25  8.22920506  2.19226333 × 10^{−10}  0.34555194  149.79495733  52.64769156  2.87908987 × 10^{−3} 
800  25  6.58249378  2.57655463 × 10^{−10}  0.34314866  190.38069917  52.99842155  2.40659465 × 10^{−3} 
600  25  4.93738274  2.27177693 × 10^{−10}  0.34433472  250.19011038  52.72470592  3.70428705 × 10^{−3} 
400  25  3.29180014  1.99109819 × 10^{−10}  0.34972198  372.27107651  52.42424407  1.44743443 × 10^{−3} 
200  25  1.64555637  2.50815014 × 10^{−10}  0.34381397  769.17560620  52.94945965  1.23547582 × 10^{−3} 
Fixed  Variable  
1000  25  8.22811095  2.49012735 × 10^{−10}  0.34410634  152.34953496  52.92528529  5.10117026 × 10^{−3} 
1000  40  8.30308470  2.50259970 × 10^{−9}  0.34496529  149.56870789  52.70878667  4.12556209 × 10^{−3} 
1000  55  8.37565108  2.31628311 × 10^{−8}  0.34480573  153.53100022  52.79148663  8.96621362 × 10^{−3} 
1000  70  8.45187588  1.62391869 × 10^{−7}  0.34518787  146.10502751  52.62434432  1.10992599 × 10^{−2} 
Method  Case  Radiation  Temperature  Describe 

FDBTLABC [96]  SM55, ST40, KC200GT  √  √  Experiments were designed for five sets of irradiances at 25 °C and three sets of temperature at 1000 W/m^{2}, with RMSEs consistently lying in the order of 1 × 10^{−5} in the three modules, much better than LSHADE, LSHADEEPSIN, and LSHADESPACMA. 
IADE [68]  SL80CE36M  √  √  Four sets of discriminative parameters and minimum RMSEs (0.0115, 0.006, 0.0071, 0.0154) were obtained from experiments fitting PV data for four different sets of environmental parameters at two temperatures and two irradiances in random combinations. 
DE3P [23]  SM55, RSM50, ST40  √  √  Experiments were carried out with five sets of irradiances at constant temperature and three sets of temperature at constant irradiance, with a maximum RMSE of 0.0148 in the results, which is still an acceptable error. 
EJADE [69]  SM55, KC200GT  √  √  The optimal average RMSE was obtained consistently with eight competing algorithms for experiments at different irradiances and temperatures. The RMSEs were of order 1 × 10^{−4} at 25 °C for 200~800 W/m^{2} and 1 × 10^{−3} for the other experiments. 
AGA [64]      √  A PV cell fitting experiment at different temperatures was designed, and the initial and postsimulation parameter values for the standard case were given. 
GWO [98]      √  Ten sets of experiments at different temperatures (−5 °C~45 °C) were designed and showed an enormous advantage in comparison experiments with MMA, with RMSEs almost of order 1 × 10^{−3} overall. 
OLBGWO [100]  ST40, KC200GT  √  √  The experimental design was the same as that of FDBTLABC. The ST40 module’s RMSEs were at or near the 1 × 10^{−4} order of magnitude. In the KC200GT module, the RMSEs were at or near the 1 × 10^{−3} order of magnitude. 
EJAYA [111]  SM55, KC200GT  √  √  The experimental design was the same as EJADE. The SM55 experiments’ RMSEs were in order 1 × 10^{−4}, and the other experiments’ RMSEs were in order 1 × 10^{−3}. 
MPSO [81]  SM55, ST40, KC200GT  √  √  The experimental design was the same as FDBTLABC. In the KC200GT, the RMSEs were of order 1 × 10^{−3}; in the other experiments, the RMSEs were of order 1 × 10^{−4}. 
GCPSO [82]  Sharpe NDR250A5  √  √  Five experiments with different temperatures and irradiances were designed to obtain high fitting accuracy, with an RMSE of order 1 × 10^{−3}. 
DEDIWPSO [85]  JKM330P  √  √  Experiments were designed for five different irradiances and temperatures, RMSE values were obtained consistently, and all RMSEs were of order 1 × 10^{−3}. 
PSOST [87,88]  JKM330P  √  √  The same experimental design as DEDIWPSO, with RMSEs of order 1 × 10^{−3} and standard deviations of RMSEs on order 1 × 10^{−17}. 
PSOCS [88]  SM55, ST40, KC200GT  √  √  The experimental design was the same as FDBTLABC, with RMSE concentrated at the order of magnitude 1 × 10^{−2} and 1 × 10^{−3}. 
EOTLBO [21]  Sharpe NDR250A5  √  √  The experimental design was the same as GCPSO, with RMSEs concentrated at orders 1 × 10^{−2} and 1 × 10^{−3}, and significantly better than the ten comparative algorithms in the text. 
MTLBO [119]  SM55, ST40  √  √  The experimental design was the same as FDBTLABC, whose RMSEs were concentrated on orders 1 × 10^{−3} and 1 × 10^{−4} and converged slightly faster than ITLBO. 
WOA [124]  KC200GT  √  √  The fitting experiments were implemented with SDM, DDM, and TDM. The SDM error was 1.6%, the DDM error was 0.3%, and the TDM error was 0.08%. It indicates that, with sufficient computational resources, TDM > DDM > SDM in terms of accuracy. 
ISNMWOA [126]  SM55, ST40, KC200GT  √  √  The experimental design was the same as FDBTLABC, with the RMSEs concentrated on orders 1 × 10^{−3} and 1 × 10^{−4}. It showed that ISNMWOA still has high accuracy at low temperatures and irradiance. 
SWOA [125]  SM55, SW255, KC200GT  √  √  Experiments were designed for five irradiances and seven temperatures. The RMSEs were concentrated around 1 × 10^{−2} for the irradiance experiments and around 1 × 10^{−3} for the temperature experiments. 
DE/WOA [127]  JAM660295W4BB  √  √  Experiments with five irradiances and four temperatures were implemented. Significantly better RMSEs were consistently achieved compared to seven competing algorithms, and all results were concentrated around 1 × 10^{−5}. 
HPSODOX [47]    \  √  Seven sets of experiments from −5 to 25 °C were designed. Of these, the RMSEs were located in order 1 × 10^{−9} at 25 °C and in order 1 × 10^{−8} at different temperatures. 
TLBOBSA [134]  SM55, KC200GT  √  √  The experimental design was the same as EJADE. The experimental results were similar to EJAYA and slightly worse overall. 
IGSK [136]  SM55, ST40  √  √  The experimental design was the same as MTLBO, with 11 RMSEs at the 1 × 10^{−4} order of magnitude and 6 RMSEs at the 1 × 10^{−3} order of magnitude in 17 experiments. 
Case  I_{ph}/A  I_{ssd}/μA  n  R_{s}/Ω  R_{sh}/Ω  RMSE 

STC  8.22879884  2.32498946 × 10^{−10}  1.37930864 × 10^{0}  602.77198763  211.10041272  1.31085496 × 10^{−6} 
PSC1  8.40661915  3.20394383 × 10^{−15}  1.62587931 × 10^{−16}  18.94997935  149.17780560  6.96889061 × 10^{−1} 
PSC2  6.93947342  1.16187272 × 10^{−14}  2.40441463 × 10^{−16}  20.81282985  155.76285151  3.71532656 × 10^{−1} 
PSC3  6.52880635  5.19579219 × 10^{−12}  1.10570546 × 10^{−14}  28.77275463  188.22179994  4.55796025 × 10^{−1} 
Parameter  IBES MSDM  TFWO MSDM  IBES MDDM  TFWO MDDM  IBES MTDM  TFWO MTDM 

I_{ph}/A  0.760713  0.760774525  0.760494  0.760783023  0.760473235  0.760780283 
R_{s}/Ω  0.032091  0.037372671  0.015196  0.036835645  0.013865736  0.036749141 
R_{sh}/Ω  54.30519  53.7186078  54.05261  55.8909553  55.47156858  55.52672891 
R_{sm}/Ω  0.00352  0.5  0.02792  0.01025276  0.027870684  0.5 
I_{ssd}_{1}/μA  3.71 × 10^{−7}  3.23 × 10^{−7}  1.00 × 10^{−10}  9.17 × 10^{−7}  1.00 × 10^{−10}  7.63 × 10^{−7} 
I_{ssd}_{2}/μA      6.69 × 10^{−7}  2.07 × 10^{−7}  7.52 × 10^{−7}  2.47 × 10^{−9} 
I_{ssd}_{3}/μA          1.00 × 10^{−10}  2.24 × 10^{−7} 
n_{1}  1.4835  1.48118376  1.00  1.999992291  1.133059042  2 
n_{2}      1.525277  1.443600817  1.537322148  2 
n_{3}          1.004574508  1.450312839 
PE5DSSE    2.5278 × 10^{−5}    2.51 × 10^{−5}    2.509 × 10^{−5} 
MIN RMSE  9.61 × 10^{−4}    7.49 × 10^{−4}    7.39055 × 10^{−4}   
Mean RMSE  1.507 × 10^{−3}    1.201 × 10^{−3}    7.64 × 10^{−4}   
MAX RMSE  2.847 × 10^{−3}    3.378 × 10^{−3}    7.81 × 10^{−4}   
STD of RMSE  7.61 × 10^{−4}    8.95 × 10^{−4}    2.21 × 10^{−5}   
Type  Positive  Negative 

GAs 
 
DEs 


PSOs 


ABCs 
 
GWOs 
 
JAYAs 
 
TLBOs 
 
WOAs 


GSKs 
 
SDOs 


HHOs 
 
TGAs 


SOSs 


FPOAs 


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Gu, Z.; Xiong, G.; Fu, X. Parameter Extraction of Solar Photovoltaic Cell and Module Models with Metaheuristic Algorithms: A Review. Sustainability 2023, 15, 3312. https://doi.org/10.3390/su15043312
Gu Z, Xiong G, Fu X. Parameter Extraction of Solar Photovoltaic Cell and Module Models with Metaheuristic Algorithms: A Review. Sustainability. 2023; 15(4):3312. https://doi.org/10.3390/su15043312
Chicago/Turabian StyleGu, Zaiyu, Guojiang Xiong, and Xiaofan Fu. 2023. "Parameter Extraction of Solar Photovoltaic Cell and Module Models with Metaheuristic Algorithms: A Review" Sustainability 15, no. 4: 3312. https://doi.org/10.3390/su15043312