Estimation of Parameters of Different Equivalent Circuit Models of Solar Cells and Various Photovoltaic Modules Using Hybrid Variants of Honey Badger Algorithm and Artificial Gorilla Troops Optimizer
Abstract
:1. Introduction
- A new metaheuristic algorithm for estimating parameters of equivalent circuit models of solar cells and PV modules has been proposed.
- Two types of hybridization of algorithms used have been proposed.
- Statistical analysis of the results of these algorithms is examined.
- Performance of the proposed algorithms is compared with several well-known algorithms used in parameter estimation problems.
- The three equivalent circuit models of solar cells are addressed and investigated.
- The applicability and efficiency of the proposed methods are tested on commercial PV modules for different levels of temperature and irradiance.
2. Solar Cell Equivalent Circuits
3. Proposed Hybrid Algorithms
Algorithm 1: Complete pseudo-code of the artificial gorilla troops optimizer-honey badger algorithm (GTO-HBA) (Proposed 1). |
1: Set parameters N, C, β, and tmax |
2: Initialize the population using the GTO algorithm [60]: 3: Evaluate the fitness of each badger xi and assign it to fi 4: Save the best position xprey and assign it to fprey |
5: for t = 1 to tmax |
6: Update factor α 7: for i = 1 to N |
8: Calculate intensity Ii 9: if r < 0.5 |
10: Update the positions according to the digging phase 11: else 12: Update the positions according to the honey phase |
13: endif 14: Evaluate new positions and assign them to fnew 15: if fnew ≤ fi 16: set xi = xnew and fi = fnew |
17: endif 18: if fnew ≤ fprey 19: set xprey = xnew and fprey = fnew |
20: endif 21: end for 22: end for 23: Return xprey—the optimal solution |
Algorithm 2: Complete pseudo-code of the honey badger algorithm and artificial gorilla troops optimizer (HBA-GTO) (Proposed 2). |
1: Set parameters N, N1, N2, p, β, and tmax |
2: Initialize the population of gorillas using HBA [30]: 3: Evaluate the fitness of each gorilla |
4: for t = 1 to tmax |
5: Update L and C 6: Conduct the exploration phase and calculated population GX(t) |
7: Evaluate the fitness of each gorilla and update the population X(t) 8: Determine the best gorilla—Silverback |
9: end for 10: Return Xsilverback—the optimal solution |
4. Numerical Results
5. Results Obtained for a Commercial PV Module
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ABC | Artificial bee colony |
ABC-DE | Artificial bee colony-differential evolution |
ABC-TRR | Artificial bee colony-trust-region reflective algorithm |
A&I | Analytical- and iterative-based methods |
BC | Bézier curves |
BIA | Bio-inspired algorithms |
BHCS | Biogeography-based heterogeneous cuckoo search |
BPFPA | Bee pollinator flower pollination algorithm |
CGBO | Improved gradient-based optimization algorithm with chaotic drifts |
CLSHADE | Chaotic successful history-based adaptive DE variants with linear population size reduction algorithm |
CNMSMA | Chaotic Nelder–Mead slime mould algorithm |
COA | Chaotic optimization approach |
CPMPSO | Classified perturbation mutation-based particle swarm optimization |
CS | Cuckoo search optimization |
CSO | Cat swarm optimization |
DDM | Double-diode model |
DE | Differential evolution |
DE-WOA | Hybrid DE with whale optimization algorithm |
DSO | Drone squadron optimization |
EHA–NMS | Eagle-based hybrid adaptive Nelder–Mead simplex algorithm |
EHHO | Enhanced Harris hawk optimization |
EO | Equilibrium optimizer method |
GA | Genetic algorithm |
GAMNU | Genetic algorithm based on non-uniform mutation |
GBO | Gradient-based optimizer |
GOFPANM | Generalized opposition-flower pollination algorithm-Nelder–Mead simplex method |
GSK | Gaining–sharing knowledge-based algorithm |
GTO | Gorilla troops optimizer |
HBA | Honey badger algorithm |
IJAYA | Improved JAYA optimization |
IMO | Ions motion algorithm |
ISCE | Improved shuffled complex evolution |
ITLBO | Improved teaching–learning-based optimization |
IWOA | Improved whale optimization algorithm |
MADE | Memetic adaptive DE |
MAE | Mean absolute error |
MAPE | Mean absolute percentage error |
MLBSA | Multiple learning backtracking search algorithm |
MPA | Marine-predators algorithm |
MPSO | Modified particle swarm optimization |
MSSO | Modified simplified swarm optimization algorithm |
MSX 60 | Solarex’s multicrystalline 60 watts solar module |
MTLBO | Modified teaching-–earning-based optimization |
NM | Newton method |
OBWOA | Opposition-based whale optimization algorithm |
ORcr-IJADE | Onlooker-ranking-based and improved adaptive and differential evolution |
PGJAYA | Performance-guided JAYA algorithm |
Photowatt PWP | Photowatt solar panel of model PWP |
PSO | Particle swarm optimization |
PV | Photovoltaic |
RESs | Renewable energy sources |
RTC | RadioTechnique Compelec |
SDM | Single-diode model |
SMA | Slime mould algorithm |
SM55 | Shell monocrystalline PV module |
STLBO | Simplified teaching–learning-based optimization |
TDM | Triple-diode model |
TLABC | Teaching–learning-based artificial bee colony |
TLBO | Teaching–learning-based optimization |
TLO | Teaching–learning optimization |
TSO | Transient search optimization |
TVA-CPSO | Time-varying acceleration coefficients PSO |
WHHO | Whippy Harris hawks optimization |
WOA | Whale optimization algorithm |
WDO | Wind-driven optimization |
Appendix A
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# | Refs. | First Author | Year | Method | Model | Root Mean Square Error (RMSE) | Mean Absolute Error (MAE) | Mean Absolute Percentage Error (MAPE) |
---|---|---|---|---|---|---|---|---|
1 | [32] | Ndi | 2021 | EO | SDM | 0.000776865 | 0.000678644363621 | 0.462865302508924 |
2 | [21] | Naeijian | 2021 | WHHO | SDM | 0.000791502 | 0.000667595306139 | 0.344470169829233 |
3 | [13] | Saadaou | 2021 | GAMNU | SDM | 0.000812621 | 0.000719474973281 | 0.643237501038952 |
4 | [17] | Xiong | 2021 | GSK | SDM | 0.000776134 | 0.000676554109096 | 0.451972461015800 |
5 | [33] | Kumar | 2020 | SMA | SDM | 0.000795243 | 0.000667150561147 | 0.332742958125476 |
6 | [34] | Jiao | 2020 | EHHO | SDM | 0.000786704 | 0.000701818945693 | 0.558833901459953 |
7 | [22] | Gude | 2020 | CSO | SDM | 0.000860194 | 0.000663573496324 | 0.210089090921584 |
8 | [18] | Li | 2019 | ITLBO | SDM | 0.000777792 | 0.000687239590168 | 0.502104166185744 |
9 | [35] | Yu | 2019 | PGJAYA | SDM | 0.000777792 | 0.000687239590168 | 0.502104166185744 |
10 | [29] | Chen | 2019 | BHCS | SDM | 0.000775415 | 0.000679675374715 | 0.455550255014124 |
11 | [23] | Merchaoui | 2018 | MPSO | SDM | 0.004359909 | 0.002889258774089 | 4.353156563261146 |
12 | [19] | Chen | 2018 | TLABC | SDM | 0.000775416 | 0.000679670632200 | 0.455459033518709 |
13 | [36] | Lin | 2017 | MSSO | SDM | 0.000809159 | 0.000665110052013 | 0.295109693517836 |
14 | [14] | Ram | 2017 | BPFPA | SDM | 0.000955513 | 0.000824210723789 | 0.736974713224005 |
15 | [37] | Derick | 2017 | WDO | SDM | 0.000894818 | 0.000721091048657 | 0.410871168713455 |
16 | [38] | Yu | 2017 | IJAYA | SDM | 0.000776055 | 0.000674909321295 | 0.443697941771721 |
17 | [17] | Xiong | 2021 | GSK | DDM | 0.000765347 | 0.000674714400538 | 0.477776103165468 |
18 | [13] | Saadaou | 2021 | GAMNU | DDM | 0.000795540 | 0.000671452693614 | 0.333198261209489 |
19 | [32] | Ndi | 2021 | EO | DDM | 0.006348583 | 0.006174565636472 | 2.943474469938229 |
20 | [21] | Naeijian | 2021 | WHHO | DDM | 0.000774553 | 0.000654593080672 | 0.327472776645842 |
21 | [39] | Liu | 2021 | CNMSMA | DDM | 0.000757922 | 0.000662676325841 | 0.426575266450123 |
22 | [33] | Kumar | 2020 | SMA | DDM | 0.007025646 | 0.004360131396396 | 7.646965757100302 |
23 | [34] | Jiao | 2020 | EHHO | DDM | 0.000764087 | 0.000671304856402 | 0.454160791097682 |
24 | [22] | Gude | 2020 | CSO | DDM | 0.000869770 | 0.000680544614180 | 0.300124951077260 |
25 | [26] | Ćalasan | 2019 | COA | DDM | 0.000757686 | 0.000667871337617 | 0.450126256899350 |
26 | [24] | Abd Elaziz | 2018 | ABC | TDM | 0.000990246 | 0.000771873120355 | 0.505954728856906 |
27 | 2018 | OBWOA | TDM | 0.000823136 | 0.000650108387227 | 0.218668597114990 | ||
28 | 2018 | STLBO | TDM | 0.000823698 | 0.000649122444713 | 0.215757981839370 | ||
29 | [40] | Premkumar | 2020 | R-II | TDM | 0.005125476 | 0.003367928190167 | 5.136372818754378 |
30 | 2020 | R-III | TDM | 0.002249998 | 0.001572560907759 | 2.495078551153684 | ||
31 | 2020 | PSO | TDM | 0.002171714 | 0.001543183004978 | 2.383178745442769 | ||
32 | 2020 | CS | TDM | 0.004569170 | 0.003033484788679 | 4.539593940311719 | ||
33 | 2020 | ABC | TDM | 0.002471743 | 0.001761292412332 | 2.292317731497820 | ||
34 | 2020 | TLO | TDM | 0.000779584 | 0.000654100267008 | 0.331628211492756 | ||
35 | Proposed Algorithm 1 | SDM | 0.000774655 | 0.000681168150469 | 0.455157210140345 | |||
36 | Proposed Algorithm 2 | SDM | 0.000774656 | 0.000681221910233 | 0.455412179465424 | |||
37 | Proposed Algorithm 1 | DDM | 0.000756129 | 0.000668726140277 | 0.457389890766874 | |||
38 | Proposed Algorithm 2 | DDM | 0.000755910 | 0.000662136081515 | 0.426224519512442 | |||
39 | Proposed Algorithm 1 | TDM | 0.000751879 | 0.000659656489694 | 0.420986462546710 | |||
40 | Proposed Algorithm 2 | TDM | 0.000752053 | 0.000663697106339 | 0.440229380526819 |
# | Ipv (A) | I01 (μA) | n1 | RS (Ω) | RP (Ω) | I02 (μA) | n2 | I03 (μA) |
---|---|---|---|---|---|---|---|---|
1 | 0.7607597037 | 0.32628893 | 1.48219300 | 0.03634099 | 54.20659400 | - | - | - |
2 | 0.76077551 | 0.32302031 | 1.48110808 | 0.03637710 | 53.71867407 | - | - | - |
3 | 0.76077400 | 0.32559540 | 1.48209600 | 0.03634020 | 53.89686000 | - | - | - |
4 | 0.76080000 | 0.32310000 | 1.48120000 | 0.03640000 | 53.72270000 | - | - | - |
5 | 0.76076000 | 0.32314000 | 1.48114000 | 0.03637000 | 53.71489000 | - | - | - |
6 | 0.76077500 | 0.32300000 | 1.48123800 | 0.03637500 | 53.74282000 | - | - | - |
7 | 0.76080000 | 0.32300000 | 1.48100000 | 0.03640000 | 53.71850000 | - | - | - |
8 | 0.76080000 | 0.32300000 | 1.48120000 | 0.03640000 | 53.71850000 | - | - | - |
9 | 0.76080000 | 0.32300000 | 1.48120000 | 0.03640000 | 53.71850000 | - | - | - |
10 | 0.76078000 | 0.32302000 | 1.48118000 | 0.03638000 | 53.71852000 | - | - | - |
11 | 0.76078700 | 0.31068300 | 1.47526200 | 0.03654600 | 52.88971000 | - | - | - |
12 | 0.76078000 | 0.32302000 | 1.48118000 | 0.03638000 | 53.71636000 | - | - | - |
13 | 0.76077700 | 0.32356400 | 1.48124400 | 0.03637000 | 53.74246500 | - | - | - |
14 | 0.76000000 | 0.31060000 | 1.47740000 | 0.03660000 | 57.71510000 | - | - | - |
15 | 0.76080000 | 0.32230000 | 1.48080000 | 0.03676800 | 57.74614000 | - | - | - |
16 | 0.76080000 | 0.32280000 | 1.48110000 | 0.03640000 | 53.75950000 | - | - | - |
17 | 0.76080000 | 0.25950000 | 1.46270000 | 0.03660000 | 54.93300000 | 0.47910000 | 1.99830000 | - |
18 | 0.76082700 | 0.32245246 | 1.48102800 | 0.03636440 | 53.11079000 | 0.00027392 | 1.47010100 | - |
19 | 0.76792000 | 0.39999000 | 2.00000000 | 0.03659000 | 54.17614000 | 0.26605000 | 1.46451000 | - |
20 | 0.76078094 | 0.22857400 | 1.45189500 | 0.03672887 | 55.42643282 | 0.727182 | 2 | - |
21 | 0.76078100 | 0.22597600 | 1.45101700 | 0.036740 | 55.48545 | 0.75068100 | 1.9999990 | - |
22 | 0.76076000 | 0.74874000 | 2.00000000 | 0.03677 | 55.71456 | 0.22652000 | 1.4546300 | - |
23 | 0.760769017 | 0.58618400 | 1.968451449 | 0.036598831 | 55.63943956 | 0.24096500 | 1.456910409 | - |
24 | 0.76080 | 0.22730 | 1.45130 | 0.03670 | 55.43270 | 0.73840000 | 1.99990 | - |
25 | 0.76078 | 0.22597 | 1.45102 | 0.03674 | 55.48542 | 0.749346 | 2.00000 | - |
26 | 0.760700 | 0.2000 | 1.4414 | 0.03687 | 55.8344 | 0.500000 | 1.90000 | 0.2100 |
27 | 0.760770 | 0.2353 | 1.4543 | 0.03668 | 55.4448 | 0.221300 | 2.00000 | 0.4573 |
28 | 0.760800 | 0.2349 | 1.4541 | 0.0367 | 55.2641 | 0.229700 | 2.00000 | 0.4443 |
29 | 0.760792 | 0.2600 | 1.4608 | 0.03660 | 54.9149 | 0.000006 | 1.14660 | 0.5700 |
30 | 0.760791 | 0.2100 | 1.7714 | 0.03670 | 55.3571 | 0.220000 | 1.45130 | 0.9900 |
31 | 0.760782 | 0.2500 | 1.4601 | 0.03660 | 55.3133 | 0.041000 | 1.74090 | 1.0000 |
32 | 0.760776 | 0.1400 | 1.4872 | 0.03630 | 53.7218 | 0.190000 | 1.47710 | 0.0310 |
33 | 0.760790 | 0.3200 | 1.8666 | 0.03670 | 55.4411 | 0.230000 | 1.45210 | 0.7400 |
34 | 0.760763 | 0.2800 | 1.4684 | 0.03650 | 55.3821 | 0.000670 | 1.54680 | 1.0000 |
35 | 0.76077537 | 0.320741243 | 1.48046987 | 0.0364 | 53.5397184 | - | - | - |
36 | 0.76077541 | 0.3207412 | 1.48047001 | 0.0364 | 53.5397 | - | - | - |
37 | 0.7607801 | 0.84162 | 1.999999 | 0.03679 | 55.73 | 0.2154505 | 1.44706 | - |
38 | 0.76078 | 0.841611 | 2.00000 | 0.0367905 | 55.72835 | 0.2154501 | 1.44704 | - |
39 | 0.7607602 | 0.876504 | 1.99504 | 0.0369201 | 55.6798 | 0.20441 | 1.442401 | 0.0001805 |
40 | 0.7607601 | 0.876499 | 1.99501 | 0.0369202 | 55.6801 | 0.204401 | 1.44241 | 0.0001801 |
# | Refs. | First Author | Year | Method | Model | RMSE | MAE | MAPE |
---|---|---|---|---|---|---|---|---|
1 | [42] | Bana | 2018 | NM | SDM | 0.101844933535061 | 0.086404559671331 | 7.989316753756794 |
2 | [41] | Szabo | 2018 | BC | SDM | 0.030722505654028 | 0.023915966897748 | 1.928605918749928 |
3 | [43] | Silva | 2016 | A&I | SDM | 0.018106614648430 | 0.015234044936426 | 1.804005972558074 |
4 | [44] | Villalva | 2009 | A&I | SDM | 0.028396627361794 | 0.020903325782359 | 1.703387713558635 |
5 | [12] | Calasan | 2021 | CLSHADE | DDM | 0.012028665165887 | 0.008871675551380 | 1.300255779491913 |
6 | [45] | Qais | 2020 | TSO | TDM | 0.017009785983445 | 0.014438913645570 | 1.467713460523862 |
7 | Proposed Algorithm 1 | SDM | 0.012105788990909 | 0.009207999217896 | 1.210171037317782 | |||
8 | Proposed Algorithm 2 | SDM | 0.012120811620560 | 0.009345995684596 | 1.276143583474973 | |||
9 | Proposed Algorithm 1 | DDM | 0.011955126049429 | 0.008847188231494 | 1.292653674324527 | |||
10 | Proposed Algorithm 2 | DDM | 0.011896989581563 | 0.008827736037378 | 1.286768018642119 | |||
11 | Proposed Algorithm 1 | TDM | 0.011683038647976 | 0.008837712415575 | 1.260645716394877 | |||
12 | Proposed Algorithm 2 | TDM | 0.011660925987728 | 0.008830639239597 | 1.256151650040435 |
# | Ipv (A) | I01 (μA) | n1 | RS (Ω) | RP (Ω) | I02 (μA) | n2 | I03 (μA) |
---|---|---|---|---|---|---|---|---|
1 | 3.8084 | 4.8723 × 10−10 | 1.0003 | 0.3692 | 169.0471 | - | - | - |
2 | 3.808 | 1.22 × 10−9 | 1.045 | 0.316 | 146.08 | - | - | - |
3 | 3.7983 | 6.79 × 10−8 | 1.28 | 0.251 | 582.7278 | - | - | - |
4 | 3.808244 | 1.21946 × 10−9 | 1.045334 | 0.316000 | 146.081207 | - | - | - |
5 | 3.812527 | 0.12311 × 10−6 | 1.32290 | 0.226800 | 800 | 7.29990 × 10−11 | 1.98800 | - |
6 | 3.8019 | 3.3525 × 10−7 | 1.9346 | 0.22724 | 450.13 | 1 × 10−12 | 1.7208 | 6.4568 × 10−8 |
7 | 3.8127 | 0.14051 × 10−6 | 1.332513 | 0.22351 | 1105.5869 | - | - | - |
8 | 3.81268 | 0.14 × 10−6 | 1.3325 | 0.2235 | 1155.6258 | - | - | - |
9 | 3.812527 | 0.12312 × 10−6 | 1.32288 | 0.226805 | 805.46 | 7.30 × 10−11 | 1.98800 | - |
10 | 3.81252689 | 0.1231199 × 10−6 | 1.32286 | 0.226801 | 807.11 | 7.299 × 10−11 | 1.9881 | - |
11 | 3.81252 | 0.12314 × 10−6 | 1.32274 | 0.226756 | 831.01000 | 7.29990 × 10−11 | 1.98888 | 1.24 × 10−10 |
12 | 3.81253 | 0.12312 × 10−6 | 1.32271 | 0.2267586 | 827.51000 | 7.30000 × 10−11 | 1.99060 | 1.2488 × 10−10 |
# | Refs. | First Author | Year | Method | Model | RMSE | MAE | MAPE |
---|---|---|---|---|---|---|---|---|
1 | [27] | Premkumar | 2021 | CGBO | SDM | 0.002203160582196 | 0.001777355730246 | 0.391412974711076 |
2 | GBO | SDM | 0.002203160582196 | 0.001777355730246 | 0.391412974711076 | |||
3 | [46] | Basset | 2021 | MTLBO | SDM | 0.002192702293887 | 0.001732693097767 | 0.386396089379751 |
4 | [47] | Gnetchejo | 2021 | DSO | SDM | 0.005525262416993 | 0.004319124678700 | 6.249226276809913 |
5 | [25] | Ridha | 2020 | MPA | SDM | 0.002741282553112 | 0.002131950064861 | 0.661561491439685 |
6 | [48] | Basset | 2020 | EO | SDM | 0.002307739416553 | 0.001831385873737 | 0.525272290565770 |
7 | [61] | Liang | 2020 | CPMPSO | SDM | 0.002192702238676 | 0.001732692519390 | 0.386403196851621 |
8 | [35] | Yu | 2019 | PGJAYA | SDM | 0.002193558995652 | 0.001733161807074 | 0.384469167044506 |
9 | [62] | Muangkote | 2019 | ORcr-IJADE | SDM | 0.002192747605064 | 0.001732930882957 | 0.383436962669269 |
10 | [18] | Li | 2019 | ITLBO | SDM | 0.002192702300691 | 0.001732692943681 | 0.386396861783031 |
11 | 2019 | TLBO | SDM | 0.004291553746717 | 0.003496972143159 | 1.247781769889620 | ||
12 | [15] | Li | 2019 | MADE | SDM | 0.002192702238262 | 0.001732692528770 | 0.386403149832207 |
13 | [28] | Xiong | 2018 | WOA | SDM | 0.002657115956104 | 0.002085699153659 | 0.539623953519785 |
14 | [50] | Yu | 2018 | MLBSA | SDM | 0.002162931772907 | 0.001693675233514 | 0.388880476705581 |
15 | [28] | Xiong | 2018 | DE-WOA | SDM | 0.002192747607804 | 0.001732930797684 | 0.383437390120559 |
16 | [51] | Wu | 2018 | ABC-TRR | SDM | 0.002192747605338 | 0.001732930874429 | 0.383437005413906 |
17 | [16] | Gao | 2018 | ISCE | SDM | 0.002192747603968 | 0.001732930917066 | 0.383436791688368 |
18 | [28] | Xiong | 2018 | IWOA | SDM | 0.002192213422029 | 0.001731871744843 | 0.389108171505321 |
19 | [52] | Xu | 2017 | GOFPANM | SDM | 0.002192747602872 | 0.001732930951174 | 0.383436620706835 |
20 | [53] | Elazab | 2017 | WOA | SDM | 0.002335740096957 | 0.001841026675079 | 0.332600274029797 |
21 | [54] | Jordehi | 2016 | TVACPSO | SDM | 0.003934939903764 | 0.003196946998661 | 4.232444252386350 |
22 | [55] | Chen | 2016 | EHA-NMS | SDM | 0.002192747604790 | 0.001732930891484 | 0.383436919923165 |
23 | [58] | Javidy | 2015 | IMO | SDM | 0.002835333050835 | 0.002165750688947 | 0.381968187687215 |
24 | [27] | Premkumar | 2021 | CGBO | DDM | 0.002199165255522 | 0.001759965636308 | 0.343756630837216 |
25 | 2021 | GBO | DDM | 0.002199691952382 | 0.001769207464245 | 0.368397908487905 | ||
26 | [48] | Basset | 2020 | EO | DDM | 0.002416169330585 | 0.001882811345434 | 0.375619719216614 |
27 | [58] | Javidy | 2015 | IMO | DDM | 0.003177249323240 | 0.002272124722926 | 0.743764711488892 |
28 | Proposed Algorithm 1 | SDM | 0.002101381507033 | 0.001770256665782 | 0.529618617926409 | |||
29 | Proposed Algorithm 2 | SDM | 0.002104650458946 | 0.001774133525922 | 0.460871551281877 | |||
30 | Proposed Algorithm 1 | DDM | 0.002076434123783 | 0.001706530046156 | 1.026218805598722 | |||
31 | Proposed Algorithm 2 | DDM | 0.002072962280362 | 0.001701420988536 | 1.006077058292598 | |||
32 | Proposed Algorithm 1 | TDM | 0.002040806557869 | 0.001676862715116 | 0.667708048509709 | |||
33 | Proposed Algorithm 2 | TDM | 0.002041811785061 | 0.001685648251157 | 0.656010002550055 |
# | Ipv (A) | I01 (μA) | n1 | RS (Ω) | RP (Ω) | I02 (μA) | n2 | I03 (μA) |
---|---|---|---|---|---|---|---|---|
1 | 1.0305 | 3.48 | 48.6428 | 1.2013 | 981.9821 | - | - | - |
2 | 1.0305 | 3.48 | 48.6428 | 1.2013 | 981.9821 | - | - | - |
3 | 1.0305143 | 3.4823 | 48.6428349 | 1.2012710 | 981.9823732 | - | - | - |
4 | 1.032357 | 2.496596 | 47.33406 | 1.240547 | 748.32309 | - | - | - |
5 | 1.0273 | 4.51 | 49.6486 | 1.1781 | 1977.6535 | - | - | - |
6 | 1.0296 | 3.76 | 48.9340 | 1.1943 | 1139.0284 | - | - | - |
7 | 1.0305143 | 3.4823 | 48.6428348 | 1.2012710 | 981.9822493 | - | - | - |
8 | 1.0305 | 3.4818 | 48.642372 | 1.2013 | 981.8545 | - | - | - |
9 | 1.030514 | 3.482263 | 48.64284 | 1.201271 | 981.98224 | - | - | - |
10 | 1.0305143 | 3.4823 | 48.6428349 | 1.201271 | 981.9821925 | - | - | - |
11 | 1.0357161 | 4.13 | 49.2820100 | 1.2222703 | 999.6274934 | - | - | - |
12 | 1.0305143 | 3.4823 | 48.6428348 | 1.2012710 | 981.9822603 | - | - | - |
13 | 1.0280 | 4.75 | 49.8593 | 1.1680 | 1712.8543 | - | - | - |
14 | 1.0309977 | 3.4279 | 48.583600 | 1.2026154 | 931.9237428 | - | - | - |
15 | 1.030514 | 3.482263 | 48.64284 | 1.201271 | 981.98214 | - | - | - |
16 | 1.030514 | 3.482263 | 48.64284 | 1.201271 | 981.98223 | - | - | - |
17 | 1.030514 | 3.482263 | 48.64284 | 1.201271 | 981.98228 | - | - | - |
18 | 1.0305 | 3.4717 | 48.631284 | 1.2016 | 978.6771 | - | - | - |
19 | 1.030514 | 3.482263 | 48.64284 | 1.201271 | 981.98232 | - | - | - |
20 | 1.0294212 | 3.8525 | 49.0306622 | 1.1906302 | 1179.9442886 | - | - | - |
21 | 1.031435 | 2.6386 | 47.556648 | 1.235611 | 821.59514 | - | - | - |
22 | 1.030514 | 3.482263 | 48.64284 | 1.201271 | 981.98225 | - | - | - |
23 | 1.0264 | 3.45 | 48.5924 | 1.2112 | 1899.6737 | - | - | - |
24 | 1.0305 | 3.48 | 48.6428 | 1.2013 | 981.8874 | 3.89 × 10−6 | 34.7828 | - |
25 | 1.0305 | 3.47 | 48.6314 | 1.2016 | 981.2677 | 0 | 50 | - |
26 | 1.0288 | 9.38 × 10−4 | 47.1325 | 1.1896 | 1310.6705 | 3.96 | 49.1369 | - |
27 | 1.0251 | 0 | 45.7618 | 1.2339 | 1849.8346 | 3.07 | 48.1472 | - |
28 | 1.03241 | 2.5538 | 47.48801 | 1.2386 | 752.8111 | - | - | - |
29 | 1.0323 | 2.554 | 47.48563 | 1.23861 | 772.8905 | - | - | - |
30 | 1.03242 | 2.5130 | 47.418 | 1.2393 | 744.724 | 3.89 × 10−6 | 50 | - |
31 | 1.0325 | 2.5150 | 47.421 | 1.23928 | 743.666 | 3.8885 × 10−6 | 49.88 | - |
32 | 1.0323818 | 2.512908 | 47.42295 | 1.2393 | 743.724 | 1.86 × 10−4 | 48.88 | 1.35 × 10−6 |
33 | 1.032383 | 2.512914 | 47.423 | 1.2393 | 753.659 | 1.16 × 10−3 | 48.93 | 1.05 × 10−6 |
Algorithms | Best | Worst | Mean | Median | Standard Deviation |
---|---|---|---|---|---|
Proposed 1 | 7.7465 × 10−4 | 7.8447 × 10−4 | 7.7591 × 10−4 | 7.7468 × 10−4 | 3.5901 × 10−6 |
Proposed 2 | 7.7466 × 10−4 | 7.8842 × 10−4 | 7.7504 × 10−4 | 7.7472 × 10−4 | 3.9844 × 10−6 |
GTO | 7.7488 × 10−4 | 7.8447 × 10−4 | 7.7501 × 10−4 | 7.7501 × 10−4 | 3.711 × 10−6 |
HBA | 7.7524 × 10−4 | 8.5089 × 10−4 | 7.8427 × 10−4 | 7.7921 × 10−4 | 1.4697 × 10−5 |
AO | 16.000 × 10−4 | 95.000 × 10−4 | 51.000 × 10−4 | 49.000 × 10−4 | 18.000 × 10−4 |
PSO | 7.7453 × 10−4 | 8.5089 × 10−4 | 7.9619 × 10−4 | 7.9570 × 10−4 | 1.9585 × 10−5 |
Algorithms | Proposed 1 Versus Proposed 2 | Proposed 1 Versus HBA | Proposed 1 Versus GTO | Proposed 1 Versus AO | Proposed 1 Versus PSO |
---|---|---|---|---|---|
p-value | 8.5641 × 10−4 | 8.1465 × 10−5 | 0.0103 | 3.01 × 10−11 | 2.8314 × 10−8 |
Algorithms | Proposed 2 versus Proposed 1 | Proposed 2 versus HBA | Proposed 2 versus GTO | Proposed 2 versus AO | Proposed 2 versus PSO |
p-value | 8.5641 × 10−4 | 5.1857 × 10−7 | 0.3112 | 3.01 × 10−11 | 2.9215 × 10−9 |
Parameters | Ipv (A) | I0 (μA) | RS (Ω) | RP (Ω) | n |
---|---|---|---|---|---|
Value | 3.45884 | 0.041477 | 0.3876853 | 549.98057 | 1.28087 |
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Rawa, M.; Abusorrah, A.; Al-Turki, Y.; Calasan, M.; Micev, M.; Ali, Z.M.; Mekhilef, S.; Bassi, H.; Sindi, H.; Aleem, S.H.E.A. Estimation of Parameters of Different Equivalent Circuit Models of Solar Cells and Various Photovoltaic Modules Using Hybrid Variants of Honey Badger Algorithm and Artificial Gorilla Troops Optimizer. Mathematics 2022, 10, 1057. https://doi.org/10.3390/math10071057
Rawa M, Abusorrah A, Al-Turki Y, Calasan M, Micev M, Ali ZM, Mekhilef S, Bassi H, Sindi H, Aleem SHEA. Estimation of Parameters of Different Equivalent Circuit Models of Solar Cells and Various Photovoltaic Modules Using Hybrid Variants of Honey Badger Algorithm and Artificial Gorilla Troops Optimizer. Mathematics. 2022; 10(7):1057. https://doi.org/10.3390/math10071057
Chicago/Turabian StyleRawa, Muhyaddin, Abdullah Abusorrah, Yusuf Al-Turki, Martin Calasan, Mihailo Micev, Ziad M. Ali, Saad Mekhilef, Hussain Bassi, Hatem Sindi, and Shady H. E. Abdel Aleem. 2022. "Estimation of Parameters of Different Equivalent Circuit Models of Solar Cells and Various Photovoltaic Modules Using Hybrid Variants of Honey Badger Algorithm and Artificial Gorilla Troops Optimizer" Mathematics 10, no. 7: 1057. https://doi.org/10.3390/math10071057