An Innovative Hunter-Prey-Based Optimization for Electrically Based Single-, Double-, and Triple-Diode Models of Solar Photovoltaic Systems
Abstract
:1. Introduction
1.1. Motivation
1.2. Literature Survey of Related Work
1.3. Research Gap
1.4. Paper Contribution
- A promising algorithm is demonstrated in the field of photovoltaic technologies, modelling with real applications on a commercial STM6-40/36 module and RTC France cell;
- The simulated results demonstrate that the developed PV system equivalent model relying on the HPO technique is extremely efficient and produces superior outcomes when compared to other reported techniques;
- The convergence rate for the proposed HPO is great, with a high speed in focusing the search around the area of the global optimization of the minimum RMSE;
- The proposed HPO technique provides high accuracy in extracting the electrical PV parameters with significant coincidence between the simulated and experimental I–V and P–V characteristics.
1.5. Key Segments of the Paper
2. Mathematical Model of the Hunter–Prey-Based Optimization
3. Mathematical Model of the Electrical Representations of Solar PV Systems
3.1. Single-Diode Model
3.2. Double-Diode Model
3.3. Photovoltaic Triple-Diode Model
3.4. PV Modules Handling
3.5. Objective Function Formulation
4. Simulation Results
4.1. Simulation Results for STM6_40/36 PV Module
4.1.1. Case 1: Single-Diode Model
4.1.2. Case 2: Double-diode Model of STM6_40/36 PV Module
4.1.3. Case 3: Triple-Diode Model of STM6_40/36 PV Module
4.2. Simulation Results for RTC France Silicon Cell
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | STM6-40/36 PV Module | RTC France PV Cell | ||
---|---|---|---|---|
lb | ub | lb | ub | |
IPh (A) | 0 | 2 | 0 | 1 |
RS (Ω) | 0 | 0.36 | 0 | 0.5 |
1 | 2 | 1 | 2 | |
Rsh (Ω) | 0 | 100 | 0 | 100 |
(μA) | 0 | 50 | 0 | 1 |
Optimizer | IPh (A) | RS (Ω) | Rsh (Ω) | RMSE | Improvement % | ||
---|---|---|---|---|---|---|---|
Proposed HPO | 1.663905 | 1.74 | 0.004275 | 15.92749 | 1.520269 | 1.729814 × 10−3 | - |
EO [48] | 1.663629 | 1.78 | 0.004205 | 16.24408 | 1.523146 | 1.733 × 10−3 | 0.1838 |
MPA [48] | 1.65702 | 2.46 | 0.003831 | 31.50673 | 1.559041 | 3.496 × 10−3 | 50.5202 |
EMPA [48] | 1.663418 | 2.03 | 0.003788 | 16.878 | 1.537713 | 1.769 × 10−3 | 2.2151 |
GTO [48] | 1.663905 | 1.74 | 0.004274 | 15.92829 | 1.520303 | 1.73 × 10−3 | 0.0108 |
HBA [48] | 1.661527 | 5.51 | 0.00001 | 23.6426 | 1.658694 | 3.33 × 10−3 | 48.0536 |
JFS [48] | 1.662589 | 1.84 | 0.004105 | 16.96607 | 1.526795 | 1.807 × 10−3 | 4.2715 |
ImCSA [49] | 1.663971 | 2 | 0.002914 | 15.84051 | 1.5335 | 1.794 × 10−3 | 3.5778 |
FBI [50] | 1.66391 | 1.74 | 0.004281 | 15.91743 | 1.520073 | 1.73 × 10−3 | 0.0108 |
ISCE [19] | 1.66390478 | 1.74 | 0.004274 | 15.9283 | 1.5203 | 1.73 × 10−3 | 0.0108 |
BHCS [38] | 1.6639 | 1.74 | 0.00427 | 15.9283 | 1.5203 | 1.73 × 10−3 | 0.0108 |
TPBA [51] | 1.6632 | 2.77 | 0.004186 | 16.7328 | 1.5656 | 1.774 × 10−3 | 2.4908 |
SA [52] | 1.6609 | 5.90 | 0.0049499 | 26.7742 | 1.66602 | 3.399 × 10−3 | 49.1081 |
Optimizer | IPh (A) | RS (Ω) | Rsh (Ω) | RMSE | Improvement % | ||||
---|---|---|---|---|---|---|---|---|---|
HPO | 1.663702 | 4.06 | 5.57 × 10−4 | 0.008726 | 17.82614 | 1.688851 | 1 | 1.696271 × 10−3 | - |
EPSO [53] | 1.6648 | 16.70 | 6.21 × 10−6 | 0.5000 | 16.858 | 1.16649 | 1.87067 | 1.8307 × 10−3 | 7.3430 |
LCROA [54] | 1.6637 | 72.2 | 3.28 × 10−6 | 0.16717 | 16.7419 | 1.5739 | 2.000 | 1.712 × 10−3 | 0.9187 |
BA [55] | 1.637941 | 1.59 | 3.94 × 10−5 | 0.003887 | 24.6958 | 1.504536 | 1.4783 | 2.194577 × 10−2 | 92.2706 |
DBA [55] | 1.663860 | 1.80 | 3.66 × 10−6 | 0.004167 | 16.066503 | 1.524098 | 1.43939 | 1.731960 × 10−3 | 2.0606 |
NBA [55] | 1.662865 | 6.60 | 1.61 × 10−6 | 0.004653 | 16.694049 | 1.678806 | 1.511867 | 1.82684 × 10−3 | 7.1473 |
FC-EPSO [56] | 1.6634 | 1.85 | 9.72 × 10−5 | 0.01101 | 16.5914 | 1.5818 | 1.5445 | 1.772 × 10−3 | 4.2736 |
Optimizer | Min | Improvement % | Mean | Improvement % | Max | Improvement % | Std | Improvement % |
---|---|---|---|---|---|---|---|---|
HPO | 0.001696271 | - | 0.003222066 | - | 0.003329899 | - | 0.000410222 | - |
BA [55] | 2.1946 × 10−2 | 2.0250 | 0.092023 | 8.8801 | 0.01448059 | 1.1151 | 2.407 × 10−2 | 2.3660 |
DBA [55] | 1.7319 × 10−3 | 0.0036 | 0.004934 | 0.1712 | 0.01372796 | 1.0398 | 2.893 × 10−3 | 0.2483 |
NBA [55] | 1.8268 × 10−3 | 0.0131 | 0.0041404 | 0.0918 | 0.007598 | 0.4268 | 1.430 × 10−3 | 0.1020 |
LCROA [54] | 1.712 × 10−3 | 0.0016 | − | - | − | - | − | - |
FC-EPSO [56] | 1.772 × 10−3 | 0.0076 | − | - | − | - | − | - |
EPSO [53] | 1.8307 × 10−3 | 0.0134 | − | - | − | - | − | - |
Point | Vexp | Iexp | Isim | Pexp | Psim | Absolut IAE | Absolut PAE |
---|---|---|---|---|---|---|---|
1 | 0 | 1.663 | 1.66155158 | 0 | 0 | 0.00144842 | 0 |
2 | 0.118 | 1.663 | 1.661412044 | 0.196234 | 0.196047 | 0.001587956 | 0.000187379 |
3 | 2.237 | 1.661 | 1.658898411 | 3.715657 | 3.710956 | 0.002101589 | 0.004701254 |
4 | 5.434 | 1.653 | 1.655006769 | 8.982402 | 8.993307 | 0.002006769 | 0.010904785 |
5 | 7.26 | 1.65 | 1.652569075 | 11.979 | 11.99765 | 0.002569075 | 0.018651483 |
6 | 9.68 | 1.645 | 1.648317804 | 15.9236 | 15.95572 | 0.003317804 | 0.032116347 |
7 | 11.59 | 1.64 | 1.642153043 | 19.0076 | 19.03255 | 0.002153043 | 0.024953773 |
8 | 12.6 | 1.636 | 1.63618594 | 20.6136 | 20.61594 | 0.00018594 | 0.002342849 |
9 | 13.37 | 1.629 | 1.629108637 | 21.77973 | 21.78118 | 0.000108637 | 0.00145248 |
10 | 14.09 | 1.619 | 1.619252298 | 22.81171 | 22.81526 | 0.000252298 | 0.003554873 |
11 | 14.88 | 1.597 | 1.602754697 | 23.76336 | 23.84899 | 0.005754697 | 0.085629887 |
12 | 15.59 | 1.581 | 1.580023152 | 24.64779 | 24.63256 | 0.000976848 | 0.015229061 |
13 | 16.4 | 1.542 | 1.539581627 | 25.2888 | 25.24914 | 0.002418373 | 0.039661322 |
14 | 16.71 | 1.524 | 1.518250212 | 25.46604 | 25.36996 | 0.005749788 | 0.096078953 |
15 | 16.98 | 1.5 | 1.49621083 | 25.47 | 25.40566 | 0.00378917 | 0.064340108 |
16 | 17.13 | 1.485 | 1.482357816 | 25.43805 | 25.39279 | 0.002642184 | 0.045260619 |
17 | 17.32 | 1.465 | 1.462947873 | 25.3738 | 25.33826 | 0.002052127 | 0.035542835 |
18 | 17.91 | 1.388 | 1.38662746 | 24.85908 | 24.8345 | 0.00137254 | 0.024582184 |
19 | 19.08 | 1.118 | 1.127166992 | 21.33144 | 21.50635 | 0.009166992 | 0.174906208 |
20 | 21.02 | 0 | −0.001376261 | 0 | −0.02893 | 0.001376261 | 0.028928997 |
IPh | Rs | Rsh | IS1 | η1 | IS2 | η2 | IS3 | η3 | RMSE |
---|---|---|---|---|---|---|---|---|---|
1.663466 | 0.007732 | 19.21541 | 1.4 × 10−5 | 2 | 3.82 × 10−8 | 1.213937 | 0 | 2 | 1.7334461 × 10−3 |
Optimizer | Min (RMSE) | Improvement % |
---|---|---|
Proposed HPO | 1.733446 × 10−3 | - |
African Vultures Optimization (AVO) | 3.5398 × 10−3 | 0.1806 |
HBO | 3.331 × 10−3 | 0.1598 |
MPA | 2.596 × 10−3 | 0.0863 |
JFS | 2.113 × 10−3 | 0.0380 |
EMPA | 1.850 × 10−3 | 0.0117 |
EO | 1.738 × 10−3 | 0.0005 |
Social network search (SNS) [57] | 2.30797 × 10−3 | 0.0575 |
Point | Vexp | Iexp | Isim | Pexp | Psim | Absolut IAE | Absolut PAE |
---|---|---|---|---|---|---|---|
1 | 0 | 1.663 | 1.662793111 | 0 | 0 | 0.000206889 | 0 |
2 | 0.118 | 1.663 | 1.662621462 | 0.196234 | 0.196189 | 0.000378538 | 4.46675 × 10−5 |
3 | 2.237 | 1.661 | 1.659523942 | 3.715657 | 3.712355 | 0.001476058 | 0.003301942 |
4 | 5.434 | 1.653 | 1.654692858 | 8.982402 | 8.991601 | 0.001692858 | 0.009198993 |
5 | 7.26 | 1.65 | 1.651650964 | 11.979 | 11.99099 | 0.001650964 | 0.011985997 |
6 | 9.68 | 1.645 | 1.646510854 | 15.9236 | 15.93823 | 0.001510854 | 0.014625064 |
7 | 11.59 | 1.64 | 1.639749954 | 19.0076 | 19.0047 | 0.000250046 | 0.002898033 |
8 | 12.6 | 1.636 | 1.633709538 | 20.6136 | 20.58474 | 0.002290462 | 0.028859815 |
9 | 13.37 | 1.629 | 1.626837989 | 21.77973 | 21.75082 | 0.002162011 | 0.02890609 |
10 | 14.09 | 1.619 | 1.617488836 | 22.81171 | 22.79042 | 0.001511164 | 0.0212923 |
11 | 14.88 | 1.597 | 1.602039545 | 23.76336 | 23.83835 | 0.005039545 | 0.074988431 |
12 | 15.59 | 1.581 | 1.580589913 | 24.64779 | 24.6414 | 0.000410087 | 0.00639326 |
13 | 16.4 | 1.542 | 1.541877255 | 25.2888 | 25.28679 | 0.000122745 | 0.002013016 |
14 | 16.71 | 1.524 | 1.521049642 | 25.46604 | 25.41674 | 0.002950358 | 0.049300474 |
15 | 16.98 | 1.5 | 1.499402663 | 25.47 | 25.45986 | 0.000597337 | 0.010142784 |
16 | 17.13 | 1.485 | 1.485687804 | 25.43805 | 25.44983 | 0.000687804 | 0.011782077 |
17 | 17.32 | 1.465 | 1.466312804 | 25.3738 | 25.39654 | 0.001312804 | 0.022737767 |
18 | 17.91 | 1.388 | 1.388788295 | 24.85908 | 24.8732 | 0.000788295 | 0.014118357 |
19 | 19.08 | 1.118 | 1.11763777 | 21.33144 | 21.32453 | 0.00036223 | 0.006911339 |
20 | 21.02 | 0 | 1.56513 × 10−5 | 0 | 0.000329 | 1.56513 × 10−5 | 0.000328991 |
Model | Single Diode | Double Diode | Triple Diode |
---|---|---|---|
IPh (A) | 0.760776 | 0.760779 | 0.76078 |
IS1 (μA) | 0.323 | 0.252 | 0 |
IS2 (μA) | - | 0.534 | 6.6 × 10−7 |
IS3 (μA) | - | - | 2.36 × 10−7 |
η1 | 1.481183 | 1.460079 | 1 |
η2 | - | 2 | 2 |
η3 | - | - | 1.454796 |
RS (Ω) | 0.036377 | 0.036629 | 0.036694 |
Rsh (Ω) | 53.71846 | 54.94474 | 55.25778 |
RMSE (×10−4) | 9.8602 | 9.83 | 9.825 |
Algorithms | RMSE (×10−4) |
---|---|
Proposed HPO | 9.8602 |
GAMNU [25] | 9.8618 |
BBO-M [58] | 9.8634 |
TLBO [59] | 9.8733 |
JAYA [62] | 9.8946 |
IADE [59] | 9.89 |
CSA [59] | 9.91184 |
HS [61] | 9.95146 |
CLPSO [63] | 9.9633 |
ABC [60] | 10 |
HHO [15] | 12.6479 |
CPSO [59] | 13.8607 |
GWO [29] | 75.011 |
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Elshahed, M.; El-Rifaie, A.M.; Tolba, M.A.; Ginidi, A.; Shaheen, A.; Mohamed, S.A. An Innovative Hunter-Prey-Based Optimization for Electrically Based Single-, Double-, and Triple-Diode Models of Solar Photovoltaic Systems. Mathematics 2022, 10, 4625. https://doi.org/10.3390/math10234625
Elshahed M, El-Rifaie AM, Tolba MA, Ginidi A, Shaheen A, Mohamed SA. An Innovative Hunter-Prey-Based Optimization for Electrically Based Single-, Double-, and Triple-Diode Models of Solar Photovoltaic Systems. Mathematics. 2022; 10(23):4625. https://doi.org/10.3390/math10234625
Chicago/Turabian StyleElshahed, Mostafa, Ali M. El-Rifaie, Mohamed A. Tolba, Ahmed Ginidi, Abdullah Shaheen, and Shazly A. Mohamed. 2022. "An Innovative Hunter-Prey-Based Optimization for Electrically Based Single-, Double-, and Triple-Diode Models of Solar Photovoltaic Systems" Mathematics 10, no. 23: 4625. https://doi.org/10.3390/math10234625
APA StyleElshahed, M., El-Rifaie, A. M., Tolba, M. A., Ginidi, A., Shaheen, A., & Mohamed, S. A. (2022). An Innovative Hunter-Prey-Based Optimization for Electrically Based Single-, Double-, and Triple-Diode Models of Solar Photovoltaic Systems. Mathematics, 10(23), 4625. https://doi.org/10.3390/math10234625