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Figure 10.
Figure 11.
Experimental current (I) and voltage (V) data for RTC France PV cells using SDM and DDM_
| Parameter | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| I (Ampere) | 0.764 | 0.762 | 0.7605 | 0.7605 | 0.76 | 0.759 | 0.757 | 0.7557 | 0.755 |
| V (Volt) | −0.2057 | −0.1291 | −0.0588 | 0.0057 | 0.0666 | 0.1183 | 0.1678 | 0.2152 | 0.2618 |
| Parameter | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| I (Ampere) | 0.754 | 0.7505 | 0.746 | 0.7385 | 0.728 | 0.706 | 0.673 | 0.632 | 0.573 |
| V (Volt) | 0.2924 | 0.3269 | 0.385 | 0.3837 | 0.4173 | 0.4573 | 0.4798 | 0.4784 | 0.5119 |
| Parameter | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | |
| I (Ampere) | 0.499 | 0.413 | 0.316 | 0.212 | 0.103 | −0.01 | −0.123 | −0.21 | |
| V (Volt) | 0.5319 | 0.5266 | 0.3983 | 0.5321 | 0.5533 | 0.5736 | 0.5833 | 0.59 | |
The SDM parameters estimated at the best RMSE
| Algorithm | Iph(A) | Isd1(μA) | Rs (Ω) | Rsh (Ω) | n | RMSE |
|---|---|---|---|---|---|---|
| WSO-HO | 0.76079 | 0.31069 | 0.036547 | 52.8899 | 1.4773 | 7.729856E-04 |
| WSO | 0.76078 | 0.31069 | 0.03654 | 52.889 | 1.47727 | 7.730056E-04 |
| HO | 0.76774 | 0.54060 | 0.03164 | 19.31912 | 1.53746 | 8.753850E-04 |
| GOANM (Amiri et al., 2024) | 0.76079 | 0.31069 | 0.036547 | 52.8899 | 1.4773 | 7.729900E-04 |
| GOA (Amiri et al., 2024) | 0.76070 | 0.34001 | 0.036182 | 55.7021 | 1.4864 | 7.870400E-04 |
| IMFOL (Qaraad et al., 2023) | 0.76078 | 0.32302 | 0.036377 | 53.7186 | 1.4812 | 9.860200E-04 |
| RTLBO (Yu et al., 2023) | 0.76078 | 0.32302 | 0.036377 | 53.7185 | 1.4812 | 9.860200E-04 |
| DLMVO (Ekinci et al., 2024) | 0.7608 | 0.3230 | 0.0364 | 53.7185 | 1.4812 | 9.860200E-04 |
| OBL-RSACM (Li et al., 2023) | 0.76080 | 0.32203 | 0.03643 | 53.3521 | 1.4812 | 9.845200E-04 |
| AHO (Bogar, 2023) | 0.76079 | 0.31086 | 0.036540 | 52.8595 | 1.2155 | 7.730600E-04 |
| PSOCS (Fan et al., 2022) | 0.76078 | 0.32302 | 0.036377 | 53.7185 | 1.4812 | 9.860200E-04 |
| ELADE (Gu et al., 2023) | 0.76077 | 0.30839 | 0.036555 | 52.8267 | 1.4765 | 7.754700E-04 |
| ILSA (Huang et al., 2020) | 0.76077 | 0.32302 | 0.036377 | 53.7185 | 1.4812 | 9.860200E-04 |
| IHGS (Xu et al., 2022) | 0.76078 | 0.32302 | 0.0364 | 53.7178 | 1.4812 | 9.860200E-04 |
| BES (Alsattar et al., 2020) | 0.7607 | 0.3230 | 0.0364 | 53.7185 | 1.4812 | 9.860200E-04 |
| DE (Yu et al., 2022) | 0.7607 | 0.3209 | 0.0363 | 54.1134 | 1.4709 | 7.769200E-04 |
| BES (Nicaire et al., 2021) | 0.7683 | 0.3262 | 0.0367 | 54.2557 | 1.4958 | 9.860000E-04 |
| ITSA (Arandian et al., 2022) | 0.7606 | 0.3298 | 0.0363 | 56.5694 | 1.4832 | 9.933900E-04 |
Analysis of RMSE for Single and Double PV models
| Model | Algorithm | Min | Mean | Max | STD |
|---|---|---|---|---|---|
| SDM | WSO-HO | 7.72985671E-04 | 7.7308567E-04 | 7.7410567E-04 | 6.138516E-17 |
| WSO | 7.73005671E-04 | 8.1665894E-04 | 0.002083 | 2.3920836E-04 | |
| HO | 8.75385E-04 | 0.00233 | 0.00629359 | 1.33368-03 | |
| GOA [Amiri, H. H et al., 2024] | 7.5810E–04 | 7.7695E–04 | 8.8385E–04 | 2.4314E–05 | |
| GOANM [Amiri, H. H et al., 2024] | 7.4339E–04 | 7.5263E–04 | 7.6714E–04 | 7.3732E–06 | |
| ELAD [Gu, Z. et al., 2023] | 9.8602E-04 | 9.8602E-04 | 9.8605E-04 | 1.753E-10 | |
| DE [Yu, S., 2022] | 9.811E-04 | 1.02874E-03 | 1.0813E-03 | 2.94961E-05 | |
| ISCA [Chen, H., 2019] | 7.3423E-04 | 7.2302E-04 | 7.4592E-04 | 1.30287E-06 | |
| ITSA [Nicaire, N. F., et al., 2021] | 9.86E-04 | 7.730062E-04 | 9.89E-04 | 5.70E-16 | |
| DDM | WSO-HO | 7.420691E-04 | 7.4967098E-04 | 7.72985671E-04 | 1.08074E-05 |
| WSO | 7.4378257E-04 | 8.3867102E-04 | 0.00099892 | 1.6562955E-04 | |
| HO | 8.55885e-04 | 0.00265008 | 0.006542 | 1.74708E-03 | |
| GOA [Amiri, H.H et al., 2024] | 7.5810E–04 | 7.7695E–04 | 8.8385E–04 | 2.4314E–05 | |
| GOANM [Amiri, H.H et al., 2024] | 7.4339E–04 | 7.5263E–04 | 7.6714E–04 | 7.3732E–06 | |
| ELAD [Gu, Z. et al., 2023] | 9.8252E-04 | 1.32602E-03 | 1.000562E-03 | 9.15E-12 | |
| DE [Yu, S., 2022] | 9.8607E-04 | 9.8874E-04 | 7.730062E-04 | 2.4696E-06 | |
| ISCA [Chen, H., 2019] | 2.2142E-04 | 1.66043E-02 | 9.93218E-04 | 1.30287E-06 | |
| ITSA [Nicaire, N. F., et al., 2021] | 9.9804E-04 | 9.99991E-04 | 3.799062E-02 | 6.33E-06 | |
The boundaries of extracted PV parameters for SDM and DDM
| Parameter | Lower bound | Upper bound |
|---|---|---|
| Iph (A) | 0 | 1 |
| Isd, Isd1, Isd2, (μA) | 0 | 1 |
| Rs (Ω) | 0 | 1 |
| Rsh(Ω) | 0 | 100 |
| n, n1, n2 | 1 | 2 |
The DDM Parameters Estimated at the best RMSE
| Algorithm | Iph (A) | Isd1 (μA) | Isd2 (μA) | Rs (Ω) | Rsh (Ω) | n1 | n2 | RMSE |
|---|---|---|---|---|---|---|---|---|
| WSO-HO | 0.760805 | 0.0854343 | 0.9991529 | 0.0376485 | 56.0775146 | 1.37756104 | 1.81810675 | 7.42069103E-04 |
| WSO | 0.760804 | 0.069334 | 0.884680 | 0.0376813 | 55.918552 | 1.3648682 | 1.7688404 | 7.4378257E-04 |
| HO | 0.7607879 | 0.3106909 | 0.3106909 | 0.0365467 | 52.8899092 | 1.47727164 | 1.47727160 | 8.55885e-04 |
| GOANM [Amiri, H.H et al., 2024] | 0.76081 | 0.11624 | 0.9768 | 0.037459 | 55.7298 | 1.3994 | 1.8597 | 7.4339E-04 |
| GOA [Amiri, H.H et al., 2024] | 0.76079 | 0.19704 | 0.4356 | 0.03688 | 54.2616 | 1.4417 | 1.8186 | 7.5810E-04 |
| IMFOL [Qaraad, M. et al., 2023] | 0.76078 | 0.76632 | 0.2251 | 0.036731 | 55.6567 | 2.0000 | 1.4508 | 9.8252E-04 |
| RTLBO [Yu, X. et al., 2023] | 0.76078 | 0.22597 | 0.7494 | 0.03674 | 55.4855 | 1.4510 | 2.0000 | 9.8248E-04 |
| DLMVO [Ekinci,S., et al., 2024] | 0.7608 | 0.7493 | 0.2260 | 0.0367 | 55.4854 | 2.0000 | 1.4510 | 9.8248E-04 |
| OBL-RSACM [ Li, J. et al., 2023] | 0.76033 | 0.39986 | 0.2677 | 0.03669 | 56.0102 | 1.4151 | 2.0000 | 9.8237E-04 |
| AHO [Bogar,E., 2023] | 0.76078 | 0.27988 | 0.2768 | 0.036530 | 54.2856 | 1.9563 | 1.4682 | 9.8401E-04 |
| PSOCS [Fan, Y., et al., 2022] | 0.76078 | 0.22598 | 0.7493 | 0.036740 | 55.4855 | 1.4510 | 2.0000 | 9.8248E-04 |
| ELADE [Gu, Z. et al., 2023] | 0.76072 | 0.24468 | 0.3802 | 0.036927 | 53.5130 | 1.4564 | 1.9899 | 7.6480E-04 |
| ILSA [Huang, T., et al., 2020] | 0.76078 | 0.50569 | 0.2557 | 0.036609 | 54.9246 | 2.0000 | 1.4614 | 9.8270E-04 |
| IHGS [Xu, B., et al., 2022] | 0.76078 | 0.74935 | 0.2260 | 0.03674 | 55.48542 | 2.0000 | 1.45102 | 9.8248E-04 |
| BES [Alsattar, H. A., et al., 2020] | 0.7608 | 0.2259 | 0.7493 | 0.0367 | 55.4854 | 1.4510 | 2.0000 | 9.8248E-04 |
| DE [Yu, S., 2022] | 0.7605 | 0.42322 | 0.1873 | 0.02061 | 51.9345 | 1.8758 | 1.4360 | 7.6300E-04 |
| ITSA [Nicaire, N. F., et al., 2021] | 0.7608 | 0.9731 | 0.1679 | 0.0369 | 53.8368 | 1.9213 | 1.4281 | 9.82E-04 |