**5. Results and discussions**

The following **Table 3** presents PV parameters results for the all classified optimization-based method discussed in Section 2.

From the above **Table 3** it is clear that for the traditional methods, the LM is more accurate than Newton's method, which in turn outperforms Kashif's method. Then, for the metaheuristic methods for each of their category as follow.

• Evolution-based:

It is observed that ISCE, Rcr-IJADE, and PCE outperform PS, which in turn is better than GA and SA.

**43**

**Table 3.**

*diode model.*

*Study of a New Hybrid Optimization-Based Method for Obtaining Parameter Values of Solar Cells*

**Methods Parameters IL (A) Ids(A) n Rs(**Ω**) Rsh(**Ω**) RMSE**

1.200000 0.014000 19.000032 7.090000e-02

1.479182 0.036461 53.271523 9.8680e- 4

0.7608 0.3223 1.4837 0.0364 53.7634 9.70E−03

0.760776 0.32302 1.48118 0.03638 53.7185 9.8602E−04

0.76077 0.32454 1.48165 0.03636 53.8550 9.8606E−04

0.76077 0.3239 1.4812 0.03636 53.7987 9.8602E−04

PCE 0.760776 0.323021 1.481074 0.03638 53.7185 9.8602E−04

ABSO [38] 0.7608 0.30623 1.47583 0.03659 52.2903 9.9124E−04 BMO [37] 0.76077 0.32479 1.48173 0.03636 53.8716 9.8608E−04 CSO [41] 0.76078 0.323 1.48118 0.03638 53.7185 9.8602E−04

BFA [31] 0.7602 0.8000 1.6951 0.0325 50.8691 0.029 HS [30] 0.7607 0.305 1.4754 0.0366 53.5946 9.95E−04 STLBO [32] 0.76078 0.32302 1.48114 0.03638 53.7187 9.8602E−04

EFO [29] 0.760776 0.323022 1.481184 0.036377 53.718646 9.860219E-04 GSA [29] 0.760977 0.847206 1.585214 0.032130 82.871489 2.166195E-03 EMA [29] 0.760590 0.329155 1.483019 0.036365 57.025188 9.972880E-04 WSA [29] 0.754454 1.000000 1.607072 0.027957 97.854073 7.702232E-03

LMSA [19] 0.7608 0.3185 1.4798 0.0364 53.3264 9.86E−04

NM-MPSO 0.76078 0.32306 1.4812 0.03638 53.7222 9.8602E−04

0.760776 0.32302 1.48118 0.03638 53.7185 9.8602E−04

0.760776 0.32302 1.48118 0.03638 53.7185 9.8602E−04

0.76077 0.32302 1.47986 0.03637 53.7185 9.8602E−04

0.76078 0.32302 1.48118 0.03638 53.7164 9.8602E−04

**Swarm-based**

**Human-based**

**Physic-based**

**Hybrid** LM-GWO 0.760776 0.32306 1.48118 0.03637 53.7222 9.8601E-04

*Parameter extraction results for 57-mm diameter R.T.C. France commercial silicon solar cell using the single* 

**Evolution-based** GA [25] 0.7619 0.8087 1.5751 0.0299 42.3729 0.019 SA [26] 0.762 0.4798 1.5172 0.0345 43.1034 0.019 PS [21] 0.7617 0.998 1.6 0.0313 64.1026 0.0149 ISCE [27] 0.760776 0.32302 1.48118 0.03638 53.7185 9.8602E−04

09

07

*DOI: http://dx.doi.org/10.5772/intechopen.93324*

**Traditional** Kashif [16] 0.760300 2.624738e-

Newton [17]

Rcr-IJADE [28]

PSO [35, 36]

CWOA [40]

EHA-NMS [27]

ABC-TRR [43]

ABC-DE [43]

TLABC [43]

**Metaheuristics** LM [19] 0.760782 3.166611e-


*Study of a New Hybrid Optimization-Based Method for Obtaining Parameter Values of Solar Cells DOI: http://dx.doi.org/10.5772/intechopen.93324*

#### **Table 3.**

*Parameter extraction results for 57-mm diameter R.T.C. France commercial silicon solar cell using the single diode model.*

#### **Figure 7.**

*Fitted I-V curve characteristic for the RTC silicon solar cell, using the hybrid LM-GWO method.*

• Swarm-based:

All the swarm-based used outperform ABSO in terms of precision.

• Human-based:

CSO and STBLO outperform HS, which is better than BFA.

• Physics-based

EFO is more accurate than EMA, which is more accurate than WSA, which is more accurate then GSA.

It is mentioned that the swarm-based got the best results compared to the other metaheuristic's category.

Finally, for the hybrid methods, it is clear that all of them have achieved the highest best optimized (minimum) values for RMSE, until now with the value of (9.8601E−04).

In addition, the hybrid methods outperform the metaheuristics, which in turn outperform the traditional methods.

The fitting obtained curves of real and simulated data, using the proposed LMGWO are illustrated in **Figure 7**.

The best approximation gotten from the fitted curves in **Figure 7** has proved the effectiveness of our hybrid LMGWO method.
