Efficient approach for optimal parameter estimation of PV using Pelican Optimization Algorithm

Figures & data

Table 1. An overview of the several methods for determining all the parameters of a PV cell/module/panel.

Techniques/ algorithm name	Analytical/ Numerical/MH	Model	Objective function/metrics	Other performance criteria	Data availability	References
Trust-Region-Dogleg Algorithm (TRDLA)	Analytical	MSX60 polycrystalline silicon solar panel	RMSE, MAE, SSE	–	No	Hali and Khlifi (2021)
Modified five parameters	Analytical	SDM	RMSE	–	No	Mares et al. (2015)
Lambert W functions	Analytical	SDM	RMSE	Max, Min, Mean	Yes	Gao et al. (2018)
Iterative method	Analytical	SDM	RE	–	Yes	Muhammadsharif (2022)
Ndegwa	Analytical	BP3235T, KC200GT, BP-SX 150, and MSX60 PV modules	error	–	Yes	Ndegwa et al. (2020)
Aichotomy method	Numerical	PWP201, Shell S115, Shell SM55, Shell ST20 panel	RMSE, IAE	–	No	Elhammoudy et al. (2023)
Analytical and Numerical/ Iterative approaches	Numerical	Shell SP70 module	RMSE MAPE, MABE, AE	Max, Min	No	Lidaighbi et al. (2022)
Runge–Kutta Method	Numerical	SDM	RMSE	Min, Max, Mean, Std	No	Shaban et al. (2021)
PGJAYA	MH	RTC France, d Photo Watt-PWP 201	RMSE	IAE, Min, Mean, Max, std	Yes	Yu et al. (2019)
I-CPA	MH	RTC France, Photowatt-PWP201, KC200GT, and STM6-40/36	RMSE	Min, Mean, Max, Std	No	Beşkirli and Dağ (2023)
SCA	MH	RTC France, and Photowat-PWP201 PV module	RMSE	IAE, RE, Mean, Worst, and Std	Yes	Yu et al. (2022)
HBO	MH	R.T.C France solar cell	RMSE	Mean, and Std.	No	AbdElminaam et al., 2022)
GSK	MH	RTC France, STM6-40/36, STP6-120/36 and Photowat-PWP201 PV module	RMSE	IAE, Mean, Worst, Std	Yes	Xiong et al. (2021)
GO	MH	RTC France and Kyocera KC200GT PV modules	RMSE	Min, worst	No	Aribia et al. (2023)
HKOA	MH	Photowatt-PWP201, STP6-120/36, Ultra 85-P, and STM6-40/36	RMSE	Mean, Worst and Std.	No	Mohamed et al. (2024)
AHT	MH	STM6-40/36, KC200GT and Photowatt-PWP201 modules	RMSE	MAE, Mean, Worst and Std	No	El-Sehiemy et al. (2023)
MSSA	MH	RTC France and Photowatt-PWP201	RMSE	Mean, Worst and Std	No	Yaghoubi et al. (2022)
MIGTO	MH	R.T.C. France, Photowatt-PWP201, STM6-40/36, and STP6-120/36	RMSE	IAE, Mean, Worst and Std	Yes	Abdel-Basset et al. (2022)
TSA	MH	RTC France, and Photowatt-PWP201	RMSE	–	Yes	Beşkirli and Dağ (2022)

Figure 1. Organization of paper.

Figure 2. Single diode model of photovoltaic panel module.

Figure 3. Flowchart of POA algorithm.

Table 2. The range of variables or parameters in the PV model.

		Parameters
PV models		Iph (A)	Isd (µA)	Rsh (Ω)	Rs (Ω)	n
SDM	LB	0	0	0	0	1
	UB	1	1	100	0.5	2
Photowatt-PW201	LB	0	0	0	0	1
	UB	2	50	2000	2	50
STM6-40/36	LB	0	0	0	0	1
	UB	2	50	1000	0.36	60
STP6-120/36	LB	0	0	0	0	1
	UB	8	50	1500	0.36	50

Table 3. Results of different PV Modules obtained using POA.

PV module	RMSE			Iph (A)	Isd (µA)	Rsh (Ω)	Rs (Ω)	n
	STD	Mean	Min
RTC	6.3881E-04	1.4916E-03	7.7298E-04	0.76078	3.1080E-01	0.036543	52.8843	1.4773
Photowatt-PWP201 PV module	1.6603E-04	2.1177E-03	2.0528E-03	1.0314	2.6427	1.2354	822.0692	49.4707
STM6-40/36 PV module	6.5963E-04	2.4304E-03	1.7220E-03	1.6639	1.7301	0.15445	571.9996	57.9284
STP6-120/36 module	1.0873E-03	1.5416E-02	1.4458E-02	7.4755	1.9419	549.9069	0.16867	48.037

Figure 4. The measured and calculated curves’ characteristics of SDM: (a) V–I curve, (b) V–P curve and (c) convergence characteristics.

Table 4. The results of POA's computed current and absolute error for a SDM.

S. No	Vl (V)	Il (Measured)(A)	Ie (Estimated) (A)	IAE (A)	Pl (W)	Pe (W)	IAE (W)
1	−0.2057	0.764	0.764150304	0.000150304	−0.1571548	−0.15718572	3.09E-05
2	−0.1291	0.762	0.762702842	0.000702842	−0.0983742	−0.09846494	9.07E-05
3	−0.0588	0.7605	0.761374328	0.000874328	−0.0447174	−0.04476881	5.14E-05
4	0.0057	0.7605	0.760154936	0.000345064	0.00433485	0.004332883	1.97E-06
5	0.0646	0.76	0.759039368	0.000960632	0.049096	0.049033943	6.21E-05
6	0.1185	0.759	0.758010965	0.000989035	0.0899415	0.089824299	0.000117
7	0.1678	0.757	0.757045806	4.58056E-05	0.1270246	0.127032286	7.69E-06
8	0.2132	0.757	0.756084832	0.000915168	0.1613924	0.161197286	0.000195
9	0.2545	0.7555	0.75502224	0.00047776	0.19227475	0.19215316	0.000122
10	0.2924	0.754	0.753597107	0.000402893	0.2204696	0.220351794	0.000118
11	0.3269	0.7505	0.751326833	0.000826833	0.24533845	0.245608742	0.00027
12	0.3585	0.7465	0.747304698	0.000804698	0.26762025	0.267908734	0.000288
13	0.3873	0.7385	0.740083774	0.001583774	0.28602105	0.286634446	0.000613
14	0.4137	0.728	0.727425165	0.000574835	0.3011736	0.300935791	0.000238
15	0.4373	0.7065	0.707024961	0.000524961	0.30895245	0.309182015	0.00023
16	0.459	0.6755	0.675399762	0.000100238	0.3100545	0.310008491	4.6E-05
17	0.4784	0.632	0.630998447	0.001001553	0.3023488	0.301869657	0.000479
18	0.496	0.573	0.572176133	0.000823867	0.284208	0.283799362	0.000409
19	0.5119	0.499	0.499541563	0.000541563	0.2554381	0.255715326	0.000277
20	0.5265	0.413	0.413488337	0.000488337	0.2174445	0.217701609	0.000257
21	0.5398	0.3165	0.317165324	0.000665324	0.1708467	0.171205842	0.000359
22	0.5521	0.212	0.212019934	1.99335E-05	0.1170452	0.117056205	1.1E-05
23	0.5633	0.1035	0.102638694	0.000861306	0.05830155	0.057816376	0.000485
24	0.5736	−0.01	−0.009298605	0.000701395	−0.005736	−0.00533368	0.000402
25	0.5833	−0.123	−0.124364338	0.001364338	−0.0717459	−0.07254172	0.000796
26	0.59	−0.21	−0.209107554	0.000892446	−0.1239	−0.12337346	0.000527
Sum of IAE				0.017639233			0.006484

Table 5. Comparison of POA results with other MH optimization methods in RTC literature (SDM).

Optimization	RMSE			Iph (A)	Isd (μA)	Rs (Ω)	Rsh (Ω)	n
	STD	Mean	Min
POA	6.3881E-04	1.4916E-03	7.7298E-04	7.6078E-01	3.1080E-01	0.036543	52.8843E + 00	1.4773E + 00
ALO	1.3173E-03	2.7705E-03	9.8617E-04	7.6076E-01	3.2043E-01	0.036411	53.6604E + 00	1.4803E + 00
AVOA	1.3363E-03	2.1769E-03	1.0763E-03	7.6017E-01	3.4299E-01	0.03627	65.18990E + 00	1.4870E + 00
BES	1.6367E-10	9.8602E-04	9.8602E-04	7.6077E-01	3.2302E-01	0.036377	53.7185E + 00	1.4811E + 00
GTO	1.7558E-06	9.8634E-04	9.8602E-04	7.6077E-01	3.2302E-01	0.036377	53.7185 E + 00	1.4811E + 00
GWO	1.5063E-03	1.1225E-02	1.2590E-03	7.6121E-01	3.35753E-01	0.0357606	45.4430E + 00	1.4853E + 00
WOA	1.8235E-02	1.4357E-02	1.2841E-03	7.6106E-01	4.4482E-01	0.034944	53.2525E + 00	1.5143E + 00
HBO (AbdElminaam et al., 2022)	4.0944E-04	1.5065E-04	9.8869E-04	7.6086E-01	3.19E-01	0.036398	52.156E + 00	1.4800E + 00
MSSA (Yaghoubi et al., 2022)	3.01E-07	9.85E-04	986E-04	7.683E-01	3.262E-01	0.0367	54.255E + 00	1.4958E + 00
CLRao-1 (Ridha et al., 2022)	0.3084E-16	0.98602E-03	0.98602E-03	7.60776E-01	3.2302E-01	0.036377	53.7185E + 00	1.4811E + 00
IAOA (Krishnan et al., 2023)	3.205E-04	1.3800E-03	9.8602E-04	7.60775E-01	3.2321E-01	0.036375	53.732E + 00	1.4810E + 00
PSO (Yaghoubi et al., 2022)	2.01E-04	2.26E-03	1.43E-03	7.383E-01	3.19E-01	0.0364	53.409E + 00	1.4799E + 00
AVOA (Diab et al., 2022)	1.009E-02	8.8533E-04	7.8565E-04	7.6097E-01	3.0518E-01	0.036564	50.0736E + 00	1.4755E + 00
SSA (Yaghoubi et al., 2022)	2.86E-05	3.43E-03	9.93E-03	7.607E-01	3.397E-01	0.0361	54.7062E + 00	1.4863E + 00
HSOA (Long et al., 2022)	5.383E-05	1.0479E-03	9.8602E-04	7.6077E-01	3.2304E-01	0.03637	53.7060E + 00	1.4811E + 00
TSA (Yaghoubi et al., 2022)	2.23E-04	2.64E-03	2.03E-03	7.616E-01	3.33E-01	0.0370	56.874E + 00	1.4799E + 00
MLBSA (Yu et al., 2018)	9.146E-12	9.860E-04	9.8602E-04	7.608E-01	3.230E-01	0.0364	53.7185E + 00	1.4812E + 00
FA (Yaghoubi et al., 2022)	8.55E-04	2.19E-03	1.23E-04	7.600E-01	3.993E-01	0.0356	62.3174E + 00	1.5029E + 00
CPMPSO (Liang et al., 2020)	2.175E-17	9.8602E-04	9.8602E-04	7.6077E-01	3.2302E-01	0.03637	53.71852E + 00	1.4811E + 00
MVO (Yaghoubi et al., 2022)	1.07E-04	6.82E-03	9.95E-04	7.607E-01	3.162E-01	0.0363	52.3178E + 00	4.7910E + 00
AOA (Krishnan et al., 2023)	7.1158E-02	9.1901E-02	1.2745E-03	7.6058E-01	4.917E-01	0.03466	68.7028E + 00	1.5245E + 00
Rao-2 (Premkumar et al., 2020)	7.490E-04	1.9387E-03	9.8602E-04	7.6077E-01	3.2301E-01	0.03639	53.71854E + 00	1.4811E + 00
IMPA (Abdel-Basset et al., 2021)	1.718E-17	9.8602E-04	9.8602E-04	7.6077E-01	3.2302E-01	0.03637	53.7185E + 00	1.4811E + 00
HBA-OBL (Koç et al., 2023)	0.2235E-09	0.98602E-03	0.98602E-03	7.608E-01	3.230E-01	0.0364	53.7185E + 00	1.4812E + 00

Figure 5. The measured and calculated curves’ characteristics of Photowatt-PWP201 PV module: (a) V–I curve, (b) P–V curve and (c) convergence curve.

Table 6. The results of POA’s computed current and absolute error for a Photowatt-PWP201 PV module.

S. No	Vl (V)	Il (Measured)(A)	Ie (Estimated) (A)	IAE(A)	Pl (W)	Pe (W)	IAE (W)
1	0.1248	1.0315	1.029733	0.001767	0.128511	0.128731	0.000221
2	1.8093	1.03	1.027667	0.002333	1.859358	1.863579	0.004221
3	3.3511	1.026	1.025731	0.000269	3.437328	3.438229	0.0009
4	4.7622	1.022	1.023841	0.001841	4.875735	4.866968	0.008767
5	6.0538	1.018	1.021822	0.003822	6.185904	6.162768	0.023136
6	7.2364	1.0155	1.019331	0.003831	7.376288	7.348564	0.027724
7	8.3189	1.014	1.015741	0.001741	8.449848	8.435365	0.014483
8	9.3097	1.01	1.009985	1.49E-05	9.402658	9.402797	0.000139
9	10.2163	1.0035	1.000414	0.003086	10.22053	10.25206	0.031527
10	11.0449	0.988	0.984745	0.003255	10.87641	10.91236	0.035954
11	11.8018	0.963	0.960188	0.002812	11.33195	11.36513	0.033186
12	12.4929	0.9255	0.923871	0.001629	11.54183	11.56218	0.020353
13	13.1231	0.8725	0.873563	0.001063	11.46385	11.4499	0.013949
14	13.6983	0.8075	0.8082	0.0007	11.07097	11.06138	0.00959
15	14.2221	0.7265	0.72855	0.00205	10.3615	10.33236	0.029149
16	14.6995	0.6345	0.636636	0.002136	9.358229	9.326833	0.031396
17	15.1346	0.5345	0.535433	0.000933	8.103561	8.089444	0.014118
18	15.5311	0.4275	0.428206	0.000706	6.650512	6.639545	0.010967
19	15.8929	0.3185	0.317858	0.000642	5.051679	5.061889	0.01021
20	16.2229	0.2085	0.207016	0.001484	3.358397	3.382475	0.024077
21	16.5241	0.101	0.097653	0.003347	1.613623	1.668934	0.055311
22	16.7987	−0.008	−0.00859	0.000586	−0.14423	−0.13439	0.009839
23	17.0499	−0.111	−0.11097	2.79E-05	−1.89206	−1.89254	0.000475
24	17.2793	−0.209	−0.20861	0.000389	−3.60465	−3.61137	0.006721
25	17.4885	−0.303	−0.30093	0.002066	−5.26289	−5.29902	0.036126
Sum of IAE				0.04253			0.452538

Table 7. Comparison of POA results with other MH optimization techniques in Photowatt-PWP201 PV module.

Optimization	RMSE			Iph (A)	Isd (μA)	Rs (Ω)	Rsh (Ω)	n
	STD	Mean	Min
POA	1.6603E-04	2.1177E-03	2.0528E-03	1.0314E + 00	2.6427	1.2354	822.0692	49.4707E + 00
ALO	4.9479E-02	1.2491E-02	2.4721E-03	1.0289E + 00	4.0651	1.1864	1312.4047	49.2392E + 00
AVOA	4.9509E-02	1.2203E-02	2.4981E-03	1.0282E + 00	3.8966	1.1932	1436.4835	49.0696E + 00
BES	5.1212E-02	1.1781E-02	2.4250E-03	1.0305E + 00	3.4822	1.2012	981.9823	48.6428E + 00
GTO	4.9631E-02	1.1486E-02	2.4250E-03	1.0305E + 00	3.4822	1.2012	981.9823	48.6428E + 00
GWO	1.6390E-03	3.7650E-03	2.6008E-03	1.0295E + 00	4.7468	1.1655	1287.6329	49.8638E + 00
WOA	6.9316E-02	2.5429E-02	2.5235E-03	1.0329E + 00	3.3045	1.2023	748.4805	48.4524E + 00
Rao-2 (Premkumar et al., 2020)	6.253E-04	3.3517E-03	2.8109E-03	1.0342E + 00	1.3214	1.256	559.68	45.198E + 00
SNSA (Shaheen, Elsayed, et al., 2022)	2.600E-05	2.4680E-03	2.4347E-03	1.0307E + 00	3.57606	3.33	274.98	1.35404E + 00
MIGTO (Abdel-Basset et al., 2022)	1.13E-17	2.425074E-03	2.4250E-03	1.0246E + 00	20.336	0.0267	1323.48	1.57093E + 00
MLBSA (Yu et al., 2018)	4.3367E-10	2.425E-03	2.4250E-3	1.0305E + 00	3.4823	1.2013	981.98	48.642E + 00
IAOA (Krishnan et al., 2023)	7.90183E-01	2.9397E-01	2.4643E-03	1.03052 E + 00	3.4777	1.2014	980.553	48.631E + 00
CPMPSO(Liang et al., 2020)	1.51595E −17	2.4250E-03	2.4250E-03	1.03051E + 00	3.4823	1.2012	981.98	48.642E + 00
SDO (Ginidi et al., 2021)	1.560E − 17	2.425E-03	2.425E-03	1.03051E + 00	3.48	3.3369	27.277E + 00	1.3511E + 00
TLABC (Duman et al., 2022)	0.112E-03	0.24856E-02	2.4251E-03	1.0306E + 00	1.0306	1.2017	972.93	48.631E + 00
ITLBO (Li et al., 2019)	0.346E-13	0.24251E-02	0.24251E-02	1.0305E + 00	3.4823	1.2013	981.982	48.19E + 00
AOA (Krishnan et al., 2023)	7.9018E-01	2.9397E-01	0.24643E-02	1.0298E + 00	3.3497	1.2091	1082.52	48.482E + 00
RTLBO (Xiong et al., 2018)	0.498E-04	0.25413E-02	0.24251E-02	1.0305E + 00	3.5033	1.2006	988.560	48.666E + 00
CLRao-1 (Farah et al., 2022)	0.3814E-04	0.24250E-02	0.24250E-02	1.03181E + 00	3.2773	1.20118	983.678	48.132E + 00
PS (AlHajri et al., 2012)	–	–	1.18E-02	1.031E + 00	3.1756	1.205	714.285	48.288E + 00
Rcr-IJADE (Gong & Cai, 2013)	–	–	2.425E-03	1.03051E + 00	3.4822	1.2021	981.982	48.642E + 00
ImCSA (Kang et al., 2018)	–	–	2.425E-03	1.03051E + 00	3.4822	1.2012	981.98	48.660E + 00
CARO (Yuan et al., 2015)	–	–	2.427E-03	1.03185E + 00	3.284	1.2055	841.321	48.436E + 00
EHA-NMS (Chen et al., 2016)	–	–	2.425E-03	1.03051E + 00	3.48226	1.20127	981.982	48.642E + 00

Figure 6. The measured and calculated curves’ characteristics of STM6-40/36 PV module: (a) V–I curve, (b) V–P curve and (c) convergence curve.

Table 8. The results of POA's computed current and absolute error for a STM6-40/36 PV module.

S. No	Vl (V)	Il (A)	Ie (A)	IAE (A)	Pl (W)	Pe (W)	IAE (W)
1	1.66349	1.663	1.66349	0.00049	2.766384	2.767199	0.000815
2	1.663284	1.663	1.663284	0.000284	2.766041	2.766512	0.000472
3	1.659573	1.661	1.659573	0.001427	2.756551	2.754184	0.002368
4	1.653923	1.653	1.653923	0.000923	2.733935	2.735461	0.001527
5	1.650567	1.65	1.650567	0.000567	2.723435	2.724371	0.000936
6	1.645423	1.645	1.645423	0.000423	2.70672	2.707416	0.000696
7	1.639222	1.64	1.639222	0.000778	2.688324	2.687049	0.001275
8	1.633703	1.636	1.633703	0.002297	2.672738	2.668985	0.003753
9	1.627277	1.629	1.627277	0.001723	2.650835	2.648032	0.002803
10	1.618306	1.619	1.618306	0.000694	2.620038	2.618916	0.001122
11	1.603063	1.597	1.603063	0.006063	2.560092	2.569811	0.009719
12	1.581586	1.581	1.581586	0.000586	2.500487	2.501413	0.000926
13	1.542334	1.542	1.542334	0.000334	2.378279	2.378793	0.000515
14	1.521233	1.524	1.521233	0.002767	2.318359	2.31415	0.004209
15	1.499215	1.5	1.499215	0.000785	2.248822	2.247644	0.001177
16	1.48528	1.485	1.48528	0.00028	2.205641	2.206057	0.000416
17	1.465652	1.465	1.465652	0.000652	2.147181	2.148137	0.000956
18	1.387605	1.388	1.387605	0.000395	1.925995	1.925447	0.000548
19	1.118351	1.118	1.118351	0.000351	1.250316	1.250708	0.000392
20	4.62E-05	0	4.62E-05	4.62E-05	0	2.13E-09	2.13E-09
Sum of IAE				0.021863			0.034625

Table 9. Comparison of POA results with other MH optimization techniques in STM6-40/36 PV Module.

Optimization	RMSE			Iph (A)	Isd (µA)	Rs (Ω)	Rsh (Ω)	n
	STD	Mean	Min
POA	6.5963E-04	2.4304E-03	1.7220E-03	1.6639	1.7301	0.15445	571.9996	57.9284 E + 00
ALO	2.4571E-03	5.2867E-03	2.0721E-03	1.6615	2.5884	0.1114	727.6120	56.3478
AVOA	2.2681E-03	4.9448E-03	2.0834E-03	1.6615	2.6019	0.11207	731.4281	56.3697 E + 00
BES	3.5566E-13	1.7298E-03	1.7298E-03	1.6639	1.7386	0.1538	573.4185	54.7309 E + 00
GTO	1.5616E-08	1.7298E-03	1.7298E-03	1.6639	1.7386	0.1538	573.4185	54.7309 E + 00
GWO	2.6502E-03	6.2182E-03	2.5592E-03	1.6633	2.6885	0.0813	597.4032	56.5132 E + 00
WOA	1.0836E-02	1.5140E-03	2.2512E-03	1.6612	1.4816	0.1812	659.2058	54.097 E + 00
CLRao-1 (Farah et al., 2022)	7.938E-04	2.22E-03	1.729E-03	1.659	1.65901	0.0866	1000.00	1.597E + 00
AOA (Krishnan et al., 2023)	7.6522E-03	6.6389E-03	2.0458E-03	1.667	0.9766	0.007801	13.3770	1.4650 E + 00
HBA-OBL (Koç et al., 2023)	0.10079E-07	0.17298E-02	0.17298E-02	1.663	1.7380	0.1539	573.418	55.7631 E + 00
Chaotic HBA (Düzenli̇ et al., 2022)	0.44220E-10	0.17298E-02	0.17298E-02	1.663	1.7387	0.1539	573.418	55.7631 E + 00
MIGTO(Abdel-Basset et al., 2022)	4.60E-18	1.7298E-03	1.72981E-03	1.663	1.9693	0.00386	16.6569	1.5341 E + 00
IAOA (Krishnan et al., 2023)	6.6298E-05	1.8347E-03	1.7943E-03	1.663	2.000	2.9136	15.8405	1.5327 E + 00
HBA (Düzenli̇ et al., 2022)	4.6718E-09	1.72E-03	1.7298E-03	1.663	1.7387	0.1539	573.418	55.7631 E + 00
SNSA (Shaheen, Elsayed, et al., 2022)	9.078E-05	1.89E-03	1.7516E-03	1.663	1.8087	0.oo412355	16.4521	1.524640 E + 00
SDO (Ginidi et al., 2021)	0.437E-17	0.173 E-02	0.173 E-02	1.663	1.74	0.004274	15.9282	1.520303 E + 00
ESNSA (Shaheen, Elsayed, et al., 2022)	1.401E-17	1.72E-03	1.7298E-03	1.663	1.7386	0.0042737	15.9282	1.52030 E + 00
CIABC (Oliva et al., 2017)	–	–	1.819E-03	1.6642	1.6760	4.40	15.617	1.4976 E + 00
CSA (Kang et al., 2018)	–	–	1.7943E-03	1.663	2.000	0.29129	15.8407	1.53349 E + 00
ImCSA (Kang et al., 2018)	–	–	1.794E-03	1.663	2.00	2.9136	15.840	1.53349 E + 00

Figure 7. The measured and computed curves’ characteristics of STP6-120/36 module: (a) V–I curve (b) V–P curve and (c) convergence curve.

Table 10. The results of POA's computed current and absolute error for a STP6-120/36 module.

S. No	Vl (V)	Il (Measured)(A)	Ie (Estimated) (A)	IAE (A)	Pl (W)	Pe (W)	IAE (W)
1	0	7.48	7.473299	0.006701	0	0	0
2	9.06	7.45	7.450174	0.000174	67.497	67.49858	0.001576
3	9.47	7.42	7.446889	0.026889	70.2674	70.52204	0.254636
4	10.32	7.44	7.436577	0.003423	76.7808	76.74547	0.035329
5	11.17	7.41	7.417949	0.007949	82.7697	82.85849	0.088794
6	11.81	7.38	7.393945	0.013945	87.1578	87.32249	0.164687
7	12.36	7.37	7.361868	0.008132	91.0932	90.99269	0.100506
8	12.74	7.34	7.33057	0.00943	93.5116	93.39146	0.120137
9	13.16	7.29	7.283855	0.006145	95.9364	95.85554	0.080862
10	13.59	7.23	7.21823	0.01177	98.2557	98.09574	0.159957
11	14.17	7.1	7.089655	0.010345	100.607	100.4604	0.14659
12	14.58	6.97	6.960626	0.009374	101.6226	101.4859	0.136678
13	14.93	6.83	6.817447	0.012553	101.9719	101.7845	0.187413
14	15.39	6.58	6.570693	0.009307	101.2662	101.123	0.143232
15	15.71	6.36	6.351286	0.008714	99.9156	99.7787	0.136902
16	16.08	6	6.039435	0.039435	96.48	97.11412	0.63412
17	16.34	5.75	5.778055	0.028055	93.955	94.41342	0.458419
18	16.76	5.27	5.27352	0.00352	88.3252	88.3842	0.058998
19	16.9	5.07	5.081137	0.011137	85.683	85.87121	0.188214
20	17.1	4.79	4.784231	0.005769	81.909	81.81035	0.098645
21	17.25	4.56	4.544105	0.015895	78.66	78.38581	0.274192
22	17.41	4.29	4.271163	0.018837	74.6889	74.36095	0.327953
23	17.65	3.83	3.828777	0.001223	67.5995	67.57792	0.021585
24	19.21	0	0.0035	0.0035	0	0.067233	0.067233
Sum of IAE				0.272222			3.886659

Table 11. Comparison of POA results with other MH optimization techniques in STP6-120/36 module.

Optimization	RMSE			Iph (A)	Isd (µA)	Rsh (Ω)	Rs (Ω)	n
	STD	Mean	Min
POA	1.0873E-03	1.5416E-02	1.4458E-02	7.4755	1.9419	549.9069	0.16867	48.037 E + 00
ALO	2.9185E-03	1.8446E-02	1.6787E-02	7.4733	2.2637	717.3285	0.1658	49.993 E + 00
AVOA	1.8219E-02	2.2906E-02	1.6787E-02	7.4732	2.2680	721.2412	0.1658	50.00 E + 00
BES	2.5476E-01	6.3298E-02	1.6785E-02	7.4722	2.2681	768.9442	0.1658	49.999 E + 00
GTO	2.410E-05	1.6793E-02	1.6785E-02	7.4722	2.2681	768.9440	0.1658	50.00 E + 00
GWO	4.3727E-03	1.9285E-02	1.6814E-02	7.4678	2.2685	1043.26506	0.1659	50.00 E + 00
WOA	1.8059E-02	2.7614E-02	1.6867E-02	7.4647	2.2700	1425.4392	0.1659	50.00 E + 00
GOTLBO (Chen, Yu, et al., 2016)	0.2158E-01	0.1668E-01	0.16683E-01	7.4563	2.2559	22.4749	0.00450	1.2566 E + 00
AOA (Krishnan et al., 2023)	1.876E + 00	2.2445E-2	2.4074E-02	7.54054	1.8597	4.9285	0.0052372	1.2476 E + 00
HBA-OBL (Koç et al., 2023)	0.1318E-04	0.1660E-01	0.16016E-01	7.4725	2.3350	799.8886	0.1654	46.789 E + 00
SDO (Ginidi et al., 2021)	7.61E-17	1.6601E-2	1.6601E-02	7.47253	2.330	22.2199	0.004595	1.2601 E + 00
GSK (Xiong et al., 2021)	0.144E-15	0.1660E-01	0.16601E-01	7.4725	2.3350	22.2199	0.0046	1.2601 E + 00
MIGTO (Abdel-Basset et al., 2022)	5.30E-17	1.6600E-02	1.6600E-02	7.47189	3.725	297.36	0.00437	1.3004 E + 00
Chaotic HBA (Düzenli̇ et al., 2022)	0.9018E-06	0.1660E-01	0.16016E-01	7.4725	2.3350	799.9	0.1654	46.789 E + 00
BES (Nicaire et al., 2021)	1.1219E −04	1.678E −02	1.6782E-02	7.4716	2.3218	23.0265	0.0042	1.2596 E + 00
HBA (Diab et al., 2022)	0.1324E-04	0.1660E-01	0.16016E-01	7.4725	2.335	799.9290	0.1654	46.789 E + 00
IAOA (Krishnan et al., 2023)	2.078E-04	1.6032E-02	1.5865E-02	7.48277	1.0000	10.000	0.0538	1.197 E + 00
CLRao-1 (Farah et al., 2022)	0.6318E-01	0.4107E-02	0.15557E-01	7.45668	1.08068	1500.00	0.19385	1.2180 E + 00
ImCSA (Kang et al., 2018)	–	–	1.5865E-02	7.4827	1.00	10.00	0.00538	1.197 E + 00
CIABC (Oliva et al., 2017)	–	–	1.6286E-02	7.4841	1.29	9.89	0.00510	1.2148 E + 00

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Data availability statement

All the necessary data pertaining to the simulations has been included in the manuscript in the form of tables and figures. Additional information will be provided on request.