A New Optimization Approach for Maximizing the Photovoltaic Panel Power Based on Genetic Algorithm and Lagrange Multiplier Algorithm

Table 4

Effect of changing the initial module voltage on the module power at 6:10 AM.

Initial solution	Independent variables			Dependant variables			𝐼^𝑀 (A)	𝑃pv (W)
[Σ^∘0,𝜑^∘𝑐0, 𝑉^𝑀0]	Σ^∘	𝜑^∘𝐶	𝑉^𝑀 (V)	𝐺𝐶 (Kw/m^2)	𝐼0 (A)	𝑇 (°C)
𝑈0 = [45, 41, 0]	51.8224	44.5636	43.3348	0.0872	4.4921∗10^−6	31.8439	0.4162	18.1819
𝑈0 = [45, 41, 2]	56.3961	45.0000	43.4018	0.0899	4.5301∗10^−6	31.9350	0.4291	18.8057
𝑈0 = [45, 41, 4]	76.0000	44.9427	43.2811	0.0957	4.6123∗10^−6	32.1299	0.4567	19.7672
𝑈0 = [45, 41, 6]	53.7614	44.8565	43.4569	0.0859	4.4740∗10^−6	31.8003	0.4100	18.5142
𝑈0 = [45, 41, 8]	54.9695	44.5616	43.4382	0.0889	4.5158∗10^−6	31.9008	0.4242	18.6007
𝑈0 = [45, 41, 10]	76.0000	45.0000	43.3597	0.0958	4.6131∗10^−6	32.1318	0.4570	19.8132
𝑈0 = [45, 41, 12]	53.1965	44.7522	43.4134	0.0875	4.4960∗10^−6	31.8533	0.4175	18.4128
𝑈0 = [45, 41, 14]	76.0000	44.9767	43.3995	0.0957	4.6127∗10^−6	32.1308	0.4568	19.8273
𝑈0 = [45, 41, 16]	75.7500	45.0000	43.4834	0.0957	4.6129∗10^−6	32.1313	0.4569	19.8698
𝑈0 = [45, 41, 18]	75.8750	45.0000	43.4408	0.0949	4.6006∗10^−6	32.1023	0.4528	19.8504
𝑈0 = [45, 41, 20]	75.7500	45.0000	43.4871	0.0958	4.6131∗10^−6	32.1318	0.4570	19.8716
𝑈0 = [45, 41, 22]	76.0000	45.0000	43.4579	0.0958	4.6131∗10^−6	32.1318	0.4569	19.8581
𝑈0 = [45, 41, 24]	75.7500	45.0000	43.4499	0.0955	4.6092∗10^−6	32.1227	0.4557	19.8545
𝑈0 = [45, 41, 26]	75.7500	45.0000	43.4741	0.0949	4.6003∗10^−6	32.1017	0.4527	19.8728
𝑈0 = [45, 41, 28]	75.7500	45.0000	43.4839	0.0958	4.6131∗10^−6	32.1318	0.4569	19.8701
𝑈0 = [45, 41, 30]	76.0000	45.0000	43.4818	0.0958	4.6130∗10^−6	32.1316	0.4569	19.8776
𝑈0 = [45, 41, 32]	75.7500	45.0000	43.4565	0.0956	4.6115∗10^−6	32.1281	0.4564	19.8575
𝑈0 = [45, 41, 34]	75.7500	45.0000	43.4324	0.0957	4.6129∗10^−6	32.1313	0.4569	19.8466
𝑈0 = [45, 41, 36]	75.6875	45.0000	43.4969	0.0958	4.6131∗10^−6	32.1318	0.4570	19.8760
𝑈0 = [45, 41, 38]	75.7500	45.0000	43.4403	0.0958	4.6130∗10^−6	32.1317	0.4569	19.8501
𝑈0 = [45, 41, 40]	75.7500	45.0000	43.4393	0.0958	4.6131∗10^−6	32.1318	0.4569	19.8497
𝐔𝟎 = [45, 41, 42]	76.0000	45.0000	43.5000	0.0957	𝟒.𝟔𝟏𝟐𝟗∗𝟏𝟎^−𝟔	32.1315	0.4569	19.8778
𝑈0 = [45, 41, 43]	75.5625	45.0000	43.4655	0.0955	4.6098∗10^−6	32.1241	0.4559	19.8615
𝑈0 = [45, 41, 43.5]	75.5000	45.0000	43.5000	0.0958	4.6130∗10^−6	32.1317	0.4564	19.8772