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

Table 2

Effect of changing the initial tilt angle 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^∘	𝜑𝐶^∘	𝑉^𝑀 (V)	𝐺𝐶 (Kw/m^2)	𝐼0 (A)	𝑇 (°C)
𝑈0 = [0, 5, 30]	56.5384	44.4320	43.4848	0.0887	4.5125∗10^−6	31.8929	0.4231	18.7692
𝑈0 = [3, 5, 30]	51.2944	44.7359	43.4484	0.0877	4.4992∗10^−6	31.8609	0.4186	18.1864
𝑈0 = [6, 5, 30]	54.6782	44.8905	43.3716	0.0887	4.5131∗10^−6	31.8944	0.4233	18.5889
𝑈0 = [9, 5, 30]	58.7500	45.0000	43.4777	0.0915	4.5519∗10^−6	31.9871	0.4365	19.0712
𝑈0 = [12, 5, 30]	63.5000	45.0000	43.5000	0.0932	4.5768∗10^−6	32.0463	0.4448	19.4612
𝑈0 = [15, 5, 30]	49.6782	44.9171	43.3964	0.0843	4.4509∗10^−6	31.7443	0.4021	17.9730
𝑈0 = [18, 5, 30]	49.2228	44.5000	43.3857	0.0833	4.4368∗10^−6	31.7098	0.3972	17.8469
𝑈0 = [21, 5, 30]	56.2744	44.8397	43.2505	0.0887	4.5122∗10^−6	31.8921	0.4230	18.7031
𝑈0 = [24, 5, 30]	47.3468	42.7325	43.4541	0.0816	4.4142∗10^−6	31.6547	0.3894	17.3567
𝑈0 = [27, 5, 30]	51.5620	44.9079	43.2911	0.0862	4.4777∗10^−6	31.8091	0.4112	18.1797
𝑈0 = [30, 5, 30]	67.2500	44.9020	43.4535	0.0941	4.5888∗10^−6	32.0746	0.4489	19.6382
𝑈0 = [33, 5, 30]	73.7500	45.0000	43.4414	0.0956	4.6110∗10^−6	32.1269	0.4563	19.8390
𝑈0 = [36, 5, 30]	74.7500	45.0000	43.4958	0.0957	4.6129∗10^−6	32.1313	0.4569	19.8724
𝑈0 = [39, 5, 30]	75.7500	45.0000	43.4894	0.0957	4.6126∗10^−6	32.1307	0.4568	19.8726
𝑈0 = [42, 5, 30]	76.0000	45.0000	43.3601	0.0953	4.6063∗10^−6	32.1160	0.4547	19.8134
𝐔𝟎 = [45, 5, 30]	75.8125	45.0000	43.4999	0.0958	𝟒.𝟔𝟏𝟑𝟏∗𝟏𝟎^−𝟔	32.1318	0.4570	19.8774
𝑈0 = [48, 5, 30]	75.7500	45.0000	43.3796	0.0953	4.6069∗10^−6	32.1173	0.4549	19.8224
𝑈0 = [51, 5, 30]	76.0000	45.0000	43.3997	0.0958	4.6130∗10^−6	32.1317	0.4569	19.8315
𝑈0 = [54, 5, 30]	75.7500	45.0000	43.4689	0.0958	4.6131∗10^−6	32.1318	0.4569	19.8632
𝑈0 = [67, 5, 30]	75.8125	45.0000	43.4989	0.0957	4.6129∗10^−6	32.1313	0.4569	19.8769
𝑈0 = [70, 5, 30]	75.8125	45.0000	43.4903	0.0958	4.6131∗10^−6	32.1318	0.4570	19.8730
𝑈0 = [73, 5, 30]	75.8125	45.0000	43.4989	0.0958	4.6131∗10^−6	32.1318	0.4570	19.8769
𝑈0 = [76, 5, 30]	75.7500	45.0000	43.4963	0.0955	4.6099∗10^−6	32.1243	0.4559	19.8757
𝑈0 = [80, 5, 30]	75.7813	45.0000	43.4966	0.0958	4.6130∗10^−6	32.1317	0.4569	19.8759