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

Table 3

Effect of changing the initial collector azimuth 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^∘	𝜑^∘𝐶	𝑉^𝑀 (V)	𝐺𝐶 (Kw/m^2)	𝐼0 (A)	𝑇 (°C)
𝑈0 = [45, −45, 30]	50.6146	44.5382	43.4679	0.0867	4.4841∗10^−6	31.8246	0.4134	18.0765
𝑈0 = [45, −40, 30]	53.9220	44.9146	43.3693	0.0880	4.5023∗10^−6	31.8683	0.4196	18.5043
𝑈0 = [45, −35, 30]	56.1325	44.2593	43.4265	0.0888	4.5140∗10^−6	31.8966	0.4236	18.6752
𝑈0 = [45, −30, 30]	55.7048	44.9776	43.3350	0.0874	4.4944∗10^−6	31.8495	0.4170	18.6999
𝑈0 = [45, −25, 30]	57.7381	44.7576	43.3907	0.0870	4.4883∗10^−6	31.8348	0.4149	18.8992
𝑈0 = [45, −20, 30]	53.4386	44.7737	43.2897	0.0877	4.4994∗10^−6	31.8615	0.4187	18.3925
𝑈0 = [45, −15, 30]	75.7500	44.9988	43.4602	0.0957	4.6130∗10^−6	32.1316	0.4569	19.8591
𝑈0 = [45, −10, 30]	75.7500	44.8301	43.4955	0.0956	4.6102∗10^−6	32.1250	0.4560	19.8452
𝑈0 = [45, −5, 30]	54.9162	44.5165	43.4248	0.0891	4.5189∗10^−6	31.9083	0.4253	18.5822
𝑈0 = [45, 0, 30]	76.0000	44.7835	43.4785	0.0956	4.6104∗10^−6	32.1255	0.4561	19.8290
𝑈0 = [45, 5, 30]	75.7500	45.0000	43.4714	0.0955	4.6100∗10^−6	32.1246	0.4559	19.8774
𝑈0 = [45, 10, 30]	75.7500	45.0000	43.4771	0.0953	4.6062∗10^−6	32.1155	0.4547	19.8670
𝑈0 = [45, 15, 30]	75.7500	45.0000	43.4837	0.0953	4.6069∗10^−6	32.1173	0.4549	19.8700
𝑈0 = [45, 20, 30]	75.7500	45.0000	43.4731	0.0958	4.6131∗10^−6	32.1318	0.4570	19.8651
𝑈0 = [45, 25, 30]	75.7500	45.0000	43.4553	0.0957	4.6122∗10^−6	32.1298	0.4567	19.8570
𝑈0 = [45, 30, 30]	76.0000	45.0000	43.4579	0.0952	4.6052∗10^−6	32.1133	0.4543	19.8581
𝑈0 = [45, 32, 30]	75.7500	45.0000	43.4983	0.0953	4.6068∗10^−6	32.1171	0.4549	19.8767
𝑈0 = [45, 34, 30]	76.0000	45.0000	43.4766	0.0957	4.6124∗10^−6	32.1303	0.4567	19.8667
𝑈0 = [45, 36, 30]	75.7500	45.0000	43.4935	0.0958	4.6130∗10^−6	32.1317	0.4569	19.8744
𝑈0 = [45, 37, 30]	76.0000	45.0000	43.4558	0.0944	4.5943∗10^−6	32.0877	0.4507	19.8572
𝑈0 = [45, 39, 30]	75.7500	45.0000	43.4837	0.0958	4.6130∗10^−6	32.1317	0.4569	19.8700
𝐔𝟎 = [45, 41, 30]	75.7500	45.0000	43.4997	0.0957	𝟒.𝟔𝟏𝟐𝟔∗𝟏𝟎^−𝟔	32.1307	0.4568	19.8776
𝑈0 = [45, 43, 30]	75.7500	45.0000	43.4516	0.0957	4.6118∗10^−6	32.1289	0.4565	19.8553
𝑈0 = [45, 45, 30]	75.7500	45.0000	43.4834	0.0953	4.6063∗10^−6	32.1160	0.4547	19.8698