Modified Differential Evolution Algorithm for Governing Virtual Inertia of an Isolated Microgrid Integrating Electric Vehicles

Table 1

Statistical analysis of the proposed method on benchmark functions.

Functions	Methods	Best	Worst	Mean	SD
F1	MDE	4.68E − 21	7.36E − 19	7.41E − 20	1.85E − 19
	DE	6.78E − 22	1.19E − 14	2.39E − 16	1.67E − 15
	TLBO	1.44E − 91	3.38E − 89	1.26E − 89	1.10884E − 89
F2	MDE	2.58E − 21	2.27E − 16	3.32E − 17	7.12E − 17
	DE	8.38E − 13	1.72E − 11	4.46E − 12	3.42E − 12
	TLBO	2.49E − 44	2.13E − 43	1.00E − 43	6.02063E − 44
F3	MDE	1.80E − 05	0.013169	0.00188	0.00303
	DE	0.000615	0.532483	0.049855	0.090053
	TLBO	1.77E − 20	2.74E − 16	3.63E − 17	8.02234E − 17
F4	MDE	7.57E − 06	6.2443	0.64133	1.6845
	DE	5.73E − 06	15.27477	0.867372	2.910621
	TLBO	1.88E − 37	2.06E − 36	1.30E − 36	5.88547E − 37
F5	MDE	0.0001369	0.22622	0.17203	0.12704
	DE	0.08269	21.13767	6.189471	2.75689
	TLBO	24.62261	25.73328	25.14059	0.36851
F6	MDE	3.537E − 24	4.049E − 20	2.2988E − 20	3.53592E − 20
	DE	7.79E − 22	7.83E − 19	8.74E − 20	1.56E − 19
	TLBO	1.32E − 07	7.44E − 05	1.64E − 05	2.35864E − 05
F7	MDE	0.0013	0.00757	0.0037	0.0018
	DE	0.000761	0.018048	0.005162	0.002945
	TLBO	0.000543	0.001908	0.001354	0.000389
F8	MDE	−4189.83	−3634.99	−3902.1344	158.86
	DE	−4079.23	−3558.16	−3847.11	202.5658
	TLBO	−1670.31	−1468.19	−1556.2	64.26864
F9	MDE	1.99	12.93	6.89	3.06
	DE	4.10	13.72706	8.052266	3.152745
	TLBO	9.061606	14.9362	12.07996	1.600468
F10	MDE	2.075E − 12	1.019E − 10	3.562E − 11	3.803E − 11
	DE	1.98E − 11	4.55E − 10	1.22E − 10	7.89E − 11
	TLBO	19.99999996	20	19.99999996	1.45389E − 09
F11	MDE	9.554E − 06	0.16982	0.055	0.054
	DE	1.11E − 16	0.271709	0.069238	0.069303
	TLBO	0	0	0	0
F12	MDE	1.58E − 26	3.81E − 21	4.294E − 22	1.052E − 21
	DE	1.11E − 22	0.29231	0.005846	0.040923
	TLBO	4.21E − 09	1.40E − 06	2.43E − 07	3.98225E − 07
F13	MDE	1.2315E − 21	9.78E − 20	2.46E − 20	2.65E − 20
	DE	1.51E − 21	5.75E − 19	3.92E − 20	8.74E − 20
	TLBO	1.151E − 05	0.206965	0.084465	0.068102