A Simplified Sine Cosine Algorithm for the Solution of Optimal Reactive Power Dispatch

Table 1

Statistical analysis of different methods (best values are presented in bold).

	SSCA Mean ± SD	SCA Mean ± SD	BBO Mean ± SD	MFO Mean ± SD	PSO Mean ± SD
F1	9.77E-29 ± 1.64E-28	1.058E-10 ± 2.048E-10	9.318E-20 ± 2.266E-19	6.217E-12 ± 1.058E-11	1.063E-18 ± 2.243E-18
F2	1.65E-17 ± 1.73E-17	3.93E-09 ± 6.24E-09	5.6E-12 ± 8.95E-12	1.78E-08 ± 2.59E-08	9.1E-13 ± 1.84E-12
F3	9.87E-17 ± 2.02E-16	0.02295 ± 0.041731	0.04077 ± 0.04197	0.657616 ± 0.441665	0.001023 ± 0.001323
F4	5.56E-10 ± 9.22E-10	0.007677 ± 0.019162	0.961993 ± 2.017756	5.546965 ± 5.085424	0.002221 ± 0.001851
F5	4.809174 ± 0.637807	7.542727 ± 0.442341	6.309724 ± 1.613368	119.3389 ± 231.1894	6.072164 ± 2.416001
F6	0.184376 ± 0.160825	0.516629 ± 0.202489	3.884666 ± 2.861071	3.89E-11 ± 1.1E-10	1.92E-20 ± 3.32E-20
F7	0.00149 ± 0.000851	0.005295 ± 0.006349	0.005182 ± 0.001862	0.019673 ± 0.014721	0.002788 ± 0.001546
F8	-2798.49 ± 172.9513	-2104.07 ± 155.2715	-3915.95 ± 189.4259	-3238.98 ± 310.8421	-2298.53 ± 346.1811
F9	0.519919 ± 1.644128	0.554686 ± 1.748545	7.987651 ± 3.170098	22.884 ± 10.14656	13.43193 ± 5.185881
F10	3E-14 ± 8E-15	0.000324 ± 0.000583	7.04E-11 ± 4.4E-11	3.51E-07 ± 1.99E-07	7.48E-11 ± 1.89E-10
F11	0.042491 ± 0.043416	0.218004 ± 0.272418	0.054998 ± 0.047894	0.139545 ± 0.087655	0.083155 ± 0.072638
F12	0.031975 ± 0.026942	0.133127 ± 0.091179	1.68E-13 ± 5.33E-13	0.311232 ± 0.587118	2.14E-20 ± 6.59E-20
F13	0.131962 ± 0.08203	0.373384 ± 0.094815	1.097407 ± 0.314339	3.731186 ± 4.656249	5.692137 ± 4.747002