Table 14 Dynamic responses of the system.

Controller	Optim. Algorithm	∆f₁		∆f₂		∆P_tie		V_out1			V_out2
Controller	Optim. Algorithm	MO_∆f1 (Hz)	MU_∆f1 (Hz)	MO_∆f2 (Hz)	MU_∆f2 (Hz)	MO_∆P (p.u)	MU_∆P (p.u)	MP_− V1 (p.u)	T_r−V1 (Sec.)	T_s−V1 (Sec.)	MP_− V2 (p.u)	T_r−V2 (Sec.)	T_s−V2 (Sec.)
PID	PSO	1.188	−0.977	0.188	−0.332	0.093	−0.145	0.379	0.543	9.133	0.398	0.430	6.311
PID	GTO	0.695	−1.196	0.350	−1.214	0.054	−0.048	0.465	0.432	11.602	0.364	0.386	5.230
PID	MPA	0.208	−0.445	0.049	−0.146	0.011	−0.059	0.477	0.558	6.601	0.751	0.268	16.110
PIDD²	PSO	0.010	−0.065	0.010	−0.065	0.000	0.000	0.364	0.067	3.703	0.364	0.067	3.703
PIDD²	GTO	0.033	−0.083	0.053	−0.102	0.003	−0.003	0.314	0.200	2.593	0.248	0.171	1.891
PIDD²	MPA	0.014	−0.063	0.013	−0.065	0.001	−0.001	0.444	0.257	4.721	0.434	0.188	3.356
FPIDD²+PIDD²	PSO	0.018	−0.041	0.001	−0.031	0.000	0.000	0.315	0.068	17.796	0.153	0.154	4.311
FPIDD²+PIDD²	GTO	0.003	−0.022	0.001	−0.012	0.000	−0.001	0.179	0.174	1.824	0.191	0.186	1.873
FPIDD²+PIDD²	MPA	0.001	−0.014	0.001	−0.023	0.001	0.000	0.454	0.191	3.263	0.355	0.181	4.112

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