Table 17 Optimal controllers’ settings for the LFC loop in the first and second area.

Controller	Optim Algorithm	\(\:{LFC\|}_{Area1}\)								\(\:{LFC\|}_{Area2}\)
Controller	Optim Algorithm	K_P	K_I	K_D1	N₁	K_D2	N₂	K_E	K_CE	K_P	K_I	K_D1	N₁	K_D2	N₂	K_E	K_CE
PID	PSO	18.5	2.0	2.0	1.1	-	-	-	-	92.9	1.3	1.8	1.5	-	-	-	-
PID	GTO	0.2	0.2	0.2	0.1	-	-	-	-	3.2	1.3	0.2	0.1	-	-	-	-
PID	MPA	0.1	1.7	1.9	0.2	-	-	-	-	2.9	0.1	2.0	0.2	-	-	-	-
PIDD²	PSO	100.0	2.0	2.0	2.0	10.0	100.0	-	-	100.0	2.0	0.8	2.0	10.0	100.0	-	-
PIDD²	GTO	100.0	2.0	1.2	1.6	10.0	100.0	-	-	100.0	2.0	2.0	1.4	1.1	98.1	-	-
PIDD²	MPA	100.0	2.0	2.0	2.0	4.2	96.1	-	-	100.0	2.0	2.0	1.8	3.2	94.8	-	-
FPIDD²+PIDD²	PSO	65.5	2.0	2.0	1.8	10.0	100.0	2.0	0.1	91.6	2.0	1.6	2.0	7.7	54.5	1.9	0.1
FPIDD²+PIDD²	GTO	100.0	2.0	0.1	2.0	1.3	100.0	2.0	0.1	100.0	2.0	2.0	2.0	0.1	100.0	2.0	0.1
FPIDD²+PIDD²	MPA	100.0	2.0	2.0	2.0	8.4	47.0	2.0	0.1	99.5	2.0	2.0	1.7	4.8	98.2	2.0	0.1

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