Grasshopper optimization algorithm optimized multistage controller for automatic generation control of a power system with FACTS devices

Protection and Control of Modern Power Systems

Table 6 Peak deviation & Settling time for GOA optimized PDF plus (1 + PI) controller with different loading conditions

Loading Condition	Peak Overshoot (+)			Peak Undershoot (−)			Settling Time in seconds
Loading Condition	∆f₁ *(Hz)*	∆f₂ *(Hz)*	∆P_tie1–2(pu)	∆f₁ *(Hz)*	∆f₂ *(Hz)*	∆P_tie1–2(pu)	∆f₁ *(Hz)*	∆f₂ *(Hz)*	∆P_tie1–2(pu)
Nominal	0.000740	0.000735	0.000551	0.007415	0.007567	0.006845	34.22	37.07	38.12
+ 25%	0.001748	0.001654	0.001726	0.009492	0.009536	0.009445	41.92	41.74	42.20
- 25%	0.001600	0.001611	0.001633	0.009544	0.009483	0.009418	41.53	40.91	41.53
+ 50%	0.002308	0.002278	0.002236	0.009575	0.009551	0.009554	42.02	41.89	42.23
- 50%	0.001582	0.001576	0.001586	0.009531	0.009548	0.009493	40.98	41.48	41.84
+ 75%	0.001844	0.001802	0.001852	0.009551	0.009475	0.009548	41.23	41.96	42.39
- 75%	0.001485	0.001553	0.001513	0.009547	0.009546	0.009557	40.58	40.35	41.02