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Table 8 Performance parameters of LFC with ISCA, SCA, ALO, SSA, and PSO for the three-area system with physical constraints with SLD of 1% in area-1

From: Design of a 2-DOF-PID controller using an improved sine–cosine algorithm for load frequency control of a three-area system with nonlinearities

Algorithm

\(\Delta F_{1}\)

\(\Delta F_{2}\)

\(\Delta F_{3}\)

\(\Delta P_{1 - 2}\)

\(\Delta P_{2 - 3}\)

\(\Delta P_{3 - 1}\)

ISCA

Settling time

31.621

26.6702

28.5448

42.842

39.097

40.1447

Maximum deviation

− 0.02454

− 0.023358

− 0.029188

− 0.01268

− 0.00799

− 0.00229

SCA

Settling time

32.5734

27.6502

29.062

43.354

48.7748

46.7889

Maximum deviation

− 0.026958

− 0.02543

− 0.02992

− 0.01287

0.00799

− 0.002646

ALO

Settling time

39.784

35.3731

35.239

48.2348

47.7947

44.776

Maximum deviation

− 0.026958

− 0.024985

− 0.0301

− 0.01290

0.00800

− 0.00170

SSA

Settling time

32.208

38.6619

38.269

49.212

45.4856

43.0036

Maximum deviation

− 0.026124

− 0.02618

− 0.030177

− 0.01259

0.00800

− 0.002651

PSO

Settling time

36.3844

31.8903

34.141

43.6058

45.0462

47.3151

Maximum deviation

− 0.029081

− 0.028708

− 0.032206

− 0.01224

0.00755

− 0.002642