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Table 4 Performance parameters of LFC with ISCA, SSA, ALO, SCA and PSO, in the case of SLD of 2% in area-1 and area-2

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

9.1448

14.0824

15.083

21.615

12.7501

15.8758

Maximum deviation

− 0.00623

− 0.00561

− 0.00135

− 0.0005317

− 0.00029

0.000827

SCA

Settling time

9.2762

16.243

17.671

22.612

19.1867

19.3867

Maximum deviation

− 0.06831

− 0.00984

− 0.00136

− 0.001047

− 0.00139

0.00173

ALO

Settling time

9.2933

16.528

17.5261

22.703

17.6988

202,057

Maximum deviation

− 0.07899

− 0.01042

− 0.00172

− 0.001257

− 0.00167

0.002021

SSA

Settling time

9.741

18.943

18.517

23.7924

19.4814

251.7936

Maximum deviation

− 0.01259

− 0.01262

− 0.00220

− 0.0017981

− 0.002047

0.002391

PSO

Settling time

9.9342

19.224

19.3311

24.5246

19.802

22.7163

Maximum deviation

− 0.01748

− 0.01316

− 0.00221

− 0.001281

− 0.001581

0.002284