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Table 10 Performance parameters of LFC with ISCA, SSA, ALO, SCA and PSO in the case of SLD of 2% in area-1 of the four-area system

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

\(\Delta F_{1}\)

\(\Delta F_{2}\)

\(\Delta F_{3}\)

\(\Delta F_{4}\)

\(\Delta P_{12}\)

\(\Delta P_{13}\)

\(\Delta P_{14}\)

\(\Delta P_{23}\)

ISCA

Settling time

2.970

17.849

15.691

12.691

22.791

14.912

16.803

20.652

Max. deviation

− 0.00669

− 0.00021

− 0.00058

− 0.00022

− 0.00121

0.00038

0.00044

0.00038

SCA

Settling time

4.0291

20.9288

17.460

15.8243

16.5011

15.3838

17.5558

21.2028

Max. deviation

− 0.01177

− 0.00161

− 0.00081

− 0.00199

− 0.00339

0.00126

0.00118

0.00097

ALO

Settling time

6.0434

22.342

16.762

19.234

15.501

15.420

17.6839

21.6339

Max. deviation

− 0.01522

− 0.00140

− 0.00099

− 0.00172

− 0.0.003

0.01275

0.00125

0.00101

SSA

Settling time

6.0534

12.5877

16.893

15.8216

15.936

15.963

18.4623

22.017

Max. deviation

− 0.01013

− 0.00082

− 0.00238

− 0.00097

− 0.00232

0.00070

0.00089

0.00087

PSO

Settling time

6.0644

8.9364

17.4604

154,219

14.691

16.721

19.3793

22.3421

Max. deviation

− 0.01702

− 0.00251

− 0.00052

− 0.00318

− 0.00444

0.00166

0.00155

0.00122