Table 11 Optimal controller gain with non-linearities under the presence of EV.

From: Frequency stability improvement in EV-integrated power systems using optimized fuzzy-sliding mode control and real-time validation

Controller

Optimization

Area controller

\(K_{p1}\)

\(K_{i1}\)

\(K_{pf}\)

\(K_{df}\)

\(x\)

\(y\)

\(z\)

\(K_{xi}\)

FSMC

GOA

\(x_{1}\)

5.0000

5.0000

5.0000

2.9525

− 7.2843

10.0000

6.1724

0.9000

\(x_{2}\)

5.0000

5.0000

5.0000

4.0287

9.2608

6.2136

8.6596

0.9000

\(x_{3}\)

5.0000

5.0000

5.0000

5.0000

− 4.4269

4.3559

10.0000

0.9000

\(x_{4}\)

5.0000

5.0000

5.0000

1.1085

6.6710

8.7793

2.1738

0.9000

\(x_{5}\)

5.0000

5.0000

2.5023

4.9034

9.9933

9.4321

− 1.1746

0.9000

MGOA

\(x_{1}\)

10.000

8.0000

8.0000

4.2690

− 10.0000

10.0000

7.0407

0.9000

\(x_{2}\)

9.0000

8.0000

7.0000

1.9933

7.2539

8.8113

8.8694

0.9000

\(x_{3}\)

5.0000

5.0000

5.0000

5.0000

− 8.0371

5.8543

5.8765

0.9000

\(x_{4}\)

5.0000

5.0000

5.0000

0.5619

8.6689

7.7820

0.9216

0.9000

\(x_{5}\)

5.0000

5.0000

4.7668

4.9515

7.0476

10.0000

− 0.1861

0.9000