Table 7 Optimal controller gains with 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

\(x_{1}\)

9.0374

0.1943

1.5489

9.0000

− 7.6628

− 0.9867

0.3431

0.8000

\(x_{2}\)

2.2906

6.6612

6.9924

0.8131

2.1200

− 9.0961

− 9.4435

0.8000

\(x_{3}\)

0.0100

7.0000

3.4310

7.0000

− 5.4876

4.6952

− 5.5857

0.7411

\(x_{4}\)

3.3289

5.9155

6.2604

0.3120

1.4998

− 3.4882

6.4911

0.6198

\(x_{5}\)

6.1297

3.4270

7.0000

1.8337

− 9.5407

7.3619

− 0.5905

0.6984

MGOA

\(x_{1}\)

9.0374

2.0943

1.5489

9.0000

− 7.6628

− 0.9867

0.3431

0.8000

\(x_{2}\)

5.5290

6.6612

6.9924

0.8131

2.1200

− 9.0961

− 9.4435

0.8000

\(x_{3}\)

0.0100

7.0000

3.4310

7.0000

− 5.4876

4.6952

− 5.5857

0.7411

\(x_{4}\)

3.3289

5.9155

6.2604

0.3120

1.4998

− 3.4882

6.4911

0.6198

\(x_{5}\)

6.1297

3.4270

7.0000

1.8337

− 9.5407

7.3619

− 0.5905

0.6984