Table 2 The optimum gains of the PD-PI and PID controllers in LFC during low renewable penetration.

From: Advanced control strategy based on hybrid energy storage system for frequency stability of interconnected power system with high renewables penetration

Alg.

Con.No.

Dual PID

PID

PD-PI

Kp

Ki

Kd

Kp

Ki

Kd

Kp1

Kd

Kp2

Ki

EEFO

C1

9.9946

8.2426

9.5479

9.9739

9.7166

8.1922

9.5870

9.5235

9.9474

9.9718

C2

0.0017

3.6836

0.7061

9.0106

2.5040

2.9932

9.8263

2.5768

9.9079

9.6726

C3

5.2286

1.7491

7.3345

9.3976

9.3230

8.1821

9.4867

9.7661

9.3700

9.2886

C4

9.9812

4.9395

4.9987

9.8834

9.9691

9.9135

9.9117

9.5799

9.7853

9.4924

C5

9.9542

6.6291

3.3332

8.0110

0.9909

3.8227

9.9752

2.2848

9.8171

4.1358

C6

9.9913

2.8968

8.1610

9.9989

7.9836

9.7017

9.5980

6.8762

9.6917

9.5869

BWO

C1

-

-

-

-

-

-

9.4915

7.1249

10.0000

7.1882

C2

-

-

-

-

-

-

9.7062

0.0000

9.5229

3.0203

C3

-

-

-

-

-

-

10.0000

7.1361

10.0000

0.0000

C4

-

-

-

-

-

-

10.0000

4.2843

9.5941

4.8689

C5

-

-

-

-

-

-

10.0000

1.2405

10.0000

0.0000

C6

-

-

-

-

-

-

10.0000

7.2572

10.0000

7.3231

SSO

C1

-

-

-

-

-

-

7.0605

3.5166

4.3141

5.4701

C2

-

-

-

-

-

-

5.9490

0.3054

2.9198

2.5181

C3

-

-

-

-

-

-

5.1805

6.4762

6.9627

5.1442

C4

-

-

-

-

-

-

7.6903

7.3784

9.1213

6.9253

C5

-

-

-

-

-

-

4.8448

0.9859

1.2487

7.5195

C6

-

-

-

-

-

-

6.2735

4.1159

3.1194

2.8150

IWD

C1

-

-

-

-

-

-

8.5827

7.8689

4.3973

4.8506

C2

-

-

-

-

-

-

9.1858

3.8091

7.8197

4.3120

C3

-

-

-

-

-

-

10.0000

8.1975

8.0374

8.1958

C4

-

-

-

-

-

-

3.9358

8.0611

3.7858

4.3294

C5

-

-

-

-

-

-

7.8342

4.0398

8.6190

8.6430

C6

-

-

-

-

-

-

8.1969

4.3457

8.1324

7.6283

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