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Table 1 Optimal controller parameter values and convergence values under different algorithms and input conditions

From: Stability enhancement of wind energy integrated hybrid system with the help of static synchronous compensator and symbiosis organisms search algorithm

Input conditions

Applied algorithms

Optimal parameters (Kp, Ki, Kd, N, T, Tc and Td)

Fitness value

0.97,0.4752

GSA

3.4994

4.0611

28.9541

0.5440

0.0010

0.9337

0.0010

10,567

BGA

99.6484

88.3984

13.5156

1.2207

0.6596

99.6529

0.0050

656.8861

SOS

0.0010

1.0000

0.0010

0.0256

0.0010

0.0032

0.0010

566.4984

0.97,1.08

GSA

3.6868

7.6381

13.3414

0.2605

0.0010

0.9587

0.0010

10,567

BGA

99.6484

88.3984

44.1016

1.9221

1.3766

99.6529

0.0050

656.8784

SOS

0.0010

1.0000

0.0010

0.0010

0.0010

0.3665

0.0775

566.4984

0.99,1.08

GSA

5.6881

5.9764

14.7117

0.0045

0.0709

0.8912

0.0010

10,568

BGA

99.6484

99.6484

32.5000

1.2363

1.3688

99.6534

0.0050

656.8323

SOS

0.0010

1.0000

0.0010

0.0010

0.0017

0.0466

0.0058

566.4984

1.0,0.93

GSA

3.2616

3.9840

31.4257

0.0010

0.4622

0.9228

0.0010

673.9469

BGA

99.6484

94.0234

32.8516

1.5013

1.2519

99.6532

0.0050

656.6698

SOS

0.0010

4.8426

0.0010

0.0010

0.0010

0.0065

0.0010

566.4984

1.0,1.08

GSA

7.2108

8.1683

22.7107

0.4192

0.0010

0.9856

0.0010

674.3396

BGA

99.6484

99.6484

43.7500

1.9221

1.1895

99.6534

0.0050

656.7532

SOS

0.0010

1.0000

0.0010

0.0017

0.0010

0.0794

0.0094

566.4984

1.01,0.752

GSA

0.0010

1.1428

3.2945

0.9497

0.1482

0.0010

26.6038

782.2997

BGA

99.6484

99.6484

32.5000

1.5013

1.1272

99.6534

0.0050

656.7778

SOS

0.0010

3.9871

0.0010

0.0010

0.0010

0.3827

0.0584

566.4984

1.01,0.97

GSA

2.6124

7.3855

10.2151

0.0801

0.0026

0.7518

0.0010

671.2094

BGA

99.6484

94.0234

32.8516

1.5013

1.2519

99.6532

0.0054

656.8762

SOS

0.0010

1.0000

0.0010

0.0010

0.0010

0.1047

0.0223

566.4984

1.01,1.08

GSA

0.0010

1.0000

27.2641

0.7052

0.0876

0.0010

19.1757

664.9852

BGA

99.6484

99.6484

62.3828

1.8753

1.7506

99.6534

0.0050

656.8446

SOS

0.0010

1.0000

0.0010

0.0010

0.0137

0.0827

0.0200

566.4984