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Table 2 Optimized PID/FOPID controller

From: Comparative performance analysis of hybrid differential evolution and pattern search technique for frequency control of the electric power system

Gains

AC link

Parallel AC-DC link

DE:PID

DE:FOPID

hDE-PS:FOPID

PID

FOPID

hDE-PS:FOPID

KP1

− 0.3968

− 1.4056

− 1.5207

− 1.6106

− 1.9956

− 1.9353

KP2

− 1.3719

0.6266

0.7151

− 1.6106

0.8880

0.5400

KP3

− 1.0413

0.5321

0.5485

− 1.7589

− 1.5540

1.2598

KI1

− 0.5039

− 1.5322

− 1.5974

− 1.1799

− 0.0381

− 1.9478

KI2

− 0.6308

− 1.6221

− 1.6299

1.5177

− 1.8206

− 1.7133

KI3

− 1.0121

− 1.6514

− 1.7125

− 0.6086

− 0.1188

− 1.0104

KD1

− 0.9209

− 1.6221

− 1.5017

− 0.2533

− 1.8206

− 1.5401

KD2

− 1.0952

− 1.1721

− 1.1193

− 1.4752

− 0.3613

− 0.0660

KD3

− 1.8923

1.8160

1.7229

0.6136

0.4604

− 0.3920

λ1

0.0145

0.0201

0.9227

0.3294

λ2

0.9426

0.9456

0.7883

0.8545

λ3

0.0299

0.0440

0.9693

0.4782

μ1

0.9681

0.7557

0.1812

0.2327

μ2

0.2841

0.3846

0.0367

0.0410

μ3

0.5121

0.3166

0.0759

0.2442