Table 11 The optimal feedback gain matrices for the T-H-G system with OARs.

EHVAC

0.4837

0.6864

21.6671

− 5.0190

0.5680

3.0981

6.3466

− 6.7353

1.5505

1.8577

1.6270

0.1133

0.8221

− 0.1140

0.0212

0.5410

0.7636

− 1.1746

0.3668

0.1824

0.2563

− 0.1281

− 4.0062

− 0.5362

− 0.8441

0.0571

0.7845

6.7963

− 1.7844

0.0628

0.0455

0.1396

− 1.6534

0.0058

− 0.0025

− 0.1191

− 0.0008

5.2744

− 0.8793

0.4206

1.9232

3.9186

− 11.7290

1.1103

1.2476

1.7111

− 0.6912

1.1423

− 0.8441

0.5362

HVDC

0.1053

0.9278

19.7452

− 4.7585

0.5043

1.8192

4.0971

− 5.2050

0.8419

1.1802

1.2534

0.1028

2.3259

− 0.3020

0.0785

1.5987

2.8199

− 1.7564

0.9940

0.9129

0.6861

− 0.2740

0.2190

− 0.6671

− 0.745

0.3858

0.5892

6.9812

− 1.6856

0.0899

0.8378

1.5640

− 2.4210

0.4366

0.4034

0.1454

0.0054

4.3986

− 0.7583

0.3910

1.2994

2.6401

− 11.5254

0.7754

0.8335

1.3764

− 0.5572

0.0228

− 0.745

0.6671

Parallel EHVAC/DC tie− lines (Delta Pdc as CV)

− 0.1808

− 0.2562

11.5030

− 2.6766

0.4158

1.2492

2.8461

− 2.4561

0.5894

0.9137

1.1280

0.0981

− 1.5989

0.2374

− 0.0549

− 1.0523

− 2.2053

2.1438

− 0.5608

− 0.6878

− 0.6597

0.2808

− 2.7708

− 0.0012

− 0.8563

− 0.2654

0.2064

5.9918

− 1.7148

0.0348

− 0.8364

− 1.6536

− 0.7165

− 0.418

− 0.4255

− 0.4494

− 0.0069

2.7251

− 0.4001

0.3636

0.7150

1.4750

− 6.0482

0.4527

0.5414

0.7912

− 0.2581

0.9172

− 0.9991

0.0235

1.4454

0.5795

4.7327

− 1.0964

0.0652

0.3413

− 0.5042

− 0.7619

0.4311

− 0.1440

− 0.9833

− 0.0292

1.3399

− 0.3287

− 0.0236

0.4207

0.7562

− 3.6673

0.2298

0.1602

0.2429

− 0.1612

0.1217

0.0435

0.516