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Table 4 Relative stability and minimum damping ratio for ±30% changes in machine inertia constant (M)

From: Design of a robust PID-PSS for an uncertain power system with simplified stability conditions

Q

p.u.

%

M

P in p.u.

0.2

0.4

0.6

0.8

1

1.2

Relative Stability(σmax)

−0.4

+ 30

− 0.6026

− 0.9114

−1.2797

− 1.2690

− 1.2551

− 1.2400

− 30

− 0.5956

−0.8983

− 1.2757

−1.2713

− 1.2647

−1.2571

− 0.2

+ 30

− 1.2207

− 1.2870

− 1.3128

−1.3186

− 1.3151

−1.3069

− 30

−1.2629

− 1.3023

− 1.3234

−1.3305

− 1.3309

−1.3280

0

+ 30

−1.3869

−1.3558

− 1.3678

−1.3758

− 1.3770

−1.3733

−30

−1.4846

−1.3943

− 1.3932

−1.3980

− 1.4001

−1.3994

0.2

+ 30

−1.7087

−1.5090

− 1.4679

−1.4577

− 1.4529

−1.4479

− 30

−1.8812

− 1.5722

− 1.5084

−1.4905

− 1.4838

−1.4796

0.4

+ 30

− 2.2016

−1.7473

− 1.6206

− 1.5733

−1.5509

− 1.5372

−30

− 2.4677

− 1.8335

−1.6755

− 1.6164

−1.5895

− 1.5748

Minimum damping ratio (ζmin)

−0.4

+ 30

0.4230

0.4024

0.3980

0.3960

0.3946

0.3935

−30

0.3089

0.2932

0.2899

0.2886

0.2878

0.2873

−0.2

+ 30

0.5275

0.4379

0.4126

0.4023

0.3970

0.3938

−30

0.3870

0.3202

0.3013

0.2937

0.2899

0.2876

0

+ 30

0.6247

0.4869

0.4391

0.4173

0.4057

0.3988

−30

0.4554

0.3559

0.3208

0.3048

0.2963

0.2913

0.2

+ 30

0.6329

0.5339

0.4689

0.4366

0.4183

0.4071

−30

0.5038

0.3882

0.3419

0.3185

0.3053

0.2972

0.4

+ 30

0.6203

0.5748

0.4973

0.4566

0.4325

0.4172

−30

0.5333

0.4135

0.3609

0.3323

0.3151

0.3041