Table 23 Dynamic responses of the system.

From: A hybrid fuzzy-PIDD² control strategy for coordinated LFC and AVR in renewable-integrated multi-area power systems

Controller

Optim Algorithm

∆f1

∆f2

Ptie

Vout1

Vout2

MO∆f1

(Hz)

MU∆f1

(Hz)

MO∆f2

(Hz)

MU∆f2

(Hz)

MOP

(p.u)

MUP

(p.u)

MP− V1

(p.u)

Tr−V1

(Sec.)

Ts−V1

(Sec.)

MP− V2

(p.u)

Tr−V2

(Sec.)

Ts−V2

(Sec.)

PID

PSO

0.417

−1.276

0.772

−1.464

0.103

−0.162

0.471

0.531

12.073

0.699

0.252

13.652

PID

GTO

0.511

−1.588

0.522

−1.574

0.077

−0.130

0.380

0.397

8.483

0.674

0.254

11.746

PID

MPA

0.331

−1.170

0.746

−1.483

0.116

−0.143

0.483

0.610

12.364

0.697

0.252

12.830

PIDD²

PSO

0.010

−0.079

0.009

−0.078

0.001

−0.001

0.436

0.102

2.620

0.156

0.145

3.146

PIDD²

GTO

0.012

−0.086

0.009

−0.083

0.001

−0.001

0.230

0.151

2.146

0.196

0.152

2.906

PIDD²

MPA

0.012

−0.064

0.008

−0.059

0.001

−0.001

0.459

0.077

3.214

0.195

0.145

3.188

FPIDD²+PIDD²

PSO

0.002

−0.015

0.001

−0.016

0.000

0.000

0.423

0.111

2.971

0.183

0.170

3.009

FPIDD²+PIDD²

GTO

0.028

−0.046

0.008

−0.034

0.000

−0.001

0.384

0.112

4.806

0.164

0.144

3.272

FPIDD²+PIDD²

MPA

0.002

−0.015

0.011

−0.036

0.002

0.000

0.467

0.246

4.135

0.220

0.200

2.589