Skip to main content

Table 6 Comparative performance of ITAE value (for \(t_{\text{sim}} = 10\) s), settling times (for 2% tolerance band) and peak overshoots for multi-area multi-unit power system (test system-2)

From: Combined load frequency and terminal voltage control of power systems using moth flame optimization algorithm

Optimization techniques

ZN-tuned PID [39]

SA PID (ISE) [39]

MFO PID (ISE)

MFO PID (ITAE)

MFO FOPID (ITAE)

Frequency deviation in area-1 \(\Delta F_{1}\)

 Maximum overshoot (OS) × 10−4 (p.u.)

4.9444

0.5532

0.2016

0.3285

0.3009

 Minimum undershoot (US) × 10−4 (p.u.)

− 14.6118

− 38.9115

− 2.2533

− 5.1166

− 5.2424

 Settling time (s) \(\left( {T_{\text{s}} } \right)\)

10.02

4.22

4.99

1.96

1.4

Frequency deviation in area-2 \(\Delta F_{2}\)

 Maximum overshoot (OS) × 10−4(p.u.)

4.6249

0.3729

0.0885

0.0008

0.0001

 Minimum undershoot (US) × 10−4 (p.u.)

− 9.259

− 1.1566

− 0.6219

− 1.5482

− 1.5194

 Settling time (s) \(\left( {T_{\text{s}} } \right)\)

9.4

4.39

3.67

2.09

1.7

Tie-line power deviation \(\Delta P_{Tie}\)

 Maximum overshoot (OS) × 10−4 (p.u.)

0.4528

0.0536

0.0259

0.0000

0.0000

 Minimum undershoot (US) × 10−4 (p.u.)

− 3.1312

− 0.4437

− 0.2593

− 0.5077

− 0.4908

 Settling time (s) \(\left( {T_{\text{s}} } \right)\)

6.23

2.31

3.02

1.79

1.23

Terminal voltage deviation in area-1 \(\left( {\Delta V_{t1} } \right)\)

 Maximum overshoot (OS) × 10−4(p.u.)

14.6051

2.6419

1.0969

2.3557

0.2391

 Minimum undershoot (US) × 10−4 (p.u.)

− 0.1870

0.0000

− 0.4479

− 0.3424

− 0.0138

 Settling time (s) \(\left( {T_{\text{s}} } \right)\)

8.17

7.7

7.4

3.66

0.167

Terminal voltage deviation in area-2 \(\left( {\Delta V_{t2} } \right)\)

 Maximum overshoot (OS) × 10−4 (p.u.)

11.3510

2.0202

0.9069

1.2567

0.1330

 Minimum undershoot (US) × 10−4 (p.u.)

0.0000

− 0.0000

− 0.1951

− 0.0050

− 0.0015

 Settling time (s) \(\left( {T_{\text{s}} } \right)\)

10.02

8.2

7.1

3.2

1.013

ITAE

0.1098

0.0139

0.0103

0.0032

0.0030