Table 5 Statistical measures of TARTPS system with different controllers.

From: A quasi-oppositional FBI algorithm driven fuzzy cascaded fractional-order controller for enhancing transient stability in hybrid power systems

Controllers

Statistical measures

Undershoot (Us × 10−3)

Overshoot (Os × 10−3)

Settling time (Ts)

ITAE

ΔF1

ΔF2

ΔPtie

ΔF1

ΔF2

ΔPtie

ΔF1

ΔF2

ΔPtie

QOFBI FFOPID(1 + FOPI)

− 1.2081

− 0.4766

− 0.1896

0

0

0

1.11

4.35

0.0008

FBI FFOPID(1 + FOPI)

− 2.6950

− 0.7203

− 0.2904

0

0

0

1.37

1.70

4.02

0.0015

ICA FPIDN-FOI32

− 2.6615

− 1.1254

0.4895

0

0

0

1.35

2.04

4.58

0.0211

FBI FPID(1 + PI)

− 1.8523

− 1.1092

− 0.4562

0.6561

0.5346

0.1819

3.43

4.21

6.32

0.1211

FBI FFOPID

− 6.1754

− 2.8125

− 1.1092

0

0

0

3.76

4.43

9.55

0.1654

FBI FPID

− 6.3923

− 3.7262

− 1.0611

0

0

0

5.66

6.75

9.56

0.2110

FBI FOPID

− 8.7664

− 8.0516

− 2.2863

0.5719

0

0

5.68

3.85

10.10

0.5214

FBI PID

− 14.1442

− 9.6933

− 2.9442

0.7296

4.2513

0.1551

7.36

8.30

13.81

0.8598

  1. Significant values are in [bold].