Table 7 Time domain parameters for frequency variation in three areas for case study III.

From: A novel TID + IDN controller tuned with coatis optimization algorithm under deregulated hybrid power system

Contract violation

Controller

\(\Delta {F_1}\)

\(\Delta {F_2}\)

\(\Delta {F_3}\)

ITAE

Optimization techniques

Ush × 10−3 (Hz)

Osh × 10−3 (Hz)

Ts (sec)

Ush × 10−3 (Hz)

Osh × 10−3 (Hz)

Ts (sec)

Ush × 10−3 (Hz)

Osh × 10−3 (Hz)

Ts (sec)

(COA) driven Controllers

TID + IDN

−66.6

11.36

5.799

−11.2

1.41

6.808

−24.3

63.09

6.13

0.4822

TID

−142.4

49.61

12.68

62.45

24.39

7.22

−91.44

39.15

12.5

0.6132

IDN

−143.7

43.47

13.81

−63.89

23.41

12.92

−89.51

32.32

14.5

0.7123