Table 2 Transient performance indices for Tie-line power in three areas for case study I.

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

Controller

\(\Delta {P_{12}}\)

\(\Delta {P_{23}}\)

\(\Delta {P_{31}}\)

ITAE

Ush × 10−3 (in p.u)

Osh × 10−3 (in p.u)

Ts (in sec)

Ush × 10−3 (in p.u)

Osh × 10−3 (in p.u)

Ts (in sec)

Ush × 10−3 (in p.u)

Osh × 10−3 (in p.u)

Ts (in sec)

PSO driven TID + IDN

−12.31

4.54

10.54

−2.807

6.423

10.02

−2.105

6.025

6.188

0.8345

SSA driven TID + IDN

−17.27

6.137

9.153

−4.01

9.036

14.02

−2.395

8.416

11.44

0.7724

ISSA driven TID + IDN

−18.15

4.926

12.71

−8.915

2.947

11.74

−2.314

8.47

8.776

0.4132

COA driven TID + IDN

−4.321

1.793

8.129

−0.56

0.358

3.72

−0.481

0.081

2.254

0.1233

COA driven TID

−14.84

4.075

7.912

−1.91

7.576

8.306

−2.425

7.554

11.27

0.6127

COA driven IDN

−21.36

8.767

10.86

−6.044

11.39

13.13

−3.163

10.21

12.04

0.8971