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Table 2 Comparative performance of peak overshoots and settling times (for 2% tolerance band) with different objective function value for isolated power system (test system 1)

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

Techniques/objective function

Frequency deviation \(\Delta \omega\)

Terminal voltage deviation \(\left( {\Delta V_{t} } \right)\)

Maximum overshoot (OS) × 10−4 (p.u.)

Minimum undershoot (US) × 10−4 (p.u.)

Settling time (s) (TS) for 2% tolerance band

Maximum overshoot (OS) × 10−4 (p.u.)

Minimum undershoot (US) × 10−4(p.u.)

Settling time (s) (Ts) for 2% tolerance band

MFO PID/IAE

6.6059

− 33.1111

23.077

3.0245

− 0.6085

7.149

MFO PID/ITAE

2.7904

− 34.2661

21.838

3.3676

− 0.3439

8.287

MFO PID/ISE

13.1665

− 31.1161

38.794

2.5433

− 1.0643

7.154

MFO PID/ITSE

9.1126

− 32.2547

31.528

2.7048

− 0.7529

7.692

  1. Ttalics values are showing the best value in column wise