Table 3 Controller parameters, settling times (for 2% tolerance band) and ITAE value (for \(t_{\text{sim}} = 60\) s) for test system 1
Optimization techniques | PSO PID | DE PID | GWO PID | MFO PID | MFO FOPID |
|---|---|---|---|---|---|
Controller parameters | |||||
 LFC loop | \(K_{P} = 1. 8 0 4 8\) | \(K_{P} = 1. 8 5 3 7\) | \(K_{P} = 1.9975\) | \(K_{P} = 1. 9 9 9 6\) | \(K_{P} = 1. 9 9 9 8\) |
\(K_{I} = 0.1257\) | \(K_{I} = 0. 0 1 6 6\) | \(K_{I} = 0.0005\) | \(K_{I} = 0. 0 0 1 2\) | \(K_{I} = 0. 2 4 6 7\) | |
\(K_{D} = 1.376\) | \(K_{D} = 1. 6 4 9 3\) | \(K_{D} = 1.7869\) | \(K_{D} = 1. 7 9 4 7\) | \(K_{D} = 1. 9 9 9 9\) \(\lambda = 0. 9 9 9 7\),\(\mu = 0. 0 2 7 4\) | |
 AVR loop | \(K_{P} = 1. 0 6 7 5\) | \(K_{P} = 1. 5 3 4 7\) | \(K_{P} = 0. 3 9 6 7\) | \(K_{P} = 0. 3 9 5 9\) | \(K_{P} = 0. 1 3 1 5\) |
\(K_{I} = 1. 9 9 9 8\) | \(K_{I} = 1. 9 9 4 3\) | \(K_{I} = 1. 9 8 8 6\) | \(K_{I} = 1. 9 9 9 8\) | \(K_{I} = 1. 9 9 9 8\) | |
\(K_{D} = 0. 0 2 9 2\) | \(K_{D} = 0. 4 4 5 5 3\) | \(K_{D} = 0. 5 4 4 9\) | \(K_{D} = 0. 5 4 6 1\) | \(K_{D} = 1. 9 9 9 7\) \(\lambda = 0. 9 9 9 9\),\(\mu = 0. 8 5 6 5\) | |
Frequency deviation Δω | |||||
 Maximum overshoot (OS) × 10−4 (p.u.) | 5.6702 | 3.5635 | 2.7935 | 2.7904 | 2.3417 |
 Minimum undershoot (US) × 10−4 (p.u.) | − 34.3803 | − 34.4585 | − 34.2913 | − 34.2661 | − 30.8683 |
 Settling time (s) (Ts) | 23.413 | 23.02 | 21.843 | 21.838 | 17.006 |
Terminal voltage deviation (ΔVt) | |||||
 Maximum overshoot (OS) × 10−4 (p.u.) | 3.0991 | 2.8851 | 3.3871 | 3.3676 | 3.7541 |
 Minimum undershoot (US) × 10−4 (p.u.) | − 0.5106 | − 0.3006 | − 0.3432 | − 0.3439 | − 0.4237 |
 Settling time (s) (Ts) | 7.997 | 9.001 | 8.314 | 8.287 | 6.543 |
ITAE | 0.3159 | 0.292 | 0.2714 | 0.271 | 0.1869 |