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Table 3 Controller parameters, settling times (for 2% tolerance band) and ITAE value (for \(t_{\text{sim}} = 60\) s) for test system 1

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

Optimization techniquesPSO PIDDE PIDGWO PIDMFO PIDMFO 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.)5.67023.56352.79352.79042.3417
 Minimum undershoot (US) × 10−4 (p.u.)− 34.3803− 34.4585− 34.2913− 34.2661− 30.8683
 Settling time (s) (Ts)23.41323.0221.84321.83817.006
Terminal voltage deviation (ΔVt)
 Maximum overshoot (OS) × 10−4 (p.u.)3.09912.88513.38713.36763.7541
 Minimum undershoot (US) × 10−4 (p.u.)− 0.5106− 0.3006− 0.3432− 0.3439− 0.4237
 Settling time (s) (Ts)7.9979.0018.3148.2876.543
ITAE0.31590.2920.27140.2710.1869