Table 5 PID controller parameters value of a multi-area multi-unit power system (test system 2)
Controllers | Thermal | Hydro | AVR loop | ||||||
|---|---|---|---|---|---|---|---|---|---|
\(K_{P}\) | \(K_{I}\) | \(K_{D}\) | \(K_{P}\) | \(K_{I}\) | \(K_{D}\) | \(K_{P}\) | \(K_{I}\) | \(K_{D}\) | |
Area 1 | |||||||||
 ZN-tuned PID [39] | 0.9522 | 1.36 | 0.167 | 0.9522 | 1.36 | 0.167 | 1 | 0.25 | 0.28 |
 SA PID(ISE) [39] | 5.1 | 9.0999 | 4.1 | 5.0025 | 8.9003 | 4.0995 | 1 | 0.25 | 0.28 |
 MFO PID(ISE) | 9.9969 | 9.9914 | 0.9999 | 9.9101 | 0.0059 | 0.35566 | 0.9999 | 0.9989 | 0.9997 |
 MFO PID (ITAE) | 8.5057 | 9.9998 | 1.7339 | 9.9997 | 1.4207 | 0 | 0.9979 | 0.9994 | 0.2294 |
 MFO FOPID (ITAE) | 8.5137 | 9.9995 | 2.5477 | 9.9999 | 9.9998 | 8.7089 | 1 | 0.8732 | 0.2241 |
\(\lambda = 0. 9 9 9 9\)\(\mu = 0. 9 9 9 4\) | \(\lambda = 0. 5 9 2 5\)\(\mu = 0. 6 5 9 4\) | \(\lambda = 0. 9 9 9 6\)\(\mu = 0. 7 5 7 4\) | |||||||
Area 2 | |||||||||
 ZN-tuned PID [39] | 0.9522 | 1.36 | 0.167 | 0.9522 | 1.36 | 0.167 | 1 | 0.25 | 0.28 |
 SA PID(ISE) [39] | 5.0098 | 9.0725 | 3.922 | 4.9008 | 9.0994 | 4.087 | 1 | 0.25 | 0.28 |
 MFO PID(ISE) | 9.9995 | 9.9879 | 7.3843 | 9.9728 | 0 | 8.7954 | 0.9986 | 0.9995 | 0.9999 |
 MFO PID (ITAE) | 9.9999 | 9.9996 | 4.1483 | 9.9986 | 0.7939 | 6.6882 | 0.9998 | 0.9996 | 0.2499 |
 MFO FOPID (ITAE) | 9.3921 | 9.9926 | 6.4457 | 0.0001 | 9.9999 | 1.3576 | 0.2345 | 0.9999 | 0.9998 |
\(\lambda = 0. 9 9 9 3\)\(\mu = 0. 7 7 5 2\) | \(\lambda = 0. 1 0 9 7\)\(\mu = 0. 8 3 8 6\) | \(\lambda = 0. 9 9 9 9\)\(\mu = 0. 0 9 1 5\) | |||||||