Table 5 Optimized controller parameters, ST and JITAE results of Test-system-4
Algorithm | ISFS: PID [1] | DSA: FOPID [23] | DSA: FOPI–FOPD [23] | CGO: FOPID–FOPI |
|---|---|---|---|---|
Controller parameters | Area 1: Thermal | Area 1: Thermal | Area 1: Thermal | Area 1: Thermal |
\({K}_{P}=1.1539*{10}^{-12}\) | \({K}_{P}=0.0001\) | \({K}_{P1}=0.0316\) | \({K}_{P1}=1.9248\) | |
\({K}_{I}=0.0577\) | \({K}_{I}=0.1253\) | \({K}_{P2}=0.3346\) | \({K}_{P2}=1.4875\) | |
\({K}_{D}=0.1606\) | \({K}_{D}=0.1206\) | \({K}_{I}=0.3424\) | \({K}_{I1}=0.3518\) | |
Area 2: Thermal | \(\lambda =1.0000\) | \({K}_{D}=0.0271\) | \({K}_{I2}=\) 1e−12 | |
\({K}_{P}=1.1539*{10}^{-12}\) | \(\mu =0.5004\) | \(\lambda =1.0000\) | \({K}_{D}=1.8881\) | |
\({K}_{I}=0.0577\) | Area 2: Thermal | \(\mu =0.6354\) | \({\lambda }_{1}=1.0000\) | |
\({K}_{D}=0.1606\) | \({K}_{P}=0.0001\) | Area 2: Thermal | \({\lambda }_{2}=0.0930\) | |
Area 3: Hydro | \({K}_{I}=0.1253\) | \({K}_{P1}=0.0316\) | \(\mu =1.000\) | |
\({K}_{P}=1.1539*{10}^{-12}\) | \({K}_{D}=0.1206\) | \({K}_{P2}=0.3346\) | Area 2: Thermal | |
\({K}_{I}=0.0577\) | \(\lambda =1.0000\) | \({K}_{I}=0.3424\) | \({K}_{P1}=0.9875\) | |
\({K}_{D}=0.1606\) | \(\mu =0.5004\) | \({K}_{D}=0.0271\) | \({K}_{P2}=1.7e{-}7\) | |
Area 3: Hydro | \(\lambda =1.0000\) | \({K}_{I1}=0.2773\) | ||
\({K}_{P}=0.0001\) | \(\mu =0.6354\) | \({K}_{I2}=1.3016\) | ||
\({K}_{I}=0.0264\) | Area 3: Hydro | \({K}_{D}=1.9500\) | ||
\({K}_{D}=0.0350\) | \({K}_{P1}=0.0316\) | \({\lambda }_{1}=1.0000\) | ||
\(\lambda =1.0000\) | \({K}_{P2}=0.3346\) | \({\lambda }_{2}=1e{-}5\) | ||
\(\mu =0.7376\) | \({K}_{I}=0.3424\) | \(\mu =1.0000\) | ||
\({K}_{D}=0.0271\) | Area 3: Hydro | |||
\(\lambda =1.0000\) | \({K}_{P1}=0.0020\) | |||
\(\mu =0.6354\) | \({K}_{P2}=0.5422\) | |||
\({K}_{I1}=0.0305\) | ||||
\({K}_{I2}=0.4657\) | ||||
\({K}_{D}=0.1605\) | ||||
\({\lambda }_{1}=1.0000\) | ||||
\({\lambda }_{2}=0.1376\) | ||||
\(\mu =1.0000\) | ||||
Ts (s) (2% band) | ||||
\(\Delta {F}_{1}\) | 107.6 | 137.5 | 90.3 | 60.59 |
\(\Delta {F}_{2}\) | 107.6 | 137.5 | 90.3 | 60.59 |
\(\Delta {F}_{3}\) | 107.6 | 137.6 | 90.0 | 58.71 |
\(\Delta {P}_{tie12}\) | 65.28 | 109.1 | 68.7 | 77.43 |
\(\Delta {P}_{tie13}\) | 65.28 | 109.1 | 68.7 | 77.43 |
\(\Delta {P}_{tie23}\) | 94.83 | 130.9 | 74.7 | 62.47 |
\({J}_{ITAE}\) | n/a | 156.32 | 147.56 | 82.67 |