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Table 2 Optimized controller parameters and ST and JITAE results of Test-system-1

From: Novel chaos game optimization tuned-fractional-order PID fractional-order PI controller for load–frequency control of interconnected power systems

Algorithm

ISFS: PID [1]

DSA: FOPID [23]

DSA: FOPI–FOPD [23]

CGO: FOPID–FOPI

Controller parameters

\({K}_{P}=1.6293\)

\({K}_{P}=2.0331\)

\({K}_{P1}=1.2485\)

\({K}_{P1}=3.0000\)

 

\({K}_{I}=2.0000\)

\({K}_{I}=2.9999\)

\({K}_{P2}=2.9999\)

\({K}_{P2}=0.9700\)

 

\({K}_{D}= 0.5882\)

\({K}_{D}=0.4670\)

\({K}_{I}=2.9998\)

\({K}_{I1}=2.975\)

  

\(\lambda =1.0007\)

\({K}_{D}=3.0000\)

\({K}_{I2}=3.0000\)

  

\(\mu =1.0517\)

\(\lambda =1.1007\)

\({K}_{D}=2.1678\)

   

\(\mu =0.6312\)

\({\lambda }_{1}=0.0298\)

    

\({\lambda }_{2}=0.9977\)

    

\(\mu =0.9078\)

ST (s) (2% band)

    

\(\Delta {F}_{1}\)

2.15

1.13

0.72

0.46

\(\Delta {F}_{2}\)

3.66

2.73

1.48

1.18

\(\Delta {P}_{tie12}\)

3.01

2.23

0.86

0.61

\({J}_{ITAE}\)

n/a

0.0778

0.0180

0.0091