Table 5 Frequency/Voltage deviation characteristics and PID gains under different step function (∆Pl).

From: Enhancement of PID controller performance for a combined LFC and AVR single- and two-area model using exponential distribution optimization technique

ITAE

Freq

Voltage

Md (p.u)

tp (sec.)

ts (sec.) ± 5%

Ess (p.u)

Mp (p.u)

tp (sec.)

ts (sec.) ± 2%

Ess (p.u)

EDO (∆Pl = 0.2)

− 6.115 × 10–3

0.6847

8.84

− 2.824 × 10–4

0.9998

0.7675

1.415

3 × 10–6

EDO (∆Pl = 0.3)

− 6.684 × 10–3

0.6847

8.85

− 3.309 × 10–4

0.9999

0.7674

1.415

− 7.27 × 10–5

EDO (∆Pl = 0.4)

− 7.265 × 10–3

0.7674

8.72

− 3.785 × 10–4

0.9999

0.7674

1.415

− 4.23 × 10–5

FA (∆Pl = 0.2)9

− 6.674 × 10–3

0.6874

8.73

− 2.798 × 10–4

1.0129

0.7705

1.422

− 1 × 10–4

FA (∆Pl = 0.3)9

− 7.273 × 10–3

0.6873

8.20

− 3.255 × 10–4

1.01294

0.7704

1.415

− 1.9 × 10–4

FA (∆Pl = 0.4)9

− 8.002 × 10–3

0.4940

8.17

− 3.723 × 10–4

1.01299

0.7704

1.422

− 1.8 × 10–4

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