Table 7 Optimal gains for HAO-MGO, MGO and AO techniques for case-2.

From: Real time frequency and voltage stabilization in multi area hybrid power systems using hybrid MGOAO optimized PID and FOPID controllers

Method

Control parameters

Optimal gains

HAO-MGO-PID

\(\:{K}_{P1\_LFC}\)

2.5211

\(\:{K}_{I1\_LFC}\)

2.0122

\(\:{K}_{D1\_LFC}\)

1.5004

\(\:{K}_{P2\_LFC}\)

3.1221

\(\:{K}_{I2\_LFC}\)

2.0412

\(\:{K}_{D2\_LFC}\)

1.5101

\(\:{K}_{P1\_AVR}\)

2.0121

\(\:{K}_{I1\_AVR}\)

1.1021

\(\:{K}_{D1}\) AVR

0.5011

\(\:{K}_{P2\_AVR}\)

1.0003

\(\:{K}_{I2}\) AVR

1.1211

\(\:{K}_{D2\_AVR}\)

1.0101

MGO-PID

\(\:{K}_{P1\_LFC}\)

3.1105

\(\:{K}_{I1\_LFC}\)

2.2660

\(\:{K}_{D1\_LFC}\)

3.4696

\(\:{K}_{P2\_LFC}\)

4.9676

\(\:{K}_{I2\_LFC}\)

2.6716

\(\:{K}_{D2\_LFC}\)

2.9542

\(\:{K}_{P1}\) AVR

2.9035

\(\:{K}_{I1\_AVR}\)

1.1277

\(\:{K}_{D1\_AVR}\)

0.8010

\(\:{K}_{P2}AVR\)

2.8698

\(\:{K}_{I2}\) AVR

3.0104

\(\:{K}_{D2\_AVR}\)

2.4276

AO-PID

\(\:{K}_{P1\_LFC}\)

3.5026

\(\:{K}_{I1\_LFC}\)

2.7497

\(\:{K}_{D1\_LFC}\)

2.2074

\(\:{K}_{P2\_LFC}\)

4.0578

\(\:{K}_{I2\_LFC}\)

3.6587

\(\:{K}_{D2\_LFC}\)

3.0103

\(\:{K}_{P1}\) _AV R

2.0454

\(\:{K}_{I1\_AVR}\)

1.7424

\(\:{K}_{D1}\) _AV R

1.3719

\(\:{K}_{P2\_AVR}\)

2.8222

\(\:{K}_{I2}{\:}^{AVR}\)

2.0241

\(\:{K}_{D2\_AVR}\)

1.7585