Table 11 Optimal gains for PID controller with BESS and without BESS for case-3.

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

Without BESS-PID

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

2.5976

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

2.1956

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

1.5675

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

3.2651

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

2.2101

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

1.5211

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

2.1013

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

1.0021

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

2.0012

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

1.1128

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

3.2141

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

3.0001

With BESS-PID

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

2.5

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

3.3288

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

1.6616

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

4.8968

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

2.1479

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

2.057

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

2.4565

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

2.4372

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

0.7944

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

1.3056

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

1.033

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

0.1.2597