Table 7 Upper and lower bounds of tuning parameters for LFC and AVR systems.

From: A hybrid fuzzy-PIDD² control strategy for coordinated LFC and AVR in renewable-integrated multi-area power systems

Tuning Parameter

LFC Bounds

AVR Bounds

Basis for Selection

Lower

Upper

Lower

Upper

\(\:{\text{K}}_{\text{P}}\)

0.1

100

0.1

2

Proportional range for system stability; prevents excessive actuation

\(\:{\text{K}}_{\text{I}}\)

0.1

2

0.1

2

Ensures integral action eliminates ESS without causing slow recovery.

\(\:{\text{K}}_{\text{D}1}\)

0.1

2

0.1

2

Avoids amplification of high-frequency noise while maintaining damping.

\(\:{\text{N}}_{1}\)

0.1

2

0.1

2

Provides adequate derivative filtering bandwidth

\(\:{\text{K}}_{\text{D}2}\)

0.1

10

0.1

2

Avoids amplification of high-frequency noise while maintaining damping.

\(\:{\text{N}}_{2}\)

0.1

100

0.1

100

Provides adequate derivative filtering bandwidth

\(\:{\text{K}}_{\text{E}}\)

0.01

2

-

-

Maintains normalized fuzzy I/O mapping for adaptive control stability.

\(\:{\text{K}}_{\text{C}\text{E}}\)

0.01

0.1

-

-

  1. where “–” indicates parameters not used in the AVR controller structure.