Table 8 Percentage improvements in \({O}_{sh}\) and \({U}_{sh}\) for Case A.2.

From: Frequency regulation in a hybrid renewable power grid: an effective strategy utilizing load frequency control and redox flow batteries

Controller structures

\({\Delta {\text{f}}}_{{\text{a}}}\)

\({\Delta {\text{f}}}_{{\text{b}}}\)

\({\Delta {\text{P}}}_{{\text{tie}}}\)

\({U}_{sh}\)

\({O}_{sh}\)

\({U}_{sh}\)

\({O}_{sh}\)

\({U}_{sh}\)

\({O}_{sh}\)

FO-(PD-PI)-optimized via MRFO3

26.2

26.39

36.36

37.56

40.65

42.44

Fuzzy-PID + (T \({{\varvec{I}}}^{{\varvec{\lambda}}}{{\varvec{D}}}^{{\varvec{\mu}}}\))-optimized via COA

88.03

88.93

75.57

79.93

71.18

69.46

  1. Optimal percentage values are highlighted in bold format.