Table 2 Transfer Function of components of Dz\(\mu\) with their values46.

From: Bayat-driven FOPID controller design for biogas-based microgrid with real-time validation

Distributed Generating Units (DGUs)

Component

Transfer Function

Parameters

Solar photovoltaic (SPV)47

\(TF_{PV}(s) = \frac{K_{PV}}{1 + sT_{PV}}\)

\(K_{PV}=1\), \(T_{PV}=1.8\)

Wind turbine generator (WTG)47

\(TF_{WTG}(s) = \frac{K_{WTG}}{1 + sT_{WTG}}\)

\(K_{WTG}=1\), \(T_{WTG}=1.5\)

Microturbine generator (MTG)47

\(TF_{MTG}(s) = \frac{K_{MTG}}{1 + sT_{MTG}}\)

\(K_{MTG}=1\), \(T_{MTG}=1.5\)

Biodiesel engine generator (BEG)23

\(TF_{BEG}(s) \approx \frac{K_{BEG}}{1 + sT_{BEG}}\)

\(K_{BEG}=1\), \(T_{BEG}=0.55\)

Biogas turbine generator (BTG)23

\(TF_{BTG}(s) \approx \frac{K_{BTG}}{1 + sT_{BTG}}\)

\(K_{BTG}=1\), \(T_{BTG}=1.48\)

Diesel engine generator (DEG)47

\(TF_{DEG}(s) = \frac{K_{DEG}}{1 + sT_{DEG}}\)

\(K_{DEG}=0.003\), \(T_{DEG}=2\)

Battery energy storage system (BESS)47

\(TF_{BESS}(s) = \frac{K_{BESS}}{1 + sT_{BESS}}\)

\(K_{BESS} = -0.003\), \(T_{BESS} = 0.1\)

Flywheel energy storage system (FESS)47

\(TF_{FESS}(s) = \frac{K_{FESS}}{1 + sT_{FESS}}\)

\(K_{FESS} = -0.01\), \(T_{FESS} = 0.1\)

Ultracapacitor (UC)48

\(TF_{UC}(s) = \frac{K_{UC}}{1 + sT_{UC}}\)

\(K_{UC} = -0.7\), \(T_{UC} = 0.9\)

Electric vehicle (EV)47

\(TF_{EV}(s) \approx \frac{K_{EV}}{1 + sT_{EV}}\)

\(K_{EV} = 1\), \(T_{EV} = 1\)

Inertia and damping47

\(TF_{Dz\mu G}(s) = \frac{1}{D + sM}\)

\(D = 0.03\), \(M = 0.4\)