Table 3 Parametrized mathematical models of system components.

PV generator

\({\text{I}}_{{{\text{pv}}}} = {\text{ n}}_{{\text{p}}} \cdot {\text{I}}_{{{\text{ph}}}} - {\text{n}}_{{\text{s}}} \cdot {\text{I}}_{{{\text{sat}}}} \left( {{\text{e}}^{{\frac{{{\text{q}}\left( {{\text{V}}_{{{\text{pv}}}} + {\text{R}}_{{\text{s}}} \cdot {\text{I}}_{{{\text{pv}}}} } \right)}}{{{\text{n}}_{{\text{s}}} \cdot {\text{A}} \cdot {\text{K}} \cdot {\text{T}}_{{\text{j}}} }}}} - 1} \right) - {\text{I}}_{{{\text{sh}}}}\)

^32,58,61

P_PV

80 W_p

I_mpp

4.58 A

V_mpp

17.5 V

I_sc

4.95A

V_oc

21.9 V

α_sc

3.00 mA/°C

β_oc

− 150.00 V/°C

Wind turbine

\(\left\{ {\begin{array}{*{20}l} {{\text{P}}_{{{\text{Tb}}}} = \left( {1/2} \right) \cdot {\text{C}}_{{\text{p}}} \cdot {\uprho } \cdot {\uppi } \cdot {\text{R}}_{{{\text{Tb}}}}^{2} \cdot {\text{V}}_{{{\text{wind}}}}^{3} } \hfill \\ {{\text{P}}_{{{\text{Tb}} - {\text{opt}}}} = \left( {1/2} \right) \cdot {\text{C}}_{{{\text{pmax}}}} \left( {{\uplambda }_{{{\text{opt}}}} } \right) \cdot {\uprho } \cdot {\uppi } \cdot {\text{R}}_{{{\text{Tb}}}}^{2} \cdot {\text{V}}_{{{\text{wind}}}}^{3} } \hfill \\ \end{array} } \right.\)

\(\left\{ {\begin{array}{*{20}c} {{\text{T}}_{{{\text{Tb}}}} = \left( {1/2} \right).{\text{C}}_{{\text{p}}} .{\uprho }.{\uppi }.{\text{R}}_{{{\text{Tb}}}}^{5} .\frac{{{\upomega }_{{{\text{Tb}}}}^{2} }}{{{\uplambda }_{{}}^{3} }}} \\ {{\text{T}}_{{{\text{Tb}} - {\text{opt}}}} = \left( {1/2} \right).{\text{C}}_{{{\text{p}} - {\text{opt}}}} .{\uprho }.{\uppi }.{\text{R}}_{{{\text{Tb}}}}^{5} .\frac{{{\upomega }_{{{\text{Tb}}}}^{2} }}{{{\uplambda }_{{{\text{opt}}}}^{3} }}} \\ \end{array} } \right.\)

\({\text{J}} \cdot \left( {{\text{d}}\upomega _{{{\text{Tb}}}} /{\text{dt}}} \right) = {\text{T}}_{{{\text{Tb}}}} - {\text{T}}_{{{\text{em}}}} - {\text{f}} \cdot\upomega _{{{\text{Tb}}}}\)

^33,58

Blades

03

λ_opt

8.1

C_p

0.48

V_w-Rated

12.5 m/s

V_w-cut-in

3.4 m/s

R_Tb

1.05 m

PMSG

\(\left\{ {\begin{array}{*{20}c} {{\text{V}}_{{{\text{sd}}}} = {\text{R}}_{{{\text{st}}}} {\text{I}}_{{{\text{sd}}}} + {\text{L}}_{{\text{d}}} \left( {\frac{{{\text{dI}}_{{{\text{sd}}}} }}{{{\text{dt}}}}} \right) - {\text{L}}_{{\text{q}}} {\omega I}_{{{\text{sq}}}} } \\ {{\text{V}}_{{{\text{sq}}}} = {\text{R}}_{{{\text{st}}}} {\text{I}}_{{{\text{sq}}}} + {\text{L}}_{{\text{q}}} \left( {{\text{dI}}_{{{\text{sq}}}} /{\text{dt}}} \right) + {\text{L}}_{{\text{d}}} {\omega I}_{{{\text{sd}}}} + {\Phi }_{{\text{f}}} {\upomega }} \\ {{\upomega } = {\text{P}}\Omega } \\ \end{array} } \right.\)

\({\text{T}}_{{{\text{em}}}} = \left( {3/2} \right)\left[ {{\Phi }_{{\text{f}}} .{\text{I}}_{{{\text{sq}}}} + \left( {{\text{L}}_{{\text{d}}} - {\text{L}}_{{\text{q}}} } \right).{\text{I}}_{{{\text{sd}}}} .{\text{I}}_{{{\text{sq}}}} } \right]\)

^58,61

P_N

900 W

\({\text{R}}_{{\text{S}}}\)

0.49 Ω

\({\text{L}}_{{\text{S}}}\)

0.0016 H

P

5

\({\Phi }_{{\text{f}}}\)

0.148 Wb

R_Tb

1.05 m

J

0.016 kg/m²

Batteries

\(\left\{ {\begin{array}{*{20}c} {{\text{V}}_{{{\text{Batt}}}} = {\text{E}}_{0} - {\text{R}}_{{{\text{Batt}}}} .{\text{I}}_{{{\text{Batt}}}} - {\text{k}}.\smallint \left( {\frac{{{\text{I}}_{{{\text{Batt}}}} }}{{\text{Q}}}} \right).{\text{dt}}} \\ {{\text{SOC}} = 1 - \frac{{{\text{I}}_{{{\text{Batt}}}} .{\text{t}}}}{{{\text{C}}_{{{\text{Batt}}}} }}} \\ \end{array} } \right.\)

^37,61

V_Batt

12 V

C_Batt

100 Ah

R_Batt

0.795 Ω

X_Batt

0.07 Ω

C_Batt

44.96 mF

Supercapacities

\(\left\{ {\begin{array}{*{20}c} {{\text{U}}_{{{\text{sc}}}} = {\text{N}}_{{{\text{sc}} - {\text{s}}}} .{\text{V}}_{{{\text{sc}}}} = {\text{N}}_{{{\text{sc}} - {\text{s}}}} .\left( {{\text{V}}_{1} + {\text{R}}_{1} .{\text{I}}_{{{\text{sc}}}} } \right)} \\ { = {\text{N}}_{{{\text{sc}} - {\text{s}}}} .\left( {{\text{V}}_{1} + {\text{R}}_{1} .\frac{{{\text{i}}_{{{\text{sc}}}} }}{{{\text{N}}_{{{\text{sc}} - {\text{p}}}} }}} \right)} \\ \end{array} } \right.\)

\({\text{V}}_{2} = \frac{1}{{{\text{C}}_{2} }}\smallint {\text{i}}_{2} \left( {\text{t}} \right).{\text{dt}}\frac{1}{{{\text{C}}_{2} }}\smallint \frac{1}{{{\text{R}}_{2} }}\left( {{\text{v}}_{1} - {\text{v}}_{2} } \right).{\text{dt}}\)

\({\text{Q}}_{2} = \smallint {\text{i}}_{2} \left( {\text{t}} \right).{\text{dt}}\)

\({\text{i}}_{1} = {\text{i}}_{{{\text{sc}}}} - {\text{i}}_{2}\)

^60,61

C_N

165 F

ESR_DC

60 m Ω

IR_DC

100A

V_N

48 V

E_sc

53 Wh

V_max

51 V

I_max

1900 A

V_series

750 V

C_cells

3000 F

E_sc-cell

3.0 Wh

N_cells

18