## 2 Harvesting System
### Electro-Mechanical Equivalent Model of the Mini Wind Harvester or Reactor  
#### 3.3.1 Equivalent Model Description  
Figure 16 provides the mixed behavioral and structural-electric model of the mini wind harvester. The wind energy and the conversion of energy to mechanical and electrical is modeled through mathematical equations, voltage and controlled current sources and passive components. The basis of this equivalent circuit were taken from reference [36], and the values were adapted to the wind harvester presented in this work and the circuit to a three-phase system. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Ref**} & **Size** & **Voltage** & **Wind Velocity** & **Max Output** & **Cp** & **Power Density** & **Topology** \\  & **(mm)** & **(V)** & **(m/s)** & **Power (mW)** & **(\%)** & **(mW \(\times\) cm\({}^{2}\))** & **Topology** \\ \hline
[20] & \(10\,\upomega\) & 80 & 2.7 & 18.3 & - & 0.58 & Electrostatic \\
[19] & \(40\,\upomega\) & 450 & 10 & 1.8 & 0.24 & 0.143 & Electrostatic \\
[17] & \(161\times 250\) & 30 & 5.8 & 53 & - & 0.13 & Piezoelectric \\
[22] & \(30\times 12.5\) & 14 & 160.2 & 2.56 & - & 0.68 & Piezoelectric \\
[24] & \(70\times 20\) & 7.86 & 14 & 0.061 & - & 0.004 & Piezoelectric \\
[17] & \(490\times 20\) & 6 & 7 & 70 & 3.46 & 0.71 & Electromagnetic \\
[39] & \(26\,\upomega\) & 2.2 & 10 & 7 mW & 11 & 1.07 & Electromagnetic \\
[40] & \(42\,\upomega\) & 2.6 & 11.8 & 130 & - & 2.34 & Electromagnetic \\ This work & \(32\,\upomega\) & 2.45 & 10 & 333 & 28 & 10.32 & Electromagnetic \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Comparison of the performances of wind energy harvesters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Torque (\(\mu\)Nm)**} \\ \hline \multirow{2}{*}{**Load**} & \multicolumn{4}{c}{**Velocity (m/s)**} \\ \cline{2-5}  & **4** & **5** & **6** & **7** \\ \hline
1 & 8.26 & 9.27 & 14.55 & 16.37 \\
11 & 17.15 & 17.25 & 57.67 & 67.30 \\
27 & 25.41 & 39.10 & 55.37 & 62.23 \\
51 & 22.97 & 29.06 & 42.34 & 50.43 \\
100 & 13.26 & 18.25 & 27.83 & 31.93 \\
270 & 6.99 & 8.67 & 12.35 & 14.33 \\
510 & 4.28 & 5.39 & 6.85 & 7.74 \\
1000 & 2.23 & 2.83 & 3.74 & 4.10 \\
2000 & 1.20 & 1.46 & 1.86 & 2.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Measured values for torque representation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Power (mW)**} \\ \hline \multirow{2}{*}{**Velocity**} & \multicolumn{4}{c}{**Resistor Load (f)**} \\ \cline{2-5}  & **1** & **27** & **11** & **100** \\ \hline
3 & 1.61 & 15.28 & 7.77 & 1.87 \\
4 & 3.45 & 31.16 & 12.54 & 13.64 \\
5 & 6.72 & 55.49 & 16.93 & 26.91 \\
6 & 11.04 & 111.02 & 89.15 & 61.34 \\
7 & 13.68 & 160.72 & 129.94 & 79.25 \\
8 & 16.80 & 239.69 & 182.70 & 100.87 \\
9 & 21.21 & 272.54 & 246.13 & 134.79 \\
10 & 26.86 & 333.15 & 313.92 & 164.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Measured power at different conditions with the three-phase generator. \(I_{torque}\) is the equivalent electrical representation of the mechanical torque of the wind harvester, \(V_{electric1,2,3}\) and \(I_{gen1,2,3}\) are the electric voltage and current generated by each phase coil, and \(V_{out1,2,3}\) are the voltage produced by the coils but with the corresponding phase shift, \(0^{\circ}\), \(120^{\circ}\) and \(240^{\circ}\). The equivalent model presented is based on different equations and elements equivalent to the harvester work operation principles and the electro-mechanical characteristics of the system [37]. The following lines describe the three parts that constitute the circuit. The first part of the schematic includes the wind and mechanical elements. Wind power is characterized by the amplitude of the input sinusoidal current source. The drive torque (\(T^{*}_{drive}\)) is deduced as Equation (12) of [41].