## 2 Harvesting System
### Theoretical Principles of Mini Wind Harvester Operation
#### 3.2.1 Work Operation at Open Space Environment  
The parameter wind flow is obtained by multiplying harvester area with flow velocity. Finally, for \(P_{wind}\), \(P_{aero}\), \(C_{p}(\lambda,\theta)\), \(\lambda_{i}\) and \(\lambda\) parameters, calculation was performed from Equations (4)-(7), respectively. Table 3 and Figure 6 show the achieved results. In this case, the mechanical design seems to be unsuitable for this purpose. \(P_{wind}\) and \(P_{aero}\) are sometimes lower than achieved results on the test. Moreover, the electrical efficiency will be near zero as Table 3 shows. However, despite these results, it was decided to continue with the calculation [36] of the electric power harvested to verify whether or not the theory was valid for this system. After the harvester captures the wind kinetic energy, the rotor rotates at a specific angular velocity under the drive torque, as in Equation (8). \[T_{drive}=\frac{P_{aero}}{\omega}=\frac{\rho v_{1}^{3}AC_{p}(\lambda,\theta)}{2 \omega} \tag{8}\]  
The drive torque (\(T_{drive}\)) is proportional to the cube of the wind velocity, power coefficient and inversely proportional to the angular velocity of the rotor, \(\omega\). Moreover, when the harvester rotates at a low tip speed ratio, the ratio of \(C_{p}=\omega\) remained mostly constant. Therefore, the drive torque is expressed in Equation (8) and could be treated as a constant if the ambient wind speed remains constant. For this system, the values obtained from \(T_{drive}\) are shown in Table 4 and Figure 7. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\mathbf{C_{p}}\) Coefficient & \(\mathbf{c_{1}}\) & \(\mathbf{c_{2}}\) & \(\mathbf{c_{3}}\) & \(\mathbf{c_{4}}\) & \(\mathbf{c_{5}}\) & \(\mathbf{c_{6}}\) & \(\mathbf{c_{7}}\) & \(\mathbf{c_{8}}\) & \(\mathbf{c_{9}}\) \\ \hline CSMWT & 0.6 & 160 & 0.93 & 0 & 0 & 9.3 & 9.8 & 0.037 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Used Betz power coefficients for mathematical calculation of operation parameters. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\mathbf{\omega}\) (rpm) & \(\mathbf{\omega}\) (rad/s) & **Velocity (m/s)** & \(\mathbf{P_{wind}}\) (mW) & \(\mathbf{P_{aero}}\) (mW) & \(C_{p}(\lambda,\theta)\) & \(\lambda_{i}\) & \(\lambda\) & **Q (m3/s)** \\ \hline
9495 & 997 & 3 & 13.719 & 3.622 & 0.264 & 2.454 & 1.180 & 0.002 \\
14,271 & 1498 & 4 & 32.518 & 9.104 & 0.280 & 2.605 & 1.330 & 0.003 \\
19,344 & 2031 & 5 & 63.513 & 18  
The electro-mechanical coefficient, \(G\) (Volt/rad/s), is obtained with a linear relationship between the generated voltage, \(V\) (V), and the angular velocity, \(\omega\) (rad/s): Equation (9). \[G=\frac{V}{\omega} \tag{9}\]  
Electro-mechanical coefficient results for different air velocities (3-10 m/s) are presented in Table 5 and Figure 8.  
Then, harvested power is calculated at load with Equation (10):  
\[P_{e\_load}=\frac{G^{2}\omega^{2}R_{L}}{\left(R_{L}+R_{in}\right)^{2}} \tag{10}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Angular Velocity** & \(T_{drive}\) \\ (**rad/s**) & (**mW/rad/s**) \\ \hline
997 & 0.0036 \\
1498.51 & 0.0061 \\
2031.14 & 0.0089 \\
2526 & 0.0124 \\
2749 & 0.0180 \\
3219.99 & 0.0231 \\
3779.50 & 0.0281 \\
4159.75 & 0.0350 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical values of the torque vs. angular velocity. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Velocity (m/s)** & **Voltage (V)** & \(\omega\) **(rad/s)** & \(G\) **(Volt/rad/s)** \\ \hline
3 & 2.05 & 997 & 0.00205 \\
4 & 3.02 & 1498.51 & 0.00202 \\
5 & 4.17 & 2031.14 & 0.00205 \\
6 & 5.32 & 2526 & 0.00211 \\
7 & 5.98 & 2749 & 0.00218 \\
8 & 6.66 & 3219.99 & 0.00207 \\
9 & 7.57 & 3779.50 & 0.00200 \\
10 & 8.38 & 4159.75 & 0.00202 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Numerical values of the electro-mechanical coefficient for different air velocities. Figure 7: Torque vs. angular velocity.