## 4 Results and Discussions  
The numerical simulations of the dynamic model presented in Section 3, developed for the wind turbine with counter-rotating electric generator described in Section 2, aim to highlight the evolution in time of the mechanical power parameters (i.e., torque and angular speed) for input and output shafts, as well as the angular acceleration and the system mechanical efficiency, in the conditions of sudden changes of the wind speed. Thus, we considered a wind turbine with a rated power of 10 kW at a nominal wind speed of 8 m/s, characterised by the parameters from Table 1, in a operating scenario in which the wind turbine started under the action of a 8 m/s wind (stage I), after which the wind speed dropped sharply to 6 m/s after 8 s (stage II) and then returned to 8 m/s after 15 s (stage III). Since the linear model adopted for the mechanical characteristic of the wind rotor is valid only on the useful area of this characteristic (see Figure 5, zone C), in stage I the initial starting phase was ignored (which is not the object of this research) and the time of 0 s was chosen at the moment when the angular speed of the wind rotor reached the value corresponding to the maximum power \(max\)\(P_{R}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **Parameter** & **Value** & **Unit** \\ \hline Wind rotor & & & \\ \(v_{w}=8\) m/s & \(a_{R}\) & 111.16 & Nm/s \\  & \(b_{R}\) & 2388.2 & Nm \\ \(v_{w}=6\) m/s & \(a_{R}\) & 83.208 & Nm/s \\  & \(b_{R}\) & 1341 & Nm \\ Speed increase & & \(i_{1\_2}\) & \(-9\) & - \\  & \(i_{3\_2}\) & 2.25 & - \\  & \(i_{1\_3}\) & \(-4\) & - \\  & \(\eta_{2\_3}=\eta_{3\_1}\) & 0.975 & - \\  & \(\eta_{2\_1}\) & 0.9506 & - \\  & \(s_{3}\) & 3 & - \\ Electric generator & & \(a_{G}\) & 3 & Nm/s \\  & \(b_{G}\) & \(-395\) & Nm \\ Inertial parameters & & \(J_{1}\) & 2.5 & kgm\({}^{2}\) \\  & \(J_{2}\) & 75 & kgm\({}^{2}\) \\  & \(J_{3}\) & 0.25 & kgm\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of the 10 kW wind turbine with counter-rotating generator. The dynamic analytical model of the wind turbine was implemented in the Simulink module from Matlab by MathWorks. The obtained graphical results including the mechanical efficiency of the wind system are systematised in: Figure 6 for the input (wind rotor \(R\)) and output components (electric generator \(G\)), Figure 7 for the rotor \(GR\) and the stator \(GS\) of the electric generator, and the distributions of the torque and power of the wind rotor on the two branches towards the speed increase input and towards the stator \(GS\) are illustrated in Figure 8.  
Figure 6: The dynamic behaviour of the wind rotor \(R\) and electric generator \(G\) in relation to wind speed modification: (**a**) angular speed; (**b**) angular acceleration; (**c**) torque; (**d**) mechanical power; and (**e**) mechanical efficiency. In stage I of the considered operating scenario, the wind turbine passed through a transient period until entering the steady-state, i.e., characterised by constant values of the kinematic parameters and torques, Figure 6a-d. Typically, the beginning of the steady-state regime is identified when the angular accelerations become null, Figure 6b. In this transient stage, the system was accelerated, a significant part of the wind rotor power \(P_{R}\) was used to overcome the inertial resistance of the mechanical components and the accumulation of kinetic energy, implicitly. The electric generator started producing electricity only when the speed \(\omega_{G}\) became equal to the value \(b_{G}/a_{G}=131.67\) rad/s (see also Figure 4), shortly (about 0.1 s) after the entry of the wind rotor into the active area of its mechanical characteristic. At each operating time, the ratio between the angular speeds \(\omega_{G}\) and \(\omega_{R}\) and the ratio between  
Figure 8: The dynamic distribution on gear 2 and the generator stator \(GS\) of the: (**a**) torque and (**b**) mechanical power generated by the wind rotor \(R\).