## 4 Results and Discussions
Figure 7: The dynamic behaviour of the generator rotor \(GR\) and stator \(GS\) in relation to wind speed modification: (**a**) angular speed; (**b**) angular acceleration; (**c**) torque; and (**d**) mechanical power. the angular accelerations \(\varepsilon_{G}\) and \(\varepsilon_{R}\), respectively, was constant and equal in this case to \(i_{G\_R}=-10\). In the steady-state operating regime during 4 to 8 s, the electric generator was operated with a power of 10 kW (Figure 6d) at an angular speed = 153.4 rad/s (Figure 6d). The decrease in the wind speed to 6 m/s after 8 s of operation (Stage II) caused the change in the mechanical characteristic of the wind rotor (see Table 1) and also the crossing of a transient stage (of about 3 s) towards a new steady-state operation, Figure 6a-d. The significant decrease in the wind rotor power \(P_{R}\) to \(\sim\)2.67 kW and of the driving power of the electric generator \(P_{G}\) to \(\sim\)2.56 kW, i.e., a reduction of \(\sim\)25% of the rated power when the wind speed has dropped to only 75% of its nominal value, is noted in Figure 6d. This significant decrease in power is due mainly to the large decrease in torques (Figure 6c) and less of the angular speeds (Figure 6a). It is also worth noting the atypical evolution of the mechanical efficiency \(\eta\), which became supraunitary under the conditions of the definition from Equation (37): according to Figure 6d, the power of the wind rotor \(P_{R}\) decreased suddenly with the decrease in the wind speed, but the power \(P_{G}\) changed progressively due to the active effect of the kinetic energy, accumulated in the previous stage, which was added to the mechanical energy produced by the wind rotor. The efficiency \(\eta\) in a steady-state regime was higher than the efficiency of the speed increase (\(\eta_{2\_1}\)), i.e., 95.53% vs. 95.06%. In stage III of the numerical simulation scenario, the wind speed returned suddenly to the nominal value \(v_{w}=8\) m/s, after 15 s of operation. The variation in the functional parameters was relatively similar to the one from stage II, symmetrically to the horizontal axis. A sudden decrease in efficiency can be noted (Figure 6e) given that the power of the wind rotor was used at the beginning mainly to accelerate the mechanical system and less to increase the power \(P_{G}\). The evolution in time of the kinematic parameters and torques for the two mobile components of the electric generator, in the three stages of the simulation scenario, are presented in Figure 7. The generator rotor \(GR\) had an angular speed increased by \(i_{GR\_R}=-9\) and higher than speed of the stator \(GS\), implicitly (\(i_{GS\_R}=1\)), Figure 6a. The angular accelerations \(\varepsilon_{GR}\) and \(\varepsilon_{GS}\) (Figure 7b) had similar evolutions to those illustrated in Figure 6b, given that \(\varepsilon_{GS}=\varepsilon_{R}\) and \(\varepsilon_{GR}=\varepsilon_{G}+\varepsilon_{GS}\), which are derived from Equations (11) and (5), respectively. The symmetry of the torques curves for the two components of the electric generator (Figure 7c), characterised by the connection relationship from Equation (24), could also be observed. Since the torques \(T_{GS}\) and \(T_{GR}\) were equal in absolute value, the variation of the powers \(P_{GS}\) and \(P_{GR}\) depended significantly on the values of the angular speeds \(\omega_{GS}\) and \(\omega_{GR}\). As a result, the leading share of power was brought by the rotor \(GR\), characterised by an angular speed higher than the stator \(GS\) speed; at the same time, the rotor \(GR\) also had the most significant power drop with the decrease in wind speed in stage II, Figure 7d. The torque \(T_{R}\) generated by the wind rotor \(R\) was dynamically distributed on two branches to gear 2 (speed increase input) and the generator stator \(GS\), the relation between these torques being influenced by the system inertia in the acceleration/deceleration phases, according to the dynamic relations from Equations (10), (12), and (18).