# A Comparative Performance Analysis of Four Wind Turbines with Counter-Rotating Electric Generators
## 4 Numerical Simulations and Discussions
### Power Flow  
In all four cases, the speed increase contains a branched circuit of mechanical power, and the direction of the power flow in each branch depends on the \(k_{t}\) and \(k_{\omega}\) values; moreover, the three-rotor version (Case A) allows obtaining the other three cases by appropriate customizations: Case B (\(\omega_{R2}=\omega_{9}=\omega_{H_{1}}=0\)), Case C (\(T_{R3}=T_{8}=0\)) and Case D (\(\omega_{R2}=\omega_{9}=\omega_{H_{1}}=0\) and \(T_{R3}=T_{8}=0\)). Case A  
Figure 6: Variations of the planetary transmission efficiency, depending on \(k_{t}\) (Case A). Six distinct simulation variants, defined by the distinct combinations of the \(k_{t}\) and \(k_{\omega}\) values, are addressed in Case A (see Figure 2a). The numerical results on the power flow are depicted in Figure 7, and the values of certain representative parameters are shown in Table 5. Based on the obtained data, the following aspects can be highlighted:  
* The secondary rotors \(R2\) and \(R3\) influence each other when the pitch angle changes, their powers depending on both ratios \(k_{\omega}\) (adjustment for \(R2\)) and \(k_{t}\) (adjustment for \(R3\)). * Ratio \(k_{t}\) significantly influences both the power values and the directions of the power flows as follows:
* \(k_{t}=0\): that is, Case C, in which the energetic contribution of rotor \(R3\) is zero, such as \(T_{R3}=0\);
* \(0<k_{t}<1\) (red lines, Figure 7a,b): the powers of rotors \(R1\), \(R2\) and \(R3\) flow branched and convergent towards the rotor and stator of the generator;
* \(k_{t}=1\) (blue lines, Figure 7a,b): in this limit situation (when \(T_{R2}=0\) and \(P_{R2}=0\), see Tables 2 and 3), rotor \(R2\) and the planetary gear set I are idling, and the power of rotor \(R1\) flows through gear set II to \(GR\), while the power of the rotor \(R3\) branches into two flows: one directly to GS and another, through gear set II, to \(GR\). It can be noticed that both the mechanical power of the generator and the transmission efficiency are higher compared with the previous situation (\(0<k_{t}<1\));
* The power \(|P_{C}|\) received by the electric generator increases with the increase of the ratio \(k_{t}\). - The power supply to the mobile stator \(GS\) increases with the increase of ratio \(k_{\omega}\) (i.e., from 10% \(P_{G}\) for \(k_{\omega}=0\) to 13.3% \(P_{G}\) for \(k_{\omega}=1\)). - The amplification ratio \(i_{a}\) does not depend on ratio \(k_{t}\) and increases with the increase of ratio \(k_{\omega}\) (i.e., from 15 for \(k_{\omega}=0\) to 30 for \(k_{\omega}=1\), Table 5). * Case B  Case B  Case B is derived from Case A by engaging clutch C1 (i.e., C1 = 1) and disengaging clutch C2 (i.e., C2 = 0 => \(T_{R2}=0\)), accompanied by rotor \(R2\) blocking (\(\omega_{R2}=0\) = \(>k_{\omega}=0\)). Comparing the best scenarios in Case A (\(k_{\omega}=1\) and \(k_{t}=1\)) and in Case B (\(k_{t}=1\), see Table 5 and Figure 8): the rotor \(R3\) power decreases about 2.66 times, the total input power and the output power decrease two times and the power input of the stator \(GS\) decreases to 10% of \(P_{G}\). * Case C  Case C  Case C (Figure 2c) is obtained from Case A by eliminating rotor \(R3\) (\(T_{R3}=0\Rightarrow k_{t}=0\)) and the flows related to it; according to Figure 9, the flow corresponding to the value \(k_{\omega}=0\) is missing, because in this situation, Case C turns into Case D.  
Figure 8: Reduced power flows of the 1-DOF and \(L=4\) system (Case B) for: \(k_{t}=0.5\) (red), 1 (blue) and 1.5 (green).