## 4 Simulation Results
### Tracking Performance  
To validate the effectiveness of the proposed control strategy, multiple traction-recovery cycles are conducted at a wind speed of 8 m/s. The cable length ranges from 100 m to 150 m, as illustrated in Figure 13a. Figure 13b,c illustrate the DC-link voltage and the grid currents throughout the cycles.  
In the traction phase, the machine rotor speed is controlled so that the tether's reeling-out speed is 1/3 of the wind speed component along the tether direction, which is its optimal value [21]. A fast reel-in speed is used in the recovery phase for more efficiency of the system.  
A comparative analysis of the three control methods reveals distinct performance characteristics. The IP controller, as observed in Figure 14, offers stable transitions between traction and recovery phases, with relatively small peaks in the controller output (q-axis current) as shown in Figure 15. However, its tracking performance in the traction phase is poor, exhibiting a noticeable delay because of the periodic component in speed reference.  
Figure 13: Simulation results of the grid-connected PKGS. (**a**) Tether length; (**b**) DC-link voltage; (**c**) Grid-phase currents.  
The conventional MFC, illustrated in Figure 16, demonstrates good tracking performance for periodically changing speeds during the traction phases. However, it faces challenges during transition phases, where the controller output becomes excessively high due to derivative action. As a result, rather than achieving true dynamic control, the system dynamics are constrained by the saturation limits [\(-\)10,10], as shown in Figure 17.  
Figure 16: Simulation result of the machine speed with the conventional MFC.  
Figure 14: Simulation result of the machine speed with the IP controller.  
Figure 15: Simulation result of q-axis current response when using the IP controller.  
In contrast, the PMFC, as shown in Figures 18 and 19, achieves excellent tracking performance for periodically changing speeds in the traction phase while simultaneously maintaining stable transition phases. Notably, the PMFC's output remains smooth with smaller peaks than the IP controller, indicating more efficient, controlled, and stable operation throughout.  
Figure 19: Simulation result of q-axis current response when using the PMFC.  
Figure 17: Simulation result of q-axis current response when using the conventional MFC.  
Figure 18: Simulation result of the machine speed with the PMFC.  
To evaluate the control strategy scalability to different PKGS sizes, we conducted simulations by varying the kite's area to 6 m\({}^{2}\) with a wind speed of 8 m/s. The results, shown in Figures 23 and 24, reveal that the control performance remained consistent across different kite sizes, with no controller retuning required when scaling the kite area. The system maintained stable operation despite the significant change in aerodynamic forces, while control signal magnitudes appropriately scaled with the change in kite size. This size-independent performance represents one of the core advantages of the MFC approach, and since the controller does not rely on system parameters or model-based calculations, it naturally adapts to changes in the physical system's scale.