## 5 Conclusions  
This paper presented a generalized dynamic modelling approach of the mechanical system of a single-rotor wind turbine with counter-rotating \(DC\) generator, which integrates a mechanical speed increase on the power flow to the generator rotor \(GR\) and a direct connection of the generator stator \(GS\) to the wind rotor \(R\). The proposed modelling algorithm considered, besides the dynamic equations of the component rigid bodies, the linear mechanical characteristics of the electric generator and wind rotor.  
The analytical study and the numerical simulations of the considered case study in a functional scenario with three stages drew the following conclusions:  
* The proposed dynamic modelling algorithm, synthetically explained in Figure 2 and detailed in Section 3, is a novel and general approach for the class of wind turbines with a single wind rotor and a counter-rotating electric generator. It enabled us to derive the motion equation and obtain the dynamic response and operating point of the mechanical system in a number and a well-defined sequence of steps, regardless of the type of components of the wind system.
* The proposed modelling for the linearization of the active sector of the mechanical characteristic of the wind rotor simplified the analytical modelling of the dynamic response, without introducing significant errors in relation to their nonlinear model regardless of the value of wind speed \(v_{w}\): the obtained linear functions are characterized by higher values of the statistical parameter R-squared (R\({}^{2}>0.998\) for the case study of a 10 kW wind turbine, Figure 5b).
* The proposed analytical approach enabled us to identify the wind system dynamic behaviour at wind speed change both in a transient regime and a steady-state regime, in a particular case characterised by zero angular accelerations.
* The use of a counter-rotating generator in a wind turbine has the advantage of higher mechanical efficiency and kinematic ratio \(i_{G\_R}\) than in a wind turbine of identical power that contains a conventional electric generator (with fixed stator).
* The proposed diagrams depicted in Figures 6-8, i.e., the variation of the mechanical power parameters, enabled us to draw valuable conclusions for the functional optimization of the wind turbine.  
The authors aim to extend in future the simplified modelling of the mechanical characteristic of the wind rotor through a succession of linear functions covering the entire range of angular speed \(\omega_{R}\) variation, which will enable the complete identification of the dynamic behaviour in the starting phase. We also intend to validate the theoretical results by using specialised rigs experimentally.  
Conceptualization, M.N. and R.S.; methodology, M.N., R.S. and C.J.; software, M.N. and R.S.; validation, M.N., R.S., C.J. and I.N.; formal analysis, M.N., R.S., C.J. and I.N.; investigation, M.N., R.S., C.J. and I.N.; writing--original draft preparation, M.N., R.S., C.J. and I.N.; writing--review and editing, M.N., R.S., C.J. and I.N.; visualization, M.N., R.S., C.J. and I.N.; supervision, M.N. and C.J. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.