## 1 Introduction
developed in [29] a dynamic model for a multistage planetary gear transmission by using the lumped parameter method to obtain the load-sharing coefficients for each planet gear pair under variable input speed and internal excitation. Unlike the previously presented results that refer to gear transmissions used as speed increasers, ref. [30] proposes a new variant of a cycloidal planetary transmission for renewable energy systems and analyses its dynamic behaviour, the efficiency values being experimentally validated. A general approach to the steady-state efficiency analysis of speed increasers with both one or two inputs and one or two outputs is proposed in [31]. The authors concluded that the in-parallel or split-power transmissions used in wind turbines with either two counter-rotating rotors or a counter-rotating generator have higher efficiency than serial transmissions. Another approach in dynamic modelling is the use of controllers adapted for wind turbines with a double-fed induction generator, which allows the estimation in real time of dynamic behaviour compensating for the external disturbances action [32]. The optimal design of proportional-integral controllers integrated in on-grid permanent magnet synchronous generators from variable-speed wind turbines is addressed by [PERSON] et al. in [33] by proposing a transient search optimization algorithm. Aiming to improve the performance of the electric generators for wind turbines, a counter-rotating generator with permanent magnets for built environment applications is proposed and analysed in [34; 35; 36]; the counter-rotating generator is proved to have a higher efficiency than the conventional one, with a low starting torque, it is compact and scalable. The literature survey concludes that the dynamic behaviour is performed only for systems with one input and one output or two inputs and one output, i.e., wind turbines with a conventional electric generator. In the vast majority of the presented research, the wind rotor and generator have nonlinear models, which lead to a dynamic model with a high complexity. In addition, some onshore theoretical models consider the wind turbines operating under constant wind speed. Generally, the numerical simulations are performed on high-power wind systems using Matlab-Simulink. As a result, the authors did not identify in the literature relevant results regarding the generalized dynamic modellingof the mechanical system for the class of wind turbines with single wind rotor and a counter-rotating electric generator, which would enable obtaining, in a simpler way, the dynamic response under variable wind speed. The paper aims to cover the gap by proposing a novel algorithm for dynamic modelling of single-rotor wind systems that include a counter-rotating electric generator and a speed increase with one input (connection to the wind rotor) and two outputs (connections to the rotor and stator of the electric generator), meant also to be used in real very attracting low-power applications, e.g., in the built environment. The power generated by the wind rotor is branched to the generator rotor and stator, a solution that brings several advantages compared to the conventional wind turbines (with fixed stator): higher mechanical efficiencies, a more compact speed increase (with lower kinematic ratio), and a self-balancing electric generator in operation. The dynamic modelling is performed under variable wind conditions. It combines the classical equations associated with the rigid bodies with fixed-axis rotational motion (mechanical moments of inertia, kinematic transmission ratios, and the efficiency of the cylindrical gear set) with the linear equations associated with the mechanical characteristics for both the direct current (DC) generator and the wind rotor, respectively, on its quasilinear active working sector in operation. The linear equations of the wind rotor mechanical characteristic are expressed as functions of wind speed.