Reduced order analytical modelling of micro wind turbine rotordynamics with tower shadow effects

Micro scale wind turbines (μWTs) in the order of 10 kW or less, suffer high vibration levels compared to larger ones. This can be attributed to the fact that they rotate at higher rotational speeds. For simplicity, blades are directly attached to a permanent magnet generator (PMG) of an outer rotor type with no need to install a gearbox. Also due to their small size, a tail vane represents a cost-effective solution for aligning the turbine with the wind direction. Those tail vanes generate significant yaw rates as a consequence of the unpredictable variations in wind direction. High yaw rates, along with increased rotational speeds, generate considerable gyroscopic loads. Therefore, μWTs involve a unique dynamic loading condition. Considering that the existing software packages are primarily designed for large wind turbines, a thorough investigation into the dynamics of μWTs is essential. In this study, we address the peculiarity of dynamics of μWTs using a simple mathematical model that helps in providing better dynamical insights than numerical calculations. Using the mathematical model, a parametric study is conducted involving two parameters: the generator's bearing span and the position of the rotor's centre of gravity (CG) along the rotor axis. The parametric study revealed that increasing the bearing span yields a decrease in vibrations. Also, shifting the centre of gravity of the rotor towards the generator's rear bearing reduces vibrations across all considered degrees of freedom, except for the rotor's vertical vibrations and pitching, which achieve a minimum value. An optimal placement of the centre of gravity is calculated and used afterwards to improve the design of an existing μWT. A case study highlights this improvement in terms of root mean square vibrations. The presented model can thereby help designers to build μWTs with better performance and longer lifespan offering a better understanding of the dynamical effects of design parameters.