Shaft speed ripples in wind turbines caused by tower shadow and wind shear

Wind turbines are an important source of renewable energy. Although the amount of wind turbine installations has known a considerable increase in recent years, technological improvements are still needed to increase their efficiency. An important subject is the presence of vibrations. For instance, ripples can be present in the torque and shaft speed, which can be caused by turbulence of the air flow, resonance or mechanical problems. Furthermore, tower shadow and wind shear are able to cause significant torque oscillations. In literature, a mathematical model of the torque oscillations has been presented for three-bladed horizontal-axis upwind turbines. However, it remains unclear what the impact is of these torque oscillations on the shaft speed. When ripples are present in the shaft speed, they affect the back-electromotive force and electrical power of the generator and could propagate further in the system. Therefore this study investigates whether this effect is large enough to have a considerable impact on the system. The turbine inertia and size are both relevant parameters in this research. However, it will be shown by mathematical proof that the relative amount of shaft speed ripples caused by tower shadow and wind shear is independent of the turbine size.