Individual pitch control for 2-bladed wind turbines via multiblade multilag transformation

Two-bladed wind turbines have regained the attention of the community thanks to the advantages in manufacturing cost provided by the lower number of blades and the ease of implementation of effective passive systems for load reduction (ie, teetering pin). Considering both teetering and nonteetering architectures, the dynamics of 2-bladed turbines is different from that of 3-bladed machines especially in terms of how multiples of the rotor frequencies in blade signals are translated on the fixed system. Such characteristics have hampered the adoption of active control laws for load mitigation based on individual pitch control, extensively studied for 3-bladed turbines. A basic element for control development allowing to capture the essence of the relationship between signals on the blades and the fixed system on 2-bladed turbines-represented by the Coleman transformation for 3-bladed turbines-has not been identified yet. The present paper tries to fill the gap, presenting an extended transformation-called multiblade multilag-applicable to turbines with an arbitrary number of blades, providing a systematic way to link rotor signals to fixed system signals, thus allowing the application of control algorithms for individual pitch control developed for 3-bladed turbines to the 2-bladed case. The paper addresses the problem first at a theoretical level, and subsequently providing applicative results from simulations on virtual models of teetering and nonteetering 2-bladed turbines. The proposed transformation algorithm and control laws allow to effectively reduce some relevant loads and motions respectively in the nonteetering and teetering scenarios, through a cyclic pitch input.