A novel methodology for analyzing modal dynamics of multi-rotor wind turbines

A multi-rotor wind turbine (MRWT) is accepted as a novel solution in reducing the rotor size without decreasing the energy harvesting capability compared to a single-rotor wind turbine (SRWT). However, there is no systematic methodology available for obtaining the modal properties of MRWTs. This paper presents a novel methodology and systematic modeling method of modal dynamics with comprehensive numerical simulations and analyses of MRWTs. In the methodology, Coleman transformation is employed to convert the nonlinear time-variant dynamics formulation of a MRWT into a set of linear time-invariant dynamic equations. Using HAWC2 and HAWCStab2 a method to establishing high-fidelity linear time-invariant dynamic models is presented. The structural modal dynamics of a tri-rotor wind turbine is systematically investigated by using modal analysis theory and interpreting the rotor speed-dependent dynamics visualized in a Campbell diagram. The investigation shows that rotor modes on a MRWT have similar behavior as for a SRWT and that low torsional stiffness of the rotor attachment point affects the first flapwise backward whirling modes by decreasing the corresponding natural frequencies. Moreover, the low torsional stiffness results in a delayed splitting of the asymmetric flapwise rotor modes. The simulations and analyses result verified the proposed dynamic modeling method. The major contributions in this paper provide the essential insights and guidance in the design of MRWTs but also for SRWT with slender towers.