Modal Analysis of a Quad-Rotor Wind Turbine

Unlike Single-Rotor wind turbines, stability analysis of Multi-Rotor wind turbines is still in its initial stages. This paper presents the modal analysis of a Quad-Rotor wind turbine and identifies the new modes or possible instability modes that are otherwise not present on a Single-Rotor wind turbine. Multi-Blade Coordinate transformation scheme is adapted to a Quad-Rotor wind turbine to write the system's equation of motion in fixed-reference frame followed by Eigenvalue analysis to determine the natural frequencies and mode shapes of the Quad-Rotor wind turbine. A Campbell diagram of the Quad-Rotor wind turbine is presented. Results indicate that the Quad-Rotor turbine is soft-soft to the first tower modes (fore-aft, side-side, and torsion). Furthermore, the modes with low natural frequency other than the tower modes are a combination of tower, boom, and blade modes. Therefore, due to the presence of blade modes, the modal frequency of these modes increases or decreases with increasing rotor speed due to centrifugal stiffening.