Modal Analysis of a Quad-Rotor Wind Turbine

Abstract

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.

Wake steering of multirotor wind turbines

“…In tackling the problems associated with rotor upscaling, a promising solution is that of multirotor turbines. This concept involves installing a number of smaller rotors on a single support structure, rather than just one large rotor 30‐33 . Primarily, this alleviates the growing expense of rotor manufacture since the total material volume associated with the smaller rotor components is less, leading to lower production costs.…”

Aeroelastic load analysis of a co‐rotating quad‐rotor wind turbine

“…While there is a larger variation in the FA boom tip displacement (compared to the UD tip deflection), the design driver in terms of boom stiffness is determined by the UD boom tip displacement, which is orders of magnitude greater than FA boom tip displacement (see Figure 6E). Looking closely at Figure 6E, the spike in boom UD displacement (at 7 m/s for top and 9 m/s for bottom rotors) is caused by dynamic excitation close to boom resonance initiated by 3p rotor frequencies as shown in the Campbell diagram of the quad‐rotor wind turbine 23 . Therefore, it is necessary to consider the resonance of the boom (excitation of the boom natural frequency by 3p rotor frequency) in determining the boom properties.…”

“…Looking closely at Figure 6E, the spike in boom UD displacement (at 7 m/s for top and 9 m/s for bottom rotors) is caused by dynamic excitation close to boom resonance initiated by 3p rotor frequencies as shown in the Campbell diagram of the quad-rotor wind turbine. 23 Therefore, it is necessary to consider the resonance of the boom (excitation of the boom natural frequency by 3p rotor frequency) in determining the boom properties. An alternative design for the booms to carry the same tip mass without drooping (large UD boom tip deflection) could be to place the booms in a shallow V-shape configuration and attach a cable between the booms and the tower.…”

Aeroelastic Stability Analysis of a Quad-Rotor Wind Turbine

“…(ii) direct application of Floquet theory [7,8,9]. This paper builds on the previous work [12] and presents a method for stability analysis of quad-rotor wind turbine. The non-linear model of a 6MW quad-rotor wind turbine is linearized around a quasi-steady point; followed by MBC transformation of the LTP system yielding LTI model.…”

“…Conversely, few modal analyses of multi-rotor wind turbines are available; among the few, [10] presents a method to analyse the modal dynamics of multi-rotor wind turbines and demonstrates the capability of the method on a three-rotor configuration supported on a single tower; the same authors present a follow up work [11] where the aerodynamic loads are considered in the stability analysis of a tri-rotor wind turbine. Furthermore, [12] presents a modal analysis of a quad-rotor wind turbine. The published work so far on Eigen analyses of multi-rotor wind turbines focuses mainly on evaluating the natural frequency and the associated mode shapes.…”