# STABCON Résumé de rapport

Project ID:
ENK5-CT-2002-00627

Financé au titre de:
FP5-EESD

Pays:
Germany

## ARLIS - Aeroelastic Analysis of Rotating Linear Systems

ARLIS is the acronym for Aero-elastic analysis of Rotating Linear Systems. The program-system many years ago was specifically developed for the stability analysis of horizontal axis wind turbines. In the framework of the Project it was adopted to state-of-the-art computers and further refined. Applying Floquet's Theory it is capable to handle wind turbines in operation with one, two and more blades. It is, however, restricted to constant r.p.m. of the wind turbine.

For the dynamic analysis of the coupled rotor-tower-system the separated systems are described by finite element models, using any appropriate Finite Element Program System. The eigen modes are calculated for both systems separately, which are then reduced via condensation to small systems with only a few generalised degrees of freedom (eigen modes) which are assumed to be sufficient for the description of the dynamics and the stability of the system. The displacements are assumed to be small enough to work with linearised equations of motions. The validity of this assumption can be checked by the dynamic response of the system. In the case of large stationary displacements the stability analysis can be conducted around the equilibrium state of the deformed structure.

Tower and rotor are connected via one nodal point (coupling point) with 6 degrees of freedom. The drive train is modelled by a simple FE-model allowing a ``stiffness and/or damping coupling to ground' of the generator, thus allowing a modelling of synchronous and asynchronous generators. ARLIS takes over the matrices of the condensed systems and builds up the matrices of the linearised-coupled rotor-tower-system, including quasisteady aerodynamics. Since, in general, the matrices of the coupled system have periodic coefficients the stability analysis is carried out using Floquet's theory.

Furthermore, steady state and transient response of the coupled system can be calculated taking into account loads due to deadweight, wind shear, gusts, unbalance, etc. The generalised displacements are given back to the Finite Element System, where nodal point displacements, stresses, forces etc. are computed in the usual manner.

For the dynamic analysis of the coupled rotor-tower-system the separated systems are described by finite element models, using any appropriate Finite Element Program System. The eigen modes are calculated for both systems separately, which are then reduced via condensation to small systems with only a few generalised degrees of freedom (eigen modes) which are assumed to be sufficient for the description of the dynamics and the stability of the system. The displacements are assumed to be small enough to work with linearised equations of motions. The validity of this assumption can be checked by the dynamic response of the system. In the case of large stationary displacements the stability analysis can be conducted around the equilibrium state of the deformed structure.

Tower and rotor are connected via one nodal point (coupling point) with 6 degrees of freedom. The drive train is modelled by a simple FE-model allowing a ``stiffness and/or damping coupling to ground' of the generator, thus allowing a modelling of synchronous and asynchronous generators. ARLIS takes over the matrices of the condensed systems and builds up the matrices of the linearised-coupled rotor-tower-system, including quasisteady aerodynamics. Since, in general, the matrices of the coupled system have periodic coefficients the stability analysis is carried out using Floquet's theory.

Furthermore, steady state and transient response of the coupled system can be calculated taking into account loads due to deadweight, wind shear, gusts, unbalance, etc. The generalised displacements are given back to the Finite Element System, where nodal point displacements, stresses, forces etc. are computed in the usual manner.