C I R E D 18 th International Conference on Electricity Distribution Turin, 6-9 June 2005 ENTIRE WIND-TO-POWER REPRESENTATION OF A WIND TURBINE UNIT IN ELECTRICAL POWER SYSTEM STUDIES Stephan GEERTS † , Joris SOENS*, Johan DRIESEN*, Ronnie BELMANS*, Charles HIRSCH † † Department of Fluid Mechanics, Vrije Universiteit Brussel Belgium stephan.geerts@vub.ac.be *Electrotechnical Department ESAT – ELECTA, K.U.Leuven Belgium joris.soens@esat.kuleuven.ac.be INTRODUCTION In studying the impact and interaction of wind power systems connected to an electrical network, often a detailed electrical model is used, completed with a simplified turbine representation to provide the input torque. On the other hand, in studies on the mechanical loading of the wind turbine system, the electrical power components are represented in limited manner, in fact ignoring interactions due to dynamic phenomena in the grid. To be able to perform truly dynamic studies, an entire wind-to-power representation is required for a wind turbine system. In this paper, a dynamical model of a wind turbine (WT model) extended with a fourth-order state-space model of an induction generator is compared with a measurements on a 600 kW wind turbine. In a second part of this paper, the entire wind-to-power transfer function is simplified to a first or second-order transfer function. WIND TURBINE MODELLING The working principle of a wind turbine encompasses two conversion processes, which are carried out by its main components: the rotor, which extracts kinetic energy from the wind and converts it into a shaft torque, and the generator, which converts this torque into electricity. Other components, such as gearboxes, controllers etc only facilitate the functioning of the principle components. To simulate the various impacts of wind power system, simulation models for each of the above simulation approaches must be developed. Therefore, the simulation model is divided in different subsystems, namely an aerodynamic, a mechanical, an electrical and a controller model. Not only a thorough understanding of the various wind turbine types and their subsystems is necessary, but also the assumptions on which these simulation approaches are based. In the next sections, the subsystems of the various wind turbines concepts will be discussed. AERODYNAMIC MODELLING To determine the structural response of wind turbines to dynamic excitation, a dynamical model of a wind turbine, based on a Lagrange approach of three degrees of freedom for each subcomponent (tower and three blades) has been developed, to calculate the response of the turbine to prescribed wind conditions ([1], [2] and [3]). To derive the equations of motion, the relative velocity of an arbitrary point of the turbine has to be calculated. A series of translations and rotations were calculated that relate the inertial frame attached to the tower to a rotating frame at a point of the blade. From these coordinate systems all matrices and forces may be determined in straightforward manner. The equations of motion are then expressed in terms of the generalized coordinates from the subcomponents. The Lagrange principle is used to determine the equations of motion of the couple rotor-tower system, namely: i i i i i Q h F h U h T h T dt d = ∂ ∂ + ∂ ∂ + ∂ ∂ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ (1) where T and U are respectively the kinetic and potential energy of the entire system. h i are the generalized coordinates. F is the dissipation function. The generalized forces are Q i . The equation provides a set of n equations where n is the number of independent generalized coordinates. To obtain the kinetic and potential energy and the damping terms, the velocity of an arbitrary point of the blade has to be calculated. This velocity can be expressed in the local frame, after lengthy algebraic manipulations. From this equation the energy terms of the blades may be calculated. With insertion of an expression for the blade displacements in the model, the energy terms may then be expressed into the generalized coordinates. Applying the Lagrange equations finally leads to the equations of motion. The equations of motion result in a second-degree non-linear system of differential equations, in terms of generalized coordinates. The equation of motion are respectively (2): [ ] [ ] [ ] [ ] ( ) [ ] [ ] [ ] [ ] [ ] ( ) ( ) Q y K K K K K y C C C y M a c p g s g a s = + + + Ω + + Ω + Ω + + . . . 2 . .. (2) where [M] is the structural mass matrix, [C a ], [C s ] and [C g ] are aerodynamic, structural and gyroscopic damping matrices, [K s ], [K g ], [K p ], [K c ] and [K a ] are respectively