Dynamic Modelling of Wind Turbines

Pedro A. Galvani

I. Modelling

A. Aerodynamic model

1. Local loads definition

The angle of attack is given by equation (1) = (1)

Where is the local pitch angle, which can be calculated by = b +, where b is the blade pitch angle,and is the twist angle. Furthermore, can be calculated by:

tan() =(1 a)V0(1 + a)r

(2)

Where a is the axial induction factor, a is the tangential induction factor, V0 is the wind speed, r is theradius, and is the angular velocity of the rotor. The induction factors were initialized as zero.

Then cn and ct were calculated by:

Cn = Cl cos() + Cd sin() (3)

Ct = Cl sin() Cd cos() (4)From figure 1, the following relations can be derived

Vrel sin() = (1 a)V0 (5)

Vrel cos() = (1 + a)r (6)

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American Institute of Aeronautics and Astronautics

Figure 1. Velocities on the rotor plane

Figure 2. Local loads on a blade.

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American Institute of Aeronautics and Astronautics