Modeling

In this section the main modeling options are discussed. We will start with the wind module library.

I.2.1 Wind module library

DAWIDUM's wind module consists of two submodules, viz.: "deterministic" and "stochastic" as illustrated in Fig. I.3. The deterministic submodule allows the following undisturbed wind inputs to be specified: a uniform wind field (i.e. Vw is constant both in space and time), a sequence of upward and downward stepwise changes in the wind velocity, and the undisturbed wind velocity can be read from a user specified WindData.mat file.

[^Library: WTML/Wind

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[^Library: WTML/Wind

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Figure I.3: Wind module library consisting of two submodules: deterministic and stochastic. The stochastic submodule is able to read the output generated by the wind field generator SWING-4.

The stochastic submodule is able to read the output generated by SWING-4. This stochastic wind generator calculates the Fourier coefficients (for each radial position and for each time step specified in the input file) expressed in the harmonics of the azimuth. The interested reader is referred to Bierbooms [11, 13] for detailed information about SWING-4.

The SWING-4 interface converts the aforementioned coefficients during simulation into the required stochastic wind velocity components U (longitudinal) and V (tangential) for each rotor blade Nb and blade section (or blade element) Ns. The user must ensure that the radial positions for which the SWING-4 output is generated are identical to the blade element positions at which the aerodynamic forces are to be calculated. In addition, the azimuth ^ of blade 1 (pointing upwards at t = 0) needs to be available during simulation. The interface is coded as an M-File S-Function named Swing consisting of the following two files: SwingInit.m, and SwingCalc.m.

The file SwingInit loads the output of a SWING-4 simulation and initializes the data to be used in SwingCalc. In the latter file the actual calculation takes place. The S-Function is shown in Fig. I.4. The number of rotor blade is specified in the "S-Function parameters" field.

The size of the output vector is 2 NbNs, with Nb number of rotor blades and Ns number of blade elements. It is checked in SwingCalc if the specified simulation stop time of DAWIDUM exceeds that of the SWING-4 output (and if that is the case an error is displayed). It is preferable that the step size of the integration routine used for time-domain simulation equals that of the one used to generate the SWING output, although a linear interpolation scheme is included in SwingCalc.

I[^swing4

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File Edit View Simulation Format Tools Help

D ËBI ft H V <S> ► ■ (Normal

Psi

n

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Figure I.4: SWING-4 interface in DAWIDUM. Input: and outputs: U = [U1(1 : Ns), ■ ■ ■ ,UNb (1 : Ns )] and V = [Vi(1 : Ns), ■ ■ ■ ,VNb (1 : Ns )] for each blade element Ns and rotor blade Nb.

I.2.2 Aerodynamic module library

The aerodynamic module is coded as an M-File S-Function named BEM. The S-Function is shown in Fig. I.5 and is built up out of the following two files: AeroInit.m, and AeroCalc.m. The file AeroInit provides an initial guess for both the axial and tangential induction factor, and loads the specified turbulent wake state model. This model is specified in the "S-Function parameters" field. In AeroCalc.m deterministic effects as wind shear, tower shadow and the ten-minute average wind speed at hub height are added to the zero-mean stochastic components of SWING-4 before the aerodynamic forces are computed.

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File Edit View Simulation Format Tools Help |

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Vpb,Vtb]

Vpb,Vtb]

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Figure I.5: Aerodynamic module in DAWIDUM. Inputs: [Vpb,Vtb]: blade element velocities x, and [U, V]: SWING-4 output. Outputs: [Fp, Ft] = [FPj1(1 : Ns) FM(1 : Ns) • • • Fp,Nb (1 : Ns) Ft,Nb (1 : Ns)] the aerodynamic forces Faero with Ns the number of blade elements and Nb the number of rotor blades).

I.2.3 Mechanical module library

The mechanical module library contains four submodules describing the structural dynamics at different level of complexity: Rotor blade, Rotor (3-bladed), Tower (plus foundation), and Wind turbine (3-bladed) (see Fig. I.6). These modules form the basis of all different developed (and those to be developed) mechanical models of (flexible) wind turbines. All submodules can be opened by double-clicking, and each submodule contains several models. The model complexity ranges from rigid models that have no effect on the system dynamics to flexible models consisting of a collection of superelements. The selection of number of superelements depends on the stiffness of the wind turbine under investigation. The library can be modified by dragging new modules or models onto it and saving the resulting system.

[^Library: WTML Mechanical

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[^Library: WTML Mechanical

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Figure I.6: Mechanical module library.

Automated structural modeling procedure: performance

The performance of the automated structural modeling procedure implemented in DAWIDUM can be best illustrated by considering the following two situations:

• Create a new structural model from scratch;

• Modify an existing structural model from the mechanical module library. In this case we have to make a distinction between:

— Model configuration and/or complexity changes;

— Parameter changes.

Obviously, to create a new wind turbine model from scratch will be more time-consuming than changing the model configuration (e.g. two or three rotor blades), model complexity (i.e. number of degrees of freedom) or adapting some model parameters (e.g. replacing the rotor blades by another type). The latter change requires only a few minutes, while changing the model configuration and/or complexity will take a few hours. The time to develop a new model from scratch will range from a couple of hours to a few days depending on the wind turbine configuration under investigation.

To emphasize that the time needed to generate the equations of motion is negligible with respect to the time to make the aforementioned changes, consider the CPU times required to generate the equation of motion of several DAWIDUM models listed in Table I.1. These timings demonstrate that the formulation of one set of equations (even for the most complex structural models) takes only a few seconds.

Timing comparisons

DAWIDUM model

CPU time

Complexity

Beamlsd

0.10 s

2

Beam3sd

1.25 s

6

Beam6sd

1.57 s

12

Beam9sd

1.90 s

18

SDLW1

2.38 s

20

SDLW2

3.77 s

36

SDLW3

5.13 s

52

Table I.1: Overview of the CPU time used to generate the equations of motion of several DAWIDUM models on a PC with a 700 MHz Pentium II processor running Winddows-2K with 384 MB RAM. The total number of degrees of freedom (including fictitious ones) has been used as a measure of complexity.

Rotor blade

The equations implemented in BladePM to compute the centroidal mass moments of inertia, and center of gravity of all rigid bodies within each superelement will now be presented. Recall that the mass as well as the flexural rigidity in the two principal bending directions need to be supplied by either the blade designer or the blade manufacturer. The center of gravity of each rigid body with respect to its base is determined as follows:

Renewable Energy 101

Renewable Energy 101

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