## Modeling Wind Turbine Towers and Modal Analysis Assessment

**General**

This is a master thesis project which demonstrates the implementation of a design tool for onshore wind turbine towers. The master thesis is performed in collaboration with the Fraunhofer Institute for Wind Energy and Energy System Technology (IWES). The idea is to provide the engineer / user with a product that gives the flexibility to define various types of tower models from coarse to more detailed. Each model describes the tower in a different type of discretization and redundant information is avoided. The type of tower model that is used depends on the kind of analysis that the user wants to proceed. The key concept is to design the tower once, and then generate simulatable code for every solver. Because this is an ongoing project very limited information will be provided here.

In the beginning, in order to obtain the global loads, the whole wind turbine is analysed as a system. To extract these global loads, a coupled aero-elastic simulation is needed. Simulating wind turbine response in time, using Finite Element Methods, is computationally intensive. Time simulations are therefore generally made using beam elements to reduce the system’s degrees of freedom. Consequently, a beam tower model is implemented that is used in this step. The output of this simulation are global loads in time series acting on the wind turbine components caused by external forces (wind, electricity grid, waves). These loads are contained and linked to the beam model. After this stage, various types of analysis can take place (buckling, fatigue) using a more complicated tower model.

**Tower modeling approach**

For the description of a wind turbine tower different levels of complexity exist. In the most fundamental stage, the tower can be seen as a tubular shaped geometrical object with a height, a base taper angle, and a base diameter. By increasing the hierarchy of the tower model one has to consider segments and a variation in thickness and diameter along the amplitude of the tower. This variation of diameter and thickness inside each segment can be approximated as linear. In the most detailed model, the description of tower include the segments, a more accurate capture of the variation of structural properties, bolted joints, door, ladder, coating, e.t.c.

This approach of splitting the complexity of the tower into various models is significant and useful in the object oriented software development of such models but also in the simulation stage when a specific kind of analysis is required (dynamic analysis, stability analysis, modal analysis).

First, it obeys the idea of object oriented programming and all the advantages that are followed by this, such as reuse of the software, maintenance and modification of the code. Second, these tower models can be combined with other components of the wind turbine such as blades, nacelle, rotor, to form a wind turbine system. Hence, at the end various wind turbine systems exist and each one of them represents the same physical structure in different level of detail. What level of complexity is going to be used, depends on the type of analysis that is intended to be done. For instance, the results of an modal analysis won’t be so different if the door is modeled, but this is not true in the case of a buckling analysis.

Moreover, the graphical user interface for the design of the tower and in general for the wind turbine system is based on these tower models and it has the form of a wizard which assists the user with a sequence of dialogue boxes. Tasks that are complex, both in the analysis phase(modal analysis, buckling analysis, fatigue) or in the design phase (creating tower models) are much easier to perform and less error prone.

**The vibration of the tower**

One of the primary considerations of a tower is its overall stiffness. The towers are categorized with respect to its natural frequencies in the following way:

- Soft – Soft Tower: The natural frequency of the tower is below both the rotor frequency and the blade passing frequency.
- Soft – Stiff Tower: The natural frequency of the tower is between the blade passing frequency and the rotor frequency.
- Stiff- Stiff Tower: The natural frequency of the tower is above the blade passing frequency. The main advantage to this type of tower is that it is not so sensitive to the motions of the turbine itself. However, it is heavy and therefore costly.

Comprehensive analysis of tower natural frequencies is done with the finite element methods.

**Some Modeling Concepts**

- Discretization of tower with Bernoulli space beam elements (three displacements and three rotations per node)
- Linear interpolation of wall thickness and diameter along the height of the tower
- Concentrated masses such as flanges modeled as tip masses in the respected nodes
- Rotor nacelle sub-assembly as rigid body

**Validation of Natural Frequencies and Mode Shapes**

The results of the implemented modal analysis tool (OWTModal) are compared with two major programs that are widely used in the industry; BModes and Adams.

**Tower without Tip Mass**

**Tower with Tip Mass**