The history books of tomorrow will remember the start of this millennium by the global energy dilemma. The literature will portray the initial skepticism towards the first signs of global warming and the depletion of unsustainable energy sources. It will lay out how the evolution of mild symptoms into hard realities -such as the exponential increase in droughts, hurricanes and other natural disasters-drove these polarized opinions to a unified global belief that radical measures in energy policy needed to be taken. The accounts will continue by describing how the global discussion then moved to the implementation of sustainable energy alternatives. And they might explain how this drove the competition between solar and wind energy industries, which in turn pushed the development of their technologies.
Even though dynamic substructuring might not star in those passages, I believe it will contribute to the technological evolution needed to sustainably meet tomorrow’s energy demand. This includes the field of wind turbines. Dynamic substructuring is in essence a linear structural dynamic analysis methodology that models a structure by the assembly of a set of substructure models, hence segmenting the normal linear model. By the implementation of this approach, components can be validated individually and reduction techniques can be tailored to the characteristics of and interaction between the components. Moreover, processing costs can be reduced via parallel computing and the ability to interchange component models without having to re-build the entire dynamic structural model.
However, when operational analyses such as time integration are required and the model or its components are expected to undergo large rotations or displacements, the dynamic substructuring methodology needs to be integrated into a formulation that includes rotational effects, such as the floating frame of reference formulation (FFR). This formulation places the linear structure model into a floating reference frame. The body’s deformations within this frame remain linear, but the frame’s kinematic description is highly non-linear. This often leads to major reductions in processing efficiency, diminishing the competitive advantage that dynamic substructuring offers in comparison to other formulations.
In the case of the operational analyses of multi-megawatt wind turbines on the other hand, rotation forces on the important turbine sub-systems tend to be relatively low. Hence the engineer’s gut feel leads to the belief that the floating frame of reference formulation can be significantly simplified. By (partly) linearizing the terms in this formulation, processing costs might significantly reduce at the loss of only little accuracy in the analyses. This leads to the main research question of this thesis:
To what extent can the rotational effects be simplified for various wind turbine operational analyses without significantly impacting their dynamic characteristics?
In order to answer this question, a simple wind turbine dynamic model is constructed in the floating frame of reference formulation. The terms in this formulation are subsequently simplified by various approaches and evaluated in terms of accuracy and processing costs in three different time simulations. This findings of the analysis will indicate which simplification approach will provide accurate results at minimal processing cost.
The results indicate that the processing cost of the 2.3 megawatt turbine model can be reduced to less than one percent with respect to the reference model in steady operation, at negligible accuracy loss. In more transient cases, such as the simulation of startup or (emergency) shut down, the degree of simplification needs to be reduced to maintain the accuracy of the model. this leads to a smaller reduction in processing cost, now to twenty percent in of the original processing costs. The research demonstrates that the simplification of rotational effects in turbine models is feasible and has a significant effect on the processing times of the codes.
The thesis hence recommends further development of the simplified FFR formulations. The formulations could be implemented into dynamic substructuring tools, allowing the analysis of operational dynamic interaction of a system’s subcomponents at competitive processing costs. Also, turbines of other sizes could be investigated, possibly leading to a presentation of the simplifications in non-dimensional form. In result, tailored simplifications of rotational effects can be applied to any wind turbine model.
From the theoretical perspective the thesis recommends further research into simplifying the FFR formulations using other parametrization techniques, such as Euler parameters and Rodriguez parameters. These might pose new opportunities in terms of processing efficiency.
The optimization of dynamic turbine modeling will contribute to speedier design iterations that result in more cost effective turbine designs. With a little bit of luck this industry might consequently turn wind into a leading global supplier of energy. And who knows, the odd history book might mention the contribution of dynamic substructuring to this process.