Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Advanced rotor technologies' taking place on Tuesday, 11 March 2014 at 11:15-12:45. The meet-the-authors will take place in the poster area.

**Federico Gualdoni**Politecnico di Milano, Italy

Co-authors:

Federico Gualdoni (1)

^{F}

^{P}Carlo Luigi Bottasso (3) Alessandro Croce (1)

(1) Politecnico di Milano, Milano, Italy (2) Technische Universität München, Munich, Germany (3) Technische Universität München, Politecnico di Milano, Munich, Germany

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## Abstract

**Simultaneous structural sizing of wind turbine rotor and tower
****Introduction**

This paper focuses on aerostructural optimization procedures for wind turbines under development at Politecnico di Milano [1], [2], [9]. The main purpose of this project is the definition of a suite of methods for the multidisciplinary optimization of wind turbines, using physics based models.

In particular the present work reports the addition of a simultaneous blade-tower design capability. The motivation resides in the fact that these components are coupled together, so that it is more effective to find the optimal compromise in terms of a minimum for the Cost of Energy (CoE), by designing them together rather than individually.

**Approach**

The algorithmic structure, developed on two layers, is reported in figure 1 .

At the beginning a model parameterization is developed according to the optimization variables. These variables define properties for a discrete number of sections along blade and tower. Considering the blade, the thickness of structural elements is taken into account, while a classical steel tubular shape solution is considered for the tower. The blade properties are studied by cross sectional analysis, employing the finite element discretization of ANBA [4]. This code allows to compute all structural couplings in the stiffness matrix. Moreover stress and strain distributions are evaluated on the blade section when external loads are applied. Considering the simple geometry of the tower, structural properties and stress distributions are determined by the analytical theory of beam sections.

The developed parameterization is translated into an aeroservoelastic model implemented in the wind turbine simulation environment Cp-Lambda [5]. Multibody techniques are adopted: blades and tower are modeled by geometrically exact beams. Time marching is performed by an unconditionally stable integration scheme, allowing for the introduction of high frequency decay [7]. External control laws are used to regulate the machine. All dynamic simulations defined by international standards are performed [6]. The obtained load envelope determines the ultimate stresses and strains, while turbulent load time histories are used to compute fatigue damage. Moreover, the design procedures consider also the placement of the system natural frequencies, as well as the clearance between blade tip and tower. These verifications, together with manufacturing conditions, are included as constraints of the optimization procedure. The optimization is performed by minimizing CoE[3] by a sequential quadratic programming SQP algorithm, implemented in Matlab [8].

When convergence on the aeroelastical model is achieved, a refined 3D finite element model of the blade is generated. All verifications performed at the coarse level are repeated, highlighting the critical points due to local effects. Using the results of the detailed analysis, the constraints of the aeroelastic optimization are updated by a heuristic approach. This constraints updating process tends to converge after a limited number of iterations between the two description levels.

**Main body of abstract**

A 2MW wind turbine with a 90 meter rotor diameter is considered to demonstrate the structural optimization of blade and tower by the proposed design procedures. The two components are first optimized simultaneously, and then independently, this second approach representing the usual approach. Figure 2 and figure 3 show the nondimensional tower diameter and thickness distribution along the tower nondimensional height. The coupled approach limits the diameter at tower half height, ensuring a larger clearance between blade tip and tower structure. The construction of a lighter and more flexible blade is possible at the expense of a heavier tower, therefore the tower thickness increases to balance the stiffness reduction due to the diameter reduction. The best compromise is automatically identified by considering the CoE as the figure of merit of the monolithic algorithm, generating the best blade-tower configuration. The effect of clearance is apparent at the level of the blade structure as well: figure 4 reports the different thickness distributions of the external shell along the blade nondimensional span. Figure 5 reports the value for the tower constraints vs. the nondimensional height for selected quantities. The figure shows that the root region is sized by fatigue damage, while at the tower top by the buckling constraint.

The presented results show how the blade-tower clearance affects the design. Considering the classical horizontal axis wind turbine configuration, several parameters influence the clearance, as rotor cone angle, blade prebend and rotor uptilt. The uptilt angle and the cone angle are selected to perform a sensitivity study for the 2MW wind turbine considered here, with the goal of identifying the configuration of best compromise. Clearly, by changing the uptilt angle, one affects both power production and blade-tower clearance, which in turn affects the blade and tower sizing. To better understand these effects, a family of optimized wind turbines was generated under the same constraint conditions, differing only by the uptilt angle. Increasing the uptilt value, the annual energy production (AEP) decreases because the misalignment between rotor axis and wind grows. On the other hand, if the uptilt angle increases, the blade-tower clearance grows, which allows for higher blade deflections (and hence a lighter blade) and larger tower diameters.

These contrasting effects on AEP and initial investment are taken into account by the CoE merit function, as shown in figure 6 . The best compromise is identified in an uptilt angle of about 6 degrees that, for the current configuration, gives the lowest CoE value.

A similar study is presented considering the rotor cone angle. Also in this case a family of comparable wind turbines is generated enforcing the same constraints set. A similar trend regarding the initial investment is highlighted: the sum of the cost of three blades and the tower tends to decrease if the cone angle grows, ensuring a larger clearance and allowing for the construction of lighter structures. At the same time, the AEP remains almost constant because an increment of the cone angle slightly affects the misalignment between the rotor axis and mean wind direction. Also in this case the CoE allows to identify the best compromise, obtained by a cone angle value equal to 2 degrees as shown in figure 7 .

**Conclusion**

The abstract has described some new additions to the wind turbine design procedures under development at the POLI-Wind Lab. After a general overview, the results section shows the application of the code to the structural design of the rotor and tower of a representative 2 MW machine. The results show the advantages of a combined approach with respect to an iterative one. The importance of the blade-tower clearance is remarked, and it is shown how the sizing process is influenced by this parameters. The best compromise obtained by coupled optimization is then used to perform a parametric study on the effect of the uptilt angle and the cone angle, revealing the shape of the solution domain. In this process is fundamental the adoption of a physical merit figure. Cost of energy model proves to be the best choice, scaling by the correct amount all the constitutive contributions of the wind turbine system and allowing for the utilization of the standard optimization techniques.

Considering the significant coupling of parameters defining the wind turbine configuration, it appears that the use of monolithic optimization procedures is useful for the identification of optimal solution in an automated and robust manner. Considerable time saving is achieved, reducing the number of the loops performed during the design process between different project teams. The general approach allows the optimal solution to emerge without no artifice. Although the authors are aware that is impossible obtaining a full automated design, it is believed that the presented tool appears to be considerably helpful if used by an experienced designer.

**Learning objectives**

The project highlights the importance of global approach in wind turbine optimization. The presented techniques allow to identify the best structural design of rotor blades and the tower of a wind turbine, considering all the physical coupling by a high fidelity simulation environment. Despite the high level of generality, the low computational time permits to apply the current techniques during the design phase on standard computers, revealing itself useful for wind turbine designers.

**References**

[1] Bottasso, C.L., Croce, A., and Campagnolo, F., 2012, “Multi-Disciplinary Constrained Optimization of Wind Turbines”. Multibody System Dynamics, Volume 27, p. 21-53

[2] Gualdoni, F., 12th-13th September 2012, “Cp-Max: A Blade Design Optimization Environment”, 8th Phd Seminar on Wind Energy in Europe

[3] Fingersh, L., Hand, M., and Laxson, A., December 2006, “Wind Turbine Desing Cost and Scaling Model”, Technical Report NREL

[4] Giavotto, V., Borri, M., Mantegazza, P., Ghiringhelli, G.L., Carmaschi, V., Maffioli, G.C., and Mussi, F., 1983, “Anisotropic Beam Theory and Applications”, Computers & Structures, Volume 16, p. 403-413

[5] Bottasso, C.L., and Croce, A., 2006-2013, “Cp-Lambda: User’s Manual”, Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano

[6] Ed 2010, “Guideline for the Certification of Wind Turbines”, Germanischer Lloyd Industrial Services GmbH, Renewables Certification, Brooktorkai 10, 20457 Hamburg, Germany

[7] Bauchau, O. A., Bottasso, C. L., and Trainelli L., 2003,“Robust integration schemes for flexible multibody systems” Comput. Meth. Appl. Mech. Eng., Volume 192, p. 395–420

[8] Matlab, The MathWorks Inc., www.mathworks.com

[9] Gualdoni, F., Bottasso, C.L., Croce, A., 18th-21th September 2013, “Aerostructural optimization of wind turbines”, 9th Phd Seminar on Wind Energy in Europe

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