Advanced aeroelastically optimized tip extensions are among rotor innovation concepts which could contribute to the higher performance and lower cost of wind turbines. A novel design optimization framework for wind turbine blade tip extensions based on surrogate aeroelastic modeling is presented. An academic wind turbine is modeled in an aeroelastic code equipped with a near-wake aerodynamic module, and tip extensions with complex shapes are parametrized using 11 design variables. The design space is explored via full aeroelastic simulations in extreme turbulence, and a surrogate model is fitted to the data. Direct optimization is performed based on the surrogate model seeking to maximize the power of the retrofitted turbine within the ultimate load constraints. The presented optimized design achieves a load-neutral gain of up to 6 % in annual energy production. Its performance is further evaluated in detail by means of the near-wake model used for the generation of the surrogate model and compared with a higher-fidelity aerodynamic module comprising a hybrid filament-particle-mesh vortex method with a lifting-line implementation. A good agreement between the solvers is obtained at low turbulence levels, while differences in predicted power and flapwise blade root bending moment grow with increasing turbulence intensity.

The trend of reducing the levelized cost of energy (LCOE) of horizontal axis wind turbines through increasing rotor size has long been established. To
achieve this, the challenges of scale must be overcome through innovative turbine design and control strategies

The existing bibliography relevant to wind turbine applications typically focuses on winglets and aerodynamic tip shapes purely from an aerodynamics
point of view

Design variables and their range. Minimum (min) and maximum (max) values of planform design variables result in the “tip 1” and “tip 2” shapes shown in Fig.

In this work, the tip extensions are designed with the objective of maximizing annual energy production (AEP) gain within the existing operational load constraints. The relevant business case is associated with improving the performance of existing rotors or customizing rotors for different site conditions while investing less in new full blade production costs. Due to the fact that full time-domain aeroelastic simulations are utilized for the power and load evaluation, a surrogate-based optimization (SBO) approach is pursued in order to avoid issues with gradient evaluations which normally require the simplification of the evaluation cases. Furthermore, the parametrization of the tip extension is detailed enough to represent a blade design optimization approach now in a modular way focusing only on the tip. This includes the capability of producing complex shapes with large sweep and prebend, which are typically not used in a traditional blade design.

A time-domain aeroelastic model of the onshore version of the IEA 10

A surrogate-based optimization framework was then wrapped around the baseline model of the IEA 10

The following sections provide further details of the different components involved in the above-described workflow.

The aeroelastic simulations performed in the present work relied on the commercial software HAWC2

The in-house multi-fidelity vortex solver MIRAS

The power performance and ultimate loads of every design are evaluated in a single load case, comprising an IEC-specific DLC1.3

Planform for two reference tips at the borders of the design space. Vertical dashed lines indicate the location of the control points.

Blade centerline for two reference tips at the borders of the design space. Vertical dashed lines indicate the location of the control points.

Mass and flapwise stiffness for two reference tips at the borders of the design space. Vertical dashed lines indicate the location of the control points.

The definition of the tip extension design variables and their design space is probably the most important step in the described optimization
process. The variables have been chosen in a way which enables a general blade stretching design capability. Their range is a result of many prior
parametric studies, and it is limited to ensure the validity of the aerodynamic modeling

For every design evaluation loop, the HAWC2 case files are pre-processed, executed, and post-processed on a single CPU. The top-level process is shown
in Fig.

In the post-processing of the MATLAB script, the output time-series files of HAWC2 are processed, and performance statistics are extracted. For the optimization, the mean generator power and the ultimate blade root flapwise bending moment are extracted. For detailed evaluation purposes of the designs, all other component load statistics and blade-distributed outputs are also extracted.

SBO setup top-level diagram.

The SBO framework is set up based on the MATLAB code package MATSuMoTo

Generate initial design sets.

Do the costly function evaluations at the points generated in the previous step.

Fit a surrogate model to the data.

Use the surrogate model to predict the objective function values at unsampled points in the variable domain to decide at which points to do the next expensive function evaluations.

Do the expensive function evaluations at the points selected in the previous step.

Check if the stopping criterion has been reached. If not, go back to the third step. If the stopping criterion has been met, stop.

The objective function is a very important part of this study since it determines which direction in the design space the SBO takes by evaluating
new design variable sets. The objective function is defined as a weighted sum of the mean generator power and the ultimate blade root flapwise bending
moment. Since we do not pursue any purely load-alleviation-driven designs but load-neutral power-increase designs, the objective function is based
only on the maximization of power when the loads are neutral or negative compared to the baseline. When the increase in loads is higher than 2 %
(an empirical limit accounting for model uncertainty), the objective has a 90 % weight on loads and 10 % on power. A smooth Gaussian filter is
used for the transition between neutral and higher loads (Fig.

Power and load objective function weights as a function of load increase.

For generating the initial sample set, MATLAB's Latin hypercube design is used with the maximin option and 20 iterations. The minimum sample size
used is

Using the fitted surrogate model on the initial set, a global optimization approach is followed utilizing MATLAB's genetic algorithm with default settings. The best-performing design point is chosen for a HAWC2 evaluation, together with points created by randomly perturbing the best point found so far. In addition, a set of points that is uniformly selected from the whole variable domain is generated (using again a Latin hypercube design) and is added to the evaluation set. Hence, it is possible to improve the global fit of the surrogate model, and new areas of the variable domain where the global optimum may be located can be detected. Using 7 CPUs, 20 iterations are performed, resulting in a total of 174 HAWC2 evaluations, including the initial sample set of 34 points.

The progress of the optimization and the results for the whole set of evaluated design samples is discussed here. The characteristics of the best converged design are also discussed in detail.

Optimized design variables.

The progress plot showing the best value of the objective function during the evaluation of each sample is shown in Fig.

Progress plot of the objective function value.

Pareto front of the evaluated samples.

Blade 3D surface comparison between baseline geometry (in black) and optimized tip
extension (in red).

Blade centerline of the optimized design.

Planform of the optimized design.

Mass and flapwise stiffness of the optimized design (zoom-in of the tip).

The best design in terms of the minimum value of the objective function comprises a tip extension with a length close to the limit of the defined
length (7 %), with all 11 design variables listed in Table

Comparison of AEP predictions for the baseline and optimized designs between HAWC2-NW and HAWC2-MIRAS.

Power curve comparison between HAWC2-NW and HAWC2-MIRAS:

The blade centerline of the optimized design is compared to the baseline in Fig.

Differences in power in the function of turbulence intensity

The performance of the optimized design is evaluated in terms of AEP in its IEC wind class I and the lowest average wind speed class III. The
“clean” power curve is defined by steady uniform wind speed inflow from cut-in to cut-out with 1

Statistics of the power and flapwise root bending moment predicted in the extreme turbulence case by HAWC2-NW and HAWC2-BEM with respect to HAWC2-LL predictions. The table shows the difference in percentages.

The performance of the optimized design is also evaluated in the DLC1.3 (ETM) case which is used in the optimization and is performed with the NW method
against two different fidelity models. The blade element momentum (BEM) model implemented in HAWC2 is used as the lower-fidelity method, and the lifting line aerodynamic module
implemented in MIRAS is employed as the higher-fidelity solver. To ensure a meaningful comparison between the solvers, simulations of the
extreme turbulent case have been carried out as follows. Firstly, to run a free turbulent simulation in MIRAS, the velocity-defined Mann turbulent box
used in the optimization procedure has been transformed into a particle cloud by computing the curl of the velocity field. This cloud is slowly
released one diameter upstream of the turbine, and it develops as it convects downstream towards the rotor plane. The released turbulent particles
interact freely with the turbine wake. Vortex simulations with and without the turbine are performed. In the simulation without a turbine, the local
velocities are extracted every time step at the rotor plane position in a

Differences in flapwise root bending moment in the function of turbulence intensity

Aerodynamic power signal

General statistics of the aerodynamic power and the flapwise root bending moment are presented in Table

In order to study the influence of the turbulence level in the results, the extreme turbulence level of the DLC 1.3 (40 %) has been downscaled to
obtain inflow fields with a range of turbulence intensities from 0 % to 40 %. Statistics of the difference in the BEM and NW predictions with
respect to the LL simulations in the function of the turbulence level are presented in what follows. Figure

A detailed analysis is carried out for the 40 % turbulent case. Figure

The time variation in the predicted flapwise root bending moment is shown in Fig.

Flapwise root bending moment for MxBR

The radial distributions of mean and standard deviation of area of attack (AOA) for the baseline blade (solid lines) and extended blade (dashed lines) are shown in
Fig.

Angle of attack

The mean and standard deviation of the in-plane force are shown in Fig.

In-plane force

Similar effects can be seen in the out-of-plane forces in Fig.

Out-of-plane force

Mean values of the aerodynamic efficiency,

A novel surrogate-based optimization framework for aeroelastic design of tip extensions on modern wind turbines is presented in this work. The design of tip extensions is performed in a realistic design space and aeroelastic operation of the wind turbine, and it is highly efficient in terms of the use of computational resources. The optimized design achieving load-neutral 6 % AEP gain is evaluated in detail with two levels of aerodynamic model fidelity. The aeroelastic response predictions of the complex tip shape with the near-wake aerodynamic module agree fairly well with the higher-fidelity MIRAS simulations. A detailed comparison including a BEM model shows that local load distributions are predicted better by the near-wake model, but the improvement in terms of mean power and blade root loading over the BEM model is not clear. This indicates that the coupling factor computation in the near-wake model should be revisited. The agreement between the lower-fidelity BEM model, the near-wake model, and the higher-fidelity MIRAS model worsens with increasing turbulence intensity, which should be investigated in more detail in future work. The tip extension design concept resulting from the SBO process has high potential in terms of actual implementation in a real rotor upscaling with a potential business case in reducing the LCOE of future large wind turbine rotors. Future work will focus on introducing multi-fidelity optimization methods but also concept innovations which could further increase the achieved performance potential.

The SBO-framework basic Matlab code is freely available at

TB performed the aeroelastic model setup, optimization framework setup, design parametrization, design optimization, and design evaluation. NRG performed the MIRAS simulations and contributed to the design evaluation. GRP contributed to the aeroelastic model setup, design parametrization, and design evaluation. SGH contributed to the design parametrization and design evaluation.

The authors declare that they have no conflict of interest.

This research was supported by the project Smart Tip (Innovation Fund Denmark 7046-00023B), in which DTU Wind Energy and Siemens Gamesa Renewable Energy explore optimized tip designs. The following persons have also contributed to the presented work: Helge Aagard Madsen, Flemming Rasmussen, Niels Nørmark Sørensen, Peder Bay Enevoldsen, and Jesper Monrad Laursen.

This research has been supported by the Innovation Fund Denmark (grant no. 7046-00023).

This paper was edited by Mingming Zhang and reviewed by Niels Adema and Rad Haghi.