This work presents and compares two formulations for the co-design optimization of a wind turbine blade under non-linear transient loads: the Nested Analysis and Design (NAND) and the Simultaneous Analysis and Design (SAND) approaches. Analytic sensitivies are used in order to ensure the convergence of the optimization within reasonable computational resources. The two formulations are compared on a mass minimization problem with dynamic constraints, solved with the interior-point method in IPOPT, for a gust input and a turbulent input. Results shows that the NAND and SAND approaches converge towards the same optimum with similar performances. The SAND approach benefits from a simpler design sensitivity analysis and a sparse jacobian of the constraints.

In wind turbine optimization, the standard power regulation strategy follows a constrained trajectory based on the maximum power coefficient. It can be updated automatically during the optimization process by solving a nested maximization problem at each iteration. We argue that this model does not take advantage of the load alleviation potential of the regulation strategy and additionally requires significant computational effort. An alternative approach is proposed, where the rotational speed and pitch angle control points for the entire operation range are set as design variables, changing the problem formulation from nested to one-level. The nested and one-level formulations are theoretically and numerically compared on different aerodynamic blade design optimization problems for AEP maximization. The aerodynamics are calculated with a steady-state blade element momentum method. The onelevel approach increases the design freedom of the problem and allows introducing a secondary objective in the design of the regulation strategy. Numerical results indicate that a standard regulation strategy can still emerge from a one-level optimization. Second, we illustrate that novel optimal regulation strategies can emerge from the one-level optimization approach. This is demonstrated by adding a thrust penalty term and a constraint on the maximum thrust. A region of minimal thrust tracking and a peak-shaving strategy appear automatically in the optimal design.control co-design, multi-disciplinary analysis and optimization, power regulation strategy, wind turbine blade design | INTRODUCTIONDesigning a modern wind turbine is a complex engineering task, due to the multi-disciplinary nature and the uncertain environment it must operate in. Many different objectives and requirements need to be considered during the design process: power extraction, reduction of costs, stability, noise, and so forth. In addition, the designer has to take into account the different disciplines involved with the goals of (i) accurately forecast the behavior of the final design and (ii) take advantage of the potential couplings between disciplines to improve the design. This makes numerical optimization an ideal tool to be used for wind turbine design. Numerous studies have focused on the development of numerical tools for optimization with the goal of handling the multi-disciplinary aspect of wind turbine design. For example, Bottasso et al 1 take in account the aero-elastic

This work compares nodal, spline and interpolation parametrization schemes for wind turbine blade planform design. The comparison is done on a power coefficient maximization problem, where the aerodynamic properties of the blade are computed using the Blade Element Method. The problem is solved using a gradient-based interior-point method with analytic gradients. We show the variation in planform design for each parametrization scheme when the degrees of freedom of the parametrization varies. We compare how the power coefficient converges with increasing degrees of freedom for each scheme. Our results shows that the B´ezier spline, the Piecewise Cubic Hermite Interpolation Polynomial (PCHIP) and Lagrange interpolation schemes present the best grid convergence out of all studied schemes.

Abstract. Control co-design is a promising approach for wind turbine design due to the importance of the controller in power production, stability and load alleviation. However, the high computational effort required to solve optimization problems with added control design variables is a major obstacle to quantify the benefit of this approach. In this work, we propose a methodology to identify if a design problem can benefit from control co-design. The estimation method, based on post-optimum sensitivity analysis, quantifies how the optimal objective value varies with a change in control tuning. The performance of the method is evaluated on a tower design optimization problem, where fatigue load constraints are a major driver, and using a Linear Quadratic Regulator targeting fatigue load alleviation. We use the gradient-based multi-disciplinary optimization framework Cp-max. Fatigue damage is evaluated with time-domain simulations corresponding to the certification standards. The estimation method applied to the optimal tower mass and optimal levelized cost of energy show good agreement with the results of the control-co design optimization, while using only a fraction of the computational effort. Our results additionally show that there may be little benefit to use control co-design in the presence of an active frequency constraint. However, for a soft-soft tower configuration where the resonance can be avoided with active control, using control co-design results in a higher tower with reduced mass.