The aim of a wind turbine is to transform the kinetic energy in the wind into electrical power. The kinetic energy per time (power) that passes an area, A, perpendicular to the wind velocity and the available aerodynamic efficiency is thus naturally defined as the fraction of the actual produced power to the available power in the so-called power coefficient. To remove kinetic energy from the wind, it is necessary to design a rotor that produces an upstream force, denoted by the thrust T, which reduces the wind speed behind the rotor, as sketched in Figure 1.1. The wind speed through the rotor is gradually reduced from far upstream, V_o, to, u, at the rotor plane and finally to u 1 in the wake. Due to conservation of mass, the streamlines that divide the airflow going through the rotor from the one passing are expanding as shown in Figure 1.1. In order to transform the extracted power into useful work and not simply dissipate it into internal heat, a mechanical torque should also be produced by the rotor as input to the shaft of an electrical generator. Figure 1.2 shows how the aerodynamic loads produce a normal load on the blades to reduce the wind speed and at the same time a tangential load to drive a generator.

This chapter presents models and methods for the automated design optimization of wind turbine rotors, possibly with a somewhat skewed view toward the approaches developed by the authors. This discipline is relatively new and is expected to quickly evolve in the years to come, spurred by a need to support ever more challenging designs. The material presented in this chapter is intimately related with Chapter 7 on systems engineering. Indeed, the design of the rotor is strictly connected with the overall design of the machine and of its various components

Wind turbines have been applied offshore since 1991, when the first offshore wind farm in Vindeby, Denmark was commissioned. According to GEWEC, by the end of 2018, about 23,140 MW of cumulative offshore wind capacity has been installed, with the majority installed in the United Kingdom (7.96 GW), Germany (6.38 GW), and China (4.59 GW). Recent auctions in Europe with subsidy-free winning bids mean that offshore wind can be produced economically at a market price, making offshore wind one of the most economic sources of renewable energy, and it is expected that the capacity will grow to 100-120 GW by 2030.

In this chapter, wind turbine optimization has been demonstrated as an effective approach to exploring complex design decisions. However, it is not a push-button solution and effective use requires a multidisciplinary design team and expertise in optimization algorithms. Common techniques include using reduced-order models for computationally intensive portions of the analysis, taking advantage of gradients to solve large problems, and more recently to include UQ to allow for robust design decisions. Current efforts continue to push for increased model fidelity, more comprehensive disciplinary coverage, and incorporation of uncertainty

In this chapter, we describe how the regional grid is modeled for wind integration and provide insight into the effect of large, utility-scale wind plants, for example, on systems with high penetration.