The design of wind turbines is an iterative process in which load calculations and system performance analyses are done under various environmental conditions. Due to the complexity of wind turbine systems, fully coupled aero-hydro-servo-elastic codes are indispensable to represent the nonlinear behaviour of the system. However, nonlinear codes are known to be costly and time-consuming. In consequence, fast methods of assessing the loads on the system are required to speed up the wind turbine design process, especially in its early stages. This research comprehends a linearised version of the BHawC model and provides fast methods of evaluating wind turbine loads under turbulent inflow conditions. For wind turbines in isotropic conditions and low turbulence intensity, the model is studied as a linear time-invariant (LTI) system through the Coleman transformation, which describes the rotor degrees of freedom in the inertial frame. The dynamic response of the system is obtained through a frequency-domain procedure based on computing the system's transfer function and using the fast Fourier transform (FFT) algorithm. In addition, model-order reduction (MOR) techniques are used to lower the run times of the simulations.

The verification of the fast model is accomplished by comparing the response of the linear model with that of the Siemens in-house aeroelastic simulation tool, BHawC. The comparison is made both in the time domain and the frequency domain through the power spectra of the time series. Results of the tower-top displacements and the tower-bottom loads are presented at three operating points. From the time-domain responses, the maximum root-mean-square error of the tower-base loads related to the fore-aft and the vertical motion of the turbine is around 10%. Besides, the tower-base lateral force and moment present large discrepancies of around 20% with respect to BHawC. The fatigue side-side moment is greatly overpredicted, whereas the differences for the other load channels are less than 20%.

For isotropic conditions and high turbulence intensity, the dependency on the variations in the controller is considered by modelling the system as a linear parameter-varying (LPV) system. In this case, a discrete-time approach is used together with model-order reduction techniques to reduce the computational requirements in terms of memory and run time. The methodology requires knowledge of the state at the steady-state equilibrium. Nevertheless, the linearised BHawC model describes the rotational degrees of freedom differently to the linearised model. Therefore, the implemented methodology is instead used in an analytical wind turbine model. There, the LPV system is able to capture the variability in the system while greatly reducing the computational expense of the simulations.