Wind Turbine Load Control and Estimation: Advancements by Coordinate Transformations

Wind energy has become one of the most economically attractive energy sources thanks to technological advances, such as wind turbine upscaling. To harness higher-quality wind reachable at greater heights, wind turbine towers are made taller; to increase power capture, rotors are made with wider diameters. Mass/material reduction for the manufacture of such components is thus imperative to keep large-scale turbines profitable, resulting in more flexible structures but exacerbating fatigue loading. Therefore, the reliance on advanced control methods is ever higher to mitigate multiple wind turbine structural loads while ensuring optimal power production.

Advanced convex economic model predictive control (CEMPC) methods have garnered attention lately in the wind turbine control community. Such techniques possess several advantages apart from those inherent in being subsets of the model predictive control (MPC) family. First, it is capable of accounting for multiple economic objectives for wind turbines, such as power production optimization, fatigue load reduction, and excessive actuation limitation, in a straightforward and unified way. This also means that the trade-off calibration between the economic objectives (by weight tuning) can be done with ease. Additionally, the convexity of the underlying optimization control problem (OCP) guarantees that a globally optimal solution can be found with high numerical effectiveness, which may lead to real-time feasibility. This thesis, in particular, is focused on the development of a unified CEMPC framework, combining the potentials of two emerging CEMPCs in the wind turbine area, namely the power-and-energy CEMPC and the quasi-linear parameter-varying model predictive control (qLPV-MPC), for addressing multiple wind turbine structural loads.

The former achieves its convexity by exchanging nominal wind turbine variables, such as blade pitch, generator torque, and rotational speed, with alternative variables in terms of aerodynamic and generator powers and rotor kinetic energy. This results in the OCP containing linear dynamics, convex constraints, and concave objectives to be maximized. Being originally focused on fulfilling power gradient requirements from a grid code, a fatigue load mitigation consideration was introduced later on for fore-aft tower motion in the literature. Unfortunately, little attention was paid to the mitigation of the more weakly-damped side-side tower loading, as well as blade fatigue loads.

Such a knowledge gap is filled in this thesis; in particular, both key components' fatigue loads are mitigated by exploiting the individual blade pitching capabilities of the power-and-energy CEMPC framework. Since, in this framework, blade pitch actuation is achieved mainly by manipulating aerodynamic power inside the CEMPC, a redefinition of the latter is necessary to enable such a feature. To be precise, multiple aerodynamic powers, each representing that of a single blade, were employed as decision variables of the CEMPC instead of a single quantity. Further mapping of the aerodynamic powers into side-side blade forces, as well as augmentation of side-side tower dynamics into the CEMPC's internal model, enables counteractive control actions for reducing side-side tower load. Mapping the powers into blade and rotor moments enables alleviation of the blade loads.

On the other hand, the utilization of qLPV-MPC for deploying a passive wind turbine tower resonance prevention by dynamically optimal frequency skipping has been gaining attention in the literature. For enabling active load cancelation in this framework, however, a periodic load estimation is needed. In this thesis, such an estimation scheme is developed, employing a Kalman filtering method. Aligned with the qLPV-MPC implementation for the aforementioned passive method, the internal model of the filter is rendered in a demodulated fashion by applying a model demodulation transformation (MDT) to an extended wind turbine side-side tower dynamics. Measurement signal demodulation (MSD) is utilized for capturing the slow-varying components of wind turbine tower measurements to be fed to the Kalman filter. The filter is thus capable of not only estimating the demodulated periodic load signals but also those of the unknown and unmeasured tower states with good agreement with the ground truth.

The next challenge addressed in this thesis is the provision of an active control method specifically aimed at tackling the side-side periodic loading of the tower. A family of repetitive control methods, namely modulation\-/demodulation control (MDC), is adopted in this thesis to handle the cancellation of the periodic loading. In principle, MDC consists of output signal demodulation, projecting the frequency component of interest (namely the rotor frequency) in the signal into low-frequency quadrature and in-phase representations. On these axes, diagonal single-input, single-output (SISO) controllers can be designed, resulting in control signals, which, by a modulation process, are translated into a single control signal, being an additive generator torque signal, oscillating at the frequency of the disturbance and thereby canceling it. A phase offset, with its optimal value determined by the plant's phase at the disturbance frequency, is needed and included in the modulation. This results in the full decoupling of the control channels, as well as the correction of an occurring gain sign flip due to the varying excitation frequency, which could have deteriorated the controller's performance and induced instabilities. The MDC extends a conventional tower damper controller specifically aimed at mitigating the tower loading at its natural frequency. As a result, both the tower load components at the natural frequency and the rotor frequency are mitigated simultaneously.

This thesis has, thus, highlighted the significant role various coordinate transformations play in advancing state-of-the-art wind turbine control, be it a transformation of signals into a different set of variables in power and energy terms or into different time scales. The former has enabled the formulation of power-and-energy CEMPC for side-side tower load and blade loads mitigation, extending this framework's fatigue load mitigation capabilities. The latter transformation, demonstrated by the MDT, paves the way for estimating unknown and unmeasurable periodic load and tower states in a demodulated manner, essential in activating the periodic load cancelation feature of the novel qLPV-MPC method. The MDC method has successfully enabled active side-side periodic tower load cancelation by leveraging a modulation-demodulation scheme, another way of transforming coordinates into different time scales where convenient yet effective control system design can be made. This thesis has, therefore, provided elements required for constructing a unified CEMPC framework, where the benefits of the said coordinate transformations may be further harnessed.