Micro-wind turbines are energy conversion technologies strongly affected by fatigue, as a result of their size and the variability of loads, induced by the unsteady wind conditions, and modulated by a very high rotational speed. This work is devoted to the experimental and numerical characterization of the aeroelastic behavior of a test-case horizontal-axis wind turbine (HAWT) with a 2 m rotor diameter and a maximum power production of 3 kW. The experimental studies have been conducted at the wind tunnel of the University of Perugia and consisted of accelerometer measurements at the tower and the tail fin. The numerical setup was the Fatigue, Aerodynamics, Structures, and Turbulence (FAST) code for aeroelastic simulations, which was fed as input with the same wind conditions employed in the wind tunnel tests. The experimental and numerical analyses were coupled with the perspective of establishing a reciprocal feedback, and this has been accomplished. On one hand, the numerical model is important for interpreting the measured spectrum of tower oscillations and, for example, inspires the detection of a mass unbalance at the blades. On the other hand, the measurements inspire the question of how to interpret the interaction between the blades and the tower. The experimental spectrum of tail fin vibrations indicates that secondary elements, in terms of weight, can also transmit to the tower, giving meaningful contributions to the vibration spectra. Therefore, an integrated numerical and experimental approach is not only valuable but is also unavoidable, to fully characterize the dynamics of small wind-energy conversion systems.

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The widespread availability of wind turbine operation data has considerably boosted the research and the applications for wind turbine monitoring. It is well established that a systematic misalignment of the wind turbine nacelle with respect to the wind direction has a remarkable impact in terms of down-performance, because the extracted power is in first approximation proportional to the cosine cube of the yaw angle. Nevertheless, due to the fact that in the wind farm practice the wind field facing the rotor is estimated through anemometers placed behind the rotor, it is challenging to robustly detect systematic yaw errors without the use of additional upwind sensory systems. Nevertheless, this objective is valuable because it involves the use of data that are available to wind farm practitioners at zero cost. On these grounds, the present work is a two-steps test case discussion. At first, a new method for systematic yaw error detection through operation data analysis is presented and is applied for individuating a misaligned multi-MW wind turbine. After the yaw error correction on the test case wind turbine, operation data of the whole wind farm are employed for an innovative assessment method of the performance improvement at the target wind turbine. The other wind turbines in the farm are employed as references and their operation data are used as input for a multivariate Kernel regression whose target is the power of the wind turbine of interest. Training the model with pre-correction data and validating on post-correction data, it is estimated that a systematic yaw error of 4 ∘ affects the performance up to the order of the 1.5% of the Annual Energy Production.

Recently, a geometric approach to operator mixing in massless QCD-like theories -that involves canonical forms, obtained by means of gauge transformations, based on the Poincare'-Dulac theorem for the linear system that defines the renormalized mixing matrix in the coordinate representation Z(x, µ) -has been advocated in [1]. In particular, it has been determined under which conditions a renormalization scheme exists where the linear system -and correspondingly Z(x, µ) -may be set in a diagonal canonical form that is one-loop exact to all perturbative orders -the nonresonant diagonalizable case -according to the Poincare'-Dulac theorem. Following the aforementioned approach, in the present paper we work out the most general canonical form for the linear system above and its solution Z(x, µ). Accordingly, we point out that a new phenomenon occurs, which is hardly discussed in the literature: If the matrix γ 0 β 0 , with γ(g) = γ 0 g 2 + • • • the matrix of the anomalous dimensions and β(g) = −β 0 g 3 + • • • the beta function, either is nondiagonalizable or is diagonalizable but -according to the Poincare'-Dulac theorem -a resonant condition for its eigenvalues and the system holds, Z(x, µ) is nondiagonalizable. If γ 0 β 0 is nondiagonalizable, Z(x, µ) is modified with respect to the nonresonant diagonalizable case by a matrix factor that contains asymptotically in the UV sums of powers of logs of the running coupling, i.e., powers of loglogs of the coordinates. We observe that this is the closest analog for asymptotically free theories of logCFTs. Yet, we argue that in the gauge-invariant (Hermitian) sector of a massless QCD-like theory, which to the order of g 2 (µ) should be conformal and unitary, γ 0 β 0 should always be diagonalizable, because otherwise a nonunitary logCFT would arise to the order of g 2 (µ). Nevertheless, even if the eigenvalues of γ 0 β 0 are diagonalizable, the associated linear system may be resonant, thus realizing the second alternative above. However, we demonstrate that in the latter case the corresponding leading UV asymptotics of Z(x, µ), despite its nondiagonalizability, coincides with the one of the nonresonant diagonalizable case.

The measurement of the rotational speed of rotating machinery is typically performed based on mechanical adherence; for example, in encoders. Nevertheless, it can be of interest in various types of applications to develop contactless vision-based methodologies to measure the speed of rotating machinery. In particular, contactless rotor speed measurement methods have several potential applications for wind turbine technology, in the context of non-intrusive condition monitoring approaches. The present study is devoted exactly to this problem: a ground level video-tachometer measurement technique and an image analysis algorithm for wind turbine rotor speed estimation are proposed. The methodology is based on the comparison between a reference frame and each frame of the video through the covariance matrix: a covariance time series is thus obtained, from which the rotational speed is estimated by passing to the frequency domain through the spectrogram. This procedure guarantees the robustness of the rotational speed estimation, despite the intrinsic non-stationarity of the system and the possible signal disturbances. The method is tested and discussed based on two experimental environments with different characteristics: the former is a small wind turbine model (with a 0.45 m rotor diameter) in the wind tunnel facility of the University of Perugia, whose critical aspect is the high rotational speed (up to the order of 1500 RPM). The latter test case is a wind turbine with a 44 m rotor diameter which is part of an industrial wind farm: in this case, the critical point regards the fact that measurements are acquired in uncontrolled conditions. It is shown that the method is robust enough to overcome the critical aspects of both test cases and to provide reliable rotational speed estimates.