It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform light-cone gauge parameter. The resulting finite size effects are exponentially small in the $R$-charge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model.Comment: 12 pages, some clarifications, references adde
The worsening with age of technical systems performance is a matter of fact which is particularly timely to analyze for horizontal-axis wind turbines because they constitute a mature technology. On these grounds, the present study deals with the assessment of wind turbine performance decline with age. The selected test case is a Vestas V52 wind turbine, installed in 2005 at the Dundalk Institute of Technology campus in Ireland. Operation data from 2008 to 2019 have been used for this study. The general idea is analyzing the appropriate operation curves for each working region of the wind turbine: in Region 2 (wind speed between 5 and 9 m/s), the generator speed–power curve is studied, because the wind turbine operates at fixed pitch. In Region 2 12bevelledtrue (wind speed between 9 and 13 m/s), the generator speed is rated and the pitch control is relevant: therefore, the pitch angle–power curve is analyzed. Using a support vector regression for the operation curves of interest, it is observed that in Region 2, a progressive degradation occurs as regards the power extracted for given generator speed, and after ten years (from 2008 to 2018), the average production has diminished of the order of 8%. In Region 2 12bevelledtrue, the performance decline with age is less regular and, after ten years of operation, the performance has diminished averagely of the 1.3%. The gearbox of the test case wind turbine was substituted with a brand new one at the end of 2018, and it results that the performance in Region 2 12bevelledtrue has considerably improved after the gearbox replacement (+3% in 2019 with respect to 2018, +1.7% with respect to 2008), while in Region 2, an improvement is observed (+1.9% in 2019 with respect to 2018) which does not compensate the ten-year period decline (−6.5% in 2019 with respect to 2008). Therefore, the lesson is that for the test case wind turbine, the generator aging impacts remarkably on the power production in Region 2, while in Region 2 12bevelledtrue, the impact of the gearbox aging dominates over the generator aging; for this reason, wind turbine refurbishment or component replacement should be carefully considered on the grounds of the wind intensity distribution onsite.
Ageing of technical systems and machines is a matter of fact. It therefore does not come as a surprise that an energy conversion system such as a wind turbine, which in particular operates under non-stationary conditions, is subjected to performance decline with age. The present study presents an analysis of the performance deterioration with age of a Vestas V52 wind turbine, installed in 2005 at the Dundalk Institute of Technology campus in Ireland. The wind turbine has operated from October 2005 to October 2018 with its original gearbox, that has subsequently been replaced in 2019. Therefore, a key point of the present study is that operation data spanning over thirteen years have been analysed for estimating how the performance degrades in time. To this end, one of the most innovative approaches for wind turbine performance control and monitoring has been employed: a multivariate Support Vector Regression with Gaussian Kernel, whose target is the power output of the wind turbine. Once the model has been trained with a reference data set, the performance degradation is assessed by studying how the residuals between model estimates and measurements evolve. Furthermore, a power curve analysis through the binning method has been performed to estimate the Annual Energy Production variations and suggests that the most convenient strategy for the test case wind turbine (running the gearbox until its end of life) has indeed been adopted. Summarizing, the main results of the present study are as follows: over a ten-year period, the performance of the wind turbine has declined of the order of 5%; the performance deterioration seems to be nonlinear as years pass by; after the gearbox replacement, a fraction of performance deterioration has been recovered, though not all because the rest of the turbine system has been operating for thirteen years from its original state. Finally, it should be noted that the estimate of performance decline is basically consistent with the few results available in the literature.
Full-scale wind turbine is a mature technology and therefore several retrofitting techniques have recently been spreading in the industry to further improve the efficiency of wind kinetic energy conversion. This kind of interventions is costly and, furthermore, the energy improvement is commonly estimated under the hypothesis of ideal wind conditions, but real ones can be very different because of wake interactions and/or wind shear induced by the terrain. A precise quantification of the energy gained in real environment is therefore precious. Wind turbines are subjected to non-stationary conditions and therefore it makes little sense to compare energy production before and after an upgrade: the post-upgrade production should rather be compared to a model of the pre-upgrade production under the same conditions. Since the energy improvement is typically of the order of few percents, a very precise model of wind turbine power output is needed and therefore it should be data-driven. Furthermore, the formulation of the model is heavily affected by the features of the available data set and by the nature of the problem. The objective of this work is the discussion of some wind turbine power curve upgrades on the grounds of operational data analysis. The selected test cases are: improved start-up through pitch angle adjustment near the cut-in, aerodynamic blade retrofitting by means of vortex generators and passive flow control devices, and extension of the power curve through a soft cutout strategy for very high wind speed. The criticality of each test case is discussed and appropriate data-driven models are formulated. These are employed to estimate the energy improvement from each of the upgrades under investigation. The general outcome of this work is a catalog of generalizable methods for studying wind turbine power curve upgrades. In particular, from the study of the selected test cases, it arises that complex wind conditions might affect wind turbine operation such that the production improvement is non-negligibly different from what can be estimated under the hypothesis of ideal wind conditions. A complex wind flow might actually impact on the efficiency of vortex generators and the soft cutout strategies at high wind speeds. The general lesson is therefore that it is very important to estimate wind turbine upgrades on real environments through operational data.
We find the full interacting Lagrangian and Hamiltonian for quantum strings in a near plane wave limit of AdS 4 × CP 3 . The leading curvature corrections give rise to cubic and quartic terms in the Lagrangian and Hamiltonian that we compute in full. The Lagrangian is found as the type IIA Green-Schwarz superstring in the light-cone gauge employing a superspace construction with 32 grassmann-odd coordinates. The light-cone gauge for the fermions is nontrivial since it should commute with the supersymmetry condition. We provide a prescription to properly fix the κ-symmetry gauge condition to make it consistent with light-cone gauge. We use fermionic field redefinitions to find a simpler Lagrangian. To construct the Hamiltonian a Dirac procedure is needed in order to properly keep into account the fermionic second class constraints. We combine the field redefinition with a shift of the fermionic phase space variables that reduces Dirac brackets to Poisson brackets. This results in a completely welldefined and explicit expression for the full interacting Hamiltonian up to and including terms quartic in the number of fields.
Due to the stochastic nature of the source, wind turbines operate under non-stationary conditions and the extracted power depends non-trivially on ambient conditions and working parameters. It is therefore difficult to establish a normal behavior model for monitoring the performance of a wind turbine and the most employed approach is to be driven by data. The power curve of a wind turbine is the relation between the wind intensity and the extracted power and is widely employed for monitoring wind turbine performance. On the grounds of the above considerations, a recent trend regarding wind turbine power curve analysis consists of the incorporation of the main working parameters (as, for example, the rotor speed or the blade pitch) as input variables of a multivariate regression whose target is the power. In this study, a method for multivariate wind turbine power curve analysis is proposed: it is based on sequential features selection, which employs Support Vector Regression with Gaussian Kernel. One of the most innovative aspects of this study is that the set of possible covariates includes also minimum, maximum and standard deviation of the most important environmental and operational variables. Three test cases of practical interest are contemplated: a Senvion MM92, a Vestas V90 and a Vestas V117 wind turbines owned by the ENGIE Italia company. It is shown that the selection of the covariates depends remarkably on the wind turbine model and this aspect should therefore be taken in consideration in order to customize the data-driven monitoring of the power curve. The obtained error metrics are competitive and in general lower with respect to the state of the art in the literature. Furthermore, minimum, maximum and standard deviation of the main environmental and operation variables are abundantly selected by the feature selection algorithm: this result indicates that the richness of the measurement channels contained in wind turbine Supervisory Control And Data Acquisition (SCADA) data sets should be exploited for monitoring the performance as reliably as possible.
Condition monitoring of gear-based mechanical systems in non-stationary operation conditions is in general very challenging. This issue is particularly important for wind energy technology because most of the modern wind turbines are geared and gearbox damages account for at least the 20% of their unavailability time. In this work, a new method for the diagnosis of drive-train bearings damages is proposed: the general idea is that vibrations are measured at the tower instead of at the gearbox. This implies that measurements can be performed without impacting the wind turbine operation. The test case considered in this work is a wind farm owned by the Renvico company, featuring six wind turbines with 2 MW of rated power each. A measurement campaign has been conducted in winter 2019 and vibration measurements have been acquired at five wind turbines in the farm. The rationale for this choice is that, when the measurements have been acquired, three wind turbines were healthy, one wind turbine had recently recovered from a planetary bearing fault, and one wind turbine was undergoing a high speed shaft bearing fault. The healthy wind turbines are selected as references and the damaged and recovered are selected as targets: vibration measurements are processed through a multivariate Novelty Detection algorithm in the feature space, with the objective of distinguishing the target wind turbines with respect to the reference ones. The application of this algorithm is justified by univariate statistical tests on the selected time-domain features and by a visual inspection of the data set via Principal Component Analysis. Finally, a novelty index based on the Mahalanobis distance is used to detect the anomalous conditions at the damaged wind turbine. The main result of the study is that the statistical novelty of the damaged wind turbine data set arises clearly, and this supports that the proposed measurement and processing methods are promising for wind turbine condition monitoring.
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