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Keywords = ultra-large wind turbines

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14 pages, 2332 KiB  
Article
Motion Analysis of International Energy Agency Wind 15 MW Floating Offshore Wind Turbine under Extreme Conditions
by Zengliang Chang, Yueming Zheng, Meng Qu, Xingguo Gao, Xiaojie Tian and Guijie Liu
J. Mar. Sci. Eng. 2024, 12(7), 1166; https://doi.org/10.3390/jmse12071166 - 11 Jul 2024
Viewed by 459
Abstract
In recent years, ultra-large-scale offshore wind turbines have attracted widespread attention. However, accurately evaluating the motion responses of offshore wind turbines under extreme conditions, especially for semisubmersible floating off-shore wind turbines, is often challenging. In order to assess the operational behavior of wind [...] Read more.
In recent years, ultra-large-scale offshore wind turbines have attracted widespread attention. However, accurately evaluating the motion responses of offshore wind turbines under extreme conditions, especially for semisubmersible floating off-shore wind turbines, is often challenging. In order to assess the operational behavior of wind turbines under wind and wave loads, this paper adopted a numerical analysis method to solve the motion responses under extreme conditions. It specifically examines the motion responses of the IEA 15 MW wind turbine in terms of surge, heave, and pitch direction, focusing on environmental loads that occur once every 50 years. The results show that the wind turbine can still operate normally under the Ultimate condition. However, the average amplitude increased by 7% in the pitch direction and decreased by 4% in the heave direction compared to the rated condition. Under extreme conditions (occurring once every 50 years), with the wind turbine parked, the average amplitude in the surge direction reduced by 33%, while the average amplitude in the pitch direction reduced by 106%. Thus, it is essential to pitch the blades and brake the generator in extreme environmental conditions to ensure the safety of the wind turbine. Full article
(This article belongs to the Section Ocean Engineering)
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Figure 1

Figure 1
<p>Flowchart between AQWA and OpenFAST.</p>
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<p>General arrangement of the FOWT.</p>
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<p>Time history of wave height (<b>top</b>) and wind speed (<b>bottom</b>).</p>
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<p>Free decay time histories and natural frequency at still water line: (<b>a</b>) Surge direction, (<b>b</b>) Heave direction, (<b>c</b>) Pitch direction, (<b>d</b>) Yaw direction—Time histories; (<b>e</b>) Surge direction, (<b>f</b>) Heave direction, (<b>g</b>) Pitch direction, (<b>h</b>) Yaw direction—Natural frequencies.</p>
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<p>Motion responses of the floating offshore turbine under different conditions.</p>
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<p>Response curves of the nacelle acceleration.</p>
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<p>Nacelle acceleration response statistics.</p>
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<p>Mooring force response curves.</p>
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<p>Mooring force response statistics.</p>
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16 pages, 4686 KiB  
Article
Ultra-Short-Term Power Prediction of Large Offshore Wind Farms Based on Spatiotemporal Adaptation of Wind Turbines
by Yuzheng An, Yongjun Zhang, Jianxi Lin, Yang Yi, Wei Fan and Zihan Cai
Processes 2024, 12(4), 696; https://doi.org/10.3390/pr12040696 - 29 Mar 2024
Cited by 1 | Viewed by 695
Abstract
Accurately predicting the active power output of offshore wind power is of great significance for reducing the uncertainty in new power systems. By utilizing the spatiotemporal correlation characteristics among wind turbine unit outputs, this paper embeds the Diffusion Convolutional Neural Network (DCNN) into [...] Read more.
Accurately predicting the active power output of offshore wind power is of great significance for reducing the uncertainty in new power systems. By utilizing the spatiotemporal correlation characteristics among wind turbine unit outputs, this paper embeds the Diffusion Convolutional Neural Network (DCNN) into the Gated Recurrent Unit (GRU) for the feature extraction of spatiotemporal correlations in wind turbine unit outputs. It also combines graph structure learning to propose a sequence-to-sequence model for ultra-short-term power prediction in large offshore wind farms. Firstly, the electrical connection graph within the wind farm is used to preliminarily determine the reference adjacency matrix for the wind turbine units within the farm, injecting prior knowledge of the adjacency matrix into the model. Secondly, a convolutional neural network is utilized to convolve the historical curves of units within the farm along the time dimension, outputting a unit connection probability vector. The Gumbel–softmax reparameterization method is then used to make the probability vector differentiable, thereby generating an optimal adjacency matrix for the prediction task based on the probability vector. At the same time, the difference between the two adjacency matrices is added as a regularization term to the loss function to reduce model overfitting. The simulation of actual cases shows that the proposed model has good predictive performance in ultra-short-term power prediction for large offshore wind farms. Full article
(This article belongs to the Section Energy Systems)
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Figure 1
<p>1DCNN feature extraction process.</p>
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<p>Gated Recurrent Unit.</p>
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<p>Diffusion Convolutional Neural Network.</p>
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<p>Diffusion Convolutional Gated Recurrent Unit.</p>
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<p>GA−DCGRU−GR.</p>
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<p>GA-DCGRU-GR ultra-short-term power prediction process for wind farms.</p>
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<p>Wind Farm 1 Electrical Connection Diagram.</p>
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<p>Wind Farm 2 Electrical Connection Diagram.</p>
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<p>Visualization of adjacency matrix changes in case 1.</p>
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<p>Visualization of adjacency matrix changes in case 2.</p>
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<p>Prediction results comparison in case 1.</p>
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<p>Prediction results comparison in case 2.</p>
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20 pages, 3371 KiB  
Article
The Impact of Bend–Twist Coupling on Structural Characteristics and Flutter Limit of Ultra-Long Flexible Wind Turbine Composite Blades
by Bei Li, De Tian, Xiaoxuan Wu, Huiwen Meng and Yi Su
Energies 2023, 16(15), 5829; https://doi.org/10.3390/en16155829 - 6 Aug 2023
Viewed by 1436
Abstract
Flutter is an instability phenomenon that can occur in wind turbine blades due to fluid–structure interaction, particularly for longer and more flexible blades. Aeroelastic tailoring through bend–twist coupling is an effective method to enhance the aeroelastic performance of blades. In this study, we [...] Read more.
Flutter is an instability phenomenon that can occur in wind turbine blades due to fluid–structure interaction, particularly for longer and more flexible blades. Aeroelastic tailoring through bend–twist coupling is an effective method to enhance the aeroelastic performance of blades. In this study, we investigate the impact of bend–twist coupling on the structural performance and flutter limit of the IEA 15 MW blade, which is currently the longest reference wind turbine blade, and determine the optimal layup configuration that maximizes the flutter speed. The blade is modeled by NuMAD and iVABS, and the cross-section properties are obtained by PreComb and VABS. The accuracy of the blade model is verified in terms of stiffness and frequency. The bend–twist coupling is implemented by changing the fiber angle of the skin and spar cap considering symmetric and asymmetric layups. The flutter limits of both the baseline and the bend–twist coupled blade are evaluated based on HAWC2. The results show that the angle of spar cap carbon fiber has a greater effect on the blade’s structural properties and flutter speed than the skin fiber. Varying the spar cap carbon fiber angle increases the flutter speed, with the effect being more significant for the symmetric layup, up to 9.66% at a fiber angle of 25 degrees. In contrast, the variation in skin fiber angle has a relatively small impact on flutter speed—within ±3%. Full article
(This article belongs to the Special Issue Wind Turbine 2023)
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Figure 1
<p>Schematic diagram of the polar grid BEM.</p>
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<p>Schematic diagram of the co-ordinate system in HAWC2.</p>
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<p>Illustration of the cross-section geometry.</p>
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<p>Blade layup: (<b>a</b>) thickness of layers in the LE reinforcement; (<b>b</b>) thickness of layers in the LE and TE panel; (<b>c</b>) thickness of layers in the spar; (<b>d</b>) thickness of layers in the TE reinforcement; and (<b>e</b>) thickness of layers in the web.</p>
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<p>Blade model established by NuMAD.</p>
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<p>Cross-sectional layout at different spans locations: (<b>a</b>) s = 0; (<b>b</b>) s = 0.1; (<b>c</b>) s = 0.47; (<b>d</b>) s = 0.65; (<b>e</b>) s = 0.78; and (<b>f</b>) s = 1.</p>
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<p>Comparison of blade stiffness properties: (<b>a</b>) tension stiffness; (<b>b</b>) edgewise stiffness; (<b>c</b>) flapwise stiffness; and (<b>d</b>) torsional stiffness.</p>
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<p>(<b>a</b>) Rotor speed and wind speed; (<b>b</b>) blade tip flapwise displacement and AOA near the instability phenomenon.</p>
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<p>Variation of blade structural properties at different span locations with respect to skin fiber angle: (<b>a</b>) edge-twist coupling factor; (<b>b</b>) flap-twist coupling factor; (<b>c</b>) ROC for tension stiffness; (<b>d</b>) ROC for edgewise stiffness; (<b>e</b>) ROC for flapwise stiffness; and (<b>f</b>) ROC for torsional stiffness.</p>
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<p>Flutter speed at different ply angles for wind turbine blades with symmetric or asymmetric skin.</p>
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<p>Variation of blade structural properties at different span locations with respect to symmetric spar cap fiber angle: (<b>a</b>) edge-twist coupling factor; (<b>b</b>) flap-twist coupling factor; (<b>c</b>) ROC for tension stiffness; (<b>d</b>) ROC for edgewise stiffness; (<b>e</b>) ROC for flapwise stiffness; and (<b>f</b>) ROC for torsional stiffness.</p>
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<p>Variation of blade structural properties at different span locations with respect to asymmetric spar cap fiber angle: (<b>a</b>) edge-twist coupling factor; (<b>b</b>) flap-twist coupling factor; (<b>c</b>) ROC for tension stiffness; (<b>d</b>) ROC for edgewise stiffness; (<b>e</b>) ROC for flapwise stiffness; and (<b>f</b>) ROC for torsional stiffness.</p>
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<p>Flutter speed at different angles for wind turbine blades with symmetric or asymmetric spar cap.</p>
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17 pages, 11149 KiB  
Article
Use of Green Fs Lasers to Generate a Superhydrophobic Behavior in the Surface of Wind Turbine Blades
by Joaquín Rivera-Sahún, Luis Porta-Velilla, Germán F. de la Fuente and Luis A. Angurel
Polymers 2022, 14(24), 5554; https://doi.org/10.3390/polym14245554 - 19 Dec 2022
Cited by 2 | Viewed by 1567
Abstract
Ice generation on the surface of wind generator blades can affect the performance of the generator in several aspects. It can deteriorate sensor performance, reduce efficiency, and cause mechanical failures. One of the alternatives to minimize these effects is to include passive solutions [...] Read more.
Ice generation on the surface of wind generator blades can affect the performance of the generator in several aspects. It can deteriorate sensor performance, reduce efficiency, and cause mechanical failures. One of the alternatives to minimize these effects is to include passive solutions based on the modification of the blade surfaces, and in particular to generate superhydrophobic behavior. Ultra-short laser systems enable improved micromachining of polymer surfaces by reducing the heat affected zone (HAZ) and improving the quality of the final surface topography. In this study, a green fs laser is used to micromachine different patterns on the surface of materials with the same structure that can be found in turbine blades. Convenient optimization of surface topography via fs laser micromachining enables the transformation of an initially hydrophilic surface into a superhydrophobic one. Thus, an initial surface finish with a contact angle ca. 69° is transformed via laser treatment into one with contact angle values above 170°. In addition, it is observed that the performance of the surface is maintained or even improved with time. These results open the possibility of using lasers to control turbine blade surface microstructure while avoiding the use of additional chemical coatings. This can be used as a complementary passive treatment to avoid ice formation in these large structures. Full article
(This article belongs to the Special Issue Applications of Lasers in Polymer Science)
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Figure 1
<p>FESEM image with EBS detector of the original sample surface employed in this work. Gray particles correspond to ceramic phases.</p>
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<p>(<b>a</b>) Topography of the surface after laser machining for <span class="html-italic">d</span><sub>lines</sub> = 200 μm. (<b>b</b>) Evolution of the contact angle values with the reduction of <span class="html-italic">d</span><sub>lines</sub>. The horizontal blue line indicates the value of 68° measured in the original surface, before laser microachining. Insets show the images obtained for measuring the contact angle in the original surface, and with <span class="html-italic">d</span><sub>lines</sub> = 200 μm and <span class="html-italic">d</span><sub>lines</sub> = 35 μm.</p>
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<p>Photograph of the sample surface subjected to study, where laser treatments were carried out in air.</p>
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<p>FESEM images recorded with In Lens (<b>a</b>) and EBS (<b>b</b>) detectors at the bottom of a laser machined groove processed with <span class="html-italic">E</span><sub>pulse</sub> = 48.5 μJ/pulse, <span class="html-italic">v</span><sub>laser</sub> = 9 mm/s and <span class="html-italic">d</span><sub>lines</sub> = 60 μm.</p>
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<p>Raman spectra recorded on the original surface and on the bottom of a laser machined groove on samples processed in air and in Ar with <span class="html-italic">E</span><sub>pulse</sub> = 48.5 μJ/pulse, <span class="html-italic">v</span><sub>laser</sub> = 9 mm/s and <span class="html-italic">d</span><sub>lines</sub> = 65 μm.</p>
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<p>Evolution of contact angle values for different distances between machined lines and different laser scanning speeds.</p>
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<p>(<b>a</b>) Surface topography and (<b>b</b>) line profile in the vertical direction in the sample processed with <span class="html-italic">E</span><sub>pulse</sub> = 48.5 μJ/pulse, <span class="html-italic">v</span><sub>laser</sub> = 5 mm/s and <span class="html-italic">d</span><sub>lines</sub> = 75 μm.</p>
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<p>Different combinations of <span class="html-italic">d</span><sub>lines</sub> and <span class="html-italic">v</span><sub>laser</sub> (<span class="html-italic">E</span><sub>pulse</sub> = 48.5 μJ/pulse) that have generated a surface with contact angles above 150°.</p>
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<p>FESEM images of the surface of the samples with different <span class="html-italic">d</span><sub>lines</sub> values: (<b>a</b>) 200 μm, (<b>b</b>) 80 μm, (<b>c</b>) 55 μm and (<b>d</b>) 40 μm. The rest of the laser processing parameters were fixed: <span class="html-italic">E</span><sub>pulse</sub> = 48.5 μJ/pulse, <span class="html-italic">v</span><sub>laser</sub> = 9 mm/s and <math display="inline"><semantics> <mrow> <mo>❬</mo> <msub> <mi>F</mi> <mrow> <mn>1</mn> <mi mathvariant="normal">D</mi> </mrow> </msub> <mo>❭</mo> </mrow> </semantics></math> = 108 J/cm<sup>2</sup>.</p>
Full article ">Figure 9 Cont.
<p>FESEM images of the surface of the samples with different <span class="html-italic">d</span><sub>lines</sub> values: (<b>a</b>) 200 μm, (<b>b</b>) 80 μm, (<b>c</b>) 55 μm and (<b>d</b>) 40 μm. The rest of the laser processing parameters were fixed: <span class="html-italic">E</span><sub>pulse</sub> = 48.5 μJ/pulse, <span class="html-italic">v</span><sub>laser</sub> = 9 mm/s and <math display="inline"><semantics> <mrow> <mo>❬</mo> <msub> <mi>F</mi> <mrow> <mn>1</mn> <mi mathvariant="normal">D</mi> </mrow> </msub> <mo>❭</mo> </mrow> </semantics></math> = 108 J/cm<sup>2</sup>.</p>
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<p>(<b>a</b>) Evolution of the contact angle values with the reduction of <span class="html-italic">d</span><sub>lines</sub>. The horizontal line indicates 150°. The rest of the laser processing parameters were fixed as follows: <span class="html-italic">E</span><sub>pulse</sub> = 48.5 μJ/pulse, <span class="html-italic">v</span><sub>laser</sub> = 9 mm/s and <math display="inline"><semantics> <mrow> <mo>❬</mo> <msub> <mi>F</mi> <mrow> <mn>1</mn> <mi mathvariant="normal">D</mi> </mrow> </msub> <mo>❭</mo> </mrow> </semantics></math> = 108 J/cm<sup>2</sup>. The inset shows the profile observed in the sample processed with <span class="html-italic">d</span><sub>lines</sub> = 65 μm. (<b>b</b>) Scheme of the different types of profiles observed for two cases where grooves do not overlap (<span class="html-italic">d</span><sub>lines</sub> = 100 μm, <span class="html-italic">d</span><sub>lines</sub> = 65 μm) and for a last one (<span class="html-italic">d</span><sub>lines</sub> = 40 μm), where they overlap. Black lines show one of the previous profiles in order to show the reduction in <span class="html-italic">h</span>.</p>
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<p>FESEM images of the surface of the samples with different <span class="html-italic">E</span><sub>pulse</sub> values: (<b>a</b>) 13.6 μJ/pulse, (<b>b</b>) 18.9 μJ/pulse, (<b>c</b>) 24.3 μJ/pulse, (<b>d</b>) 31.0 μJ/pulse, (<b>e</b>) 38.7 μJ/pulse, and (<b>f</b>) 48.5 μJ/pulse. The rest of the laser processing parameters were fixed as follows: <span class="html-italic">v</span><sub>laser</sub> = 9 mm/s and <span class="html-italic">d</span><sub>lines</sub> = 65 μm.</p>
Full article ">Figure 11 Cont.
<p>FESEM images of the surface of the samples with different <span class="html-italic">E</span><sub>pulse</sub> values: (<b>a</b>) 13.6 μJ/pulse, (<b>b</b>) 18.9 μJ/pulse, (<b>c</b>) 24.3 μJ/pulse, (<b>d</b>) 31.0 μJ/pulse, (<b>e</b>) 38.7 μJ/pulse, and (<b>f</b>) 48.5 μJ/pulse. The rest of the laser processing parameters were fixed as follows: <span class="html-italic">v</span><sub>laser</sub> = 9 mm/s and <span class="html-italic">d</span><sub>lines</sub> = 65 μm.</p>
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<p>(<b>a</b>) Evolution of <span class="html-italic">h</span><sub>v</sub> as a function of ❬<span class="html-italic">F</span><sub>1D</sub>❭, in a series of experiments where the energy per pulse has been modified. The plot includes a second sample series fabricated with different laser scanning speeds. (<b>b</b>) Evolution of the contact angle dependence for both series of samples.</p>
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<p>FESEM micrographs obtained on the sample’s surfaces treated with different <span class="html-italic">v</span><sub>laser</sub> values: (<b>a</b>) 18 mm/s, (<b>b</b>) 27 mm/s, (<b>c</b>) 36 mm/s, and (<b>d</b>) 45 mm/s. The rest of the laser processing parameters are the same in all cases: <span class="html-italic">E</span><sub>pulse</sub> = 48.5 μJ/pulse and <span class="html-italic">d</span><sub>lines</sub> = 65 μm.</p>
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<p>(<b>a</b>) Relation between <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msub> <mi>θ</mi> <mrow> <mi>rW</mi> </mrow> </msub> </mrow> </semantics></math> and <span class="html-italic">r</span>. (<b>b</b>) Relation between <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msub> <mi>θ</mi> <mrow> <mi>rC</mi> </mrow> </msub> </mrow> </semantics></math> and <span class="html-italic">A</span>. Lines are eye-guides.</p>
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35 pages, 11986 KiB  
Review
Evolution of Turbine Cooled Vanes and Blades Applied for Large Industrial Gas Turbines and Its Trend toward Carbon Neutrality
by Kenichiro Takeishi
Energies 2022, 15(23), 8935; https://doi.org/10.3390/en15238935 - 25 Nov 2022
Cited by 11 | Viewed by 6369
Abstract
Photovoltaics and wind power are expected to account for a large share of power generation in the carbon-neutral era. A gas turbine combined cycle (GTCC) with an industrial gas turbine as the main engine has the ability to rapidly start up and can [...] Read more.
Photovoltaics and wind power are expected to account for a large share of power generation in the carbon-neutral era. A gas turbine combined cycle (GTCC) with an industrial gas turbine as the main engine has the ability to rapidly start up and can follow up to load fluctuations to smooth out fluctuations in power generation from renewable energy sources. Simultaneously, the system must be more efficient than today’s state-of-the-art GTCCs because it will use either Carbon dioxide Capture and Storage (CCS) when burning natural gas or hydrogen/ammonia as fuel, which is more expensive than natural gas. This paper describes the trend of cooled turbine rotor blades used in large industrial gas turbines that are carbon neutral. First, the evolution of cooled turbine stationary vanes and rotor blades is traced. Then, the current status of heat transfer technology, blade material technology, and thermal barrier coating technology that will lead to the realization of future ultra-high-temperature industrial gas turbines is surveyed. Based on these technologies, this paper introduces turbine vane and blade cooling technologies applicable to ultra-high-temperature industrial gas turbines for GTCC in the carbon-neutral era. Full article
(This article belongs to the Special Issue New Insights of Gas Turbine Cooling Systems)
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Figure 1
<p>Evolution of thermal efficiency in steam power plants [<a href="#B5-energies-15-08935" class="html-bibr">5</a>].</p>
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<p>Evolution of turbine inlet temperature, metal operating temperature, and pressure ratio over the years: (<b>a</b>) turbine inlet temperature and allowable metal operating temperature [<a href="#B7-energies-15-08935" class="html-bibr">7</a>]; (<b>b</b>) engine overall pressure ratio increase [<a href="#B7-energies-15-08935" class="html-bibr">7</a>].</p>
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<p>Evolution of turbine inlet temperature, metal operating temperature, and pressure ratio over the years: (<b>a</b>) turbine inlet temperature and allowable metal operating temperature [<a href="#B7-energies-15-08935" class="html-bibr">7</a>]; (<b>b</b>) engine overall pressure ratio increase [<a href="#B7-energies-15-08935" class="html-bibr">7</a>].</p>
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<p>Increase in operational temperature of turbine components made possible by alloy development, manufacturing technology, and TBCs [<a href="#B8-energies-15-08935" class="html-bibr">8</a>].</p>
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<p>German Jumo 004 nozzle and blade cooling flow passages [<a href="#B17-energies-15-08935" class="html-bibr">17</a>].</p>
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<p>Liquid-cooling passages in turbine blades [<a href="#B17-energies-15-08935" class="html-bibr">17</a>].</p>
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<p>Four-stage water-cooled rotor [<a href="#B18-energies-15-08935" class="html-bibr">18</a>].</p>
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<p>First stage turbine vane of the Spey engine [<a href="#B19-energies-15-08935" class="html-bibr">19</a>].</p>
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<p>First stage turbine blade of the Spey engine [<a href="#B19-energies-15-08935" class="html-bibr">19</a>].</p>
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<p>Air-cooled high-pressure turbine nozzle of CF6-80C2 engine [<a href="#B24-energies-15-08935" class="html-bibr">24</a>].</p>
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<p>Air-cooled high-pressure turbine blade of CF6-80C2 engine [<a href="#B24-energies-15-08935" class="html-bibr">24</a>].</p>
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<p>Cooling structure of Lamilloy<sup>®</sup> [<a href="#B25-energies-15-08935" class="html-bibr">25</a>].</p>
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<p>Manufacturing process of Lamilloy<sup>®</sup> and CastCool<sup>®</sup>: (<b>a</b>) Fabricated Lamilloy<sup>®</sup> airfoils [<a href="#B26-energies-15-08935" class="html-bibr">26</a>]; (<b>b</b>) single crystal structure [<a href="#B26-energies-15-08935" class="html-bibr">26</a>]; (<b>c</b>) CastCool<sup>®</sup> airfoils [<a href="#B26-energies-15-08935" class="html-bibr">26</a>,<a href="#B27-energies-15-08935" class="html-bibr">27</a>]; (<b>d</b>) structure of CastCool<sup>®</sup> [<a href="#B26-energies-15-08935" class="html-bibr">26</a>].</p>
Full article ">Figure 12 Cont.
<p>Manufacturing process of Lamilloy<sup>®</sup> and CastCool<sup>®</sup>: (<b>a</b>) Fabricated Lamilloy<sup>®</sup> airfoils [<a href="#B26-energies-15-08935" class="html-bibr">26</a>]; (<b>b</b>) single crystal structure [<a href="#B26-energies-15-08935" class="html-bibr">26</a>]; (<b>c</b>) CastCool<sup>®</sup> airfoils [<a href="#B26-energies-15-08935" class="html-bibr">26</a>,<a href="#B27-energies-15-08935" class="html-bibr">27</a>]; (<b>d</b>) structure of CastCool<sup>®</sup> [<a href="#B26-energies-15-08935" class="html-bibr">26</a>].</p>
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<p>Impingement cooling of CastCool<sup>®</sup>: (<b>a</b>) integrally cast cooling passage; (<b>b</b>) Nu distribution on a target surface [<a href="#B28-energies-15-08935" class="html-bibr">28</a>].</p>
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<p>Wafer vane cooling configuration for ERDA advanced industrial engines [<a href="#B29-energies-15-08935" class="html-bibr">29</a>].</p>
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<p>Wafer blade cooling configuration for ERDA advanced industrial engines [<a href="#B29-energies-15-08935" class="html-bibr">29</a>].</p>
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<p>Shell/Spar cooling configuration: (<b>a</b>) cooling configuration; (<b>b</b>) fabrication demonstration blade [<a href="#B30-energies-15-08935" class="html-bibr">30</a>].</p>
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<p>F100 wafer turbine first blade: (<b>a</b>) F100 radial wafer bonded block and tip cap; (<b>b</b>) Fabrication blade [<a href="#B31-energies-15-08935" class="html-bibr">31</a>].</p>
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<p>Evolution of first-stage nozzle and blade cooling structures [<a href="#B33-energies-15-08935" class="html-bibr">33</a>].</p>
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<p>Improve cooling design of D-type first nozzle and blade: (<b>a</b>) D and DA cooling configurations of the first nozzle; (<b>b</b>) D and DA cooling configurations of the first blade [<a href="#B35-energies-15-08935" class="html-bibr">35</a>].</p>
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<p>Evolution of first-stage stationary nozzle cooling structures [<a href="#B41-energies-15-08935" class="html-bibr">41</a>].</p>
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<p>Evolution of first-stage rotating blade cooling structures [<a href="#B15-energies-15-08935" class="html-bibr">15</a>].</p>
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<p>First-stage stationary nozzle structure of the water-cooled gas turbine: (<b>a</b>) Water cooled nozzle concept; (<b>b</b>) Composite construction [<a href="#B46-energies-15-08935" class="html-bibr">46</a>].</p>
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<p>First-stage rotating blade structure of the water-cooled gas turbine [<a href="#B46-energies-15-08935" class="html-bibr">46</a>].</p>
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<p>Water-cooled rotating blade concept [<a href="#B46-energies-15-08935" class="html-bibr">46</a>].</p>
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<p>H combined cycle and steam description [<a href="#B50-energies-15-08935" class="html-bibr">50</a>].</p>
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<p>H System closed loop steam-cooled nozzle: (<b>a</b>) Open loop air-cooled nozzle [<a href="#B50-energies-15-08935" class="html-bibr">50</a>,<a href="#B51-energies-15-08935" class="html-bibr">51</a>]; (<b>b</b>) H system closed loop steam-cooled nozzle [<a href="#B50-energies-15-08935" class="html-bibr">50</a>,<a href="#B51-energies-15-08935" class="html-bibr">51</a>]; (<b>c</b>) H Stage first nozzle—single crystal [<a href="#B50-energies-15-08935" class="html-bibr">50</a>].</p>
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<p>H System closed loop steam-cooled nozzle: (<b>a</b>) Open loop air-cooled nozzle [<a href="#B50-energies-15-08935" class="html-bibr">50</a>,<a href="#B51-energies-15-08935" class="html-bibr">51</a>]; (<b>b</b>) H system closed loop steam-cooled nozzle [<a href="#B50-energies-15-08935" class="html-bibr">50</a>,<a href="#B51-energies-15-08935" class="html-bibr">51</a>]; (<b>c</b>) H Stage first nozzle—single crystal [<a href="#B50-energies-15-08935" class="html-bibr">50</a>].</p>
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<p>Comparisons among alloys in terms of a combination of 1100 °C/137 MPa creep and 1100 °C oxidation resistances [<a href="#B65-energies-15-08935" class="html-bibr">65</a>].</p>
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<p>Future of turbine cooling: (<b>a</b>) “micro” cooling [<a href="#B78-energies-15-08935" class="html-bibr">78</a>]; (<b>b</b>) an example of double-wall cooling [<a href="#B79-energies-15-08935" class="html-bibr">79</a>].</p>
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<p>Example of F-type first nozzle cooling design concept of 3D printed internal cooling design [<a href="#B85-energies-15-08935" class="html-bibr">85</a>].</p>
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<p>Comparison of cooling effectiveness of F-type gas turbine nozzles: (<b>a</b>) nozzles manufactured by conventional casting and additive manufacturing [<a href="#B85-energies-15-08935" class="html-bibr">85</a>]; (<b>b</b>) cooling effectiveness distribution results of conventional and additive cooling design [<a href="#B85-energies-15-08935" class="html-bibr">85</a>].</p>
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36 pages, 4656 KiB  
Review
Electrical Generators for Large Wind Turbine: Trends and Challenges
by Amina Bensalah, Georges Barakat and Yacine Amara
Energies 2022, 15(18), 6700; https://doi.org/10.3390/en15186700 - 13 Sep 2022
Cited by 26 | Viewed by 7440
Abstract
This paper presents an overview of the emerging trends in the development of electrical generators for large wind turbines. To describe the developments in the design of electrical generators, it is necessary to look at the conversion system as a whole, and then, [...] Read more.
This paper presents an overview of the emerging trends in the development of electrical generators for large wind turbines. To describe the developments in the design of electrical generators, it is necessary to look at the conversion system as a whole, and then, the structural and mechanical performances of the drive train need to be considered. Many drive train configurations have been proposed for large wind turbines; they should ensure high reliability, long availability and reduced maintainability. Although most installed wind turbines are geared, directly driven wind turbines with permanent magnet generators have attracted growing interest in the last few years, which has been in parallel to the continuous increase of the per unit turbine power. The aim of this work is to present the recent commercial designs of electrical generators in large wind turbines. Both the strengths and weaknesses of the existing systems are discussed. The most emerging technologies in high-power, low-speed electrical generators are investigated. Furthermore, a comparative analysis of different electrical generator concepts is performed, and the generators are assessed upon a list of criteria such as the mass, cost, and mass-to-torque ratio. Within the framework of these criteria, it may help to determine whether the electrical generator is technically feasible and economically viable for high-power wind turbines. Finally, this review could help to determine suitable generators for use in large and ultra-large wind energy systems. Full article
(This article belongs to the Special Issue Trends and Innovations in Wind Power Systems)
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<p>Upwind and downwind wind turbines.</p>
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<p>Power coefficient with respect to the pitch angle and tip speed ratio <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>λ</mi> <mo>,</mo> <mi>β</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Cumulative installed renewable power capacity mix in 2020 (own representation with information from [<a href="#B33-energies-15-06700" class="html-bibr">33</a>]).</p>
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<p>Global investment in renewable energy in 2019 (own representation with information from [<a href="#B36-energies-15-06700" class="html-bibr">36</a>]).</p>
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<p>Global new offshore wind installations in 2020–by country (adapted with permission from Ref. from [<a href="#B45-energies-15-06700" class="html-bibr">45</a>]). 2020, GWEC.).</p>
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<p>Cumulative capacity of offshore wind energy in 2020–by country (adapted with permission from Ref. from [<a href="#B45-energies-15-06700" class="html-bibr">45</a>]). 2020, GWEC.).</p>
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<p>Evolution of offshore wind turbine size (Reprinted with permission from [<a href="#B45-energies-15-06700" class="html-bibr">45</a>]. 2020, GWEC).</p>
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<p>Haliade-X prototype (Reprinted with permission from [<a href="#B57-energies-15-06700" class="html-bibr">57</a>]. 2022, GE).</p>
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<p>Block diagram of dual-speed wind turbine generation.</p>
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<p>Power versus rotational speed of dual-speed wind turbine generation.</p>
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<p>Flux path in one pole pair of longitudinal and transverse. PMSG (<b>a</b>) Longitudinal. (<b>b</b>) Transverse.</p>
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<p>Haliade-X 12 MW nacelle (courtesy of GE) [<a href="#B57-energies-15-06700" class="html-bibr">57</a>].</p>
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<p>Comparison of wind turbine rotor concepts [<a href="#B121-energies-15-06700" class="html-bibr">121</a>]. (<b>a</b>) External rotor. (<b>b</b>) Internal rotor.</p>
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<p>The influence of the pole pitch reduction on PMSG’s force density. (<b>a</b>) Longitudinal PMSG. (<b>b</b>) Transverse Flux PMSG.</p>
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<p>Transverse flux permanent magnet synchronous generators [<a href="#B145-energies-15-06700" class="html-bibr">145</a>]. (<b>a</b>) Inner rotor. (<b>b</b>) Outer rotor.</p>
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<p>U-Core flux-concentrating transverse flux permanent magnet synchronous generators topologies [<a href="#B108-energies-15-06700" class="html-bibr">108</a>]. (<b>a</b>) Double-sided single-winding. (<b>b</b>) Double-sided double-winding.</p>
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21 pages, 7034 KiB  
Article
A Novel Nonsingular Terminal Sliding Mode Control-Based Double Interval Type-2 Fuzzy Systems: Real-Time Implementation
by Hooman Mohammadi Moghadam, Meysam Gheisarnejad, Maryam Yalsavar, Hossein Foroozan and Mohammad-Hassan Khooban
Inventions 2021, 6(2), 40; https://doi.org/10.3390/inventions6020040 - 4 Jun 2021
Cited by 6 | Viewed by 2602
Abstract
Extensive use of wind turbine (WT) systems brings remarkable challenges to the stability and safety of the power systems. Due to the difficulty and complexity of modeling such large plants, the model-independent strategies are preferred for the control of the WT plants which [...] Read more.
Extensive use of wind turbine (WT) systems brings remarkable challenges to the stability and safety of the power systems. Due to the difficulty and complexity of modeling such large plants, the model-independent strategies are preferred for the control of the WT plants which eliminates the need to model identification. This current work proposes a novel model-independent control methodology in the rotor side converter (RSC) part to ameliorate low voltage ride through (LVRT) ability especially for the doubly-fed induction generator (DFIG) WT. A novel model-independent nonsingular terminal sliding mode control (MINTSMC) was developed based on the principle of the ultra-local pattern. In the suggested controller, the MINTSMC scheme was designed to stabilize the RSC of the DFIG, and a sliding-mode supervisor was adopted to determine the unknown dynamics of the proposed system. An auxiliary dual input interval type 2 fuzzy logic control (DIT2-FLC) was established in a model-independent control structure to remove the estimation error of the sliding mode observer. Real-time examinations have been carried out using a Real-Time Model in Loop (RT-MiL) for validating the applicability of the proposed model-independent control in a real-time platform. To evaluate the usefulness and supremacy of the MINTSMC based DIT2-FLC, the real-time outcomes are compared with outcomes of RSC regulated conventional PI controller and MINTSMC controller. Full article
(This article belongs to the Special Issue Microgrids: Protection, Cyber Physical Issues, and Control)
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<p>Schematic diagram of the DFIG WT structure.</p>
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<p>Illustration of the design curves of the DFIG WT test system. (<b>a</b>) Output mechanical power base on wind speed and (<b>b</b>) electrical power based on the speed of the generator.</p>
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<p>The control structure of the RSC in (<b>a</b>) normal operation, and (<b>b</b>) during a grid fault.</p>
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<p>Control structure for the GSC.</p>
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<p>Illustration of the MINTSMC controller with an SM observer.</p>
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<p>Diagram of DIT2-FPI controller.</p>
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<p>Schematic of (<b>a</b>) antecedent IT2-FSs (<b>b</b>) singleton membership functions.</p>
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<p>Structure of the proposed MINTSMC scheme-based DIT2-FPI controller.</p>
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<p>Overall scheme of the real-time MiL platform.</p>
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<p>The voltage of the DC link capacitor in the DFIG system for scenario I via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.</p>
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<p>Magnitude rotor current of DFIG system under scenario I via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.</p>
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<p>Grid voltage of the DFIG system under scenario I.</p>
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<p>Grid current of the DFIG system under scenario I.</p>
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<p>The DFIG responses according to the scenario I (<b>a</b>) measured active power of DFIG WT, (<b>b</b>) measured reactive power of DFIG WT, (<b>c</b>) Generator speed of DFIG system.</p>
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<p>Capacitor DC-link voltage of the DFIG system via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.</p>
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<p>Magnitude rotor current of the DFIG system via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.</p>
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<p>Grid voltage of the DFIG system under scenario II.</p>
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<p>Grid current of the DFIG system under scenario II.</p>
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<p>The DFIG responses according to scenario II (<b>a</b>) measured active power of the DFIG WT, (<b>b</b>) measured reactive power of the DFIG WT, (<b>c</b>) generator speed of the DFIG system.</p>
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<p>DC link capacitor voltage of the DFIG system under scenario III via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.</p>
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<p>Magnitude rotor current of the DFIG system under scenario III via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.</p>
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<p>Grid voltage of the DFIG system under scenario III.</p>
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<p>Grid current of the DFIG system under scenario III.</p>
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<p>The DFIG responses according to scenario III (<b>a</b>) active power of the DFIG system, (<b>b</b>) reactive power of the DFIG system, (<b>c</b>) generator speed of the DFIG system.</p>
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18 pages, 6612 KiB  
Article
Investigation on Ultrasonic Welding Attributes of Novel Carbon/Elium® Composites
by Somen K. Bhudolia, Goram Gohel, Kah Fai Leong and Robert J. Barsotti
Materials 2020, 13(5), 1117; https://doi.org/10.3390/ma13051117 - 3 Mar 2020
Cited by 53 | Viewed by 4801
Abstract
Joining large and complex polymer–matrix composite structures is becoming increasingly important in industries such as automobiles, aerospace, sports, wind turbines, and others. Ultrasonic welding is an ultra-fast joining process and also provides excellent joint quality as a cost-effective alternative to other joining processes. [...] Read more.
Joining large and complex polymer–matrix composite structures is becoming increasingly important in industries such as automobiles, aerospace, sports, wind turbines, and others. Ultrasonic welding is an ultra-fast joining process and also provides excellent joint quality as a cost-effective alternative to other joining processes. This research aims at investigating the welding characteristics of novel methyl methacrylate Elium®, a liquid thermoplastic resin. Elium® is the first of its kind of thermoplastic resin, which is curable at room temperature and is suitable for mass production processes. The welding characteristics of Elium® composites were investigated by optimizing the welding parameters with specially designed integrated energy directors (ED) and manufactured using the Resin transfer molding process. The results showed a 23% higher lap shear strength for ultrasonically welded composite joints when compared to the adhesively bonded joints. The optimized welding time for the ultrasonic welded joint was found to be 1.5 s whereas it was 10 min for the adhesively bonded joint. Fractographic analysis showed the significant plastic deformation and shear cusps formation on the fractured surface, which are typical characteristics for strong interfacial bonding. Full article
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<p>(<b>a</b>) Mold design for flat composite laminate manufacturing; (<b>b</b>) circumferential resin strategy.</p>
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<p>Manufacturing steps for the Resin Transfer Moulding (RTM) process to manufacture composite laminate.</p>
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<p>Mold design of the Energy Director (ED) composite laminate manufacturing.</p>
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<p>Manufactured Energy Director (ED) laminate with optimized parameters.</p>
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<p>Schematic of Semi-circular ED Elium<sup>®</sup> composite_ Flat Elium<sup>®</sup> Composite (SC-ELC_FL-ELC) welding configuration.</p>
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<p>Ultrasonic welding machine test setup.</p>
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<p>Visual and microscopic pictures of initial welding trials (<b>a</b>–<b>c</b>) over-bonded (<b>d</b>) un-bonded joints.</p>
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<p>Effect of near and far-field weld parameters on the bonding of ED integrated panels.</p>
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<p>Load vs. displacement curves for the adhesively bonded Elium<sup>®</sup> composites.</p>
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<p>Failure surfaces of adhesively bonded ELC_ELC composites.</p>
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<p>Load vs. displacement curves of SC-ELC_FL-ELC configuration at different welding conditions.</p>
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<p>Welded area under all the welding conditions for the SC-ELC_FL-ELC configuration.</p>
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<p>LSS1 and LSS2 graphs for SC-ELC_FL-ELC configuration.</p>
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<p>Fracture surfaces of SC-ELC_FL-ELC specimen with maximum LSS value.</p>
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<p>Fracture surface of SC-ELC_FL-ELC specimen with minimum LSS value.</p>
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<p>Scanning Electron Microscope (SEM) fractography of SC-ELC_FL-ELC at maximum LSS.</p>
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<p>SEM fractography of the SC-ELC_FL-ELC composite for the minimum LSS.</p>
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<p>Comparison of the Lap shear stress (LSS) for the laminate joints with adhesively bonded and welded.</p>
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28 pages, 5270 KiB  
Article
Analysis of Dynamic Characteristics of an Ultra-Large Semi-Submersible Floating Wind Turbine
by Zhixin Zhao, Xin Li, Wenhua Wang and Wei Shi
J. Mar. Sci. Eng. 2019, 7(6), 169; https://doi.org/10.3390/jmse7060169 - 1 Jun 2019
Cited by 29 | Viewed by 5548
Abstract
An initial design of the platform for the moderate water depth (100 m) is performed by upscaling of an existing 5 MW braceless semi-submersible platform design to support the DTU (Danish University of Science and Technology) 10 MW wind turbine. To investigate the [...] Read more.
An initial design of the platform for the moderate water depth (100 m) is performed by upscaling of an existing 5 MW braceless semi-submersible platform design to support the DTU (Danish University of Science and Technology) 10 MW wind turbine. To investigate the dynamic characteristics of the ultra-large semi-submersible floating offshore wind turbine (FOWT), an aero-hydro-servo-elastic numerical modeling is applied to carry out the fully coupled time-domain simulation analysis. The motion responses of the ultra-large semi-submersible FOWT are presented and discussed for selected environmental conditions. Based on the quasi-static and dynamic analysis methods, the influence of the dynamic effects of the mooring lines on the platform motion responses and mooring line tension responses are discussed. Subsequently, the difference in the motion responses and structural dynamics of the DTU 10 MW and NREL (National Renewable Energy Laboratory) 5 MW FOWT is studied due to the difference in turbine properties. The simulation results reveal that the excitation of the low-frequency wind loads on the surge and pitch motions, the tower-base fore-aft bending moments and the mooring line tension response becomes more prominent when the size of the wind turbine increases, but the excitation action of the 3P effect on the structural dynamics of the 5 MW FOWT is more obvious than those of the 10 MW FOWT. Full article
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<p>A single mooring line with undercover length in a local coordinate system.</p>
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<p>Mooring line discretization and indexing.</p>
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<p>Side (<b>a</b>) and top (<b>b</b>) views of the braceless semi-submersible platform [<a href="#B23-jmse-07-00169" class="html-bibr">23</a>].</p>
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<p>Arrangement of the mooring system.</p>
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<p>Layout of the FOWT.</p>
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<p>Overview of FAST used in the fully coupled analysis.</p>
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<p>Panel mesh model of the braceless semi-submersible platform.</p>
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<p>Time histories of surge decay test.</p>
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<p>Power spectra and time histories of the platform motions for different load cases. (<b>a</b>) Time histories of surge motion; (<b>b</b>) power spectra of surge motion; (<b>c</b>) time histories of heave motion; (<b>d</b>) power spectra of heave motion; (<b>e</b>) time histories of pitch motion; (<b>f</b>) power spectra of pitch motion.</p>
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<p>Power spectra and time histories of the platform motions for different load cases. (<b>a</b>) Time histories of surge motion; (<b>b</b>) power spectra of surge motion; (<b>c</b>) time histories of heave motion; (<b>d</b>) power spectra of heave motion; (<b>e</b>) time histories of pitch motion; (<b>f</b>) power spectra of pitch motion.</p>
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<p>Comparison of power spectra of motion responses for the rated and over-rated wind speeds. (<b>a</b>) Power spectra of surge motion; (<b>b</b>) power spectra of heave motion; (<b>c</b>) power spectra of pitch motion.</p>
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<p>Comparison of time histories and power spectra of surge motion for the steady and turbulent wind cases. (<b>a</b>) Time histories of surge motion; (<b>b</b>) power spectra of surge motion; (<b>c</b>) time histories of surge motion; (<b>d</b>) power spectra of surge motion.</p>
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<p>Time histories and power spectra of mooring line tension response in the rated wind speed (LC3) case. (<b>a</b>) Time histories of mooring line tension; (<b>b</b>) power spectra of mooring line tension.</p>
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<p>Comparison of motion responses based on the dynamic and quasi-static models. (<b>a</b>) Power spectra of surge motion; (<b>b</b>) power spectra of heave motion; (<b>c</b>) power spectra of pitch motion.</p>
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<p>Comparison of motion responses based on the dynamic and quasi-static models. (<b>a</b>) Power spectra of surge motion; (<b>b</b>) power spectra of heave motion; (<b>c</b>) power spectra of pitch motion.</p>
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<p>Comparison of power spectra of platform motion responses. (<b>a</b>) Power spectra of surge motion for the LC3 case; (<b>b</b>) power spectra of pitch motion for the LC3 case; (<b>c</b>) power spectra of surge motion for the over-rated wind speed (LC6) case; (<b>d</b>) power spectra of pitch motion for the LC6 case.</p>
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<p>Comparison of power spectra of platform motion responses. (<b>a</b>) Power spectra of surge motion for the LC3 case; (<b>b</b>) power spectra of pitch motion for the LC3 case; (<b>c</b>) power spectra of surge motion for the over-rated wind speed (LC6) case; (<b>d</b>) power spectra of pitch motion for the LC6 case.</p>
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<p>Structural loads diagram of the FOWT system.</p>
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<p>Comparison of the power spectra of RootMyc1 response. (<b>a</b>) Power spectra of RootMyc1 response for the LC3 case; (<b>b</b>) power spectra of RootMyc1 response for the LC6 case.</p>
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<p>Comparison of the power spectra of TwrBsMyt response. (<b>a</b>) Power spectra of TwrBsMyt response for the LC3 case; (<b>b</b>) power spectra of TwrBsMyt response for the LC6 case.</p>
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<p>Comparison of the power spectra of TwrBsMyt response. (<b>a</b>) Power spectra of TwrBsMyt response for the LC3 case; (<b>b</b>) power spectra of TwrBsMyt response for the LC6 case.</p>
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<p>Comparison of the power spectra of Mooring line 1 (ML1) tension response. (<b>a</b>) Power spectra of ML1 tension response for the LC3 case; (<b>b</b>) power spectra of ML1 tension response for the LC6 case.</p>
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2560 KiB  
Article
A Polar Fuzzy Control Scheme for Hybrid Power System Using Vehicle-To-Grid Technique
by Mohammed Elsayed Lotfy, Tomonobu Senjyu, Mohammed Abdel-Fattah Farahat, Amal Farouq Abdel-Gawad and Hidehito Matayoshi
Energies 2017, 10(8), 1083; https://doi.org/10.3390/en10081083 - 25 Jul 2017
Cited by 14 | Viewed by 5302
Abstract
A novel polar fuzzy (PF) control approach for a hybrid power system is proposed in this research. The proposed control scheme remedies the issues of system frequency and the continuity of demand supply caused by renewable sources’ uncertainties. The hybrid power system consists [...] Read more.
A novel polar fuzzy (PF) control approach for a hybrid power system is proposed in this research. The proposed control scheme remedies the issues of system frequency and the continuity of demand supply caused by renewable sources’ uncertainties. The hybrid power system consists of a wind turbine generator (WTG), solar photovoltaics (PV), a solar thermal power generator (STPG), a diesel engine generator (DEG), an aqua-electrolyzer (AE), an ultra-capacitor (UC), a fuel-cell (FC), and a flywheel (FW). Furthermore, due to the high cost of the battery energy storage system (BESS), a new idea of vehicle-to-grid (V2G) control is applied to use the battery of the electric vehicle (EV) as equivalent to large-scale energy storage units instead of small batteries to improve the frequency stability of the system. In addition, EV customers’ convenience is taken into account. A minimal-order observer is used to estimate the supply error. Then, the area control error (ACE) signal is calculated in terms of the estimated supply error and the frequency deviation. ACE is considered in the frequency domain. Two PF approaches are utilized in the intended system. The mission of each controller is to mitigate one frequency component of ACE. The responsibility for ACE compensation is shared among all parts of the system according to their speed of response. The performance of the proposed control scheme is compared to the conventional fuzzy logic control (FLC). The effectiveness and robustness of the proposed control technique are verified by numerical simulations under various scenarios. Full article
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<p>Single line diagram of the hybrid power system.</p>
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<p>Block diagram of the proposed system. ACE, area control error.</p>
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<p>The equivalent EV model.</p>
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<p>Minimal-order observer.</p>
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<p>Polar fuzzy (PF) controllers’ scheme.</p>
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<p>PF controller model.</p>
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<p>PF phase plan.</p>
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<p>(<b>a</b>) Input membership functions for first PF controller; (<b>b</b>) output membership functions for first PF controller.</p>
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<p>(<b>a</b>) Input membership functions for the second PF controller; (<b>b</b>) output membership functions for second PF controller.</p>
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<p>Flowchart of the PF scheme design process.</p>
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<p>Singular values plot of frequency control loop (<math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msup> <mi>F</mi> <mo>*</mo> </msup> <mo>→</mo> <mo>Δ</mo> <mi>F</mi> </mrow> </semantics> </math>).</p>
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<p>Singular values plot of supply error control loop (<math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msubsup> <mi>P</mi> <mi>e</mi> <mo>*</mo> </msubsup> <mo>→</mo> <mo>Δ</mo> <msub> <mi>P</mi> <mi>e</mi> </msub> </mrow> </semantics> </math>).</p>
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<p>(<b>a</b>) First input membership functions for the first fuzzy logic control (FLC) scheme; (<b>b</b>) second input membership functions for the first FLC scheme; (<b>c</b>) output membership functions for the first FLC scheme.</p>
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<p>(<b>a</b>) First input membership functions for the second FLC scheme; (<b>b</b>) second input membership functions for the second FLC scheme; (<b>c</b>) output membership functions for for the second FLC scheme.</p>
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<p>Case 1 simulation results: PF (black), FLC (blue).</p>
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<p>Case 2 simulation results: PF (black), FLC (blue).</p>
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<p>Case 3 simulation results: PF (black), FLC (blue).</p>
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<p>(<b>a</b>) <math display="inline"> <semantics> <msub> <mrow> <mo stretchy="false">|</mo> <mo>Δ</mo> <mi>F</mi> <mo stretchy="false">|</mo> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics> </math> for system parameters variation: PF (black), FLC (blue); (<b>b</b>) <math display="inline"> <semantics> <mrow> <mrow> <mo stretchy="false">|</mo> <mo>Δ</mo> </mrow> <msub> <mi>P</mi> <mi>e</mi> </msub> <msub> <mrow> <mo stretchy="false">|</mo> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics> </math> for system parameters variation: PF (black), FLC (blue).</p>
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