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15 pages, 8029 KiB  
Article
Study on Length–Diameter Ratio of Axial–Radial Flux Hybrid Excitation Machine
by Mingyu Guo, Jiakuan Xia, Qimin Wu, Wenhao Gao and Hongbo Qiu
Processes 2024, 12(12), 2942; https://doi.org/10.3390/pr12122942 (registering DOI) - 23 Dec 2024
Abstract
To improve the flux regulation range of the Axial–Radial Flux Hybrid Excitation Machine (ARFHEM) and the utilization rate of permanent magnets (PMs), the effects of different length–diameter ratios (LDRs) on the ARFHEM performance are studied. Firstly, the principle of the flux regulation of [...] Read more.
To improve the flux regulation range of the Axial–Radial Flux Hybrid Excitation Machine (ARFHEM) and the utilization rate of permanent magnets (PMs), the effects of different length–diameter ratios (LDRs) on the ARFHEM performance are studied. Firstly, the principle of the flux regulation of the ARFHEM is introduced by means of the structure and equivalent magnetic circuit method. Then, based on the principle of the bypass effect, the analytical formulas of LDRs, the number of pole-pairs, and the flux regulation ability are derived, and then the restrictive relationship between the air-gap magnetic field, LDR, and the number of pole-pairs is revealed. On this basis, the influence of an electric LDR on motor performance is studied. By comparing and analyzing the air-gap magnetic density and no-load back electromotive force (EMF) of motors with different LDRs, the variation in the magnetic flux regulation ability of motors with different LDRs is obtained and its influence mechanism is revealed. In addition, the torque regulation ability and loss of motors with different LDRs are compared and analyzed, and the influence mechanism of the LDR on torque and loss is determined. Finally, the above analysis is verified by experiments. Full article
(This article belongs to the Section Manufacturing Processes and Systems)
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Figure 1
<p>Structure of ARFHEM.</p>
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<p>The flux path and equivalent magnetic circuit of ARFHEM in different excitation current working conditions. (<b>a</b>) Only PM working state. (<b>b</b>) Negative excitation current working state. (<b>c</b>,<b>d</b>) Positive current excitation working state.</p>
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<p>Schematic diagram of bypass structure.</p>
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<p>Air-gap flux regulation characteristic curve with LDRs. (<b>a</b>) The radial air-gap flux density varies with the excitation current. (<b>b</b>) Variation of the multiple of air-gap magnetic flux regulation with LDRs.</p>
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<p>Relation between no-load back EMF and LDR. (<b>a</b>) No-load back EMF. (<b>b</b>) Total harmonic distortion.</p>
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<p>The output torque of a motor with different LDRs varies with the excitation current.</p>
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<p>Influence of different LDRs on motor loss.</p>
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<p>The ARFHEM prototypes.</p>
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<p>The test platform of prototypes.</p>
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<p>The back EMF varies with the excitation currents. (<b>a</b>) 0A. (<b>b</b>) 1A. (<b>c</b>) 3A. (<b>d</b>) 5A.</p>
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<p>The back EMF varies with the excitation currents. (<b>a</b>) 0A. (<b>b</b>) 1A. (<b>c</b>) 3A. (<b>d</b>) 5A.</p>
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24 pages, 3125 KiB  
Article
Lithium Battery SOC Estimation Based on Type-2 Fuzzy Cerebellar Model Neural Network
by Jing Zhao, Menglei Ge, Qiyu Huang and Xungao Zhong
Electronics 2024, 13(24), 4999; https://doi.org/10.3390/electronics13244999 - 19 Dec 2024
Viewed by 278
Abstract
Accurate estimation of the state of charge (SOC) of lithium batteries is critical for the safe and optimal operation of battery management systems (BMSs). Traditional SOC estimation methods are often limited by model inaccuracy and noise interference. In this study, a novel type-2 [...] Read more.
Accurate estimation of the state of charge (SOC) of lithium batteries is critical for the safe and optimal operation of battery management systems (BMSs). Traditional SOC estimation methods are often limited by model inaccuracy and noise interference. In this study, a novel type-2 fuzzy cerebellar model neural network (Type-2 FCMNN) is proposed for accurately estimating the state of charge of lithium batteries. Based on the traditional fuzzy cerebellar model neural network (FCMNN), type-2 fuzzy rules are innovatively introduced to enhance the robustness of the model against uncertainties and noise disturbances. This enables the model to better cope with nonlinear complexity and external disturbances when dealing with SOC estimation of lithium batteries and significantly improves the accuracy of prediction. On this basis, by analyzing the working principle of lithium batteries, a battery equivalent circuit model is successfully established and simulated and tested by Simulink R2022b, which provides a theoretical basis for the selection of the size of the input parameters of the subsequent neural network. Then, this paper designs and implements the SOC estimation model based on Type-2 FCMNN and tests it in Matlab. Finally, this paper carries out simulation comparison experiments between Type-2 FCMNN and various classical neural network algorithms in Matlab R2022b including traditional FCMNN, a backpropagation neural network, radial basis function neural network, and Kalman filtering algorithm. The simulation results show that Type-2 FCMNN exhibits a significant advantage in SOC estimation accuracy, with mean absolute error and root mean square error values of only 43.1% and 36.0% of FCMNN’s, respectively, while FCMNN achieves the best results among the compared methods. Full article
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Figure 1
<p>Schematic diagram of the internal electrochemical reaction of a lithium-ion battery.</p>
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<p>Schematic diagram of the voltage rebound phenomenon of a lithium battery.</p>
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<p>Model diagram of a second-order RC equivalent circuit.</p>
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<p>Lithium battery experimental equipment and data acquisition system.</p>
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<p>Experimental-voltage-current diagram for OCV working condition at 0 °C.</p>
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<p>Simulink simulation of the second-order RC circuit model.</p>
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<p>Schematic diagram of Gaussian type-2 fuzzy affiliation function.</p>
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<p>Architecture of the Type-2 FCMNN algorithm.</p>
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<p>Organisation of Type-2 FCMNN.</p>
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<p>Flow chart of the Type-2 FCMNN SOC estimation method.</p>
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<p>Plot of Type-2 FCMNN SOC forecast SOC under OCV conditions.</p>
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<p>Plot of BPNN SOC forecast results under OCV conditions.</p>
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<p>Plot of RBFNN SOC forecast results under OCV conditions.</p>
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<p>Plot of KF SOC forecast results under OCV conditions.</p>
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<p>Plot of FCMNN SOC forecast results under OCV conditions.</p>
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<p>Experimental-voltage-current diagram for DST-FUDS under working conditions at 0 °C.</p>
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<p>Experimental voltage–current diagram for DST-FUDS under working conditions at 0 °C.</p>
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<p>Plot of Type-2 FCMNN SOC forecast results under DST-FUDS conditions.</p>
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<p>Plot of BPNN SOC forecast results under DST-FUDS conditions.</p>
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<p>Plot of RBFNN SOC forecast results under DST-FUDS conditions.</p>
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<p>Plot of KF SOC forecast results under DST-FUDS conditions.</p>
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<p>Plot of FCMNN SOC forecast results under DST-FUDS conditions.</p>
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13 pages, 800 KiB  
Article
Grape Pomace as a Source of Phenolics for the Inhibition of Starch Digestion Enzymes: A Comparative Study and Standardization of the Efficacy
by Pedapati Siva Charan Sri Harsha and Vera Lavelli
Foods 2024, 13(24), 4103; https://doi.org/10.3390/foods13244103 - 18 Dec 2024
Viewed by 358
Abstract
The increase in the incidence of hyperglycemia and diabetes poses the challenge of finding cost-effective natural inhibitors of starch digestion enzymes. Among natural compounds, phenolics have been considered as promising candidates. The aims of this study were as follows: (a) to investigate the [...] Read more.
The increase in the incidence of hyperglycemia and diabetes poses the challenge of finding cost-effective natural inhibitors of starch digestion enzymes. Among natural compounds, phenolics have been considered as promising candidates. The aims of this study were as follows: (a) to investigate the effectiveness of the inhibition of different winemaking byproducts towards intestinal brush border α-glucosidase and pancreatic α-amylase in vitro; (b) to calculate an efficacy index relative to the standard acarbose for the phenolic pool of winemaking byproducts, as well as for isolated phenolic compounds and for the phenolic pools of different plants studied in the literature, in order to rank winemaking byproducts with respect to the reference drug and other natural alternatives. Among winemaking byproducts, red grape skins showed the highest inhibitory activities towards both α-glucosidase and α-amylase, which were, on average, 4.9 and 2.6 µg acarbose equivalents/µg total phenolics (µg Ac eq/µg GAE), respectively. A correlation was observed between the total phenolic contents of red grape skins and their inhibitory effectiveness, which is useful for standardizing the efficacy of phenolic extracts obtained from different winemaking processes. In general, the inhibitory activity of the phenolic pool of grape skins was higher than those of isolated phenolic compounds, namely anthocyanins and monomeric and polymeric flavanols and flavonols, probably due to synergistic effects among compounds. Hence, bioactive phenolic fractions could be produced with the focus on functionality rather than purity, in line with the principles of sustainable processing. Based on the efficacy index developed to compare different phenolic compounds and phenolic-rich plants studied in the literature as starch digestion enzyme inhibitors, red grape skins proved to be cost-effective candidates. Full article
(This article belongs to the Section Food Nutrition)
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Graphical abstract

Graphical abstract
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<p>Correlation between enzyme inhibition efficacy and phenolic content for red grape skins (<span style="color:#7030A0">▲</span>), white grape skins (<span style="color:#FFC000">♦</span>), and grape seeds (<span style="color:#00B050">●</span>). (<b>a</b>) α-glucosidase inhibition; (<b>b</b>) α-amylase inhibition. Data for grape seeds were recalculated from Lavelli et al., 2015 [<a href="#B27-foods-13-04103" class="html-bibr">27</a>].</p>
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<p>HPLC chromatograms of red skin extract. (<b>a</b>) Major peaks identified at 520 nm: 1. delphinidin–3–O–glucoside; 2. cyanidin–3–O–glucoside; 3. petunidin 3–O–glucoside; 4. peonidin–3–O–glucoside; and 5. malvidin–3-O–glucoside. (<b>b</b>) Major peaks identified at 354 nm: 1. quercetin glucoside; 2. quercetin; and 3. kaempferol. (<b>c</b>) Major peaks identified at λex 230/λem 320: 1. procyanidin B1; 2. catechin; 3. procyanidin B2; and 4. epicatechin.</p>
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19 pages, 490 KiB  
Review
Pulsar Kick: Status and Perspective
by Gaetano Lambiase and Tanmay Kumar Poddar
Symmetry 2024, 16(12), 1649; https://doi.org/10.3390/sym16121649 - 13 Dec 2024
Viewed by 301
Abstract
The high speeds seen in rapidly rotating pulsars after supernova explosions present a longstanding puzzle in astrophysics. Numerous theories have been suggested over the years to explain this sudden “kick” imparted to the neutron star, yet each comes with its own set of [...] Read more.
The high speeds seen in rapidly rotating pulsars after supernova explosions present a longstanding puzzle in astrophysics. Numerous theories have been suggested over the years to explain this sudden “kick” imparted to the neutron star, yet each comes with its own set of challenges and limitations. Key explanations for pulsar kicks include hydrodynamic instabilities in supernovae, anisotropic neutrino emission, asymmetries in the magnetic field, binary system disruption, and physics beyond the Standard Model. Unraveling the origins of pulsar kicks not only enhances our understanding of supernova mechanisms but also opens up possibilities for exploring new physics. In this brief review, we will introduce pulsar kicks, examine the leading hypotheses, and explore future directions for this intriguing phenomenon. Full article
(This article belongs to the Section Physics)
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<p>Schematic diagram of a pulsar kick. The asymmetric supernova collapse results in the pulsar a kick.</p>
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<p>The variation in GW intensity with radiation frequency is presented, illustrating a pulsar kick driven by asymmetric neutrino emission induced via ultralight DM. Sensitivity curves of GW detectors are included for reference. The plot is adapted from [<a href="#B58-symmetry-16-01649" class="html-bibr">58</a>].</p>
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<p>The histograms display the velocity distribution of NSs for the 70 models detailed in Tables A.1–A.5 of [<a href="#B74-symmetry-16-01649" class="html-bibr">74</a>]. The solid blue and red line represents the velocity distribution at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>, and the dashed purple and magneta lines correspond to the extrapolation. The red-shaded region indicates the subset of models where NSs attain velocities exceeding <math display="inline"><semantics> <mrow> <mn>200</mn> <mspace width="3.33333pt"/> <mi>km</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math> within one second of the core bounce. The black solid line correspond to the modeled kick distribution from observed fluence and redshift of gamma ray bursts (GRBs) [<a href="#B75-symmetry-16-01649" class="html-bibr">75</a>]. The figure is adapted from [<a href="#B74-symmetry-16-01649" class="html-bibr">74</a>,<a href="#B75-symmetry-16-01649" class="html-bibr">75</a>].</p>
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20 pages, 11490 KiB  
Article
Characteristic Analysis and Error Compensation Method of Space Vector Pulse Width Modulation-Based Driver for Permanent Magnet Synchronous Motors
by Qihang Chen, Wanzhen Wu and Qianen He
Sensors 2024, 24(24), 7945; https://doi.org/10.3390/s24247945 - 12 Dec 2024
Viewed by 320
Abstract
Permanent magnet synchronous motors (PMSMs) are widely used in a variety of fields such as aviation, aerospace, marine, and industry due to their high angular position accuracy, energy conversion efficiency, and fast response. However, driving errors caused by the non-ideal characteristics of the [...] Read more.
Permanent magnet synchronous motors (PMSMs) are widely used in a variety of fields such as aviation, aerospace, marine, and industry due to their high angular position accuracy, energy conversion efficiency, and fast response. However, driving errors caused by the non-ideal characteristics of the driver negatively affect motor control accuracy. Compensating for the errors arising from the non-ideal characteristics of the driver demonstrates substantial practical value in enhancing control accuracy, improving dynamic performance, minimizing vibration and noise, optimizing energy efficiency, and bolstering system robustness. To address this, the mechanism behind these non-ideal characteristics is analyzed based on the principles of space vector pulse width modulation (SVPWM) and its circuit structure. Tests are then conducted to examine the actual driver characteristics and verify the analysis. Building on this, a real-time compensation method is proposed, physically matched to the driver. Using the volt–second equivalence principle, an input–output voltage model of the driver is derived, with model parameters estimated from test data. The driving error is then compensated with a voltage method based on the model. The results of simulations and experiments show that the proposed method effectively mitigates the influence of the driver’s non-ideal characteristics, improving the driving and speed control accuracies by 88.07% (reducing the voltage error from 0.7345 V to 0.0879 V for a drastic command voltage with a sinusoidal amplitude of 10 V and a frequency of 50 Hz) and 53.08% (reducing the speed error from 0.0130°/s to 0.0061°/s for a lower command speed with a sinusoidal amplitude of 20° and a frequency of 0.1 Hz), respectively, in terms of the root mean square errors. This method is cost-effective, practical, and significantly enhances the control performance of PMSMs. Full article
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Figure 1
<p>Drive–control system for PMSMs.</p>
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<p>(<b>a</b>) Equivalent circuit diagram of the SVPWM driver. (<b>b</b>) Vector diagram of the space voltage.</p>
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<p>Dead time effect on the IGBT conduction and output voltages. (<b>a</b>) The ideal control signals for the pair of switches. (<b>b</b>) The control signals with dead time for the pair of switches. (<b>c</b>) Electric potential of the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> </mrow> </semantics></math> connection point (a phase terminal).</p>
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<p>Schematic diagram of the internal structure of an IGBT. (<b>a</b>) Basic structure; (<b>b</b>) equivalent circuit.</p>
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<p>IGBT on–off time test circuit.</p>
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<p>(<b>a</b>) Comparison of the voltage <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>R</mi> </mrow> </msub> </mrow> </semantics></math> when switching on (<math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> <mtext> </mtext> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>). (<b>b</b>) Switch-on voltages for different resistances (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>30</mn> <mtext> </mtext> <mi mathvariant="normal">V</mi> </mrow> </semantics></math>).</p>
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<p>(<b>a</b>) Comparison of the voltage <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>R</mi> </mrow> </msub> </mrow> </semantics></math> when switching off (<math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> <mtext> </mtext> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>). (<b>b</b>) Comparison of the voltage <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>R</mi> </mrow> </msub> </mrow> </semantics></math> when switching off (<math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>9</mn> <mtext> </mtext> <mi mathvariant="normal">K</mi> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>).</p>
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<p>Steady-state voltage <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> </mrow> </semantics></math> relationship curve.</p>
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<p>(<b>a</b>) Fitting results of the turn-on process. (<b>b</b>) Fitting results of the turn-off process.</p>
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<p>(<b>a</b>) Graph of the pattern of change in <math display="inline"><semantics> <mrow> <mo>∆</mo> <mi>v</mi> </mrow> </semantics></math>. (<b>b</b>) Fitting result (<math display="inline"><semantics> <mrow> <mi>a</mi> </mrow> </semantics></math>).</p>
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<p>Schematic diagram of voltage compensation.</p>
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<p>(<b>a</b>) Phase voltage error before/after driver compensation. (<b>b</b>) Phase current error before/after driver compensation.</p>
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<p>(<b>a</b>) q-axis current before/after driver compensation. (<b>b</b>) Speed before/after driver compensation.</p>
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<p>Experimental platform.</p>
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<p>(<b>a</b>) Comparison of speed loop performance <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>20</mn> <mtext> </mtext> <mi mathvariant="normal">V</mi> </mrow> </semantics></math>. (<b>b</b>) Comparison of speed loop performance <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>30</mn> <mtext> </mtext> <mi mathvariant="normal">V</mi> </mrow> </semantics></math>.</p>
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<p>Magnitude of the synthetic voltage vector.</p>
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17 pages, 5477 KiB  
Article
A Novel Objective Method for Steel Degradation Rate Evaluation
by Justyna Kasińska, Paweł Malinowski, Piotr Matusiewicz, Włodzimierz Makieła, Leopold Barwicki and Dana Bolibruchova
Materials 2024, 17(24), 6074; https://doi.org/10.3390/ma17246074 - 12 Dec 2024
Viewed by 268
Abstract
This article introduces a novel approach for assessing microstructure, particularly its degradation after extended operation. The authors focus on creep processes in power plant components, highlighting the importance of diagnostics in this field. This article emphasizes the value of combining traditional microstructure observation [...] Read more.
This article introduces a novel approach for assessing microstructure, particularly its degradation after extended operation. The authors focus on creep processes in power plant components, highlighting the importance of diagnostics in this field. This article emphasizes the value of combining traditional microstructure observation techniques with image analysis. A non-destructive method of evaluating microstructure parameters (matrix replicas) is presented, and its accuracy is evaluated against the conventional destructive method. The assessment utilizes quantitative data derived from classical stereological principles and image analysis. Parameters like mean chord length, relative surface area, mean cross-sectional area, and mean equivalent diameter are compared for replica and metallographic specimens. The results show that the replica method accurately reproduces the microstructure. In their conclusions, the authors highlight the importance of developing visual methods alongside the application of artificial intelligence while indicating the challenges in achieving this goal. Full article
(This article belongs to the Section Advanced Materials Characterization)
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<p>Diagram of diagnostic stages for power-generating unit elements.</p>
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<p>Destructive methods in the decision-making process.</p>
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<p>Microstructure mapping using the matrix replica method [<a href="#B9-materials-17-06074" class="html-bibr">9</a>].</p>
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<p>Example of replicas: the upper one, made on an incorrectly prepared surface with visible grinding marks, and the lower one, correctly prepared on 15HM steel, ferrite, and perlite grains with a retained lamellar cementite structure.</p>
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<p>Microstructure patterns and assigned classes acc. to UDT Guidelines [<a href="#B34-materials-17-06074" class="html-bibr">34</a>].</p>
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<p>A fragment of a steam pipeline used to create the replicas.</p>
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<p>Microstructure of 13HMF steel on the metallographic sample (<b>top</b>) and on the replica (<b>bottom</b>).</p>
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<p>Chords in a single-phase alloy [<a href="#B44-materials-17-06074" class="html-bibr">44</a>].</p>
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<p>Mean grain area measurement using the planimetric method [<a href="#B44-materials-17-06074" class="html-bibr">44</a>].</p>
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<p>SEM images of the specimen (<b>top</b>) and replica (<b>bottom</b>) with marked characteristic features.</p>
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<p>Replica image after checking Adjust → Brightness/Contrast.</p>
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<p>Use of the “Find Edges” feature.</p>
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<p>Placing test lines and reading their actual length.</p>
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<p>Box plots of the mean chords measured on the specimens and replicas. *—position of extreme values.</p>
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<p>Box plots of equivalent diameters measured on the specimens and replicas. *—position of extreme values.</p>
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<p>Mean chord distributions measured on the specimens and replicas.</p>
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<p>Equivalent diameter distributions measured on the specimens and replicas.</p>
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27 pages, 3467 KiB  
Article
Computational Algorithms for Representing Aircraft Instruments with Barometric Physics (Numerical Methods Applied to Flight Simulation)
by Adan Ramirez-Lopez
Appl. Sci. 2024, 14(24), 11536; https://doi.org/10.3390/app142411536 - 11 Dec 2024
Viewed by 389
Abstract
The present work describes the development of a graphical environment to represent typical flight instruments on a computer screen. The instruments’ behavior is displayed according to information regarding the aircraft’s flight conditions. Some of the instruments represented in this work, such as the [...] Read more.
The present work describes the development of a graphical environment to represent typical flight instruments on a computer screen. The instruments’ behavior is displayed according to information regarding the aircraft’s flight conditions. Some of the instruments represented in this work, such as the altimeter, the vertical speed indicator, the aircraft speed indicator, and the Mach indicator, use air pressure principles. The algorithms and routines developed for the screen display are created using the C++ programming language and compiled independently to be included as libraries to improve the software performance. The algorithms developed for this purpose also include the corresponding relationship between the physical variables, such as the speed and displacement, and the standard atmosphere to provide an equivalent value. These algorithms are successfully tested using data information to simulate three hypothetical flights, which are divided into maneuvers with the aircraft in a stopped position, running on the ground, taking off and flying away, including some changes in directions. Moreover, the routines for displaying the aircraft path with the instruments’ animation are also successfully tested by comparison. Finally, an approach analysis as a function of the step time (Δt) used for calculation of the aircraft displacement to evaluate the efficiency of the numerical method integrated in the simulator is also described. It is proved that the aircraft instrument representation is appropriate according to the input data of the analyzed flights, and an improvement in the calculation can be easily obtained, making it possible to represent any flight condition on the aircraft instruments. Full article
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Figure 1
<p>Altimeter (computer simulation): (<b>a</b>) segmentation of the dial and movement regions, and (<b>b</b>) instrument developed for the computer simulation.</p>
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<p>Vertical speed indicator: (<b>a</b>) segmentation of the dial and movement regions, and (<b>b</b>) instrument developed for the computer simulation.</p>
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<p>Airspeed indicator: (<b>a</b>) segmentation of the dial and movement regions, and (<b>b</b>) instrument developed for the computer simulation.</p>
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<p>Machmeter: (<b>a</b>) segmentation of the dial and movement regions, and (<b>b</b>) instrument developed for the computer simulation.</p>
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<p>Fuel indicator: (<b>a</b>) segmentation of the dial and movement regions, and (<b>b</b>) instrument developed for the computer simulation.</p>
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<p>Speed components calculated for the horizontal axes (<b>a</b>) as a function of the aircraft’s horizontal speed (v<sub>x</sub>, v<sub>y</sub>) and heading angle. (<b>b</b>) Calculation of the 3D aircraft speed and displacement.</p>
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<p>Flight instruments displayed on the computer screen with the computational algorithms developed (all the instruments show initial stationary values).</p>
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<p>General flowchart (<b>a</b>) of the flight simulator developed and (<b>b</b>) a graphical representation of the flight instruments and parameter calculation.</p>
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<p>Flowchart selecting the units to be used during the simulation.</p>
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<p>Computer simulation of the aircraft’s flight showing the 2D and 3D paths conforming to the data in <a href="#applsci-14-11536-t001" class="html-table">Table 1</a> for each flight.</p>
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<p>Aircraft displacement along the axes (x, y, z) of the simulated flights: (<b>a</b>) flight (1); (<b>b</b>) flight (2); and (<b>c</b>) flight (3).</p>
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<p>Aircraft speed along the axes (x, y, z) of the simulated flights: (<b>a</b>) flight (1); (<b>b</b>) flight (2); and (<b>c</b>) flight (3).</p>
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<p>Calculation of the results for the analyzed flights based on the total aircraft displacement values for (<b>a</b>) flight (1), (<b>b</b>) flight (2), and (<b>c</b>) flight (3).</p>
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<p>Calculation of the results for the analyzed flights based on the total aircraft displacement values for (<b>a</b>) flight (1), (<b>b</b>) flight (2), and (<b>c</b>) flight (3).</p>
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<p>Calculation of the results for the analyzed flights based on the total aircraft displacement values for (<b>a</b>) flight (1), (<b>b</b>) flight (2), and (<b>c</b>) flight (3).</p>
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14 pages, 306 KiB  
Article
The Quantum Electromagnetic Field in the Weyl–Wigner Representation
by Emilio Santos
Universe 2024, 10(12), 452; https://doi.org/10.3390/universe10120452 - 9 Dec 2024
Viewed by 413
Abstract
The quantum electromagnetic (EM) field is formulated in the Weyl–Wigner representation (WW), which is equivalent to the standard Hilbert space one (HS). In principle, it is possible to interpret within WW all experiments involving the EM field interacting with macroscopic bodies, the latter [...] Read more.
The quantum electromagnetic (EM) field is formulated in the Weyl–Wigner representation (WW), which is equivalent to the standard Hilbert space one (HS). In principle, it is possible to interpret within WW all experiments involving the EM field interacting with macroscopic bodies, the latter treated classically. In the WW formalism, the essential difference between classical electrodynamics and the quantum theory of the EM field is just the assumption that there is a random EM field-filling space, i.e., the existence of a zero-point field with a Gaussian distribution for the field amplitudes. I analyze a typical optical test of a Bell inequality. The model admits an interpretation compatible with local realism, modulo a number of assumptions assumed plausible. Full article
(This article belongs to the Special Issue Quantum Field Theory, 2nd Edition)
14 pages, 9345 KiB  
Article
Effect of Oil Film Radial Clearances on Dynamic Characteristics of Variable Speed Rotor with Non-Concentric SFD
by Weijian Nie, Xiaoguang Yang, Guang Tang, Qicheng Zhang and Ge Wang
Machines 2024, 12(12), 882; https://doi.org/10.3390/machines12120882 - 5 Dec 2024
Viewed by 398
Abstract
Variable-speed aircraft engines require the power turbine rotor to operate stably within a wide range of output speeds, posing a challenge for rotor vibration reduction design. Non-concentric squeeze film dampers (NCSFDs) have been widely used in rotor vibration reduction design due to their [...] Read more.
Variable-speed aircraft engines require the power turbine rotor to operate stably within a wide range of output speeds, posing a challenge for rotor vibration reduction design. Non-concentric squeeze film dampers (NCSFDs) have been widely used in rotor vibration reduction design due to their simple structure. However, comprehensive research on the matching and applicability of NCSFDs under varying operating speeds is lacking. Therefore, this paper investigates the influence of oil film radial clearances on the dynamic characteristics of a variable-speed rotor system with an NCSFD, examining its suitability across variable speeds. This study introduces the principle of equivalent rotor dynamics similarity design, demonstrating good consistency between simulated and real rotor dynamic characteristics, with a radial clearance of 0.10 mm being deemed optimal. The vibration response variation in the rotor at a fixed speed within the range of 0.51 n to 1.0 n does not exceed 4 μm, and the vibration acceleration variation does not exceed 0.04 g, indicating a wide, stable operating speed range. This study can be helpful for the engineering design and vibration reduction design of variable-speed rotors in aircraft engines. Full article
(This article belongs to the Special Issue Power and Propulsion Engineering)
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<p>Schematic diagram of the simulated rotor structure.</p>
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<p>Structure of NCSFD.</p>
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<p>Schematic diagram of the true rotor structure.</p>
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<p>Bifurcation diagram. (<b>a</b>) <span class="html-italic">c</span> = 0.05 mm; (<b>b</b>) <span class="html-italic">c</span> = 0.10 mm; (<b>c</b>) <span class="html-italic">c</span> = 0.15 mm.</p>
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<p>Nonlinear response characteristics (<span class="html-italic">c</span> = 0.10 mm, 1.0 <span class="html-italic">n</span>). (<b>a</b>) Poincaré section; (<b>b</b>) Frequency spectrum.</p>
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<p>Nonlinear response characteristics (<span class="html-italic">c</span> = 0.15 mm, 1.0 <span class="html-italic">n</span>). (<b>a</b>) Poincaré section; (<b>b</b>) Frequency spectrum.</p>
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<p>The physical photo of the rotor on the test rig.</p>
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<p>Amplitude changes with speed under different oil film radial clearances. (<b>a</b>) D<sub>1</sub>; (<b>b</b>) D<sub>2</sub>; (<b>c</b>) D<sub>3</sub>; (<b>d</b>) D<sub>4</sub>.</p>
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<p>Composition of test equipment. Here, 1 represents a power system; 2 represents a speed-increasing system; 3 represents a support system; 4 represents a lubricating oil system; 5 represents a vacuum system; 6 represents a control system; 7 represents the testing system.</p>
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<p>Variation curve of rotor vibration amplitude with speed measured by D<sub>1</sub>~D<sub>4</sub> displacement sensors within the speed range of 0.51 <span class="html-italic">n</span>~1.0 <span class="html-italic">n</span>.</p>
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<p>Variation curve of rotor vibration acceleration with speed measured by A<sub>1</sub>~A<sub>6</sub> accelerometers within the speed range of 0.51 <span class="html-italic">n</span>~1.0 <span class="html-italic">n</span>.</p>
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15 pages, 4416 KiB  
Article
Investigation of the Fabrication Parameters’ Influence on the Tensile Strength of 3D-Printed Copper-Filled Metal Composite Using Design of Experiments
by Vasileios Kyratsis, Anastasios Tzotzis, Apostolos Korlos and Nikolaos Efkolidis
J. Manuf. Mater. Process. 2024, 8(6), 278; https://doi.org/10.3390/jmmp8060278 - 2 Dec 2024
Viewed by 621
Abstract
The present study investigates the effects of fabrication parameters such as the nozzle temperature, the flow rate, and the layer thickness on the tensile strength of copper-filled metal-composite specimens. The selected material is a polylactic acid (PLA) filament filled with 65% copper powder. [...] Read more.
The present study investigates the effects of fabrication parameters such as the nozzle temperature, the flow rate, and the layer thickness on the tensile strength of copper-filled metal-composite specimens. The selected material is a polylactic acid (PLA) filament filled with 65% copper powder. Two sets of 27 specimens each were fabricated, and equivalent tensile experiments were carried out using a universal testing machine. The experiments were planned according to the full factorial design, with three printing parameters, as well as three value levels for each parameter. The analysis revealed that the temperature and the flow rate had the greatest impact on the yielded tensile strength, with their contribution percentages being 42.41% and 22.16%, respectively. In addition, a regression model was developed based on the experimental data to predict the tensile strength of the 3D-printed copper-filled metal composite within the investigated range of parameters. The model was evaluated using statistical methods, highlighting its increased accuracy. Finally, an optimization study was carried out according to the principles of the desirability function. The optimal fabrication parameters were determined to maximize the tensile strength of the specimens: temperature equal to 220 °C, flow rate equal to 110%, and layer thickness close to 0.189 mm. Full article
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<p>The five basic steps of the study.</p>
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<p>The infill pattern, density, and printing orientation of the specimens.</p>
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<p>Macro image of the fractured cross-section and the generated stress–strain curve for specimens (<b>a)</b> No 6, (<b>b</b>) No 10, (<b>c</b>) No 13, and (<b>d</b>) No 18.</p>
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<p>Pareto chart showing the effects of contribution on tensile strength.</p>
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<p>Residual plots generated from the ANOVA: (<b>a</b>) normal probability plot showing the distribution of residuals; (<b>b</b>) residuals vs. fitted values plot highlighting the prediction capability; (<b>c</b>) error histogram with four bins; and (<b>d</b>) residuals vs. order of observation.</p>
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<p>The main effects plot for the average tensile strength with respect to the levels of the three parameters: printing temperature, flow rate, and layer thickness.</p>
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<p>Interaction plots for the printing parameters: (<b>a</b>) F vs T, (<b>b</b>) L vs T and (<b>c</b>) L vs F.</p>
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<p>Contour plots of the response with respect to the fabrication parameters: (<b>a</b>) F × T, (<b>b</b>) L × T, and (<b>c</b>) L × F.</p>
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19 pages, 357 KiB  
Review
Low-Intensity Resistance Exercise in Cardiac Rehabilitation: A Narrative Review of Mechanistic Evidence and Clinical Implications
by Jemima Jansen, Paul W. Marshall, Jocelyne R. Benatar, Rebecca Cross, Tia K. Lindbom and Michael Kingsley
J. Clin. Med. 2024, 13(23), 7338; https://doi.org/10.3390/jcm13237338 - 2 Dec 2024
Viewed by 762
Abstract
Cardiac rehabilitation, a multi-component intervention designed to mitigate the impact of cardiovascular disease, often underutilises low-intensity resistance exercise despite its potential benefits. This narrative review critically examines the mechanistic and clinical evidence supporting the incorporation of low-intensity resistance exercise into cardiac rehabilitation programmes. [...] Read more.
Cardiac rehabilitation, a multi-component intervention designed to mitigate the impact of cardiovascular disease, often underutilises low-intensity resistance exercise despite its potential benefits. This narrative review critically examines the mechanistic and clinical evidence supporting the incorporation of low-intensity resistance exercise into cardiac rehabilitation programmes. Research indicates that low-intensity resistance exercise induces hypertrophic adaptations by maximising muscle fibre activation through the size principle, effectively recruiting larger motor units as it approaches maximal effort. This activation promotes adaptation in both type I and II muscle fibres, resulting in comparable increases in myofibrillar protein synthesis and phosphorylation of key signalling proteins when compared to high-intensity resistance exercise. Low-intensity resistance exercise provides equivalent improvements in muscular strength and hypertrophy compared to high-intensity protocols while addressing barriers to participation, such as concerns about safety and logistical challenges. By facilitating engagement through a more accessible exercise modality, low-intensity resistance exercise might improve adherence rates and patient outcomes in cardiac rehabilitation. Additionally, the ability of low-intensity resistance exercise to address sarcopenia and frailty syndrome, significant determinants of cardiovascular disease progression, can enhance the recovery and overall quality of life for patients. This review establishes evidence-based recommendations for the inclusion of low-intensity resistance exercise in cardiac rehabilitation, offering a promising pathway to enhance the effectiveness of these programmes. Full article
(This article belongs to the Section Clinical Rehabilitation)
22 pages, 6353 KiB  
Article
Real-Time Short-Circuit Current Calculation in Electrical Distribution Systems Considering the Uncertainty of Renewable Resources and Electricity Loads
by Dan Liu, Ping Xiong, Jinrui Tang, Lie Li, Shiyao Wang and Yunyu Cao
Appl. Sci. 2024, 14(23), 11001; https://doi.org/10.3390/app142311001 - 26 Nov 2024
Viewed by 616
Abstract
Existing short-circuit calculation methods for distribution networks with renewable energy sources ignore the fluctuation of renewable sources and cannot reflect the impact of renewable sources and load changes on short-circuit current in real time at all times of the day and in extreme [...] Read more.
Existing short-circuit calculation methods for distribution networks with renewable energy sources ignore the fluctuation of renewable sources and cannot reflect the impact of renewable sources and load changes on short-circuit current in real time at all times of the day and in extreme scenarios. A real-time short-circuit current calculation method is proposed to take into account the stochastic nature of distributed generators (DGs) and electricity loads. Firstly, the continuous power flow of distribution networks is calculated based on the real-time renewable energy output and electricity loads. And then, equivalent DG models with low-voltage ride through (LVRT) strategies are substituted into the iterative calculation method to obtain the short-circuit currents of all main branches in real time. The effects of different renewable energy output curves on distribution network short-circuit currents are quantitatively analyzed during the fluctuation in distributed power output, which can provide an important basis for the setting calculation of distribution network relay protection and the study of new principles of protection. Full article
(This article belongs to the Special Issue State-of-the-Art of Power Systems)
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<p>Symmetrical short-circuit fault analysis: (<b>a</b>) equivalent circuit for distribution network with a fault with transition resistance; (<b>b</b>) equivalent circuit for distribution network in normal status; (<b>c</b>) equivalent circuit for the fault branch.</p>
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<p>Cluster analysis of PV output power: (<b>a</b>) spring season; (<b>b</b>) summer season; (<b>c</b>) autumn season; (<b>d</b>) winter season.</p>
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<p>Cluster analysis of PV output power: (<b>a</b>) spring season; (<b>b</b>) summer season; (<b>c</b>) autumn season; (<b>d</b>) winter season.</p>
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<p>Cluster analysis of residential loads: (<b>a</b>) ten households; (<b>b</b>) fifty households; (<b>c</b>) one hundred and fifty households; (<b>d</b>) three hundred households.</p>
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<p>An illustrative flowchart of our proposed method.</p>
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<p>Four typical daily load curves according to the cluster analysis results.</p>
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<p>Three typical daily output power curves of DGs in the distribution network.</p>
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<p>Topological structures of the distribution network in short-circuit analysis scenarios: (<b>a</b>) the first case; (<b>b</b>) the second case; (<b>c</b>) the third case.</p>
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<p>Topological structures of the distribution network in short-circuit analysis scenarios: (<b>a</b>) the first case; (<b>b</b>) the second case; (<b>c</b>) the third case.</p>
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<p>Voltage at some selected nodes on sunny days during 24 h: (<b>a</b>) node 27; (<b>b</b>) node 54.</p>
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<p>Voltage at node 27 on a sunny day, cloudy day, and rainy day for case 3.</p>
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<p>Short-circuit currents considering the fluctuation in loads in case 1.</p>
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<p>Short-circuit currents considering the fluctuation in loads and DGs in case 3: (<b>a</b>) short-circuit currents on sunny days; (<b>b</b>) short-circuit currents on cloudy days; (<b>c</b>) short-circuit currents on rainy days.</p>
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<p>Short-circuit currents considering the fluctuation in loads and DGs in case 3: (<b>a</b>) short-circuit currents on sunny days; (<b>b</b>) short-circuit currents on cloudy days; (<b>c</b>) short-circuit currents on rainy days.</p>
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<p>Short-circuit currents of branch 1–2 under different equivalent system impedance.</p>
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<p>Short-circuit currents of branch 1–2 under different fault types.</p>
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25 pages, 19929 KiB  
Article
Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible Thermodynamics
by Xin Jin, Yufei Ding, Keke Qiao, Jiamin Wang, Cheng Fang and Ruihan Hu
Appl. Sci. 2024, 14(23), 10923; https://doi.org/10.3390/app142310923 - 25 Nov 2024
Viewed by 525
Abstract
Shale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second [...] Read more.
Shale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second law of thermodynamics, the strain equivalence principle, the non-associated flow rule, and the Drucker–Prager yield criterion. This model is used to describe the mechanical behavior of shale before and after peak strength and has been implemented in ABAQUS via UMAT for numerical computation. The model comprehensively considers the quasi-brittle and anisotropic characteristics of shale, as well as the strength degradation caused by damage during both the elastic and plastic phases. A damage yield function has been established as a criterion for damage occurrence, and the constitutive integration algorithm has been derived using a regression mapping algorithm. Compared with experimental data from La Biche shale in Canada, the theoretical model accurately simulated the stress–strain curves and volumetric–axial strain curves of shale under confining pressures of 5 MPa, 25 MPa, and 50 MPa. When compared with experimental data from shale in Western Hubei and Eastern Chongqing, China, the model precisely fitted the stress–strain curves of shale at pressures of 30 MPa, 50 MPa, and 70 MPa, and at bedding angles of 0°, 22.5°, 45°, and 90°. This proves that the model can effectively predict the failure behavior of shale under different confining pressures and bedding angles. Additionally, a sensitivity analysis has been performed on parameters such as the plastic hardening rate b, damage evolution rate Bω, weighting factor r, and damage softening parameter a. This research is expected to provide theoretical support for the efficient extraction technologies of shale oil and gas. Full article
(This article belongs to the Section Civil Engineering)
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<p>Map of basins with assessed shale oil and shale gas formations [<a href="#B5-applsci-14-10923" class="html-bibr">5</a>].</p>
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<p>Loading direction and bedding plane angle <span class="html-italic">θ</span>.</p>
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<p>Principle of the regression mapping algorithm.</p>
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<p>Schematic of the calculation process for the elastoplastic damage coupled model.</p>
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<p>Stress–strain curves of theoretical and experimental for La Biche shale [<a href="#B18-applsci-14-10923" class="html-bibr">18</a>].</p>
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<p>Volumetric–axial strain curves of theoretical and experimental for La Biche shale [<a href="#B18-applsci-14-10923" class="html-bibr">18</a>].</p>
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<p>Location of Eastern Yunnan–Western Chongqing shale.</p>
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<p>Field sampling (modified from Zhang [<a href="#B110-applsci-14-10923" class="html-bibr">110</a>]).</p>
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<p>Samples in different bedding plane orientations.</p>
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<p>Fitting curve of <span class="html-italic">f</span>(<span class="html-italic">θ</span>) at 0 MPa confining pressure [<a href="#B110-applsci-14-10923" class="html-bibr">110</a>].</p>
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<p>Stress–strain curves of theoretical and experimental for Eastern Yunnan–Western Chongqing shale: (<b>a</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 0°; (<b>b</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 22.5°; (<b>c</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 45°; (<b>d</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 90° [<a href="#B110-applsci-14-10923" class="html-bibr">110</a>].</p>
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<p>Stress–strain curves of theoretical and experimental for Eastern Yunnan–Western Chongqing shale: (<b>a</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 0°; (<b>b</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 22.5°; (<b>c</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 45°; (<b>d</b>) Comparison when the bedding angle <span class="html-italic">θ</span> is 90° [<a href="#B110-applsci-14-10923" class="html-bibr">110</a>].</p>
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<p>Sensitivity analysis of <span class="html-italic">b</span>: (<b>a</b>) The relationship between axial strain and deviatoric stress; (<b>b</b>) The relationship between axial strain and damage variable <span class="html-italic">D</span>.</p>
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<p>Sensitivity analysis of <span class="html-italic">B<sub>ω</sub></span>: (<b>a</b>) The relationship between axial strain and deviatoric stress; (<b>b</b>) The relationship between axial strain and damage variable <span class="html-italic">D</span>.</p>
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<p>Sensitivity analysis of <span class="html-italic">r</span>: (<b>a</b>) The relationship between axial strain and deviatoric stress; (<b>b</b>) The relationship between axial strain and damage variable <span class="html-italic">D</span>.</p>
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<p>Sensitivity analysis of <span class="html-italic">a</span>: (<b>a</b>) The relationship between axial strain and deviatoric stress; (<b>b</b>) The relationship between axial strain and damage variable <span class="html-italic">D</span>.</p>
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13 pages, 5139 KiB  
Article
Study on Long-Term Stability of Lined Rock Cavern for Compressed Air Energy Storage
by Shaohua Liu and Duoxin Zhang
Energies 2024, 17(23), 5908; https://doi.org/10.3390/en17235908 - 25 Nov 2024
Viewed by 439
Abstract
A rock mass is mainly subjected to a high internal pressure load in the lined rock cavern (LRC) for compressed air energy storage (CAES). However, under the action of long-term cyclic loading and unloading, the mechanical properties of a rock mass will deteriorate, [...] Read more.
A rock mass is mainly subjected to a high internal pressure load in the lined rock cavern (LRC) for compressed air energy storage (CAES). However, under the action of long-term cyclic loading and unloading, the mechanical properties of a rock mass will deteriorate, affecting the long-term stability of the cavern. The fissures in the rock mass will expand and generate new cracks, causing varying degrees of damage to the rock mass. Most of the existing studies are based on the test data of complete rock samples and the fissures in the rock mass are ignored. In this paper, the strain equivalence principle is used to couple the initial damage variable caused by the fissures and the fatigue damage variable of a rock mass to obtain the damage variable of a rock mass under cyclic stress. Then, based on the ANSYS 17.0 platform, the ANSYS Parametric Design Language (APDL) is used to program the rock mass elastic modulus evolution equation, and a calculation program of the rock mass damage model is secondarily developed. The calculation program is verified by a cyclic loading and unloading model test. It is applied to the construction project of underground LRC for CAES in Northwest China. The calculation results show that the vertical radial displacement of the rock mass is 8.39 mm after the 100th cycle, which is a little larger than the 7.53 mm after the first cycle. The plastic zone of the rock mass is enlarged by 4.71 m2, about 11.49% for 100 cycles compared to the first cycle. Our calculation results can guide the design and calculation of the LRC, which is beneficial to the promotion of the CAES technology. Full article
(This article belongs to the Section D: Energy Storage and Application)
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<p>Schematic diagram of strain equivalent calculation: (<b>a</b>) A rock containing both initial damage and fatigue damage; (<b>b</b>) A rock containing only initial damage; (<b>c</b>) A rock containing only fatigue damage; (<b>d</b>) A rock containing no damage at all.</p>
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<p>Flowchart of numerical calculation.</p>
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<p>Fissure rock sample.</p>
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<p>Uniaxial compression fatigue test.</p>
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<p>Comparison of the results.</p>
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<p>Finite element model.</p>
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<p>Elastic modulus of the rock mass changes with cycle time.</p>
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<p>Air pressure changes with time.</p>
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<p>Variation curve of stress of concrete lining: (<b>a</b>) Variation curve of maximum tensile stress of concrete lining; (<b>b</b>) Variation curve of maximum compressive stress of concrete lining.</p>
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<p>Distribution of cracks in concrete lining.</p>
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<p>Variation curve of radial displacement at lining measurement points.</p>
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<p>Variation curve of stress of rock: (<b>a</b>) Variation curve of tensile stress at rock measurement points; (<b>b</b>) Variation curve of compressive stress at rock measurement points.</p>
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<p>Variation curve of radial displacement at rock measurement points.</p>
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<p>Changes in areas of plastic zone.</p>
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20 pages, 6228 KiB  
Article
DC-DC Buck Converters with Quasi-Online Estimation of Filter Capacitor Equivalent Parameters
by Dadiana-Valeria Căiman, Corneliu Bărbulescu, Sorin Nanu and Toma-Leonida Dragomir
Appl. Sci. 2024, 14(22), 10756; https://doi.org/10.3390/app142210756 - 20 Nov 2024
Viewed by 533
Abstract
The article focuses on devising solutions for monitoring the condition of the filter capacitors of DC-DC converters. The article introduces two novel DC-DC buck converter designs that monitor the equivalent series resistance (ESR) and the capacitance of capacitors using a parameter observer (PO) [...] Read more.
The article focuses on devising solutions for monitoring the condition of the filter capacitors of DC-DC converters. The article introduces two novel DC-DC buck converter designs that monitor the equivalent series resistance (ESR) and the capacitance of capacitors using a parameter observer (PO) and simple variable electrical networks (VEN). For the first scheme, the PO processes in real time the voltage at the capacitor terminals during a discharge-charge cycle. For the second scheme, the filtering is performed with two or more capacitors in parallel, and the PO processes the voltage at the terminals of each capacitor during two discharge processes without interrupting the filtering operation of the converter. The paper presents the principles and theoretical support on which the two schemes of DC-DC buck converters are based, design details regarding PO and VEN, as well as experiments performed with each of the schemes. In the experimental schemes, the PO is implemented with a microcontroller, and the parameters of some aluminum electrolytic filter capacitors are calculated in a real-time manner of about 40 ms. The calculation accuracy of the equivalent capacity is very good. Regarding the calculation accuracy of the ESR, it is shown that it depends on the fulfillment of certain ratios between the VEN resistances, on the one hand, as well as between them and the ESR, on the other hand. Full article
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<p>V curve of Equation (4).</p>
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<p>The connection of PO to the observed system OS in order to estimate the parameter <math display="inline"><semantics> <mrow> <mi>T</mi> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>. For<math display="inline"><semantics> <mrow> <mo> </mo> <mi>t</mi> <mo>∈</mo> <mfenced open="[" separators="|"> <mrow> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math> the switch SW is in position 2, and for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>∈</mo> <mfenced open="[" close="]" separators="|"> <mrow> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math> in position 1.</p>
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<p>The behavior of the system in <a href="#applsci-14-10756-f002" class="html-fig">Figure 2</a> when <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> has the Equation (7): (<b>a</b>) input signal; (<b>b</b>) the estimated time constant <math display="inline"><semantics> <mrow> <mo> </mo> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>.</p>
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<p>Parameter observer on two edges: (<b>a</b>) the structure of PO2; (<b>b</b>) the block diagram of the connection OS-PO2 for discrete time processing.</p>
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<p>The influence of the <math display="inline"><semantics> <mrow> <mi>K</mi> </mrow> </semantics></math> parameter of PO2 on<math display="inline"><semantics> <mrow> <mo> </mo> <mi>T</mi> </mrow> </semantics></math> value.</p>
Full article ">Figure 6
<p>A group of characteristics <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> of parameter <math display="inline"><semantics> <mrow> <mi>K</mi> </mrow> </semantics></math> for the case when the system observed in <a href="#applsci-14-10756-f004" class="html-fig">Figure 4</a>b generates the signal (7); <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>∈</mo> <mfenced open="{" close="}" separators="|"> <mrow> <mn>2.9</mn> <mo>,</mo> <mn>2.95</mn> <mo>,</mo> <mn>2.98</mn> <mo>,</mo> <mn>2.99</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>3.01</mn> <mo>,</mo> <mn>3.02</mn> <mo>,</mo> <mn>3.05</mn> <mo>,</mo> <mn>3.1</mn> </mrow> </mfenced> </mrow> </semantics></math>: (<b>a</b>) Highlighting the segments <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mrow> <mn>1</mn> <mo>,</mo> <mi>K</mi> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math> și<math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mrow> <mn>2</mn> <mo>,</mo> <mi>K</mi> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>; (<b>b</b>) Obtaining <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> estimates from segments <math display="inline"><semantics> <mrow> <msub> <mrow> <mo> </mo> <mover accent="true"> <mrow> <mo> </mo> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mrow> <mn>2</mn> <mo>,</mo> <mi>K</mi> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>.</p>
Full article ">Figure 7
<p>Principle schemes used for the realization of DC-DC buck converters with the estimation of the equivalent parameters of the filter capacitors: (<b>a</b>,<b>b</b>) Schemes with the monitoring of the discharging and charging of the capacitor using PO2 (<b>c</b>,<b>d</b>) Schemes with monitoring of two distinct discharges using PO.</p>
Full article ">Figure 8
<p>The time sequence for filtering capacitor parameter estimation by a discharge/charge process.</p>
Full article ">Figure 9
<p>Buck converter scheme made based on the principle scheme in <a href="#applsci-14-10756-f007" class="html-fig">Figure 7</a>a.</p>
Full article ">Figure 10
<p>Frequency characteristics of the filter capacitor <math display="inline"><semantics> <mrow> <mi>C</mi> <mn>2</mn> </mrow> </semantics></math> of the converter in <a href="#applsci-14-10756-f009" class="html-fig">Figure 9</a>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </semantics></math> characteristic; (<b>b</b>) Characteristic <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p><math display="inline"><semantics> <mrow> <mi>C</mi> <mn>2</mn> </mrow> </semantics></math> capacitor charging/discharging signal in <a href="#applsci-14-10756-f009" class="html-fig">Figure 9</a> and the result of its processing with PO2: (<b>a</b>) The signal <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> on capacitor terminal; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mrow> <mn>1</mn> <mo>,</mo> <mi>K</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mrow> <mn>2</mn> <mo>,</mo> <mi>K</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>3.291</mn> <mo> </mo> <mi mathvariant="normal">V</mi> </mrow> </semantics></math> characteristics generated by PO2.</p>
Full article ">Figure 12
<p>Buck converter scheme made based on the principle scheme in <a href="#applsci-14-10756-f007" class="html-fig">Figure 7</a>d.</p>
Full article ">Figure 13
<p>Frequency characteristics of the filter capacitors in <a href="#applsci-14-10756-f012" class="html-fig">Figure 12</a>: (<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </semantics></math> characteristics of the electrolytic capacitor <math display="inline"><semantics> <mrow> <mi>C</mi> <mn>21</mn> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <mn>470</mn> <mo> </mo> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">F</mi> <mo>/</mo> <mn>25</mn> <mo> </mo> <mi mathvariant="normal">V</mi> <mo>)</mo> </mrow> </semantics></math>; (<b>c</b>,<b>d</b>) <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </semantics></math> characteristics of electrolytic capacitor <math display="inline"><semantics> <mrow> <mi>C</mi> <mn>22</mn> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <mn>220</mn> <mo> </mo> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">F</mi> <mo>/</mo> <mn>25</mn> <mo> </mo> <mi mathvariant="normal">V</mi> </mrow> </semantics></math>).</p>
Full article ">Figure 14
<p>Experiment performed with the converter from <a href="#applsci-14-10756-f012" class="html-fig">Figure 12</a> in stage 1: (<b>a</b>) Characteristics <math display="inline"><semantics> <mrow> <msub> <mrow> <mo> </mo> <mover accent="true"> <mrow> <mo> </mo> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mrow> <mn>1</mn> <mo>_</mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mrow> <mn>2</mn> <mo>_</mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mrow> <mn>1</mn> <mo>_</mo> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> și <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mrow> <mn>2</mn> <mo>_</mo> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>; (<b>b</b>) Voltage variation <math display="inline"><semantics> <mrow> <msub> <mrow> <mo> </mo> <mi>V</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> from the terminals of capacitors <math display="inline"><semantics> <mrow> <mi>C</mi> <mn>21</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>C</mi> <mn>22</mn> </mrow> </semantics></math>; (<b>c</b>) Voltage variation <math display="inline"><semantics> <mrow> <msub> <mrow> <mo> </mo> <mi>V</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> at the load terminals.</p>
Full article ">Figure 15
<p>Integrated circuit diagram associated with the DC-DC buck converter in <a href="#applsci-14-10756-f012" class="html-fig">Figure 12</a>. The integrated chip includes 6 switches (T-sw<sub>ij,</sub> i,j = {1,2}; T-sw<sub>i,</sub> i = {3,4}), the LM2596 circuit, the LDO circuit, and the microcontroller. The unembedded components are the filtering capacitors <math display="inline"><semantics> <mrow> <mi>C</mi> <mn>21</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>C</mi> <mn>22</mn> </mrow> </semantics></math>, the VEN resistors <math display="inline"><semantics> <mrow> <msub> <mrow> <mo> </mo> <mi>R</mi> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>t</mi> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mo> </mo> <mi>R</mi> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>t</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>, the temperature sensors, the inductance L<sub>1</sub>, and the input capacitors <math display="inline"><semantics> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>C</mi> <mn>2</mn> </mrow> </semantics></math>.</p>
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