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22 pages, 3301 KiB  
Article
Parameter Identification of Distribution Zone Transformers Under Three-Phase Asymmetric Conditions
by Panrun Jin, Wenqin Song and Yankui Zhang
Eng 2025, 6(8), 181; https://doi.org/10.3390/eng6080181 (registering DOI) - 2 Aug 2025
Abstract
As a core device in low-voltage distribution networks, the distribution zone transformer (DZT) is influenced by short circuits, overloads, and unbalanced loads, which cause thermal aging, mechanical stress, and eventually deformation of the winding, resulting in parameter deviations from nameplate values and impairing [...] Read more.
As a core device in low-voltage distribution networks, the distribution zone transformer (DZT) is influenced by short circuits, overloads, and unbalanced loads, which cause thermal aging, mechanical stress, and eventually deformation of the winding, resulting in parameter deviations from nameplate values and impairing system operation. However, existing identification methods typically require synchronized high- and low-voltage data and are limited to symmetric three-phase conditions, which limits their application in practical distribution systems. To address these challenges, this paper proposes a parameter identification method for DZTs under three-phase unbalanced conditions. Firstly, based on the transformer’s T-equivalent circuit considering the load, the power flow equations are derived without involving the synchronization issue of high-voltage and low-voltage side data, and the sum of the impedances on both sides is treated as an independent parameter. Then, a novel power flow equation under three-phase unbalanced conditions is established, and an adaptive recursive least squares (ARLS) solution method is constructed using the measurement data sequence provided by the smart meter of the intelligent transformer terminal unit (TTU) to achieve online identification of the transformer winding parameters. The effectiveness and robustness of the method are verified through practical case studies. Full article
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24 pages, 1008 KiB  
Article
Variable Submodule Voltage Control for Enhanced Efficiency in DAB-Integrated Modular Multilevel Converters
by Marzio Barresi, Davide De Simone, Edoardo Ferri and Luigi Piegari
Energies 2025, 18(15), 4096; https://doi.org/10.3390/en18154096 (registering DOI) - 1 Aug 2025
Abstract
Modular multilevel converters (MMCs) are widely used in power-conversion applications, including distributed energy storage integration, because of their scalability, high efficiency, and reduced harmonic distortion. Integrating battery storage systems into MMC submodules using dual active bridge (DAB) converters provides electrical isolation and reduces [...] Read more.
Modular multilevel converters (MMCs) are widely used in power-conversion applications, including distributed energy storage integration, because of their scalability, high efficiency, and reduced harmonic distortion. Integrating battery storage systems into MMC submodules using dual active bridge (DAB) converters provides electrical isolation and reduces voltage stress, harmonics, and common-mode issues. However, voltage fluctuations due to the battery state of charge can compromise the zero-voltage switching (ZVS) operation of a DAB and increase the reactive power circulation, leading to higher losses and reduced system performance. To address these challenges, this study investigated an active control strategy for submodule voltage regulation in an MMC with DAB-based battery integration. Assuming single-phase-shift modulation, two control strategies were evaluated. The first strategy regulated the DAB voltage on one side to match the battery voltage on the other, scaled by the high-frequency transformer turns ratio, which facilitated the ZVS operation and reduced the reactive power. The second strategy optimized this voltage to minimize the total power-conversion losses. The proposed control strategies improved the efficiency, particularly at low power levels, achieving several percentage points of improvement compared to maintaining a constant voltage. Full article
17 pages, 2076 KiB  
Article
Detection and Classification of Power Quality Disturbances Based on Improved Adaptive S-Transform and Random Forest
by Dongdong Yang, Shixuan Lü, Junming Wei, Lijun Zheng and Yunguang Gao
Energies 2025, 18(15), 4088; https://doi.org/10.3390/en18154088 (registering DOI) - 1 Aug 2025
Abstract
The increasing penetration of renewable energy into power systems has intensified transient power quality (PQ) disturbances, demanding efficient detection and classification methods to enable timely operational decisions. This paper introduces a hybrid framework combining an Improved Adaptive S-Transform (IAST) with a Random Forest [...] Read more.
The increasing penetration of renewable energy into power systems has intensified transient power quality (PQ) disturbances, demanding efficient detection and classification methods to enable timely operational decisions. This paper introduces a hybrid framework combining an Improved Adaptive S-Transform (IAST) with a Random Forest (RF) classifier to address these challenges. The IAST employs a globally adaptive Gaussian window as its kernel function, which automatically adjusts window length and spectral resolution based on real-time frequency characteristics, thereby enhancing time–frequency localization accuracy while reducing algorithmic complexity. To optimize computational efficiency, window parameters are determined through an energy concentration maximization criterion, enabling rapid extraction of discriminative features from diverse PQ disturbances (e.g., voltage sags and transient interruptions). These features are then fed into an RF classifier, which simultaneously mitigates model variance and bias, achieving robust classification. Experimental results show that the proposed IAST–RF method achieves a classification accuracy of 99.73%, demonstrating its potential for real-time PQ monitoring in modern grids with high renewable energy penetration. Full article
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22 pages, 1287 KiB  
Article
Comparative Analysis of the Gardner Equation in Plasma Physics Using Analytical and Neural Network Methods
by Zain Majeed, Adil Jhangeer, F. M. Mahomed, Hassan Almusawa and F. D. Zaman
Symmetry 2025, 17(8), 1218; https://doi.org/10.3390/sym17081218 (registering DOI) - 1 Aug 2025
Abstract
In the present paper, a mathematical analysis of the Gardner equation with varying coefficients has been performed to give a more realistic model of physical phenomena, especially in regards to plasma physics. First, a Lie symmetry analysis was carried out, as a result [...] Read more.
In the present paper, a mathematical analysis of the Gardner equation with varying coefficients has been performed to give a more realistic model of physical phenomena, especially in regards to plasma physics. First, a Lie symmetry analysis was carried out, as a result of which a symmetry classification following the different representations of the variable coefficients was systematically derived. The reduced ordinary differential equation obtained is solved using the power-series method and solutions to the equation are represented graphically to give an idea of their dynamical behavior. Moreover, a fully connected neural network has been included as an efficient computation method to deal with the complexity of the reduced equation, by using traveling-wave transformation. The validity and correctness of the solutions provided by the neural networks have been rigorously tested and the solutions provided by the neural networks have been thoroughly compared with those generated by the Runge–Kutta method, which is a conventional and well-recognized numerical method. The impact of a variation in the loss function of different coefficients has also been discussed, and it has also been found that the dispersive coefficient affects the convergence rate of the loss contribution considerably compared to the other coefficients. The results of the current work can be used to improve knowledge on the nonlinear dynamics of waves in plasma physics. They also show how efficient it is to combine the approaches, which consists in the use of analytical and semi-analytical methods and methods based on neural networks, to solve nonlinear differential equations with variable coefficients of a complex nature. Full article
(This article belongs to the Section Physics)
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34 pages, 1441 KiB  
Article
Empowering the Intelligent Transformation of the Manufacturing Sector Through New Quality Productive Forces: Value Implications, Theoretical Analysis, and Empirical Examination
by Yinyan Hu and Xinran Jia
Sustainability 2025, 17(15), 7006; https://doi.org/10.3390/su17157006 (registering DOI) - 1 Aug 2025
Abstract
Achieving sustainable development goals remains a core issue in global development. In response, China has proposed the development of new quality productive forces (NQPFs) through innovative thinking, emphasizing that fostering NQPFs is both an intrinsic requirement and a pivotal focus for advancing high-quality [...] Read more.
Achieving sustainable development goals remains a core issue in global development. In response, China has proposed the development of new quality productive forces (NQPFs) through innovative thinking, emphasizing that fostering NQPFs is both an intrinsic requirement and a pivotal focus for advancing high-quality development. Concurrently, the intelligent transformation of the manufacturing sector serves as a critical direction for China’s economic restructuring and upgrading. This paper places “new quality productive forces” and “intelligent transformation of manufacturing” within the same analytical framework. Starting from the logical chain of “new quality productive forces—three major mechanisms—intelligent transformation of manufacturing,” it concretizes the value implications of new quality productive forces into a systematic conceptual framework driven by the synergistic interaction of three major mechanisms: the mechanism of revolutionary technological breakthroughs, the mechanism of innovative allocation of production factors, and the mechanism of deep industrial transformation and upgrading. This study constructs a “3322” evaluation index system for NQPFs, based on three formative processes, three driving forces, two supporting systems, and two-dimensional characteristics. Simultaneously, it builds an evaluation index system for the intelligent transformation of manufacturing, encompassing intelligent technology, intelligent applications, and intelligent benefits. Using national time-series data from 2012 to 2023, this study assesses the development levels of both NQPFs and the intelligent transformation of manufacturing during this period. The study further analyzes the impact of NQPFs on the intelligent transformation of the manufacturing sector. The research results indicate the following: (1) NQPFs drive the intelligent transformation of the manufacturing industry through the three mechanisms of innovative allocation of production factors, revolutionary breakthroughs in technology, and deep transformation and upgrading of industries. (2) The development of NQPFs exhibits a slow upward trend; however, the outbreak of the pandemic and Sino-US trade frictions have caused significant disruptions to the development of new-type productive forces. (3) The level of intelligent manufacturing continues to improve; however, from 2020 to 2023, due to the impact of the COVID-19 pandemic and Sino-US trade conflicts, the level of intelligent benefits has slightly declined. (4) NQPFs exert a powerful driving force on the intelligent transformation of manufacturing, exerting a significant positive impact on intelligent technology, intelligent applications, and intelligent efficiency levels. Full article
29 pages, 1477 KiB  
Review
Bioinformation and Monitoring Technology for Environmental DNA Analysis: A Review
by Hyo Jik Yoon, Joo Hyeong Seo, Seung Hoon Shin, Mohamed A. A. Abedlhamid and Seung Pil Pack
Biosensors 2025, 15(8), 494; https://doi.org/10.3390/bios15080494 (registering DOI) - 1 Aug 2025
Abstract
Environmental DNA (eDNA) analysis has emerged as a transformative tool in environmental monitoring, enabling non-invasive detection of species and microbial communities across diverse ecosystems. This study systematically reviews the role of bioinformation technology in eDNA analysis, focusing on methodologies and applications across air, [...] Read more.
Environmental DNA (eDNA) analysis has emerged as a transformative tool in environmental monitoring, enabling non-invasive detection of species and microbial communities across diverse ecosystems. This study systematically reviews the role of bioinformation technology in eDNA analysis, focusing on methodologies and applications across air, soil, groundwater, sediment, and aquatic environments. Advances in molecular biology, high-throughput sequencing, bioinformatics tools, and field-deployable detection systems have significantly improved eDNA detection sensitivity, allowing for early identification of invasive species, monitoring ecosystem health, and tracking pollutant degradation processes. Airborne eDNA monitoring has demonstrated potential for assessing microbial shifts due to air pollution and tracking pathogen transmission. In terrestrial environments, eDNA facilitates soil and groundwater pollution assessments and enhances understanding of biodegradation processes. In aquatic ecosystems, eDNA serves as a powerful tool for biodiversity assessment, invasive species monitoring, and wastewater-based epidemiology. Despite its growing applicability, challenges remain, including DNA degradation, contamination risks, and standardization of sampling protocols. Future research should focus on integrating eDNA data with remote sensing, machine learning, and ecological modeling to enhance predictive environmental monitoring frameworks. As technological advancements continue, eDNA-based approaches are poised to revolutionize environmental assessment, conservation strategies, and public health surveillance. Full article
(This article belongs to the Section Environmental Biosensors and Biosensing)
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25 pages, 953 KiB  
Article
Command Redefined: Neural-Adaptive Leadership in the Age of Autonomous Intelligence
by Raul Ionuț Riti, Claudiu Ioan Abrudan, Laura Bacali and Nicolae Bâlc
AI 2025, 6(8), 176; https://doi.org/10.3390/ai6080176 (registering DOI) - 1 Aug 2025
Abstract
Artificial intelligence has taken a seat at the executive table and is threatening the fact that human beings are the only ones who should be in a position of power. This article gives conjectures on the future of leadership in which managers will [...] Read more.
Artificial intelligence has taken a seat at the executive table and is threatening the fact that human beings are the only ones who should be in a position of power. This article gives conjectures on the future of leadership in which managers will collaborate with learning algorithms in the Neural Adaptive Artificial Intelligence Leadership Model, which is informed by the transformational literature on leadership and socio-technical systems, as well as the literature on algorithmic governance. We assessed the model with thirty in-depth interviews, system-level traces of behavior, and a verified survey, and we explored six hypotheses that relate to algorithmic delegation and ethical oversight, as well as human judgment versus machine insight in terms of agility and performance. We discovered that decisions are made quicker, change is more effective, and interaction is more vivid where agile practices and good digital understanding exist, and statistical tests propose that human flexibility and definite governance augment those benefits as well. It is single-industry research that contains self-reported measures, which causes research to be limited to other industries that contain more objective measures. Practitioners are provided with a practical playbook on how to make algorithmic jobs meaningful, introduce moral fail-safes, and build learning feedback to ensure people and machines are kept in line. Socially, the practice is capable of minimizing bias and establishing inclusion by visualizing accountability in the code and practice. Filling the gap between the theory of leadership and the reality of algorithms, the study provides a model of intelligent systems leading in organizations that can be reproduced. Full article
(This article belongs to the Section AI Systems: Theory and Applications)
20 pages, 1890 KiB  
Review
Laser Surface Hardening of Carburized Steels: A Review of Process Parameters and Application in Gear Manufacturing
by Janusz Kluczyński, Katarzyna Jasik, Jakub Łuszczek and Jakub Pokropek
Materials 2025, 18(15), 3623; https://doi.org/10.3390/ma18153623 (registering DOI) - 1 Aug 2025
Abstract
This article provides a comprehensive overview of recent studies concerning laser heat treatment (LHT) of structural and tool steels, with particular attention to the 21NiCrMo2 steel used for carburized gear wheels. Analysis includes the influence of critical laser processing conditions—including power output, motion [...] Read more.
This article provides a comprehensive overview of recent studies concerning laser heat treatment (LHT) of structural and tool steels, with particular attention to the 21NiCrMo2 steel used for carburized gear wheels. Analysis includes the influence of critical laser processing conditions—including power output, motion speed, spot size, and focusing distance—on surface microhardness, hardening depth, and microstructure development. The findings indicate that the energy density is the dominant factor that affects the outcomes of LHT. Optimal results, in the form of a high surface microhardness and a sufficient depth of hardening, were achieved within the energy density range of 80–130 J/mm2, allowing for martensitic transformation while avoiding defects such as melting or cracking. At densities below 50 J/mm2, incomplete hardening occurred with minimal microhardness improvement. On the contrary, densities exceeding 150–180 J/mm2 caused surface overheating and degradation. For carburized 21NiCrMo2 steel, the most effective parameters included 450–1050 W laser power, 1.7–2.5 mm/s scanning speed, and 2.0–2.3 mm beam diameter. The review confirms that process control through energy-based parameters allows for reliable prediction and optimization of LHT for industrial applications, particularly in components exposed to cyclic loads. Full article
(This article belongs to the Special Issue Advanced Machining and Technologies in Materials Science)
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37 pages, 642 KiB  
Article
The Goddess of the Flaming Mouth Between India and Tibet
by Arik Moran and Alexander Zorin
Religions 2025, 16(8), 1002; https://doi.org/10.3390/rel16081002 - 1 Aug 2025
Abstract
This article examines the evolution and potential cross-cultural adaptations of the “Goddess of the Flaming Mouth”, Jvālāmukhī (Skt.) or Kha ‘bar ma (Tib.), in Indic and Tibetan traditions. A minor figure in medieval Hindu Tantras, Jvālāmukhī is today best known through her tangible [...] Read more.
This article examines the evolution and potential cross-cultural adaptations of the “Goddess of the Flaming Mouth”, Jvālāmukhī (Skt.) or Kha ‘bar ma (Tib.), in Indic and Tibetan traditions. A minor figure in medieval Hindu Tantras, Jvālāmukhī is today best known through her tangible manifestation as natural flames in a West Himalayan temple complex in the valley of Kangra, Himachal Pradesh, India. The gap between her sparse portrayal in Tantric texts and her enduring presence at this local “seat of power” (śakti pīṭha) raises questions regarding her historical development and sectarian affiliations. To address these questions, we examine mentions of Jvālāmukhī’s Tibetan counterpart, Kha ‘bar ma, across a wide range of textual sources: canonical Buddhist texts, original Tibetan works of the Bön and Buddhist traditions, and texts on sacred geography. Regarded as a queen of ghost spirits (pretas) and field protector (kṣetrapāla) in Buddhist sources, her portrayal in Bön texts contain archaic motifs that hint at autochthonous and/or non-Buddhist origins. The assessment of Indic material in conjunction with Tibetan texts point to possible transformations of the goddess across these culturally proximate Himalayan settings. In presenting and contextualizing these transitions, this article contributes critical data to ongoing efforts to map the development, adaptation, and localization of Tantric deities along the Indo-Tibetan interface. Full article
29 pages, 959 KiB  
Review
Machine Learning-Driven Insights in Cancer Metabolomics: From Subtyping to Biomarker Discovery and Prognostic Modeling
by Amr Elguoshy, Hend Zedan and Suguru Saito
Metabolites 2025, 15(8), 514; https://doi.org/10.3390/metabo15080514 (registering DOI) - 1 Aug 2025
Abstract
Cancer metabolic reprogramming plays a critical role in tumor progression and therapeutic resistance, underscoring the need for advanced analytical strategies. Metabolomics, leveraging mass spectrometry and nuclear magnetic resonance (NMR) spectroscopy, offers a comprehensive and functional readout of tumor biochemistry. By enabling both targeted [...] Read more.
Cancer metabolic reprogramming plays a critical role in tumor progression and therapeutic resistance, underscoring the need for advanced analytical strategies. Metabolomics, leveraging mass spectrometry and nuclear magnetic resonance (NMR) spectroscopy, offers a comprehensive and functional readout of tumor biochemistry. By enabling both targeted metabolite quantification and untargeted profiling, metabolomics captures the dynamic metabolic alterations associated with cancer. The integration of metabolomics with machine learning (ML) approaches further enhances the interpretation of these complex, high-dimensional datasets, providing powerful insights into cancer biology from biomarker discovery to therapeutic targeting. This review systematically examines the transformative role of ML in cancer metabolomics. We discuss how various ML methodologies—including supervised algorithms (e.g., Support Vector Machine, Random Forest), unsupervised techniques (e.g., Principal Component Analysis, t-SNE), and deep learning frameworks—are advancing cancer research. Specifically, we highlight three major applications of ML–metabolomics integration: (1) cancer subtyping, exemplified by the use of Similarity Network Fusion (SNF) and LASSO regression to classify triple-negative breast cancer into subtypes with distinct survival outcomes; (2) biomarker discovery, where Random Forest and Partial Least Squares Discriminant Analysis (PLS-DA) models have achieved >90% accuracy in detecting breast and colorectal cancers through biofluid metabolomics; and (3) prognostic modeling, demonstrated by the identification of race-specific metabolic signatures in breast cancer and the prediction of clinical outcomes in lung and ovarian cancers. Beyond these areas, we explore applications across prostate, thyroid, and pancreatic cancers, where ML-driven metabolomics is contributing to earlier detection, improved risk stratification, and personalized treatment planning. We also address critical challenges, including issues of data quality (e.g., batch effects, missing values), model interpretability, and barriers to clinical translation. Emerging solutions, such as explainable artificial intelligence (XAI) approaches and standardized multi-omics integration pipelines, are discussed as pathways to overcome these hurdles. By synthesizing recent advances, this review illustrates how ML-enhanced metabolomics bridges the gap between fundamental cancer metabolism research and clinical application, offering new avenues for precision oncology through improved diagnosis, prognosis, and tailored therapeutic strategies. Full article
(This article belongs to the Special Issue Nutritional Metabolomics in Cancer)
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35 pages, 2730 KiB  
Review
Deep Learning and NLP-Based Trend Analysis in Actuators and Power Electronics
by Woojun Jung and Keuntae Cho
Actuators 2025, 14(8), 379; https://doi.org/10.3390/act14080379 (registering DOI) - 1 Aug 2025
Abstract
Actuators and power electronics are fundamental components of modern control systems, enabling high-precision functionality, enhanced energy efficiency, and sophisticated automation. This study investigates evolving research trends and thematic developments in these areas spanning the last two decades (2005–2024). This study analyzed 1840 peer-reviewed [...] Read more.
Actuators and power electronics are fundamental components of modern control systems, enabling high-precision functionality, enhanced energy efficiency, and sophisticated automation. This study investigates evolving research trends and thematic developments in these areas spanning the last two decades (2005–2024). This study analyzed 1840 peer-reviewed abstracts obtained from the Web of Science database using BERTopic modeling, which integrates transformer-based sentence embeddings with UMAP for dimensionality reduction and HDBSCAN for clustering. The approach also employed class-based TF-IDF calculations, intertopic distance visualization, and hierarchical clustering to clarify topic structures. The analysis revealed a steady increase in research publications, with a marked surge post-2015. From 2005 to 2014, investigations were mainly focused on established areas including piezoelectric actuators, adaptive control, and hydraulic systems. In contrast, the 2015–2024 period saw broader diversification into new topics such as advanced materials, robotic mechanisms, resilient systems, and networked actuator control through communication protocols. The structural topic analysis indicated a shift from a unified to a more differentiated and specialized spectrum of research themes. This study offers a rigorous, data-driven outlook on the increasing complexity and diversity of actuator and power electronics research. The findings are pertinent for researchers, engineers, and policymakers aiming to advance state-of-the-art, sustainable industrial technologies. Full article
(This article belongs to the Special Issue Power Electronics and Actuators—Second Edition)
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42 pages, 4490 KiB  
Review
Continuous Monitoring with AI-Enhanced BioMEMS Sensors: A Focus on Sustainable Energy Harvesting and Predictive Analytics
by Mingchen Cai, Hao Sun, Tianyue Yang, Hongxin Hu, Xubing Li and Yuan Jia
Micromachines 2025, 16(8), 902; https://doi.org/10.3390/mi16080902 (registering DOI) - 31 Jul 2025
Abstract
Continuous monitoring of environmental and physiological parameters is essential for early diagnostics, real-time decision making, and intelligent system adaptation. Recent advancements in bio-microelectromechanical systems (BioMEMS) sensors have significantly enhanced our ability to track key metrics in real time. However, continuous monitoring demands sustainable [...] Read more.
Continuous monitoring of environmental and physiological parameters is essential for early diagnostics, real-time decision making, and intelligent system adaptation. Recent advancements in bio-microelectromechanical systems (BioMEMS) sensors have significantly enhanced our ability to track key metrics in real time. However, continuous monitoring demands sustainable energy supply solutions, especially for on-site energy replenishment in areas with limited resources. Artificial intelligence (AI), particularly large language models, offers new avenues for interpreting the vast amounts of data generated by these sensors. Despite this potential, fully integrated systems that combine self-powered BioMEMS sensing with AI-based analytics remain in the early stages of development. This review first examines the evolution of BioMEMS sensors, focusing on advances in sensing materials, micro/nano-scale architectures, and fabrication techniques that enable high sensitivity, flexibility, and biocompatibility for continuous monitoring applications. We then examine recent advances in energy harvesting technologies, such as piezoelectric nanogenerators, triboelectric nanogenerators and moisture electricity generators, which enable self-powered BioMEMS sensors to operate continuously and reducereliance on traditional batteries. Finally, we discuss the role of AI in BioMEMS sensing, particularly in predictive analytics, to analyze continuous monitoring data, identify patterns, trends, and anomalies, and transform this data into actionable insights. This comprehensive analysis aims to provide a roadmap for future continuous BioMEMS sensing, revealing the potential unlocked by combining materials science, energy harvesting, and artificial intelligence. Full article
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19 pages, 1020 KiB  
Article
Optimizing Power Sharing and Demand Reduction in Distributed Energy Resources for Apartments Through Tenant Incentivization
by Janak Nambiar, Samson Yu, Jag Makam and Hieu Trinh
Energies 2025, 18(15), 4073; https://doi.org/10.3390/en18154073 (registering DOI) - 31 Jul 2025
Abstract
The increasing demand for electricity in multi-tenanted residential areas has placed unforeseen strain on sub-transformers, particularly in dense urban environments. This strain compromises overall grid performance and challenges utilities with shifting and rising peak demand periods. This study presents a novel approach to [...] Read more.
The increasing demand for electricity in multi-tenanted residential areas has placed unforeseen strain on sub-transformers, particularly in dense urban environments. This strain compromises overall grid performance and challenges utilities with shifting and rising peak demand periods. This study presents a novel approach to enhance the operation of a virtual power plant (VPP) comprising a microgrid (MG) integrated with renewable energy sources (RESs) and energy storage systems (ESSs). By employing an advanced monitoring and control system, the proposed topology enables efficient energy management and demand-side control within apartment complexes. The system supports controlled electricity distribution, reducing the likelihood of unpredictable demand spikes and alleviating stress on local infrastructure during peak periods. Additionally, the model capitalizes on the large number of tenancies to distribute electricity effectively, leveraging locally available RESs and ESSs behind the sub-transformer. The proposed research provides a systematic framework for managing electricity demand and optimizing resource utilization, contributing to grid reliability and a transition toward a more sustainable, decentralized energy system. Full article
17 pages, 438 KiB  
Article
Analytic Solutions and Conservation Laws of a 2D Generalized Fifth-Order KdV Equation with Power Law Nonlinearity Describing Motions in Shallow Water Under a Gravity Field of Long Waves
by Chaudry Masood Khalique and Boikanyo Pretty Sebogodi
AppliedMath 2025, 5(3), 96; https://doi.org/10.3390/appliedmath5030096 (registering DOI) - 31 Jul 2025
Abstract
The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly [...] Read more.
The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly and nonlinearly, acoustic waves on a crystal lattice, lengthy internal waves in density-graded oceans, and ion acoustic waves in plasma. The KdV equation is one of the most well-known soliton models, and it provides a good platform for further research into other equations. The KdV equation has several forms. The aim of this study is to introduce and investigate a (2+1)-dimensional generalized fifth-order KdV equation with power law nonlinearity (gFKdVp). The research methodology employed is the Lie group analysis. Using the point symmetries of the gFKdVp equation, we transform this equation into several nonlinear ordinary differential equations (ODEs), which we solve by employing different strategies that include Kudryashov’s method, the (G/G) expansion method, and the power series expansion method. To demonstrate the physical behavior of the equation, 3D, density, and 2D graphs of the obtained solutions are presented. Finally, utilizing the multiplier technique and Ibragimov’s method, we derive conserved vectors of the gFKdVp equation. These include the conservation of energy and momentum. Thus, the major conclusion of the study is that analytic solutions and conservation laws of the gFKdVp equation are determined. Full article
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12 pages, 441 KiB  
Article
G-Subdiffusion Equation as an Anomalous Diffusion Equation Determined by the Time Evolution of the Mean Square Displacement of a Diffusing Molecule
by Tadeusz Kosztołowicz, Aldona Dutkiewicz and Katarzyna D. Lewandowska
Entropy 2025, 27(8), 816; https://doi.org/10.3390/e27080816 (registering DOI) - 31 Jul 2025
Abstract
Normal and anomalous diffusion processes are characterized by the time evolution of the mean square displacement of a diffusing molecule σ2(t). When σ2(t) is a power function of time, the process is described by [...] Read more.
Normal and anomalous diffusion processes are characterized by the time evolution of the mean square displacement of a diffusing molecule σ2(t). When σ2(t) is a power function of time, the process is described by a fractional subdiffusion, fractional superdiffusion or normal diffusion equation. However, for other forms of σ2(t), diffusion equations are often not defined. We show that to describe diffusion characterized by σ2(t), the g-subdiffusion equation with the fractional Caputo derivative with respect to a function g can be used. Choosing an appropriate function g, we obtain Green’s function for this equation, which generates the assumed σ2(t). A method for solving such an equation, based on the Laplace transform with respect to the function g, is also described. Full article
(This article belongs to the Section Complexity)
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