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Search Results (339)

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Keywords = power system symmetry

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34 pages, 2789 KB  
Article
Investigation of the Impact of Household Energy Storage on DSO Grid Load Symmetry and Photovoltaic Energy Utilization Efficiency
by Laurynas Šriupša, Mindaugas Vaitkūnas, Artūras Baronas, Gytis Svinkūnas, Julius Dosinas, Saulius Gudžius and Gytis Vilutis
Symmetry 2026, 18(5), 879; https://doi.org/10.3390/sym18050879 (registering DOI) - 21 May 2026
Abstract
In this study, we investigate the impact of electric energy storage (EES) on phase line power flow symmetry and photovoltaic (PV) energy utilization in prosumer three-phase four-wire integrated household systems. The analysis is based on high-time-resolution (1 s) experimental data collected from a [...] Read more.
In this study, we investigate the impact of electric energy storage (EES) on phase line power flow symmetry and photovoltaic (PV) energy utilization in prosumer three-phase four-wire integrated household systems. The analysis is based on high-time-resolution (1 s) experimental data collected from a real household grid and subsequent simulations of energy flows using MATLAB/Simulink software. Two converter operation strategies were evaluated: the conventional symmetric mode and the asymmetric mode developed by the authors based on an adaptive power flow management algorithm. For both strategies, the impact of EES capacity on imbalance in the distribution system operator (DSO) grid was investigated. The methodology analyzes energy flows in each phase line separately, allowing for a detailed assessment of the imbalance between phase line phenomena and their impact on local energy consumption. Key performance parameters used for the efficiency evaluation include the self-consumption and self-sufficiency rates, which quantify the share of locally generated energy consumed within the household and the degree of independence from the DSO grid. The results show that combining adaptive asymmetric inverter control with appropriately sized energy storage allows for more efficient on-site utilization of PV energy, which, at the same time, improves the load symmetry of the phase lines in the DSO grid. Full article
24 pages, 3251 KB  
Article
Coordinated Low-Voltage Ride-Through Control of a Flywheel-Assisted Permanent-Magnet Direct-Drive Wind Power System Under Asymmetrical Grid Faults
by Dahai Guo, Guangchen Liu, Jianwei Zhang, Guizhen Tian, Sufang Wen, Zicheng He and Yan Wang
Energies 2026, 19(10), 2476; https://doi.org/10.3390/en19102476 - 21 May 2026
Abstract
To address fault-period DC-link overvoltage, the reduction in grid-side active-power regulation margin caused by reactive-current-priority operation, and the double-frequency current fluctuation induced by negative-sequence components under asymmetrical grid faults in a flywheel-assisted permanent-magnet direct-drive wind power system, this paper proposes a coordinated low-voltage [...] Read more.
To address fault-period DC-link overvoltage, the reduction in grid-side active-power regulation margin caused by reactive-current-priority operation, and the double-frequency current fluctuation induced by negative-sequence components under asymmetrical grid faults in a flywheel-assisted permanent-magnet direct-drive wind power system, this paper proposes a coordinated low-voltage ride-through (LVRT) strategy based on DC-link-voltage-threshold partitioning. According to the DC-link voltage level, the operating process is divided into a normal regulation region, a grid-side saturation region, and a flywheel activation region, thereby enabling coordinated regulation between grid-side reactive-current support and flywheel-side active-power absorption. To improve transient smoothness, an anti-windup mechanism together with a bumpless transfer scheme is incorporated into the coordinated control process to suppress integrator saturation and mitigate mode-transition disturbances. In addition, a grid-side proportional–integral–vector resonant controller (PI-VRC) is introduced to improve the suppression of double-frequency current fluctuation under asymmetrical faults and enhance converter capacity utilization. Simulation results show that the proposed strategy can effectively restrain fault-period DC-link voltage rise, improve three-phase current symmetry and grid power quality, and strengthen transient reactive-power support, thereby enhancing the asymmetrical-fault LVRT capability of the system. Full article
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29 pages, 2786 KB  
Article
Enhanced Transmission Loss and Modal Coupling in Dual-Membrane Flexible-Shell Cylindrical Waveguides: A Rigorous Mode-Matching–Galerkin Framework
by Mohammed Alkinidri
Mathematics 2026, 14(10), 1761; https://doi.org/10.3390/math14101761 - 20 May 2026
Abstract
This paper develops an analytical treatment of vibro-acoustic wave propagation in a cylindrical waveguide containing two clamped elastic membranes and a central flexible-shell segment. The acoustic field obeys the time-harmonic Helmholtz equation, the shell motion is described by Donnell–Mushtari thin-shell theory under axisymmetric [...] Read more.
This paper develops an analytical treatment of vibro-acoustic wave propagation in a cylindrical waveguide containing two clamped elastic membranes and a central flexible-shell segment. The acoustic field obeys the time-harmonic Helmholtz equation, the shell motion is described by Donnell–Mushtari thin-shell theory under axisymmetric loading, and the membrane response is governed by classical membrane theory and incorporated through a tailored Galerkin scheme. The resulting coupled fluid–structure boundary-value problem is solved by the Mode-Matching Method: the acoustic potentials are expanded in orthogonal radial eigenfunctions within each subregion, and continuity of pressure, normal velocity, and structural displacement are enforced at every interface. The mirror symmetry of the configuration is exploited by an exact decomposition into symmetric and anti-symmetric sub-problems, each of which reduces to a truncated linear algebraic system of dimension 4N+4 for the unknown modal amplitudes. Acoustic power-balance identities provide a quantitative consistency check on the numerical implementation and diagnose convergence with respect to the truncation order; structural damping is accommodated through complex-modulus substitutions for the shell and the membrane tension without altering the algebraic structure of the system. The numerical results demonstrate that the dual-membrane configuration delivers transmission-loss values exceeding 25dB across the low-frequency band relevant to HVAC and automotive applications, with a representative plateau near 13dB at the reference geometry, through resonance-driven modal coupling between the acoustic field and the compliant interfaces. Parametric studies identify the excitation frequency, the inner-membrane radius, the shell radius, and the chamber length as effective design parameters for tuning the attenuation. The formulation furnishes a unified and computationally efficient analytical tool for predicting and optimising noise attenuation in flexibly coupled cylindrical duct systems. Full article
(This article belongs to the Section E4: Mathematical Physics)
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29 pages, 5903 KB  
Article
A Symmetric Fault Diagnosis Method for Power Batteries Based on Digital Battery Passport and Knowledge Graph-Fuzzy Bayesian Network
by Tongzhou Ji and Jie Li
Symmetry 2026, 18(5), 857; https://doi.org/10.3390/sym18050857 (registering DOI) - 18 May 2026
Viewed by 69
Abstract
The safe operation of power battery systems relies on the dynamic symmetric equilibrium of electrochemical distribution and thermal management states, whereas fault occurrence is often accompanied by symmetry breaking. To achieve accurate fault diagnosis and symmetry restoration, this study proposes a symmetrical closed-loop [...] Read more.
The safe operation of power battery systems relies on the dynamic symmetric equilibrium of electrochemical distribution and thermal management states, whereas fault occurrence is often accompanied by symmetry breaking. To achieve accurate fault diagnosis and symmetry restoration, this study proposes a symmetrical closed-loop framework (DBP-KG-FBN) that integrates digital battery passport (DBP) text mining, knowledge graph (KG), and fuzzy Bayesian network (FBN). Power battery fault diagnosis is critical to new energy vehicle (NEV) safety; however, conventional methods face two key limitations: (1) they inadequately exploit multi-source heterogeneous textual data in DBPs; and (2) they fail to handle uncertainty in fault propagation. The methodology proceeds as follows. First, a BERT-BiLSTM-CRF model extracts fault-related entities and relations from unstructured DBP text, which are structured into a Neo4j-based knowledge graph. Second, via rule-based topological mapping, the KG topology is transformed into a Bayesian network through structurally symmetric transformation between the semantic and probabilistic layers, with cyclic dependencies resolved by introducing latent variables. Third, network parameters are determined by integrating fuzzy set theory with game theory-based weighting to quantify uncertainty and subjectivity in expert evaluations, thereby achieving symmetric utilization of subjective and objective information. This enables bidirectional symmetric reasoning for forward fault prediction and backward fault traceability. Experimental results demonstrate that while maintaining symmetric stability of the diagnostic knowledge topology, the proposed DBP-KG-FBN method achieves a diagnostic accuracy of 0.92 (Top-3). This symmetrical closed-loop framework significantly outperforms fault tree analysis (FTA) and event tree analysis (ETA) in diagnostic accuracy and reasoning efficiency. It transforms unstructured DBP data into computable knowledge for intelligent battery diagnosis. Future work will expand the corpus via transfer learning and optimize adaptive weighting algorithms for expert evaluations. Full article
(This article belongs to the Section Engineering and Materials)
23 pages, 3999 KB  
Article
Model-Free Predictive Synthesis Performance Optimization of DAB Converters Based on an Ultra-Local Model
by Luan Wang, Guoqiang Qiu, Bowen Chi, Dejun Liu and Yanming Cheng
Energies 2026, 19(10), 2421; https://doi.org/10.3390/en19102421 - 18 May 2026
Viewed by 90
Abstract
The dual-active-bridge (DAB) converter is the core component of the DC micro-grid system; it has the advantages of topological structure symmetry, high efficiency, and high-power density. Model predictive control (MPC) is often employed to improve the dynamic response characteristics of the system, but [...] Read more.
The dual-active-bridge (DAB) converter is the core component of the DC micro-grid system; it has the advantages of topological structure symmetry, high efficiency, and high-power density. Model predictive control (MPC) is often employed to improve the dynamic response characteristics of the system, but its strong parameter dependence is a key factor limiting the development of MPC. Therefore, a model-free predictive control (MFPC) method combining an ultra-local model with model predictive control is proposed to solve the problem of strong dependence of traditional MPC on system model parameters. Firstly, establish the ultra-local mathematical model of the DAB converter. The system’s lumped disturbances are identified using the residual prediction method and substituted into the discrete model of the system at the next time step to achieve model-free prediction. Secondly, a minimum back-flow power constraint is added to the cost function to improve the steady-state performance of the converter. Thirdly, in the extended phase shift modulation, the Lagrange multiplier method (LMM) is proposed to reduce the current stress, ultimately achieving the collaborative optimization of the comprehensive performance of the DAB. Finally, a simulation model is built using MATLAB/Simulink, and compared with traditional control methods, the voltage ripple has been reduced by 51.3%, 89.1%, and 85.1%, respectively; the current stress significantly decreases both when the output voltage reference value changes and when the load resistance changes abruptly, and both can basically achieve zero back-flow power operation. The validity and superiority of the proposed strategy have been verified. Full article
(This article belongs to the Special Issue Advances in Power Converters and Inverters)
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15 pages, 28225 KB  
Article
CBCT-Based Epidemiological Study of Root and Root Canal Anatomy in Mandibular Second Molars in an Italian Clinical Cohort
by Katia Greco, Riccardo Federico Visconti, Gaetano Paolone, Maria Teresa Sberna, Enrico Felice Gherlone and Giuseppe Cantatore
J. Clin. Med. 2026, 15(10), 3688; https://doi.org/10.3390/jcm15103688 - 11 May 2026
Viewed by 307
Abstract
Background: Mandibular second molars show notable variability in root canal structures and C-shaped morphology, with possible differences among populations. Methods: This retrospective cross-sectional CBCT study included 500 patients attending the Department of Dentistry at IRCCS Ospedale San Raffaele (Milan, Italy) with [...] Read more.
Background: Mandibular second molars show notable variability in root canal structures and C-shaped morphology, with possible differences among populations. Methods: This retrospective cross-sectional CBCT study included 500 patients attending the Department of Dentistry at IRCCS Ospedale San Raffaele (Milan, Italy) with bilateral mandibular second molars and was reported according to STROBE guidelines. CBCT scans (Hyperion X5; voxel size 0.125 mm) were assessed by two endodontists using standardized criteria. Root-based canal configurations were classified according to Vertucci in cases with complete bilateral coding of homologous mesial and distal roots; C-shaped morphology was classified using Fan’s system and analyzed separately because Vertucci coding is not applicable to C-shaped systems. Categorical variables were analyzed using χ2 or Fisher’s exact test, continuous variables with parametric or non-parametric tests, and right–left comparisons with paired-sample tests (p < 0.05). Results: Complete bilateral Vertucci coding was feasible in 494/500 patients (98.8%), yielding 988 mesial and 988 distal roots for analysis. C-shaped canal configuration was detected in 1.2% of patients (6/500; 95% CI 0.44–2.59%); females showed a higher proportion than males (2.0% vs. 0.4%), with no evidence of a sex association (Fisher’s exact test, p = 0.216). Fan subtype annotation was available for 5/6 patients and 7 teeth; C1, C3, and C4 patterns were observed. In the Vertucci dataset, mesial roots most frequently exhibited Types II (52.0%) and IV (26.5%), whereas distal roots were predominantly Type I (62.4%), followed by Type III (29.8%). Contralateral symmetry was observed in 27.3% of mesial roots (135/494; 95% CI 23.4–31.5%) and 59.1% of distal roots (292/494; 95% CI 54.6–63.5%). Mean pulp chamber roof-to-floor distance was 2.623 ± 0.263 mm on the right and 2.567 ± 0.343 mm on the left (paired p < 0.001; mean difference 0.056 mm; 95% CI 0.023–0.089 mm). Conclusions: In this cohort, C-shaped morphology was rare, and no evidence of a sex association was found, although the small number of cases limits statistical power. Mesial roots showed more variability than distal roots, and contralateral symmetry was moderate and greater for distal roots than for mesial roots, supporting contralateral anatomy as a helpful—rather than predictive—clinical reference. Full article
(This article belongs to the Section Dentistry, Oral Surgery and Oral Medicine)
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9 pages, 867 KB  
Article
Multiscale Ordinal-Pattern Dynamics and Temporal Symmetries in a Photonic Neuron with Single and Dual Delayed Feedback
by Julian Feiveson, Mateu Yearian, Maddie Jones and Andrés Aragoneses
Entropy 2026, 28(5), 538; https://doi.org/10.3390/e28050538 - 9 May 2026
Viewed by 278
Abstract
Feedback delays and the coexistence of multiple timescales are central features of complex dynamical systems, ranging from neural networks and ecosystems to electronic and optical devices. Interactions between fast and slow dynamics can give rise to rich emergent behaviors that are absent in [...] Read more.
Feedback delays and the coexistence of multiple timescales are central features of complex dynamical systems, ranging from neural networks and ecosystems to electronic and optical devices. Interactions between fast and slow dynamics can give rise to rich emergent behaviors that are absent in single-timescale systems. Here we investigate how these coupled timescales shape the dynamics of a photonic neuron with single and dual delayed feedback. Using ordinal pattern analysis and recent ordinal-based complexity measures, we characterize the temporal correlations and symmetry properties of the fast peaks and slow spikes generated by the system. Our results show that the signatures of determinism exhibited at fast and slow timescales differ markedly, revealing a strongly multiscale organization of the dynamics. Despite these differences, when represented in the symmetry-based Φ-space, all cases, fast peaks and slow spikes under both single and dual feedback, collapse onto a common curve. This universal structure indicates the presence of underlying constraints governing the system’s dynamics across temporal scales and feedback configurations. These results highlight the power of ordinal-based approaches to uncover hidden symmetries and multiscale organization in delayed nonlinear systems. Full article
(This article belongs to the Special Issue Entropy-Based Time Series Analysis: Theory and Applications)
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29 pages, 628 KB  
Article
From Asymmetry to Equilibrium: How Government Regulation Drives Sustainable Digital Asset Management on Media Platforms in China
by Shaozhen Hong and Yingqi Liu
Information 2026, 17(5), 454; https://doi.org/10.3390/info17050454 - 8 May 2026
Viewed by 268
Abstract
The rapid digitalization of the media and publishing industry has deepened systemic asymmetries in resources, power, and institutional rights. These asymmetries create fundamental barriers to the economic–institutional sustainability of digital content dissemination. Existing governance frameworks have not yet comprehensively addressed the resulting competitive [...] Read more.
The rapid digitalization of the media and publishing industry has deepened systemic asymmetries in resources, power, and institutional rights. These asymmetries create fundamental barriers to the economic–institutional sustainability of digital content dissemination. Existing governance frameworks have not yet comprehensively addressed the resulting competitive and informational imbalances. Adopting China’s publishing and media industry as a focal case, this study draws on symmetry theory to develop an integrated analytical framework. It reconceptualizes government regulation as a multi-dimensional governance mechanism operating across three dimensions: resource allocation, technological innovation, and rights protection. We test this framework empirically using Xinbang Index data covering the top 10 publishing and media enterprises from 24 January 2025 to 7 December 2025. Multiple regression analysis and Spearman rank correlation are applied to assess each dimension’s differential impact on content dissemination efficiency. The results yield four key findings. First, all three regulatory dimensions contribute positively to content dissemination efficiency. Second, technological innovation is the most potent symmetry-restoring lever, exerting a statistically robust direct effect on dissemination outcomes. Third, resource allocation provides a necessary foundational contribution, while rights protection operates conditionally—its effect is fully realized only alongside adequate technological and resource inputs. Fourth, an integrated multivariate regression confirms the cross-dimensional hierarchy: the standardized Beta coefficient for technological innovation (β = 0.394) exceeds those for rights protection (β = 0.294) and resource allocation (β = 0.125). No single regulatory instrument is sufficient to achieve dynamic equilibrium. A synergistic, technology-centered combination of all three dimensions is required. This study proposes a tripartite symmetry-based governance strategy for media platform ecosystems. The symmetry framework developed here offers an analytical template for diagnosing analogous asymmetries in other platform-dependent sectors. Empirical validation beyond the Chinese publishing and media context is recommended as a priority for future research. Full article
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19 pages, 4236 KB  
Article
Improvement in the Energy Autonomy and the Mechanical Performances of an Onboard Actuation Chain for Robotics
by Abdoul-Aziz Ahmed Hassan, Abderrezzak Cherifi, Ouahid Bouchhida, Sebastien Charles and Hassan Ali Barkad
Energies 2026, 19(10), 2258; https://doi.org/10.3390/en19102258 - 7 May 2026
Viewed by 285
Abstract
This paper aims to improve the energy autonomy and the mechanical performances of an on-board drive chain for robotics. The energy autonomy improvement is performed by reducing electrical losses in the inverter. Electrical losses are reduced by decreasing the number of switching cycles [...] Read more.
This paper aims to improve the energy autonomy and the mechanical performances of an on-board drive chain for robotics. The energy autonomy improvement is performed by reducing electrical losses in the inverter. Electrical losses are reduced by decreasing the number of switching cycles per period of the inverter’s power semiconductor switches, while maintaining a low Total Harmonic Distortion (THD). These improvements are expected thanks to a new control strategy called Pre-Calculated Pulse Width Modulation (PC PWM). The principle of this new control strategy is that all the symmetries of an ideal three-phase voltage system are assigned to the real output voltage of the inverter. Then the switching instants of the inverter’s switches are determined off line, by means of Fourier’s analysis, so that the maximum number of successive harmonics is zeroed. This allows the optimal switching sequence to be predefined, thereby reducing unnecessary commutations of the power switches. The performance of the new method (PC PWM) is evaluated through detailed simulation studies and compared with the conventional method called Sinusoidal Pulse Width Modulation (SPWM). The simulation results show that despite the reduction in the number of commutations per period, the performance of the actuation chain has been significantly improved with PC-PWM (new technique). Indeed, for the same mechanical load, the PC-PWM method allows for a lower current, a shorter transient response time and a lower torque ripple than the SPWM method. Full article
(This article belongs to the Section F3: Power Electronics)
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28 pages, 1192 KB  
Article
Disturbance Location-Aware Frequency Support in New Power Systems via Heterogeneous Nodal Frequency Response Modeling and Atlas-Based Gain Scheduling
by Lixue Gao, Shouyuan Wu, Mu Li and Futao Yang
Symmetry 2026, 18(5), 759; https://doi.org/10.3390/sym18050759 - 28 Apr 2026
Viewed by 266
Abstract
New power systems with penetration of inverter-based resources (IBRs) exhibit symmetry breaking in post-disturbance frequency, as nodal trajectories depend on disturbance location, network coupling, and heterogeneous frequency channels across synchronous generators (SGs), grid-forming (GFM) converters, and grid-following (GFL) converters with phase-locked loops (PLLs). [...] Read more.
New power systems with penetration of inverter-based resources (IBRs) exhibit symmetry breaking in post-disturbance frequency, as nodal trajectories depend on disturbance location, network coupling, and heterogeneous frequency channels across synchronous generators (SGs), grid-forming (GFM) converters, and grid-following (GFL) converters with phase-locked loops (PLLs). As a consequence, relying only on aggregated center-of-inertia/center-of-frequency (COI) metrics can underestimate asymmetric local risks, including worst-node rate of change of frequency (RoCoF), worst-node nadir, and nodal frequency split. This paper proposes a disturbance location-aware coordination framework that explicitly models and balances heterogeneous active-power frequency support across the network using an electromechanical-scale state-space formulation. First, a heterogeneous nodal frequency response (HNFR) model yields an explicit state-space input–output mapping from location-specific active power disturbances to nodal frequency outputs for both electromechanical and PLL-estimated channels. Second, a reproducible signal processing protocol computes nodal RoCoF/nadir/split indices and enables large-scale location sweeping via atlas-ready matrices that are naturally parallelizable for high-performance computing. Third, a constrained allocation layer schedules heterogeneous fast frequency response subject to converter limits and finite energy constraints, supporting an atlas-based gain scheduling implementation. Case studies demonstrate that the proposed symmetry-aware design improves worst-node security and suppresses frequency split while maintaining comparable COI behavior. Under budget-matched conditions on the modified IEEE 39-bus system, the proposed allocation reduces worst-node RoCoF by 32.2% and maximum nodal frequency split by 17.8% relative to the COI-based benchmark. Full article
(This article belongs to the Special Issue New Power System and Symmetry)
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57 pages, 13008 KB  
Article
Corrosion Diagnosis of Hydroelectric Grounding Grids Based on Voltage Distribution Symmetry Deviation via a Quantum-Inspired Candidate Pool Guided Sine Cosine Algorithm
by Xinyue Zhang, Keying Wang and Liangliang Li
Symmetry 2026, 18(5), 753; https://doi.org/10.3390/sym18050753 - 27 Apr 2026
Viewed by 251
Abstract
Hydropower stations, as critical infrastructure for basic energy supply, play a pivotal role in ensuring the reliability of power systems through their safe and stable operation. Grounding grids operating long-term in complex soil environments are prone to corrosion and degradation, disrupting current distribution [...] Read more.
Hydropower stations, as critical infrastructure for basic energy supply, play a pivotal role in ensuring the reliability of power systems through their safe and stable operation. Grounding grids operating long-term in complex soil environments are prone to corrosion and degradation, disrupting current distribution balance and causing spatial asymmetry in the voltage field, thereby compromising system safety. Corrosion branch resistance increment identification based on the electrical network method is typically modeled as a parameter inversion optimization problem. However, this problem exhibits underdetermination and other characteristics, making it difficult for traditional analytical methods to obtain stable solutions. To address this, this paper proposes a quantum perturbation scheduling candidate pool-guided sine–cosine algorithm (QSPSCA). Building upon the classical sine–cosine algorithm framework, it incorporates a dynamic candidate pool with multi-source attractor points and a quantum-inspired long-tail scheduling local refinement operator. This achieves an enhanced and smooth transition between global exploration and local refinement. Comparative experiments based on the CEC2017 benchmark and a hydropower station grounding grid corrosion diagnosis case demonstrate that QSPSCA outperforms multiple comparison algorithms in terms of average optimality and result stability. Furthermore, QSPSCA is applied to three typical engineering-constrained optimization problems. Results demonstrate that, whilst satisfying engineering constraints, this method consistently yields higher-quality feasible solutions with superior convergence accuracy and stability compared to alternative algorithms. Therefore, QSPSCA is not only applicable to underdetermined inversion diagnostics but also provides a solution framework with broad applicability for complex engineering optimization problems under structural symmetry perturbations. Full article
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11 pages, 2576 KB  
Article
Promising Thermoelectric Performance of Janus Monolayer ZrBrI
by Jingfeng Wang, Wenyan Jiao, Zihe Li and Huijun Liu
Materials 2026, 19(9), 1716; https://doi.org/10.3390/ma19091716 - 23 Apr 2026
Viewed by 383
Abstract
The Janus monolayers have recently attracted substantial interest due to their unique asymmetric structures and intriguing physical properties. In this work, we explore the thermoelectric properties of the Janus monolayer ZrBrI, using first-principles calculations and Boltzmann transport theory. We demonstrate that the system [...] Read more.
The Janus monolayers have recently attracted substantial interest due to their unique asymmetric structures and intriguing physical properties. In this work, we explore the thermoelectric properties of the Janus monolayer ZrBrI, using first-principles calculations and Boltzmann transport theory. We demonstrate that the system maintains good dynamic and thermal stability, as evidenced by the absence of imaginary phonon modes and small lattice fluctuation at a higher temperature of 600 K. The hybrid functional calculations reveal that the monolayer exhibits a relatively small indirect gap of 1.22 eV, and the energy bands near the conduction band minimum exhibit double degeneracy with weak dispersions, which is very beneficial for enhancing the n-type power factor. Meanwhile, a relatively lower lattice thermal conductivity is found due to strong lattice anharmonicity caused by the antibonding state and the symmetry breaking of the structure. Collectively, a larger ZT value of 3.9 at 600 K can be realized for the n-type Janus monolayer ZrBrI at an optimal concentration of 1.89×1013 cm2, highlighting its promising thermoelectric application in the intermediate temperature region. Full article
(This article belongs to the Section Materials Physics)
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51 pages, 10042 KB  
Article
A Symmetry-Guided Multi-Strategy Differential Hybrid Slime Mold Algorithm for Sustainable Microgrid Dispatch Under Refined Battery Degradation Models
by Xingyu Lai, Minjie Dai, Yuhang Luo and Xin Song
Symmetry 2026, 18(4), 692; https://doi.org/10.3390/sym18040692 - 21 Apr 2026
Viewed by 311
Abstract
Optimized dispatch of microgrids is crucial for improving the economic performance and long-term sustainability of modern low-carbon power systems. In particular, accurate economic dispatch modeling for battery energy storage systems (BESSs) is essential for properly evaluating the operational benefits and lifetime costs of [...] Read more.
Optimized dispatch of microgrids is crucial for improving the economic performance and long-term sustainability of modern low-carbon power systems. In particular, accurate economic dispatch modeling for battery energy storage systems (BESSs) is essential for properly evaluating the operational benefits and lifetime costs of microgrids. However, when both battery cycle aging and calendar aging are considered, the resulting scheduling model becomes highly nonlinear, high-dimensional, non-convex, and multimodal, which poses substantial challenges to conventional optimization methods. To alleviate the above problem, a symmetry-guided multi-strategy differential hybrid slime mold algorithm (MDHSMA) is introduced for the day-ahead economic dispatch of microgrids under a refined battery degradation framework. First, a chaotic bimodal mirrored Latin hypercube sampling strategy is designed to exploit symmetry during population initialization, thereby enhancing diversity and improving structured coverage of the search space. Second, a history-driven adaptive differential evolution mechanism is integrated to balance global exploration and local exploitation more effectively during the iterative search process. Third, a state-aware stagnation handling framework is incorporated to maintain population vitality and further improve convergence accuracy and robustness. MDHSMA is evaluated against 12 state-of-the-art optimizers on the CEC2017 and CEC2022 benchmark suites and two representative engineering optimization problems to verify its overall performance. In addition, it is applied to a microgrid case study with refined BESS degradation modeling. The results show that MDHSMA achieves the lowest comprehensive operating cost by effectively coordinating electricity arbitrage and battery life consumption. Moreover, it guides the energy storage system toward shallow charge–-discharge patterns, thereby mitigating accelerated degradation caused by excessive cycling. These results confirm the effectiveness and practical value of the proposed method for sustainable microgrid dispatch in complex nonconvex optimization scenarios. Full article
(This article belongs to the Special Issue Symmetry and Metaheuristic Algorithms)
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21 pages, 2743 KB  
Article
SOC and SOH Joint Estimation of Lithium-Ion Batteries Under Dynamic Current Rates Based on Machine Learning
by Mingyu Zhang, Xiaoqiang Dai, Qingjun Zeng, Ye Tian and Xiaohui Xu
Symmetry 2026, 18(4), 623; https://doi.org/10.3390/sym18040623 - 8 Apr 2026
Viewed by 540
Abstract
It is critical to accurately estimate the state of charge (SOC) and state of health (SOH) of lithium-ion batteries to ensure the safety and reliability of marine power systems, where the inherent symmetry of lithium-ion battery charge–discharge dynamics is often disrupted. However, the [...] Read more.
It is critical to accurately estimate the state of charge (SOC) and state of health (SOH) of lithium-ion batteries to ensure the safety and reliability of marine power systems, where the inherent symmetry of lithium-ion battery charge–discharge dynamics is often disrupted. However, the accuracy of conventional methods significantly deteriorates under dynamic current rates induced by fluctuating electrical loads, leading to unreliable SOC and SOH estimates. This article proposes a novel SOC and SOH joint estimation method based on a long short-term memory network with a rate awareness attention mechanism (RAAM-LSTM) and support vector regression optimized by greylag goose algorithm (GGO-SVR). RAAM-LSTM improves SOC estimation accuracy by adaptively weighting enhanced rate-related features. For SOH estimation, the GGO-SVR model incorporates the SOC as a coupling feature and applies physical constraints to ensure consistency with irreversible battery degradation. The comparative experimental results show that the error of the SOC is less than 1.6%, and that of the SOH is less than 0.5%, which are much smaller compared with those of conventional methods. Full article
(This article belongs to the Section Computer)
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16 pages, 397 KB  
Article
Symmetry and Structural Analysis of Power Congruence Graphs over a Set of Moduli
by Ahmad Almutlg and Muhammad Awais Raza
Symmetry 2026, 18(4), 582; https://doi.org/10.3390/sym18040582 - 29 Mar 2026
Viewed by 447
Abstract
In this article, we introduce and investigate a novel class of graphs that are called Power Congruence Graph PCGs, which are defined over the vertex set V ={0,1,2,,n1} where [...] Read more.
In this article, we introduce and investigate a novel class of graphs that are called Power Congruence Graph PCGs, which are defined over the vertex set V ={0,1,2,,n1} where two vertices a,bV are adjacent if akbk(modm) for some modulus mMp, where Mp={p,p2,,ptpt<n}. We thoroughly characterize the structural features of these graphs, establishing that each PCG decomposes into a union of d+1 complete components, where d=p1gcd(k,p1). The component sizes are explicitly given for n, p, and k. This decomposition highlights symmetry patterns in the component arrangement, emphasizing connectedness and structural balance. We derive key graph-theoretic metrics such as degree distribution, size, chromatic number, clique number and domination number. We also compute the adjacency and Laplacian matrices, as well as their spectra and associated graph energies to better understand the structural similarities and differences among PCGs with different exponents and prime moduli. This paper offers a systematic framework for comprehending power congruence based graph constructs, integrating number theory with structural and spectral graph theory and illustrating the natural symmetry that underpins these combinatorial structures. Full article
(This article belongs to the Special Issue Mathematics: Feature Papers 2026)
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