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Keywords = alternating direction method of multipliers

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32 pages, 2675 KB  
Article
Coordinated Scheduling of Distribution Network and Transportation System for EVs with Aggregated Flexibility and Endogenous Dynamic Pricing
by Sizu Hou, Yao Sang, Xuan Zhao, Yifan Yu and Qiwei Xue
Energies 2026, 19(18), 4245; https://doi.org/10.3390/en19184245 - 8 Sep 2026
Abstract
With the large-scale integration of Electric Vehicles (EVs) into distribution systems, the spatiotemporal uncertainty of charging loads and the interplay between user charging behavior and network operational constraints present new challenges to the safe and economical operation of the power system. To address [...] Read more.
With the large-scale integration of Electric Vehicles (EVs) into distribution systems, the spatiotemporal uncertainty of charging loads and the interplay between user charging behavior and network operational constraints present new challenges to the safe and economical operation of the power system. To address the insufficient coordination among flexibility characterization, distributed optimization, and user-side responses, this paper proposes a closed-loop collaborative dispatch strategy. The strategy integrates flexibility aggregation, endogenous dynamic pricing, and user charging-station selection behavior. Firstly, a three-tier collaborative architecture comprising the Distribution System Operator (DSO), Electric Vehicle Aggregators (EVAs), and EV users is established, with rolling updates implemented using Model Predictive Control (MPC). A flexible aggregation model is developed based on set operations of vehicle-level constraints, dynamically calculating power boundaries and energy feasibility domains. Furthermore, a distributed coordinated optimization model between the DSO and multiple EVAs is established and solved via the Alternating Direction Method of Multipliers (ADMM) under privacy-preserving conditions. By analyzing the correlation between ADMM dual variables and the marginal value of network constraints, a Distribution Locational Marginal Pricing (DLMP) -inspired dynamic price signal—endogenous to the optimization—is constructed to guide spatial reallocation of charging loads. Joint simulations based on an IEEE 33-node distribution network and the Sioux Falls transport network demonstrate that the proposed strategy reduces 24 h network losses from 9.05 MWh (uncoordinated) to 8.41 MWh, lowers user total costs from 22,200 yuan to 7100 yuan, and eliminates voltage limit violations (duration reduced from 1.50 h to 0), while exhibiting good distributed solution performance and closed-loop control capability. Full article
42 pages, 10431 KB  
Article
Non-Convex Joint Sparse and Low-Rank Optimization for Enhanced ISAR Imaging from Incomplete Data
by Chengzhi Chen, Haoran Hu, Zhen Wang, Xinyuan Zhang, Shengyao Chen and Sirui Tian
Remote Sens. 2026, 18(17), 3043; https://doi.org/10.3390/rs18173043 - 6 Sep 2026
Viewed by 90
Abstract
Conventional inverse synthetic aperture radar (ISAR) imaging techniques can produce high-resolution imagery from complete observation data. However, in practical scenarios, incomplete data caused by undersampling or missing data often leads to defocused results with traditional methods. While compressive sensing or low-rank reconstruction approaches [...] Read more.
Conventional inverse synthetic aperture radar (ISAR) imaging techniques can produce high-resolution imagery from complete observation data. However, in practical scenarios, incomplete data caused by undersampling or missing data often leads to defocused results with traditional methods. While compressive sensing or low-rank reconstruction approaches have been proposed to address this challenge, existing techniques frequently fail to fully exploit both the sparsity and low-rank properties inherent in ISAR scenes. Moreover, they typically rely on convex approximations that introduce estimation bias, weaken sparsity promotion, and increase computational complexity, ultimately degrading imaging performance. To overcome these limitations, this work presents an enhanced sparse ISAR imaging method that jointly enforces non-convex sparsity and low-rank constraints for incomplete data recovery. The imaging model incorporates both inherent sparsity priors and a low-rank constraint. The resulting non-convex optimization problem is solved via an efficient iterative algorithm based on the alternating direction method of multipliers, where the sparse component is reconstructed using an iterative reweighted scheme with a regularizer and the low-rank component is recovered through truncated singular value decomposition. Experimental results on both simulated and measured data demonstrate the efficacy and superior performance of the proposed method. Full article
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26 pages, 3795 KB  
Article
Adaptive Segmented Doppler Compensation for Forward-Looking Radar Imaging
by Yingying Wang, Yongpeng Dai, Xiurong Wang and Tian Jin
Remote Sens. 2026, 18(17), 2985; https://doi.org/10.3390/rs18172985 - 3 Sep 2026
Viewed by 127
Abstract
In long-aperture forward-looking radar, nonlinear Doppler mismatch caused by target relative motion can lead to positioning deviation and image defocusing. To address this issue, an adaptive segmented Doppler compensation method based on phase error constraints is proposed. As synthetic aperture time increases, high-order [...] Read more.
In long-aperture forward-looking radar, nonlinear Doppler mismatch caused by target relative motion can lead to positioning deviation and image defocusing. To address this issue, an adaptive segmented Doppler compensation method based on phase error constraints is proposed. As synthetic aperture time increases, high-order terms in the slant range history broaden the Doppler spectrum and enhance spatially variant phase errors. Conventional global compensation cannot achieve stable focusing, and fixed-length segmentation fails to adapt to varying motion nonlinearity. Accordingly, the high-order nonlinear characteristics of the slant range are first analyzed, and an adaptive sub-aperture partitioning criterion constrained by second-order phase error is derived, ensuring each sub-aperture satisfies the local quasi-linear hypothesis. A cross-segment mapping relationship between different sub-apertures is then established, and the compensation process is formulated as a two-dimensional separable operator. To manage the high computational complexity of solving spatially variant mapping under long apertures, the Alternating Direction Method of Multipliers (ADMM) is introduced to iteratively optimize the operator, achieving phase alignment and coherent reconstruction among sub-apertures. Simulation and experimental results show that the proposed method effectively suppresses nonlinear defocusing under long-aperture conditions. Compared with conventional global methods, it achieves superior energy concentration and focusing resolution in extended target scenarios. Full article
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31 pages, 3742 KB  
Article
Cross-Park Dispatch Optimization Strategy for Hybrid Energy Storage Power Systems Considering Carbon–Green Certificate Trading
by Chunxian Feng, Yifeng Wang, Wenxue Wang, Long Yuan, Feifei Zhang, Shuo Ren and Heng Chen
Energies 2026, 19(16), 3827; https://doi.org/10.3390/en19163827 - 14 Aug 2026
Viewed by 343
Abstract
To alleviate renewable energy curtailment and the high operating costs arising from the temporal and spatial mismatch of distributed generation, this paper develops a cross-park dispatch optimization approach for power systems under the joint participation of carbon trading and green certificate trading (GCT). [...] Read more.
To alleviate renewable energy curtailment and the high operating costs arising from the temporal and spatial mismatch of distributed generation, this paper develops a cross-park dispatch optimization approach for power systems under the joint participation of carbon trading and green certificate trading (GCT). The proposed approach aims to improve system flexibility and economic performance in coordinated multi-park operation. Specifically, adjustable resources in different parks are dispatched in a coordinated manner, and the total comprehensive operating cost is taken as the optimization objective. In addition, the Alternating Direction Method of Multipliers (ADMM) is adopted to determine inter-park electricity trading prices and exchanged power in a distributed framework. Furthermore, an asymmetric bargaining model is introduced to distribute the cooperative benefits, ensuring a balance between fairness and incentive compatibility. Simulation results demonstrate that inter-park electricity interaction reduces generation costs by 5.29%. The integration of carbon and green certificate trading further reduces costs by 7.4%. After asymmetric bargaining-based benefit allocation, the operating costs of parks with higher contributions decrease by up to 10.34%. The results conclude that the proposed strategy effectively leverages the complementary advantages of multi-park resources and optimizes the synergy between carbon markets, green certificate markets, and physical dispatch. Full article
(This article belongs to the Section F1: Electrical Power System)
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21 pages, 2280 KB  
Article
A Tailored ADMM for Chronological Production Simulation of Flexibly Interconnected Regional Power Systems
by Wenxuan Pan, Junzhou Wang, Huiying Cao, Xingyu Lin and Junjie Tang
Processes 2026, 14(16), 2593; https://doi.org/10.3390/pr14162593 - 14 Aug 2026
Viewed by 441
Abstract
In flexibly interconnected regional power systems with high penetration of renewable energy, chronological production simulation encounters combinatorial explosion and computational inefficiency, especially over medium- and long-term horizons with large-scale network constraints. Centralized approaches become intractable due to problem scale and memory limitations, while [...] Read more.
In flexibly interconnected regional power systems with high penetration of renewable energy, chronological production simulation encounters combinatorial explosion and computational inefficiency, especially over medium- and long-term horizons with large-scale network constraints. Centralized approaches become intractable due to problem scale and memory limitations, while existing alternating direction method of multipliers (ADMM) variants suffer from convergence instability and high computational cost when regional subproblems involve discrete unit commitment decisions. To address these issues, this paper establishes a network-constrained chronological production simulation model incorporating the operational characteristics of voltage-source-converter-based high-voltage direct-current (VSC-HVDC) transmission and inter-regional flexibility reserve sharing, and proposes a tailored consensus ADMM with network-constrained clustering linearization (ADMM-NCL) for an efficient parallel solution. The ADMM-NCL combines same-type unit clustering, which convexifies the unit commitment formulation for parallel solvability, with redundant network constraint screening thus retaining only the critical constraints. In representative spring and summer periods, ADMM-NCL achieves 12×~18× speedups over the centralized benchmark and 2×~10× over the tested ADMM variants; across four seasonal scenarios (spring, summer, autumn, and winter), it bounds the objective cost deviation within 0.41% while maintaining close agreement in key operational indicators. For the 8760 h case, where the centralized benchmark and several ADMM variants fail due to memory or time limits, ADMM-NCL completes the simulation within an available computational budget, thus demonstrating its scalability with respect to the full-year chronological horizon. Full article
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24 pages, 1761 KB  
Article
Superpixel-Level Joint-Sparse and Graph-Regularized Framework for Hyperspectral Image Classification
by Tugcan Dundar
Remote Sens. 2026, 18(16), 2699; https://doi.org/10.3390/rs18162699 - 11 Aug 2026
Viewed by 355
Abstract
Hyperspectral image classification (HSIC) remains challenging because high-dimensional spectral signatures must be interpreted together with spatially coherent land-cover structures, particularly when labeled samples are limited. This paper presents a superpixel-based spectral–spatial HSIC method called SJSGR, which combines joint-sparse representation with graph Laplacian regularization. [...] Read more.
Hyperspectral image classification (HSIC) remains challenging because high-dimensional spectral signatures must be interpreted together with spatially coherent land-cover structures, particularly when labeled samples are limited. This paper presents a superpixel-based spectral–spatial HSIC method called SJSGR, which combines joint-sparse representation with graph Laplacian regularization. The HSI is first partitioned into homogeneous superpixel regions so that neighbouring pixels with similar spectral characteristics can be represented jointly rather than independently. For each superpixel, a similarity-aware weighting matrix is constructed between the training dictionary and the superpixel samples, encouraging the coefficient matrix to select more label-consistent and representative training atoms. To further preserve local manifold structure, graph Laplacian regularization is incorporated into the optimization objective, enforcing smooth and coherent representation coefficients among neighboring pixels within each superpixel. The resulting unified formulation integrates spectral correlation, spatial consistency, and local geometric structure, and is solved by the alternating-direction method of multipliers (ADMM). Classification is then performed by assigning each superpixel to the class with the minimum reconstruction error. Experiments are conducted on three real-world HSI datasets called Indian Pines, Pavia University and Fanglu to compare the proposed framework with several sparse representation and graph-based HSIC methods. Experimental results on these datasets reveal the capability of the proposed method, obtaining overall accuracies of 98.12%, 98.04%, and 98.26% under 10%, 1% and 1% labeled samples, respectively. Besides obtaining nearly 1% higher overall accuracy than the compared methods under these low-training-sample distributions, the SJSGR also provided better classification performance even under much more limited numbers of training samples. The findings suggest that superpixel-guided sparse representation with local manifold regularization is a promising direction for effective spectral–spatial HSIC. Full article
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26 pages, 4093 KB  
Article
Multi-Time-Scale Distributed Voltage Optimization for AC/DC Hybrid Distribution Networks with High-Penetration Photovoltaics
by Xuerui Zheng, Yunjing Liu, Shaoshuai Wang, Bo Zhao and Zhenhao Wang
Energies 2026, 19(16), 3748; https://doi.org/10.3390/en19163748 - 10 Aug 2026
Viewed by 240
Abstract
After high-penetration distributed photovoltaics (DPVs) are integrated into AC/DC hybrid distribution networks, stochastic source-load fluctuations, AC-DC coupling, and heterogeneous response characteristics of voltage-regulation devices jointly aggravate voltage violations and rapid voltage fluctuations. This paper proposes a spatio-temporal coordinated hierarchical distributed voltage-optimization framework. Spatially, [...] Read more.
After high-penetration distributed photovoltaics (DPVs) are integrated into AC/DC hybrid distribution networks, stochastic source-load fluctuations, AC-DC coupling, and heterogeneous response characteristics of voltage-regulation devices jointly aggravate voltage violations and rapid voltage fluctuations. This paper proposes a spatio-temporal coordinated hierarchical distributed voltage-optimization framework. Spatially, the AC and DC regions are first separated according to voltage-source-converter (VSC) interfaces, and an electrical-coupling-aware modularity index is then constructed for the AC network by combining normalized bidirectional reactive-power-voltage sensitivities, available fast reactive-power support, and intra-cluster compactness. Temporally, an 1 h day-ahead model coordinates slow, discrete, or intertemporally coupled resources, including on-load tap changers, capacitor banks, energy storage systems, and flexible loads, while a 15 min intra-day rolling model coordinates DPV inverters, static var generators, and VSCs. The synchronous alternating direction method of multipliers (SADMM) is tailored to the resulting AC clusters, DC subnetworks, and VSC boundary variables to enable synchronous regional solution and boundary-consensus coordination. Studies on a modified 50-node AC/DC test system show that, under the investigated operating conditions, the framework mitigates voltage violations and intra-day fluctuations while obtaining favorable network-loss, DPV-curtailment, and solution-time performance. Full article
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21 pages, 2077 KB  
Article
Sparse Rational Polynomial Coefficient Estimation Method via Low-Rank Matrix Constraint
by Congzhen Hu, Jiajie He, Tianyu Yan, Pu Wang, Wei An and Yingqian Wang
Remote Sens. 2026, 18(15), 2547; https://doi.org/10.3390/rs18152547 - 3 Aug 2026
Viewed by 252
Abstract
The rational function model (RFM) is an important general imaging model in remote sensing image geometric processing, which is composed of many rational polynomial coefficients (RPCs). However, due to the correlation among the high-order polynomials, the RPCs can be overfitting and the design [...] Read more.
The rational function model (RFM) is an important general imaging model in remote sensing image geometric processing, which is composed of many rational polynomial coefficients (RPCs). However, due to the correlation among the high-order polynomials, the RPCs can be overfitting and the design matrix is ill-posed. Existing methods either alleviate the overfitting problem through parameter regularization or alleviate the ill-posedness of the design matrix through variable selection. However, these two problems exist simultaneously, and there is a lack of a unified optimization framework to alleviate overfitting and ill-posedness simultaneously. To address this issue, this paper proposes a sparse RPC estimation method via low-rank matrix constraint, called LRMC-RFM. The proposed method assumes that the observed design matrix constructed from GCPs is a noisy perturbation of an latent low-rank geometric design matrix. In a unified optimization framework, the latent low-rank geometric design matrix and the sparse RPCs are jointly estimated by introducing the nuclear norm and the 1 norm. To ensure computational efficiency, an alternating direction method of multipliers (ADMM)-based optimization algorithm is derived. Extensive experiments demonstrate that the proposed method achieves better performance than existing competing methods. Full article
(This article belongs to the Section Remote Sensing Image Processing)
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22 pages, 48504 KB  
Article
View-Aligned Nonlocal Low-Rank Tensor Reconstruction for Snapshot Compressive Multi-View Spectral Imaging System
by Xiaorui Yin, Lijuan Su, Yu Wang and Yan Yuan
Sensors 2026, 26(15), 4875; https://doi.org/10.3390/s26154875 - 2 Aug 2026
Viewed by 310
Abstract
Snapshot compressive multi-view spectral imaging (SC-MVSI) multiplexes view-spectral information into a single coded measurement, enabling compact acquisition with a two-dimensional detector. Because each reconstructed channel corresponds to both a selected spectral response and a view direction, direct cross-channel modeling at identical pixel coordinates [...] Read more.
Snapshot compressive multi-view spectral imaging (SC-MVSI) multiplexes view-spectral information into a single coded measurement, enabling compact acquisition with a two-dimensional detector. Because each reconstructed channel corresponds to both a selected spectral response and a view direction, direct cross-channel modeling at identical pixel coordinates can introduce structural mismatch caused by view-dependent displacement. This paper proposes a reference-guided view-aligned nonlocal low-rank tensor reconstruction method for SC-MVSI. The reconstruction is formulated as a coded inverse problem and solved using the alternating direction method of multipliers (ADMM) in a variable-splitting framework. In the prior update, a reference tensor guides block-level patch alignment before nonlocal tensor grouping, and the resulting fourth-order tensor groups are regularized by canonical polyadic (CP) low-rank approximation. Experiments on eight synthesized multispectral light-field scenes show that the proposed method achieves the highest average PSNR of 33.61 dB and the lowest average CAE of 5.69 degrees among the compared baselines, while obtaining the second-highest average SSIM of 0.8823. Real-system experiments further provide a qualitative demonstration of applying the proposed reconstruction framework to captured coded measurements. Full article
(This article belongs to the Special Issue Computational Optical Sensing and Imaging: 2nd Edition)
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36 pages, 2186 KB  
Review
A Review of Electric Vehicle Integration in Peer–to–Peer Energy Networks
by Mohammad Kamran Ikram, Mehdi Seyedmahmoudian, Gokul Thirunavukkarasu, Saad Mekhilef, Alex Stojcevski and Jose Moreira
World Electr. Veh. J. 2026, 17(8), 383; https://doi.org/10.3390/wevj17080383 - 23 Jul 2026
Viewed by 1388
Abstract
The rapid growth of electric vehicle (EV) adoption presents significant challenges for power system stability while creating new opportunities for decentralized energy management. Peer-to-peer (P2P) energy networks have emerged as a promising approach for transforming EVs from passive loads into coordinated grid assets. [...] Read more.
The rapid growth of electric vehicle (EV) adoption presents significant challenges for power system stability while creating new opportunities for decentralized energy management. Peer-to-peer (P2P) energy networks have emerged as a promising approach for transforming EVs from passive loads into coordinated grid assets. This paper presents a comprehensive review of EV-P2P integration through a three-layer architectural framework that systematically connects physical infrastructure, market mechanisms, and intelligent control strategies. The Physical Layer reviews how V2X technologies and bidirectional charging enable EVs to operate as flexible storage resources and ancillary service providers. The Transactional Layer reviews on blockchain-based platforms, auction mechanisms, and game-theoretic models for secure energy trading. The Intelligence Layer reviews advanced control strategies, including decentralized optimization methods such as the Alternating Direction Method of Multipliers (ADMM) and Deep Reinforcement Learning. Collectively, the reviewed studies demonstrate that these approaches enable EVs to operate as flexible loads, distributed storage resources, and ancillary service providers, while improving energy trading efficiency, reducing operating costs, and alleviating network congestion under simulated operating conditions. Despite these promising results, a substantial gap remains between simulation-based studies and practical implementation. Future research should prioritize integrated pilot projects to evaluate scalability, interoperability, cybersecurity, and regulatory compliance under realistic operating conditions. Full article
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23 pages, 602 KB  
Article
Prior-Assisted Hierarchical ADMM Decoding for Punctured Globally Coupled LDPC Codes
by Wenbo Shi, Wenlong Xie, Jiashen Hu and Lishan Liu
Entropy 2026, 28(7), 815; https://doi.org/10.3390/e28070815 - 17 Jul 2026
Viewed by 354
Abstract
Future wireless networks require channel coding schemes that can provide high reliability, low latency, and strong adaptability under finite-blocklength and structurally heterogeneous transmission scenarios. Globally coupled low-density parity-check (GC-LDPC) codes are promising for such systems because their coupled structure can enhance error-correction capability, [...] Read more.
Future wireless networks require channel coding schemes that can provide high reliability, low latency, and strong adaptability under finite-blocklength and structurally heterogeneous transmission scenarios. Globally coupled low-density parity-check (GC-LDPC) codes are promising for such systems because their coupled structure can enhance error-correction capability, but the additional global constraints also increase decoding complexity and make conventional fixed-parameter decoders less effective. This paper proposes a prior-assisted hierarchical alternating direction method of multipliers (ADMMs) decoding framework for GC-LDPC codes. The proposed decoder first partitions the GC-LDPC parity-check structure into two local subgraphs and performs tuned ADMM decoding on the local blocks in parallel. The local decoding outputs are then merged and verified by the full GC-LDPC parity-check matrix. If the merged local decision satisfies all global constraints, it is directly accepted, thereby avoiding unnecessary full-graph decoding. Otherwise, a global fallback ADMM decoder is activated. In this stage, the channel log-likelihood ratios are fused with soft priors extracted from the local ADMM outputs, where prior clipping and conflict scaling are introduced to control unreliable or contradictory local information. The resulting fused reliability information is used to guide full-matrix ADMM decoding. This local-to-global strategy reduces unnecessary global iterations while preserving the ability to enforce global consistency when local decoding is insufficient. Simulation-oriented metrics, including bit error rate, frame error rate, local pass rate, global fallback rate, global fallback success rate, and average iteration count, are used to evaluate reliability and decoding efficiency. The proposed framework provides an average-complexity-aware and reliability-aware decoding approach for advanced channel coding in future wireless networks. Full article
(This article belongs to the Special Issue Key Technologies Towards Future Wireless Networks)
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20 pages, 410 KB  
Article
ANM-Based DOA Estimation and Signal Detection for Multi-Tag Ambient Backscatter Communications
by Yu Ren, Qian Wang, Liping Qian and Pooi-Yuen Kam
Appl. Sci. 2026, 16(14), 7032; https://doi.org/10.3390/app16147032 - 13 Jul 2026
Viewed by 379
Abstract
Ambient backscatter communication is a promising low-power technology for the Internet of Things (IoT), yet direction of arrival (DOA) estimation and detection in multi-backscatter device (BD) scenarios remain challenging. This paper thus investigates joint DOA estimation and signal detection in multi-BD IoT systems. [...] Read more.
Ambient backscatter communication is a promising low-power technology for the Internet of Things (IoT), yet direction of arrival (DOA) estimation and detection in multi-backscatter device (BD) scenarios remain challenging. This paper thus investigates joint DOA estimation and signal detection in multi-BD IoT systems. By exploiting the Toeplitz structure of the covariance matrix of the received signals, an atomic norm minimization (ANM)-based optimization framework is first employed for DOA estimation in varying signal-to-noise ratio (SNR) conditions. Specifically, the alternating direction method of multipliers (ADMM) in combination with the estimation of signal parameters via the rotational invariance techniques (ESPRIT) algorithm is used to iteratively solve the ANM optimization issue and obtain the DOA angles. Then, the muti-BD signal detection is considered by iteratively implementing the minimum variance distortionless response beamforming with successive interference cancellation, to guarantee successive detection from the strongest to the weakest signal. Simulation results demonstrate that the proposed ANM-based scheme achieves high DOA estimation accuracy and low bit error rate (BER) of muti-BD detection across the whole SNR range of [0–20] dB. For example, the root mean square error of DOA estimation under three-tag conditions can achieve 102 at 10 dB, with the BER of BD detection being 2.9×103, validating the effectiveness of our method in multi-BD IoT scenarios. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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16 pages, 5935 KB  
Article
An Improved Space-Based ISAR Simulation Method Using Two-Line Element Data
by Wenjie Zhu, Hongxing Hao, Ronghuan Yu and Desheng Liu
Sensors 2026, 26(14), 4338; https://doi.org/10.3390/s26144338 - 8 Jul 2026
Viewed by 387
Abstract
Inverse synthetic aperture radar (ISAR) technology is widely used in the field of target recognition, and radar simulation technology is also being extensively studied. The present study focuses on the digital simulation of ISAR technology and proposes a sparse imaging simulation method for [...] Read more.
Inverse synthetic aperture radar (ISAR) technology is widely used in the field of target recognition, and radar simulation technology is also being extensively studied. The present study focuses on the digital simulation of ISAR technology and proposes a sparse imaging simulation method for spatial targets based on two-line element from satellites. The method utilizes two-line element (TLE) data from satellites as a foundation and applies an improved alternating direction method of multipliers (ADMM) for echo data processing. It enables high-resolution imaging in a simulation environment while accurately resolving the motion state of space targets relative to the radar line of sight. The present study analyzes data such as image entropy, image contrast, and normalized root mean square error for the imaging results. The proposed simulation method offers the advantages of high-sparsity imaging and low signal-to-noise ratio (SNR) imaging, enabling better simulation and application of inverse synthetic aperture radar. Full article
(This article belongs to the Section Radar Sensors)
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30 pages, 887 KB  
Article
A Maturity-Aware Proximal ADMM with NG-Route Relaxation for Dynamic Inventory Reallocation in a Multi-Echelon Mandarin Cold-Chain Network
by Baowen Liang, Linjie Ma, Yiran Zhang, Yuxuan Su, Haoyu Wang and Yiping Jiang
Mathematics 2026, 14(13), 2446; https://doi.org/10.3390/math14132446 - 7 Jul 2026
Viewed by 332
Abstract
The Vehicle Routing Problem with Time Windows (VRPTW) takes on a structurally distinct form when the goods being routed undergo first-order quality decay during transport. In this setting, distance minimisation alone underestimates the true economic cost. A per-customer minimum-quality acceptance constraint further introduces [...] Read more.
The Vehicle Routing Problem with Time Windows (VRPTW) takes on a structurally distinct form when the goods being routed undergo first-order quality decay during transport. In this setting, distance minimisation alone underestimates the true economic cost. A per-customer minimum-quality acceptance constraint further introduces a non-linear feasibility condition that does not appear in the classical formulation. This paper addresses such a setting in the context of loose-skin citrus fruit (e.g., mandarins) distribution, where stock has already undergone several days of cold storage at the origin warehouse, and remaining shelf life makes retail time windows binding rather than decorative. We formulate a Maturity-Aware Multi-Echelon Dynamic Reallocation Vehicle Routing Problem with Time Windows (MA-MEDR-VRPTW) on a three-echelon network (origin warehouse → distribution centres → stores) over a seven-day rolling horizon. A first contribution shows that the minimum-quality acceptance constraint admits an analytic transformation into a time-window tightening, which removes per-extension exponential evaluations from the subproblem solver. The algorithmic contribution is a proximal alternating direction method of multipliers (ADMM) with NG-route relaxation (padmm-ma) whose quality-loss weight is updated by a residual-balancing rule and is decoupled from the outer reallocation linear program (LP) through approximate dynamic-programming-style marginal costs. On twelve Solomon-derived mandarin instances (72 feasible algorithm–instance combinations), padmm-ma returns a mean seven-day cost of 12,638 CNY against 11,753 CNY for a subgradient baseline (+7.5%) at statistically indistinguishable arrival quality (paired Wilcoxon p=0.077 for q¯arr), while cutting mean wall-clock time from 350 to 23 s (about 15×). The method, therefore, reads as a fast operational heuristic for daily re-planning. An ablation, an exact-MIP benchmark on tractable subproblems, and a scale extension to n=100 customers round out the validation. Full article
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25 pages, 2962 KB  
Article
Flexible Voltage Control Strategy for Photovoltaic Inverters in Distribution Networks Considering Dynamic Cluster Partitioning
by Shukang Lyu, Xiaolong Xiao, Wenqiang Xie, Xiaoxing Lu and Ziran Guo
Symmetry 2026, 18(7), 1127; https://doi.org/10.3390/sym18071127 - 1 Jul 2026
Viewed by 364
Abstract
With the advancement of the carbon peaking and carbon neutrality goals, large-scale grid integration of photovoltaic (PV) systems has become a core trend in the development of distribution networks (DNs). However, this high penetration breaks the inherent spatiotemporal symmetry of power flow in [...] Read more.
With the advancement of the carbon peaking and carbon neutrality goals, large-scale grid integration of photovoltaic (PV) systems has become a core trend in the development of distribution networks (DNs). However, this high penetration breaks the inherent spatiotemporal symmetry of power flow in traditional DNs, leading to severe spatiotemporal imbalance issues, including voltage violations, reverse power flow, and a sharp increase in network power loss. To address these challenges, an optimized flexible control method for PV inverters in DNs considering cluster partitioning is proposed in this paper. First, a comprehensive performance index system integrating improved modularity, source-load matching degree, and voltage sensitivity is constructed, which quantifies the electrical coupling symmetry and source-load power symmetry within clusters, providing a rigorous quantitative basis for dynamic cluster partitioning. Moreover, based on a dynamic monitoring mechanism, an improved Particle Swarm Optimization algorithm for cluster partitioning is proposed to achieve the optimal cluster partitioning of DN nodes and the selection of key control nodes. Finally, a Q-V flexible control model of the inverter adapted to cluster control is established; thus, an optimization model with the objectives of minimizing voltage deviation, PV curtailment loss, and PV reactive power output is constructed. The distributed and efficient solution is performed using the Alternating Direction Method of Multipliers algorithm and the GUROBI solver. Simulation results based on the modified IEEE 123-node test feeder show that, compared with traditional methods, the proposed method improves the cluster partitioning effectiveness, ensures that the operating voltage deviation of the control system is within 5%, and reduces the PV curtailment loss of the system. Full article
(This article belongs to the Special Issue Symmetry with Power Systems: Control and Optimization)
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