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Keywords = lightning protection

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22 pages, 5797 KB  
Article
Computational Investigation of Lightning Strike Damage Effects on an Aircraft Fuel Tank Cover
by Feng Yue and Xiaofeng Xue
Fibers 2026, 14(5), 46; https://doi.org/10.3390/fib14050046 - 23 Apr 2026
Viewed by 202
Abstract
Fuel vapor can be ignited by lightning through various means, particularly through hot spot formation on fuel tank skins. The wing fuel tank cover and its surrounding outer plates together form part of the aerodynamic shape of an aircraft. The lightning protection design [...] Read more.
Fuel vapor can be ignited by lightning through various means, particularly through hot spot formation on fuel tank skins. The wing fuel tank cover and its surrounding outer plates together form part of the aerodynamic shape of an aircraft. The lightning protection design of the fuel system, including wing fuel tank, is of great significance for ensuring the aircraft safety. Based on the Joule heating and implosion effect, the damage response of a composite fuel tank cover subjected to lightning strikes is analyzed in this paper. The adopted method combines electrical–thermal coupling with explicit dynamics analysis. Firstly, a finite element model of the fuel tank cover is established using electrical–thermal coupling elements, and the lightning current impact simulation is carried out under given electrical boundary conditions and thermal boundary conditions. On one hand, the ablation criterion is determined by the Joule heating effect and the sublimation temperature of materials. The thermal damage of composite materials subjected to transient high currents is obtained through transient thermal analysis. On the other hand, special implosion elements are selected according to the temperature distribution obtained from the electrical–thermal coupling analysis. The original composite material model in the implosion region needs to be replaced with a new material model described by the high-explosive material model and the JWL equation of state. The von Mises stress distribution and pressure distribution on the structure after implosion are discussed in detail. The results show that concave pits are formed near the implosion zone. Unlike the thermal damage morphology defined by the ablation criterion, the implosion effect makes the damage distribution deviate from the initial fiber direction of each layer. The implosion dynamic method reveals the internal damage and pit and bulge phenomenon around the lightning attachment area to a certain extent. Full article
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16 pages, 3388 KB  
Article
A Fast Calculation Method for Electrostatic Fields in Complex Terrain Using NSGA-II and Conformal Mapping
by Xiaojian Wang, Xinyu Shi, Tianlei He, Xiaobin Cao and Ruifang Li
Electronics 2026, 15(8), 1689; https://doi.org/10.3390/electronics15081689 - 17 Apr 2026
Viewed by 220
Abstract
Rapid and accurate calculation of lightning-induced electric fields in complex terrain is essential for lightning protection and electromagnetic compatibility analysis. Although conventional full-wave numerical methods such as the finite element method can achieve high-fidelity results, they are computationally expensive and inefficient for large-scale [...] Read more.
Rapid and accurate calculation of lightning-induced electric fields in complex terrain is essential for lightning protection and electromagnetic compatibility analysis. Although conventional full-wave numerical methods such as the finite element method can achieve high-fidelity results, they are computationally expensive and inefficient for large-scale or repetitive engineering analysis. To enable efficient and reliable computation of lightning-induced electrostatic fields over complex terrain, this paper proposes a fast computational framework that integrates multi-level conformal mapping with a multi-objective optimization strategy based on the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). In the proposed method, irregular terrain boundaries are transformed into analytically tractable domains using multi-level conformal mapping, while the critical mapping parameter is reformulated as a dual-objective optimization problem that simultaneously minimizes the maximum local error and the mean global error. Unlike traditional approaches that rely on empirical tuning or exhaustive traversal of mapping parameters, the proposed framework establishes a closed-loop adaptive optimization process that generates a Pareto-optimal solution set, enabling flexible trade-off selection according to practical accuracy requirements. The method is validated against high-fidelity finite element simulations for representative terrain profiles. The results demonstrate that the proposed approach achieves comparable maximum-error performance while reducing mean error and significantly improving parameter-optimization efficiency relative to exhaustive search methods. The proposed framework provides an adaptive and efficient computational solution for preliminary assessment of lightning-induced electric fields in complex terrain environments, and lays a foundation for future extensions toward more realistic multi-dimensional and transient analyses. The improvements in computational accuracy and efficiency offer significant practical value for rapid lightning protection assessment in large-scale complex terrain engineering, enabling parametric analysis and scheme comparison during the preliminary engineering design stage with sufficient reliability. Full article
(This article belongs to the Section Artificial Intelligence)
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20 pages, 3551 KB  
Article
GMM-Based Lightning Damage Detection for Wind Turbines Under De-Rated Operation Using the Scaled Power Curve
by Takuto Matsui, Koki Naito and Kazuo Yamamoto
Energies 2026, 19(7), 1790; https://doi.org/10.3390/en19071790 - 6 Apr 2026
Viewed by 400
Abstract
Many countries are actively promoting the large-scale deployment of wind power generation, both onshore and offshore. However, damage to wind turbines caused by winter lightning has become a growing concern in Japan. Japan has made efforts since an early stage to establish legal [...] Read more.
Many countries are actively promoting the large-scale deployment of wind power generation, both onshore and offshore. However, damage to wind turbines caused by winter lightning has become a growing concern in Japan. Japan has made efforts since an early stage to establish legal frameworks for reducing lightning damage; nevertheless, lightning damage to wind turbines remains a problem that has not been completely eradicated. After a wind turbine has been struck by lightning, it is restarted only after its structural integrity has been verified; however, the current method relies on visual inspection by workers, making accurate and rapid inspections difficult. One approach to solving this problem is to use anomaly detection techniques based on SCADA data. Research is currently underway to implement this approach. However, anomaly detection methods based on SCADA data have been criticized for their limited ability to accommodate multiple operating modes, including de-rated operation. In this study, we propose the “scaled power curve” as a robust feature that is less affected by operating modes, with its effectiveness verified through anomaly detection. This method showed improved anomaly detection accuracy compared to using the original power curve as a feature; moreover, in the present case, the method remained effective under de-rated operation. By using this feature, it is expected that a lightning damage detection model can be developed, contributing to improved availability of wind turbines. Full article
(This article belongs to the Section A3: Wind, Wave and Tidal Energy)
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22 pages, 389 KB  
Article
Adaptive Multipath Proofs for Privacy Protection and Security in Payment Channel Networks
by Wenqi Li, Zijie Pan and Yunqing Yang
Mathematics 2026, 14(7), 1199; https://doi.org/10.3390/math14071199 - 3 Apr 2026
Viewed by 265
Abstract
Payment channel networks enable scalable off-chain payments, but their practical deployment remains constrained by a persistent tension among routing efficiency, liquidity visibility, transaction privacy, and settlement security. Existing multipath routing mechanisms can improve payment success under fragmented liquidity, yet they often expose sensitive [...] Read more.
Payment channel networks enable scalable off-chain payments, but their practical deployment remains constrained by a persistent tension among routing efficiency, liquidity visibility, transaction privacy, and settlement security. Existing multipath routing mechanisms can improve payment success under fragmented liquidity, yet they often expose sensitive balance information, leak structural features of payment routes, and enlarge the attack surface for probing, channel exhaustion, and selective forwarding. This paper presents a novel framework, Adaptive Multipath Proofs (AMPs), for privacy protection and security in payment channel networks. The core idea is to bind multipath routing decisions with lightweight zero-knowledge verifiability, allowing intermediate nodes to validate path feasibility, fragment consistency, and settlement constraints without learning exact channel balances, the complete payment amount, or the global route structure. AMP integrates three mechanisms: a hidden-liquidity feasibility proof that supports privacy-preserving route selection, an adaptive payment-splitting strategy that dynamically determines fragment allocation according to network congestion and balance uncertainty, and a proof-coupled settlement guard that enforces atomicity and timeout consistency across all payment fragments. Together, these mechanisms reduce information leakage while preserving robust payment execution under dynamic network conditions. Experimental evaluation on real Lightning Network topologies and synthetic stress scenarios demonstrates that AMP significantly lowers balance disclosure and endpoint inference risk, improves payment completion under skewed liquidity distributions, and introduces only moderate computational and communication overhead. The results indicate that adaptive proof-carrying multipath routing offers a practical and effective direction for building secure, privacy-preserving, and high-success payment channel networks. Full article
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20 pages, 4299 KB  
Article
Establishment Mechanism of Power-Frequency Follow-Current Arc on Medium-Voltage Insulated Conductors Under Lightning Overvoltage
by Xin Ning, Rui Yu, Longchen Liu, Jiayi Wang, Jingxin Zou, Hao Wang, Tian Tan, Huajian Peng and Xin Yang
Inventions 2026, 11(2), 28; https://doi.org/10.3390/inventions11020028 - 18 Mar 2026
Cited by 1 | Viewed by 400
Abstract
Lightning-induced breaking accidents of medium-voltage insulated conductors pose a serious threat to the safety of distribution networks, and the key cause lies in the establishment and sustained combustion of the power-frequency follow-current arc after lightning overvoltage breakdown. This paper systematically investigates the formation [...] Read more.
Lightning-induced breaking accidents of medium-voltage insulated conductors pose a serious threat to the safety of distribution networks, and the key cause lies in the establishment and sustained combustion of the power-frequency follow-current arc after lightning overvoltage breakdown. This paper systematically investigates the formation mechanism and critical conditions of power-frequency follow-current arcs using combined simulation and experimental approaches. Based on the streamer discharge theory, a lightning breakdown model was established and combined with the arc energy balance equation, revealing that the establishment of power-frequency follow-current arcs is essentially determined by the post-breakdown energy competition process. The simulation results show that the required anode electric field strength for lightning breakdown is not less than 3 kV/mm. When the power-frequency voltage reaches 10 kV, Joule heating of the arc continuously exceeds heat dissipation loss, enabling restrike after zero-crossing and sustaining stable burning. Experiments verified this voltage threshold and further revealed that the arc establishment rate exhibits nonlinear growth with increasing power-frequency voltage, exceeding 90% at power-frequency voltages ≥ 10 kV. The study also reveals that increased gap distance reduces the arc establishment rate, while the introduction of insulators can enhance it by approximately 20%. This study clarifies the energy criterion for power-frequency follow-current arc establishment and the influence patterns of key parameters, providing theoretical basis and engineering reference for lightning protection design and arc suppression in medium-voltage insulated lines. Full article
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15 pages, 32660 KB  
Article
Enhancing Lightning Strike Protection of CFRP Laminates Using Nickel-Coated Carbon Fiber Nonwoven Veils
by Minqiang Jiang, Xiaoling Liu, Chris Rudd, Guocai Li, Weiping Liu, Zhenghua Cao and Xiaosu Yi
J. Compos. Sci. 2026, 10(2), 69; https://doi.org/10.3390/jcs10020069 - 31 Jan 2026
Viewed by 616
Abstract
The lightning strike protection (LSP) performance of nickel-coated carbon fiber nonwoven veils (NiCVs) with varying areal densities, integrated onto the surface of CFRP laminates, was evaluated through simulated lightning strike tests. Post-strike damage was evaluated through visual inspection, non-destructive ultrasonic testing, residual strength [...] Read more.
The lightning strike protection (LSP) performance of nickel-coated carbon fiber nonwoven veils (NiCVs) with varying areal densities, integrated onto the surface of CFRP laminates, was evaluated through simulated lightning strike tests. Post-strike damage was evaluated through visual inspection, non-destructive ultrasonic testing, residual strength measurements, and microstructural examinations. Results indicated that the protection effectiveness improved with increasing NiCV areal density. The laminate with a 68 g/m2 NiCV layer showed substantially reduced damage—its damage volume, damage area, and maximum damage depth decreased to 18%, 40%, and 51% of those of the control laminate—and it retained 95% of the reference compression strength, demonstrating the strong post-strike protection capability of this lightweight veil. A detailed analysis suggested that the NiCV LSP performance may arise from a mechanism involving high electrical conductivity, a thermally stable coated-fiber skeleton, as well as a distributed nonwoven network architecture. These results highlight NiCV as a promising functional approach for enhancing the lightning strike protection of CFRP aerostructures. Full article
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18 pages, 5275 KB  
Article
Interference Characteristics of a Primary–Secondary Integrated Distribution Switch Under Lightning Strike Conditions Based on a Field-Circuit Hybrid Full-Wave Model
by Ge Zheng, Shilei Guan, Yilin Tian, Changkai Shi, Hui Yin, Chengbo Jiang, Meng Yuan, Yijun Fu, Yiheng Chen, Shen Lai and Shaofei Wang
Energies 2026, 19(3), 623; https://doi.org/10.3390/en19030623 - 25 Jan 2026
Cited by 1 | Viewed by 335
Abstract
As distribution networks become increasingly intelligent, primary–secondary integrated distribution switches are replacing the traditional electromagnetic type. However, the high degree of integration intensifies inherent electromagnetic compatibility (EMC) challenges. This paper presents a field-circuit hybrid full-wave model to investigate switch characteristics during lightning strikes. [...] Read more.
As distribution networks become increasingly intelligent, primary–secondary integrated distribution switches are replacing the traditional electromagnetic type. However, the high degree of integration intensifies inherent electromagnetic compatibility (EMC) challenges. This paper presents a field-circuit hybrid full-wave model to investigate switch characteristics during lightning strikes. A 3D full-wave model of the switch and a distributed parameter circuit model of the connecting lines are coupled via a network parameter matrix. This approach comprehensively accounts for the impacts of transmission lines and structural components on electromagnetic disturbances. Simulation and experimental results reveal that lightning strikes induce high-frequency damped oscillatory waves, primarily caused by traveling wave reflections along overhead lines. The characteristic frequency of disturbance is inversely proportional to the transmission line length. Additionally, internal components significantly influence this frequency; specifically, a larger voltage dividing capacitance in the voltage transformer results in a lower frequency. Model validation was performed using a 20 m transmission line setup. A 75 kV standard lightning impulse was injected into Phase B. At a distance of 500 mm from the voltage transformer, the measured radiated electric field amplitude was 14.12 kV/m (deviation < 5%), and the characteristic frequency was 1.11 MHz (deviation < 20%). These findings offer vital guidance for the lightning protection and EMC design of primary–secondary integrated distribution switches. Full article
(This article belongs to the Topic EMC and Reliability of Power Networks)
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18 pages, 5567 KB  
Article
Quantitative Analysis of Lightning Rod Impacts on the Radiation Pattern and Polarimetric Characteristics of S-Band Weather Radar
by Xiaopeng Wang, Jiazhi Yin, Fei Ye, Ting Yang, Yi Xie, Haifeng Yu and Dongming Hu
Remote Sens. 2026, 18(3), 392; https://doi.org/10.3390/rs18030392 - 23 Jan 2026
Viewed by 416
Abstract
Lightning rods, while essential for protecting weather radars from direct lightning strikes, act as persistent non-meteorological scatterers that can interfere with signal transmission and reception and thereby degrade detection accuracy and product quality. Existing studies have mainly focused on X-band and C-band systems, [...] Read more.
Lightning rods, while essential for protecting weather radars from direct lightning strikes, act as persistent non-meteorological scatterers that can interfere with signal transmission and reception and thereby degrade detection accuracy and product quality. Existing studies have mainly focused on X-band and C-band systems, and robust, measurement-based quantitative assessments for S-band dual-polarization radars remain scarce. In this study, a controllable tilting lightning rod, a high-precision Far-field Antenna Measurement System (FAMS), and an S-band dual-polarization weather radar (SAD radar) are jointly employed to systematically quantify lightning-rod impacts on antenna electromagnetic parameters under different rod elevation angles and azimuth configurations. Typical precipitation events were analyzed to evaluate the influence of the lightning rods on dual-polarization parameters. The results show that the lightning rod substantially elevates sidelobe levels, with a maximum enhancement of 4.55 dB, while producing only limited changes in the antenna main-beam azimuth and beamwidth. Differential reflectivity (ZDR) is the most sensitive polarimetric parameter, exhibiting a persistent positive bias of about 0.24–0.25 dB in snowfall and mixed-phase precipitation, while no persistent azimuthal anomaly is evident during freezing rain; the co-polar correlation coefficient (ρhv) is only marginally affected. Collectively, these results provide quantitative, far-field evidence of lightning-rod interference in S-band dual-polarization radars and provide practical guidance for more reasonable lightning-rod placement and configuration, as well as useful references for ZDR-oriented polarimetric quality-control and correction strategies. Full article
(This article belongs to the Section Engineering Remote Sensing)
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25 pages, 7150 KB  
Article
Integrating Frequency-Spatial Features for Energy-Efficient OPGW Target Recognition in UAV-Assisted Mobile Monitoring
by Lin Huang, Xubin Ren, Daiming Qu, Lanhua Li and Jing Xu
Sensors 2026, 26(2), 506; https://doi.org/10.3390/s26020506 - 12 Jan 2026
Viewed by 463
Abstract
Optical Fiber Composite Overhead Ground Wire (OPGW) cables serve dual functions in power systems, lightning protection and critical communication infrastructure for real-time grid monitoring. Accurate OPGW identification during UAV inspections is essential to prevent miscuts and maintain power-communication functionality. However, detecting small, twisted [...] Read more.
Optical Fiber Composite Overhead Ground Wire (OPGW) cables serve dual functions in power systems, lightning protection and critical communication infrastructure for real-time grid monitoring. Accurate OPGW identification during UAV inspections is essential to prevent miscuts and maintain power-communication functionality. However, detecting small, twisted OPGW segments among visually similar ground wires is challenging, particularly given the computational and energy constraints of edge-based UAV platforms. We propose OPGW-DETR, a lightweight detector based on the D-FINE framework, optimized for low-power operation to enable reliable detection. The model incorporates two key innovations: multi-scale convolutional global average pooling (MC-GAP), which fuses spatial features across multiple receptive fields and integrates spectrally motivated features for enhanced fine-grained representation, and a hybrid gating mechanism that dynamically balances global and spatial features while preserving original information through residual connections. By enabling real-time inference with minimal energy consumption, OPGW-DETR addresses UAV battery and bandwidth limitations while ensuring continuous detection capability. Evaluated on a custom OPGW dataset, the S-scale model achieves 3.9% improvement in average precision (AP) and 2.5% improvement in AP50 over the baseline. By mitigating misidentification risks, these gains improve communication reliability. As a result, uninterrupted grid monitoring becomes feasible in low-power UAV inspection scenarios, where accurate detection is essential to ensure communication integrity and safeguard the power grid. Full article
(This article belongs to the Section Internet of Things)
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18 pages, 3068 KB  
Article
Identification of Grounding Impulse Impedance Based on a Combined Improved Hanning Window and RLS Algorithm in Power System
by Jialin Wan, Jiayuan Hu, Zikang Yang, Fan Yang, Sen Liu, Shiying Hou, Yanzhi Wu and Xiaohan Wen
Processes 2026, 14(2), 253; https://doi.org/10.3390/pr14020253 - 11 Jan 2026
Viewed by 427
Abstract
To enhance the accuracy and timeliness of field testing for grounding impulse impedance in complex soil environments, this paper addresses the limitations of traditional peak-ratio methods—such as susceptibility to noise interference and the inability to reflect dynamic impedance variations—by proposing an identification method [...] Read more.
To enhance the accuracy and timeliness of field testing for grounding impulse impedance in complex soil environments, this paper addresses the limitations of traditional peak-ratio methods—such as susceptibility to noise interference and the inability to reflect dynamic impedance variations—by proposing an identification method that combines an improved Hanning window with recursive least squares (RLS). During signal preprocessing, an improved Hanning window with adjustable parameters and energy normalization is employed to enhance the main-lobe energy concentration of impulse voltage and current signals while effectively suppressing high-frequency sidelobe leakage. In the parameter estimation stage, a low-order discrete linear model is established and an RLS algorithm with a forgetting factor is introduced to achieve full-time adaptive estimation of impulse impedance. Using a simulated surge test circuit, 18 sets of typical operating conditions with varying inductance and resistance parameters are designed. The same voltage and current data are processed using three processing methods: no windowing, standard Hanning windowing, and improved Hanning windowing. Results show that the average relative error of surge impedance is 9.16% without windowing, the standard Hanning window reduced the error to 3.78%, and the modified Hanning window further decreased the error to approximately 1.51%. Comparative analysis of different forgetting factor settings indicates that a value of approximately λ = 0.98 achieves an optimal trade-off between dynamic tracking capability and steady-state smoothness. The research results demonstrate that the proposed method achieves high identification accuracy for impact impedance and exhibits satisfactory parameter robustness under strong noise and multiple operating conditions, providing a reference for grounding impact characteristic testing and lightning protection design. Full article
(This article belongs to the Section Energy Systems)
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39 pages, 1059 KB  
Systematic Review
Ground Enhancement Materials for Grounding Systems: A Systematic Review of Factors, Technologies and Advances
by Hugo Martínez Ángeles, Cesar Augusto Navarro Rubio, Luis Angel Iturralde Carrera, Leonel Díaz-Tato, José Gabriel Ríos Moreno, Mario Trejo Perea, Roberto Valentín Carrillo-Serrano and Juvenal Rodríguez-Reséndiz
Technologies 2026, 14(1), 49; https://doi.org/10.3390/technologies14010049 - 8 Jan 2026
Cited by 1 | Viewed by 1286
Abstract
Grounding Systems (GS) play a critical role in electrical safety, lightning protection, and the reliable operation of power and renewable energy infrastructures, particularly in high-resistivity soils. In this context, Ground Enhancement Materials (GEM) are widely used to reduce soil resistivity and improve grounding [...] Read more.
Grounding Systems (GS) play a critical role in electrical safety, lightning protection, and the reliable operation of power and renewable energy infrastructures, particularly in high-resistivity soils. In this context, Ground Enhancement Materials (GEM) are widely used to reduce soil resistivity and improve grounding performance. This systematic review analyzes and synthesizes recent advances (2018–2025) in GEM applied to GS, with emphasis on their electrical performance, durability, and environmental sustainability. The review covers conventional GEM, industrial waste-derived materials, and hybrid formulations, evaluating their effectiveness under different soil types and moisture conditions. Comparative analysis of the literature indicates that GEM derived from industrial byproducts and hybrid composites often exhibit superior long-term resistivity reduction due to enhanced moisture retention and material-soil interactions, especially in clay-rich and heterogeneous soils. Sustainability considerations such as environmental impact, material availability, and long-term stability are increasingly influencing GEM selection and design. Overall, this review provides a structured framework for understanding the factors governing GEM performance while highlighting current trends, challenges, and future research directions in the development of sustainable grounding solutions. Full article
(This article belongs to the Special Issue Technological Advances in Science, Medicine, and Engineering 2025)
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30 pages, 14158 KB  
Article
The Three-Dimensional Analytical Modeling of Lightning-Induced Heat Diffusion: The Critical Roles of the Continuing Current and Lightning Channel Radius in Structural Damage
by Konrad Sobolewski and Piotr Strużewski
Appl. Sci. 2026, 16(1), 452; https://doi.org/10.3390/app16010452 - 31 Dec 2025
Cited by 1 | Viewed by 722
Abstract
The utilization of metal roofing as natural air terminals is a standard practice in lightning protection; however, the risk of thermal perforation and subsequent ignition of internal hazardous atmospheres remains a critical safety concern. While current standards (e.g., IEC 62305) primarily focus on [...] Read more.
The utilization of metal roofing as natural air terminals is a standard practice in lightning protection; however, the risk of thermal perforation and subsequent ignition of internal hazardous atmospheres remains a critical safety concern. While current standards (e.g., IEC 62305) primarily focus on material thickness and total charge (Q), this study demonstrates that these parameters alone are insufficient for predicting burn-through failure. We present a comprehensive electrothermal analysis based on the method of images to simulate three-dimensional heat diffusion in finite-thickness plates (0.5–7 mm) made of aluminum, copper, and steel. Unlike simplified 1D models, our approach considers the spatial distribution of the heat source and the varying depth of the thermal penetration. The results confirm that the continuing current component (Qlong200 C) is the primary driver of volumetric melting. Crucially, the sensitivity analysis reveals that the lightning channel radius (rmbo) acts as a governing factor for perforation risk; a reduction in the lightning channel radius from 5 mm to 2 mm can shift the outcome from minor surface heating to complete perforation for thin sheets (0.5 mm), even under identical charge conditions. This paper identifies a “safety gap” in current engineering practices, demonstrating that neglecting this parameter constriction effect results in an underestimation of the thermal threat. The proposed analytical model provides a precise tool for determining the safety margins of natural air terminals, offering direct applicability for designing lightning protection systems in high-risk industrial facilities. Full article
(This article belongs to the Section Applied Thermal Engineering)
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14 pages, 939 KB  
Article
Effective Height of Mountaintop Towers Revisited: Simulation-Based Assessment for Self-Initiated Upward Lightning
by André Tiso Lobato, Liliana Arevalo and Vernon Cooray
Atmosphere 2026, 17(1), 16; https://doi.org/10.3390/atmos17010016 - 23 Dec 2025
Viewed by 512
Abstract
Mountaintop towers are highly exposed to self-initiated upward lightning flashes. Accurate estimation of their effective height—the equivalent flat-ground height yielding the same lightning exposure—is essential for reliable exposure assessment, for interpreting and calibrating measurement data at instrumented mountaintop towers, and for comparison with [...] Read more.
Mountaintop towers are highly exposed to self-initiated upward lightning flashes. Accurate estimation of their effective height—the equivalent flat-ground height yielding the same lightning exposure—is essential for reliable exposure assessment, for interpreting and calibrating measurement data at instrumented mountaintop towers, and for comparison with established protection guidelines. This study applies a two-step numerical framework that couples finite-element electrostatic simulations with a leader-inception and propagation model for representative tower–terrain configurations reflecting reference instrumented mountaintop sites in lightning research. For each configuration, the stabilization field, the minimum background electric field enabling continuous upward leader propagation to the cloud base, is determined, from which effective heights are obtained. The simulated results agree with the analytical formulation of Zhou et al. (within ~10%), while simplified or empirical approaches by Shindo, Eriksson, and Pierce exhibit larger deviations, especially for broader mountains. A normalized analysis demonstrates that the tower-to-mountain slenderness ratio (h/a) governs the scaling of effective height, following a power-law dependence with exponent −0.17 (R2 = 0.94). This compact relation enables direct estimation of effective height from geometric parameters alone, complementing detailed leader-inception modeling. The findings validate the proposed physics-based framework, quantify the geometric dependence of effective height for mountaintop towers, and provide a foundation for improving lightning-exposure assessments, measurement calibration and design standards for elevated structures. Full article
(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
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27 pages, 1773 KB  
Article
The Mathematical Modeling of a Lightning Strike in an HVAC Line Considering the Modified Hamilton–Ostrogradsky Principle
by Vitaliy Levoniuk, Andriy Chaban, Paweł Czaja, Aleksander Dydycz, Andrzej Szafraniec, Roman Kwiecień and Małgorzata Górska
Energies 2025, 18(24), 6599; https://doi.org/10.3390/en18246599 - 17 Dec 2025
Viewed by 523
Abstract
Based on the modified Hamilton–Ostrogradsky principle, a mathematical model of a distributed-parameter high-voltage HVAC line that includes lightning shield wires is proposed. A partial differential equation of a five-wire power line is produced as a result. Therefore, a methodology for looking for boundary [...] Read more.
Based on the modified Hamilton–Ostrogradsky principle, a mathematical model of a distributed-parameter high-voltage HVAC line that includes lightning shield wires is proposed. A partial differential equation of a five-wire power line is produced as a result. Therefore, a methodology for looking for boundary conditions of a long line equation in the five-wire version is proposed here. A mathematical model is introduced as an example of a section of a power line that consists of a high-voltage long line that includes shield wires operating in an equivalent concentrated-parameter power system presented in its circuit version. The system is described with both partial and ordinary derivative differential equations. Poincaré boundary conditions of the third type are applied to solve the state equations of the object discussed. A discrete line model is thus presented, described with ordinary differential equations based on the well-known straight-line method. Transient processes across the system are analysed exactly at the moment of a lightning strike against a shield wire in the middle section of the line. To this end, a mathematical lightning strike model is developed by means of cubic spline interpolation. The original system of differential equations is integrated into the implicit Euler method, considering the Seidel method. The end results of the computer simulation are presented graphically and analysed. The results show the effectiveness of the proposed method of analysing transients across ultra-high-voltage lines that include lightning protection wires and can serve as accurate calculations of power supply lightning protection at the stages of design and production. Full article
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13 pages, 2028 KB  
Article
Study on Transient Overvoltage and Surge Arrester Electrical Stresses in Offshore Wind Farms Under Multiple Lightning Strokes
by Jie Zhang, Yong Wang, Jun Xiong, Junxiang Liu, Lu Zhu, Chao Huang, Jianfeng Shi and Yongxia Han
J. Mar. Sci. Eng. 2025, 13(12), 2307; https://doi.org/10.3390/jmse13122307 - 4 Dec 2025
Viewed by 585
Abstract
Lightning strikes are a major cause of wind turbine (WT) damage, with approximately 80% of cloud-to-ground lightning strikes exhibiting a multi-stroke characteristic. Therefore, studying the transient overvoltages induced by multiple lightning strokes is essential for the effective lightning protection of offshore WTs. Firstly, [...] Read more.
Lightning strikes are a major cause of wind turbine (WT) damage, with approximately 80% of cloud-to-ground lightning strikes exhibiting a multi-stroke characteristic. Therefore, studying the transient overvoltages induced by multiple lightning strokes is essential for the effective lightning protection of offshore WTs. Firstly, a multiple-stroke lightning current model representative of Guangdong Province, China, is established based on data from the lightning location system and rocket-triggered lightning experiments. Simulations are then employed to analyze the transient overvoltage of a Guangdong offshore wind farm under multiple lightning strikes. Simulation results indicate that when a WT is subjected to a two-stroke lightning flash, with current amplitudes corresponding to a cumulative probability density of approximately 1%, the surge arrester A1 must be configured with four parallel columns to ensure the insulation safety of the equipment without sustaining damage. Additionally, adequate electrical clearance must be maintained between the power cable and the tower wall, or alternatively, a high-strength insulating material may be applied over the cable armor to prevent flashover. Moreover, it is observed that the front time of the impulse current flowing through the surge arrester is approximately 2 μs, significantly shorter than the front time specified in IEC 60099-4 for the repetitive charge transfer capability test of ZnO varistors. Hence, it is essential to consider local lightning intensity and distribution characteristics when studying the transient overvoltages in offshore wind farms, optimizing surge arrester configurations, and assessing the impulse withstand performance of ZnO varistors, in order to ensure the safe and stable operation of offshore WTs. Full article
(This article belongs to the Section Ocean Engineering)
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