A method and system for evaluating the ground loss of a very low frequency monopole antenna considering tidal effects

Abstract

The present application belongs to the technical field of very low frequency monopole antenna grounding loss evaluation, and discloses a very low frequency monopole antenna grounding loss evaluation method considering tidal effect, which comprises the following steps: a fan-shaped ring-shaped layered grounding model is established, a magnetic field weight function is defined under polar coordinates by using a monopole antenna near-zone magnetic field distribution formula to represent the contribution weight of the magnetic field intensity at different radial distances and azimuth angles to the total grounding loss; a three-dimensional model is established by FEKO full-wave simulation, and the analytical calculation results are compared and verified with the simulation results in the frequency band of 20 to 25 kHz. The present application establishes a fan-shaped ring-shaped layered grounding loss model of a very low frequency antenna under tidal coverage, and discretizes the ground net area into a normal area without tide and a tidal coverage area, wherein the tidal coverage area is further subdivided into a finite depth seawater layer and a lower soil-ground net composite structure.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of ground loss assessment technology for very low frequency monopole antennas, and particularly relates to a method for assessing ground loss of very low frequency monopole antennas considering tidal effects. Background Technology

[0002] Existing methods for assessing ground loss of very low frequency (VLF) monopole antennas have significant shortcomings and are difficult to apply to dynamic, non-uniform, and layered conductive scenarios in tidal environments. As early as the 1970s, Wait's transmission line analogy method laid the foundation for radial ground grid equivalent admittance analysis, but it assumed the ground plane to be a uniform lossy half-space and did not consider the existence of any overlay layer. Subsequently, Liu Chao et al. and Li Bin et al. further developed ground loss calculation models for VLF umbrella antennas and derived the equivalent admittance formula for ground grid lines. However, these models are still limited to ideal ground planes or uniform soil conditions and cannot handle composite conductive structures where seawater, soil, and metal ground grids coexist. Although Gao Peng et al. revealed the nonlinear relationship between ground grid density and ground loss, their research was still based on static radial ground grids and ignored changes in the external environment.

[0003] For very low frequency (VLF) transmitting antennas, tidal fluctuations periodically flood the soil surrounding the antenna, creating a spatially non-uniform, time-varying layered medium. High-conductivity seawater may provide an additional low-resistance return path in the sparsely grounded outer area, reducing grounding losses. However, as the tide further intrudes into the high-density near-field grounding, the limited-depth seawater layer generates a skin effect and shielding effect, causing current redistribution among the seawater, soil, and metal grounding. This weakens the loss reduction trend and may even lead to a non-monotonic rebound. Current technology is completely unable to describe this complex behavior because traditional models either treat the grounding plane as ideal or assume constant and uniform soil parameters, failing to reflect the admittance transformation of the layered medium or predict the loss rebound caused by current redistribution.

[0004] Furthermore, existing assessment methods have fundamental deficiencies in their dynamic simulation capabilities. Real-world antennas face periodic tidal fluctuations, such as diurnal and semi-diurnal tides, causing grounding loss resistance to exhibit asymmetrical double-peak or single-peak fluctuations with the tidal phase, and the extreme values ​​shift by approximately one hour daily. However, existing analytical models are all static assessments and cannot simulate the time-varying patterns of grounding loss throughout the day. While full-wave simulation methods like FEKO offer high accuracy, they involve enormous computational demands for large-area grounding networks, multiple frequency points, and time-varying tidal conditions, requiring remodeling and solving for each tidal change, making them unsuitable for rapid engineering assessments. Traditional analytical methods are oversimplified and fail to reflect the propagation effects of electromagnetic waves in layered media and the modulation effect of non-uniform grounding network distribution on losses. In summary, existing technologies have significant shortcomings in terms of the realism of physical models, the ability to predict non-monotonic behavior, the efficiency of dynamic time-varying simulation, and the balance between computational accuracy and cost. Therefore, a new method capable of accurately and rapidly assessing grounding loss under tidal conditions is urgently needed. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for evaluating the grounding loss of a very low frequency monopole antenna that takes into account tidal effects.

[0006] This invention is implemented as follows: a method for evaluating the grounding loss of a very low frequency monopole antenna considering tidal effects, comprising: A fan-shaped ring-shaped layered grounding model is established, dividing the ground network coverage area around the antenna into a non-tidal coverage area and a tidal coverage area; the tidal coverage area is constructed as a sub-region consisting of an upper seawater layer and a lower soil-ground network composite structure; Calculate the first equivalent conductivity of the tidal-free area; The tidal zone is equivalent to a one-dimensional lossy transmission line. Based on the physical parameters of the seawater layer and the parameters of the underlying soil-ground grid composite structure in the tidal zone, the second equivalent conductivity of the tidal zone is calculated. Based on the first equivalent conductivity and the second equivalent conductivity, a magnetic field weighting function is constructed and the magnetic field loss resistance per unit area of ​​each subdomain is calculated. The total magnetic field loss resistance is obtained by integrating the area of ​​the grounding grid coverage area, and the total magnetic field loss resistance is used as an approximation of the total grounding loss resistance.

[0007] Furthermore, the calculation of the first equivalent conductivity includes: neglecting displacement current in the very low frequency band, calculating the first equivalent conductivity by simultaneously solving the soil characteristic admittance equation and the ground grid system characteristic admittance equation composed of N radial conductors, and combining the boundary condition that the soil admittance and the ground grid admittance are equal.

[0008] Further, calculating the second equivalent conductivity includes: calculating the characteristic admittance of the seawater layer based on the seawater layer conductivity; calculating the seawater propagation constant based on the seawater layer conductivity and the operating frequency; calculating the input admittance as observed from the upper surface of the seawater layer based on the ratio of the load admittance of the lower soil-grid composite structure to the characteristic admittance of the seawater layer, and combining it with the hyperbolic function corresponding to the tidal depth; and then using the input admittance as input to back-calculate the second equivalent conductivity.

[0009] Furthermore, constructing the magnetic field weighting function includes: calculating the magnetic field weighting function based on the quotient of the radial distance at the bottom of the antenna and the square of the tangential component of the magnetic field divided by the square of the bottom current.

[0010] Furthermore, in the very low frequency band, the total magnetic field loss resistance is used as an approximation of the total grounding loss resistance; wherein, the total grounding loss resistance also includes the electric field loss resistance, and the proportion of the electric field loss resistance in the very low frequency band for large-scale radial grounding grid systems is smaller than that of the total magnetic field loss resistance.

[0011] Furthermore, it also includes a simplified calculation method: defining a tidal coverage location influence factor and a tidal depth influence factor, wherein the location influence factor is the ratio of the magnetic field loss contribution of the tidal coverage area in the non-tidal state to the non-tidal reference magnetic field loss resistance, and the depth influence factor is the ratio of the magnetic field loss of the tidal coverage area at a tidal depth of h to the magnetic field loss of the area in the non-tidal state; the total grounding loss resistance is calculated by multiplying the non-tidal reference magnetic field loss resistance, the location influence factor, and the depth influence factor.

[0012] This invention also provides a method for calculating the equivalent conductivity of the tidal coverage area for evaluating the grounding loss of a very low frequency monopole antenna, comprising: The upper seawater layer in the tidal-covered area is equivalent to a one-dimensional lossy transmission line; Calculate the characteristic admittance of the seawater layer based on its electrical conductivity. The seawater propagation constant is calculated based on the seawater layer conductivity and the operating frequency. Obtain the lower soil-grid composite structure as the load admittance; Using the admittance transformation formula, the input admittance observed from the upper surface of the seawater layer downwards is calculated based on the characteristic admittance of the seawater layer, the seawater propagation constant, the tidal depth, and the load admittance. Using the input admittance as input, the equivalent conductivity of the tidal coverage area is obtained by reverse calculation.

[0013] Furthermore, calculating the input admittance as observed from the upper surface of the seawater layer downwards includes: calculating the ratio of the load admittance to the characteristic admittance of the seawater layer, and constructing an admittance transformation relationship based on the hyperbolic tangent function corresponding to the tidal depth to calculate the input admittance.

[0014] Furthermore, the equivalent conductivity is obtained by reverse calculation by multiplying the square of the input admittance by the imaginary unit, the angular frequency, and the permeability, and then taking the real part to obtain the equivalent conductivity of the tidal coverage area.

[0015] Furthermore, the operating frequency belongs to the very low frequency band; in this frequency band, the electromagnetic wave penetrates the seawater layer to a depth less than the skin depth of the seawater, and the electromagnetic field can penetrate the seawater layer and act on the underlying soil-ground grid composite structure.

[0016] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows: This invention's physical model better reflects the actual operating conditions of tidal environments. For the first time, this invention establishes a sector-shaped, ring-shaped, layered grounding loss model for very low frequency (VLF) antennas under tidal coverage, clearly dividing the grounding network coverage area into a normal, non-tidal zone and a tidal coverage zone. The tidal coverage zone is further subdivided into a composite structure of a finite-depth seawater layer + a lower soil layer-grounding network. This model can realistically reflect the composite conductivity and current distribution mechanism among seawater, soil, and the metal grounding network, overcoming the limitations of traditional uniform grounding or ideal planar models that cannot describe layered media, non-uniform conductivity, and dynamic boundaries. Compared to the Wait transmission line analogy method and subsequent improved models (which all assume the grounding plane is a uniform lossy half-space or constant soil parameters), this invention, for the first time, simultaneously considers the skin effect, shielding effect, and admittance transformation of a finite-thickness seawater layer in an analytical model, providing an accurate physical basis for antenna performance evaluation under dynamic environments.

[0017] This invention can accurately predict non-monotonic loss changes under tidal action, a capability completely lacking in existing technologies. When the tide only covers the sparse outer edge of the grounding grid, the high-conductivity seawater layer provides an additional low-resistance return channel, reducing grounding loss. However, when the tide further intrudes into the high-density near-field grounding grid area, the finite-depth seawater layer produces a significant skin effect and shielding effect, causing a redistribution of current among the seawater layer, soil, and metal grounding grid. The current-conducting effect of the metal grounding grid is relatively weakened, and the decreasing trend of grounding loss weakens or even shows a non-monotonic increase. This invention, through equivalent conductivity inversion and magnetic field weighted integration, quantitatively reveals this complex law for the first time, resolving the long-standing misconception and technical blind spot that seawater coverage necessarily reduces loss in engineering projects.

[0018] This invention possesses rapid dynamic evaluation capabilities, filling the gap in dynamic simulation of grounding loss under tidal time-varying environments. By defining tidal depth and tidal coverage location influence factors, this invention concisely expresses the total grounding loss resistance as the product of the tidal baseline loss and the two influence factors. Loss values ​​under different tidal depths, coverage areas, grounding grid structures, and operating frequencies can be rapidly evaluated without repeated full-wave simulations. Simultaneously, this method supports diurnal and semi-diurnal tide evolution simulations, predicting the time-varying patterns of loss with tidal level fluctuations throughout the day (including asymmetric bi-peak or single-peak fluctuations, daily shifts in extreme values, etc.), providing a direct theoretical basis for transmitter dynamic tuning, runtime optimization, and adaptive impedance matching. An excellent balance is achieved between computational accuracy and engineering efficiency. In the 20kHz–25kHz frequency band, the average relative error between the analytical model of this invention and the FEKO full-wave simulation results is only 5.76%, while the computation time is reduced to less than 1% of the simulation time. Compared to pure numerical simulation methods (which require remodeling, meshing, and solving for each tidal state), this invention can complete a full evaluation in seconds, making it ideal for rapid iterative engineering design, parameter sensitivity analysis, and multi-scenario comparative studies.

[0019] This invention can directly guide the optimized design of non-uniform radial grounding grids and has clear engineering application value. By quantitatively analyzing the impact of different radial density distributions on tidal adaptability, this invention provides a design criterion for appropriately increasing the conductor density in the inner zone (near the antenna region) to enhance the mainstream return current capability, while maintaining sufficient conductivity in the outer zone (tidal-prone area) to utilize the low-resistivity seawater channel. Under the condition of limited total copper material usage, this criterion can significantly improve the robustness of the grounding system to tidal intrusion, avoid the material waste caused by blindly densifying the grounding grid, and provide an operable, economical, and efficient engineering basis for very low frequency antenna grounding systems.

[0020] This invention has significant and irreplaceable advantages over existing technologies in terms of physical realism, non-monotonic behavior prediction capability, dynamic time-varying simulation efficiency, balance between accuracy and cost, and practical engineering guidance value.

[0021] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows: This invention can be directly applied to the design, evaluation, operation, maintenance, and renovation of communication facilities, antenna systems, and related grounding projects, demonstrating clear engineering transformation value. By establishing a rapid grounding loss assessment model that considers tidal effects, this invention can quickly obtain grounding loss variation results under different tidal depths, tidal coverage areas, grounding grid radii, grounding grid densities, and operating frequencies without relying on extensive repetitive full-wave simulations. This significantly shortens the design iteration cycle of antenna grounding systems and reduces the costs of simulation modeling, manual analysis, and field testing.

[0022] Especially for engineering systems like very low frequency (VLF) antennas, which involve large-scale construction, extensive grounding networks, and high maintenance costs, this invention can predict the impact of tides on transmission efficiency and grounding loss during the design phase, avoiding rework, grounding network reinforcement, or system tuning difficulties due to insufficient estimation of the tidal environment. During operation and maintenance, it can be used to predict the daily fluctuations in grounding loss resistance based on tidal changes, providing a basis for transmitter impedance matching, dynamic tuning, operational optimization, and energy management. Because this invention shows good consistency with FEKO full-wave simulation results in the 20kHz to 25kHz frequency band, and the calculation time can be reduced to a very small proportion of the full-wave simulation, it can significantly improve evaluation efficiency while ensuring engineering accuracy.

[0023] Furthermore, this invention can also serve the optimized design of non-uniform radial grounding grids. By analyzing the coupling relationship between grounding grid density in different radial regions and tidal coverage locations, it guides a more rational grounding grid layout under limited copper material usage, reducing ineffective material input and improving the return on investment in grounding grid construction. Therefore, this invention not only has the potential for transformation into software tools, engineering consulting, and design standardization, but can also form a dedicated evaluation module or auxiliary design platform for high-power low-frequency / very low-frequency antenna systems, possessing high commercial promotion value.

[0024] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally: Most existing methods for assessing grounding loss of very low frequency (VLF) monopole antennas are based on ideal grounding planes, uniform lossy half-spaces, or static radial grounding grid models. These methods typically assume constant soil electrical parameters, a fixed grounding grid structure, and an unchanging external environment. While the Wait transmission line analogy method and subsequent equivalent grounding grid admittance models can handle equivalent grounding grid problems under certain conditions, they do not consider the layered composite conductive structure formed when seawater, soil, and metal grounding grids coexist in tidal environments. Furthermore, they cannot describe the transformation effect of a finite-depth seawater layer on the load admittance of the underlying soil-grounding grid.

[0025] This invention, for the first time, proposes a fan-shaped ring-shaped layered grounding model for VLF monopole antennas in tidal coverage scenarios. The tidal coverage area is modeled as a composite structure of an upper layer of seawater at a finite depth and a lower layer of soil-grounding network. The equivalent conductivity of the tidal coverage area is derived through one-dimensional lossy transmission line admittance transformation, making the equivalent conductivity a function of tidal depth, operating frequency, seawater conductivity, soil conductivity, and grounding network geometric parameters. This scheme overcomes the limitations of traditional models that can only handle static, uniform, single-layer grounding media, filling the technical gap of lacking a rapid analytical evaluation model for VLF antenna grounding losses in dynamic tidal, spatially non-uniform, and layered conductive environments.

[0026] Furthermore, this invention introduces a magnetic field weighting function, a tidal coverage location influence factor, and a tidal depth influence factor. This not only enables the calculation of grounding loss under a specific tidal condition but also allows for the simulation of time-varying grounding loss patterns during diurnal and semi-diurnal tidal processes. This technical system, which combines tidal dynamics, hierarchical admittance transformation, non-uniform grounding grid distribution, and rapid grounding loss assessment, represents a significant filler in the gap in existing publicly available technologies, addressing a crucial gap in the industry's assessment of the tidal adaptability of very low frequency (VLF) antennas.

[0027] (3) The technical solution of the present invention solves a technical problem that people have long wanted to solve but have never been able to solve successfully: Very low frequency (VLF) monopole antennas have long faced an engineering challenge: tidal fluctuations periodically alter the grounding environment around the antenna, causing grounding loss resistance to dynamically change with tide level, coverage area, and seawater depth. This, in turn, affects antenna transmission efficiency, impedance matching, and system operational stability. Engineers have long sought to quickly and accurately predict these tidal effects. However, traditional analytical models are overly simplistic and fail to reflect the realities of layered media and non-uniform grounding network distributions. While full-wave simulation offers high accuracy, it requires repeated modeling and solving when dealing with large-area grounding networks, multiple frequency points, multiple tide levels, and diurnal tidal evolution, resulting in enormous computational demands that hinder rapid engineering evaluation and real-time analysis.

[0028] This invention solves the long-standing technical challenge of balancing accuracy and efficiency by employing finite-depth seawater layer admittance transformation, soil-grid load admittance equivalence, magnetic field weight integration, and simplified expression of tidal influence factors. On one hand, this invention preserves the physical coupling relationship between the seawater layer, soil layer, and metal grounding grid, reflecting the variation of the equivalent conductivity of the tidal coverage area with tidal depth and frequency. On the other hand, it avoids the high cost of re-performing three-dimensional full-wave simulations for each tidal state, making grounding loss assessment under dynamic tidal conditions engineering-ready.

[0029] More importantly, this invention solves the problem of non-monotonic variation in grounding loss under tidal conditions, a problem that is difficult to explain with existing technologies. Traditional understanding often assumes that high-conductivity seawater coverage simply reduces grounding loss. However, in actual antennas, as the tide advances from the sparse outer grounding network area to the high-density near-field grounding network area, the finite-depth seawater layer generates a skin effect and shielding effect, causing a redistribution of current among the seawater, soil, and metal grounding network. This results in a complex variation in grounding loss, which may first decrease and then increase. This invention, through equivalent conductivity inversion and magnetic field weighted surface integration, can quantitatively reveal and predict this phenomenon, thus solving the long-standing technical problem of accurately modeling, rapidly calculating, and guiding the design of grounding loss variations under tidal conditions.

[0030] (4) The technical solution of the present invention overcomes technical bias: Two types of technical biases are prevalent in existing technologies. The first bias holds that in assessing grounding loss of very low frequency (VLF) antennas, the grounding plane can be approximated as uniform soil or an ideal conductive plane, and tidal seawater cover is treated merely as an external factor increasing surface conductivity; it can even be simply assumed that seawater has high conductivity, therefore tidal cover necessarily reduces grounding loss. The second bias argues that for complex layered conductive structures under tidal influence, only three-dimensional full-wave electromagnetic simulation can yield reliable results, as analytical models struggle to simultaneously account for layered media, current redistribution, and engineering computational efficiency.

[0031] This invention overcomes the aforementioned technical biases. First, it does not simply equate the tidal cover area to an infinitely thick seawater layer or a single high-conductivity region. Instead, it recognizes that at very low frequencies, the thickness of a finite-depth seawater layer may be less than or close to the skin depth of seawater, allowing electromagnetic fields to still penetrate the seawater layer and act on the underlying soil-grounding grid composite structure. Therefore, this invention treats the seawater layer as a lossy transmission line of finite thickness while retaining the influence of the load admittance of the underlying soil-grounding grid, thus overcoming the one-sided view that seawater cover can simply replace the original grounding medium.

[0032] Secondly, this invention reveals that tidal coverage does not always monotonically reduce grounding losses. When the tide covers the sparsely covered outer edge of the grounding grid area, the highly conductive seawater may indeed provide an additional low-resistance return path, reducing losses. However, when the tide further enters the near-field high-density grounding grid area, the skin effect, shielding effect, and current redistribution of the seawater layer may weaken the original conductivity of the metallic grounding grid, causing the trend of loss reduction to weaken or even rebound. This understanding breaks through the industry's empirical judgment that the deeper and more extensive the seawater coverage, the lower the grounding loss will necessarily be.

[0033] Furthermore, this invention transforms the grounding loss problem under complex tidal environments into a rapidly calculable analytical evaluation problem by using tidal coverage location influence factors and tidal depth influence factors. It demonstrates that, under reasonable physical modeling and parameter equivalence conditions, analytical methods can also obtain engineering results consistent with full-wave simulation trends and with acceptable errors, thus overcoming the technical bias that complex tidal grounding problems can only rely on high-cost full-wave simulation. In summary, this invention not only breaks through the traditional uniform grounding assumption in model construction but also forms new technical insights into loss variation patterns and engineering evaluation methods. Attached Figure Description

[0034] Figure 1 This invention provides a method for evaluating the grounding loss of a very low frequency monopole antenna that takes into account tidal effects. Figure 2 A detailed flowchart of the method for evaluating the grounding loss of a very low frequency monopole antenna considering tidal effects provided in this embodiment of the invention; Figure 3Equivalent circuit diagram of a very low frequency transmitting antenna provided in an embodiment of the present invention; Figure 4 The tidal region model provided in this embodiment of the invention; Figure 5 This invention provides an embodiment of the variation of composite equivalent conductivity of the tidal-covered area with tidal depth at different frequencies. Figure 6 The FEKO simulation models provided for embodiments of the present invention are: (a) a tidal-free model, (b) an outer edge tidal intrusion model, and (c) an inner zone tidal intrusion model. Figure 7 The embodiments of the present invention provide (a) curves showing the variation of loss resistance at different monopole heights under different tidal depths; and (b) curves showing the variation of loss resistance at different frequencies. Figure 8 The embodiments of the present invention provide (a) curves showing the variation of loss resistance at different tidal depths under different tidal coverage areas; and (b) curves showing the variation of loss resistance under different ground grid radii. Figure 9 The embodiments of the present invention provide (a) curves of loss resistance variation under different grounding grid configurations in different tidal coverage areas; and (b) curves of loss resistance variation under the same copper content in different grounding grid configurations. Figure 10 The following diagrams are provided for embodiments of the present invention: (a) tidal depth variation over 24 hours; (b) tidal intrusion range variation over 24 hours; and (c) grounding loss resistance variation over 24 hours. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0036] like Figure 1 As shown in the figure, an embodiment of the present invention provides a method for evaluating the grounding loss of a very low frequency monopole antenna considering tidal effects, comprising: S101, establish a fan-shaped ring-shaped layered grounding model, and divide the ground network coverage area around the antenna into a non-tidal coverage area and a tidal coverage area; the tidal coverage area is constructed as a fan-shaped ring-shaped sub-region composed of an upper layer of seawater with a limited depth and a lower layer of soil-ground network composite structure. S102, For the tidal-free area, based on the Wait equivalent admittance theory, the soil dielectric constant, soil electrical conductivity, soil magnetic permeability and the geometric parameters of the ground grid are used as inputs to calculate the equivalent electrical conductivity of the tidal-free area. S103, for the tidal-covered area, the finite-depth seawater layer is equivalent to a one-dimensional lossy transmission line; based on the seawater layer characteristic admittance, seawater propagation constant, tidal depth, and lower soil-grid load admittance, the input admittance observed from the upper surface of the seawater layer downwards is calculated using the admittance transformation formula; then, the input admittance is used as input to back-calculate the equivalent conductivity of the tidal-covered area, which is a function of tidal depth, operating frequency, seawater conductivity, and lower soil-grid parameters.

[0037] The present invention provides a method for calculating the equivalent conductivity of tidal-free areas as follows: Based on a ground grid system consisting of N radial conductors, the spacing between adjacent ground conductors, the radius of the covering circle, the radius of the ground conductor, and the operating frequency are obtained. According to the soil characteristic admittance equation and the ground grid system characteristic admittance equation, the displacement current is ignored in the very low frequency band. Combined with the boundary condition that the soil admittance and the ground grid admittance are equal, the equivalent conductivity of the non-tidal coverage area is obtained by simultaneous calculation and simplification.

[0038] The present invention provides a method for calculating the equivalent conductivity of tidal-covered areas as follows: The seawater layer characteristic admittance is set as the square root of the complex conductivity of seawater divided by the imaginary unit, multiplied by the angular frequency, and multiplied by the permeability; the seawater propagation constant is set as the square root of the imaginary unit, multiplied by the angular frequency, multiplied by the permeability, and multiplied by the conductivity of seawater. The transformation relationship of the input admittance is constructed by the ratio of the seawater layer characteristic admittance to the load admittance and the hyperbolic function of the tidal depth tangent; the equivalent conductivity of the tidal coverage area is equal to the square of the input admittance multiplied by the imaginary unit multiplied by the angular frequency multiplied by the permeability, and then the real part is taken.

[0039] The method provided in this embodiment of the invention is applicable to the very low frequency band, where the depth to which electromagnetic waves penetrate the seawater layer is less than the skin depth of the seawater, and the electromagnetic field can penetrate the seawater layer and act on the underlying soil-ground grid composite structure.

[0040] The embodiments of the present invention provide grounding grid geometric parameters including buried conductor spacing and conductor diameter.

[0041] Another objective of this invention is to provide a method for evaluating the ground loss of a very low frequency monopole antenna, comprising: Obtain the equivalent conductivity of the tidal-free area and the equivalent conductivity of the tidal-covered area determined by the method described above; Using the near-field magnetic field distribution formula of a monopole antenna, a magnetic field weighting function is constructed in polar coordinates. This magnetic field weighting function quantifies the contribution of the magnetic field strength at different spatial locations to the total grounding loss based on the radial distance and azimuth angle of the antenna bottom. Based on the formula for the base value of magnetic field loss resistance per unit area, the ground grid coverage area is discretized into multiple fan-shaped ring sub-domains; for the non-tidal zone, the equivalent conductivity of the non-tidal coverage area is applied, and for the tidal zone, the equivalent conductivity of the tidal coverage area is applied, and the corresponding base value of magnetic field loss resistance per unit area is calculated respectively. The total magnetic field loss resistance of the antenna system is obtained by integrating the product of the magnetic field loss resistance base and the magnetic field weighting function of each subdomain, and this total magnetic field loss resistance is used as an approximation of the total grounding loss resistance.

[0042] The embodiment of this invention provides the following method for constructing the magnetic field weighting function: The magnetic field weighting function is equal to the result of multiplying the radial distance from the bottom of the antenna by the square of the tangential component of the magnetic field and then dividing by the square of the bottom current; wherein, the tangential component of the magnetic field is determined by the bottom current of the monopole antenna, the equivalent height, and the radial distance.

[0043] The evaluation method provided in this embodiment of the invention further includes introducing a tidal coverage location influence factor and a tidal depth influence factor to simplify the calculation of total grounding loss resistance: The tidal coverage location influence factor is defined as the ratio of the magnetic field loss contribution of the tidal coverage area in the non-tidal state to the non-tidal reference magnetic field loss resistance. The tidal depth influence factor is defined as the ratio of the magnetic field loss in the tidal-covered area at a depth of h to the magnetic field loss in the same area under non-tidal conditions. The total grounding loss resistance is expressed as the product of the non-tidal reference magnetic field loss resistance, the tidal coverage location influence factor, and the tidal depth influence factor. The present invention provides that, in the very low frequency band, for large-scale radial grounding grid systems, the magnetic field loss resistance dominates the total grounding loss, the electric field loss resistance is extremely small, and the total grounding loss resistance is approximately equal to the total magnetic field loss resistance.

[0044] The embodiments of the present invention also include a method effectiveness verification step: comparing the grounding loss resistance value obtained by analytical calculation with the simulation results obtained by the three-dimensional full-wave electromagnetic simulation model in the 20 kHz to 25 kHz frequency band.

[0045] like Figure 2 As shown, this embodiment of the invention provides a method for evaluating the grounding loss of a very low frequency monopole antenna considering tidal effects. The method includes: S1: Establish a fan-shaped ring-shaped layered grounding model, dividing the ground network coverage area around the antenna into a normal area without tidal influence and a tidal coverage area. The tidal coverage area is further modeled as a fan-shaped ring-shaped sub-region composed of an upper finite-depth seawater layer and a lower soil-ground network composite structure. For the non-tidal coverage area, its equivalent characteristic admittance and equivalent conductivity are defined based on the Wait ground network equivalent admittance theory. For the tidal coverage area, the finite-thickness seawater layer is regarded as a lossy transmission line, and the input admittance observed from the upper surface of the seawater layer downward is calculated using the admittance transformation formula. S2: Using the near-field magnetic field distribution formula of a monopole antenna, a magnetic field weighting function is defined in polar coordinates to characterize the contribution weight of magnetic field strength at different radial distances and azimuth angles to the total grounding loss. Based on the formula for the magnetic field loss resistance per unit area, the grounding grid coverage area is discretized into multiple fan-shaped annular subdomains. The baseline equivalent conductivity is used in the non-tidal area, and the aforementioned equivalent conductivity is used in the tidal area. The magnetic field weighted area integral is performed on each subdomain to obtain the total magnetic field loss resistance. In the very low frequency band, magnetic field loss dominates, and the contribution of electric field loss can be ignored. To make the evaluation faster, tidal coverage location influence factors and tidal depth influence factors are defined. The total grounding loss resistance is expressed as the product of the non-tidal baseline loss and these two influence factors, which enables rapid evaluation of loss changes at different tidal intrusion locations and depths. S3: A three-dimensional model was established using FEKO full-wave simulation. The analytical calculation results and simulation results were compared and verified in the 20 to 25 kHz frequency band. The influence of different tidal depths, different tidal coverage areas, non-uniform radial grounding grid distribution, and dynamic periodic evolution of diurnal and semi-diurnal tides on grounding loss resistance was systematically analyzed, providing a theoretical basis for the tidal adaptability design of very low frequency antenna grounding systems.

[0046] 1. Equivalent Calculation Method from Figure 3 The equivalent circuit diagram for very low frequency (VLF) transmission shows that the total antenna loss is determined by multiple resistors. Among these, the tuning inductor loss and wire loss are fixed after the antenna is installed. However, the ground loss resistance is the only parameter in the equivalent circuit that fluctuates with the tides. This loss mainly consists of two parts: first, the electric field loss caused by displacement current flowing into the ground grid system; and second, the magnetic field loss generated by induced current flowing through the damaged ground layer. Establishment as follows... Figure 4 The grounding plane is shown in a regional model, with the light-colored area representing the normal operating area of ​​the grounding grid and the blue area representing the tidal coverage area. The influence of tides on the grounding grid is equivalent to a sector-shaped region model, constructing a model of a grounding plane with non-uniform conductivity distribution. Based on this, the equivalent conductivity and the loss basis per unit area are derived, and then the total grounding loss resistance is solved.

[0047] Based on the soil characteristics described in the literature for (1) In the formula Where is the dielectric constant. Indicates soil electrical conductivity. Indicates soil permeability, ω is the angular frequency.

[0048] For a grounding grid system consisting of N radial conductors, its characteristic admittance The definition is as follows: (2) in Indicates the distance between two adjacent ground lines. Indicates the radius of the covering circle. Indicates the radius of the ground wire. Let be the frequency. In the tidal-free region, for ease of calculation, the equivalent characteristic admittance of the tidal-free region is defined as: (3) In the formula This represents the equivalent conductivity in areas without tidal coverage. Since we are considering the very low frequency band, Then it can be simplified to: (4) According to Wait's conclusion, there is an equation relating the ground grid line and the soil conductivity. Then, by solving the simultaneous equations and simplifying, we get: (5) The tidal zone consists of an upper layer of seawater and an underlying soil-geological network structure. The complex electrical conductivity of seawater is defined as: Calculations show that in the very low frequency band, electromagnetic waves penetrate the seawater layer to a depth of approximately 1-2 meters. Since the seawater layer thickness is less than the skin depth, the electromagnetic field can still partially penetrate the seawater layer and act on the underlying soil-grid composite structure. Therefore, the tidal cover area cannot be simply equated to an infinitely thick seawater layer; the loading effect of the underlying soil and ground grid still needs to be considered. The tidal cover area can be viewed as a layered conductive structure loaded onto the soil-grid composite system by a finite-thickness seawater layer. Because the tidal depth is much smaller than the horizontal scale of the ground grid, this invention uses a one-dimensional lossy transmission line model to describe the admittance transformation of the seawater layer in a localized region. In this case, the input admittance observed downwards from the upper surface of the seawater layer can be expressed as: (6) in Admittance for seawater layer characteristics, Let be the seawater propagation constant. Tidal depth, This is the soil-grid load admittance. The admittance ratio is defined as: For seawater, according to Maxwell's equations and wave equations, its propagation constant is... (7) The electrical conductivity of seawater is given by [insert value here]. The characteristic admittance of seawater is [insert value here]. (8) For ease of calculation, Defined as (9) in Let be the equivalent conductivity including tides. Then, the equivalent conductivity of the tidal-covered area is calculated as follows: (10) Substituting equation 8 into equation 10 and simplifying, we get: (11) Down Figure 5 This describes the curves showing the variation of the equivalent electrical conductivity of the tidal-covered area with tidal depth at different frequencies. In the outer region, the ground grid lines are sparse, and the enhancing effect of the ground grid on electrical conductivity weakens. As tidal depth increases, a layer of highly conductive seawater covering the soil surface causes the equivalent electrical conductivity to steadily increase. When the frequency increases, the skin depth decreases, and the shielding effect of seawater on the ground grid-soil composite structure strengthens. High frequencies make this region more likely to reach a seawater-dominated state.

[0049] Baseline of magnetic field loss resistance per unit area It is given by the following formula: (12) In the formula The equivalent conductivity of a monopole antenna in areas affected by tidal forces or for normal operation of the ground network. d represents the spacing of buried conductors, and d represents the conductor diameter.

[0050] For a monopole antenna with a uniformly distributed current, the tangential component of the magnetic field is... The expression for the region much smaller than the wavelength is: (13) Vertical electric field for: (14) In the formula The distance to the bottom of the monopole antenna. For equivalent height, The relative permittivity, This is the bottom current. According to the method of base resistance per unit area magnetic field loss, the magnetic field loss resistance is... (15) In polar coordinates, Define the magnetic field weighting function as follows: (16) Under tidal conditions, the reference magnetic field loss resistance is (17) Let be the radius of the ground grid coverage area. The contribution of the tidal coverage area to the total magnetic field loss in the absence of tides is... (18) , These are the inner and outer boundaries of the tidal coverage, respectively. Let be the tidal cover angle. The tidal cover location influence factor is defined as... (19) Substituting equations (17) and (18) into equation (19) yields (20) When the tidal depth is h, the magnetic field loss in the tidal-covered area is: (twenty one) Define the tidal depth influence factor as (twenty two) Substituting equations (18) and (21) into equation (22) yields (twenty three) After tidal coverage, non-tidal areas will still use Tidal coverage area adopts Then the total magnetic field loss resistance is (twenty four) In the formula This is an area without tidal coverage. This is the tidal-covered area. Using equations (23) and (26), the total magnetic field loss resistance in equation (28) can be simplified to... (25) Electric field loss resistance is (26) For conduction current density, , The resistance per unit area of ​​electric field loss in the normal zone and the tidal zone. , , The radius of the ground network covering the area, and Let be the radius of the inner circular normal ground grid area. In the VLF band, for large-scale radial ground grid systems, magnetic field loss usually dominates. Therefore, the total loss resistance can be approximated as... (27).

[0051] like Figure 6 To verify the effectiveness of this method in calculating the grounding loss resistance including tidal currents, a FEKO simulation was used and compared with the model. The monopole antenna height was set to 300 meters, its grounding network system consisted of 100 grounding wires with an angle of 3.6°, and the grounding network system coverage radius was 1600 meters. The tidal coverage area was set at an angle of 60 degrees, covering the area from 1300 meters to 1600 meters in the outer ring. The blue area in the figure represents the tidal coverage area, with a tidal depth of 0.5 meters, a ground conductivity of 0.01 S / m, and a seawater conductivity of 4 S / m.

[0052] Table 1 Comparison of Grounding Loss Resistance Results ρ ; Table 1 compares the proposed analytical model with the FEKO simulation results. It can be seen that within the 20–25 kHz frequency band, the grounding loss resistance obtained by both methods increases with frequency, and the loss is greater without tidal coverage than with tidal coverage. Taking 20 kHz as an example, the grounding loss resistance calculated using the analytical model is 55.05 mΩ, while the FEKO simulation result is 51.88 mΩ, with a relative error of approximately 5.76%. The FEKO analytical result is slightly lower than the analytical value, mainly due to the coupling effect between the seawater layer, the grounding wire, and the boundary of the limited region in the full-wave model, as well as the mesh partitioning problem. Overall, the grounding loss resistance obtained by the two methods shows good consistency in terms of frequency variation trends and tidal loss reduction patterns. The loss reduction in this model is mainly due to the high conductivity of the seawater layer effectively diverting the current flowing through the soil, thus reducing losses. Although the improvement seems limited, this is because the current tidal region is located at the outermost edge of the grounding grid, where the current density has significantly decreased, limiting its contribution to the total loss.

[0053] 2. Grounding loss resistance at different tidal depths Figure 7 The variation of grounding loss resistance with tidal depth under tidal cover at the outer edge is presented. Since the tidal cover area is located at the outer edge of the grounding grid, the line spacing is relatively large, the original conductivity is poor, and as the tidal depth increases, the seawater layer provides additional conductive channels at the outer edge, increasing the local equivalent admittance. Therefore, overall, the grounding loss resistance shows a decreasing trend. Figure 7As shown in (a), the curves exhibit the same variation pattern at different monopole heights, but differ in terms of loss and reduction magnitude, indicating that the near-field distribution of the antenna affects the contribution of the tidal coverage area to the total loss. From Figure 7 As can be seen in (b), the loss resistance at different frequencies decreases with increasing tidal depth. Furthermore, the coupling strength between the seawater layer and the underlying geothermal-soil composite structure also causes differences between the curves at different frequencies as the frequency changes.

[0054] 3. Grounding loss resistance in different tidal coverage areas Figure 8 The variation patterns of grounding loss resistance under different tidal coverage areas are presented. Figure 8 (a) shows that as the tidal coverage area gradually expands from the outer edge of the land grid to the inner area, the loss resistance first decreases and then increases; while in the outer area, the overall loss resistance decreases with increasing tidal depth, and as the coverage area moves closer to the inner area, the loss resistance increases to a certain extent, with this trend becoming more pronounced at greater seawater depths. From Figure 8 (b) As can be seen, similar to before, under the same tidal coverage conditions, increasing the grounding grid radius can also significantly reduce the grounding loss resistance, and the curves corresponding to different grounding grid radii generally show similar trends. That is, when the grounding grid radius is small, its loss resistance is relatively high, and as the grounding grid radius increases, its loss resistance gradually decreases. Overall, the location of tidal coverage has a significant impact on grounding loss, and the magnitude of change in grounding loss resistance also changes with the continuous increase of tidal depth and grounding grid radius.

[0055] 4. Grounding loss resistance of non-uniform radial grounding grid distribution The first segment of the grounding grid covers an area of ​​0-500 meters, the second segment covers an area of ​​500-1000 meters, and the third segment covers an area of ​​1000-1600 meters. Tables 2 and 3 show the grounding grid distribution structure under different conditions.

[0056] Table 2. Distribution of several different forms of ground grid ; Table 3 Non-uniform ground grid distribution under equal copper content ; Figure 9 The modulation effect of non-uniform radial grounding grid configuration on grounding loss resistance under tidal intrusion conditions is presented. Overall, the two sets of results are similar to the regional patterns obtained in the previous paper. When the tide mainly covers the outer edge, the loss decreases as the tidal intrusion range increases; while when the tide further extends into the near zone, the decreasing trend of loss decreases and even increases slightly. Figure 9(a) The grounding grid configuration is not equal in copper quantity, but as the conductors gradually gather in the inner and middle areas and the total conductor length increases, the overall grounding loss resistance decreases. That is, increasing the grounding grid density in the main return area can effectively reduce the equivalent grounding loss. Figure 9 (b) shows a grounding grid configuration with equal copper content. The small differences between the curves indicate that the improvement from radial redistribution is limited by the total conductor length. It is worth noting that denser grounding in the inner zone does not necessarily achieve the best results across the entire tidal intrusion range; excessively sparse grounding in the outer and middle zones weakens the conduction capacity during the tidal coverage phase at the outer edge. In contrast, non-uniform grounding grid optimization schemes should not be achieved simply by increasing near-zone conductor density, but should also comprehensively consider the coupling relationship between tidal coverage location, return current weight, and the radial distribution of the grounding grid.

[0057] 5. Simulation of the time-varying evolution of grounding loss resistance during diurnal tidal dynamics Figure 10 The changes in tidal level, tidal intrusion range, and grounding loss resistance within a day are presented under the influence of diurnal and semi-diurnal tides. As can be seen from the figure, under the dominant diurnal tide condition, the tidal level experiences one rise and fall, while under the dominant semi-diurnal tide condition, two rises and falls occur within 24 hours. Correspondingly, Figure 10 (b) The tidal intrusion range expands and recedes synchronously with the tide level. Figure 10 As shown in (c), the grounding loss resistance is also affected by tides and undergoes periodic changes. When the tide advances from the outer edge inward, the loss resistance tends to decrease; when the tide continues to increase and the near-field water depth is high, the loss resistance will increase. Under semi-diurnal tide conditions, there are two loss fluctuations within a day, but the amplitudes of the two loss fluctuations are not equal, indicating that the tide type determines the variation characteristics of grounding loss. On the other hand, under different tidal models, the times when the maximum and minimum values ​​of the loss resistance occur are not the same, and the antenna transmission efficiency will also fluctuate with the tide. The tidal parameters used in this simulation show that the loss resistance is higher and the transmission efficiency is lower from morning to noon, while the opposite is true at night. It should be noted that the actual tidal phase shifts backward by about one hour each day, so the time when the extreme value of loss occurs will also shift daily.

[0058] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0059] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for evaluating the grounding loss of a very low frequency monopole antenna considering tidal effects, characterized in that, include: A fan-shaped ring-shaped layered grounding model is established, dividing the ground network coverage area around the antenna into a non-tidal coverage area and a tidal coverage area; the tidal coverage area is constructed as a sub-region consisting of an upper seawater layer and a lower soil-ground network composite structure; Calculate the first equivalent conductivity of the tidal-free area; The tidal zone is equivalent to a one-dimensional lossy transmission line. Based on the physical parameters of the seawater layer and the parameters of the underlying soil-ground grid composite structure in the tidal zone, the second equivalent conductivity of the tidal zone is calculated. Based on the first equivalent conductivity and the second equivalent conductivity, a magnetic field weighting function is constructed and the magnetic field loss resistance per unit area of ​​each subdomain is calculated. The total magnetic field loss resistance is obtained by integrating the area of ​​the grounding grid coverage area, and the total magnetic field loss resistance is used as an approximation of the total grounding loss resistance.

2. The method according to claim 1, characterized in that, The calculation of the first equivalent conductivity includes: neglecting displacement current in the very low frequency band, calculating the first equivalent conductivity by simultaneously solving the soil characteristic admittance equation and the ground grid system characteristic admittance equation composed of N radial conductors, and combining the boundary condition that the soil admittance and the ground grid admittance are equal.

3. The method according to claim 1, characterized in that, The calculation of the second equivalent conductivity includes: calculating the characteristic admittance of the seawater layer based on the seawater layer conductivity; calculating the seawater propagation constant based on the seawater layer conductivity and the operating frequency; calculating the input admittance as observed from the upper surface of the seawater layer based on the ratio of the load admittance of the lower soil-grid composite structure to the characteristic admittance of the seawater layer, and combining it with the hyperbolic function corresponding to the tidal depth; and then using the input admittance as input to back-calculate the second equivalent conductivity.

4. The method according to claim 1, characterized in that, Constructing the magnetic field weighting function includes: calculating the magnetic field weighting function based on the quotient of the radial distance at the bottom of the antenna and the square of the tangential component of the magnetic field divided by the square of the bottom current.

5. The method according to claim 1, characterized in that, In the very low frequency band, the total magnetic field loss resistance is used as an approximation of the total grounding loss resistance; wherein, the total grounding loss resistance also includes the electric field loss resistance, and the proportion of the electric field loss resistance in the very low frequency band for large-scale radial grounding grid systems is smaller than that of the total magnetic field loss resistance.

6. The method according to claim 1, characterized in that, It also includes a simplified calculation method: defining a tidal coverage location influence factor and a tidal depth influence factor. The location influence factor is the ratio of the magnetic field loss contribution of the tidal coverage area in the non-tidal state to the non-tidal reference magnetic field loss resistance. The depth influence factor is the ratio of the magnetic field loss of the tidal coverage area at a tidal depth of h to the magnetic field loss of the area in the non-tidal state. The total grounding loss resistance is calculated by multiplying the non-tidal reference magnetic field loss resistance, the location influence factor, and the depth influence factor.

7. A method for calculating the equivalent conductivity of the tidal coverage area for evaluating the grounding loss of a very low frequency monopole antenna, characterized in that, include: The upper seawater layer in the tidal-covered area is equivalent to a one-dimensional lossy transmission line; Calculate the characteristic admittance of the seawater layer based on its electrical conductivity. The seawater propagation constant is calculated based on the seawater layer conductivity and the operating frequency. Obtain the lower soil-grid composite structure as the load admittance; Using the admittance transformation formula, the input admittance observed from the upper surface of the seawater layer downwards is calculated based on the characteristic admittance of the seawater layer, the seawater propagation constant, the tidal depth, and the load admittance. Using the input admittance as input, the equivalent conductivity of the tidal coverage area is obtained by reverse calculation.

8. The method according to claim 7, characterized in that, Calculating the input admittance as viewed from the upper surface of the seawater layer includes: calculating the ratio of the load admittance to the characteristic admittance of the seawater layer, constructing an admittance transformation relationship based on the hyperbolic tangent function corresponding to the tidal depth, and calculating the input admittance.

9. The method according to claim 7, characterized in that, The equivalent conductivity is obtained by reverse calculation by multiplying the square of the input admittance by the imaginary unit, the angular frequency, and the permeability, and then taking the real part to obtain the equivalent conductivity of the tidal coverage area.

10. The method according to claim 7, characterized in that, The operating frequency is in the very low frequency band; in this frequency band, the electromagnetic wave penetrates the seawater layer to a depth less than the skin depth of the seawater, and the electromagnetic field can penetrate the seawater layer and act on the underlying soil-ground grid composite structure.

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