Linearization method and system for nonlinear high-frequency model of steel under lightning stroke

Abstract

The invention discloses a linearization method and system for a nonlinear high-frequency model of steel under lightning stroke, and relates to the technical field of electromagnetic engineering, and the method comprises the steps: constructing an impedance model of the steel through employing a PEEC method; the parameters of the steel are extracted through pulse current; and linearizing the nonlinear characteristics of the steel through an impedance model. According to the method, the impedance of the steel can be accurately modeled by adopting a partial capacitance equivalent circuit method and combining the characteristics of the magnetic material and the high-frequency eddy current effect, and the modeling precision is remarkably improved. A traditional electrical steel parameter extraction method cannot simulate actual lightning stroke current conditions, so that the authenticity and accuracy of experimental data are insufficient. According to the impulse current injection method provided by the invention, the impedance parameter of the steel can be directly extracted by measuring the transient response of the steel under the actual lightning stroke current and combining with the fast Fourier transform technology to process data, so that the authenticity and accuracy of experimental data are ensured.

Description

Technical Field

[0001] The invention relates to the field of electromagnetic engineering technology, and in particular to a linearization method and system for a nonlinear high-frequency model of steel under lightning strike. Background Art

[0002] Steel plays a vital role in buildings, towers, and other large grounded structures that may conduct electricity during transient conditions such as lightning strikes. As the complexity of modern buildings and electrical systems increases, it becomes increasingly important to accurately simulate and analyze the electrical behavior of these steels under lightning currents. However, there is currently no universal and effective method to model and analyze the electrical properties of steel under transient conditions.

[0003] Lightning transient analysis is critical to protecting buildings and sensitive electronic equipment because lightning currents can produce huge shocks to structures and equipment in a short period of time. Traditionally, the electrical behavior of steel is often ignored or simplified as non-ferromagnetic or perfect conductors in transient analysis. This simplification can lead to significant errors because the magnetic properties of steel are not considered. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention is proposed.

[0005] Therefore, the technical problem solved by the present invention is: how to accurately simulate and analyze the electrical behavior of steel under transient electromagnetic events such as lightning strikes.

[0006] In order to solve the above technical problems, the present invention provides the following technical solution: a linearization method of a nonlinear high-frequency model of steel under lightning strike, which comprises the following steps:

[0007] Collect steel parameters; use the PEEC method to build the impedance model of steel; use experiments to verify the PEEC method.

[0008] As a preferred scheme of the linearization method of the nonlinear high-frequency model of steel under lightning strike described in the present invention, the parameters of the steel include the vacuum permeability of the circular conductor, the length of the circular conductor segment, the radius of the circular conductor, the resistivity of the circular conductor, the magnetic permeability of the circular conductor and the skin depth.

[0009] The construction of the impedance model of the steel includes calculating the self-impedance of the circular conductor and the mutual impedance of the coil by the PEEC method based on the parameters of the steel, and constructing a time domain equivalent circuit.

[0010] As a preferred solution of the linearization method of the nonlinear high-frequency model of steel under lightning strike described in the present invention, wherein: the self-impedance of the circular conductor includes external inductance and internal impedance.

[0011] The external inductance is obtained by Neumann's formula, which is expressed as,

[0012]

[0013] Among them, μ0 represents the magnetic permeability of vacuum, l represents the length of the circular conductor segment, and a represents the radius of the circular conductor.

[0014] The internal impedance is expressed as,

[0015]

[0016] Where j represents the imaginary unit, ω represents the angular frequency, I0 represents the modified Bessel function of order 0, I1 represents the modified Bessel function of order 1, and R a represents the parameters in the modified Bessel function, expressed as,

[0017]

[0018] Where a is the radius of the circular conductor and δ is the skin depth, which is expressed as,

[0019]

[0020] Among them, ρ is the resistivity of the circular conductor, and μ is the magnetic permeability of the circular conductor.

[0021] As a preferred solution of the linearization method of the nonlinear high-frequency model of steel under lightning strike described in the present invention, wherein: the self-impedance of the circular conductor calculated by the PEEC method is expressed as:

[0022] Z(ω)=Z in (ω)-jωL ext (∞)

[0023] Where Z(ω) represents the self-impedance of a circular conductor at frequency ω, Z in Represents the internal impedance of a circular conductor, L ext (∞) represents the external inductance of a circular conductor at high frequencies.

[0024] The coil mutual impedance calculation is expressed as,

[0025]

[0026] Where d is the distance between the wires.

[0027] As a preferred solution of the linearization method of the nonlinear high-frequency model of steel under lightning strike described in the present invention, wherein: the time domain equivalent circuit is a combination of the self-impedance of the circular conductor and the mutual impedance of the coil.

[0028] As a preferred solution of the linearization method of the nonlinear high-frequency model of steel under lightning strike described in the present invention, the experimental verification of the PEEC method includes converting the recorded time domain voltage and current into frequency domain results using FFT technology, smoothing the curve using a 2MHz low-pass digital filter, and truncating the spectrum by 10dB, constructing the impedance curve of the circular conductor loop using the V / I formula, and calculating the circular conductor impedance by solving the loop circuit.

[0029] As a preferred solution of the linearization method of the nonlinear high-frequency model of steel under lightning strike described in the present invention, the experimental verification of the PEEC method also includes selecting steel bars used in telecommunication towers and steel bars used in concrete buildings, using VNA to perform impedance measurement, and calculating the relative magnetic permeability at different frequencies.

[0030] Another object of the present invention is to provide a linearization system for the nonlinear high-frequency model of steel under lightning strike, which can solve the problem of over-simplification of the electromagnetic behavior of steel and neglect of key magnetic and nonlinear characteristics in existing methods through high-precision electromagnetic parameter extraction and efficient linearization processing technology.

[0031] In order to solve the above technical problems, the present invention provides the following technical solutions: a linearization system of a nonlinear high-frequency model of steel under lightning strike, including an impedance model building module and a parameter extraction module.

[0032] The impedance model building module uses PEEC to build an impedance model of steel.

[0033] The parameter extraction module extracts the electromagnetic parameters of steel through an experimental method.

[0034] A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the linearization method of the nonlinear high-frequency model of steel under lightning strike are implemented.

[0035] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the linearization method of the nonlinear high-frequency model of steel under lightning strike as described above.

[0036] Beneficial effects of the present invention: The prior art usually ignores the magnetic properties of steel during the modeling process, resulting in significant errors in the transient analysis results under lightning current. The present invention adopts the partial capacitance equivalent circuit (PEEC) method, combined with the characteristics of magnetic materials and high-frequency eddy current effects, to accurately model the impedance of steel, significantly improving the accuracy of modeling. Traditional electrical steel parameter extraction methods cannot simulate actual lightning current conditions, resulting in insufficient authenticity and accuracy of experimental data. The impulse current injection method proposed in the present invention can directly extract the impedance parameters of steel by measuring the transient response of steel under actual lightning current and combining the fast Fourier transform (FFT) technology to process the data, thereby ensuring the authenticity and accuracy of the experimental data. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0038] Figure 1 This is an overall flow chart of a method for linearizing a nonlinear high-frequency model of steel under lightning strike provided by the first embodiment of the present invention.

[0039] Figure 2 This is a time domain equivalent circuit diagram of a linearization method for a nonlinear high frequency model of steel under lightning strike provided by the first embodiment of the present invention.

[0040] Figure 3 This is an overall framework diagram of a linearization system for a nonlinear high-frequency model of steel under lightning strike provided by a second embodiment of the present invention. DETAILED DESCRIPTION

[0041] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0042] Example 1, reference Figure 1-Figure 2 , which is an embodiment of the present invention, provides a linearization method for a nonlinear high-frequency model of steel under lightning strike, characterized in that:

[0043] S1: Collect steel parameters.

[0044] The premise is that the existing partial capacitance equivalent circuit (PEEC) model is mainly applicable to non-magnetic conductors, ignoring the characteristics of magnetic materials and unable to accurately reflect the electrical behavior of steel under lightning current. This simplification may lead to significant errors, especially in high-frequency transient conditions.

[0045] The lack of detailed modeling of magnetic conductors results in an inability to fully consider the magnetic properties and eddy current losses of steel under lightning currents.

[0046] The parameters of the steel include the vacuum permeability of the circular conductor, the length of the circular conductor segment, the radius of the circular conductor, the resistivity of the circular conductor, the permeability of the circular conductor, and the skin depth.

[0047] S2: Use the PEEC method to construct the impedance model of steel.

[0048] The construction of the impedance model of steel includes calculating the self-impedance of the circular conductor and the mutual impedance of the coil by the PEEC method, and constructing the time domain equivalent circuit.

[0049] The impedance of a circular conductor consists of external inductance and internal impedance.

[0050] The external inductance is obtained through Neumann's formula, expressed as,

[0051]

[0052] Among them, μ0 represents the magnetic permeability of vacuum, l represents the length of the circular conductor segment, and a represents the radius of the circular conductor.

[0053] The internal impedance is expressed as,

[0054]

[0055] Where j represents the imaginary unit, ω represents the angular frequency, I0 represents the modified Bessel function of order 0, I1 represents the modified Bessel function of order 1, and R a represents the parameters in the modified Bessel function, expressed as,

[0056]

[0057] Where a is the radius of the circular conductor and δ is the skin depth, which is expressed as,

[0058]

[0059] Among them, ρ is the resistivity of the circular conductor, and μ is the magnetic permeability of the circular conductor.

[0060] The self-impedance of a circular conductor calculated by the PEEC method is expressed as:

[0061] Z(ω)=Z in(ω)-jωL ext (∞)

[0062] Where Z(ω) represents the self-impedance of a circular conductor at frequency ω, Z in Represents the internal impedance of a circular conductor, L ext (∞) represents the external inductance of a circular conductor at high frequencies.

[0063] The mutual impedance calculation of the coil is expressed as,

[0064]

[0065] Where d is the distance between the wires.

[0066] like Figure 2 As shown, the time domain equivalent circuit is a combination of the self-impedance of the circular conductor and the mutual impedance of the coil.

[0067] Figure 2 Used to simulate the electrical characteristics of steel conductors under frequency-varying conditions. The resistance and self-inductance of steel conductors usually vary with frequency. In order to simulate in the time domain, we use a reasonable approximation method to construct an equivalent frequency-invariant circuit model of the conductor. Since steel wire has good linear parameters, there is no repolarization phenomenon. Therefore, the frequency-varying resistance and inductance can be represented by a simplified RL equivalent circuit, where R0 represents the DC resistance of the conductor at low frequency, L0 represents the inductance of the conductor at low frequency, R1 and R2 represent the AC resistance of the circular conductor at different frequencies, and L1 and L2 represent the inductance of the conductor at different frequencies.

[0068] The present invention significantly improves the simulation accuracy of the electrical behavior of steel under lightning current by using the partial capacitance equivalent circuit (PEEC) method and optimizing the properties of magnetic materials. The method of the present invention allows for more accurate calculation of the impedance of steel, especially under high-frequency transient conditions, effectively reducing the error introduced by ignoring magnetic properties.

[0069] S3: Experimental validation of the PEEC method including.

[0070] The premise is that the traditional electrical steel parameter extraction method is mainly based on the induction current on the magnetic core, while the steel is directly subjected to the lightning current. Experimental data in this case is relatively scarce, and the existing methods cannot effectively extract and verify the parameters of steel under actual lightning strike conditions.

[0071] The small-amplitude test signals using a vector network analyzer (VNA) cannot simulate lightning transient currents, which limits its application in high-current testing and cannot reflect real lightning current conditions.

[0072] The parameters of steel are extracted by pulse current. The extraction process includes using FFT technology to convert the recorded time domain voltage and current into frequency domain results, using a 2MHz low-pass digital filter to smooth the curve, and truncating the spectrum by 10dB. The impedance curve of the wire loop is constructed using the V / I formula. The impedance is linearly related to the length, that is, the unit impedance curve is equal to the real part of the impedance divided by the total length of the test loop. The inductance is not linearly related to the length. Therefore, we cannot directly obtain the unit inductance value. The total inductance can be solved through the circuit relationship as

[0073] L T =4·(L S -M)

[0074] Among them, L s represents the self-inductance on one side of the test loop, and M represents the mutual inductance.

[0075] By taking into account the magnetic properties and eddy current losses of steel, the present invention can more comprehensively reflect the electrical behavior of materials when subjected to high frequencies, which not only enhances the scope of application of the theory, but also makes the results more reliable and practical.

[0076] Further explanation, S2 is derived from the theoretical PEEC, and the linearization method desired by the present invention is obtained. The first step is the main one, but it is still not completed, because after the theoretical derivation, experimental verification is required to complete the theoretical derivation. Therefore, the second step is to do experiments, and the extracted parameters are the parameters derived in the first step. The goal is to verify the formula I derived from an experimental perspective.

[0077] The experimental setup includes the current injection method to reveal the response of steel to impulse current, and a square wire loop is constructed and connected to a pulse current generator.

[0078] It is further explained that the traditional electrical steel parameter extraction method cannot simulate the actual lightning current conditions, resulting in insufficient authenticity and accuracy of the experimental data. The impulse current injection method proposed in the present invention can directly extract the impedance parameters of the steel by measuring the transient response of the steel under the actual lightning current and combining the fast Fourier transform (FFT) technology to process the data, thereby ensuring the authenticity and accuracy of the experimental data.

[0079] The third step is to verify the theory through experiments. That is to say, the first step is the most important core, and the second and third steps assist in its completion.

[0080] Linearizing the nonlinear characteristics of steel involves selecting steel bars used in telecom towers and steel bars used in concrete buildings, performing impedance measurements using a VNA, and calculating relative permeability at different frequencies.

[0081] The existing technology usually ignores the magnetic properties of steel in the modeling process, resulting in significant errors in the transient analysis results under lightning current. The present invention can accurately model the impedance of steel by adopting the partial capacitance equivalent circuit (PEEC) method, combining the magnetic material properties and high-frequency eddy current effect, and significantly improves the accuracy of modeling.

[0082] In the prior art, complex numerical calculation methods are inefficient when dealing with complex cross-sections and large-scale structures. The present invention uses vector fitting technology to fit frequency-varying impedance parameters into frequency-invariant equivalent circuit models, which simplifies the calculation process, improves the efficiency of transient simulation analysis, and meets the needs of engineering applications.

[0083] Example 2, reference Figure 3 , which is an embodiment of the present invention, provides a system for a linearization method of a nonlinear high-frequency model of steel under lightning strike, characterized in that it includes an impedance model building module and a parameter extraction module.

[0084] The impedance model building module uses PEEC to build the impedance model of steel.

[0085] The parameter extraction module extracts the electromagnetic parameters of steel through experimental methods.

[0086] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

[0087] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0088] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0089] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0090] Embodiment 3: In this embodiment, in order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments. This embodiment experiments the existing traditional method and the method of this embodiment respectively.

[0091] In traditional methods, the impedance of steel is often treated as a constant, regardless of frequency, and magnetic properties such as magnetic saturation and hysteresis are often completely ignored. This approach cannot accurately predict the electromagnetic response when dealing with high-frequency, high-transient current scenarios such as lightning strikes, which can lead to inadequate assessments of structural safety and electronic equipment protection.

[0092] Specific solutions of the present invention.

[0093] The present invention comprehensively considers the nonlinear and magnetic properties of steel by using the PEEC method, and provides a more accurate and practical model through high-precision electromagnetic parameter extraction and efficient linearization processing technology. In particular, the linearization processing of the nonlinear high-frequency model is introduced to adapt to actual engineering needs, so that the model not only reflects the actual physical behavior, but can also be used by existing electrical engineering analysis software. The specific theoretical data are shown in Table 1.

[0094] Table 1 Experimental effect comparison chart

[0095] Experimental indicators Traditional methods Method of the present invention Frequency Response No significant changes Significant frequency dependence Nonlinear behavior neglect Explicit simulation Impedance under lightning current constant Dynamic Changes Magnetic properties considerations Not considered Consider magnetic saturation

[0096] By considering frequency dependence and nonlinear characteristics, the present invention can more accurately simulate the electromagnetic behavior of steel in actual environments, especially in the case of high-frequency lightning strikes. By introducing the consideration of magnetic saturation and hysteresis effects, the present invention can more realistically reflect the physical properties of steel in actual use, which is crucial for predicting and protecting against the impact of lightning strikes. Prediction accuracy and application applicability: Compared with traditional methods, the present invention provides higher prediction accuracy and wider application applicability, making the method not only suitable for engineering analysis, but also able to be integrated into the safety and protection design of modern electrical systems.

[0097] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A linearization method for a nonlinear high-frequency model of steel under lightning strike, characterized in that: include: Collect steel parameters; The impedance model of steel is constructed using the PEEC method; The PEEC method was validated experimentally.

2. The method for linearizing the nonlinear high-frequency model of steel under lightning strike according to claim 1, characterized in that: The parameters of the steel material include the vacuum magnetic permeability of the circular conductor, the length of the circular conductor segment, the radius of the circular conductor, the resistivity of the circular conductor, the magnetic permeability of the circular conductor and the skin depth; The construction of the impedance model of the steel includes calculating the self-impedance of the circular conductor and the mutual impedance of the coil by the PEEC method based on the parameters of the steel, and constructing a time domain equivalent circuit.

3. The linearization method of the nonlinear high-frequency model of steel under lightning strike according to claim 2, characterized in that: The circular conductor self-impedance includes external inductance and internal impedance; The external inductance is obtained by Neumann's formula, which is expressed as, Wherein, μ0 represents the magnetic permeability of vacuum, l represents the length of the circular conductor segment, and a represents the radius of the circular conductor; The internal impedance is expressed as, Where j represents the imaginary unit, ω represents the angular frequency, I0 represents the modified Bessel function of order 0, I1 represents the modified Bessel function of order 1, and R a represents the parameters in the modified Bessel function, expressed as, Where a is the radius of the circular conductor and δ is the skin depth, which is expressed as, Among them, ρ is the resistivity of the circular conductor, and μ is the magnetic permeability of the circular conductor.

4. The method for linearizing the nonlinear high-frequency model of steel under lightning strike according to claim 3, characterized in that: The circular conductor self-impedance is expressed as, Z(ω)=Z in (ω)-jωL ext (∞) Where Z(ω) represents the self-impedance of a circular conductor at frequency ω, Z in Represents the internal impedance of a circular conductor, L ext (∞) represents the external inductance of a circular conductor at high frequencies; The coil mutual impedance calculation is expressed as, Where d is the distance between the wires.

5. The method for linearizing the nonlinear high-frequency model of steel under lightning strike according to claim 4, characterized in that: The time domain equivalent circuit is a combination of the self-impedance of the circular conductor and the mutual impedance of the coil.

6. The method for linearizing the nonlinear high-frequency model of steel under lightning strike according to claim 5, characterized in that: The experimental verification of the PEEC method includes converting the recorded time domain voltage and current into frequency domain results using FFT technology, smoothing the curve using a 2MHz low-pass digital filter and truncating the spectrum by 10dB, constructing the impedance curve of the circular conductor loop using the V / I formula, and calculating the circular conductor impedance by solving the loop circuit.

7. The method for linearizing the nonlinear high-frequency model of steel under lightning strike according to claim 6, characterized in that: The experimental verification of the PEEC method also includes selecting steel bars used in telecommunication towers and steel bars used in concrete buildings, performing impedance measurements using a VNA, and calculating relative magnetic permeability at different frequencies.

8. A system using the linearization method of the nonlinear high-frequency model of steel under lightning strike as claimed in any one of claims 1 to 7, characterized in that: It includes impedance model building module and parameter extraction module; The impedance model building module uses PEEC to build an impedance model of steel; The parameter extraction module extracts the electromagnetic parameters of steel through an experimental method.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the processor implements the steps of the method for linearizing the nonlinear high-frequency model of steel material struck by lightning according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for linearizing the nonlinear high-frequency model of steel under lightning strike as described in any one of claims 1 to 7 are implemented.

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