Modeling method for rapid electrothermal simulation of metal oxide varistor

Abstract

The invention relates to a modeling method for rapid electrothermal simulation of a metal oxide varistor, which comprises the following steps: acquiring a local voltage-current curve of the metal oxide varistor under the conditions of a small current region and a large current region through an experiment, and acquiring a global resistance-voltage logarithmic curve based on the local voltage-current curve; based on a continuous voltage-current peak-time curved surface of different peak currents in a preset current range in the large current region under the action of a standard 8 / 20us pulse current, constructing a data mapping matrix of the large current region; calculating the average loss of the metal oxide varistor based on the data mapping matrix, and calculating an equivalent sinusoidal voltage based on the global resistance-voltage logarithmic curve and the average loss; calculating the space loss density distribution of the metal oxide varistor; and based on the space loss density distribution, solving the transient heat conduction equation to obtain transient space temperature distribution of the metal oxide varistor. Compared with the prior art, the electric heating characteristic simulation method of the MOV is rapid and high in precision.

Description

Technical Field

[0001] This invention relates to the field of power equipment simulation technology, and in particular to a modeling method for rapid simulation of the electrothermal properties of metal oxide varistors. Background Technology

[0002] Traditional electrothermal coupling simulation of metal oxide varistors (MOVs) has significant drawbacks: due to the nonlinear impedance characteristics of MOVs, bidirectional coupling simulation requires solving complex equations for time-varying electric fields and transient temperature fields, resulting in excessively long computation times. For example, full-time domain simulation of a single pulse current impact process takes more than one hour, while simulation of multiple pulse impact conditions such as moving loads takes more than 10 hours. This fails to meet the needs of engineering optimization design. Although existing technologies attempt to simplify calculations through equivalent circuit models, they struggle to accurately characterize the time-varying characteristics of nonlinear impedance under high-frequency transient responses, and still rely on time-domain solutions when calculating spatial electromagnetic loss distribution, failing to fundamentally improve computational efficiency. Chinese patent application CN115422870A employs an equivalent circuit model based on piecewise linear interpolation, including a current source, a voltage measurement module, and a voltage-current substitution module. By measuring the voltage in real time and calculating the equivalent current based on pre-acquired voltage-current substitution relationships, it simplifies the simulation process. While this avoids complex volt-ampere characteristic relationship calculations, it still suffers from the following drawbacks:

[0003] 1. The method of extracting N discrete sample voltage values ​​from the volt-ampere characteristic curve of the varistor and performing linear interpolation cannot accurately characterize the strong nonlinear impedance characteristics of the MOV under lightning impulse (8 / 20us wave), resulting in the accumulation of simulation errors in the high-frequency region and distortion of high-frequency transient response.

[0004] 2. Since it relies on FPGA lookup table calculation, it is necessary to compare voltage ranges cyclically. In this process, counters, comparators and multi-level memory need to work together, resulting in large hardware resource overhead and making it difficult to meet the real-time calculation requirements of multi-MOV parallel scenarios.

[0005] 3. By measuring the voltage in real time and calculating the equivalent current based on the pre-obtained voltage-current substitution relationship, only the electrical characteristics of the MOV can be simulated, without considering the Joule heating and temperature rise of the MOV.

[0006] The balance between high-frequency nonlinear response accuracy and multi-physics coupling efficiency is the core bottleneck of MOV electrothermal modeling. Chinese patent application CN115422870A cannot overcome this modeling bottleneck due to the above-mentioned shortcomings. Therefore, this paper proposes a method that considers the balance between high-frequency nonlinear response accuracy and multi-physics coupling efficiency during the modeling process, thereby achieving higher accuracy MOV simulation modeling. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a modeling method for rapid simulation of the electrothermal properties of metal oxide varistors. Addressing the problems of low computational efficiency and difficulty in nonlinear solutions in traditional methods, this invention adopts the average loss equivalence principle to convert transient pulse current excitation into sinusoidal steady-state excitation, and combines a frequency domain-transient decoupling algorithm to separate the electric field and temperature field solution processes, thereby achieving rapid and accurate simulation of MOV electrothermal properties.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] According to a first aspect of the present invention, a modeling method for rapid simulation of the electrothermal properties of metal oxide varistors is provided, comprising:

[0010] S1. Divide the current into a small current region, a medium current region, and a large current region. Obtain the local voltage-current curve of the metal oxide varistor under the conditions of the small current region and the large current region through experiments. Obtain the global resistance-voltage logarithmic curve of the metal oxide varistor based on the local voltage-current curve.

[0011] S2. The voltage waveforms of different peak currents in the preset current range under the action of standard 8 / 20us pulse current are collected by pulse current experiment and plotted on the same three-dimensional coordinate axis. A continuous voltage-current peak-time surface is constructed using interpolation algorithm. A data mapping matrix of the large current region is constructed based on the continuous voltage-current peak-time surface.

[0012] S3. Based on the data mapping matrix, calculate the average loss of the metal oxide varistor within a preset time of the standard 8 / 20us pulse current, and calculate the equivalent sinusoidal voltage based on the global resistance-voltage logarithmic curve and the average loss.

[0013] S4. Calculate the spatial loss density distribution of the metal oxide varistor under the equivalent sinusoidal voltage.

[0014] S5. Based on the aforementioned spatial loss density distribution, the transient spatial temperature distribution of the metal oxide varistor is obtained by solving the transient heat conduction equation.

[0015] As a preferred technical solution, the global resistance-voltage logarithmic curve is as follows:

[0016]

[0017] Where R represents the resistance of the metal oxide varistor; A0, A1, and A2 all represent fitting coefficients; and U represents the voltage across the metal oxide varistor.

[0018] As a preferred technical solution, the average loss is:

[0019]

[0020] Among them, LOSS avg This represents the average loss of the metal oxide varistor within a preset time under a standard 8 / 20µs pulse current; T s Indicates the preset time; V g (t) represents the time-domain voltage across the metal oxide varistor, and the time-domain voltage under any peak current is obtained through the data mapping matrix described above; I g (t) represents the normalized 8 / 20µs pulse current.

[0021] As a preferred technical solution, the method for calculating the equivalent sinusoidal voltage includes:

[0022] Using the energy conservation principle, a transient-steady-state equivalent relationship between pulse signals and sinusoidal signals is established based on the aforementioned average loss. Its expression is:

[0023]

[0024] Among them, LOSS avg This represents the average loss of the metal oxide varistor within a preset time under a standard 8 / 20µs pulse current; T s Indicates the preset time; V g (t) represents the time-domain voltage across the metal oxide varistor, and the time-domain voltage under any peak current is obtained through the data mapping matrix described above; I g (t) represents the standardized 8 / 20µs pulse current; V eq (t) represents the equivalent sinusoidal time-domain voltage signal under a sinusoidal signal; I eq (t) represents the equivalent sinusoidal current signal;

[0025] Based on the relationship between the equivalent sinusoidal time-domain voltage signal and the equivalent sinusoidal voltage, and between the equivalent sinusoidal current signal and the equivalent sinusoidal current, the transient-steady-state equivalent relationship can be rewritten as follows:

[0026]

[0027] Among them, I eq V represents the equivalent sinusoidal current; eq Represents the equivalent sinusoidal voltage; f represents the frequency; The phase angle represents the equivalent sinusoidal voltage and the equivalent sinusoidal current;

[0028] Based on the aforementioned global resistance-voltage logarithmic curve, the equivalent sinusoidal voltage solution is obtained from the rewritten transient-steady-state equivalent relationship:

[0029]

[0030] Where A0, A1, and A2 all represent fitting coefficients;

[0031] Based on the aforementioned formula for solving the equivalent sinusoidal voltage, an objective function is constructed, and the equivalent sinusoidal voltage is solved using the Newton-Raphson iteration method based on the objective function.

[0032] As a preferred technical solution, the objective function is:

[0033]

[0034] Where A0, A1, and A2 all represent fitting coefficients; V eq Represents the equivalent sinusoidal voltage; LOSS avg This indicates the average loss of the metal oxide varistor within a preset time under the action of a standard 8 / 20µs pulse current.

[0035] As a preferred technical solution, the method for calculating the spatial loss density distribution includes:

[0036] The frequency domain Maxwell equations for a metal oxide varistor under an equivalent sinusoidal voltage are constructed as follows:

[0037]

[0038] Where J represents the current density; σE represents the conduction current density; jωD represents the displacement current density; J e The input current density source is represented by E; electric field strength is represented by D; electric displacement vector is represented by V; electric potential is represented by σ; conductivity is represented by j; and angular frequency is represented by ω.

[0039] Based on the boundary electrical insulation condition of the metal oxide varistor under the equivalent sinusoidal voltage, excluding the input terminal and the ground terminal, i.e., n·J=0, the frequency domain Maxwell equations are solved using the BiCGStab iterative method to obtain the electric field strength and current density; n represents the normal vector of the vertical edge.

[0040] The spatial loss density distribution is calculated based on the aforementioned electric field strength and current density, and its expression is as follows:

[0041] P loss =J·E.

[0042] As a preferred technical solution, the transient heat conduction equation is:

[0043]

[0044] Where ρ represents the density of the metal oxide varistor solid material; C p This represents the heat absorbed or released per unit mass of material in a metal oxide varistor when its temperature changes under constant pressure, i.e., constant-pressure heat capacity; T represents temperature; t represents the time during which the thermal process occurs; u represents the fluid velocity vector. P represents the net heat outflow rate caused by heat conduction. loss Represents the spatial loss density distribution; Q ted Indicates the external heat source term; This represents the temperature gradient.

[0045] As a preferred technical solution, the method for obtaining the transient spatial temperature distribution includes:

[0046] Data on metal oxide varistors were obtained by differential scanning calorimetry and fitted to obtain a quadratic temperature function relating to the thermal capacity parameter of the metal oxide varistor.

[0047] Construct boundary conditions for thermal convection and thermal radiation on the surface of a metal oxide varistor;

[0048] Based on the aforementioned quadratic temperature function and boundary conditions, the transient thermal conduction equation is solved using a numerical discretization method to obtain the transient spatial temperature distribution of the metal oxide varistor.

[0049] As a preferred technical solution, the secondary temperature function is:

[0050] C p =C0 + C1×T - C2×T 2 ,

[0051] Among them, C p The constant pressure heat capacity represents the heat absorbed or released per unit mass of material in a metal oxide varistor when the temperature changes under constant pressure; C0, C1, and C2 all represent fitting coefficients; T represents temperature.

[0052] As a preferred technical solution, the boundary conditions are as follows:

[0053]

[0054] Where n represents the normal vector of the vertical edge; k represents the thermal conductivity of the metal oxide varistor; Represents the temperature gradient; h represents the convective heat transfer coefficient; T amb Indicates ambient temperature; T sur ε represents the surface temperature of the metal oxide varistor; ε represents the emissivity of the metal oxide varistor surface; σ1 represents the Stefan-Boltzmann constant.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] 1) This invention maps the voltage-current peak-time characteristics of the high current region under a standard 8 / 20µs pulse current to the same coordinate system, and uses an interpolation algorithm to construct a three-dimensional continuous mapping surface based on the voltage-current peak-time characteristics. Combined with the accurate nonlinear conductance model of MOV, it not only accurately characterizes the strong nonlinear impedance characteristics of MOV under the action of pulse current, but also directly correlates the conductance performance of MOV with the voltage waveform under arbitrary lightning current amplitude, thereby avoiding table lookup and comparison operations and improving simulation efficiency.

[0057] 2) This invention converts transient pulse current excitation into sinusoidal steady-state voltage excitation by calculating the average loss of lightning cycles, thereby transforming a nonlinear time-domain problem into a linear frequency-domain problem. This reduces the complexity of electromagnetic field calculations and avoids the problems of piecewise interpolation errors and nonlinear time-domain solutions in traditional MOV electrothermal bidirectional coupling simulation.

[0058] 3) Considering that the temperature field distribution of an MOV depends on both heat generation and heat dissipation, when it is in operation, heat generation is mainly caused by its own losses, i.e., electromagnetic losses, while heat dissipation is mainly caused by its exchange of heat with the external environment as a heat source. Therefore, it is necessary to consider three forms of heat transfer: conduction, radiation, and convection. Based on this, this invention adopts a unidirectional coupling strategy to separate the calculation of electromagnetic space loss from the solution of the temperature field. The frequency domain electromagnetic space loss is substituted into the time domain transient heat conduction equation, which includes heat convection, heat conduction, heat radiation, and Joule heating, to solve the transient temperature field unidirectional data transfer. This can separate the bidirectional iterative calculation while ensuring physical accuracy. While ensuring the accuracy of the physical mechanism, it greatly optimizes the computational resource requirements and achieves high-precision simulation of the electrothermal properties of MOV. Attached Figure Description

[0059] Figure 1 This is a flowchart of the method of the present invention;

[0060] Figure 2 The global resistance-voltage logarithmic curve of the MOV of this invention;

[0061] Figure 3 The global voltage-current curve of the MOV of this invention;

[0062] Figure 4 The voltage waveforms of different peak currents within a preset current range in the high current region under the action of the standard 8 / 20us pulse current of this invention are shown.

[0063] Figure 5 This is a schematic diagram of the data mapping matrix of the present invention;

[0064] Figure 6This is a schematic diagram of the electric field boundary conditions of the MOV of the present invention. Detailed Implementation

[0065] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0066] To address the problems of low computational efficiency and difficulty in nonlinear solutions in traditional methods, this invention provides a modeling method for rapid electrothermal simulation of metal oxide varistors (MOVs). First, a dynamic resistance model of the MOV is established. Second, a three-dimensional mapping function is used to correlate the peak value of the pulse current with the voltage waveform of the MOV under the pulse current. Then, the periodic average loss of the MOV under an arbitrary peak pulse current is calculated, and its equivalent sinusoidal excitation is solved. Finally, the temperature field distribution is obtained through frequency domain electromagnetic calculations and transient heat conduction solutions. The process is as follows: Figure 1 As shown.

[0067] Detailed, including:

[0068] S1. Divide the current into small current region, medium current region and large current region. Obtain the local voltage-current curve of MOV under the conditions of small current region and large current region through experiments. Obtain the global resistance-voltage logarithmic curve of MOV based on the local voltage-current curve.

[0069] For the MOV volt-ampere characteristic curve in the low current region (around 1mA), voltage and current data were measured using a DC parameter tester; for the MOV volt-ampere characteristic curve in the high current region (kA level), voltage and current data were obtained by pulse current measurement.

[0070] In the medium current region, the MOV may burn out or even explode due to overheating during TOV testing. Therefore, the UI data for this part cannot be directly obtained through experimental measurement. Furthermore, the experimental data for the MOV in the low current and high current regions differ significantly in magnitude. Therefore, to ensure the accuracy of the global volt-ampere characteristics, it is necessary to first calculate the equivalent impedance of the MOV according to Ohm's law, then take the logarithm of the MOV's impedance and voltage, and finally perform nonlinear fitting based on the logarithmic impedance and voltage to obtain the global resistance-voltage logarithmic curve of the MOV. Where R represents the resistance of the MOV; A0, A1, and A2 are all fitting coefficients, with A0 = -1.41505, A1 = 84469902612.6741, and A2 = -22.33938; U represents the voltage across the MOV, and the corresponding global resistance-voltage logarithmic curve is shown below. Figure 2 As shown.

[0071] according to Figure 2 The global lgR-lgU curve shown is obtained as follows: Figure 3 The complete UI curve of the MOV shown.

[0072] S2. Collect different peak currents I within a preset current range in the high-current region under the action of a standard 8 / 20µs pulsed current through a pulsed current experiment. peak The voltage waveforms are mapped onto the same three-dimensional coordinate axis, and a continuous voltage-current-time surface is constructed using an interpolation algorithm. Based on the continuous voltage-current-time surface, a data mapping matrix for the high current region is constructed.

[0073] The I collected in this embodiment peak The preset current range is 4.67-21.61kA, corresponding to each I... peak 3D mapping such as Figure 4 As shown, the Renka-Cline interpolation algorithm is used, with an interpolation interval of 10A. Figure 4 Interpolating the voltage waveform of the discrete three-dimensional mapping shown, we obtain a three-dimensional continuous mapping surface, i.e., a continuous voltage-current-time surface, thus obtaining... Figure 5 The data mapping matrix shown is stored in CSR sparse format.

[0074] This step enables the rapid acquisition of the MOV value at any I using a data mapping matrix. peak Voltage curves under 8 / 20µs pulse current range.

[0075] S3. Based on the data mapping matrix, calculate the average loss of MOV within Ts = 80us under the action of the standard 8 / 20us pulse current, and calculate the equivalent sinusoidal voltage based on the global resistance-voltage logarithmic curve and the average loss.

[0076] S31. Integrate the energy over the standard 8 / 20µs pulse current duration to obtain the average loss, which is expressed as follows:

[0077]

[0078] Among them, LOSS avg This represents the global average loss of the MOV within a preset time under a standard 8 / 20µs pulse current; T s Indicates the preset time; V g (t) represents the time-domain voltage across the MOV, and the time-domain voltage under any peak current is obtained through a data mapping matrix; I g (t) represents the normalized 8 / 20µs pulse current.

[0079] S32. Using the energy conservation principle, establish the transient-steady-state equivalent relationship between pulse signals and sinusoidal signals based on average loss.

[0080] In detail, the equivalent principle is that the periodic average loss of transient lightning is equal to the periodic average loss of sinusoidal excitation. In order to construct the spatial distribution matrix of pulse current loss, the average loss is used to equivalence V. g (t) and I g (t) is converted into an equivalent sinusoidal time-domain voltage signal V. eq (t) and equivalent sinusoidal current signal I eq (t).

[0081] Its expression is:

[0082]

[0083] Among them, LOSS avg This represents the average loss of the MOV within a preset time under a standard 8 / 20µs pulse current; T s Indicates the preset time; V g (t) represents the time-domain voltage across the MOV, and the time-domain voltage under any peak current is obtained through a data mapping matrix; I g (t) represents the standardized 8 / 20µs pulse current; V eq (t) represents the equivalent sinusoidal time-domain voltage signal under a sinusoidal signal; I eq (t) represents the equivalent sinusoidal current signal.

[0084] S33. Rewrite the transient-steady-state equivalent relationship based on the relationship between the equivalent sinusoidal time-domain voltage signal and the equivalent sinusoidal voltage, and the equivalent sinusoidal current signal and the equivalent sinusoidal current.

[0085] In detail, the relationship between the equivalent sinusoidal time-domain voltage signal and the equivalent sinusoidal voltage is as follows: Where f represents frequency; The phase angle represents the equivalent sinusoidal voltage; the relationship between the equivalent sinusoidal current signal and the equivalent sinusoidal current is: This represents the phase angle of the equivalent sinusoidal current.

[0086] Then we have: Due to LOSS avg This represents the average loss over one cycle, and its value is independent of the frequency f. Therefore, when studying electrothermal energy conversion, the capacitive and inductive components of the MOV impedance have relatively small effects and can be ignored. make have: Among them, I eq V represents the equivalent sinusoidal current;eq Represents the equivalent sinusoidal voltage; f represents the frequency; The phase angle represents the equivalent sinusoidal voltage and the equivalent sinusoidal current.

[0087] S34. Based on the global resistance-voltage logarithmic curve, obtain the equivalent sinusoidal voltage solution from the rewritten transient-steady-state equivalent relationship:

[0088]

[0089] Where A0, A1, and A2 all represent fitting coefficients.

[0090] S35. Construct an objective function based on the solution formula of the equivalent sinusoidal voltage, and solve for the equivalent sinusoidal voltage using the Newton-Raphson iteration method based on the objective function.

[0091] In detail, the objective function is:

[0092]

[0093] Where A0, A1, and A2 all represent fitting coefficients; V eq Represents the equivalent sinusoidal voltage; LOSS avg This indicates the average loss of the MOV within a preset time under the action of a standard 8 / 20µs pulse current;

[0094] Its iterative process is as follows:

[0095]

[0096] in, Let F(·) represent the equivalent sinusoidal voltage in the k-th iteration; F(·) represents the objective function calculation. Let the initial value be... V g,max For MOV in I g The residual pressure under (t)

[0097] And set the convergence condition as |F(V) eq )|<0.001×LOSS avg .

[0098] S4. Calculate the spatial loss density distribution of the MOV under the action of an equivalent sinusoidal voltage.

[0099] S41. Construct the frequency domain Maxwell equations for the MOV under the action of an equivalent sinusoidal voltage. The expression is as follows:

[0100]

[0101] Where J represents current density, that is, current per unit area, with units of A / m. 2σE represents the conduction current density; jωD represents the displacement current density; J e σ represents the applied current density source; E represents the electric field strength, with units of V / m, and the direction of the electric field is the direction in which the electric potential decreases the fastest. Since the magnitude of the electric field is proportional to the rate of change of the electric potential, the electric field strength can be expressed as the negative gradient of the electric potential; D represents the electric displacement vector; V represents the electric potential; σ represents the conductivity; j represents the imaginary unit; and ω represents the angular frequency.

[0102] S42. Based on the boundary electrical insulation condition of the MOV (excluding the input and ground terminals) under the equivalent sinusoidal voltage, i.e., n·J=0, the BiCGStab iterative method is used with a residual tolerance of 0.01 to solve the frequency domain Maxwell equations, obtaining the electric field strength and current density; n represents the normal vector of the vertical edge. In detail, in this step, V... eq As a sinusoidal voltage source (frequency f is arbitrary), it is applied to the MOV model, such as Figure 6 As shown.

[0103] S43. Calculate the spatial loss density distribution based on electric field strength and current density, in W / m². 3 Its expression is:

[0104] P loss =J·E.

[0105] S5. Based on the spatial loss density distribution, the transient spatial temperature distribution of the MOV is obtained by solving the transient heat conduction equation.

[0106] The temperature field distribution of an MOV depends on both heat generation and heat dissipation. When it is in operation, heat generation is mainly caused by its own losses, namely electromagnetic losses, while heat dissipation is mainly due to its exchange of heat with the external environment as a heat source. Therefore, it is necessary to consider three forms of heat transfer: conduction, radiation, and convection.

[0107] S51, P loss The transient heat conduction equation is given by:

[0108]

[0109] Where ρ represents the density of the MOV solid material, in kg / m³. 3 C p The constant pressure heat capacity (CPC) represents the amount of heat absorbed or released per unit mass of material when the temperature changes at constant pressure. The unit is J / (kg×K); T represents temperature; t represents the time during which the thermal process occurs. The unit is K; u represents the fluid velocity vector, which indicates the velocity and direction of the fluid in space. The unit is m / s. This represents the convective heat transfer rate caused by fluid motion (convection term); P represents the net heat outflow rate due to heat conduction (conduction term); loss This represents the spatial loss density distribution, i.e., the heat generated per unit volume due to factors such as electrical energy conversion; Q ted This refers to the external heat source term, which represents the heat generated or absorbed per unit volume due to external factors (such as radiation, convection, etc.), and is expressed in W / m³. 3 ; This represents the temperature gradient.

[0110] S52. Obtain the data of MOV measured by differential scanning calorimetry, and fit it to obtain the quadratic temperature function of MOV heat capacity parameter, as follows:

[0111] C p =C0 + C1×T - C2×T 2 ,

[0112] Among them, C p The constant pressure heat capacity represents the amount of heat absorbed or released per unit mass of material under constant pressure when the temperature is changed per unit volume; C0, C1, and C2 all represent fitting coefficients; T represents temperature.

[0113] S53. Construct the boundary conditions for thermal convection and thermal radiation on the MOV surface as follows:

[0114]

[0115] Where n represents the normal vector of the vertical edge; k represents the thermal conductivity of the MOV; Represents the temperature gradient; h represents the convective heat transfer coefficient; T amb Indicates ambient temperature; T sur ε represents the surface temperature of the MOV; ε represents the emissivity of the MOV surface; σ1 represents the Stefan-Boltzmann constant.

[0116] S54. The transient spatial temperature distribution of the MOV is obtained by solving the transient heat conduction equation based on the quadratic temperature function and boundary conditions using a numerical discretization method.

[0117] In detail, the numerical discretization method selected in this embodiment is the second-order backward difference scheme discretization. The time step of the lightning action stage is set to Δt = 1us, and the time step of the heat dissipation stage is adaptively adjusted to Δt = 1~100s.

[0118] Furthermore, this embodiment also provides an electronic device for rapid electrothermal simulation of metal oxide varistors, including a central processing unit (CPU), which can execute various appropriate actions and processes according to computer program instructions stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). The RAM can also store various programs and data required for device operation. The CPU, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0119] Multiple components in the device are connected to the I / O interface, including: input units such as keyboards and mice; output units such as various types of displays and speakers; storage units such as disks and optical discs; and communication units such as network interface cards (NICs), modems, and wireless transceivers. The communication unit allows the device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0120] The processing unit executes the various methods and processes described above, such as methods S1 to S5. For example, in some embodiments, methods S1 to S5 may be implemented as computer software programs tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program may be loaded and / or installed on the device via ROM and / or a communication unit. When the computer program is loaded into RAM and executed by the CPU, one or more steps of methods S1 to S5 described above may be performed. Alternatively, in other embodiments, the CPU may be configured to execute methods S1 to S5 by any other suitable means (e.g., by means of firmware).

[0121] The functions described above in this document can be performed, at least in part, by one or more hardware logic components. For example, exemplary types of hardware logic components that can be used, without limitation, include: Field Programmable Gate Arrays (FPGAs), Application-Specific Integrated Circuits (ASICs), Application Standard Products (ASSPs), System-on-Chip (SoCs), Complex Programmable Logic Devices (CPLDs), and so on.

[0122] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0123] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0124] 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 person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A modeling method for rapid simulation of the electrothermal properties of metal oxide varistors, characterized in that, include: S1. Divide the current into a small current region, a medium current region, and a large current region. Obtain the local voltage-current curve of the metal oxide varistor under the conditions of the small current region and the large current region through experiments. Obtain the global resistance-voltage logarithmic curve of the metal oxide varistor based on the local voltage-current curve. S2. The voltage waveforms of different peak currents in the preset current range under the action of standard 8 / 20us pulse current are collected by pulse current experiment and mapped to the same three-dimensional coordinate axis. A continuous voltage-current peak-time surface is constructed using interpolation algorithm. A data mapping matrix of the large current region is constructed based on the continuous voltage-current peak-time surface. S3. Based on the data mapping matrix, calculate the average loss of the metal oxide varistor within a preset time of the standard 8 / 20us pulse current, and calculate the equivalent sinusoidal voltage based on the global resistance-voltage logarithmic curve and the average loss. S4. Calculate the spatial loss density distribution of the metal oxide varistor under the equivalent sinusoidal voltage described above. S5. Based on the aforementioned spatial loss density distribution, the transient spatial temperature distribution of the metal oxide varistor is obtained by solving the transient heat conduction equation.

2. The modeling method for rapid electrothermal simulation of metal oxide varistors according to claim 1, characterized in that, The global resistance-voltage logarithmic curve is as follows: Where R represents the resistance of the metal oxide varistor; A0, A1, and A2 all represent fitting coefficients; and U represents the voltage across the metal oxide varistor.

3. The modeling method for rapid electrothermal simulation of metal oxide varistors according to claim 1, characterized in that, The average loss is: Among them, LOSS avg This represents the average loss of the metal oxide varistor within a preset time under a standard 8 / 20µs pulse current; T s Indicates the preset time; V g (t) represents the time-domain voltage across the metal oxide varistor, and the time-domain voltage under any peak current is obtained through the data mapping matrix described above; I g (t) represents the normalized 8 / 20µs pulse current.

4. The modeling method for rapid electrothermal simulation of metal oxide varistors according to claim 1, characterized in that, The method for calculating the equivalent sinusoidal voltage includes: Using the energy conservation principle, a transient-steady-state equivalent relationship between pulse signals and sinusoidal signals is established based on the aforementioned average loss. Its expression is: Among them, LOSS avg This represents the average loss of the metal oxide varistor within a preset time under a standard 8 / 20µs pulse current; T s Indicates the preset time; V g (t) represents the time-domain voltage across the metal oxide varistor, and the time-domain voltage under any peak current is obtained through the data mapping matrix described above; I g (t) represents the standardized 8 / 20µs pulse current; V eq (t) represents the equivalent sinusoidal time-domain voltage signal under a sinusoidal signal; I eq (t) represents the equivalent sinusoidal current signal; Based on the relationship between the equivalent sinusoidal time-domain voltage signal and the equivalent sinusoidal voltage, and between the equivalent sinusoidal current signal and the equivalent sinusoidal current, the transient-steady-state equivalent relationship can be rewritten as follows: Among them, I eq V represents the equivalent sinusoidal current; eq Represents the equivalent sinusoidal voltage; f represents the frequency; The phase angle represents the equivalent sinusoidal voltage and the equivalent sinusoidal current; Based on the aforementioned global resistance-voltage logarithmic curve, the equivalent sinusoidal voltage solution is obtained from the rewritten transient-steady-state equivalent relationship: Where A0, A1, and A2 all represent fitting coefficients; Based on the aforementioned formula for solving the equivalent sinusoidal voltage, an objective function is constructed, and the equivalent sinusoidal voltage is solved using the Newton-Raphson iteration method based on the objective function.

5. The modeling method for rapid electrothermal simulation of metal oxide varistors according to claim 4, characterized in that, The objective function is: Where A0, A1, and A2 all represent fitting coefficients; V eq Represents the equivalent sinusoidal voltage; LOSS avg This indicates the average loss of the metal oxide varistor within a preset time under the action of a standard 8 / 20µs pulse current.

6. The modeling method for rapid electrothermal simulation of metal oxide varistors according to claim 1, characterized in that, The method for calculating the spatial loss density distribution includes: The frequency domain Maxwell equations for a metal oxide varistor under an equivalent sinusoidal voltage are constructed as follows: Where J represents the current density; σE represents the conduction current density; jωD represents the displacement current density; J e The input current density source is represented by E; electric field strength is represented by D; electric displacement vector is represented by V; electric potential is represented by σ; conductivity is represented by j; and angular frequency is represented by ω. Based on the boundary electrical insulation condition of the metal oxide varistor under the equivalent sinusoidal voltage, excluding the input terminal and the ground terminal, i.e., n·J=0, the frequency domain Maxwell equations are solved using the BiCGStab iterative method to obtain the electric field strength and current density; n represents the normal vector of the vertical edge. The spatial loss density distribution is calculated based on the aforementioned electric field strength and current density, and its expression is as follows: Q loss =J·E。 7. The modeling method for rapid electrothermal simulation of metal oxide varistors according to claim 1, characterized in that, The transient heat conduction equation is as follows: Where ρ represents the density of the metal oxide varistor solid material; C p This represents the heat absorbed or released per unit mass of material in a metal oxide varistor when its temperature changes under constant pressure, i.e., constant-pressure heat capacity; T represents temperature; t represents the time during which the thermal process occurs; u represents the fluid velocity vector. P represents the net heat outflow rate caused by heat conduction. loss Represents the spatial loss density distribution; Q ted Indicates the external heat source term; This represents the temperature gradient.

8. The modeling method for rapid electrothermal simulation of metal oxide varistors according to claim 1, characterized in that, The method for obtaining the transient spatial temperature distribution includes: Data on metal oxide varistors were obtained by differential scanning calorimetry and fitted to obtain a quadratic temperature function relating to the thermal capacity parameter of the metal oxide varistor. Construct boundary conditions for thermal convection and thermal radiation on the surface of a metal oxide varistor; Based on the aforementioned quadratic temperature function and boundary conditions, the transient thermal conduction equation is solved using a numerical discretization method to obtain the transient spatial temperature distribution of the metal oxide varistor.

9. The modeling method for rapid electrothermal simulation of metal oxide varistors according to claim 8, characterized in that, The aforementioned quadratic temperature function is: C p =C0+C1×T-C2×T 2 , Among them, C p The constant pressure heat capacity represents the heat absorbed or released per unit mass of material in a metal oxide varistor when the temperature changes under constant pressure; C0, C1, and C2 all represent fitting coefficients; T represents temperature.

10. The modeling method for rapid electrothermal simulation of metal oxide varistors according to claim 8, characterized in that, The boundary conditions are as follows: Where n represents the normal vector of the vertical edge; k represents the thermal conductivity of the metal oxide varistor; The temperature gradient is represented by h; the convective heat transfer coefficient is represented by T. amb Indicates ambient temperature; T sur ε represents the surface temperature of the metal oxide varistor; ε represents the emissivity of the metal oxide varistor surface; σ1 represents the Stefan-Boltzmann constant.

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