Simplified mathematical model simulation method and system for cable single-phase earth fault arc

Abstract

The invention relates to a cable single-phase earth fault arc simplified mathematical model simulation method and system. The method comprises the steps of designing a geometric model, boundary conditions and medium physical property parameters for magnetofluid MHD simulation; a fault arc physical model is obtained through magnetofluid MHD simulation; calculating simulation arc voltage, arc current and arc energy; arc conductance, dissipation power and a time constant are calculated, and functions of the dissipation power and the time constant about the arc conductance are obtained through fitting; replacing the dissipated power and the time constant in the classic Mayr arc model with a function about arc conductance to obtain an improved Mayr arc model; the obtained improved Mayr arc model is substituted into an ATP-EMTP power distribution network model, a cable single-phase earth fault simulation waveform is obtained, and a reliable and effective arc model can be provided for power distribution network cable single-phase earth fault simulation.

Description

Technical Field

[0001] The present application relates to the field of model simulation, and in particular to a simplified mathematical model simulation method and system for a cable single-phase grounding fault arc. Background Art

[0002] Currently, equivalent circuit simulation is a commonly used fault analysis method for single-phase grounding cable faults. The fault arc model is an important part of the accuracy of the simulation results. Existing mathematical arc models are mainly based on the voltage and current values in the circuit. The arc is equivalent to a variable resistor with an overall shape that tends to be cylindrical and a resistance that changes with the transient state of the circuit. Commonly used models include the Mayr and Cassie arc models, as well as improved models based on the two models.

[0003] 1) Cassie model

[0004] The Cassie model's core consideration is the cooling effect of gas convection. Furthermore, it makes several assumptions. The model assumes that the gas flows through a cylindrical channel with a fixed arc channel diameter. For arcs exceeding the arc channel diameter, the model assumes extremely high resistance, a uniform temperature distribution across the cross section, and a proportional relationship between energy magnitude and energy diffusion.

[0005] 2) Mayr model

[0006] The Mayr model mainly considers the heat conduction effect, assuming that the arc column is cylindrical with a fixed diameter and the arc voltage drop is constant. It does not consider the intrinsic relationship between electrode diffusion, axial heat loss, arc temperature change and the thermophysical properties of the gas.

[0007] In addition to mathematical models, arc physics models are also used in the study of various arc faults. The physical model of the arc is usually referred to as the arc magnetohydrodynamic model (MHD). The establishment of a magnetohydrodynamic model is usually based on theories from disciplines such as thermodynamics, electromagnetic field theory, plasma physics, and fluid mechanics, using differential and integral equations to describe the dynamic relationship between arc parameters. During MHD modeling and simulation, the particle composition is statistically determined through macroscopic thermodynamics. This is then combined with the Navier-Stokes equations to describe fluid motion and the electromagnetic equations to describe electric field properties. Finally, the arc magnetohydrodynamic model can effectively reflect the dynamic mechanism and transient characteristics of the arc.

[0008] Existing arc models used for equivalent circuit simulation primarily make judgments based on the voltage and current values in the circuit, equating the arc to a variable resistor with a cylindrical overall shape and a resistance that varies with the circuit's transient state. This method is suitable for analyzing line arcs and switch arcs. However, for single-phase grounding cable arcs, which are complex structures and diverse environments, constructing an equivalent simulation circuit based on the arc mathematical model for fault characteristic analysis has significant limitations in the study of distribution network cable faults. Furthermore, applying the arc physical model to the equivalent circuit is computationally intensive and difficult to converge. Therefore, there is an urgent need for an arc model simulation method that can assist in the detection and treatment of single-phase grounding faults in distribution networks. Summary of the Invention

[0009] The purpose of the embodiments of the present application is to provide a simplified mathematical model simulation method and system for a cable single-phase grounding fault arc, so as to solve the problem that the existing arc model has a narrow scope of application and is not suitable for the study of medium-voltage cable single-phase grounding faults.

[0010] To achieve the above objectives, this application provides the following technical solutions:

[0011] In a first aspect, an embodiment of the present application provides a simplified mathematical model simulation method for a single-phase grounding fault arc in a cable, comprising the following steps:

[0012] Design geometric models, boundary conditions, and medium physical properties for magnetic fluid MHD simulation;

[0013] The physical model of the fault arc is obtained through magnetic fluid MHD simulation;

[0014] Calculate and simulate arc voltage, arc current and arc energy;

[0015] Calculate arc conductance, dissipated power and time constant, and fit the functions of dissipated power and time constant related to arc conductance;

[0016] The improved Mayr arc model is obtained by replacing the dissipated power and time constant in the classic Mayr arc model with functions related to arc conductance;

[0017] The improved Mayr arc model is introduced into the ATP-EMTP distribution network model to obtain the simulation waveform of the cable single-phase grounding fault.

[0018] The geometric model, boundary conditions and medium physical parameters designed for magnetic fluid MHD simulation are specifically as follows:

[0019] Design and simplify the geometric model based on the actual fault conditions and cable structure; determine the electric field boundary conditions based on the external applied circuit of the actual structure; and determine the physical properties of the dielectric used for arc discharge based on the actual fault environment.

[0020] The control equations involved in the magnetic fluid simulation in the fault arc physical model obtained by the magnetic fluid MHD simulation include three conservation equations of fluid mechanics and Maxwell's equations. The three conservation equations of fluid mechanics are shown in formula (1), formula (2), and formula (3); the Maxwell's equations are shown in formula (4), formula (5), formula (6), and formula (7);

[0021] Mass conservation equation:

[0022] (1)

[0023] in, is the density, For speed,

[0024] Momentum conservation equation:

[0025] (2)

[0026] in, is the pressure, is the current, is the dynamic viscosity coefficient, is the current density, is the magnetic induction intensity;

[0027] Energy conservation equation:

[0028] (3)

[0029] in, is the enthalpy per unit mass, is the thermal conductivity, is the specific heat capacity at constant pressure, is the conductivity, is the electric field strength, is the total volume radiant energy, is dissipated energy;

[0030] Maxwell's equations:

[0031] (4)

[0032] (5)

[0033] (6)

[0034] (7)

[0035] in, is the electric displacement vector, is the space charge density, is the magnetic field strength, is the electric field strength.

[0036] The calculation simulation arc voltage, arc current and arc energy are specifically as follows:

[0037] The potential change at both ends of the arc is calculated based on the electromagnetic field distribution in the physical model; the arc current density is calculated based on the electromagnetic field distribution in the physical model; the overall arc energy is calculated based on the electromagnetic field distribution in the physical model,

[0038] The calculation of arc voltage and arc current is shown in equations (8), (9), and (10);

[0039] (8)

[0040] (9)

[0041] (10)

[0042] Where, is the conductivity, is the electric potential, is the current density, For speed, is the magnetic induction intensity, is the arc energy.

[0043] The arc conductance, dissipated power and time constant are calculated, and the functions of the dissipated power and time constant with respect to the arc conductance are obtained by fitting, specifically:

[0044] The arc conductance is calculated based on the arc voltage and arc current, the dissipated power is calculated based on the distribution and change of the energy field, and the function of the dissipated power with respect to the arc conductance is obtained by fitting.

[0045] The calculation of dissipated power and time constant is shown in equations (11) and (12);

[0046] (11)

[0047] (12)

[0048] Where, is the arc voltage, is the arc current, For the The energy of electrons within a fluid cluster; is the duration, is the arc conductance.

[0049] The function of the dissipated power on the arc conductance is obtained by fitting, and the fitting equations are as follows: (13) and (14);

[0050] (13)

[0051] (14).

[0052] In a second aspect, an embodiment of the present application provides a simplified mathematical model simulation system for a cable single-phase grounding fault arc, comprising a memory and a processor, wherein the memory includes a program for a simplified mathematical model simulation method for a cable single-phase grounding fault arc, and when the program for the simplified mathematical model simulation method for a cable single-phase grounding fault arc is executed by the processor, the following steps are implemented:

[0053] Design geometric models, boundary conditions, and medium physical properties for magnetic fluid MHD simulation;

[0054] The physical model of the fault arc is obtained through magnetic fluid MHD simulation;

[0055] Calculate and simulate arc voltage, arc current and arc energy;

[0056] Calculate arc conductance, dissipated power and time constant, and fit the functions of dissipated power and time constant related to arc conductance;

[0057] The improved Mayr arc model is obtained by replacing the dissipated power and time constant in the classic Mayr arc model with functions related to arc conductance;

[0058] The improved Mayr arc model is introduced into the ATP-EMTP distribution network model to obtain the simulation waveform of the cable single-phase grounding fault.

[0059] In a third aspect, an embodiment of the present application provides a computer-readable storage medium, which stores program code. When the program code is executed by a processor, it implements the steps of the simplified mathematical model simulation method for a single-phase grounding fault arc of a cable as described above.

[0060] In a fourth aspect, an embodiment of the present application provides an electronic device, including:

[0061] Memory for storing computer programs;

[0062] The processor is configured to execute the steps of the simplified mathematical model simulation method for a single-phase grounding fault arc in a cable as described above when executing the computer program stored in the memory.

[0063] Compared with the prior art, the present invention has the following advantages: 1) Based on actual operating conditions, a geometric model for MHD simulation is established. Based on finite element calculations, simulation research of multiple physical fields is realized, the transient evolution and dynamic characteristics of the cable single-phase grounding fault arc in different scenarios are analyzed, and the evolution mechanism of the single-phase grounding arc is analyzed. 2) Based on the various characteristic quantities of the arc output by the simulation, the transient characteristics of the arc are analyzed and extracted, and a mathematical model of the arc is constructed based on which the resistance value responds to the changes in the loop input in a timely manner. This is used to establish an arc mathematical model suitable for simulating single-phase grounding faults in medium-voltage distribution network cables. 3) The distribution network model is established using EMTP software, and the improved mathematical model is introduced into the corresponding distribution network model to simulate the fault waveform, achieving accurate simulation of the actual fault. The present invention can be used for simulating medium-voltage cable grounding faults in distribution networks with complex structures and diverse environments. By combining MHD simulation and arc mathematical models, a large amount of computational cost is saved while maintaining high computational accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments of the present application. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0065] Figure 1 is a flow chart of the method of the present invention;

[0066] Figure 2 is the geometric model of the MHD simulation of the present invention;

[0067] Figure 3 is the temperature field change in the MHD simulation result of the present invention;

[0068] Figure 4 is the change of arc energy and arc conductance over time in the MHD simulation results of the present invention;

[0069] Figure 5 is the fitting curve of the time constant and dissipated power with respect to conductance in the MHD simulation results of the present invention;

[0070] Figure 6 The present invention relates to an ATP-EMTP single-phase grounding fault simulation model;

[0071] Figure 7 It is an actual single-phase grounding fault current waveform of the present invention and a simulated current waveform of a cable single-phase grounding fault based on an improved Mayr arc model;

[0072] Figure 8The present invention provides an actual single-phase grounding fault voltage waveform and a simulated voltage waveform of a cable single-phase grounding fault based on an improved Mayr arc model. DETAILED DESCRIPTION

[0073] The technical solutions in the embodiments of the present application will be described below in conjunction with the accompanying drawings. It should be noted that similar reference numerals and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0074] The terms "comprises," "comprising," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not preclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0075] The terms "first," "second," etc. are only used to distinguish one entity or operation from another entity or operation, and are not to be understood as indicating or implying relative importance, nor are they to be understood as requiring or implying any actual relationship or order between these entities or operations.

[0076] like Figure 1 As shown, the embodiment of the present application provides a simplified mathematical model simulation method for a cable single-phase grounding fault arc, including the following specific steps:

[0077] S1-1: Design and simplify the geometric model based on the actual fault situation and cable structure; S1-2: Determine the electric field boundary conditions based on the external applied circuit of the actual structure; S1-3: Determine the physical properties of the dielectric used for arc discharge based on the actual fault environment;

[0078] S2-1 obtains the fault arc physical model through magnetic fluid dynamics (MHD) simulation based on the geometric model designed in S1-1, the boundary conditions given in S1-2, and the dielectric physical parameters involved in S1-3;

[0079] S3-1: Calculate the arc potential change at both poles based on the electromagnetic field distribution in the physical model S2-1; S3-2: Calculate the arc current density based on the electromagnetic field distribution in the physical model S2-1; S3-3: Calculate the overall arc energy based on the electromagnetic field distribution in the physical model S2-1;

[0080] S4-1: Calculate arc conductance according to S3-1 and S3-2, calculate dissipated power according to the distribution and change of energy field in S3-3, and obtain the function of dissipated power with respect to arc conductance by fitting; S4-2: Calculate arc conductance according to S3-1 and S3-2, calculate time constant according to the distribution and change of energy field in S3-3, and obtain the function of time constant with respect to arc conductance by fitting;

[0081] S5-1: The dissipated power and time constant in the classic Mayr arc model are replaced by the functions of S4-1 and S4-2 on arc conductance to obtain the improved Mayr arc model;

[0082] S6-1: The improved Mayr arc model obtained in S5-1 is introduced into the ATP-EMTP distribution network model to obtain the cable single-phase grounding fault simulation waveform.

[0083] See also Figure 1 、 Figure 2 and Figure 3 , embodiments of the present invention include:

[0084] A simplified mathematical model simulation method for cable single-phase grounding fault arc based on MHD is proposed to solve the problem that the existing arc model has a narrow scope of application and is not suitable for the study of medium-voltage cable single-phase grounding fault. The specific implementation method is as follows:

[0085] Step 1: Design and simplify the geometric model based on the actual fault conditions and cable structure;

[0086] Step 2: Determine the electric field boundary conditions based on the external applied circuit of the actual structure;

[0087] Step 3: Determine the physical properties of the dielectric used for arc discharge based on the actual fault environment;

[0088] Step 4: Based on the geometric model designed in the first step, the given boundary conditions and the physical properties of the medium involved, the fault arc physical model is obtained through magnetic fluid dynamics (MHD) simulation. The control equations involved in the magnetic fluid dynamics simulation include the three conservation equations of fluid dynamics, as shown in Equations (1), (2), and (3); and Maxwell's equations, as shown in Equations (4), (5), (6), and (7).

[0089] Mass conservation equation:

[0090] (1)

[0091] in, is the density, For speed.

[0092] Momentum conservation equation:

[0093] (2)

[0094] in, is the pressure, is the current, is the dynamic viscosity coefficient, is the current density, is the magnetic induction intensity.

[0095] Energy conservation equation:

[0096] (3)

[0097] in, is the enthalpy per unit mass, is the thermal conductivity, is the specific heat capacity at constant pressure, is the conductivity, is the electric field strength, is the total volume radiant energy, For dissipated energy.

[0098] Maxwell's equations:

[0099] (4)

[0100] (5)

[0101] (6)

[0102] (7)

[0103] in, is the electric displacement vector, is the space charge density, is the magnetic field strength, is the electric field strength.

[0104] Step 5: Calculate the arc voltage, arc current and arc energy based on the electromagnetic field distribution in the fault arc physical model obtained in step 4. The calculation of arc voltage and arc current is shown in equations (8), (9) and (10).

[0105] (8)

[0106] (9)

[0107] (10)

[0108] Where, is the conductivity, is the electric potential, is the current density, For speed, is the magnetic induction intensity, is the arc energy.

[0109] Step 6: Calculate the arc conductance based on the arc voltage and arc current in the previous step, and calculate the dissipated power and time constant based on the distribution and change of the arc voltage, arc current and arc energy field in the previous step, such as Figure 4 As shown, the calculation of dissipated power and time constant is shown in equations (11) and (12);

[0110] (11)

[0111] (12)

[0112] Where, is the arc voltage, is the arc current, For the The energy of electrons within a fluid cluster; is the duration, is the arc conductance.

[0113] Step 7: Based on the arc conductance, time constant and dissipated power calculated in step 6, the function of dissipated power on arc conductance and the function of time constant on arc conductance are fitted. The fitting result curve is as follows: Figure 5 As shown, the fitting equations are as follows (13) and (14);

[0114] (13)

[0115] (14).

[0116] Step 8: Replace the dissipated power and time constant in the classic Mayr arc model with the dissipated power and time constant functions of arc conductance obtained in step 7 to obtain the improved Mayr arc model. The classic Mayr model is shown in Equation (15);

[0117] (15)

[0118] is the conductance of the Mayr arc model; is the arc time constant; is the arc dissipation power. In the Mayr arc model, the arc time constant, heat dissipation power, and arc voltage are all constants.

[0119] The improved Mayr arc model based on MHD simulation is shown in Equation (16);

[0120] (16)

[0121] Where, and Different from the definitions in the Mayr model, they are not constants, but functions obtained in the seventh step that change with the arc state (conductance), namely, equations (13) and (14).

[0122] Step 9: Bring the improved Mayr model obtained in step 8 into an example ATP-EMTP single-phase ground fault simulation model. The distribution network equivalent model is as follows: Figure 6 As shown, the Model part is a user-defined arc model, which is the Mayr model improved based on MHD simulation in the present invention.

[0123] The final obtained cable single-phase grounding fault current and voltage waveform is as follows: Figure 7 , Figure 8 shown.

[0124] An embodiment of the present application provides a simplified mathematical model simulation system for a cable single-phase grounding fault arc, comprising a memory and a processor, wherein the memory comprises a program for a simplified mathematical model simulation method for a cable single-phase grounding fault arc, and when the program for the simplified mathematical model simulation method for a cable single-phase grounding fault arc is executed by the processor, the steps of the simplified mathematical model simulation method for a cable single-phase grounding fault arc as described above are implemented.

[0125] An embodiment of the present application provides a computer-readable storage medium storing program code. When the program code is executed by a processor, the steps of the simplified mathematical model simulation method for a single-phase grounding fault arc in a cable are implemented as described above.

[0126] An embodiment of the present application provides an electronic device, including:

[0127] Memory for storing computer programs;

[0128] The processor is configured to execute the steps of the simplified mathematical model simulation method for a single-phase grounding fault arc in a cable as described above when executing the computer program stored in the memory.

[0129] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0130] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0131] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0132] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0133] In a typical configuration, a computing device includes one or more processors (CPUs), input / output interfaces, network interfaces, and memory.

[0134] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0135] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can be implemented using any method or technology to store information. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change RAM (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory computer-readable media such as modulated data signals and carrier waves.

[0136] The above description is merely an embodiment of the present application and is not intended to limit the scope of protection of the present application. For those skilled in the art, various modifications and variations of the present application are possible. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A simplified mathematical model simulation method for a single-phase grounding fault arc in a cable, characterized in that: The following steps are involved: Design geometric models, boundary conditions, and medium physical properties for magnetic fluid MHD simulation; Based on the geometric model, boundary conditions and dielectric physical parameters, the fault arc physical model is obtained through magnetic fluid MHD simulation; Calculate and simulate arc voltage, arc current and arc energy based on the fault arc physical model; According to the simulated arc voltage, arc current and arc energy, the arc conductance, dissipated power and time constant are calculated, and the functions of the dissipated power and time constant with respect to the arc conductance are obtained by fitting. The improved Mayr arc model is obtained by replacing the dissipated power and time constant in the classic Mayr arc model with functions related to arc conductance; The improved Mayr arc model is introduced into the ATP-EMTP distribution network model to obtain the simulation waveform of the cable single-phase grounding fault.

2. The simplified mathematical model simulation method for a cable single-phase grounding fault arc according to claim 1, characterized in that: The geometric model, boundary conditions and medium physical parameters designed for magnetic fluid MHD simulation are specifically as follows: Design and simplify the geometric model based on the actual fault conditions and cable structure; determine the electric field boundary conditions based on the external applied circuit of the actual structure; and determine the physical properties of the dielectric used for arc discharge based on the actual fault environment.

3. The simplified mathematical model simulation method for a cable single-phase grounding fault arc according to claim 1, characterized in that: The control equations involved in the magnetic fluid simulation in the fault arc physical model obtained by the magnetic fluid MHD simulation include three conservation equations of fluid mechanics and Maxwell's equations. The three conservation equations of fluid mechanics are shown in formula (1), formula (2), and formula (3); the Maxwell's equations are shown in formula (4), formula (5), formula (6), and formula (7); Mass conservation equation: （1） in, is the density, For speed, Momentum conservation equation: （2） in, is the pressure, is the current, is the dynamic viscosity coefficient, is the current density, is the magnetic induction intensity; Energy conservation equation: （3） in, is the enthalpy per unit mass, is the thermal conductivity, is the specific heat capacity at constant pressure, is the conductivity, is the electric field strength, is the total volume radiant energy, is dissipated energy; Maxwell's equations: （4） （5） （6） （7） in, is the electric displacement vector, is the space charge density, is the magnetic field strength, is the electric field strength.

4. The simplified mathematical model simulation method for a cable single-phase grounding fault arc according to claim 1, characterized in that: The calculation simulation arc voltage, arc current and arc energy are specifically as follows: The potential change at both ends of the arc is calculated based on the electromagnetic field distribution in the physical model; the arc current density is calculated based on the electromagnetic field distribution in the physical model; the overall arc energy is calculated based on the electromagnetic field distribution in the physical model, The calculation of arc voltage and arc current is shown in equations (8), (9), and (10); (8) (9) (10) Where, is the conductivity, is the electric potential, is the current density, For speed, is the magnetic induction intensity, is the arc energy.

5. The simplified mathematical model simulation method for a cable single-phase grounding fault arc according to claim 1, characterized in that: The arc conductance, dissipated power and time constant are calculated, and the functions of the dissipated power and time constant with respect to the arc conductance are obtained by fitting, specifically: The arc conductance is calculated based on the arc voltage and arc current, the dissipated power is calculated based on the distribution and change of the energy field, and the function of the dissipated power with respect to the arc conductance is obtained by fitting.

6. A simplified mathematical model simulation method for a cable single-phase grounding fault arc according to claim 5, characterized in that: The calculation of dissipated power and time constant is shown in equations (11) and (12); (11) (12) Where, is the arc voltage, is the arc current, For the The energy of electrons within a fluid cluster; is the duration, is the arc conductance.

7. The simplified mathematical model simulation method for a cable single-phase grounding fault arc according to claim 5, characterized in that: The function of the dissipated power on the arc conductance is obtained by fitting, and the fitting equations are as follows: (13) and (14); (13) (14)。 8. A simplified mathematical model simulation system for a cable single-phase grounding fault arc, characterized in that: The invention comprises a memory and a processor, wherein the memory comprises a program of a simplified mathematical model simulation method for a cable single-phase grounding fault arc, and when the program of the simplified mathematical model simulation method for a cable single-phase grounding fault arc is executed by the processor, the following steps are implemented: Design geometric models, boundary conditions, and medium physical properties for magnetic fluid MHD simulation; Based on the geometric model, boundary conditions and dielectric physical parameters, the fault arc physical model is obtained through magnetic fluid MHD simulation; Calculate and simulate arc voltage, arc current and arc energy according to the physical model of the fault arc; According to the simulated arc voltage, arc current and arc energy, the arc conductance, dissipated power and time constant are calculated, and the functions of the dissipated power and time constant with respect to the arc conductance are obtained by fitting. The improved Mayr arc model is obtained by replacing the dissipated power and time constant in the classic Mayr arc model with functions related to arc conductance; The improved Mayr arc model is introduced into the ATP-EMTP distribution network model to obtain the simulation waveform of the cable single-phase grounding fault.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores program code, and when the program code is executed by a processor, the steps of the simplified mathematical model simulation method for a cable single-phase grounding fault arc are implemented as described in any one of claims 1 to 7.

10. An electronic device, characterized in that: include: Memory for storing computer programs; The processor is configured to execute the steps of the simplified mathematical model simulation method for a cable single-phase grounding fault arc as claimed in any one of claims 1 to 7 when executing the computer program stored in the memory.

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