Method and system for constructing mayr arc model based on dynamic arc radius and random length

Abstract

The application relates to the technical field of high-voltage power transmission and distribution, and provides a Mayr arc model construction method and system based on a dynamic arc radius and a random length, which comprises the following steps: generating a multi-dimensional random state vector representing micro-instability in the arc; calculating a random effective arc length and a dynamic arc radius according to the multi-dimensional random state vector, an instantaneous arc current and a mechanical contact spacing; calculating a dynamic time constant, a heat dissipation power and an arc voltage correction amount based on the random effective arc length and the dynamic arc radius, and solving an improved Mayr differential equation to update an arc conductance; feeding back and modulating evolution parameters of the multi-dimensional random state vector according to a power imbalance degree calculated by the arc conductance, and adjusting secondary empirical coefficients in the dynamic arc radius and the dynamic time constant; and generating the Mayr arc model after complete time domain iteration. The method generates a high-fidelity Mayr model which can reflect arc physical randomness and is suitable for probabilistic evaluation.

Description

Technical Field

[0001] This application relates to the field of high-voltage power transmission and transformation technology, and in particular to a method and system for constructing a Mayr arc model based on dynamic arc radius and random length. Background Technology

[0002] High-voltage circuit breakers are core equipment for ensuring the safe operation of power systems, and their breaking capacity mainly depends on the accurate control and prediction of the electric arc generated by the fault current. The Mayr arc model, as a classic theory describing the transient energy balance of the arc, has long provided a basic computational framework for circuit breaker design and performance evaluation.

[0003] However, the traditional Mayr model and its improved versions treat the electric arc as a plasma channel with a defined shape, assuming that its radius and length are fixed values ​​or change according to simple laws. This completely ignores the inherent dynamic evolution and random fluctuation characteristics of the radial and axial morphology of the actual electric arc under strong turbulence, magnetic field and electrode movement. As a result, the model cannot reflect the inherent randomness of electric arc physics, and it is difficult to predict the statistical distribution law of the breaking result (success or failure). This seriously limits its application accuracy in the high reliability design of circuit breakers and probabilistic safety verification. Summary of the Invention

[0004] In view of this, the present invention provides a method and system for constructing a Mayr arc model based on dynamic arc radius and random length, so as to solve the problems mentioned in the background art.

[0005] Firstly, this application provides a method for constructing a Mayr arc model based on dynamic arc radius and random length, including: Establish and solve a coupled stochastic differential equation system to generate a multidimensional stochastic state vector characterizing the microscopic instability inside the electric arc; Based on the multidimensional random state vector, the instantaneous arc current, and the mechanical distance between the contacts, the random effective arc length and the dynamic arc radius are calculated using a nonlinear mapping function. Based on the random effective arc length and the dynamic arc radius, the dynamic time constant, the morphology-related heat dissipation power and the arc voltage correction are calculated, and the improved Mayr differential equation is solved to update the arc conductance. Based on the power imbalance calculated from the arc conductance, the evolution parameters of the multidimensional random state vector are fed back and modulated, and the secondary empirical coefficients in the dynamic arc radius and the dynamic time constant are adaptively adjusted. After a complete time domain iteration, a Mayr arc model containing a fixed parameter mapping function and a core state equation is generated.

[0006] Secondly, this application provides a Mayr arc model construction system based on dynamic arc radius and random length, comprising: The module is used to build and solve coupled stochastic differential equation systems to generate multidimensional stochastic state vectors characterizing the microscopic instability inside the electric arc. The first calculation module is used to calculate the random effective arc length and dynamic arc radius based on the multidimensional random state vector, the instantaneous arc current and the mechanical distance between the contacts, through a nonlinear mapping function. The second calculation module is used to calculate the dynamic time constant, the morphology-related heat dissipation power and the arc voltage correction based on the random effective arc length and the dynamic arc radius, and to solve the improved Mayr differential equation to update the arc conductance. The modulation module is used to feed back the evolution parameters of the multidimensional random state vector based on the power imbalance calculated by the arc conductance, and to adaptively adjust the secondary empirical coefficients in the dynamic arc radius and the dynamic time constant. After a complete time domain iteration, a Mayr arc model containing a fixed parameter mapping function and a core state equation is generated.

[0007] This application provides a method and system for constructing a Mayr arc model based on dynamic arc radius and random length. Firstly, by establishing independent microscopic random state vectors and using their evolution to drive macroscopic morphology, the inherent randomness and dynamism of arc length and radius are mathematically represented at their root, enabling the model to reflect the physical instability of real arcs. Secondly, by coupling random length and dynamic radius in real-time to the calculation of key parameters such as time constant, heat dissipation power, and voltage, the spatiotemporal evolution of the morphology is fully embedded into the classical energy balance equation framework, improving the simulation accuracy of the model in critical transients such as current zero crossing. Thirdly, by constructing a closed-loop system that modulates microscopic random evolution from energy balance state feedback and adaptively adjusts secondary coefficients, self-tuning and consistency optimization of the model's internal parameters are achieved during simulation. Ultimately, a customized Mayr arc model with fixed parameters and rules, capable of accurately reproducing the breaking behavior of specific circuit breakers, is generated, providing a directly usable tool for probabilistic breaking assessment. Attached Figure Description

[0008] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0009] Figure 1A flowchart illustrating the method for constructing a Mayr arc model based on dynamic arc radius and random length, provided in this application embodiment; Figure 2 A schematic block diagram of the Mayr arc model construction system based on dynamic arc radius and random length provided in the embodiments of this application. Detailed Implementation

[0010] 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 are within the scope of protection of the present invention.

[0011] The flowchart shown in the attached diagram is for illustrative purposes only and does not necessarily include all content and operations / steps, nor does it require execution in the described order. For example, some operations / steps can be broken down, combined, or partially merged, so the actual execution order may change depending on the actual situation.

[0012] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the scope of the application. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0013] It should also be further understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the relevant listed items and all possible combinations, and includes such combinations.

[0014] The following detailed description of some embodiments of this application is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0015] Please see Figure 1 , Figure 1 A flowchart illustrating the Mayr arc model construction method based on dynamic arc radius and random length provided in this application embodiment is shown below. Figure 1 As shown, the Mayr arc model construction method based on dynamic arc radius and random length provided in this application embodiment includes steps S1 to S4.

[0016] Step S1: Establish and solve the coupled stochastic differential equation system to generate a multidimensional stochastic state vector characterizing the microscopic instability inside the electric arc.

[0017] Specifically, a microscopic stochastic state vector with four components is constructed to comprehensively describe the internal latent variables driving the random changes in the macroscopic morphology of the electric arc. These four components are defined as follows: the first component corresponds to the turbulence intensity random factor, reflecting the instability of gas flow; the second component corresponds to the cathode spot jumping activity, characterizing the disordered movement of attachment points on the electrode surface; the third component corresponds to the metal vapor concentration fluctuation, reflecting the non-uniformity of electrode material evaporation; and the fourth component corresponds to the local thermodynamic imbalance of the arc column, describing the deviation of the energy transfer process. The evolution of these components is described by a four-dimensional stochastic differential equation system containing a state transition matrix and a diffusion coefficient matrix. The elements of the state transition matrix are functions of the current instantaneous arc current and the arc-extinguishing chamber geometry, allowing the evolution rate of the microstate to respond to external circuit conditions and the arc-extinguishing chamber structure. The diffusion coefficient matrix, similarly dependent on the current and geometry parameters, determines the intensity of the stochastic excitation. Within each simulation time step, four independent sets of standard normally distributed random numbers are generated by calling a pseudo-random number generator as increments for the Wiener process. Subsequently, numerical methods suitable for stochastic differential equations are used to solve the above stochastic differential equation system, thereby updating the four-dimensional microscopic stochastic state vector at the current moment. This vector is the sole source of randomness in all subsequent calculations of macroscopic parameters.

[0018] Step S2: Based on the multidimensional random state vector, the instantaneous arc current, and the mechanical distance between the contacts, the random effective arc length and the dynamic arc radius are calculated using a nonlinear mapping function.

[0019] Specifically, firstly, the random effective arc length is calculated, which consists of three superimposed parts: the first part is a deterministic fundamental length based on the mechanical distance between the contacts and the instantaneous arc current, reflecting the effects of mechanical and electromagnetic stretching of the arc; the second part is a length fluctuation term driven by the turbulence intensity component in the microscopic random state vector, the amplitude of which is proportional to the square root of the current and the mechanical distance; the third part is a length fluctuation term driven by the rate of change of the speckle jump activity component in the microscopic random state vector, simulating the instantaneous path change caused by the jump at the electrode attachment point. Adding these three parts yields the random effective arc length. Secondly, the dynamic arc radius is calculated based on a quasi-steady-state force balance principle. This balance considers three types of pressure: first, the magnetic pressure expansion force generated by the arc's own current, the intensity of which is proportional to the square of the current; second, the radiation contraction pressure caused by the arc's thermal radiation, the magnitude of which is obtained through iterative calculation of the current arc temperature and the radius at the previous moment; and third, the aerodynamic pressure and random pressure disturbance caused by the combined effects of external airflow and the metal vapor concentration fluctuation component in the microscopic random state vector. By constructing an implicit equation about the radius and solving it using the Newton-Raphson iterative method, the dynamic arc radius that satisfies the force equilibrium condition can be obtained.

[0020] Step S3: Based on the random effective arc length and the dynamic arc radius, calculate the dynamic time constant, the morphology-related heat dissipation power and the arc voltage correction, and use these to solve the improved Mayr differential equation to update the arc conductance.

[0021] Specifically, firstly, the dynamic time constant is calculated based on the arc heat capacity represented by the dynamic arc radius, combined with the modulation effect of the thermodynamic imbalance component in the micro-random state vector on the energy relaxation rate. Secondly, the morphology-related heat dissipation power consists of three parts: convective heat dissipation power, whose value is proportional to the heat dissipation surface area formed by the dynamic arc radius and the random effective arc length, as well as the temperature difference between the arc temperature and the environment; radiative heat dissipation power, also based on the aforementioned heat dissipation surface area, and proportional to the fourth power of the arc temperature according to the Stefan-Boltzmann law; and turbulence-enhanced heat dissipation term, obtained by multiplying the convective heat dissipation power by the turbulence intensity component in the micro-random state vector as a modulation factor, reflecting the enhancing effect of turbulence on heat dissipation. Thirdly, the arc voltage correction consists of two parts: one is a linear term proportional to the random effective arc length, representing the arc column voltage drop; the other is a nonlinear function term with the speckle jump activity component in the micro-random state vector as input, representing the random fluctuation of the electrode voltage drop. Finally, the calculated dynamic time constant, morphology-dependent heat dissipation power, and arc voltage correction, along with the instantaneous arc current from the external circuit, are substituted into the improved Mayr differential equation. This equation, based on the classical form, adds a nonlinear term related to the arc conductance and dynamic arc radius to simulate the potential "collapse" effect of the arc column cross-section before and after the current crosses zero. The Gill algorithm, suitable for rigid differential equations, is used to numerically integrate the equation, solving and updating the arc conductance at the current moment.

[0022] Step S4: Based on the power imbalance calculated by the arc conductance, the evolution parameters of the multidimensional random state vector are fed back and modulated, and the secondary empirical coefficients in the dynamic arc radius and the dynamic time constant are adaptively adjusted. After a complete time domain iteration, a Mayr arc model containing a fixed parameter mapping function and a core state equation is generated.

[0023] Specifically, firstly, based on the updated arc conductance, arc voltage correction, and morphology-related heat dissipation power in step S3, the power imbalance of the arc at the current moment, i.e., the difference between the input power and the heat dissipation power, is calculated. Secondly, the absolute value of this power imbalance is used as a feedback signal to dynamically adjust specific elements in the state transition matrix of the stochastic differential equation system described in step S1, such as parameters affecting the relaxation rate of the thermodynamic imbalance component. This forms a negative feedback loop: when the arc moves away from energy equilibrium, the evolution behavior of its microscopic thermodynamic state is modulated accordingly. Simultaneously, based on the time-varying rate of change of the arc conductance, the coefficients used in step S2 to calculate the length fluctuation term caused by turbulence are adjusted. Thirdly, throughout the entire simulation time domain, key indicators such as the ratio of radiative to convective heat dissipation are continuously monitored, and based on the real-time values ​​of these indicators, several secondary empirical coefficients used in steps S2 and S3 are fine-tuned to ensure that the macroscopic performance of the model remains consistent with the known characteristics of the target circuit breaker type. Finally, after all the time-domain iterative calculations from the start to the end of the simulation are completed, the program does not only output data curves, but also packages and solidifies the mapping function used to calculate the random effective arc length and dynamic arc radius, the rules used to calculate the dynamic time constant and morphology-related heat dissipation power, and the final core state equation—the improved Mayr differential equation—to form a Mayr arc model instance that can be independently called and run.

[0024] The method provided in this embodiment, on the one hand, establishes an independent microscopic random state vector and uses its evolution to drive the macroscopic morphology, mathematically representing the inherent randomness and dynamics of the arc length and radius from the root, enabling the model to reflect the physical instability of the real arc; on the other hand, by coupling the random length and dynamic radius in real time to the calculation of key parameters such as time constant, heat dissipation power, and voltage, the spatiotemporal evolution of the morphology is fully embedded into the classical energy balance equation framework, improving the simulation accuracy of the model in key transients such as current zero crossing; furthermore, by constructing a closed-loop system that modulates the microscopic random evolution from the energy balance state feedback and adaptively adjusts the secondary coefficients, the self-tuning and consistency optimization of the model's internal parameters are realized during the simulation process, ultimately generating a customized Mayr arc model with solidified parameters and rules that can accurately reproduce the breaking behavior of a specific circuit breaker, providing a directly usable tool for probabilistic breaking assessment.

[0025] In some embodiments, establishing and solving the coupled stochastic differential equation system to generate a multidimensional stochastic state vector characterizing the microscopic instability within the electric arc includes: Step S11: Define the four components of the multidimensional random state vector, which correspond to turbulence intensity, cathode spot jumping activity, metal vapor concentration and thermodynamic imbalance, respectively.

[0026] Specifically, the implementation of this step involves establishing a clear mathematical framework for representing the microscopic randomness of the electric arc. In the computer program, a state array with four elements is first declared to store the multidimensional random state vector. The first element is designated as a scalar representing turbulence intensity, which physically quantifies the severity of vortices and disordered motion in the flow of the arc-extinguishing medium (such as SF6 gas), influenced by the nozzle shape and airflow velocity. The second element is designated as a scalar representing the cathode spot jumping activity, which physically quantifies the frequency and randomness of the movement of current convergence points on the cathode surface, related to electrode material, current density, and magnetic field conditions. The third element is designated as a scalar representing the fluctuation of metal vapor concentration, which physically quantifies the non-uniformity and time-varying nature of the distribution of metal vapor evaporated from the electrode surface in the arc gap, relating to the arc's conductivity and cooling characteristics. The fourth element is designated as a scalar representing the thermodynamic imbalance, which physically quantifies the degree to which the local temperature and particle energy distribution of the arc plasma deviate from equilibrium, affecting the energy relaxation process. These four components together constitute a complete set of latent variables describing the microscopic instability inside the electric arc, providing a clear mathematical object for subsequent stochastic evolution.

[0027] Step S12: Input the instantaneous arc current and the geometric parameters of the arc-extinguishing chamber as time-varying coefficients into the preset stochastic differential equation.

[0028] Specifically, this step involves dynamically injecting external conditions into the microscopic stochastic evolution process. The preset stochastic differential equation adopts the Itô form, and its general expression is: In this formula, Represents time A four-dimensional microscopic random state vector. It is a 4×4 state transition matrix, which determines the vector The deterministic evolutionary trend. The key implementation detail lies in the matrix. Each element in Neither of them are constants, but rather functions of two time-varying or steady-state parameters: one is the instantaneous arc current scalar value from the external circuit solution interface. The other is the geometric parameter vector describing the structure of the arc-extinguishing chamber. This vector, read from the configuration file at the start of the simulation, contains constants such as nozzle diameter, length, and contraction ratio. For example, it includes matrix elements connecting the turbulence intensity component and the metal vapor concentration component. It may be designed as ,in and These are model constants. This refers to the nozzle contraction ratio in the geometric parameter vector. This means that a large current and a high contraction ratio enhance the influence of metallic vapor on turbulent evolution. Similarly, It is a 4×4 diffusion coefficient matrix that determines the strength of the random perturbation, and its elements depend on the diffusion coefficient matrix in a similar way. and . This represents the differential increment of a four-dimensional independent standard Wiener process. Through this design, the external circuit state (current) and the fixed structure of the arc-extinguishing chamber jointly modulate the evolution of microscopic randomness.

[0029] Step S13: Solve the stochastic differential equation using numerical methods to obtain a micro-stochastic state vector consisting of four random variables at each time step.

[0030] Specifically, this step is implemented by using a numerical algorithm to advance the stochastic differential equation in discrete time. Since the equation contains both deterministic drift terms and stochastic diffusion terms, a specialized numerical solution method is required. At each discrete time step... First, four independent groups need to be generated, with a mean of 0 and a variance of 0. Normally distributed random numbers , , , ΔW1, this is obtained by using a computer's pseudo-random number generator and applying a transformation. To achieve this, in which These are standard normally distributed random numbers. Subsequently, the Euler-Maruyama method is used to numerically integrate the stochastic differential equation. The iterative formula for this method is: in, Indicates the current time step. Indicates the previous time step, The program calculates according to this formula: first, it uses the state vector from the previous time step. and the currently known current and fixed parameters Calculate matrix and Then perform matrix and vector multiplication and addition operations; finally, add a random perturbation term. After the calculation is completed, the updated four-dimensional microscopic random state vector at the current time is obtained. This vector is stored in memory and immediately used for the calculation of macroscopic morphological parameters in step S2.

[0031] The method provided in this embodiment, on the one hand, establishes a structured mathematical description foundation for the microscopic randomness of the electric arc by clearly defining four latent variable components with clear physical meaning: turbulence intensity, spot activity, metal vapor concentration, and thermodynamic imbalance, so that the subsequent stochastic evolution has a clear physical correspondence; on the other hand, by designing the instantaneous current and arc-extinguishing chamber geometric parameters as functional inputs to the coefficient matrix of the stochastic differential equation, the evolution law of the microscopic random state can dynamically respond to the constraints of external circuit conditions and arc-extinguishing chamber structure, thus organically coupling external macroscopic conditions with internal microscopic randomness; furthermore, by using numerical algorithms such as the Euler-Maruyama method to solve the stochastic differential equation, a set of state vectors containing four related random variables can be stably generated at each discrete time step, thereby providing a continuous, self-consistent, and reproducible source of microscopic randomness for the entire model.

[0032] In some embodiments, the step of calculating the random effective arc length and dynamic arc radius based on the multidimensional random state vector, the instantaneous arc current, and the mechanical distance between the contacts using a nonlinear mapping function includes: Step S21: Substitute the contact mechanical spacing and the instantaneous arc current into the first mapping function to generate a deterministic base length.

[0033] Specifically, the implementation of this step involves calculating the deterministic portion of the arc length, which is determined by both mechanical separation and electromagnetic stretching. The contact mechanical spacing... It is time The function, calculated by integration from the circuit breaker's tripping speed curve, represents the linear geometric distance between the moving and stationary contacts. The instantaneous arc current... Provided by external circuit simulation. The first mapping function is designed as a nonlinear relationship containing an arctangent function, specifically in the form of: In this formula, Represents time The calculated deterministic basic arc length. It is time The mechanical spacing of the contacts. It is a dimensionless empirical coefficient used to adjust the intensity of the effect of current on arc stretching. It is time The instantaneous arc current. This is a reference current value used to normalize the current, making the independent variable of the arctangent function dimensionless. This function indicates that the base length increases linearly as the contacts separate; simultaneously, as the current increases, the arc is further stretched under the influence of electromagnetic force, adding a current-related increment to the mechanical distance.

[0034] Step S22: Combine the rate of change of the turbulence intensity component and the speckle jump component in the multidimensional random state vector with the instantaneous arc current and the contact mechanical distance to calculate the length random fluctuation term.

[0035] Specifically, this step involves quantifying the random fluctuations in the arc path caused by turbulence and electrode spot motion. First, the length fluctuation term caused by turbulence is calculated. This calculation requires the use of microscopic random state vectors. The first component in the equation, namely the turbulence intensity component. and instantaneous arc current mechanical spacing with contacts The calculation formula is as follows: In this formula, It is a proportionality coefficient used to transform dimensionless random state components into fluctuation values ​​with length dimensions. The introduction of this concept is based on physical considerations, assuming that the effect of turbulence on length fluctuations is related to the square root of the arc scale. (Absolute value of current) The product represents the modulation of turbulence intensity by the current magnitude. Next, the length fluctuation term caused by cathode spot jumping is calculated. This calculation requires the use of microscopic random state vectors. The second component, namely the speckle jump activity component. Since speckle skipping causes instantaneous changes in the path, it is more reasonable to use the time rate of change (difference) of this component to drive the fluctuations. The calculation formula is as follows: In this formula, It is another proportionality coefficient. This is the simulation time step. (Molecules) It represents the change in spot activity over the most recent time step, and its rate of change reflects the intensity of attachment point jumps, which causes rapid random fluctuations in the effective conductive path length.

[0036] Step S23: Superimpose the base length with each of the random fluctuation terms of the length to obtain the random effective arc length.

[0037] Specifically, this step involves synthesizing the deterministic base length with a random fluctuation term to obtain the final arc length representation. This is a simple linear superposition process, and its calculation formula is as follows: In this formula, That is, in time The desired random effective arc length will be derived from the deterministic base length obtained in step S21. , turbulent wave length from step S22 and the length of the spot jump fluctuation Direct addition. Through this superposition, the final arc length incorporates both the main trend determined by mechanical motion and electromagnetic force, and the rapid fluctuations driven by microscopic random processes, thus realistically simulating the physical picture of the actual arc length randomly varying around its average value. The calculated... This will be directly used in the calculation of heat dissipation power and arc voltage in the subsequent step S3.

[0038] Step S24: Substitute the instantaneous arc current, the dynamic arc radius of the previous moment, and the metal vapor concentration component in the multidimensional random state vector into the implicit equation based on the principle of force balance, and obtain the dynamic arc radius by iterative solution.

[0039] Specifically, this step involves determining the instantaneous equivalent radius of the electric arc by solving a force balance equation. This equation is based on the quasi-steady-state assumption, meaning that the expansion and contraction forces acting radially on the arc are instantaneously balanced. The expansion force is primarily provided by the magnetic pressure (Lorentz force) generated by the arc's own current. The contraction force mainly consists of two parts: first, the thermal contraction pressure caused by the arc's surface radiation; and second, the pressure generated by external airflow dynamics and metal vapor disturbance. The specific form of the balance equation is as follows: This equation represents the dynamic arc radius. The implicit equation. The left side of the equation represents the magnetic expansion force per unit area, where... It is the vacuum permeability. It is the instantaneous arc current. is the radius of the electric arc at the current moment, which needs to be determined. The right side of the equation represents the total contraction pressure, where... It is the static pressure of the arc-extinguishing medium; It is radiation pressure, which is the current arc temperature. The function, and It needs to be done through another relation. Arc conductance at the previous moment Current radius to be determined and current arc length Iterative solution, here It is a function of plasma conductivity as a function of temperature; It is a coefficient; This is the metal vapor concentration component in the microscopic random state vector, and this term introduces random pressure perturbations. During the solution process, the known... , , and Substituting the values, numerical iterative algorithms such as the Newton-Raphson method are used to solve the above coupled equations until convergence, ultimately obtaining the dynamic arc radius at the current moment that satisfies the force equilibrium condition. .

[0040] The method provided in this embodiment, on the one hand, uses a nonlinear mapping containing an arctangent function to calculate the base length, thereby reasonably characterizing the electromagnetic stretching effect of current on the arc and avoiding the limitations of a simple linear model; on the other hand, by combining the microscopic random state components and their rate of change with the macroscopic current and spacing to construct independent random fluctuation terms, it achieves the separation and quantitative modeling of the length randomness caused by two different physical mechanisms, turbulence and speckle motion; furthermore, by constructing implicit equations based on the balance of magnetic pressure, radiation pressure and random aerodynamic pressure to solve for the radius, it physically couples the dynamic evolution of the arc radius with multiple factors such as current, temperature, conductivity and random disturbances, so that the determination of the radius is transformed from a simple parameterized assumption to a calculation result based on physical principles.

[0041] In some embodiments, substituting the instantaneous arc current, the dynamic arc radius of the previous moment, and the metal vapor concentration component in the multidimensional random state vector into an implicit equation based on the principle of force balance, and obtaining the dynamic arc radius through iterative solution, includes: Step S241: Construct a force balance equation that includes a magnetic pressure expansion term, a radiation contraction term, and an aerodynamic pressure term.

[0042] Specifically, the implementation of this step involves establishing a mathematical expression for the physical equilibrium relationship governed by the arc radius. The core idea of ​​this equation is that at any given instant, the pressure causing the arc column to expand outwards is balanced with the pressure causing it to contract inwards. The expansion force originates solely from the self-generated magnetic field produced by the electric current, i.e., magnetic pressure. The contraction force mainly considers two mechanisms: first, the arc radiates energy outwards due to its high temperature, and the recoil effect of this radiation is equivalent to an inward radiation pressure; second, the dynamic pressure of the external cooling airflow (such as SF6) compresses the arc, as well as any possible random disturbances. Therefore, the constructed force balance equation formally makes the magnetic pressure per unit area equal to the sum of the radiation pressure and the aerodynamic pressure per unit area. The left side of the equation is the magnetic pressure term, expressed as follows: ,in It is the vacuum permeability constant. It is instantaneous current. The dynamic arc radius is the unknown quantity. The inverse relationship between the square of the current and the square of the radius reflects the physical nature of magnetic pressure. The right side of the equation is the contraction pressure term, which is constructed as the sum of several parts: a radiation contraction term. It is the radius. and arc temperature Functions; aerodynamic pressure term It is the airflow speed. The function; and a reserved additional term to accommodate random perturbations introduced in subsequent steps.

[0043] Step S242: Input the square value of the instantaneous arc current into the calculation function of the magnetic pressure expansion term.

[0044] Specifically, this step involves providing a definite expansion force drive for the force balance equations. In the computer program, the instantaneous arc current value at the current simulation time step is read in real-time from the external circuit solution interface. Then, immediately calculate the square of the current value, i.e. This squared value is directly substituted into the expression for the magnetobaric expansion term on the left-hand side of the force balance equation constructed in step S241, serving as the key input for calculating the magnitude of the magnetobaric pressure at the current moment. Specifically, this involves calculating... This term. Because the equation is implicit (radius). (Appearing on both sides of the equation simultaneously), in the iterative solution process, a radius value is assumed for each iteration. They all need to use this fixed one. This is used to calculate the corresponding magnetic pressure value. The introduction of the square of the current accurately reflects the quadratic relationship between electromagnetic force and current intensity, and is the main factor determining whether an electric arc can maintain a large cross-section.

[0045] Step S243: Input the dynamic arc radius of the previous moment and the instantaneous arc current into an algebraic relationship about the arc temperature to calculate the current arc temperature, and input the current arc temperature into the calculation function of the radiation contraction term.

[0046] Specifically, this step involves establishing the relationship between arc temperature and radius, current, and conductance, and using this relationship to calculate radiation pressure. First, it is necessary to establish a mechanism for solving for arc temperature from known quantities. The algebraic relationship is based on the plasma conductivity formula and Ohm's law. The specific formula is: This formula is used to iteratively solve for the current temperature. Wherein, It is the arc conductance known at the previous moment. and These are characteristic constants of plasma materials. It is the Boltzmann constant. It is the dynamic arc radius that was obtained at the previous moment. This is the current effective arc length at any given moment (already calculated by S23). In solving for the current radius... In the iterative process, a current temperature is needed to estimate the radiation pressure. The temporary value. At this point, the radius from the previous time step can be used. As Substituting the initial guess into the above relationship, we can solve for the corresponding estimated arc temperature. Then, this estimated temperature value... Substitute the terms into the calculation function for the radiation contraction term. The radiation contraction term is usually expressed in the form of the Stefan-Boltzmann law: in, It is the radiation coefficient of the electric arc. It is the Stefan-Boltzmann constant. In this way, the current, the radius at the previous moment, and the current length are linked through temperature, and the corresponding radiation pressure is calculated.

[0047] Step S244: Add the metal vapor concentration component in the multidimensional random state vector as a random pressure disturbance term to the aerodynamic pressure term.

[0048] Specifically, this step involves introducing microscopic randomness into aerodynamic pressure to simulate the stochastic effects of metal vapor splashing on arc cooling and stability. This is achieved by using the current-moment microscopic random state vector stored in memory. From this, we extract its third component, namely the metal vapor concentration fluctuation component. This component is a random variable with a mean of zero, and its value can be positive or negative, representing a random deviation from the average concentration. This component is then multiplied by a preset pressure disturbance coefficient. This forms a random pressure disturbance term. Finally, this term is combined with the fundamental aerodynamic pressure term determined by the airflow velocity. Add them together to form a complete aerodynamic pressure term. On the right-hand side of the force balance equation constructed in step S241, this synthesized aerodynamic pressure term will be added to the radiation contraction term. Through this operation, the originally deterministic aerodynamic pressure is endowed with the characteristics of random fluctuations, so that the arc radius is not only affected by the average airflow during the solution process, but also by the additional pressure disturbances caused by the random fluctuations in metal vapor concentration, thus more realistically reflecting the complex multiphase flow random interactions within the arc-extinguishing chamber.

[0049] Step S245: Based on the force balance equation, the dynamic arc radius that satisfies the balance condition is solved by a numerical iterative algorithm.

[0050] Specifically, this step involves determining a unique equilibrium radius through numerical calculation. The complete force equilibrium equation, prepared after steps S242, S243, and S244, is used as the objective function. : Notice, It is itself through the relation in S243 and It is calculated using its iterative current value and known quantities, therefore it is also The function is solved using the Newton-Raphson iterative method: First, an initial guess is given, for example, using the radius from the previous time step. Then, the iteration loop begins. In the... In the next iteration, the current radius guess is used. : (1) Calculate the current temperature estimate (Using the S243 relation, Alternative (Inverse solution).

[0051] (2) Calculate the function value and its impact derivative (The dependence of temperature on radius needs to be considered).

[0052] (3) Update the formula according to Newton's method: .

[0053] (4) Check the convergence conditions, for example ( (This is the preset tolerance). If satisfied, then... That is, the dynamic arc radius at the current moment. If not satisfied, then let Return to step (1) and continue iterating until convergence or the maximum number of iterations is reached.

[0054] The method provided in this embodiment, on the one hand, elevates the determining factors of the arc radius from empirical correlation to a quantitative relationship based on fundamental principles by explicitly constructing a force balance physical equation based on magnetic pressure, radiation pressure, and aerodynamic pressure; on the other hand, it achieves close interaction between energy state and mechanical balance by establishing a coupled calculation process that uses the conductivity, radius, and current length of the previous moment to iteratively solve for the current temperature and correlates the temperature with the fourth power of the radiation pressure; furthermore, by directly adding the random component of the metal vapor concentration as a pressure disturbance term to the aerodynamic pressure, microscopic randomness is introduced at the mechanical balance level, making the final solved arc radius a dynamic variable affected by random processes, rather than a deterministic value.

[0055] In some embodiments, the step of calculating the dynamic time constant, morphology-related heat dissipation power, and arc voltage correction based on the random effective arc length and the dynamic arc radius, and then solving the improved Mayr differential equation to update the arc conductance, includes: Step S31: Calculate the dynamic time constant based on the dynamic arc radius and the thermodynamic imbalance component in the multidimensional random state vector.

[0056] Specifically, this step involves calculating the energy relaxation timescale based on the thermal inertia characteristics of the electric arc and its deviation from equilibrium. The time constant in the Mayr model... Essentially, it reflects the thermal time constant of the electric arc, that is, the rate at which the arc temperature (or conductivity) responds to changes in input power. Its implementation is based on the following physical understanding: the heat capacity of the arc is related to the volume of the arc column, i.e., to the dynamic arc radius. It is proportional to the square of the energy; however, the rate of energy relaxation may be affected by whether the local arc plasma is in thermodynamic equilibrium. The calculation formula is designed as follows: In this formula, Represents time The dynamic time constant. It is a basic proportional coefficient. It is the equivalent density of the electric arc plasma. It is its equivalent specific heat capacity, therefore Heat capacity per unit volume. The molecule represents the cross-sectional area of ​​an electric arc per unit length. It is proportional to the heat capacity per unit length of the electric arc. It is the equivalent thermal conductivity, representing the ease with which heat is dissipated. Ratio Having a time dimension, it constitutes the physical basis of the time constant, indicating that the larger the radius, the greater the heat capacity, and the slower the heat dissipation, the longer the time constant. It is a modulation coefficient. It is a microscopic random state vector The fourth component is the thermodynamic imbalance component. Random modulation was introduced: when When (deviating from equilibrium), the time constant is amplified, indicating that relaxation slows down; when When the time constant is reduced, it indicates that relaxation is accelerated. Thus, the time constant becomes a dynamic parameter related to the instantaneous shape and microscopic random state of the electric arc.

[0057] Step S32: Based on the dynamic arc radius and the random effective arc length, calculate the convective heat dissipation power and the radiative heat dissipation power respectively, and generate a turbulence-enhanced heat dissipation term according to the turbulence intensity component in the multidimensional random state vector to correct the convective heat dissipation power, so as to obtain the morphology-related heat dissipation power.

[0058] Specifically, this step involves quantifying the rate at which the electric arc loses energy across its surface, while considering the enhancement of heat dissipation efficiency by turbulence. The calculation of heat dissipation power depends on the heat dissipation surface area of ​​the electric arc. First, the heat dissipation surface area is calculated. : in, It is the dynamic arc radius. It is the random effective arc length. This is the lateral surface area of ​​the equivalent cylindrical electric arc column.

[0059] Convection heat dissipation power The calculation uses Newton's law of cooling: in, It is the convective heat transfer coefficient. It is the current arc temperature (which can be calculated by relating it to the current conductance, radius, and length using the formula in S243). It refers to the ambient temperature.

[0060] Radiant heat dissipation power The calculations use the Stefan-Boltzmann law: in, It is the radiation coefficient of the electric arc. It is the Stefan-Boltzmann constant.

[0061] Turbulence-enhanced heat dissipation This is used to simulate the enhancing effect of turbulent mixing on convective heat dissipation. It is based on convective heat dissipation power and consists of turbulence intensity components in a microscopic random state vector. Modulation: in, It is an enhancement factor. Because... It is a random variable, and this term adds a random fluctuation component to the heat dissipation power.

[0062] Finally, the total heat dissipation power related to the form factor. The sum of the three: This power figure comprehensively reflects the combined effects of arc size (radius, length), temperature, and turbulent randomness on heat dissipation capacity.

[0063] Step S33: The random effective arc length and the speckle jump component in the multidimensional random state vector are used as inputs for linear and nonlinear terms, respectively, to generate the arc voltage correction amount.

[0064] Specifically, the implementation of this step involves constructing a complete expression for the arc voltage, which includes the arc column voltage drop and the electrode voltage drop, the latter being random. Classical models often simplify the arc voltage to... This step involves making corrections. Arc voltage correction amount. The calculation formula is: The formula contains three terms. The first term... It is a classic arc-column resistor voltage drop, in which For instantaneous current, This represents the arc conductance at the previous moment. (Second term) It is a linear term, where It is the constant electric field strength (voltage drop per unit length) of the arc column. This is the random effective arc length. This term reflects the fundamental physical relationship that voltage increases linearly with arc length, and transmits the randomness of the length to the voltage. (Third term) This is a nonlinear term used to simulate the random fluctuations in the cathode and anode voltage drops. It is the nominal amplitude of the electrode voltage drop. It is the speckle jump activity component in the micro-random state vector. It is the hyperbolic tangent function, which is used to transform a random variable... The value is smoothly limited to Within the range. Random fluctuations in electrode voltage drop originate from the unstable motion of the cathode spot; this term directly maps this microscopic randomness to random fluctuations in voltage output.

[0065] Step S34: Substitute the dynamic time constant, the morphology-related heat dissipation power, and the arc voltage correction into the improved Mayr differential equation, and combine it with the instantaneous arc current to update the arc conductance through numerical integration.

[0066] Specifically, this step involves numerically solving the core energy balance differential equation of the model. The improved Mayr differential equation takes the following form: The left side of the equation is the arc conductance. Regarding time The derivative of . The first term on the right-hand side of the equation is in the form of the classic Mayr equation, but with different parameters. , , All have been replaced with dynamic values ​​calculated by the aforementioned steps S31, S32, and S33. This is the instantaneous current. This term describes the energy input. With heat dissipation How does the imbalance lead to changes in conductivity? The second term on the right-hand side of the equation is a newly added nonlinear term, in which... It is a coefficient. It is a very small lower limit of conductivity. This is the current dynamic arc radius. This simulation is performed under conditions of zero current crossing and conductance... Approaching At that time, due to intense heat dissipation, the arc column may experience a cross-sectional "collapse" or "fracture" effect. Its strength is inversely proportional to the cube of its radius; that is, the smaller the radius, the stronger the collapse effect. In the simulation, at time step... The known place , , , , and the arc conductance at the previous moment Substitute into the right side of the equation. Since the equation may be rigid, use a numerical integrator suitable for rigid differential equations, such as the Gear algorithm, to calculate from... arrive The change in conductance is used to update the arc conductance at the current moment. .

[0067] The method provided in this embodiment, on the one hand, establishes a functional relationship between the time constant and the square of the dynamic radius and the thermodynamic random state components, enabling the energy relaxation rate to adaptively change with the arc size and micro-equilibrium state, thus breaking through the limitation of the fixed time constant in traditional models; on the other hand, it constructs a heat dissipation power model that is precisely coupled with the instantaneous geometry and random flow state of the arc by calculating convective and radiative heat dissipation based on the surface area of ​​the arc shape and introducing an enhancement term modulated by the turbulent random component; furthermore, by explicitly introducing a linear term proportional to the random length and a nonlinear electrode voltage drop term related to the speckle jump random component into the arc voltage expression, it completely maps the macroscopic length fluctuations and the randomness of the micro-electrode process into random fluctuations of the voltage output, providing a more realistic input for the energy balance equation.

[0068] In some embodiments, the step of calculating convective heat dissipation power and radiative heat dissipation power based on the dynamic arc radius and the random effective arc length, respectively, and generating a turbulence-enhanced heat dissipation term based on the turbulence intensity component in the multidimensional random state vector to correct the convective heat dissipation power to obtain the morphology-related heat dissipation power includes: Step S321: Multiply the dynamic arc radius by the random effective arc length to obtain the arc heat dissipation surface area.

[0069] Specifically, the implementation method of this step involves calculating the effective area for heat exchange between the electric arc and the surrounding medium. The calculation formula is directly as follows: In this formula, Represents time The surface area for arc heat dissipation. It is the dynamic arc radius at the current moment. It is the current random effective arc length. (Constant) This formula originates from the calculation of the lateral surface area (circumference) when an electric arc is approximated as a cylinder. Multiply by length This calculation forms the basis for all subsequent heat dissipation power calculations, fusing the two-dimensional morphological information of the electric arc (radial and axial dimensions) into a single key geometric feature. This surface area dynamically changes with the expansion or contraction of the radius, and the stretching or random fluctuation of the length.

[0070] Step S322: Calculate the convective heat dissipation power based on the difference between the arc heat dissipation surface area and the arc temperature and ambient temperature.

[0071] Specifically, this step involves applying Newton's law of cooling to calculate the power lost by the electric arc through convection. The formula is as follows: In this formula, Represents time Convection heat dissipation power. It is the convective heat transfer coefficient, which is a parameter related to the properties of the arc-extinguishing medium (such as SF6 gas) and the flow state (laminar or turbulent). It is usually preset before simulation. The surface area for arc heat dissipation is calculated from step S321. This is the current arc temperature, a value that needs to be obtained through other relationships (e.g., by inversely calculating the plasma conductivity formula from the current conductivity, radius, and length). This refers to the ambient temperature or the background temperature of the arc-quenching medium. The formula shows that convective heat dissipation power is directly proportional to the heat transfer area, the heat transfer coefficient, and the temperature difference between the arc and the environment. This is one of the main mechanisms of heat dissipation, especially in the medium and low temperature ranges.

[0072] Step S323: Calculate the radiative heat dissipation power based on the fourth power of the arc heat dissipation surface area and the arc temperature.

[0073] Specifically, this step involves applying the Stefan-Boltzmann law to calculate the power lost by the electric arc through thermal radiation. The calculation formula is as follows: In this formula, Represents time Radiative heat dissipation power. It is the emissivity (or emissivity) of the arc plasma, with a value between 0 and 1, indicating how close it is to blackbody radiation. It is the Stefan-Boltzmann constant, a physical constant. The surface area for arc heat dissipation is calculated from step S321. This is the current arc temperature. The formula shows that radiative heat dissipation is proportional to the surface area, the emissivity, and also proportional to the fourth power of the absolute temperature. Due to this high-power dependence of temperature, radiative heat dissipation will become the dominant heat dissipation mechanism during the high-temperature phase of the arc (e.g., near the current peak).

[0074] Step S324: The turbulence intensity component in the multidimensional random state vector is used as a modulation factor and multiplied with the convective heat dissipation power to generate the turbulence-enhanced heat dissipation term.

[0075] Specifically, this step involves quantifying the stochastic enhancement effect of turbulence on heat dissipation efficiency. The calculation formula is as follows: In this formula, Represents time Turbulence-enhanced heat dissipation. It is a positive enhancement factor used to adjust the intensity of turbulence effects. It is the microscopic random state vector at the current moment. The first component in the equation is the turbulence intensity random factor. This component is a random variable with zero mean, obtained in the simulation by solving stochastic differential equations. This is the convective heat dissipation power calculated in step S322. The turbulence intensity component... As a modulation factor and Multiplication means when When, convective heat dissipation is enhanced; when At this time, convective heat dissipation is reduced (but the total heat dissipation power will not be negative, because this term is added to the total power, and usually...). (To ensure physical plausibility). This simulates how turbulent mixing randomly enhances energy exchange in the thermal boundary layer.

[0076] Step S325: Add the convective heat dissipation power, the radiative heat dissipation power and the turbulence-enhanced heat dissipation term to obtain the morphology-related heat dissipation power.

[0077] Specifically, this step involves summing all heat dissipation mechanisms to obtain the total heat dissipation power. The calculation formula is as follows: In this formula, Convection heat dissipation power calculated in step S322 1. Radiative heat dissipation power calculated in step S323 And the turbulence-enhanced heat dissipation term calculated in step S324 The linear superposition of these factors. This total power comprehensively reflects: the heat dissipation surface area determined by the dynamic radius and random length of the electric arc (influenced by...). and Temperature, determined by the energy state of the electric arc (affects) and ), and the random fluctuations in heat dissipation efficiency determined by the microscopic random turbulence state (affecting) This total power will be directly used in the improved Mayr differential equation as a dissipation term in the energy balance.

[0078] The method provided in this embodiment, on the one hand, provides a unified, time-evolving geometric basis for all heat dissipation mechanisms by accurately calculating the arc heat dissipation surface area based on the dynamic radius and random length; on the other hand, it distinguishes and quantifies the two main heat dissipation mechanisms based on different physical principles by calculating the convection and radiation power according to Newton's law of cooling and Stefan-Boltzmann's law respectively; furthermore, by introducing the turbulent random component as a modulation factor into the convection heat dissipation term, it embeds the random efficiency fluctuation driven by flow instability into the heat dissipation model, so that the total heat dissipation power not only depends on the average state, but also includes the physically real random disturbance component.

[0079] In some embodiments, the step of feeding back the evolution parameters of the multidimensional random state vector based on the power imbalance calculated from the arc conductance, and adaptively adjusting the secondary empirical coefficients in the dynamic arc radius and the dynamic time constant, and generating a Mayr arc model containing a fixed parameter mapping function and a core state equation after a complete time-domain iteration, includes: Step S41: Calculate the instantaneous power imbalance based on the arc conductance, the arc voltage correction, and the morphology-related heat dissipation power.

[0080] Specifically, this step involves real-time assessment of the arc energy balance and power imbalance. Defined as the difference between the instantaneous input power and the instantaneous heat dissipation power of the electric arc. Its calculation formula is: In this formula, Represents time Instantaneous power imbalance. It is the arc voltage correction amount calculated in step S33. It is the instantaneous arc current from an external circuit. Therefore, It represents the electrical power input from the circuit to the electric arc per unit time. The morphology-dependent heat dissipation power calculated in step S32 represents the heat power lost by the electric arc to the environment per unit time through various mechanisms. The difference between the two is... This reflects the net heat gain (or net heat loss) rate of the electric arc. When When the electric arc gains net energy, it tends to heat up and expand; when At this time, the electric arc loses net energy and tends to cool and contract. This value is an important basis for subsequent feedback regulation.

[0081] Step S42: Using the absolute value of the instantaneous power imbalance as input, dynamically adjust the state transition matrix elements in the stochastic differential equation of the multidimensional random state vector.

[0082] Specifically, the implementation of this step involves establishing a negative feedback loop from macroscopic energy states to microscopic stochastic evolution laws. Specifically, the focus is on adjusting the state transition matrix of the stochastic differential equation system described in step S1. Select the component in the matrix that corresponds to the thermodynamic disequilibrium degree. diagonal elements related to the self-relaxation rate As the parameter to be adjusted, its adjustment rules are designed as follows: In this formula, It is the value of the state transition matrix element after adjustment at the current moment. This is its base value (default value). It is a positive feedback strength coefficient. It is the absolute value of the instantaneous power imbalance calculated in step S41. This formula shows that when the power imbalance is severe ( When the arc is large, the electric arc state is far from equilibrium. A decrease in the value of indicates that the thermodynamic imbalance component The slower rate of regression to its mean allows the random component to deviate more significantly, which can affect the time constant via S31, and consequently the evolution of conductance, forming a regulatory loop. Conversely, when power approaches equilibrium, When the system approaches the baseline value, it evolves according to a default random pattern.

[0083] Step S43: Adjust the coefficients of the turbulence fluctuation term used to calculate the random effective arc length based on the time derivative of the arc conductance.

[0084] Specifically, this step involves linking the rapid changes in the arc state with the turbulence intensity. The turbulence fluctuation term coefficient refers to the coefficient calculated in step S22. The coefficient used at that time Its adjustment rule is based on the rate of change of arc conductance. (Numerically, it can be expressed as a difference) approximate): In this formula, It is the coefficient of the turbulence fluctuation term adjusted at the current moment. This is its base value. It is a positive sensitivity coefficient. It is the absolute value of the rate of change of arc conductivity. This rule means that when conductivity decreases rapidly (e.g., when the arc extinguishes violently before or after the current crosses zero), the amplitude of the length fluctuation caused by turbulence will be amplified. (Increase). This physically corresponds to the possibility that the drastic cooling and contraction process may induce stronger fluid instabilities (turbulence). Adjusted This will be immediately used for the random effective arc length in the next time step (or the next iteration of the current step). The calculation.

[0085] Step S44: During the simulation, based on the real-time ratio of the dynamic arc radius to the radiative heat dissipation power, fine-tune the secondary empirical coefficients used in calculating the dynamic arc radius and the dynamic time constant.

[0086] Specifically, this step involves online optimization of some empirical parameters based on the internal state of the model during runtime. First, a real-time scaling factor is calculated. : This factor approximately reflects the relative importance of radiative heat dissipation in the current total heat dissipation (compared to a reference radiative power). Then, according to The value of is used to fine-tune some secondary empirical coefficients used in calculating the dynamic arc radius and dynamic time constant. For example, a simple linear adjustment rule can be set: if Continuously above the threshold Over a period of time, the coefficient related to radiation pressure is slightly increased, or the base value of the time constant is decreased. The adjustments are made to make the model behavior more consistent with the high-temperature arc characteristics, which are dominated by radiative heat dissipation; conversely, adjustments are made to make the model behavior less consistent with the known experimental characteristics of the target circuit breaker. This fine-tuning is smooth and slow, aiming to make the model's macroscopic performance (such as the average arc voltage level) throughout the simulation process consistent with the known experimental characteristics of the target circuit breaker.

[0087] Step S45: After completing the time-domain iterative calculation for a preset duration, output the mapping function for calculating the random effective arc length and the dynamic arc radius, the calculation rule for the dynamic time constant and the heat dissipation power related to the shape, and the improved Mayr differential equation, which together constitute the Mayr arc model.

[0088] Specifically, this step involves solidifying the dynamic simulation process into a static, reusable model. From the initial moment... until the end time After the complete time loop ends, the program performs the following packaging operations: (1) Extract and solidify the packaging material finally determined in steps S21, S22, and S23, which is used to package the product from the packaging process. , , calculate All functions and coefficients (including the final ones adjusted by S43) (2) Extract and solidify the value finally determined in step S24, used to extract from , , , Calculation The force balance equations, iterative algorithms, and related parameters (including the correlation coefficients after fine-tuning in S44) are extracted and solidified. (3) The parameters finally determined in steps S31, S32, and S33 are used for calculation. , , All formulas and coefficients (including the relevant time constant coefficients after S44 fine-tuning). (4) Record the final form of the improved Mayr differential equations (the equations in S134). Encapsulate these elements into a data structure or configuration file to generate the Mayr arc model. This model contains all parameter mappings and core dynamic equations optimized for the specific operating conditions (current, circuit breaker type) represented by this simulation, and can be independently called to predict arc behavior under similar excitations.

[0089] The method provided in this embodiment, on the one hand, establishes a dynamic correlation between the micro-random process and the macro-energy balance state by using the instantaneous power imbalance feedback to modulate the micro-random state evolution matrix, thereby achieving adaptive coordination of the model's internal state; on the other hand, by adjusting the length turbulence coefficient according to the rate of change of conductivity, it links the severity of the overall arc decay with local flow instability, enhancing the physical realism of the model in transient processes such as current zero crossing; furthermore, by proportionally fine-tuning the secondary coefficients based on the runtime heat dissipation mechanism, the model can perform subtle self-calibration for different operating points without changing the core physical framework, ultimately outputting a customized Mayr arc model instance that has undergone complete operating condition iterative optimization, has solidified parameter rules, and can be directly used for probabilistic simulation.

[0090] Please see Figure 2 , Figure 2 A schematic block diagram of the Mayr arc model construction system 100 based on dynamic arc radius and random length provided in this application embodiment is shown below. Figure 2 As shown in the embodiment of this application, the Mayr arc model construction system 100 based on dynamic arc radius and random length includes: Module 110 is used to establish and solve a coupled stochastic differential equation system to generate a multidimensional stochastic state vector characterizing the microscopic instability inside the electric arc.

[0091] The first calculation module 120 is used to calculate the random effective arc length and dynamic arc radius based on the multidimensional random state vector, the instantaneous arc current and the mechanical distance between the contacts, through a nonlinear mapping function.

[0092] The second calculation module 130 is used to calculate the dynamic time constant, the morphology-related heat dissipation power and the arc voltage correction based on the random effective arc length and the dynamic arc radius, and to solve the improved Mayr differential equation to update the arc conductance.

[0093] The modulation module 140 is used to feed back the evolution parameters of the multidimensional random state vector based on the power imbalance calculated by the arc conductance, and to adaptively adjust the secondary empirical coefficients in the dynamic arc radius and the dynamic time constant. After a complete time domain iteration, a Mayr arc model containing a fixed parameter mapping function and a core state equation is generated.

[0094] It should be noted that those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system and its modules described above can be referred to in the aforementioned embodiment of the Mayr arc model construction method based on dynamic arc radius and random length, and will not be repeated here.

[0095] The above description is merely a specific embodiment of this application, but the scope of protection of this application 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 this application, and these modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for constructing a Mayr arc model based on dynamic arc radius and random length, characterized in that, include: Establish and solve a coupled stochastic differential equation system to generate a multidimensional stochastic state vector characterizing the microscopic instability inside the electric arc; Based on the multidimensional random state vector, the instantaneous arc current, and the mechanical distance between the contacts, the random effective arc length and the dynamic arc radius are calculated using a nonlinear mapping function. Based on the random effective arc length and the dynamic arc radius, the dynamic time constant, the morphology-related heat dissipation power and the arc voltage correction are calculated, and the improved Mayr differential equation is solved to update the arc conductance. Based on the power imbalance calculated from the arc conductance, the evolution parameters of the multidimensional random state vector are fed back and modulated, and the secondary empirical coefficients in the dynamic arc radius and the dynamic time constant are adaptively adjusted. After a complete time domain iteration, a Mayr arc model containing a fixed parameter mapping function and a core state equation is generated.

2. The method for constructing a Mayr arc model based on dynamic arc radius and random length according to claim 1, characterized in that, The establishment and solution of the coupled stochastic differential equation system to generate a multidimensional stochastic state vector characterizing the microscopic instability within the electric arc includes: The four components of the multidimensional random state vector are defined, and the four components correspond to turbulence intensity, cathode spot jumping activity, metal vapor concentration and thermodynamic disequilibrium, respectively. The instantaneous arc current and the geometric parameters of the arc-extinguishing chamber are input as time-varying coefficients into a preset stochastic differential equation; The stochastic differential equation is solved using numerical methods, and a micro-stochastic state vector consisting of four random variables is obtained at each time step.

3. The method for constructing a Mayr arc model based on dynamic arc radius and random length according to claim 1, characterized in that, The step of calculating the random effective arc length and dynamic arc radius based on the multidimensional random state vector, instantaneous arc current, and contact mechanical distance using a nonlinear mapping function includes: Substitute the contact mechanical spacing and the instantaneous arc current into the first mapping function to generate a deterministic base length; The rate of change of the turbulence intensity component and the speckle jump component in the multidimensional random state vector are combined with the instantaneous arc current and the mechanical distance between the contacts to calculate the length random fluctuation term. The base length is superimposed with each of the random fluctuation terms of the length to obtain the random effective arc length; The instantaneous arc current, the dynamic arc radius of the previous moment, and the metal vapor concentration component in the multidimensional random state vector are substituted into an implicit equation based on the principle of force balance, and the dynamic arc radius is obtained by iterative solution.

4. The method for constructing a Mayr arc model based on dynamic arc radius and random length according to claim 3, characterized in that, The step of substituting the instantaneous arc current, the dynamic arc radius of the previous moment, and the metal vapor concentration component in the multidimensional random state vector into an implicit equation based on the principle of force balance, and obtaining the dynamic arc radius through iterative solution, includes: Construct a force balance equation that includes magnetopressure expansion, radiation contraction, and aerodynamic pressure terms; The square of the instantaneous arc current is input into the calculation function of the magnetic pressure expansion term; The dynamic arc radius of the previous moment and the instantaneous arc current are input into an algebraic relationship about the arc temperature to calculate the current arc temperature, and the current arc temperature is input into the calculation function of the radiation contraction term. The metal vapor concentration component in the multidimensional random state vector is added to the aerodynamic pressure term as a random pressure perturbation term. Based on the force balance equation, the dynamic arc radius that satisfies the equilibrium condition is solved using a numerical iterative algorithm.

5. The method for constructing a Mayr arc model based on dynamic arc radius and random length according to claim 1, characterized in that, The process involves calculating the dynamic time constant, morphology-related heat dissipation power, and arc voltage correction based on the random effective arc length and the dynamic arc radius, and then solving the improved Mayr differential equation to update the arc conductance, including: The dynamic time constant is calculated based on the dynamic arc radius and the thermodynamic imbalance component in the multidimensional random state vector. Based on the dynamic arc radius and the random effective arc length, the convective heat dissipation power and the radiative heat dissipation power are calculated respectively. A turbulence-enhanced heat dissipation term is generated according to the turbulence intensity component in the multidimensional random state vector to correct the convective heat dissipation power, so as to obtain the morphology-related heat dissipation power. The random effective arc length and the speckle jump component in the multidimensional random state vector are used as inputs to the linear and nonlinear terms, respectively, to generate the arc voltage correction amount. Substituting the dynamic time constant, the morphology-related heat dissipation power, and the arc voltage correction into the improved Mayr differential equation, and combining it with the instantaneous arc current, the arc conductance is updated by numerical integration.

6. The method for constructing a Mayr arc model based on dynamic arc radius and random length according to claim 5, characterized in that, The convective heat dissipation power and radiative heat dissipation power are calculated based on the dynamic arc radius and the random effective arc length, respectively. A turbulence-enhanced heat dissipation term is generated based on the turbulence intensity component in the multidimensional random state vector to correct the convective heat dissipation power, thereby obtaining the morphology-related heat dissipation power. This includes: Multiply the dynamic arc radius by the random effective arc length to obtain the arc heat dissipation surface area; The convective heat dissipation power is calculated based on the difference between the arc heat dissipation surface area and the arc temperature and ambient temperature. The radiative heat dissipation power is calculated based on the fourth power of the arc heat dissipation surface area and the arc temperature. The turbulence intensity component in the multidimensional random state vector is used as a modulation factor and multiplied by the convective heat dissipation power to generate the turbulence-enhanced heat dissipation term; The convective heat dissipation power, the radiative heat dissipation power, and the turbulence-enhanced heat dissipation term are added together to obtain the morphology-related heat dissipation power.

7. The method for constructing a Mayr arc model based on dynamic arc radius and random length according to claim 1, characterized in that, The process involves using the power imbalance calculated based on the arc conductance to feed back and modulate the evolution parameters of the multidimensional random state vector, and adaptively adjusting the secondary empirical coefficients in the dynamic arc radius and the dynamic time constant. After a complete time-domain iteration, a Mayr arc model containing a fixed parameter mapping function and a core state equation is generated, including: The instantaneous power imbalance is calculated based on the arc conductance, the arc voltage correction, and the morphology-related heat dissipation power. The absolute value of the instantaneous power imbalance is used as input to dynamically adjust the elements of the state transition matrix in the stochastic differential equation of the multidimensional random state vector. The coefficients for the turbulence fluctuation term used to calculate the random effective arc length are adjusted based on the time derivative of the arc conductance. During the simulation, the secondary empirical coefficients used in calculating the dynamic arc radius and the dynamic time constant are fine-tuned based on the real-time ratio of the dynamic arc radius to the radiative heat dissipation power. After completing the time-domain iterative calculation for a preset duration, the output functions for calculating the mapping function between the random effective arc length and the dynamic arc radius, the calculation rules for the dynamic time constant and the heat dissipation power related to the shape, and the improved Mayr differential equation are used to constitute the Mayr arc model.

8. A Mayr arc model construction system based on dynamic arc radius and random length, characterized in that, include: The module is used to build and solve coupled stochastic differential equation systems to generate multidimensional stochastic state vectors characterizing the microscopic instability inside the electric arc. The first calculation module is used to calculate the random effective arc length and dynamic arc radius based on the multidimensional random state vector, the instantaneous arc current and the mechanical distance between the contacts, through a nonlinear mapping function. The second calculation module is used to calculate the dynamic time constant, the morphology-related heat dissipation power and the arc voltage correction based on the random effective arc length and the dynamic arc radius, and to solve the improved Mayr differential equation to update the arc conductance. The modulation module is used to feed back the evolution parameters of the multidimensional random state vector based on the power imbalance calculated by the arc conductance, and to adaptively adjust the secondary empirical coefficients in the dynamic arc radius and the dynamic time constant. After a complete time domain iteration, a Mayr arc model containing a fixed parameter mapping function and a core state equation is generated.

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