A spatiotemporal evolution model of short circuit arc to secondary arc evolution process

Abstract

The application establishes a short-circuit arc to a potential arc evolution process space-time evolution model, specifically including a short-circuit arc internal space electric field model and a potential arc evolution model with randomness. A large number of ions and electrons exist in the short-circuit arc channel, and the internal electric field of the short-circuit arc model cannot be directly calculated. The application establishes a short-circuit arc internal space electric field model based on a particle swarm algorithm and a simulation charge method to further obtain the short-circuit arc internal space electric field strength. Based on the above short-circuit arc internal electric field model, the short-circuit arc internal space electric field is used as an independent variable of the potential arc development to establish a short-circuit arc to a potential arc evolution model with randomness, and the space form of the potential arc at the evolution time is obtained. The application combines the physical characteristics of the short-circuit arc to the potential arc evolution, realizes the short-circuit arc to the potential arc evolution model based on the existing optimization algorithm, and provides technical support for the potential arc suppression in engineering.

Description

Technical Field

[0001] This invention relates to a method for calculating the spatiotemporal evolution of short-circuit arcs to latent arcs based on particle swarm optimization and simulated charge method, belonging to the field of latent arcs in high-voltage transmission lines. Background Technology

[0002] In my country, renewable energy bases are located far from load centers. To overcome the problem of unbalanced spatial distribution of power resources, long-distance power transmission is essential. According to statistics on faults in existing long-distance, high-voltage transmission lines, single-phase ground faults occur in over 90% of cases. The resulting surging arcs caused by single-phase ground faults severely impact the stability and reliability of the power system. The evolution of short-circuit arcs into surging arcs leads to differences in the initial spatial location of the surging arc, which in turn significantly affects the arc's burning time. Therefore, it is imperative to conduct in-depth research into the development mechanism and physical characteristics of surging arcs.

[0003] In recent years, there has been extensive research on the physical characteristics, formation mechanism, and motion morphology of surging arcs. A short-circuit model based on a chain arc model has been proposed, which incorporates the short-circuit condition of the arc column to better reflect its motion characteristics and closely approximate the actual arc motion. An arc simulation model considering the randomness of the initial position of the surging arc has also been proposed. This model assumes that the spatial position of the surging arc is related to the spatial conductivity, resulting in a dispersed arcing time. This model better reflects the dispersed arcing time characteristic of surging arcs in engineering practice. Other scholars have used nonlinear time-varying resistors to simulate the arc column characteristics of surging arcs, supplementing the extinguishing criteria for surging arcs. Overall, most existing simulation models of surging arcs focus on their volt-ampere characteristics, with only a few models simulating the impact of the surging arc evolution process on the dispersion of arcing time. Therefore, there is still considerable room for research on the evolution process from short-circuit arcs to surging arcs, and it is necessary to improve the evolution mechanism of surging arcs and establish a stochastic model of their evolution. Summary of the Invention

[0004] To address the aforementioned problems, this invention establishes a method for calculating the spatiotemporal evolution of a short-circuit arc to a latent arc based on particle swarm optimization and simulated charge method. Specifically, it includes an internal spatial electric field model of the short-circuit arc and a latent arc evolution model incorporating randomness. The method is characterized by comprising:

[0005] The spatial location of simulated point charges within the short-circuit arc's internal electric field at the instant of its evolution from a short-circuit arc to a latent arc is used as the variable to be optimized. Matching points are set, uniformly distributed on the surface of the short-circuit arc. These matching points can be reasonably simplified using the arc dynamic resistance model. At the moment of evolution, the arc exhibits resistivity, and its resistance value is constant. The surface potential of the short-circuit arc is calculated from the experimentally measured arc voltage. Compared to the traditional simulated charge method where matching points correspond one-to-one with the number of simulated charges, the number of matching points is far greater than the number of simulated charges. No additional verification points are needed when calculating the fitness value, solving the problem of reduced computational efficiency caused by setting verification points. The average potential error function of the potentials at several matching points on the short-circuit arc surface is used as the fitness function, and an improved particle swarm optimization algorithm is used for optimization. Based on the optimal simulated charge obtained through optimization, the internal electric field strength of the short-circuit arc is calculated as the independent variable for the development of the latent arc. An evolution model from a short-circuit arc to a latent arc incorporating randomness is established to obtain the spatial morphology of the latent arc at the moment of evolution.

[0006] Optionally, the method includes:

[0007] S1: Construct a spatial morphology model of the short-circuit arc at the moment of evolution from short-circuit arc to potential arc, set matching points, which are evenly distributed on the surface of the short-circuit arc. The model can be reasonably simplified by the arc dynamic resistance model. At the moment of evolution, the arc exhibits resistance and the resistance value is constant. The surface potential of the short-circuit arc is solved by the arc voltage measured by experiment.

[0008] S2: Initialization parameters, including the number of particles N and the number of simulated charges M in each particle. csm The optimization variable dimension D includes four dimensions: the radial distance r of the simulated charge in cylindrical coordinates with the z-axis, the angle θ between the simulated charge and the positive x-axis, the coordinate z along the z-axis, and the charge q carried by the simulated charge; individual learning factor c1; group learning factor c2; and initial inertia weight factor ω. start Termination inertia weight factor ω end .

[0009] S3: Using the spatial location and charge quantity of the simulated charge as optimization variables, randomly generate an initial particle swarm within the feasible region of the simulated charge.

[0010] S4: Using the spatial location and charge of the simulated point charge, calculate the potential of the above matching point, and calculate the relative error with the known potential of the matching point. Average the error of each point to obtain the fitness function.

[0011] S5: Compare the fitness values ​​of each particle and select the individual extreme value P. best And the group extreme value G within the example group best .

[0012] S6: Incorporate a nonlinearly decreasing inertial weight factor ω. In the initial stage of iteration, a larger weight factor can ensure that the particles have a better global search capability and avoid getting trapped in local conditions. As the iteration progresses and the optimal particle range is determined, a smaller weight factor can ensure the ability to search locally and improve search efficiency.

[0013] S7: Adaptively adjust the optimization variables within each particle based on individual and group extreme values.

[0014] S8: Determine whether the maximum number of iterations has been reached, or whether the fitness value of the optimal particle meets the accuracy requirement, or whether the fitness value of the optimal particle changes less than the preset accuracy for several consecutive iterations. If not, return to S4; if so, output the current optimal position and the optimal charge.

[0015] S9: Based on the spatial morphology of the short-circuit arc, the center position of the cathode arc root is determined as the starting point for the development of the latent arc. The potential development direction of the latent arc is centered on the current development point G. step The upper hemisphere with radius .

[0016] S10: Based on the position and charge information of the optimal simulated charge obtained in S8, calculate the electric field intensity of all potential development points in S9.

[0017] S11: Based on the electric field strength obtained in S10 above, the probability distribution function is obtained and incorporated into the stochastic analysis to obtain the current development position.

[0018] S12: Determine whether the anode forced regression condition is met. If not, return to S9; if it is met, the development of the submerged arc terminates at the anode position.

[0019] Optionally, compared to the traditional analog charge method where the matching points correspond one-to-one with the number of analog charges, the number of matching points set in S1 is much greater than the number of analog charges. Therefore, no additional verification points are needed when calculating the fitness value, which solves the problem of reduced calculation efficiency when setting verification points.

[0020] Optionally, the fitness function in S4 is:

[0021]

[0022] In the formula, i represents the i-th particle; M represents the number of matching points. Calculate values ​​for the matching points; The theoretical value of the j-th matching point.

[0023] The search space for the optimization variable is:

[0024] subject to:positionm(m=1,2,3,…,M)∈Dac

[0025] In the formula, D ac It is the set of boundary spaces of short-circuit arcs.

[0026] Optionally, the inertia weighting factor that is nonlinearly reduced in S6 is:

[0027]

[0028] In the formula, ω(k) is the inertia weight factor at the kth iteration, ω start ω is the initial inertia weighting factor. end To terminate the inertia weighting factor, T max This represents the maximum number of iterations.

[0029] Optionally, the particle position is adaptively adjusted in S7:

[0030]

[0031]

[0032] In the formula, V id X represents the velocity of the i-th particle as it searches in the d-th dimension. id This represents the optimal position of the i-th particle in the d-th dimension, where c1 is the individual learning factor and c2 is the group learning factor, both of which are non-negative constants. 1+ c2∈[0,8], r1 and r2 are random numbers between 0 and 1.

[0033] Optionally, the process of calculating the simulated point charge value using the potential of the matching point includes:

[0034] Use Q j Let j represent the j-th simulated charge, j∈[1,M]. csm ]; Using M i Let i represent the i-th matching point, j∈[1,M], and let the potential of the matching point be...

[0035] According to the superposition principle, the potential at each matching point is generated by the superposition of all simulated charges. Therefore, a system is constructed using M... csm A set of potential equations composed of simulated charges:

[0036]

[0037] Construct equivalent matrix equations:

[0038]

[0039] Where matrix P is the potential coefficient matrix, and its elements P ij P represents the potential coefficient generated by the j-th simulated charge at the i-th matching point;ij It depends only on the simulated charge and the location of the matching point, and is independent of the magnitude of the charge; Let Q be the potential matrix of the matching point; solve the simulated charge matrix Q using the Gaussian column pivoting elimination method.

[0040] Optionally, the method is based on the particle swarm optimization algorithm and the simulated charge method for calculating the electric field intensity inside the short-circuit arc. It calculates the electric field inside the short-circuit arc at the moment of evolution from the short-circuit arc to the potential arc, calculates the probability distribution function of all potential development points, incorporates the probability distribution function into the stochastic analysis process, determines the position of the next development point, and ends the evolution process when the anode forced regression condition is met.

[0041] Optionally, the development direction of the latent arc in S9 is as follows:

[0042]

[0043] In the formula, i represents the i-th development point, and β is the current development point G. i With potential development point G i+1 The angle between the vector formed and the positive z-axis is α, where α is the angle between the projection of this vector onto the xoy plane and the positive x-axis.

[0044] Optionally, the probability distribution function of all potential development points of the potential arc in the current development stage in S10 is:

[0045]

[0046] In the formula, n is the number of possible values ​​for angle α; m is the number of possible values ​​for angle β; E(i,j) represents the electric field intensity amplitude at the potential development point; and P(i,j) represents the probability that the potential development point becomes the next development point.

[0047] Optionally, the probability of each potential development point in S11 is regarded as a probability column vector P. mn×1 One element in the vector transforms the elements in the column vector above:

[0048]

[0049] In the formula, PPi is the new probability column vector PP mn×1 The i-th element in P j It is the j-th element in the original probability column vector.

[0050] In each development process of the submerged arc, PP mn×1 The elements within are subtracted sequentially from the random number k generated by the random distribution function in [0,1]. The process stops when the difference first becomes negative, and the position of the element at this point is recorded, indicating that the element has successfully progressed to that position.

[0051] Optionally, the forced regression condition for the anode arc root in S12 is:

[0052]

[0053] In the formula, x s y s , z s Here are the coordinates of the arc position, x, y, z are the coordinates of the anode electrode, and l s This is the critical distance.

[0054] This invention uses the spatial location and charge of simulated point charges within the space outside the short-circuit arc as optimization variables, and the average potential error of matching points on the surface of the short-circuit arc as the fitness function. It employs an improved particle swarm optimization algorithm for optimization, avoiding the artificial introduction of simulated charge locations in traditional simulated charge methods, thus improving the accuracy of electric field calculations to a certain extent. Addressing the unclear mechanism of the evolution from a short-circuit arc to a latent arc, this invention uses the electric field strength within the short-circuit arc as a condition for the evolution of the latent arc, providing a new approach for determining the evolution mechanism and offering valuable insights. The evolution image of the short-circuit arc to a latent arc obtained by this invention more closely matches the actual arc morphology, and the arcing time of the latent arc calculated by the model obtained by this invention exhibits dispersion, which better reflects the certain randomness inherent in the actual arcing process of a latent arc. Attached Figure Description

[0055] Figure 1 This is a spatial distribution diagram of simulated charges in the optimal particle according to an embodiment of the present invention.

[0056] Figure 2 This is a graph showing the change in fitness value during the optimization iteration process in an embodiment of the present invention.

[0057] Figure 3 This is a schematic diagram illustrating the development direction of the potential arc during the evolution of embodiments of the present invention.

[0058] Figure 4 This is a flowchart of an embodiment of the present invention.

[0059] Figure 5 This diagram illustrates the different spatial morphologies of the latent power arc during the evolution of embodiments of the present invention.

[0060] Figure 6 This is a comparison diagram of the calculated and measured latent arc shape at 0.2s in an embodiment of the present invention.

[0061] Figure 7 This is a schematic diagram illustrating the arcing time dispersion in an embodiment of the present invention. Detailed Implementation

[0062] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0063] The basic principles of this invention will first be introduced below.

[0064] 1. Simulated Charge Method: The simulated charge method is a commonly used numerical solution method in electrostatic field calculations. Based on the uniqueness theorem of electromagnetic fields, it replaces the continuously distributed free charges on the surface of electrodes or conductors, or the bound charges at dielectric interfaces, with a finite number of virtual charges discretely distributed at certain geometric locations outside the target field. Based on the principle of superposition of electric fields, it approximates the electric field intensity generated at any point in three-dimensional space. The application steps of the simulated charge method are as follows:

[0065] 1) Set M inside the electrode csm A simulated charge, represented by Q j Let j represent the j-th simulated charge, j∈[1,M]. csm ];

[0066] 2) Set M matching points at the boundary of the specific field, M i Let i represent the i-th matching point, j∈[1,M], and let the potential of the matching point be...

[0067] 3) According to the superposition principle, the potential at each matching point is generated by the superposition of all simulated charges. Therefore, a system is constructed using M... csm A set of potential equations composed of simulated charges:

[0068]

[0069] Construct equivalent matrix equations:

[0070]

[0071] Where matrix P is the potential coefficient matrix, and its elements P ij P represents the potential coefficient generated by the j-th simulated charge at the i-th matching point; ij It depends only on the simulated charge and the location of the matching point, and is independent of the magnitude of the charge; The potential matrix of the matching points;

[0072] 4) Solve for the simulated charge matrix Q using the Gaussian column pivoting elimination method.

[0073] 2. Particle Swarm Optimization (PSO) is a commonly used method for solving optimal problems. First, particles are initialized at random positions within the feasible region of the variables. Each particle represents a solution to the optimization problem. Depending on the specific problem, the information carried by each particle varies, but the indicators representing the particle's state are fixed: its position, velocity, and fitness function value. Each position update within the feasible region is considered an iteration. After each iteration, the optimal solution for each particle is recorded and assigned to an individual extreme value P. best In all P best The optimal value is selected from the population and assigned to the population extreme value G. best Guided by the population extreme value and the individual extreme value, the particle moves continuously until the fitness function value meets the requirements or reaches the preset number of iterations.

[0074] 1) The inertia weight factor that decreases nonlinearly in the particle swarm optimization algorithm is:

[0075]

[0076] In the formula, ω(k) is the inertia weight factor at the kth iteration, ω start ω is the initial inertia weighting factor. end To terminate the inertia weighting factor, T max This represents the maximum number of iterations.

[0077] 2) Adaptive adjustment of particle positions in particle swarm optimization:

[0078]

[0079] In the formula, V id X represents the velocity of the i-th particle as it searches in the d-th dimension. id This represents the optimal position of the i-th particle in the d-th dimension, where c1 is the individual learning factor and c2 is the group learning factor, both of which are non-negative constants. 1+ c2∈[0,8], r1 and r2 are random numbers between 0 and 1.

[0080] 3. According to empirical formulas, the arc diameter is proportional to the square root of the effective value of the arc current. The diameter of a short-circuit arc is much larger than that of a latent arc. The spatial location of the latent arc's evolution is uncertain, and the development of the short-circuit arc channel is also uncertain. Therefore, an evolution model from a short-circuit arc to a latent arc that incorporates randomness is established. The application steps are as follows.

[0081] 1) Determine the development direction of potential electric arc:

[0082] The specific development direction of the potential arc flash is determined by the following formula:

[0083]

[0084] In the formula, i represents the i-th development point, and β is the current development point G. i With potential development point G i+1 The angle between the vector formed and the positive z-axis is α, where α is the angle between the projection of this vector onto the xoy plane and the positive x-axis.

[0085] 2) Determine the probability distribution function of all potential development points of the potential arc in the current development stage:

[0086]

[0087] In the formula, n is the number of possible values ​​for angle α; m is the number of possible values ​​for angle β; E(i,j) represents the electric field intensity amplitude at the potential development point; and P(i,j) represents the probability that the potential development point becomes the next development point.

[0088] 3) Treat the probability of potential development points as a probability column vector P mn×1 One element in the vector transforms the elements in the column vector above:

[0089]

[0090] In the formula, PPi is the new probability column vector PP mn×1 The i-th element in P j It is the j-th element in the original probability column vector.

[0091] 4) During each development process of the potential arc, PP will be used. mn×1 The elements within are subtracted sequentially from the random number k generated by the random distribution function in [0,1]. The process stops when the difference first becomes negative, and the position of the element at this point is recorded, indicating that the element has successfully progressed to that position.

[0092] 5) The termination of the submerged arc development satisfies the forced regression condition of the anode arc root:

[0093]

[0094] In the formula, x s y s , z s Here are the coordinates of the arc position, x, y, z are the coordinates of the anode electrode, and l s This is the critical distance.

[0095] Example 1:

[0096] This embodiment provides a method for calculating the spatiotemporal evolution process from a short-circuit arc to a latent arc.

[0097] Considering the actual evolution process from a short-circuit arc to a latent arc, the evolution time is set to 0.1s, at which point the short-circuit current is 1.456kA and the instantaneous arc voltage is 2.05kV. First, the spatial position of the simulated point charge within the simulated short-circuit arc's internal electric field at the moment of evolution is used as the variable to be optimized. The average potential error function of the potential at the matching points set on the short-circuit arc surface is used as the fitness function. An improved particle swarm optimization algorithm is used for optimization. Then, based on the optimal simulated charge obtained from the above optimization, the electric field strength value within the short-circuit arc is calculated as the independent variable for the development of the latent arc. A short-circuit arc to latent arc evolution model incorporating randomness is established to obtain the spatial morphology of the latent arc at the moment of evolution.

[0098] Finding the optimal simulated charge using an improved particle swarm optimization algorithm includes:

[0099] 1. Determine the optimization quantity

[0100] In the simulated charge method, the potential coefficient determines the calculation of the simulated charge quantity. As mentioned earlier, the calculation of the potential coefficient is only related to the location of the simulated charge and the matching point, and is independent of the charge quantity of the simulated charge. In a typical transmission line model, the location of the simulated charge can be manually specified. However, a short-circuit arc is no longer a clearly axisymmetric model compared to a transmission line; its spatial shape is more tortuous. Manually specifying the simulated point charge obviously has the drawback of large errors. Furthermore, in the traditional simulated charge method, the matching point is set in a one-to-one correspondence with the simulated charge, and the charge quantity of the simulated charge can only be obtained through Gaussian column pivoting elimination of the matrix equation, increasing the computational complexity. Therefore, this example uses both the spatial location and charge quantity of the simulated point charge as optimization variables. Figure 1 The spatial distribution of point charges and their mirror charges within the optimal particle is shown. This distribution is formed because the simulated charge positions are outside the short-circuit arc channel and the number is much smaller than the number of matching points. In order to satisfy the boundary conditions, they will not be symmetrically distributed on the channel surface.

[0101] 2. Construct the fitness function

[0102] In this embodiment, matching points are set at the boundaries of the short-circuit arc, and their number is much greater than the number of simulated charges. Therefore, there is no need to set separate verification points. The potential at all matching points is calculated using the optimization variables generated in the previous step, and the relative error is calculated with the known potential. The errors of all matching points are averaged to obtain the fitness function. Through continuous iteration, the fitness value is minimized. The optimization function is as follows:

[0103]

[0104] In the formula, i represents the i-th particle; M represents the number of matching points. Calculate values ​​for the matching points; The theoretical value of the j-th matching point.

[0105] The search space for the optimization variable is:

[0106] subject to: position m (m=1,2,3,…,M)∈D ac

[0107] In the formula, D ac It is the set of boundary spaces of short-circuit arcs.

[0108] In this embodiment, the change in the fitness function value with iteration is as follows: Figure 2 As shown, the particle's fitness value surges during iteration; however, the algorithm automatically adjusts to move the particle towards the spatial optimum. An improved simulated charge method is used to solve for the spatial electric field within the short-circuit arc channel, thus providing a computational basis for incorporating it into the spatiotemporal model of stochastic latent arc evolution.

[0109] 3. Parameter initialization

[0110] Before applying the particle swarm optimization algorithm, parameters should be initialized, including the number of particles N and the number of simulated charges M in each particle. csm The optimization variable dimension D includes four dimensions: the radial distance r of the simulated charge in cylindrical coordinates with the z-axis, the angle θ between the simulated charge and the positive x-axis, the coordinate z along the z-axis, and the charge q carried by the simulated charge; individual learning factor c1; group learning factor c2; and initial inertia weight factor ω. start Termination inertia weight factor ω end .

[0111] The spatial morphology of the latent arc at the moment of evolution from a short-circuit arc to a latent arc is calculated using the internal electric field intensity of the short-circuit arc, including:

[0112] 1. Determining the starting position of the submerged arc

[0113] In actual evolution, the electron beam ejected from the metal electrode only occurs at the arc root. The length of the latent arc root is much smaller than the arc column length, so only the randomness of the arc column needs to be considered. The cathode is the main source of electrons inside the arc channel, and the electron concentration and electron velocity are the highest at the cathode. Therefore, in this embodiment, the starting position of the latent arc is set at the center of the cathode arc root.

[0114] 2. Potential development direction identified

[0115] Figure 3 This indicates that the development direction of the potential arc supply is based on the current development point G. i With the center of the circle, l step The upper hemisphere with radius is , where β is The angle between the vector and the positive z-axis, α is the angle between the projection of this vector onto the xoy plane and the positive x-axis. i With G i+1 The spatial coordinate relationships are as follows:

[0116]

[0117] 3. Termination methods of submerged arc power development

[0118] The subsurface arc does not develop indefinitely. Due to the large amount of plasma at the anode position, the subsurface arc cannot detach from the electrode and thus terminates at the anode position, i.e., it is forced to return to the anode root. When the distance between the subsurface arc development point and the anode is less than the critical distance, the subsurface arc breaks down with the anode, where the short-circuit arc radius is used as the critical distance.

[0119] The spatiotemporal evolution model from short-circuit arc to latent arc in this embodiment is as follows: Figure 4 As shown, the specific process includes the following steps:

[0120] S1: Construct a spatial morphology model of the short-circuit arc at the moment of evolution from short-circuit arc to potential arc, set matching points, which are evenly distributed on the surface of the short-circuit arc. The model can be reasonably simplified by the arc dynamic arc resistance model. At the moment of evolution, the arc exhibits resistance and the resistance value is constant. The surface potential of the short-circuit arc is solved by the arc voltage measured by the experiment.

[0121] S2: Initialization parameters, including the number of particles N and the number of simulated charges M in each particle. csm The optimization variable dimension D includes four dimensions: the radial distance r of the simulated charge in cylindrical coordinates with the z-axis, the angle θ between the simulated charge and the positive x-axis, the coordinate z along the z-axis, and the charge q carried by the simulated charge; individual learning factor c1; group learning factor c2; and initial inertia weight factor ω. start Termination inertia weight factor ω end ;

[0122] S3: Using the spatial location and charge quantity of the simulated charge as optimization variables, randomly generate an initial particle swarm within the feasible region of the simulated charge;

[0123] S4: Using the spatial location and charge of the simulated point charge, calculate the potential of the above matching point, and calculate the relative error with the known potential of the matching point. Average the error of each point to obtain the fitness function.

[0124] S5: Compare the fitness values ​​of each particle and select the individual extreme value P. best And the group extreme value G within the example group best ;

[0125] S6: Incorporate a nonlinearly decreasing inertia weight factor ω. In the initial stage of iteration, a larger weight factor can ensure that the particles have a better global search capability and avoid getting trapped in local conditions. As the iteration progresses and the optimal particle range is determined, a smaller weight factor can ensure the ability to search locally and improve search efficiency.

[0126] S7: Adaptively adjust the optimization variables within each particle based on individual and group extreme values;

[0127] S8: Determine whether the maximum number of iterations has been reached, or whether the fitness value of the optimal particle meets the accuracy requirement, or whether the fitness value of the optimal particle changes less than the preset accuracy for several consecutive iterations. If not, return to S4; if so, output the current optimal position and the optimal charge.

[0128] S9: Based on the spatial morphology of the short-circuit arc, the center position of the cathode arc root is determined as the starting point for the development of the latent arc. The potential development direction of the latent arc is centered on the current development point G. step The upper hemisphere with radius [ ].

[0129] S10: Based on the position and charge information of the optimal simulated charge obtained in S8, calculate the electric field intensity of all potential development points in S9;

[0130] S11: Based on the electric field intensity obtained in S10 above, the probability distribution function is obtained and incorporated into the stochastic analysis to obtain the current development position;

[0131] S12: Determine whether the anode forced regression condition is met. If not, return to S9; if it is met, the development of the submerged arc terminates at the anode position.

[0132] Applying the simulated charge spatial location and charge obtained above to the calculation of the evolution from a short-circuit arc to a latent arc, which incorporates randomness, yields the following results: Figure 5 The spatial morphology of the latent arc at the end of the evolution process, as shown, reveals a significant degree of randomness in the spatial morphology of the latent arc at each evolution moment when the present invention is applied. Combining this invention with a multi-field coupled chain arc model allows for the acquisition of the spatial morphology of the latent arc at any given arcing moment. Figure 6 This displays different spatial morphologies of the latent arc when the arcing time is 0.2 s, and compares them with arc images obtained from physical experiments under the same conditions. It can be found that both exhibit a spiraling upward spatial morphology, and the spatial morphology of the arc column portion of the latent arc is also quite similar. Furthermore, to verify the influence of the spatial morphology of the latent arc at the evolution moment on the subsequent arcing time and to validate the accuracy of this model, the dispersion of arcing time under different latent currents calculated by this invention is shown below. Figure 7As shown, the arcing time under different inrush currents exhibits a certain degree of dispersion, which can better reflect the randomness of the inrush arc during the actual arcing process, and the average arcing time is also closer to the average value of the actual arcing time.

[0133] This invention uses the spatial location and charge of simulated point charges in the space outside the short-circuit arc as optimization variables, and the average potential error of the matching points on the surface of the short-circuit arc as the fitness function. It uses an improved particle swarm optimization algorithm for optimization, which avoids the artificial introduction of simulated charge positions in the traditional simulated charge method and improves the calculation accuracy of the electric field to a certain extent.

[0134] This invention addresses the unclear mechanism of the evolution from a short-circuit arc to a latent arc by using the internal electric field strength of the short-circuit arc as a condition for the evolution of the latent arc. This provides a new approach for determining the evolution mechanism of the short-circuit arc to the latent arc and has reference value. The evolution image of the short-circuit arc to the latent arc obtained by this invention more closely matches the actual arc morphology. The arcing time of the latent arc calculated by the model obtained by this invention has dispersion, which can better reflect the certain randomness that latent arcs exhibit in the actual arcing process.

Claims

1. A method for modeling the evolution of short-circuit arcs to latent arcs incorporating randomness, characterized in that, include: S1: Obtain the internal spatial electric field intensity of the short-circuit arc at the moment of its evolution from a short-circuit arc to a latent arc; S2: Based on the spatial morphology of the short-circuit arc, determine the center position of the cathode arc root as the starting point for the development of the potential arc; S3: Based on the current development point G With the center, and l step Using a radius, determine the potential development direction of the latent arc within the upper hemisphere and obtain the potential development point; the potential development direction of the latent arc is: In the formula, i Indicates the first i One development point, β Current development point G i With potential development points G i+1 The vector formed by z The angle along the positive direction of the axis. α Is this vector in xoy Projection of a plane and x The angle between the positive axis and the axis; S4: according to the short-circuit arc internal space electric field intensity, calculate the electric field intensity amplitude at all potential development points in the current development stage E ( i, j ). S5: Amplitude of the electric field strength at all potential development points according to the current development stage E i, j , obtaining the probability distribution function of all potential development points of the potential supply arc:​ In the formula, n It's an angle. α The number of possible values; m It's an angle. β The number of possible values; E ( i , j () represents the amplitude of the electric field strength at the potential development point; P ( i , j () represents the probability that a potential development point will become the next development point; S6: Consider the probability of each potential development point as a probability column vector P mn×1 transforming the elements within the column vector to obtain a new probability column vector PP mn×1 : In the formula, PP i For the new probability column vector PP mn×1 The first i One element, P j The first probability in the original probability column vector j One element; In each development process of the latent supply arc PP mn×1 The elements in the array are sequentially subtracted from the random numbers generated by the random distribution function in [0, 1] k The difference value stops when the negative value first appears, and the element position at this time is recorded, that is, the successful development to the element position; S7: Determine whether the anodic forced regression condition is met; If the conditions are not met, the current development position will be used as the new current development point and the system will return to S3. If satisfied, the development of the latent arc terminates at the anode position, yielding the spatial morphology of the latent arc from the short-circuit arc to the moment of its evolution; wherein, the anode forced regression condition is: wherein x s , y s , z s is the position coordinate of the arc, x , y , z is the position coordinate of the anode electrode, l s is the critical distance.

2. The short circuit arc to arc strike modeling method of claim 1, wherein, The electric field strength inside the short-circuit arc in step S1 is obtained according to the following steps: S1: Construct a spatial morphological model of the short-circuit arc at the moment of evolution from short-circuit arc to potential arc, and set matching points, which are evenly distributed on the surface of the short-circuit arc; S2: The arc dynamic resistance model is simplified to make the arc resistive at the evolution time constant and the resistance value constant, and the short-circuit arc surface potential is solved by the arc voltage measured by the experiment. S3: Initialize particle swarm parameters, including the number of particles. N The number of simulated charges within each particle M csm Optimizing the dimensions of variables D The dimension includes the analog charge in cylindrical coordinates and z radial distance of the axis r ,and x Angle in the positive direction of the axis θ , z Coordinates in the axial direction z The amount of electricity carried by the simulated charge q These four dimensions, individual learning factors c 1. Group learning factor c 2. Initial inertia weighting factor ω start Termination inertia weight factor ω end ; S4: Using the spatial location and charge quantity of the simulated charge as optimization variables, randomly generate an initial particle swarm within the feasible region of the simulated charge; S5: Using the spatial location and charge of the simulated point charge, calculate the potential of the above matching point, and calculate the relative error with the known potential of the matching point. Average the error of each point to obtain the fitness function. S6: Compare the fitness values ​​of each particle and select the individual extreme value. P best and the group extreme value within the example group G best ; S7: Incorporating an inertia weighting factor that reduces nonlinearity. ω In the initial stage of iteration, a larger weight factor can ensure that the particles have a better global search capability. As the iteration progresses and the optimal particle range is determined, a smaller weight factor can ensure the local search capability and improve the search efficiency. Subsequently, the optimization variables within each particle are adaptively adjusted according to the individual extreme value and the group extreme value. S8: Determine whether the maximum number of iterations has been reached, or whether the fitness value of the optimal particle meets the accuracy requirement, or whether the fitness value of the optimal particle changes less than the preset accuracy for several consecutive iterations. If not, return to S5; if so, output the current optimal position and the optimal charge. S9: Based on the current optimal position and optimal charge, calculate the internal spatial electric field intensity of the short-circuit arc at the moment of evolution from the short-circuit arc to the latent arc.

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