Anode temperature value evaluation method in arc diffusion process in arc starting stage of circuit breaker

Abstract

The invention discloses an anode temperature value evaluation method in an arc diffusion process in an arc starting stage of a circuit breaker, and belongs to the technical field of electric power safety. According to the invention, on the basis of the known transient change of the arc to the anode energy flux density distribution in a certain time period, the energy flux density distribution of the fine arc diffusion stage from the 0 moment to the starting point of the time period can be evaluated; the problem that the energy flux density in the fine arc state cannot be evaluated due to the fact that high-density and high-energy fine arc parameters are difficult to stably calculate is solved, and the electrode ablation condition can be evaluated more accurately.

Description

Technical Field

[0001] The invention belongs to the technical field of electric power safety, and in particular relates to a method for numerically evaluating anode temperature in an arc diffusion process during an arc starting stage of a circuit breaker. Background Art

[0002] Circuit breakers are one of the most important electrical equipment in the high voltage field. They play a role in protecting and controlling the power system and need to reliably cut off the load current or short-circuit current. During the circuit breaker opening process, a high-energy arc will be generated between the circuit breakers. Due to the self-contraction effect of the arc, the arc will cause strong ablation of the anode, especially in the arc starting stage, when the arc gradually spreads from a thin arc to the entire electrode plane. At this time, the arc energy will concentrate on a certain area of ​​the electrode and the energy flow density will be extremely high.

[0003] For the transient numerical analysis method of anode temperature distribution, the energy flux density distribution from the arc region is the most important parameter, and the energy flux density distribution depends on the parameter distribution inside the arc. Considering that the plasma density and temperature of the arc are extremely high during the arc starting stage, it is difficult for the existing numerical analysis method to obtain a stable convergent solution. Therefore, the start time of the numerical calculation is generally after 0.5ms after the arc starting.

[0004] However, due to the extremely intense ablation in the arc starting stage, the existing assessment of transient anode temperature distribution will be significantly underestimated. In order to more accurately evaluate the anode ablation state, a method needs to be proposed to solve the problem of energy flux density assessment of fine arc ablation in the arc starting stage. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the numerical evaluation method of the anode temperature of the arc diffusion process in the arc starting stage of the circuit breaker provided by the present invention solves the problem that the existing arc model is difficult to stably calculate the plasma parameters and energy flux density of the fine arc in the arc starting stage, and thus cannot accurately evaluate the ablation state of the electrode.

[0006] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a method for numerically evaluating anode temperature of an arc diffusion process in an arc starting stage of a circuit breaker, comprising the following steps: S1, in time step dt In this case, a transient arc simulation model considering the arc diffusion process is used to calculate the arc diffusion from the initial moment. t 0 to end time t 1 arc plasma parameters, and obtain the energy flux density of the arc to the anode at each moment in this time period q ( x ); S2, energy flux density q ( x ) to process the data and obtain the arc root range at each time step. t 0~t 1 The instantaneous arc radius during the arc diffusion process from the arc starting point to the edge r ( t ); S3. r (0) = 0 added to r ( t ), through numerical fitting and interpolation methods, dt For time step evaluation from 0~ t 0, and add the best evaluation result to the instantaneous arc radius r ( t ) to form 0 ~ t 1. The instantaneous arc radius range of the full time range during the period; S4. Within the instantaneous arc radius, the energy flux density distribution of the arc to the anode at each moment q ( x ) to obtain the coordinates of each point t 0~ t 1 Energy flux density of the arc to the anode during the time period ; S5, t 0~ t 1 Based on the energy flow density data in the time period, dt Evaluate for time steps 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) , and combined with t 0~ t 1 Energy flux density of the arc to the anode during the time period , get 0 ~ t 1 Energy flux density of the arc to the anode during the time period ;in, r ( t 0) t = t The instantaneous arc radius at time 0; S6, add 0~ t 1 Energy flux density of the arc to the anode during the time period Q ( t ) to get 0~ t 1 The energy flux density of the arc to the anode at each moment in the time period And the coordinate position at each moment is greater than the instantaneous arc radius r ( t ) is set to zero; S7. Modeling is performed based on the actual structure of the electrode to evaluate the energy flux density over the entire time range. Import and calculate the transient anode temperature based on the anode energy balance equation.

[0007] Furthermore, in step S1, the initial moment satisfies: At the initial moment, the stable solution of arc plasma parameters can be calculated by transient arc simulation model; The initial moment approaches 0; Also, at the initial moment, the arc burning range does not cover the entire electrode plane.

[0008] Further, in step S3, the interpolation method is cubic spline interpolation; The numerical fitting method includes polynomial function fitting, Gaussian function fitting, exponential function fitting and sinusoidal function fitting.

[0009] Furthermore, the number of fitting functions is selected according to the amount of energy flux density data; When the data volume is 2, the fitting function includes a linear function and a linear exponential function; When the data volume is 3, the fitting functions include quadratic function, linear Gaussian function, quadratic exponential function and linear sine function; When the data volume is 4, the fitting functions include cubic function, linear Gaussian function, quadratic exponential function and linear sine function; When the data volume is 5, the fitting functions include quartic function, linear Gaussian function, quadratic exponential function and linear sine function; When the data volume is 6, the fitting functions include quintic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function; When the data volume is 7, the fitting functions include sextic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function; When the data volume is 8, the fitting functions include the seventh-order function, the quadratic Gaussian function, the quadratic exponential function, and the quadratic sine function; When the data volume is 9 to 11, the fitting functions include octane function, cubic Gaussian function, quadratic exponential function and cubic sine function; When the data volume is 12-14, the fitting functions include octonic function, quartic Gaussian function, quadratic exponential function and quartic sine function; When the data volume is 15-17, the fitting functions include octane function, quintic Gaussian function, quadratic exponential function and quintic sine function; When the data volume is 18-20, the fitting functions include octane function, sextaneous Gaussian function, quadratic exponential function and sextaneous sine function; When the data volume is 21-23, the fitting functions include octahedral function, septahedral Gaussian function, quadratic exponential function and septahedral sine function; When the data volume is greater than 24, the fitting functions include octahedral function, octahedral Gaussian function, quadratic exponential function and octahedral sine function.

[0010] Further, in step S5, the evaluation 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) The specific method is: S51. Assume that the current time to be evaluated is t x = t 0– dt ; S52, according to each coordinate point t x + dt ~ t Time-varying energy flux density of the arc to the anode during a period of 1 Q ( t ), using different numerical fitting methods, calculate the corresponding t x The energy flux density of the arc to the anode at the moment; S53, calculate the standard deviation of the energy flux density obtained by different numerical fitting methods, and use the result obtained by the method with the minimum standard deviation as t x The energy flux density of the arc to the anode at the moment, and add it to the time-varying energy flux density In, forming t x ~ t 1. The energy flux density of the arc to the anode during the time period; S54, subtract the current time to be evaluated from dt , update the current time to be evaluated, and determine whether the updated current time to be evaluated is less than 0; If yes, proceed to step S6; If not, return to step S52 until 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) .

[0011] Furthermore, in step S7, the energy balance equation based on the anode is:

[0012] In the formula, represents the electrode material density, represents the specific heat capacity of the electrode material, represents the electrode temperature, represents the thermal conductivity of the electrode material, represents the direction perpendicular to the anode surface, represents the surface normal, represents the distribution of energy flux density in the radial direction of the electrode at the current moment, represents the Hamiltonian operator.

[0013] The beneficial effects of the present invention are: The present invention can evaluate the energy flux density distribution in the fine arc diffusion stage from time 0 to the starting point of the time period based on the transient change of the arc energy flux density distribution to the anode within a known time period, thereby solving the problem that the energy flux density cannot be evaluated in the fine arc state due to the inability to implement arc calculation, so as to more accurately evaluate the electrode ablation situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 A flow chart of a method for numerically evaluating anode temperature during an arc diffusion process in an arc starting stage of a circuit breaker provided by the present invention.

[0015] Figure 2 The present invention provides different numerical processing methods for predicting the arc diffusion process.

[0016] Figure 3 The basis provided by the present invention q ( x ) obtained at some coordinate points Q ( t )curve.

[0017] Figure 4 The 0mm position provided by the present invention Q ( t ) curve original data and evaluation data processing results.

[0018] Figure 5 The 5.5 ms time provided by the present invention q ( x ) Error comparison between original data and evaluation data. DETAILED DESCRIPTION

[0019] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0020] The embodiment of the present invention provides a method for numerically evaluating the anode temperature of the arc diffusion process during the arc starting stage of a circuit breaker. Figure 1As shown, the following steps are included: S1, in time step dt In this case, a transient arc simulation model considering the arc diffusion process is used to calculate the arc diffusion from the initial moment. t 0 to end time t 1 arc plasma parameters, and obtain the energy flux density of the arc to the anode at each moment in this time period q ( x ); S2, energy flux density q ( x ) to process the data and obtain the arc root range at each time step. t 0~ t 1 The instantaneous arc radius during the arc diffusion process from the arc starting point to the edge r ( t ); S3. r (0) = 0 added to r ( t ), through numerical fitting and interpolation methods, dt For time step evaluation from 0~ t 0, and add the best evaluation result to the instantaneous arc radius r ( t ) to form 0 ~ t 1. The instantaneous arc radius range of the whole time range during the period; S4. Within the instantaneous arc radius, the energy flux density distribution of the arc to the anode at each moment q ( x ) to obtain the coordinates of each point t 0~ t 1 Energy flux density of the arc to the anode during the time period ; S5, t 0~ t 1 Based on the energy flow density data in the time period, dt Evaluate for time steps 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) , and combined with t 0~ t 1 Energy flux density of the arc to the anode during the time period , get 0 ~ t 1 Energy flux density of the arc to the anode during the time period ;in, r ( t 0) t =t The instantaneous arc radius at time 0; S6, add 0~ t 1 Energy flux density of the arc to the anode during the time period Q ( t ) to get 0~ t 1 The energy flux density of the arc to the anode at each moment in the time period And the coordinate position at each moment is greater than the instantaneous arc radius r ( t ) is set to zero; S7. Modeling is performed based on the actual structure of the electrode to evaluate the energy flux density over the entire time range. Import and calculate the transient anode temperature based on the anode energy balance equation.

[0021] In step S1 of the embodiment of the present invention, the initial time satisfies: At the initial moment, the stable solution of arc plasma parameters can be calculated by transient arc simulation model; The initial moment approaches 0; Also, at the initial moment, the arc burning range does not cover the entire electrode plane.

[0022] In step S3 of the embodiment of the present invention, the interpolation method is a cubic spline interpolation method; Numerical fitting methods include polynomial function fitting, Gaussian function fitting, exponential function fitting and sinusoidal function fitting.

[0023] Furthermore, the number of fitting functions is selected according to the amount of energy flux density data; When the data volume is 2, the fitting function includes a linear function and a linear exponential function; When the data volume is 3, the fitting functions include quadratic function, linear Gaussian function, quadratic exponential function and linear sine function; When the data volume is 4, the fitting functions include cubic function, linear Gaussian function, quadratic exponential function and linear sine function; When the data volume is 5, the fitting functions include quartic function, linear Gaussian function, quadratic exponential function and linear sine function; When the data volume is 6, the fitting functions include quintic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function; When the data volume is 7, the fitting functions include sextic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function; When the data volume is 8, the fitting functions include the seventh-order function, the quadratic Gaussian function, the quadratic exponential function, and the quadratic sine function; When the data volume is 9 to 11, the fitting functions include octane function, cubic Gaussian function, quadratic exponential function and cubic sine function; When the data volume is 12-14, the fitting functions include octonic function, quartic Gaussian function, quadratic exponential function and quartic sine function; When the data volume is 15-17, the fitting functions include octane function, quintic Gaussian function, quadratic exponential function and quintic sine function; When the data volume is 18-20, the fitting functions include octane function, sextaneous Gaussian function, quadratic exponential function and sextaneous sine function; When the data volume is 21-23, the fitting functions include octahedral function, septahedral Gaussian function, quadratic exponential function and septahedral sine function; When the data volume is greater than 24, the fitting functions include octahedral function, octahedral Gaussian function, quadratic exponential function and octahedral sine function.

[0024] In step S5 of the embodiment of the present invention, the evaluation 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) The specific method is: S51. Assume that the current time to be evaluated is t x = t 0– dt ; S52, according to each coordinate point t x + dt ~ t Time-varying energy flux density of the arc to the anode during a period of 1 Q ( t ), using different numerical fitting methods, calculate the corresponding t x The energy flux density of the arc to the anode at the moment; S53, calculate the standard deviation of the energy flux density obtained by different numerical fitting methods, and use the result obtained by the method with the minimum standard deviation as t x The energy flux density of the arc to the anode at the moment, and add it to the time-varying energy flux density In, form t x ~ t 1. The energy flux density of the arc to the anode during the time period; S54, subtract the current time to be evaluated from dt , update the current time to be evaluated, and determine whether the updated current time to be evaluated is less than 0; If yes, proceed to step S6; If not, return to step S52 until 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) .

[0025] In step S7 of the embodiment of the present invention, the energy balance equation based on the anode is:

[0026] In the formula, represents the electrode material density, represents the specific heat capacity of the electrode material, represents the electrode temperature, represents the thermal conductivity of the electrode material, represents the direction perpendicular to the anode surface, represents the surface normal, represents the distribution of energy flux density in the radial direction of the electrode at the current moment, represents the Hamiltonian operator.

[0027] In the embodiment of the present invention, the closing arc under 2kA DC current is used as an example, the closing speed is 1m / s, the arc radial diffusion speed is 5m / s, and the arc plasma parameters within 0.5 ~ 1.25ms are calculated with a time step of 5μs through the arc transient model, and then the arc energy flux density distribution to the anode at each moment in this time period is obtained. q ( x ).

[0028] Then, for the time period q ( x ) to perform numerical analysis and obtain the value within 0.5~1.25ms r ( t ), since the amount of data in this time period is 151, such as Figure 2 As shown in the figure, the octahedral function fitting, octahedral Gaussian function fitting, octahedral sine function fitting and cubic spline interpolation method are selected to evaluate the time interval between 0 and 0.5 ms. r ( t ), and the evaluation results are displayed for selection of the best processing result. In this example, the evaluation result of the cubic spline interpolation method is more accurate, so the result obtained by this method is used as r ( t ) is a value between 0 and 0.5 ms.

[0029] Then each moment q ( x ) distribution is converted to each coordinate point Curve (such as Figure 3 ), in this exampler ( t 0) is 2.5mm. The energy flux density in the area outside 2.5mm has been accurately calculated by the transient arc model. Therefore, it is necessary to calculate the energy flux density in the 0~0.5ms time period within the coordinate range of 0~2.5mm. Distribution is evaluated.

[0030] At 0mm Distribution as an example, first according to The data within 0.5 ~ 1.25ms are fitted with functions, and the standard deviation of the fitted functions is evaluated. The function with the smallest standard deviation is selected and t x = 0.495ms Substitute this into the function as the value at 0mm The evaluation results at 0.495ms (such as Figure 4 Then based on The data within 0.495 ~1.25ms is evaluated in the same way at 0mm The result at 0.49ms is repeated until the full range of energy flow density from 0 to 1.25ms is completed. Evaluate.

[0031] Finally, the time between 0 and 1.25 ms completed at each coordinate point is calculated. Q ( t ) curve is converted to each moment Distribution, based on The anode energy balance equation is used to calculate the transient anode temperature distribution based on the actual anode structure.

[0032] Furthermore, if Figure 5 As shown in Figure 2, in order to verify the accuracy of the method, in this example, the arc plasma parameters within 0.5~1.25ms are calculated with a time step of 5μs, and then the arc to anode energy flux density distribution within this time period is obtained. q ( x ). Then the energy flux density distribution calculated within 0.6 ~ 1.25ms q ( x ) Evaluate the energy flux density distribution within 0.5 ~ 0.6ms q '( x ), and q '( x ) and the calculated 0.5 ~ 0.6ms q ( x ) compared with the actual value, the error is within 8%.

[0033] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0034] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for numerically evaluating anode temperature during arc diffusion in a circuit breaker in the arc starting phase, characterized in that: The following steps are involved: S1, in time step dt In this case, a transient arc simulation model considering the arc diffusion process is used to calculate the arc diffusion from the initial moment. t 0 to end time t 1 arc plasma parameters, and obtain the energy flux density of the arc to the anode at each moment in this time period q ( x ); S2, energy flux density q ( x ) to process the data and obtain the arc root range at each time step. t 0~ t 1 The instantaneous arc radius during the arc diffusion process from the arc starting point to the edge r ( t ); S3. r (0) = 0 added to r ( t ), through numerical fitting and interpolation methods, dt For time step evaluation from 0~ t 0, and add the best evaluation result to the instantaneous arc radius r ( t ) to form 0 ~ t 1. The instantaneous arc radius range of the whole time range during the period; S4. Within the instantaneous arc radius, the energy flux density distribution of the arc to the anode at each moment q ( x ) to obtain each coordinate point t 0~ t 1 Energy flux density of the arc to the anode during the time period ; S5, t 0~ t 1 Based on the energy flow density data in the time period, dt Evaluate for time steps 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) , and combined with t 0~ t 1 Energy flux density of the arc to the anode during the time period , get 0 ~ t 1 Energy flux density of the arc to the anode during the time period ;in, r ( t 0) t = t The instantaneous arc radius at time 0; S6, add 0~ t 1 Energy flux density of the arc to the anode during the time period Q ( t ) to get 0~ t 1 The energy flux density of the arc to the anode at each moment in the time period And the coordinate position at each moment is greater than the instantaneous arc radius r ( t ) is set to zero; S7. Modeling is performed based on the actual structure of the electrode to evaluate the energy flux density over the entire time range. Import and calculate the transient anode temperature based on the anode energy balance equation.

2. The method for numerically evaluating anode temperature during arc diffusion process in the arc starting stage of a circuit breaker according to claim 1, characterized in that: In step S1, the initial moment satisfies: At the initial moment, the stable solution of arc plasma parameters can be calculated by transient arc simulation model; The initial moment approaches 0; Also, at the initial moment, the arc burning range does not cover the entire electrode plane.

3. The method for numerically evaluating anode temperature during arc diffusion process in the arc starting stage of a circuit breaker according to claim 1, characterized in that: In step S3, the interpolation method is cubic spline interpolation; The numerical fitting method includes polynomial function fitting, Gaussian function fitting, exponential function fitting and sinusoidal function fitting.

4. The method for numerically evaluating anode temperature during arc diffusion process in the arc starting stage of a circuit breaker according to claim 3, characterized in that: Select the number of fitting functions according to the amount of energy flux density data; When the data volume is 2, the fitting function includes a linear function and a linear exponential function; When the data volume is 3, the fitting functions include quadratic function, linear Gaussian function, quadratic exponential function and linear sine function; When the data volume is 4, the fitting functions include cubic function, linear Gaussian function, quadratic exponential function and linear sine function; When the data volume is 5, the fitting functions include quartic function, linear Gaussian function, quadratic exponential function and linear sine function; When the data volume is 6, the fitting functions include quintic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function; When the data volume is 7, the fitting functions include sextic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function; When the data volume is 8, the fitting functions include the seventh-order function, the quadratic Gaussian function, the quadratic exponential function, and the quadratic sine function; When the data volume is 9 to 11, the fitting functions include octane function, cubic Gaussian function, quadratic exponential function and cubic sine function; When the data volume is 12-14, the fitting functions include octonic function, quartic Gaussian function, quadratic exponential function and quartic sine function; When the data volume is 15-17, the fitting functions include octane function, quintic Gaussian function, quadratic exponential function and quintic sine function; When the data volume is 18-20, the fitting functions include octane function, sextaneous Gaussian function, quadratic exponential function and sextaneous sine function; When the data volume is 21-23, the fitting functions include octahedral function, septahedral Gaussian function, quadratic exponential function and septahedral sine function; When the data volume is greater than 24, the fitting functions include octahedral function, octahedral Gaussian function, quadratic exponential function and octahedral sine function.

5. The method for numerically evaluating anode temperature during arc diffusion process in the arc starting stage of a circuit breaker according to claim 1, characterized in that: In step S5, the evaluation 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) The specific method is: S51. Assume that the current time to be evaluated is t x = t 0 – dt ; S52, according to each coordinate point t x + dt ~ t Time-varying energy flux density of the arc to the anode during a period of 1 Q ( t ), using different numerical fitting methods, calculate the corresponding t x The energy flux density of the arc to the anode at the moment; S53, calculate the standard deviation of the energy flux density obtained by different numerical fitting methods, and use the result obtained by the method with the minimum standard deviation as t x The energy flux density of the arc to the anode at the moment, and add it to the time-varying energy flux density In, forming t x ~ t 1. The energy flux density of the arc to the anode during the time period; S54, subtract the current time to be evaluated from dt , update the current time to be evaluated, and determine whether the updated current time to be evaluated is less than 0; If yes, proceed to step S6; If not, return to step S52 until 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) .

6. The method for numerically evaluating anode temperature during arc diffusion process in the arc starting stage of a circuit breaker according to claim 1, characterized in that: In step S7, the energy balance equation based on the anode is: In the formula, represents the electrode material density, represents the specific heat capacity of the electrode material, represents the electrode temperature, represents the thermal conductivity of the electrode material, represents the direction perpendicular to the anode surface, represents the surface normal, represents the distribution of energy flux density in the radial direction of the electrode at the current moment, represents the Hamiltonian operator.

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