Numerical evaluation method of anode temperature in arc diffusion process in arc initiation stage of circuit breaker

Abstract

The application discloses an anode temperature numerical evaluation method for an arc diffusion process in an arc striking stage of a circuit breaker and belongs to the technical field of power safety. The application can realize evaluation of energy flux density distribution of a fine arc diffusion stage starting from 0 time to the starting point of a certain time period on the basis of transient change of the energy flux density distribution of the arc to the anode in the certain time period, solves the problem that the energy flux density cannot be evaluated in the fine arc state due to difficulty in stable calculation of high-density high-energy fine arc parameters, and more accurately evaluates the electrode ablation condition.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power safety, and particularly relates to an anode temperature numerical evaluation method for an arc diffusion process in an arc initiation stage of a circuit breaker. BACKGROUND

[0002] The circuit breaker is one of the most important electrical devices in the high-voltage field, and plays a role in power system protection and control, and needs to reliably cut off the load current or short-circuit current. In the breaking process of the circuit breaker, a high-energy arc is generated between the circuit breakers. Due to the self-pinching effect of the arc, the arc will cause strong ablation to the anode, especially in the arc initiation stage, the arc gradually diffuses from a thin arc to the entire electrode plane, at this time, the arc energy will concentrate to ablate a certain area of the electrode, and the energy flux density is extremely large.

[0003] For the transient numerical analysis method of the 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 in the arc. Considering that the plasma density and temperature of the thin arc in the arc initiation stage are extremely high, the existing numerical analysis method is difficult to obtain a stable convergent solution, and therefore the starting time of the numerical calculation is generally after 0.5 ms after the arc initiation.

[0004] However, due to the extremely strong ablation in the arc initiation stage, the existing evaluation of the transient anode temperature distribution is obviously low. In order to more accurately evaluate the ablation state of the anode, a method needs to be proposed to solve the problem of evaluating the energy flux density of the thin arc ablation in the arc initiation stage. SUMMARY

[0005] In view of the above problems in the prior art, the anode temperature numerical evaluation method for the arc diffusion process in the arc initiation stage of the circuit breaker provided by the application solves the problem that the existing arc model is difficult to stably calculate the plasma parameters and energy flux density of the thin arc in the arc initiation stage, and further cannot accurately evaluate the ablation state of the electrode.

[0006] In order to achieve the above application purposes, the technical scheme adopted by the application is as follows: the anode temperature numerical evaluation method for the arc diffusion process in the arc initiation stage of the circuit breaker, comprising the following steps:

[0007] S1, at a time step dt , a transient arc simulation model considering the arc diffusion process is used to calculate the arc plasma parameters from an initial time t 0 to a termination time t 1, so as to obtain the energy flux density of the arc to the anode at each time in the time period q ( x );

[0008] S2, the energy flux density q ( xdata processing, the arc root range at each time step is obtained, and the arc root range at each time step is obtained t 0~ t 1arc radius during the arc diffusion process from the starting point to the edge r ( t );

[0009] S3, the r (0) = 0 is supplemented to r ( t ) is evaluated by numerical fitting and interpolation method, and the best evaluation result is supplemented to the transient arc radius dt ( t ) to form the transient arc radius range during 0 ~ r 1; t t S4, in the transient arc radius range, the energy flow density distribution of the arc to the anode at each time (

[0010] ) is processed, and the energy flow density of the arc to the anode at each coordinate point during 0 ~ q 1time period x ; t t

[0011] S5, based on the energy flow density data during 0 ~ t 1time period, the energy flow density during 0 ~ t 0time period and coordinate range within 0 ~ dt ( t 0) is evaluated with r as the time step, and the energy flow density of the arc to the anode during 0 ~ t 1time period is obtained by combining the energy flow density of the arc to the anode during 0 ~ 1time period t ; wherein, t ( 0) is the transient arc radius at t = 0; r t S6, the energy flow density of the arc to the anode at each coordinate point during 0 ~ t 1time period t ( ) is processed, and the energy flow density of the arc to the anode at each time during 0 ~

[0012] 1time period t ; Q t t ​​​​​​And the coordinate position at each moment is greater than the instantaneous arc radius r ( t ) is set to zero;

[0013] S7. Model the electrode according to its actual structure and evaluate the energy flux density over the entire time range. Import and calculate the transient anode temperature based on the anode energy balance equation.

[0014] Furthermore, in step S1, the initial moment satisfies:

[0015] At the initial moment, the stable solution of arc plasma parameters can be obtained by calculating the transient arc simulation model;

[0016] The initial time is close to 0;

[0017] Also, at the initial moment, the arc burning range does not cover the entire electrode plane.

[0018] Furthermore, in step S3, the interpolation method is a cubic spline interpolation method;

[0019] The numerical fitting method includes polynomial function fitting, Gaussian function fitting, exponential function fitting and sine function fitting.

[0020] Furthermore, the number of fitting functions is selected according to the amount of energy flux density data;

[0021] When the data volume is 2, the fitting function includes a linear function and a linear exponential function;

[0022] When the data volume is 3, the fitting functions include quadratic function, linear Gaussian function, quadratic exponential function and linear sine function;

[0023] When the data size is 4, the fitting functions include cubic function, linear Gaussian function, quadratic exponential function and linear sine function;

[0024] When the data volume is 5, the fitting functions include quartic function, linear Gaussian function, quadratic exponential function and linear sine function;

[0025] When the data size is 6, the fitting functions include quintic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function;

[0026] When the data size is 7, the fitting functions include sextic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function;

[0027] When the data size is 8, the fitting functions include the septillic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function;

[0028] When the data volume is 9 to 11, the fitting functions include octant function, cubic Gaussian function, quadratic exponential function and cubic sine function;

[0029] When the data size is 12 to 14, the fitting functions include octant function, quartic Gaussian function, quadratic exponential function and quartic sine function;

[0030] When the data volume is 15-17, the fitting functions include octant function, quintic Gaussian function, quadratic exponential function and quintic sine function;

[0031] When the data size is 18 to 20, the fitting functions include octant function, sextant Gaussian function, quadratic exponential function and sextant sine function;

[0032] When the data volume is 21-23, the fitting functions include octant function, septad Gaussian function, quadratic exponential function and septad sine function;

[0033] When the data volume is greater than 24, the fitting functions include octant function, octant Gaussian function, quadratic exponential function, and octant sine function.

[0034] Furthermore, in step S5, the evaluation 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) energy flux density The specific method is:

[0035] S51. Assume that the current time to be evaluated is t x = t 0– dt ;

[0036] S52, according to each coordinate point t x + dt ~ t Time-varying energy flux density of the arc to the anode during a time period 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;

[0037] 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 the formation t x ~ t 1. The energy flux density of the arc to the anode during the time period;

[0038] 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;

[0039] If yes, proceed to step S6;

[0040] If not, return to step S52 until 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) energy flux density .

[0041] Furthermore, in step S7, the energy balance equation based on the anode is:

[0042]

[0043] Where, 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, Indicates 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.

[0044] The beneficial effects of the present invention are:

[0045] The present invention can evaluate the energy flux density distribution in the thin 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 in the thin arc state cannot be evaluated due to the inability to implement arc calculation, so as to more accurately evaluate the electrode ablation situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of the method for numerically evaluating the anode temperature during the arc diffusion process of a circuit breaker in the arc starting stage provided by the present invention.

[0047] Figure 2 This is the prediction result of the arc diffusion process using different numerical processing methods provided by the present invention.

[0048] Figure 3 The basis provided by the present invention q ( x ) obtained at some coordinate points Q ( t )curve.

[0049] Figure 4 The 0mm position provided by the present invention Q ( t ) curve original data and evaluation data processing results.

[0050] Figure 5 The 5.5ms time provided by the present invention q ( x ) Error comparison between original data and evaluation data. DETAILED DESCRIPTION

[0051] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0052] The embodiment of the present invention provides a method for numerically evaluating the anode temperature of the arc diffusion process during the arc starting phase of a circuit breaker. Figure 1 As shown, the following steps are included:

[0053] S1, in time step dt In this case, a transient arc simulation model considering the arc diffusion process is used to calculate the arc state from the initial moment t 0 to the 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 );

[0054] S2, energy flux density q ( x ) to process the data and obtain the arc root range at each time step, and obtain t 0~ t 1 The instantaneous arc radius during the arc diffusion process from the arc starting point to the edge r ( t );

[0055] 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 results to the instantaneous arc radius r ( t ), forming 0 ~t 1. The instantaneous arc radius range of the entire time range during the period;

[0056] S4. Within the instantaneous arc radius, the energy flux density distribution of the arc to the anode at each moment q ( x ) to process and obtain the coordinates of each point t 0~ t 1. Energy flux density of the arc to the anode during the time period ;

[0057] S5, t 0~ t 1. Based on the energy flow density data within the time period, dt Evaluate for time steps 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) energy flux density , and combined with t 0~ t 1. Energy flux density of the arc to the anode during the time period , and 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;

[0058] S6, add 0~ t 1. Energy flux density of the arc to the anode during the time period Q ( t ) is processed to obtain 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;

[0059] S7. Model the electrode according to its actual structure and evaluate the energy flux density over the entire time range. Import and calculate the transient anode temperature based on the anode energy balance equation.

[0060] In step S1 of the embodiment of the present invention, the initial moment satisfies:

[0061] At the initial moment, the stable solution of arc plasma parameters can be obtained by calculating the transient arc simulation model;

[0062] The initial time is close to 0;

[0063] Also, at the initial moment, the arc burning range does not cover the entire electrode plane.

[0064] In step S3 of the embodiment of the present invention, the interpolation method is a cubic spline interpolation method;

[0065] Numerical fitting methods include polynomial function fitting, Gaussian function fitting, exponential function fitting and sine function fitting.

[0066] Furthermore, the number of fitting functions is selected according to the amount of energy flux density data;

[0067] When the data volume is 2, the fitting function includes a linear function and a linear exponential function;

[0068] When the data volume is 3, the fitting functions include quadratic function, linear Gaussian function, quadratic exponential function and linear sine function;

[0069] When the data size is 4, the fitting functions include cubic function, linear Gaussian function, quadratic exponential function and linear sine function;

[0070] When the data volume is 5, the fitting functions include quartic function, linear Gaussian function, quadratic exponential function and linear sine function;

[0071] When the data size is 6, the fitting functions include quintic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function;

[0072] When the data size is 7, the fitting functions include sextic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function;

[0073] When the data size is 8, the fitting functions include the septillic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function;

[0074] When the data volume is 9 to 11, the fitting functions include octant function, cubic Gaussian function, quadratic exponential function and cubic sine function;

[0075] When the data size is 12 to 14, the fitting functions include octant function, quartic Gaussian function, quadratic exponential function and quartic sine function;

[0076] When the data volume is 15-17, the fitting functions include octant function, quintic Gaussian function, quadratic exponential function and quintic sine function;

[0077] When the data size is 18 to 20, the fitting functions include octant function, sextant Gaussian function, quadratic exponential function and sextant sine function;

[0078] When the data volume is 21-23, the fitting functions include octant function, septad Gaussian function, quadratic exponential function and septad sine function;

[0079] When the data volume is greater than 24, the fitting functions include octant function, octant Gaussian function, quadratic exponential function, and octant sine function.

[0080] In step S5 of the embodiment of the present invention, the evaluation 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) energy flux density The specific method is:

[0081] S51. Assume that the current time to be evaluated is t x = t 0– dt ;

[0082] S52, according to each coordinate point t x + dt ~ t Time-varying energy flux density of the arc to the anode during a time period 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;

[0083] 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 the formation t x ~ t 1. The energy flux density of the arc to the anode during the time period;

[0084] 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;

[0085] If yes, proceed to step S6;

[0086] If not, return to step S52 until 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) energy flux density .

[0087] In step S7 of the embodiment of the present invention, the energy balance equation based on the anode is:

[0088]

[0089] Where, 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, Indicates 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.

[0090] 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, and the arc radial diffusion speed is 5m / s. 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 to anode energy flux density distribution at each moment in this time period is obtained. q ( x ).

[0091] Then, within the time period q ( x ) to conduct 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, the octave function fitting, octave Gaussian function fitting, octave sine function fitting and cubic spline interpolation method are selected to evaluate the time within 0 ~ 0.5ms. 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 0.5ms.

[0092] Then each moment q ( x ) distribution is converted to each coordinate point Curve (such as Figure 3 In this example, r ( 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.

[0093] At 0mm Distribution as an example, first according to Perform function fitting on data within 0.5 ~ 1.25ms, evaluate the standard deviation of the fitted function, select the function with the smallest standard deviation, and t x = 0.495ms is substituted 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 deduced and so on until the full range of energy flow density from 0 to 1.25ms is completed. Evaluate.

[0094] Finally, the time between 0 and 1.25 ms for evaluating each coordinate point is calculated. Q ( t ) curve is converted to the Distribution, based on The anode energy balance equation is used to calculate the transient anode temperature distribution based on the actual anode structure.

[0095] Further, if Figure 5 As shown, 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 flow 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%.

[0096] Specific embodiments are used in the present invention 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 ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0097] Those skilled in the art will appreciate that the embodiments described herein are presented for purposes of illustration and that the inventive principles are not limited to these particular embodiments. Other variations and modifications can be made to the embodiments without departing from the spirit and scope of the inventive principles.

Claims

1. A method for numerically evaluating anode temperature during arc diffusion during the arc starting phase of a circuit breaker, 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 state from the initial moment t 0 to the 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, and obtain 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 results to the instantaneous arc radius r ( t ), forming 0 ~ t 1. The instantaneous arc radius range of the entire 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 process and 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 within the time period, dt Evaluate for time steps 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) energy flux density , and combined with t 0~ t 1. Energy flux density of the arc to the anode during the time period , and 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 ) is processed to obtain 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. Model the electrode according to its actual structure and 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 in a circuit breaker arc starting phase 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 obtained by calculating the transient arc simulation model; The initial time is close to 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 in a circuit breaker arc starting phase 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 sine function fitting.

4. The method for numerically evaluating anode temperature during arc diffusion in a circuit breaker arc starting phase 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 size 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 size is 6, the fitting functions include quintic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function; When the data size is 7, the fitting functions include sextic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function; When the data size is 8, the fitting functions include the septillic function, quadratic Gaussian function, quadratic exponential function and quadratic sine function; When the data volume is 9 to 11, the fitting functions include octant function, cubic Gaussian function, quadratic exponential function and cubic sine function; When the data size is 12 to 14, the fitting functions include octant function, quartic Gaussian function, quadratic exponential function and quartic sine function; When the data volume is 15-17, the fitting functions include octant function, quintic Gaussian function, quadratic exponential function and quintic sine function; When the data size is 18 to 20, the fitting functions include octant function, sextant Gaussian function, quadratic exponential function and sextant sine function; When the data volume is 21-23, the fitting functions include octant function, septad Gaussian function, quadratic exponential function and septad sine function; When the data volume is greater than 24, the fitting functions include octant function, octant Gaussian function, quadratic exponential function, and octant sine function.

5. The method for numerically evaluating anode temperature during arc diffusion in a circuit breaker arc starting phase according to claim 1, characterized in that: In step S5, the evaluation 0 ~ t 0 time period, coordinate range is 0 ~ r ( t 0) energy flux density 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 time period 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 the formation 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) energy flux density .

6. The method for numerically evaluating anode temperature during arc diffusion in a circuit breaker arc starting phase according to claim 1, characterized in that: In step S7, the energy balance equation based on the anode is: Where, 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, Indicates 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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