CN109492339B - Arc model construction method and system - Google Patents

Abstract

The present application discloses a method and system for constructing an arc model. The method is to calculate the arc conductance according to the obtained arc data, and then obtain the mayr arc resistance and the cassie arc resistance, and set a proportional coefficient. By adding the mayr arc resistance And the cassie arc resistance is connected in series according to the proportional coefficient to obtain an arc stabilizing resistance. Then establish the first functional relational expression and the second functional relational expression. Finally, according to the first functional relational expression and the second functional relational expression, an arc model is constructed based on the principle equation of the mayr arc model and the principle equation of the cassie arc model. Compared with the prior art, the arc model constructed by the present application has a wide application range, and can dynamically construct the arc model for high-resistance arcs and low-resistance arcs by setting the proportional coefficient reasonably, so as to realize the control of arc voltage and arc current. Accurate simulation effectively improves the efficiency of arc experiment research.

Description

A method and system for building an arc model

technical field

The present application relates to the technical field of power system fault detection and protection, in particular to a method and system for constructing an arc model.

Background technique

During the breaking period of the high-voltage circuit breaker, the gap between the contacts of the high-voltage circuit breaker is prone to arc due to breakdown. The arc is a gas discharge phenomenon, which poses a great threat to the safe operation of the power system. Therefore, the research on the arc Dynamic behavior is of great significance for improving the breaking performance of high-voltage circuit breakers and ensuring the safe operation of power systems. In the prior art, experiments are usually conducted to conduct simulation research on the dynamic behavior of the arc, so as to further achieve the purpose of improving the breaking performance of the high voltage circuit breaker.

In the process of simulating the dynamic behavior of the arc, it is generally realized by establishing an arc model. At present, the commonly used arc model is black-box modeling. Black-box modeling is based on the change process of arc current and arc voltage during the test of the high-voltage circuit breaker, combined with a given differential equation, and derives the arc model used to study the dynamic behavior of the arc. Typical black box models include cassie arc model and mayr arc model. It can be seen from their establishment process that the cassie arc model and the mayr arc model describe the arc qualitatively in the high current region and the small current region respectively, that is to say, the cassie arc model is suitable for the simulation experiment research of the arc with low resistance and high current. The mayr arc model is suitable for the simulation experiment research of the arc with high resistance and small current.

However, the inventor found in the research process of the present application that the above two arc models in the prior art have a relatively small scope of application. For the cassie arc model, only low-resistance arcs can be accurately simulated, but the simulation for high-resistance arcs is not accurate. Similarly, for the mayr arc model, only high-resistance arcs can be accurately simulated, but the simulation for low-resistance arcs is not accurate. In the prior art, two kinds of arc models are needed to carry out simulation test research for different arc states, and in practical application, the efficiency of arc test research is reduced.

Contents of the invention

In order to solve the problem that the range of application of the arc model provided in the prior art is relatively small, resulting in a reduction in the efficiency of arc test research, the present application discloses a method and system for constructing an arc model through the following embodiments.

In the first aspect of the present application, a method for constructing an arc model is disclosed, including:

Acquiring arc data, the arc data including arc voltage, arc current and arc stable arc voltage;

Obtaining arc conductance according to the arc voltage and the arc current;

Obtaining the mayr arc resistance and the cassie arc resistance, and setting the proportional coefficient, by connecting the mayr arc resistance and the cassie arc resistance in series according to the proportional coefficient, obtaining the arc stabilizing resistance;

Establishing a first functional relationship according to the arc stable arcing voltage, the proportional coefficient and the arc stable resistance;

According to the arc current, the stable arc voltage of the arc and the conductance of the arc, the time constant of the arc and the power dissipation are fitted with a function to establish a second functional relational expression, the time constant of the arc includes a mayr arc time Constant and cassie arc time constant, the second functional relational expression includes the functional relational expression of the mayr arc time constant, the functional relational expression of the cassie arc time constant and the functional relational expression of the dissipated power;

An arc model is constructed based on the first functional relational expression and the second functional relational expression, based on the principle equation of the mayr arc model and the principle equation of the cassie arc model.

Optionally, the proportional coefficient includes a first proportional coefficient and a second proportional coefficient, the first proportional coefficient is the proportional coefficient of the mayr arc resistance, and the second proportional coefficient is the proportional coefficient of the cassie arc resistance .

Optionally, the arc stabilizing resistance is calculated by the following formula:

R _arc =K ₁ R _m +K ₂ R _c ;

Wherein, R _arc is the arc stabilizing resistance, K ₁ is the first proportionality coefficient, K ₂ is the second proportionality coefficient, R _m is the mayr arc resistance, R _c is the cassie arc resistance.

Optionally, according to the arc current, the arc stable arc voltage and the arc conductance, performing function fitting on the time constant and power dissipation of the arc to establish a second functional relationship, including:

The functional relational expression of described mayr arc time constant is set up by following formula:

Wherein, τ _m is the mayr arc time constant, i is the arc current, U _arc is the arc stable arc voltage, g is the arc conductance, and t is time;

The functional relational expression of described cassie arc time constant is established by the following formula:

Wherein, τ _c is described cassie arc time constant;

The functional relationship of the dissipated power is established by the following formula:

p = U _arc |i|;

Wherein, p is the dissipated power.

Optionally, the principle equation of the mayr arc model is:

Wherein, g _m is the mayr arc conductance, the mayr arc conductance is inversely proportional to the mayr arc resistance, τ _m is the mayr arc time constant, u is the arc voltage, i is the arc current, and p is said dissipated power;

The principle equation of the cassie arc model is:

Wherein, g _c is the conductance of the cassie arc, and the conductance of the cassie arc is inversely proportional to the resistance of the cassie arc, τ _c is the time constant of the cassie arc, and U _arc is the stable arcing voltage of the arc.

In a second aspect of the present application, an arc model construction system is disclosed, including:

An arc data acquisition module, configured to acquire arc data, the arc data including arc voltage, arc current and arc stable arc voltage;

an arc conductance acquisition module, configured to acquire arc conductance according to the arc voltage and the arc current;

The arc stabilizing resistance acquisition module is used to acquire the mayr arc resistance and the cassie arc resistance, and set the proportional coefficient, and obtain the arc stabilizing resistance by connecting the mayr arc resistance and the cassie arc resistance in series according to the proportional coefficient;

A first functional relationship establishment module, configured to establish a first functional relationship according to the arc stable arc ignition voltage, the proportional coefficient and the arc stable resistance;

The second functional relationship establishment module is used to perform function fitting on the time constant and dissipated power of the arc according to the arc current, the arc stable arc voltage and the arc conductance, and establish a second functional relationship, The time constant of the arc includes a mayr arc time constant and a cassie arc time constant, and the second functional relational expression includes a functional relational expression of the mayr arc time constant, a functional relational expression of the cassie arc time constant, and the consumption The functional relationship of the dissipation power;

An arc model building module, configured to construct an arc model based on the principle equation of the mayr arc model and the principle equation of the cassie arc model according to the first functional relational expression and the second functional relational expression.

Optionally, the arc stabilization resistance acquisition module includes:

The arc stabilizing resistance calculation unit is used to calculate the arc stabilizing resistance by the following formula:

R _arc =K ₁ R _m +K ₂ R _c ;

Wherein, R _arc is the arc stabilizing resistance, K ₁ is the first proportional coefficient, and the first proportional coefficient is the proportional coefficient of the mayr arc resistance, K ₂ is the second proportional coefficient, and the second proportional coefficient is The proportional coefficient of the cassie arc resistance, R _m is the mayr arc resistance, and R _c is the cassie arc resistance.

Optionally, the second functional relationship building module includes:

The mayr arc time constant functional relational expression establishment unit is used to establish the functional relational expression of the mayr arc time constant by the following formula:

Wherein, τ _m is the mayr arc time constant, i is the arc current, U _arc is the arc stable arc voltage, g is the arc conductance, and t is time;

The cassie arc time constant functional relational expression establishment unit is used to establish the functional relational expression of the cassie arc time constant by the following formula:

Wherein, τ _c is described cassie arc time constant;

Dissipated power functional relational expression establishment unit, used for establishing the functional relational expression of described dissipated power by the following formula:

p = U _arc |i|;

Wherein, p is the dissipated power.

The present application discloses a method and system for constructing an arc model. The method is based on the cassie arc model and the mayr arc model in the prior art, and the mayr arc resistance and the cassie arc resistance are connected in series according to a certain proportional coefficient. By setting the size of the proportional coefficient, different arc stable arc resistances can be obtained, and an arc model can be constructed on the basis of different arc stable resistances. Compared with the cassie arc model suitable for the low-resistance arc state and the mayr arc model suitable for the high-resistance arc state in the prior art, the arc model constructed by the application has a wide range of applications, and can be flexibly set by setting the proportional coefficient reasonably. For high-resistance arcs and low-resistance arcs, the arc model is dynamically constructed to realize accurate simulation of arc voltage and arc current, which effectively improves the efficiency of arc test research.

Description of drawings

In order to illustrate the technical solution of the present application more clearly, the accompanying drawings that need to be used in the embodiments will be briefly introduced below. Obviously, for those of ordinary skill in the art, on the premise of not paying creative work, there are also Additional figures can be derived from these figures.

Fig. 1 is a schematic workflow diagram of an arc model construction method disclosed in the embodiment of the present application;

Fig. 2 is an arc simulation waveform diagram of the established arc model using an arc model construction method disclosed in the embodiment of the present application;

Fig. 3 is a schematic structural diagram of an arc model building system disclosed in an embodiment of the present application.

Detailed ways

In order to solve the problem that the range of application of the arc model provided in the prior art is relatively small, resulting in a reduction in the efficiency of arc test research, the present application discloses a method and system for constructing an arc model through the following embodiments.

The first embodiment of the present application discloses a method for constructing an arc model. Referring to the schematic workflow diagram shown in FIG. 1, the method includes:

Step S11, acquiring arc data, the arc data includes arc voltage, arc current and arc stable arcing voltage.

Specifically, in actual operation, the arc data is obtained by conducting an electrode arcing experiment. The process of the electrode arcing experiment is as follows: first, the copper electrode and the carbon electrode are set in a contact state, and then the copper electrode is pulled by the motor to generate an arc . By measuring the arc generated during the electrode arcing experiment, a series of arc data such as arc voltage, arc current and arc stable arc burning voltage are obtained.

Step S12, obtaining arc conductance according to the arc voltage and the arc current.

Specifically, according to the arc voltage and the arc current, the arc conductance is calculated by the following formula:

Wherein, g is the arc conductance, i is the arc current, and u is the arc voltage.

Step S13, obtaining the mayr arc resistance and the cassie arc resistance, and setting a proportional coefficient, and obtaining the arc stabilizing resistance by connecting the mayr arc resistance and the cassie arc resistance in series according to the proportional coefficient.

By assuming that the arc model to be constructed in this application is composed of two nonlinear arc resistances Rm and Rc connected in series, the cassie arc model and mayr arc model can be connected in series according to the preset proportional coefficient, which can overcome the single cassie arc model, mayr arc model and single The proportional cassie-mayr arc model is insufficient. In practical applications, different arc stability resistances can be obtained by adjusting the proportional coefficient.

Step S14, establishing a first functional relationship according to the stable arc ignition voltage, the proportional coefficient and the stable arc resistance.

Specifically, when the arc voltage is constant, changing the proportional coefficient will result in different arc stabilizing resistances. Based on this, by changing the arc voltage, the relationship between the arc stabilizing resistance, arc voltage and the proportional coefficient will be obtained, and then the arc stabilizing arc voltage, the proportional coefficient and the arc stabilizing resistance will be established. A functional relationship, that is, the first functional relationship: R _arc =f(U _arc , K), wherein, R _arc is the arc stabilization resistance, U _arc is the arc voltage, and K is the proportional coefficient.

In the process of establishing the first functional relational expression, pscad software can be used for establishment, and pscad software is a widely used electromagnetic transient simulation software. Specifically, multiple arc stable arc voltage data are acquired through measurement, and by continuously adjusting the value of the proportional coefficient, the simulated arc stable resistance is equal to the actual arc stable resistance, and multiple different arc stable resistance data are obtained. In this way, multiple sets of data of arc stable arc voltage, arc stable resistance and proportional coefficient can be obtained. According to the obtained multiple sets of data, corresponding proportional coefficients under different arc voltages can be integrated to establish the first functional relational expression. Through the established first functional relationship, select the corresponding arc stable arc voltage and proportional coefficient, then the only corresponding arc stable resistance can be determined, and then the arc voltage and arc current can be accurately simulated for the arc stable resistance .

Step S15, according to the arc current, the arc stable arc voltage and the arc conductance, perform function fitting on the time constant of the arc and the dissipated power, and establish a second functional relationship, the time constant of the arc includes The mayr arc time constant and the cassie arc time constant, the second functional relational expression includes the functional relational expression of the mayr arc time constant, the functional relational expression of the cassie arc time constant and the functional relational expression of the dissipated power.

In practical application, you can use Origin software to perform function fitting on the arc time constant and dissipated power. Origin software is a kind of data analysis software.

Step S16 , constructing an arc model based on the first functional relational expression and the second functional relational expression, based on the principle equation of the mayr arc model and the principle equation of the cassie arc model.

Wherein, the established second functional relational expression is essentially a calculation formula for relevant parameters in the finally constructed arc model, and the finally constructed arc model is a combination of a mayr arc model and a cassie arc model. Therefore, the second functional relational expression is mainly used to calculate the arc time constant and power dissipation used in the principle equation of the mayr arc model and the principle equation of the cassie arc model.

The present application discloses a method for constructing an arc model. The method is based on the cassie arc model and the mayr arc model in the prior art. The mayr arc resistance and the cassie arc resistance are connected in series according to a certain proportional coefficient. By setting According to the size of the proportional coefficient, different arc stable arc resistances can be obtained, and the arc model can be constructed on the basis of different arc stable resistances. Compared with the cassie arc model suitable for the low-resistance arc state and the mayr arc model suitable for the high-resistance arc state in the prior art, the arc model constructed by the application has a wide range of applications, and can be flexibly set by setting the proportional coefficient reasonably. For high-resistance arcs and low-resistance arcs, the arc model is dynamically constructed to realize accurate simulation of arc voltage and arc current, which effectively improves the efficiency of arc test research.

Further, the proportional coefficient includes a first proportional coefficient and a second proportional coefficient, the first proportional coefficient is the proportional coefficient of the mayr arc resistance, and the second proportional coefficient is the proportional coefficient of the cassie arc resistance.

Specifically, the relationship between the first proportional coefficient and the second proportional coefficient is: K ₁ +K ₂ =1, where K ₁ is the first proportional coefficient and K ₂ is the second proportional coefficient. In the first functional relationship disclosed above, the proportional coefficient K may be the first proportional coefficient K ₁ or the second proportional coefficient K ₂ .

Further, the arc stabilizing resistance is calculated by the following formula:

R _arc =K ₁ R _m +K ₂ R _c ;

Wherein, R _arc is the arc stabilizing resistance, K ₁ is the first proportionality coefficient, K ₂ is the second proportionality coefficient, R _m is the mayr arc resistance, R _c is the cassie arc resistance.

Further, according to the arc current, the arc stable arc voltage and the arc conductance, function fitting is performed on the time constant and power dissipation of the arc, and a second functional relationship is established, including:

The functional relational expression of described mayr arc time constant is set up by following formula:

Wherein, τ _m is the mayr arc time constant, i is the arc current, U _arc is the arc stable arc voltage, g is the arc conductance, and t is time;

The functional relational expression of described cassie arc time constant is established by the following formula:

Wherein, τ _c is described cassie arc time constant;

The functional relationship of the dissipated power is established by the following formula:

p = U _arc |i|;

Wherein, p is the dissipated power.

further,

The principle equation of the mayr arc model is:

Wherein, g _m is the mayr arc conductance, and the mayr arc conductance is inversely proportional to the mayr arc resistance, τ _m is the mayr arc time constant, u is the arc voltage, i is the arc current, and p is said dissipated power;

The principle equation of the cassie arc model is:

Wherein, g _c is the conductance of the cassie arc, and the conductance of the cassie arc is inversely proportional to the resistance of the cassie arc, τ _c is the time constant of the cassie arc, and U _arc is the stable arcing voltage of the arc.

An arc model construction method disclosed in the present application finally constructs a Cassie-Mayr arc model with variable coefficients based on Origin parameter fitting. The arc model uses Origin software to analyze the arc data measured in experiments, and uses The fitting method obtains the function of each parameter in the arc model. When the arc test system is working normally, the arc model has a high conductance value, which is equivalent to a wire, and will not affect the arc test system. When the electromagnetic transient phenomenon occurs in the arc test system, arc discharge will occur at the line fracture or weak insulation. At this time, the arc model is equivalent to a nonlinear resistor. By combining the cassie arc model and mayr arc model according to a certain proportion, And according to the established time constant and the function relationship of parameters such as power dissipation, the characteristics of the arc near the large current area and the current zero area can be accurately simulated. Referring to shown in Fig. 2, Fig. 2 is to utilize the arc model constructed by the present application to simulate the waveform diagram of arc voltage and current, the abscissa in the figure is time, the unit is s, and the ordinate is arc current or arc voltage, corresponding The unit is kA or kV. It can be seen from the figure that the arc model constructed by this application can accurately simulate the test arc, thus further improving the accuracy of line electromagnetic transient simulation calculation.

The following are system embodiments of the present application, which can be used to implement the method embodiments of the present application. For details not disclosed in the system embodiments of the present application, please refer to the method embodiments of the present application.

Correspondingly, another embodiment of the present application discloses an arc model construction system, as shown in FIG. 3 , the system includes:

An arc data acquisition module 10, configured to acquire arc data, the arc data including arc voltage, arc current and arc stable arc voltage;

An arc conductance acquisition module 20, configured to acquire arc conductance according to the arc voltage and the arc current;

The arc stabilizing resistance acquisition module 30 is used to acquire the mayr arc resistance and the cassie arc resistance, and set the proportional coefficient, and obtain the arc stabilizing resistance by connecting the mayr arc resistance and the cassie arc resistance in series according to the proportional coefficient;

A first functional relationship establishment module 40, configured to establish a first functional relationship according to the arc stable arcing voltage, the proportional coefficient and the arc stable resistance;

The second functional relationship establishment module 50 is used to perform function fitting on the time constant and dissipated power of the arc according to the arc current, the arc stable arc voltage and the arc conductance, and establish a second functional relationship , the time constant of the arc includes a mayr arc time constant and a cassie arc time constant, and the second functional relational expression includes a functional relational expression of the mayr arc time constant, a functional relational expression of the cassie arc time constant, and the Functional relation of dissipated power;

The arc model construction module 60 is configured to construct an arc model based on the principle equation of the mayr arc model and the principle equation of the cassie arc model according to the first functional relational expression and the second functional relational expression.

Further, the arc stabilization resistance acquisition module 30 includes:

The arc stabilizing resistance calculation unit is used to calculate the arc stabilizing resistance by the following formula:

R _arc =K ₁ R _m +K ₂ R _c ;

Wherein, R _arc is the arc stabilizing resistance, K ₁ is the first proportional coefficient, and the first proportional coefficient is the proportional coefficient of the mayr arc resistance, K ₂ is the second proportional coefficient, and the second proportional coefficient is The proportional coefficient of the cassie arc resistance, R _m is the mayr arc resistance, and R _c is the cassie arc resistance.

Further, the second functional relationship establishment module 50 includes:

The mayr arc time constant functional relational expression establishment unit is used to establish the functional relational expression of the mayr arc time constant by the following formula:

Wherein, τ _m is the mayr arc time constant, i is the arc current, U _arc is the arc stable arc voltage, g is the arc conductance, and t is time;

The cassie arc time constant functional relational expression establishment unit is used to establish the functional relational expression of the cassie arc time constant by the following formula:

Wherein, τ _c is described cassie arc time constant;

Dissipated power functional relational expression establishment unit, used for establishing the functional relational expression of described dissipated power by the following formula:

p = U _arc |i|;

Wherein, p is the dissipated power.

Those skilled in the art can clearly understand that the technologies in the embodiments of the present application can be implemented by means of software plus a necessary general-purpose hardware platform. Based on this understanding, the technical solution in the embodiment of the present application is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a storage medium, such as ROM/RAM , magnetic disk, optical disk, etc., including several instructions to enable a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present application.

The present application has been described in detail above in conjunction with specific implementations and illustrative examples, but these descriptions should not be construed as limiting the present application. Those skilled in the art understand that without departing from the spirit and scope of the present application, various equivalent replacements, modifications or improvements can be made to the technical solutions and implementations of the present application, all of which fall within the scope of the present application. The scope of protection of the present application is subject to the appended claims.

Claims (3)

1. A method for building an electric arc model, comprising: Acquiring arc data, the arc data including arc voltage, arc current and arc stable arc voltage; Obtaining arc conductance according to the arc voltage and the arc current; Obtaining the mayr arc resistance and the cassie arc resistance, and setting the proportional coefficient, by connecting the mayr arc resistance and the cassie arc resistance in series according to the proportional coefficient, obtaining the arc stabilizing resistance; The proportional coefficient includes a first proportional coefficient and a second proportional coefficient, the first proportional coefficient is the proportional coefficient of the mayr arc resistance, and the second proportional coefficient is the proportional coefficient of the cassie arc resistance; The formula for calculating the arc stabilizing resistance is as follows: R _arc =K ₁ R _m +K ₂ R _c ; Wherein, R _arc is the arc stabilizing resistance, K ₁ is the first proportional coefficient, K ₂ is the second proportional coefficient, R _m is the mayr arc resistance, R _c is the cassie arc resistance; Change the arc voltage to obtain the relationship between the arc stabilizing resistance, arc voltage and proportional coefficient, and establish the first functional relationship between the arc stabilizing arc voltage, the proportional coefficient and the arc stabilizing resistance: R _arc = f(U _arc , K), wherein, R _arc is the arc stabilizing resistance, U _arc is the arc voltage, and K is the proportional coefficient; According to the arc current, the stable arc voltage of the arc and the conductance of the arc, the time constant of the arc and the power dissipation are fitted with a function to establish a second functional relational expression, the time constant of the arc includes a mayr arc time Constant and cassie arc time constant, the second functional relational expression includes the functional relational expression of the mayr arc time constant, the functional relational expression of the cassie arc time constant and the functional relational expression of the dissipated power; The functional relational expression of described mayr arc time constant is set up by following formula:

Wherein, τ _m is the mayr arc time constant, i is the arc current, U _arc is the arc stable arc voltage, g is the arc conductance, and t is time; The functional relational expression of described cassie arc time constant is established by the following formula:

Wherein, τ _c is described cassie arc time constant; The functional relationship of the dissipated power is established by the following formula: p = U _arc i; Wherein, p is described dissipated power; An arc model is constructed based on the first functional relational expression and the second functional relational expression, based on the principle equation of the mayr arc model and the principle equation of the cassie arc model. 2. The method of claim 1, wherein, The principle equation of the mayr arc model is:

Wherein, g _m is the mayr arc conductance, and the mayr arc conductance is inversely proportional to the mayr arc resistance, τ _m is the mayr arc time constant, u is the arc voltage, i is the arc current, and p is said dissipated power; The principle equation of the cassie arc model is:

Wherein, g _c is the conductance of the cassie arc, and the conductance of the cassie arc is inversely proportional to the resistance of the cassie arc, τ _c is the time constant of the cassie arc, and U _arc is the stable arcing voltage of the arc. 3. An electric arc model building system, characterized in that, comprising: An arc data acquisition module, configured to acquire arc data, the arc data including arc voltage, arc current and arc stable arc voltage; an arc conductance acquisition module, configured to acquire arc conductance according to the arc voltage and the arc current; The arc stabilizing resistance acquisition module is used to acquire the mayr arc resistance and the cassie arc resistance, and set the proportional coefficient, and obtain the arc stabilizing resistance by connecting the mayr arc resistance and the cassie arc resistance in series according to the proportional coefficient; The arc stabilizing resistance acquisition module includes: The arc stabilizing resistance calculation unit is used to calculate the arc stabilizing resistance by the following formula: R _arc =K ₁ R _m +K ₂ R _c ; Wherein, R _arc is the arc stabilizing resistance, K ₁ is the first proportional coefficient, and the first proportional coefficient is the proportional coefficient of the mayr arc resistance, K ₂ is the second proportional coefficient, and the second proportional coefficient is The proportional coefficient of the cassie arc resistance, R _m is the mayr arc resistance, R _c is the cassie arc resistance; The first functional relationship building module is used to change the arc voltage to obtain the relationship between the arc stabilizing resistance, arc voltage and proportional coefficient, and establish the relationship between the arc stabilizing arc voltage, the proportional coefficient and the arc stabilizing resistance The first functional relationship of the functional relationship: R _arc =f(U _arc , K), wherein, R _arc is the arc stabilization resistance, U _arc is the arc voltage, and K is the proportional coefficient; The second functional relationship establishment module is used to perform function fitting on the time constant and dissipated power of the arc according to the arc current, the arc stable arc voltage and the arc conductance, and establish a second functional relationship, The time constant of the arc includes a mayr arc time constant and a cassie arc time constant, and the second functional relational expression includes a functional relational expression of the mayr arc time constant, a functional relational expression of the cassie arc time constant, and the consumption The functional relationship of the dissipation power; The second functional relational formula building module includes: The mayr arc time constant functional relational expression establishment unit is used to establish the functional relational expression of the mayr arc time constant by the following formula:

Wherein, τ _m is the mayr arc time constant, i is the arc current, U _arc is the arc stable arc voltage, g is the arc conductance, and t is time; The cassie arc time constant functional relational expression establishment unit is used to establish the functional relational expression of the cassie arc time constant by the following formula:

Wherein, τ _c is described cassie arc time constant; Dissipated power functional relational expression establishment unit, used for establishing the functional relational expression of described dissipated power by the following formula: p = U _arc i; Wherein, p is described dissipated power; An arc model building module, configured to construct an arc model based on the principle equation of the mayr arc model and the principle equation of the cassie arc model according to the first functional relational expression and the second functional relational expression.

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