CN113138310A - AC arc black box model, computing device and storage medium - Google Patents
AC arc black box model, computing device and storage medium Download PDFInfo
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Abstract
The invention relates to the technical field of high voltage, in particular to an alternating current arc black box model which passes through a transition function sigma (I)arc) The method combines a Mayr model and a Cassie model, can accurately describe three stages of arc striking, stable arc burning and arc extinguishing of the alternating current arc and the change process of the instantaneous arc resistance, improves the simulation accuracy of the alternating current arc, and can accurately obtain the instantaneous arc resistance R of the alternating current arc at any momentarc(ii) a The invention also provides a computer device for storing and operating the alternating current arc black box model and a storage medium for storing the alternating current arc black box model.
Description
Technical Field
The invention relates to the technical field of high voltage, in particular to an alternating current arc black box model, a computing device for operating the alternating current arc black box model and a storage medium for storing the alternating current arc black box model.
Background
The existing alternating current arc model mainly comprises an exponential arc resistance model, a hyperbolic arc resistance model, a segmented arc model, a black box model and the like; the first three focus on studying the internal characteristics of the arc, while the black box model only studies the external characteristics of the arc. In the black box model, the alternating current arc is taken as a component of a circuit to be researched, the internal physical process is omitted, and only the connection between the alternating current arc and an external circuit is researched, so that the arc can be better described.
The existing common basic black box model comprises a Mayr model and a Cassie model, wherein the two models regard an electric arc as a resistive two-end element; among them, the Mayr model is suitable for describing arc characteristics when the current of the ac arc is small, and the Cassie model is suitable for describing arc characteristics when the current of the ac arc is large, so that both models have limitations.
The prior art also provides an ac arc black box model obtained by combining a step function with a Mayr model and a Cassie model, which can be specifically expressed as follows: rarc＝e1(t)Rcassie+e2(t)RmayrWherein e is1(t)、e2(t) is a step function, which can be expressed as:
since the step function is a combination of finite-segment piecewise constant functions, i.e. a1、b1、a2、b2Are all constants. If a step function is used instead of the transition function according to the invention, a fixed ratio R is used when the instantaneous arc current is less than the transition current, the instantaneous arc current is greater than the transition current, and the instantaneous arc current is equal to the transition currentcassieAnd a fixed ratio of RmayrThe instantaneous arc resistance is represented, resulting in an inability to accurately describe the actual rate of change and trend of the instantaneous arc resistance of the ac arc.
Based on the background, the invention constructs a comprehensive alternating current arc black box model, which accurately describes three stages of arc starting, stable arc burning and arc extinguishing of an alternating current arc and a change process of arc resistance of the alternating current arc based on a Mayr model and a Cassie model.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an alternating current arc black box model which can accurately describe alternating current by combining a Mayr model and a Cassie model through a transition function sigma (Iarc)The three stages of arc starting, stable arc burning and arc extinguishing and the change process of the instantaneous arc resistance improve the simulation accuracy of the alternating current arc and can accurately obtain the instantaneous arc resistance R of the alternating current arc at any momentarc(ii) a The calculating device for operating the alternating current arc black box model can accurately describe three stages of arc starting, stable arc burning and arc extinguishing of the alternating current arc and the change process of the instantaneous arc resistance, improve the simulation accuracy of the alternating current arc, and accurately obtain the instantaneous arc resistance R of the alternating current arc at any momentarc(ii) a A storage medium storing the AC arc black box model is also provided.
In order to achieve the purpose, the invention adopts the following technical scheme:
an AC arc black box model calculates instantaneous arc resistance R of AC arc by the following methodarc：
Preferably, the first and second liquid crystal materials are,
said transition function
Wherein, λ is a transition function parameter, λ > 1; i istransIs the transition current, in units of A.
Preferably, the instantaneous arc current IarcAmplitude of > transition current ItransAnd instantaneous arc current IarcWith increasing amplitude of the instantaneous arc current IarcIncrease in amplitude of, σ (I)arc) Gradually approaches to
The instantaneous arc current IarcIs equal to the transition current ItransWhen, σ (I)arc) Is taken as
The instantaneous arc current IarcAmplitude of < transition current ItransAnd instantaneous arc current IarcWith the instantaneous arc current I gradually decreasing in amplitudearcOf the amplitude of (c), σ (I)arc) Gradually approaches 0.
Preferably, the transition function parameter λ and the transition current ItransObtained by the following method:
step 1s, starting from the arc starting stage of the alternating current arc, setting a plurality of measuring moments in the arc starting, stable arc burning and arc extinguishing stages of the alternating current arc, and measuring the arc burning duration of each measuring moment and the instantaneous arc voltage value U of each measuring momentarcAnd instantaneous arc current value Iarc(ii) a According to
Calculating the instantaneous arc resistance R at each measurement instantarc；
Step 2s, respectively calculating the instantaneous arc resistance R at each measuring moment according to a Cassie model and a Mayr modelcassieAnd an instantaneous arc resistance Rmayr；
Step 3s, comparing R of each measurement time obtained in step 1s and step 2scassie、RmayrAnd RarcSubstituted into Rarc＝σ(Iarc)Rcassie+(1-σ(Iarc))RmayrCalculating a transition function sigma (I) at each measurement instantarc) A value of (d);
preferably, the transition function σ (I) is dependent on each measurement instantarc) Value of (d), instantaneous arc current value I at each measurement instantarcAnd according to
Obtaining a transition function parameter lambda and a transition current I through curve fittingtransThe value of (a).
Preferably, the time interval between adjacent measurement instants is ti，0≤ti≤1ms。
Preferably, the first and second liquid crystal materials are,
the Cassie model is characterized by the following expression
Wherein, taucassieIs the time constant of the Cassie model in s.
Preferably, the first and second liquid crystal materials are,
the Mayr model has a characteristic expression of
Wherein, taumayrIs the time constant of the Mayr model in s.
A computer device stores and runs the alternating current arc black box model.
A storage medium storing said ac arc black box model, which is read by a computer to run said ac arc black box model.
The invention relates to an alternating current arc black box model which uses an instantaneous arc current IarcTransition function sigma (I) as an argumentarc) The combination being adapted to high resistanceThe Mayr model and the Cassie model with different proportions can be selected according to the instantaneous arc current change of the three stages of arcing, stable arcing and arc extinguishing of the alternating current arc, and the description functions of the Mayr model and the Cassie model in different proportions in a specific arc current range are fully exerted, so that the three stages of arcing, stable arcing and arc extinguishing of the alternating current arc and the instantaneous arc resistance R of the alternating current arc are accurately describedarcThe change process of the alternating current arc simulation system improves the simulation accuracy of the alternating current arc, and can accurately obtain the instantaneous arc resistance R of the alternating current arc at any momentarc。
Furthermore, the transition function σ (I)arc) Using an exponential function with e as base, a transition function parameter lambda and a transition current ItransIn the transition process among three different stages of arc combustion, the model can describe the change of the arc resistance rate more accurately, describe the arc striking stage and the arc extinguishing stage of the alternating current arc, and adjust the parameter lambda of the transition function and the transition current ItransThe value of (3) can accurately reflect different severe change trends of the arc resistance of each type of compressed arc and the arc resistance of each type of free arc in the arc starting stage and the arc extinguishing stage; in addition, the alternating current arc black box model can measure the instantaneous arc voltage and the instantaneous arc current of each type of arc resistor, and can measure the transition function parameter lambda and the transition current ItransAnd the correction is carried out, the response is quick, and the accuracy of the alternating current arc black box model is ensured when various types of arc resistors are described.
The computer device can accurately describe three stages of arc starting, stable arc burning and arc extinguishing of the alternating current arc and the change process of the instantaneous arc resistance of the alternating current arc, and can also accurately obtain the instantaneous arc resistance R of the alternating current arc at any momentarc。
The storage medium can conveniently and quickly provide the alternating current arc black box model for a computer to accurately describe three stages of arc starting, stable arc burning and arc extinguishing of an alternating current arc and the change process of the instantaneous arc resistance of the alternating current arc, and can also accurately obtain the instantaneous arc resistance R of the alternating current arc at any momentarc。
Drawings
FIG. 1 is a diagram of a transition function curve cluster under different transition function parameters according to the present invention;
FIG. 2 is a schematic diagram of a family of transition function curves for different transition currents in accordance with the present invention;
FIG. 3 is a simulation block diagram of the 10kV power transmission and distribution system of the present invention;
FIG. 4 is a block diagram of a simulation of the AC arc black box model of the present invention;
FIG. 5 is a schematic diagram of an arc resistance simulation curve according to the present invention.
Detailed Description
The following description will further describe embodiments of the ac arc black box model, the computer device and the storage medium according to the present invention with reference to the embodiments shown in fig. 1 to 5. The alternating current arc black box model, the computer apparatus and the storage medium of the present invention are not limited to the description of the following embodiments.
The invention relates to an alternating current arc black box model, which calculates the instantaneous arc resistance R of an alternating current arc by the following methodarc：
The invention relates to an alternating current arc black box model which uses an instantaneous arc current IarcTransition function sigma (I) as an argumentarc) The Mayr model and the Cassie model with different proportions can be selected according to the instantaneous arc current change of the three stages of arcing, stable arcing and arc extinguishing of the alternating current arc by combining the Mayr model suitable for high-resistance small current and the Cassie model suitable for low-resistance large current, and the description functions of the Mayr model and the Cassie model in different proportions in a specific arc current range are fully exerted, so that the three stages of arcing, stable arcing and arc extinguishing of the alternating current arc and the instantaneous arc resistance R are accurately describedarcThe change process of the alternating current arc simulation model improves the simulation accuracy of the alternating current arc, and can accurately calculate the instantaneous arc resistance R of the alternating current arc at any momentarc。
Preferably, the transition function
Wherein, λ is a transition function parameter, λ > 1; i istransIs the transition current, in units of A.
The invention relates to an alternating current arc black box model, the transition function sigma (I) of whicharc) Applying an exponential function with e as base, a transition function parameter lambda and a transition current ItransIn the transition process among three different stages of arc combustion, the model can describe the change of the arc resistance rate more accurately, describe the arc striking stage and the arc extinguishing stage of the alternating current arc, and adjust the parameter lambda of the transition function and the transition current ItransThe value of (3) can accurately reflect different severe change trends of the arc resistance of each type of compressed arc and the arc resistance of each type of free arc in the arc starting stage and the arc extinguishing stage; in addition, the alternating current arc black box model can measure the instantaneous arc voltage and the instantaneous arc current of each type of arc resistor, and can measure the transition function parameter lambda and the transition current ItransThe correction is carried out, the response is quick, and the alternating current arc black box model of the invention is ensured to describe various typesAccuracy of instantaneous arc resistance of the type AC arc.
The invention also discloses a computer device which stores and runs the alternating current arc black box model and can accurately describe three stages of arc starting, stable arc burning and arc extinguishing of the alternating current arc, so that the change process of the instantaneous arc resistance of each type of alternating current arc can be more accurately described.
The invention also discloses a storage medium which stores the alternating current arc black box model and is read by a computer to operate the alternating current arc black box model.
The AC arc black box model of the present invention will be further described with reference to the drawings and the specific embodiments.
The following is one embodiment of the ac arc black box model of the present invention.
In the AC arc black box model of the present embodiment, the instantaneous arc resistance R of the AC arc is calculated by the following methodarc：
In particular, the instantaneous arc current IarcAmplitude of > transition current ItransAnd instantaneous arc current IarcWith increasing amplitude of the instantaneous arc current IarcIncrease in amplitude of, σ (I)arc) Gradually approaches to
(that is, in the AC arc black box model of the present embodiment, the Cassie model is almost only used to describe the arc characteristics and the instantaneous arc resistance R when the arc current is largearc) (ii) a The instantaneous arc current IarcIs equal to the transition current ItransWhen, σ (I)arc) Is taken as
(that is, in the AC arc black box model of the present embodiment, the Mayr model and the Cassie model are used to describe the arc characteristics and the transient arc resistance RarcAnd the proportionality coefficients of the two are the same); the instantaneous arc current IarcAmplitude of < transition current ItransAnd instantaneous arc current IarcWith the instantaneous arc current I gradually decreasing in amplitudearcOf the amplitude of (c), σ (I)arc) The value of (a) gradually approaches to 0 (that is, in the ac arc model of the present embodiment, the Mayr model is almost only used to describe the arc characteristics and the instantaneous arc resistance R when the arc current is small (before and after zero crossing)arc) (ii) a Therefore, for the alternating current arc with the arc current attenuating, the arc resistance and the arc characteristics at any instant of time can be accurately described by applying the alternating current arc black box model of the embodiment when the arc voltage and the arc current of the alternating current arc change continuously.
Preferably, the transition function
Wherein, λ is a transition function parameter, λ > 1; i istransIs the transition current, in units of A.
Specifically, as shown in FIG. 1, let the transition current ItransWhen the transition function parameter λ is equal to 360A, the values are 5, 10, and 15, respectively, and the transition function σ (I) is plottedarc) It can be seen that the transition function σ (I) increases with the increase of the value of the transition function parameter λarc) The faster the rate of change of the value of (c) at the inflection point.
Specifically, as shown in fig. 2, let the transition function parameter λ be 10, and let the transition current I betransRespectively taking the values of 90A, 360A and 630A, and drawing a transition function sigma (I)arc) Can be seen as a function of the transition current ItransIncreasing the value, the transition function σ (I)arc) The slower the rate of change of the value of (c) at the inflection point and the larger the occupancy of the Mayr model used in the description of the arc characteristics.
It should be noted that the value of the transition function parameter λ is related to the actual ac arc type, and the change rates of the instantaneous arc resistances of different types of ac arcs in the arc striking, stable arc burning and arc extinguishing phases are different, and the time when the instantaneous arc resistance starts to change drastically is also different, for example:
in the process of running of a high-speed rail, the bow net off-line electric arc is subjected to a strong air arc blowing effect, so that the heat dissipation power of the bow net off-line electric arc is higher, the arc quenching speed is higher, the change of the instantaneous electric arc resistance is more violent, and the total arc burning duration is shorter; meanwhile, the pantograph-catenary offline electric arc is positioned between the pantograph and the suspension line, and the arc length is continuously increased along with the increase of the pantograph-catenary offline distance, so that the arc quenching speed is also increased.
For switching arcs, the arc length is not changed greatly, and the air blowing effect is very small, so that the electrical characteristics of the arcs are greatly different from those of bow net off-line arcs.
Therefore, the alternating current arc black box model of the invention is realized by correcting the parameter lambda of the transition function and the transition current ItransThe electrical characteristics of different types of alternating arcs and the change process of the instantaneous arc resistance can be described more accurately.
It should be noted that the alternating current arc black box model of the present invention is used for describing the electrical characteristics of a certain type of alternating current arc and the transient arc resistance change processFunction parameter lambda and transition current ItransThe method can measure the arcing duration of the type of alternating-current arc after the starting of the arcing stage, the corresponding instantaneous arc voltage and instantaneous arc current at each measuring moment for multiple times, and then according to the instantaneous arc resistance RarcPerforming curve fitting to obtain a transition function parameter lambda and a transition current ItransThe value of (2) specifically comprises the following steps:
step 1s, starting from an arc starting stage of the alternating-current arc, setting a plurality of measuring moments (the number of the measuring moments is determined according to measuring intervals of measuring instruments, the more the measuring moments are, the better the measuring moments are) at the arc starting, stable arc burning and arc extinguishing stages, and recording arc burning duration (the duration from the arc starting stage to each current measuring moment) of each measuring moment and an instantaneous arc voltage value U of each measuring momentarcInstantaneous arc current value Iarc(ii) a According to
Calculating the instantaneous arc resistance R at each measurement instantarc；
Step 2s, then the following two differential equations (the expressions of the Cassie model and the Mayr model, respectively) are solved: the Cassie model and the Mayr model respectively calculate the instantaneous arc resistance R at each measurement momentcassieAnd an instantaneous arc resistance RmayrI.e., solving the following two differential equations,
the general solutions are obtained respectively as follows:
step 3s, comparing R of each measurement time obtained in step 1s and step 2scassie、RmayrAnd RarcSubstituting into the instantaneous arc resistance RarcThe calculation formula of (2): rarc＝σ(Iarc)Rcassie+(1-σ(Iarc))RmayrCalculating a transition function sigma (I) at each measurement instantarc) A value of (d);
step 4s, according to the transition function σ (I) at each measurement instantarc) Value of (d), instantaneous arc current value I at each measurement instantarcAnd according to
Obtaining a transition function parameter lambda and a transition current I through curve fittingtransThe value of (a).
Preferably, the time interval between adjacent measurement instants is ti，0＜ti≤1ms。
Specifically, in step 1s, the number of the measurement times is related to the total arcing duration of the ac arc. For example, for an offline pantograph-catenary arc, the maximum possible arcing time of the arc is from the separation of the pantograph from the catenary suspension line to the maximum offline distance between the pantograph and the catenary suspension line until the pantograph and the catenary suspension line are contacted again, the pantograph can be regarded as vibrating in simple resonance in the process, and the total time of the whole process is about 0.7 s. Within 0.7s, the bow net off-line arc may also be extinguished in advance and not reignited, but the maximum possible arcing duration is 0.7s, so at least 0.7s should be measured for such bow net off-line arcs, in which case the number of measurement instants should be ≧ 700.
Preferably, the Cassie model feature expression is as follows:
wherein, taucassieIs the time constant of the Cassie model,the unit is s.
Note that the Cassie model assumes: the arc column of the alternating current arc is a cylinder with a constant diameter, the temperature of the cross section of the arc column is uniformly distributed, the diameter of the arc column changes along with the change of the arc current, the temperature of the arc remains constant, and the heat dissipation power of the arc energy also continuously increases along with the increase of the cross section area of the arc column.
Preferably, the characteristic expression of the Mayr model is as follows:
wherein, taumayrIs the time constant of the Mayr model in s.
Note that the Mayr model assumes: the arc column of the alternating current arc is a cylinder with a constant diameter, the farther the arc column is away from the axis of the cylinder, the lower the temperature of the arc is, the temperature of the arc changes along with the radial distance and time change of the axis of the arc column, the dissipation of the arc power is not influenced by air convection, and the heat dissipation power is a fixed value.
The alternating current arc black box model improves the obtained instantaneous arc resistance R of the alternating current arcarcThe accuracy of (2) in practical use is applicable to and not limited to the following fields:
(1) the field of power switches, such as the manufacture of high-voltage circuit breakers (vacuum interrupters);
(2) the field of welding, such as correction of arc welding process parameters;
(3) in the field of railway transportation, such as treatment of high-speed railway pantograph-catenary offline electric arcs, the alternating-current electric arc black box model can be used for simulating the high-speed railway pantograph-catenary offline electric arcs under the actual operation condition to obtain the transient overvoltage characteristics of the arcing stage of the pantograph-catenary offline electric arcs under the actual operation condition, and can be used for selecting a parallel capacitor, a grounding resistor and a voltage mutual inductance excitation inductor to inhibit overvoltage and improve the safety and reliability of power supply.
As shown in fig. 3 and 4, a simulation model of a single-phase grounding arc of a power transmission line in a 10kV system built in Simulink utilizes a controllable current source to achieve the purpose of simulating arc resistance with time sequence variation by adjusting the current of the controllable current source.
Setting: the system power supply is 10kV, the frequency is 50Hz, the load is 10MW, the impedance of the power transmission line is 0.45ohms/km, the inductive reactance is 0.25mH/km, and the capacitive reactance is 0.33 muF/km; in the Mayr model, τmayrIs 0.5ms, P0Is 50 kW; in the Cassie model,. tau.cassie1.1ms, U0Is 3.2 kV; in the AC arc black box model of the embodiment, the parameter lambda of the transition function is 10, and the transition current I istrans0.032 kA; the simulation step length is 1 mus, and the total simulation time length is 0.2 s.
The following is a script code of an MATLAB fusion module of the simulation system, wherein eps is applied in the script code, namely the difference value epsilon of the maximum double-precision floating point number in the MATLAB is 2-52The method is used for representing the minimum positive number in the MATLAB, and avoiding the situation that a possible singular value occurs because the denominator is 0 in the simulation calculation, and specifically:
(1) MATLAB Function module arc synthesis black box model part1, including the code for Mayr model and Cassie model:
function[pRm，pRc]＝arc_model1(Uarc，Iarc，Rm，Rc，tau-m，tau-c，P0，U0)
pRm＝(1-Uarc*Iarc/P0)*(Rm+eps)/tau_m；
pRc＝(1-Uarc^2/U0^2)*(Rc+eps)/tac_c；
end
(2) the MATLAB Function module arc synthesis black box model part2 is a code of the ac arc black box model of this embodiment:
functionRarc＝arc_mode12(Rm，Rc，sigma)
Rarc＝eps+sigma*Rc+(1-sigma)*Rm；
end
(3) MATLAB Function module transition Function, which is a transition Function σ (I)arc) The code of (2):
functionsigma＝trans_fcn(1ambda，Itrans，Iarc)
sigma＝1/(1+exp(-lambda*(1-Itrans^2/(Iarc^2+eps))))；
end
as shown in fig. 5, the arc resistance change curve observed from an oscilloscope shows that: the arc resistance has a transient high resistance state in the arc starting and arc extinguishing stages, and presents a low resistance state in the stable arc burning stage, which accords with the theoretical basis of a comprehensive model, namely, in the arc starting stage, because the current is small, the proportion of a Mayr model suitable for low-current high-resistance is very large, and transient overvoltage can occur at the moment; with the increase of the arc current, when the absorbed power of the arc is higher than the heat dissipation power, the temperature of the arc rises, the resistance of the arc drops, and due to the influence of transient overvoltage, the drop of the resistance of the arc is more severe and quickly drops to be very small immediately after the arcing stage; with the continuous increase of the current, entering a stable arcing stage, the Cassie model suitable for large current and low resistance has a very large proportion; when the current in the period reaches the maximum value, the arc temperature also reaches the maximum value, then along with the reduction of the voltage and the current, when the arc voltage is lower than the voltage required by stable arcing, the arc resistance starts to increase sharply, when the amplitude of the arc current is lower than the transition current, the arc model is represented as a comprehensive model taking a Mayr model as the main part, and the arc current has zero-rest time until the arc is extinguished or the beginning of the arcing phase of the next reignition period.
It is to be noted that the transition function parameter λ and the transition current I are used to simulate a specific arctransFor determining the value, during the simulation, the instantaneous arc current I at the current simulation momentarcMeasuring the instantaneous arc voltage U at the current simulation timearcInstantaneous arc resistance R calculated in previous simulation momentarc(ii) a For example, in the simulation model of the single-phase earth arc of the power transmission line, the total simulation time is defined to be 0.2s, and the instantaneous arc resistance R is defined before the simulation is startedcassieAnd RmayrInitial value R ofcassie0And Rmayr0Are all 210 Ω, and the instantaneous arc voltage UarcIs 0, instantaneous arc current IarcIs 0, and by running the arc black box model part2 module, R can be calculatedarcInitial value R ofarc0. At the first simulation moment, an arc is generated, and the program measures the instantaneous arc electricityPress UarcAccording to
Calculating the instantaneous arc current IarcThen program according to Uarc、Iarc、Rcassie0And Rmayr0Running an arc black box model part1 module to obtain RcassieAnd RmayrDerivative of (pR)cAnd pRmThe program operates the transition function module again, calculates the function value sigma of the transition function, substitutes the function value sigma into the arc black box model part2 module and operates the arc black box model to obtain the instantaneous arc resistance R at the simulation momentarcAnd calculating the next simulation moment. Thereafter, at each simulation instant, the process measures the instantaneous arc voltage UarcAnd then calculating the instantaneous arc resistance R according to the previous simulation momentarcAccording to
Calculating the instantaneous arc current IarcAnd sequentially executing the arc black box model part1 module, the transition function module and the arc black box model part2 module until the simulation time reaches the specified total simulation duration.
One embodiment of the computer apparatus of the present invention is: and the computer device stores and runs the alternating current arc black box model. Further, the computer device comprises a processor and a memory, the alternating current arc black box model is stored in the memory, and the processor retrieves and runs the alternating current arc black box model from the memory.
One embodiment of the storage medium of the present invention is: the storage medium stores the alternating current arc black box model, and the storage medium is read by a computer to operate the alternating current arc black box model. Further, the storage medium may be a removable hard disk or a usb disk.
It should be noted that the ac arc black box model is stored in the form of program code in a computer device or storage medium.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (9)
1. An AC arc black box model is characterized in that the instantaneous arc resistance R of an AC arc is calculated by the following methodarc：
Step 1, obtaining instantaneous arc voltage U of alternating current arcarcStable arcing voltage U of AC arc in stable arcing stage0Instantaneous arc current I of an AC arcarcAnd the heat dissipation power P of the alternating current arc in the stable arcing stage0Instantaneous arc voltage UarcAnd stabilizing the arcing voltage U0In units of V, instantaneous arc current IarcHas a unit of A, heat dissipation power P0The unit of (a) is W; instantaneous arc resistance R of alternating current arc according to Cassie modelcassie(ii) a Instantaneous arc resistance R of alternating current arc according to Mayr modelmayr；
Step 2, according to the R obtained in the step 1cassieAnd RmayrCalculating the instantaneous arc resistance R of the AC arcarc，Rarc＝σ(Iarc)Rcassie+(1-σ(Iarc))Rmayr(ii) a Wherein, σ (I)arc) In order to be a function of the transition,
Rarc、Rcassieand RmayrAll units of (2) are omega.
2. The alternating current arc black box model of claim 1, wherein:
said transition function
Wherein, λ is a transition function parameter, λ > 1; i istransIs the transition current, in units of A.
3. The alternating current arc black box model of claim 2, wherein:
the instantaneous arc current IarcAmplitude of > transition current ItransAnd instantaneous arc current IarcWith increasing amplitude of the instantaneous arc current IarcIncrease in amplitude of, σ (I)arc) Gradually approaches to
The instantaneous arc current IarcIs equal to the transition current ItransWhen, σ (I)arc) Is taken as
The instantaneous arc current IarcAmplitude of < transition current ItransAnd instantaneous arc current IarcWith the instantaneous arc current I gradually decreasing in amplitudearcOf the amplitude of (c), σ (I)arc) Gradually approaches 0.
4. The alternating current arc black box model of claim 2, wherein: the transition function parameter lambda and the transition current ItransObtained by the following method:
step 1s, starting from the arc starting stage of the alternating current arc, setting a plurality of measuring moments in the arc starting, stable arc burning and arc extinguishing stages of the alternating current arc, and measuring the arc burning duration of each measuring moment and the instantaneous arc voltage value U of each measuring momentarcAnd instantaneous arc current value Iarc(ii) a According to
Calculating the instantaneous arc resistance R at each measurement instantarc；
Step 2s, classifying according to Cassie model and Mayr modelCalculating the instantaneous arc resistance R at each measuring timecassieAnd an instantaneous arc resistance Rmayr；
Step 3s, comparing R of each measurement time obtained in step 1s and step 2scassie、RmayrAnd RarcSubstituted into Rarc＝σ(Iarc)Rcassie+(1-σ(Iarc))RmayrCalculating a transition function sigma (I) at each measurement instantarc) A value of (d);
step 4s, according to the transition function σ (I) at each measurement instantarc) Value of (d), instantaneous arc current value I at each measurement instantarcAnd according to
Obtaining a transition function parameter lambda and a transition current I through curve fittingtransThe value of (a).
5. The alternating current arc black box model of claim 4, wherein: the time interval between adjacent measurement moments is ti，0≤ti≤1ms。
6. The alternating current arc black box model of claim 1, wherein:
the Cassie model is characterized by the following expression
Wherein, taucassieIs the time constant of the Cassie model in s.
7. The alternating current arc black box model of claim 1, wherein:
the Mayr model has a characteristic expression of
Wherein, taumayrTime constant for Mayr modelNumber, in units of s.
8. A computer device storing and operating the ac arc black box model of any one of claims 1-7.
9. A storage medium storing the ac arc black box model of any one of claims 1 to 7, read by a computer to run the ac arc black box model.
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