Long-gap in-oil arc test platform and energy calculation method

Abstract

The invention provides a long-gap in-oil arc test platform and an energy calculation method, and relates to the technical field of in-oil arc energy calculation, the long-gap in-oil arc test platform comprises a current source loop and a discharge loop, the current source loop is used for providing large current for the discharge loop, and the discharge loop is used for providing large current for the discharge loop. The discharge loop comprises an in-oil arc test tank body, a voltage measuring instrument, a current measuring instrument, a temperature measuring instrument, an image acquisition instrument and N metal probes, wherein N is a positive integer. According to the energy calculation method, short arc injection energy and loss energy are calculated through piecewise linear discretization, and energy calculation errors are reduced; meanwhile, the arc energy space-time distribution characteristics are obtained, and a theoretical basis is provided for research of an arc dynamic breakdown mechanism.

Description

Technical Field

[0001] The present invention relates to the technical field of arc energy calculation in oil, and particularly relates to a long-gap arc test platform in oil and an energy calculation method. Background Art

[0002] As the heart of the power grid, power transformers play a crucial role in the power system. However, after long-term operation of the transformer, internal insulation is inevitably damaged, and faults such as inter-turn short circuits, phase-to-phase short circuits, or ground short circuits are likely to occur. The high-energy arc generated by the short-circuit fault will cause the insulating oil to quickly vaporize, resulting in a sudden increase in the pressure inside the fuel tank. If the power is not cut off in time or the pressure relief valve does not act immediately, accidents such as deflagration are extremely likely to occur. Among them, due to the large arc energy, large contact area between the arc and the transformer oil, and more gas generated by the long-gap arc, it is easier to cause serious accidents such as transformer explosion and combustion, seriously affecting the safe and stable operation of the power system. Therefore, it is necessary to propose a calculation method for the energy of the long-gap arc in oil to provide theoretical guidance and data support for the internal pressure calculation and explosion-proof design of the transformer.

[0003] Currently, the research on arc energy is limited to the case of short arcs, and the calculation method for the energy of long-gap arcs is not yet clear. The arc diameter distribution of short-gap arcs is relatively uniform. Therefore, it can be considered that the short-arc channel has a uniform conductivity, and the short-arc resistance is linearly related to the length. Based on this, the current method of integrating arc voltage and current can be used to calculate the energy of short arcs.

[0004] The long-gap arc in oil is affected by the coupling of the temperature gradient, flow rate, and bubble distribution of the insulating oil, and its conductivity shows significant spatial non-uniform characteristics, resulting in that the resistance model of the long arc cannot be simplified to an idealized assumption linearly related to the length. At this time, if the arc voltage-current integration method is used to calculate the arc energy, significant errors will occur. Summary of the Invention

[0005] The purpose of the present invention is to provide a long-gap arc test platform in oil and an energy calculation method, which are used to solve the problems that the calculation method for the energy of long-gap arcs in the prior art is not yet clear and there are significant errors in the calculation of the energy of long-gap arcs. It can calculate the energy of long-gap arcs, reduce the error in the calculation of the energy of long-gap arcs, and obtain the spatio-temporal distribution characteristics of arc energy, providing a theoretical basis for the research on the dynamic breakdown mechanism of arcs.

[0006] To achieve the above purpose, in the first aspect, the present invention provides a long-gap arc test platform in oil, including a current source circuit and a discharge circuit. The current source circuit is used to provide a large current for the discharge circuit. The discharge circuit includes an arc test tank in oil, a voltage measuring instrument, a current measuring instrument, a temperature measuring instrument, an image acquisition instrument, and N metal probes, where N is a positive integer; The oil medium arc test tank is provided with insulating oil and two opposite metal rod electrodes. After a large current is passed through the two metal rod electrodes, a long-gap arc is generated; N metal probes divide the long-gap arc into N + 1 segments of arcs, and a voltage measuring instrument is used to measure the voltage of the i-th segment of arc. U i , and a current measuring instrument is used to measure the current of the long-gap arc at time t. I t , a temperature measuring instrument is used to measure the temperature of the long-gap arc and the temperature of the insulating oil, and an image acquisition instrument is used to acquire n images of the long-gap arc and the discharge duration, where n is a positive integer.

[0007] According to a long-gap oil medium arc test platform provided by the present invention, the voltage measuring instrument includes N oscilloscopes, and the N metal probes are respectively connected to the N oscilloscopes through different high-voltage probes. According to a long-gap oil medium arc test platform provided by the present invention, the metal rod electrode is a copper rod electrode.

[0008] According to a long-gap oil medium arc test platform provided by the present invention, the metal probe is a tungsten probe.

[0009] According to a long-gap oil medium arc test platform provided by the present invention, the current measuring instrument is a Rogowski coil.

[0010] According to a long-gap oil medium arc test platform provided by the present invention, the temperature measuring instrument is a sapphire optical fiber.

[0011] According to a long-gap oil medium arc test platform provided by the present invention, the image acquisition instrument is a high-speed camera. Observation windows are provided on both sides of the oil medium arc test tank. The high-speed camera is arranged at one observation window, and a fill light is arranged at the other observation window.

[0012] According to a long-gap oil medium arc test platform provided by the present invention, the current source circuit includes a capacitor C i , an inductor L i , a closing circuit breaker, and an auxiliary circuit breaker. The first end of the capacitor C i is connected to the first end of the inductor L i , the second end of the inductor L i is connected to the first end of the closing circuit breaker, the second end of the closing circuit breaker is connected to the first end of the auxiliary circuit breaker, the second end of the auxiliary circuit breaker is connected to one metal rod electrode, and the other metal rod electrode and the second end of the capacitor C i are both grounded.

[0013] According to a long-gap oil medium arc test platform provided by the present invention, in the current source circuit, the capacitor C i and the inductor L i generate a test current through resonance I 1, the test currentI The expression of 1 is:

[0014]

[0015] In the formula, U 0 represents the initial charging voltage of capacitor C i ; ω represents the resonance frequency; β is the attenuation coefficient of the current source loop; C , L and R are respectively the total capacitance, total inductance and total resistance of the current source loop; t is the time.

[0016] In the second aspect, the present invention provides a method for calculating the energy of a long-gap arc in oil, including: Construct the long-gap arc test platform in oil of the first aspect; The current source loop supplies a large current to the discharge loop; Measure the voltage of the i-th arc segment through a voltage measuring instrument U i , measure the current of the long-gap arc at time t through a current measuring instrument I t , measure the temperature of the long-gap arc and the temperature of the insulating oil through a temperature measuring instrument, and collect n images and the discharge duration of the long-gap arc through an image acquisition instrument, where n is a positive integer; Use the edge segmentation algorithm to obtain the average arc diameter and length of the i-th arc segment in the j-th image of the long-gap arc. Consider the i-th arc segment as a cylinder, and calculate the surface area of the cylinder, that is, the contact area between the i-th arc segment and the insulating oil S ij ; Calculate the injected energy of the long-gap arc as:

[0017] In the formula, t0 is the discharge duration of the long-gap arc; Calculate the dissipated energy of the long-gap arc as:

[0018] In the formula, k is the thermal conductivity of the insulating oil, T ij is the temperature difference between the temperature of the i-th arc segment and the temperature of the insulating oil in the j-th image, is the acquisition interval of the image acquisition instrument, is the distance between the long-gap arc temperature measurement point and the insulating oil temperature measurement point, his the convective heat transfer coefficient; Furthermore, the energy of the long-gap arc is obtained as: W = W 1 －W 2.

[0019] The present invention at least has the following technical effects: The present invention provides a long-gap arc test platform in oil and an energy calculation method. By multi-electrode configuration, the long-gap arc is discretized into a series of short arcs. After measuring the short-arc voltage and current separately, the input energy of the short arcs is calculated respectively. Further considering the heat transfer energy loss during the arc combustion process, the net energy of a series of short arcs is accumulated to obtain the total energy of the long-gap arc in oil. Compared with the traditional electrode terminal voltage-current global integration method, the method of the present invention calculates the injected energy and loss energy of the short arcs through piecewise linear discretization, reducing the error of energy calculation; at the same time, the spatio-temporal distribution characteristics of the arc energy are obtained, providing a theoretical basis for the study of the arc dynamic breakdown mechanism. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the implementation examples or the prior art descriptions. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0021] In the drawings: Figure 1 is the structural schematic diagram of the long-gap arc test platform in oil of the present invention; Figure 2 is the equivalent circuit diagram of the current source circuit of the present invention; Figure 3 is the structural schematic diagram of the discharge circuit of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0022] To make the objectives, technical solutions and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions in the present invention with reference to the drawings in the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0023] The following will describe some embodiments of the present invention in detail with reference to the drawings. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0024] A method for calculating the energy of a long-gap arc in oil proposed by the present invention implements multi-electrode configuration through a high-energy arc test platform, and uses the voltage-current integration method to measure the energy input of discretized arc units; on this basis, the heat transfer losses between the arc and the electrodes and insulating oil are further considered. Finally, the net energy of the long-gap arc in oil is obtained through the energy conservation equation.

[0025] Please refer to Figure 1 , an embodiment of the present invention provides a long-gap arc test platform in oil, including a current source circuit and a discharge circuit. The current source circuit is used to provide a large current for the discharge circuit. The discharge circuit includes an oil arc test tank, a voltage measuring instrument, a current measuring instrument, a temperature measuring instrument, an image acquisition instrument, and N metal probes, where N is a positive integer; There is insulating oil and two opposite metal rod electrodes in the oil arc test tank. After passing a large current through the two metal rod electrodes, a long-gap arc is generated; the N metal probes divide the long-gap arc into N + 1 arc segments, and the voltage measuring instrument is used to measure the voltage of the i-th arc segment U i , and the current measuring instrument is used to measure the current of the long-gap arc at time t I t , the temperature measuring instrument is used to measure the temperature of the long-gap arc and the temperature of the insulating oil, and the image acquisition instrument is used to acquire n images of the long-gap arc and the discharge duration, where n is a positive integer.

[0026] In some embodiments, as Figure 3 shown, the voltage measuring instrument includes N oscilloscopes. The N metal probes are respectively connected to the N oscilloscopes through different high-voltage probes, and the upper metal rod electrode is connected to the oscilloscope through a high-voltage probe, so as to measure the potential of the upper metal rod electrode. The N oscilloscopes respectively measure the potentials of the N metal probes, and then the voltages of N + 1 arc segments can be obtained, that is, segmented voltage measurement is performed. The metal rod electrode is a copper rod electrode. The metal probe is a tungsten probe. The current measuring instrument is a Rogowski coil. The temperature measuring instrument is a sapphire optical fiber. The image acquisition instrument is a high-speed camera. Observation windows are provided on both sides of the oil arc test tank. The high-speed camera is arranged at one observation window, and a supplementary light is arranged at the other observation window.

[0027] Specifically, the current source circuit includes a capacitor C i , an inductor L i , a closing circuit breaker CB, and an auxiliary circuit breaker AB. The first end of the capacitor C i is connected to the first end of the inductor L i , the second end of the inductor L i is connected to the first end of the closing circuit breaker CB, the second end of the closing circuit breaker CB is connected to the first end of the auxiliary circuit breaker AB, the second end of the auxiliary circuit breaker AB is connected to a metal rod electrode, and the other metal rod electrode is connected to the capacitor Ci The second ends of both are grounded.

[0028] In the current source loop, C i and L i serve as the capacitor and inductor of the current source respectively, and generate power frequency test current through resonance oscillation. The Rogowski coil includes an integrator Int, and the two are used together to measure the breaking current. The closing circuit breaker CB is used to control the discharge of the capacitor C i The auxiliary circuit breaker AB is used to protect the current source loop. The initial state of the closing circuit breaker CB is open, and the initial state of the auxiliary circuit breaker AB is closed. When the test starts, after a certain delay, the closing circuit breaker CB closes, thus triggering the discharge of the capacitor Ci and introducing the short-circuit current into the current source loop. At this time, the power frequency test current will pass through the discharge loop I 1.

[0029] As Figure 2 shown, it is the equivalent circuit of the current source loop. Among them C, L, and R are the total capacitance, total inductance and total resistance of the current source loop respectively. After the capacitor C i is charged and discharges, if the resistance of the arc is not considered at this time, the current source loop is a passive second-order RLC circuit. The test current I 1 in the current source loop is controlled by the initial charging voltage of the capacitor C i , and its calculation formula is as follows:

[0030]

[0031] Among them, U 0 represents the initial charging voltage of the capacitor C i ; ω represents the resonance frequency, which is 50 Hz of the power frequency here; β is the attenuation coefficient of the current source loop; C , L and R are the total capacitance, total inductance and total resistance of the current source loop respectively; t is the time.

[0032] By controlling the capacitor C i and the initial charging voltage U 0, the current peak value can be controlled. By controlling the total inductance and total resistance, the loop attenuation coefficient β can be controlled.

[0033] Specifically, as Figure 3As shown, the oil arc test tank is a cylindrical tank welded from high-strength Q345 steel plates. It has a diameter of 800 mm, a height of 1000 mm, and a capacity of 502.7 L. The top and bottom covers are 900 mm in diameter, leaving ample space for securing screws. Observation windows are located in the center of each side of the tank: one for supplemental lighting and the other for a high-speed camera to capture the arc morphology. A high-voltage bushing is located at the top and bottom of the tank, connecting the internal metal rod electrodes to the external current source circuit. The metal rod electrodes are a pair of copper rods, with an arc starter wire installed between them. The high short-circuit current applied by the current source circuit generates significant heat in the arc starter wire, causing it to melt and generate a long gap arc between the two copper rod electrodes.

[0034] The arc diameter of a long-gap electric arc is unevenly distributed in space, and it cannot be equivalent to a cylinder with uniform conductivity using the short-arc method. Based on the idea of piecewise linearization, another embodiment of the present invention provides a method for calculating the energy of a long-gap electric arc in oil, including: Step 1: Build the long-gap arc-in-oil test platform of the above embodiment; Specifically, at the beginning of the test, it is necessary to ensure that the measuring part is securely installed; adjust the distance between the electrodes and secure the arc-starting wire; inject transformer insulating oil through the oil filling valve at the bottom of the tank, leaving a certain amount of gas space to prevent a sudden increase in internal tank pressure caused by the arc cracking the insulating oil and producing gas; and perform a vacuum treatment to remove the outside air introduced during oil filling and prevent explosions inside the tank. Check whether the closing position of each circuit breaker in the current source circuit is correct and whether the measuring device, signal transmission device, etc. are functioning properly. After the inspection is correct, perform the charging operation. Record the data during the arcing process. After 80ms, the circuit breaker reliably operates and the arc is extinguished. After the discharge is completed, ensure that the circuit breaker is reliably disconnected, and then use the oil filter to extract the transformer insulating oil from the tank in preparation for the next test.

[0035] Step 2: The current source circuit provides a large current to the discharge circuit; Step 3: Measure the voltage of the arc segment i using a voltage meter. U i , measure the current of the long gap arc at time t by the current measuring instrument I t , measuring the temperature of the long gap arc and the temperature of the insulating oil by a temperature measuring instrument, and collecting n images of the long gap arc and the discharge duration by an image acquisition instrument, where n is a positive integer; In a specific embodiment of the present invention, 4 tungsten probes (tungsten has a high melting point to prevent damage by the high temperature of the arc) are used to divide the long-gap arc into 5 segments, and each segment of the arc can be regarded as a time-varying resistor. The 4 tungsten probes are connected to different oscilloscopes through 4 different high-voltage probes to avoid interference caused by the formation of a loop in the oscilloscope ground wire. The voltages of the 5 segments of the arc are respectively denoted as U i ( i = 1, 2, 3, 4, 5).

[0036] The melting point of the sapphire optical fiber is around 2300K and can withstand the high temperature generated by the arc. Moreover, it measures temperature in the form of an optical signal and is not affected by the electromagnetic interference generated by the arc. Therefore, two segments of sapphire optical fiber can be used. One segment is arranged in the arc area to measure the arc temperature; the other segment is arranged 10 mm around the arc to measure the temperature of the insulating oil around the arc.

[0037] The arc current is actually the current flowing through the current source loop. Therefore, only by installing a Rogowski coil on the wire side of the current source loop can the measurement of the arc current be realized.

[0038] The image acquisition device is a high-speed camera, which cooperates with a fill light to complete image acquisition. The high-speed camera has two triggering methods: manual triggering and pulse triggering. Here, the second method is adopted. After the oscilloscope records the conduction current of the current source loop through the Rogowski coil, it immediately outputs a pulse wave to the high-speed camera to control its shooting. The shooting duration is 3 - 4 power frequency cycles, that is, 60 ms - 80 ms. Therefore, there are certain requirements for the frame rate of the high-speed camera. Here, a high-speed camera with a frame rate of 2000 FPS is selected.

[0039] Step 4: Use the edge segmentation algorithm to obtain the average arc diameter and length of the i-th segment of the arc in the j-th image of the long-gap arc. Regarding the i-th segment of the arc as a cylinder, calculate the surface area of the cylinder, that is, the contact area between the i-th segment of the arc and the insulating oil in the j-th image S ij ; Step 5: Calculate the injection energy of the long-gap arc as:

[0040] In the formula, t0 is the discharge duration of the long-gap arc; Specifically, by segmenting the long-gap arc, each segment of the arc can be regarded as an equivalent resistor with uniform conductivity according to the treatment method of a short arc. At this time, the voltage U i and current I t between the N + 1 segments of the arc divided by N tungsten electrodes can be used to calculate the energy of the arc.

[0041] Step 6. Calculate the dissipated energy of the long-gap arc as follows:

[0042] In the formula, k is the thermal conductivity of the insulating oil; T ij is the temperature difference between the temperature of the i-th segment of the arc and the temperature of the insulating oil in the j-th image; is the acquisition interval of the image acquisition device; is the distance between the long-gap arc temperature measurement point and the insulating oil temperature measurement point; h is the convective heat transfer coefficient; It should be noted that the arc dissipated energy mainly occurs through two ways: ① heat conduction loss W t ; ② heat convection loss W c . The arc loss energy W The calculation formula is as follows:

[0043] The arc dissipates energy in the form of heat, mainly including three forms: heat conduction, heat convection, and heat radiation. Among them, heat conduction and heat convection are the main ways of arc heat dissipation. In the experiment, a 2000 FPS high-speed camera was used to take n images of the arc discharge in oil, and the shooting interval between adjacent two images is 0.5 ms. Through the image recognition algorithm, the arc channel morphology every 0.5 ms is extracted, and the average arc diameter and contact area S ij of the arc segments are calculated, and based on this, the heat conduction heat dissipation power and heat convection heat dissipation power of the arc within every 0.5 ms are calculated. If the discharge lasts for 4 cycles, that is, the discharge duration is t0= 80 ms, then n = 80 / 0.5 = 160 images can be taken. And based on this, the heat conduction loss W t is:

[0044] Among them, k is the thermal conductivity of the insulating oil; A t is the conduction heat transfer area. When studying the heat transfer between the arc column and the insulating oil, it is the surface area of the i-th segment of the arc in the j-th image obtained after processing the arc image S ij ; Δ T i is the temperature difference between the temperature of the i-th segment of the arc measured by the sapphire optical fiber and the temperature of the insulating oil; dIt is the heat transfer distance, i.e., the distance between the temperature measurement point of the long-gap arc and the temperature measurement point of the insulating oil.

[0045] Heat convection loss W c is:

[0046] In the formula, h is the convective heat transfer coefficient; A c is the convective heat transfer area, which is the surface area of the i-th segment of the arc in the j-th image obtained after processing the arc image S ij .

[0047] Step 7. Furthermore, the energy of the long-gap arc is obtained as: W = W 1 －W 2.

[0048] In summary, the present invention proposes a long-gap oil arc test platform and an energy calculation method. By multi-electrode configuration, the long-gap arc is discretized into a series of short arcs. After measuring the short-arc voltage and current segment by segment, the input energy of the short arcs is calculated respectively. Further, the heat transfer energy loss during the arc combustion process is considered. The total energy of the long-gap oil arc is obtained by accumulating the net energies of a series of short arcs. Compared with the traditional electrode terminal voltage-current global integration method, the method of the present invention calculates the injected energy and loss energy of the short arcs by piecewise linear discretization, reducing the error of energy calculation; at the same time, the spatio-temporal distribution characteristics of the arc energy are obtained, providing a theoretical basis for the research on the dynamic breakdown mechanism of the arc.

[0049] After considering the specification and the embodiments disclosed herein, those skilled in the art will readily conceive of other embodiments of the present invention. The present invention is intended to cover any variations, uses, or adaptations of the present invention, which follow the general principles of the present invention and include the common general knowledge or conventional technical means in the technical field not disclosed by the present invention. It should be understood that the present invention is not limited to the exact structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present invention is only limited by the appended claims.

Claims

1. A long-gap arc-in-oil test platform, characterized in that It includes a current source circuit and a discharge circuit. The current source circuit is used to provide a large current for the discharge circuit. The discharge circuit includes an oil-immersed arc test tank, a voltage measuring instrument, a current measuring instrument, a temperature measuring instrument, an image acquisition instrument, and N metal probes, where N is a positive integer; The oil arc test tank is provided with insulating oil and two opposite metal rod electrodes. After passing the large current through the two metal rod electrodes, a long-gap arc is generated; N metal probes divide the long-gap arc into N + 1 segments of arcs, and a voltage measuring instrument is used to measure the voltage of the i-th segment of arc. U i , and a current measuring instrument is used to measure the current of the long-gap arc at time t. I t , a temperature measuring instrument is used to measure the temperature of the long-gap arc and the temperature of the insulating oil, and an image acquisition instrument is used to acquire n images of the long-gap arc and the discharge duration, where n is a positive integer.

2. The long-gap arc-in-oil test platform according to claim 1, wherein, The voltage measuring instrument includes N oscilloscopes, and the N metal probes are respectively connected to the N oscilloscopes through different high-voltage probes.

3. The long-gap arc-in-oil test platform according to claim 1, characterized in that The metal rod electrode is a copper rod electrode.

4. The long-gap arc-in-oil test platform according to claim 1, characterized in that, The metal probe is a tungsten probe.

5. The long-gap arc-in-oil test platform according to claim 1, wherein The current measuring instrument is a Rogowski coil.

6. The long-gap arc-in-oil test platform according to claim 1, wherein, The temperature measuring instrument is a sapphire optical fiber.

7. The long-gap arc-in-oil test platform according to claim 1, characterized in that, The image acquisition instrument is a high-speed camera. Observation windows are provided on both sides of the oil-immersed arc test tank. The high-speed camera is arranged at one observation window, and a fill light is arranged at the other observation window.

8. The long-gap arc-in-oil test platform according to claim 1, wherein The current source circuit includes a capacitor C i , an inductor L i , a closing breaker and an auxiliary breaker. The first end of the capacitor C i is connected to the first end of the inductor L i . The second end of the inductor L i is connected to the first end of the closing breaker. The second end of the closing breaker is connected to the first end of the auxiliary breaker. The second end of the auxiliary breaker is connected to a metal rod electrode, and the other metal rod electrode and the second end of the capacitor C i are both grounded.

9. The long-gap oil arc test platform according to claim 8, characterized in that, In the current source circuit, the capacitor C i and the inductor L i generate a test current through resonance I 1, and the expression of the test current I 1 is: In the formula, U 0 represents the initial charging voltage of capacitor C i ; ω represents the resonance frequency; β is the attenuation coefficient of the current source loop; C , L and R are the total capacitance, total inductance and total resistance of the current source loop respectively; t is the time.

10. A method for calculating the energy of an arc in oil with a long gap, characterized in that, It includes: Construct a long-gap oil-immersed arc test platform as described in any one of claims 1 to 9; The current source circuit provides a large current to the discharge circuit; Measure the voltage of the i-th arc segment with a voltage measuring instrument U i , measure the current of the long-gap arc at time t with a current measuring instrument I t , measure the temperature of the long-gap arc and the temperature of the insulating oil with a temperature measuring instrument, and collect n images of the long-gap arc and the discharge duration with an image acquisition instrument, where n is a positive integer; Using the edge segmentation algorithm, obtain the average arc diameter and length of the \(i\)-th arc segment in the \(j\)-th image of the long-gap arc. Consider the \(i\)-th arc segment as a cylinder, and calculate the surface area of this cylinder, which is the contact area between the \(i\)-th arc segment and the insulating oil in the \(j\)-th image S ij ; Calculate the injected energy of the long-gap arc as: In the formula, t0 is the discharge duration of the long-gap arc; Calculate the dissipated energy of the long-gap arc as: In the formula, k is the thermal conductivity of the insulating oil, T ij is the temperature difference between the temperature of the i-th segment of the arc and the temperature of the insulating oil in the j-th image, is the acquisition interval of the image acquisition instrument, is the distance between the long-gap arc temperature measurement point and the insulating oil temperature measurement point, h is the convective heat transfer coefficient; Furthermore, the energy of the long-gap arc is obtained as follows: W = W 1 －W 2.

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