Safety evaluation method and system for tank based on arc discharge in transformer insulating oil

Abstract

A safety evaluation method for a transformer tank comprises: dividing an interior of the transformer tank into a plurality of regions and determining a maximum tolerable pressure tolerable for each re

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of transformers, and in particular to a safety evaluation method and system for a tank based on arc discharge in transformer insulating oil. BACKGROUND

[0002] This section is merely intended to provide background information related to the present disclosure, and does not necessarily constitute the prior art.

[0003] Transformers are among the most important components of transmission and distribution systems, and they are the key equipment used for power transmission. During operation, arc discharge-induced faults in the transformer are unavoidable. In case of an inter-tum short circuit fault in the transformer, an arc releases energy, such that a temperature of surrounding insulating oil rises instantaneously and the insulating oil vaporizes, rapidly increasing a pressure in the tank. Once the pressure exceeds a limit that can be borne by the tank, and the tank is ruptured, combustible gas in the tank comes in contact with oxygen. This can lead to ignition and explosion to cause damage of the equipment, regional power failure and fires at a substation. Serious accidents of this kind can cause casualties, significant economic loss, and huge social impacts.

[0004] For the transformer, a local strong electric field formed by an inter-turn short circuit and an inter-layer short circuit of a winding as well as degradation of the insulating oil often induces insulation breakdown to cause high-energy arc faults. In response to arc discharge, insulating structures make a violent physical and chemical reaction. With a high gas production rate caused by a high temperature of the arc, dissolved gas escapes in a form of bubbles and rapidly expands to accumulate in the transformer. The huge pressure in the transformer cannot be released by a pressurerelease valve timely, which poses an explosion hazard or even causes fires. The pressure rise caused by expansion and massive accumulation of bubbles in the arc discharge is the most direct cause of the explosion of the transformer tank. A strong electric field arises before the arc discharge, and the temperature and pressure in the transformer continue to increase during development of the arc until the explosion occurs. The process of evolution of the arc discharge in the transformer before the explosion involves the coupling of a strong electromagnetic field, a high-temperature field, a strong stress field, etc.

[0005] In the prior art, related research has been devoted with respect to the mechanism of evolution of discharge in the transformer insulating oil, the gas production of the arc in the insulating oil and the stress acting on the tank, the relationship between the pressure rise of the liquid and generation of arc bubbles in the insulating oil, the pressure rise caused by the arc fault in the transformer, and arc discharge-induced faults in the tank on an ascending flanged base at a network side of the transformer. The research has explored the characteristics of abnormal discharge in the transformer insulating oil, including the form, the generation of degraded gas, and the spatiotemporal evolution. Researchers have derived the internal changes in pressure caused by arc discharge-induced faults in the tank, and used it to examine the temperature, vibration, deformation of the tank and related characteristics.

[0006] However, the research has placed a greater emphasis on physical mechanisms of the streamer and the partial discharge of the transformer insulating oil. Although the arc discharge is the main cause of the explosion of the transformer tank, there lacks enough in-depth research on arc discharge laws in the insulating oil, and particularly there lacks a connection between macroscopic fault characteristics such as the inter-turn short circuit and the inter-layer short circuit of the winding in the transformer and microscopic arc discharge laws. In addition, the currently available results do not organically link the action of the arc with development of the pressure in the tank. The law of pressure transfer in the transformer tank due to the presence of a large number of bubbles following arc discharge thus remains unclear. SUMMARY

[0007] In order to solve the above-mentioned problems, the present disclosure provides a safety evaluation method and system for a tank based on arc discharge in transformer insulating oil. The present disclosure takes arc discharge caused by an inter-turn short circuit of a winding in transformer insulating oil as well as a temperature field and a stress field under the action of the arc discharge as objects of research. The present disclosure theoretically analyzes and deduces energy and gas production characteristics of an arc fault caused by the inter-turn short circuit through a topology of a circuit, an alternating-current (AC) system and properties of the insulating oil to establish a quantitative relationship between the inter-turn short circuit of the winding and an arc discharge law at a macroscopic level, thereby obtaining a quantitative relationship among the energy of the arc fault in the transformer, an occurrence position of the arc fault and a pressure finally acting on the tank. In combination with a tolerable pressure of each portion of the tank, the present disclosure determines whether the tank is ruptured or even exploded in a very short time when the arc is located at a particular position in the transformer and has an energy value under a fault.

[0008] In some implementations, the following technical solutions are employed:

[0009] The present disclosure provides a safety evaluation method for a tank based on arc discharge in transformer insulating oil, including:

[0010] dividing an interior of a transformer tank into a plurality of different regions, and determining a maximum pressure tolerable to each of the regions;

[0011] solving energy generated by arc discharge caused by dielectric breakdown arising from an inter-turn short circuit fault of a winding due to insulation damage of the winding of a region in a transformer, and calculating a transient pressure when insulating oil in the region changes from a liquid state to a gaseous state, as well as a transient pressure when the pressure acts on other regions of the tank; and

[0012] comparing a transient pressure of each region with the maximum pressure tolerable to the region, and determining whether the tank has a risk of rupture.

[0013] In other implementations, the following technical solutions are employed:

[0014] The present disclosure provides a safety evaluation system for a tank based on arc discharge in transformer insulating oil, including:

[0015] a maximum pressure calculation module configured to divide an interior of a transformer tank into a plurality of different regions, and determining a maximum pressure tolerable to each of the regions;

[0016] a transient pressure calculation module configured to solve energy generated by arc discharge caused by dielectric breakdown arising from an inter-turn short circuit fault of a winding due to insulation damage of the winding of a region in a transformer, and calculate a transient pressure when insulating oil in the region changes from a liquid state to a gaseous state, as well as a transient pressure when the pressure acts on other regions of the tank; and

[0017] a tank safety evaluation module configured to compare a transient pressure of each region with the maximum pressure tolerable to the region, and determining whether the tank has a risk of rupture.

[0018] In other implementations, the following technical solutions are employed:

[0019] The present disclosure provides a terminal device, including a processor and a memory, where the processor is configured to realize an instruction; the memory is configured to store a plurality of instructions; and the instruction is suitable for being loaded by the processor and executing the safety evaluation method for a tank based on arc discharge in transformer insulating oil.

[0020] In other implementations, the following technical solutions are employed:

[0021] The present disclosure provides a computer-readable storage medium, storing a plurality of instructions, where the instructions is suitable for being loaded by a processor of a terminal device and executing the safety evaluation method for a tank based on arc discharge in transformer insulating oil.

[0022] Compared with the prior art, the present disclosure has the following beneficial effects:

[0023] (1) The present disclosure takes arc discharge caused by an inter-tum short circuit of a winding in transformer insulating oil as well as a temperature field and a stress field under the action of the arc discharge as objects of research. The present disclosure theoretically analyzes and deduces energy and gas production characteristics of an arc fault caused by the inter-turn short circuit through a topology of a circuit, an AC system and properties of the insulating oil to establish a quantitative relationship between the inter-turn short circuit of the winding and an arc discharge law at a macroscopic level, thereby obtaining a quantitative relationship among the energy of the arc fault in the transformer, an occurrence position of the arc fault and a pressure finally acting on the tank. In combination with a tolerable pressure of each portion of the tank, the present disclosure determines whether the tank is ruptured or even exploded in very short time when the arc is located at a particular position in the transformer and has an energy value under a fault.

[0024] (2) The present disclosure explains generation and transfer laws for the pressure of the tank in the arc fault, brings a protective line for the fault of the transformer forward, and provides an explosion-proof solution for the transformer tank from the source, thereby ensuring operation safety of a high-voltage direct-current (DC) transmission system. The present disclosure can lay a solid theoretical foundation and provide a key technical support to design the forward protective line in "active" protection for the explosion of the transformer, and has an important theoretical significance and an important application value.

[0025] Other features and additional advantages of the present disclosure will be partially provided in the following description, and partially become apparent in the following description or understood through the practice of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] FIG. 1 shows an equivalent circuit in a short-circuit fault on a primary side of a single-phase double-winding transformer according to an embodiment of the present disclosure;

[0027] FIG. 2 shows a relationship between an arc length and an arc voltage according to an embodiment of the present disclosure;

[0028] FIG. 3 shows a change trend in arc energy with arc time according to an embodiment of the present disclosure;

[0029] FIG. 4 shows changes in arc energy over time with different numbers of short-circuit turns according to an embodiment of the present disclosure;

[0030] FIG. 5 shows a relationship between arc energy and gas production according to an embodiment of the present disclosure;

[0031] FIG. 6 shows propagation of an initial pressure wave according to an embodiment of the present disclosure;

[0032] FIG. 7 shows a change in a propagation distance of an initial pressure wave with a pressure according to an embodiment of the present disclosure;

[0033] FIG. 8 shows an overall geometric model of a transformer tank according to an embodiment of the present disclosure;

[0034] FIG. 9 shows an occurrence position of an initial arc of a transformer tank according to an embodiment of the present disclosure;

[0035] FIG. 10 shows multiple monitoring points of a transformer tank according to an embodiment of the present disclosure;

[0036] FIG. 11 shows a finite-element mesh division model of a transformer tank according to an embodiment of the present disclosure;

[0037] FIGS. 12A-12C show distribution of an isosurface of a pressure in a transformer tank according to an embodiment of the present disclosure;

[0038] FIG. 13 shows a simulation result of a pressure on a wall of a transformer tank over time according to an embodiment of the present disclosure;

[0039] FIG. 14 shows a relationship among a number of short-circuit turns, arc energy and a pressure on a wall of a tank according to an embodiment of the present disclosure;

[0040] FIG. 15 shows a time-domain distribution of a dynamic pressure on a wall of a tank according to an embodiment of the present disclosure;

[0041] FIG. 16 shows a frequency-domain distribution of a dynamic pressure on a wall of a tank according to an embodiment of the present disclosure;

[0042] FIGS. 17A-17D show change of a variable of a tank over time according to an embodiment of the present disclosure;

[0043] FIG. 18 shows top views of modeling in A, B, and C cases according to an embodiment of the present disclosure;

[0044] FIGS. 19A-19C show comparison of a pressure in A, B, and C cases according to an embodiment of the present disclosure; and

[0045] FIG. 20 shows propagation of a transient pressure wave according to an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] It should be noted that the following detailed descriptions are exemplary and are intended to provide further descriptions of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present disclosure belongs.

[0047] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit exemplary embodiments according to the present disclosure. As used herein, unless otherwise specified herein, the singular forms are also intended to include the plural forms. In addition, it should also be understood that when the terms "comprise" and / or "include" are used in this specification, they specify the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0048] Embodiment 1

[0049] In one or more implementations, the present disclosure provides a safety evaluation method for a tank based on arc discharge in transformer insulating oil, specifically including the following steps:

[0050] (1) An interior of a transformer tank is divided into a plurality of different regions, and a maximum pressure tolerable to each of the regions is determined.

[0051] In the embodiment, tolerable pressures of structures in different regions of the transformer tank are analyzed. By constantly increasing an internal pressure until the tank in a region deforms, a maximum pressure tolerable to the tank in the region is determined. When a pressure on the tank is less than the maximum pressure, the tank does not deform. Weak regions more prone to deformation and rupture under a pressure for a manufacturing process and a component connection in the tank, such as a comer of the tank, an attachment weld on a wall of the tank, a position of a high-pressure sleeve and a low-pressure sleeve, and a flange fixed position, are analyzed emphatically.

[0052] (2) Energy generated by arc discharge caused by dielectric breakdown arising from an interturn short circuit fault of a winding due to insulation damage of the winding of a region in a transformer is solved, and a transient pressure when insulating oil in the region changes from a liquid state to a gaseous state, as well as a transient pressure when the pressure acts on other regions of the tank, is calculated.

[0053] (3) A transient pressure of each region is compared with the maximum pressure tolerable to the region, and whether the tank has a risk of rupture is determined.

[0054] (4) A connection and a comparison are made according to an occurrence position of an arc in the tank and a stress finally acting on the region of the tank to determine a position and a region of an arc causing deformation in the tank, thereby determining critical values at which deformation occurs at different regions of the tank corresponding to different positions of the arc, and obtaining a corresponding relationship between energy of an arc fault in the transformer tank and deformation of the tank to serve as a basis for determining rupture of the transformer tank to conduct explosion-proof work of the transformer tank. A 5.35% (26 turns) inter-turn short circuit of an A-phase high-voltage winding of an SZ11-50000 / 110 oil-immersed transformer is used as an example for analysis. It is assumed that a fault occurs at t=0 ms, and a fault arc lasts for 60 ms. A pressure distribution and a pressure change in the tank after 60 ms of the fault are analyzed. The stress on the wall of the tank is distributed non-uniformly, and is reduced with a distance away from the fault. The stress is mainly concentrated on the wall of the tank directly opposite to a fault point, and a weld between a heat dissipation tube and the tank. Within 10 ms after the fault occurs, the stress on the wall of the tank is not obvious. From 20 ms, the stress on the wall of the tank rises quickly, and the stress at a middle of the wall of the tank and at the front side of the A-phase winding is up to 100 MPa. At 40 ms, the stress at the middle of the wall of the tank and at the front side of the A-phase winding is up to 400 MPa, and the tank causes unrecoverable deformation. At 60 ms, the stress on the wall of the tank, at the front side of the A-phase winding and at the weld between the heat dissipation tube and the tank is greater than a tensile strength 460 MPa of the steel material, and the tank is ruptured. Therefore, this value can be taken as the critical value for the rupture of the tank in the fault.

[0055] (5) A position of a pressure-release valve close to the arc is set reasonably. By improving a Young's modulus of the material of the wall, a risk of rupture and explosion in a pressure shock can be reduced.

[0056] As a specific implementation solution, the embodiment has the following specific implementation process:

[0057] 1. Analysis on characteristics of arc discharge and gas production laws in the transformer insulating oil

[0058] A. Arc energy in case of the inter-turn short circuit of the winding

[0059] A small number of turns can usually lead to insulation breakdown and arc discharge in case of an inter-turn short circuit fault in the transformer insulating oil, which cannot be detected by differential protection of the transformer. In response to the fault, insulation damage occurs in the part of the winding of the transformer where the inter-turn short circuit occurs. The damaged position of the winding and the insulating oil are broken down under the action of a large electric field (voltage), and arc discharge in the insulating oil occurs.

[0060] Dry and clean insulating oil has a considerably high breakdown voltage. Generally, domestic insulating oil has a breakdown voltage of 40 kV or more, or even 60 kV or more. In case of free water, dissolved water or a solid, since the foreign matter has a higher conductivity and a higher dielectric constant than the oil, a conducting bridge is formed under the action of the electric field (voltage). By reducing the breakdown voltage of the oil, the insulating oil is broken down to cause the arc discharge.

[0061] In case of the inter-turn short circuit of the transformer, arc discharge occurs in the oil. At this time, the faulty winding is short-connected, and arc generation renders it a closed loop. This is equivalent to generating a new "short-circuit transformer" with a high ratio of turns of the coil, as shown in FIG. 1. Ni is a number of turns on a primary side of the transformer, N2 is a number of turns on a secondary side of the transformer, and Nb is a number of turns in the inter-turn short circuit in FIG. 1. Therefore, the winding of the original transformer includes an inter-turn short circuit winding and a remaining portion that are connected in parallel.

[0062] An equivalent arc resistance rarc with respect to a flowing current iare is analyzed from short-circuit turns. Given a saturation factor of the transformer, even though the inter-turn short circuit occurs, a magnetic flux in an iron core does not change significantly. It is assumed in FIG. 1 that the primary side has an induced potential ui, and an impedance Zi, and the short-circuit turns Nb have an induced potential UNb=(Nb / Nl)ui. Due to a small impedance Zb=Zi(Nb / Nl)2 of the short-circuit turns, a huge short-circuit current in=UNb / Zb arises. According to an empirical equation for calculating arc energy, the arc energy E(J) is an integral function of an arc current iarc(t), an arc voltage Uarc(t), and time tarc(s), and is given by:

[0063] E=^'C Uarc^t)-iarc{t}dt (1)

[0064] According to the empirical equation for calculating the arc energy, it is necessary to know a functional relationship between a voltage and a current at both ends of the arc over time.

[0065] According to analysis on FIG. 1, the arc current iarc(t) can be calculated by:

[0066] ^Wn(0+*i2(0 (2)

[0067] in is a current passing through the winding when the arc fault occurs. Assuming that a rated current originally passing through the coil of the transformer is in, then in is expressed as:

[0068] j (t) = 411 n sin(2;rft+ (p) (3)

[0069] For ii2=uNb / Zb, assuming that the coil of the transformer has a rated voltage of Ue, then the following can be derived: fl N

[0070] il2f) =—--±Ue sm(17ift + (p) (4) A

[0071] Therefore, the arc current may be expressed as:

[0072]

[0073] The arc current is derived by ignoring a change in impedance of the new "short-circuit transformer" generated by the short circuit. As a matter of fact, the impedance of the arc generated in the circuit is dynamic. Once the arc resistance is considered, the arc current in is given by: flN,Nh r , .

[0074] / 12 ( / ) = -.......-..............................? If sin(2,T ft + (p) (6)

[0075] Therefore, the arc current is expressed as:

[0076] t '(f = 411,,+---41flf-- -^(171 ft+ (p)(f

[0077] In addition to the rated voltage and the rated current of the transformer in operation, the arc current generated by the inter-turn short circuit in Eq. (7) is further associated with a number of turns at a short-circuit point and a dynamic resistance of the arc.

[0078] The energy generated by the arc can be obtained from Eq. (1) based on the current and the voltage of the arc. According to research on the empirical equation, the arc voltage is related to the arc length. As shown in FIG. 2, the voltage of a 100 mm long arc is approximately 1,000 V. A curve fitted at each point in the figure is roughly a directly proportional line:

[0079] (7„.=10xZ„(8)

[0080] To sum up, the arc energy generated by the inter-turn short circuit can be expressed by: ,r f r Jin N 'i ,

[0081] V24 + 1 b G I • |sin(2^ + <p)\dt (9) V b )

[0082] Larc is the arc length, tare is arc time, I„ is the rated current originally passing through the coil of the transformer, N\ is the number of turns on the primary side of the transformer, Nb is the number of turns in the inter-turn short circuit, is the equivalent arc resistance, Ue is the rated voltage of the coil of the transformer, f represents a frequency that a current passes through the winding when the arc fault occurs, t represents a duration after the arc fault occurs, and represents an initial phase of the current passing through the winding in the arc fault.

[0083] According to Eq. (9), the number Nb of turns at the short-circuit point, the arc time tarc, the arc length Larc, as well as the model, the rated current In and the rated voltage Ue of the transformer are main variables influencing the arc energy.

[0084] B Law of development of the arc energy under the action of multiple factors

[0085] Through tests, an approximate relationship between the fault-induced arc energy of the transformer and the gas production is given by:

[0086] vgas = ln(Warc + r) - (P (10)

[0087] &is a coefficient of conversion, which is generally set to 0.44.

[0088] The transformer with a model of SFPZ11-120000 / 220 is used as an example for analysis.

[0089] It is assumed that a 5% inter-turn short circuit occurs in the single-phase high-voltage winding of the transformer. A total number of turns of the high-voltage winding is 531, Ni=531. A number of short-circuit turns in the 5% inter-turn short circuit is 27, Nb=27. The high-voltage winding has a rated current of 315 A, In=315 A, and a rated voltage of 220 kV, Ue=315A. The high-voltage winding has a height of 1,750 mm, which means that each turn of the winding has a height of about 3.3 mm. The winding in the inter-turn short circuit has a height of about 89 mm. According to relevant equations of the transformer, the winding has an impedance of about 90.79 Q. The resistance of the arc is on the order of mO.

[0090] By taking the arc time tarc as the independent variable, the above parameters are plotted to explore a change trend of the arc energy with increasing arc time, as shown in FIG. 3.

[0091] According to a curve of the arc energy obtained in case of the 5% inter-turn short circuit in simulation of the single-phase high-voltage winding of the transformer in FIG. 3, the energy released by the arc is accumulated gradually over time.

[0092] The number of short-circuit turns is extracted according to Eq. (9). The type of the fault and the number Nb of short-circuit turns are used as independent variables to obtain Eq. (11):

[0093] = (11) y b J

[0094] Because the arc length Larc is directly proportional to the number of short-circuit turns, Larc can be expressed as kNb. Eq. (11) can thus be approximated as Eq. (12): |0095| 105 / 2kN, ,, ft arc | . z — / ■ \ I t +----------1 Ue I |sin(2^ft + ^)| dt (12) Zj J 0

[0096] It is evident from Eq. (12) that the relationship between the number Nb of short-circuit turns and the arc energy is a linear function. That is, as the number of short-circuit turns increases, cumulative fault-induced arc energy increases approximately linearly over time. FIG. 4 shows a plot generated using different numbers of short-circuit turns in the equation. It is clear that slopes of two curves are closely related to a severity of the fault, namely the number of short-circuit turns.

[0097] Eq. (10) indicates that there is a logarithmic relationship between the gas production and the arc energy. By substituting the arc energy equation into Eq. (10), the relationship between the gas production and the arc energy can be obtained, as shown in FIG. 5.

[0098] A logarithmic relationship is observed between the fault-induced arc energy and the gas production. When the arc energy reaches a certain value, the slope of the curve decreases rapidly and gradually tends to saturation. This is caused by saturation of the arc during vaporization of the insulating oil.

[0099] To sum up, according to the arc discharge in the inter-turn short circuit fault, the expression of the arc energy, the relationships of the arc energy with multiple different variables such as the arc discharge time, the number of short-circuit turns of the winding, the model of the transformer, and the arc length, and the relationship between the arc energy and the gas production in the insulating oil are analyzed.

[0100] C. Pressure transfer in the oil and the tank under the action of the arc

[0101] The temperature near the arc is approximately 4,000-5,000 K, while the highest temperature at a center of an arc column is 104 K. The burning point of mineral oil that is generally used in the transformer is approximately 400 K. The insulating oil near the arc is instantaneously gasified and decomposed owing to the ultra-high temperature. At this time, the energy released by the arc is mainly converted into energy absorbed by degradation and decomposition of the insulating oil, energy thermally radiated out, and energy absorbed by the evaporation of the oil led to the production of gas.

[0102] Warc=Woll+Wgas+Wrad (13)

[0103] The insulating oil near the arc is evaporated into combustible gas instantaneously. Under a standard pressure, when the arc energy is 1 kJ, the corresponding gas production is approximately 5.8 10u m3 / kJ. According to the above analysis, the arc generates a gas amount of 10’5 m2 in a short time. This is much smaller than the gas generated by 1 kJ of arc energy, and can thus be ignored when fluctuations in temperature of the oil are calculated. According to the law of heat conduction, the heat transfer and temperature rise of the insulating oil according to the distance from the arc can be calculated by:

[0104] Toi; =^--(Tarc^Toa) + ToU (14) mcoaL

[0105] represents a temperature of the arc and a coefficient of thermal conductivity, which is generally 0.15 W(mK)'1 in the insulating oil, S represents an area of heat transfer between the insulating oil and the arc, TM represents an initial temperature of the insulating oil, Tj represents a real-time temperature of the insulating oil, L represents a distance between the insulating oil and the arc during heat conduction, m is a unit mass of the insulating oil, and cM is a specific heat capacity of the insulating oil.

[0106] It is clear from Eq. (14) that the heat transfer in the insulating oil is mainly influenced by the arc heat, and it gradually decreases with an increase in its distance to the arc.

[0107] Volume expansion of the insulating oil has a hysteresis effect relative to production of the gas. The transient pressure of the gas generated by the arc continues to drastically increase with the discharge time of the high-energy arc. Therefore, a high pressure is obtained at an interface between the gas and the insulating oil during phase transition reaction, which spreads around in the form of a pressure wave in the oil and acts on the wall of the tank. This causes the tank to bear the corresponding stress and deform once the pressure exceeds a certain limit, or to even accumulate too much energy in a short time such that it burst. The change in the phase of the insulating oil from liquid to gas follows the law of the conservation of mass. The mass of the vaporized oil can then be obtained according to the mechanism of vaporization-induced evaporation of the mineral oil. 101081

[0109] mog is a mass of the insulating oil undergoing a phase change, Tga, represents a transient temperature of the generated gas, and AO* is latent heat of vaporization of the insulating oil per unit mass (heat absorbed by a certain liquid per unit mass during vaporization when the temperature is constant). Components of gas generated by combustion of the arc in the insulating oil are analyzed, mainly including 7.85% of ethylene, 13.96% of methane, 14.87% of methanol, 22.17% of acetylene, and 30.77% of propane. According to a method for calculating a molar mass of the mixed gas, a molar mass of the gas generated in the insulating oil is approximately 28.99 g / mol. According to an ideal gas equation, the pressure of the gas can be calculated by Eq. (16):

[0110] PgMVgM = nRTgas (16)

[0111] The transient pressure of the generated gas can then be obtained by substituting (10) and (15) into (16): W RT ‘°1121 ^8.99^4^(7^ <17>

[0113] n is an amount of matter in the mixed gas, is the energy thermally radiated out in the energy released by the arc, Tal represents the initial temperature of the insulating oil, cal is the specific heat capacity of the insulating oil, is the transient temperature of the generated gas, AO* is the latent heat of vaporization of the insulating oil per unit mass, R is a molar gas constant, with a typical value of 8.31451 J / (moTK), and Vgas is a volume of the generated gas.

[0114] As shown in FIG. 5, when the energy released by arc combustion over time accumulates to a certain value, the gas production approaches saturation. It is thus assumed that the gas production does not change in calculation of the transient pressure and transfer of the internal pressure. The initial pressure of the generated gas is approximately proportional to the arc energy.

[0115] A difference in initial pressure at the occurrence position of the arc in the insulating oil is calculated by:

[0116] = Pgas -p0~ Potlgh (18)

[0117] po is an atmospheric pressure, and is 1.01325* 105Pa, pM is a density of the insulating oil, g is a gravitational constant, and h is a depth of an occurrence position of the arc discharge from a surface of the oil.

[0118] The propagation of a pressure wave in the insulating oil is analyzed below. The generated gas pressure is regarded as a source of transient pressure Pv (t) that can provide initial shock-induced excitation in the tank. The coupling of two-phase gas-liquid flow is calculated by using the volume function model (VOF). The shock induced by the source of transient pressure Pv (?) in the tank is transmitted to the insulating oil in the form of waves and acts on the wall of the tank, causing it to strain.

[0119] The insulating oil is compressible and viscous. The greater the viscosity of the fluid, the worse the fluidity. Therefore, the viscosity of the oil weakens the transmission of the pressure wave. 12 As shown in FIG. 6, it is assumed that a pressure wave propagates in the insulating oil at a velocity v due to a compressibility of the oil. In response to a pressure difference between gas and the surrounding insulating oil, a pressure at a distance Sx from the gas increases instantaneously by Ap. The pressure at the distance Sx is then transferred to an adjacent liquid surface Sx, such that a pressure of the adjacent liquid surface increases by Ap and a velocity of the pressure wave of the adjacent liquid surface changes from zero to v. By the same reasoning, an initial pressure wave having a magnitude Ap and propagating at the velocity v toward a surrounding wall of the tank is formed.

[0120] As shown in FIG. 7, the propagation of the pressure wave increases the pressure of the insulating oil by &p. The pressure wave travels over a distance ^Sx = vAt within time St, causing the pressure of water within this distance to rise by Ap , while P(j+P0ligh remains unchanged in the section in which the wave does not propagate. There is no reflection if a source of transient pressure Pv ( / ) is generated in a frictionless and infinitely large container, and the pressure wave is indefinitely transmitted. However, the energy of the pressure wave continuously decreases during propagation in the actual transformer tank due to a viscosity of the insulating oil and an elastic structure on the wall of the tank. While the pressure wave is propagated to the wall of the tank and reflected, the energy is transmitted to the wall of the tank.

[0121] During propagation of the pressure wave of the arc fault in the tank, due to the viscosity of the insulating oil and the elastic structure on the wall of the tank, kinetic energy of the pressure wave is attenuated and lost. For propagation of a pressure wave of a bubble source in surrounding insulating oil, a wave equation of a transient pressure is given by:

[0122] 1 d2Pt pc1 dr V i pp W • I / / I * pc J dt

[0123] c is a propagation velocity of the pressure wave in the insulating oil, p is a medium density, pc2 is a volumetric modulus of elasticity, t is time, p is a dynamic viscosity, / / b is a coefficient of viscosity, and Pt is an intensity of a pressure field, including an initial pressure Po (a differential pressure AP between inside and outside of the bubble) and an intensity Pb of a background pressure field (an intensity of a pressure field in the tank at a previous timepoint), namely:

[0124] pt=p0+pb=Sp + pb.

[0125] In the embodiment, finite element simulation software is used to perform finite element simulation on the pressure in the tank, thereby calculating changes of the pressure in the transformer tank once an internal fault has occurred. According to a size of the actual transformer, a transformer tank is simulated by considering only three key components of the transformer. The overall geometric model of the transformer tank is shown in FIG. 8. The tank has a length of 4 m, a width of 1.4 m, and a height of 2 m. A model including an iron core and a winding is provided inside the tank. Stiffeners are provided at suitable positions outside the tank.

[0126] In analysis, the whole model of the tank is divided into the tank, and the winding and the iron core.

[0127] In simulated analysis on the model of the tank, the thickness of the wall of the tank is set to 16 mm. The model is mainly used to simulate the propagation of the pressure wave on the wall. The model of the iron core is formed by superimposing multiple silicon steel sheets. The winding circuit is simulated by using a virtual circuit in COMSOL. The coil includes a primary coil and a second coil. The model is mainly used to simulate a distribution of magnetic circuits and a distribution of forces in the propagation of the pressure wave.

[0128] In the simulated analysis on the changes of the pressure in the transformer tank once the internal fault has occurred, the occurrence position of an initial arc (that is, the initial position of generation of a bubble-induced pressure) in the finite element simulation is varied. Multiple probes are provided at different positions in the tank and its wall for measurements, as shown in FIG. 9 and FIG. 10.

[0129] A finite-element mesh division in COMSOL simulation software is used, as shown in FIG. 11. The pressure transfer inside the transformer tank under the action of the source of transient pressure and the distribution of pressure on the wall of the tank can be simulated according to the position of the initial arc. Based on a diagram of the isosurface of the pressure distribution, the propagation of the pressure wave is analyzed intuitively.

[0130] Inter-turn short circuit faults occur commonly in the winding of the power transformer, which can cause significant damage. Position 2 at which the initial arc occurs is selected to analyze the propagation of the pressure wave as well as the pressure on the tank. The simulated distribution of the isosurface of the pressure in the tank at t=l ms, t=6 ms and t=10 ms is as shown in in FIGS. 12A-12C. (a) to (d) in FIG. 13 respectively show simulation results of the pressure on the wall of the transformer tank at t=l ms, t=5 ms,t=20 ms and t=60 ms.

[0131] As can be observed from FIGS. 12A-12C, when the inter-turn short circuit of the winding of the transformer occurs and the initial arc is formed at position 2, the pressure in the transformer tank first rises at position 2 because the insulating oil near the arc is instantaneously vaporized for an ultra-high temperature. Owing to the hysterical effect of the volumetric expansion of the insulating oil relative to the production of gas, the transient pressure of the gas increases drastically with the duration of discharge of the high-energy arc.

[0132] As can be obviously observed from (a) to (d) in FIG. 13, the pressure in the tank increases over time from position 2 and spread around to gradually act on the wall of the transformer tank. The pressure on the wall of the transformer tank continues to increase over time, spreading from position 2 at which the initial arc occurs. 1 ms after the fault has occurred, the sidewall of the tank closest to the arc deforms and expands. Approximately 20 ms after the fault has occurred, the deformation has distributed throughout the transformer tank. The entire wall of the tank expands and deforms under the action of pressure 60 ms after the fault has occurred.

[0133] It is clear from the distribution of the isosurface of pressure in the transformer tank and the diagram of change in pressure on its wall over time that the pressure wave is transmitted from the initial position of the arc to the periphery after the fault has occurred. The pressure on the wall of the tank increases with time.

[0134] A relationship between the initial position of the arc and the distribution of pressure on the wall of the tank is analyzed below.

[0135] The insulating oil in the transformer tank is viscous and compressible. The greater the viscosity of the fluid, the worse the fluidity. Therefore, the viscosity of the insulating oil weakens the transmission of the pressure wave. Pressures at each monitoring point under three initial positions of the arc are compared. Arc 1 is located in the primary coil of the side winding, arc 2 is located in the primary coil of the middle winding, and arc 3 is located in the secondary coil of the side winding. A comparison of the above three cases shows that the pressure measured at the monitoring point closest to the occurrence position of the arc is the highest, while the pressure measured at the monitoring point farthest from it is the lowest. This is consistent with the previous derivation. The viscosity of the insulating oil in the transformer tank as well as the refraction and reflection of the internal components of the tank to the pressure wave reduces the energy of the pressure wave in the oil.

[0136] A relationship between the arc energy and the pressure on the wall of the tank is analyzed below.

[0137] In case of the inter-turn short circuit of the winding of the transformer, the arc energy is related to the number of short-circuit turns. Changing the number of short-circuit turns affects the arc energy, and the pressure on the wall of the tank. In the COMSOL simulation software, different numbers of short-circuit turns are provided to research a relationship among the number of short-circuit turns, the arc energy and the pressure on the wall of the tank, as shown in FIG. 14. A time domain and a frequency domain of pressure data obtained in the simulation are analyzed to obtain the relationship macroscopically and microscopically.

[0138] With analysis on FIG. 14, since the number of short-circuit turns is directly related to the arc length in breakdown, as the arc energy and the number of short-circuit turns increase, the pressure acting on the wall of the tank increases obviously. According to simulated data, when the short-circuit turns account for 8%, a peak pressure acting on the wall of the tank reaches a critical pressure, and the tank has a high risk of rupture.

[0139] In order to better analyze the pressure acting on the wall of the tank after the inter-tum short circuit fault occurs, a time domain and a frequency domain of the transient pressure on the wall of the tank are analyzed, as shown in FIGS. 15-20.

[0140] As shown in FIG. 15, a waveform of the pressure on the wall of the tank in the time domain is oscillated and slowed down, and both the peak pressure and the oscillation amplitude decrease over time. As shown in FIG. 16, with analysis on the frequency domain of the pressure on the wall of the tank, a peak oscillation frequency appears near 600 Hz, and other frequencies has a small amplitude.

[0141] Cross-over analysis is made to parameters influencing the pressure on the wall of the tank, including arc energy, a transient pressure of initial generated gas, a pressure generated by initial gas, and a density of the insulating oil. Under the four parameters, changes of the pressure on the wall of the tank over time are shown in FIGS. 17A-17D.

[0142] According to in FIGS. 17A-17D, the arc energy, the transient pressure of the initial generated gas, and the pressure generated by initial gas are positively related to the pressure on the wall of the tank. The density of the insulating oil is negatively related to the positively related. The larger the density of the insulating oil, the more obvious the "rubbing action" on transmission of the pressure wave in the oil.

[0143] Impacts of a position of a pressure-release valve and a material of the tank on a shock are analyzed below.

[0144] The pressure-release valve is a device used to protect the transformer from excessively high pressure. In case of a fault in the transformer tank, the pressure in the tank rises sharply due to gas generated by oil decomposition. If the pressure-release valve is opened in time, it can isolate part of the transformer oil and reduce the pressure in the tank. A relationship between the mounting position of the pressure-release valve and the pressure on the tank is examined by changing the experimental parameters. Research with the initial arc occurring at position 2 and measured the pressure at monitoring point 3 is conducted. The pressure-release valve is opened at point A directly above the initial arc, at point B directly to a side of the initial arc, and at point C behind the initial arc, as shown in (a) to (c) in FIG. 18. Measured values of the static pressure on the wall under these three conditions are shown in in FIGS. 19A-19C.

[0145] As shown in FIGS. 19A-19C, the pressure-release valve at points A and B reduces the pressure on the wall of the tank, while the pressure-release valve at point C cannot reduce the pressure on the wall. The pressure-release valve has the most prominent effect in terms of reducing the pressure when it is set at point A. For the pressure-release valve at point A, the propagation of the transient pressure is shown in FIG. 20.

[0146] It is clear from FIG. 20 that part of the pressure wave is directly discharged upward through the pressure-release valve rather than spreading around when the pressure-release valve is located directly above the occurrence position of the arc. This led to a reduction in the pressure on the wall of the tank. Meanwhile, in case of the fault in the transformer tank, the strength of the material of the tank is also related to a bearing capacity of the pressure. Young's modulus is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. Poisson's ratio refers to a ratio of transverse normal strain to axial normal strain when the material is pulled or stressed unidirectionally. It reflects an elastic coefficient of transverse deformation of the material.

[0147] The strength of the material is changed by changing the Young's modulus and the Poisson's ratio of the material of the wall of the tank, thereby determining parameters influencing deformation of the tank under the pressure wave. It can be concluded that materials with different Young's moduli affect a displacement in a direction perpendicular to the wall of the tank after 5 ms of the arc, and materials with different Poisson's ratios do not affect the displacement in the direction perpendicular to the wall of the tank. By reasonably providing the position of the pressure-release valve, and selecting the material of the wall of the tank with the high Young's modulus, the risk of rupture and explosion can be reduced in case of the fault in the transformer tank.

[0148] Embodiment 2

[0149] In one or more implementations, the present disclosure provides a safety evaluation system for a tank based on arc discharge in transformer insulating oil, including: a maximum pressure calculation module, a transient pressure calculation module, and a tank safety evaluation module.

[0150] The maximum pressure calculation module is configured to divide an interior of a transformer tank into a plurality of different regions, and determining a maximum pressure tolerable to each of the regions.

[0151] The transient pressure calculation module is configured to solve energy generated by arc discharge caused by dielectric breakdown arising from an inter-turn short circuit fault of a winding due to insulation damage of the winding of a region in a transformer, and calculate a transient pressure when insulating oil in the region changes from a liquid state to a gaseous state, as well as a transient pressure when the pressure acts on other regions of the tank.

[0152] The tank safety evaluation module is configured to compare a transient pressure of each region with the maximum pressure tolerable to the region, and determining whether the tank has a risk of rupture.

[0153] The specific implementation of each module is the same as that in Embodiment 1.

[0154] Embodiment 3

[0155] In one or more implementations, the present disclosure provides a terminal device, including a server. The server includes a memory, a processor, and a computer program stored on the memory and executable on the processor. The processor executes the program to realize the safety evaluation method for a tank based on arc discharge in transformer insulating oil in Embodiment 1. For brevity, details are not repeated herein.

[0156] Embodiment 4

[0157] In one or more implementations, the present disclosure provides a computer-readable storage medium, storing a plurality of instructions. The instructions is suitable for being loaded by a processor of a terminal device and executing the safety evaluation method for a tank based on arc discharge in transformer insulating oil in Embodiment 1.

[0158] The above describes the specific implementations of the present disclosure with reference to the accompanying drawings, but is not intended to limit the protection scope of the present disclosure. Those skilled in the art should understand that any modifications or variations made by those skilled in the art based on the technical solutions of the present disclosure without creative efforts still fall within the protection scope of the present disclosure.

Claims

1. A safety evaluation method for a tank based on arc discharge in transformer insulating oil, comprising:dividing an interior of a transformer tank into a plurality of different regions, and determining a maximum pressure tolerable to each of the regions;solving energy generated by arc discharge caused by dielectric breakdown arising from an inter-turn short circuit fault of a winding due to insulation damage of the winding of a region in a transformer, and calculating a transient pressure when insulating oil in the region changes from a liquid state to a gaseous state, as well as a transient pressure when the pressure acts on other regions of the tank; andcomparing a transient pressure of each region with the maximum pressure tolerable to the region, and determining whether the tank has a risk of rupture.

2. The safety evaluation method for a tank based on arc discharge in transformer insulating oil according to claim 1, further comprising:making a connection and a comparison according to an occurrence position of an arc in the tank and a stress finally acting on the region of the tank to determine a position and a region of an arc causing deformation in the tank, thereby determining critical values at which deformation occurs at different regions of the tank corresponding to different positions of the arc, and obtaining a corresponding relationship between energy of an arc fault in the transformer tank and deformation of the tank to serve as a basis for determining rupture of the transformer tank.

3. The safety evaluation method for a tank based on arc discharge in transformer insulating oil according to claim 1, further comprising: providing a pressure-release valve directly above an occurrence position of the arc discharge, thereby reducing a risk of rupture and explosion in a pressure shock.

4. The safety evaluation method for a tank based on arc discharge in transformer insulating oil according to claim 1, wherein the solving energy generated by arc discharge caused by dielectric breakdown arising from an inter-turn short circuit fault of a winding due to insulation damage of the winding of a region in a transformer specifically comprises:e t ( i- J2N N ,Jo I J 1wherein, Larc is an arc length, tarc is arc time, 1,, is a rated current originally passing through a coil of the transformer, N\ is a number of turns on a primary side of the transformer, Nb is a number of turns in the inter-turn short circuit, rarc is an equivalent arc resistance, Ue is a rated voltage of the coil of the transformer, f represents a frequency that a current passes through the winding when an arc fault occurs, t represents a duration after the arc fault occurs, and represents an initial phase of the current passing through the winding in the arc fault.

5. The safety evaluation method for a tank based on arc discharge in transformer insulating oil according to claim 1, wherein the calculating a transient pressure when insulating oil in the region changes from a liquid state to a gaseous state specifically comprises:W RTn =_________________8<>s 8™________________gas 28.99 xK \cAt I \ \oAwherein, Wgas is energy thermally radiated out in energy released by an arc, TM represents an initial temperature of the insulating oil, cal is a specific heat capacity of the insulating oil, Tgas is a transient temperature of generated gas, / \Q* is latent heat of vaporization of the insulating oil per unit mass, Risa molar gas constant, and Vgas is a volume of the generated gas.

6. The safety evaluation method for a tank based on arc discharge in transformer insulating oil according to claim 1, wherein the calculating a transient pressure when the pressure acts on other regions of the tank specifically comprises:assuming that a pressure wave propagates in the insulating oil at a velocity v due to a compressibility of the oil, wherein in response to a pressure difference between gas and the surrounding insulating oil, a pressure at a distance Sx from the gas increases instantaneously by Ap; the pressure at the distance dx is then transferred to an adj acent liquid surface Sx, such that a pressure of the adjacent liquid surface increases by Ap, and a velocity of the pressure wave of the adjacent liquid surface changes from zero to v; and by the same reasoning, an initial pressure wave having a magnitude and propagating at the velocity v toward a surrounding wall of the tank is formed;energy of the pressure wave continuously decreases during propagation in an actual transformer tank due to a viscosity of the insulating oil and an elastic structure on the wall of the tank; and while the pressure wave is propagated to the wall of the tank and reflected, the energy is transmitted to the wall of the tank; andfor propagation of a pressure wave of a bubble source in the surrounding insulating oil, a waveequation of a transient pressure is given by:pc1 dt2 _ p1 I 4 / / — + pc \ 3= 0wherein, c is a propagation velocity of the pressure wave in the insulating oil, p is a medium density, pc2 is a volumetric modulus of elasticity, t is time, p is a dynamic viscosity, p® is a coefficient of viscosity, and Pt is an intensity of a pressure field, comprising an initial pressure Po and an intensity Pb of a background pressure field.

7. The safety evaluation method for a tank based on arc discharge in transformer insulating oil according to claim 6, wherein the amplitude &p is specifically given by:= Poilghwherein, Pgas is the transient pressure when the insulating oil in the region changes from the liquid state to the gaseous state, p0 is an atmospheric pressure, pM is a density of the insulating oil, g is a gravitational constant, and h is a depth of an occurrence position of the arc discharge from a surface of the oil.

8. A safety evaluation system for a tank based on arc discharge in transformer insulating oil, comprising:a maximum pressure calculation module configured to divide an interior of a transformer tank into a plurality of different regions, and determining a maximum pressure tolerable to each of the regions;a transient pressure calculation module configured to solve energy generated by arc discharge caused by dielectric breakdown arising from an inter-turn short circuit fault of a winding due to insulation damage of the winding of a region in a transformer, and calculate a transient pressure when insulating oil in the region changes from a liquid state to a gaseous state, as well as a transient pressure when the pressure acts on other regions of the tank; anda tank safety evaluation module configured to compare a transient pressure of each region with the maximum pressure tolerable to the region, and determining whether the tank has a risk of rupture.

9. A terminal device, comprising a processor and a memory, wherein the processor is configured to realize an instruction; the memory is configured to store a plurality of instructions; and the instruction is suitable for being loaded by the processor and executing the safety evaluation method for a tank based on arc discharge in transformer insulating oil according to any one of claims 1 to 7.

10. A computer-readable storage medium, storing a plurality of instructions, wherein the instructions is suitable for being loaded by a processor of a terminal device and executing the safety evaluation method for a tank based on arc discharge in transformer insulating oil according to any one of claims 1 to 7.

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