Modeling analysis method and device for temperature rise of winding area of oil-immersed distribution transformer
By establishing an oil temperature calculation model at the outlet of the oil channel and building a single-phase winding thermal network model, the problem of difficult to accurately obtain the hot spot temperature and temperature distribution of the winding of the oil-immersed distribution transformer is solved, and efficient and real-time temperature analysis is achieved.
Patent Information
- Application Number
- CN202411716568.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-27
- Publication Date
- 2025-02-21
AI Technical Summary
The prior art is difficult to accurately and quickly obtain the hot spot temperature and internal temperature distribution of the oil-immersed distribution transformer winding, resulting in poor monitoring blind spots and real-time performance.
By establishing an oil temperature calculation model at the outlet of the oil duct based on fluid mechanics and heat transfer theory, the basic heat transfer units of the thermal network are divided, and a single-phase winding thermal network model is constructed, and the temperature distribution of the winding area is obtained.
It realizes accurate acquisition of the hot spot temperature and internal temperature distribution of the distribution transformer during operation, and has the advantages of easy calculation, good real-time and high accuracy, and is suitable for ensuring the safe and efficient operation of the transformer.
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Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of modeling and analysis, and in particular relates to a method and device for modeling and analyzing regional temperature rise of a winding of an oil-immersed distribution transformer. Background Art
[0002] In recent years, with the rapid development of the economy, the demand for electric energy has increased day by day, and the requirements for the reliability of transmission and transformation equipment have also increased. As the terminal equipment of the medium-voltage distribution network, oil-immersed distribution transformers are widely distributed and numerous. The hot spot temperature of the winding insulation system is the main determinant of its load capacity. When the hot spot temperature of the winding exceeds the long-term allowable operating temperature of the insulation at that location, it will cause insulation damage or loss of life.
[0003] At present, the main methods for obtaining transformer hot spot temperature are measurement method and calculation method. The measurement method first estimates the hottest spot location, then buries multiple temperature sensors near the predicted location, and selects the highest measured temperature as the hot spot temperature. The measurement method has high accuracy, but the measured data is restricted by the sensor layout scheme, and it is always impossible to achieve continuous temperature collection in space, and it is difficult to obtain the accurate value of the hottest spot temperature, and there is a large monitoring blind area. In addition, the burial of sensors will also have an adverse effect on the insulation and heat dissipation of the winding.
[0004] The calculation methods mainly include numerical calculation method, artificial intelligence algorithm and thermal circuit model method. The numerical calculation method solves the heat transfer process of the transformer based on the heat transfer and fluid mechanics equations. Compared with other methods, it can obtain the temperature field and fluid field distribution inside the transformer. However, the numerical calculation method has high requirements on computer performance, complex modeling process, long calculation time, and poor real-time and universality.
[0005] Therefore, obtaining the hot spot temperature and hottest position of the transformer winding through accurate and fast calculation methods is of great significance for tapping the load potential and ensuring the safe and efficient operation of the transformer. Summary of the invention
[0006] In view of the above deficiencies in the prior art, the purpose of the present invention is to provide a method and device for modeling and analyzing the regional temperature rise of the winding of an oil-immersed distribution transformer, which can accurately obtain the hot spot temperature and internal temperature distribution during the operation of the distribution transformer through modeling and analysis.
[0007] To achieve the above objectives, the technical solution adopted by the present invention is a method for modeling and analyzing the regional temperature rise of windings of an oil-immersed distribution transformer, comprising the following steps: S1. For the winding area of the oil-immersed distribution transformer including the low-voltage winding, the high-voltage winding and the vertical oil channel, an oil temperature calculation model at the oil channel outlet is established based on the fluid mechanics and heat transfer theory. The modeling steps are as follows: S1.1. Establish a calculation formula for the buoyancy of the oil flow inside the oil channel, the friction of the transformer oil during flow, and the gravity of the transformer oil; S1.2, simplify and integrate the three calculation formulas in S1.1; S1.3. Establish a calculation formula for the heat absorbed by the oil channel and the total heat absorbed by each oil channel; S1.4. Establish the expressions of convective heat transfer coefficient, Nusselt number correlation, Reynolds number, Rayleigh number and Prandtl number in the process of flow heat transfer; S2. Based on the oil temperature calculation model at the oil channel outlet, the oil temperature at the outlet of each vertical oil channel is obtained by simultaneous solution; S3, dividing the winding area into heat network basic heat transfer units, and solving the temperature distribution of the winding area; S4. Based on the basic heat transfer unit of the thermal network, a single-phase winding thermal network model is constructed to obtain the outermost axial temperature distribution of the winding. The oil temperature at the outlet of each vertical oil channel and the outermost axial temperature distribution of the winding are introduced into the single-phase winding thermal network model to solve the temperature distribution of the winding area.
[0008] As a preferred embodiment of the present invention, in S1.1, since the temperature of the transformer oil rises and the density decreases after absorbing heat, the transformer oil in the vertical oil channel flows upward under the action of buoyancy. During the flow process, the transformer oil is also affected by friction and gravity. When the oil flow velocity no longer changes, the force reaches a balanced state. The calculation formula for the buoyancy of the oil flow inside the oil channel is: (1); In the formula, is the buoyancy of the oil flow in the i-th oil channel; is the density of transformer oil; g is the acceleration due to gravity; is the axial height of the i-th oil channel; is the flow area of the i-th oil channel; β is the volume expansion coefficient of transformer oil; is the average temperature of transformer oil; The calculation formula of the friction force on transformer oil during flow is: (2); In the formula, is the friction force on the transformer oil in the i-th oil channel during its flow; is the hydraulic diameter of the i-th oil channel; is the oil flow rate of the i-th oil channel; is the viscosity of transformer oil; The calculation formula for the gravity of transformer oil is: (3); In the formula, is the gravity of the transformer oil in the i-th oil channel; is the bottom oil temperature; is the oil temperature difference between the inlet and outlet of the i-th oil channel.
[0009] As a preferred embodiment of the present invention, in S1.2, the simplified integration process is that when the oil flow rate is stable, the buoyancy force on the transformer oil is equal to the sum of gravity and friction: (4); Substitute equation (1), equation (2), and equation (3) into equation (4) and simplify them to express as: (5).
[0010] As a preferred solution of the present invention, in S1.3, according to the law of conservation of energy, that is, the heat emitted by the windings on both sides of the oil channel in steady state is equal to the energy required to maintain the temperature rise of the oil channel, the calculation formula for the heat absorbed by the oil channel is: (6); In the formula, is the heat absorbed by the i-th oil channel; is the specific heat capacity of transformer oil; The total heat absorbed by each oil channel is further calculated according to Newton's cooling formula: (7); In the formula, , are the average temperatures of the windings on both sides of the i-th oil channel; , are the convective heat transfer coefficients between the winding and the oil channel on both sides of the i-th oil channel; , are the heat transfer areas between the winding and the oil channel on both sides of the i-th oil channel.
[0011] As a preferred embodiment of the present invention, in S1.4, the convective heat transfer coefficient h in the flow heat transfer process is expressed as: (8); In the formula, is the thermal conductivity of the fluid; is the Nusselt number in the convective heat transfer process between fluid and solid; L is the characteristic size of convective heat transfer; The heat transfer between each winding and the oil channel is regarded as the convection heat transfer between the vertical slot and the internal fluid, and the Nusselt number correlation formula is expressed as: (9); In the formula, is the Reynolds number; Pr is the Prandtl number; is the viscosity of the transformer oil at the average temperature of the winding; D is the hydraulic diameter of the oil channel; H is the axial height of the oil channel; The heat transfer between the outermost side of the high-voltage winding and the transformer oil is regarded as the convection heat transfer between the fluid and the vertical plate, and the Nusselt number correlation is expressed as: (10); is the Rayleigh number with L as the characteristic size; The expressions for the Reynolds number, Rayleigh number, and Prandtl number are: (11); In the formula, is the average temperature of the winding; is the transformer oil temperature; is the thermal conductivity of transformer oil; v is the oil flow velocity in the oil channel.
[0012] As a preferred embodiment of the present invention, in S2, it is measured and , substitute equations (8), (9), (10) and (11) into equation (7), and solve them together with equations (5) and (6) to obtain the oil temperature at the outlet of each vertical oil channel.
[0013] As a preferred embodiment of the present invention, in S3, the heat network basic heat transfer unit includes a copper conductor, a winding insulation wrapped around the copper conductor, and an oil channel on the outer surface of the winding insulation. Heat diffuses around the copper conductor. When the heat is transferred to the outer surface of the winding insulation, it is transferred to the transformer oil in the oil channel by heat convection, and the conduction thermal resistance of the copper conductor itself is ignored. The basic heat transfer unit is divided into a conductor unit and an oil channel unit. The conductor unit only involves the winding conduction thermal resistance, while the oil channel unit involves the oil channel conduction thermal resistance and convection thermal resistance. In the basic heat transfer unit of the thermal network, the axial conduction thermal resistance characterizes the heat transfer process in the axial direction of the winding and the oil channel. The calculation formula of the axial conduction thermal resistance of the winding is as follows: (12); In the formula, is the thermal conductivity of winding insulation; is the insulation thickness of the winding unit in the axial direction; is the axial heat transfer area of the winding unit; is the axial conduction thermal resistance of the winding; The oil channel outlet temperature meets the following requirements: (13); In the formula, is the oil temperature at the outlet of the i-th oil channel; is the transformer oil mass flow rate flowing through the i-th oil channel; the oil channel inlet temperature is the same; According to the principles of heat transfer: (14); In the formula, is the conduction thermal resistance of the i-th oil channel; N is the number of axial segments of the winding; Substituting formula (13) into formula (14), it is expressed as: (15); The convection thermal resistance between the winding and the transformer oil is expressed as: (16); In the formula, is the convection thermal resistance between the winding and the transformer oil in the i-th oil channel; is the convection heat transfer coefficient between the winding and the transformer oil in the i-th oil channel; is the heat exchange area between the winding and the transformer oil in the i-th oil channel.
[0014] As a preferred embodiment of the present invention, in the S4, a single-phase winding thermal network model is constructed by using each thermal network basic heat transfer unit and the end insulation provided at the upper and lower ends of the winding, and the convective heat transfer thermal resistance between the end insulation and the transformer oil is ignored during the construction.
[0015] As a preferred embodiment of the present invention, in the above S4, the temperature value at the outlet of each oil channel is obtained by the oil temperature calculation model at the outlet of the oil channel, and the axial temperature distribution of the outermost side of the winding is considered to be a linear distribution with the top oil temperature and the bottom oil temperature as the endpoints; the top oil temperature Calculated by traditional heat circuit model; the bottom oil temperature calculation formula is: (17); In the formula, is the external ambient temperature of the transformer; At this point, the oil temperature at the outlet of each vertical oil channel and the outermost axial temperature distribution of the winding are introduced into the single-phase winding thermal network model and solved to obtain the temperature distribution of the winding area.
[0016] A device for modeling and analyzing regional temperature rise of windings of an oil-immersed distribution transformer, comprising: a memory having a computer processing program stored thereon; The processor is used to execute the computer processing program in the memory to implement the above-mentioned oil-immersed distribution transformer winding regional temperature rise modeling and analysis method.
[0017] The beneficial effects of the present invention are: The oil-immersed distribution transformer winding regional temperature rise modeling and analysis method proposed in the present invention can accurately obtain the hot spot temperature and internal temperature distribution of the distribution transformer during operation through modeling and analysis, obtain the winding regional temperature distribution, and realize the description of the transformer heat transfer process in the form of a circuit; it has the advantages of convenient calculation, good real-time performance and high accuracy, and at the same time, no modification is required for the transformer, and it is highly practical. It can accurately and quickly obtain the transformer winding hot spot temperature and the hottest point position, which is of great significance for ensuring the safe and efficient operation of the transformer. BRIEF DESCRIPTION OF THE DRAWINGS
[0018] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 is a schematic diagram of a heat transfer unit of a heat network foundation in an embodiment of the present invention; Figure 3 is a schematic diagram of a geometric model of a distribution transformer during the verification process of the present invention; Figure 3 (a) is a schematic diagram of the internal structure; Figure 3 (b) is a schematic diagram of the external fuel tank; Figure 4 It is a diagram of the calculation results of the finite element model during the verification process of the present invention; Figure 4 (a) is a schematic diagram of the temperature distribution of the transformer oil tank; Figure 4 (b) is a schematic diagram of the temperature distribution of the transformer winding and core; Figure 4 (c) is a schematic diagram of the temperature distribution of the transformer core metal clamp; Figure 5 It is the axial temperature distribution diagram of the finite element model and the thermal network model during the verification process of the present invention; Figure 6 It is a radial temperature distribution diagram of the finite element model and the thermal network model during the verification process of the present invention. DETAILED DESCRIPTION
[0019] The embodiments of the present invention are further described below in conjunction with the accompanying drawings: Example 1: Figure 1 As shown, a method for modeling and analyzing the regional temperature rise of an oil-immersed distribution transformer winding includes the following steps: S1. For the winding area of the oil-immersed distribution transformer including the low-voltage winding, the high-voltage winding and the vertical oil channel, an oil temperature calculation model at the oil channel outlet is established based on the fluid mechanics and heat transfer theory. The modeling steps are as follows: S1.1. Establish a calculation formula for the buoyancy of the oil flow inside the oil channel, the friction of the transformer oil during flow, and the gravity of the transformer oil; S1.2, simplify and integrate the three calculation formulas in S1.1; S1.3. Establish a calculation formula for the heat absorbed by the oil channel and the total heat absorbed by each oil channel; S1.4. Establish the expressions of convective heat transfer coefficient, Nusselt number correlation, Reynolds number, Rayleigh number and Prandtl number in the process of flow heat transfer; S2. Based on the oil temperature calculation model at the oil channel outlet, the oil temperature at the outlet of each vertical oil channel is obtained by simultaneous solution; S3, dividing the winding area into heat network basic heat transfer units, and solving the temperature distribution of the winding area; S4. Based on the basic heat transfer unit of the thermal network, a single-phase winding thermal network model is constructed to obtain the outermost axial temperature distribution of the winding. The oil temperature at the outlet of each vertical oil channel and the outermost axial temperature distribution of the winding are introduced into the single-phase winding thermal network model to solve the temperature distribution of the winding area.
[0020] In order to improve the heat dissipation capacity of transformer windings and reduce the hot spot temperature, several vertical oil channels are usually set in the winding area during the design and manufacturing stage. The transformer oil at the oil inlet of the oil channel has undergone a cooling process, and the temperature after releasing heat is low. It is generally believed that the oil temperature here is equal to the bottom oil temperature. The outer side of the high-voltage winding has a large area and strong heat dissipation capacity. The oil temperature distribution in the outer axial direction is approximately linear with the top oil temperature and the bottom oil temperature as endpoints. Compared with the outside of the high-voltage winding, the heat dissipation capacity of the oil channel inside the winding is limited. Therefore, the temperature at the outlet of the oil channel inside the winding is higher than the top oil temperature. Based on the winding structure and spatial size layout of the distribution transformer, the approximate temperature distribution of the oil channel.
[0021] From the above analysis, it can be seen that the oil temperature at the oil channel outlet is higher than the top oil temperature. Since there is a more complex flow relationship between the oil at the oil channel outlet and the top oil, it is difficult to describe the numerical relationship between the two by means of thermal resistance. Therefore, a calculation model for the oil temperature at the oil channel outlet is established based on the theory of heat transfer and fluid mechanics.
[0022] In S1.1, the transformer oil in the vertical oil channel flows upward under the action of buoyancy because the temperature rises and the density decreases after the transformer oil absorbs heat. During the flow, the transformer oil is also affected by friction and gravity. When the oil flow velocity no longer changes, the force reaches a balanced state. The calculation formula for the buoyancy of the oil flow inside the oil channel is: (1); In the formula, is the buoyancy of the oil flow in the i-th oil channel; is the density of transformer oil; g is the acceleration due to gravity; is the axial height of the i-th oil channel; is the flow area of the i-th oil channel; β is the volume expansion coefficient of transformer oil; is the average temperature of transformer oil; The calculation formula of the friction force on transformer oil during flow is: (2); In the formula, is the friction force on the transformer oil in the i-th oil channel during its flow; is the hydraulic diameter of the i-th oil channel; is the oil flow rate of the i-th oil channel; is the viscosity of transformer oil; The calculation formula for the gravity of transformer oil is: (3); In the formula, is the gravity of the transformer oil in the i-th oil channel; is the bottom oil temperature; is the oil temperature difference between the inlet and outlet of the i-th oil channel.
[0023] In S1.2, the simplified integration process is that when the oil flow rate is stable, the buoyancy force on the transformer oil is equal to the sum of gravity and friction: (4); Substitute equation (1), equation (2), and equation (3) into equation (4) and simplify them to express as: (5).
[0024] In S1.3, according to the law of conservation of energy, that is, the heat emitted by the windings on both sides of the oil channel in steady state is equal to the energy required to maintain the temperature rise of the oil channel, the calculation formula for the heat absorbed by the oil channel is: (6); In the formula, is the heat absorbed by the i-th oil channel; is the specific heat capacity of transformer oil; The windings of oil-immersed distribution transformers mostly adopt a cylindrical structure. The heat absorbed by each oil channel of the cylindrical winding is closely related to the windings on both sides of the oil channel, and the total heat absorbed by the oil channel is not easy to obtain; therefore, the total heat absorbed by each oil channel is further calculated according to the Newton cooling formula: (7); In the formula, , are the average temperatures of the windings on both sides of the i-th oil channel; , are the convective heat transfer coefficients between the winding and the oil channel on both sides of the i-th oil channel; , are the heat transfer areas between the winding and the oil channel on both sides of the i-th oil channel.
[0025] In S1.4, the convective heat transfer coefficient h in the flow heat transfer process is expressed as: (8); In the formula, is the thermal conductivity of the fluid; is the Nusselt number in the convective heat transfer process between fluid and solid; L is the characteristic size of convective heat transfer; The heat transfer between each winding and the oil channel is regarded as the convection heat transfer between the vertical slot and the internal fluid, and the Nusselt number correlation formula is expressed as: (9); In the formula, is the Reynolds number; Pr is the Prandtl number; is the viscosity of the transformer oil at the average temperature of the winding; D is the hydraulic diameter of the oil channel; H is the axial height of the oil channel; The heat transfer between the outermost side of the high-voltage winding and the transformer oil is regarded as the convection heat transfer between the fluid and the vertical plate, and the Nusselt number correlation is expressed as: (10); is the Rayleigh number with L as the characteristic size; The expressions for the Reynolds number, Rayleigh number, and Prandtl number are: (11); In the formula, is the average temperature of the winding; is the transformer oil temperature; is the thermal conductivity of transformer oil; v is the oil flow velocity in the oil channel.
[0026] In S2, it is measured and , substitute equations (8), (9), (10) and (11) into equation (7), and solve them together with equations (5) and (6) to obtain the oil temperature at the outlet of each vertical oil channel.
[0027] In S3, the basic heat transfer unit of the heat network includes the copper conductor, the winding insulation wrapped around the copper conductor, and the oil channel on the outer surface of the winding insulation. The heat diffuses around the copper conductor. When the heat is transferred to the outer surface of the winding insulation, it is transferred to the transformer oil in the oil channel by heat convection. The thermal conductivity of the copper conductor is thousands of times that of the insulation wrapped around it, so its thermal resistance is extremely small compared to the thermal resistance of the insulation. Therefore, the conduction thermal resistance of the copper conductor itself is ignored, and only the conduction thermal resistance of the winding insulation is considered; The basic heat transfer unit is divided into a conductor unit and an oil channel unit. The conductor unit only involves the winding conduction thermal resistance, while the oil channel unit involves the oil channel conduction thermal resistance and convection thermal resistance. In the basic heat transfer unit of the thermal network, the axial conduction thermal resistance characterizes the heat transfer process in the axial direction of the winding and the oil channel. The calculation formula of the axial conduction thermal resistance of the winding is as follows: (12); In the formula, is the thermal conductivity of winding insulation; is the insulation thickness of the winding unit in the axial direction; is the axial heat transfer area of the winding unit; is the axial conduction thermal resistance of the winding; The oil channel outlet temperature meets the following requirements: (13); In the formula, is the oil temperature at the outlet of the i-th oil channel; is the transformer oil mass flow rate flowing through the i-th oil channel; According to the principles of heat transfer: (14); In the formula, is the conduction thermal resistance of the i-th oil channel; N is the number of axial segments of the winding; Substituting formula (13) into formula (14), it is expressed as: (15); The convection thermal resistance between the winding and the transformer oil is expressed as: (16); In the formula, is the convection thermal resistance between the winding and the transformer oil in the i-th oil channel; is the convection heat transfer coefficient between the winding and the transformer oil in the i-th oil channel; is the heat exchange area between the winding and the transformer oil in the i-th oil channel.
[0028] An example of a specific heat network basic heat transfer unit is as follows Figure 2 As shown, Figure 2 middle, , , , They represent the conduction thermal resistance of the winding in four directions, indicating the heat transfer to the surroundings; , denote the convection thermal resistance between the winding and the transformer oil in the i-th oil channel in the left and right directions respectively; , They represent the thermal conduction resistance in the upward and downward directions of the i-th oil channel, respectively, indicating the heat transfer in the upward and downward directions; Indicates the winding node temperature; Represents the temperature of the i-th oil channel node.
[0029] In S4, a single-phase winding thermal network model is constructed through each thermal network basic heat transfer unit and the end insulation set at the upper and lower ends of the winding, and the convection heat transfer thermal resistance between the end insulation and the transformer oil is ignored during construction. During construction, the radial number of the winding can be represented by r in the subscript, and the axial number of the winding can be represented by a in the subscript, which is the node number in the thermal network model, used to distinguish each thermal network basic heat transfer unit.
[0030] In S4, the temperature value at the outlet of each oil channel is obtained by the oil temperature calculation model at the oil channel outlet. The axial temperature distribution of the outermost side of the winding is considered to be a linear distribution with the top oil temperature and the bottom oil temperature as the endpoints; the top oil temperature Calculated by traditional heat circuit model; the bottom oil temperature calculation formula is: (17); In the formula, is the external ambient temperature of the transformer; At this point, the oil temperature at the outlet of each vertical oil channel and the outermost axial temperature distribution of the winding are introduced into the single-phase winding thermal network model and solved to obtain the temperature distribution of the winding area.
[0031] The existing standard GB1094.2-2013 points out that for oil-immersed self-cooling transformers of 2500kVA and below, the average oil temperature rise above the ambient temperature can be taken as 80% of the top oil temperature rise. Since the axial oil temperature distribution outside the high-voltage winding is assumed to be a linear distribution with the top oil temperature and the bottom oil temperature as endpoints, it can be considered that the transformer bottom oil temperature rise can be taken as 60% of the top oil temperature rise.
[0032] The verification process is: A S13-M-200 / 10 distribution transformer is taken as the research object (case transformer), and its finite element model is established considering the core, end insulation, winding and other components. Its geometric model is as follows Figure 3 The electrical parameters are shown in Table 1.
[0033] Table 1 Case transformer electrical parameters
[0034] In Table 1, the connection mode dyn means that the high voltage side of the transformer is connected in a triangle, while the low voltage side is connected in a star, and the low voltage side has a neutral line. In the Dyn11 connection method, the high voltage side is connected in a triangle, the low voltage side is connected in a star with a neutral line, and the high voltage and low voltage have a phase difference of 30 degrees.
[0035] The commercial software Fluent Meshing was used to mesh the geometric model. The total number of meshes was about 3.8 million, and the minimum mesh quality was 0.187, which met the calculation requirements.
[0036] Transformer oil plays a vital role in the cooling process of oil-immersed transformers, so its physical properties are extremely important for the calculation of temperature field. The physical performance parameters of transformer oil are shown in Table 2.
[0037] Table 2 Physical properties of transformer oil
[0038] In Table 2, T represents temperature, and the unit is Kelvin.
[0039] During the verification process, the transformer winding used was wound with enameled wire and then wrapped with insulating paper. The thickness of the lacquer layer and insulating paper is only at the millimeter level. If the influence of the two is considered during the modeling process, it will increase the difficulty of winding modeling, and the number of networks will increase sharply, making it difficult to implement. For this reason, the equivalent thermal conductivity of the winding is calculated by thermal parameter equivalence to reduce the influence of ignoring the insulating layer on the temperature field calculation results. The calculation formulas for the radial and axial equivalent thermal conductivity of the winding are obtained by equations (18) and (19).
[0040] (18); In the formula, is the radial equivalent thermal conductivity of the winding; , , They are the thermal conductivity of copper, insulating varnish and insulating cardboard respectively; , , They are the thickness of copper, insulating varnish and insulating paperboard in the radial direction of the winding respectively; is the total thickness of the winding in the radial direction; (19); In the formula, is the axial equivalent thermal conductivity of the winding; , is the thickness of the winding axial copper and insulating varnish; It is the total height of the winding in the axial direction.
[0041] The end insulation materials at the upper and lower ends of the winding are made of insulating paper, the oil tank is a steel structure, and the iron core is made of stacked silicon steel sheets. The physical performance parameters of each material of the transformer are shown in Table 3.
[0042] Table 3 Physical performance parameters of transformer materials
[0043] The heat transfer modes of transformers include convection heat transfer, radiation heat transfer and heat conduction. The radiation heat transfer inside the transformer has little effect on the temperature field calculation results and can be ignored. Therefore, only convection heat transfer and heat conduction are considered on the internal wall, and coupled boundary conditions are set for the internal wall. By setting the convection-radiation composite heat transfer coefficient on the outer wall of the transformer to simulate the convection and radiation heat transfer process between the transformer and the outside world, the composite heat transfer coefficient It can be obtained by formula (20).
[0044] (20); In the formula, , are the convection heat transfer coefficient and radiation heat transfer coefficient of the oil tank surface respectively; is the fuel tank temperature; is the surface emissivity of the object, which takes a value of 0.95; is the Boltzmann constant, with a value of 5.67×10 –8 W / (m 2 ×K 4 ); is the thermal conductivity of air; is the Nusselt number with L as the characteristic dimension; The finite element model is used to calculate the temperature distribution of the case transformer and the temperature distribution cloud diagram of each component under rated working conditions and an ambient temperature of 5.55°C. Figure 4 As shown. Figure 4 It can be seen that since the three-phase winding losses are roughly the same, the temperature distribution of the three-phase windings is basically the same. The hot spot temperature is 72.38°C, which is located on the low-voltage winding. This is because the low-voltage winding has a higher unit heat source and is located at the innermost part of the winding, resulting in a poor heat dissipation environment. The temperature of the transformer box gradually rises from the bottom to the top, with the highest temperature reaching 50.93°C, and the temperature at the bottom of the oil tank is 29.03°C.
[0045] The distribution transformer is a central axis symmetrical structure. According to the finite element calculation results, it can be seen that the temperature distribution of the three-phase windings A, B, and C is roughly the same. Therefore, taking phase B as an example, a case transformer thermal network model (that is, a single-phase winding thermal network model of the case transformer) is established according to the method in this embodiment. The high-voltage winding of the case transformer has a total of 1546 turns and 13 layers, with a vertical oil channel set between the layers. The low-voltage winding has a total of 34 turns, divided into 2 layers, and a vertical oil channel is set between the layers. If each turn of the low-voltage winding is taken as a basic unit, the entire winding can be divided into 17 sections axially and each layer can be divided into one section radially. In this way, the thermal network model of the case transformer is established, and the temperature distribution of the winding area of the distribution transformer can be obtained by solving the thermal network model.
[0046] In order to verify the accuracy of the thermal network model, the short-circuit method was used to conduct a steady-state temperature rise test on the case transformer. The ambient temperature was 5.55℃, and the temperature rise test results are shown in Table 4.
[0047] Table 4 Transformer temperature rise test results
[0048] According to GB / T1094.7-2008 "Power Transformers Part 7: Load Guidelines for Oil-Immersed Power Transformers", the calculation formula for the winding hot spot temperature is shown in formula (21).
[0049] (twenty one); In the formula, is the hot spot temperature; E is the winding hot spot coefficient; The average temperature of the winding at the end of the temperature rise test; The hot spot temperature values obtained by the finite element model, the thermal network model calculation value and the temperature rise test are shown in Table 5. As can be seen from Table 5, the difference between the hot spot temperature values obtained by the thermal network model and the hot spot temperature values obtained by the finite element model and the temperature rise test is less than 2°C, which proves the effectiveness and accuracy of the thermal network model.
[0050] Table 5 Comparison of calculation results of each model
[0051] According to the calculation results of the thermal network model, the hot spot temperature is located at the first layer and the first turn of the low-voltage winding. The axial temperature distribution at the corresponding position of the finite element model is compared with the calculation results of the thermal network model, such as Figure 5 As shown in the figure, the winding temperature increases with the increase of axial height. The hot spot temperature obtained by the thermal network is located at 97.08% of the winding axial height, and the hot spot temperature obtained by the finite element is located at 97.96% of the winding axial height. The calculation results of the hot spot positions of the two are basically the same. It can also be seen from the figure that the relative error of the calculation results of the two models at various axial positions is less than 5%.
[0052] At the axial height of the hot spot, a straight line is drawn from the innermost side of the winding to the outermost side of the winding in the radial direction. The temperature distribution of the two models on this straight line is as follows: Figure 6 As shown in the figure. The relative error of the calculation results of the two models at each position is less than 10%. By comparing the axial and radial temperature calculation results of the winding area of the two models, it can be seen that the temperature distribution calculation results of the two models are not much different, which once again proves the feasibility of the established thermal network model. On a workstation equipped with an Intel Xeon CPU E5-2680 V4, the finite element model calculation time is about 8 hours, while the thermal network calculation time is about 3 minutes, which greatly shortens the calculation time.
[0053] Embodiment 2: A device for modeling and analyzing regional temperature rise of windings of an oil-immersed distribution transformer, comprising: a memory having a computer processing program stored thereon; The processor is used to execute the computer processing program in the memory to implement the modeling and analysis method in Example 1.
Claims
1. A method for modeling and analyzing the regional temperature rise of oil-immersed distribution transformer windings, characterized in that The following steps are involved: S1. For the winding area of the oil-immersed distribution transformer including the low-voltage winding, the high-voltage winding and the vertical oil channel, an oil temperature calculation model at the oil channel outlet is established based on the fluid mechanics and heat transfer theory. The modeling steps are as follows: S1.
1. Establish a calculation formula for the buoyancy of the oil flow inside the oil channel, the friction of the transformer oil during flow, and the gravity of the transformer oil; S1.2, simplify and integrate the three calculation formulas in S1.1; S1.
3. Establish a calculation formula for the heat absorbed by the oil channel and the total heat absorbed by each oil channel; S1.
4. Establish the expressions of convective heat transfer coefficient, Nusselt number correlation, Reynolds number, Rayleigh number and Prandtl number in the process of flow heat transfer; S2. Based on the oil temperature calculation model at the oil channel outlet, the oil temperature at the outlet of each vertical oil channel is obtained by simultaneous solution; S3, dividing the winding area into heat network basic heat transfer units, and solving the temperature distribution of the winding area; S4. Based on the basic heat transfer unit of the thermal network, a single-phase winding thermal network model is constructed to obtain the outermost axial temperature distribution of the winding. The oil temperature at the outlet of each vertical oil channel and the outermost axial temperature distribution of the winding are introduced into the single-phase winding thermal network model to solve the temperature distribution of the winding area.
2. The method for modeling and analyzing the regional temperature rise of windings of an oil-immersed distribution transformer according to claim 1, characterized in that: In S1.1, the transformer oil in the vertical oil channel flows upward under the action of buoyancy because the temperature rises and the density decreases after the transformer oil absorbs heat. During the flow, the transformer oil is also affected by friction and gravity. When the oil flow velocity no longer changes, the force reaches a balanced state. The calculation formula for the buoyancy of the oil flow inside the oil channel is: （1）； In the formula, is the buoyancy of the oil flow in the i-th oil channel; is the density of transformer oil; g is the acceleration due to gravity; is the axial height of the i-th oil channel; is the flow area of the i-th oil channel; β is the volume expansion coefficient of transformer oil; is the average temperature of transformer oil; The calculation formula of the friction force on transformer oil during flow is: （2）； In the formula, is the friction force on the transformer oil in the i-th oil channel during its flow; is the hydraulic diameter of the i-th oil channel; is the oil flow rate of the i-th oil channel; is the viscosity of transformer oil; The calculation formula for the gravity of transformer oil is: （3）； In the formula, is the gravity of the transformer oil in the i-th oil channel; is the bottom oil temperature; is the oil temperature difference between the inlet and outlet of the i-th oil channel.
3. The method for modeling and analyzing the regional temperature rise of windings of an oil-immersed distribution transformer according to claim 2 is characterized in that: In S1.2, the simplified integration process is that when the oil flow rate is stable, the buoyancy force on the transformer oil is equal to the sum of gravity and friction: （4）； Substitute equation (1), equation (2), and equation (3) into equation (4) and simplify them to express as: （5）。 4. The method for modeling and analyzing the regional temperature rise of windings of an oil-immersed distribution transformer according to claim 3 is characterized in that: In S1.3, according to the law of conservation of energy, that is, the heat emitted by the windings on both sides of the oil channel in steady state is equal to the energy required to maintain the temperature rise of the oil channel, the calculation formula for the heat absorbed by the oil channel is: （6）； In the formula, is the heat absorbed by the i-th oil channel; is the specific heat capacity of transformer oil; The total heat absorbed by each oil channel is further calculated according to Newton's cooling formula: （7）； In the formula, , are the average temperatures of the windings on both sides of the i-th oil channel; , are the convective heat transfer coefficients between the winding and the oil channel on both sides of the i-th oil channel; , are the heat transfer areas between the winding and the oil channel on both sides of the i-th oil channel.
5. The method for modeling and analyzing the regional temperature rise of windings of an oil-immersed distribution transformer according to claim 4, characterized in that: In S1.4, the convective heat transfer coefficient h in the flow heat transfer process is expressed as: （8）； In the formula, is the thermal conductivity of the fluid; is the Nusselt number in the convective heat transfer process between fluid and solid; L is the characteristic size of convective heat transfer; The heat transfer between each winding and the oil channel is regarded as the convection heat transfer between the vertical slot and the internal fluid, and the Nusselt number correlation formula is expressed as: （9）； In the formula, is the Reynolds number; Pr is the Prandtl number; is the viscosity of the transformer oil at the average temperature of the winding; D is the hydraulic diameter of the oil channel; H is the axial height of the oil channel; The heat transfer between the outermost side of the high-voltage winding and the transformer oil is regarded as the convection heat transfer between the fluid and the vertical plate, and the Nusselt number correlation is expressed as: （10）； is the Rayleigh number with L as the characteristic size; The expressions for the Reynolds number, Rayleigh number, and Prandtl number are: （11）； In the formula, is the average temperature of the winding; is the transformer oil temperature; is the thermal conductivity of transformer oil; v is the oil flow velocity in the oil channel.
6. The method for modeling and analyzing regional temperature rise of windings of an oil-immersed distribution transformer according to claim 5, characterized in that: In the S2, it is measured and , substitute equations (8), (9), (10) and (11) into equation (7), and solve them together with equations (5) and (6) to obtain the oil temperature at the outlet of each vertical oil channel.
7. The method for modeling and analyzing regional temperature rise of windings of an oil-immersed distribution transformer according to claim 6, characterized in that: In the above S3, the heat network basic heat transfer unit includes a copper conductor, a winding insulation wrapped around the copper conductor, and an oil channel on the outer surface of the winding insulation. Heat diffuses around the copper conductor. When the heat is transferred to the outer surface of the winding insulation, it is transferred to the transformer oil in the oil channel by heat convection, and the conduction thermal resistance of the copper conductor itself is ignored. The basic heat transfer unit is divided into a conductor unit and an oil channel unit. The conductor unit only involves the winding conduction thermal resistance, while the oil channel unit involves the oil channel conduction thermal resistance and convection thermal resistance. In the basic heat transfer unit of the thermal network, the axial conduction thermal resistance characterizes the heat transfer process in the axial direction of the winding and the oil channel. The calculation formula of the axial conduction thermal resistance of the winding is as follows: （12）； In the formula, is the thermal conductivity of winding insulation; is the insulation thickness of the winding unit in the axial direction; is the axial heat transfer area of the winding unit; is the axial conduction thermal resistance of the winding; The oil channel outlet temperature meets the following requirements: （13）； In the formula, is the oil temperature at the outlet of the i-th oil channel; is the transformer oil mass flow rate flowing through the i-th oil channel; According to the principles of heat transfer: （14）； In the formula, is the conduction thermal resistance of the i-th oil channel; N is the number of axial segments of the winding; Substituting formula (13) into formula (14), it is expressed as: （15）； The convection thermal resistance between the winding and the transformer oil is expressed as: （16）； In the formula, is the convection thermal resistance between the winding and the transformer oil in the i-th oil channel; is the convection heat transfer coefficient between the winding and the transformer oil in the i-th oil channel; is the heat exchange area between the winding and the transformer oil in the i-th oil channel.
8. The method for modeling and analyzing regional temperature rise of windings of an oil-immersed distribution transformer according to claim 7, characterized in that: In the above S4, a single-phase winding thermal network model is constructed by using each thermal network basic heat transfer unit and the end insulation provided at the upper and lower ends of the winding, and the convection heat transfer thermal resistance between the end insulation and the transformer oil is ignored during the construction.
9. The method for modeling and analyzing regional temperature rise of windings of an oil-immersed distribution transformer according to claim 8, characterized in that: In S4, the temperature value at the outlet of each oil channel is obtained by the oil temperature calculation model at the oil channel outlet. The axial temperature distribution of the outermost side of the winding is considered to be a linear distribution with the top oil temperature and the bottom oil temperature as endpoints; the top oil temperature Calculated by traditional heat circuit model; the bottom oil temperature calculation formula is: （17）； In the formula, is the external ambient temperature of the transformer; At this point, the oil temperature at the outlet of each vertical oil channel and the outermost axial temperature distribution of the winding are introduced into the single-phase winding thermal network model and solved to obtain the temperature distribution of the winding area.
10. A device for modeling and analyzing the regional temperature rise of windings of an oil-immersed distribution transformer, characterized in that: include: a memory having a computer processing program stored thereon; A processor is used to execute a computer processing program in a memory to implement the oil-immersed distribution transformer winding regional temperature rise modeling and analysis method as described in any one of claims 1 to 9.