Method and system for analyzing cable temperature rise at different environment temperatures

Abstract

The invention discloses a method and a system for analyzing cable temperature rise at different environment temperatures. The method comprises the following steps: establishing a temperature field and a fluid field; calculating a radiation angle coefficient; assuming that the air velocity on the outer surface of the cable and the inner wall of the cable trench is zero, and determining the boundary condition of the external soil environment of the cable; building a cable simulation model according to the cable heat flow coupling condition, the radiation angle coefficient, the boundary condition and the cable duct laying mode; dividing each part of the cable simulation model into grids with different fineness; simplifying the cable simulation model into a two-dimensional model; and calculating and analyzing the temperature rise of the cable at different environment temperatures by using the two-dimensional model. The model obtained by the embodiment is more in line with the actual condition of cable laying; determining boundary conditions of all boundaries of the model to enable the boundary conditions to accord with complex cable laying conditions; and each part of the model is divided into grids with different finesses, and the grids are simplified into a two-dimensional model, so that the model construction difficulty is reduced, and the operation is more efficient.

Description

Technical Field

[0001] Embodiments of the present disclosure relate to the technical field of cable temperature rise analysis, and in particular, to a method and system for analyzing the temperature rise of cables under different ambient temperatures. Background Art

[0002] In the construction practice of power distribution projects, cable laying technology, as a key technology, has shown many irreplaceable advantages in its application. Cable laying technology can not only effectively ensure the stability and safety of power transmission, but also play an important role in improving the flexibility and reliability of the power network. However, in the actual application process, some inevitable problems and challenges have also emerged. For example, after cable laying, the ambient temperature has a huge impact on the thermal performance and current-carrying capacity of the cable. In the specific laying environment of the underground cable channel, the influence of the ambient temperature needs to comprehensively consider two aspects: air temperature and soil temperature. The influence of soil temperature on the heat dissipation ability of the cable is particularly significant.

[0003] Therefore, analyzing the temperature rise of cables in different environments is an important problem to be solved in this field.

[0004] In the related art, the boundary conditions used for analyzing the cable temperature rise cannot meet the requirements of specific cable laying scenarios, and the design is complex with a large amount of calculation, resulting in a slow calculation speed and a long time consumption, thus leading to low calculation efficiency.

[0005] Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions.

[0006] It should be noted that this part aims to provide background or context for the technical solutions of the present disclosure stated in the claims. The descriptions herein are not admitted to be prior art just because they are included in this part. Summary of the Invention

[0007] The purpose of the embodiments of the present disclosure is to provide a method and system for analyzing the temperature rise of cables under different ambient temperatures, thereby at least to a certain extent overcoming one or more problems caused by the limitations and defects of the related art.

[0008] The embodiments of the present disclosure first provide a method for analyzing the temperature rise of cables under different ambient temperatures, including:

[0009] Establishing the temperature field and fluid field of cables laid in underground conduits to analyze the heat flow coupling situation of the cables;

[0010] Calculating the radiation view factor to simulate the heat transfer mode of the cables;

[0011] Assume that the air flow velocity on the outer surface of the cable and the inner wall of the cable trench is zero, and determine the boundary conditions of the external soil environment of the cable;

[0012] Build a cable simulation model according to the cable heat flow coupling situation, the radiation view factor, the boundary conditions and the cable duct laying method;

[0013] Perform mesh division on the cable simulation model, and divide each part of the cable simulation model into meshes with different fineness;

[0014] Simplify the cable simulation model into a two-dimensional model;

[0015] Use the two-dimensional model to calculate and analyze the cable temperature rise under different environmental temperatures, and obtain the temperature rise analysis result.

[0016] In an embodiment of the present disclosure, the heat transfer modes of the cable include: heat conduction, heat convection and heat radiation.

[0017] In an embodiment of the present disclosure, the process of determining the boundary conditions of the external soil environment of the cable includes:

[0018] Set the temperature value of the lower boundary of the external soil of the cable;

[0019] Set the heat flow amount of the left and right boundaries of the external soil of the cable;

[0020] Determine the heat exchange intensity of the upper boundary according to the convective heat transfer coefficient and the fluid temperature of the upper boundary of the external soil of the cable.

[0021] In an embodiment of the present disclosure, the control equation of the lower boundary is:

[0022] T(x, y)| Γ =f(x, y)| Γ ;

[0023] The control equations of the left and right boundaries are:

[0024] The control equation of the upper boundary is:

[0025] Wherein, x and y are coordinates in the two-dimensional model; f is the boundary scalar function, n is the outer normal direction of the boundary; Γ is the regional boundary; T is the temperature, T f is the external environmental temperature, K is the medium thermal conductivity, q is the heat flux density, and h is the convective heat transfer coefficient of the surface air.

[0026] In an embodiment of the present disclosure, the process of performing mesh division on the cable simulation model and dividing each part of the cable simulation model into meshes with different fineness includes:

[0027] Perform first-level meshing on the cable part, second-level meshing on the surface of the cable duct and the air part, and third-level meshing on the soil area. Among them, the fineness of the first-level meshing, second-level meshing, and third-level meshing decreases in sequence.

[0028] In an embodiment of the present disclosure, after the step of simplifying the cable simulation model into a two-dimensional model, the following steps are further included:

[0029] Conduct a feasibility test on the two-dimensional model.

[0030] In an embodiment of the present disclosure, the cable duct laying method includes: 2×4 type cable duct laying and 2×2 type cable duct laying.

[0031] In an embodiment of the present disclosure, the process of calculating and analyzing the cable temperature rise at different ambient temperatures by using the two-dimensional model to obtain the temperature rise analysis result includes:

[0032] Set the temperature change range of the groundwater where the cable is located to be -5°C to 42°C;

[0033] Use the finite element simulation method to calculate and analyze the steady-state temperature conditions of the cable conductor and the outer sheath within the temperature change range.

[0034] In an embodiment of the present disclosure, the calculation and analysis of the steady-state temperature conditions include: analyzing the time when the cable core temperature reaches the steady state and the time when the cable core temperature reaches 90°C; analyzing the steady-state value of the cable core temperature and the steady-state value of the outer sheath temperature.

[0035] The embodiments of the present disclosure also provide a system for analyzing the cable temperature rise at different ambient temperatures. The system includes:

[0036] A non-isothermal flow module, which is used to establish the temperature field and fluid field of the cable laid in the underground duct to analyze the cable heat flow coupling situation;

[0037] A radiation view factor calculation module, which is used to calculate the radiation view factor to simulate the heat transfer method of the cable;

[0038] A boundary condition determination module, which is used to assume that the air flow velocity on the outer surface of the cable and the inner wall of the cable trench is zero and determine the boundary conditions of the external soil environment of the cable;

[0039] A cable simulation model building module, which is used to build a cable simulation model according to the cable heat flow coupling situation, the radiation view factor, the boundary conditions, and the cable duct laying method;

[0040] The mesh generation module is used to perform mesh generation on the cable simulation model, and divide each part of the cable simulation model into meshes with different fineness levels;

[0041] The model simplification module is used to simplify the cable simulation model into a two-dimensional model;

[0042] The calculation and analysis module is used to calculate and analyze the cable temperature rise at different ambient temperatures by using the two-dimensional model, and obtain the temperature rise analysis result.

[0043] The technical solution provided by the embodiments of the present disclosure may include the following beneficial effects:

[0044] In a method and system for analyzing the cable temperature rise at different ambient temperatures in the embodiments of the present disclosure, a cable simulation model is built by using the cable heat flow coupling condition, the radiation angle factor, the boundary condition, and the cable trench laying method, so that the obtained model is more in line with the actual situation of cable laying; and the boundary conditions of each boundary of the model are determined to make it conform to the complex cable laying conditions; each part of the model is divided into meshes with different fineness levels and simplified into a two-dimensional model, so that the model construction difficulty is reduced and the operation is more efficient. Description of the Drawings

[0045] The drawings here are incorporated into the specification and constitute a part of this specification, showing the embodiments consistent with the present disclosure, and are used together with the specification to explain the principles of the present disclosure. Obviously, the drawings in the following description are only some embodiments of the present disclosure, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0046] Figure 1 A flowchart showing the method for analyzing the cable temperature rise at different ambient temperatures in the exemplary embodiments of the present disclosure;

[0047] Figure 2 A diagram showing the cable simulation model in the exemplary embodiments of the present disclosure;

[0048] Figure 3 A diagram showing the cable laying model in the exemplary embodiments of the present disclosure;

[0049] Figure 4 A diagram showing the 2×4 cable laying three-dimensional model simulation in the exemplary embodiments of the present disclosure;

[0050] Figure 5 A diagram showing the 2×2 cable laying three-dimensional model simulation in the exemplary embodiments of the present disclosure;

[0051] Figure 6 A diagram showing the 2×4 cable laying environment overall mesh generation three-dimensional diagram in the exemplary embodiments of the present disclosure;

[0052] Figure 7 Shows the three-dimensional diagram of the overall grid division of the 2×2 cable laying environment in an exemplary embodiment of the present disclosure;

[0053] Figure 8 Shows the grid division diagram of the simplified two-dimensional cable local model in an exemplary embodiment of the present disclosure;

[0054] Figure 9 Shows the simulation diagram of the 2×4 pipe laying two-dimensional model in an exemplary embodiment of the present disclosure;

[0055] Figure 10 Shows the simulation diagram of the 2×2 pipe laying two-dimensional model in an exemplary embodiment of the present disclosure;

[0056] Figure 11 Shows the grid division diagram of the 2×4 cable two-dimensional model in an exemplary embodiment of the present disclosure;

[0057] Figure 12 Shows the grid division diagram of the 2×2 cable two-dimensional model in an exemplary embodiment of the present disclosure;

[0058] Figure 13 Shows the overall temperature distribution diagram of the cable under 3D pipe laying in an exemplary embodiment of the present disclosure;

[0059] Figure 14 Shows the overall temperature distribution diagram of the cable under 2D pipe laying in an exemplary embodiment of the present disclosure;

[0060] Figure 15 Shows the temperature rise curves of the cable core and sheath under 2×4 pipe laying and different ambient temperatures in an exemplary embodiment of the present disclosure;

[0061] Figure 16 Shows the operation diagram of the cable under 2×4 pipe laying in an exemplary embodiment of the present disclosure;

[0062] Figure 17 Shows the temperature rise curves of the cable core and sheath under 2×2 pipe laying and different ambient temperatures in an exemplary embodiment of the present disclosure;

[0063] Figure 18 Shows the operation diagram of the cable under 2×2 pipe laying in an exemplary embodiment of the present disclosure. Detailed implementation manners

[0064] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art. The features, structures, or characteristics described may be combined in any suitable manner in one or more embodiments.

[0065] In addition, the accompanying drawings are only schematic illustrations of the embodiments of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus repeated descriptions thereof will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0066] In this example embodiment, a method for analyzing the temperature rise of cables at different ambient temperatures is first provided. Please refer to Figure 1 , which may include: step S101 - step S107. Specifically as follows:

[0067] Step S101, establish the temperature field and fluid field of the underground pipe - laid cable to analyze the cable heat - flow coupling situation. For example, COMSOL finite - element simulation software can be used to establish the temperature field and fluid field to analyze the influence of the thermal - force coupling of the cable in the cable trench.

[0068] Step S102, calculate the radiation view factor to simulate the heat transfer mode of the cable. The heat transfer modes of the cable include: heat conduction, heat convection, and heat radiation. The radiation heat transfer of the cable is simulated by adding a face - to - face radiation module, and the radiation view factor is calculated using the Hemicube method, thereby simulating the three heat transfer modes of heat conduction, heat convection, and heat radiation of the cable in the pipe. Specifically, heat conduction is mainly described by the thermal conductivity of the cable and pipe materials; heat convection is calculated by coupling the velocity field and temperature field in the fluid field; heat radiation is calculated by the radiation module for the radiation heat transfer between the cable surface and the inner wall of the pipe. Through this method of multi - physical - field coupling, the temperature distribution and heat dissipation of the cable in the pipe can be more accurately simulated, providing a theoretical basis for the cable laying design and operation and maintenance.

[0069] Step S103, assume that the air flow velocities on the outer surface of the cable and the inner wall of the cable trench are zero, and determine the boundary conditions of the external soil environment of the cable. In this application, different boundary conditions are adopted for each boundary of the external soil environment of the cable to conform to the complex boundary characteristics of the actual cable laying environment.

[0070] Step S104: Build a cable simulation model according to the cable heat flow coupling situation, the radiation angle factor, the boundary conditions, and the cable tray laying method. When building the model, since the steel frames supporting the cables only exist in some areas of the channel, the existence of the steel frames is ignored during the simulation process. In this application, the cable tray laying methods are set as: 2×4 type tray laying and 2×2 type tray laying.

[0071] Step S105: Perform mesh division on the cable simulation model, and divide each part of the cable simulation model into meshes with different fineness. If the model is divided into meshes of the same size, if the division accuracy is too high, the calculation accuracy is high, but the calculation efficiency is low. If the mesh accuracy is too low, the calculation accuracy will be affected. Therefore, in this application, according to the fineness requirements of each part of the cable, different fineness mesh divisions are performed on it, which not only meets the calculation accuracy requirements but also improves the calculation efficiency.

[0072] Step S106: Simplify the cable simulation model into a two-dimensional model. The cable simulation model is a three-dimensional model. Since the structure of the cable three-dimensional model is relatively complex and it is difficult during the simulation process, in this application, the three-dimensional model is simplified into a two-dimensional model to improve the research efficiency using the two-dimensional model. The two-dimensional model significantly reduces the calculation cost. Due to the simplification of the two-dimensional model in geometric dimensions, the number of grid points and degrees of freedom it requires are greatly reduced. This means that under the same hardware conditions, two-dimensional simulation can occupy less memory and CPU resources, thus achieving a faster simulation speed. This improvement in calculation efficiency is particularly important for the simulation of large-scale cable systems because it can significantly shorten the simulation cycle and accelerate the R & D process.

[0073] In addition, the results of the two-dimensional model are more intuitive and are easy to visualize and analyze in depth. On the two-dimensional plane, key information such as the structure of the cable system, temperature distribution, and electromagnetic field intensity can be clearly presented, which enables this application to capture the key features in the simulation results faster. This intuitiveness not only helps to understand the behavior mechanism of the cable system but also provides strong visual support for subsequent design optimization. More importantly, these advantages of the two-dimensional model can be directly translated into an improvement in research efficiency and design optimization ability. Through a faster simulation speed and a more intuitive result display, the design scheme can be iterated faster, and the influence of different parameters on the performance of the cable system can be verified. Therefore, this application simplifies the three-dimensional cable model into a two-dimensional model.

[0074] Step S107: Use the two-dimensional model to calculate and analyze the cable temperature rise under different ambient temperatures to obtain the temperature rise analysis results. Input different ambient temperatures into the two-dimensional model to calculate and analyze the cable temperature rise situation. For example, the cable temperature rise situation can be calculated for different ambient temperature values within the range of -11°C to 42°C.

[0075] In this embodiment, a cable simulation model is built by using the cable heat flow coupling situation, the radiation angle factor, the boundary conditions, and the cable tray laying method, so that the obtained model is more in line with the actual situation of cable laying; and the boundary conditions of each boundary of the model are determined to make it conform to complex cable laying conditions; each part of the model is divided into meshes with different fineness and simplified into a two-dimensional model, reducing the model construction difficulty and making the operation more efficient.

[0076] The following uses specific test examples to illustrate the method of the present application.

[0077] I. Theoretical analysis

[0078] 1. Cable structure analysis

[0079] As Figure 2 shown, the structure of the cable consists of a conductor core, a conductor shielding layer, an insulating layer, an insulating shielding layer, a buffer layer, a metal sheath, and an outer sheath in sequence.

[0080] Conductor: It is the main carrier for transmitting current. Generally, copper and aluminum with high conductivity are selected for the material to reduce the loss of transmitted electric energy while ensuring economy.

[0081] Conductor shielding layer: A material with low resistivity is preferably used, and its thickness is thinner than other layers. Essentially, it improves the distribution of the electric field, suppresses the growth of electrical tree branches, and reduces partial discharge, etc.

[0082] Insulating layer: It is an important part of high-voltage cables. The material is generally composed of cross-linked polyethylene or polyvinyl chloride. Its function is to ensure that the cable is insulated from the surrounding environment, and its performance such as heat resistance, electrical resistance, and stability is the main factor determining the current-carrying capacity of the cable.

[0083] Metal shielding: It is made of copper wire winding or soft copper tape and is located outside the insulating layer. It provides a low-voltage electrode for the insulation of the cable. The electrode maintains a zero potential through grounding, provides a path for capacitive current, and protects the cable from the influence of other electric fields.

[0084] Outer sheath: It protects each layer of the cable from being damaged due to changes in external conditions and is located on the outermost layer of the cable.

[0085] 2. Heat transfer method

[0086] (1) Heat conduction

[0087] Heat conduction is expressed by Fourier's law:

[0088]

[0089] In the formula: A represents the area of the flat plate, and the unit is m2 ; Φ represents the heat flowing through the flat plate, with the unit of W; λ is the thermal conductivity, and dt / dx is the temperature change rate of a point on the flat plate in the x direction.

[0090] (2) Heat convection

[0091] Heat convection generally refers to the macroscopic displacement between fluids, accompanied by heat conduction, which is a heat transfer process on the surface of an object. The calculation formula is:

[0092] Φ = hAΔt

[0093] In the formula: h is the convective heat transfer coefficient, a measure of the heat exchange intensity, with the unit of W / m 2 ·K; Δt is the difference between the solid surface temperature t1 and the fluid temperature t2, with the unit of K.

[0094] (3) Heat radiation

[0095] The heat radiation expression is:

[0096] Q = ξAσ b ΔT 4

[0097] In the formula: T represents the temperature of the object surface, A represents the surface area of the object radiation, with the unit of m 2 , σ b is the blackbody radiation constant, generally taking the value of 5.67x10 -8 W / (m 2 ·K), ξ is the emissivity. Since the radiation ability of the object is numerically smaller than that of the blackbody radiation, the emissivity is less than 1 in value.

[0098] 3. Loss calculation

[0099] (1) Conductor loss

[0100] The loss generated by the conductor core in the power cable when carrying a load is:

[0101] Wc = I 2 R

[0102] In the formula: W c means the resistance loss generated by the copper conductor per unit length due to heating, with the unit of W / m; I is the load flowing into the conductor, with the unit of A; R means the AC resistance per unit length at a certain temperature, with the unit of Ω / m.

[0103] The unit resistance value at 293K is 0.0283Ω / km, and the unit resistance value of the cable at 363K is 0.0383Ω / km.

[0104] The following formula is the calculation formula for the AC resistance R of the cable conductor:

[0105] R = R′(1 + y s + y p )

[0106] wherein, R' represents the DC resistance per unit length at a certain temperature, with the unit of Ω / m, and y s represents the skin effect factor, and y p represents the proximity effect factor of the cable.

[0107] (2) Insulation loss

[0108] When alternating current is applied to the cable, a part of the energy is consumed in the insulating layer medium and converted into dielectric loss. The insulation loss per unit length is:

[0109]

[0110] wherein, w = 2πf, f is 50 Hz; c is the capacitance of the cable per unit length, with the unit of F / m; U0 is the rated phase voltage of the cable, with the unit of V; tanδ is the dielectric loss factor of the insulation, and its value is related to the voltage level and the cable insulation material.

[0111] The calculation formula for the cable capacitance C is as follows:

[0112]

[0113] wherein, ε is the dielectric constant of the insulation material; D i is the diameter of the insulation layer, with the unit of mm; d c is the outer diameter of the conductor with the shielding layer, with the unit of mm.

[0114] II. Model construction

[0115] 1. Modeling assumptions

[0116] To reduce the model calculation amount and improve the calculation efficiency, the following simplifications are made during modeling: ① Assume that the cable in the trench is infinitely long, without considering the influence of axial heat transfer, equivalent the three-dimensional model to a two-dimensional model, and at the same time ignore the influence of the cable support in the trench; ② The Joule loss of the conductor and the dielectric loss are the main heat sources of the cable, and the influence of the metal sheath loss is ignored in the model; ③ In the case of pipe laying, the natural convection velocity of the enclosed air domain in the pipe is relatively low, and the air in the trench can be considered as an incompressible fluid, and the Boussinesq approximation is adopted.

[0117] 2. Boundary conditions

[0118] Figure 3 is the cable simulation model diagram, Figure 3 in which each boundary condition is shown.

[0119] (1) The lower boundary of the soil outside the cable applies the first type of boundary condition. The lower boundary is the soil, and the temperature is the same as that of the deep soil. The first type of boundary condition refers to the situation where the boundary temperature is known, that is, a specific temperature value on the soil boundary is set. This condition directly reflects the thermal state of the soil boundary and is crucial for solving the heat conduction equation.

[0120] The governing equation corresponding to the first type of boundary condition is:

[0121] T(x,y)| Γ =f(x,y)| Γ

[0122] (2) The left and right boundaries of the soil outside the cable apply the second type of boundary condition. The influence of the cable on the left and right boundaries can be ignored. At this time, the temperature gradient of the cable in the horizontal direction is 0. The second type of boundary condition is based on the known normal heat flux density on the boundary, that is, the heat flow situation through the unit area of the soil boundary per unit time is set. This condition helps to accurately evaluate the heat transfer process between the soil and the external environment.

[0123] The governing equation corresponding to the second type of boundary condition is:

[0124]

[0125] (3) The upper boundary of the soil outside the cable applies the third type of boundary condition.

[0126] The governing equation corresponding to the third type of boundary condition is:

[0127]

[0128] Among them, x and y are coordinates in the two-dimensional model; f is the boundary scalar function, n is the direction of the outer normal of the boundary; Γ is the boundary of the region; T is the soil temperature, T f is the external environment temperature, K is the thermal conductivity of the medium, q is the heat flux density, and h is the convective heat transfer coefficient of the surface air.

[0129] According to the complex boundary characteristics of the actual cable laying environment, when analyzing the thermal characteristics of the cable trench model, this application adopts different boundary conditions to simulate the heat exchange situation on various interfaces. For the deep soil located on the lower side of the cable trench model, since this area is far from the ground surface, less affected by the external environment, and the thermal conductivity of the soil is stable, this application can reasonably adopt the first type of boundary condition, that is, set the temperature of the deep soil to a constant value of 293K (equivalent to 20°C) to simulate the thermal state of this area.

[0130] For the boundaries on both sides of the cable trench in contact with the soil, considering that these areas are mainly affected by cable heating and heat conduction within the soil, and the heat exchange with the external environment is relatively weak, the second type of boundary condition is adopted, that is, the normal heat flux density q on these boundaries is set to 0 W / m 2 , which means that no heat flows to the external environment through heat conduction on these boundaries.

[0131] As for the surface part, since it is directly exposed to the atmosphere and affected by various factors such as solar radiation, wind speed, and temperature, its heat exchange process is more complex. To accurately simulate the heat exchange between the surface and the external environment, the third type of boundary condition, that is, the convective boundary condition, is selected. Under this condition, the convective heat transfer coefficient is set to 12.5 W / (m 2 ·K), and this value reflects the intensity of the heat exchange between the surface and the external air. At the same time, the temperature of the external air is taken as 293 K (equivalent to 20 °C) to simulate the heat exchange process between the surface and the air.

[0132] For the fluid-solid interfaces such as the outer surface of the cable and the inner wall of the cable trench, based on the basic principles of fluid mechanics, there is a significant phenomenon: due to the existence of fluid viscous forces, the air molecules adhering to these solid walls will be subject to frictional resistance from the walls, resulting in their relative movement speed with respect to the walls being reduced to zero. This phenomenon, usually referred to as the "no-slip condition", is an important boundary condition in fluid dynamics.

[0133] When constructing the cable trench model, in order to accurately simulate the heat exchange and flow characteristics between the air layer in the trench and the cable and the trench wall, the outer surface of the cable and the inner wall of the cable trench are set as no-slip walls, that is, it is assumed that the air flow velocity on these walls is zero, serving as the boundary condition for the fluid field of the enclosed air layer in the trench. This setting ensures that the model can accurately reflect the interaction between the fluid and the solid wall during the simulation process, especially the influence of viscous forces on fluid flow and heat exchange. The corresponding boundary equation is:

[0134] u = v = 0

[0135] In the formula, u and v are the air flow velocities in the horizontal and vertical directions respectively, with the unit of m / s.

[0136] 3. Governing equations

[0137] According to Fourier's basic law and the law of conservation of energy in heat transfer, the heat conduction differential equation in the heat source region can be expressed as:

[0138]

[0139] Among them, T is the temperature at the point (x, y), and the same applies to the following formula; q v$q$ is the heat generation rate per unit volume of the heat source; $\lambda$ is the thermal conductivity of the medium.

[0140] The heat conduction equation for the heat source-free region (other layers of the cable, external soil, etc.) in the model can be expressed as:

[0141]

[0142] 4. Simulation model construction

[0143] The research objects are the 2×2 pipe laying model and the 2×4 pipe laying model. The power cable model is the single-core cross-linked polyethylene cable of ZC-YJLW02, 190 / 330 kV, 1×2500 mm 2 type. The center distance between the pipes is 450 mm. The cable protection pipe is CPVC (Φ300 mm) with a wall thickness of 16 - 24 mm. The simulation diagrams of the pipe laying models are as shown in Figure 4 and Figure 5 shown.

[0144] (1) Material parameters and physical field settings

[0145] When defining the physical field, the physical fields can be added separately, and the corresponding limiting conditions and boundary conditions can be defined under the corresponding physical field settings.

[0146] When estimating the current-carrying capacity of the cable under different laying methods, a finite element simulation software based on numerical methods can be used to establish a cable simulation model for the cable body and the surrounding environment, and different fineness grid divisions can be carried out according to the different research objects to simulate the cable temperature field and calculate more accurate results. The actual operating environment of the cable is relatively complex. Therefore, when establishing the simulation model, considering the differences in laying methods and laying conditions, the selected physical fields will be different, and the coupled fields required for calculating the current-carrying capacity of the cable will also be different.

[0147] When the cable is laid in a cable trench, there is air flow between the cable body and the trench wall. The heat conduction method of the cable is the same as that when the cable is laid in a pipe buried underground, including three methods: heat conduction, heat convection, and heat radiation. Among them, the heat conduction of the soil outside the trench and the cable body is mainly in the form of heat conduction, while inside the trench, due to the presence of air, there are heat convection and heat radiation heat conduction methods between the cable surface and the inner trench wall. Therefore, when establishing the model, the mutual coupling between the electromagnetic field, temperature field, and fluid field needs to be considered.

[0148] (2) Mesh division

[0149] This application uses a user-controlled grid to perform grid meshing on the cable laid in pipes, which has the advantages of fast calculation speed, high utilization efficiency of calculation resources, and good convergence. Different degrees of grid refinement are adopted: the parts of the power cable are extremely refined (first-level meshing), the surface of the pipe and the air are relatively refined (second-level meshing), and the soil area is coarsely meshed (third-level meshing), as Figure 6 and Figure 7 shown.

[0150] (3) Simplification of the simulation model

[0151] Due to the complexity of the three-dimensional model structure of the cable, it is too difficult in the COMSOL simulation process. Therefore, this application chooses to simplify the three-dimensional cable model into a two-dimensional model. The two-dimensional model shows significant advantages in many aspects compared with the three-dimensional model in the cable system simulation. These advantages are not only reflected in the technical level but also deeply affect the research efficiency and the design optimization process.

[0152] From a technical perspective, the two-dimensional model significantly reduces the calculation cost. Due to the simplification of the two-dimensional model in geometric dimensions, the number of grid points and degrees of freedom it requires are greatly reduced. This means that under the same hardware conditions, two-dimensional simulation can occupy less memory and CPU resources, thus achieving a faster simulation speed. The improvement of this calculation efficiency is particularly important for the simulation of large-scale cable systems because it can significantly shorten the simulation cycle and accelerate the R & D process.

[0153] In addition, the results of the two-dimensional model are more intuitive and easy to visualize and analyze in depth. On the two-dimensional plane, key information such as the structure of the cable system, temperature distribution, and electromagnetic field strength can be clearly presented, which enables this application to capture the key features in the simulation results faster. This intuitiveness not only helps to understand the behavior mechanism of the cable system but also provides strong visual support for subsequent design optimization. More importantly, these advantages of the two-dimensional model can be directly transformed into the improvement of research efficiency and design optimization ability. Through a faster simulation speed and more intuitive result display, the design scheme can be iterated faster to verify the influence of different parameters on the performance of the cable system. Therefore, this application chooses to simplify the three-dimensional cable model into a two-dimensional model.

[0154] As an embodiment, the simplification process of this application is as follows:

[0155] First, three-dimensional feature extraction is performed, and then the minimum energy projection method is used to determine the optimal two-dimensional plane to obtain a two-dimensional coordinate system including the elevation correction factor:

[0156]

[0157] In the formula, α and β are projection angles, k is the energy compensation coefficient, E i3D represents the energy density of the \(i\)-th unit in the three-dimensional model, \(E\) i 2D represents the energy density of the corresponding unit in the two-dimensional projection plane.

[0158] After that, dynamic mesh generation is performed.

[0159] Then, the physical field equivalent calculation is carried out:

[0160] The two-dimensional plane equivalent capacitance matrix is calculated using the virtual displacement method:

[0161] The plane stress model is corrected using the pseudo-thickness factor: \(\sigma\) 2D =\(\sigma_{3D}\cdot(1 + 0.3\delta)\).

[0162] In the formula, \(C\) eq represents the two-dimensional plane equivalent capacitance matrix, \(\epsilon\) r is the relative permittivity of the cable insulation material, \(W\) e represents the electric field energy storage in the three-dimensional model, \(V\) represents the volume; \(\sigma\) 2D represents the two-dimensional plane equivalent stress, \(\sigma\) 3D represents the three-dimensional original stress, \(\delta\) represents the pseudo-thickness factor, \(0\leqslant\delta\leqslant1\).

[0163] Finally, verification is carried out. In addition, when the error \(> 5\%\), the adaptive feedback adjustment module is triggered.

[0164] The simplified 2×4 row pipe laying model and the simulation diagrams of the 2×2 row pipe laying two-dimensional model are respectively as Figure 9 and Figure 10 shown. The mesh division of the cable two-dimensional model is as Figure 8 , Figure 11 and Figure 12 shown.

[0165] 5. Feasibility test of simulation model simplification

[0166] During the simulation, the same soil conditions (soil thermal conductivity is 1.09), ambient temperature (ambient temperature is \(20^{\circ}C\)), laying environment (laying environment is flat laying method), and load current magnitude (1850 A) are applied to the three-dimensional model and the two-dimensional model. The simulation results are as Figure 13 and Figure 14 shown.

[0167] The simulation results show that the two-dimensional simplified model and the three-dimensional model exhibit high consistency in key parameters such as temperature distribution. The difference in the cable surface temperature calculated by the two-dimensional model and the three-dimensional model is less than 5%, and the distribution of heat flux density is also basically consistent. In addition, the two-dimensional model is significantly superior to the three-dimensional model in terms of computational efficiency, with the calculation time reduced by approximately 70% while the accuracy loss is within an acceptable range. These results preliminarily prove the rationality of the simplified two-dimensional model and provide theoretical support for further experimental verification.

[0168] Through comparative simulation, while simplifying the geometric structure, the two-dimensional model can still accurately capture the main heat transfer characteristics of the cable. This simplification not only reduces the computational complexity but also provides an efficient tool for subsequent optimization design and engineering applications.

[0169] III. Analysis of Cable Temperature Rise Characteristics under Different Ambient Temperatures

[0170] (1) 2×4 Cable Laying Method

[0171] In this experiment, the soil thermal conductivity was set to 1.09, the load current was 1850 A, and the laying environment was the 2×4 cable laying method. The temperature change results of the power cable were calculated at ambient temperatures of -11°C, 0°C, 10°C, 25°C, 30°C, 33°C, 35°C, 37°C, 40°C, and 42°C respectively. The steady-state values of the cable core and outer sheath at different ambient temperatures are shown in Table 1.

[0172] Table 1 Steady-State Values of Cable Core and Outer Sheath at Different Ambient Temperatures

[0173]

[0174]

[0175] Please refer to Figure 16 , Figure 16 for the 2×4 cable laying operation diagram. The temperature rise curves of the cable core and outer sheath at different ambient temperatures can be seen in Figure 15 .

[0176] As can be seen from Table 1 above, on the premise that other influencing factors remain unchanged, as the ambient temperature increases, the cable core temperature rises significantly. When the ambient temperature rises from -11°C to 42°C, the cable core temperature rises from 85.42°C to 106.09°C. For every 10°C increase in ambient temperature, the cable core temperature rises by an average of about 3°C - 4°C. This change trend indicates that the ambient temperature has a significant impact on the cable core temperature, especially at high ambient temperatures, where the cable core temperature quickly approaches or exceeds the heat resistance limit of the insulating material.

[0177] The temperature of the outer sheath also rises with the increase of the ambient temperature, but the increase amplitude is relatively smaller than that of the cable core temperature. When the ambient temperature rises from -11°C to 42°C, the temperature of the outer sheath rises from 54.43°C to 73.18°C. The rising trend of the outer sheath temperature is similar to that of the cable core temperature, but at high ambient temperatures, the rising speed of the outer sheath temperature is significantly lower than that of the cable core temperature.

[0178] At low ambient temperatures (such as -11°C), the temperature difference between the cable core and the outer sheath is small (30.54°C), indicating that the heat dissipation condition of the cable is good at this time, and the heat can be dissipated through the outer sheath relatively quickly. As the ambient temperature rises, the temperature difference between the cable core and the outer sheath gradually decreases. At 42°C, the temperature difference is 32.91°C. The increase in the temperature difference indicates that as the ambient temperature rises, the heat dissipation capacity of the outer sheath gradually weakens, resulting in the accumulation of heat inside the cable core.

[0179] By analyzing T1 and T2, it can be found that as the ambient temperature rises, T1 (the time for the cable core temperature to reach a steady state) gradually extends. At -11°C, T1 is 100 hours. At 42°C, T1 increases to 235 hours. This indicates that as the ambient temperature rises, the time required for the cable to reach thermal equilibrium significantly extends. T2 (the time for the cable core temperature to reach 90 degrees Celsius) significantly shortens with the increase of the ambient temperature. At 0°C, T2 is 220 hours. At 42°C, T2 shortens to 81 hours. This indicates that as the ambient temperature rises, the time required for the cable core temperature to reach 90°C significantly decreases.

[0180] (2) 2×2 type cable laying method

[0181] In this experiment, the soil thermal conductivity is set to 1.09, the load current is 1850A, and the laying environment is the 2×2 type cable laying method. The temperature change results of the power cable at ambient temperatures of -11°C, 0°C, 10°C, 25°C, 30°C, 33°C, 35°C, 37°C, 40°C, and 42°C are calculated respectively. The steady-state values of the cable core and the outer sheath at different ambient temperatures are shown in Table 2.

[0182] Table 2 Steady-state values of the cable core and the outer sheath at different ambient temperatures

[0183] Ambient temperature / degC Steady-state value of core temperature / °C Steady-state value of outer sheath temperature / °C <![CDATA[T1 / h]]> <![CDATA[T2 / h]]> -11 / ℃ 86.97 55.04 100 0 / ℃ 92.26 60.05 140 232 10 / ℃ 96.99 64.54 180 135 20 / ℃ 102.26 69.54 185 100 25 / ℃ 104.29 71.57 195 91 30 / ℃ 106.91 73.96 200 82 33 / ℃ 108.41 75.37 210 78 35 / ℃ 109.28 76.21 220 75 37 / ℃ 110.26 77.13 220 73 40 / ℃ 111.12 78.21 225 70 42 / ℃ 112.53 79.29 230 68

[0184] Please refer to Figure 18 , Figure 18 For the 2×2 type cable laying operation diagram, the temperature rise curves of the cable core and the sheath at different ambient temperatures are shown in Figure 17 .

[0185] From Table 2 and Figure 17It can be seen that, on the premise that other influencing factors remain unchanged, as the ambient temperature rises, the core temperature of the cable rises significantly. When the ambient temperature rises from -11°C to 42°C, the core temperature rises from 86.97°C to 112.53°C. For every 10°C increase in the ambient temperature, the core temperature rises by approximately 5°C to 6°C on average. This trend indicates that the ambient temperature has a significant impact on the core temperature, especially at high ambient temperatures, where the core temperature rapidly approaches or exceeds the heat resistance limit of the insulating material.

[0186] The outer sheath temperature also rises with the increase in ambient temperature, but the increase amplitude is relatively smaller than that of the core temperature. When the ambient temperature rises from -11°C to 42°C, the outer sheath temperature rises from 55.04°C to 79.29°C. The rising trend of the outer sheath temperature is similar to that of the core temperature, but at high ambient temperatures, the rising speed of the outer sheath temperature is significantly lower than that of the core temperature.

[0187] At low ambient temperatures (such as -11°C), the temperature difference between the core and the outer sheath is small (31.93°C), indicating that the heat dissipation condition of the cable is good at this time, and heat can be dissipated through the outer sheath relatively quickly. As the ambient temperature rises, the temperature difference between the core and the outer sheath gradually decreases. At 42°C, the temperature difference is 33.24°C. The increase in the temperature difference indicates that as the ambient temperature rises, the heat dissipation capacity of the outer sheath gradually weakens, resulting in the accumulation of heat inside the core.

[0188] By analyzing T1 and T2, it can be found that as the ambient temperature rises, T1 (the time for the core temperature to reach a steady state) gradually extends. At -11°C, T1 is 100 hours. At 42°C, T1 increases to 230 hours. This shows that as the ambient temperature rises, the time required for the cable to reach thermal equilibrium significantly extends. T2 (the time for the core temperature to reach 90 degrees Celsius) significantly shortens with the increase in ambient temperature. At 0°C, T2 is 232 hours. At 42°C, T2 shortens to 68 hours. This indicates that as the ambient temperature rises, the time required for the core temperature to reach 90°C significantly decreases.

[0189] Through the comparative analysis of two cable laying methods, namely 2×2 laying and 2×4 laying, it can be known that at the same ambient temperature, the steady-state temperatures of the core and the outer sheath of 2×4 laying are generally lower, the temperature rise amplitude is smaller, and the time (T2) required for the core temperature to reach 90°C is longer, indicating that its heat accumulation speed is slower and the heat dissipation condition is better. In addition, the temperature difference between the core and the outer sheath of 2×4 laying is smaller, and the heat distribution is more uniform, further proving that its heat dissipation performance is better. Although the time (T1) for the core temperature of 2×4 laying to reach a steady state is slightly longer than that of 2×2 laying, its overall heat dissipation effect is significantly improved, and it is more suitable for the operation of cables in high-load or high-temperature environments.

[0190] As can be seen from this application, as the ambient temperature gradually increases, the temperatures of the cable core and the outer sheath will both rise accordingly, and the time to reach the stable temperature will also be significantly shortened. As the ambient temperature increases, the heat dissipation efficiency of the outer sheath gradually decreases, resulting in a further increase in the temperature difference between the cable core temperature and the outer sheath temperature. This is of crucial significance for evaluating the thermal stability and safety of the cable in a high-temperature environment.

[0191] The embodiment of this application also provides a system for analyzing the temperature rise of a cable under different ambient temperatures. The system includes:

[0192] A non-isothermal flow module for establishing the temperature field and fluid field of the cable laid in the underground pipe to analyze the heat-fluid coupling situation of the cable;

[0193] A radiation view factor calculation module for calculating the radiation view factor to simulate the heat transfer mode of the cable;

[0194] A boundary condition determination module for assuming the air flow velocity on the outer surface of the cable and the inner wall of the cable trench to be zero and determining the boundary conditions of the external soil environment of the cable;

[0195] A cable simulation model building module for building a cable simulation model according to the heat-fluid coupling situation of the cable, the radiation view factor, the boundary conditions, and the cable laying method in the pipe;

[0196] A mesh generation module for performing mesh generation on the cable simulation model and dividing each part of the cable simulation model into meshes with different fineness;

[0197] A model simplification module for simplifying the cable simulation model into a two-dimensional model;

[0198] A calculation and analysis module for using the two-dimensional model to calculate and analyze the temperature rise of the cable under different ambient temperatures and obtaining the temperature rise analysis result.

[0199] In this embodiment, the technical effects of the system are as described in the foregoing method and will not be elaborated here.

[0200] Regarding the system in the above embodiment, the specific manners in which each module performs operations have been described in detail in the embodiment related to the method and will not be elaborated here.

[0201] It should be noted that although several modules of the system for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to the embodiments of the present invention, the features and functions of two or more of the above-described modules can be embodied in one module. Conversely, the features and functions of one module described above can be further divided and embodied by multiple modules. The components shown as modules may or may not be physical units, that is, they may be located in one place or distributed over multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the present invention. A person of ordinary skill in the art can understand and implement it without creative efforts.

[0202] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative rather than restrictive. Under the inspiration of the present invention, without departing from the spirit of the present invention and the scope protected by the claims, a person of ordinary skill in the art can still make many forms, and these all fall within the protection scope of the present invention.

Claims

1. A method for analyzing the temperature rise of a cable under different ambient temperatures, characterized in that: include: Establish the temperature field and fluid field of underground pipe laying cables to analyze the thermal-fluid coupling of cables; Calculate the radiation angle factor to simulate the heat transfer behavior of the cable; The air velocity on the outer surface of the cable and the inner wall of the cable trench is assumed to be zero, and the boundary conditions of the soil environment outside the cable are determined; Building a cable simulation model according to the cable thermal-fluid coupling condition, the radiation angle coefficient, the boundary conditions and the cable conduit laying method; Meshing the cable simulation model, dividing each part of the cable simulation model into meshes of different finenesses; Simplifying the cable simulation model into a two-dimensional model; The two-dimensional model is used to calculate and analyze the cable temperature rise under different ambient temperatures to obtain temperature rise analysis results.

2. The method for analyzing the temperature rise of a cable under different ambient temperatures according to claim 1, characterized in that: The heat transfer modes of the cable include: heat conduction, heat convection and heat radiation.

3. The method for analyzing the temperature rise of a cable under different ambient temperatures according to claim 1, characterized in that: The process of determining the boundary conditions of the soil environment outside the cable includes: Setting the temperature value of the lower boundary of the soil outside the cable; Setting the heat flow at the left and right boundaries of the soil outside the cable; The heat exchange intensity of the upper boundary is determined according to the convection heat transfer coefficient of the upper boundary of the soil outside the cable and the fluid temperature.

4. The method for analyzing the temperature rise of a cable under different ambient temperatures according to claim 3 is characterized in that: The governing equation for the lower boundary is: T(x, y)| Γ =f(x,y)| Γ ; The governing equations for the left and right boundaries are: The governing equation for the upper boundary is: Where x and y are the coordinates in the two-dimensional model; f is the boundary scalar function, n is the normal direction outside the boundary; Γ is the regional boundary; T is the soil temperature, T f is the external environment temperature, K is the thermal conductivity of the medium, q is the heat flux density, and h is the convection heat transfer coefficient of the surface air.

5. The method for analyzing the temperature rise of a cable under different ambient temperatures according to claim 1, characterized in that: The process of meshing the cable simulation model and dividing each part of the cable simulation model into meshes of different finenesses includes: The cable part is divided into a primary segmentation, the pipe surface and the air part are divided into a secondary segmentation, and the soil area part is divided into a tertiary segmentation, wherein the fineness of the primary segmentation, the secondary segmentation and the tertiary segmentation decreases successively.

6. The method for analyzing the temperature rise of a cable under different ambient temperatures according to claim 1, characterized in that: After the step of simplifying the cable simulation model into a two-dimensional model, the method further includes: The feasibility of the two-dimensional model is tested.

7. The method for analyzing cable temperature rise under different ambient temperatures according to claim 1, characterized in that: The cable conduit laying methods include: 2×4 type conduit laying and 2×2 type conduit laying.

8. The method for analyzing the temperature rise of a cable under different ambient temperatures according to any one of claims 1 to 7, characterized in that: The process of calculating and analyzing the cable temperature rise under different ambient temperatures using the two-dimensional model to obtain the temperature rise analysis result includes: The temperature range of the underground water where the cable is located is set to -5°C to 42°C; The finite element simulation method is used to calculate and analyze the steady-state temperature conditions of the cable conductor and the outer sheath within the temperature variation range.

9. The method for analyzing cable temperature rise under different ambient temperatures according to claim 8, characterized in that: The calculation and analysis of the steady-state temperature condition includes: analyzing the time when the cable core temperature reaches a steady state and the time when the cable core temperature reaches 90° C.; analyzing the steady-state value of the cable core temperature and the steady-state value of the outer sheath temperature.

10. A system for analyzing the temperature rise of cables under different ambient temperatures, characterized in that: The system comprises: The non-isothermal flow module is used to establish the temperature field and fluid field of underground pipe laying cables to analyze the thermal-fluid coupling of the cables; The radiation angle coefficient calculation module is used to calculate the radiation angle coefficient to simulate the heat transfer mode of the cable; A boundary condition determination module is used to assume that the air velocity on the outer surface of the cable and the inner wall of the cable trench is zero, and determine the boundary conditions of the soil environment outside the cable; A cable simulation model building module, used to build a cable simulation model according to the cable thermal-fluid coupling condition, the radiation angle coefficient, the boundary conditions and the cable conduit laying method; A mesh generation module, used for performing mesh generation on the cable simulation model, dividing each part of the cable simulation model into meshes of different finenesses; A model simplification module, used for simplifying the cable simulation model into a two-dimensional model; The calculation and analysis module is used to calculate and analyze the temperature rise of the cable under different ambient temperatures using the two-dimensional model to obtain a temperature rise analysis result.

Images