Low-voltage single-core cable temperature evolution trend prediction method

Abstract

The invention discloses a method for predicting the temperature evolution trend of a low-voltage single-core cable. The method comprises the following steps: S1, establishing a transient heat balance equation of each layer of the low-voltage single-core cable based on a heat transfer theory principle; s2, dividing the cable into grids by adopting a finite difference method, discretizing time and space, representing the established transient thermal equilibrium equation of each layer of the low-voltage single-core cable, and constructing a temperature evolution trend prediction model of the low-voltage single-core cable; and S3, performing simulation calculation by adopting an MATLAB writing program, and solving the temperature of each layer of the single-core cable. According to the method, the complexity of the calculation model is low, the calculation precision is improved, and the method has guiding significance in early warning of fire caused by overload of the power cable.

Description

Technical Field

[0001] This invention belongs to the field of power system technology, specifically relating to a method for predicting the temperature evolution trend of low-voltage single-core cables. Background Technology

[0002] Low-voltage cables refer to cables used to transmit power or signals at voltages of 1kV and below. These cables are widely used in residential, commercial buildings, industrial facilities, and public infrastructure for power distribution and electrical equipment connections. From a safety perspective, they need to carry not only the normal operating current from the power source to the equipment but also fault currents under various fault conditions. Therefore, low-voltage cable design must meet stringent safety standards to prevent electrical faults and fires. Furthermore, urbanization and new city construction have driven the demand for low-voltage cables. The application of new environmentally friendly materials and manufacturing technologies has promoted product upgrades.

[0003] In modern power systems and industrial applications, low-voltage cables serve as the primary medium for power transmission, and their performance and reliability directly impact the safety and stable operation of the system. The cable insulation layer, a critical component of low-voltage cables, has a significant impact on cable lifespan and the effectiveness of power transmission due to its temperature condition. As the insulation temperature gradually increases, the insulation material ages and its performance deteriorates. Coupled with prolonged overload conditions, this frequently leads to cable fires, causing significant personal injury and direct property damage. Therefore, establishing a mathematical model for calculating the temperature of low-voltage single-core cables, and accurately calculating and predicting their temperature, can provide a reference for cable fire early warning and prevention.

[0004] Domestic and international methods for estimating cable temperature mainly include thermal circuit models, finite element coupled calculation models, artificial intelligence and finite element combined models, and temperature rise test methods. For example, Riba Jordi Roger et al., Chang Hangrui et al., and Hou Aogang et al. used temperature rise test methods to consider the thermal characteristics of cable materials, cable insulation defects, and different environments, obtaining the internal temperature rise of the cable. However, it is difficult to observe temperature changes in real time. Therefore, Zhan et al., Zhang Xuran, and Wang Weiping adopted a transient radial thermal circuit model for cables, which can invert the core temperature in real time. However, due to the low accuracy of thermal circuit models, Tai Baoyu, Chen Xingang, Zhang Di, and Wei Wenqing et al. used finite element coupled calculation models to simulate the internal temperature of cables, which can realistically and effectively reflect the temperature of high-voltage cables under overload, prevent thermal aging of cable insulation, and improve accuracy, but increase the computational load. Therefore, Chen, Lin Jinghuai, Weixing Han, and Pang Kai et al. used a combination of artificial intelligence and finite element methods to invert the cable core temperature, which not only improved the accuracy of predicting the internal temperature of the cable but also reduced the calculation time. However, it increased the model complexity.

[0005] In summary, on the one hand, although traditional temperature calculation models can calculate the internal temperature of the cable, they require knowledge of the temperature of the outermost layer of the cable to obtain the internal temperature field distribution; on the other hand, the improvement of the accuracy of traditional models comes at the cost of increasing model complexity. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for predicting the temperature evolution trend of low-voltage single-core cables, which addresses the shortcomings of the prior art. The method has low computational model complexity, improves computational accuracy, and provides guidance for early warning of fires caused by overload of power cables.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for predicting the temperature evolution trend of low-voltage single-core cables, the method comprising the following steps:

[0008] Step S1: Establish the transient thermal balance equations for each layer of the low-voltage single-core cable based on the principles of heat transfer.

[0009] Step S2: Using the finite difference method, the cable is divided into a grid, and time and space are discretized to represent the transient thermal balance equations of each layer of the low-voltage single-core cable, thus constructing a predictive model for the temperature evolution trend of the low-voltage single-core cable.

[0010] Step S3: Use MATLAB to write a program to simulate and calculate the temperature of each layer of the single-core cable.

[0011] The above-mentioned method for predicting the temperature evolution trend of low-voltage single-core cables also includes step S4, which uses an experimental method to verify the accuracy and feasibility of the temperature evolution trend prediction model for low-voltage single-core cables.

[0012] In the above-mentioned method for predicting the temperature evolution trend of a low-voltage single-core cable, when establishing the transient thermal balance equation of each layer of the single-core cable based on the principle of heat transfer in step S1, a micro-element is taken from the single-core cable to perform thermal conductivity and thermal balance analysis, and the transient thermal balance equation of each layer of the single-core cable is established using a cylindrical coordinate system.

[0013] The above-mentioned method for predicting the temperature evolution trend of low-voltage single-core cables, specifically the process in step S1 of establishing the transient thermal balance equations for each layer of the single-core cable using a cylindrical coordinate system, is as follows:

[0014] Step S101: Import the total heat flux of the micro-element:

[0015]

[0016] Where λ is the thermal conductivity; T is the temperature; r is the radius; θ is the included angle of the infinitesimal element; and z is the height of the infinitesimal element.

[0017] By Taylor expansion:

[0018] f(x+Δx)=f(x)+f'(x)(x+Δx-x) (F2)

[0019] The total heat flux of the derived infinitesimal element is:

[0020]

[0021] Importing and exporting heat flux yields:

[0022]

[0023] According to the law of conservation of energy, the infinitesimal element has the following thermal equilibrium relationship at any given time interval: Total heat flux introduced into the infinitesimal element + Heat generated by the heat source within the infinitesimal element = Total heat flux removed from the infinitesimal element + Increase in internal energy of the infinitesimal element. The transient thermal equilibrium equation without an internal heat source is shown in equation (F5):

[0024]

[0025] Dividing both sides of equation (F5) by the volume of the infinitesimal element rdrdθdz, we obtain the final transient thermal equilibrium equation as shown in equation (F6):

[0026]

[0027] Where ρ is density, C is specific heat capacity, and t is time;

[0028] The conductor generates heat under the thermal effect of electric current and transfers it to the insulation layer. Simultaneously, the insulation layer dissipates heat to the external environment. The Joule heat Q generated by the conductor is:

[0029] Q = I 2 RΔt(F7)

[0030]

[0031] Where I is the effective current value; R is the resistance per unit length (Ω / m); Δt is the energizing time; and A is the cross-sectional area of ​​the wire core (m²). 2 L is the length of the wire core in meters. It is the conductivity of the wire core at T0℃; T0 represents the initial temperature of each point in the cable;

[0032] The relationship between conductivity and temperature is:

[0033]

[0034] In the formula, γ(T) is the conductivity of the wire core at T℃; a is the temperature coefficient of the material;

[0035] Based on the relationship that the heat required for the conductor to rise by ΔT per unit time and unit volume = the heat generated by the conductor per unit time and unit volume - the heat transferred from the outer surface of the conductor to the insulation layer per unit time and unit volume, the heat balance equation for the conductor is established:

[0036]

[0037] In the formula, ρ c C is the material density of the wire core. c λ is the specific heat capacity of the conductor material; c r is the thermal conductivity of the wire core material; r1 is the radius of the wire core;

[0038] The transient thermal equilibrium equation for the insulating layer is established as follows:

[0039]

[0040] In the formula, ρ x C is the material density of the insulating layer. x λ is the specific heat capacity of the insulating layer material. x r1 is the thermal conductivity of the insulating layer material; r2 is the radius of the insulating layer.

[0041] The third type of boundary condition in the above-mentioned method for predicting the temperature evolution trend of low-voltage single-core cables is:

[0042]

[0043] In the formula, ε x T is the emissivity of the insulating layer material; f T is the temperature of the outer surface of the insulating layer. ∞ ρ is the air temperature; h is the convective heat transfer coefficient; σ is the Stefan-Boltzmann constant;

[0044] The fourth type of boundary condition in the above-mentioned method for predicting the temperature evolution trend of low-voltage single-core cables is:

[0045]

[0046] In the above-mentioned method for predicting the temperature evolution trend of a low-voltage single-core cable, the following assumptions are made when establishing the transient thermal balance equations for each layer of the single-core cable based on the principle of heat transfer in step S1:

[0047] Assuming that the heat transfer inside the cable is by conduction, and the heat transfer between the insulation layer and the environment is by radiation and convection;

[0048] Assuming uniform temperature distribution in the cable core;

[0049] Assume that heat transfer in the cable occurs only radially, and not axially;

[0050] Assuming that the cable layers are in close contact with each other and there is no contact thermal resistance;

[0051] Assume that the material inside the cable is homogeneous and has a known density ρ, thermal conductivity λ, and specific heat capacity C, all of which are constant and do not change with temperature;

[0052] Assume there is no external heat source, only Joule heating as the heat source;

[0053] Assume the initial temperature at all points on the cable is T0;

[0054] Assume the cable laying environment is air, and the air circulation is natural convection.

[0055] The above-mentioned method for predicting the temperature evolution trend of low-voltage single-core cables, in step S2, employs the finite difference method to divide the cable into a grid, discretizing time and space, and the specific process of representing the established transient thermal balance equations for each layer of the low-voltage single-core cable is as follows:

[0056] Time discretization:

[0057]

[0058] Where i is a natural number;

[0059] Spatial discretization:

[0060]

[0061]

[0062] Where j is a natural number;

[0063] The difference form of the transient thermal equilibrium equation for the wire core:

[0064]

[0065] Difference form of the insulation layer equation:

[0066]

[0067] Difference form of boundary conditions:

[0068]

[0069]

[0070] Formula for convective heat transfer coefficient:

[0071]

[0072] Nu = c(GrPr) n (F14)

[0073]

[0074]

[0075]

[0076]

[0077] Where g is the acceleration due to gravity; Nu is the Nusselt number; λ a ρ is the thermal conductivity of air; D is the diameter of the cable; Gr is the Grashof number; v is the dynamic viscosity of air; α is the thermal diffusivity of air; Pr is the Prandtl number of air; β is the coefficient of thermal expansion; T f T is the surface temperature of the outermost layer of the cable. ∞ T represents the fluid temperature. m For T f and T ∞ The average value.

[0078] The above-mentioned method for predicting the temperature evolution trend of low-voltage single-core cables is derived from the formula for the convective heat transfer coefficient:

[0079]

[0080] Compared with existing technologies, this invention has the following advantages: It proposes a temperature calculation model that can calculate temperature in real time without needing to know the outermost layer temperature, and improves calculation accuracy without increasing the complexity of the calculation model; based on the principles of heat transfer, this invention establishes transient thermal balance equations for each layer of a single-core cable, describes in detail the underlying assumptions and mathematical expressions of the model, then uses the finite difference method to represent the established equations and uses a MATLAB program to solve for the temperature of each layer of the cable; finally, experimental methods are used to verify the accuracy and feasibility of the model; this has guiding significance for early warning of fires caused by overload of power cables.

[0081] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0082] Figure 1 This is a flowchart of the method of the present invention;

[0083] Figure 2 This is a schematic diagram of the micro-element structure of the single-core cable of the present invention;

[0084] Figure 3 This is a cross-sectional structural diagram of the single-core cable of the present invention;

[0085] Figure 4 This is a comparison chart of the surface temperature evolution trends of the insulating layer under two types of boundary conditions when the present invention is not overloaded;

[0086] Figure 5 This is a comparison chart of the surface temperature evolution trends of the insulating layer under two types of boundary conditions when the present invention is overloaded by 1.1 times.

[0087] Figure 6 This is a comparison chart showing the evolution trend of the surface temperature of the insulating layer under two types of boundary conditions when the present invention is overloaded by 1.4 times.

[0088] Figure 7 This is a temperature field distribution diagram of the single-core cable of the present invention;

[0089] Figure 8 This is a graph showing the trend of radial distance versus temperature in this invention.

[0090] Figure 9 This is a schematic diagram of the experimental platform of the present invention;

[0091] Figure 10 This is a comparison chart of experimental and MATLAB simulation results when the invention is not overloaded;

[0092] Figure 11 This is a comparison chart of experimental and MATLAB simulation results when the present invention is overloaded by 1.1 times.

[0093] Figure 12 This is a comparison chart of experimental and MATLAB simulation results when the present invention is overloaded by 1.4 times. Detailed Implementation

[0094] The theoretical basis for constructing the temperature evolution trend prediction model for low-voltage single-core cables is as follows:

[0095] Heat conduction

[0096] Heat conduction refers to the process of heat transfer within an object. Its basic principle is that heat is spontaneously transferred from a high-temperature region to a low-temperature region. This transfer process is achieved through the collision and vibration of molecules within the substance. Specifically, when a part of an object is heated, the molecules vibrate faster, thereby driving the vibration of surrounding molecules and causing heat to diffuse to the surroundings. It is usually calculated using Fourier's law, which states that the amount of heat passing through a unit area per unit time is proportional to the rate of temperature change perpendicular to that area.

[0097] Fourier's law is:

[0098]

[0099] In the formula, q r The heat flux density transferred along the n-direction is expressed in W / m³. 2 The negative sign indicates that the heat transfer is from high temperature to low temperature, and λ is the thermal conductivity of the material, with units of W / (m·K). Let n be the rate of temperature change of the object along the n-direction;

[0100] thermal radiation

[0101] All objects with a temperature above absolute zero (0 K) emit thermal radiation; that is, a temperature difference produces thermal radiation. However, the thermal radiation of solids and liquids is only manifested on the surface of the object and cannot penetrate it; the opposite is true for gases. The Stefan-Boltzmann law is generally used to solve this problem.

[0102] The Stefan-Boltzmann law is as follows:

[0103]

[0104] In the formula, q f The heat flux density transferred by thermal radiation, expressed in W / m³. 2 ε is the emissivity of the object, and its value is less than 1; σ is the Stefan-Boltzmann constant, and its value is 5.67 × 10⁻⁶. -8 W / (m 2 ·K 4 ); T is temperature, in K.

[0105] thermal convection

[0106] Thermal convection refers to the phenomenon of heat being transferred from one point in space to another through a flowing medium. Thermal convection is divided into natural convection and forced convection; natural convection often occurs naturally due to temperature differences; forced convection is a phenomenon where external influences cause fluid flow, transferring heat from one point to another; it is generally calculated using Newton's law of cooling.

[0107] Newton's Law of Cooling:

[0108] q=h(T f -T ∞ )

[0109] In the formula, q is the heat flux density transferred by heat convection, with units of W / m³. 2 h is the convective heat transfer coefficient, with units of W / (m³). 2 ·K); T f The surface temperature of an object, expressed in Kelvin (K); T ∞ The fluid temperature is expressed in Kelvin (K).

[0110] like Figure 1 As shown, the method for predicting the temperature evolution trend of low-voltage single-core cables according to the present invention includes the following steps:

[0111] Step S1: Establish the transient thermal balance equations for each layer of the low-voltage single-core cable based on the principles of heat transfer.

[0112] Step S2: Using the finite difference method, the cable is divided into a grid, and time and space are discretized to represent the transient thermal balance equations of each layer of the low-voltage single-core cable, thus constructing a predictive model for the temperature evolution trend of the low-voltage single-core cable.

[0113] Step S3: Use MATLAB to write a program to simulate and calculate the temperature of each layer of the single-core cable.

[0114] In this embodiment, the present invention further includes step S4, which uses an experimental method to verify the accuracy and feasibility of the temperature evolution trend prediction model for low-voltage single-core cables.

[0115] In this embodiment, when establishing the transient thermal balance equations for each layer of the single-core cable based on the principles of heat transfer in step S1, a micro-element is taken from the single-core cable for thermal conductivity and thermal balance analysis, such as... Figure 2 As shown, since the cable has a multi-layer cylindrical structure, the transient thermal balance equations of each layer of the single-core cable are established using a cylindrical coordinate system.

[0116] In this embodiment, the specific process of establishing the transient thermal balance equations for each layer of the single-core cable using a cylindrical coordinate system in step S1 is as follows:

[0117] Step S101: Import the total heat flux of the micro-element:

[0118]

[0119] Where λ is the thermal conductivity, in W / (m·K); T is the temperature, in K; r is the radius; θ is the included angle of the infinitesimal element; and z is the height of the infinitesimal element.

[0120] By Taylor expansion:

[0121] f(x+Δx)=f(x)+f'(x)(x+Δx-x) (F2) gives the total heat flux of the derived infinitesimal element as:

[0122]

[0123] Importing and exporting heat flux yields:

[0124]

[0125] According to the law of conservation of energy, the infinitesimal element has the following thermal equilibrium relationship at any given time interval: Total heat flux introduced into the infinitesimal element + Heat generated by the heat source within the infinitesimal element = Total heat flux removed from the infinitesimal element + Increase in internal energy of the infinitesimal element. The transient thermal equilibrium equation without an internal heat source is shown in equation (F5):

[0126]

[0127] Dividing both sides of equation (F5) by the volume of the infinitesimal element rdrdθdz, we obtain the final transient thermal equilibrium equation as shown in equation (F6):

[0128]

[0129] Where ρ is density, C is specific heat capacity, and t is time;

[0130] The conductor generates heat under the thermal effect of electric current and transfers it to the insulation layer. Simultaneously, the insulation layer dissipates heat to the external environment. The Joule heat Q generated by the conductor is:

[0131] Q = I 2 RΔt(F7)

[0132]

[0133] Where I is the effective current value, in A; R is the resistance per unit length, in Ω / m; Δt is the energizing time, in s; and A is the cross-sectional area of ​​the wire core, in m². 2 L is the core length, in meters; γ T0 It is the conductivity of the wire core at T0℃; T0 represents the initial temperature of each point in the cable;

[0134] The γ T0 The value is 5.7 × 10 8 S / m;

[0135] The relationship between conductivity and temperature is:

[0136]

[0137] In the formula, γ(T) is the conductivity of the wire core at T℃; a is the temperature coefficient of the material;

[0138] The value of 'a' is 0.004℃. -1 ;

[0139] The heat conducted from the conductor to the insulation layer is the same heat transferred to the insulation layer. Therefore, to establish the heat balance equation for the insulation layer, we must first establish the heat balance equation for the conductor. Based on the relationship that the heat required for the conductor to rise ΔT per unit time and unit volume = the heat generated by the conductor per unit time and unit volume (Joule heat) - the heat transferred from the outer surface of the conductor to the insulation layer per unit time and unit volume, we can establish the heat balance equation for the conductor.

[0140]

[0141] In the formula, ρ c The density of the wire core is expressed in kg / m. 3 C cλ represents the specific heat capacity of the conductor material, expressed in J / (kg·K); c ρ is the thermal conductivity of the wire core material, in W / (m·K); r1 is the radius of the wire core, in meters.

[0142] The transient thermal equilibrium equation (temperature calculation model) for the insulating layer is established as follows:

[0143]

[0144] In the formula, ρ x The density of the insulating layer material is expressed in kg / m³. 3 C x λ is the specific heat capacity of the insulating layer material, expressed in J / (kg·K); x ρ is the thermal conductivity of the insulating layer material, in W / (m·K); r2 is the radius of the insulating layer, in m.

[0145] In this embodiment, the third type of boundary condition is:

[0146]

[0147] In the formula, ε x T is the emissivity of the insulating layer material; f Temperature of the outer surface of the insulation layer, in K; T ∞ The temperature of the air is expressed in Kelvin (K); h is the convective heat transfer coefficient, expressed in W / (m³). 2 ·K); σ is the Stefan-Boltzmann constant, with a value of 5.67 × 10⁻⁶. -8 W / (m 2 ·K 4 );

[0148] The ε x The value is 0.9;

[0149] In this embodiment, the fourth type (contact surface) boundary condition is:

[0150]

[0151] In this embodiment, when establishing the transient thermal balance equations for each layer of a single-core cable based on the principle of heat transfer in step S1, the following assumptions were made:

[0152] Assuming that the heat transfer inside the cable is by conduction, and the heat transfer between the insulation layer and the environment is by radiation and convection;

[0153] Assuming the cable core has a uniform temperature distribution, i.e. the core is a good conductor and the temperature is approximately equal;

[0154] Assume that heat transfer in the cable occurs only radially, and not axially;

[0155] Assuming that the cable layers are in close contact with each other and there is no contact thermal resistance;

[0156] Assume that the material inside the cable is homogeneous and has a known density ρ, thermal conductivity λ, and specific heat capacity C, all of which are constant and do not change with temperature;

[0157] Assume there is no external heat source, only Joule heating as the heat source;

[0158] Assuming the initial temperature at all points on the cable is T0; the initial temperature set in this invention is 24.5℃;

[0159] Assuming the cable laying environment is air, and the airflow is natural convection; the convective heat transfer coefficient h is generally 2–25 W / (m²). 2 ·K).

[0160] In this embodiment, a single-core cable of 220 / 380V BV 1×2.5mm is selected. 2 The type is the research object. Figure 3 This is a diagram of the cable structure.

[0161] In this embodiment, the specific process of using the finite difference method in step S2 to divide the cable into a grid, discretize time and space, and represent the transient thermal balance equations of each layer of the low-voltage single-core cable is as follows:

[0162] Time discretization:

[0163]

[0164] Where i is a natural number of 0, 1, 2, ...

[0165] Spatial discretization:

[0166]

[0167]

[0168] Where j is a natural number of 0, 1, 2, ...

[0169] The difference form of the transient thermal equilibrium equation for the wire core:

[0170]

[0171] Difference form of the insulation layer equation:

[0172]

[0173] Difference form of boundary conditions:

[0174]

[0175]

[0176] Formula for convective heat transfer coefficient:

[0177]

[0178] Nu = c(GrPr) n (F14)

[0179]

[0180]

[0181]

[0182]

[0183] Where g is the acceleration due to gravity, with units of m / s². 2 Nu is the Nusselt number; λ a is the thermal conductivity of air, measured in W / (m·K); D is the diameter of the cable; Gr is the Grashof number; v is the dynamic viscosity of air, v = 22.81 × 10⁻⁶. -6 m 2 / s; α is the thermal diffusivity of air, taken as 2.2 × 10⁻⁶. -5 m 2 / s; Pr is the Prandtl number of air; coefficient of thermal expansion β, in K⁻¹; T f The surface temperature of the outermost layer of the cable, in K; T ∞ T represents fluid temperature, expressed in Kelvin (K). m For T f and T ∞ The average value.

[0184] c is set to 0.6, and n is set to 0.25.

[0185] In this embodiment, the convective heat transfer coefficient formula is used to obtain:

[0186]

[0187] In this embodiment, when using MATLAB to simulate and calculate the temperature of each layer of the single-core cable in step S3, the material parameters of each layer of the single-core cable are shown in Table 1:

[0188] Table 1 Material Parameters of Single-Core Cables

[0189]

[0190] Using the first and third type of boundary conditions, temperature calculations were performed on the mathematical model of heat transfer in a single-core cable, yielding the following results: Figure 4 , 5 The temperature evolution trend is shown in Figure 6. Comparing the two types of boundary conditions, it can be concluded that the temperature evolution trend of the third type of boundary condition is more consistent with reality and COMSOL simulation.

[0191] Solving the transient heat transfer equilibrium equation of a single-core cable based on the third type of boundary conditions yields the following results: Figure 7 and Figure 8 Three-dimensional graph of cable temperature and curves showing the variation of copper core with radial distance over different time periods.

[0192] When the current is 45A, from Figure 7 The internal temperature distribution of a single-core cable can be obtained from this. From... Figure 8 The cable temperature distribution can be observed, with the highest temperatures on the inner side of the PVC layer, at 58.3℃, 75℃, 83.3℃, ​​and 85℃ respectively. As the cable overload time increases, the temperatures of the cable core and insulation also increase. Due to the different thermodynamic properties of copper and PVC, the core temperature is more uniformly distributed and reaches its highest point. The insulation temperature decreases with distance from the core.

[0193] In this embodiment, when verifying the accuracy and feasibility of the low-voltage single-core cable temperature evolution trend prediction model using an experimental method in step S4, the experimental cable is connected between the DC power supply and the load, and a multi-channel MT500X thermometer is used to measure the surface temperature of the cable core and insulation layer; the experimental platform is as follows: Figure 9 As shown;

[0194] The single-core cable current carrying capacities in the experiments were 25, 35, and 45 A. To further analyze the accuracy of the simulation model, the simulated and experimental values ​​of the core and insulation temperatures were compared. The results are shown below. Figure 10 , 11 12 and Table 2.

[0195] Table 2 Comparison of Simulation Results and Experimental Results

[0196]

[0197] from Figure 10 It can be seen that, under no-overload conditions, the simulated and experimental cable core temperatures differ by 2.4℃, and the insulation layer temperatures differ by 0.1℃; from Figure 11 As can be seen, when the overload is 1, the temperature of the cable core in the simulation and the experimental simulation are very different, with a maximum difference of 4℃, and the temperature of the insulation layer is 0.4℃ different. Figure 12 As can be seen, at an overload of 1.3 times, the simulated and experimental cable core temperatures differ by 7.2℃, and the insulation layer temperatures differ by 1.2℃. Since the experiment involved cutting the cable open to measure the core temperature, the heat dissipation from the core in the experiment was greater than in the simulation, hence the larger temperature difference.

[0198] In summary, the maximum temperature difference between the simulated and experimental values ​​for the cable insulation layer is 1.2℃, and the maximum temperature difference between the simulated and experimental values ​​for the cable core temperature is 7.2℃. The results show that under different load conditions, the simulated and experimental values ​​for the cable insulation layer temperature agree well, and the model has high accuracy. With the increase of the overload factor, the temperature rise rate gradually increases, and the temperature difference between the simulated and experimental results gradually widens, indicating that the cable temperature rises faster.

[0199] In summary, this invention proposes a temperature calculation model and uses MATLAB simulation to obtain the internal temperature field distribution of a single-core cable under normal operating conditions and different overload conditions. Based on the established temperature calculation model for the insulation layer of a single-core cable, the main conclusions of this invention are as follows:

[0200] (1) Compared with traditional temperature calculation models, the established model is less complex, requires less computation, and has higher accuracy. An experimental platform was built to verify the model's accuracy. Experimental results show that under different load conditions, the maximum temperature difference between the simulated and experimental values ​​of the cable insulation layer at steady state is 1.2℃.

[0201] (2) The temperature rise trend of the insulation layer was obtained by solving the problem using the finite difference method. The temperature rise rate is relatively fast in the initial stage of energization, and gradually slows down after a period of time, eventually reaching a certain temperature value and remaining constant.

[0202] (3) If the cable is overloaded by 1.3 times, it will reach the cable’s allowable operating temperature of 70°C, which will cause damage to the insulation layer and thus cause a fire.

[0203] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for predicting the temperature evolution trend of a low-voltage single-core cable, characterized in that, The method includes the following steps: Step S1: Establish the transient thermal balance equations for each layer of the low-voltage single-core cable based on the principles of heat transfer. Step S2: Using the finite difference method, the cable is divided into a grid, and time and space are discretized to represent the transient thermal balance equations of each layer of the low-voltage single-core cable, thus constructing a predictive model for the temperature evolution trend of the low-voltage single-core cable. Step S3: Use MATLAB to write a program to simulate and calculate the temperature of each layer of the single-core cable.

2. The method for predicting the temperature evolution trend of a low-voltage single-core cable according to claim 1, characterized in that, It also includes step S4, which uses an experimental method to verify the accuracy and feasibility of the temperature evolution trend prediction model for low-voltage single-core cables.

3. A method for predicting the temperature evolution trend of a low-voltage single-core cable according to claim 1 or 2, characterized in that: In step S1, when establishing the transient thermal balance equations for each layer of a single-core cable based on the principle of heat transfer, a micro-element is taken from the single-core cable to perform thermal conductivity and thermal balance analysis, and the transient thermal balance equations for each layer of the single-core cable are established using a cylindrical coordinate system.

4. The method for predicting the temperature evolution trend of a low-voltage single-core cable according to claim 3, characterized in that: The specific process of establishing the transient thermal balance equations for each layer of a single-core cable using a cylindrical coordinate system in step S1 is as follows: Step S101: Import the total heat flux of the micro-element: Where λ is the thermal conductivity; T is the temperature; r is the radius; θ is the included angle of the infinitesimal element; and z is the height of the infinitesimal element. By Taylor expansion: f(x+Δx)=f(x)+f'(x)(x+Δx-x) (F2) The total heat flux of the derived infinitesimal element is: Importing and exporting heat flux yields: According to the law of conservation of energy, the infinitesimal element has the following thermal equilibrium relationship at any given time interval: Total heat flux introduced into the infinitesimal element + Heat generated by the heat source within the infinitesimal element = Total heat flux removed from the infinitesimal element + Increase in internal energy of the infinitesimal element. The transient thermal equilibrium equation without an internal heat source is shown in equation (F5): Dividing both sides of equation (F5) by the volume of the infinitesimal element rdrdθdz, we obtain the final transient thermal equilibrium equation as shown in equation (F6): Where ρ is density, C is specific heat capacity, and t is time; The conductor generates heat under the thermal effect of electric current and transfers it to the insulation layer. Simultaneously, the insulation layer dissipates heat to the external environment. The Joule heat Q generated by the conductor is: Q=I 2 RΔt(F7) Where I is the effective current value; R is the resistance per unit length (Ω / m); Δt is the energizing time; and A is the cross-sectional area of ​​the wire core (m²). 2 L is the length of the wire core in meters. It is the conductivity of the wire core at T0℃; T0 represents the initial temperature of each point in the cable; The relationship between conductivity and temperature is: In the formula, γ(T) is the conductivity of the wire core at T℃; a is the temperature coefficient of the material; Based on the relationship that the heat required for the conductor to rise by ΔT per unit time and unit volume = the heat generated by the conductor per unit time and unit volume - the heat transferred from the outer surface of the conductor to the insulation layer per unit time and unit volume, the heat balance equation for the conductor is established: In the formula, ρ c C is the material density of the wire core. c λ is the specific heat capacity of the conductor material; c r is the thermal conductivity of the wire core material; r1 is the radius of the wire core; The transient thermal equilibrium equation for the insulating layer is established as follows: In the formula, ρ x C is the material density of the insulating layer. x λ is the specific heat capacity of the insulating layer material. x r1 is the thermal conductivity of the insulating layer material; r2 is the radius of the insulating layer.

5. The method for predicting the temperature evolution trend of a low-voltage single-core cable according to claim 4, characterized in that: The third type of boundary condition is: In the formula, ε x T is the emissivity of the insulating layer material; f T is the temperature of the outer surface of the insulating layer. ∞ ν is the air temperature; h is the convective heat transfer coefficient; σ is the Stefan-Boltzmann constant.

6. The method for predicting the temperature evolution trend of a low-voltage single-core cable according to claim 5, characterized in that: The fourth type of boundary condition is:

7. A method for predicting the temperature evolution trend of a low-voltage single-core cable according to claim 6, characterized in that: In step S1, when establishing the transient thermal balance equations for each layer of a single-core cable based on heat transfer principles, the following assumptions were made: Assuming that the heat transfer inside the cable is by conduction, and the heat transfer between the insulation layer and the environment is by radiation and convection; Assuming uniform temperature distribution in the cable core; Assume that heat transfer in the cable occurs only radially, and not axially; Assuming that the cable layers are in close contact with each other and there is no contact thermal resistance; Assume that the material inside the cable is homogeneous and has a known density ρ, thermal conductivity λ, and specific heat capacity C, all of which are constant and do not change with temperature; Assume there is no external heat source, only Joule heating as the heat source; Assume the initial temperature at all points on the cable is T0; Assume the cable laying environment is air, and the air circulation is natural convection.

8. A method for predicting the temperature evolution trend of a low-voltage single-core cable according to claim 6, characterized in that: The specific process described in step S2, which involves using the finite difference method to divide the cable into a grid and discretize time and space to represent the transient thermal balance equations for each layer of the established low-voltage single-core cable, is as follows: Time discretization: Where i is a natural number; Spatial discretization: Where j is a natural number; The difference form of the transient thermal equilibrium equation for the wire core: Difference form of the insulation layer equation: Difference form of boundary conditions: Formula for convective heat transfer coefficient: No=c(GrPr) n (F14) Where g is the acceleration due to gravity; Nu is the Nusselt number; λ a ρ is the thermal conductivity of air; D is the diameter of the cable; Gr is the Grashof number; v is the dynamic viscosity of air; α is the thermal diffusivity of air; Pr is the Prandtl number of air; β is the coefficient of thermal expansion; T f T is the surface temperature of the outermost layer of the cable. ∞ T represents the fluid temperature. m For T f and T ∞ The average value.

9. A method for predicting the temperature evolution trend of a low-voltage single-core cable according to claim 8, characterized in that: The formula for convective heat transfer coefficient is obtained as follows:

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