Simulation system and method for medium-voltage cable

Abstract

The invention discloses a simulation system and method for a medium-voltage cable, and particularly relates to the field of cable performance experiments. The device comprises an electric heating bidirectional coupling unit, and the electric heating bidirectional coupling unit comprises an electric field module which loads corresponding excitation current into a cable model according to different simulation working conditions, and a conductor in the cable model generates Joule heat; and the solid heat transfer module takes the Joule heat as a heat source, the electric field module and the solid heat transfer module are combined to obtain the temperature distribution of the cable, at the moment t, the temperature change generates new conductivity, and the new conductivity is fed back to the electric field module. The problems of high cost, difficulty in data acquisition, high safety risk, insufficient dynamic detection capability and the like in the existing medium-voltage cable thermal performance test are solved.

Description

Technical Field

[0001] This invention relates to the field of cable performance testing, and in particular to a simulation system and method for medium-voltage cables. Background Technology

[0002] Medium-voltage cables are widely used in power transmission and urban distribution networks. Temperature rise under extreme conditions such as short circuits or overloads directly affects the thermal aging life and operational safety of the cable insulation system. Traditional research on the temperature rise of 8.7 / 15kV XLPE insulated medium-voltage cables under short circuits and overloads mainly relies on physical experimental methods. However, analytical methods based on physical testing have the following technical drawbacks: 1. High experimental cost: Short-circuit or overload experiments require the construction of high-power power supply systems, consuming a large number of cable samples, resulting in high costs; 2. Difficult data acquisition: Under short-circuit conditions, the temperature can rise instantaneously to over 250℃, making sensors prone to failure, leading to large temperature measurement errors or even data loss; 3. Significant safety risks: High-current experiments may be accompanied by problems such as arc discharge and insulation breakdown, posing significant risks to personnel and equipment; 4. Inability to achieve full-process simulation: Traditional methods are mostly based on discrete time-point measurements, making it difficult to comprehensively acquire the temperature field changes throughout the entire short-circuit or overload process, especially the heat dissipation process after the fault is cleared. Therefore, there is an urgent need for a medium-voltage cable temperature rise analysis system with high modeling accuracy, strong safety, and the ability to dynamically detect the thermal behavior of short circuits and overloads throughout the entire process, in order to solve the above-mentioned problems existing in the current technology. Summary of the Invention

[0003] In view of the above-mentioned deficiencies of the prior art, the present invention provides a simulation system and method for medium-voltage cables to solve the problems of high cost, difficulty in data acquisition, high safety risks and insufficient dynamic detection capabilities in the existing thermal performance testing of medium-voltage cables.

[0004] The first aspect of this invention provides a simulation system for medium-voltage cables, including an electrothermal bidirectional coupling unit, the electrothermal bidirectional coupling unit comprising:

[0005] The electric field module applies the corresponding excitation current to the cable model according to different simulation conditions, causing Joule heating in the conductors of the cable model.

[0006] The solid heat transfer module uses Joule heat as a heat source. By solving the control equation of the solid heat transfer module, the temperature distribution of the cable is obtained. Based on the obtained cable temperature, the current new conductivity is updated and fed back into the electric field model.

[0007] Furthermore, the simulation system includes an input unit, which includes an excitation current module for providing excitation current.

[0008] Furthermore, the control equations for the electric field module are as follows:

[0009]

[0010] in, σ is the vector differential operator; J is the current density vector; σ is the conductivity; ε0 is the vacuum permittivity; ε is the relative permittivity; t is time; E is the electric field vector; e is the externally injected current density; U is the electric potential.

[0011] Furthermore, the control equation for the solid heat transfer module is:

[0012]

[0013] Where ρ is density; C p θ is the constant pressure heat capacity; t is the temperature; u is the time; k is the velocity vector; k is the thermal conductivity; and Q is the heat output power per unit volume of the heat source.

[0014] Furthermore, the boundary conditions of the governing equations of the solid heat transfer module include: the specific temperature of the known boundary, the heat flux density on the known boundary, the type of fluid in the surrounding environment and the external natural convection heat transfer coefficient h of the object on the known boundary, and the temperature of the surrounding medium.

[0015] Furthermore, the conductivity function is:

[0016]

[0017] Where σ(θ) is the conductivity; α is the resistivity at temperature θ0; β is the temperature coefficient of resistance of copper; and θ is the core temperature.

[0018] A second aspect of the present invention provides a simulation method for medium-voltage cables, comprising the following steps:

[0019] According to different simulation conditions, the corresponding excitation current is applied to the cable model, and the conductor in the cable model generates Joule heating;

[0020] The solid heat transfer module uses Joule heat as a heat source. By solving the control equation of the solid heat transfer module, the temperature distribution of the cable is obtained. Based on the obtained cable temperature, the current new conductivity is updated and fed back into the electric field model.

[0021] Furthermore, the simulated operating conditions include short-circuit conditions and overload conditions.

[0022] Furthermore, under the short-circuit condition, the excitation current is a step current; under the overload condition, the excitation current is a cyclic overload current.

[0023] Compared with the prior art, the present invention has the following technical effects:

[0024] The simulation system and method of this invention require few resources and support rapid deployment and reuse. During operation, there is no need to build a high-voltage experimental platform, avoiding safety hazards and significantly saving costs. It can replace traditional high-cost and high-risk short-circuit and overload physical tests, and complete the temperature rise detection of the entire process through a virtual simulation platform, greatly improving experimental safety.

[0025] This invention employs a bidirectional electrothermal coupling modeling approach. By establishing a two-dimensional model of the insulated cable, it accurately predicts the temperature distribution and temperature rise process of the cable under short-circuit and overload conditions, achieving high-precision and high-efficiency temperature rise prediction. Through a multi-physics coupling mechanism, it dynamically feedbacks the relationship between conductor conductivity and Joule heating, combined with convection and radiation boundary condition modeling, replacing traditional experimental methods. This significantly reduces costs and operational complexity. Furthermore, the simulation results of specific embodiments show that the error between simulation and actual experiments is controlled within 4%, verifying a significant improvement in simulation accuracy and a high degree of consistency between simulation results and experimental data. This provides a reliable theoretical and engineering application basis for cable thermal performance evaluation.

[0026] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the cable simulation system according to a specific embodiment of the present invention;

[0028] Figure 2 This is a schematic diagram of the structure of an electrothermal bidirectional coupling unit according to a specific embodiment of the present invention;

[0029] Figure 3 This is a flowchart illustrating a method for detecting the temperature rise performance of a cable under short circuit and overload conditions, provided in a specific embodiment of the present invention.

[0030] Figure 4 A geometric model diagram of a cable cross-section is provided for a specific embodiment of the present invention;

[0031] Figure 5 This is a schematic diagram of the temperature distribution of a PP cable within 1 to 7 seconds under short-circuit conditions in a specific embodiment of the present invention;

[0032] Figure 6 This is a schematic diagram of the temperature distribution of an XLPE cable within 1 to 7 seconds under short-circuit conditions in a specific embodiment of the present invention.

[0033] Figure 7 This is a simulation result of the temperature distribution range of PP and XLPE cables during a short-circuit test in a specific embodiment of the present invention; wherein, Figure 7 'a' represents the simulation results of the short-circuit temperature distribution range of the PP cable. Figure 7 b represents the simulation results of the short-circuit temperature distribution range of the XLPE cable;

[0034] Figure 8 This is a simulation result of the overload test temperature of PP and XLPE cables over time in a specific embodiment of the present invention; wherein, Figure 8 'a' represents the simulation results of the temperature changes of the core, metal sheath, and outer sheath of the PP cable over time within an 8-hour single thermal cycle overload test. Figure 8 b represents the simulation results of the temperature changes of the core, metal sheath, and outer sheath of the XLPE insulated cable over time within an 8-hour single thermal cycle overload test.

[0035] Reference numerals: 1. Conductor core; 2. Conductor shield; 3. Insulation layer; 4. Insulation shield layer; 5. Metal shield layer; 6. Non-woven wrapping tape; 7. Outer sheath. Detailed Implementation

[0036] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0037] In one specific embodiment, a medium-voltage cable simulation system is provided, such as... Figure 1 As shown, it includes a two-dimensional model processing unit, a parameter setting unit, a finite element model unit, an electrothermal bidirectional coupling unit, and an output unit.

[0038] The two-dimensional model processing unit is used to establish a proportional model based on the actual cable size. In this embodiment, the model is a two-dimensional axisymmetric model, including multiple structural layers such as conductor, insulation layer, metal sheath and outer sheath. The heat conduction direction in the simulation area is set to radial, and the axial heat dissipation effect is ignored.

[0039] The parameter setting unit includes an excitation current module and a parameter module. The excitation current module is used to set the corresponding excitation current according to different operating conditions. When the system is operating under short-circuit conditions, the excitation current is a step current. When the system is operating under overload conditions, the excitation current is a periodic overload loop current.

[0040] The parameter module is used to input cable material parameters and boundary conditions. The cable material parameters are obtained from the system's built-in material parameter database, which includes temperature-dependent properties such as thermal conductivity, specific heat capacity, and electrical conductivity of common cable materials like XLPE, copper, and PVC. This data is used to dynamically update the physical field characteristics during the simulation process. The boundary conditions include natural convection and surface thermal radiation, and the boundary parameters are stored as global variables, facilitating rapid switching between different operating conditions and cable types. In practical applications, the model can be extended to different voltage levels such as 10kV and 35kV, and various cable materials such as PP and XLPE, giving the parameterized model constructed by this invention strong adaptability, good versatility, and engineering promotion potential.

[0041] In this embodiment, the parameter module includes a parameterized model and a boundary model. The parameterized model refers to the material parameter library built into the simulation system of this application, which stores various physical properties of commonly used cable materials such as XLPE, copper, and PVC. These properties (such as electrical conductivity) are not fixed constants but are defined as functions that change with temperature. For example, the electrical conductivity of copper decreases as temperature increases; the model uses a mathematical formula to describe this relationship:

[0042]

[0043] Where σ(θ) is the conductivity; α is the resistivity at temperature θ0; β is the temperature coefficient of resistance of copper; and θ is the core temperature.

[0044] The model's boundary conditions (such as surface heat dissipation coefficient and ambient temperature) and certain geometric features (such as insulation thickness) are also set as parameterized forms, allowing users to "quickly switch between different operating conditions and cable types." For example, to simulate the difference between cables laid in air and cables laid in pipes, simply call different boundary condition templates and modify variables such as the convective heat transfer coefficient; there is no need to reset complex physical fields.

[0045] The finite element model elements are used to convert the two-dimensional model into a finite element model through adaptive mesh generation. In this embodiment, the existing adaptive mesh generation technology built into the COMSOL Multiphysics finite element simulation software is used. Through axisymmetric simplification modeling method and adaptive mesh optimization mechanism, the calculation time for a single working condition simulation is less than 5 minutes and the memory usage is less than 2GB, balancing computational efficiency and resource consumption.

[0046] The electrothermal bidirectional coupling unit includes an electric field module, a solid heat transfer module, and a conductivity model. To accurately reflect the multi-field coupling scheme of the physical mechanism, a bidirectional real-time feedback mechanism between physical fields is adopted. The electric field module applies corresponding excitation currents to the cable model according to different simulation conditions, generating Joule heating in the conductors of the cable model. The solid heat transfer module uses this Joule heating as a heat source, and by combining the electric field module and the solid heat transfer module, the temperature distribution of the cable is obtained. At time t, the temperature change generates a new conductivity, which is fed back to the electric field module. Based on the constructed fully parameterized material database and boundary condition templates, it not only includes the precise relationship between material properties and temperature changes, but also globalizes the key geometric, material, and excitation parameters of the model. This allows the system to quickly adapt to different cable types (e.g., 10kV, 35kV) and operating conditions by modifying parameters, demonstrating excellent versatility and scalability.

[0047] In one embodiment, the control equation of the electric field module is shown in equation (2):

[0048]

[0049] In the formula, J is the vector differential operator; J is the current density vector, A / m. 3 σ is the conductivity, S / m; ε0 is the vacuum permittivity, F / m; ε is the relative permittivity; t is time, s; E is the electric field vector, V / m; e is the externally injected current density, A / m 3 U represents electric potential, V.

[0050] The control equations for the solid heat transfer module are shown in equation (3):

[0051]

[0052] In the formula, ρ is the density, kg / m³ 3 C p θ is the constant-pressure heat capacity, J / (kg·K); θ is the temperature, K; t is the time, s; u is the velocity vector, m / s; k is the thermal conductivity, W / (m·K); Q is the heat output per unit volume of the heat source, W / m³ 3 This governing equation is an energy conservation equation, and the fundamental parameter for solving it is temperature.

[0053] During cable operation, the heat source is the Joule heat generated by the current flowing through the current-carrying conductor. The control equation of the electrothermal coupling module is shown in formula (4):

[0054]

[0055] The output unit is used to output temperature cloud maps, radial temperature gradients, hotspot evolution curves, etc., which makes it easier for designers to accurately identify the weakest part of the cable.

[0056] In one specific embodiment, a simulation method for medium-voltage cables is provided, such as... Figure 3 As shown, it includes the following steps:

[0057] S1. Establish a scaled model based on the actual dimensions of the medium-voltage cable;

[0058] S2. Import relevant insulation and shielding material parameters into the model to provide accurate material property data for simulation analysis. In this embodiment, the insulation and shielding material parameters include the thermal and electrical parameters of the structural layer, such as thermal conductivity, electrical conductivity, and specific heat capacity. The thermal conductivity, electrical conductivity, and specific heat capacity are all derived from measured data and change dynamically with temperature.

[0059] like Figure 2 As shown, during the experiment, the electrothermal coupling process was achieved by using a multi-physics coupling method, which simultaneously considered two physical processes: "current generates Joule heat to drive temperature rise" (electricity → heat) and "temperature rise causes changes in material conductivity, which in turn affects current distribution and Joule heat intensity" (heat → electricity), thus achieving a bidirectional coupling effect.

[0060] S3. Establish an electric field model, a solid heat transfer model, and an electrothermal coupling model to simulate the electric field distribution, heat transfer process, and the effect of Joule heat generated by current on temperature inside the cable, respectively, to achieve comprehensive simulation of the cable under different operating conditions; set the boundary conditions of each model according to the application environment and laying conditions to simulate the heat exchange and temperature change of the cable under different operating conditions.

[0061] According to different simulation conditions, the corresponding excitation current is applied to the cable model, and Joule heating is generated in the cable model. The Joule heating is used as a heat source, and the electric field module and solid heat transfer module are combined to obtain the temperature distribution of the cable. The temperature change at time t generates a new conductivity, and the new conductivity is fed back to the electric field model.

[0062] In this embodiment, the operating conditions include short-circuit and overload conditions; under each condition, the Joule heat generated by the excitation current is used as a heat source input to the solid heat transfer module. The simulation couples the electric field with the heat transfer physical field, and the conductivity of the copper conductor changes with temperature in real time, feeding back to the electric field equation to achieve bidirectional electrothermal coupling. The simulation settings include realistic boundary conditions such as natural air convection and thermal radiation. The system can automatically calculate the temperature response of the core, insulation layer, and outer sheath, forming a complete temperature rise-time evolution curve.

[0063] In this embodiment, in order to study the temperature changes and temperature rise of various parts of the PP and XLPE cables under short-circuit and overload tests, both short-circuit and overload tests were conducted indoors, with the cable loop placed in the air. Therefore, it is necessary to determine the boundary conditions of the model to simulate the actual cable laying environment and surrounding medium. Three types of boundary conditions are set when solving the solid heat conduction differential equation. The first type of boundary condition is the specific temperature of the known boundary, as shown in Equation (5); the second type of boundary condition is the heat flux density on the known boundary, as shown in Equation (6); the third type of boundary condition is the type of fluid in the surrounding environment and the external natural convection heat transfer coefficient h of the object on the boundary and the temperature of the surrounding medium, as shown in Equation (7).

[0064] θ(x,y)| Γ =f(x,y)| Γ (5)

[0065]

[0066] In the formula, f(x,y) is the temperature of the object boundary, in °C; λ is the thermal conductivity of air, in W / (m·K); and h is the convective heat transfer coefficient between the object surface and the air, in W / (m²·K). 2 ·K).

[0067] Since the object of this model simulation is a single-phase power cable in an air-based radiation environment, the heat absorption of the cable surface by the surrounding environment is ignored; and since the cable radiation environment in the short-circuit experiment is indoors, the heat dissipation caused by air flow is ignored. The cable is initially at room temperature. At the same time, since the core temperature can reach up to 250℃ under short-circuit conditions, the influence of thermal radiation on the cable temperature needs to be considered. The expression for the thermal radiation of the cable surface to the surrounding environment is shown in equation (8):

[0068] Q=Aεσ b (θ 4 -θ f 4 (8)

[0069] In the formula, A is the surface area of ​​the outer sheath of the cable per unit length, in meters. 2 ε is the thermal emissivity of the cable surface, typically taken as 0.95; σ b Let σ be the blackbody radiation constant. b =5.67×10 -8 W / (m 2 K 4 ).

[0070] Under the overload condition, the excitation current is a cyclic overload current. A periodic thermal cycling current (411A, period of 8 hours) is set according to GB / T 12706.2-2020 standard to simulate the steady-state temperature rise of the cable under continuous current-carrying conditions. By analyzing the thermal response of the conductor and outer sheath, the system can determine whether there is heat accumulation or localized overheating.

[0071] S4. Solve the above model to obtain the temperature distribution at different times under different operating conditions.

[0072] In one specific embodiment, the above embodiments are further illustrated by the following experiment;

[0073] In this embodiment, the Comsol Multiphysics platform is used for modeling and solving, supporting simulation analysis of two types of working conditions: short circuit and overload. It features strong scalability, high computational efficiency, and zero safety risk.

[0074] After constructing a two-dimensional model based on a simplified two-dimensional axisymmetric method, an adaptive mesh generation method is used to construct a finite element model, which optimizes computational efficiency, keeping the simulation time for a single short circuit or overload within 5 minutes and the memory usage within 2GB. Furthermore, the system features rapid model copying, batch parameter modification, and result visualization (output functions, including temperature contour maps, radial temperature gradients, and hotspot evolution curves), facilitating designers to accurately identify the weakest points in cables.

[0075] The method for rapid model replication includes: First, creating a standard, parameterized "medium-voltage cable temperature rise simulation model template." This template contains all preset physical fields (current, solid-state heat transfer, multiphysics coupling), a two-dimensional axisymmetric geometric framework, mesh generation settings, and boundary conditions. When analyzing a new type of cable or a new operating condition, users do not need to start from scratch. They can simply copy the model template file directly from the COMSOL file system to generate an identical model copy. Parameters can then be modified according to the required operating conditions and the actual cable type for calculation.

[0076] The method for batch modification of parameters includes defining all variable quantities in the system (such as the radius of the cable conductor, the thickness of the insulation layer, the magnitude of the short-circuit current, the material type, etc.) as "global parameters" and managing them in a single parameter table.

[0077] The visualization method for the results includes generating a temperature distribution cloud map, an evolution curve, and a radial temperature gradient map based on the solved temperature data. The temperature distribution cloud map visually displays where the temperature is highest (hot spot) on the cable cross-section during a short circuit or overload, and the temperature gradient. The evolution curve plots the changes in core temperature, metal sheath temperature, and outer sheath temperature over overload time, dynamically demonstrating the temperature rise process. The radial temperature gradient map plots the temperature distribution along the cable radius, accurately analyzing the maximum temperature difference the insulation layer can withstand.

[0078] Traditional simulation modeling requires adding physics fields, defining variables, and setting couplings. This system completely skips these repetitive tasks by copying templates. All new models based on template copying follow unified setup standards and processes, ensuring the consistency, comparability, and reliability of simulation results and avoiding model errors caused by human error. These functions significantly reduce modeling time. Temperature contour maps clearly show the weakest points of the cable (usually the insulation layer near the core), allowing for targeted design improvements. Time evolution curves reveal the cable's dynamic thermal response, showing not only steady-state temperature rise but also analyzing the speed of transient processes, which is crucial for evaluating the appropriateness of the protective switch's operating time after a short-circuit fault.

[0079] During short-circuit and overload simulations, the system automatically couples the electric field module and the solid heat transfer module for joint solution, with the Joule heat generated by the conductor serving as the heat source input to the heat transfer equation. During the simulation, the conductivity of the copper conductor exhibits linear feedback with temperature, forming a bidirectional electrothermal coupling relationship. After the short-circuit or overload simulation is completed, the natural dissipation process is calculated for a time interval after the excitation current is removed to simulate the cooling process and thermal decay behavior of the cable insulation layer.

[0080] The simulated heat dissipation process in this embodiment is achieved through the continuous action of natural convection and surface thermal radiation boundary conditions within the solid heat transfer physical field. When the short-circuit current is removed or the overload cycle enters the cooling phase, the system automatically resets the Joule heat source to zero and continues transient calculations, thereby simulating the natural cooling of the cable. Operationally, users only need to set the total simulation time or select the standard cooling cycle in the parametric system; no model adjustments are required. The natural heat dissipation process is fully applicable to both short-circuit and overload conditions, achieving accurate simulation of the cable's full thermal process.

[0081] The above embodiments will be further explained through specific experimental procedures below.

[0082] In this embodiment, the 8.7 / 15kV PP and XLPE medium-voltage cables are modeled to scale using Comsol finite element software. The geometric dimensions of the cable are shown in Table 1, where D represents the diameter and h represents the thickness. A two-dimensional simulation model of the cable is established. The following assumptions are made when establishing the finite element simulation model:

[0083] (1) Since the cable length is much greater than the diameter under actual operating conditions, axial heat transfer is ignored. It is assumed that the cable only has a temperature gradient in the radial direction, and the heat is conducted in one dimension in the radial direction.

[0084] (2) The thermal conductivity of the conductor and metal sheath of the cable is much greater than that of the insulation and sheath. That is, the conductor and metal shield are considered to be isothermal bodies with uniform temperature. At the same time, the multi-core stranded conductor is constructed to make the conductor part of the cable a single-core round conductor with the same cross-sectional area.

[0085] (3) The thermal conductivity of each layer of the cable is constant and does not change with physical conditions such as temperature and field strength. Moreover, each layer has the same thermal conductivity and the surface temperature of the cable is the same.

[0086] This embodiment simulates a commercial medium-voltage XLPE insulated power cable, whose geometric dimensions are shown in Table 1. The cable model is YJV-8.7 / 15kV 1×70mm², with an insulation thickness of 4.5mm, and is a copper core cable as the research object. The cable mainly consists of the conductor core, conductor shield, insulation layer, insulation shield, metal shield, non-woven fabric wrapping tape, and outer sheath. The insulation is XLPE; the metal sheath is copper; the wrapping tape is non-woven fabric; and the outer sheath is PVC. In the simulation, heat conduction is assumed to be only along the radial direction, and axial heat transfer is ignored. The geometric model of the cable cross-section is shown in Table 1. Figure 4 As shown, the thermal and electrical parameters of all structural layers in this embodiment, such as thermal conductivity, electrical conductivity, and specific heat capacity, are all derived from measured data and change dynamically with temperature.

[0087] Table 1. Geometric Dimensions of 8.7 / 15kV Medium Voltage Cables

[0088]

[0089]

[0090] The material parameters of the PP and XLPE insulated power cables in this embodiment are shown in Table 2. The insulation and shielding material parameters of the PP and XLPE cables were obtained experimentally. Since the cable temperature is high under short-circuit conditions, the conductivity of the conductor and sheath needs to be defined as the temperature characteristics of the materials during electromagnetic-thermal multiphysics coupling simulation. The conductor and sheath are both copper, and the conductivity of copper is a function of temperature as shown in Equation (9):

[0091]

[0092] In the formula, σ(θ) is the electrical conductivity of copper, S / m; 0.017241×10 -8 θ is the resistivity of copper at 20℃, in Ω·m; 0.00393 is the temperature coefficient of resistance of copper, in 1 / ℃; θ is the core temperature, in ℃.

[0093] Table 2 Material parameters for PP and XLPE insulated cables

[0094]

[0095] Since the object of this model simulation is a single-phase power cable in an air-based radiation environment, the heat absorption of the cable surface by the surrounding environment is ignored; and since the cable radiation environment in the short-circuit experiment is indoors, the heat dissipation caused by air flow is ignored. The cable is initially at room temperature. At the same time, since the core temperature can reach up to 250℃ under short-circuit conditions, the influence of thermal radiation on the cable temperature needs to be considered. The expression for the thermal radiation of the cable surface to the surrounding environment is shown in equation (10):

[0096] Q=Aεσ b (θ 4 -θ f 4 (10)

[0097] In the formula, A is the surface area of ​​the outer sheath of the cable per unit length, in meters. 2 ε is the thermal emissivity of the cable surface, typically taken as 0.95; σ b Blackbody radiation constant, σ b =5.67×10 -8 W / (m 2 K 4 ).

[0098] 1. Short-circuit temperature rise verification experiment

[0099] In this embodiment, based on the Comsol electromagnetic-thermal coupling theory and multiphysics simulation model, the Joule heat generated by the maximum allowable short-circuit current of PP and XLPE cables from 1 to 7 seconds is used as a heat source and coupled with the solid heat transfer module. The actual current values ​​collected in the 1-7s short-circuit experiment in Table 3 are applied to the cable core, and a step function with a step size of 1-7 seconds is used to simulate the process of the cable switching from no-load to short-circuit during the 1-7s short circuit. The simulation system and method of the above embodiment are used to calculate the temperature rise change of the cable model caused by the Joule heat generated by the current in the PP and XLPE cables during the 1-7s short circuit. Figure 5 Simulation results of temperature distribution during a short circuit of a PP insulated cable from 1 to 7 seconds are presented. Figure 6 Simulation results of temperature distribution during a short circuit of an XLPE insulated cable from 1 to 7 seconds.

[0100] Table 3 Actual values ​​of short-circuit test current from 1 to 7 seconds and maximum temperature of cable core

[0101]

[0102] like Figure 5 The data shows that the short-circuit current is large and the duration is short within 1-7 seconds of a short circuit. Due to the high thermal resistance of the cable insulation and sheath, the cable cannot dissipate heat sufficiently at the end of the short circuit. Therefore, the heat generated during the short circuit mainly exists in the cable conductor, and the highest temperature of the cable core at this time is close to 250℃. (Comparison) Figure 5 The temperature changes of various parts of the cable structure during a short circuit of 1 to 7 seconds show that as the short circuit time gradually increases from 1 second to 7 seconds, the conductor has more time to transfer heat outwards, and the insulation temperature near the conductor shield changes significantly with increasing short circuit time. Therefore, during a short circuit, the insulation near the conductor shield experiences a higher temperature. The temperature change trends of various parts of the PP and XLPE insulated cables are relatively consistent after a short circuit. After a short circuit, the core temperature of the XLPE insulated cable is slightly lower than that of the PP insulated cable. This phenomenon is related to the fact that XLPE has a slightly higher thermal conductivity than PP, and its heat dissipation capacity is slightly higher than that of PP.

[0103] Will Figure 5 and 6 The simulation results were compared with the core temperatures of PP and XLPE cables in the short-circuit test in Table 3. The finite element simulation results showed that the temperature variation range of PP cable was 248-241℃, and that of XLPE cable was 241-230℃. The short-circuit test results were 245-255℃. It can be seen that the error between the simulation results and the experimental results is within 4%. The COMSOL finite element simulation results are basically consistent with the data of the short-circuit test, and the temperature rise and the trend of change have a high degree of consistency.

[0104] The temperature change of the cable is related to the ambient temperature and the time it takes for the heat to dissipate. Figure 5 and Figure 6The temperature rise of PP and XLPE cables from 1 to 7 seconds after a short circuit was calculated. However, due to the short circuit time, the heat generated is mainly concentrated in the cable core, and the process of dissipating heat to room temperature usually takes several hours or even more than ten hours. During this process, the cable insulation layer is subjected to a high temperature. To investigate the overall temperature change of the cable and the temperature distribution range of the insulation during a short circuit fault, it is necessary to simulate the short-term heat dissipation process after the cable short circuit, and calculate the temperature rise of the cable caused by the heat generated by the short circuit current in PP and XLPE cables during the heat dissipation process after the short circuit ends. The simulation results of the short circuit experiment show that the cable core has sufficient time to dissipate heat during the 7-second short circuit, and the insulation layer is subjected to the highest temperature during the 7-second short circuit. Therefore, the 7-second short circuit experiment simulation was selected as the research object. With appropriate current excitation, the simulation was carried out to simulate the rapid temperature rise to 250°C after the cable short circuit occurred for 7 seconds, and then the natural heat dissipation of the PP and XLPE cables from the 7-second short circuit to 300 seconds after all heat sources were removed. Figure 7 The simulation results show the temperature changes of the main parts of the PP and XLPE insulated medium-voltage cables over time and the temperatures of the inner and outer insulation layers during the above process.

[0105] Figure 7 As shown in Figures a and b, a significant temperature gradient exists between the inner and outer insulation layers during the heat dissipation process after a short circuit. The highest temperature endured by the inner PP insulation layer approaches 180℃, while the highest temperature endured by the inner XLPE insulation layer approaches 160℃. At this point, the temperatures endured by both PP and XLPE insulation exceed their respective melting temperatures. Under high-temperature conditions, the structural characteristics and macroscopic properties of polymer materials are significantly affected. Therefore, the results of this study provide a reference for subsequent research on the evaluation of the insulation performance of PP and XLPE after a short circuit.

[0106] 2.130℃ Overload Test Temperature Rise Simulation Verification

[0107] A periodic current excitation is applied to the conductor of the cable model to simulate overload operation of the cable under thermal cycling conditions. According to GB / T 12707.2-2020 standard, the thermal cycling process of medium-voltage cables should be no less than 8 hours, with the heating process no less than 2 hours and the heat dissipation process no less than 3 hours. Therefore, a periodic current of 411A is applied according to the above-mentioned time limits. The temperature distribution of the cable during overload thermal cycling is calculated. Figure 8 Simulation results of temperature changes over time for the core, metal sheath, and outer sheath of PP and XLPE insulated cables during a single thermal cycle overload test over 8 hours.

[0108] Will Figure 8The simulation results of a and b are compared with the temperatures of the PP and XLPE insulated cable cores, metal sheaths, and outer sheaths collected by the temperature monitoring system in the overload experiment (Table 4). Changes in thermal conductivity and constant-pressure heat capacity with temperature and field strength during the simulation are ignored. The comparison between the simulation and the overload experiment results shows that the error between the simulation and the experiment is within 3%. The results of the Comsol finite element overload simulation analysis are largely consistent with those of the overload experiment. Therefore, the finite element simulation model proposed in this paper is effective in evaluating temperature changes under overload conditions. It can be applied in engineering practice to predict temperature distribution under cable overload and thermal cycling conditions, and provides a reference for subsequent research.

[0109] Table 4. Temperature readings of main structures in PP and XLPE cables during overload tests.

[0110]

[0111] After the above simulation is completed, the system continues to simulate the natural heat dissipation process for up to 300 seconds after the short-circuit current is removed, accurately capturing the thermal decay trend of the insulation layer and effectively evaluating the insulation material's ability to withstand extreme thermal stress and its safety margin.

[0112] The above embodiments demonstrate that the simulation system of this invention, with its highly realistic structural model, flexible parameterized database, and efficient computing platform, achieves accurate, controllable, and efficient simulation of the thermal performance of medium-voltage cables within limited time and space resources. This provides strong technical support for cable system safety assessment, product selection, and lifespan prediction. Furthermore, it can continuously simulate the heat dissipation process for up to 300 seconds after a short circuit, filling the technical gap in traditional experiments that cannot capture continuous changes in insulation heat load. The simulation process fully models boundary conditions, ensuring good adaptability to complex operating environments. The visualized temperature output throughout the process facilitates maintenance decisions and failure warnings for engineers. This invention can be coupled with an optimization algorithm platform for multi-objective comprehensive optimization of conductor cross-section, insulation thickness, and current carrying capacity, helping to accelerate the development of new cable products and shorten the R&D cycle. Based on virtual simulation, the system achieves full-process thermal behavior tracking, avoiding traditional testing risks such as electric arcs and electric shocks, realizing a "zero-emission, zero-hazard" green testing path, and responding to the national "dual-carbon" strategic goal.

[0113] The simulation system and method of this invention can accurately, efficiently and safely simulate the temperature behavior of medium-voltage cables under extreme thermal conditions, avoid the safety hazards of traditional high-power tests, save test costs, and provide important basis for cable fault early warning, operation and maintenance decision-making and insulation material evaluation through full-process temperature rise prediction.

[0114] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A simulation system for medium-voltage cables, characterized in that, Includes an electrothermal bidirectional coupling unit, the electrothermal bidirectional coupling unit comprising: The electric field module applies the corresponding excitation current to the cable model according to different simulation conditions, causing Joule heating in the conductors of the cable model. The solid heat transfer module uses Joule heat as a heat source. By solving the control equation of the solid heat transfer module, the temperature distribution of the cable is obtained. Based on the obtained cable temperature, the current new conductivity is updated and fed back into the electric field model.

2. The simulation system for a medium-voltage cable according to claim 1, characterized in that, The simulation system includes an input unit, which includes an excitation current module for providing excitation current.

3. The simulation system for medium-voltage cables according to claim 1, characterized in that, The control equation for the electric field module is: Where ▽ is the vector differential operator; J is the current density vector; σ is the conductivity; ε0 is the vacuum permittivity; ε is the relative permittivity; t is time; E is the electric field vector; e is the externally injected current density; and U is the electric potential.

4. The simulation system for a medium-voltage cable according to claim 3, characterized in that, The control equation for the solid heat transfer module is: Where ρ is density; C p θ is the constant pressure heat capacity; t is the temperature; u is the time; k is the velocity vector; k is the thermal conductivity; and Q is the heat output power per unit volume of the heat source.

5. The simulation system for a medium-voltage cable according to claim 4, characterized in that, The boundary conditions of the governing equations of the solid heat transfer module include: the specific temperature of the known boundary, the heat flux density on the known boundary, the type of fluid in the surrounding environment and the external natural convection heat transfer coefficient h of the object on the known boundary, and the temperature of the surrounding medium.

6. The simulation system for a medium-voltage cable according to claim 4, characterized in that, The conductivity function is: Where σ(θ) is the conductivity; α is the resistivity at temperature θ0; β is the temperature coefficient of resistance of copper; and θ is the core temperature.

7. A simulation method for medium-voltage cables, characterized in that, Includes the following steps: According to different simulation conditions, the corresponding excitation current is applied to the cable model, and the conductor in the cable model generates Joule heating; The solid heat transfer module uses Joule heat as a heat source. By solving the control equation of the solid heat transfer module, the temperature distribution of the cable is obtained. Based on the obtained cable temperature, the current new conductivity is updated and fed back into the electric field model.

8. The simulation method for a medium-voltage cable according to claim 7, characterized in that, The simulated operating conditions include short-circuit conditions and overload conditions.

9. The simulation method for a medium-voltage cable according to claim 8, characterized in that, Under the short-circuit condition, the excitation current is a step current; under the overload condition, the excitation current is a cyclic overload current.

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