A cable life prediction method based on an improved electromagnetic-thermal field coupling model

Abstract

The application discloses a cable life prediction method based on an improved electromagnetic-thermal field coupling model, and comprises the following steps: firstly, a temperature coefficient and a proportional coefficient are used to respectively establish an insulation material thermal conductivity coefficient and temperature relationship and a convection heat transfer coefficient and temperature relationship, and the two relationships are used together with a conductor resistivity and temperature relationship as an electromagnetic-thermal field coupling relationship, thereby forming an improved electromagnetic-thermal field coupling model; then, a chaotic grey wolf optimization algorithm is used to identify the optimal temperature coefficient and the proportional coefficient of the insulation material in the improved electromagnetic-thermal field coupling model, and on this basis, the conductor temperature is calculated; finally, a multivariate linear regression is used to establish a conductor temperature analytical model, and an Arrhenius model is used to establish a cable life analytical model. The application solves the problem of large error of a traditional electromagnetic-thermal field coupling calculation method under a high temperature operation condition of a cable, and realizes online prediction of the cable life.

Description

Technical Field

[0001] This invention belongs to the field of wire and cable health management, specifically involving a cable life prediction method based on an improved electromagnetic-thermal field coupling model. Background Technology

[0002] Cables are crucial equipment in power systems, and their reliability is a key factor in ensuring safe power supply. Real-time monitoring of cable operating status and lifetime prediction using sensors can effectively assess cable health. Current research on cable lifetime prediction mainly focuses on physical lifetime models and data-driven lifetime models. Physical lifetime models are established based on the aging mechanisms of materials under different environmental stresses. Data-driven lifetime models are degradation models established based on aging characteristics collected by sensors. Data-driven lifetime models do not consider cable failure mechanisms; they only make real-time predictions based on sensor data. Physical lifetime models have clear physical meaning and can reflect cable lifetime changes with current and ambient temperature with high fidelity. The conductor temperature generated by the combined effects of current and ambient temperature is the main factor affecting cable lifetime. Traditional electromagnetic-thermal coupling models only consider the relationship between conductor resistivity and temperature, suitable for cables with low operating temperatures, such as cross-linked polyethylene cables. For cables with high operating temperatures, such as aerospace-grade fluoropolymer cables, traditional electromagnetic-thermal coupling models that only consider the temperature characteristics of conductor parameters have significant errors. Therefore, in the process of electromagnetic-thermal field coupling iterative calculation, it is necessary to consider the changes in the temperature characteristics of both the conductor material and the insulation material. Based on this, it is urgent to improve the traditional electromagnetic-thermal field coupling model to obtain an accurate conductor temperature, which is essential for accurate cable life prediction. The unknown coefficients in the relationship between the thermal characteristics of the cable insulation material and temperature are difficult to obtain experimentally, and iteratively searching for the optimal parameters using an ergonomic method would be time-consuming. Therefore, a heuristic optimization algorithm is needed to search for the optimal parameters to obtain an accurate relationship between the thermal characteristics of the insulation material and temperature. After collecting cable current and ambient temperature data, the improved electromagnetic-thermal field coupling model can be used to accurately calculate the cable conductor temperature, which can then be combined with the Arrhenius model to achieve online prediction of cable life. Summary of the Invention

[0003] The purpose of this invention is to address the problem that traditional electromagnetic-thermal field coupling models are not applicable to high-temperature operating conditions of cables, thus leading to inaccurate life prediction. This invention proposes a cable life prediction method based on an improved electromagnetic-thermal field coupling model, which can quickly and accurately calculate the conductor temperature of the cable and realize online prediction of cable life, which is of great significance for cable health management.

[0004] To achieve the above-mentioned objectives, this invention proposes a cable life prediction method based on an improved electromagnetic-thermal field coupling model, characterized by comprising:

[0005] The relationship between the thermal conductivity of the cable insulation material and temperature is established using the temperature coefficient of the cable insulation material to be determined. The temperature coefficient of the cable insulation material represents the relationship between the temperature change and the thermal conductivity change of the cable insulation material.

[0006] A formula for the relationship between the convective heat transfer coefficient of the cable insulation material and temperature is established using the proportional coefficient of the cable insulation material to be determined. The proportional coefficient of the cable insulation material represents the ratio of the thermal conductivity to the convective heat transfer coefficient of the cable insulation material.

[0007] The relationship between the thermal conductivity and temperature of the cable insulation material and the relationship between the convective heat transfer coefficient and temperature are incorporated into the traditional electromagnetic-thermal field coupling model to form an improved electromagnetic-thermal field coupling model.

[0008] Based on the improved electromagnetic-thermal coupling model, the cable conductor temperature under different cable insulation material temperature coefficients and cable insulation material proportional coefficients is calculated. The error analysis of the improved electromagnetic-thermal coupling model is performed based on the cable conductor temperature calculation results, and a mathematical model is established for the average absolute error of the output temperature and the cable insulation material temperature coefficient and cable insulation material proportional coefficient.

[0009] Using the mathematical model as the objective function, the optimal temperature coefficient and the optimal proportional coefficient of the cable insulation material in the improved electromagnetic-thermal field coupling model are identified by the chaotic gray wolf optimization algorithm, thus forming an improved electromagnetic-thermal field coupling model with material parameter adaptive correction function.

[0010] Based on the improved electromagnetic-thermal field coupling model with adaptive material parameter correction function, the final cable conductor temperature is obtained through electromagnetic-thermal field coupling calculation. Then, a multivariate linear regression is used to establish an analytical model of cable conductor temperature. Finally, an analytical model of cable life is established by combining the Arrhenius model. Based on the analytical model of cable life, cable life is predicted.

[0011] Preferably, in the conventional electromagnetic-thermal field coupling model, the relationship between the resistivity of the cable conductor and temperature is shown in equation (1):

[0012] ρ c =ρ 20 [1+α c (T) c -20)] (1)

[0013] In the formula ρ c ρ is the resistivity of the cable conductor. 20α is the resistivity of the cable conductor at 20℃. c T is the temperature coefficient of the cable conductor. c This refers to the temperature of the cable conductor.

[0014] Preferably, the relationship between the thermal conductivity and temperature and the relationship between the convective heat transfer coefficient and temperature of the cable insulation material are shown in (2) and (3), respectively:

[0015] λ i =a i T c +λ0 (2)

[0016]

[0017] In the formula λ i T represents the thermal conductivity of the cable insulation material. c For the temperature of the cable conductor, a i η is the temperature coefficient of the cable insulation material, λ0 is the initial value of the thermal conductivity of the cable insulation material, and η is the initial value of the thermal conductivity of the cable insulation material. i d is the convective heat transfer coefficient of the cable insulation material. i This is the proportional coefficient for cable insulation materials.

[0018] Preferably, the optimal temperature coefficient and the optimal proportional coefficient of the cable insulation material are obtained by using formula (4) as the objective function and solving them through the chaotic gray wolf optimization algorithm; the position update formulas of α, β and δ gray wolves in the chaotic gray wolf optimization algorithm are shown in formulas (5) to (7) respectively, and the update formula of the objective function value is shown in formula (8). Tent chaotic factor is introduced into each gray wolf position update formula to enhance the convergence speed and optimization accuracy of the gray wolf optimization algorithm. The calculation formula of Tent chaotic factor is shown in (9):

[0019] e m =b1+b2d i +b3a i +b4d i 2 +b5d i a i +b6a i 2 (4)

[0020] In the formula e m The mean absolute error is given, and b1 to b6 are undetermined coefficients. i d represents the temperature coefficient of the cable insulation material. i This is the proportional coefficient for cable insulation materials.

[0021] X1 = X α -A1|C1X α -mX| (5)

[0022] X2 = X β -A2|C2X β -mX| (6)

[0023] X3 = X δ -A3|C1X δ -mX| (7)

[0024] X(t+1)=(X1+X2+X3) / 3 (8)

[0025]

[0026] In the formula, m is the chaos factor, X a Let X be the position of α wolf. β X represents the position of the β wolf. δ Let δ be the position of the wolf, X be the objective function value determined by the positions of α, β, and δ, X1 be the objective function value determined only by the position of α, X2 be the objective function value determined only by the position of β, and X3 be the objective function value obtained only by the position of δ, i be the number of gray wolves, and t be the number of iterations.

[0027] Preferably, the electromagnetic-thermal field coupling calculation process is an iterative calculation process. After each calculation, the cable conductor temperature is extracted and the cable conductor resistivity, the thermal conductivity of the cable insulation material, and the convective heat transfer coefficient of the cable insulation material are updated until the convergence formula (10) is satisfied:

[0028] |T n+1 -T n |≤ε (10)

[0029] In the formula T n+1 Let T be the temperature of the cable conductor in the (n+1)th iteration. n Let ε be the temperature of the cable conductor at the nth time, and ε be the temperature deviation value.

[0030] Preferably, the analytical model for cable conductor temperature is shown in formula (11), the Arrhenius model is shown in formula (12), and the analytical model for cable life is shown in formula (13):

[0031] T c =c1+c2I+c3T a +c4I 2 +c5IT a +IT a 2 (11)

[0032]

[0033]

[0034] In the formula, c1 to c6 are the undetermined coefficients of the analytical model of cable conductor temperature, I is the cable conductor current, and T is the current in the cable conductor. a For ambient temperature, T c Let t be the cable conductor temperature, a and b be the undetermined coefficients of the Arrhenius model, and t be the cable life.

[0035] The beneficial effects of this invention are as follows:

[0036] 1. In the electromagnetic-thermal field coupling calculation, the temperature characteristics of the cable conductor material parameters and insulation material parameters were considered, and the optimal undetermined coefficients in the relationship between insulation material parameters and temperature were optimized using the chaotic gray wolf optimization algorithm, thus realizing the accurate calculation of cable temperature.

[0037] 2. An analytical model of cable conductor temperature was established using the calculation results of the improved electromagnetic-thermal field coupling model, and combined with the Arrhenius model to achieve rapid prediction of cable life.

[0038] The cable life prediction method based on the improved electromagnetic-thermal field coupling model of the present invention solves the problem of large error in the traditional electromagnetic-thermal field coupling calculation method under high temperature operation conditions of cables. It can accurately and quickly calculate the internal temperature of the cable and realize online prediction of cable life. Attached Figure Description

[0039] Figure 1 This is a flowchart of Example 1;

[0040] Figure 2 The temperature iterative change curve;

[0041] Figure 3 Comparison curves of calculated and measured values ​​from traditional models under different working conditions;

[0042] Figure 4 The iterative curve of the optimization process of the Chaotic Gray Wolf Optimization Algorithm;

[0043] Figure 5 Improve the comparison curves of calculated and measured values ​​for different working conditions;

[0044] Figure 6 A bar chart showing the temperature of the cable conductor under operating conditions;

[0045] Figure 7 This is a 3D diagram of the cable's lifespan. Detailed Implementation

[0046] Comparative Example 1

[0047] This comparative example uses an AWG12 type ethylene-tetrafluoroethylene copolymer insulated cable as an example to provide the calculation process for the cable conductor temperature based on a traditional electromagnetic-thermal field coupling model. The cable conductor radius is 1.05 mm, the insulation radius is 1.3 mm, the initial value of the thermal conductivity of XETFE is taken as 0.17 W / m / K, and the initial value of the convective heat transfer coefficient is taken as 30 W / m. 2 / ℃, the thermal conductivity of copper is taken as 400W / m / K.

[0048] The traditional electromagnetic-thermal coupling model only considers the relationship between the resistivity of the cable conductor and temperature, as shown in equation (1):

[0049] ρ c =ρ 20 [1+α c (T c -20)] (1)

[0050] In the formula ρ c ρ is the resistivity of the cable conductor. 20 α is the resistivity of the cable conductor at 20℃. c T is the temperature coefficient of the cable conductor. c This refers to the temperature of the cable conductor.

[0051] A finite element model was established based on the cable structure parameters, and corresponding material properties were assigned to the conductor and insulation layer. Electromagnetic-thermal field coupling calculations were performed based on formula (1). The results of 10 iterations of the cable conductor temperature and surface temperature calculations are as follows: Figure 2 As shown.

[0052] The cable surface temperature was calculated using the above calculation process under different operating conditions, and measured using a PT100 temperature sensor. The cable current range was 10–60 A, and the ambient temperature was 43.78–84.20 °C. Based on the traditional electromagnetic-thermal field coupling model, the calculated and measured values ​​of the cable surface temperature under different operating conditions are as follows: Figure 3 As shown.

[0053] It is evident that the traditional electromagnetic-thermal coupling model, which only considers the temperature characteristics of the cable conductor parameters, is only applicable to cables with low operating temperatures. For cables with high operating temperatures, such as aviation-grade fluoropolymer cables with ethylene-tetrafluoroethylene copolymer insulation, the traditional electromagnetic-thermal coupling model has significant errors.

[0054] Example 1

[0055] This embodiment uses the AWG12 type ethylene-tetrafluoroethylene copolymer insulated cable from Comparative Example 1 as an example to provide a cable life prediction method based on an improved electromagnetic-thermal field coupling model, such as... Figure 1 As shown, it includes the following steps:

[0056] Step S01: Define the temperature coefficient of cable insulation material to represent the relationship between the temperature change and the thermal conductivity change of cable insulation material; define the proportionality coefficient of cable insulation material to represent the ratio of the thermal conductivity to the convective heat transfer coefficient of cable insulation material; and establish the relationship between the thermal conductivity and temperature and the convective heat transfer coefficient of cable insulation material using the temperature coefficient and proportionality coefficient to be determined, as shown in formulas (2) and (3), respectively.

[0057] λ i =a i T c +λ0 (2)

[0058]

[0059] In the formula λ i T represents the thermal conductivity of the cable insulation material. c For the temperature of the cable conductor, a i η is the temperature coefficient of the cable insulation material, λ0 is the initial value of the thermal conductivity of the cable insulation material, and η is the initial value of the thermal conductivity of the cable insulation material. i d is the convective heat transfer coefficient of the cable insulation material. i This is the proportional coefficient for cable insulation materials.

[0060] In the traditional electromagnetic-thermal coupling model, the thermal conductivity and convective heat transfer coefficient of the cable insulation material are constants during the calculation process. After optimization by this invention, these two parameters are two relationships affected by temperature, and the calculation process is a continuous iterative update process.

[0061] Step S02: Add the above-mentioned relationship between the thermal conductivity of the cable insulation material and temperature (2) and the relationship between the convective heat transfer coefficient and temperature (3) to the traditional electromagnetic-thermal field coupling model, and together with the above-mentioned relationship between the resistivity of the cable conductor and temperature (1), as the coupling relationship of the electromagnetic-thermal field coupling model, to form an improved electromagnetic-thermal field coupling model.

[0062] Step S03: Set several different temperature coefficients and proportional coefficients of cable insulation materials. Based on the above improved electromagnetic-thermal field coupling model, calculate the cable conductor temperature under different temperature coefficients and proportional coefficients of cable insulation materials. Perform error analysis on the improved electromagnetic-thermal field coupling model through the cable conductor temperature calculation results, and establish a mathematical model of the average absolute error of the output temperature and the temperature coefficients and proportional coefficients of cable insulation materials, as shown in formula (4).

[0063] e m =b1+b2d i +b3a i+b4d i 2 +b5d i a i +b6a i 2 (4)

[0064] In the formula e m The mean absolute error is given, and b1 to b6 are undetermined coefficients. i d represents the temperature coefficient of the cable insulation material. i This is the proportional coefficient for cable insulation materials.

[0065] Step S04: Using the mean absolute error expressed by formula (4) as the objective function, the optimal undetermined parameters of the improved electromagnetic-thermal field coupling model are identified by the chaotic gray wolf optimization algorithm, namely the optimal temperature coefficient of the cable insulation material and the optimal proportional coefficient of the cable insulation material.

[0066] The optimal temperature coefficient for the cable insulation material was found to be 2.51 × 10⁻⁶. -４ The optimal ratio factor for cable insulation material is 6.6 × 10⁻⁶. -3 The minimum mean absolute error is 0.5676. The iterative curve of the optimization process is shown below. Figure 4 As shown.

[0067] After obtaining the optimal temperature coefficient and proportional coefficient of the cable insulation material, an improved electromagnetic-thermal field coupling model with adaptive correction function of material parameters is obtained.

[0068] Step S05: Perform electromagnetic-thermal field coupling calculations based on an improved electromagnetic-thermal field coupling model with adaptive material parameter correction capabilities, and output the cable conductor temperature. Calculated and measured values ​​of the cable surface under different operating conditions are shown below. Figure 5 As shown in the figure. The bar chart shows the cable conductor temperature under different operating conditions. Figure 6 As shown, the cable surface temperature calculated based on the improved electromagnetic-thermal field coupling model is still close to the actual value even under conditions of high current and high ambient temperature.

[0069] The cable conductor temperature was fitted using formula (5) under different currents and ambient temperatures, yielding the following parameters: c1 = 7.08, c2 = -0.72, c3 = 0.97, and c4 = 3.91 × 10⁻⁶. -2 c5 is 3.3 × 10 -3 c6 is -1.24 × 10 -４ .

[0070] T c =c1+c2I+ac3T a +c4I 2 +c5ITa +IT a 2 (5)

[0071] In the formula, c1 to c6 are undetermined coefficients, I is the conductor current, and T is the conductor current. a For ambient temperature, T c The conductor temperature.

[0072] The failure times of ethylene-tetrafluoroethylene copolymer insulated cables at different temperatures are shown in Table 1. The failure times were fitted using formula (6) under different temperatures, yielding undetermined coefficients a = 14884.06 and b = -22.54. Combining formulas (5) and (6), the analytical model for cable life is obtained as shown in formula (7). Figure 7 This is a 3D diagram of the cable's lifespan.

[0073] Table 1. Cable insulation failure time at different temperatures

[0074]

[0075]

[0076]

[0077] In the formula, a and b are undetermined coefficients of the Arrhenius model, and t is the cable life.

Claims

1. A method for predicting cable life based on an improved electromagnetic-thermal field coupling model, characterized in that, include: The relationship between the thermal conductivity of the cable insulation material and temperature is established using the temperature coefficient of the cable insulation material to be determined. The temperature coefficient of the cable insulation material represents the relationship between the temperature change and the thermal conductivity change of the cable insulation material. A formula for the relationship between the convective heat transfer coefficient of the cable insulation material and temperature is established using the proportional coefficient of the cable insulation material to be determined. The proportional coefficient of the cable insulation material represents the ratio of the thermal conductivity to the convective heat transfer coefficient of the cable insulation material. The relationship between the thermal conductivity and temperature and the convective heat transfer coefficient of the cable insulation material are incorporated into the traditional electromagnetic-thermal field coupling model to form an improved electromagnetic-thermal field coupling model. Based on the improved electromagnetic-thermal coupling model, the cable conductor temperature under different cable insulation material temperature coefficients and cable insulation material proportional coefficients is calculated. The error analysis of the improved electromagnetic-thermal coupling model is performed based on the cable conductor temperature calculation results, and a mathematical model is established for the average absolute error of the output temperature and the cable insulation material temperature coefficient and cable insulation material proportional coefficient. Using the mathematical model as the objective function, the optimal temperature coefficient and the optimal proportional coefficient of the cable insulation material in the improved electromagnetic-thermal field coupling model are identified by the chaotic gray wolf optimization algorithm, thus forming an improved electromagnetic-thermal field coupling model with material parameter adaptive correction function. Based on the improved electromagnetic-thermal field coupling model with adaptive material parameter correction function, the final cable conductor temperature is obtained through electromagnetic-thermal field coupling calculation. Then, a multivariate linear regression is used to establish an analytical model of cable conductor temperature. Finally, an analytical model of cable life is established by combining the Arrhenius model. Based on the analytical model of cable life, cable life is predicted.

2. The cable life prediction method based on an improved electromagnetic-thermal field coupling model as described in claim 1, characterized in that, In the traditional electromagnetic-thermal coupling model, the relationship between the resistivity of the cable conductor and temperature is shown in equation (1): ρ c ＝ ρ 20 [1＋ α c ( T c －20)] (1) In the formula ρ c ρ is the resistivity of the cable conductor. 20 α is the resistivity of the cable conductor at 20℃. c T is the temperature coefficient of the cable conductor. c This refers to the temperature of the cable conductor.

3. The cable life prediction method based on an improved electromagnetic-thermal field coupling model as described in claim 1, characterized in that, The relationships between the thermal conductivity and temperature, and between the convective heat transfer coefficient and temperature of the cable insulation material are shown in (2) and (3), respectively: λ i ＝ a i T c ＋ λ 0 (2) (3) In the formula λ i T represents the thermal conductivity of the cable insulation material. c For the cable conductor temperature, a i η is the temperature coefficient of the cable insulation material, λ0 is the initial value of the thermal conductivity of the cable insulation material, and η is the initial value of the thermal conductivity of the cable insulation material. i d is the convective heat transfer coefficient of the cable insulation material. i This is the proportional coefficient for cable insulation materials.

4. The cable life prediction method based on an improved electromagnetic-thermal field coupling model as described in claim 1, characterized in that, The optimal temperature coefficient and the optimal proportional coefficient of the cable insulation material are obtained by using formula (4) as the objective function and solving them through the chaotic gray wolf optimization algorithm. The position update formulas for α, β and δ wolves in the chaotic gray wolf optimization algorithm are shown in formulas (5) to (7), and the update formula for the objective function value is shown in formula (8). The Tent chaos factor is introduced into each gray wolf position update formula to enhance the convergence speed and optimization accuracy of the gray wolf optimization algorithm. The calculation formula for the Tent chaos factor is shown in formula (9). e m ＝ b 1＋ b 2 d i ＋ b 3 a i ＋ b 4 d i 2 ＋ b 5 d i a i ＋ b 6 a i 2 (4) In the formula e m Let b1~b6 be the mean absolute error, and a be the coefficients to be determined. i d represents the temperature coefficient of the cable insulation material. i This refers to the proportionality coefficient of cable insulation material; X 1＝ X α － A 1 |C 1 X α － mX| (5) X 2＝ X β － A 2 |C 2 X β － mX| (6) X 3＝ X δ － A 3 |C 1 X δ － mX| (7) X （ t ＋1）＝（ X 1＋ X 2＋ X 3） / 3 (8) (9) In the formula, m is the chaos factor, X α Let X be the position of α wolf. β X represents the position of the β wolf. δ Let δ be the position of the wolf, X be the objective function value determined by the positions of α, β, and δ, X1 be the objective function value determined only by the position of α, X2 be the objective function value determined only by the position of β, and X3 be the objective function value obtained only by the position of δ, i be the number of gray wolves, and t be the number of iterations.

5. The cable life prediction method based on an improved electromagnetic-thermal field coupling model as described in claim 1, characterized in that, The electromagnetic-thermal field coupling calculation process is an iterative calculation process. After each calculation, the cable conductor temperature is extracted and the cable conductor resistivity, the thermal conductivity of the cable insulation material, and the convective heat transfer coefficient of the cable insulation material are updated until the convergence formula (10) is satisfied: | T n＋1 － T n | ≤ ε (10) In the formula T n+1 Let T be the temperature of the cable conductor in the (n+1)th iteration. n Let ε be the temperature of the cable conductor at the nth time, and ε be the temperature deviation value.

6. The cable life prediction method based on an improved electromagnetic-thermal field coupling model as described in claim 1, characterized in that, The analytical model for cable conductor temperature is shown in formula (11), the Arrhenius model is shown in formula (12), and the analytical model for cable life is shown in formula (13). T c ＝ c 1＋ c 2 I ＋ c 3 T a ＋ c 4 I 2 ＋ c 5 IT a ＋ IT a 2 (11) (12) (13) In the formula, c1~c6 are the undetermined coefficients of the analytical model of cable conductor temperature, I is the cable conductor current, and T is the current in the cable conductor. a For ambient temperature, T c Let t be the cable conductor temperature, a and b be the undetermined coefficients of the Arrhenius model, and t be the cable life.

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