Method for Calculating and Monitoring Maximum Permissible Deformation of Cables Based on Thermo-Mechanical Stress

Abstract

This invention proposes a method for calculating and monitoring the maximum permissible deformation of cables based on thermo-mechanical stress. The maximum permissible deformation of cables is calculated, and the cable deformation is monitored by tracking the real-time deformation of large-section cables. This invention considers the irreversible damage to cable insulation caused by deformation and proposes a method for monitoring the maximum permissible deformation of large-section cables. This method can effectively prevent internal insulation damage caused by thermo-mechanical stress, provides a clear monitoring scheme, supplements and improves cable laying regulations, supports the standardization of cable construction, improves construction safety, and helps ensure the safe operation of the power grid.

Description

Technical Field

[0001] This invention belongs to the field of power technology and relates to safe cable construction. It is a method for calculating and monitoring the maximum permissible deformation of large-section cables based on thermo-mechanical stress. Background Technology

[0002] Currently, research on large-section cables mainly focuses on their electrical performance, temperature field, and current carrying capacity, with little research on the operational characteristics of cables under thermo-mechanical stress caused by temperature changes. When large-section cables are laid in a straight line, they are subjected to enormous thermo-mechanical stress due to temperature variations, causing localized deformation of the cable line. Over time, this accumulated deformation can lead to excessive bending of the cable. If this bending is allowed to continue unchecked, it will damage the cable's original structure.

[0003] The "Technical Regulations for the Design of Urban Power Cable Lines" currently published for engineering practice provides preliminary solutions to the thermal strain generated during cable operation. Based on existing cable operation and management experience and power grid operation technical standards, two measures are generally adopted to alleviate the thermal stress and thermal strain caused by load changes when laying large-section cables in engineering: one is to lay them in a serpentine manner in tunnels, and the other is to use an expansion arc structure at both ends of the cable intermediate joint.

[0004] Current regulations stipulate that the size of the expansion arc in cable laying must meet the requirement that the metal sheath of the cable should not experience fatigue during its lifespan. However, no clear recommendations are given regarding the maximum permissible deformation of large-section cables, and effective monitoring methods are lacking. Summary of the Invention

[0005] The problem this invention aims to solve is that the thermo-mechanical stress generated by temperature changes in cables can affect their safe operation. Existing technologies do not quantitatively define the impact of cable deformation on safety and cannot effectively monitor whether current cable deformation will affect cable operation.

[0006] The technical solution of this invention is: a method for calculating and monitoring the maximum permissible deformation of cables based on thermo-mechanical stress, comprising the following steps:

[0007] Step 1: Establish a thermo-mechanical stress model for a large-section cable, including temperature and stress distribution diagrams. The large section refers to a cable cross-section of 2000 mm². 2 and above;

[0008] Step 2: As can be seen from Step 1, large-section cables undergo deformation during operation. The large-section cable is equivalent to a catenary. The deformation of any point M on the vertical arc of the large-section cable is calculated according to the catenary equation function.

[0009] Step 3: Based on the deformation calculation in Step 2, and combined with the catenary function of the cable arc, calculate the maximum allowable deformation of the cable;

[0010] Step 4: Acquire cable images and monitor the real-time deformation of large-section cables through image processing;

[0011] Step 5: When the monitored real-time deformation exceeds the cable's maximum allowable deformation, send monitoring information to issue an early warning.

[0012] Furthermore, in step 1, a strain distribution map of the large-section cable is established, and the lowest point of the cable is determined by the strain distribution map.

[0013] The present invention proposes a method for calculating and monitoring the maximum allowable deformation of large-section cables based on thermo-mechanical stress. This method supplements and improves the existing safety standards for cables, specifically the provisions on cable laying in the "Technical Specifications for Design of Urban Power Cable Lines" (DL / T 5221-2016). Currently, there is no solution for detecting the impact of cable deformation on safe operation; most methods rely on manual experience to judge the cable's operating status. This invention proposes a clear method for calculating deformation, providing support for the standardization of cable construction.

[0014] The beneficial effects of this invention are as follows: This invention proposes a method for calculating and monitoring the maximum permissible deformation of large-section cables based on thermo-mechanical stress. This method can effectively prevent internal insulation damage to cables caused by thermo-mechanical stress, provides a clear monitoring scheme, and can significantly reduce the probability of cable operation accidents, thus ensuring the safe operation of the power grid. This invention supplements and improves cable laying regulations, provides support for the standardization of cable construction, improves construction safety, and helps ensure the safe operation of the power grid. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention.

[0016] Figure 2 Temperature field distribution diagram of large cross-section cable established for embodiments of the present invention.

[0017] Figure 3 The stress distribution diagram of a large cross-section cable established for an embodiment of the present invention.

[0018] Figure 4 The strain distribution diagram of a large cross-section cable established for an embodiment of the present invention.

[0019] Figure 5 This is a cable-catenary model in an embodiment of the present invention. Detailed Implementation

[0020] This invention, based on a thermo-mechanical stress model, derives a method for calculating the maximum permissible deformation of cables. Furthermore, considering the damage caused by deformation to cable insulation, it proposes a method for monitoring the maximum permissible deformation of large-section cables. The method of this invention is described in detail below. Figure 1 As shown.

[0021] Step 1: Establish a thermo-mechanical stress model for large-section cables. Large-section refers to cables with a cross-section of 2000 mm². 2 And above. A three-dimensional coordinate system is established with the lowest point of the sag arc of the large-section cable as the origin, and the distribution of thermo-mechanical stress is calculated.

[0022] 1) Establish a temperature field distribution diagram for large cross-section cables.

[0023]

[0024] In the formula: t represents a certain operating moment of the large-section cable; T represents the temperature at any point (x, y, z) on the large-section cable; λ represents the thermal conductivity of the material; q v Represents heat generation rate per unit volume; ρ represents material density; c p This indicates the specific heat capacity of a material. For regions containing heat sources, such as conductors and metallic sheaths, q represents... v Not zero; however, for areas without heat sources, such as buffer layers and outer sheaths, q v Then simply take 0.

[0025] 2) Establish a stress distribution diagram for large-section cables:

[0026]

[0027] In the formula: σ x , σ y , σ z δ represents the stress along the x, y, and z axes; xy δ yz δ zx The stress components in the xy, yz, zx planes are represented by H and G; Lamé constants are represented by β; the coefficient of thermal expansion of the cable sheath is represented by β; ΔT represents the temperature difference between the cable sheath and the environment during power grid operation; ε x , ε y , ε z γ represents the strain in the x, y, and z axes; xy γ yz γ zx D represents the components of strain in the xy, yz, zx planes; v D represents volumetric strain. v =ε x +ε y +ε z .

[0028] The stress σ at any point on a large cross-section cable is:

[0029] σ=σ x +σ y +σ z (7)

[0030] 3) Establish a thermal strain distribution diagram for large-section cables:

[0031]

[0032] In the formula: u, v, w represent the displacement components along the x, y, and z axes, respectively; f x f y f z The force components in each direction of the cable are represented sequentially. If the cable is fixed along the x-direction, then u can be set to 0, and so on for other directions.

[0033] Due to gravity, the maximum allowable deformation exists at the bottom of the cable sag. However, in reality, the bottom of the cable is an arc segment, and the y-coordinate on the arc segment does not change much, making it difficult to intuitively determine the lowest point. Selecting a point in the arc segment can be used to calculate the maximum allowable deformation. To make the maximum allowable deformation in this invention more accurate, this invention further establishes a strain distribution diagram of the cable and uses strain analysis to determine the coordinates of the lowest point at the bottom of the cable sag.

[0034] Step 2: As shown in the model analysis in Step 1, large-section cables will deform due to temperature during operation. When the cable is laid in a serpentine pattern, it can be approximated as a catenary. Based on the catenary equation, the formula for calculating the deformation of any point M on the sag of the large-section cable can be derived.

[0035]

[0036] In the formula: g is the specific load of the cable conductor's self-weight; l is the distance between the two fixed points A and B of the large cross-section cable; x is the abscissa of any point M on the arc; and σ is the stress at point M.

[0037] Step 3: Calculate the maximum allowable deformation of the cable.

[0038] 1) Analogizing a large-section cable to a catenary, simplify the formula for calculating the deformation of any point M on the vertical arc obtained in step 2:

[0039]

[0040] In the formula: l A l B Let M be the horizontal distance from any point M on the cable arc to the fixed points A and B at both ends of the cable.

[0041] 2) The maximum allowable deformation of the cable exists at the bottom of the installation. Since the laid cable can be approximated as an axisymmetric curve, we take l as the maximum allowable deformation. A =l B = l / 2, we can get:

[0042]

[0043] In the formula, σ0 represents the stress at the lowest point of the cable, and d represents the maximum allowable deformation. The lowest point of the cable is preferably determined through strain distribution analysis.

[0044] Step 4: Monitor the deformation of large-section cables.

[0045] 1) Existing power grids often have image monitoring systems for cables. The watershed algorithm is used to extract key information from images collected by these systems, thereby monitoring the real-time deformation of the cables. The watershed represents the maximum point of the input image. To obtain the edge information of the image, the gradient image is usually used as the input image, i.e.

[0046]

[0047] In the formula, f(x,y) represents the original image, and grad represents the gradient operation.

[0048] 2) To prevent the watershed algorithm from over-segmenting image information, thresholding can be applied to the gradient image to eliminate over-segmentation caused by small changes in grayscale.

[0049] g(x,y)=max{grad(f(x,y)),g(θ)} (8)

[0050] In the formula, g(θ) represents the threshold.

[0051] The cable in the cable image is segmented using the watershed algorithm, and the real-time deformation at the bottom of the cable is calculated. The watershed algorithm is existing technology and will not be described in detail here. Other image processing schemes can also be used to monitor deformation through real-time cable images.

[0052] Step 5: When the monitored value is greater than the maximum allowable deformation of the large cross-section cable, send the monitoring information to the back-end operation and maintenance personnel.

[0053] This implementation case uses a city with a voltage of 220kV and a cross-sectional area of ​​2500mm². 2 Taking a large-section cable as an example, we will simulate, analyze, calculate, and monitor the cable.

[0054] Step 1: Using the finite element method, establish a voltage of 220kV and a cross-sectional area of ​​2500mm². 2 Temperature field distribution, stress, and thermal strain distribution of large cross-section cables, such as Figures 2-4As shown, it can be seen that when the cable is in operation, the internal conductor will squeeze the insulation layer, and the aluminum sheath will squeeze the outer sheath. Long-term squeezing will cause irreversible damage to the insulation layer and the outer sheath.

[0055] Step 2: Take any point M on the cable and calculate the deformation f(x) that occurs during operation, such as... Figure 5 As shown.

[0056] Step 3: Due to gravity, the maximum allowable deformation exists at the bottom of the cable's sag. In this embodiment, the distance between the two fixed points A and B of the cable is l = 6m. l can usually be measured at the cable laying site. According to formula (6), the deformation of the cable at its lowest point during operation is 7mm.

[0057] Step 4: A fluorescent sticker is placed at the lowest point of the cable for location marking. A video monitoring system monitors the lowest point of the cable at any given time. A watershed algorithm is used to extract keyframes from the acquired image information and compares them with those under normal cable conditions, controlling the deformation to not exceed the 7mm calculated in Step 4. This monitoring system can effectively monitor large-section cables and, to a certain extent, suppress insulation damage caused by thermo-mechanical stress. This matches actual operating conditions, demonstrating the effectiveness and feasibility of the invention.

[0058] The above description is only one embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating and monitoring the maximum permissible deformation of cables based on thermo-mechanical stress, characterized in that: Includes the following steps: Step 1: Establish a thermo-mechanical stress model for a large-section cable, including temperature and stress distribution diagrams. The large section refers to a cable cross-section of 2000 mm². 2 and above; Step 2: As can be seen from Step 1, large-section cables undergo deformation during operation. The large-section cable is equivalent to a catenary. The deformation of any point M on the vertical arc of the large-section cable is calculated according to the catenary equation function. Step 3: Based on the deformation calculation in Step 2, and combined with the catenary function of the cable arc, calculate the maximum allowable deformation of the cable; Step 4: Acquire cable images and monitor the real-time deformation of large-section cables through image processing; Step 5: When the monitored real-time deformation exceeds the cable's maximum allowable deformation, send monitoring information to issue an early warning.

2. The method for calculating and monitoring the maximum permissible deformation of cables based on thermo-mechanical stress according to claim 1, characterized in that: Step 1 is as follows: 1) Establish a three-dimensional coordinate system with the lowest point of the sag of the large-section cable as the origin, and obtain the temperature field distribution diagram of the large-section cable: In the formula: t represents a certain operating moment of the large-section cable; T represents the temperature at any point (x, y, z) on the large-section cable; λ represents the thermal conductivity of the cable material; q v The cable's heat generation rate per unit volume is represented by ρ; the material density is represented by c. p Indicates the specific heat capacity of the material; 2) Establish a stress distribution diagram for large-section cables: In the formula: σ x , σ y , σ z δ represents the stress along the x, y, and z axes; xy δ yz δ zx The stress components in the xy, yz, zx planes are represented by H and G; Lamé constants are represented by β; the coefficient of thermal expansion of the cable sheath is represented by β; ΔT represents the temperature difference between the cable sheath and the environment during power grid operation; ε x , ε y , ε z γ represents the strain in the x, y, and z axes; xy γ yz γ zx D represents the components of strain in the xy, yz, zx planes; v D represents volumetric strain. v =ε x +ε y +ε z ; The stress σ at any point on a large cross-section cable is: s = s x +s y +s z (3)。 3. The method for calculating and monitoring the maximum permissible deformation of cables based on thermo-mechanical stress according to claim 1 or 2, characterized in that: According to the catenary equation, the deformation calculation formula for any point M on the sag arc of the large-section cable in step 2 is: In the formula: g is the specific load of the cable conductor's self-weight; l is the distance between the two fixed points A and B of the large cross-section cable; x is the abscissa of any point M on the arc; and σ is the stress at point M.

4. The method for calculating and monitoring the maximum permissible deformation of cables based on thermo-mechanical stress according to claim 3, characterized in that: In step 3, the cable is compared to a catenary, further simplifying the variable calculation formula: In the formula: l A l B These are the horizontal distances from point M on the cable arc to fixed points A and B at both ends of the cable; The maximum permissible deformation of the cable exists at the lowest point of the sag during installation, taken as l. A =l B = l / 2, resulting in: In the formula, σ0 is the stress at the lowest point of the cable, and d is the maximum allowable deformation of the cable.

5. The method for calculating and monitoring the maximum permissible deformation of cables based on thermo-mechanical stress according to claim 4, characterized in that: Step 1 also involves establishing a strain distribution diagram for the large-section cable, and using the strain distribution diagram to determine the lowest point of the cable.

6. The method for calculating and monitoring the maximum permissible deformation of cables based on thermo-mechanical stress according to claim 5, characterized in that: A three-dimensional coordinate system is established with the lowest point of the sag arc of the large-section cable as the origin, and the strain distribution diagram of the large-section cable is as follows: In the formula: u, v, w represent the displacement components along the x, y, and z axes, respectively; f x f y f z The components of the force acting on the cable in each direction are represented sequentially. Based on the strain distribution diagram of the cable, the point of maximum deformation on the cable is determined, that is, the stress at the lowest point of the cable is obtained, which is used to calculate the maximum allowable deformation.

7. The method for calculating and monitoring the maximum permissible deformation of cables based on thermo-mechanical stress according to claim 1, characterized in that: The real-time deformation of large-section cables is monitored by extracting keyframe information and using a watershed algorithm.

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