Grounding resistance thermal-electric coupling prediction method and system suitable for various soil scenes

Abstract

The invention discloses a grounding resistance thermal-electric coupling prediction method and system suitable for various soil scenes. The method comprises the following steps: acquiring an electrode parameter, a soil parameter, a grounding fault parameter and initial temperatures of an electrode and soil; calculating an electrode current and a soil leakage current of the time step based on the electrode and soil resistivity of the time step; based on the electrode current and the soil leakage current of the time step, calculating the electrode temperature, the soil radial temperature distribution and the grounding potential rise of the time step by adopting a finite difference method; based on the electrode temperature and soil radial temperature distribution of the time step, updating the electrode resistivity and the soil resistivity of the time step + 1; if the end of the fault time is not reached, returning to continuously calculate the temperature of the electrode and the soil at the time step + 1; otherwise, outputting the electrode temperature and soil radial temperature distribution of each time step. According to the invention, thermal-electric dynamic coupling is considered, and accurate evaluation of the performance of the grounding system is realized.

Description

Technical Field

[0001] This invention belongs to the field of power system grounding protection technology, specifically, it relates to a grounding resistance thermo-electric coupling prediction method and system applicable to various soil scenarios. Background Technology

[0002] The grounding electrode is a core protective component of a power system. Its function is to safely discharge fault currents (such as lightning strikes and short-circuit currents) into the earth, ensuring the safety of personnel and the integrity of equipment. However, under fault conditions, the grounding electrode will experience a severe thermo-electric coupling effect due to Joule heating: both the internal resistance of the electrode and the leakage current in the soil will generate heat, causing the temperature of the electrode and the surrounding soil to rise. The increase in temperature will change the resistivity of the grounding electrode and the soil—the resistivity of the grounding electrode increases with increasing temperature, while the resistivity of the soil decreases with increasing temperature, thereby changing the current distribution and heat generation efficiency, forming a nonlinear feedback loop of "temperature-resistivity-current-temperature".

[0003] Existing techniques for predicting current or temperature fields have significant drawbacks:

[0004] (1) Most models only calculate the current field or temperature field in isolation and do not effectively integrate this dynamic thermo-electric coupling relationship. Especially in the scenario of multi-layered heterogeneous soil and significant differences in resistivity between layers, which are common in actual engineering, existing models either ignore the influence of soil stratification on the current leakage path or do not include the temperature-dependent resistivity of the layered soil in the coupling calculation, resulting in significant deviations between the predicted results of current distribution and temperature field and the actual situation. For example, when calculating grounding resistance, existing studies often assume that the soil resistivity is constant, which cannot reflect the sudden increase in resistivity caused by soil heating and dehydration during the fault process. This leads to an overestimation of the fault current dissipation capacity of the grounding system, which may result in the distortion of safety parameters such as step voltage and contact voltage, and may create hidden dangers of electric shock to personnel or damage to equipment.

[0005] (2) Traditional analytical or finite element methods have a rough handling of heat conduction at the electrode-soil interface and do not optimize the discretization strategy for the transient characteristics of short-term faults, which easily leads to calculation divergence. Existing methods are difficult to adapt to different electrode structures, materials and soil types, and cannot accurately identify hot spots such as corners and current injection points, resulting in overly conservative or unsafe designs. Summary of the Invention

[0006] This invention provides a grounding resistance thermal-electric coupling prediction method and system applicable to various soil scenarios, solving the problem of missing thermal-electric dynamic coupling and achieving accurate performance evaluation of grounding systems.

[0007] To achieve the above technical objectives, the present invention adopts the following technical solution:

[0008] A grounding resistance thermo-electric coupling prediction method applicable to various soil scenarios includes:

[0009] Step 1: Obtain the inherent parameters and initial resistivity of the electrodes, the inherent parameters and initial resistivity of the soil, the grounding fault parameters, and the initial temperatures of the electrodes and soil;

[0010] Step 2, based on time step Electrode resistivity and soil resistivity, calculation time step Electrode current and soil leakage current;

[0011] Step 3, based on time step The electrode current and soil leakage current were calculated using the finite difference method for the time step. Electrode temperature and soil radial temperature distribution;

[0012] Step 4, based on time step Electrode temperature and soil radial temperature distribution, update time step +1 electrode resistivity and soil resistivity;

[0013] Step 5, if time step If the fault time has not ended by +1, return to step 2 and continue with the time step. +1 is used to calculate the electrode and soil temperatures; otherwise, the electrode temperature and soil radial temperature distribution at each time step are output.

[0014] Furthermore, the electrode current is calculated based on electrode resistivity, and the soil leakage current is calculated based on soil resistivity, respectively:

[0015]

[0016]

[0017] In the formula, For the first The segment electrode at time step The current; For the first The segment electrode at time step temperature, For the first The segment electrode at a temperature of resistivity at that time For the first The potential at the beginning of the segment electrode, For the first The resistance of the segment electrode, Electrode resistivity, Where is the electrode radius. The depth of the electrode embedding wire. For electrode length, For the first The radial region of the soil of the segment electrode Each node at time step The soil temperature; For the first The soil at the segment electrode at time step Leakage current, For the first The radial region of the soil at the segment electrode Each node is at a temperature of The resistivity at that time.

[0018] Furthermore, the finite difference method is used to calculate the time step. Electrode temperature and soil radial temperature distribution;

[0019] Among them, the radial region of the soil at any segment electrode is the first Each node at time step temperature The calculation formula is:

[0020]

[0021] in, For the radial region of soil Each node at time step temperature, ; The time step for dividing the fault period, The distance between adjacent nodes in the radial division of the soil. , Where is the electrode radius. The depth of the electrode burial wire; the nodes are numbered sequentially from the electrode surface to the ground surface. , For the first The distance from each node to the center line of the electrode; The soil thermal diffusivity, , For soil density, For soil thermal conductivity, The specific heat capacity of soil at constant pressure; Soil leakage current The power density of heat production;

[0022] Arbitrary segment electrode at time step temperature The calculation formula is:

[0023]

[0024] in, For discrete coefficients, For the current time step, For the next time step; Electrode thermal conductivity, The electrode thermal diffusivity, For time steps The electrode temperature, For the radial region of soil Each node at time step The temperature.

[0025] Furthermore, the power density of heat generated by soil leakage current The formula for calculation is:

[0026]

[0027] in, For soil leakage current, For electrode length, For electrode temperature, Soil radial region node At electrode temperature resistivity under the given conditions Soil radial region node At electrode temperature The power density of heat generated by leakage current under certain conditions.

[0028] Furthermore, step 3 also includes calculating the grounding potential rise of each segment of the electrode, the calculation method being:

[0029]

[0030] in, Indicates the first The grounding potential rise of the segment electrode, For the first The segment electrode at time step The current, It is the first The sum of the internal resistance of the segment electrode and the leakage resistance of the radial region of the soil where it is located. Total current: .

[0031] Furthermore, based on time steps electrode temperature Update time step +1 electrode resistivity The update expression is:

[0032]

[0033] in, The initial temperature of the electrode. For the electrode at the initial temperature resistivity under the given conditions This is the temperature coefficient of electrode resistivity;

[0034] Based on time step Soil radial temperature distribution update time step +1 soil resistivity The update expression can be any of the following computational models:

[0035]

[0036]

[0037]

[0038] in, Soil radial region node At the initial temperature resistivity under the given conditions This is the temperature coefficient of soil resistivity.

[0039] A system based on the grounding resistance thermal-electric coupling prediction method described in any one of the above claims, comprising:

[0040] The parameter acquisition module is used to: acquire the inherent parameters and initial resistivity of the electrode, the inherent parameters and initial resistivity of the soil, the grounding fault parameters, and the initial temperature of the electrode and the soil;

[0041] The current calculation module is used for: time step-based calculation. Electrode resistivity and soil resistivity, calculation time step Electrode current and soil leakage current;

[0042] Thermo-electric coupling prediction module, used for: time step-based prediction The electrode current and soil leakage current were calculated using the finite difference method for the time step. Electrode temperature, soil radial temperature distribution, and grounding potential rise;

[0043] The resistivity update module is used for: time step-based updates. Electrode temperature and soil radial temperature distribution, update time step +1 electrode resistivity and soil resistivity;

[0044] The iterative judgment and output module is used to: determine the time step. +1 indicates the fault timeout has ended. If so, execute the current calculation module to continue calculating the time step. +1 for electrode and soil temperature; otherwise, output the electrode temperature and soil radial temperature distribution at each time step.

[0045] Beneficial effects

[0046] This invention provides a grounding resistance thermo-electric coupling prediction method and system applicable to various soil scenarios. By correlating the temperature dependence of the internal resistance of the electrode with the soil leakage resistance, it dynamically calculates the distribution of the current inside the electrode and the leakage current in the soil, and then synchronously updates the Joule heat generation rate and temperature field evolution, effectively avoiding the deviation caused by isolated calculation of the current field or temperature field, and improving the prediction accuracy.

[0047] This invention calculates the potential and temperature distribution of each electrode segment by segmenting the electrode and analyzing the current density. Based on the fact that the electrode segment in the low resistivity soil layer has a higher temperature, it accurately identifies the current concentration effect at the geometric discontinuity of the electrode (corners, exposed ends), the current injection point, and the contact area with the low resistivity soil. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the electrothermal coupling of a buried cylindrical conductor according to an embodiment of this application. Detailed Implementation

[0049] The embodiments of the present invention will be described in detail below. These embodiments are based on the technical solutions of the present invention and provide detailed implementation methods and specific operation processes to further explain the technical solutions of the present invention.

[0050] Example 1

[0051] This embodiment provides a grounding resistance thermal-electric coupling prediction method applicable to various soil scenarios. Through a cycle of "time segmentation - current calculation - temperature update - resistivity correction," it achieves dynamic coupling prediction of thermal and electrical parameters, including the following steps:

[0052] Step 1: Obtain the inherent parameters and initial resistivity of the electrodes, the inherent parameters and initial resistivity of the soil, the grounding fault parameters, and the initial temperatures of the electrodes and the soil.

[0053] Electrode inherent parameters include electrode structure (horizontal structure, vertical rod), material (e.g., copper, galvanized steel), and radius. ,length Thermal conductivity Soil intrinsic parameters include soil type (homogeneous, three-layered heterogeneous), thermal conductivity, etc. Thermal diffusivity Ground fault parameters include fault current. Failure time Initial electrode temperature and any node in the radial region of the soil initial temperature All are set to the temperature of the soil surface. Same; initial resistivity of electrodes That is, at the initial temperature Resistivity under certain conditions, i.e. ; any node in the radial region of the soil initial resistivity That is, at the initial temperature Resistivity under certain conditions, i.e. .

[0054] Step 2, based on time step Electrode resistivity and soil resistivity, calculation time step Electrode current and soil leakage current.

[0055] The specific calculation formula is as follows:

[0056]

[0057]

[0058] In the formula, For the first The segment electrode at time step The current; For the first The segment electrode at time step temperature, For the first The segment electrode at a temperature of resistivity at that time For the first The potential at the beginning of the segment electrode, For the first The resistance of the segment electrode, Electrode resistivity, Where is the electrode radius. The depth of the electrode embedding wire. For electrode length, For the first The radial region of the soil of the segment electrode Each node at time step The soil temperature; For the first The soil at the segment electrode at time step Leakage current, For the first The radial region of the soil at the segment electrode Each node is at a temperature of The resistivity at that time.

[0059] The method for calculating the potential at the beginning and end of each electrode segment is as follows: First, for any given segment... The current balance equation for the segment electrode is as follows:

[0060]

[0061] Summarized as follows:

[0062] (1)

[0063] Set boundary conditions, current injection point (j=1):

[0064] (2)

[0065] Where U is the fault voltage, and the terminal node (j=N):

[0066] (3)

[0067] Summarized as follows:

[0068] (4)

[0069] Combining the above formulas (1), (2), (3), and (4), we can calculate... .

[0070] In addition, the method for calculating the ground potential rise is as follows:

[0071]

[0072] in, Indicates the first The grounding potential rise of the segment electrode, For the first The segment electrode at time step The current, It is the first The sum of the internal resistance of the segment electrode and the leakage resistance of the radial region of the soil where it is located.

[0073] Step 3, based on time step The electrode current and soil leakage current were calculated using the finite difference method for the time step. Electrode temperature, soil radial temperature distribution, and grounding potential rise.

[0074] First, regarding the heat exchange process between the horizontally buried cylindrical grounding electrode and the surrounding soil, this embodiment establishes a set of heat conduction equations based on two types of Joule heat sources: heat generation inside the electrode and heat generation from soil leakage current.

[0075] (1) Heat generation inside the electrode: generated by the longitudinal current along the electrode axis (Through the internal resistivity of the electrode) ) is generated, with a power density of:

[0076]

[0077] in, Where is the electrode radius. The resistivity of the electrode is a temperature function. This represents the longitudinal current of the electrode (unit: A).

[0078] (2) Heat generation from soil leakage current: generated by leakage current on the electrode surface (Produced by flowing into the soil), with a power density of:

[0079]

[0080] in, For electrode length, Radial distance of soil (unit: m). The temperature-radial function of soil resistivity Soil leakage current (unit: A).

[0081] (3) Soil heat conduction equation: Based on the law of heat conduction, considering the transient heat exchange between the electrode and the soil, the following soil heat conduction equation is established (radial one-dimensional, applicable area). , The radius of the soil outer boundary is equal to the electrode burial depth. ):

[0082]

[0083] in, Radial temperature distribution of soil (unit: °C). Soil thermal diffusivity (unit: ), Soil thermal conductivity (unit: ), For soil density, The specific heat capacity of soil at constant pressure.

[0084] (4) Electrode-soil interface boundary conditions:

[0085]

[0086] in, Electrode thermal conductivity (unit: ), Electrode thermal diffusivity (unit: ), For electrode volume, The electrode surface area. The temperature at the electrode-soil interface is continuous.

[0087] (5) Soil outer boundary conditions:

[0088]

[0089] in, This represents the ambient temperature of the soil surface, with a default value of 20℃.

[0090] Then, the finite difference method is used to separate the heat dissipation and conduction equations to ensure the transient calculation accuracy and stability of short-term faults, and a discrete strategy is adopted.

[0091] (1) Spatial discretization: the radial region of the soil Divided into Segment, step length ,get Nodes ( , , ).

[0092] (2) Time discretization: The total fault time Divided into Segment, step length The convergence condition is met. To avoid numerical divergence.

[0093] (3) Discretize the heat conduction equations established above to obtain

[0094] ① Soil internal nodes Temperature update formula:

[0095]

[0096] in, For the radial region of soil Each node at time step temperature, ; The time step for dividing the fault period, The distance between adjacent nodes in the radial division of the soil. , Where is the electrode radius. The depth of the electrode burial wire; the nodes are numbered sequentially from the electrode surface to the ground surface. , For the first The distance from each node to the center line of the electrode; The soil thermal diffusivity, , For soil density, For soil thermal conductivity, The specific heat capacity of soil at constant pressure; The power density of heat generated by soil leakage current is calculated using the following formula:

[0097]

[0098] in, For soil leakage current, For electrode length, For electrode temperature, Soil radial region node At electrode temperature resistivity under the given conditions Soil radial region node At electrode temperature The power density of heat generated by leakage current under certain conditions.

[0099] ②Electrode temperature update formula, i.e., electrode-soil interface node Temperature update formula (combined with thermal continuity boundary):

[0100]

[0101] in, For the electrode at time step temperature, For discrete coefficients, For the current time step, For the next time step; Electrode thermal conductivity, The electrode thermal diffusivity, For time steps The electrode temperature, For the radial region of soil Each node at time step The temperature.

[0102] Step 4, based on time step Electrode temperature and soil radial temperature distribution, update time step +1 electrode resistivity and soil resistivity.

[0103] A differentiated model was adopted to address the resistivity-temperature characteristics of electrodes (metals) and soil, covering different electrode materials and soil types.

[0104] (1) Electrode resistivity model: The resistivity of a metal increases exponentially with increasing temperature. Based on time step... electrode temperature Update time step +1 electrode resistivity The formula is:

[0105]

[0106] in, Reference temperature (default 25°C) For the electrode at the reference temperature Resistivity under certain conditions (e.g., copper): Galvanized steel: , ), Temperature coefficient of resistivity (copper: 0.0039°C) -1 ), This is the temperature coefficient of electrode resistivity.

[0107] (2) Soil resistivity model: In this embodiment, three soil resistivity models are established to cover different nonlinear characteristics of soils. Soil resistivity decreases with increasing temperature. Based on time step Soil radial temperature distribution update time step For soil resistivity of +1, use any of the following calculation models:

[0108] ①Exponential Decrease Model: ;

[0109] ② Mixed function model: ;

[0110] ③ Reciprocal linear model: ;

[0111] in, Soil radial region node At reference temperature resistivity under the given conditions This refers to the temperature coefficient in various soil resistivity calculation models; in specific embodiments, it can be taken as a value of [value missing]. , , , , .

[0112] Step 5, if time step If the fault time has not ended by +1, return to step 2 and continue with the time step. +1 is used to calculate the electrode and soil temperatures; otherwise, the electrode temperature and soil radial temperature distribution at each time step are output.

[0113] Example 2

[0114] This embodiment performs thermo-electric coupling prediction of contact resistance in a homogeneous soil scenario. That is, the soil parameters of each node in the radial direction of the soil in Embodiment 1 are the same, and the temperature and resistivity of each different node are only related to the distance to the electrode. All steps are performed in the same way as in Embodiment 1.

[0115] Example 3

[0116] This embodiment performs thermo-electric coupling prediction of contact resistance under three different soil parameter scenarios. The temperature and resistivity of different nodes in each soil layer are related not only to the distance to the electrode but also to the soil parameters of the corresponding soil layer. This embodiment starts from the surface downwards, focusing on the first soil layer region. The initial resistivity is ; Second soil layer area The initial resistivity is This is a low-resistivity layer; the third soil layer area. initial resistivity This is a high-resistivity layer. For each soil layer, the resistivity temperature-dependent model from Example 1 was applied to update the resistivity based on temperature. All other steps were performed in the same manner as in Example 1.

[0117] Even within the same soil layer, the resistivity of different nodes may still differ. This is because:

[0118] In electrode segmentation modeling, each node (electrode segment) has an independent temperature. Soil resistivity varies with temperature, and the uneven temperature distribution at different locations leads to differences in resistivity across soil layers. This embodiment uses... This represents the resistivity of the k-th soil layer at a local temperature, rather than assuming it to be constant.

[0119] For homogeneous soil, leakage current is calculated based on the equivalent resistance between the electrode and the ground. For a length of... , radius is The cylindrical electrode has a resistance to ground of: The leakage current in homogeneous soil is: .

[0120] In this embodiment, the electrode is vertically inserted into the stratum, and the leakage current is distributed in layers. The vertical rod is in the soil layer. Leakage current It is inversely proportional to the resistivity of this layer, as shown in the formula:

[0121]

[0122] in, This is the total fault current. For the electrode in the soil layer Length, soil layer Temperature-dependent resistivity.

[0123] The above embodiments are preferred embodiments of this application. Those skilled in the art can make various changes or improvements based on them. Without departing from the overall concept of this application, these changes or improvements should fall within the scope of protection claimed in this application.

Claims

1. A grounding resistance thermo-electric coupling prediction method applicable to various soil scenarios, characterized in that, include: Step 1: Obtain the inherent parameters and initial resistivity of the electrodes, the inherent parameters and initial resistivity of the soil, the grounding fault parameters, and the initial temperatures of the electrodes and soil; Step 2, based on time step Electrode resistivity and soil resistivity, calculation time step Electrode current and soil leakage current; Step 3, based on time step The electrode current and soil leakage current were calculated using the finite difference method for the time step. Electrode temperature and soil radial temperature distribution; Step 4, based on time step Electrode temperature and soil radial temperature distribution, update time step +1 electrode resistivity and soil resistivity; Step 5, if time step If the fault time has not ended by +1, return to step 2 and continue with the time step. +1 is used to calculate the electrode and soil temperatures; otherwise, the electrode temperature and soil radial temperature distribution at each time step are output.

2. The method for predicting grounding resistance thermal-electric coupling according to claim 1, characterized in that, Electrode current is calculated based on electrode resistivity, and soil leakage current is calculated based on soil resistivity, respectively: ； ； In the formula, For the first The segment electrode at time step The current; For the first The segment electrode at time step temperature, For the first The segment electrode at a temperature of resistivity at that time For the first The potential at the beginning of the segment electrode, For the first The resistance of the segment electrode, Electrode resistivity, Where is the electrode radius. The depth of the electrode embedding wire. For electrode length, For the first The radial region of the soil of the segment electrode Each node at time step The soil temperature; For the first The soil at the segment electrode at time step Leakage current, For the first The radial region of the soil at the segment electrode Each node is at a temperature of The resistivity at that time.

3. The method for predicting grounding resistance thermal-electric coupling according to claim 1, characterized in that, The time step is calculated using the finite difference method. Electrode temperature and soil radial temperature distribution; Among them, the radial region of the soil at any segment electrode is the first Each node at time step temperature The calculation formula is: ； in, For the radial region of soil Each node at time step temperature, ; The time step for dividing the fault period, The distance between adjacent nodes in the radial division of the soil. , Where is the electrode radius. The depth of the electrode burial wire; the nodes are numbered sequentially from the electrode surface to the ground surface. , For the first The distance from each node to the center line of the electrode; The soil thermal diffusivity, , For soil density, For soil thermal conductivity, The specific heat capacity of soil at constant pressure; Soil leakage current The power density of heat production; Arbitrary segment electrode at time step temperature The calculation formula is: ； in, For discrete coefficients, For the current time step, For the next time step; Electrode thermal conductivity, The electrode thermal diffusivity, For time steps The electrode temperature, For the radial region of soil Each node at time step The temperature.

4. The method for predicting grounding resistance thermal-electric coupling according to claim 3, characterized in that, Power density of heat generated by soil leakage current The formula for calculation is: ； in, For soil leakage current, For electrode length, For electrode temperature, Soil radial region node At electrode temperature resistivity under the given conditions Soil radial region node At electrode temperature The power density of heat generated by leakage current under certain conditions.

5. The method for predicting grounding resistance thermal-electric coupling according to claim 1, characterized in that, Step 3 also includes calculating the grounding potential rise of each segment of the electrode. The calculation method is as follows: ； in, Indicates the first The grounding potential rise of the segment electrode, For the first The segment electrode at time step The current, It is the first The sum of the internal resistance of the segment electrode and the leakage resistance of the radial region of the soil where it is located.

6. The method for predicting grounding resistance thermal-electric coupling according to claim 1, characterized in that, Based on time step electrode temperature Update time step +1 electrode resistivity The update expression is: ； in, The initial temperature of the electrode. For the electrode at the initial temperature resistivity under the given conditions This is the temperature coefficient of electrode resistivity; Based on time step Soil radial temperature distribution update time step +1 soil resistivity The update expression can be any of the following computational models: ； ； ； in, Soil radial region node At the initial temperature resistivity under the given conditions This is the temperature coefficient of soil resistivity.

7. A system based on the grounding resistance thermo-electric coupling prediction method according to any one of claims 1-6, characterized in that, include: The parameter acquisition module is used to: acquire the inherent parameters and initial resistivity of the electrode, the inherent parameters and initial resistivity of the soil, the grounding fault parameters, and the initial temperature of the electrode and the soil; The current calculation module is used for: time step-based calculation. Electrode resistivity and soil resistivity, calculation time step Electrode current and soil leakage current; Thermo-electric coupling prediction module, used for: time step-based prediction The electrode current and soil leakage current were calculated using the finite difference method for the time step. Electrode temperature, soil radial temperature distribution, and grounding potential rise; The resistivity update module is used for: time step-based updates. Electrode temperature and soil radial temperature distribution, update time step +1 electrode resistivity and soil resistivity; The iterative judgment and output module is used to: determine the time step. +1 indicates the fault timeout has ended. If so, execute the current calculation module to continue calculating the time step. +1 for electrode and soil temperature; otherwise, output the electrode temperature and soil radial temperature distribution at each time step.

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