Ground potential rise calculation method and system considering grounding inter-electrode propagation time

Abstract

The invention discloses a ground potential rise calculation method and system considering the propagation time between grounding electrodes, and the method comprises the steps: calculating the self-grounding resistance of each grounding electrode, and the mutual grounding resistance and electric field propagation time between the grounding electrode and other grounding electrodes according to the structure parameter and soil parameter of the grounding electrode; wherein the number is the number of grounding electrodes of the grounding system; obtaining the current of each grounding electrode at the target moment and the current of other grounding electrodes at the moment; and calculating the ground potential rise of each grounding electrode at the target moment according to the calculated and obtained current of the self-grounding resistance and the mutual grounding resistance. According to the method, the earth inter-electrode electric field propagation time is incorporated into the grounding resistance model, so that the calculation precision of the ground potential rise is improved.

Description

Technical Field

[0001] This invention belongs to the field of power system grounding protection technology. Specifically, it relates to a method and system for calculating ground potential rise that takes into account the propagation time between grounding electrodes. It can be applied to the design and electromagnetic transient analysis of power facilities such as substations and transmission lines. Background Technology

[0002] In power systems, the grounding system is a core component ensuring the safe operation of equipment and the safety of personnel. Its design must simultaneously meet the dual requirements of personnel safety and equipment safety. Among these parameters, grounding resistance, as a key parameter for measuring the performance of the grounding system, directly determines the magnitude of ground potential rise (GPR) and the distribution pattern of surge current, playing a decisive role in the accuracy of surge analysis results.

[0003] Existing grounding resistance models are generally based on traditional circuit theory, and their core assumption is "no delay in electric field propagation," which ignores the difference in electric field propagation speed between soil and air media—the actual electric field propagation speed in soil (typically 50 m / μs–300 m / μs) is much lower than the speed of light in air (3 × 10⁻⁶ m / s). 8 When there is a certain distance between the grounding electrodes (GE), a non-negligible electric field propagation time will occur between the grounding electrodes.

[0004] When the grounding electrode is connected via an overhead lead or a grounding conductor in the soil, the difference in propagation time between the lead and the grounding conductor further exacerbates the response delay of the mutual grounding resistance. Traditional models, which do not consider this delay, lead to a critical problem in surge analysis: significant errors in GPR calculation during the surge front stage, especially when the surge front time is short, the error can reach 20%–50%.

[0005] Currently, although some simulation methods based on electromagnetic field theory can indirectly reflect propagation time, these methods require direct solution of Maxwell's equations, resulting in high computational complexity and time consumption. They are difficult to integrate into commonly used electromagnetic transient response (EMTP) programs and cannot meet the engineering and efficiency requirements of power system design. Therefore, there is an urgent need for a grounding resistance modeling method that balances computational accuracy and engineering practicality, and can accurately incorporate the propagation time between grounding electrodes. Summary of the Invention

[0006] This invention provides a method and system for calculating ground potential rise that takes into account the propagation time between grounding electrodes. By incorporating the propagation time of the electric field between grounding electrodes into the grounding resistance model, the calculation accuracy of ground potential rise is improved.

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

[0008] A method for calculating ground potential rise that considers the propagation time between grounding electrodes includes:

[0009] Step 1, for each grounding electrode The self-grounding resistance is calculated based on its structural parameters and soil parameters. and other grounding electrodes Inter-grounding resistance Electric field propagation time ;in, , , This refers to the number of grounding electrodes in the grounding system.

[0010] Step 2, obtain each grounding electrode In the target Current at any moment Other grounding electrodes exist Current at any moment ;

[0011] Step 3: Based on the self-grounding resistance and mutual grounding resistance obtained in Step 1, and the current obtained in Step 2, calculate the grounding electrode's resistance at the target. Ground potential rise at time:

[0012] (1)

[0013] in, For the first The ground potential rises at each grounding electrode.

[0014] Furthermore, the grounding structure parameters include: shape, size, number N, and inter-electrode distance; the soil parameters include resistivity and electric field propagation velocity.

[0015] Furthermore, the grounding electrode Self-grounding resistance The formula for calculation is:

[0016]

[0017] in, grounding electrode The grounding electrode structure parameters, This refers to soil resistivity.

[0018] Furthermore, based on the theory of electromagnetic induction and interelectrode distance... Soil resistivity Calculate the grounding electrode using the integral method With ground electrode between :

[0019]

[0020] in, The length of the induced grounding electrode. This is the radius of the grounding electrode.

[0021] Furthermore, the grounding electrode With ground electrode electric field propagation time between The calculation formula is:

[0022]

[0023] in, Indicates the grounding electrode With ground electrode The distance between them Let be the speed at which the electric field propagates.

[0024] Further, step 3 calculates the ground potential rise for each grounding electrode, specifically as follows:

[0025] Construct the equivalent circuit according to equation (1): diagonal matrix For N independent self-grounding resistance branches, the induced matrix For voltage or current sources with delay characteristics, the voltage value is the sum of the products of the mutual grounding resistance and the historical current of the other grounding electrode.

[0026] Set the simulation step size of the electromagnetic transient process simulation tool EMTP The equivalent circuit is imported into EMTP and the simulation is run. The output shows the position of each ground electrode in the target. The rise in ground potential at a given moment.

[0027] A ground potential rise calculation system that considers the propagation time between grounding electrodes includes:

[0028] The self-grounding resistance calculation module is used to calculate the resistance of each grounding electrode based on its structural parameters and soil parameters. Self-grounding resistance ;

[0029] The mutual grounding resistance calculation module is used to calculate the resistance between two different grounding electrodes based on their structural parameters and soil parameters. Inter-grounding resistance ;

[0030] The electric field propagation time calculation module is used to: calculate the propagation time based on two different grounding electrodes. Distance between and electric field propagation speed Calculate the two different grounding electrodes. electric field propagation time between ;

[0031] The current acquisition module is used to: acquire the current of each grounding electrode at the target time. Current at any moment Other grounding electrodes exist Current at any moment ;

[0032] The ground potential rise calculation module is used to: calculate the ground potential rise of each grounding electrode at the target grounding electrode according to the following expression, based on the self-grounding resistance, mutual grounding resistance, and current calculated and obtained by other modules. Ground potential rise at time:

[0033] (1)

[0034] in, For the first The ground potential rises at each grounding electrode.

[0035] Compared with the prior art, the present invention has the following technical effects:

[0036] (1) Higher accuracy: This invention incorporates the propagation time of the electric field between grounding electrodes into the grounding resistance model for the first time. The wavefront error between GPR and current is reduced from 20%-50% in the traditional grounding resistance model to below 8%, meeting the requirements of high-precision design.

[0037] (2) More practical for engineering: Through equivalent circuit conversion, it can be directly integrated into commonly used engineering simulation tools such as EMTP. The time for a single simulation is only 20s-100s, which is much lower than the electromagnetic field theory method (more than 1000s), and the efficiency is improved by 10-50 times.

[0038] (3) Better scalability: It adopts an N-order matrix structure, supports the calculation of ground potential rise of multiple grounding electrodes, and is suitable for different scale scenarios such as substations and transmission line tower foundations;

[0039] (4) Higher computational stability: Establish a "propagation speed - time step" adaptation rule to ensure and The matching performance is improved, the convergence of numerical calculation is enhanced, and the simulation divergence problem caused by improper step size is avoided;

[0040] (5) Better cost-effectiveness: An accurate grounding resistance model can avoid the problems of "over-protection" (such as increasing the number of grounding electrodes) or "insufficient protection" (such as omitting the coupling effect) in traditional design, reduce engineering costs by 15%-30%, and improve the safety of power system operation. Attached Figure Description

[0041] Figure 1 It is a mutual inductance voltage source model of a multi-grounding electrode grounding system to grounding electrode l.

[0042] Figure 2 It is a mutual inductance current source model of a multi-grounding electrode grounding system to grounding electrode k.

[0043] Figure 3 It is the grounding resistance that takes into account the propagation time of the electric field. Detailed Implementation

[0044] 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.

[0045] Example 1

[0046] This embodiment provides a method for calculating ground potential rise that considers the propagation time between grounding electrodes, including:

[0047] Step 1, for each grounding electrode The self-grounding resistance is calculated based on its structural parameters and soil parameters. and other grounding electrodes Inter-grounding resistance Electric field propagation time ;in, , , This refers to the number of grounding electrodes in the grounding system.

[0048] In this invention, the structural parameters of the grounding electrode include shape, size, and quantity. Interpolar distance Soil parameters include resistivity electric field propagation speed Voltage source parameters include type, amplitude, and waveform parameters.

[0049] (1) Calculate the self-grounding resistance. Calculate the resistance of any grounding electrode using the equipotential profile of the grounding electrode. Self-grounding resistance :

[0050]

[0051] in, grounding electrode The grounding electrode structure parameters, This refers to soil resistivity.

[0052] (2) Calculate the mutual grounding resistance. Based on the electromagnetic induction theory and using the integral method, calculate the resistance of different grounding electrodes. With ground electrode Inter-grounding resistance .

[0053] (3) Electric field propagation time. Based on the interelectrode distance. With soil electric field propagation speed Calculate the electric field propagation time between any two grounding electrodes. .

[0054] Step 2, obtain each grounding electrode In the target Current at any moment Other grounding electrodes exist Current at any moment .

[0055] Step 3: Based on the self-grounding resistance and mutual grounding resistance obtained in Step 1, and the current obtained in Step 2, calculate the grounding electrode's resistance at the target. The rise in ground potential at a given moment.

[0056] Based on the data obtained in steps 1 and 2, construct an N×N order grounding resistance matrix, with the diagonal elements representing self-grounding resistance terms. , [ [This is the Dirac function, representing the instantaneous response], with off-diagonal elements being the mutual ground resistance terms with propagation time. , [ [Characterizing delayed response]. The formula is shown below:

[0057]

[0058] in, For the first The ground potential rise of each grounding electrode. Further transformation of the above formula yields:

[0059]

[0060] The above transformation formula can convert the decomposed "self-grounding resistance diagonal matrix + mutual grounding resistance induced matrix" into an engineering-realizable equivalent circuit—the diagonal matrix corresponds to N independent self-grounding resistance branches, and the induced matrix corresponds to a voltage source or current source with delay characteristics. The voltage source value is the sum of the products of the mutual grounding resistance and the historical current of other grounding electrodes. For example... Figure 1 As shown.

[0061] This embodiment further incorporates the equivalent circuit into EMTP, based on propagation speed. Set the simulation time step (Value range 0.001μs—0.1μs), configure simulation parameters (total duration, output variables), run the simulation and output the ground potential rise of N grounding electrodes at the target time. Among them, the time step Based on the propagation speed of the electric field Adaptive settings: When the electric field propagation speed Smaller (e.g.) (When can be taken) When the electric field propagation speed Larger (e.g.) (When can be taken) ,make sure for This reduces numerical truncation error by 0.5 to 2 times.

[0062] This invention employs the delayed form of the Dirac function. The time response of the mutual grounding resistance is characterized by integrating the two-dimensional characteristics of "resistance value - propagation time" into matrix elements to achieve accurate quantification of the coupling effect between grounding electrodes. Then, the complex time delay term is transformed into a simple circuit structure of "resistance + voltage / current source" through matrix decomposition, avoiding direct solution of electromagnetic field equations, reducing computational complexity by more than 80%, and is compatible with the EMTP modeling specifications.

[0063] Example 2

[0064] 1. Implementation conditions.

[0065] Based on Example 1, the following implementation conditions are set:

[0066] (1) Grounding electrode parameters: rod-shaped grounding electrode, radius r=5mm, length L=2m, quantity N=2, distance between electrodes D 12 =2m;

[0067] (2) Soil parameters: The soil type is sandy soil, the resistivity is ρ=100Ω·m, and the electric field propagation speed is v=100m / μs;

[0068] (3) Voltage source parameters: an exponential function voltage source simulating ground electrode surge, ground electrode 1: Grounding electrode 2: ;

[0069] (4) Simulation parameters: time step Δt = 0.01 μs, total simulation time = 0.5 μs, series line impedance Zs1 = Zs2 = 10Ω.

[0070] 2. Implementation steps.

[0071] (1) Resistance calculation:

[0072] Self-grounding resistance Rs: Based on the equipotential profile of the reference rod-shaped grounding electrode, the structural parameters of the rod-shaped grounding electrode are calculated as follows: A = 1 / (2πL) × ln(4L / r-1) = 1 / (2π×2) × ln(4×2 / 0.005-1) ≈ 0.0318 × ln(1600-1) ≈ 0.0318 × 7.37 ≈ 0.234m -1 Rs1 =R s2 =ρA=100×0.234≈23.4Ω;

[0073] Inter-grounding resistance Rm: Based on electromagnetic induction theory, R is calculated through integration. m12 =ρ / (2πD 12 )×ln(4L / r-1)=100 / (2π×2)×7.37≈0.0796×7.37≈5.87Ω.

[0074] (2) Calculation of propagation time: τ 12 =D 12 / v=2m / (100m / μs)=0.02μs;

[0075] (3) Matrix construction: Construct a second-order grounding resistance matrix:

[0076]

[0077] (4) Generation of equivalent circuit:

[0078] First, decompose the matrix into a diagonal matrix. and induced matrix Then, construct the equivalent circuit of the voltage source: the two grounding electrodes are connected in series with a 23.4Ω self-grounding resistor, and each is connected in parallel with a voltage source - the voltage source of V1 is 5.87I2(t-0.02), and the voltage source of V2 is 5.87I1(t-0.02).

[0079] (5) EMTP Integration: The equivalent circuit is introduced into the EMTP, and voltage sources E1 and E2 are connected to series impedances Zs1 and Zs2. Δt = 0.01μs (τ 12 =0.02μs is twice Δt, indicating good matching), run the simulation.

[0080] 3. Implementation results.

[0081] (1) GPR wavefront error: Compared with the traditional propagation time-free model, the GPR calculation error in the wavefront stage (0-0.05μs) is reduced from 35% to below 8%;

[0082] (2) Computational efficiency: A single simulation takes about 20 seconds, which is only 1 / 50 of the finite difference method in the time domain (a numerical method that directly solves Maxwell's equations by simulating the propagation of electromagnetic fields), thus meeting the efficiency requirements of engineering design.

[0083] In other embodiments, besides the rod shape described above, the grounding electrode can also be plate-shaped, tubular, mesh-shaped, etc., requiring only adjustment of the calculation method for the structural constant A. If current source modeling in EMTP is more convenient, the voltage source equivalent circuit can be converted into a current source circuit using Norton's theorem. ,in, grounding electrode Equivalent current source after applying Norton's theorem; Number the grounding electrode. N is the total number of grounding electrodes. grounding electrode Self-grounding resistance, grounding electrode For the grounding electrode Inter-grounding resistance, such as Figure 2 As shown.

[0084] Because the propagation of an electric field in the soil takes time, even though the self-grounding resistance is theoretically constant in steady state, the effective grounding resistance changes over time during transient processes. Initially, the electric field only covers the area near the grounding electrode, resulting in a small effective grounding resistance; as time progresses, the electric field propagates over a wider area, and the resistance gradually increases to its steady-state value. Similarly, the mutual grounding resistance also exhibits time dependence and is significantly affected by the propagation speed of the electric field. Figure 3 Different curves correspond to different propagation velocities (v=50, 100, 300 m / μs), demonstrating how propagation velocity affects the transient process. This phenomenon explains why propagation time must be considered during the wavefront phase; otherwise, significant errors will occur.

[0085] 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 method for calculating ground potential rise considering the propagation time between grounding electrodes, characterized in that, include: Step 1, for each grounding electrode The self-grounding resistance is calculated based on its structural parameters and soil parameters. and other grounding electrodes Inter-grounding resistance Electric field propagation time ;in, , , This refers to the number of grounding electrodes in the grounding system. Step 2, obtain each grounding electrode In the target Current at any moment Other grounding electrodes exist Current at any moment ; Step 3: Based on the self-grounding resistance and mutual grounding resistance obtained in Step 1, and the current obtained in Step 2, calculate the grounding electrode's resistance at the target. Ground potential rise at time: （1） in, For the first The ground potential rises at each grounding electrode.

2. The method for calculating ground potential rise considering the propagation time between grounding electrodes according to claim 1, characterized in that, The grounding structure parameters include: shape, size, number N, and inter-electrode distance; the soil parameters include resistivity and electric field propagation velocity.

3. The method for calculating ground potential rise considering the propagation time between grounding electrodes according to claim 1, characterized in that, Grounding electrode Self-grounding resistance The formula for calculation is: ； in, grounding electrode The grounding electrode structure parameters, This refers to soil resistivity.

4. The method for calculating ground potential rise considering the propagation time between grounding electrodes according to claim 1, characterized in that, Based on electromagnetic induction theory and interelectrode distance Soil resistivity Calculate the grounding electrode using the integral method With ground electrode Between : ； in, The length of the induced grounding electrode. This is the radius of the grounding electrode.

5. The method for calculating ground potential rise considering the propagation time between grounding electrodes according to claim 1, characterized in that, Grounding electrode With ground electrode electric field propagation time between The calculation formula is: ； in, Indicates the grounding electrode With ground electrode The distance between them Let be the speed at which the electric field propagates.

6. The method for calculating ground potential rise considering the propagation time between grounding electrodes according to claim 1, characterized in that, Step 3 calculates the ground potential rise for each grounding electrode, specifically as follows: Construct the equivalent circuit according to equation (1): diagonal matrix For N independent self-grounding resistance branches, the induced matrix For voltage or current sources with delay characteristics, the voltage value is the sum of the products of the mutual grounding resistance and the historical current of the other grounding electrode. Set the simulation step size of the electromagnetic transient process simulation tool EMTP The equivalent circuit is imported into EMTP and the simulation is run. The output shows the position of each grounding electrode in the target. The rise in ground potential at a given moment.

7. A ground potential rise calculation system considering the propagation time between grounding electrodes, characterized in that, include: The self-grounding resistance calculation module is used to calculate the resistance of each grounding electrode based on its structural parameters and soil parameters. Self-grounding resistance ; The mutual grounding resistance calculation module is used to calculate the resistance between two different grounding electrodes based on their structural parameters and soil parameters. Inter-grounding resistance ; The electric field propagation time calculation module is used to: calculate the propagation time based on two different grounding electrodes. Distance between and electric field propagation speed Calculate the two different grounding electrodes. electric field propagation time between ; The current acquisition module is used to: acquire the current of each grounding electrode at the target time. Current at any moment Other grounding electrodes exist Current at any moment ; The ground potential rise calculation module is used to: calculate the ground potential rise of each grounding electrode at the target grounding electrode according to the following expression, based on the self-grounding resistance, mutual grounding resistance, and current calculated and obtained by other modules. Ground potential rise at time: （1） in, For the first The ground potential rises at each grounding electrode.

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