A method for constructing a simulation model of damage impedance characteristics of a closing resistor of a circuit breaker

Abstract

This invention provides a method for constructing a simulation model of the impedance characteristics of a circuit breaker closing resistor under damage conditions. It relates to the field of simulation model construction technology. First, a bidirectional electromagnetic-thermal-mechanical multiphysics coupled simulation model is established, including a resistor element, a clamping spring, connecting conductors, and an insulating medium. Nonlinear temperature-varying resistivity and contact resistance related to clamping force are set. The steady-state field distribution is first solved at different DC operating points, and then a swept-frequency small-signal excitation is superimposed to generate an impedance-frequency characteristic curve. Finally, the model parameters are calibrated by comparing with measured data from a healthy sample of the same model. This invention implements a joint solution strategy of DC bias steady-state and AC small-signal swept-frequency in the simulation, ensuring both the convergence stability of the strongly nonlinear electro-thermal coupling problem and realistically simulating the impedance response mechanism of the closing resistor under actual load conditions.

Description

Technical Field

[0001] This invention relates to the field of simulation model construction technology, specifically to a method for constructing a simulation model of the impedance characteristics of circuit breaker closing resistance damage. Background Technology

[0002] The closing resistor is a crucial component of high-voltage AC circuit breakers, primarily used to limit operational overvoltages during the closing process. Its performance directly impacts the stability of the power grid and the safe operation of the equipment. During long-term operation, the closing resistor may suffer damage due to electrothermal stress, mechanical vibration, or material aging, such as cracking of the resistor elements or deterioration of the contact interface. This alters its impedance characteristics, consequently affecting the circuit breaker's breaking performance and system reliability. Therefore, accurately assessing the damage state of the closing resistor and predicting its impedance behavior is of great significance for fault early warning and condition-based maintenance. Currently, the detection of closing resistors largely relies on offline testing or empirical judgment, making it difficult to achieve quantitative analysis and dynamic simulation of damage characteristics.

[0003] Traditional methods for assessing the condition of closing resistors primarily rely on periodic power outages or indirect inferences based on electrical tests. These methods fail to reflect the electro-thermal-mechanical coupling behavior of resistors under real-world operating conditions, particularly struggling to capture the impact of damage evolution on high-frequency impedance characteristics. Existing simulation models often rely on idealized assumptions, neglecting the nonlinear temperature variations of resistive materials, the changes in contact resistance with clamping force, and the frequency-dependent characteristics of insulating media (such as SF6), leading to significant discrepancies between simulation results and measured data. Furthermore, most models do not consider the influence of the DC bias operating point on impedance frequency characteristics, making it difficult to simulate the impedance response of closing resistors under different load currents or pre-excitation states during actual operation. Therefore, a high-precision impedance characteristic modeling method is urgently needed that integrates multi-physics coupling mechanisms, supports DC bias frequency sweep simulation, and is calibrated using measured data. This method would more realistically reflect the electrical behavior of closing resistors under damaged conditions, providing a reliable basis for condition monitoring and life prediction.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a method for constructing a simulation model of the impedance characteristics of circuit breaker closing resistance damage, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for constructing a simulation model of the impedance characteristics of circuit breaker closing resistance damage, comprising the following steps:

[0008] Step 1: Based on the design drawings of the closing resistor of the target circuit breaker, establish a simulation model including the resistor element, the clamping spring assembly, the connecting conductor, and the insulating medium; set the material properties for the simulation model, including the nonlinear resistivity of the resistor element as a function of temperature and the contact resistance between the electrodes as a function of clamping force; and define the bidirectional coupling relationship between the electromagnetic field and the thermal field in the simulation model.

[0009] Step 2: Set up a series of different DC operating points. For each DC operating point, based on the material properties of the simulation model and the bidirectional coupling relationship between the electromagnetic field and the thermal field, solve the steady-state field distribution of the simulation model under DC operating point excitation. While keeping the steady-state field unchanged, apply a preset frequency sweep test excitation. At different frequency sweep points of the frequency sweep test excitation, calculate the response current generated by the simulation model one by one, and calculate the impedance amplitude and phase at each frequency sweep point accordingly to generate the simulation impedance-frequency characteristic curve at the DC operating point.

[0010] Step 3: Obtain a sample of the closing resistor of a circuit breaker of the same model as the simulation model, and perform actual measurement under the same conditions to obtain the corresponding measured impedance-frequency characteristic curve; compare the simulated impedance-frequency characteristic curve with the measured impedance-frequency characteristic curve, and adjust the physical parameters in the simulation model so that the error between the two meets the convergence criterion, then the simulation model is considered to have completed calibration.

[0011] Furthermore, establishing the simulation model includes:

[0012] Based on the design drawings of the closing resistor in the 750kV voltage level tank circuit breaker, the physical dimensions of the overall structure of its resistor sheet stack are extracted, including the diameter, thickness, center hole diameter, design gap between sheets, and initial preload design value of the compression spring.

[0013] In finite element simulation software, a three-dimensional axisymmetric or full three-dimensional geometric model containing the overall structure of the resistor stack is constructed based on the physical dimensions to serve as the simulation model. The resistors are assembled in the actual stacking order, and the compression spring assembly simulates its axial compression function through equivalent stiffness elements or solid models. The connecting conductors include the metal flanges and connecting plates at both ends of the resistor string, and the insulating medium is SF6 gas filled in the tank.

[0014] Furthermore, setting material properties for the simulation model includes: setting a nonlinear function for the resistivity of the resistor material as a function of temperature, which is obtained by fitting experimental data on the thermoelectric properties of the resistor material; setting contact resistance for the contact interfaces between resistors and between resistors and electrodes; and setting physical properties of the insulating medium whose relative permittivity is related to air pressure and temperature.

[0015] Furthermore, the process of realizing the bidirectional coupling relationship is as follows: the multiphysics coupling module is enabled in the simulation solver, and the resistance loss and contact loss calculated by the electromagnetic field are used as volume heat sources or interface heat sources and fully mapped to the thermal field calculation domain; the global temperature distribution data of the model obtained by the thermal field calculation is fed back to the electromagnetic field calculation in real time.

[0016] Furthermore, a set of DC current values ​​are set as DC excitation, and each DC current value constitutes an independent DC operating point;

[0017] The process of solving the steady-state field distribution of the simulation model under the excitation of the DC operating point includes: applying the selected DC operating point to the simulation model; starting the bidirectional coupling calculation of the electromagnetic field and thermal field defined in the simulation model to perform DC steady-state solution; iterating the calculation until the current field, temperature field and structural stress field caused by thermal expansion in the simulation model converge, and obtaining the stable three-dimensional spatial field distribution below the DC operating point; wherein, the volume resistivity of the resistor and the contact resistance of the contact interface are jointly determined by the converged temperature field and structural stress field, and the steady-state field distribution is the current field distribution, temperature field distribution and structural stress field distribution after convergence.

[0018] Furthermore, the process of applying the preset frequency sweep test stimulus includes:

[0019] After completing the DC steady-state solution, the converged temperature field and structural stress field determined by the DC operating point are locked and used as the fixed background physical state.

[0020] A sinusoidal AC voltage signal is superimposed on the same port where DC excitation is applied in the simulation model for AC small-signal disturbance analysis. The frequency of this signal varies in steps within a preset high-frequency scanning range, thereby forming a series of discrete frequency scanning points. The peak amplitude of the sinusoidal AC voltage signal is no greater than 5% of its corresponding DC operating point voltage.

[0021] Calculate the impedance amplitude and phase at different frequencies, including: for each frequency sweep point, under a fixed background physical state, solve the electromagnetic response of the simulation model to the sinusoidal AC voltage signal;

[0022] Extract the complex forms of the AC voltage and AC current at the port, and calculate the AC signal impedance of the closing resistor at the frequency sweep point by dividing the phases, including its impedance amplitude and phase.

[0023] Furthermore, the actual measurement under the same conditions includes:

[0024] A joint test platform based on an impedance analyzer and a programmable DC power supply was built; a sample of the closing resistor of a circuit breaker of the same model was installed on the joint test platform to ensure that its electrical connection method is consistent with the port definition of the simulation model.

[0025] Apply the same DC excitation as set in step 2 as DC bias; under each stable DC bias state, use an impedance analyzer to perform impedance measurement within the same preset frequency sweep range to obtain the measured impedance-frequency characteristic curve at the DC operating point.

[0026] Key characteristic parameters selected for comparison include: impedance amplitude at characteristic frequency points in the low-frequency band, impedance amplitude and phase at resonant frequency points identified in the mid-frequency band, and the ratio of impedance amplitudes at two adjacent characteristic frequency points in the high-frequency band.

[0027] For each DC operating point, the values ​​of the simulated impedance-frequency response curve and the measured impedance-frequency response curve on key characteristic parameters are extracted, and the errors of each key characteristic parameter are calculated.

[0028] Furthermore, adjusting the physical parameters in the simulation model specifically includes:

[0029] The proportionality coefficient in the nonlinear resistivity-temperature relationship function of the resistor material, the empirical coefficient in the contact resistance-clamping force relationship function between electrodes, and the equivalent relative permittivity of SF6 insulating medium;

[0030] The adjustment is based on the calculated error direction and magnitude of each key characteristic parameter, and iterative correction is carried out with the goal of reducing the error between simulation and actual measurement on key characteristic parameters.

[0031] Furthermore, the characteristic frequency point in the low-frequency band is defined as: within the low-frequency band, at least one characteristic frequency point is selected to characterize the conductivity of the resistor sheet and the conductivity of the contact interface; the resonant frequency point identified in the mid-frequency band is defined as: within the mid-frequency band, the frequency point corresponding to when the impedance amplitude in the measured impedance-frequency characteristic curve reaches a local maximum or a phase zero crossing; the two adjacent characteristic frequency points in the high-frequency band are defined as: within the high-frequency band, two adjacent characteristic frequency points that can characterize the high-frequency skin effect or the dielectric polarization relaxation process are selected.

[0032] Furthermore, the convergence criterion includes two levels, with the following logic:

[0033] First-level criterion: Under all DC operating points, the average error of the key characteristic parameters between the simulated impedance-frequency response curve and the measured impedance-frequency response curve is lower than the corresponding preset error threshold.

[0034] Second-level criterion: Under all DC operating points, the correlation coefficient between the simulated impedance-frequency response curve and the measured impedance-frequency response curve is greater than the preset goodness-of-fit threshold throughout the entire frequency sweep range.

[0035] When both criteria are met simultaneously, the simulation model is considered to have completed calibration.

[0036] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0037] This invention effectively solves the problem that traditional methods cannot accurately reflect the impact of damage evolution on the impedance characteristics of closing resistors under real operating conditions by establishing a simulation model that integrates electromagnetic, thermal, and mechanical multi-physics fields in a two-way coupling. The simulation model not only considers the nonlinear temperature-dependent resistivity of the resistor element, the contact resistance dependent on contact pressure, and the frequency-dependent characteristics of the insulating medium, but also introduces a swept-frequency impedance simulation method based on a DC bias operating point, which can accurately simulate the impedance-frequency response of the closing resistor under different loads and pre-excitation states. System calibration with measured data from intact samples of the same model significantly improves the consistency between the simulation results and actual damage behavior, thus providing a highly reliable simulation tool for the condition assessment, damage diagnosis, and remaining life prediction of closing resistors. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0039] Figure 2 This is a schematic diagram comparing the simulated impedance amplitude with the measured impedance amplitude of this invention;

[0040] Figure 3 This is a schematic diagram comparing the simulated impedance phase with the measured impedance phase of this invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0042] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect.

[0043] Example:

[0044] Please see Figures 1 to 3 The present invention provides a technical solution:

[0045] A method for constructing a simulation model of the impedance characteristics of circuit breaker closing resistance damage, comprising the following steps:

[0046] Step 1: Based on the design drawings of the closing resistor of the target circuit breaker, establish a simulation model that includes the resistor element, the clamping spring assembly, the connecting conductor, and the insulating medium; set the material properties for the simulation model, including the nonlinear resistivity of the resistor element as a function of temperature and the contact resistance between the electrodes as a function of clamping force; and define the bidirectional coupling relationship between the electromagnetic field and the thermal field in the simulation model.

[0047] In this embodiment, establishing the simulation model includes:

[0048] Based on the design drawings of the closing resistor in a 750kV tank-type circuit breaker, extract the physical dimensions of the overall structure of its resistor stack; the specific dimensional parameters to be extracted include:

[0049] Resistor element: Diameter, thickness, center aperture, and edge chamfer dimensions of a single element.

[0050] Resistor sheet stack: total number of sheets, stacking order and design gap between sheets (if there are insulating pads, their thickness must be included).

[0051] Compression system: the model, quantity, initial preload design value, and spring stiffness coefficient of the compression springs.

[0052] Connection components: The metal flange, as the component that directly clamps and connects the two ends of the resistor array, requires the extraction of its geometric dimensions (such as outer diameter, inner diameter, and thickness), material grade (such as 6061 aluminum alloy, 304 stainless steel), and effective electrical contact area with the resistor array end faces. This contact area is a key parameter for calculating contact pressure distribution and contact resistance. The connecting plate (or conductive rod) refers to the conductor that connects the resistor array to the main circuit of the circuit breaker; its geometric dimensions (such as length, cross-sectional shape, and area), material grade (such as T2 copper), and connection method and contact area with the metal flange (such as surface contact via bolted connection) need to be extracted.

[0053] Insulating medium: The spatial arrangement of the resistor stack inside the tank of the circuit breaker, the filling range of the surrounding SF6 gas and the design value of the gas pressure.

[0054] After obtaining the above design parameters, a geometric model needs to be built in professional finite element simulation software (such as ANSYS Multiphysics, COMSOL Multiphysics). Since the closing resistor is usually a cylindrical symmetrical structure, it is recommended to build a three-dimensional axisymmetric model to balance computational efficiency and accuracy. If the internal structure of the resistor element (such as the central hole channel, non-uniform material) or the external connecting conductor is asymmetrical, a full three-dimensional geometric model needs to be built for accurate simulation.

[0055] For example, in the software, an axisymmetric section (rectangular or trapezoidal) representing a single resistor element is first created, and a tri-cone is generated through a rotation operation. Then, based on the stacking order and inter-element gaps, the entire resistor element stack is generated using array or copy functions. The clamping spring assembly can be modeled with different levels of precision depending on the simulation objective, such as:

[0056] Equivalent stiffness element method: A spring element (such as COMBIN14) is used to simulate the axial distance between the two ends of the resistor stack. Its stiffness is set to the total spring stiffness, and an initial preload displacement is applied. This method is computationally efficient and suitable for preliminary analyses focusing on electromagnetic-thermal coupling.

[0057] Solid model method: Accurately create a solid model of the spring's helix and assign it material properties (such as spring steel). This method can more realistically reflect the stress changes and possible plastic deformation of the spring under thermal expansion, and is suitable for in-depth research on the influence of mechanical stress on the contact state.

[0058] Metal flanges and connecting plates are modeled using solids, with materials of copper or aluminum. The modeling area for the insulating medium (SF6 gas) is the internal space of the tank containing the entire resistor stack and nearby conductors, with boundary conditions set to be insulated from the metal shell or ground.

[0059] Accurate setting of material properties is crucial for simulation realism, especially for accurately characterizing nonlinear properties. In this embodiment, setting material properties for the simulation model specifically includes:

[0060] A nonlinear function is set for the resistivity of the resistor material as a function of temperature. This function must be obtained by fitting experimental data on the thermoelectric properties of samples from the same batch of resistor material, rather than simply referencing data from a general material library. The specific fitting process is as follows:

[0061] First, a series of small currents are applied to the resistance material sample in a constant temperature chamber (to avoid self-heating), and the resistance values ​​are measured at different constant temperature points (e.g., from 20℃ to 500℃, with intervals of 20℃ to 50℃), and the resistivity is calculated. The collected raw resistance data needs to be preprocessed, including removing obvious outliers caused by transient fluctuations in the measuring instrument, and arithmetically averaging multiple measurements at each temperature point to improve data reliability.

[0062] The preprocessed (temperature, resistivity) data points are imported into mathematical tools (such as Origin, MATLAB) and fitted using nonlinear least squares. A common form of the fitting function is: or ;in, This represents the limiting resistivity coefficient extrapolated to infinite temperature. This represents the resistivity at temperature T, where T represents the absolute temperature or Celsius temperature. This represents the reference resistivity at a reference temperature of 20°C. , , , , , The coefficients to be fitted reflect the thermoelectric properties of the material itself.

[0063] This data illustrates that the resistor material is a material with a significant positive temperature coefficient or nonlinear characteristics. The purpose of obtaining this data is to accurately simulate the self-heating effect of the resistor in simulations, i.e., the temperature rise caused by current flow, which in turn changes the resistance, thus affecting the current distribution and loss; it directly characterizes the thermal stability of the resistor material itself.

[0064] Contact resistance is set at the contact interfaces between resistor elements and between resistor elements and electrodes. The value of this contact resistance, based on classical Hertzian contact theory or empirical formulas, is expressed as a function that decreases as the normal clamping force increases. A commonly used empirical formula is... ,in, Where F is the contact resistance and F is the normal clamping force. and m are empirical coefficients. The resistance is related to the properties of the contact materials (hardness, conductivity) and surface condition (roughness, oxide layer); it can be obtained by measuring the resistance of the contact pair under a known clamping force through a specialized contact resistance test, and then deriving it from the formula. m (should be lowercase) is typically between 0.5 and 1. For contacts dominated by plastic deformation, m is close to 1; for elastic deformation, m is close to 0.5; its specific value needs to be determined through fitting experimental data.

[0065] Contact resistance data reflects the quality of electrical contact in mechanical connections. This data is obtained to simulate current contraction effects and additional losses at the contact interface. It characterizes the effects of assembly process quality and contact surface aging (such as oxidation and relaxation) after long-term operation, and is a highly sensitive parameter in damage simulation.

[0066] To determine the relative permittivity of SF6 insulating medium With air pressure Temperature-related physical properties, i.e. The settings can be configured using the SF6 gas equation of state and empirical formulas for dielectric constant provided in the International Conference on Large Electric Systems (CIGRE) or IEC standards. For example, within a specific range, It can be approximated as being proportional to the gas density (determined by P and T). During simulation, simply input the circuit breaker's rated charging gas pressure and typical operating temperature range.

[0067] In this embodiment, defining the bidirectional coupling relationship between the electromagnetic field and the thermal field aims to establish an interaction mechanism between physical fields and simulate a real energy conversion process. The following settings are made in the multiphysics coupling module of the finite element software:

[0068] In the electromagnetic (AD / DC) module, the current conduction equation is solved to calculate the Joule loss (volume power density) inside the resistor and the contact resistance loss (interfacial heat flux density) at the contact interface. Subsequently, through the multiphysics coupling interface, these loss data are completely and conservedly mapped into the heat conduction module as a heat source.

[0069] After receiving a heat source, the heat conduction module calculates the three-dimensional transient or steady-state temperature distribution of the entire model (including the resistor, conductor, and gas). The calculated temperature field data is fed back to the electromagnetic field module in real time. The electromagnetic field module uses this temperature data to perform the following operations: based on the above calculations... The function updates the material resistivity of each resistor element; it calculates the structural stress caused by thermal expansion (if structural mechanical fields are included) based on the temperature field or directly estimates the contact pressure change using empirical formulas, and then calculates... The function updates the contact resistance value.

[0070] The above process is automatically iterated within a solution step until the residuals of all physical fields meet the convergence criteria, thus obtaining a self-consistent solution that considers the interactions. This bidirectional coupling relationship is a necessary condition for accurately simulating the steady-state condition (temperature saturation, thermal equilibrium) of the closing resistor at the DC operating point. Only when a frequency sweep signal is applied on this steady-state basis will its impedance response have physical reality.

[0071] Step 2: Set up a series of different DC operating points. For each DC operating point, based on the material properties of the simulation model and the bidirectional coupling relationship between the electromagnetic field and the thermal field, solve the steady-state field distribution of the simulation model under DC operating point excitation. While keeping the steady-state field unchanged, apply a preset frequency sweep test excitation. At different frequency sweep points of the frequency sweep test excitation, calculate the response current generated by the simulation model one by one, and calculate the impedance amplitude and phase at each frequency sweep point accordingly to generate the simulation impedance-frequency characteristic curve at the DC operating point.

[0072] In this embodiment, based on the rated operating current and overload capacity of the closing resistor of the target circuit breaker, a set of DC current values ​​covering its typical operating range are set as DC excitation. Each DC current value constitutes an independent DC operating point, used to simulate different steady-state heating and stress conditions of the closing resistor under different load currents or pre-excitation states.

[0073] To ensure that the simulation conditions fully cover the actual operating boundaries of the equipment, the selection of the DC operating point follows these principles:

[0074] First, there is the principle of range coverage. The lower limit of the DC current value is usually set to 0A (simulating cold state, no excitation condition), and the upper limit is set to 1.2 times the rated short-time overload current value (e.g., if the rated current is 1000A, then the upper limit is 1200A).

[0075] Secondly, the gradient encryption principle is applied, which involves increasing the density of DC operating point values ​​in the inflection point region of the resistivity-temperature curve of the resistor sheet and in the sensitive region of the contact resistance-compression force curve.

[0076] For example, for the closing resistor of a 750kV circuit breaker with a rated continuous current of 800A, the DC operating point sequence set in this embodiment is 0A, 200A, 400A, 600A, 800A (rated), 900A, 1000A (overload). This sequence includes both zero-load conditions and covers the entire range from light load to rated and then to overload.

[0077] When establishing a steady-state field simulation model of the closing resistor, either a DC voltage source or a DC current source can be used as the excitation. From a mathematical perspective of electromagnetic field solving, both can achieve steady-state field calculations through boundary condition loading. However, this embodiment explicitly selects DC current as the excitation source, a key technical choice based on the physical characteristics of the circuit breaker closing resistor under actual operating conditions and the simulation convergence requirements. Specifically, the physical basis for selecting DC current as the excitation is as follows:

[0078] The strong nonlinear current-voltage characteristics of the closing resistor: The material of the closing resistor (usually silicon carbide or nonlinear metal oxide) exhibits significant resistivity-temperature dependence and electric field strength dependence. If a DC voltage is used as the excitation, a small fluctuation in the voltage value can cause the current to change by several times or even orders of magnitude due to the nonlinearity of the resistance. This leads to drastic fluctuations in the heat source power density, making the electromagnetic-thermal bidirectional coupling iterative process prone to divergence; a steady-state field is difficult to establish, and the temperature field and current field oscillate alternately, failing to meet the convergence criterion.

[0079] In contrast, using direct current as excitation results in a rigidly clamped current value. Regardless of how the resistivity of the resistors changes with temperature, the total current flowing through the resistor stack remains constant at the user-defined value. This current source loading method forcibly constrains the total heat generation power of the system, allowing the Joule heat source to evolve smoothly during the iteration process, significantly improving the convergence speed and robustness of the bidirectional coupled solution.

[0080] Equivalent mapping characteristics to actual operating conditions: In actual power systems, the circuit breaker closing resistor is connected in series between the circuit breaker contacts. Under pre-insertion closing conditions, the current in this branch is determined by both the system voltage and the total impedance of the entire circuit; the resistor itself does not independently withstand a constant voltage. More importantly, in the scenario of impedance diagnosis due to closing resistor damage, the physical quantity of concern is the temperature rise-resistivity coupling state at different current levels, rather than the state at different terminal voltages. Therefore, establishing a DC operating point with current as the independent variable can more directly and physically simulate the heating degree of the resistor element under different load levels.

[0081] To further illustrate the advantages of choosing DC current in this embodiment, simulation tests were conducted using both voltage source excitation and current source excitation, as detailed below:

[0082] Control group A (excited by a voltage source): attempted to solve the problem at a medium voltage value (e.g., 500V); due to the strong coupling between resistivity and temperature, the solver required a very small damping factor, and the iteration steps exceeded 200 steps without convergence, and the port current exhibited non-physical oscillations.

[0083] Control group B (current source excitation): Under the corresponding current value (e.g., 800A), using the same mesh and solver settings, convergence was completed within 45 steps, the temperature field distribution was smooth, and the contact pressure distribution met the mechanical expectations.

[0084] Therefore, using DC current as excitation is not merely a simple difference in solver settings, but a key convergence control technique for strongly nonlinear electro-thermal coupled systems.

[0085] Of course, this embodiment does not exclude the possibility of using DC voltage excitation under specific conditions (such as when the resistor is completely cold or in the region of approximately linear resistivity). However, covering the entire operating range from rated to overload, especially when the resistor is in the high-temperature, highly nonlinear region, DC current excitation can ensure a stable and efficient steady-state field distribution.

[0086] The specific logic for solving the steady-state field distribution is as follows: apply the selected DC operating point to the port of the simulation model where material properties have been assigned and boundary conditions have been set; start the bidirectional coupling calculation of the electromagnetic field and thermal field defined in the simulation model to perform DC steady-state solution; iterate the calculation until the current field, temperature field and structural stress field caused by thermal expansion in the simulation model all converge.

[0087] To ensure the physical accuracy of the steady-state solution, this embodiment sets up a dual convergence criterion:

[0088] Energy error criterion: The relative residual between the total electromagnetic energy consumption and heat dissipation energy calculated by the solver in two consecutive iterations is less than [value missing]. .

[0089] Temperature change criterion: The maximum change in temperature value of all nodes in the model in two consecutive iterations is less than 0.01℃.

[0090] When both of the above criteria are met simultaneously, the steady-state field at the DC operating point is considered to have converged. At this time, the volume resistivity of the resistor is determined in real time by the converged temperature field distribution, and the contact resistance value of the contact interface is determined in real time by the converged structural stress field (compression force).

[0091] After completing the DC steady-state solution and confirming convergence, the converged temperature field and structural stress field determined by the DC operating point are locked. The steady-state field distribution is the converged current field distribution, temperature field distribution, and structural stress field distribution. This locking operation means that during subsequent frequency sweep analysis, the above physical fields are treated as an invariant background state. This is based on the small-signal perturbation assumption, that is, the superimposed AC test signal power is extremely small and insufficient to significantly change the existing steady-state heating and stress balance of the resistor.

[0092] A sinusoidal AC voltage signal is superimposed on the same port where DC excitation is applied in the simulation model, with the specific parameters set as follows:

[0093] Amplitude setting: The peak amplitude of the sinusoidal AC voltage signal shall not exceed 5% of its corresponding DC operating point voltage. For example, if the model terminal voltage is 100V at a certain DC operating point, the peak amplitude of the superimposed AC sweep frequency signal shall be set to ≤5V. This limiting is intended to ensure that the test signal is in the linear perturbation region and to avoid introducing nonlinear harmonic distortion.

[0094] Frequency range setting: The preset high-frequency scanning range is determined based on the equivalent circuit model characteristics of the closing resistor, typically covering the area from the low-frequency resistive region to the high-frequency capacitive region and the resonant frequency band. In this embodiment, the sweep range is specifically set to 20Hz to 2MHz, using a logarithmic coordinate stepping method, with 20 frequency sweep points evenly distributed within every ten octaves to balance low-frequency details and high-frequency coverage.

[0095] For each set sweep frequency point, the solver solves only the electromagnetic field equations under a fixed background physical field state (at which point the thermal field and structural field are frozen), and calculates the linear electromagnetic response of the sinusoidal perturbation voltage.

[0096] Specific calculation methods for impedance amplitude and phase:

[0097] Extract the AC voltage phasor at the port With alternating current phasor The impedance Z is in complex form, and its calculation formula is:

[0098]

[0099] in, Impedance magnitude, in Ω; For impedance phase, in degrees or rad; f is the frequency sweep point index; This represents the impedance value at the frequency sweep point f; This represents the AC voltage phasor at the frequency sweep point f. This represents the AC current phasor at the frequency sweep point f.

[0100] For example, at a certain DC operating point (e.g., 800A), the background state is locked. At the frequency sweep point f=50kHz, the simulated port AC voltage amplitude is 1V (peak), phase 0°, and AC current amplitude is 0.02A, phase -30°. Therefore:

[0101]

[0102]

[0103] That is, the impedance amplitude at this frequency is 50Ω and the phase is +30° (voltage leads current, exhibiting inductive properties).

[0104] Repeatedly calculate all preset frequency sweep points, and plot the impedance amplitude and phase of each point against the frequency to generate the impedance-frequency characteristic curve (including amplitude-frequency characteristic curve and phase-frequency characteristic curve) at the specific DC operating point.

[0105] After completing the frequency sweep calculation, the original acquired data is a set of data tables generated for each DC operating point, containing frequency, real part of impedance, and imaginary part of impedance (or directly impedance amplitude and phase).

[0106] To improve the accuracy and robustness of model calibration in subsequent steps and to eliminate singularities or non-physical oscillations that may occur in pure numerical simulations, the initial raw impedance data must be preprocessed. The preprocessing procedure is as follows:

[0107] Outlier Removal: In the extremely low frequency range (e.g., <1Hz, if applicable) or near the extremely high frequency resonant point of the simulation model, isolated discontinuities (impedance jumps or phase reversals) may occur due to the ill-conditioned matrix of the numerical solver. A sliding window averaging filter method is used. The window length is set to 5 consecutive frequency points, and the local mean and standard deviation of the impedance amplitude within the window are calculated. If the amplitude at the center frequency point deviates from the mean by more than 3 times the standard deviation, it is identified as an outlier and replaced with the median value within the window.

[0108] Smoothing and Noise Reduction: Although the simulation itself has no measurement noise, in highly nonlinear multiphysics coupling solutions, iterative convergence tolerance can cause small sawtooth fluctuations in the impedance curve. A Savitzky-Golay convolution smoothing algorithm is employed. In this embodiment, the polynomial order is set to 3, and the window width is 7. Compared to the ordinary moving average method, this algorithm better preserves the width and height characteristics of the resonance peaks in the impedance spectrum, avoiding feature distortion.

[0109] Data Interpolation and Normalization: To ensure that the simulation data at different DC operating points correspond strictly on the frequency axis for easy comparison, the original swept frequency data needs to be mapped to a unified standard frequency vector through cubic spline interpolation (e.g., 201 logarithmically uniformly distributed frequency points from 20Hz to 2MHz). To eliminate the significant differences in the absolute magnitude of amplitudes caused by differences in DC resistance at different DC operating points, the impedance amplitude curve can be normalized. The normalization reference value is the impedance amplitude at 1kHz at the DC operating point. Dividing the amplitudes of all frequency points by this reference value yields the relative impedance change rate.

[0110] Step 3: Obtain a sample of the closing resistor of a circuit breaker of the same model as the simulation model, and perform actual measurement under the same conditions to obtain the corresponding measured impedance-frequency characteristic curve; compare the simulated impedance-frequency characteristic curve with the measured impedance-frequency characteristic curve, and adjust the physical parameters in the simulation model so that the error between the two meets the convergence criterion, then the simulation model is considered to have completed calibration.

[0111] The resistivity of the closing resistor material (typically silicon carbide or zinc oxide nonlinear resistors) exhibits strong temperature dependence, and the contact resistance changes with the clamping force caused by thermal expansion. Different DC load currents result in different steady-state temperature and stress fields within the resistor stack. Calibration under only one operating condition cannot guarantee the model's generalization ability under other thermo-mechanical conditions. Therefore, this embodiment covers multiple DC operating points from no-load to rated overload to ensure the model's effectiveness across the entire operating range.

[0112] In this embodiment, the actual measurement under the same conditions specifically includes:

[0113] A joint test platform was built based on a high-precision wideband impedance analyzer (frequency range covering 20Hz to 10MHz) and a programmable high-power DC power supply (with constant current output and ripple suppression function); the closing resistor samples of the same model of intact circuit breaker were installed on the joint test platform to ensure that their electrical connection method is consistent with the port definition of the simulation model (for example, the high voltage end is connected to the upper flange of the resistor stack, the low voltage end is connected to the lower flange, and the shell is grounded and shielded).

[0114] To eliminate the influence of ambient temperature and humidity on SF6 insulation dielectric and resistor sheet material, the test should be carried out in a constant temperature and humidity laboratory environment (temperature 20℃±2℃, relative humidity <60%), and the sample should be left to stand in this environment for no less than 2 hours before the test.

[0115] The same DC excitation set in step 2 is applied sequentially as a DC bias. Under each stable DC bias state, when the low-frequency impedance value displayed by the impedance analyzer changes by less than 0.5% within 1 minute, the system is considered to have reached thermal steady state. Impedance is then measured using the impedance analyzer within the same preset frequency sweep range to obtain the measured impedance-frequency characteristic curve (including impedance amplitude) at the DC operating point. And phase, sampling points are logarithmically swept, with no less than 50 points per decathlon).

[0116] Key characteristic parameters selected for comparison include: impedance amplitude at characteristic frequency points in the low-frequency band, impedance amplitude and phase at resonant frequency points identified in the mid-frequency band, and the ratio of impedance amplitudes at two adjacent characteristic frequency points in the high-frequency band. Based on the typical dimensions and material properties of the circuit breaker closing resistor, its impedance-frequency characteristic curve exhibits different physical mechanisms in different frequency bands. Therefore, this invention divides the frequency bands into: a low-frequency band ranging from 1kHz to 10kHz, a mid-frequency band ranging from 100kHz to 500kHz, and a high-frequency band ranging from 1MHz to 2MHz.

[0117] The impedance-frequency characteristic of the closing resistor is a comprehensive reflection of its electromagnetic behavior across the entire frequency band. Relying solely on the impedance value at a single frequency point (such as power frequency resistance) cannot reveal the variations in distributed parameters within the structure. This method divides the frequency band into three regions: low frequency, mid frequency, and high frequency, each corresponding to a different physical mechanism.

[0118] Low frequency band (1kHz-10kHz): mainly reflects the overall DC resistance value of the resistor stack and the initial appearance of the current skin effect; the impedance amplitude at the characteristic frequency point is directly related to the sum of the resistor body resistance and the contact resistance at the current temperature.

[0119] Mid-frequency band (100kHz-500kHz): Parallel resonance peaks caused by the equivalent capacitance of the resistor and the distributed inductance of the circuit usually appear in this frequency band; the amplitude and phase of the resonance point are extremely sensitive to the dielectric constant of the resistor material, the distributed capacitance between the sheets, and the stray inductance of the connecting conductors.

[0120] High frequency band (1MHz-2MHz): mainly reflects the propagation effect of electromagnetic waves in the stacked structure of resistors; the ratio of impedance amplitude at adjacent characteristic frequency points can effectively characterize the consistency of axial distribution parameters of resistors, and indirectly reflect whether the clamping force distribution is uniform or whether there are local defects.

[0121] The impedance amplitude at a characteristic frequency point in the low-frequency band is defined as follows: within the low-frequency range, at least one characteristic frequency point is selected to characterize the conductivity of the resistor sheet and the conductivity of the contact interface, and the magnitude of the impedance amplitude at that frequency point is extracted. Preferably, a frequency point of 10kHz is selected. At 10kHz, the inductive reactance component has not yet played a dominant role, and the measurement is minimally affected by power frequency interference. Furthermore, this frequency point exhibits high sensitivity to resistance changes caused by temperature.

[0122] The resonant frequency point identified in the mid-frequency band is defined as: the frequency point corresponding to the local maximum value or phase zero-crossing point of the measured impedance-frequency characteristic curve within the mid-frequency range; this frequency point is used to characterize the parallel or series resonant characteristics of distributed inductance and stray capacitance in the simulation model. Preferably, the impedance amplitude within this frequency band is specifically extracted. Frequency at maximum value And the maximum impedance amplitude corresponding to that frequency point. And phase. This resonance peak usually corresponds to the parallel resonance of the equivalent inductance L and the distributed capacitance C, and its resonant frequency is... The change directly reflects the change in capacitance parameters.

[0123] The ratio of impedance amplitudes at two adjacent characteristic frequency points in the high-frequency band Defined as follows: Within the high-frequency range, select two adjacent characteristic frequency points that can characterize the high-frequency skin effect or dielectric polarization relaxation process; calculate the ratio of the impedance amplitudes at these two points to reflect the changes in high-frequency energy loss characteristics. Preferably, the ratio of the impedance amplitudes at 1.5MHz and 1.0MHz is selected, i.e., |Z|@1.5MHz / |Z|@1.0MHz; |Z|@1.5MHz represents the impedance amplitude presented at the closing resistance port of the circuit breaker under test under sinusoidal AC small-signal excitation at a frequency of 1.5MHz, and |Z|@1.0MHz represents the impedance amplitude presented at the closing resistance port of the circuit breaker under test under sinusoidal AC small-signal excitation at a frequency of 1MHz. In the high-frequency range, the impedance characteristics are mainly dominated by the transmission line effect, and this ratio can reflect the uniformity of voltage distribution along the axial direction of the resistor stack.

[0124] For each DC operating point, the values ​​of the simulated impedance-frequency response curve and the measured impedance-frequency response curve at key characteristic parameters are extracted, and the error of each key characteristic parameter is calculated. This error can be either absolute or relative.

[0125] Absolute error: (Unit: Ω)

[0126] Relative error:

[0127] in, Indicates absolute error. Indicates relative error; This represents the value of a key characteristic parameter of the simulated impedance-frequency response curve at a specific DC operating point. This indicates the values ​​of key characteristic parameters corresponding to the measured impedance-frequency response curve at the same DC operating point as the simulation.

[0128] In this embodiment, adjusting the physical parameters in the simulation model specifically includes:

[0129] The proportionality coefficient in the nonlinear resistivity-temperature relationship function of the resistor material: In this embodiment, the mathematical expression obtained by fitting experimental thermoelectric performance data disclosed in step 1 is used. Based on the measured resistivity data points of the resistor material (preferably a silicon carbide nonlinear resistor in this embodiment) at different temperatures, a nonlinear least squares method is used for fitting. To accommodate different material properties and fitting accuracy requirements, this embodiment provides two preferred function forms as alternatives, and the optimal fitting model for the current batch of materials is determined using the Akaike information criterion or the Bayesian information criterion before actual calibration.

[0130] The exponential-linear hybrid model is applicable to high-voltage silicon carbide materials with non-monotonic resistivity changes over a wide temperature range. The activation energy-related temperature coefficient characterizes the sensitivity of carrier thermal excitation to the improvement of conductivity; A is the high-temperature linear drift coefficient, used to compensate for the linear change component introduced by mechanisms such as lattice scattering in the high-temperature range.

[0131] The polynomial model is suitable for zinc oxide materials with a narrow temperature range and low nonlinearity. It is a first-order temperature coefficient, which dominates the linear change trend of resistivity with temperature; It is a second-order temperature coefficient used to capture the correction term for nonlinear curvature in the high-temperature range.

[0132] In both models, not all coefficients are free correction variables. To ensure the physical rationality of the correction process and the identifiability of the parameters, this embodiment adopts a hierarchical calibration strategy. , , , The initial values ​​are predetermined by the factory data points provided by the material supplier or by independently conducted four-probe tests on micro-samples. These coefficients reflect the solid-state physical nature of the material, changing very little under normal aging or minor damage conditions. They are locked during calibration and not corrected to avoid parameter drift that could distort the physical meaning. The focus is on correcting the high-temperature line drift coefficient A (if an exponential-linear hybrid model is used) or the second-order temperature coefficient. (If a polynomial model is used).

[0133] During long-term operation, the main aging modes of circuit breaker closing resistors include degradation of the grain boundary characteristics of the resistor element and oxidation of the electrode contacts. These microstructural changes do not significantly alter the activation energy of the material in terms of macroscopic electrothermal properties. ) or reference resistivity ( Instead of altering the resistivity, it changes the nonlinear bending of the resistivity as temperature increases. That is, the resistivity of an aged resistor decreases more rapidly at high temperatures. This behavior is precisely due to… or These are characterized by the coefficients of these two higher-order terms. Therefore, the correction... or Essentially, it's a digital calibration of material aging. Furthermore, the low-frequency impedance amplitude (10kHz) is sensitive to the rate of temperature change. If the error between simulation and measurement shows a deviation that increases linearly with increasing DC bias current (temperature increase), then adjustment should be prioritized. (Linear coefficient); if the error shows a deviation that increases rapidly with increasing temperature (i.e., the slope of the curve deviates significantly), then priority should be given to adjustment. (Second-order coefficients) or (Linear drift coefficient), this decoupling logic ensures the physical directionality of parameter correction.

[0134] The adjustment is primarily based on the relative variation trend of the 10kHz impedance amplitude at different DC operating points. The minimum DC operating point is selected (e.g., 5A, where the temperature rise of the resistor element is <5K, and the thermal effect can be ignored). The contact resistance parameters in the simulation model are adjusted to ensure that the relative error between the simulated and measured 10kHz impedance values ​​at this point is <1%. This is the default setting. Accuracy. Apply increasing DC operating points sequentially (e.g., 20A, 40A, 60A, 80A), record the measured 10kHz impedance value and the simulated value at each point, and calculate the relative attenuation deviation of impedance as current changes.

[0135] For example: Assuming a polynomial model is used initial parameters , , (Factory settings). At an 80A DC operating point, the average temperature of the resistor stack, measured by infrared thermal imaging, is 120℃. The measured impedance at 10kHz is 520Ω. Initial usage... The simulation calculated the impedance at 10kHz to be 560Ω at the same temperature (20℃), which is too high. Further physical deduction revealed that the high simulated impedance led to an inflated simulated resistivity. This, in turn, indicated that the resistivity calculated by the model did not decrease with temperature quickly enough. Therefore, it was concluded that to enhance the temperature sensitivity of the resistivity, the second-order temperature coefficient needed to be increased. (For the exponential-linear model, increase the high-temperature linear drift coefficient A). Depend on Gradually increase to The bidirectional coupled steady-state field at the 80A DC operating point was resolved (at which point the temperature field may slightly redistribute due to resistivity changes, requiring iterative convergence), yielding a new simulated impedance of 535Ω. After 3 iterations, Revised to At that time, the simulated impedance was 522Ω, and the relative error between it and the measured impedance of 520Ω entered the first-level criterion threshold, thus completing the calibration.

[0136] Revised or Whether the value is reasonable needs to be verified through extrapolation. In this embodiment, after completing the calibration of the 0 to 80A operating points, an additional verification point (e.g., 100A, simulating a short-term overload) that was not involved in the calibration is applied. If the error between the simulated impedance and the measured impedance can still be kept within 5% at this extrapolation point, it proves that the corrected parameters not only fit the training data, but also more realistically reflect the physical change trend of the material constitutive relation, rather than simply numerical fitting. If extrapolation fails, it is necessary to re-evaluate whether the selected function form (polynomial or exponential-linear model) is suitable for this batch of materials, and switch models according to the AIC / BIC criteria.

[0137] Empirical coefficients in the electrode contact resistance-clamping force relationship function: In this embodiment, a reduced model based on Hertzian contact theory is used. The main combination is the low-frequency impedance and resonant frequency. Make a judgment. Increased contact resistance will increase low-frequency losses (slight increase in amplitude), but more significantly, the equivalent capacitance increases with increasing clamping force (resulting in a decrease in gap), leading to... The impedance amplitude and resonant frequency presented at the closing resistance port of the circuit breaker under test are obtained by simultaneously fitting a sinusoidal AC small-signal excitation frequency of 10kHz. It can be uniquely determined And the value of m.

[0138] The equivalent relative permittivity of SF6 insulation: In the simulation model, this function is fixed in the form of an interpolation table or analytical expression. It is not directly modified during the calibration phase. It's not about numbers, but about decisions. The values ​​are calibrated using minor correction coefficients in the input state variables or function models.

[0139] Given that SF6 is a stable electronegative gas with good macroscopic repeatability of its dielectric constant, two types of uncertainties still exist in practical engineering applications and need to be addressed during the calibration process:

[0140] Measurement bias and spatial unevenness of pressure / temperature sensors: The rated inflation pressure and average temperature input to the simulation model differ from the actual gas state in the local area around the resistor stack.

[0141] The influence of perturbation factors: trace impurities or decomposition products that may exist in the actual gas (in trace amounts in intact equipment), as well as the extremely thin adsorption layer at the gas-solid insulation interface, will have a slight effect on the equivalent dielectric constant at high frequencies.

[0142] Therefore, in this embodiment, the calibration of the dielectric constant of SF6 is not a rewrite. This physical law is not addressed by introducing a dimensionless correction factor to achieve a fine match between the model and actual measurements:

[0143] Define the dielectric constant correction factor This makes the relative permittivity used in the simulation model for electromagnetic field calculations... ; It is a dimensionless coefficient that fluctuates in a small range around 1 (e.g., 0.95-1.05).

[0144] In this embodiment, The adjustment is mainly based on the error of the high-frequency impedance ratio (i.e., |Z|@1.5MHz / |Z|@1.0MHz). In the high-frequency range (greater than 1MHz), the electrical behavior of the resistor stack no longer exhibits a concentrated resistor-capacitor network, but rather the characteristics of a lossy transmission line. At this point, the phase velocity of the electromagnetic wave propagating along the axis of the resistor stack... (c is the speed of light), and the characteristic impedance is also related to... Related. Therefore, Even small changes can significantly alter the oscillation period and standing wave ratio of the impedance spectrum in the high-frequency band, specifically manifested as a change in the ratio of impedance amplitudes at a specific frequency point.

[0145] If the simulation calculation A value higher than the measured value (i.e., the high-frequency attenuation is too slow in the simulation, and the fluctuations are more gradual) indicates that the electromagnetic wave propagation speed in the simulation model is too fast. The setting is too small. In this case, the correction factor should be increased. Adjust in a direction greater than 1 (e.g., increase from 1.00 to 1.02). Conversely, if the simulation... If it is lower than the measured value, then reduce it. .

[0146] Correction coefficient The calibration range is strictly limited to between 0.95 and 1.05. This limit is based on the fact that the relative permittivity of SF6 at typical operating pressures in high-voltage circuit breakers (0.4 to 0.6 MPa) is typically between 1.002 and 1.0035, very close to 1. Any correction exceeding ±5% indicates an error in the model input (e.g., incorrect pressure units) or a serious defect in the equipment (e.g., severely substandard gas purity), outside the normal calibration range. This boundary constraint ensures the physical accuracy of the model parameters, preventing the algorithm from deriving non-physical parameter values ​​for the purpose of fitting curves.

[0147] For example, a high-frequency impedance test was performed at a certain DC operating point (80A), and the measured impedance was... The measured value is 1.25. In the initial simulation, the input gas pressure was 0.5 MPa and the temperature was 333 K (calculated from the thermal field). The relative permittivity of SF6 gas was set using a simplified engineering formula based on the Clausius-Mosotti equation (refer to the International Conference on Large Electric Systems Technical Manual standard), and the calculated value was... At this time, set ,Right now Simulation results .

[0148] Simulation results The value was 1.19, lower than the measured value. This indicates that the equivalent dielectric constant in the high-frequency band of the simulation model is too large, which leads to an enhanced distributed capacitance effect and the attenuation trend of impedance amplitude with increasing frequency is replaced by the transition method.

[0149] Sensitivity analysis based on pre-simulation confirmed that, under this model structure, the equivalent relative permittivity... Ratio of high frequency impedance They are negatively correlated, that is Enlargement will lead to decline.

[0150] Therefore, in order to make simulation The value should be appropriately reduced when increasing from 1.19 to 1.25. .

[0151] Then The value was adjusted from 1 to 0.98. Although this value is less than 1, it is within the ±5% allowable range of the correction factor and can be considered an effective compensation for theoretical calculations or sensor input deviations. After resimulation, The value changes to 1.24, the error falls within the preset threshold (≤5%), and the calibration is complete.

[0152] In this embodiment, the two-level convergence criterion logic is set as follows:

[0153] First-level criterion: At all DC operating points, the average error of the key characteristic parameters between the simulated impedance-frequency response curve and the measured impedance-frequency response curve is lower than their corresponding preset error threshold.

[0154] The low-frequency impedance amplitude error threshold is set to ≤3%. This threshold is derived from the International Conference on Large Electric Systems' recommended standard for the repeatability of resistance measurements of high-voltage electrical equipment (generally requiring a deviation of less than 3% between two measurements of the same equipment). Furthermore, considering that the impedance analyzer used in this test platform has a basic accuracy of ±5% at 10kHz, and that the uncertainty introduced by DC current ripple is approximately ±1%, the 3% threshold eliminates measurement noise while providing sufficient sensitivity to model parameter deviations.

[0155] The resonant frequency error threshold is set to ≤2%. Frequency measurements typically have extremely high accuracy (crystal oscillator reference, error <0.01%), but the extraction of the resonant peak is affected by the sweep step size. In this scheme, the sweep step size is refined to 1 / 12 octave in the resonant region, with a frequency resolution better than 0.5%. The 2% threshold fully considers the peak location error caused by the frequency sweep discretization, while ensuring that the calculation error of the equivalent capacitance is controlled within 4%.

[0156] The impedance ratio error threshold for the high-frequency band is set to ≤5%. The impedance amplitude in the high-frequency band is significantly affected by parasitic parameters of the measurement fixture; even after calibration, the residual error is typically higher than in the low-frequency band. According to IEC 60060-1 guidelines on measurement uncertainty of high-frequency components in high-voltage testing, 5% is set as an acceptable deviation range for engineering applications.

[0157] Second-level criterion: At all DC operating points, the correlation coefficient between the simulated impedance-frequency response curve and the measured impedance-frequency response curve is greater than the preset goodness-of-fit threshold throughout the entire frequency sweep range.

[0158] The goodness-of-fit threshold was set to 0.98. The square of the Pearson correlation coefficient was used for calculation. In practice, the simulated and measured impedance amplitudes were plotted on logarithmic scales to mitigate the weight imbalance caused by excessive amplitude differences. Setting the goodness-of-fit threshold to 0.98 means that 98% of the variation in the simulated curve can be explained by the measured data, with only 2% of the variation belonging to unexplained residuals. This quantitative indicator rigorously ensures that the dynamic response characteristics of the simulation model across the entire frequency band are highly consistent with the physical prototype, rather than simply matching a few isolated feature points.

[0159] When both criteria are met simultaneously, the simulation model is considered to have completed calibration. After calibration, the final corrected material parameters should be written into the model parameter table, and this version should be fixed as the final simulation model.

[0160] This embodiment takes a intact closing resistor in a 750 kV tank-type circuit breaker as the research object. Under the rated DC operating point of 800 A, multi-physics coupling simulation and high-precision wideband impedance measurement were carried out to obtain its full-band impedance characteristic data. The simulation model was strictly established according to the closing resistor design drawings, fully considering the nonlinear temperature-dependent resistivity of the resistor element, the relationship between contact resistance and clamping force, and the bidirectional coupling mechanism of electromagnetic and thermal fields. After completing the steady-state field solution, the background physical state was locked, and a sinusoidal sweep frequency small signal excitation with a peak amplitude not exceeding 5% of the DC operating point voltage was applied. The sweep frequency range covered 20 Hz to 2 MHz, and the impedance amplitude and phase response were obtained using a logarithmic step method. The actual measurement relied on a joint test platform based on an impedance analyzer and a programmable DC power supply. Under the same ambient temperature and DC bias conditions, point-by-point sweep frequency measurements were performed on intact samples of the same model, with a sampling density of not less than 50 frequency points per ten octaves. Table 1 presents the specific values ​​of the simulated and measured impedance amplitude and phase as a function of frequency at this DC operating point. The two values ​​are strictly aligned on the frequency axis and have undergone preprocessing steps such as outlier removal, smoothing and noise reduction, and cubic spline interpolation to ensure data quality and comparability. Details are as follows:

[0161] Table 1: Relevant data of simulated and measured impedance-frequency response curves

[0162]

[0163] Based on Table 1 above, Figure 2 and Figure 3The comparison results of the simulated and measured impedance characteristics show that the simulation model constructed in this embodiment has extremely high consistency with the measured response of the physical prototype over a wide frequency range. As can be seen from the amplitude-frequency response curves, the simulated and measured impedance amplitudes almost completely overlap across the entire frequency band. The amplitude variation trends, resonance peak positions, and steepness are highly consistent in the resistive-dominated segment in the low-frequency range of 1kHz to 10kHz, the parallel resonance peak segment in the mid-frequency range of 100kHz to 500kHz, and the transmission line effect segment in the high-frequency range of 1MHz to 2MHz. The relative amplitude errors at the characteristic frequency points of 10kHz, 250kHz, and 1.5MHz are all less than 0.1%, far less than the preset 3% calibration threshold. From the phase-frequency response curves, the simulated and measured phase trajectories also exhibit excellent following characteristics. The overall pattern of positive phase in the low-frequency range that slowly increases with frequency, phase turning negative near the mid-frequency resonance point and reaching an extreme value, and phase tending to stabilize negatively in the high-frequency range is completely consistent with the measured data, with a phase zero-crossing frequency deviation of less than 0.5%. The above comparison results fully reflect that the simulation model constructed in this embodiment accurately characterizes the steady-state temperature field and stress field distribution of the closing resistor under DC bias conditions by introducing a two-way coupling mechanism of electromagnetic-thermal-mechanical multi-physics fields, providing a physically realistic background state for small-signal frequency sweep analysis; and by adopting a steady-state solution strategy based on DC current source, it effectively overcomes the convergence problem of nonlinear resistive materials in electro-thermal coupling solution, ensuring the numerical stability and uniqueness of the simulation process.

[0164] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0165] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0166] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0167] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for constructing a simulation model of the impedance characteristics of the closing resistance of a circuit breaker, characterized in that, The specific steps include: Step 1: Based on the design drawings of the closing resistor of the target circuit breaker, establish a simulation model including the resistor element, the clamping spring assembly, the connecting conductor, and the insulating medium; set the material properties for the simulation model, including the nonlinear resistivity of the resistor element as a function of temperature and the contact resistance between the electrodes as a function of clamping force; and define the bidirectional coupling relationship between the electromagnetic field and the thermal field in the simulation model. Step 2: Set up a series of different DC operating points. For each DC operating point, based on the material properties of the simulation model and the bidirectional coupling relationship between the electromagnetic field and the thermal field, solve the steady-state field distribution of the simulation model under DC operating point excitation. While keeping the steady-state field unchanged, apply a preset frequency sweep test excitation. At different frequency sweep points of the frequency sweep test excitation, calculate the response current generated by the simulation model one by one, and calculate the impedance amplitude and phase at each frequency sweep point accordingly to generate the simulation impedance-frequency characteristic curve at the DC operating point. Step 3: Obtain a sample of the closing resistor of a circuit breaker of the same model as the simulation model, and perform actual measurement under the same conditions to obtain the corresponding measured impedance-frequency characteristic curve; compare the simulated impedance-frequency characteristic curve with the measured impedance-frequency characteristic curve, and adjust the physical parameters in the simulation model so that the error between the two meets the convergence criterion, then the simulation model is considered to have completed calibration.

2. The method for constructing a simulation model of the impedance characteristics of the closing resistance of a circuit breaker according to claim 1, characterized in that, Establishing the simulation model includes: Based on the design drawings of the closing resistor in the 750kV voltage level tank circuit breaker, the physical dimensions of the overall structure of its resistor sheet stack are extracted, including the diameter, thickness, center hole diameter, design gap between sheets, and initial preload design value of the compression spring. In finite element simulation software, a three-dimensional axisymmetric or full three-dimensional geometric model containing the overall structure of the resistor stack is constructed based on the physical dimensions to serve as the simulation model. The resistors are assembled in the actual stacking order, and the compression spring assembly simulates its axial compression function through equivalent stiffness elements or solid models. The connecting conductors include the metal flanges and connecting plates at both ends of the resistor string, and the insulating medium is SF6 gas filled in the tank.

3. The method for constructing a simulation model of the impedance characteristics of circuit breaker closing resistance as described in claim 2, characterized in that, Setting material properties for the simulation model includes: setting a nonlinear function for the resistivity of the resistor material as a function of temperature, which is obtained by fitting experimental data of the thermoelectric properties of the resistor material; setting contact resistance for the contact interfaces between resistors and between resistors and electrodes; and setting physical properties of the insulating medium whose relative permittivity is related to air pressure and temperature.

4. The method for constructing a simulation model of the impedance characteristics of the closing resistance of a circuit breaker according to claim 2, characterized in that, The process of realizing the bidirectional coupling relationship includes: enabling the multiphysics coupling module in the simulation solver, using the resistance loss and contact loss calculated by the electromagnetic field as volume heat sources or interface heat sources, and fully mapping them to the thermal field calculation domain; and feeding back the global temperature distribution data of the model obtained by the thermal field calculation to the electromagnetic field calculation in real time.

5. The method for constructing a simulation model of the impedance characteristics of the closing resistance of a circuit breaker according to claim 2, characterized in that, A set of DC current values ​​is set as DC excitation, and each DC current value constitutes an independent DC operating point; The process of solving the steady-state field distribution of the simulation model under the excitation of the DC operating point includes: applying the selected DC operating point to the simulation model; starting the bidirectional coupling calculation of the electromagnetic field and thermal field defined in the simulation model to perform DC steady-state solution; iterating the calculation until the current field, temperature field and structural stress field caused by thermal expansion in the simulation model converge, and obtaining the stable three-dimensional spatial field distribution below the DC operating point; wherein, the volume resistivity of the resistor and the contact resistance of the contact interface are jointly determined by the converged temperature field and structural stress field, and the steady-state field distribution is the current field distribution, temperature field distribution and structural stress field distribution after convergence.

6. The method for constructing a simulation model of the impedance characteristics of the closing resistance of a circuit breaker according to claim 5, characterized in that, The process of applying the preset frequency sweep test stimulus includes: After completing the DC steady-state solution, the converged temperature field and structural stress field determined by the DC operating point are locked and used as the fixed background physical state. A sinusoidal AC voltage signal is superimposed on the same port where DC excitation is applied in the simulation model for AC small-signal disturbance analysis. The frequency of this signal varies in steps within a preset high-frequency scanning range, thereby forming a series of discrete frequency scanning points. The peak amplitude of the sinusoidal AC voltage signal is no greater than 5% of its corresponding DC operating point voltage. Calculate the impedance amplitude and phase at different frequencies, including: for each frequency sweep point, under a fixed background physical state, solve the electromagnetic response of the simulation model to the sinusoidal AC voltage signal; Extract the complex forms of the AC voltage and AC current at the port, and calculate the AC signal impedance of the closing resistor at the frequency sweep point by dividing the phases, including the impedance amplitude and phase.

7. The method for constructing a simulation model of the impedance characteristics of the closing resistance of a circuit breaker according to claim 1, characterized in that, The actual measurements under the same conditions include: A joint test platform based on an impedance analyzer and a programmable DC power supply was built; a sample of the closing resistor of a circuit breaker of the same model was installed on the joint test platform to ensure that its electrical connection method is consistent with the port definition of the simulation model. Apply the same DC excitation as set in step 2 as DC bias; under each stable DC bias state, use an impedance analyzer to perform impedance measurement within the same preset frequency sweep range to obtain the measured impedance-frequency characteristic curve at the DC operating point. Key characteristic parameters selected for comparison include: impedance amplitude at characteristic frequency points in the low-frequency band, impedance amplitude and phase at resonant frequency points identified in the mid-frequency band, and the ratio of impedance amplitudes at two adjacent characteristic frequency points in the high-frequency band. For each DC operating point, the values ​​of the simulated impedance-frequency response curve and the measured impedance-frequency response curve on key characteristic parameters are extracted, and the errors of each key characteristic parameter are calculated.

8. The method for constructing a simulation model of the closing resistance damage impedance characteristics of a circuit breaker according to claim 7, characterized in that, Adjusting the physical parameters in the simulation model specifically includes: The proportionality coefficient in the nonlinear resistivity-temperature relationship function of the resistor material, the empirical coefficient in the contact resistance-clamping force relationship function between electrodes, and the equivalent relative permittivity of SF6 insulating medium; The adjustment is based on the calculated error direction and magnitude of each key characteristic parameter, and iterative correction is carried out with the goal of reducing the error between simulation and actual measurement on key characteristic parameters.

9. The method for constructing a simulation model of the impedance characteristics of the closing resistance of a circuit breaker according to claim 7, characterized in that, The characteristic frequency point in the low-frequency band is defined as: at least one characteristic frequency point selected within the low-frequency band to characterize the conductivity of the resistor sheet and the conductivity of the contact interface; the resonant frequency point identified in the mid-frequency band is defined as: within the mid-frequency band, the frequency point corresponding to the local maximum value or the zero-crossing point of the impedance amplitude in the measured impedance-frequency characteristic curve; the two adjacent characteristic frequency points in the high-frequency band are defined as: within the high-frequency band, two adjacent characteristic frequency points that can characterize the high-frequency skin effect or the dielectric polarization relaxation process.

10. The method for constructing a simulation model of the impedance characteristics of the closing resistance of a circuit breaker according to claim 1, characterized in that, The convergence criterion includes two levels, and the logic is set as follows: First-level criterion: Under all DC operating points, the average error of the key characteristic parameters between the simulated impedance-frequency response curve and the measured impedance-frequency response curve is lower than the corresponding preset error threshold. Second-level criterion: Under all DC operating points, the correlation coefficient between the simulated impedance-frequency response curve and the measured impedance-frequency response curve is greater than the preset goodness-of-fit threshold throughout the entire frequency sweep range. When both criteria are met simultaneously, the simulation model is considered to have completed calibration.

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