A broadband electromagnetic transient model modeling method, system, device and storage medium

Abstract

This invention belongs to the field of transformers and discloses a broadband electromagnetic transient modeling method, system, device, and storage medium, including the following processes: Based on the transformer's geometric dimensions and magnetization characteristics, a frequency-varying magnetoresistive topology network is established; the broadband equivalent capacitance matrix and part of the inductance matrix of the transformer windings are extracted and integrated to construct a broadband admittance matrix of the windings; the geometric steady-state resistance of the plasma arc column is calculated, and a dynamic differential equation for the time-varying arc resistance of the plasma arc column is established; an augmented state-space equation describing the dynamic evolution of the transformer before and after a fault is constructed; the above are integrated to construct a time-domain multiphysics joint solution model, and the time-domain multiphysics joint solution model is verified by time-domain joint solution and frequency-domain impedance scanning to obtain a broadband electromagnetic transient model. This enables accurate simulation of complex broadband transient processes inside the transformer.

Description

Technical Field

[0001] This invention belongs to the field of transformers and relates to a broadband electromagnetic transient modeling method, system, device and storage medium. Background Technology

[0002] During the long-term operation of power transformers, the winding insulation gradually ages under the combined effects of thermal stress, electrodynamic forces, and environmental factors. When the local insulation strength decreases to a certain level, local breakdown may occur inside the winding, forming a discharge channel under the influence of an electric field. Under specific operating conditions, this discharge process can develop into an arc channel that penetrates the structure of adjacent conductors, thus forming an inter-stage arc fault.

[0003] The arc channel, composed of high-temperature plasma, exhibits significant nonlinear and time-varying characteristics due to the combined influence of current, temperature, and channel geometry. Under alternating current voltage, the periodic zero-crossing of the current causes the arc to repeatedly undergo extinction and reignition processes, resulting in a rapid change in the equivalent resistance of the arc channel within an extremely short time. This process not only alters the local current distribution but also generates electromagnetic disturbance signals with broadband characteristics within the system.

[0004] Due to the complex spatial coupling relationships within the transformer windings, the aforementioned broadband disturbances can propagate within the equipment through electromagnetic coupling paths between windings and distributed capacitance networks, forming multi-scale transient responses at different spatial locations. These responses include magnetomotive force changes at the power frequency scale, as well as fast pulse characteristics in the mid-to-high frequency range, resulting in significant multi-time-scale coupling characteristics in the electromagnetic processes within the transformer.

[0005] Meanwhile, in this type of transient process, the response characteristics of the iron core magnetic circuit under different frequency excitations, the transmission capability of the winding structure to high-frequency signals, and the dynamic evolution behavior of the arc channel itself are coupled with each other and jointly determine the overall electromagnetic response characteristics of the system. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a broadband electromagnetic transient modeling method, system, device and storage medium, thereby realizing accurate simulation of complex broadband transient processes inside transformers.

[0007] To achieve the above objectives, the present invention employs the following technical solution: A broadband electromagnetic transient modeling method includes the following steps: A frequency-varying magnetoresistive topology network is established based on the geometric dimensions and magnetization characteristics of the transformer. The broadband equivalent capacitance matrix and part of the inductance matrix of the transformer winding are extracted, and the broadband equivalent capacitance matrix and part of the inductance matrix are integrated to construct the broadband admittance matrix of the winding. The geometric steady-state resistance of the plasma arc column is calculated, and based on the geometric steady-state resistance, a dynamic differential equation for the time-varying arc resistance of the plasma arc column is established. Construct an augmented state-space equation to describe the dynamic evolution of a transformer before and after a fault; By integrating the frequency-varying magnetoresistive topology network, the wideband admittance matrix of the winding, the dynamic differential equation, and the augmented state-space equation, a joint solution model for the time-domain multiphysics field is constructed. The joint solution model for the time-domain multiphysics field is verified by time-domain joint solution and frequency-domain impedance scanning to obtain a wideband electromagnetic transient model.

[0008] Optionally, based on the transformer's geometry and magnetization characteristics, a frequency-varying magnetoresistive topology network is established, including: A solid-domain geometric model of the transformer is established, and the core magnetic circuit and winding entity in the solid-domain geometric model of the transformer are equivalent to a two-dimensional longitudinal section structure. The two-dimensional longitudinal section structure is discretized into a grid along the horizontal and vertical directions to construct a magnetic network unit, which includes core unit and winding unit. Calculate the high-frequency magnetic flux penetration depth of the core unit at different frequency points, and calculate the effective magnetic cross-sectional area based on the high-frequency magnetic flux penetration depth and the thickness of a single silicon steel sheet. The frequency-varying reluctance is calculated based on the effective magnetic cross-sectional area. All core units corresponding to the frequency-varying reluctance are assembled according to the topological adjacency relationship to obtain the frequency-varying reluctance topology network.

[0009] Optionally, the broadband equivalent capacitance matrix and part of the inductance matrix of the transformer winding are extracted, and then integrated to construct the broadband admittance matrix of the winding, including: The grid-side winding and valve-side winding of the transformer are discretized into multiple winding units along the axial direction; A partial inductance matrix is ​​obtained by performing three-dimensional volume integral extraction on any two winding units; A three-dimensional electrostatic field numerical model is established to extract the potential coefficient matrix, and the broadband equivalent capacitance matrix is ​​obtained by inverting the potential coefficient matrix. Based on a partial inductance matrix and a wideband equivalent capacitance matrix, the capacitive and inductive branches in the winding unit are integrated in the frequency domain using operator-based methods to construct a wideband admittance matrix for the winding.

[0010] Optionally, the geometric steady-state resistance of the plasma arc column is calculated, and based on the geometric steady-state resistance, a dynamic differential equation for the time-varying arc resistance of the plasma arc column is established, including: An extended equation for the diameter of the plasma arc column was established to reflect the evolution of the plasma channel geometry driven by the interstage short-circuit circulation. The equivalent arc diameter in the extended equation of plasma arc column diameter is transformed into the circuit equivalent parameter, and the geometric steady-state resistance of plasma arc column under the current drive is derived. By combining the traction effect of the geometric steady-state resistance with the thermal inertia constraint of the plasma channel, a dynamic differential equation for the time-varying arc resistance is established.

[0011] Optionally, an augmented state-space equation describing the dynamic evolution of the transformer before and after a fault is constructed, including: The definition encompasses the system state vector of the transformer, which includes macroscopic electrical quantities and microscopic internal variables. These macroscopic electrical quantities and microscopic internal variables include grid-side transient current, valve-side transient current, interstage short-circuit circulating current, and core main magnetic flux. The magnetomotive force balance constraints before and after transformer faults are uniformly incorporated into the augmented state space framework. By combining the system state vector and its time derivative, the system matrix containing time-varying system parameters, the input matrix, and the external AC voltage excitation vector, an augmented state space equation describing the dynamic evolution before and after transformer faults is constructed. The total number of turns is kept constant during the evolution of the augmented state space equations.

[0012] Optionally, perform joint time-domain solution on the time-domain multiphysics joint solution model, including: Time-domain step-by-step iteration is performed based on augmented state-space equations. At each simulation time, the frequency-varying reluctance of the core unit is obtained from the frequency-varying reluctance topology network and updated to the system matrix. The winding unit current calculated by the augmented state space equation is converted into a magnetomotive force excitation vector. The magnetomotive force excitation vector is injected into the frequency-varying reluctance topology network to solve the system magnetic node equation and obtain the real-time magnetic flux distribution. The time rate of change of the real-time magnetic flux distribution is extracted and fed back to the circuit system to generate an induced electromotive force. The induced electromotive force (EMF) in the faulty winding unit is extracted from the induced EMF. The induced EMF in the faulty winding unit is injected into the arc dynamic evolution logic to solve the local fault state equation, update the inter-stage short-circuit circulating current and the time-varying arc resistance, and feed the updated time-varying arc resistance back to the augmented state space equation for global state calculation.

[0013] Optionally, the solution results of the time-domain multiphysics joint solution model are verified by frequency-domain impedance scanning to obtain a broadband electromagnetic transient model, including: A sinusoidal sweep frequency injection signal is superimposed at the input end of the time-domain multiphysics joint solution model, and the sweep frequency points are selected at logarithmic intervals within a set frequency band. Record the port response current phasor at each frequency sweep point, and calculate the port input impedance based on the sinusoidal frequency sweep injection signal and the port response current phasor. The wideband impedance spectrum curve is obtained by arranging the port input impedances corresponding to each sweep frequency point in frequency order. A frequency domain consistency comparison is performed between the broadband impedance spectrum curve and the broadband admittance matrix of the winding. When the comparison error meets the set conditions, a broadband electromagnetic transient model is established.

[0014] A broadband electromagnetic transient modeling system, comprising: The network establishment module is used to establish a frequency-varying magnetoresistive topology network based on the geometric dimensions and magnetization characteristics of the transformer. The matrix construction module is used to extract the broadband equivalent capacitance matrix and part of the inductance matrix of the transformer winding, integrate the broadband equivalent capacitance matrix and part of the inductance matrix, and construct the broadband admittance matrix of the winding. The equation-building module is used to calculate the geometric steady-state resistance of the plasma arc column. Based on the geometric steady-state resistance, the dynamic differential equation of the time-varying arc resistance of the plasma arc column is established. The space construction module is used to construct augmented state-space equations that describe the dynamic evolution of a transformer before and after a fault. The model solution verification module is used to integrate the frequency-varying magnetoresistive topology network, the winding broadband admittance matrix, the dynamic differential equation and the augmented state space equation, and then construct a time-domain multi-physics joint solution model. The time-domain joint solution and frequency-domain impedance scanning verification of the time-domain multi-physics joint solution model are performed to obtain a broadband electromagnetic transient model.

[0015] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the broadband electromagnetic transient modeling method.

[0016] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the broadband electromagnetic transient modeling method.

[0017] Compared with the prior art, the present invention has the following beneficial effects: This invention overcomes the limitations of traditional low-frequency or quasi-steady-state transformer models in dealing with high-frequency disturbances. It integrates a frequency-variable magnetoresistive network reflecting the high-frequency attenuation characteristics of the spatial magnetic circuit, a broadband admittance matrix reflecting the complex spatial coupling of the windings, and an arc model reflecting the dynamic evolution of plasma. This achieves bidirectional interaction between macroscopic electromagnetic energy transmission and microscopic high-frequency transient pulses (such as arcing spikes), thereby enabling high-fidelity reconstruction of the complex multi-scale, broadband electromagnetic transient response of a transformer during interstage arcing faults.

[0018] Furthermore, based on the eddy current shielding principle under high-frequency magnetic fields, the effective magnetic cross-sectional area of ​​the core is dynamically corrected by calculating the penetration depth of high-frequency magnetic flux inside the silicon steel sheet of the core, thereby deriving a frequency-dependent magnetoresistive model. This overcomes the deficiency of conventional static magnetoresistive models in characterizing the high-frequency skin effect, restores the real phenomenon of decreased permeability and increased loss in the transformer core under medium- and high-frequency excitation, and ensures the accuracy of the calculation of the propagation characteristics of high-frequency transient pulses in the magnetic circuit.

[0019] Furthermore, by utilizing the partial-element equivalent circuit method and three-dimensional electrostatic field numerical calculations, the winding is subjected to high-dimensional spatial discretization and volume integral extraction. This method not only rigorously preserves the self-inductance and mutual inductance characteristics of the winding, but also captures the microscopic stray capacitance and distributed capacitance network that are highly dependent on the propagation of high-frequency electromagnetic waves. By constructing a high-order broadband admittance matrix, a broadband propagation channel is provided for the local extremely steep wavefront arc excitation signal, improving the simulation accuracy of high-frequency resonance and voltage transient distribution.

[0020] Furthermore, abandoning the traditional fixed resistor or simple nonlinear resistor model, the dynamic expansion / contraction process of the arc column geometric diameter driven by short-circuit current is integrated with the thermal inertia time constant of the arc channel. Based on the time-varying arc resistance described by differential equations, it can simulate the extinction and reignition phenomenon of the arc near the zero-crossing point of the AC current due to energy dissipation and reionization, and restore the characteristics of the highly destructive nonlinear and broadband disturbance source at the fault point.

[0021] Furthermore, an augmented state-space equation containing singular matrices is introduced, unifying the differential equations representing the dynamic process and the algebraic equations representing the ampere-turn balance constraints within a single mathematical framework for solution. At the instant of an inter-stage short circuit, abrupt changes in topology, or abrupt changes in the number of damaged turns in the transformer, the system does not require a forced interruption and reconstruction of the solver due to changes in constraints. Instead, it maintains the magnetomotive force conservation law simply by updating the parameters, eliminating numerical oscillations caused by topology switching and ensuring extremely high stability across time scales.

[0022] Furthermore, a step-by-step iteration and feedback mechanism for the "field-circuit-arc" triad was established, particularly employing a strategy combining local closed-loop solution and global state update for the nonlinear arc branch. This forward mapping (current to magnetomotive force) and reverse feedback (magnetic flux rate to induced electromotive force) mechanism follows Faraday's law of electromagnetic induction and Ampere's circuital law. The local real-time correction of high-frequency abrupt fault branches effectively avoids convergence disruption caused by strong nonlinear factors in the global large-step matrix solution, balancing the accuracy and computational efficiency of multi-physics joint solution.

[0023] Furthermore, after completing the time-domain modeling, a swept-frequency signal is injected at the port to extract the broadband impedance spectrum and cross-compare it with the original distributed parameter matrix. This is equivalent to verifying the impulse response of the time-domain model through an equivalent mapping in the discrete Fourier domain. This mechanism constructs a rigorous logical closed loop, proving that the constructed time-domain multiphysics system retains the broadband transmission properties of the original physical structure after undergoing complex spatiotemporal discretization and algebraic order reduction, providing a numerical criterion for the reliability of the electromagnetic transient model. Attached Figure Description

[0024] Figure 1 This is a flowchart of a broadband electromagnetic transient modeling method for analyzing inter-stage arc faults in transformers, as described in an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the two-dimensional geometric structure of the transformer and the setting of the inter-stage short-circuit fault area in an embodiment of the present invention.

[0026] Figure 3 This is a broadband electromagnetic transient model diagram used for inter-stage arc fault analysis in an embodiment of the present invention.

[0027] Figure 4 This is a diagram illustrating the overall architecture of broadband electromagnetic transient multiphysics co-simulation for inter-stage arc fault analysis in this invention.

[0028] Figure 5 This is a transient waveform response result diagram of a transformer when an inter-stage short-circuit fault occurs in an embodiment of the present invention. Detailed Implementation

[0029] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0030] Example 1: This embodiment provides a broadband electromagnetic transient modeling method. The broadband electromagnetic transient model is used for inter-stage arc fault analysis in transformers. It aims to fill the gap in the applicability of conventional low-frequency or quasi-steady-state electromagnetic transient models when dealing with high-frequency arc disturbances. In view of the high-frequency eddy current effect, the broadband transmission requirement of high-frequency signals and the dynamic evolution mechanism of plasma channels that are unique to arc faults, a broadband transient analysis scheme with self-consistent physical mechanism is proposed, so as to achieve accurate simulation of complex broadband transient processes inside transformers.

[0031] The ZZDFPZ-509400 / 500-400 single-phase, two-column, side-yoke converter transformer, typical of ±800kV UHVDC converter stations, is used as the research and modeling object. Its rated capacity is 509.4 MVA, and its rated voltage combination is 306 / 99.77 kV. The diameter of its core column is 1400 mm, and the width and height of the iron window are 760 mm and 2595 mm, respectively. The windings, from the inside out, are the regulating winding, the grid-side winding, and the valve-side winding. The total number of turns in the grid-side winding is... N pri =611 turns, total number of turns in the valve-side winding N sec =179 turns, the voltage regulating winding consists of 14 identical segments, each with 7 turns. This invention provides a broadband electromagnetic transient modeling method for inter-stage arc fault analysis in transformers, the overall process of which is as follows: Figure 1 As shown, it includes the following steps: (1) Based on the geometric dimensions and magnetization characteristics of the transformer, a frequency-varying magnetoresistive topology network is established.

[0032] (2) Extract the broadband equivalent capacitance matrix and part of the inductance matrix of the transformer winding, integrate the broadband equivalent capacitance matrix and part of the inductance matrix, and construct the broadband admittance matrix of the winding.

[0033] (3) Calculate the geometric steady-state resistance of the plasma arc column, and based on the geometric steady-state resistance, establish the dynamic differential equation of the time-varying arc resistance of the plasma arc column.

[0034] (4) Construct an augmented state-space equation to describe the dynamic evolution of the transformer before and after a fault.

[0035] (5) Integrate the frequency-varying magnetoresistive topology network, the wideband admittance matrix of the winding, the dynamic differential equation and the augmented state space equation, and then construct a time-domain multi-physics joint solution model. Perform time-domain joint solution and frequency-domain impedance scanning verification on the time-domain multi-physics joint solution model to obtain a wideband electromagnetic transient model.

[0036] The specific steps (1) are as follows: A solid-domain geometric model of the transformer was established using geometric modeling software. To reduce computational complexity while meeting simulation accuracy requirements, structural details in the longitudinal depth direction of the core were ignored. The core magnetic circuit and winding entity were represented as a two-dimensional longitudinal section structure, and the mesh was discretized along both the transverse and longitudinal directions, ultimately constructing 40 magnetic network elements of 10×4. The magnetic network elements include core elements and winding elements, such as... Figure 2 As shown. The effective magnetic path length of the iron core unit in the magnetic network unit is... l m Set to 259.5mm, geometric cross-sectional area S mThe dimensions are set at 3848.5 cm².

[0037] To address the physical phenomenon that the rapid pulse characteristics in the mid-to-high frequency range are significantly modulated by the eddy currents in the iron core, this embodiment selects 30Q130 grain-oriented silicon steel for the iron core, whose resistivity is... Single-piece thickness initial relative permeability Vacuum permeability for .

[0038] Based on the principle of eddy current effect, the simulation focuses on the frequency band. Each frequency point within Calculate the penetration depth of high-frequency magnetic flux inside the silicon steel sheet. :

[0039] The value is pi, and then based on the high-frequency magnetic flux penetration depth... and the thickness of a single silicon steel sheet Calculate the effective magnetic cross-sectional area that exhibits frequency-dependent shrinkage due to eddy current shielding. :

[0040] in, This represents the geometric cross-sectional area of ​​a transformer core unit. exp This represents an exponential function with the natural constant e as its base.

[0041] Substituting the effective magnetic cross-sectional area into the basic formula for reluctance, we obtain the frequency-varying reluctance of the core unit, which characterizes the broadband transmission characteristics of the magnetic circuit. :

[0042] in, This indicates the effective magnetic circuit length of the core unit. For the core material at magnetic flux density B The relative permeability at this level, in this embodiment, is used to decouple the macroscopic frequency variation effect from the intrinsic saturation characteristics of the core material. The magnetization curves were obtained directly from the basic magnetization curves of silicon steel sheet samples; for the winding and insulation regions, the relative permeability was taken as a linear constant of 1.0; for the core region, It exhibits a nonlinear function that varies with magnetic flux density. Based on the actual magnetization characteristics of silicon steel sheets, as the iron core gradually moves from the linear operating region into the deep saturation region, The value drops nonlinearly and monotonically from around 40,000 in the high permeability state to around 500 in the deep saturation state.

[0043] Frequency-varying reluctance of all core units By assembling according to topological adjacency, a frequency-varying magnetoresistive topology network is finally obtained, which reflects the wideband transmission characteristics of the overall transformer magnetic circuit. This network characterizes the wideband transmission characteristics of the magnetic circuit under high-frequency excitation and provides a high-frequency self-consistent magnetic circuit-side description for subsequent multi-physics field integration with the circuit side.

[0044] Step (2) includes the following steps: This step uses the partial element equivalent circuit method to construct a complete winding broadband admittance matrix.

[0045] First, the grid-side winding and the valve-side winding are discretized into several winding units along the axial direction. In this embodiment, the grid-side winding is discretized into 61 segments, each with approximately 10 turns; the valve-side winding is discretized into 18 segments, each with approximately 10 turns; and the voltage regulating winding is discretized into 14 segments, each with 7 turns, according to its actual structure. Each segment is considered as a partial equivalent circuit unit with an independent current distribution.

[0046] Secondly, for any two winding units i and k The partial inductance matrix is ​​extracted based on the analytical integral formula of the partial equivalent circuit. L partial Elements in:

[0047] when i = k The time was the i Partial self-inductance of each winding unit, when i ≠ k The time was the i The and the first k Partial mutual inductance between each winding unit. Among them, i and k These represent the index numbers of the winding units in the spatial discretization sequence; Represents a partial inductance matrix L partial The elements in, when i = k The time was the i Partial self-inductance of each winding unit, when i ≠ k The time was the i The and the first k Partial mutual inductance between individual winding units; Indicates the permeability of free space; and They represent the first i The and the first k The cross-sectional area of ​​each winding unit; and These represent the volumes of the corresponding winding units; and These represent the integral infinitesimal vectors along the corresponding winding directions; and Let each represent the position vector of the two integral infinitesimals; This represents the Euclidean distance between two infinitesimal elements. Others indicate that they are not related to the first i The three-dimensional spatial region where the first winding unit is located and the first k Volume integral operations are performed on the three-dimensional spatial region where each winding unit is located.

[0048] In this embodiment, a three-dimensional parasitic parameter extraction and analysis tool is used to perform three-dimensional volume integration on the partial equivalent circuit units to extract a 93×93 order partial inductance matrix. L partial .

[0049] Using a partial inductance matrix and based on the principles of charge conservation and electrostatic field integration, the broadband equivalent capacitance matrix between winding units and to ground is calculated. C cap The process first involves extracting the potential coefficient matrix by establishing a three-dimensional electrostatic field numerical model. P Its elements P ik The calculation formula is:

[0050] in, Denotes the vacuum permittivity, taking... ; This represents the relative permittivity of the winding insulation medium, taken as 3.5; and They represent the first i The and the first k Surface area of ​​each winding unit; To represent the differential; Others indicate that they are not related to the first i The outer surface area where the first winding unit is located and the first winding unit k The area integral operation is performed on the outer surface region where each winding unit is located.

[0051] Through the pairing coefficient matrix P Perform the inverse operation to obtain the broadband equivalent capacitance matrix. C cap :

[0052] in, Represents the bit coefficient matrix P The inverse matrix, whose internal elements C ik Used to characterize thei The and the first k Capacitive coupling strength between winding units; Finally, based on the partial inductance matrix and the broadband equivalent capacitance matrix, the capacitive branches (broadband equivalent capacitance matrix) and inductive branches (partial inductance matrix) of each winding unit are integrated in the frequency domain using operator-based methods to construct a winding broadband admittance matrix that reflects the broadband transmission path of the winding. :

[0053] in, f Indicates the frequency point; j Represents the imaginary unit; R dc This represents a diagonal matrix composed of the DC resistances of each winding unit, and is composed of the geometric dimensions of the equivalent circuit units of each component and the resistivity of the copper conductor. The calculation yields the result. The wideband admittance matrix of the winding transforms the physical winding structure of the transformer into a complete electrical frequency conversion network, thereby establishing a wideband transmission channel in the winding and providing a mathematical carrier for the subsequent wideband transmission of high-frequency arc excitation signals within the winding.

[0054] Step (3) includes the following steps: This step involves connecting the custom C model component in the multiphysics system simulation software to the time-varying calculation module for arc impedance at the specified weak inter-level insulation nodes.

[0055] First, we establish the plasma column diameter expansion equation, which reflects the evolution of the arc plasma channel geometry driven by current:

[0056] in, D arc The equivalent arc diameter represents the dynamic expansion or contraction of the plasma arc column as the arc current changes. K 1 represents a constant parameter that determines the extension of the arc geometry; in this embodiment, it is taken as 0.00015. i flt For interstage short-circuit circulating current flowing through the arc channel, K 2 represents the exponential constant parameter that determines the extension of the arc geometry; in this embodiment, it is taken as 0.52.

[0057] Secondly, the equivalent arc diameter D arc Converting these parameters into corresponding circuit equivalent parameters, we can derive the geometric steady-state resistance that the plasma arc column should achieve under the current drive. R a,geo :

[0058] Among them, the equivalent resistivity of the plasma arc column arc length The geometric spacing between the two winding units corresponding to the selected inter-stage breakdown point is taken. Considering the tap lead and contact insulation structure of the voltage regulating winding in this embodiment, the insulation breakdown geometric spacing between two adjacent taps (electrically separated by 7 turns) is set to 4.5mm.

[0059] Finally, summarizing the geometric steady-state resistance... The traction effect and thermal inertial constraint of the plasma channel are used to establish the time-varying arc resistance. The dynamic differential equation:

[0060] in, R a The time-varying arc resistance of the plasma arc column. t Indicates the time parameter. T a The time constant representing the thermal inertia of the electric arc model is taken as 0.1. , d This is the differential. The dynamic differential equation is solved in real time within each simulation step, and its output is... It serves as the core broadband nonlinear excitation source in the subsequent augmented state-space equations, used to accurately simulate the nonlinear zero-dimensional characteristics of inter-stage short-circuit arcs.

[0061] Step (4) includes the following steps: To ensure the rigor of energy conversion between internal and external physical systems and to achieve a smooth parameterized switching of constraint conditions before and after a fault, this step integrates the magnetic potential balance constraints under both operating conditions into the same augmented state space framework.

[0062] Define a system state vector that encompasses both macroscopic electrical quantities and microscopic internal variables of a transformer. ,in Indicates the grid-side transient current. This represents the transient current on the valve side. Indicates interstage short-circuit circulating current. This represents the main magnetic flux of the iron core. The superscript T is the transpose symbol, indicating that the system's state vector should be treated as a column vector in matrix operations.

[0063] Construct an augmented state-space equation that uniformly describes the dynamic evolution before and after a fault:

[0064] in, E This represents the description matrix containing magnetic potential balance constraints. State vector The derivative with respect to time,A ( t ) represents the system matrix containing time-varying system parameters. B The input matrix is ​​represented by the following expression: Its physical significance lies in mapping the driving voltage of the external power supply into the grid-side circuit equations, serving as the external excitation source driving the electromagnetic transient evolution of the entire system. External AC voltage excitation vector. u ( t ) The formula defines a peak value as V, a 50Hz power frequency sinusoidal AC voltage excitation source; Indicates the time parameter.

[0065] For the description matrix E Its expression is:

[0066] in, and These represent the equivalent leakage inductances of the grid-side and valve-side windings, respectively, which are taken as 8.6mH and 0.31mH in this embodiment. The local equivalent leakage inductance of the faulty unit is represented by 85. For inter-stage short-circuit faults occurring in the middle of the voltage regulating winding, the number of damaged turns is set. Turns, which refers to the number of effective turns on the network side that were not short-circuited after the fault occurred. Turns. Matrix E The last row of elements is all 0, which corresponds to the magnetic potential balance constraint row in the system. Its singularity is used to achieve a unified solution of differential equations and algebraic constraints.

[0067] The system matrix A ( t The specific expression for ) is:

[0068] in, The equivalent DC resistance of the transformer grid-side winding is taken as 1.85. ; and These represent the resistance of the valve-side winding and the load resistance, respectively, both taken as 0.018. With 4.81 ; This represents the time-varying arc resistance, which is generated in real time by the dynamic differential equation in step (3); This represents the frequency-varying reluctance calculated in step (1). The transient equivalent magnetoresistance parameters are obtained after time-domain equivalent transformation. The last row of this matrix corresponds to the description matrix. EThe all-zero rows in the state space are used to enforce the magnetic potential balance constraint.

[0069] Throughout the state-space evolution process, the constraint of conservation of the total number of turns is always satisfied:

[0070] in, This represents the total number of turns in the grid-side winding.

[0071] This augmented state-space framework eliminates the need to switch solvers or reconstruct equations during fault introduction; instead, it allows for operation solely through matrices. E and The parameterized update of the number of turns-related elements can complete the smooth switching of constraints, thereby ensuring the continuity and numerical stability of the macroscopic ampere-turn balance and the local electromagnetic evolution logic before and after the arc fault.

[0072] Step (5) includes the following steps: The frequency-varying magnetoresistive topology network of step (1), the dynamic differential equation of the time-varying arc resistance of step (3), and the augmented state-space framework of step (4) are integrated into an electromagnetic transient co-simulation platform based on MATLAB (Matrix Laboratory) / Simulink (a multi-domain dynamic system simulation software), forming a... Figure 5 The time-domain multiphysics joint solution model is shown; the winding broadband admittance matrix in step (2) is also shown. It is synchronously connected to the simulation platform as a frequency domain reference benchmark to independently verify the accuracy of the wideband response of the port impedance of the time-domain multi-physics joint solution model.

[0073] First, time-domain step-by-step iteration is performed based on the augmented state-space equation established in step (4). The total simulation duration is 60ms, with a maximum step size of 10µs, which is automatically reduced to 0.05µs after the arc dynamic process is triggered. At each simulation moment, for the closed time-domain differential equation, a recursive convolution algorithm is used to convert the frequency-varying reluctance of the magnetoresistive system established in step (1) into a closed time-domain differential equation. Converted to transient equivalent magnetoresistance parameters at this calculation step size The calculated result Dynamically updated to system matrix The fourth row and fourth column; then perform a forward mapping from the circuit side to the magnetic circuit side, which will be determined by the state vector. The calculated winding unit current is converted into a magnetomotive force excitation vector through the line-turn coupling relationship. Then, the magnetomotive force excitation vector is used as a field source and injected into the frequency-varying magnetoresistive topology network established in step (1). The magnetic node equation of the system is solved based on Ohm's law of magnetic circuits, thereby calculating the real-time magnetic flux distribution of each discrete unit in the core and leakage magnetic space at that moment. Subsequently, reverse feedback from the magnetic circuit side to the circuit side is executed, the time rate of change of the real-time magnetic flux distribution is extracted and fed back to the circuit system according to Faraday's law of electromagnetic induction to form an induced electromotive force.

[0074] Secondly, a local closed-loop solution is performed for the arc fault branch. The induced electromotive force within the faulty winding unit is extracted from the induced electromotive force. E ind,flt And inject it into the arc dynamic evolution logic maintained by step (3). Using the state variables at the current moment, solve the local fault state equation:

[0075] Real-time calculation and correction of the inter-stage short-circuit circulating current The circulating current value is then synchronously fed back into the differential equation of step (3) to update the time-varying arc resistance at the next moment. And participate as a state component in the global state solution in step (4).

[0076] To reduce the impact of transient components at the moment of fault input on simulation stability, the matrix is ​​updated parametrically after 30 ms of simulation. E and The number of turns-related elements in the circuit triggers an inter-stage short-circuit fault in the air arc.

[0077] The simulation continues from the moment the fault is triggered until the set total simulation duration. During this process, the frequency-varying magnetoresistive topology network, the time-varying arc resistance dynamic differential equation, and the augmented state-space equation are solved jointly in the time domain multiphysics field within each simulation time step, completely recording the time-domain evolution trajectory of each state variable before and after the fault, thereby forming a broadband electromagnetic transient model to be verified.

[0078] Finally, for the broadband electromagnetic transient model to be verified, frequency domain impedance scanning verification is performed at the port of the time-domain multiphysics joint solution model. This is achieved by superimposing a sinusoidal frequency sweep injection signal at the input of the time-domain multiphysics joint solution model. :

[0079] in, The amplitude of the injected signal is set to 1V, and the frequency of the sweep point is... In order to be in A total of 401 frequency points were selected at logarithmic intervals. The port response current phasors were recorded. And calculate the port input impedance. :

[0080] in, For the injected voltage phasor, For the response current phasor.

[0081] right Repeat the above sinusoidal injection and response extraction process for each of the 401 swept frequency points within the frequency band, and input the corresponding port impedance of each frequency point. Arranged in frequency order, the simulated broadband impedance spectrum curve is obtained.

[0082] By comparing the frequency domain consistency of the wideband impedance spectrum curve obtained by simulation with the admittance characteristics extracted in step (2), the relative error of the amplitude of the two is less than 5% and the absolute error of the phase is less than 3° in the full frequency band of 50Hz–10MHz. The frequency domain perspective verifies the accuracy of the response of the constructed wideband electromagnetic transient model under wideband excitation, and thus formally establishes the wideband electromagnetic transient model.

[0083] like Figure 3 As shown, the transformer's core and windings are finely divided into two-dimensional magnetic network units, and the frequency-varying reluctance of each grid is quantified. It accurately maps the distribution characteristics of the internal spatial magnetic field of the equipment under broadband excitation; at the same time, the broadband electromagnetic transient model allows for flexible setting of inter-stage short-circuit fault regions at specified winding segments, laying a physical spatial foundation for simulating local disturbances.

[0084] like Figure 4 As shown, the external three-phase AC power supply of the transformer ( E A 、E B and E C (Connected via a macroscopic port. In the diagram, L1, L2, and L3 represent core posts 1, 2, and 3, respectively; GSW represents the grid-side winding; VSW represents the valve-side winding; S represents the interstage fault short-circuit switch; and SPR represents the six-pulse rectifier.) R d This represents the DC-side equivalent resistance. L d PCC represents the converter bus, while the smoothing reactor represents the converter bus. The broadband electromagnetic transient model of the transformer deeply integrates the broadband admittance matrix of the partial element equivalent circuit method. Dynamic arc branch based on plasma channel diameter evolution This collaborative architecture enables low-level bidirectional interaction between macroscopic circuits, spatial magnetic fields, and microscopic arc dynamics under the ampere-turn conservation constraint enforced by the augmented state space.

[0085] Figure 5 This is the transient response result of the transformer after an inter-stage short-circuit fault occurs at 30 ms, calculated based on the broadband electromagnetic transient model of this invention. Specifically: Figure 5 The top-level subplot shows the transient waveforms of the interstage short-circuit circulating current (blue curve, left ordinate) and the arc voltage (orange curve, right ordinate). 30ms after the fault trigger, a large electromotive force is induced in the fault section of the voltage regulating winding, driving the short-circuit circulating current to a peak value exceeding 50kA. Simultaneously, near the zero-crossing point of the power frequency current, the arc plasma channel undergoes a violent deionization and re-ignition process, resulting in a steep, step-like arc voltage spike (peak value close to 1.8kV) at this moment. This waveform highly replicates the "zero-rest" dynamic characteristics of the nonlinear time-varying arc, proving the effectiveness of the dynamic differential equation for the time-varying arc resistance in this model.

[0086] Figure 5 The middle layer subplot shows the time-domain waveform of the grid-side current. Before the fault occurs (0~30ms), the grid-side current exhibits a standard trapezoidal flat-top waveform due to the commutation characteristics of the converter valve. When a sudden inter-stage short circuit occurs at 30ms, the huge short-circuit energy breaks the original magnetomotive force balance, resulting in a significant increase in the amplitude of the grid-side current, and the waveform is severely distorted from a trapezoidal flat-top to a triangular pointed-top shape.

[0087] Figure 5 The bottom subplot shows the time-domain waveform of the valve-side current (secondary current). Simulation results show that although there are sharp current surges and waveform distortions on the grid side and in the fault circuit, the overall transformer voltage ratio change caused by a small number of inter-turn short-circuit faults (such as 7 turns in this embodiment) is relatively small. Therefore, the valve-side current does not exhibit significant amplitude abrupt changes before and after the fault, maintaining a trapezoidal flat-top wave shape with a peak value of approximately 4.7 kA. This difference in multi-port transient response closely matches the actual physical evolution of an UHVDC converter system when an internal transformer fault occurs.

[0088] The aforementioned time-domain waveform evolution and quantitative characteristic analysis, along with the concurrent port broadband impedance spectrum comparison results, corroborate each other: after the fault occurs, the port impedance exhibits significant resonant point shifts and amplitude drops in the tens of kHz to MHz frequency band, corresponding to the reconfiguration of capacitive coupling paths caused by changes in winding distributed capacitance and the number of damaged turns. This not only highly matches the actual physical evolution mechanism of inter-stage arc faults but also fully verifies the synergistic effectiveness of the model in characterizing nonlinear dynamic disturbance sources, high-frequency capacitive coupling links, and broadband transmission characteristics of the magnetic circuit, providing a highly reliable numerical basis for the accurate evaluation of the broadband electromagnetic transient characteristics inside the transformer.

[0089] This embodiment has the following beneficial effects: A full-bandwidth response analysis encompassing eddy current effects and spatial distribution characteristics is achieved: This embodiment overcomes the limitation of traditional lumped-parameter models in taking into account high-frequency characteristics. By coupling a frequency-variable magnetoresistive network and a wideband admittance matrix based on the partial-element equivalent circuit method, it fully considers the modulation effects of core eddy current effects and spatially distributed electromagnetic effects of windings on transient processes. This scheme can accurately simulate the wideband transmission of multi-scale electromagnetic disturbances within complex winding structures mentioned in the background art, filling the gap in high-frequency characteristic analysis of conventional models.

[0090] Significantly improved simulation accuracy of interstage arc nonlinear excitation characteristics: This embodiment abandons the traditional method of equating the fault point to a fixed resistor and introduces a dynamic arc model based on the geometric evolution of the plasma channel. This model can deeply characterize the extinction and reignition mechanism of the arc near the zero-crossing point of the AC current, and reproduce the arc voltage spike and current zero-crossing phenomenon with high fidelity. It provides a nonlinear broadband excitation source that conforms to the physical mechanism for transformer fault analysis, and solves the problem of simulation distortion of the arc dynamic evolution process in the background technology.

[0091] To ensure the physical consistency and computational stability of the evolution process across time scales, this embodiment constructs a mathematical framework based on an augmented state space, utilizing a singular descriptive matrix to deeply integrate the magnetomotive force balance constraint with the electromagnetic transient differential equations. This architecture guarantees a seamless parameterized switching of the transformer from a healthy magnetomotive force balance to a fault-prone damaged magnetomotive force balance. While strictly adhering to the underlying magnetomotive force conservation law of the transformer, it improves the numerical stability and computational accuracy of the broadband electromagnetic transient model when dealing with extreme nonlinear drastic processes.

[0092] This embodiment provides comprehensive time-frequency joint diagnostic and panoramic characteristic analysis methods: Through the integrated application of time-domain multiphysics joint solution and port broadband impedance scanning, it achieves the joint output of time-domain transient waveforms and frequency-domain impedance spectra. This multi-dimensional collaborative analysis capability can not only reproduce time-domain waveform distortion caused by arc faults, but also reflect changes in the internal structure of the winding through impedance spectrum characteristics, providing more complete numerical tools and theoretical support for transformer insulation diagnosis and condition assessment.

[0093] Example 2: In this embodiment, a broadband electromagnetic transient modeling system is provided. This broadband electromagnetic transient modeling system can be used to implement the above-mentioned broadband electromagnetic transient modeling method. Specifically, the broadband electromagnetic transient modeling system includes a network establishment module, a matrix construction module, an equation establishment module, a space construction module, and a model solution verification module.

[0094] The network establishment module is used to establish a frequency-varying magnetoresistive topology network based on the geometric dimensions and magnetization characteristics of the transformer.

[0095] The matrix construction module is used to extract the broadband equivalent capacitance matrix and part of the inductance matrix of the transformer winding, integrate the broadband equivalent capacitance matrix and part of the inductance matrix, and construct the broadband admittance matrix of the winding.

[0096] The equation-building module is used to calculate the geometric steady-state resistance of the plasma arc column. Based on the geometric steady-state resistance, the dynamic differential equation of the time-varying arc resistance of the plasma arc column is established.

[0097] The space construction module is used to construct augmented state-space equations that describe the dynamic evolution of a transformer before and after a fault.

[0098] The model solution verification module is used to integrate the frequency-varying magnetoresistive topology network, the winding broadband admittance matrix, the dynamic differential equation and the augmented state space equation, and then construct a time-domain multi-physics joint solution model. The time-domain joint solution and frequency-domain impedance scanning verification of the time-domain multi-physics joint solution model are performed to obtain a broadband electromagnetic transient model.

[0099] Example 3: This embodiment provides a computer device, which includes a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve corresponding method flows or corresponding functions. The processor described in this embodiment can be used for operating a broadband electromagnetic transient modeling method, including: establishing a frequency-varying magnetoresistive topology network based on the transformer's geometric dimensions and magnetization characteristics; and extracting the broadband equivalent capacitance matrix and part of the inductance matrix of the transformer windings. A broadband equivalent capacitance matrix and a partial inductance matrix are integrated to construct a broadband admittance matrix for the winding. The geometric steady-state resistance of the plasma arc column is calculated, and based on the geometric steady-state resistance, a dynamic differential equation for the time-varying arc resistance of the plasma arc column is established. An augmented state-space equation describing the dynamic evolution of the transformer before and after a fault is constructed. The frequency-varying magnetoresistive topology network, the broadband admittance matrix of the winding, the dynamic differential equation, and the augmented state-space equation are integrated to construct a time-domain multiphysics joint solution model. The time-domain joint solution model is verified by time-domain joint solution and frequency-domain impedance scanning to obtain a broadband electromagnetic transient model.

[0100] Example 4: This embodiment provides a computer-readable storage medium (Memory), which is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM (Random Access Memory) or non-volatile memory, such as at least one disk storage device.

[0101] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the broadband electromagnetic transient model modeling method in the above embodiments. One or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps: Based on the geometric dimensions and magnetization characteristics of the transformer, a frequency-varying magnetoresistive topology network is established; the broadband equivalent capacitance matrix and part of the inductance matrix of the transformer winding are extracted, and the broadband equivalent capacitance matrix and part of the inductance matrix are integrated to construct the broadband admittance matrix of the winding; the geometric steady-state resistance of the plasma arc column is calculated, and based on the geometric steady-state resistance, a dynamic differential equation for the time-varying arc resistance of the plasma arc column is established; an augmented state space equation describing the dynamic evolution of the transformer before and after the fault is constructed; the frequency-varying magnetoresistive topology network, the broadband admittance matrix of the winding, the dynamic differential equation and the augmented state space equation are integrated to construct a time-domain multi-physics joint solution model, and the time-domain multi-physics joint solution model is verified by time-domain joint solution and frequency-domain impedance scanning to obtain the broadband electromagnetic transient model.

[0102] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, etc.) containing computer-usable program code.

[0103] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0104] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0105] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0106] In the above embodiments of this application, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0107] The above description is only a preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

[0108] It should be understood that the above description is for illustrative purposes and not for limitation. Many embodiments and applications beyond the examples provided will become apparent to those skilled in the art upon reading the above description.

Claims

1. A broadband electromagnetic transient model modeling method, characterized in that, Includes the following processes: A frequency-varying magnetoresistive topology network is established based on the geometric dimensions and magnetization characteristics of the transformer. The broadband equivalent capacitance matrix and part of the inductance matrix of the transformer winding are extracted, and the broadband equivalent capacitance matrix and part of the inductance matrix are integrated to construct the broadband admittance matrix of the winding. The geometric steady-state resistance of the plasma arc column is calculated, and based on the geometric steady-state resistance, a dynamic differential equation for the time-varying arc resistance of the plasma arc column is established. Construct an augmented state-space equation to describe the dynamic evolution of a transformer before and after a fault; By integrating the frequency-varying magnetoresistive topology network, the wideband admittance matrix of the winding, the dynamic differential equation, and the augmented state-space equation, a joint solution model for the time-domain multiphysics field is constructed. The joint solution model for the time-domain multiphysics field is verified by time-domain joint solution and frequency-domain impedance scanning to obtain a wideband electromagnetic transient model.

2. The broadband electromagnetic transient modeling method of claim 1, wherein, Based on the transformer's geometry and magnetization characteristics, a frequency-varying reluctance topology network is established, including: A solid-domain geometric model of the transformer is established, and the core magnetic circuit and winding entity in the solid-domain geometric model of the transformer are equivalent to a two-dimensional longitudinal section structure. The two-dimensional longitudinal section structure is discretized into a grid along the horizontal and vertical directions to construct a magnetic network unit, which includes core unit and winding unit. Calculate the high-frequency magnetic flux penetration depth of the core unit at different frequency points, and calculate the effective magnetic cross-sectional area based on the high-frequency magnetic flux penetration depth and the thickness of a single silicon steel sheet. The frequency-varying reluctance is calculated based on the effective magnetic cross-sectional area. All core units corresponding to the frequency-varying reluctance are assembled according to the topological adjacency relationship to obtain the frequency-varying reluctance topology network.

3. The broadband electromagnetic transient modeling method of claim 1, wherein, The broadband equivalent capacitance matrix and part of the inductance matrix of the transformer winding are extracted, and then integrated to construct the broadband admittance matrix of the winding, including: The grid-side winding and valve-side winding of the transformer are discretized into multiple winding units along the axial direction; A partial inductance matrix is ​​obtained by performing three-dimensional volume integral extraction on any two winding units; A three-dimensional electrostatic field numerical model is established to extract the potential coefficient matrix, and the broadband equivalent capacitance matrix is ​​obtained by inverting the potential coefficient matrix. Based on a partial inductance matrix and a wideband equivalent capacitance matrix, the capacitive and inductive branches in the winding unit are integrated in the frequency domain using operator-based methods to construct a wideband admittance matrix for the winding.

4. The broadband electromagnetic transient modeling method according to claim 1, characterized in that, The geometric steady-state resistance of the plasma arc column is calculated. Based on this geometric steady-state resistance, the dynamic differential equation for the time-varying arc resistance of the plasma arc column is established, including: An extended equation for the diameter of the plasma arc column was established to reflect the evolution of the plasma channel geometry driven by the interstage short-circuit circulation. The equivalent arc diameter in the extended equation of plasma arc column diameter is transformed into the circuit equivalent parameter, and the geometric steady-state resistance of plasma arc column under the current drive is derived. By combining the traction effect of the geometric steady-state resistance with the thermal inertia constraint of the plasma channel, a dynamic differential equation for the time-varying arc resistance is established.

5. The broadband electromagnetic transient modeling method according to claim 1, characterized in that, Construct an augmented state-space equation describing the dynamic evolution of the transformer before and after a fault, including: The definition encompasses the system state vector of the transformer, which includes macroscopic electrical quantities and microscopic internal variables. These macroscopic electrical quantities and microscopic internal variables include grid-side transient current, valve-side transient current, interstage short-circuit circulating current, and core main magnetic flux. The magnetomotive force balance constraints before and after transformer faults are uniformly incorporated into the augmented state space framework. By combining the system state vector and its time derivative, the system matrix containing time-varying system parameters, the input matrix, and the external AC voltage excitation vector, an augmented state space equation describing the dynamic evolution before and after transformer faults is constructed. The total number of turns is kept constant during the evolution of the augmented state space equations.

6. The broadband electromagnetic transient modeling method according to claim 1, characterized in that, The time-domain joint solution of the multiphysics joint solution model includes: Time-domain step-by-step iteration is performed based on augmented state-space equations. At each simulation time, the frequency-varying reluctance of the core unit is obtained from the frequency-varying reluctance topology network and updated to the system matrix. The winding unit current calculated by the augmented state space equation is converted into a magnetomotive force excitation vector. The magnetomotive force excitation vector is injected into the frequency-varying reluctance topology network to solve the system magnetic node equation and obtain the real-time magnetic flux distribution. The time rate of change of the real-time magnetic flux distribution is extracted and fed back to the circuit system to generate an induced electromotive force. The induced electromotive force (EMF) in the faulty winding unit is extracted from the induced EMF. The induced EMF in the faulty winding unit is injected into the arc dynamic evolution logic to solve the local fault state equation, update the inter-stage short-circuit circulating current and the time-varying arc resistance, and feed the updated time-varying arc resistance back to the augmented state space equation for global state calculation.

7. The broadband electromagnetic transient modeling method according to claim 1, characterized in that, The solution results of the time-domain multiphysics joint solution model were verified by frequency-domain impedance scanning to obtain a broadband electromagnetic transient model, including: A sinusoidal sweep frequency injection signal is superimposed at the input end of the time-domain multiphysics joint solution model, and the sweep frequency points are selected at logarithmic intervals within a set frequency band. Record the port response current phasor at each frequency sweep point, and calculate the port input impedance based on the sinusoidal frequency sweep injection signal and the port response current phasor. The wideband impedance spectrum curve is obtained by arranging the port input impedances corresponding to each sweep frequency point in frequency order. A frequency domain consistency comparison is performed between the broadband impedance spectrum curve and the broadband admittance matrix of the winding. When the comparison error meets the set conditions, a broadband electromagnetic transient model is established.

8. A broadband electromagnetic transient modeling system, characterized in that, include: The network establishment module is used to establish a frequency-varying magnetoresistive topology network based on the geometric dimensions and magnetization characteristics of the transformer. The matrix construction module is used to extract the broadband equivalent capacitance matrix and part of the inductance matrix of the transformer winding, integrate the broadband equivalent capacitance matrix and part of the inductance matrix, and construct the broadband admittance matrix of the winding. The equation-building module is used to calculate the geometric steady-state resistance of the plasma arc column. Based on the geometric steady-state resistance, the dynamic differential equation of the time-varying arc resistance of the plasma arc column is established. The space construction module is used to construct augmented state-space equations that describe the dynamic evolution of a transformer before and after a fault. The model solution verification module is used to integrate the frequency-varying magnetoresistive topology network, the winding broadband admittance matrix, the dynamic differential equation and the augmented state space equation, and then construct a time-domain multi-physics joint solution model. The time-domain joint solution and frequency-domain impedance scanning verification of the time-domain multi-physics joint solution model are performed to obtain a broadband electromagnetic transient model.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the broadband electromagnetic transient modeling method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the broadband electromagnetic transient modeling method as described in any one of claims 1 to 7.

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