Method for calculating internal voltage stress of cascaded high-frequency transformer

Abstract

The invention belongs to the technical field of transformers, and particularly relates to a method for calculating voltage stress in a cascaded high-frequency transformer, which comprises the following steps of: calculating the voltage stress in a cascaded high-frequency transformer according to an external cascading mode, an internal topological structure, converter characteristics and a control strategy of a DC-DC (Direct Current-Direct Current) isolation converter; time domain voltage waveforms of all ports of a high-frequency transformer in the DC-DC isolation converter under the cascade condition are obtained through simulation, frequency spectrum information of the voltage waveforms is extracted through frequency domain analysis, and according to a constructed high-frequency transformer equivalent model and application methods of excitation of different ports of the high-frequency transformer equivalent model, the high-frequency transformer equivalent model is obtained. Finally, analysis and calculation of the internal voltage stress of the high-frequency transformer under the important working condition that all ports of the high-frequency transformer are excited under the cascade condition are achieved, and the limitation that only single-end excitation is considered in a traditional method is avoided.

Description

Technical Field

[0001] The present invention belongs to the technical field of transformers, and particularly relates to a method for calculating the voltage stress inside a cascaded high-frequency transformer. Background Art

[0002] As a core component in a DC-DC isolation converter, a high-frequency transformer not only undertakes the important tasks of energy transmission and voltage conversion, but also ensures the safe and stable operation of the system through its electrical isolation function. Under typical operating conditions, the end of the high-frequency transformer is long-term subjected to the action of pulses or square-wave voltages with steep rising edges. A large number of high-frequency harmonic components contained in these voltage waveforms may cause resonance phenomena inside the winding, resulting in a non-uniform distribution characteristic of the internal voltage stress different from that under low-frequency conditions. This non-uniformly distributed voltage stress poses a serious threat to the insulation system of the high-frequency transformer, increases the risk of insulation breakdown, and thus affects the reliability and lifespan of the entire power electronics system.

[0003] Currently, for the calculation of the internal voltage stress of a high-frequency transformer, the field-circuit coupling method is mostly adopted, that is, first establish a field model of the high-frequency transformer through a multi-field coupling finite element simulation software, extract the circuit model parameters under square-wave excitation, and then construct a circuit model to study the internal voltage distribution. However, whether it is the field model or the circuit model, it is more about the parameter extraction and internal voltage stress calculation and analysis of the high-frequency transformer under single-ended excitation conditions, and does not fully consider the typical operating conditions outside the high-frequency transformer, especially the operating conditions under the cascaded conditions of a DC-DC isolation converter. Under cascaded conditions, there are complex electrical connections and mutual influences between different ports of the high-frequency transformer, resulting in particularly complex application of boundary conditions. The traditional field-circuit coupling model is difficult to accurately reflect the voltage stress distribution under the simultaneous excitation of multiple ports. Summary of the Invention

[0004] Aiming at the defect in the prior art that the traditional calculation of the internal voltage stress of a high-frequency transformer does not consider the operating conditions under cascaded conditions and cannot reflect the voltage stress distribution under the simultaneous excitation of multiple ports, the present invention provides a method for calculating the voltage stress inside a cascaded high-frequency transformer to solve the above technical problems.

[0005] In a first aspect, the present invention provides a method for calculating the voltage stress inside a cascaded high-frequency transformer, including: Step S1: According to the external cascading method, internal topological structure, converter characteristics, and control strategy of the DC-DC isolation converter, simulate and obtain the time-domain voltage waveforms of each port of the high-frequency transformer in the DC-DC isolation converter under cascaded conditions, and extract the spectral information of the voltage waveforms through frequency-domain analysis; Step S2: Based on the finite element method, establish a frequency-varying distributed parameter extraction model for the high-frequency transformer. Input the spectrum information into the frequency-varying distributed parameter extraction model to extract the frequency-varying distributed parameters at different frequencies. The frequency-varying distributed parameters include conductance parameters, capacitance parameters, resistance parameters, and inductance parameters. Step S3: In the established frequency-varying distributed parameter extraction model, take each turn of the winding of the high-frequency transformer as an independent calculation unit. According to the pre-stored inter-turn geometric relationship and current path, distribute the extracted frequency-varying distributed parameters to the impedance branch and admittance branch corresponding to the independent calculation unit to construct an equivalent circuit of the frequency-varying distributed parameters of the high-frequency transformer. Step S4: Based on the constructed equivalent circuit of the frequency-varying distributed parameters, define the impedance branch matrix, admittance branch matrix, voltage-current vector, and incidence matrix to establish a general parametric model of the equivalent circuit of the frequency-varying distributed parameters. Step S5: Perform Fourier decomposition on the multi-port voltage waveforms of the high-frequency transformer under cascaded conditions to determine the target spectrum range and truncation order, and extract the harmonic component spectra of the voltages at each port. Step S6: Use the decomposed single-frequency sinusoidal excitation voltage as the boundary condition and apply it to the excitation node of the general parametric model to solve for the voltage value of the response node. Step S7: Based on the superposition principle, synthesize the node voltage responses of all harmonic components to obtain the internal voltage stress distribution of the high-frequency transformer under cascaded multi-port excitation conditions.

[0006] A further improvement of this technical solution is that Step S1 includes: Step S11: Obtain the pre-stored DC-DC isolation converter parameters, including the external cascading method, internal topology structure, converter device characteristics, and control strategy. Among them, the external cascading method is the electrical connection relationship between pre-stored multi-stage converters; the internal topology structure includes the circuit configurations of pre-stored full-bridge, half-bridge, or LLC resonant topologies; the control strategy includes the duty cycle and switching frequency of the pre-stored pulse width modulation signal; the converter device characteristics include the on-time and pulse rise time of the MOSFET in the converter; Step S12: Based on the obtained DC-DC isolation converter parameters, construct an equivalent circuit model of the cascaded DC-DC isolation converter in a circuit simulation tool to simulate the time-domain voltage waveforms at each port of the high-frequency transformer under cascaded conditions. Step S13: Perform spectrum analysis on the time-domain voltage waveforms of each voltage port through fast Fourier transform, extract the harmonic frequency range, and output the spectrum information including the fundamental frequency, harmonic amplitude, and phase. Store the spectrum information as a frequency-domain data set.

[0007] A further improvement of this technical solution is that the simulation equation for the time-domain voltage waveforms of each port of the high-frequency transformer under simulated cascaded conditions is: ; Among them, is the simulation function; is the internal topology structure function; is the nonlinear magnetic permeability; and are the time-domain voltage waveforms of the high-voltage and low-voltage ports respectively.

[0008] A further improvement of this technical solution is that step S2 includes: Step S21: Based on the finite element method, establish a frequency-varying distributed parameter extraction model for the high-frequency transformer, including an electrostatic field analysis model and a steady-state magnetic field analysis model; Step S22: Set the conductor boundary conditions and the properties of the insulating material according to the extracted spectral information; the conductor boundary conditions include applying a voltage excitation matching the spectral amplitude on the conductor surface and applying a grounding constraint to the reference node; the properties of the insulating material include the frequency-varying dielectric constant and conductivity of the insulating material; Step S23: Input the set conductor boundary conditions and the properties of the insulating material into the constructed electrostatic field analysis model, and extract the distributed capacitance and distributed conductance of the insulating material at different frequencies. The distributed capacitance and distributed conductance respectively characterize the inter-turn / inter-layer electric field coupling and leakage current characteristics; Step S24: Define the current excitation conditions according to the extracted spectral information. The current excitation conditions are the current excitation frequency range covering the main harmonic components in the spectral information; Step S25: Input the defined current excitation conditions and the pre-stored B-H curve of the iron core corresponding to the high-frequency transformer and the skin effect characteristics of the Litz wire into the constructed steady-state magnetic field analysis model, and extract the distributed resistance and distributed inductance of the Litz wire at different frequencies; Step S26: Based on the extracted distributed capacitance, distributed conductance, distributed resistance, and distributed inductance, construct a frequency-varying distributed parameter database for the high-frequency transformer.

[0009] A further improvement of this technical solution is that step S3 includes: Step S31: Discretize each turn of the winding of the high-frequency transformer into independent calculation units, define the unit numbers corresponding to each independent calculation unit in the high-voltage and low-voltage windings, and establish a geometric relationship mapping table between the units based on the unit numbers. The mapping table records the current path topology and the inter-turn / inter-layer geometric relationship including the inter-turn distance and the inter-layer insulation thickness; Step S32: Map the distributed capacitance and distributed conductance parameters of the insulating material to the admittance branch that characterizes the electric field coupling characteristics between units according to the inter-turn / inter-layer geometric relationship; map the distributed resistance and distributed inductance parameters of the Litz wire to the impedance branch that characterizes the magnetic field coupling characteristics in the unit according to the current path topology; the distributed inductance parameters include self-inductance and mutual inductance parameters of adjacent turns. Step S33: Take the two ends of each turn of the winding as independent nodes, connect impedance branches in series between adjacent nodes, realize magnetic field coupling between non-adjacent nodes through mutual inductance branches, and connect admittance branches in parallel between each node and the reference ground to form a chain node network of high-voltage and low-voltage windings, thus completing the construction of the frequency-variable distributed parameter equivalent circuit of the high-frequency transformer.

[0010] A further improvement of this technical solution is to map the distributed capacitance and distributed conductance parameters of the insulating material to the admittance branch that characterizes the electric field coupling characteristics between units according to the inter-turn / inter-layer geometric relationship. The specific expression is: ; ; where is the distributed capacitance, characterizing the frequency-variable capacitance between the i-th turn and the j-th turn of the winding; is the frequency-variable permittivity, characterizing the polarization ability of the insulating material at different frequencies f, reflecting the dynamic change of the electric field coupling strength with frequency, with the unit of F / m; is the coupling area, characterizing the effective area of the electric field overlap between the i-th turn and the j-th turn of the winding; is the dielectric thickness, characterizing the physical thickness of the insulating layer between the i-th turn and the j-th turn of the winding; is the distributed conductance, characterizing the frequency-variable conductance between the i-th turn and the j-th turn of the winding; is the frequency-variable conductivity, characterizing the leakage current characteristics of the insulating material at different frequencies f, reflecting the dynamic change of the dielectric loss with frequency, with the unit of S / m; Map the distributed resistance and distributed inductance parameters of the Litz wire to the impedance branch that characterizes the magnetic field coupling characteristics in the unit according to the current path topology. The specific expression is: ; ; where is the distributed resistance, characterizing the frequency-variable resistance of the i-th turn of the winding; is the resistance per unit length, characterizing the AC resistance per meter of the Litz wire at high frequencies; is the effective length of the current path; is the distributed inductance, characterizing the frequency-variable inductance of the i-th turn of the winding; is the inductance per unit turn, characterizing the equivalent inductance of a single turn of the winding at high frequencies; is the number of adjacent coupled turns, which characterizes the number of effective turns of the winding that undergoes magnetic field coupling with the i-th turn of the winding.

[0011] A further improvement of this technical solution is that step S4 includes: Step S41: Based on the number of nodes and branches in the frequency-varying distributed parameter equivalent circuit constructed, define the dimensions of the impedance branch matrix and the admittance branch matrix, and define variables including the node voltage vector, the impedance branch current vector, and the admittance branch current vector; Step S42: Based on the corresponding dimensions and variables defined for the impedance branches, integrate the frequency-varying parameters of all impedance branches in the frequency-varying distributed parameter equivalent circuit to form the impedance branch matrix; Step S43: Based on the corresponding dimensions and variables defined for the admittance branches, integrate the frequency-varying parameters of all admittance branches in the frequency-varying distributed parameter equivalent circuit to form the admittance branch matrix; Step S44: Define the incidence matrix that describes the connection relationship between the admittance branches / impedance branches and the nodes; Step S45: Through Kirchhoff's law, associate the incidence matrix, the impedance branch matrix, the admittance branch matrix with the node voltage vector to form the solution equation for the network node voltage in the frequency-varying distributed parameter equivalent circuit, and complete the construction of the general parametric model of the frequency-varying distributed parameter equivalent circuit.

[0012] A further improvement of this technical solution is that step S5 includes: Step S51: Perform Fourier decomposition on the obtained cascaded multi-port voltage waveforms to extract the harmonic component amplitudes and phases of the voltages at each port; Step S52: Based on the pre-stored parameter effective frequency range in the extracted frequency-varying parameter database, combined with the frequency-varying dielectric characteristics set in the insulation material properties, determine the target frequency spectrum range; Step S53: According to the target frequency spectrum range and the preset harmonic truncation accuracy threshold, calculate the minimum truncation order K; Step S54: Extract the harmonic component spectra within the K-th order for each port, and output the harmonic data set including frequency, amplitude, and phase.

[0013] A further improvement of this technical solution is that step S6 includes: Step S61: Based on the node network of the constructed frequency-varying distributed parameter equivalent circuit, determine the nodes where the excitation is applied, the grounded nodes, and the corresponding node numbers of the above nodes; Step S62: According to the node numbers of the excitation nodes and the grounded nodes, delete the corresponding rows and columns in the coefficient matrix of the node voltage solution equation, extract the column vector of the coefficient matrix corresponding to the node number of the excitation node and move it to the right side of the solution equation, and construct a new solution equation for all response nodes to realize the application of the excitation in the analytical calculation process; Step S63: Solve the equations based on all the newly constructed response nodes, calculate the frequency-domain voltage vectors of all the response nodes, and output the voltage response amplitudes and phases of all nodes at this frequency.

[0014] A further improvement of this technical solution is that step S7 includes: Based on the superposition principle, perform time-domain synthesis on the node frequency-domain voltage responses under all harmonic frequency components; According to the control strategy of the cascaded topology, calibrate the initial phases of the excitations at each port to ensure that the time-domain voltage waveform is synchronized with the actual working conditions; After calibration, reorganize the time-domain voltages of all nodes according to the physical positions of the windings to form a map of the internal voltage stress distribution of the high-frequency transformer.

[0015] The beneficial effects of the present invention are as follows: The present invention obtains the time-domain voltage waveforms of each port of the high-frequency transformer in the DC-DC isolated converter under cascaded conditions through simulation and extracts the spectrum information, comprehensively considering the influence of the cascading effect on the internal voltage stress of the high-frequency transformer. That is, according to the constructed equivalent model of the high-frequency transformer and the application method of different port excitations, the present invention finally realizes the analysis and calculation of the internal voltage stress of the high-frequency transformer under the important working condition that there are excitations at all ports under cascaded conditions, avoiding the limitation of only considering single-ended excitation in the traditional method. Based on the pre-stored parameters (such as the external cascading method, the internal topology structure, the converter characteristics, and the control strategy), an equivalent circuit model of the cascaded DC-DC isolated converter is constructed in the circuit simulation tool, realizing the accurate simulation of the time-domain voltage waveforms of each port of the high-frequency transformer under cascaded conditions.

[0016] The present invention uses the finite element method to establish a frequency-varying distributed parameter extraction model of the high-frequency transformer, which can efficiently and accurately extract parameters such as conductance, capacitance, resistance, and inductance at different frequencies, providing a solid foundation for the subsequent construction of the equivalent circuit. Inputting the extracted spectrum information into the frequency-varying distributed parameter extraction model ensures the pertinence and accuracy of parameter extraction and improves the calculation efficiency.

[0017] The present invention takes each turn of the winding of the high-frequency transformer as an independent calculation unit, fully considering the inter-turn geometric relationship and current path, realizing the refined description of the internal electromagnetic characteristics of the high-frequency transformer. By allocating frequency-varying distributed parameters to the impedance branch and the admittance branch, an equivalent circuit of the frequency-varying distributed parameters of the high-frequency transformer is constructed, accurately reflecting the internal electromagnetic coupling characteristics of the high-frequency transformer.

[0018] Based on the constructed equivalent circuit of the frequency-varying distributed parameters, the present invention defines the impedance branch matrix, the admittance branch matrix, the voltage and current vectors, and the incidence matrix, and establishes a general parametric model of the equivalent circuit of the frequency-varying distributed parameters.

[0019] The present invention performs Fourier decomposition on the multi-port voltage waveforms of a high-frequency transformer under cascaded conditions, extracts the harmonic component spectra of the voltages at each port, and provides accurate data support for subsequent calculations. The decomposed single-frequency sinusoidal excitation voltage is used as a boundary condition and applied to the excitation node and the ground node of the general parametric model, achieving an accurate simulation of the multi-port voltage excitation condition. Based on the superposition principle, the node voltage responses of all harmonic components are synthesized to obtain the internal voltage stress distribution of the high-frequency transformer under the cascaded multi-port excitation condition. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0021] Figure 1 It is a schematic flowchart of the method according to an embodiment of the present invention.

[0022] Figure 2 It is the frequency-variable distributed parameter equivalent circuit of the constructed high-frequency transformer.

[0023] Figure 3 It is a schematic structural diagram of a terminal provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] In order to make the objectives, features, and advantages of the present invention more obvious and understandable, the following will clearly and completely describe the technical solutions in the present invention with reference to the drawings in the specific embodiments of the present invention. Obviously, the embodiments described below are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present application.

[0025] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field of the present invention. The terms used in the description of the present invention in this specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0026] Figure 1 It is a schematic flowchart of a method for calculating the internal voltage stress of a cascaded high-frequency transformer provided by the present invention. According to different requirements, the order of the steps in this flowchart can be changed, and some can be omitted.

[0027] As Figure 1 shown, the method includes: Step S1: According to the pre-stored external cascading method, internal topology, converter characteristics, and control strategy of the DC-DC isolation converter, simulate to obtain the time-domain voltage waveforms of each port of the high-frequency transformer in the DC-DC isolation converter under cascading conditions, and extract the spectral information of the voltage waveforms through frequency-domain analysis; Step S2: Based on the finite element method, establish a frequency-varying distributed parameter extraction model of the high-frequency transformer, and input the spectral information into the frequency-varying distributed parameter extraction model to extract the frequency-varying distributed parameters at different frequencies. The frequency-varying distributed parameters include conductance parameters, capacitance parameters, resistance parameters, and inductance parameters; Step S3: In the established frequency-varying distributed parameter extraction model, take each turn of the winding of the high-frequency transformer as an independent calculation unit, and distribute the extracted frequency-varying distributed parameters to the impedance branch and admittance branch corresponding to the independent calculation unit according to the pre-stored inter-turn geometric relationship and current path, and construct an equivalent circuit of the frequency-varying distributed parameters of the high-frequency transformer; Step S4: Based on the constructed equivalent circuit of the frequency-varying distributed parameters, define the impedance branch matrix, admittance branch matrix, voltage-current vector, and incidence matrix, and establish a general parametric model of the equivalent circuit of the frequency-varying distributed parameters; Step S5: Perform Fourier decomposition on the multi-port voltage waveforms of the high-frequency transformer under cascading conditions, determine the target spectral range and truncation order, and extract the harmonic component spectra of the voltages of each port; Step S6: Take the decomposed single-frequency sinusoidal excitation voltage as the boundary condition and apply it to the excitation node of the general parametric model to solve the voltage value of the response node; Step S7: Based on the superposition principle, synthesize the node voltage responses of all harmonic components to obtain the internal voltage stress distribution of the high-frequency transformer under the cascaded multi-port excitation condition.

[0028] Among them, Step S1 includes: Step S11: Obtain the pre-stored DC-DC isolation converter parameters, including the external cascading method, internal topology, converter device characteristics, and control strategy; among them, the external cascading method is the electrical connection relationship between pre-stored multi-stage converters; the internal topology includes the circuit configurations of pre-stored full-bridge, half-bridge, or LLC resonant topologies; the control strategy includes the duty cycle of the pre-stored pulse width modulation signal and switching frequency ; the converter device characteristics include the conduction time of the MOSFET in the converter and pulse rise time ; Step S12: Based on the obtained DC-DC isolation converter parameters, construct an equivalent circuit model of the cascaded DC-DC isolation converter in a circuit simulation tool to simulate the time-domain voltage waveforms of each port of the high-frequency transformer under cascading conditions; Step S13: Perform spectral analysis on the time-domain voltage waveforms of each voltage port through fast Fourier transform, extract the harmonic frequency range, and output the spectral information including the fundamental frequency, harmonic amplitude, and phase. Store the spectral information as a frequency-domain data set.

[0029] Further, the simulation equation for the time-domain voltage waveforms of each port of the high-frequency transformer under cascaded conditions is: ; Where is the simulation function, which internally includes Kirchhoff's law, device transient models (such as MOSFET switch models, diode reverse recovery models), and magnetic core nonlinear models; is the internal topology function, which characterizes the circuit connection relationship of the full-bridge LLC topology (such as the on-off logic of the upper and lower tubes of the H-bridge); is the nonlinear magnetic permeability; and are the time-domain voltage waveforms of the high-voltage and low-voltage ports respectively.

[0030] Taking "2 full-bridge LLC converters cascaded (IPOS topology)" as the object, retrieve the electrical connection drawings of the corresponding model converters from the preset cascaded topology library (such as the "input parallel - output series (IPOS)" topology diagram), clarify the port connection relationship between multiple converters (such as the high-voltage sides HV1 and HV2 in parallel, and the low-voltage sides LV1 and LV2 in series), and mark the physical interface and terminal connection correspondence of the high-voltage port (parallel input, voltage 800V), and the low-voltage port (series output, target voltage 1600V).

[0031] Call the circuit configuration file in the preset power topology library (such as the CAD drawing of the full-bridge LLC topology), identify the layout of the core power devices (internal topology structure), and build an equivalent circuit in a circuit simulation tool (such as PLECS) according to the circuit principle of the full-bridge LLC topology - the primary-side H-bridge (generating high-frequency square waves) consists of 4 MOSFETs, and the secondary side consists of 2 synchronous rectifier diodes ((model IDW30G65C5)), with an intermediate series resonant capacitor and a high-frequency transformer (including the exciting inductance , leakage inductance ).

[0032] Export the PWM (Pulse Width Modulation) signal parameters from the control board parameter configuration system - the duty cycle (determines the conduction pulse of the PWM square wave, set according to the power adjustment requirement), the switching frequency (Determine the fundamental frequency of the PWM square wave, which is matched by the resonator design), determine the fundamental frequency and pulse width of the voltage waveform, and maximize the resonance gain of the LLC (Low-Loss Coupling) topology.

[0033] Obtain the characteristics of the converter devices: MOSFET characteristics: Refer to the data sheet of the used model (such as IPW60R041C6) to extract the turn-on time of the MOSFET (A time constant representing the transition of the MOSFET from the off high-impedance state to the on low-impedance state, representing the switching speed ( The larger it is, the slower the drain-source resistance drops, and the drain-source voltage has a flatter falling edge, indirectly resulting in a lower slope of the rising edge of the load current and the port voltage)), pulse rise time (During the turn-off stage of the MOSFET, the time when the drain-source voltage drops from 90% of the rated value to 10% of the rated value, reflecting the turn-off speed ( The smaller it is, the lower the turn-off loss and the better the voltage spike suppression effect)); Core characteristics (retrieve the N87 ferrite data from the pre-stored magnetic core material library): Based on the retrieved B-H curve of the N87 core, calculate the non-linear permeability (When the magnetic field strength H changes, the permeability adjusts dynamically. When the magnetic field strength is reached, the permeability is approximately constant; where is the saturation threshold of the magnetic field strength), and embed it into the excitation inductance model of the high-frequency transformer (N is the number of turns, is the cross-sectional area of the magnetic core, is the magnetic path length).

[0034] Based on the above parameters, simulate the time-domain voltage waveform at the port of the high-frequency transformer under cascade conditions according to the above simulation equation.

[0035] For the time-domain voltage waveform obtained by simulation (such as the HV port , ), set the sampling frequency to 10 times the switching frequency (1 MHz), that is, the sampling frequency ), to avoid high-frequency harmonic aliasing.

[0036] Apply a Blackman-Harris window to the sampled time-domain signal (to suppress spectral leakage), and decompose it through the fast Fourier transform (FFT) to obtain the frequency, amplitude, and phase of each harmonic: Fundamental frequency , and the corresponding amplitude is times the effective value of the port voltage (such as the fundamental amplitude of the HV port is about 752 V); Harmonic frequencies such as the 3rd and 5th harmonics are , , and their amplitudes are jointly determined by the topological harmonic characteristics (such as the resonance gain of the LLC topology) and device characteristics (such as the high-frequency oscillations introduced).

[0037] Organize the extracted spectral information into a standardized data set (such as in JSON format), including: Fundamental wave information: frequency 100 kHz, amplitude 752.3 V, phase -0.12 rad; Harmonic information: 3rd harmonic (300 kHz, 85.1 V, 2.1 rad), 5th harmonic (500 kHz, 42.7 V, -1.9 rad), etc.

[0038] Through the transient solver of the simulation tool, iteratively calculate the differential equation after coupling the above parameters, and finally output the time-domain voltage waveforms at the high / low voltage ports of the high-frequency transformer , .

[0039] Directly correlate the fundamental wave frequency in the frequency-domain data set with the control strategy in step S11 ( ), and correlate the harmonic amplitudes and phases with the characteristics of the converter devices in step S12, ensuring the closure of the technical chain of "time domain - frequency domain - device characteristics", ensuring the accuracy and reliability of the simulation results, and providing a strong guarantee for the optimal design of the high-frequency transformer and the reliability assessment of the insulation system.

[0040] The present invention ensures the comprehensiveness and accuracy of the simulation model by obtaining and integrating multi-dimensional parameters such as the external cascading method, internal topological structure, converter device characteristics, and control strategy. The external cascading method clarifies the electrical connection relationship between multiple-level converters, the internal topological structure defines the circuit configuration, the control strategy determines the fundamental frequency and pulse width of the voltage waveform, and the converter device characteristics correct the on / off transient characteristics of the power devices, providing a solid physical basis for the simulation. By consulting the data manuals and magnetic core material libraries, Based on the circuit principle of the full-bridge LLC (L-network linked coupled inductor) topology, an equivalent circuit is built in a circuit simulation tool in the present invention, realizing the accurate mapping of the topology structure and the control strategy. By integrating the device characteristics into the simulation model, the present invention can accurately simulate the conduction voltage drop of the power device, the turn-off overshoot, and the saturation effect of the magnetic core, so as to obtain more realistic simulation results. By introducing simulation equations including Kirchhoff's law, device transient models, and magnetic core nonlinear models, the present invention realizes the refined simulation of the time-domain voltage waveforms at each port of the high-frequency transformer. Parameters such as the internal topology structure function and the nonlinear magnetic permeability in the simulation equations enable the simulation results to accurately reflect the working state of the actual circuit.

[0041] The present invention performs spectral analysis on the time-domain voltage waveforms obtained by simulation through the fast Fourier transform, efficiently extracting key spectral information such as the harmonic frequency range, fundamental frequency, harmonic amplitude, and phase. This method not only improves the analysis efficiency but also ensures the accuracy of the spectral information.

[0042] In addition, step S2 includes: Step S21, based on the finite element method, establish a frequency-varying distributed parameter extraction model of the high-frequency transformer including an electrostatic field analysis model and a steady-state magnetic field analysis model; Step S22, set the conductor boundary conditions and the properties of the insulating material according to the extracted spectral information; the conductor boundary conditions include applying a voltage excitation matching the spectral amplitude on the conductor surface and applying a grounding constraint to the reference node; the properties of the insulating material include the frequency-varying dielectric constant and conductivity of the insulating material; Step S23, input the set conductor boundary conditions and the properties of the insulating material into the constructed electrostatic field analysis model, and extract the distributed capacitance and distributed conductance of the insulating material at different frequencies. The distributed capacitance and distributed conductance respectively characterize the inter-turn / inter-layer electric field coupling and leakage current characteristics; Step S24, define the current excitation conditions according to the extracted spectral information, and the current excitation conditions are the current excitation frequency range covering the main harmonic components in the spectral information; Step S25, input the defined current excitation conditions and the pre-stored B-H curve of the iron core corresponding to the high-frequency transformer and the skin effect characteristics of the Litz wire into the constructed steady-state magnetic field analysis model, and extract the distributed resistance and distributed inductance of the Litz wire at different frequencies (that is, extract the distributed resistance and distributed inductance of the Litz wire considering the frequency-dependent electrical effect of the iron core (the B-H curve of the iron core reflects the nonlinear relationship between the magnetic induction intensity B and the magnetic field strength H, and this relationship changes with frequency (eddy currents intensify at high frequencies, the equivalent magnetic permeability decreases, and the slope of the B-H curve decreases)) at different frequencies); Step S26: Construct a frequency-varying distributed parameter database for the high-frequency transformer based on the extracted distributed capacitance, distributed conductance, distributed resistance, and distributed inductance.

[0043] In finite element software (such as Ansys Maxwell), construct an electrostatic field analysis model (focusing on the insulating medium to extract electric field parameters) and a steady-state magnetic field analysis model (focusing on the conductor and magnetic core to extract magnetic field parameters) respectively: Electrostatic field model: Simulate the electric field distribution of inter-turn / inter-layer insulation and output the distributed capacitance (characterizing the electric field coupling strength) and the distributed conductance (characterizing the leakage current loss); Steady-state magnetic field model: Simulate the magnetic field distribution of the Litz wire and magnetic core and output the distributed resistance (characterizing the skin effect loss) and the distributed inductance (characterizing the magnetic field energy storage and the nonlinearity of the magnetic core).

[0044] Geometric model and mesh generation: Import the three-dimensional geometric model of the high-frequency transformer (including the number of winding turns, insulation thickness, and magnetic core size), and refine the meshes in the regions with large electric field gradients (such as the inter-turn gap and inter-layer insulation) and large magnetic field gradients (such as the surface of the Litz wire and the air gap of the magnetic core) (mesh size ≤ 1 / 5 skin depth or the characteristic length of electric field change) to ensure the simulation accuracy (such as the calculation error of the electric field strength < 5%).

[0045] Conductor boundary conditions (associated with the spectrum in step S13): Voltage excitation: Apply a multi-frequency voltage excitation matching the frequency-domain data set in step S13 on the surface of the winding conductor - the fundamental wave amplitude is taken as the fundamental wave amplitude of the high-voltage port (such as 752.3V, corresponding to ), and the amplitudes of the 3rd and 5th harmonics are taken as the corresponding components (such as 85.1V, 42.7V, corresponding to and ) to simulate the voltage stress spectrum under the cascaded condition; Grounding constraint: Set the reference node of the transformer magnetic core or the low-voltage winding to ground (potential 0V) to restore the potential reference logic of the actual circuit and ensure that the electric field calculation boundary is consistent with the engineering scenario.

[0046] Properties of insulating materials (frequency-varying characteristics): Frequency-varying dielectric constant : Consult the frequency-varying dielectric spectrum of the insulating material (such as polyimide film) (obtained from the supplier's technical manual or measured data), input the dielectric constant values at different frequencies (such as at 100 kHz and at 1 MHz) to reflect the frequency dependence of the polarization ability of the insulating material (such as the attenuation of the dielectric constant caused by the lag of molecular polarization at high frequencies).

[0047] Frequency-dependent conductivity Similarly, the frequency-dependent conductivity of the input insulating material (e.g., at 100 kHz , at 1 MHz ) characterizes the dynamic change of the leakage current in the insulating material at high frequencies (e.g., the increase in the conductivity due to the improvement of the high-frequency ion mobility).

[0048] Physical principle of parameters: Distributed capacitance : Reflects the electric field coupling strength between turns / layers of insulation, and satisfies the relationship with the relative permittivity of the insulating material , the coupling area A between turns, and the insulation thickness d ; Distributed conductance : Reflects the leakage current characteristics of the insulating medium, and satisfies the relationship with the conductivity of the insulating material , the coupling area A between turns, and the insulation thickness d .

[0049] Electrostatic field simulation and parameter extraction: Input the multi-frequency voltage excitation (fundamental wave + harmonics), ground constraint, and frequency-dependent properties of the insulating material in step S22 ( , ) into the electrostatic field analysis model, and solve the Maxwell's electric field equation (when there is no free charge) to obtain the electric field distribution at different frequencies.

[0050] Current excitation frequency range: Refer to the main harmonic components (fundamental wave , 3rd harmonic , 5th harmonic ) in the frequency-domain data set in step S13, and define the current excitation frequencies as 100 kHz, 300 kHz, and 500 kHz, covering the main harmonic components of the litz wire current under the LLC topology to ensure that the magnetic field parameter extraction matches the actual current spectrum.

[0051] Current amplitude matching: The amplitude of the current excitation is derived from the load current in the simulation equation in step S12 (e.g., for a 10 kW converter, the full-load current is about 12.5 A, and the amplitude of the fundamental wave current is about 17.7 A), ensuring that the excitation current intensity is consistent with the actual working conditions.

[0052] Physical principle of parameters: Distributed resistance : Reflects the high-frequency skin effect of the litz wire. The higher the frequency, the smaller the skin depth ( is the angular frequency, is the copper conductivity), the effective conductive area decreases, and the resistance increases; Distributed inductance : Reflects the self - inductance of the Litz wire, the mutual inductance between turns, and the non - linear magnetic permeability of the iron core Resulting in the inductance frequency dependence (when magnetic saturation occurs, attenuation, and the inductance decreases synchronously).

[0053] Magnetic field simulation and parameter extraction: Input the multi - frequency current excitation (amplitude + frequency) in step S24, the B - H curve of the iron core (input the non - linear magnetic permeability , such as the measured magnetization curve of ferrite N87), the skin effect characteristics of the Litz wire (input the copper conductivity , the magnetic permeability of vacuum μ0 = 4π×10 −7 H / m, calculate the skin depth ) into the steady - state magnetic field analysis model, and solve the Maxwell magnetic field equation , ( is the vector magnetic potential).

[0054] Store data in the dimension of "frequency - spatial position - parameter", and the example is as follows (structured description): Frequency dimension: Covers the main harmonic frequencies in step S13 (100kHz, 300kHz, 500kHz, etc.); Spatial position dimension: Distinguish "between turns" (such as between the 1st turn and the 2nd turn), "between layers" (such as between the 1st layer and the 2nd layer); Parameter dimension: Store the distributed capacitance , the distributed conductance , the distributed resistance , the distributed inductance .

[0055] For example: At 100kHz, the distributed capacitance between turns of the windings between the 1st layer and the 2nd layer is 22.3pF, and the distributed conductance is 1.5nS; the distributed resistance of the 1st turn of the Litz wire is 0.05Ω, and the distributed inductance is 120nH.

[0056] Based on the finite - element method, the present invention establishes an electrostatic field analysis model and a steady - state magnetic field analysis model for high - frequency transformers, focusing on the electric and magnetic field characteristics of the insulating medium and the conductor and the magnetic core respectively, and realizes a comprehensive analysis of the frequency - variable distributed parameters of high - frequency transformers. This multi - dimensional analysis model construction method ensures the accuracy and comprehensiveness of parameter extraction. During the model construction process, the present invention fully considers physical principles such as the frequency - variable dielectric constant and conductivity of insulating materials, the skin effect of Litz wires, and the non - linear magnetic permeability of iron cores, making the simulation results closer to the actual physical process.

[0057] Based on the spectral information extracted in step S13, the present invention applies a voltage excitation on the conductor surface that matches the spectral amplitude and applies a ground constraint to the reference node. This precisely matched setting of the conductor boundary conditions ensures the accuracy and reliability of the voltage excitation during the simulation process, providing a solid foundation for subsequent parameter extraction. By referring to the frequency-dependent dielectric spectra and conductivity data of the insulating material, the present invention inputs the permittivity and conductivity values at different frequencies into the simulation model, accurately reflecting the polarization ability and leakage current characteristics of the insulating material at different frequencies.

[0058] By inputting the set conductor boundary conditions and insulating material properties into the electrostatic field analysis model, the present invention successfully extracts the distributed capacitance and distributed conductance of the insulating material at different frequencies. These parameters respectively characterize the inter-turn / inter-layer electric field coupling and leakage current characteristics. At the same time, through the steady-state magnetic field analysis model, the present invention extracts the distributed resistance and distributed inductance of the Litz wire at different frequencies. These parameters reflect the high-frequency skin effect and magnetic field energy storage characteristics of the Litz wire. During the geometric model and mesh generation process, the present invention performs encrypted mesh processing on regions with large electric field gradients and large magnetic field gradients, ensuring the simulation accuracy. At the same time, by defining current excitation conditions that match the actual current spectrum, the present invention improves the efficiency and accuracy of magnetic field parameter extraction.

[0059] Based on the extracted distributed capacitance, distributed conductance, distributed resistance, and distributed inductance, the present invention constructs a frequency-dependent distributed parameter database for the high-frequency transformer. This database stores data in the dimension of "frequency - spatial position - parameter", realizing the structured management and efficient query of the frequency-dependent distributed parameters of the high-frequency transformer.

[0060] In addition, step S3 includes: Step S31: Discretize each turn of the winding of the high-frequency transformer into independent calculation units, define the unit numbers corresponding to each independent calculation unit in the high-voltage and low-voltage windings, and establish a geometric relationship mapping table between the units based on the unit numbers. The mapping table records the current path topology and the inter-turn / inter-layer geometric relationship including the inter-turn distance and the inter-layer insulation thickness; Step S32: Map the distributed capacitance and distributed conductance parameters of the insulating material to the admittance branches between the units that characterize the electric field coupling characteristics according to the inter-turn / inter-layer geometric relationship; map the distributed resistance and distributed inductance parameters of the Litz wire to the impedance branches in the units that characterize the magnetic field coupling characteristics according to the current path topology; the distributed inductance parameters include self-inductance and mutual inductance parameters between adjacent turns; Step S33: Take the two ends of each turn of the winding as independent nodes, connect impedance branches in series between adjacent nodes, realize magnetic field coupling between non-adjacent nodes through mutual inductance branches, and connect admittance branches in parallel between each node and the reference ground to form a chain node network of the high-voltage and low-voltage windings, completing the construction of the frequency-dependent distributed parameter equivalent circuit of the high-frequency transformer.

[0061] Furthermore, the distributed capacitance and distributed conductance parameters of the insulating material are mapped to the admittance branch that characterizes the electric field coupling characteristics between units according to the inter-turn / inter-layer geometric relationship. The specific expression is as follows: ; ; where, is the distributed capacitance, characterizing the frequency-varying capacitance between the i-th turn and the j-th turn of the winding; is the frequency-varying permittivity, characterizing the polarization ability of the insulating material at different frequencies f, reflecting the dynamic change of the electric field coupling strength with frequency, with the unit of F / m; is the coupling area, characterizing the effective area of the electric field overlap between the i-th turn and the j-th turn of the winding; is the dielectric thickness, characterizing the physical thickness of the insulating layer between the i-th turn and the j-th turn of the winding; is the distributed conductance, characterizing the frequency-varying conductance between the i-th turn and the j-th turn of the winding; is the frequency-varying conductivity, characterizing the leakage current characteristics of the insulating material at different frequencies f, reflecting the dynamic change of the dielectric loss with frequency, with the unit of S / m; The distributed resistance and distributed inductance parameters of the Litz wire are mapped to the impedance branch that characterizes the magnetic field coupling characteristics in the unit according to the current path topology. The specific expression is as follows: ; ; where, is the distributed resistance, characterizing the frequency-varying resistance of the i-th turn of the winding; is the resistance per unit length, characterizing the AC resistance of the Litz wire per meter at high frequencies; is the effective length of the current path; is the distributed inductance, characterizing the frequency-varying inductance of the i-th turn of the winding; is the inductance per unit turn, characterizing the equivalent inductance of a single-turn winding at high frequencies; is the number of adjacent coupled turns, characterizing the effective number of winding turns that magnetically couple with the i-th turn of the winding.

[0062] Taking the high-frequency transformer of a 10kW full-bridge LLC converter as an example (20 turns on the primary side and 5 turns on the secondary side, using Litz wire windings), each turn on the primary side and each turn on the secondary side are divided into independent calculation units. Define the primary side unit number as , and the secondary side as , and clarify the correspondence relationship of "unit number → physical winding position" (e.g., corresponds to the innermost first turn on the primary side).

[0063] Measure and record the current path topology and turn - to - turn / layer - to - layer geometric parameters between units to form a two - dimensional table: Current path topology: The primary winding is wound in a clockwise spiral, and the current flows in from the head end and out from the tail end; The secondary winding is wound in a counter - clockwise spiral, and the current flows in from the head end and out from the tail end.

[0064] For unit pairs (such as ), combine the frequency - varying distributed capacitance extracted in step S23, the distributed conductance, and the geometric parameters in the mapping table, calculate through the above formula, and use the frequency - varying distributed capacitance and the distributed conductance as the admittance branch parameters to connect and the corresponding nodes to characterize the turn - to - turn electric - field coupling strength and leakage - current loss.

[0065] For a single unit (such as ), combine the frequency - varying distributed resistance extracted in step S25, the distributed inductance (including self - inductance and mutual inductance between adjacent turns), the current - path length, the number of adjacent coupled turns, calculate through the above formula, and use the frequency - varying distributed resistance and the distributed inductance as the impedance - branch parameters to connect in series between the head - end and tail - end nodes to characterize the high - frequency skin effect loss and magnetic - field energy - storage characteristics of the Litz wire.

[0066] Set the head - end and tail - end of each turn of the winding as independent nodes (such as the head - end is node and the tail - end is node ; the head - end is and the tail - end is , and so on), and establish a "unit → double - node" mapping relationship.

[0067] Branch - topology integration: Series impedance branch: Connect the impedance branches of the corresponding units in series between adjacent nodes (such as connect in series of , ; connect in series of , ); Mutual inductance branch connection: Magnetic field coupling is achieved between non - adjacent units through mutual inductance branches (such as and there is mutual inductance , then between () end) and () end), a mutual inductance branch is connected ); Admittance branch to ground: A shunt admittance branch is connected between each node and the reference ground (such as shunt - connected to ground , where , are the distributed capacitance and conductance between Figure 2 and ground). The frequency - dependent distributed parameter equivalent circuit of the constructed high - frequency transformer is as shown in

[0068] In the present invention, each turn of the winding of the high - frequency transformer is discretized into independent calculation units, and the number of each unit is defined, realizing a refined description of the internal structure of the transformer. This discretization method makes subsequent parameter mapping and circuit construction more accurate. Based on the unit numbers, a geometric relationship mapping table between units is established, recording the current path topology and the geometric relationship between turns / layers, providing a basis for subsequent parameter mapping. This mapping relationship ensures the accuracy and consistency of parameter mapping.

[0069] In the present invention, the distributed capacitance and distributed conductance parameters of the insulating material are mapped to the admittance branches representing the electric - field coupling characteristics between units according to the geometric relationship between turns / layers, and specific mathematical expressions are given. This mapping method accurately reflects the electric - field coupling strength and leakage - current characteristics of the insulation between turns / layers, providing key parameters for the construction of the circuit model. The distributed resistance and distributed inductance parameters of the Litz wire are mapped to the impedance branches representing the magnetic - field coupling characteristics in the unit according to the current - path topology, and specific mathematical expressions are also given. This mapping method takes into account the high - frequency skin effect and magnetic - field energy - storage characteristics of the Litz wire, making the circuit model closer to the actual physical process.

[0070] In the present invention, both ends of each turn of the winding are used as independent nodes, impedance branches are connected in series between adjacent nodes, magnetic - field coupling is achieved between non - adjacent nodes through mutual inductance branches, and a shunt admittance branch is connected between each node and the reference ground. This definition method of nodes and branches forms a chain - type node network for the high - and low - voltage windings, providing a structural basis for the construction of the circuit model. Through the integration of series impedance branches, mutual inductance - branch connections, and admittance branches to ground, a complete frequency - dependent distributed parameter equivalent circuit of the high - frequency transformer is constructed. This circuit model can accurately reflect the electrical characteristics of the high - frequency transformer at different frequencies, providing strong support for subsequent circuit simulation and analysis.

[0071] After that, step S4 includes: Step S41: Based on the number of nodes and branches in the constructed frequency-varying distributed parameter equivalent circuit, define the dimensions of the impedance branch matrix and the admittance branch matrix, and define variables including the node voltage vector, the impedance branch current vector, and the admittance branch current vector; Step S42: Based on the corresponding dimensions and variables defined for the impedance branches, integrate the frequency-varying parameters of all impedance branches in the frequency-varying distributed parameter equivalent circuit to form the impedance branch matrix; Step S43: Based on the corresponding dimensions and variables defined for the admittance branches, integrate the frequency-varying parameters of all admittance branches in the frequency-varying distributed parameter equivalent circuit to form the admittance branch matrix; Step S44: Define the incidence matrix that describes the connection relationship between the admittance branches / impedance branches and the nodes; Step S45: Through Kirchhoff's law, associate the incidence matrix, the impedance branch matrix, the admittance branch matrix with the node voltage vector to form the solution equation for the network node voltage in the frequency-varying distributed parameter equivalent circuit, and complete the construction of the general parametric model of the frequency-varying distributed parameter equivalent circuit.

[0072] Specifically, taking the example of "each of the high-voltage and low-voltage windings contains n = 2 units" (primary side , ; secondary side , ), define the matrix dimensions and variables according to the following rules: Number of nodes: For a single-winding with n units, it corresponds to n + 1 nodes (such as for the primary side , corresponding to nodes , , ), and for a double-winding, they share 1 reference ground node , so the total number of nodes is 2n + 2 = 6 (node list: , , , , , ).

[0073] (1) The matrix is used to represent all the impedance branches composed of resistors and inductors in the distributed parameter model, with a total of 2n impedance branches (in accordance with both the high-voltage and low-voltage windings having n units and n + 1 nodes, the same below).

[0074] (2) The matrix It is used to represent the admittance branches composed of all conductances and capacitances in the distributed parameter model, a total of 2n+2 admittance branches.

[0075] (3) Column vector , and They represent the node voltage, impedance branch current and admittance branch current respectively, and their orders are 2n+2, 2n and 2n+2 respectively.

[0076] Incidence Matrix It can be expressed as: (4) Combining equations (1) to (4), we can get the relationship between the voltage and current of the high-frequency transformer winding distributed parameter network: (5) Combining equation (5), we can get the solution equation of network node voltage under the condition of no external voltage: (6) in, To solve the coefficient matrix of the equation; by implementing the above equations (1) to (6) through programming, a general parameterized model of the frequency-variable distributed parameter equivalent circuit of the high-frequency transformer can be constructed.

[0077] The present invention establishes a systematic model framework in step S4 by defining the dimensions of the impedance branch matrix, the admittance branch matrix, and variables such as the node voltage vector, the impedance branch current vector, and the admittance branch current vector. This systematic model construction method enables the electrical characteristics of the high-frequency transformer to be accurately described in the form of a mathematical matrix, providing a basis for subsequent circuit analysis and optimization. By defining a unified matrix dimension and variable naming rules, step S4 ensures the consistency and comparability of high-frequency transformers of different specifications and types in model construction. This unified standard helps technicians share experience and exchange technology between different projects.

[0078] The present invention forms a complete impedance branch matrix in step S4 by integrating the frequency-dependent parameters of all impedance branches in the frequency-dependent distributed parameter equivalent circuit. The matrix can accurately reflect the resistance and inductance characteristics of the high-frequency transformer at different frequencies, and provides key parameters for circuit simulation and analysis. Similarly, by integrating the frequency-dependent parameters of all admittance branches, step S4 forms a complete admittance branch matrix. The matrix can accurately reflect the conductance and capacitance characteristics of the high-frequency transformer at different frequencies, and further improves the description of the circuit model.

[0079] Through defining the incidence matrix that describes the connection relationship between the admittance branch / impedance branch and the nodes, step S4 clarifies the topological relationship between each branch and the nodes in the circuit model. This way of defining the incidence matrix makes the structure of the circuit model clearer, facilitating circuit analysis and fault troubleshooting for technicians. By applying Kirchhoff's laws to associate the incidence matrix, impedance branch matrix, admittance branch matrix with the node voltage vector, step S4 forms a solution equation for a complete frequency-varying distributed parameter equivalent circuit. This equation can accurately describe the electrical characteristics of the high-frequency transformer under different working conditions, providing a mathematical basis for circuit simulation and analysis.

[0080] The present invention realizes the above solution equation through programming. Step S4 constructs a general parametric model of the frequency-varying distributed parameter equivalent circuit of the high-frequency transformer. This model has good versatility and scalability and can be applied to high-frequency transformers of different specifications and types. By simply adjusting the matrix dimension and parameter values, the rapid construction and simulation analysis of the model can be achieved. By constructing the general parametric model, step S4 provides strong support for the circuit simulation and analysis of the high-frequency transformer. Technicians can use this model to conduct circuit simulations under different working conditions, predict the electrical performance of the high-frequency transformer, and optimize and improve the design.

[0081] Step S5 includes: Step S51: Perform Fourier decomposition on the obtained cascaded multi-port voltage waveform to extract the harmonic component amplitudes and phases of each port voltage; Step S52: Based on the pre-stored parameter effective frequency range in the extracted frequency-varying parameter database, combined with the frequency-varying dielectric characteristics set in the insulation material properties, determine the target frequency spectrum range; Step S53: Calculate the minimum truncation order K according to the target frequency spectrum range and the preset harmonic truncation accuracy threshold; Step S54: Extract the harmonic component spectra within the Kth order of each port and output a harmonic data set including frequency, amplitude, and phase.

[0082] Based on the method in step S1, the voltage waveforms V i (t) of different ports of the high-frequency transformer under the cascaded condition of the DC-DC isolation converter are obtained, where i is the port number of the high-frequency transformer. If the voltage is an ideal square wave with a period T (T = 1 / f s ), f s is the fundamental frequency of the voltage wave, D i is its duty cycle. Within each period, the amplitude of V i (t) is V i in the first D i T time, and the amplitude of V i (t) is -V i in the subsequent (1 - D iBy performing independent Fourier decomposition on the square wave of each port, the following can be obtained: (7) In the formula, ; , where k represents the kth harmonic.

[0083] The actual square wave has a finite rise time and fall time , and the waveform is closer to a trapezoidal wave. At this time, the Fourier coefficients need to be corrected, and according to the Shannon sampling theorem, the key parameters are truncated, where K is the truncation order ( , is the highest frequency of concern): (8) where is the phase shift (determined by timing control).

[0084] For the kth harmonic component of each excitation port i, the excitation vector is set as: (9) The frequency-domain expressions of the voltages of each port in Equation (9) are the boundary conditions of the network parameterization model in step S4, where is the transpose operator.

[0085] In the present invention, by performing Fourier decomposition on the obtained cascaded multi-port voltage waveforms, step S5 can accurately extract the amplitudes and phases of the harmonic components of the voltages of each port. This decomposition method enables complex periodic voltage waveforms to be decomposed into the superposition of a series of simple sine waves and cosine waves, facilitating subsequent analysis and processing. The extracted amplitude and phase information of the harmonic components provides technicians with a comprehensive understanding of the harmonic characteristics of the voltage waveforms, which helps to analyze the electrical performance of high-frequency transformers under different operating conditions.

[0086] Based on the effective frequency range of the parameters pre-stored in the extracted frequency-variable parameter database and combined with the frequency-variable dielectric characteristics set in the insulating material properties, step S5 can accurately determine the target frequency spectrum range. This determination method ensures the pertinence and effectiveness of subsequent analysis, avoiding unnecessary calculation and analysis burdens. By accurately determining the target frequency spectrum range, step S5 enables the frequency spectrum analysis to focus on the frequency range that has the greatest impact on the electrical characteristics of high-frequency transformers, improving the accuracy and efficiency of the analysis.

[0087] According to the target frequency spectrum range and the preset harmonic truncation accuracy threshold, step S5 can reasonably calculate the minimum truncation order K. This calculation method ensures that the error between the waveform after harmonic truncation and the original waveform is within an acceptable range, guaranteeing the accuracy of the analysis. By reasonably calculating the minimum truncation order K, step S5 avoids unnecessary harmonic calculations and analyses, optimizing the utilization efficiency of computing resources.

[0088] The present invention extracts the harmonic component spectra within the Kth order for each port and outputs a harmonic data set including frequency, amplitude, and phase. Step S5 realizes the comprehensive integration and output of key harmonic information. Such a data set provides rich data support for the subsequent construction of the network parametric model and simulation analysis. The output harmonic data set has traceability and reusability, facilitating data sharing and reuse among technicians in different projects, and improving work efficiency and data utilization rate.

[0089] For the kth harmonic component of each excitation port i, the present invention sets the excitation vector as an expression including frequency, amplitude, and phase. Step S5 realizes the accurate construction of the excitation vector. This construction method enables the excitation vector to accurately reflect the harmonic characteristics of the actual voltage waveform, providing accurate boundary conditions for the solution of the subsequent network parametric model. By precisely setting the boundary conditions, step S5 improves the accuracy of the solution of the network parametric model, making the simulation results closer to the actual electrical characteristics.

[0090] Aiming at the finite rise time and fall time of the actual square wave, step S5 effectively processes the non-ideal square wave by correcting the Fourier coefficients and truncating the key parameters according to the Shannon sampling theorem. This processing method makes the analysis closer to the actual working conditions and improves the practicability and reliability of the model.

[0091] Step S6 includes: Step S61: Based on the node network of the frequency-varying distributed parameter equivalent circuit constructed, determine the nodes where the excitation is applied, the grounding nodes, and the corresponding node numbers of the above nodes; Step S62: According to the node numbers of the excitation nodes and the grounding nodes, delete the corresponding rows and columns in the coefficient matrix of the node voltage solution equation, extract the column vector of the coefficient matrix corresponding to the node number of the excitation node and move it to the right side of the solution equation, and construct a new solution equation for all response nodes to realize the application of the excitation in the analytical calculation process; Step S63: Based on the newly constructed solution equation for all response nodes, calculate the frequency-domain voltage vector of all response nodes and output the voltage response amplitudes and phases of all nodes at this frequency.

[0092] In step S5, the square-wave excitation voltage of different port classes in Equation (9) is decomposed into sine excitations within a certain frequency spectrum. The sine voltages within the target frequency spectrum of all ports are applied to the parametric model at different frequencies respectively, and the nodal voltages in this state are calculated (single-frequency excitation). Finally, the superposition principle is used to solve the total response waveform.

[0093] The present invention proposes the following method for applying single-frequency excitation boundary conditions: Take the numbers of all excitation nodes, grounding nodes, and response nodes in the distributed parameter model to form sets d, g, and r. Delete all elements in the d-th row and d-th column and the g-th row and g-th column of the coefficient matrix M in Equation (6) of step four to form a new square matrix N of order (2n + 2 - numel(d) - numel(g)); After deleting the d-th and g-th elements from the d-th column of M, form a new column vector N of dimension (2n + 2 - numel(d) - numel(g)) d , to form a new equation: (10) where, U r is the original nodal voltage column vector U after deleting the known voltages U d and U g elements, consisting of all (2n + 2 - numel(d) - numel(g)) unknown nodal voltage values to be solved, that is, all voltages with the numbers of response node numbers r. Using Equation (10), the single-frequency excitation voltage boundary conditions of all ports can be applied to the distributed parameter network of the high-frequency transformer to solve the voltage values of all unknown response nodes.

[0094] Specifically, in combination with the 6-node chain equivalent circuit constructed in step S3 ( , , primary side with 2 turns + secondary side with 2 turns + shared reference ground), clarify the physical meanings and numbering rules of the three types of nodes: 1. Excitation nodes (set d): The voltage application nodes for the parallel input on the primary side, select the first end of the first turn on the primary side , the first end of the second turn on the primary side , numbered ( , , , , , The nodes are sorted in order).

[0095] 2. Grounding nodes (set g): The circuit reference ground node , numbered (the potential of the grounding node is constantly 0V).

[0096] 3. Response Node (Number Set r): The secondary side series output node for which the voltage needs to be solved, select the end of the first turn of the secondary side and the end of the second turn of the secondary side , numbered .

[0097] Based on the general parametric model in Step S4, the core equation for solving the node voltage is Equation (6) in Step Four (homogeneous equation without applied voltage, and the applied voltage is embedded through boundary conditions). Combining the excitation node d and the grounding node g, perform the following matrix operations: 1. Coefficient Matrix Cropping: The original coefficient matrix has a dimension of 6×6 (corresponding to 2n + 2 nodes).

[0098] Delete the rows / columns corresponding to the excitation node d: Remove the first and second rows and the first and second columns (corresponding to , the rows and columns); Delete the rows / columns corresponding to the grounding node g: Remove the sixth row and the sixth column (corresponding to the rows and columns); After cropping, the new matrix has a dimension of (6−2−1)×(6−2−1)=3×3 (the remaining nodes are , , ).

[0099] 2. Excitation Column Vector Extraction: The d-th column of the original coefficient matrix (the column corresponding to the excitation node), after deleting the first and second rows (the rows of the excitation node itself) and the sixth row (the row of the grounding node), form a new column vector with a dimension of 3×1.

[0100] 3. Reorganize the Solving Equation: In the original node voltage column vector , the voltage of the excitation node (determined by the fundamental / harmonic amplitude of the frequency domain data set in Step S13) and the grounding voltage are known quantities, and the remaining unknown quantity is the voltage of the response node (with a dimension of 3×1, corresponding to the voltages , , ). The final reorganized equation is: .

[0101] Taking the fundamental frequency f1 = 100 kHz as an example, combining the frequency-domain data set in step S13 with the distribution parameters in step S2, the solution of the response node voltage and the characteristic output are completed: 1. Excitation voltage assignment: Obtain the excitation node from the frequency-domain data set in step S13 、 fundamental voltage: Amplitude: 、 , paralleled on the primary side, with equal voltage amplitudes; Phase: both are (synchronized triggering by the control strategy, with consistent PWM initial phases).

[0102] 2. Matrix inversion and voltage solution: Substitute the trimmed coefficient matrix (including the frequency-varying distribution parameters extracted in step S2: the distributed resistance 、distributed inductance of the Litz wire, the inter-turn distributed capacitance 、distributed conductance -mapped admittance / impedance) into the recombination equation , and obtain the response node voltage through matrix inversion operation: (voltage at the end of the first turn of the secondary side ): The amplitude is determined by the electric field coupling strength between the primary excitation and the inter-turn distributed capacitance , and the measured value is about 376.1 V; (voltage at the end of the second turn of the secondary side ): The amplitude is determined by the magnetic field coupling strength between the primary excitation and the inter-layer distributed inductance , and the measured value is about 376.1 V; (voltage at the end of the second turn of the primary side ): The amplitude is determined by the midpoint voltage of the primary H-bridge topology, and the measured value is about 376.1 V.

[0103] 3. Voltage characteristic output: Output the amplitude and phase of the response node voltage: Amplitude: Reflects the voltage distribution characteristics of the cascaded topology (the voltages of the two nodes on the secondary side are superimposed to approach the primary side voltage, verifying the series boost logic); Phase: 、 (in antiphase with the primary excitation phase, conforming to the voltage transfer phase characteristics of the full-bridge LLC topology).

[0104] Based on the node network of the frequency-varying distributed parameter equivalent circuit constructed by the present invention, step S6 can accurately identify the nodes to which excitation needs to be applied and the preset grounding nodes. This identification method ensures that the excitation voltage can be accurately applied to the target nodes, providing a basis for subsequent voltage response calculation. By accurately identifying the excitation nodes and grounding nodes, step S6 improves the accuracy of constructing the frequency-varying distributed parameter equivalent circuit model, making the model closer to the actual circuit situation.

[0105] The present invention converts the single-frequency components in the extracted harmonic data set into frequency-domain complex voltage excitations. Step S6 realizes the conversion from the time domain to the frequency domain, providing convenience for subsequent frequency-domain analysis. By accurately applying the frequency-domain complex voltage excitations to the identified excitation nodes and grounding nodes, step S6 ensures that the excitation voltage can act on the circuit as expected, improving the accuracy of voltage response calculation.

[0106] The present invention inputs the frequency-domain complex voltage excitations into the solution equation of the frequency-varying distributed parameter equivalent circuit. Step S6 can efficiently calculate the frequency-domain voltage vectors of the response nodes. This calculation method avoids complex time-domain simulations and improves the calculation efficiency. By calculating the frequency-domain voltage vectors of the response nodes, step S6 can comprehensively obtain the voltage response amplitudes and phases of all nodes at this frequency, providing rich data support for subsequent insulation evaluation and design.

[0107] The single-frequency excitation boundary condition application method proposed by the present invention realizes the effective application of the single-frequency excitation voltage boundary condition by deleting specific elements in the coefficient matrix and forming a new equation. This method simplifies the calculation process and improves the solution efficiency. Using the new equation, step S6 can accurately solve the voltage values of all unknown response nodes, providing a key basis for subsequent voltage stress distribution analysis and insulation design.

[0108] The node voltage response under single-frequency excitation calculated in step S6 of the present invention provides basic data for subsequent solving the total response waveform using the superposition principle. This close connection ensures the coherence and accuracy of the entire analysis process. Through the node voltage response data obtained in step S6, technicians can further conduct insulation evaluation and design optimization to improve the insulation performance and reliability of high-frequency transformers.

[0109] Based on the constructed equivalent model of the high-frequency transformer and the method for applying different port excitations, the present invention finally realizes the analysis and calculation of the internal voltage stress under the important condition that there are excitations at all ports of the high-frequency transformer under cascade conditions, avoiding the limitation of only considering single-end excitation in traditional methods.

[0110] Step S7 includes: Based on the superposition principle, perform time-domain synthesis on the node frequency-domain voltage responses at all harmonic frequency components; According to the control strategy of the cascade topology, calibrate the initial phases of the excitations of each port to ensure that the time-domain voltage waveform is synchronized with the actual working conditions; After calibration, reorganize the time-domain voltages of all nodes according to the physical positions of the windings to form a map of the internal voltage stress distribution of the high-frequency transformer.

[0111] Specifically, select the main harmonic components (fundamental wave , 3rd harmonic , 5th harmonic ) of the frequency-domain data set in step S13, and for each node in the general parametric model in step S4 (such as the first-turn head node of the primary side , the first-turn tail node of the secondary side , etc.), synthesize the time-domain voltage according to the superposition principle, that is, the voltage distribution of each node under all harmonic components of the multi-port sinusoidal excitation in the target frequency band: (11) wherein, is the harmonic response amplitude of each node (node n) at frequency , which is derived from the analytical solution result in step S6, and its magnitude is directly related to the frequency-varying distribution parameters extracted in step S2 (such as the inter-turn distributed capacitance determines the electric field coupling strength. If increases, the harmonic amplitude will be amplified); is the harmonic response phase of node n at frequency , which is obtained by solving in step S6, and its phase difference reflects the perturbation of the device characteristics in the simulation equation. Based on Equation (11), the internal voltage stress distribution of the high-frequency transformer under the final cascade multi-port excitation condition can be obtained, which is used to evaluate the voltage borne by the insulation of the high-frequency transformer under the cascade condition of the DC-DC isolation converter, and provides a reference for the insulation design of the high-frequency transformer.

[0112] For example, fundamental wave , V, ; 3rd harmonic , V, ; 5th harmonic , V, ; the synthesized time-domain terminal voltage is: .

[0113] Taking the IPOS cascade topology as an example, combining the control strategy and the device characteristic parameters in the simulation equation, the phase calibration is implemented in two layers: Based on the control strategy of "input parallel synchronization, output series in-phase" of the IPOS cascade topology, calibrate the initial phases of the port excitations in two layers: 1. Phase reference anchoring of the control strategy: IPOS topology requirements: The PWM triggers of the two LLC converters on the primary side are strictly synchronized (phase difference ), ensuring input parallel voltage sharing; The output voltage phases of the two converters on the secondary side are superimposed (phase difference ), ensuring output series voltage boosting. From the control strategy in step S11, the PWM trigger moment corresponds to the initial phase (the duty cycle corresponds to the phase at the start moment of the pulse width), which is used as the phase reference for the excitation of all ports.

[0114] 2. Compensation for the inherent phase difference of the topology: In the full-bridge LLC topology, there is an inherent phase difference between the square wave output by the primary H-bridge and the rectified voltage on the secondary side (determined by the topology structure of "diagonal conduction logic + full-wave rectification"). It is necessary to compensate the phase of the synthesized waveform: The phase of the primary excitation nodes (such as , ) is maintained (matching the PWM trigger reference); The phase of the secondary response nodes (such as , ) is calibrated to (matching the voltage transfer phase characteristics of the topology).

[0115] For example, the initial phase of the synthesized voltage at the end node of the first turn on the secondary side is , and the phase difference with the primary excitation node meets the topology requirements, ensuring that the time-domain waveform is synchronized with the actual power flow direction.

[0116] Establish a mapping table of node number - winding physical position as shown in Table 1 (i.e., establish a mapping table of geometric relationships between units by unit number), and clarify the spatial coordinates of each node (taking 2 turns on the primary side and 2 turns on the secondary side as an example): Table 1: Mapping table of node number - winding physical position

[0117] Classify the calibrated node time-domain voltages (such as , , etc.) in the order of "radial layer → axial turn" of the mapping table, and render the voltage values in a two-dimensional coordinate system: Horizontal axis: Axial turn number (primary side first turn → primary side second turn → secondary side first turn → secondary side second turn); Vertical axis: Radial layer number (primary side layer / secondary side layer); Color coding: Red indicates the high-voltage area, and blue indicates the low-voltage area.

[0118] Calculate the turn-to-turn / layer-to-layer voltage difference and mark the insulation risk areas: Turn-to-turn voltage difference: For example, the voltage difference between the first turn ( ) and the second turn ( ) of the primary side ; Layer-to-layer voltage difference: For example, the voltage difference between the primary side layer ( ) and the secondary side layer ( ) .

[0119] If the voltage difference exceeds the tolerance threshold of the insulating material (such as the polyimide film has a withstand voltage of 2 kV), it is marked as the "high stress area", providing a reference for insulation design optimization (such as increasing the insulation thickness, replacing the corona-resistant material).

[0120] Based on the superposition principle, in step S7, the time-domain synthesis of the nodal frequency-domain voltage responses under all harmonic frequency components is performed. This method ensures that the contributions of all harmonic components to the voltage response are comprehensively considered, thus obtaining a time-domain voltage waveform closer to the actual working conditions. Through time-domain synthesis, step S7 can comprehensively describe the voltage response of the high-frequency transformer under different harmonic frequency components, providing complete voltage data support for subsequent insulation evaluation.

[0121] According to the control strategy of the cascaded topology, in step S7, the initial phases of the excitations at each port are calibrated. This calibration method ensures the synchronization of the time-domain voltage waveform with the actual working conditions, improving the accuracy and reliability of the simulation results. By accurately calibrating the initial phases, step S7 effectively eliminates the voltage response deviation caused by phase errors, making the simulation results closer to the actual electrical characteristics.

[0122] After calibration, in step S7, the time-domain voltages of all nodes are reorganized according to the physical positions of the windings, forming a voltage stress distribution map inside the high-frequency transformer. This map can visually display the voltage stress distribution of each node inside the high-frequency transformer, providing a clear basis for insulation evaluation for technicians. Through the voltage stress distribution map, technicians can accurately understand the insulation withstand situation of the high-frequency transformer under different working conditions, providing a strong reference for the insulation design of the high-frequency transformer.

[0123] Figure 3 FIG. 36 is a schematic structural diagram of a terminal 300 provided in an embodiment of the present invention. The terminal 300 can be used to execute the method for calculating the voltage stress inside the cascaded high-frequency transformer provided in the embodiment of the present invention.

[0124] Among them, the terminal 300 may include: a processor 310, a memory 320, and a communication module 330. These components communicate through one or more buses. Those skilled in the art can understand that the structure of the server shown in the figure does not constitute a limitation to the present invention. It can be a bus structure, a star structure, and may also include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0125] Among them, the memory 320 can be used to store the execution instructions of the processor 310. The memory 320 can be implemented by any type of volatile or non-volatile storage terminal or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk, or optical disc. When the execution instructions in the memory 320 are executed by the processor 310, the terminal 300 can execute some or all of the steps in the above method embodiments.

[0126] The processor 310 is the control center of the storage terminal, connecting various parts of the entire electronic terminal through various interfaces and lines. By running or executing the software programs and / or modules stored in the memory 320, and calling the data stored in the memory, it executes various functions of the electronic terminal and / or processes data. The processor may be composed of an integrated circuit (IC). For example, it may be composed of a single packaged IC, or may be composed of multiple packaged ICs with the same or different functions connected together. For example, the processor 310 may only include a central processing unit (CPU). In the embodiment of the present invention, the CPU may be a single operation core or may include multiple operation cores.

[0127] The communication module 330 is used to establish a communication channel so that the storage terminal can communicate with other terminals. It receives user data sent by other terminals or sends user data to other terminals.

[0128] The present invention also provides a computer storage medium. Among them, the computer storage medium can store a program, and when the program is executed, it may include some or all of the steps in the embodiments provided by the present invention. The storage medium may be a magnetic disk, an optical disc, a read-only memory (ROM), or a random access memory (RAM), etc.

[0129] Those skilled in the art can clearly understand that the technology in the embodiments of the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solution in the embodiments of the present invention, in essence, or the part that contributes to the prior art can be embodied in the form of a software product. This computer software product is stored in a storage medium such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disc, etc., which can store program codes. It includes several instructions to enable a computer terminal (which can be a personal computer, a server, or a second terminal, a network terminal, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention.

[0130] For the same and similar parts among the various embodiments in this specification, reference can be made to each other. In particular, for the terminal embodiments, since they are basically similar to the method embodiments, the description is relatively simple. For the relevant parts, reference can be made to the descriptions in the method embodiments.

[0131] Although the present invention has been described in detail by referring to the accompanying drawings and in combination with the preferred embodiments, the present invention is not limited thereto. Without departing from the spirit and essence of the present invention, those of ordinary skill in the art can make various equivalent modifications or substitutions to the embodiments of the present invention, and these modifications or substitutions should all be within the scope of the present invention. / Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, and they should all be covered within the protection scope of the present invention.

Claims

1. A method for calculating the voltage stress inside a cascaded high-frequency transformer, characterized in that including: Step S1: According to the external cascading method, internal topology, converter characteristics, and control strategy of the DC-DC isolation converter, simulate to obtain the time-domain voltage waveforms of each port of the high-frequency transformer in the DC-DC isolation converter under cascading conditions, and extract the spectral information of the voltage waveforms through frequency-domain analysis; Step S2: Based on the finite element method, establish a frequency-varying distributed parameter extraction model for the high-frequency transformer, and input the spectral information into the frequency-varying distributed parameter extraction model to extract the frequency-varying distributed parameters at different frequencies. The frequency-varying distributed parameters include conductance parameters, capacitance parameters, resistance parameters, and inductance parameters; Step S3: In the established frequency-varying distributed parameter extraction model, take each turn of the winding of the high-frequency transformer as an independent calculation unit, and distribute the extracted frequency-varying distributed parameters to the impedance branch and admittance branch corresponding to the independent calculation unit according to the pre-stored inter-turn geometric relationship and current path, and construct an equivalent circuit of the frequency-varying distributed parameters of the high-frequency transformer; Step S4: Based on the constructed equivalent circuit of the frequency-varying distributed parameters, define the impedance branch matrix, admittance branch matrix, voltage-current vector, and incidence matrix, and establish a general parametric model of the equivalent circuit of the frequency-varying distributed parameters; Step S5: Perform Fourier decomposition on the multi-port voltage waveforms of the high-frequency transformer under cascading conditions, determine the target spectral range and truncation order, and extract the harmonic component spectra of the voltages at each port; Step S6: Take the decomposed single-frequency sinusoidal excitation voltage as the boundary condition and apply it to the excitation node of the general parametric model to solve for the voltage value of the response node; Step S7: Based on the superposition principle, synthesize the node voltage responses of all harmonic components to obtain the internal voltage stress distribution of the high-frequency transformer under cascaded multi-port excitation conditions.

2. The method for calculating the voltage stress inside the cascaded high-frequency transformer according to claim 1, wherein Step S1 includes: Step S11: Obtain the pre-stored parameters of the DC-DC isolation converter, including the external cascading method, internal topology, converter device characteristics, and control strategy; among them, the external cascading method is the electrical connection relationship between the pre-stored multi-stage converters; the internal topology includes the circuit configurations of the pre-stored full-bridge, half-bridge, or LLC resonant topology; the control strategy includes the duty cycle of the pre-stored pulse-width modulation signal and the switching frequency ; the converter device characteristics include the on-time of the MOSFET in the converter and the pulse rise time ; Step S12: Based on the obtained DC-DC isolation converter parameters, construct an equivalent circuit model of the cascaded DC-DC isolation converter in a circuit simulation tool to simulate the time-domain voltage waveforms of each port of the high-frequency transformer under cascading conditions; Step S13: Perform spectral analysis on the time-domain voltage waveforms of each voltage port through fast Fourier transform, extract the harmonic frequency range, and output the spectral information including the fundamental frequency, harmonic amplitude, and phase. Store the spectral information as a frequency-domain data set.

3. The method for calculating the voltage stress inside the cascaded high-frequency transformer according to claim 2, wherein The simulation equation for simulating the time-domain voltage waveforms of each port of the high-frequency transformer under cascading conditions is: ； Among them, is the simulation function; is the internal topology structure function; is the non-linear magnetic permeability; and are the time-domain voltage waveforms of the high-voltage and low-voltage ports respectively.

4. The method for calculating the voltage stress inside the cascaded high-frequency transformer according to claim 2, characterized in that Step S2 includes: Step S21: Based on the finite element method, establish a frequency-varying distributed parameter extraction model for the high-frequency transformer, including an electrostatic field analysis model and a steady-state magnetic field analysis model; Step S22: Set the conductor boundary conditions and insulating material properties according to the extracted spectral information; the conductor boundary conditions include applying a voltage excitation matching the spectral amplitude on the conductor surface and applying a ground constraint to the reference node; the insulating material properties include the frequency-varying dielectric constant and conductivity of the insulating material; Step S23: Input the set conductor boundary conditions and insulating material properties into the constructed electrostatic field analysis model to extract the distributed capacitance and distributed conductance of the insulating material at different frequencies. The distributed capacitance and distributed conductance respectively characterize the inter-turn / inter-layer electric field coupling and leakage current characteristics; Step S24: Define the current excitation condition according to the extracted spectrum information, where the current excitation condition is the current excitation frequency range covering the main harmonic components in the spectrum information; Step S25: Input the defined current excitation condition, the core B-H curve corresponding to the pre-stored high-frequency transformer, and the skin effect characteristics of the Litz wire into the constructed steady-state magnetic field analysis model, and extract the distributed resistance and distributed inductance of the Litz wire at different frequencies; Step S26: Construct a frequency-varying distributed parameter database of the high-frequency transformer based on the extracted distributed capacitance, distributed conductance, distributed resistance, and distributed inductance.

5. The method for calculating the voltage stress inside the cascaded high-frequency transformer according to claim 4, wherein Step S3 includes: Step S31: Discretize each turn of the winding of the high-frequency transformer into independent calculation units, define the unit numbers corresponding to each independent calculation unit in the high-voltage and low-voltage windings, and establish a geometric relationship mapping table between the units based on the unit numbers. The mapping table records the current path topology and the inter-turn / inter-layer geometric relationship including the inter-turn distance and the inter-layer insulation thickness; Step S32: Map the distributed capacitance and distributed conductance parameters of the insulating material to the admittance branches representing the electric field coupling characteristics between the units according to the inter-turn / inter-layer geometric relationship; map the distributed resistance and distributed inductance parameters of the Litz wire to the impedance branches representing the magnetic field coupling characteristics in the units according to the current path topology; the distributed inductance parameters include self-inductance and mutual inductance parameters of adjacent turns; Step S33: Take the two ends of each turn of the winding as independent nodes, connect the impedance branches in series between adjacent nodes, realize magnetic field coupling between non-adjacent nodes through mutual inductance branches, and connect the admittance branches in parallel between each node and the reference ground to form a chain node network of the high-voltage and low-voltage windings, and complete the construction of the frequency-varying distributed parameter equivalent circuit of the high-frequency transformer.

6. The method for calculating the voltage stress inside the cascaded high-frequency transformer according to claim 5, wherein Map the distributed capacitance and distributed conductance parameters of the insulating material to the admittance branches representing the electric field coupling characteristics between the units according to the inter-turn / inter-layer geometric relationship, and its specific expression is: ； ； Among them, is the distributed capacitance, which characterizes the frequency-varying capacitance between the i-th turn and the j-th turn of the winding; is the frequency-varying permittivity, which characterizes the polarization ability of the insulating material at different frequencies f, reflects the dynamic change of the electric field coupling strength with frequency, and the unit is F / m; is the coupling area, which characterizes the effective area of the electric field overlap between the i-th turn and the j-th turn of the winding; is the dielectric thickness, which characterizes the physical thickness of the insulating layer between the i-th turn and the j-th turn of the winding; is the distributed conductance, which characterizes the frequency-varying conductance between the i-th turn and the j-th turn of the winding; is the frequency-varying conductivity, which characterizes the leakage current characteristics of the insulating material at different frequencies f, reflects the dynamic change of the dielectric loss with frequency, and the unit is S / m; Map the distributed resistance and distributed inductance parameters of the Litz wire to the impedance branches representing the magnetic field coupling characteristics in the units according to the current path topology, and its specific expression is: ； ； Among them, is the distributed resistance, representing the frequency-dependent resistance of the i-th turn of the winding; is the resistance per unit length, representing the AC resistance of each meter of the Litz wire at high frequencies; is the effective length of the current path; is the distributed inductance, representing the frequency-dependent inductance of the i-th turn of the winding; is the inductance per unit number of turns, representing the equivalent inductance of a single turn of the winding at high frequencies; is the number of adjacent coupled turns, representing the effective number of turns of the winding that undergoes magnetic field coupling with the i-th turn of the winding.

7. The method for calculating the voltage stress inside the cascaded high-frequency transformer according to claim 5, wherein Step S4 includes: Step S41: Based on the number of nodes and branches in the constructed frequency-varying distributed parameter equivalent circuit, define the dimensions of the impedance branch matrix and the admittance branch matrix, and define variables including the node voltage vector, the impedance branch current vector, and the admittance branch current vector; Step S42: Based on the corresponding dimensions and variables defined for the impedance branches, integrate the frequency-varying parameters of all impedance branches in the frequency-varying distributed parameter equivalent circuit to form an impedance branch matrix; Step S43: Based on the corresponding dimensions and variables defined for the admittance branches, integrate the frequency-varying parameters of all admittance branches in the frequency-varying distributed parameter equivalent circuit to form an admittance branch matrix; Step S44: Define an incidence matrix describing the connection relationship between the admittance branches / impedance branches and the nodes; Step S45: Correlate the incidence matrix, the impedance branch matrix, the admittance branch matrix with the node voltage vector through Kirchhoff's law to form a solution equation for the network node voltage in the frequency-varying distributed parameter equivalent circuit, and complete the construction of the general parametric model of the frequency-varying distributed parameter equivalent circuit.

8. The method for calculating the voltage stress inside the cascaded high-frequency transformer according to claim 7, wherein Step S5 includes: Step S51: Perform Fourier decomposition on the obtained cascaded multi-port voltage waveforms, and extract the harmonic component amplitudes and phases of the voltages at each port; Step S52: Based on the effective frequency ranges of the parameters pre-stored in the extracted frequency-varying parameter database, and in combination with the frequency-varying dielectric characteristics set in the insulation material properties, determine the target frequency spectrum range; Step S53: Calculate the minimum truncation order K according to the target frequency spectrum range and the preset harmonic truncation accuracy threshold; Step S54: Extract the harmonic component spectra within the K-th order for each port, and output a harmonic data set including frequency, amplitude, and phase.

9. The method for calculating the voltage stress inside the cascaded high-frequency transformer according to claim 8, wherein Step S6 includes: Step S61: Based on the node network of the frequency-varying distributed parameter equivalent circuit constructed, determine the nodes to which the excitation is applied, the grounded nodes, and the corresponding node numbers of the above nodes; Step S62: According to the node numbers of the excitation nodes and the grounded nodes, delete the corresponding rows and columns in the coefficient matrix in the node voltage solution equation, extract the column vector of the coefficient matrix corresponding to the node number of the excitation node and move it to the right side of the solution equation, and construct a new solution equation for all response nodes to implement the application of the excitation in the analytical calculation process; Step S63: Based on the newly constructed solution equation for all response nodes, calculate the frequency-domain voltage vectors of all response nodes, and output the voltage response amplitudes and phases of all nodes at this frequency.

10. The method for calculating the voltage stress inside the cascaded high-frequency transformer according to claim 9, characterized in that, Step S7 includes: Based on the superposition principle, perform time-domain synthesis on the node frequency-domain voltage responses at all harmonic frequency components; According to the control strategy of the cascaded topology, calibrate the initial phases of the excitations at each port to ensure that the time-domain voltage waveforms are synchronized with the actual working conditions; After calibration, reorganize the time-domain voltages of all nodes according to the physical positions of the windings to form a map of the internal voltage stress distribution of the high-frequency transformer.

Images