A method for calculating voltage stress inside cascaded high-frequency transformers

Abstract

The present invention belongs to the technical field of transformers and specifically relates to a method for calculating voltage stress within a cascaded high-frequency transformer. The method comprises simulating and obtaining the time-domain voltage waveforms at each port of the high-frequency transformer in the DC-DC isolation converter under cascade conditions based on the external cascade mode, internal topology, converter characteristics, and control strategy of the DC-DC isolation converter, extracting spectral information of the voltage waveform through frequency-domain analysis, and finally, analyzing and calculating the internal voltage stress of the high-frequency transformer under the important operating condition of excitation at all ports of the cascaded converter based on a constructed equivalent model of the high-frequency transformer and a method for applying excitation to different ports. This method avoids the limitation of traditional methods that only consider single-ended excitation.

Description

Technical Field

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

[0002] As a core component in DC-DC isolation converters, high-frequency transformers not only perform the crucial tasks of energy transmission and voltage conversion but also ensure safe and stable system operation through electrical isolation. Under typical operating conditions, the ends of high-frequency transformers are subjected to long-term exposure to pulsed or square-wave voltages with steep rise times. These voltage waveforms contain a large number of high-frequency harmonic components, which can induce resonance within the windings, resulting in internal voltage stress exhibiting a non-uniform distribution characteristic that differs from that observed under low-frequency conditions. This non-uniform distribution of voltage stress poses a serious threat to the high-frequency transformer's insulation system, increasing the risk of insulation breakdown and, in turn, impacting the reliability and lifespan of the entire power electronics system.

[0003] Currently, the calculation of internal voltage stress in high-frequency transformers is often performed using a field-circuit coupling approach. This involves first establishing a field model of the high-frequency transformer using multi-field coupling finite element simulation software, extracting circuit model parameters under square wave excitation, and then constructing a circuit model to study the internal voltage distribution. However, both field and circuit models primarily focus on extracting parameters and calculating and analyzing internal voltage stress under single-ended excitation conditions, without fully considering the typical external operating conditions of the high-frequency transformer, particularly those operating under cascaded DC-DC isolation converters. Under cascaded conditions, complex electrical connections and interactions exist between the different ports of the high-frequency transformer, making the application of boundary conditions particularly complex. Traditional field-circuit coupling models struggle to accurately reflect the voltage stress distribution under simultaneous excitation of multiple ports. Summary of the Invention

[0004] In view of the defects in the prior art of traditional calculation of internal voltage stress of high-frequency transformers, which does not take into account the operating conditions under cascade conditions and cannot reflect the voltage stress distribution under 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 voltage stress inside a cascaded high-frequency transformer, comprising:

[0006] Step S1: according to the external cascade mode, internal topology, converter characteristics and control strategy of the DC-DC isolation converter, simulate and obtain the time domain voltage waveform of each port of the high frequency transformer in the DC-DC isolation converter under the cascade condition, and extract the spectrum information of the voltage waveform through frequency domain analysis;

[0007] Step S2: Based on the finite element method, a frequency-dependent distributed parameter extraction model of the high-frequency transformer is established, and the spectrum information is input into the frequency-dependent distributed parameter extraction model to extract the frequency-dependent distributed parameters at different frequencies. The frequency-dependent distributed parameters include conductance parameters, capacitance parameters, resistance parameters, and inductance parameters;

[0008] Step S3: In the established frequency-variable distributed parameter extraction model, each winding of the high-frequency transformer is used as an independent calculation unit. According to the pre-stored inter-turn geometric relationship and current path, the extracted frequency-variable distributed parameters are distributed to the impedance branch and admittance branch corresponding to the independent calculation unit, thereby constructing the frequency-variable distributed parameter equivalent circuit of the high-frequency transformer;

[0009] Step S4: Based on the constructed frequency-variable distributed parameter equivalent circuit, define the impedance branch matrix, the admittance branch matrix, the voltage and current vectors, and the correlation matrix, and establish a universal parameterized model of the frequency-variable distributed parameter equivalent circuit;

[0010] Step S5: performing Fourier decomposition on the multi-port voltage waveform of the high-frequency transformer under the cascade condition, determining the target spectrum range and truncation order, and extracting the harmonic component spectrum of each port voltage;

[0011] Step S6: Using the decomposed single-frequency sinusoidal excitation voltage as a boundary condition, and applying it to the excitation node of the general parameterized model, and solving the voltage value of the response node;

[0012] Step S7: 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 cascade multi-port excitation condition.

[0013] A further improvement of this technical solution is that step S1 includes:

[0014] Step S11, obtaining pre-stored DC-DC isolation converter parameters, including external cascade mode, internal topology, converter device characteristics and control strategy; wherein the external cascade mode is the pre-stored electrical connection relationship between the multi-level converters; the internal topology includes the pre-stored circuit configuration of the full-bridge, half-bridge or LLC resonant topology; the control strategy includes the pre-stored duty cycle of the pulse width modulation signal and switching frequency ;Converter device characteristics include the on-time of the MOSFET in the converter and pulse rise time ;

[0015] Step S12: Based on the acquired 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 waveform of each port of the high-frequency transformer under the cascade condition;

[0016] Step S13: Perform spectrum analysis on the time-domain voltage waveform of each voltage port by fast Fourier transform, extract the harmonic frequency range, and output spectrum information including fundamental frequency, harmonic amplitude and phase, and store the spectrum information as a frequency domain data set.

[0017] A further improvement of this technical solution is that the simulation equation of the time domain voltage waveform of each port of the high-frequency transformer under the simulated cascade condition is:

[0018] ;

[0019] in, is the simulation function; is the internal topological structure function; is the nonlinear magnetic permeability; and These are the time domain voltage waveforms of the high and low voltage ports respectively.

[0020] A further improvement of this technical solution is that step S2 includes:

[0021] Step S21: Based on the finite element method, a frequency-dependent distributed parameter extraction model of the high-frequency transformer is established, including an electrostatic field analysis model and a steady-state magnetic field analysis model;

[0022] Step S22: setting conductor boundary conditions and insulation material properties based on the extracted spectrum information; the conductor boundary conditions include applying a voltage excitation matching the spectrum amplitude on the conductor surface and applying a ground constraint to the reference node; the insulation material properties include the frequency-dependent dielectric constant and conductivity of the insulation material;

[0023] Step S23: Input the set conductor boundary conditions and insulation material properties into the constructed electrostatic field analysis model to extract the distributed capacitance and distributed conductance of the insulation material at different frequencies. The distributed capacitance and distributed conductance respectively characterize the inter-turn / inter-layer electric field coupling and leakage current characteristics;

[0024] Step S24: defining a current excitation condition based on the extracted spectrum information, where the current excitation condition is a current excitation frequency range covering the main harmonic components in the spectrum information;

[0025] Step S25: input the defined current excitation conditions and the pre-stored core BH curve and skin characteristics of the Litz wire corresponding to the high-frequency transformer into the constructed steady-state magnetic field analysis model to extract the distributed resistance and distributed inductance of the Litz wire at different frequencies;

[0026] Step S26: constructing a frequency-dependent distributed parameter database of the high-frequency transformer based on the extracted distributed capacitance, distributed conductance, distributed resistance, and distributed inductance.

[0027] A further improvement of this technical solution is that step S3 includes:

[0028] Step S31: Discretize each winding of the high-frequency transformer into an independent calculation unit, define the unit number corresponding to each independent calculation unit in the high and low voltage windings, and establish a geometric relationship mapping table between units based on the unit number. The mapping table records the current path topology and the inter-turn / inter-layer geometric relationship including the inter-turn distance and inter-layer insulation thickness;

[0029] Step S32: Mapping the distributed capacitance and distributed conductance parameters of the insulating material to the admittance branch representing the electric field coupling characteristics between the units according to the inter-turn / inter-layer geometric relationship; mapping the distributed resistance and distributed inductance parameters of the Litz wire to the impedance branch representing 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;

[0030] Step S33: Treat the two ends of each winding as independent nodes, connect impedance branches in series between adjacent nodes, achieve magnetic field coupling between non-adjacent nodes through mutual inductance branches, and connect an admittance branch in parallel between each node and the reference ground to form a chain node network of high and low voltage windings, completing the construction of the frequency-variable distributed parameter equivalent circuit of the high-frequency transformer.

[0031] 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 representing the electric field coupling characteristics between units according to the geometric relationship between turns / layers. The specific expression is:

[0032] ;

[0033] ;

[0034] in, is the distributed capacitance, representing the frequency-dependent capacitance between the i-th and j-th turns of the winding; The frequency-dependent dielectric constant characterizes the polarization ability of the insulating material at different frequencies f and reflects the dynamic change of the electric field coupling strength with frequency. The unit is F / m. is the coupling area, which represents the effective area of ​​the electric field overlap between the i-th and j-th turns of the winding; is the dielectric thickness, which represents the physical thickness of the insulation layer between the i-th and j-th turns of the winding; is the distributed conductance, representing the frequency-dependent conductance between the i-th and j-th turns of the winding; Frequency-dependent conductivity, which characterizes the leakage current characteristics of insulating materials at different frequencies f, reflects the dynamic change of dielectric loss with frequency, and its unit is S / m;

[0035] The distributed resistance and distributed inductance parameters of the Litz wire are mapped to the impedance branch in the unit that represents the magnetic field coupling characteristics according to the current path topology. The specific expression is:

[0036] ;

[0037] ;

[0038] in, is the distributed resistance, representing the frequency-dependent resistance of the i-th winding turn; The resistance per unit length characterizes the AC resistance of Litz wire per meter at high frequencies. is the effective length of the current path; is the distributed inductance, representing the frequency-varying inductance of the i-th winding turn; is the inductance per unit turn, which represents the equivalent inductance of a single-turn winding at high frequency; is the number of adjacent coupled turns, representing the number of effective winding turns that have magnetic field coupling with the i-th winding turn.

[0039] A further improvement of this technical solution is that step S4 includes:

[0040] Step S41: Based on the number of nodes and branches in the constructed frequency-dependent 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;

[0041] Step S42: Based on the corresponding dimensions and variables defined for the impedance branches, the frequency-variant parameters of all impedance branches in the frequency-variant distributed parameter equivalent circuit are integrated to form an impedance branch matrix;

[0042] Step S43: Based on the corresponding dimensions and variables defined by the admittance branches, frequency-varying parameters of all admittance branches in the frequency-varying distributed parameter equivalent circuit are integrated to form an admittance branch matrix;

[0043] Step S44: defining an association matrix describing the connection relationship between the admittance branch / impedance branch and the node;

[0044] Step S45: Correlate the correlation matrix, the impedance branch matrix, the admittance branch matrix, and the node voltage vector using Kirchhoff's law to form a solution equation for the network node voltage in the frequency-variable distributed parameter equivalent circuit, thereby completing the construction of a universal parameterized model of the frequency-variable distributed parameter equivalent circuit.

[0045] A further improvement of this technical solution is that step S5 includes:

[0046] Step S51: Perform Fourier decomposition on the acquired cascade multi-port voltage waveform to extract the amplitude and phase of the harmonic components of each port voltage;

[0047] Step S52: determining a target frequency spectrum range based on the extracted parameter effective frequency range pre-stored in the frequency-variable parameter database and the frequency-variable dielectric characteristics set in the insulating material properties;

[0048] Step S53: Calculate the minimum truncation order K based on the target spectrum range and the preset harmonic truncation accuracy threshold;

[0049] Step S54: extract the harmonic component spectrum of each port within the Kth order, and output a harmonic data set including frequency, amplitude and phase.

[0050] A further improvement of this technical solution is that step S6 includes:

[0051] Step S61: Based on the constructed node network of the frequency-dependent distributed parameter equivalent circuit, determine the node to which the excitation is applied, the grounding node, and the node numbers corresponding to the above nodes;

[0052] Step S62: Delete the corresponding rows and columns in the coefficient matrix of the node voltage solution equation according to the node number of the excitation node and the node number of the grounding node, extract the coefficient matrix column vector corresponding to the node number of the excitation node and move it to the right side of the equation solution, and construct a new equation solution for all response nodes to implement the application of excitation in the analytical calculation process;

[0053] Step S63: Solve equations based on all newly constructed 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.

[0054] A further improvement of this technical solution is that step S7 includes:

[0055] Based on the superposition principle, the node frequency domain voltage responses under all harmonic frequency components are synthesized in the time domain;

[0056] According to the control strategy of the cascade topology, the initial phase of each port excitation is calibrated to ensure that the time domain voltage waveform is synchronized with the actual working conditions;

[0057] After calibration, the time domain voltages of all nodes are reorganized according to the physical positions of the windings to form a voltage stress distribution map inside the high-frequency transformer.

[0058] The beneficial effects of the present invention are:

[0059] The present invention simulates and obtains the time-domain voltage waveforms at each port of the high-frequency transformer in a cascaded DC-DC isolation converter, extracting spectral information. This fully considers the impact of the cascade effect on the internal voltage stress of the high-frequency transformer. Specifically, based on the constructed equivalent model of the high-frequency transformer and the method for applying excitation to its different ports, the present invention ultimately achieves the analysis and calculation of the internal voltage stress of the high-frequency transformer under the critical operating condition of excitation at all ports of the cascaded converter, avoiding the limitation of traditional methods that only consider single-ended excitation. Based on pre-stored parameters (such as the external cascade method, internal topology, converter characteristics, and control strategy), an equivalent circuit model of the cascaded DC-DC isolation converter is constructed in a circuit simulation tool, achieving accurate simulation of the time-domain voltage waveforms at each port of the high-frequency transformer under cascade conditions.

[0060] This paper uses the finite element method to establish a frequency-dependent distributed parameter extraction model for high-frequency transformers. This model efficiently and accurately extracts parameters such as conductance, capacitance, resistance, and inductance at different frequencies, providing a solid foundation for subsequent equivalent circuit construction. Inputting the extracted spectral information into the frequency-dependent distributed parameter extraction model ensures targeted and accurate parameter extraction and improves computational efficiency.

[0061] This method treats each turn of a high-frequency transformer as an independent calculation unit, fully considering the inter-turn geometry and current paths, enabling a refined description of the transformer's internal electromagnetic characteristics. By assigning frequency-dependent distributed parameters to impedance and admittance branches, a frequency-dependent distributed parameter equivalent circuit for the high-frequency transformer is constructed, accurately reflecting the transformer's internal electromagnetic coupling characteristics.

[0062] Based on the constructed frequency-varying distributed parameter equivalent circuit, the present invention defines the impedance branch matrix, admittance branch matrix, voltage and current vectors and correlation matrix, and establishes a universal parameterized model of the frequency-varying distributed parameter equivalent circuit.

[0063] This paper performs Fourier decomposition on the multi-port voltage waveforms of high-frequency transformers under cascade conditions, extracting the harmonic component spectra of each port voltage, providing accurate data support for subsequent calculations. The decomposed single-frequency sinusoidal excitation voltage is applied as a boundary condition to the excitation and ground nodes of a universal parameterized model, enabling accurate simulation of multi-port voltage excitation conditions. 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 cascade multi-port excitation conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0065] Figure 1 A schematic flow chart of a method according to an embodiment of the present invention.

[0066] Figure 2 The frequency-variable distributed parameter equivalent circuit of the constructed high-frequency transformer.

[0067] Figure 3 A schematic diagram of the structure of a terminal provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0068] In order to make the purpose, features, and advantages of the present invention more obvious and easy to understand, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the specific embodiments. Obviously, the embodiments described below are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0069] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in this specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0070] Figure 1 This is a schematic flow chart of a method for calculating voltage stress inside a cascaded high-frequency transformer provided by the present invention. According to different requirements, the order of the steps in the flow chart can be changed, and some can be omitted.

[0071] like Figure 1 As shown, the method includes:

[0072] Step S1: Based on the pre-stored external cascade mode, internal topology, converter characteristics, and control strategy of the DC-DC isolation converter, simulate and obtain the time domain voltage waveform of each port of the high-frequency transformer in the DC-DC isolation converter under the cascade condition, and extract the spectrum information of the voltage waveform through frequency domain analysis;

[0073] Step S2: Based on the finite element method, a frequency-dependent distributed parameter extraction model of the high-frequency transformer is established, and the spectrum information is input into the frequency-dependent distributed parameter extraction model to extract the frequency-dependent distributed parameters at different frequencies. The frequency-dependent distributed parameters include conductance parameters, capacitance parameters, resistance parameters, and inductance parameters;

[0074] Step S3: In the established frequency-variable distributed parameter extraction model, each winding of the high-frequency transformer is used as an independent calculation unit. According to the pre-stored inter-turn geometric relationship and current path, the extracted frequency-variable distributed parameters are distributed to the impedance branch and admittance branch corresponding to the independent calculation unit, thereby constructing the frequency-variable distributed parameter equivalent circuit of the high-frequency transformer;

[0075] Step S4: Based on the constructed frequency-variable distributed parameter equivalent circuit, define the impedance branch matrix, the admittance branch matrix, the voltage and current vectors, and the correlation matrix, and establish a universal parameterized model of the frequency-variable distributed parameter equivalent circuit;

[0076] Step S5: performing Fourier decomposition on the multi-port voltage waveform of the high-frequency transformer under the cascade condition, determining the target spectrum range and truncation order, and extracting the harmonic component spectrum of each port voltage;

[0077] Step S6: Using the decomposed single-frequency sinusoidal excitation voltage as a boundary condition, and applying it to the excitation node of the general parameterized model, and solving the voltage value of the response node;

[0078] Step S7: 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 cascade multi-port excitation condition.

[0079] Wherein, step S1 includes:

[0080] Step S11, obtaining pre-stored DC-DC isolation converter parameters, including external cascade mode, internal topology, converter device characteristics and control strategy; wherein the external cascade mode is the pre-stored electrical connection relationship between the multi-level converters; the internal topology includes the pre-stored circuit configuration of the full-bridge, half-bridge or LLC resonant topology; the control strategy includes the pre-stored duty cycle of the pulse width modulation signal and switching frequency ;Converter device characteristics include the on-time of the MOSFET in the converter and pulse rise time ;

[0081] Step S12: Based on the acquired 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 waveform of each port of the high-frequency transformer under the cascade condition;

[0082] Step S13: Perform spectrum analysis on the time-domain voltage waveform of each voltage port by fast Fourier transform, extract the harmonic frequency range, and output spectrum information including fundamental frequency, harmonic amplitude and phase, and store the spectrum information as a frequency domain data set.

[0083] Furthermore, the simulation equations for the time domain voltage waveforms of each port of the high-frequency transformer under the simulated cascade condition are:

[0084] ;

[0085] in, It is a simulation function that includes Kirchhoff's law, device transient model (such as MOSFET switching model, diode reverse recovery model), and core nonlinear model; It is the internal topology structure function, which characterizes the circuit connection relationship of the full-bridge LLC topology (such as the upper and lower tube conduction logic of the H-bridge); is the nonlinear magnetic permeability; and These are the time domain voltage waveforms of the high and low voltage ports respectively.

[0086] Taking "two full-bridge LLC converters cascaded (IPOS topology)" as the object, retrieve the electrical connection diagram of the corresponding converter model from the preset cascade topology library (such as the "input parallel - output series (IPOS)" topology diagram), clarify the port connection relationship between the multi-stage converters (such as high-voltage side HV1 and HV2 in parallel, low-voltage side LV1 and LV2 in series), and mark the high-voltage port (Parallel input, voltage 800V), low voltage port (Series output, target voltage 1600V) physical interface and terminal correspondence.

[0087] Call the circuit configuration file in the preset power topology library (such as the CAD drawing of the full-bridge LLC topology), identify the core power device layout (internal topology structure), and build an equivalent circuit in a circuit simulation tool (such as PLECS) based on the circuit principle of the full-bridge LLC topology - the primary side H-bridge (generating high-frequency square waves) consists of 4 MOSFETs, the secondary side consists of 2 synchronous rectifier diodes (model IDW30G65C5), and the middle series resonant capacitor With high frequency transformer (including excitation inductor , leakage inductance ).

[0088] Export PWM (Pulse Width Modulation) signal parameters - duty cycle from the control board parameter configuration system (determines the on-pulse of the PWM square wave, set by power regulation requirements), switching frequency (Determines the fundamental frequency of the PWM square wave, which is matched by the resonant cavity design), determines the fundamental frequency and pulse width of the voltage waveform, and maximizes the resonant gain of the LLC (Low-Loss Coupling) topology.

[0089] Converter device characteristics acquisition:

[0090] MOSFET characteristics: Consult the data sheet of the model used (such as IPW60R041C6) to extract the MOSFET's on-time (characterizes the time constant of the MOSFET transition from the off high-resistance state to the on low-resistance state, characterizes the switching rate ( The larger the value, the slower the drain-source resistance decreases, and the drain-source voltage The flatter the falling edge, the lower the rising slope of the load current and the port voltage.) Pulse rise time (During the MOSFET turn-off phase, the time it takes for the drain-source voltage to drop from 90% of the rated value to 10% of the rated value reflects the turn-off speed. The smaller it is, the lower the turn-off loss is and the better the voltage spike suppression effect is);

[0091] Core characteristics (recall N87 ferrite data from the pre-stored core material library): Calculate nonlinear permeability based on the retrieved N87 core BH curve (When the magnetic field strength H changes, the magnetic permeability is adjusted dynamically. When the magnetic permeability is approximately constant; among them, is the saturation threshold of the magnetic field strength), and embeds it into the excitation inductance model of the high-frequency transformer (N is the number of turns, is the core cross-sectional area, is the magnetic path length).

[0092] Based on the above parameters, the time domain voltage waveform of the high-frequency transformer port under the cascade condition is simulated according to the above simulation equation.

[0093] The time domain voltage waveform obtained by simulation (such as HV port 、 ), set the sampling frequency to 10 times the switching frequency (1MHz), that is, the sampling frequency ), to avoid high-frequency harmonic aliasing.

[0094] Apply a Blackman-Harris window to the sampled time domain signal (to suppress spectrum leakage), and decompose it through fast Fourier transform (FFT) to obtain the frequency, amplitude, and phase of each harmonic:

[0095] Fundamental frequency , the corresponding amplitude is the effective value of the port voltage times (e.g. the fundamental amplitude of the HV port is about 752 V);

[0096] The third and fifth harmonic frequencies are 、 , whose amplitude is determined by the topological harmonic characteristics (such as the resonant gain of the LLC topology) and the device characteristics (such as The high-frequency oscillation introduced by the

[0097] Organize the extracted spectrum information into a standardized dataset (e.g., JSON format), including:

[0098] Fundamental wave information: frequency 100 kHz, amplitude 752.3 V, phase −0.12 rad;

[0099] Harmonic information: 3rd harmonic (300kHz, 85.1V, 2.1rad), 5th harmonic (500kHz, 42.7V, −1.9rad), etc.

[0100] The transient solver of the simulation tool is used to iteratively calculate the differential equation after the above parameters are coupled, and finally the time domain voltage waveform of the high / low voltage port of the high-frequency transformer is output. 、 .

[0101] Directly associate the fundamental frequency in the frequency domain data set with the control strategy of step S11 ( ), the converter device characteristics of step S12 of harmonic amplitude and phase correlation ensure the closure of the technical chain of "time domain-frequency domain-device characteristics", ensure the accuracy and reliability of the simulation results, and provide a strong guarantee for the optimization design of high-frequency transformers and the reliability evaluation of insulation systems.

[0102] The present invention ensures the comprehensiveness and accuracy of the simulation model by acquiring and integrating multi-dimensional parameters such as external cascade mode, internal topology, converter device characteristics and control strategy. The external cascade mode clarifies the electrical connection relationship between the multi-stage converters, the internal topology defines the circuit configuration, the control strategy determines the base frequency and pulse width of the voltage waveform, and the converter device characteristics correct the on / off transient characteristics of the power device, providing a solid physical foundation for the simulation. By consulting the data sheet and the core material library,

[0103] Based on the circuit principle of the full-bridge LLC (L-network linked coupled inductor) topology, the present invention builds an equivalent circuit in the circuit simulation tool, realizing the precise 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 on-state voltage drop, turn-off overshoot and saturation effect of the magnetic core of the power device, thereby obtaining simulation results that are closer to reality. By introducing simulation equations containing Kirchhoff's law, device transient model and magnetic core nonlinear model, the present invention realizes the refined simulation of the time domain voltage waveform of each port of the high-frequency transformer. The internal topology structure function and nonlinear permeability and other parameters in the simulation equation enable the simulation results to accurately reflect the working state of the actual circuit.

[0104] The present invention uses fast Fourier transform to perform spectrum analysis on the simulated time-domain voltage waveform, efficiently extracting key spectrum information such as harmonic frequency range, fundamental frequency, harmonic amplitude, and phase. This method not only improves analysis efficiency but also ensures the accuracy of spectrum information.

[0105] In addition, step S2 includes:

[0106] Step S21: Based on the finite element method, a frequency-dependent distributed parameter extraction model of the high-frequency transformer is established, including an electrostatic field analysis model and a steady-state magnetic field analysis model;

[0107] Step S22: setting conductor boundary conditions and insulation material properties based on the extracted spectrum information; the conductor boundary conditions include applying a voltage excitation matching the spectrum amplitude on the conductor surface and applying a ground constraint to the reference node; the insulation material properties include the frequency-dependent dielectric constant and conductivity of the insulation material;

[0108] Step S23: Input the set conductor boundary conditions and insulation material properties into the constructed electrostatic field analysis model to extract the distributed capacitance and distributed conductance of the insulation material at different frequencies. The distributed capacitance and distributed conductance respectively characterize the inter-turn / inter-layer electric field coupling and leakage current characteristics;

[0109] Step S24: defining a current excitation condition based on the extracted spectrum information, where the current excitation condition is a current excitation frequency range covering the main harmonic components in the spectrum information;

[0110] Step S25: Input the defined current excitation conditions and the pre-stored core BH curve and skin characteristics of the Litz wire corresponding to the high-frequency transformer into the constructed steady-state magnetic field analysis model to extract the distributed resistance and distributed inductance of the Litz wire at different frequencies (i.e., extract the distributed resistance and distributed inductance of the Litz wire at different frequencies, taking into account the core frequency-electric effect (the core BH curve reflects the nonlinear relationship between magnetic induction intensity B and magnetic field intensity H, and this relationship varies with frequency (eddy currents intensify at high frequencies, equivalent magnetic permeability decreases, and the slope of the BH curve decreases));

[0111] Step S26: constructing a frequency-dependent distributed parameter database of the high-frequency transformer based on the extracted distributed capacitance, distributed conductance, distributed resistance, and distributed inductance.

[0112] In finite element software (such as Ansys Maxwell), construct an electrostatic field analysis model (focusing on the insulating medium and extracting the electric field parameters) and a steady-state magnetic field analysis model (focusing on the conductor and magnetic core and extracting the magnetic field parameters):

[0113] Electrostatic field model: simulates the electric field distribution of inter-turn / inter-layer insulation and outputs distributed capacitance (characterizing the electric field coupling strength), distributed conductivity (characterizes leakage current loss);

[0114] Steady-state magnetic field model: simulates the magnetic field distribution of Litz wire and magnetic core, and outputs distributed resistance (characterizing skin effect loss), distributed inductance (Characterizing magnetic field energy storage and core nonlinearity).

[0115] Geometric model and mesh division:

[0116] Import the 3D geometric model of the high-frequency transformer (including the number of winding turns, insulation thickness, and core size), and refine the mesh (mesh size ≤ 1 / 5 of the skin depth or the characteristic length of the electric field change) in areas with large electric field gradients (such as inter-turn gaps and interlayer insulation) and large magnetic field gradients (such as the Litz wire surface and the core air gap) to ensure simulation accuracy (such as the calculated error of the electric field strength < 5%).

[0117] Conductor boundary conditions (associated with step S13 spectrum):

[0118] 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 amplitude is the fundamental amplitude of the high voltage port (e.g. 752.3V, corresponding to ), the 3rd and 5th harmonic amplitudes take the corresponding components (such as 85.1V, 42.7V, corresponding 、 ), simulates the voltage stress spectrum under cascade conditions;

[0119] Grounding constraint: Set the reference node of the transformer core or 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.

[0120] Insulation material properties (frequency-varying characteristics):

[0121] Frequency-dependent dielectric constant : Look up the frequency-dependent dielectric spectrum of insulating materials (such as polyimide film) (obtained from the supplier's technical manual or measured data), enter the dielectric constant values ​​at different frequencies (such as 100kHz). , at 1MHz ), which reflects the frequency dependence of the polarization ability of insulating materials (such as the attenuation of dielectric constant caused by molecular polarization hysteresis at high frequencies).

[0122] Frequency-variable conductivity : Similarly, input the frequency-variable conductivity of the insulating material (e.g. at 100kHz , at 1MHz ), characterizing the dynamic changes in the leakage current of insulating materials at high frequencies (such as the increase in high-frequency ion mobility leading to an increase in conductivity).

[0123] Parameter physics principle:

[0124] Distributed capacitance : reflects the electric field coupling strength of inter-turn / inter-layer insulation and the dielectric constant of the insulation material , inter-turn coupling area A, insulation thickness d meet ;

[0125] Distributed conductance : Reflects the leakage current characteristics of the insulating medium and the conductivity of the insulating material , inter-turn coupling area A, insulation thickness d meet .

[0126] Electrostatic field simulation and parameter extraction:

[0127] The multi-frequency voltage excitation (fundamental wave + harmonics), grounding constraint, insulation material frequency-varying properties ( , ) Input the electrostatic field analysis model and solve Maxwell's electric field equations (When there is no free charge), the electric field distribution at different frequencies is obtained.

[0128] Current excitation frequency range:

[0129] Refer to step S13 for the main harmonic components of the frequency domain data set (fundamental , 3rd harmonic , 5th harmonic ), the current excitation frequencies are defined as 100kHz, 300kHz, and 500kHz, covering the main harmonic components of the Litz wire current in the LLC topology, ensuring that the magnetic field parameter extraction matches the actual current spectrum.

[0130] Current amplitude matching:

[0131] The current excitation amplitude is derived from the load current in the simulation equation of step S12 (e.g., the full-load current of a 10kW converter is approximately 12.5A, and the fundamental current amplitude is approximately 17.7A), ensuring that the current intensity of the excitation is consistent with the actual working conditions.

[0132] Parameter physics principle:

[0133] Distributed resistance : Reflects the high-frequency skin effect of Litz wire. The higher the frequency, the deeper the skin depth. The smaller ( is the angular frequency, is the conductivity of copper), the effective conductive area decreases and the resistance increases;

[0134] Distributed inductance : Reflects the self-inductance of the Litz wire, the mutual inductance between turns, and the nonlinear magnetic permeability of the core The resulting frequency dependence of the inductance (at magnetic saturation, attenuates, and the inductance decreases synchronously).

[0135] Magnetic field simulation and parameter extraction:

[0136] The multi-frequency current excitation (amplitude + frequency) of step S24, the core BH curve (input nonlinear permeability , such as the measured magnetization curve of ferrite N87), skin characteristics of Litz wire (input copper conductivity , vacuum magnetic permeability μ0=4π×10 −7 H / m, calculate skin depth ) Input the steady-state magnetic field analysis model and solve Maxwell's magnetic field equations , ( is the vector magnetic potential).

[0137] The data is stored in the dimensions of "frequency-spatial position-parameter". The example is as follows (structured description):

[0138] Frequency dimension: covers the main harmonic frequency of step S13 (100kHz, 300kHz, 500kHz, etc.);

[0139] Spatial location dimension: distinguish between "turns" (such as the first turn and the second turn) and "layers" (such as the first layer and the second layer);

[0140] Parameter dimension: storage distributed capacitance , distributed conductivity , distributed resistance , distributed inductance .

[0141] For example, at 100kHz, the inter-turn distributed capacitance between the first and second winding layers is 22.3pF, and the distributed conductance is 1.5nS; the distributed resistance of the first turn of the Litz wire is 0.05Ω, and the distributed inductance is 120nH.

[0142] Based on the finite element method, the present invention establishes an electrostatic field analysis model and a steady-state magnetic field analysis model for a high-frequency transformer, focusing on the electric field and magnetic field characteristics of the insulating medium, the conductor, and the magnetic core, respectively, to achieve a comprehensive analysis of the frequency-variable distributed parameters of the high-frequency transformer. This multi-dimensional analysis model construction method ensures the accuracy and comprehensiveness of parameter extraction. In the process of model construction, the present invention fully considers physical principles such as the frequency-variable dielectric constant and conductivity of the insulating material, the skin effect of the Litz wire, and the nonlinear magnetic permeability of the iron core, so that the simulation results are closer to the actual physical process.

[0143] Based on the spectrum information extracted in step S13, the present invention applies a voltage excitation matching the spectrum amplitude to the conductor surface and applies a ground constraint to the reference node. This precisely matched conductor boundary condition setting ensures the accuracy and reliability of the voltage excitation during the simulation process, providing a solid foundation for subsequent parameter extraction. By consulting the frequency-dependent dielectric spectrum and conductivity data of the insulating material, the present invention inputs the dielectric constant 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.

[0144] By inputting the set conductor boundary conditions and insulating material properties into the electrostatic field analysis model, the present invention successfully extracted 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 extracted 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. In the process of geometric model and mesh division, the present invention performs encrypted mesh processing on areas with large electric field gradients and large magnetic field gradients to ensure 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.

[0145] Based on the extracted distributed capacitance, distributed conductance, distributed resistance, and distributed inductance, this paper constructs a frequency-dependent distributed parameter database for high-frequency transformers. This database stores data using the "frequency-spatial location-parameter" dimension, enabling structured management and efficient querying of frequency-dependent distributed parameters of high-frequency transformers.

[0146] In addition, step S3 includes:

[0147] Step S31: Discretize each winding of the high-frequency transformer into an independent calculation unit, define the unit number corresponding to each independent calculation unit in the high and low voltage windings, and establish a geometric relationship mapping table between units based on the unit number. The mapping table records the current path topology and the inter-turn / inter-layer geometric relationship including the inter-turn distance and inter-layer insulation thickness;

[0148] Step S32: Mapping the distributed capacitance and distributed conductance parameters of the insulating material to the admittance branch representing the electric field coupling characteristics between the units according to the inter-turn / inter-layer geometric relationship; mapping the distributed resistance and distributed inductance parameters of the Litz wire to the impedance branch representing 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;

[0149] Step S33: Treat the two ends of each winding as independent nodes, connect impedance branches in series between adjacent nodes, achieve magnetic field coupling between non-adjacent nodes through mutual inductance branches, and connect an admittance branch in parallel between each node and the reference ground to form a chain node network of high and low voltage windings, completing the construction of the frequency-variable distributed parameter equivalent circuit of the high-frequency transformer.

[0150] Furthermore, the distributed capacitance and distributed conductance parameters of the insulating material are mapped to the admittance branch between units that characterizes the electric field coupling characteristics according to the inter-turn / inter-layer geometric relationship. The specific expression is:

[0151] ;

[0152] ;

[0153] in, is the distributed capacitance, representing the frequency-dependent capacitance between the i-th and j-th turns of the winding; The frequency-dependent dielectric constant characterizes the polarization ability of the insulating material at different frequencies f and reflects the dynamic change of the electric field coupling strength with frequency. The unit is F / m. is the coupling area, which represents the effective area of ​​the electric field overlap between the i-th and j-th turns of the winding; is the dielectric thickness, which represents the physical thickness of the insulation layer between the i-th and j-th turns of the winding; is the distributed conductance, representing the frequency-dependent conductance between the i-th and j-th turns of the winding; Frequency-dependent conductivity, which characterizes the leakage current characteristics of insulating materials at different frequencies f, reflects the dynamic change of dielectric loss with frequency, and its unit is S / m;

[0154] The distributed resistance and distributed inductance parameters of the Litz wire are mapped to the impedance branch in the unit that represents the magnetic field coupling characteristics according to the current path topology. The specific expression is:

[0155] ;

[0156] ;

[0157] in, is the distributed resistance, representing the frequency-dependent resistance of the i-th winding turn; The resistance per unit length characterizes the AC resistance of Litz wire per meter at high frequencies. is the effective length of the current path; is the distributed inductance, representing the frequency-varying inductance of the i-th winding turn; is the inductance per unit turn, which represents the equivalent inductance of a single-turn winding at high frequency; is the number of adjacent coupled turns, representing the number of effective winding turns that have magnetic field coupling with the i-th winding turn.

[0158] Taking the high-frequency transformer of a 10kW full-bridge LLC converter as an example (with 20 turns on the primary side and 5 turns on the secondary side, using Litz wire winding), each turn on the primary side and each turn on the secondary side is divided into independent calculation units. The primary unit number is defined as , the secondary side is , clarify the correspondence between "unit number → physical winding position" (such as Corresponding to the first turn of the innermost layer of the original side).

[0159] Measure and record the inter-unit current path topology and inter-turn / inter-layer geometric parameters to form a two-dimensional table:

[0160] Current path topology: The primary winding is wound in a clockwise spiral, and the current flows from Head end inflow, The secondary side is a counterclockwise spiral, and the current flows from Head end inflow, The end flows out.

[0161] For unit pairs (such as ), combined with the frequency-dependent distributed capacitance extracted in step S23 , distributed conductivity , and the geometric parameters in the mapping table ( , ), calculated by the above formula, and the frequency-dependent distributed capacitance , distributed conductivity As the admittance branch parameter, connect and The corresponding nodes represent the inter-turn electric field coupling strength and leakage current loss.

[0162] For a single unit (such as ), combined with the frequency-dependent distributed resistance extracted in step S25 , distributed inductance (including self-inductance and mutual inductance of adjacent turns), and the current path length , adjacent coupling turns , calculated by the above formula, the frequency-dependent distributed resistance , distributed inductance As the impedance branch parameter, in series Between the head end and the end node, the high-frequency skin loss and magnetic field energy storage characteristics of the Litz wire are characterized.

[0163] Set the beginning and end of each winding as independent nodes (such as The first end is the node , the end is a node ; The first end is , the end is , and so on), establish a “unit→double node” mapping relationship.

[0164] Branch topology integration:

[0165] Series impedance branch: The impedance branch of the corresponding unit in series between adjacent nodes (such as Series of 、 ; Series of 、 );

[0166] Mutual inductance branch connection: Magnetic field coupling is achieved between non-adjacent units through mutual inductance branches (such as and Mutual induction , then in ( end) and ( End) between connecting mutual inductance branches );

[0167] Admittance branch to ground: A parallel admittance branch is connected between each node and the reference ground (such as Parallel connection to ground ,in 、 for The frequency-variable distributed parameter equivalent circuit of the high-frequency transformer constructed is as follows: Figure 2 shown.

[0168] This invention discretizes each turn of a high-frequency transformer into an independent computational unit and assigns a number to each unit, achieving a refined description of the transformer's internal structure. This discretization method enables more accurate subsequent parameter mapping and circuit construction. Based on the unit numbering, a geometric relationship mapping table between units is established, recording the current path topology and the inter-turn / inter-layer geometric relationships, providing a foundation for subsequent parameter mapping. This mapping relationship ensures the accuracy and consistency of parameter mapping.

[0169] The present invention maps the distributed capacitance and distributed conductance parameters of the insulating material to the admittance branch between units that characterizes the electric field coupling characteristics according to the inter-turn / inter-layer geometric relationship, and provides a specific mathematical expression. This mapping method accurately reflects the electric field coupling strength and leakage current characteristics of the inter-turn / inter-layer insulation, and provides 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 branch in the unit that characterizes the magnetic field coupling characteristics according to the current path topology, and a specific mathematical expression is 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.

[0170] The present invention treats the two ends of each winding turn as independent nodes, connects impedance branches in series between adjacent nodes, achieves magnetic field coupling between non-adjacent nodes via mutual inductance branches, and connects an admittance branch in parallel between each node and the reference ground. This node and branch definition creates a chain node network for the high and low voltage windings, providing a structural foundation for the construction of circuit models. By integrating the series impedance branch, the mutual inductance branch connection, and the ground admittance branch, 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.

[0171] Then, step S4 includes:

[0172] Step S41: Based on the number of nodes and branches in the constructed frequency-dependent 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;

[0173] Step S42: Based on the corresponding dimensions and variables defined for the impedance branches, the frequency-variant parameters of all impedance branches in the frequency-variant distributed parameter equivalent circuit are integrated to form an impedance branch matrix;

[0174] Step S43: Based on the corresponding dimensions and variables defined by the admittance branches, frequency-varying parameters of all admittance branches in the frequency-varying distributed parameter equivalent circuit are integrated to form an admittance branch matrix;

[0175] Step S44: defining an association matrix describing the connection relationship between the admittance branch / impedance branch and the node;

[0176] Step S45: Correlate the correlation matrix, the impedance branch matrix, the admittance branch matrix, and the node voltage vector using Kirchhoff's law to form a solution equation for the network node voltage in the frequency-variable distributed parameter equivalent circuit, thereby completing the construction of a universal parameterized model of the frequency-variable distributed parameter equivalent circuit.

[0177] Specifically, take "high and low voltage windings each contain n=2 units" as an example (primary side , Secondary side , ), define the matrix dimensions and variables according to the following rules:

[0178] Number of nodes:

[0179] A single winding with n units corresponds to n+1 nodes (e.g. primary side , Corresponding node , , ), the dual windings share one reference ground node , so the total number of nodes is 2n+2=6 (node ​​list: , , , , , ).

[0180] (1)

[0181] matrix It is used to represent the impedance branches composed of all resistances and inductances in the distributed parameter model, with a total of 2n impedance branches (according to the high and low voltage windings, there are n units and n+1 nodes, the same below).

[0182] (2)

[0183] matrix Used to represent the admittance branches composed of all conductances and capacitances in the distributed parameter model, a total of 2n+2 admittance branches.

[0184] (3)

[0185] 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.

[0186] Correlation Matrix It can be expressed as:

[0187] (4)

[0188] Combining equations (1) to (4), we can obtain the relationship between the voltage and current of the high-frequency transformer winding distributed parameter network:

[0189] (5)

[0190] Combining equations (5), we can obtain the solution equation for the network node voltage under the condition of no external voltage:

[0191] (6)

[0192] in, To solve the coefficient matrix of the equation, the above equations (1) to (6) are implemented through programming to construct a universal parameterized model of the frequency-variable distributed parameter equivalent circuit of the high-frequency transformer.

[0193] 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 the model construction of high-frequency transformers of different specifications and types. This unified standard helps technicians share experience and exchange technology between different projects.

[0194] 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. This matrix accurately reflects the resistance and inductance characteristics of the high-frequency transformer at different frequencies, providing 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. This matrix accurately reflects the conductance and capacitance characteristics of the high-frequency transformer at different frequencies, further improving the description of the circuit model.

[0195] The present invention defines an association matrix that describes the connection relationship between the admittance branch / impedance branch and the node, and step S4 clarifies the topological relationship between each branch and the node in the circuit model. This definition of the association matrix makes the structure of the circuit model clearer, making it easier for technicians to perform circuit analysis and troubleshooting. By applying Kirchhoff's law to associate the association matrix, impedance branch matrix, admittance branch matrix and node voltage vector, step S4 forms a solution equation for a complete frequency-dependent distributed parameter equivalent circuit. This equation can accurately describe the electrical characteristics of the high-frequency transformer under different operating conditions, providing a mathematical basis for circuit simulation and analysis.

[0196] The present invention implements the aforementioned equation solving through programming. Step S4 constructs a universal parameterized model of the frequency-dependent distributed parameter equivalent circuit of a high-frequency transformer. This model has excellent versatility and scalability, and can be applied to high-frequency transformers of different specifications and types. Rapid model construction and simulation analysis can be achieved by simply adjusting the matrix dimensions and parameter values. By constructing a universal parameterized model, step S4 provides strong support for circuit simulation and analysis of high-frequency transformers. Technicians can use this model to perform circuit simulations under different operating conditions, predict the electrical performance of high-frequency transformers, and optimize and improve designs.

[0197] Step S5 includes:

[0198] Step S51: Perform Fourier decomposition on the acquired cascade multi-port voltage waveform to extract the amplitude and phase of the harmonic components of each port voltage;

[0199] Step S52: determining a target frequency spectrum range based on the extracted parameter effective frequency range pre-stored in the frequency-variable parameter database and the frequency-variable dielectric characteristics set in the insulating material properties;

[0200] Step S53: Calculate the minimum truncation order K based on the target spectrum range and the preset harmonic truncation accuracy threshold;

[0201] Step S54: extract the harmonic component spectrum of each port within the Kth order, and output a harmonic data set including frequency, amplitude and phase.

[0202] Based on the method in step S1, the voltage waveform V at different ports of the high-frequency transformer under the cascade condition of the DC-DC isolation converter is obtained. i (t), i is the port number of the high-frequency transformer. If the voltage is period T (T=1 / f s ) of an ideal square wave, f s is the voltage wave fundamental frequency, D i Its duty cycle, in each cycle, the front D i V in T time i (t) amplitude is V i , after (1-Di )T time V i (t) The amplitude is -V i Performing independent Fourier decomposition on the square wave of each port yields:

[0203] (7)

[0204] Where, ; , where k represents the kth harmonic.

[0205] A real square wave has a finite rise time and fall time , the waveform is closer to a trapezoidal wave. At this time, the Fourier coefficients need to be corrected, and the key parameters are truncated according to the Shannon sampling theorem. K is the truncation order ( , To focus on the highest frequency):

[0206] (8)

[0207] in, is the phase offset (determined by the timing control).

[0208] For each excitation port i, the kth harmonic component , set the excitation vector to:

[0209] (9)

[0210] The frequency domain expression of the voltage at each port in formula (9) is the boundary condition of the network parameterization model in step S4, where: is the transpose operator.

[0211] The present invention performs Fourier decomposition on the acquired cascaded multi-port voltage waveform, and step S5 accurately extracts the amplitude and phase of the harmonic components of each port voltage. This decomposition method allows complex periodic voltage waveforms to be decomposed into a series of simple sine and cosine waves, facilitating subsequent analysis and processing. The extracted harmonic component amplitude and phase information provides technicians with a comprehensive understanding of the harmonic characteristics of the voltage waveform, helping to analyze the electrical performance of high-frequency transformers under different operating conditions.

[0212] Based on the effective frequency range of parameters pre-stored in the extracted frequency-variable parameter database and combined with the frequency-variable dielectric properties set in the insulation material properties, step S5 can accurately determine the target spectrum range. This determination method ensures the targeted and effective nature of subsequent analysis and avoids unnecessary calculation and analysis burdens. By accurately determining the target spectrum range, step S5 enables spectrum analysis to focus on the frequency range that has the greatest impact on the electrical characteristics of the high-frequency transformer, improving the accuracy and efficiency of the analysis.

[0213] Based on the target spectrum range and a preset harmonic truncation accuracy threshold, step S5 of the present invention 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, thus ensuring the accuracy of the analysis. By reasonably calculating the minimum truncation order K, step S5 avoids unnecessary harmonic calculation and analysis, optimizing the utilization of computing resources.

[0214] The present invention extracts the K-order harmonic component spectrum of each port and outputs a harmonic dataset containing frequency, amplitude, and phase. Step S5 fully integrates and outputs key harmonic information. This dataset provides rich data support for subsequent network parameterization model construction and simulation analysis. The output harmonic dataset is traceable and reusable, facilitating data sharing and reuse among different projects by technicians, improving work efficiency and data utilization.

[0215] For the kth harmonic component of each excitation port i, the present invention sets the excitation vector as an expression containing frequency, amplitude, and phase. Step S5 achieves precise 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 subsequent solution of the network parameterized model. By precisely setting the boundary conditions, step S5 improves the accuracy of the network parameterized model solution, making the simulation results more closely aligned with the actual electrical characteristics.

[0216] In this paper, the present invention addresses the finite rise and fall times of real square waves. Step S5 corrects the Fourier coefficients and truncates key parameters according to Shannon's sampling theorem, effectively processing non-ideal square waves. This approach makes the analysis more realistic and improves the practicality and reliability of the model.

[0217] Step S6 includes:

[0218] Step S61: Based on the constructed node network of the frequency-dependent distributed parameter equivalent circuit, determine the node to which the excitation is applied, the grounding node, and the node numbers corresponding to the above nodes;

[0219] Step S62: Delete the corresponding rows and columns in the coefficient matrix of the node voltage solution equation according to the node number of the excitation node and the node number of the grounding node, extract the coefficient matrix column vector corresponding to the node number of the excitation node and move it to the right side of the equation solution, and construct a new equation solution for all response nodes to implement the application of excitation in the analytical calculation process;

[0220] Step S63: Solve equations based on all newly constructed 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.

[0221] In step S5, equation (9) decomposes the square wave excitation voltages of different ports into sinusoidal excitations within a certain spectrum range. The sinusoidal voltages within the target spectrum range of all ports are applied to the parameterized model at different frequencies and the node voltages in this state are calculated (single-frequency excitation). Finally, the superposition principle is used to solve the total response waveform.

[0222] The present invention proposes the following method for applying single-frequency excitation boundary conditions: the numbers of all excitation nodes, grounding nodes and response nodes in the distributed parameter model are taken to form a number set d, g and r, and the elements of the d-th row and d-th column and the g-th row and g-th column of the coefficient matrix M in step four (6) are all deleted to form a new (2n+2-numel(d)-numel(g))-order square matrix N; after deleting the d-th and g-th elements of the d-th column elements in M, a new (2n+2-numel(d)-numel(g))-dimensional column vector N is formed. d , forming a new equation:

[0223] (10)

[0224] Among them, U r Delete the known voltage U from the original node voltage column vector U d and U g The total (2n+2-numel(d)-numel(g)) unknown node voltage values ​​to be solved after the elements are formed, that is, all voltages of all response nodes numbered r. Using Equation (10), the single-frequency excitation voltage boundary conditions of all ports can be applied to the high-frequency transformer distributed parameter network to solve the voltage values ​​of all unknown response nodes.

[0225] Specifically, combined with the 6-node chain equivalent circuit constructed in step S3 ( , , 2 turns on the primary side + 2 turns on the secondary side + shared reference ground), clarify the physical meaning and numbering rules of the three types of nodes:

[0226] 1. Incentive node (data set d):

[0227] The voltage application node of the primary parallel input is selected from the first turn of the primary side. 、The first end of the second turn of the original side , numbered ( , , , , , Nodes are sorted sequentially).

[0228] 2. Ground node (data set g):

[0229] Circuit reference ground node , numbered (The ground node potential is always 0V).

[0230] 3. Response node (data set r):

[0231] The secondary side series output node where the voltage needs to be solved is selected at the end of the first turn of the secondary side. , the end of the second turn of the secondary side , numbered .

[0232] Based on the general parameterized model of step S4, the core equation for solving the node voltage is step 4 (6) (Homogeneous equations when there is no applied voltage; the applied voltage is embedded through boundary conditions.) Combined with the excitation node d and the ground node g, perform the following matrix operations:

[0233] 1. Coefficient matrix Crop:

[0234] Original coefficient matrix The dimension is 6×6 (corresponding to 2n+2 nodes).

[0235] Delete the rows / columns corresponding to the excitation node d: remove the 1st and 2nd rows and the 1st and 2nd columns (corresponding to , rows and columns);

[0236] Delete the row / column corresponding to the ground node g: remove the 6th row and the 6th column (corresponding to rows and columns); the new matrix after clipping The dimension is (6−2−1)×(6−2−1)=3×3 (the remaining nodes are , , ).

[0237] 2. Excitation column vector Extraction:

[0238] Original coefficient matrix After deleting the dth column (corresponding to the excitation node) of , the 1st and 2nd rows (the excitation node rows) and the 6th row (the ground node row) are formed to form a new column vector The dimensions are 3×1.

[0239] 3. Reorganize and solve the equation:

[0240] Original node voltage column vector In the example, the excitation node voltage (determined by the fundamental / harmonic amplitude of the frequency domain data set in step S13) and the ground voltage is a known quantity, and the remaining unknown quantity is the response node voltage (Dimension 3×1, corresponding voltage , , The final rearranged equation is: .

[0241] Taking the fundamental frequency f1 = 100 kHz as an example, the frequency domain data set of step S13 and the distributed parameters of step S2 are combined to complete the solution and characteristic output of the response node voltage:

[0242] 1. Excitation voltage assignment:

[0243] Get the excitation node from the frequency domain data set in step S13 、 Fundamental voltage:

[0244] Amplitude: 、 , the primary sides are connected in parallel, and the voltage amplitudes are equal;

[0245] Phase: Both (Control strategies are triggered synchronously, and the initial PWM phases are consistent).

[0246] 2. Matrix inversion and voltage solution:

[0247] The trimmed coefficient matrix (Including the frequency-dependent distributed parameters extracted in step S2: Litz wire distributed resistance , distributed inductance , inter-turn distributed capacitance , distributed conductivity Mapped admittance / impedance) into the reorganized equation , the response node voltage is obtained by matrix inversion operation:

[0248] (End of the first turn of the secondary side Voltage): The amplitude is determined by the primary excitation and the inter-turn distributed capacitance The electric field coupling strength is determined by the actual measurement, which is about 376.1V;

[0249] (End of the 2nd turn on the secondary side Voltage): The amplitude is determined by the primary excitation and the interlayer distributed inductance The magnetic field coupling strength is determined by the actual measurement of about 376.1V;

[0250] (The end of the second turn of the primary side Voltage): The amplitude is determined by the midpoint voltage of the primary H-bridge topology and is measured to be approximately 376.1V.

[0251] 3. Voltage characteristic output:

[0252] The amplitude and phase of the output response node voltage:

[0253] Amplitude: reflects the voltage distribution characteristics of the cascade topology (the voltage of the two nodes on the secondary side is close to the primary side voltage after superposition, verifying the series boost logic);

[0254] Phase: 、 (It is in anti-phase with the primary side excitation phase, which conforms to the voltage transfer phase characteristics of the full-bridge LLC topology).

[0255] Based on the node network of the frequency-dependent distributed parameter equivalent circuit constructed in the present invention, step S6 can accurately identify the node to be excited and the preset ground node. This identification method ensures that the excitation voltage can be accurately applied to the target node, providing a basis for subsequent voltage response calculations. By accurately identifying the excitation node and the ground node, step S6 improves the accuracy of the frequency-dependent distributed parameter equivalent circuit model, making the model more accurate to the actual circuit conditions.

[0256] The present invention converts the single-frequency components in the extracted harmonic data set into frequency-domain complex voltage excitations. Step S6 achieves the conversion from the time domain to the frequency domain, facilitating subsequent frequency-domain analysis. Accurately applying the frequency-domain complex voltage excitations to the identified excitation and ground nodes ensures that the excitation voltages act as intended on the circuit, improving the accuracy of the voltage response calculation.

[0257] The present invention applies frequency-domain complex voltage excitation to the solved equations of the frequency-dependent distributed parameter equivalent circuit. Step S6 efficiently calculates the frequency-domain voltage vector of the response node. This calculation method avoids complex time-domain simulation and improves computational efficiency. By calculating the frequency-domain voltage vector of the response node, step S6 comprehensively obtains the voltage response amplitude and phase of all nodes at this frequency, providing rich data support for subsequent insulation evaluation and design.

[0258] The proposed single-frequency excitation boundary condition application method effectively applies single-frequency excitation voltage boundary conditions by deleting specific elements from the coefficient matrix and forming a new equation. This method simplifies the calculation process and improves solution efficiency. Using this new equation, step S6 accurately determines the voltage values ​​of all unknown response nodes, providing a key basis for subsequent voltage stress distribution analysis and insulation design.

[0259] The node voltage response under single-frequency excitation calculated in step S6 of the present invention provides basic data for the subsequent use of the superposition principle to solve the overall response waveform. This close connection ensures the consistency and accuracy of the entire analysis process. Using the node voltage response data obtained in step S6, technicians can further perform insulation evaluation and design optimization to improve the insulation performance and reliability of the high-frequency transformer.

[0260] Based on the constructed high-frequency transformer equivalent model and the method of applying excitation to different ports, the present invention ultimately realizes the analysis and calculation of the internal voltage stress of the high-frequency transformer under the important working condition that all ports are excited under cascade conditions, avoiding the limitation of only considering single-ended excitation in traditional methods.

[0261] Step S7 includes:

[0262] Based on the superposition principle, the node frequency domain voltage responses under all harmonic frequency components are synthesized in the time domain;

[0263] According to the control strategy of the cascade topology, the initial phase of each port excitation is calibrated to ensure that the time domain voltage waveform is synchronized with the actual working conditions;

[0264] After calibration, the time domain voltages of all nodes are reorganized according to the physical positions of the windings to form a voltage stress distribution map inside the high-frequency transformer.

[0265] Specifically, the main harmonic component (fundamental) of the frequency domain data set in step S13 is selected , 3rd harmonic , 5th harmonic ), for each node in the general parameterized model of step S4 (such as the first end node of the primary side , the end node of the first turn of the secondary side etc.), and synthesize the time domain voltage according to the superposition principle, that is, the voltage distribution of each node under all harmonic components of multi-port sinusoidal excitation in the target frequency band:

[0266] (11)

[0267] in, For each node (node ​​n) at frequency The harmonic response amplitude under the condition of ΔH is derived from the analytical solution of step S6, and its magnitude is directly related to the frequency-dependent distribution parameters extracted in step S2 (such as the inter-turn distributed capacitance). Determine the electric field coupling strength, if increases, the harmonic amplitude will be amplified); For node n at frequency The harmonic response phase under the condition of is obtained by solving step S6, and its phase difference reflects the disturbance 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. This is used to evaluate the voltage withstand of the high-frequency transformer insulation under the condition of cascaded DC-DC isolation converters, providing a reference for the insulation design of high-frequency transformers.

[0268] For example, the fundamental , V, ; 3rd harmonic , V, ; 5th harmonic , V, ; The synthesized time domain terminal voltage is: .

[0269] Taking the IPOS cascade topology as an example, phase calibration is implemented in two layers by combining the control strategy with the device characteristic parameters in the simulation equation:

[0270] Based on the "parallel synchronous input and serial in-phase output" control strategy of the IPOS cascade topology, the initial phase of the port excitation is calibrated in two layers:

[0271] 1. Phase reference anchoring of control strategy:

[0272] IPOS topology requirements:

[0273] The PWM triggering of the two LLC converters on the primary side is strictly synchronized (phase difference ), ensure the input parallel voltage equalization;

[0274] The output voltage phase of the two converters on the secondary side is superimposed (phase difference ), to ensure the output series boost. From the control strategy of step S11, the PWM triggering moment corresponds to the initial phase (Duty Cycle The phase corresponding to the starting moment of the pulse width) is used as the phase reference for all port excitations.

[0275] 2. Topological inherent phase difference compensation:

[0276] In the full-bridge LLC topology, there is an inherent difference between the primary H-bridge output square wave and the secondary rectifier voltage. Phase difference (determined by the topology of "diagonal conduction logic + full-wave rectification"). The phase of the synthesized waveform needs to be compensated:

[0277] Primary side excitation node (such as , ) phase hold (matching PWM trigger reference);

[0278] Secondary side response node (such as , ) is the phase calibration (voltage transfer phase characteristics of the matching topology).

[0279] For example, the end node of the first turn of the secondary side The initial phase of the composite voltage is , and the primary side excitation node of The phase difference meets the topology requirements and ensures that the time domain waveform is synchronized with the actual power flow direction.

[0280] Establish a mapping table of node numbers and winding physical positions as shown in Table 1 (i.e., a mapping table of geometric relationships between units established by unit numbers), 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):

[0281] Table 1: Node number winding physical location mapping table

[0282]

[0283] The calibrated node time domain voltage (such as 、 etc.) are classified according to the order of "radial layer → axial turn" in the mapping table, and the voltage values ​​are rendered in a two-dimensional coordinate system:

[0284] Horizontal axis: axial turns (1st turn on primary side → 2nd turn on primary side → 1st turn on secondary side → 2nd turn on secondary side);

[0285] Vertical axis: radial layer number (primary edge layer / secondary edge layer);

[0286] Color coding: red indicates high voltage areas and blue indicates low voltage areas.

[0287] Calculate turn-to-turn / layer voltage differences and mark insulation risk areas:

[0288] Turn-to-turn voltage difference: For example, the first turn of the primary side ( ) and the second turn ( ) voltage difference ;

[0289] Voltage difference between layers: such as the primary layer ( ) and the secondary side layer ( ) voltage difference .

[0290] If the voltage difference exceeds the insulation material's tolerance threshold (e.g., the polyimide film's tolerance voltage is 2kV), it is marked as a "high stress area," providing a reference for optimizing insulation design (e.g., increasing insulation thickness, replacing corona-resistant materials).

[0291] Based on the superposition principle, step S7 of the present invention performs time-domain synthesis of the node frequency-domain voltage responses for all harmonic frequency components. This approach ensures that the contributions of all harmonic components to the voltage response are comprehensively considered, resulting in a time-domain voltage waveform that more closely reflects actual operating conditions. Through time-domain synthesis, step S7 can comprehensively describe the voltage response of the high-frequency transformer for different harmonic frequency components, providing complete voltage data support for subsequent insulation evaluation.

[0292] Based on the control strategy of the cascade topology, step S7 of the present invention calibrates the initial phase of each port's excitation. This calibration method ensures the synchronization of the time-domain voltage waveform with the actual operating conditions, improving the accuracy and reliability of the simulation results. By accurately calibrating the initial phase, step S7 effectively eliminates voltage response deviations caused by phase errors, making the simulation results more accurate and consistent with the actual electrical characteristics.

[0293] After calibration, step S7 reconstructs the time-domain voltages of all nodes according to the physical location of the windings, forming a voltage stress distribution map within the high-frequency transformer. This map visually displays the voltage stress distribution at each node within the high-frequency transformer, providing technicians with a clear basis for insulation assessment. This voltage stress distribution map allows technicians to accurately understand the insulation withstand capacity of the high-frequency transformer under different operating conditions, providing a powerful reference for insulation design.

[0294] Figure 3 This is a structural diagram of a terminal 300 provided in an embodiment of the present invention. The terminal 300 can be used to execute the voltage stress calculation method inside the cascade high-frequency transformer provided in an embodiment of the present invention.

[0295] The terminal 300 may include a processor 310, a memory 320, and a communication module 330. These components communicate via one or more buses. Those skilled in the art will appreciate that the server structure shown in the figure does not limit the present invention. The server structure may be a bus structure or a star structure, and may include more or fewer components than shown, or may combine certain components or arrange the components differently.

[0296] Memory 320 can be used to store execution instructions of processor 310. Memory 320 can be implemented by any type of volatile or non-volatile storage device, 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 disk. When the execution instructions in memory 320 are executed by processor 310, terminal 300 can perform some or all of the steps in the above-described method embodiments.

[0297] The processor 310 is the control center of the storage terminal. It uses various interfaces and lines to connect various parts of the entire electronic terminal. It executes various functions of the electronic terminal and / or processes data by running or executing software programs and / or modules stored in the memory 320, and calling data stored in the memory. The processor can be composed of an integrated circuit (IC), for example, it can be composed of a single packaged IC, or it can be composed of multiple packaged ICs with the same or different functions. For example, the processor 310 can only include a central processing unit (CPU). In the embodiment of the present invention, the CPU can be a single computing core or multiple computing cores.

[0298] The communication module 330 is used to establish a communication channel so that the storage terminal can communicate with other terminals, receive user data sent by other terminals, or send user data to other terminals.

[0299] The present invention also provides a computer storage medium, wherein the computer storage medium may store a program that, when executed, may include some or all of the steps of each embodiment provided herein. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0300] Those skilled in the art will clearly understand that the techniques in the embodiments of the present invention can be implemented using software plus a necessary general-purpose hardware platform. Based on this understanding, the technical solutions in the embodiments of the present invention, or the portion 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 drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, among other media capable of storing program code, and includes instructions for causing 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 various embodiments of the present invention.

[0301] In this specification, the same or similar parts between the various embodiments can be referred to each other. In particular, for the terminal embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the description in the method embodiment.

[0302] Although the present invention has been described in detail with reference to the accompanying drawings and in conjunction with preferred embodiments, the present invention is not limited thereto. Without departing from the spirit and essence of the present invention, persons of ordinary skill in the art may make various equivalent modifications or substitutions to the embodiments of the present invention, and such modifications or substitutions shall be within the scope of the present invention. Any changes or substitutions that can be easily conceived by persons skilled in the art within the technical scope disclosed in the present invention shall be within the scope of protection of the present invention.

Claims

1. A method for calculating voltage stress inside a cascaded high-frequency transformer, characterized in that: include: Step S1: according to the external cascade mode, internal topology, converter characteristics and control strategy of the DC-DC isolation converter, simulate and obtain the time domain voltage waveform of each port of the high frequency transformer in the DC-DC isolation converter under the cascade condition, and extract the spectrum information of the voltage waveform through frequency domain analysis; Step S2: Based on the finite element method, a frequency-dependent distributed parameter extraction model of the high-frequency transformer is established, and the spectrum information is input into the frequency-dependent distributed parameter extraction model to extract the frequency-dependent distributed parameters at different frequencies. The frequency-dependent distributed parameters include conductance parameters, capacitance parameters, resistance parameters, and inductance parameters; Step S3: In the established frequency-variable distributed parameter extraction model, each winding of the high-frequency transformer is used as an independent calculation unit. According to the pre-stored inter-turn geometric relationship and current path, the extracted frequency-variable distributed parameters are distributed to the impedance branch and admittance branch corresponding to the independent calculation unit, thereby constructing the frequency-variable distributed parameter equivalent circuit of the high-frequency transformer; Step S4: Based on the constructed frequency-variable distributed parameter equivalent circuit, define the impedance branch matrix, the admittance branch matrix, the voltage and current vectors, and the correlation matrix, and establish a universal parameterized model of the frequency-variable distributed parameter equivalent circuit; Step S5: performing Fourier decomposition on the multi-port voltage waveform of the high-frequency transformer under the cascade condition, determining the target spectrum range and truncation order, and extracting the harmonic component spectrum of each port voltage; Step S6: Using the decomposed single-frequency sinusoidal excitation voltage as a boundary condition, and applying it to the excitation node of the general parameterized model, and solving the voltage value of the response node; Step S7: 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 cascade multi-port excitation condition.

2. The method for calculating voltage stress inside a cascaded high-frequency transformer according to claim 1, characterized in that: Step S1 includes: Step S11, obtaining pre-stored DC-DC isolation converter parameters, including external cascade mode, internal topology, converter device characteristics and control strategy; wherein the external cascade mode is the pre-stored electrical connection relationship between the multi-level converters; the internal topology includes the pre-stored circuit configuration of the full-bridge, half-bridge or LLC resonant topology; the control strategy includes the pre-stored duty cycle of the pulse width modulation signal and switching frequency ;Converter device characteristics include the on-time of the MOSFET in the converter and pulse rise time ; Step S12: Based on the acquired 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 waveform of each port of the high-frequency transformer under the cascade condition; Step S13: Perform spectrum analysis on the time-domain voltage waveform of each voltage port by fast Fourier transform, extract the harmonic frequency range, and output spectrum information including fundamental frequency, harmonic amplitude and phase, and store the spectrum information as a frequency domain data set.

3. The method for calculating voltage stress inside a cascaded high-frequency transformer according to claim 2, characterized in that: The simulation equation of the time domain voltage waveform of each port of the high-frequency transformer under the simulated cascade condition is: ； in, is the simulation function; is the internal topological structure function; is the nonlinear magnetic permeability; and These are the time domain voltage waveforms of the high and low voltage ports respectively.

4. The method for calculating voltage stress inside a cascaded high-frequency transformer according to claim 2, wherein: Step S2 includes: Step S21: Based on the finite element method, a frequency-dependent distributed parameter extraction model of the high-frequency transformer is established, including an electrostatic field analysis model and a steady-state magnetic field analysis model; Step S22: setting conductor boundary conditions and insulation material properties based on the extracted spectrum information; the conductor boundary conditions include applying a voltage excitation matching the spectrum amplitude on the conductor surface and applying a ground constraint to the reference node; the insulation material properties include the frequency-dependent dielectric constant and conductivity of the insulation material; Step S23: Input the set conductor boundary conditions and insulation material properties into the constructed electrostatic field analysis model to extract the distributed capacitance and distributed conductance of the insulation 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: defining a current excitation condition based on the extracted spectrum information, where the current excitation condition is a current excitation frequency range covering the main harmonic components in the spectrum information; Step S25: input the defined current excitation conditions and the pre-stored core BH curve and skin characteristics of the Litz wire corresponding to the high-frequency transformer into the constructed steady-state magnetic field analysis model to extract the distributed resistance and distributed inductance of the Litz wire at different frequencies; Step S26: constructing a frequency-dependent 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 voltage stress inside a cascaded high-frequency transformer according to claim 4, characterized in that: Step S3 includes: Step S31: Discretize each winding of the high-frequency transformer into an independent calculation unit, define the unit number corresponding to each independent calculation unit in the high and low voltage windings, and establish a geometric relationship mapping table between units based on the unit number. The mapping table records the current path topology and the inter-turn / inter-layer geometric relationship including the inter-turn distance and inter-layer insulation thickness; Step S32: Mapping the distributed capacitance and distributed conductance parameters of the insulating material to the admittance branch representing the electric field coupling characteristics between the units according to the inter-turn / inter-layer geometric relationship; mapping the distributed resistance and distributed inductance parameters of the Litz wire to the impedance branch representing 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: Treat the two ends of each winding as independent nodes, connect impedance branches in series between adjacent nodes, achieve magnetic field coupling between non-adjacent nodes through mutual inductance branches, and connect an admittance branch in parallel between each node and the reference ground to form a chain node network of high and low voltage windings, completing the construction of the frequency-variable distributed parameter equivalent circuit of the high-frequency transformer.

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

7. The method for calculating voltage stress inside a cascaded high-frequency transformer according to claim 5, characterized in that: Step S4 includes: Step S41: Based on the number of nodes and branches in the constructed frequency-dependent 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, the frequency-variant parameters of all impedance branches in the frequency-variant distributed parameter equivalent circuit are integrated to form an impedance branch matrix; Step S43: Based on the corresponding dimensions and variables defined by the admittance branches, frequency-varying parameters of all admittance branches in the frequency-varying distributed parameter equivalent circuit are integrated to form an admittance branch matrix; Step S44: defining an association matrix describing the connection relationship between the admittance branch / impedance branch and the node; Step S45: Correlate the correlation matrix, the impedance branch matrix, the admittance branch matrix, and the node voltage vector using Kirchhoff's law to form a solution equation for the network node voltage in the frequency-variable distributed parameter equivalent circuit, thereby completing the construction of a universal parameterized model of the frequency-variable distributed parameter equivalent circuit.

8. The method for calculating voltage stress inside a cascaded high-frequency transformer according to claim 7, characterized in that: Step S5 includes: Step S51: Perform Fourier decomposition on the acquired cascade multi-port voltage waveform to extract the amplitude and phase of the harmonic components of each port voltage; Step S52: determining a target frequency spectrum range based on the extracted parameter effective frequency range pre-stored in the frequency-variable parameter database and the frequency-variable dielectric characteristics set in the insulating material properties; Step S53: Calculate the minimum truncation order K based on the target spectrum range and the preset harmonic truncation accuracy threshold; Step S54: extract the harmonic component spectrum of each port within the Kth order, and output a harmonic data set including frequency, amplitude and phase.

9. The method for calculating voltage stress inside a cascaded high-frequency transformer according to claim 8, characterized in that: Step S6 includes: Step S61: Based on the constructed node network of the frequency-dependent distributed parameter equivalent circuit, determine the node to which the excitation is applied, the grounding node, and the node numbers corresponding to the above nodes; Step S62: Delete the corresponding rows and columns in the coefficient matrix of the node voltage solution equation according to the node number of the excitation node and the node number of the grounding node, extract the coefficient matrix column vector corresponding to the node number of the excitation node and move it to the right side of the equation solution, construct a new equation solution for all response nodes, and implement the application of excitation in the analytical calculation process; Step S63: Solve equations based on all newly constructed 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 voltage stress inside a cascaded high-frequency transformer according to claim 9, characterized in that: Step S7 includes: Based on the superposition principle, the node frequency domain voltage responses under all harmonic frequency components are synthesized in the time domain; According to the control strategy of the cascade topology, the initial phase of each port excitation is calibrated to ensure that the time domain voltage waveform is synchronized with the actual working conditions; After calibration, the time domain voltages of all nodes are reorganized according to the physical positions of the windings to form a voltage stress distribution map inside the high-frequency transformer.

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