Winding potential distribution Gaussian fitting calculation method, system, medium and equipment

Abstract

The invention discloses a high-frequency transformer winding potential distribution Gaussian fitting calculation method, system, medium and equipment, and the method comprises the steps: measuring the complex permeability of a high-frequency transformer magnetic core material and the complex dielectric constant of a packaging epoxy material; a finite element model is built according to the actual structure and size of the high-frequency transformer, magnetic core complex permeability and epoxy complex permittivity are substituted, equivalent electrical parameters of the high-frequency transformer are extracted through simulation analysis, and a broadband equivalent circuit model of the high-frequency transformer is built; heating the high-frequency transformer by using a drying oven, and measuring the impedance amplitude and phase angle frequency response of the high-frequency transformer to obtain the impedance frequency response at the corresponding temperature; and taking the measured impedance frequency response characteristic curve as a target function, multiplying equivalent parameters in the initial broadband equivalent circuit model by a frequency-dependent scaling coefficient formed by a multi-peak Gaussian function, and determining optimal Gaussian function fitting parameters by using an optimization algorithm so as to obtain an accurate broadband frequency-variable equivalent circuit model.

Description

Technical Field

[0001] The present invention relates to the technical field of power electronic transformers, and in particular to a Gaussian fitting calculation method, system, medium and equipment for high-frequency transformer winding potential distribution. Background Art

[0002] In the field of high-frequency transformers and their insulation technology, research has shown that increasing the operating frequency can significantly reduce the size and weight of transformers. However, due to factors such as parasitic capacitance and rapid high-voltage rise times, high-frequency transformer windings are prone to uneven potential distribution, which can cause ringing overvoltage and subject the insulation to more stringent electric field requirements. To address these issues, traditional analysis methods for power-frequency transformers are often extended to the medium-frequency or higher-frequency range, such as using multi-conductor transmission line models or wideband sweep analysis to determine the winding resonant characteristics. Taking power-frequency transformers as an example, some scholars have conducted frequency response tests on the winding impedance and node voltage at different frequencies to diagnose deformation or fault conditions, demonstrating that changes in amplitude and phase angle within a specific frequency band are closely related to the winding state. However, this method operates at a relatively low frequency and cannot directly and accurately predict overvoltage problems in the range of tens of kilohertz to several megahertz, and lacks more sophisticated potential distribution modeling. For medium-frequency transformers, some literature (e.g., Andrea Cremasco et al.) combines multi-conductor transmission line models with finite element methods, focusing on how the fast-rise-time PWM signals generated by wide-bandgap devices trigger resonance and voltage amplification within the windings. This allows for, to a certain extent, prediction of possible ringing overvoltages and resonant peaks in medium-frequency transformer windings. However, existing models typically rely on data such as material permeability and dielectric constant provided by manuals or suppliers to calculate winding inductance and capacitance. Differences in material batches, geometric configurations, and processing techniques often result in discrepancies between the measured L and C parameters and the theoretical values. Once resonance or parasitic coupling occurs during testing, it becomes difficult to maintain stability in the measured values, thereby reducing the accuracy of the prediction of the winding potential distribution. Based on this, this application proposal proposes that after measuring the broadband impedance characteristic curve, the material parameters and winding parasitic characteristics are corrected through multiple iterations of Gaussian fitting, so that the model input parameters are more consistent with the measured data, enabling a more accurate assessment of the potential distribution and ringing overvoltage risk of high-frequency transformers over a wide frequency range.

[0003] In summary, frequency-domain analysis methods for power-frequency transformers primarily address winding deformation diagnosis at low frequencies. They lack the ability to predict waveform ringing and overvoltage in the high-frequency range from tens of kilohertz to several megahertz, and they struggle to precisely characterize the winding potential gradient distribution caused by fast rising edges. While multi-conductor transmission line models for medium-frequency transformers can account for higher frequencies and faster voltage rises, they generally rely on empirical manuals or supplier parameters, ignoring variations in actual L and C characteristics caused by material batches, geometric variations, and processing techniques. Once resonance or coupling effects occur during testing, measured data often struggles to stabilize, leading to a mismatch between model input and actual parameters and an inability to accurately assess the broadband potential distribution and peak ringing overvoltage of the winding. Furthermore, existing technologies do not address the significant variations in material parameters in high-temperature environments or under high dv / dt conditions, lacking sufficient guidance for insulation design, and thus exposing the risk of overfields in interturn or main insulation under high-frequency, high-stress conditions. Existing technologies remain deficient in accurately predicting interturn potential and ringing overvoltage, and lack targeted guidance for insulation design.

[0004] The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the Invention

[0005] The present invention provides a Gaussian fitting calculation method, system, medium and equipment for the potential distribution of high-frequency transformer windings. By measuring the broadband impedance curve and fitting the Gaussian function, the traditional parameter measurement errors are corrected to obtain material and winding parasitic parameters that are more consistent with the actual working conditions. In this way, the potential distribution and ringing overvoltage amplitude of the winding nodes can be accurately predicted within a wider frequency and temperature range, and assistance can be provided for the optimized design and safety assessment of inter-turn insulation and main insulation. It overcomes the problem of insufficient accuracy caused by the existing technology's excessive reliance on theoretical manual data, and avoids parameter distortion caused by resonance or parasitic coupling in measurement, laying a more reliable technical foundation for the design and application of high-frequency transformers, obtaining more accurate potential distribution calculations, and providing stronger support for the reliability of inter-turn and main insulation.

[0006] The present invention discloses a Gaussian fitting calculation method for the potential distribution of a high-frequency transformer winding, comprising:

[0007] Determine the complex magnetic permeability of high-frequency transformer core materials and the complex dielectric constant of encapsulating epoxy materials;

[0008] A finite element model is constructed based on the actual structure and size of the high-frequency transformer, and the complex magnetic permeability and the complex dielectric constant are substituted into the model. The equivalent electrical parameters of the resistance R, inductance L, and capacitance C of the high-frequency transformer are extracted through simulation analysis of the finite element model;

[0009] Construct a broadband equivalent circuit model for a high-frequency transformer, in which the winding is divided into several trapezoidal units, each of which corresponds to one or more turns of the winding. A top-down multi-node network model is constructed based on the equivalent electrical parameters of the resistance, inductance, and capacitance of the trapezoidal units as the broadband equivalent circuit model of the high-frequency transformer. The resistance and inductance in each trapezoidal unit in the broadband equivalent circuit model of the high-frequency transformer are connected in series to form a corresponding impedance branch. Different impedance branches are coupled through mutual inductance. Based on the equivalent circuit model, the corresponding node voltage equation is constructed. That is, each node in the network is modeled based on Kirchhoff's current law, forming a complex frequency domain solution framework for the node potential response.

[0010] Use an oven to heat the high-frequency transformer, measure the amplitude and phase angle frequency response of the high-frequency transformer's impedance, and obtain the impedance characteristic frequency response curve at the corresponding temperature;

[0011] Taking the measured impedance amplitude and phase angle frequency response characteristics of the high-frequency transformer as the objective function, the equivalent electrical parameters of the resistance R, inductance L, and capacitance C in the initial broadband equivalent circuit model are multiplied by the frequency-dependent scaling coefficients constructed by the multi-peak Gaussian function. The multi-peak Gaussian model coefficients are continuously adjusted through an adaptive genetic algorithm to minimize the difference between the theoretical impedance and the measured impedance. This determines the optimal multi-peak Gaussian function fitting parameters and obtains the broadband frequency-varying equivalent circuit model. At the same time, the corresponding node voltage equations are updated.

[0012] The broadband frequency-variable equivalent circuit model is applied to solve the node equations to obtain the potential frequency response of each node. On this basis, the corresponding time domain waveform is synthesized to evaluate the reliability of the main insulation design and the inter-turn insulation design.

[0013] The Gaussian fitting calculation method for the high-frequency transformer winding potential distribution further includes:

[0014] In time domain analysis, the ideal square wave is first expanded into a superposition of several odd harmonics through Fourier series, where the harmonic frequency is an odd multiple of the fundamental frequency, and the harmonic amplitude decays successively according to the 1 / n law. r , using the empirical formula f cutoff =0.35 / t r The highest harmonic frequency of the truncated Fourier series is determined, and an approximate square wave excitation signal is constructed based on this. The amplitude and phase response data of each node at the determined harmonic frequency are used to superimpose all harmonic frequency components and reconstruct the time domain voltage waveform of each node. By analyzing the voltage change rate dv / dt, overshoot amplitude, oscillation duration and its frequency components in the waveform, the resonant response or local insulation stress concentration caused by square wave excitation can be identified.

[0015] In the Gaussian fitting calculation method for the potential distribution of high-frequency transformer windings, a multi-peak Gaussian function is used to form a frequency-dependent scaling coefficient model, which is used to adjust the equivalent resistance R, inductance L, and capacitance C parameters extracted by finite element simulation. The effective j values ​​of resistance R, inductance L, and capacitance C at different frequency points are determined by the product of their initial simulation values ​​and the Gaussian function scaling coefficient at the corresponding frequency, thereby achieving a fine fitting of the frequency response of the equivalent circuit model. The resistance is defined as

[0016]

[0017] Where f represents frequency, ln f represents logarithmic frequency; N is the number of Gaussian peaks, k i is the amplitude coefficient of the i-th Gaussian peak, μ i is the logarithmic frequency of the Gaussian peak, σ i is the width parameter,

[0018] Definition of inductance and capacitance:

[0019]

[0020] Where M is the number of Gaussian peaks in the inductance fitting, p j is the amplitude coefficient of the jth Gaussian peak, ν j is the central logarithmic frequency of the Gaussian peak, δ j is the width parameter,

[0021] C scaled (f) = a0 + b0lnf

[0022] Where a0 and b0 are fitting constant coefficients;

[0023] The measured impedance amplitude and phase frequency response are compared with the impedance of R scaled (f), L scaled (f), C scaled (f) The calculated theoretical impedance is compared, and the difference between the two is used as the optimization objective function. The adaptive genetic algorithm is used to dynamically adjust k i ,μ i ,σ i ,p j ,ν j ,δ j ,a0,b0 coefficients, thereby minimizing the difference between the theoretical impedance and the measured impedance.

[0024] In the Gaussian fitting calculation method for the high-frequency transformer winding potential distribution, the optimization algorithm used for fitting the scaling coefficient of the multi-peak Gaussian function is an adaptive genetic algorithm, which includes the following steps:

[0025] Initialize the population: Randomly generate several sets of candidate Gaussian function parameters within the set parameter boundary range as the initial population;

[0026] Individual selection: A tournament selection method is used to select individuals with smaller fitting errors from the current population to enter the next generation;

[0027] Crossover operation: Generate a new generation of individuals using a simulated binary crossover operator;

[0028] Mutation operation: Use polynomial mutation operators to perturb individual parameters and enhance local search capabilities;

[0029] Adaptive strategy: When the optimal fitness does not improve for several consecutive generations, dynamically increase the mutation rate or randomly restart part of the population to improve the global search capability.

[0030] The adaptive genetic algorithm uses the measured impedance amplitude and phase angle frequency response curve as the objective function, and minimizes the error between the measured impedance and the impedance calculated by the equivalent circuit model as the fitness criterion. It optimizes the parameters of the Gaussian function scaling coefficient and finally obtains the frequency-dependent scaling function parameter set with the minimum fitting error, thereby improving the broadband frequency-varying equivalent circuit model.

[0031] In the Gaussian fitting calculation method for the potential distribution of a high-frequency transformer winding, the complex magnetic permeability of the nanocrystalline material and the complex dielectric constant of the epoxy are obtained by testing an annular nanocrystalline magnetic ring and an epoxy resin sample, respectively. The measured impedance of the ring is:

[0032]

[0033] Where μ′ is the real part of magnetic permeability, μ″ is the imaginary part of magnetic permeability, n is the number of turns, l is the average length of the ring, A m is the effective cross-sectional area of ​​the magnetic ring, and the complex magnetic permeability is calculated as:

[0034]

[0035] The dielectric constant is measured by measuring the admittance of the epoxy resin sample. The complex dielectric constant is related to C p With R p The expression:

[0036] C p Represents the equivalent circuit capacitance, R p represents the electrical loss of epoxy resin, ε′ is the real part of the dielectric constant, ε″ is the imaginary part of the dielectric constant, A e is the area of ​​the silver-plated electrode, and d is the distance between the upper and lower electrodes.

[0037] In the Gaussian fitting calculation method for the potential distribution of the high-frequency transformer winding, in the broadband equivalent circuit model of the high-frequency transformer, the relationship between the admittance branch current and the node voltage is: M·U=0

[0038] in

[0039] The vector U contains three types of voltage nodes, the excitation node d, whose voltage vector is U d , ground node g, whose voltage vector is U g , and the response node r, whose voltage vector is U r , where U d Set to 1, U g Set to 0, which is a known voltage. Excluding the excitation voltage and the ground voltage, the remaining voltage is the voltage to be determined, U rem ,

[0040] Delete all elements in the dth row and dth column and the gth row and gth column of the matrix M to form a new (2n+2-numel(d)-numel(g))-order square matrix N; delete the dth and gth elements in the dth column of M to form a new (2n+2-numel(d)-numel(g))-dimensional column vector N d , and move it to the right side of the formula, so that the voltage U of other nodes except the excitation node and the ground node can be solved rem :

[0041] U rem =-N -1 ·N d

[0042] The broadband impedance of the circuit is obtained by dividing the current of the first winding unit by the excitation voltage. The calculation method of the branch current matrix is:

[0043]

[0044] Calculate the total impedance of the circuit:

[0045] In the Gaussian fitting calculation method for the high-frequency transformer winding potential distribution, obtaining the potential responses of all nodes at different frequencies includes the following steps:

[0046] At each discrete frequency point, the optimized equivalent parameters of resistance, inductance, and capacitance with frequency-dependent scaling factors are substituted into the broadband equivalent circuit model of the high-frequency transformer;

[0047] Based on this model, the frequency domain circuit coefficient matrix M is constructed. The matrix represents the complex relationship between node voltage and branch current in the frequency domain, wherein the matrix elements are derived according to the circuit topology and the frequency domain impedance calculation rules;

[0048] Classify all nodes into excitation nodes, grounding nodes and nodes to be solved, and remove the rows and columns related to known excitation and grounding in the matrix M to form the reduced matrix N and the right terminal vector N d ;

[0049] Solve the linear equation system U rem =-N -1 ·N d , obtain the voltage response of the remaining nodes at this frequency;

[0050] Repeat the above steps to complete the scan of all frequency points within the set frequency range, and finally obtain the amplitude and phase angle response curves of the potential of all winding nodes changing with frequency, which are used to evaluate the electrical behavior characteristics and potential distribution law of the winding structure under high-frequency excitation conditions.

[0051] The present invention also discloses a system for implementing the method, comprising:

[0052] An extraction unit is used to extract the complex magnetic permeability of the high-frequency transformer core and magnetic ring material and the complex dielectric constant of the encapsulating epoxy material;

[0053] A finite element modeling unit is used to construct a finite element model according to the structure and size of the high-frequency transformer, and to extract the equivalent electrical parameters of resistance, resistance, and capacitance based on the finite element model;

[0054] An equivalent circuit modeling unit is used to build a broadband equivalent circuit model of a high-frequency transformer. The winding is divided into a number of trapezoidal units, each of which corresponds to one or more turns of the winding. A top-down multi-node network model is constructed based on the resistance, inductance, and capacitance parameters of the trapezoidal units as the broadband equivalent circuit model of the high-frequency transformer. The resistance and inductance in each trapezoidal unit in the broadband equivalent circuit model of the high-frequency transformer are connected in series to form a corresponding impedance branch, and different impedance branches are coupled through mutual inductance.

[0055] A measuring unit, which uses an oven to heat the high-frequency transformer, measures the amplitude and phase angle frequency response of the impedance of the high-frequency transformer, and obtains a temperature-dependent impedance characteristic curve;

[0056] The Gaussian fitting optimization unit is used to construct a frequency-dependent scaling coefficient model using a multi-peak Gaussian function. The error between the measured impedance frequency response and the theoretical impedance of the equivalent circuit model is used as the objective function. An adaptive genetic algorithm is used to dynamically optimize the amplitude, center frequency, and broadening coefficient of the Gaussian function to minimize the fitting error between the theoretical impedance curve output by the model and the measured data.

[0057] The calculation unit calculates the node potential response of each node, optimizes the obtained parameters and substitutes them into the broadband equivalent circuit model of the high-frequency transformer. By constructing the frequency domain circuit equation and solving the node voltage at all frequency points, the potential amplitude and phase angle response of each node of the transformer winding at different frequencies are obtained.

[0058] The present invention also discloses a computer storage medium, which includes computer instructions. When the computer instructions are executed on a computer, the computer executes the method.

[0059] The present invention also discloses an electronic device, comprising:

[0060] A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein:

[0061] When the processor executes the program, the method described is implemented.

[0062] Compared with the existing technology, the present invention has the following advantages: the present invention combines finite element extraction with multi-peak Gaussian function fitting, overcomes the difference between material models and real transformers, and introduces multi-peak Gaussian functions after finite element extraction to adjust and correct the nonlinear changes of R, L, and C with frequency. In this way, the actual test impedance curve can be better fitted in the high frequency band, compensating for the differences caused by relying solely on the material database or the initial finite element model, so that the frequency response of the winding potential and impedance characteristics after fitting is closer to the measured data. Expanding to temperature-dependent impedance characteristic parameter adjustment, more accurate winding distribution can be obtained for different operating conditions. The impact of temperature changes on the core, insulation material properties and conductive loss is taken into account, and the real and imaginary parts of the impedance at different temperatures are measured and recorded as the target function. By introducing the measured impedance characteristic curve for Gaussian function fitting within multiple temperature ranges, reliable RLC parameter distribution of the transformer under various temperature conditions can be obtained, and thus the simulation results can still be guaranteed to be consistent with the actual operating conditions in complex operating environments such as hot, high voltage, and high current. The broadband equivalent circuit model is integrated with the objective function parameter adjustment to achieve a higher matching degree in the high-frequency band. The measurement data within the broadband range (especially the high-frequency resonant section) is introduced into the multi-peak Gaussian function fitting process, and iterative optimization is performed in conjunction with the broadband equivalent circuit. This not only identifies the main resonant points but also continuously improves simulation accuracy from tens of kilohertz to several megahertz, minimizing the deviation between "measurement and simulation". This further enhances compatibility with temperature-dependent operating conditions and measurement error correction, and can more accurately predict voltage distribution and impedance characteristics in the medium and high frequency ranges, making it more adaptable and practical in actual engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are intended only to illustrate preferred embodiments and are not to be construed as limiting the present invention. It should be understood that the drawings described below are merely examples of the present invention, and that those skilled in the art will be able to derive other drawings from these drawings without inventive effort. Throughout the drawings, identical reference numerals are used to denote identical components.

[0064] In the attached figure:

[0065] Figure 1 It is a schematic diagram of steps of an embodiment of the present invention;

[0066] FIG2(a) and FIG2(b) are schematic diagrams of a magnetic ring sample test according to an embodiment of the present invention, wherein FIG2(a) is a schematic diagram of a magnetic ring wire; FIG2(b) is an equivalent circuit;

[0067] FIG3(a) and FIG3(b) are schematic diagrams of epoxy sample testing according to an embodiment of the present invention, wherein FIG3(a) is a schematic diagram of an epoxy sample; FIG3(b) is an equivalent circuit;

[0068] Figure 4 is a schematic diagram of an epoxy testing device according to one embodiment of the present invention;

[0069] Figure 5 1 is a schematic diagram of a parameter-raising transformer modeling according to an embodiment of the present invention;

[0070] Figure 6 1 is a schematic diagram of an equivalent model of a high-frequency transformer ladder network simplified to a 4:4 turns ratio according to an embodiment of the present invention;

[0071] Figure 7 The impedance characteristic response and R of the optimized parameters of one embodiment of the present invention are scaled (f), L scaled (f), C scaled (f) Schematic diagram of various parameters;

[0072] Figure 8 is a schematic diagram of a calculated winding potential response according to one embodiment of the present invention;

[0073] Figure 9 is a schematic diagram of a synthesized winding square wave waveform according to one embodiment of the present invention;

[0074] Figure 10 This is a comparison chart of simulation values ​​and measured values ​​after 5 iterations of one embodiment of the present invention;

[0075] Figure 11This is a comparison chart of simulation values ​​and measured values ​​after 40 iterations of an embodiment of the present invention.

[0076] The present invention will be further explained below with reference to the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0077] Specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0078] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present invention, but the description is based on the general principles of the specification and is not intended to limit the scope of the invention. The scope of protection of the present invention shall be as defined in the attached claims.

[0079] To facilitate understanding of the embodiments of the present invention, further explanation will be given below using specific embodiments as examples in conjunction with the accompanying drawings, and the accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0080] like Figures 1 to 11 As shown, the Gaussian fitting calculation method for the high-frequency transformer winding potential distribution includes the following steps:

[0081] Determine the complex magnetic permeability of the high-frequency transformer core material and the complex dielectric constant of the encapsulating epoxy material.

[0082] A finite element model was constructed based on the actual structure and dimensions of the high-frequency transformer. The frequency-variable complex permeability of the core and the frequency-variable complex dielectric constant of the epoxy were substituted into the model. The equivalent electrical parameters of the high-frequency transformer's resistance (R), inductance (L), and capacitance (C) were extracted through simulation analysis of the finite element model.

[0083] Build a broadband equivalent circuit model for a high-frequency transformer. The winding is divided into several trapezoidal units, each of which corresponds to one or more turns of the winding. A top-down multi-node network model is constructed based on the equivalent electrical parameters of the trapezoidal units, such as resistance (R), inductance (L), and capacitance (C). In the broadband equivalent circuit model, the resistance and inductance within each trapezoidal unit are connected in series to form a corresponding impedance branch. Different impedance branches are coupled through mutual inductance, and parasitic capacitance factors such as inter-turn capacitance, inter-layer capacitance, and ground capacitance are considered between nodes.

[0084] Use an oven to heat the high-frequency transformer, measure the amplitude and phase angle frequency response of the high-frequency transformer's impedance, and obtain the impedance characteristic frequency response curve at the corresponding temperature;

[0085] Using the measured impedance amplitude and phase-angle frequency response characteristics of high-frequency transformers as the objective function, the resistance (R), inductance (L), and capacitance (C) parameters in the initial broadband equivalent circuit model are multiplied by the frequency-dependent scaling coefficients constructed using a multi-peak Gaussian function. An adaptive genetic algorithm is then used to continuously adjust the multi-peak Gaussian model coefficients to minimize the difference between the theoretical and measured impedances. This approach then determines the optimal multi-peak Gaussian function fitting parameters and obtains an accurate broadband frequency-variable equivalent circuit model. Specifically, multiple Gaussian functions are superimposed to construct a frequency-dependent multi-peak model. The measured impedance data is then compared with the theoretical impedance generated by this multi-peak model. The difference between the two is used as the optimization objective function, and an adaptive genetic algorithm is introduced to dynamically adjust the Gaussian function coefficients, ultimately obtaining a multi-peak Gaussian function expression with high fitting accuracy.

[0086] By applying the broadband frequency-varying equivalent circuit model to solve the node equations, the potential frequency response (amplitude and phase angle) of each node can be further obtained, and the corresponding time domain waveform can be synthesized on this basis to evaluate the reliability of the main insulation design and inter-turn insulation design.

[0087] Finite element extraction is combined with multi-peak Gaussian parameter adjustment: First, the finite element model is used to combine the complex magnetic permeability and complex dielectric constant of the nanocrystalline core and epoxy insulation material to extract the preliminary electrical parameters of the medium-frequency transformer (including self-inductance, mutual inductance, leakage inductance, ground capacitance, and inter-winding capacitance). On this basis, a multi-peak Gaussian model is introduced to further correct the frequency dependence of R, L, and C. By using the measured impedance characteristic curve as the target function for quadratic fitting and optimization, accuracy in the high-frequency range is ensured.

[0088] The tuning idea of ​​frequency-dependent impedance characteristics at different temperatures as the objective function is as follows:

[0089] By measuring the real and imaginary impedance parts of the medium-frequency transformer under different temperature environments and different high-frequency ranges, the impedance curve that changes with frequency is obtained; this measured impedance data is compared with the calculation results of the broadband equivalent circuit model, and the R, L, and C parameters are adjusted and corrected with the goal of minimizing the error between the two.

[0090] Energy method combined with material parameters to extract equivalent resistance, inductance, and capacitance:

[0091] The quasi-static magnetic field (MQS) equation is used to solve the field energy when a single winding is energized or multiple windings are energized simultaneously using energy integration, and the self-inductance, mutual inductance, and corresponding equivalent resistance are extracted. The electrostatic field (ES) equation is used to calculate the electric field energy between the windings and to the ground under different excitation and grounding conditions of multiple windings, and the capacitance to ground and mutual capacitance are extracted. Combined with the complex magnetic permeability and complex dielectric constant of the material, the RLC value of the transformer over a wider frequency range is comprehensively obtained.

[0092] Broadband equivalent circuit model and node potential-impedance frequency response calculation:

[0093] The extracted R, L, and C parameters are divided into trapezoidal units to construct a multi-node network, generating equivalent circuits for each turn of the high and low voltage windings. By solving Kirchhoff's current law (KCL) or matrix-form node equations, the voltage distribution at any node under the scanning frequency and the transformer port impedance frequency response are obtained. This method not only derives the overall impedance characteristics but also accurately analyzes the potential distribution at various locations in the winding, providing a reference for high-frequency insulation design and loss assessment.

[0094] Use the Fourier transform of the potentials at different nodes to synthesize a square wave:

[0095] In time-domain simulation, the optimized broadband equivalent circuit model is treated as a multi-point coupled system, allowing the interception of several odd harmonics and their superposition using the Fourier series method to generate square-wave excitation. The time-domain voltage response of each node is output, analyzing transient phenomena such as voltage overshoot and oscillation that may occur under square-wave excitation, providing a basis for square-wave drive and resonance risk control in actual operating conditions. Comprehensively covering everything from material property measurements to the winding potential and impedance response under final square-wave excitation conditions, this approach more accurately characterizes the actual operating state of medium-frequency transformers and provides a comprehensive and effective technical approach for optimizing related equipment.

[0096] The Gaussian fitting calculation method for the high-frequency transformer winding potential distribution further includes:

[0097] In time domain analysis, the ideal square wave is first expanded into a superposition of several odd harmonics through Fourier series, where the harmonic frequency is an odd multiple of the fundamental frequency and the harmonic amplitude decays successively according to the 1 / n law. According to engineering experience, the rise time t of the square wave can be used to calculate the r , using the empirical formula fcutoff =0.35 / t r The highest harmonic frequency of the truncated Fourier series is determined, and an approximate square wave excitation signal is constructed based on this frequency. Subsequently, the amplitude and phase response data of each node at the determined harmonic frequency are superimposed on all harmonic frequency components to reconstruct the time-domain voltage waveform at each node. By analyzing the voltage change rate (dv / dt), overshoot amplitude, oscillation duration, and frequency content in the waveform, resonant responses or localized insulation stress concentrations caused by square wave excitation can be identified. Overshoot is defined as the ratio of the difference between the highest transient voltage value and the steady-state voltage amplitude within the waveform cycle to the steady-state voltage amplitude, which quantifies the voltage stress caused by transient voltage on the winding insulation. Furthermore, by analyzing the differences in voltage waveforms at different node locations, the distribution of the instantaneous potential difference between turns within the winding can be further clarified, providing a reliable theoretical basis for the selection and optimization of winding structure, electrical spacing, and insulation materials. This effectively reduces the risk of insulation failure caused by square wave drive and improves the insulation performance and operational reliability of the equipment.

[0098] The multi-peak Gaussian function constitutes a frequency-dependent scaling coefficient model, which is used to adjust the equivalent resistance (R), inductance (L), and capacitance (C) parameters extracted by finite element simulation. Specifically, the effective values ​​of resistance (R), inductance (L), and capacitance (C) at different frequency points are determined by the product of their initial simulation values ​​and the Gaussian function scaling coefficient at the corresponding frequency, thereby achieving a precise fit of the frequency response of the equivalent circuit model. Resistance is defined as:

[0099] Where f represents frequency, ln f represents logarithmic frequency; N is the number of Gaussian peaks, k i is the amplitude coefficient of the i-th Gaussian peak, μ i is the logarithmic frequency of the Gaussian peak, σ i is the width parameter,

[0100] Definition of inductance and capacitance:

[0101]

[0102] Where M is the number of Gaussian peaks in the inductance fitting, p j is the amplitude coefficient of the jth Gaussian peak, ν j is the central logarithmic frequency of the Gaussian peak, δ j is the width parameter.

[0103] C scaled (f)=a0+b0lnf.

[0104] Where a0 and b0 are fitting constant coefficients;

[0105] The measured impedance amplitude and phase frequency response are compared with the impedance of R scaled (f), L scaled (f), C scaled (f) The calculated theoretical impedance is compared, and the difference between the two is used as the optimization objective function. The adaptive genetic algorithm is used to dynamically adjust k i ,μ i ,σ i ,p j ,ν j ,δ j ,a0,b0 coefficients, thereby minimizing the difference between the theoretical impedance and the measured impedance.

[0106] The optimization algorithm used in the method for fitting the scaling coefficients of the multi-peak Gaussian function is an adaptive genetic algorithm, which includes the following steps:

[0107] Initialize the population: Randomly generate several sets of candidate Gaussian function parameters within the set parameter boundary range as the initial population;

[0108] Individual selection: Using the tournament selection method, individuals with smaller fitting errors are selected from the current population to enter the next generation;

[0109] Crossover operation: Generate a new generation of individuals using the Simulated Binary Crossover (SBX) operator;

[0110] Mutation operation: Use the polynomial mutation operator to perturb individual parameters and enhance local search capabilities;

[0111] Adaptive strategy: When the optimal fitness does not improve for several consecutive generations, dynamically increase the mutation rate or randomly restart part of the population to improve the global search capability.

[0112] The adaptive genetic algorithm uses the measured impedance amplitude and phase angle frequency response curve as the objective function, and minimizes the error between the measured impedance and the impedance calculated by the equivalent circuit model as the fitness criterion. It optimizes the parameters of the Gaussian function scaling coefficient, ultimately obtaining a set of frequency-dependent scaling function parameters with the smallest fitting error, thereby improving the broadband frequency-variable equivalent circuit model. In a preferred embodiment of the Gaussian fitting calculation method for the potential distribution of a high-frequency transformer winding, the complex magnetic permeability of the nanocrystalline material and the complex dielectric constant of the epoxy are obtained by testing an annular nanocrystalline magnetic ring and an epoxy resin sample, respectively. The measured impedance of the annular ring is:

[0113]

[0114] Where μ′ is the real part of magnetic permeability, μ″ is the imaginary part of magnetic permeability, n is the number of turns, l is the average length of the ring, A m is the effective cross-sectional area of ​​the magnetic ring, and the complex magnetic permeability is calculated as:

[0115]

[0116] The dielectric constant is measured by measuring the admittance of the epoxy resin sample. The complex dielectric constant is related to C p With R p The expression:

[0117] C p Represents the equivalent circuit capacitance, R p represents the electrical loss of epoxy resin, ε′ is the real part of the dielectric constant, ε″ is the imaginary part of the dielectric constant, A e is the area of ​​the silver-plated electrode, and d is the distance between the upper and lower electrodes.

[0118] In a preferred embodiment of the Gaussian fitting calculation method for the high-frequency transformer winding potential distribution, in the broadband equivalent circuit model of the high-frequency transformer, the relationship between the admittance branch current and the node voltage is: M·U=0

[0119] in

[0120] The vector U contains three types of voltage nodes, the excitation node d, whose voltage vector is U d , ground node g, whose voltage vector is U g , and the response node r, whose voltage vector is U r , where U d Set to 1, U g Set to 0, which is a known voltage. Excluding the excitation voltage and the ground voltage, the remaining voltage is the voltage to be determined, U rem ,

[0121] Delete all elements in the dth row and dth column and the gth row and gth column of the matrix M to form a new (2n+2-numel(d)-numel(g))-order square matrix N; delete the dth and gth elements in the dth column of M to form a new (2n+2-numel(d)-numel(g))-dimensional column vector N d , and move it to the right side of the formula, so that the voltage U of other nodes except the excitation node and the ground node can be solved rem :

[0122] U rem =-N -1 ·N d

[0123] The broadband impedance of the circuit is obtained by dividing the current of the first winding unit by the excitation voltage. The calculation method of the branch current matrix is:

[0124]

[0125] Calculate the total impedance of the circuit:

[0126] In the Gaussian fitting calculation method for the high-frequency transformer winding potential distribution, obtaining the potential responses of all nodes at different frequencies includes the following steps:

[0127] At each discrete frequency point, the optimized equivalent resistance, inductance, and capacitance parameters with frequency-dependent scaling factors are substituted into the broadband equivalent circuit model of the high-frequency transformer;

[0128] Construct a frequency domain circuit coefficient matrix based on this model The matrix represents the complex relationship between node voltage and branch current in the frequency domain, wherein the matrix elements are derived according to the circuit topology and the frequency domain impedance calculation rules;

[0129] Classify all nodes into excitation nodes, grounding nodes and nodes to be solved, and remove the rows and columns related to known excitation and grounding in the matrix M to form the reduced matrix N and the right terminal vector N d ;

[0130] Solve the linear equation system U rem =-N -1 ·N d , obtain the voltage response of the remaining nodes at this frequency;

[0131] Repeat the above steps to complete the scan of all frequency points within the set frequency range, and finally obtain the amplitude and phase angle response curves of the potential of all winding nodes changing with frequency, which are used to evaluate the electrical behavior characteristics and potential distribution law of the winding structure under high-frequency excitation conditions.

[0132] The system includes,

[0133] An extraction unit is used to extract the complex magnetic permeability of the high-frequency transformer core and magnetic ring material and the complex dielectric constant of the encapsulating epoxy material;

[0134] A finite element modeling unit is used to construct a finite element model according to the structure and size of the high-frequency transformer, and to extract equivalent electrical parameters of the high-frequency transformer such as equivalent resistance, resistance, and capacitance based on the finite element model;

[0135] An equivalent circuit modeling unit is used to build a broadband equivalent circuit model of a high-frequency transformer. The winding is divided into a number of trapezoidal units, each of which corresponds to one or more turns of the winding. A top-down multi-node network model is constructed based on the resistance, inductance, and capacitance parameters of the trapezoidal units as the broadband equivalent circuit model of the high-frequency transformer. The resistance and inductance in each trapezoidal unit in the broadband equivalent circuit model of the high-frequency transformer are connected in series to form a corresponding impedance branch, and different impedance branches are coupled through mutual inductance;

[0136] A measuring unit, which uses an oven to heat the high-frequency transformer, measures the amplitude and phase angle frequency response of the impedance of the high-frequency transformer, and obtains a temperature-dependent impedance characteristic curve;

[0137] The Gaussian fitting optimization unit is used to construct a frequency-dependent scaling coefficient model using a multi-peak Gaussian function. The error between the measured impedance frequency response and the theoretical impedance of the equivalent circuit model is used as the objective function. An adaptive genetic algorithm is used to dynamically optimize the amplitude, center frequency, and broadening coefficient of the Gaussian function to minimize the fitting error between the theoretical impedance curve output by the model and the measured data.

[0138] The calculation unit calculates the node potential response of each node, optimizes the obtained parameters and substitutes them into the broadband equivalent circuit model of the high-frequency transformer. By constructing the frequency domain circuit equation and solving the node voltage at all frequency points, the potential amplitude and phase angle response of each node of the transformer winding at different frequencies are obtained.

[0139] By measuring the material's frequency-dependent characteristics and the impedance curves of high-frequency transformers at different temperatures, combined with a Gaussian fitting algorithm, we can accurately predict the node voltage waveforms, ringing overvoltages, and insulation risks caused by uneven potential distribution during rapid switching transients in high-frequency transformers. This method can assist designers in assessing the safety margin of interturn insulation under high-frequency, rapid switching conditions and also provides valuable insights into main insulation design, thereby improving the overall reliability and operating efficiency of high-frequency transformers.

[0140] In one embodiment, Figure 1 As shown, the method includes: material property measurement, finite element modeling and electrical parameter extraction, broadband trapezoidal equivalent circuit modeling and frequency response calculation, transformer impedance characteristic extraction, adaptive genetic algorithm based on multi-peak Gaussian function, node potential frequency response calculation and square wave synthesis.

[0141] Extraction of complex permeability of magnetic ring and complex dielectric constant of epoxy:

[0142] By testing the annular nanocrystalline magnetic ring and epoxy resin samples, the complex magnetic permeability of the nanocrystalline material and the complex dielectric constant of the epoxy can be obtained respectively.

[0143] The equivalent circuit of the toroidal winding inductor is represented by R s -L sThe series circuit is shown in Figure 2(a) and Figure 2(b).

[0144] Figure 2(a) and Figure 2(b) are schematic diagrams of a magnetic ring sample measurement according to an embodiment of the present invention, wherein Figure 2(a) is a schematic diagram of a magnetic ring wire; Figure 2(b) is an equivalent circuit. By measuring the series impedance of the sample at different frequencies, the real part R s and inductive reactance ωL s , and then convert the real and imaginary parts of the complex magnetic permeability.

[0145] The impedance analyzer measures the total complex impedance Z = R s +jωL s ;

[0146] For each frequency point, extract the real part R s and the imaginary part X s =ωL s .

[0147] Using the magnetic circuit model, the corresponding relationship between inductive reactance and core structure size is substituted into:

[0148]

[0149] in:

[0150] μ r ′: real part of complex magnetic permeability;

[0151] μ r ″: imaginary part of complex permeability (reflecting loss);

[0152] l m : average length of magnetic circuit;

[0153] A e : effective core cross-sectional area;

[0154] N: number of turns of the excitation coil;

[0155] μ0: magnetic permeability of vacuum.

[0156] L s Indicates the inductance generated by the magnetic flux passing through the core plus the leakage flux, R s Represents the losses in the core and windings. The equivalent series inductance and resistance of the magnetic toroid were measured using a Wenke 6500B impedance analyzer. During the test, the impedance analyzer was calibrated using an air-core inductor with the same number of turns. To ensure stable test results, four turns of thin wire were wound around the magnetic toroid at a distance to reduce inter-turn capacitance.

[0157] The measured impedance of the measured ring can be expressed as follows:

[0158]

[0159] Where μ′ is the real part of magnetic permeability, μ″ is the imaginary part of magnetic permeability. n is the number of turns, l is the average length of the ring surface, A m is the effective cross-sectional area of ​​the magnetic ring. From (1.1), the complex magnetic permeability can be calculated as:

[0160]

[0161] The dielectric constant is measured by measuring the admittance of the epoxy resin sample. The measurement adopts the parallel plate capacitor model, as shown in Figure 3(a) and Figure 3(b). The equivalent circuit uses capacitor C p Indicates the dielectric properties of epoxy resin, with R p Represents the electrical loss of epoxy resin. Figure 3(a) Schematic diagram of epoxy sample, where the disc-shaped electrode clamps the insulating sample (such as epoxy resin original sheet) to form a dielectric capacitor structure; Figure 3(b) is its parallel equivalent circuit model in the frequency domain, with the capacitor C p and the resistor R in parallel with it p express. Figure 4 Schematic diagram of an epoxy testing device according to one embodiment. An epoxy resin sheet sample with a thickness of d and an area of ​​A is prepared;

[0162] Conductive electrode sheets (such as metal foil or silver spraying) are attached to the upper and lower sides to form a standard parallel plate capacitor structure.

[0163] The sample is sandwiched between the electrodes of a dielectric spectrometer (e.g. Novocontrol Concept80);

[0164] Sweep frequency (e.g. 10Hz–10MHz) and measure complex impedance

[0165] The real and imaginary parts of the dielectric constant are obtained from the measured impedance Z(ω):

[0166]

[0167] in:

[0168] ε′: energy storage capacity, corresponding to capacitance;

[0169] ε″: loss capacity, indicating polarization hysteresis;

[0170] ε0: vacuum dielectric constant;

[0171] Loss tangent.

[0172] like Figure 4 As shown in Figure 1, the test was performed using the Concept80 broadband dielectric spectrum analyzer from Novocontrol, Germany. The admittance is expressed as formula (1.3).

[0173]

[0174] Where ε′ is the real part of the dielectric constant, ε″ is the imaginary part of the dielectric constant, and A e is the area of ​​the silver-plated electrode, and d is the distance between the upper and lower electrodes. From (1.3), the complex dielectric constant can be calculated with respect to C p With R p The expression:

[0175]

[0176] Finite element model construction and transformer equivalent electrical parameter extraction:

[0177] At this stage, we first need to build a high-frequency transformer according to its actual structure and size. Figure 5 The geometric model shown. Figure 5 The diagram shows the core winding structure layout and core window diagram of the tap numbering of an example physical high-frequency transformer. It is the core structure diagram for equivalent circuit modeling, node potential calculation and simulation verification.

[0178] For example, the dimensions of the core, the number and arrangement of winding turns, the distribution of insulation materials, and any components that may affect the distribution of the electromagnetic field must be clearly defined.

[0179] Subsequently, in terms of material properties, corresponding physical parameters are assigned to the magnetic core and insulating materials: the magnetic core part usually uses the complex magnetic permeability (including real and imaginary parts) based on experimental measurements to accurately describe the magnetic properties of the iron core at high frequencies; the winding and insulation parts are based on measured complex dielectric constant (also including real and imaginary parts) and conductivity and other information.

[0180] Once the model is built, it is necessary to solve the quasi-static magnetic field (MQS) and electrostatic field (ES) equations. MQS field solutions are typically used to extract the magnetic field distribution, induced current distribution, and power loss in the windings and core; ES field solutions are primarily used to extract the potential distribution and capacitive coupling relationships in the transformer windings and the surrounding dielectric.

[0181] The quasi-static magnetic field (MQS) model is used to determine the magnetic field distribution within the transformer windings and core. After obtaining the magnetic flux density B and magnetic field strength H, the energy method is used to calculate the self-inductance and mutual inductance of each winding, as well as the corresponding equivalent resistance.

[0182] When current I is applied to only one winding, the energy can be integrated using formula (1.5) to obtain the self-inductance and self-resistance of the winding at that frequency:

[0183] I.I* (R eff +jωL eff )=∫ V jωB·H * dV.(1.5)

[0184] Where B = ▽ × A is the magnetic vector potential, the asterisk represents the complex conjugate, R eff With L eff Corresponding to equivalent resistance and inductance respectively.

[0185] When current is applied to the i-th and j-th windings simultaneously, the off-diagonal terms (mutual inductance and mutual resistance) can be obtained using a similar energy integration method, such as:

[0186]

[0187] In the above formula, the subscript i+j represents the field component when the two windings are energized at the same time, and i and j represent the field components when they are energized separately.

[0188] Under the electrostatic field (ES) model, solve

[0189] -▽·(ε▽V)=0 (1.7)

[0190] The potential distribution V and electric field strength E=-▽V between windings and between windings and ground are obtained from this.

[0191] When voltage U is applied only to the i-th winding and the other windings are grounded, the diagonal term (capacitance to ground) C can be obtained by integrating the electric field energy. i :

[0192]

[0193] In the magnetic ring test, the outer diameter and inner diameter are selected. When voltage is applied to the two windings at the same time, the non-diagonal term (mutual capacitance) C can be obtained by comparing the electric field energy difference when applied separately and simultaneously. ij .

[0194]

[0195] Method for building broadband equivalent circuit model of high-frequency transformer

[0196] The purpose of establishing a broadband equivalent circuit model for a high-frequency transformer is to accurately characterize the voltage and current distribution characteristics of the transformer under high-frequency excitation. To this end, the actual winding must first be divided into several trapezoidal units, each corresponding to one or more turns of the winding. Based on the unit's resistance, inductance, and capacitance (R, L, C) parameters, a top-down multi-node network model is constructed. Because the wavelength of voltage harmonics is much larger than the size of a single-turn winding in the high-frequency range considered (especially the tens of kilohertz to several megahertz common in medium-frequency transformers), the electric field and current distribution in each turn can be assumed to be uniform, making it a feasible and effective approximation to consider a single turn as a basic network unit. In addition to self-inductance and mutual inductance, distributed capacitance and coupling capacitance must also be considered between nodes to fully describe high-frequency parasitic effects. Figure 6 The present invention shows an equivalent model of a high-frequency transformer ladder network simplified to a 4:4 turns ratio (mutual inductance and mutual resistance are omitted in the figure). The model divides the winding into 4:4 electrical units, each unit consisting of a series inductor and a resistor to form an impedance branch, and the branches are interconnected through the winding inter-turn capacitance in the blue area and the node-to-ground capacitance and the main winding inter-layer capacitance in the red area. The insulation coupling capacitance forms a complete multi-node coupling network. The broadband equivalent circuit model established by the present invention belongs to a frequency-dependent RLC network modeling method based on node segmentation. The model uses finite element analysis to extract the complex permeability of the core and the complex dielectric constant of epoxy, and constructs a frequency domain coupling network, taking into account the parasitic coupling effects between turns, between layers, on both sides of the main insulation, and between the winding and the ground, so as to accurately characterize the potential response and resonant behavior inside the winding under high-frequency excitation.

[0197] The impedance branch is defined as the branch consisting of the series connection of resistance and inductance in each ladder unit in the ladder equivalent network. Different impedance branches are coupled by mutual inductance. Obviously, the ladder network with n units in both high and low voltage windings has a total of 2n impedance branches. The following 2n-order square matrix M can be defined: IMB Describe it:

[0198]

[0199] The definition of admittance branch is the branch composed of all distributed capacitances at the same node in the ladder equivalent network. The admittance branch connects different network nodes. There are obviously 2n+2 nodes in the ladder network, so the number of admittance branches is also 2n+2. The definition of 2n+2 order square matrix M is as follows ADB Describe all admittance branches of the network:

[0200]

[0201] Define column vector U as the voltage of all nodes to be calculated in the trapezoidal equivalent network. It is consistent with the number of nodes, which is 2n+2 in total. Its form is:

[0202] U=[U1,…,U s ,…,U 2(n+1) ] T .(1.12)

[0203] Define the 2n-dimensional column vector I respectively IMB and 2n+2 dimensional column vector I ADB is the impedance branch current and admittance branch current to be determined in the ladder equivalent network. Its form is:

[0204]

[0205] Where I Ii represents the current in the i-th impedance branch, I Aj Represents the current in the jth admittance branch.

[0206] According to Kirchhoff's current law, the relationship between impedance current and admittance current can be derived:

[0207]

[0208] Based on the relationship between impedance current and admittance current, the correlation matrix Γ is defined as:

[0209]

[0210] Using Γ to express the relationship between the impedance branch current and the admittance branch current in (1.14), we have:

[0211] I ADB =ΓI IMB (1.16)

[0212] From the impedance branch voltage and current relationship, we can get:

[0213]

[0214] Combining (1.10), (1.16), and (1.17), we can obtain the relationship between the impedance branch current and the node voltage:

[0215] M IMB I IMB =-Γ T U(1.18)

[0216] From the voltage-current relationship of the admittance branch, we can get:

[0217]

[0218] Combining (1.11), (1.16), and (1.19), we can obtain the relationship between the admittance branch current and the node voltage:

[0219] M ADB U=I ADB (1.20)

[0220] Simplifying (1.12), (1.18), and (1.20), we can obtain:

[0221] M·U=0(1.21)

[0222] in

[0223] The vector U contains three types of voltage nodes, the excitation node d, whose voltage vector is U d , ground node g, whose voltage vector is U g , and the response node r, whose voltage vector is U r . Among them U d Set to 1, U g Set to 0, which is a known voltage. Excluding the excitation voltage and the ground voltage, the remaining voltage is the voltage to be determined, U rem (Including U r ).

[0224] Delete all elements in the dth row and dth column and the gth row and gth column of the matrix M to form a new (2n+2-numel(d)-numel(g))-order square matrix N; delete the dth and gth elements in the dth column of M to form a new (2n+2-numel(d)-numel(g))-dimensional column vector N d , and move it to the right side of the formula, so that the voltage U of other nodes except the excitation node and the ground node can be solved rem :

[0225] U rem =-N -1 ·N d (1.22)

[0226] The broadband impedance of the circuit is obtained by dividing the current of the first winding unit by the excitation voltage. The calculation method of the branch current matrix is ​​obtained by transforming formula (1.18):

[0227]

[0228] Calculate the total impedance of the circuit from (1.24):

[0229]

[0230] Extract temperature-dependent impedance characteristic curve

[0231] The medium frequency transformer is heated in an oven, and the real and imaginary impedance of the medium frequency transformer in the medium and high frequency bands are measured using a Wenke 6500B impedance analyzer, that is, the impedance amplitude and phase angle frequency response are measured.

[0232] Multi-peak Gaussian function modeling

[0233] Finite element modeling based solely on the material's inherent properties often results in significant differences from the actual transformer. Therefore, this method proposes further parameter adjustment and fitting. Based on the finite element parameter extraction, the impedance response of the medium-frequency transformer is calculated using a broadband equivalent circuit model. In view of the nonlinear variation characteristics of different components (R, L, C) at high frequencies, multiple Gaussian functions are used to construct a frequency-dependent multi-peak model. Let f represent frequency and lnf represent logarithmic frequency; for a certain parameter (such as resistance), it can be defined as (1.25):

[0234]

[0235] Where N is the number of Gaussian peaks, k i is the amplitude coefficient of the i-th Gaussian peak, μ i is the center position of the Gaussian peak (logarithmic frequency), σ i is the width parameter. Similarly, for inductance and capacitance, we can define:

[0236]

[0237] C scaled (f) = a0 + b0 lnf. (1.27)

[0238] The above forms can be flexibly expanded or combined to form multi-peak or linear superposition functions to more accurately describe the relationship between R, L, and C as they change with frequency;

[0239] The measured actual impedance (amplitude and phase) of the intermediate frequency transformer is compared with the impedance of R scaled (f), L scaled (f), C scaled (f) The calculated theoretical impedance is compared, and the difference between the two is used as the optimization objective function;

[0240] Adaptive genetic algorithm is used to dynamically adjust k i ,μ i ,σ i ,p j ,ν j ,δ j ,a0,b0 and other coefficients, so as to minimize the difference between the theoretical impedance and the measured impedance. The adaptive genetic algorithm includes the following steps:

[0241] Initialize the population: randomly generate multiple candidate solutions within the parameter boundary;

[0242] Selection: Use tournament selection method to select individuals with higher fitness (smaller error);

[0243] Crossover: Generate new individuals using simulated binary crossover (SBX);

[0244] Mutation: fine-tune parameters locally through operators such as polynomial mutation;

[0245] Adaptive strategy: If the optimal fitness does not improve over several consecutive generations, increase the mutation rate or partially restart the population, taking into account both global and local searches.

[0246] Calculate the node potential response of each node

[0247] After adjusting the RLC parameters of the medium-frequency transformer using a multi-peak Gaussian function and an adaptive optimization algorithm, the optimized parameters can be substituted into a broadband equivalent circuit model. By solving the node equations at each frequency point, the potential distribution of all nodes at the corresponding frequency can be obtained. Specifically, at each discrete frequency point, the optimized R, L, and C parameters are first substituted into the established broadband equivalent circuit equations. Then, Kirchhoff's law (KCL) or a matrix-based node analysis method is applied to solve for the voltage response of each node. Finally, after scanning the entire frequency range, a response curve of the potential of each node as it changes with frequency can be obtained, which can be used to evaluate the electrical characteristics of different parts of the transformer under high-frequency excitation conditions.

[0248] FFT synthesis of square waves

[0249] In practical applications or simulation analysis, in order to verify the transient response of the medium-frequency transformer under square wave excitation, the Fourier series can be used to synthesize the square wave in frequency bands.

[0250] Through Fourier analysis, we can see that an ideal square wave can be regarded as a DC component plus the superposition of an infinite number of sine waves, which only contain odd harmonics. Its general form can be written as shown in (1.28):

[0251]

[0252] Among them, U square represents the amplitude of the square wave, f base is the fundamental angular frequency.

[0253]

[0254] Among them, U square represents the amplitude of the square wave, f base is the fundamental angular frequency, |U r | represents the amplitude response of the frequency point, ∠U r Indicates the phase angle response at this frequency point.

[0255] Due to the high frequency attenuation of the actual system and the limitation of computing resources, only a limited number of odd harmonics can be used to approximately synthesize square wave excitation. According to the required simulation or experimental frequency band, k intercepts up to a certain highest harmonic n max Finally, the square wave can be represented as a finite superposition of odd harmonic terms.

[0256] Figure 8 The frequency response characteristic curves for a node in a high-frequency transformer under broadband excitation are shown. The red curve represents the voltage amplitude response, and the blue curve represents the phase angle response. As can be seen, at approximately 3.05 MHz, the voltage at this node experiences a significant amplitude peak (6.85 times the excitation voltage), accompanied by a rapid phase angle jump, indicating strong local resonance. This analysis can be used to identify possible ringing overvoltage points, assisting in potential distribution analysis and insulation risk assessment.

[0257] In the time domain simulation, the time series of each odd harmonic component is first generated in sequence according to the number of intercepted harmonics; then these harmonic components are superimposed at the same time step to obtain an approximate square wave waveform. Figure 9 Schematic diagram of the synthesized winding square wave waveform. Figure 9 The figure shows the time domain voltage response waveform of the winding of a certain node synthesized under square wave excitation in one embodiment. It can be observed that at each rising and falling edge, the voltage has a significant overshoot phenomenon, with an amplitude of about twice the steady-state value, followed by high-frequency attenuation ringing. This phenomenon indicates that the node is affected by the high-frequency parasitic coupling channel inside the winding, and there is a certain distributed parameter resonance effect, which may cause the potential difference between turns to increase sharply in an instant. If the time axis is further enlarged, detailed features such as the ringing frequency, decay time and oscillation period can be observed more clearly. This waveform can be used to evaluate the transient voltage stress and breakdown risk faced by the insulation system during operation.

[0258] Figure 10 and Figure 11 Comparing the differences between the simulation values ​​and the measured values ​​after 5 iterations and 40 iterations, it can be clearly seen that after 40 iterations, the simulation values ​​match the measured values ​​better in the high frequency band, which shows the effect of the continuous simulation accuracy of this model.

[0259] For the present invention, it should be noted that:

[0260] The complex permeability of the high-frequency transformer core material and the complex dielectric constant of the encapsulating epoxy material are measured. By testing the annular nanocrystalline magnetic ring and epoxy resin samples, the complex permeability and complex dielectric constant of the materials can be obtained, respectively. This is crucial for accurately simulating the electromagnetic behavior of high-frequency transformers at different frequencies. This provides accurate material property parameters for subsequent finite element modeling.

[0261] A finite element model was constructed based on the actual structure and dimensions of the high-frequency transformer. Finite element analysis (FEA) was used to extract electrical parameters such as equivalent resistance (R), inductance (L), and capacitance (C), combining the extracted frequency-dependent complex permeability of the core and the frequency-dependent complex dielectric constant of the epoxy. This ensures that the model accurately reflects the physical characteristics of the actual device.

[0262] A broadband equivalent circuit model of a high-frequency transformer is constructed, dividing the winding into multiple trapezoidal units. A complex multi-node network model is constructed based on the resistance, inductance, and capacitance parameters of each unit. This enables accurate characterization of the potential distribution and resonance phenomena within the winding.

[0263] The high-frequency transformer is heated in an oven, and its impedance amplitude and phase-angle frequency response are measured. The impedance characteristic curve of the high-frequency transformer is obtained at the corresponding temperature, which serves as the basis for optimizing the equivalent circuit model. This is important for verifying the model's accuracy and temperature dependence.

[0264] A multi-peak Gaussian function is used for fitting and an adaptive genetic algorithm is used for optimization. A frequency-dependent scaling coefficient model is constructed using the multi-peak Gaussian function. By adjusting the parameters in this model, the theoretically calculated impedance is as close as possible to the measured data. An adaptive genetic algorithm is used for parameter optimization, aiming to minimize the difference between the two. The key goal is to improve the model's fitting accuracy in the high-frequency range, thereby enhancing predictive capabilities.

[0265] By solving node equations and calculating the potential frequency response, the optimized broadband equivalent circuit model is used to determine the voltage response at each node, which is then synthesized into a time-domain waveform. This step not only assesses the overall impedance characteristics but also provides a detailed analysis of the internal distribution of the winding. This is particularly important for identifying potential insulation risk points, providing a basis for design optimization.

[0266] The winding is divided into several trapezoidal units, each of which corresponds to one or several turns of the winding. A top-down multi-node network model is constructed based on the equivalent electrical parameters of the trapezoidal units, such as resistance, inductance, and capacitance, as a broadband equivalent circuit model of the high-frequency transformer. In the broadband equivalent circuit model of the high-frequency transformer, an impedance branch is composed of resistance and inductance connected in series in each trapezoidal unit. Different impedance branches are coupled through mutual inductance, and parasitic capacitance factors such as inter-turn capacitance, inter-layer capacitance, and ground capacitance are considered between nodes. This accurately simulates the complex electric field distribution and interaction inside the winding, especially the capture of parasitic effects in the high-frequency range, laying the foundation for the simulation and analysis of the present invention.

[0267] An adaptive genetic algorithm dynamically adjusts coefficients to minimize the difference between theoretical and measured impedance. This algorithm improves model fitting accuracy, ensuring that theoretical calculations accurately reflect actual conditions, particularly at high frequencies.

[0268] Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments and application fields. The above-mentioned specific embodiments are merely illustrative and instructive, and are not restrictive. A person skilled in the art, guided by this specification and without departing from the scope of protection of the claims of the present invention, may also devise various forms, all of which fall within the scope of protection of the present invention.

Claims

1. A Gaussian fitting calculation method for high-frequency transformer winding potential distribution, characterized in that: The steps include: Determine the complex magnetic permeability of high-frequency transformer core materials and the complex dielectric constant of encapsulating epoxy materials; A finite element model is constructed based on the actual structure and size of the high-frequency transformer, and the complex magnetic permeability and the complex dielectric constant are substituted into the model. The equivalent electrical parameters of the resistance R, inductance L, and capacitance C of the high-frequency transformer are extracted through simulation analysis of the finite element model; Construct a broadband equivalent circuit model for a high-frequency transformer, in which the winding is divided into several trapezoidal units, each of which corresponds to one or more turns of the winding. A top-down multi-node network model is constructed based on the equivalent electrical parameters of the resistance, inductance, and capacitance of the trapezoidal units as the broadband equivalent circuit model of the high-frequency transformer. The resistance and inductance in each trapezoidal unit in the broadband equivalent circuit model of the high-frequency transformer are connected in series to form a corresponding impedance branch. Different impedance branches are coupled through mutual inductance. Based on the equivalent circuit model, the corresponding node voltage equation is constructed. That is, each node in the network is modeled based on Kirchhoff's current law, forming a complex frequency domain solution framework for the node potential response. Use an oven to heat the high-frequency transformer, measure the amplitude and phase angle frequency response of the high-frequency transformer's impedance, and obtain the impedance characteristic frequency response curve at the corresponding temperature; Taking the measured impedance amplitude and phase angle frequency response characteristics of the high-frequency transformer as the objective function, the equivalent electrical parameters of the resistance R, inductance L, and capacitance C in the initial broadband equivalent circuit model are multiplied by the frequency-dependent scaling coefficients constructed by the multi-peak Gaussian function. The multi-peak Gaussian model coefficients are continuously adjusted through an adaptive genetic algorithm to minimize the difference between the theoretical impedance and the measured impedance. This determines the optimal multi-peak Gaussian function fitting parameters and obtains the broadband frequency-varying equivalent circuit model. At the same time, the corresponding node voltage equations are updated. The broadband frequency-variable equivalent circuit model is applied to solve the node equations to obtain the potential frequency response of each node. On this basis, the corresponding time domain waveform is synthesized to evaluate the reliability of the main insulation design and the inter-turn insulation design.

2. The Gaussian fitting calculation method for high-frequency transformer winding potential distribution according to claim 1, characterized in that: Preferably, it also includes, In time domain analysis, the ideal square wave is first expanded into a superposition of several odd harmonics through Fourier series, where the harmonic frequency is an odd multiple of the fundamental frequency, and the harmonic amplitude decays successively according to the 1 / n law. r , using the empirical formula f cutoff =0.35 / t r The highest harmonic frequency of the truncated Fourier series is determined, and an approximate square wave excitation signal is constructed based on this. The amplitude and phase response data of each node at the determined harmonic frequency are used to superimpose all harmonic frequency components and reconstruct the time domain voltage waveform of each node. By analyzing the voltage change rate dv / dt, overshoot amplitude, oscillation duration and its frequency components in the waveform, the resonant response or local insulation stress concentration caused by square wave excitation can be identified.

3. The Gaussian fitting calculation method for high-frequency transformer winding potential distribution according to claim 1, characterized in that: A frequency-dependent scaling coefficient model is constructed using a multi-peak Gaussian function to adjust the equivalent resistance R, inductance L, and capacitance C parameters extracted by finite element simulation. The effective j values ​​of resistance R, inductance L, and capacitance C at different frequency points are determined by the product of their initial simulation values ​​and the Gaussian function scaling coefficient at the corresponding frequency, thereby achieving a fine fitting of the frequency response of the equivalent circuit model. The resistance is defined as Where f represents frequency, lnf represents logarithmic frequency; N is the number of Gaussian peaks, k i is the amplitude coefficient of the i-th Gaussian peak, μ i is the logarithmic frequency of the Gaussian peak, σ i is the width parameter, Definition of inductance and capacitance: Where M is the number of Gaussian peaks in the inductance fitting, p j is the amplitude coefficient of the jth Gaussian peak, ν j is the central logarithmic frequency of the Gaussian peak, δ j is the width parameter, C scaled (f)=a0+b0lnf Where a0 and b0 are fitting constant coefficients; The measured impedance amplitude and phase frequency response are compared with the impedance of R scaled (f), L scaled (f), C scaled (f) The calculated theoretical impedance is compared, and the difference between the two is used as the optimization objective function. The adaptive genetic algorithm is used to dynamically adjust k i ,μ i ,σ i ,p j ,ν j ,δ j ,a0,b0 coefficients, thereby minimizing the difference between the theoretical impedance and the measured impedance.

4. The Gaussian fitting calculation method for high-frequency transformer winding potential distribution according to claim 1, characterized in that: The optimization algorithm used for fitting the scaling coefficients of the multi-peak Gaussian function is an adaptive genetic algorithm, which includes the following steps: Initialize the population: Randomly generate several sets of candidate Gaussian function parameters within the set parameter boundary range as the initial population; Individual selection: A tournament selection method is used to select individuals with smaller fitting errors from the current population to enter the next generation; Crossover operation: Generate a new generation of individuals using a simulated binary crossover operator; Mutation operation: Use polynomial mutation operators to perturb individual parameters and enhance local search capabilities; Adaptive strategy: When the optimal fitness does not improve for several consecutive generations, dynamically increase the mutation rate or randomly restart part of the population to improve the global search capability. The adaptive genetic algorithm uses the measured impedance amplitude and phase angle frequency response curve as the objective function, and minimizes the error between the measured impedance and the impedance calculated by the equivalent circuit model as the fitness criterion. It optimizes the parameters of the Gaussian function scaling coefficient and finally obtains the frequency-dependent scaling function parameter set with the minimum fitting error, thereby improving the broadband frequency-varying equivalent circuit model.

5. The Gaussian fitting calculation method for high-frequency transformer winding potential distribution according to claim 1, characterized in that: The complex magnetic permeability of the nanocrystalline material and the complex dielectric constant of the epoxy resin were obtained by testing the annular nanocrystalline magnetic ring and the epoxy resin sample, respectively. The measured impedance of the ring is: Where μ′ is the real part of magnetic permeability, μ″ is the imaginary part of magnetic permeability, n is the number of turns, l is the average length of the ring, A m is the effective cross-sectional area of ​​the magnetic ring, and the complex magnetic permeability is calculated as: The dielectric constant is measured by measuring the admittance of the epoxy resin sample. The complex dielectric constant is related to C p With R p The expression: C p Represents the equivalent circuit capacitance, R p represents the electrical loss of epoxy resin, ε′ is the real part of the dielectric constant, ε″ is the imaginary part of the dielectric constant, A e is the area of ​​the silver-plated electrode, and d is the distance between the upper and lower electrodes.

6. The Gaussian fitting calculation method for high-frequency transformer winding potential distribution according to claim 1, characterized in that: In the broadband equivalent circuit model of a high-frequency transformer, the relationship between the admittance branch current and the node voltage is: M·U=0 in The vector U contains three types of voltage nodes, the excitation node d, whose voltage vector is U d , ground node g, whose voltage vector is U g , and the response node r, whose voltage vector is U r , where U d Set to 1, U g Set to 0, which is a known voltage. Excluding the excitation voltage and the ground voltage, the remaining voltage is the voltage to be determined, U rem , Delete all elements in the dth row and dth column and the gth row and gth column of the matrix M to form a new (2n+2-numel(d)-numel(g))-order square matrix N; delete the dth and gth elements in the dth column of M to form a new (2n+2-numel(d)-numel(g))-dimensional column vector N d , and move it to the right side of the formula, so that the voltage U of other nodes except the excitation node and the ground node can be solved rem : U rem =-N- 1 ·N d The broadband impedance of the circuit is obtained by dividing the current of the first winding unit by the excitation voltage. The calculation method of the branch current matrix is: Calculate the total impedance of the circuit:

7. The Gaussian fitting calculation method for high-frequency transformer winding potential distribution according to claim 1, characterized in that: Obtaining the potential responses of all nodes at different frequencies includes the following steps: At each discrete frequency point, the optimized equivalent parameters of resistance, inductance, and capacitance with frequency-dependent scaling factors are substituted into the broadband equivalent circuit model of the high-frequency transformer; Based on this model, the frequency domain circuit coefficient matrix M is constructed. The matrix represents the complex relationship between node voltage and branch current in the frequency domain, wherein the matrix elements are derived according to the circuit topology and the frequency domain impedance calculation rules; Classify all nodes into excitation nodes, grounding nodes and nodes to be solved, and remove the rows and columns related to known excitation and grounding in the matrix M to form the reduced matrix N and the right terminal vector N d ; Solve the linear equation system U rem =-N -1 ·N d , obtain the voltage response of the remaining nodes at this frequency; Repeat the above steps to complete the scan of all frequency points within the set frequency range, and finally obtain the amplitude and phase angle response curves of the potential of all winding nodes changing with frequency, which are used to evaluate the electrical behavior characteristics and potential distribution law of the winding structure under high-frequency excitation conditions.

8. A system for implementing the method according to any one of claims 1 to 7, characterized in that: It includes: An extraction unit is used to extract the complex magnetic permeability of the high-frequency transformer core and magnetic ring material and the complex dielectric constant of the encapsulating epoxy material; A finite element modeling unit is used to construct a finite element model according to the structure and size of the high-frequency transformer, and to extract the equivalent electrical parameters of resistance, resistance, and capacitance based on the finite element model; An equivalent circuit modeling unit is used to build a broadband equivalent circuit model of a high-frequency transformer. The winding is divided into a number of trapezoidal units, each of which corresponds to one or more turns of the winding. A top-down multi-node network model is constructed based on the resistance, inductance, and capacitance parameters of the trapezoidal units as the broadband equivalent circuit model of the high-frequency transformer. The resistance and inductance in each trapezoidal unit in the broadband equivalent circuit model of the high-frequency transformer are connected in series to form a corresponding impedance branch, and different impedance branches are coupled through mutual inductance; A measuring unit, which uses an oven to heat the high-frequency transformer, measures the amplitude and phase angle frequency response of the impedance of the high-frequency transformer, and obtains a temperature-dependent impedance characteristic curve; The Gaussian fitting optimization unit is used to construct a frequency-dependent scaling coefficient model using a multi-peak Gaussian function. The error between the measured impedance frequency response and the theoretical impedance of the equivalent circuit model is used as the objective function. An adaptive genetic algorithm is used to dynamically optimize the amplitude, center frequency, and broadening coefficient of the Gaussian function to minimize the fitting error between the theoretical impedance curve output by the model and the measured data. The calculation unit calculates the node potential response of each node, optimizes the obtained parameters and substitutes them into the broadband equivalent circuit model of the high-frequency transformer. By constructing the frequency domain circuit equation and solving the node voltage at all frequency points, the potential amplitude and phase angle response of each node of the transformer winding at different frequencies are obtained.

9. A computer storage medium, characterized in that The storage medium includes computer instructions, which, when executed on a computer, enable the computer to perform the method according to any one of claims 1 to 7.

10. An electronic device, characterized in that: The electronic device comprises: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method according to any one of claims 1 to 7 is implemented.

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