An electromagnetic structure optimization method of high-frequency transformer based on intelligent optimization algorithm

Abstract

The application relates to a high-frequency transformer electromagnetic structure optimization technology, in particular to a high-frequency transformer electromagnetic structure optimization method based on an intelligent optimization algorithm, which comprises the following steps: step one, setting system parameters, selecting fixed parameters and decision variables, and obtaining the minimum voltage phase-shifting angle of zero-voltage switching based on the equivalent circuit of a BDA transformer; step two, performing parameterization processing on the magnetic core and winding structure in the high-frequency transformer and calculating the magnetic core loss and winding loss, constructing a leakage inductance calculation model, establishing a multiple insulation structure and calculating the insulation distance; step three, establishing a multi-objective optimization mathematical model of the high-frequency transformer; and step four, seeking an optimal solution on the basis of the multi-objective optimization mathematical model of the high-frequency transformer, and manufacturing a 60kVA, 400V / 400V, 10kHz high-frequency transformer prototype according to the optimal solution.The application has the beneficial effect that a 60kVA / 10kHz, 400V / 400V high-frequency transformer prototype can be optimized, the efficiency is 99.65%, and the power density is 71.7kW / m<3>. 3 ​

Description

Technical Field

[0001] This invention relates to the field of electromagnetic structure optimization technology for high-frequency transformers, and in particular to a method for optimizing the electromagnetic structure of high-frequency transformers based on intelligent optimization algorithms. Background Technology

[0002] With the increasing application of power electronic transformers in medium and high voltage AC / DC power grids, the development and research of high-frequency transformers are booming. Improving the overall efficiency, power density, and reliability of power electronic devices has become the mainstream trend in their development. Improvements in switching device performance and the widespread application of novel magnetic materials such as nanocrystals are driving power electronic devices towards higher frequencies and higher power densities. Today, high-frequency transformers have become core components in AC / DC hybrid distribution networks and electric traction power conversion fields, playing a crucial role in voltage conversion and isolation. They are widely used in photovoltaic power generation, offshore wind power, and other new energy DC collection systems, as well as railway electric traction systems. Accurate and effective high-frequency transformer design can not only improve efficiency and power density but also ensure the reliability and stability of equipment operation.

[0003] High-frequency transformers impose more stringent requirements on the comprehensive evaluation of indicators such as losses, insulation, and leakage inductance. Because high-frequency transformers typically operate under complex excitation conditions, the various optimization objectives conflict and are difficult to balance. Therefore, the optimal design of high-frequency transformers is a multi-objective optimization process that needs to consider the influence of numerous factors. Under high-frequency conditions, the eddy current effect in transformers is significant, leading to increased core and winding losses. The complex winding structure makes accurate calculation of winding losses difficult. Furthermore, the compact size and significantly increased power density of high-frequency transformers present serious challenges to electromagnetic design.

[0004] Currently, many research institutions and experts at home and abroad have achieved certain results in the optimization design of high-power high-frequency transformers. Wang Jianing, Zou Qiang, Hu Jiawen, Pei Wei, Zhao Yushun, et al. proposed a multi-winding medium-frequency transformer with a special magnetic core structure and winding structure operating in an LLC resonant converter in their paper "Optimization Design Method of Medium-Voltage Insulated High-Power Medium-Frequency Transformer" [J]. Journal of Electrical Engineering, 2022, 37(12):3048-3060. They designed a 200kW / 30kHz air-cooled medium-frequency transformer prototype using the free parameter scanning method, achieving an efficiency of 99.18%. However, the insulation structure was not considered in the design process. Cao Xiaopeng of Southeast University optimized the design of a high-frequency transformer with a power of 3.52kW and a frequency of 20kHz based on a genetic algorithm. However, the algorithm suffers from problems such as uneven population distribution and easy local convergence. Chen Bin's team designed a 15kW / 5kHz, 500V / 500V nanocrystalline alloy high-power medium-frequency three-phase transformer based on the free parameter scanning method, achieving an efficiency of 98.6% and a power density of 8.29MW / m². 3 However, the aforementioned three-phase transformers do not consider the influence of the end magnetic field component on the leakage inductance analytical method. Furthermore, when there are many optimization objectives and parameters, parameter scanning generates numerous valid design schemes, making it difficult to select the optimal design scheme. Therefore, those skilled in the art need an electromagnetic field modeling method based on high-frequency effect and structural effect analysis to perform multi-objective collaborative optimization of high-frequency transformers. Summary of the Invention

[0005] The purpose of this invention is to solve the above problems by designing an electromagnetic structure optimization method for high-frequency transformers based on intelligent optimization algorithms.

[0006] The technical solution of the present invention to achieve the above objectives is a method for optimizing the electromagnetic structure of a high-frequency transformer based on an intelligent optimization algorithm, which includes the following steps:

[0007] Step 1: Set the system specifications of the DAB converter, select fixed parameters and decision variables based on the magnetic core, winding structure and insulation material, establish the design scheme of the square Litz wire high-frequency transformer structure, parameterize the magnetic core and winding structure within the magnetic core window and calculate all structural parameters;

[0008] Step 2: Based on the electrical and structural parameters determined in Step 1, establish calculation models for the core loss and winding loss of the high-frequency transformer, construct a leakage inductance calculation model, establish a multi-insulation structure, and calculate the insulation distance.

[0009] Step 3: Based on the calculations and analysis in Step 2, establish a multi-objective optimization mathematical model for the high-frequency transformer;

[0010] Step four: Based on the multi-objective optimization mathematical model of the high-frequency transformer, the NSGA-II model is improved, and the free parameter scanning method is combined to seek the global optimal solution. A high-frequency transformer prototype is then manufactured based on the selected optimal solution.

[0011] In step one, the DAB converter controls the input bridge and output bridge and inductors... L σ Applying full voltage causes the two square wave voltage waveforms on both sides of the transformer to shift, resulting in a phase shift angle. φ Among them, leakage L σ As a power transmission element, it controls the shape of the current. I T1 The waveform is a piecewise linear waveform containing fundamental and harmonic components, and its effective value expression is shown in equation (1):

[0012] (1)

[0013] in,

[0014]

[0015]

[0016] To achieve soft switching upon turn-on, the anti-parallel diodes of each switch should begin conducting before the turn-on moment. To reduce the number of components and achieve higher power density, the series inductor can be integrated into the leakage inductance of the high-frequency transformer;

[0017] The calculation of all structural parameters within the magnetic core window in step two is as follows:

[0018] The cross-sectional area of ​​the magnetic core is:

[0019] (2)

[0020] In the formula, D Duty cycle, N 2 represents the total number of turns in the secondary winding. N 2= m 2 N l2 , K c It is the lamination factor of the magnetic core;

[0021] The length of the magnetic core cross-section is:

[0022] (3)

[0023] Based on the turns ratio of the primary winding to the secondary winding of the transformer nThe total number of turns in the primary winding of the high-frequency transformer can be obtained from this:

[0024] (4)

[0025] Number of strands in a single turn of Litz wire in the primary and secondary windings:

[0026] (5)

[0027] in, J max To determine the maximum permissible current density, based on the current-carrying capacity and cooling method selected in this application, J max =3.82A / mm 2 ;

[0028] To improve the fill factor and reduce the size of the high-frequency transformer, this application assumes that each turn of Litz wire is square. Therefore, the number of sub-rows of a single turn of Litz wire in the primary and secondary windings is:

[0029] (6)

[0030] The side lengths of the single-turn Litz wire for the primary and secondary windings are:

[0031] (7)

[0032] The number of layers in a primary winding is:

[0033] (8)

[0034] The heights of the primary and secondary windings are:

[0035] (9)

[0036] The height of the core window is:

[0037] (10)

[0038] The widths of the primary and secondary windings are:

[0039] (11)

[0040] The width of the core window is:

[0041] (12)

[0042] The average turn length of the primary winding is:

[0043] (13)

[0044] The average turn length of the secondary winding is:

[0045] (14)

[0046] The average turn length of the leakage flux channel between windings is:

[0047] (15)

[0048] The volume of the magnetic core is:

[0049] (16)

[0050] The volume of the winding is:

[0051] (17).

[0052] In step two, the expression for calculating core loss is the modified IGSE. The formula for IGSE before modification is:

[0053] (18)

[0054] in,

[0055] (19)

[0056] according to α The range of values ​​and curve fitting yielded the following:

[0057] (20)

[0058] Within a cycle B The rate of change is:

[0059] (twenty one)

[0060] The revised expression for IGSE is as follows:

[0061] (twenty two).

[0062] In step two, the winding loss calculation is based on the principle of area equivalence and linearization of complex functions, deriving an approximate Dowell model suitable for Litz wire windings. First, under the condition that the number of turns and layers of the Litz wire winding remains unchanged, square strands are used to replace round strands, introducing an equivalent square strand side length. d seq The relationship between the side length of the square strand and the diameter of the round strand is shown in equation (23):

[0063] (twenty three)

[0064] Then, keeping the number of layers in the Litz wire winding constant, the square strand winding is equivalent to an ideal foil winding. However, this equivalence changes the effective conductive cross-sectional area of ​​the winding. To ensure that the DC conductivity of the winding is the same, a porosity is considered. η The conductivity of the winding conductor is corrected as shown in equation (24):

[0065] (twenty four)

[0066] Since the copper foils in foil windings need to be evenly distributed, the interlayer insulation distance needs to be equivalent to the insulation distance between the foils. d i :

[0067] (25)

[0068] The winding losses of a high-frequency transformer can be calculated as follows:

[0069] (26)

[0070] F r,n The AC resistivity of the winding is... R dc1 , R dc2 These are the DC resistances of the primary and secondary winding conductors, respectively. I rms,n for n The root mean square value of the primary excitation current of the transformer under subharmonics;

[0071] (27)

[0072] (28)

[0073] (29)

[0074] In equation (27), Δ s For the penetration rate of the winding, ξ 1. ξ 2 represents the skin effect correction factor and proximity correction factor of the winding. δ w The skin depth of the winding at the operating frequency;

[0075] (30)

[0076] (31)

[0077] (32)

[0078] In equation (32), f For operating frequency, μ 0 represents the permeability of free space.

[0079] Due to the induction of eddy currents at high frequencies, the skin effect and proximity effect of the windings are enhanced, the current density is no longer uniform, and the AC resistivity increases. F r This also increases accordingly. To achieve more accurate calculations of square Litz wire windings at high frequencies, this application derives an approximate Dowell model suitable for square Litz wire windings based on area equivalence. By linearizing the hyperbolic and trigonometric functions in the Dowell model, the AC resistivity is obtained. F r The approximate expression is shown in equation (33):

[0080] (33)

[0081] In step two, the leakage inductance calculation model needs to introduce a Rogowski factor to correct the winding height by adjusting the magnetic field path length, as shown in equation (34):

[0082] (34)

[0083] In the formula, K R Rogowski factor h weq The equivalent height of the winding;

[0084] Based on the integration of the magnetic field energy generated by the leakage magnetic field, a leakage inductance calculation model considering winding end effects and structural effects is obtained, as follows:

[0085] The calculation of leakage inductance is divided into two parts: one part is the frequency-dependent region, that is, the leakage inductance generated in the region where the winding is located. L σb The other part is the frequency-unrelated region, namely the leakage inductance generated by the interlayer insulation region of the winding and the leakage magnetic channel region. L σy ;

[0086] The total leakage inductance of the high-frequency transformer L σ It can be calculated as:

[0087] (35)

[0088] For the leakage inductance of the frequency-dependent part, a frequency dependence factor that takes into account the winding structure effect is introduced. k f ,but Lσb The following can be calculated:

[0089] (36)

[0090] (37)

[0091] In the formula,

[0092] (38)

[0093] in γ The conductivity coefficient, γ= ( 1+j ) / δ w For leakage inductance in frequency-independent components, L σy The following can be calculated:

[0094] (39)

[0095] The process of establishing the multi-objective optimization mathematical model for the high-frequency transformer in step three is as follows:

[0096] First, the selected decision variables are:

[0097] Number of magnetic cores stacked n c The side length of the magnetic core cross-section A The diameter of the Lids wire strands in the primary and secondary windings d s1 , d s2 Number of secondary winding layers m 2. Number of turns in the primary and secondary windings N l1 、N l2 and maximum magnetic induction intensity B m Its upper boundary is determined by the saturation magnetic flux density of the material. B sat set up.

[0098] Second, the two objective functions selected are:

[0099] Objective function 1: To minimize the core loss and winding loss of the high-frequency transformer, and maximize its efficiency.

[0100] (40)

[0101] Objective function 2: Minimize the volume of the high-frequency transformer and maximize power density.

[0102] (41)

[0103] Under the minimum insulation voltage level U iso Under these conditions, to ensure zero-voltage switching, the leakage inductance must be greater than the minimum leakage inductance value required to meet the minimum isolation requirement. L σ-min Therefore, the constraints selected in this application are:

[0104] (42)

[0105] in, x l It is the lower bound of the decision variable. x u It is the upper bound of the decision variable;

[0106] Third, the improved non-dominated sorting genetic algorithm introduces dynamic clustering distance and improves the crossover operation of NSGA-II using an arithmetic crossover operator; wherein, the arithmetic crossover operator is set as follows: X i t 、X j t The first t If we encode the real values ​​of the decision variables at the intersection of two individuals, then the decision variables for the two individuals after the intersection are as follows:

[0107] (43)

[0108] in, a , b They are random numbers uniformly distributed on [0,1]; while the dynamic aggregation distance of individuals i The dynamic aggregation distance is calculated as follows:

[0109] (44)

[0110] in,

[0111] (45)

[0112] (46)

[0113] In the formula, I i For individuals i The gathering distance, M For the target dimension, I i,k For the first i The individual in the first kThe sorted function values ​​on the target dimension.

[0114] Step four involves performing 580,000 parameter scans across all decision variables using the free parameter scanning method, generating 260,000 effective design schemes within a specific range. This yields a distribution cloud map of volumetric power density and efficiency within the 10Hz-100kHz range, where each point represents a design scheme. This is then used as the initial population in the improved NSGA-II for iterative calculations. The improved NSGA-II is then used to globally optimize all design schemes obtained from the free parameter scanning, resulting in a globally optimal design scheme. This design scheme is then used to design and manufacture a high-frequency transformer prototype.

[0115] Compared with the prior art, the present invention has the following beneficial effects:

[0116] 1. This application establishes a core loss calculation model that combines low cost and high efficiency by fitting the complex integral function in IGSE under high-frequency non-sinusoidal excitation waveform;

[0117] 2. Based on the principle of area equivalence and linearization of complex functions, this application derives an approximate Dowell model that considers winding structure effects and eddy current effects, thereby achieving high-precision calculation of winding losses.

[0118] 3. This application proposes a leakage inductance calculation model that considers winding end effects and structural effects, reducing the dependence of leakage inductance on geometry and frequency; based on long-term and short-term dielectric strength, a novel multi-insulation structure is adopted to improve the insulation withstand voltage level between windings during the operation of high-frequency transformers;

[0119] 4. This application introduces Dynamic Clustering Distance (DCD) and Arithmetic Crossover Operator NSGA-II for improvement, uses ZDT1 and ZDT3 functions for testing, and establishes an optimization design process for high-frequency transformers by combining the free parameter scanning method. A high-frequency transformer prototype was made based on the selected optimal design scheme. Attached Figure Description

[0120] Figure 1 This is a flowchart of an electromagnetic structure optimization method for a high-frequency transformer based on an intelligent optimization algorithm, as described in this invention.

[0121] Figure 2 This is the system parameter table of the DAB converter described in this invention;

[0122] Figure 3 This is the equivalent circuit diagram of the DAB converter described in this invention;

[0123] Figure 4 This is a diagram showing the voltage and current waveforms of the DAB converter under steady-state conditions as described in this invention.

[0124] Figure 5 This is the design scheme of the high-frequency transformer structure described in this invention;

[0125] Figure 6 This is a diagram showing the general three-level voltage waveform generated by the converter described in this invention and the characteristic magnetic induction intensity waveform caused by it;

[0126] Figure 7 This is a physical image of the nanocrystalline magnetic ring loss data measurement platform described in this invention;

[0127] Figure 8 This is a loss curve of the nanocrystalline magnetic ring measured under square waves of different frequencies as described in this invention.

[0128] Figure 9 This is an equivalent process diagram of the Litz wire winding described in this invention;

[0129] Figure 10 This is a simulation diagram of the two-dimensional finite element eddy current field within the magnetic core window described in this invention;

[0130] Figure 11 This is the current density distribution diagram of the 110kHz square Litz wire winding described in this invention;

[0131] Figure 12 This is a comparison chart of the AC resistance coefficient curves of the primary winding obtained by the Dowell model and finite element simulation as described in this invention;

[0132] Figure 13 The different from those described in this invention m AC resistivity of square Litz wire windings F r about d s / δ w A graph showing the changes (solid line: Dowell's equation, dashed line: approximate Dowell's equation).

[0133] Figure 14 The different from those described in this invention η AC resistivity of square Litz wire windings F r about d s / δ w A graph showing the changes;

[0134] Figure 15 This is a top cross-sectional view of the magnetic core window of the high-frequency transformer described in this invention;

[0135] Figure 16 This is a finite element simulation result of the leakage magnetic field inside the magnetic core window at 110kHz as described in this invention;

[0136] Figure 17 This is a comparison chart of leakage inductance obtained by analytical method and finite element simulation as described in this invention;

[0137] Figure 18 This is a diagram of the novel multi-insulation structure described in this invention;

[0138] Figure 19 This is the Pareto front plot of the test function before and after introducing the DCD and arithmetic crossover operators as described in this invention;

[0139] Figure 20 This is a cloud map showing the distribution of volumetric power density and efficiency in the 10Hz-100kHz range described in this invention;

[0140] Figure 21 This is the Pareto front plot of power density-efficiency as described in this invention;

[0141] Figure 22 These are three-dimensional structural diagrams and prototype images of the high-frequency transformer described in this invention;

[0142] Figure 23 This is a physical image of the no-load loss and thermal measurement experimental platform described in this invention;

[0143] Figure 24 This invention describes the voltage and current waveforms on the primary side of the transformer at 10kHz and the corresponding hysteresis loop diagram of the magnetic core.

[0144] Figure 25 This is a graph of hot spot temperatures measured during the 5-hour hot operation described in this invention;

[0145] Figure 26 This is a thermal image of the high-frequency transformer under no-load steady-state conditions as described in this invention.

[0146] Figure 27 This is the design parameter table described in this invention;

[0147] Figure 28 This is a comparison table of core loss and winding loss of the high-frequency transformer described in this invention. Detailed Implementation

[0148] The present invention will now be described in detail with reference to the accompanying drawings, such as... Figure 1-28 As shown;

[0149] Dual-active bridge (DAB) converters are characterized by easy soft-switching, bidirectional power transfer, modularity, and symmetrical structure, making them increasingly used in high-power applications and a crucial component of DC distribution networks. Their system parameter table is as follows: Figure 2 As shown, the equivalent circuit of the DAB converter is as follows: Figure 3As shown, the voltage and current waveforms generated in steady state are as follows: Figure 4 As shown, by controlling the input bridge and output bridge, and in the inductor L σ Applying full voltage causes the two square wave voltage waveforms on both sides of the transformer to shift, resulting in a phase shift angle. φ Among them, leakage inductance L σ As a power transmission element, it controls the shape of the current. I T1 The waveform is a piecewise linear waveform containing fundamental and harmonic components, and its effective value expression is shown in equation (1):

[0150] (1)

[0151] in,

[0152]

[0153]

[0154] To achieve soft switching upon turn-on, the anti-parallel diodes of each switch should begin conducting before the turn-on moment. To reduce the number of components and achieve higher power density, the series inductor can be integrated into the leakage inductance of the high-frequency transformer.

[0155] The design scheme for a square Litz wire high-frequency transformer structure is described, and all structural dimensions within the core window are parameterized, such as... Figure 5 As shown, and calculated as follows:

[0156] The cross-sectional area of ​​the magnetic core is:

[0157] (2)

[0158] In the formula, D Duty cycle, N 2 represents the total number of turns in the secondary winding. N 2= m 2 N l2 , K c It is the lamination factor of the magnetic core;

[0159] The length of the magnetic core cross-section is:

[0160] (3)

[0161] Based on the turns ratio of the primary winding to the secondary winding of the transformer n The total number of turns in the primary winding of the high-frequency transformer can be obtained from this:

[0162] (4)

[0163] The number of strands in a single turn of Litz wire in the primary and secondary windings is:

[0164] (5)

[0165] in, J max To determine the maximum permissible current density, based on the current-carrying capacity and cooling method selected in this application, J max =3.82A / mm 2 ;

[0166] To improve the fill factor and reduce the size of the high-frequency transformer, this application assumes that each turn of Litz wire is square. Therefore, the number of sub-rows of a single turn of Litz wire in the primary and secondary windings is:

[0167] (6)

[0168] The side lengths of the single-turn Litz wire for the primary and secondary windings are:

[0169] (7)

[0170] The number of layers in a primary winding is:

[0171] (8)

[0172] The heights of the primary and secondary windings are:

[0173] (9)

[0174] The height of the core window is:

[0175] (10)

[0176] The widths of the primary and secondary windings are:

[0177] (11)

[0178] The width of the core window is:

[0179] (12)

[0180] The average turn length of the primary winding is:

[0181] (13)

[0182] The average turn length of the secondary winding is:

[0183] (14)

[0184] The average turn length of the leakage flux channel between windings is:

[0185] (15)

[0186] The volume of the magnetic core is:

[0187] (16)

[0188] The volume of the winding is:

[0189] (17).

[0190] Because IGSE offers high accuracy and good fit within its operating range, and requires only three empirical coefficients, it is a more suitable expression for calculating core losses under high-frequency non-sinusoidal excitation waveforms. Its voltage and magnetic flux density waveforms are as follows: Figure 6 As shown. To avoid the increased computational cost due to the complex integral function in IGSE, this application modifies the formula, as follows:

[0191] The formula before the IGSE correction was:

[0192] (18)

[0193] in,

[0194] (19)

[0195] according to α The range of values ​​and curve fitting yielded the following:

[0196] (20)

[0197] Figure 6 In a cycle B The rate of change is:

[0198] (twenty one)

[0199] In summary, the revised IGSE expression is calculated as follows:

[0200] (twenty two)

[0201] Establish a measurement platform for nanocrystalline magnetic ring loss data, such as Figure 7 As shown. Loss data of nanocrystalline magnetic rings measured under sinusoidal induction waveform. The effect of core loss on the operating point of the magnetic material was simulated using Matlab. f , B mThe dependency relationship of IGSE is shown in Table 1. Table 1 is the empirical coefficient table for IGSE, and its specific contents are as follows:

[0202] empirical coefficient numerical values 1.397 2.296 <![CDATA[4.229×10 -5 ]]>

[0203] Meanwhile, loss data of nanocrystalline magnetic rings at different frequencies were measured under square wave conditions, such as... Figure 8 As shown, within the region below the saturation flux density, the loss gradually increases with increasing flux density. In the core loss separation model, hysteresis loss dominates at low frequencies, being proportional to the first power of the frequency, while eddy current loss is not significant. Therefore, the increase in core loss is slow, and the curve is relatively flat. However, as the frequency increases, eddy current loss within the core becomes increasingly larger and proportional to the square of the frequency. Consequently, the higher the frequency, the faster the loss increases, and the steeper the curve. Therefore, in the optimized design of high-frequency transformers, selecting appropriate frequency and flux density is crucial for improving efficiency.

[0204] The Dowell one-dimensional assumption of the electromagnetic field within the core window only applies to ideal foil-wound transformers. For transformers with Litz wire windings, winding equivalence is required. The equivalence process is as follows: Figure 9 As shown.

[0205] Based on the principle of area equivalence, under the condition that the number of turns and layers of the Litz wire winding remain unchanged, square strands are used to replace round strands, introducing an equivalent square strand side length. d seq The relationship between the side length of the square strand and the diameter of the round strand is shown in equation (23):

[0206] (twenty three)

[0207] Then, keeping the number of layers in the Litz wire winding constant, the square strand winding is equivalent to an ideal foil winding. However, this equivalence changes the effective conductive cross-sectional area of ​​the winding. To ensure that the DC conductivity of the winding is the same, a porosity is considered. η The conductivity of the winding conductor is corrected as shown in equation (24):

[0208] (twenty four)

[0209] Since the copper foils in foil windings need to be evenly distributed, the interlayer insulation distance needs to be equivalent to the insulation distance between the foils. d i :

[0210] (25)

[0211] A DAB converter contains a large number of high-order harmonics; therefore, the total winding loss is the sum of the winding losses under each individual harmonic. The winding losses of a high-frequency transformer can be calculated as follows:

[0212] (26)

[0213] F r,n The AC resistivity of the winding is... R dc1 , R dc2 These are the DC resistances of the primary and secondary winding conductors, respectively. I rms,n for n The root mean square value of the primary excitation current of the transformer under subharmonics;

[0214] (27)

[0215] (28)

[0216] (29)

[0217] In equation (27), Δ s For the penetration rate of the winding, ξ 1. ξ 2 represents the skin effect correction factor and proximity correction factor of the winding. δ w The skin depth of the winding at the operating frequency;

[0218] (30)

[0219] (31)

[0220] (32)

[0221] In equation (32), f For operating frequency, μ 0 represents the permeability of free space.

[0222] Due to the induction of eddy currents at high frequencies, the skin effect and proximity effect of the windings are enhanced, the current density is no longer uniform, and the AC resistivity increases. F r This also increases accordingly. To achieve more accurate calculations of square Litz wire windings at high frequencies, this application derives an approximate Dowell model suitable for Litz wire windings based on area equivalence. By linearizing the hyperbolic and trigonometric functions in the Dowell model, the AC resistivity is obtained. F rThe approximate expression is shown in equation (33):

[0223] (33)

[0224] To verify the effectiveness and accuracy of the Dowell equivalence, this application conducts two-dimensional eddy current field finite element simulations on the actual core window structure and the equivalent core window structure. The simulation results are as follows: Figure 10 As shown.

[0225] from Figure 10 It can be seen that the magnetic field strength and magnetic energy of the equivalent magnetic core window structure are significantly smaller than those of the actual magnetic core window structure, and the distribution of magnetic field strength and magnetic energy is also more uniform, with no obvious skin effect and proximity effect.

[0226] The AC resistance of a square Litz wire winding in a high-frequency transformer was simulated and calculated using the finite element method. The current density distribution of the winding at 110kHz is shown below. Figure 11 As shown. The square Litz wire has a strand diameter of 0.1 mm and contains 100 strands. At high frequencies, the Litz wire exhibits a uniform current density distribution and minimal skin effect.

[0227] Figure 12 The AC resistivity curves of the broadband primary winding obtained from the Dowell model and finite element simulation are shown. It can be seen that the AC resistivity calculated using the Dowell model agrees well with the simulation results, and this model can be used to derive an approximate Dowell model.

[0228] At high frequencies, the skin effect and proximity effect of the winding are enhanced. To investigate the impact of the skin depth on winding losses, the number of winding layers is increased. m Porosity varies within the range of 1-20. η= 0.8, the obtained AC resistivity F r about d s / δ w The changing curve is as follows Figure 13 As shown. Then maintain the number of winding layers. m =1 remains unchanged, so that the porosity η Variation within the range of 0.6-1 yields the following results. F r about d s / δ w The changing curve is as follows Figure 14 As shown.

[0229] from Figure 13-14The following conclusions can be drawn: In the design of high-frequency transformers, in order to minimize the error between the winding losses calculated by the approximate Dowell model and the calculation results of the Dowell model, it is necessary to make the following as much as possible. d s / δ w ≤2.

[0230] The porosity of the winding has a significant impact on the uniformity of the leakage magnetic field distribution, and the reasonable design of the insulation distance is crucial for the calculation of the leakage inductance of high-frequency transformers. Therefore, this application introduces the Rogowski factor to correct the winding height by adjusting the magnetic field path length, as shown in Equation (34), thereby reducing the dependence of magnetic field strength and magnetic energy distribution on the winding structure.

[0231] (34)

[0232] In the formula, K R Rogowski factor h weq This represents the equivalent height of the winding.

[0233] Compared to directly applying the Dowell model, this correction allows for more accurate estimation of various parameter values ​​when designing high-frequency transformers. As the operating frequency increases, a transverse magnetic field component appears at the winding ends, causing the calculated leakage inductance to be underestimated. Therefore, this application proposes a leakage inductance calculation model that considers winding end effects and structural effects, as follows:

[0234] The calculation of leakage inductance is divided into two parts, such as Figure 15 As shown, one part is the frequency-dependent region, indicated by blue, which represents the leakage inductance generated in the area where the winding is located. L σb The other part is the frequency-unrelated region, indicated in yellow, which is the leakage inductance generated by the interlayer insulation region of the winding and the leakage magnetic channel region. L σy .

[0235] The total leakage inductance of the high-frequency transformer L σ It can be calculated as:

[0236] (35)

[0237] For the leakage inductance of the frequency-dependent portion represented by the blue area, a frequency-dependent factor considering the winding geometry is introduced. k f ,but L σb The following can be calculated:

[0238] (36)

[0239] (37)

[0240] In the formula,

[0241] (38)

[0242] in γ The conductivity coefficient, γ= ( 1+j ) / δ w For the leakage inductance in the frequency-independent portion represented by the yellow area, L σy The following can be calculated:

[0243] (39)

[0244] Figure 16 The finite element simulation results of the leakage magnetic field of a high-frequency transformer at 110kHz are shown. It can be seen that the maximum magnetic field strength of the high-frequency transformer is located at the leakage magnetic channel. Therefore, to obtain an accurate value of the leakage inductance, the width of the leakage magnetic channel needs to be appropriately designed. d iso The leakage inductance curves obtained from analytical methods and finite element simulations are as follows: Figure 17 As shown, the leakage inductance calculated analytically is basically consistent with the simulation results. At frequencies above 100kHz, the leakage inductance calculated analytically is slightly lower than the finite element simulation results, but still within the acceptable error range. This model can be applied to the optimization design of high-frequency transformers. To reduce the risk of insulation reliability degradation caused by thermal aging and other problems during the operation of high-frequency transformers, and to improve the insulation withstand voltage level between windings, this application adopts a novel multi-layer insulation structure in the design process, such as... Figure 18 As shown, a semiconductor varnish is applied to the outer layer of the magnetic core and windings to enhance structural strength and reduce noise; epoxy resin with excellent dielectric properties is poured inside the magnetic core window, significantly reducing the required insulation distance compared to air insulation; single-strand conductors are wound with polyurethane film, and Litz wire adopts a double-layer insulation design, with an inner layer wrapped with polyimide film and an outer layer wrapped with Nomex T410 insulating paper, confining electrical stress within the main insulation layer. This avoids partial discharge problems caused by excessively high field strength in the air outside the insulation layer and softens the electrical stress in the main insulation layer. Figure 18 The insulation distances within the novel multi-insulation structure can be calculated as follows:

[0245] Minimum insulation distance between primary and secondary windings:

[0246]

[0247] To ensure zero-voltage switching of the DAB converter, a safety factor is required. k saf =30%.

[0248] Horizontal and vertical insulation distances between the winding and the upper and lower yokes:

[0249]

[0250] Insulation distance between the secondary winding and the center post of the magnetic core:

[0251]

[0252] Wherein, Eins-s is the short-term dielectric strength, that is, the breakdown field strength at power frequency.

[0253] The dimensions of the winding inter-turn insulation and inter-layer insulation are only related to the breakdown field strength of the inter-turn insulation material under high-frequency square wave voltage, and can be calculated as follows:

[0254]

[0255]

[0256] in, E ins-l Long-term dielectric strength refers to the breakdown field strength of an insulating material under a high-frequency square wave voltage. U t-t This refers to the inter-turn voltage of the winding under long-term high-frequency square wave voltage. U l-l These are the interlayer voltages of the windings under long-term high-frequency square wave voltage.

[0257] The decision variables selected in this application are:

[0258] Number of magnetic cores stacked n c The side length of the magnetic core cross-section A The diameter of the Lids wire strands in the primary and secondary windings d s1 , d s2 Number of secondary winding layers m 2. Number of turns in the primary and secondary windings N l1 、N l2 and maximum magnetic induction intensity B m Its upper boundary is determined by the saturation magnetic flux density of the material. B sat set up.

[0259] The two objective functions selected in this application are:

[0260] Objective function 1: Minimize the core loss and winding loss of the high-frequency transformer to maximize efficiency.

[0261] (40)

[0262] Objective function 2: Minimize the volume of the high-frequency transformer and maximize power density.

[0263] (41)

[0264] Under the minimum insulation voltage level U iso Under these conditions, to ensure zero-voltage switching, the leakage inductance must be greater than the minimum leakage inductance value required to meet the minimum isolation requirement. L σ-min Therefore, the constraints selected in this application are:

[0265] (42)

[0266] in, x l It is the lower bound of the decision variable. x u It is the upper bound of the decision variable. Since NSGA-II still has problems such as uneven population distribution and easy getting trapped in local convergence during the optimization design of high-frequency transformers, in order to improve the algorithm with better global search capabilities, this application introduces DCD and arithmetic crossover operators to improve NSGA-II, enhance the breadth and uniformity of population distribution, and improve global optimization efficiency.

[0267] set up X i t 、X j t The first t If we encode the real values ​​of the decision variables at the intersection of two individuals, then the decision variables for the two individuals after the intersection are as follows:

[0268] (43)

[0269] in, a , b These are random numbers uniformly distributed on [0,1].

[0270] individual i The dynamic aggregation distance is calculated as follows:

[0271] (44)

[0272] in,

[0273] (45)

[0274] (46)

[0275] In the formula, I i For individuals i The gathering distance, M For the target dimension, I i,k For the first i The individual in the first k The function values ​​after sorting over the target dimension. The improved algorithm was debugged using the Matlab platform and tested using the ZDT1 and ZDT3 functions. The population size used in the algorithm. N p =100, number of generations Gen =200, number of tests tr =8, crossover probability p c =0.8, mutation probability p m =1 / n v ,in n v It is the number of decision variables, the cross-distribution index. mu =80, variation distribution index mum =20. Compare the Pareto fronts of the test functions obtained before and after the algorithm improvement, such as... Figure 19 As shown. From Figure 19 It can be seen that after the improvement of the NSGA-II algorithm, the Pareto front curve of the test function is smoother and the distribution of each solution is more uniform. It is evident that the improved NSGA-II is more suitable for multi-objective optimization design of high-frequency transformers.

[0276] This application, based on the free parameter scanning method, performs 580,000 parameter scans within their respective ranges for the selected decision variables, generating 260,000 effective design schemes within a specific range. This yields distribution cloud maps of volumetric power density and efficiency in the 10Hz-100kHz range, as shown below. Figure 20 As shown in the figure. Each point represents a design scheme, which is used as the initial population in the improved NSGA-II for iterative calculation. Figure 27 This paper summarizes the design parameters required in the design process of high-frequency transformers. Based on the optimized design flowchart, a global optimization is performed on all design schemes obtained through free parameter scanning using the improved NSGA-II, yielding the power density-efficiency Pareto front as follows: Figure 21 As shown. A globally optimal design scheme is found based on the principle of maximizing power density, indicated by a red asterisk. A high-frequency transformer prototype is designed and manufactured using this design scheme; its 3D structural diagram and prototype image are shown below. Figure 22 As shown. For the prototype shell-type high-frequency transformer, the magnetic core uses Antainano nanocrystalline material from Antai Technology, with specifications of CN-154*87*28*35. The diameter of each strand in the square Litz wire winding is 0.2mm. The Litz wire structure is 16×137 strands, that is, 2192 strands are twisted into 16 sub-bundles, each sub-bundle containing 137 strands, and then the 16 sub-bundles are twisted together into one turn of Litz wire. The dimensions of a single turn of Litz wire are 11.65mm×11.65mm, and the insulation thickness is 0.3mm. The upper yoke of the magnetic core is connected at the front and rear using Z-shaped stainless steel clamps, and the lower yoke is connected at the front and rear using U-shaped stainless steel plates as structural clamps, and the overall structure is firmly formed by screws. Example

[0277] The leakage inductance and AC resistance of a high-frequency transformer prototype were measured using a Tonghui TH2840B impedance analyzer. During the measurement, the secondary winding of the high-frequency transformer prototype was short-circuited, and the primary winding was open-circuited, neglecting the influence of magnetizing inductance. The leakage inductance measurement result was 7.92 μH, with an error of 2.2% compared to the leakage inductance value attributed to the primary side. The AC resistance measurement result was 3.1 mΩ. The winding loss was calculated based on the measured AC resistance value and the root mean square value of the rated harmonic current. In actual manufacturing, the insulation distance between the high-frequency transformer frame and windings differed from the design value, causing the measured leakage inductance value to not match the design value. (The text then abruptly shifts to a different topic: "Assembly as...") Figure 23 The experimental platform for measuring no-load loss and thermal activity is shown. The excitation source is a WF1974 signal generator with an NF4520A power amplifier, which generates a square wave voltage with an amplitude of 400V and an operating frequency of 10kHz. The secondary winding is kept open. An LMG500 power analyzer is used to read the values ​​of voltage, current and core loss. Figure 24 The voltage and current waveforms on the primary side of the high-frequency transformer under no-load conditions, as well as the corresponding hysteresis loop of the magnetic core, are displayed. A three-dimensional model of the high-frequency transformer was established in SolidWorks software and imported into Ansys software for finite element analysis. The core loss and winding loss calculated at a frequency of 10kHz are shown below. Figure 28 As shown. Figure 28 This is a comparison table of core losses and winding losses in high-frequency transformers. To verify the thermal characteristics of the designed high-frequency transformer prototype, it was subjected to 5 hours of hot-running operation under no-load and rated voltage excitation until it reached a stable state, at an ambient temperature of 20℃. The temperatures of each hot spot were recorded using a NAPUL TP230X temperature recorder. The measurement results are as follows: Figure 25 As shown. Figure 26 The image shows a thermal photograph of a high-frequency transformer under steady-state operation, captured by a FLUKE Ti32 infrared thermal imager. Under no-load conditions, the windings are primarily heated via thermal coupling, resulting in a low magnetization current and winding temperature. At this point, the main issue within the high-frequency transformer is core loss. It can be seen that the core temperature is the highest, reaching 135.7℃ under stable operating conditions, but still within the safe operating range, and the temperature rise meets the expected design requirements.

[0278] The above technical solutions only embody the preferred technical solutions of the present invention. Any modifications that may be made by those skilled in the art to certain parts thereof embody the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A method for optimizing the electromagnetic structure of a high-frequency transformer based on an intelligent optimization algorithm, characterized in that, The method includes the following steps: Step 1: Set the system specifications of the DAB converter, select fixed parameters and decision variables based on the magnetic core, winding structure and insulation material, establish the design scheme of the square Litz wire high-frequency transformer structure, parameterize the magnetic core and winding structure within the magnetic core window and calculate all structural parameters; Step 2: Based on the electrical and structural parameters determined in Step 1, establish calculation models for the core loss and winding loss of the high-frequency transformer, construct a leakage inductance calculation model, establish a multi-insulation structure, and calculate the insulation distance. Step 3: Based on the calculations and analysis in Step 2, establish a multi-objective optimization mathematical model for the high-frequency transformer. The process is as follows: First, the selected decision variables are: The number of magnetic cores stacked n c The side length A of the magnetic core cross-section, and the diameter d of the Litz wire strands in the primary and secondary windings. s1 d s2 Number of secondary winding layers m2, number of turns N in primary and secondary windings l1 N l2 and the maximum magnetic induction intensity B m Its upper boundary is determined by the material's saturation magnetic flux density B. sat set up; Second, the two objective functions selected are: Objective function 1: To minimize the core loss and winding loss of the high-frequency transformer, and maximize its efficiency. Objective function 2: Minimize the volume of the high-frequency transformer and maximize power density. Under the minimum insulation voltage level U iso Under these conditions, to ensure zero-voltage switching, the leakage inductance must be greater than the minimum leakage inductance value L required to meet the minimum isolation requirement. σ-min Therefore, the constraints selected in this application are: Where, x l It is the lower bound of the decision variable, x u It is the upper bound of the decision variable; Third, the improved non-dominated sorting genetic algorithm introduces dynamic clustering distance and uses an arithmetic crossover operator to improve the crossover operation of NSGA-II; Step four: Based on the multi-objective optimization mathematical model of the high-frequency transformer, the NSGA-II model is improved, and the free parameter scanning method is combined to seek the global optimal solution. A high-frequency transformer prototype is then manufactured based on the selected optimal solution.

2. The electromagnetic structure optimization method for a high-frequency transformer based on an intelligent optimization algorithm according to claim 1, characterized in that, In step one, the DAB converter controls the input bridge and output bridge, and in the leakage inductance L σ Applying full voltage causes the two square wave voltage waveforms on both sides of the transformer to shift, resulting in a phase shift angle. Among them, leakage inductance L σ As a power transmission element, I controls the shape of the current. T1 The waveform is a piecewise linear waveform, containing fundamental and harmonic components, and its effective value expression is shown in equation (1): in, Where f is the operating frequency; to achieve soft switching upon turn-on, the anti-parallel diode of each switch should begin conducting before the turn-on moment; to reduce the number of components and achieve higher power density, the series inductor can be integrated into the leakage inductance of the high-frequency transformer.

3. The electromagnetic structure optimization method for a high-frequency transformer based on an intelligent optimization algorithm according to claim 2, characterized in that, The calculation of all structural parameters within the magnetic core window in step two is as follows: The cross-sectional area of ​​the magnetic core is: In the formula, D is the duty cycle, N2 is the total number of turns of the secondary winding, and N2 = m2N l2 K c It is the lamination factor of the magnetic core; The length of the magnetic core cross-section is: Based on the turns ratio n of the primary winding to the secondary winding of the transformer, the total number of turns in the primary winding of the high-frequency transformer can be calculated: N1=nm2Nl2 (4) Number of strands in a single turn of Litz wire in the primary and secondary windings: Among them, J max To determine the maximum permissible current density, J depends on the selected Litz wire current rating and cooling method. max =3.82A / mm 2 ; Therefore, the number of sub-rows of a single-turn Litz wire in the primary and secondary windings is: The side lengths of the single-turn Litz wire for the primary and secondary windings are: The number of layers in a primary winding is: The heights of the primary and secondary windings are: The height of the core window is: H = hw1 + 2dch (10) The widths of the primary and secondary windings are: The width of the core window is: G=d cv +m1(2d int1 +d b1 )+(m1-1)d m1 +m2(2d int2 +d b2 )+(m2-1)d m2 +d iso +d cf (12) The average turn length of the primary winding is: The average turn length of the secondary winding is: The average turn length of the leakage flux channel between windings is: The volume of the magnetic core is: V c =4n c AB(H+2A+G) (16) The volume of the winding is: Vw=hw1(MLT1+πW1) (17).

4. The electromagnetic structure optimization method for a high-frequency transformer based on an intelligent optimization algorithm according to claim 3, characterized in that, In step two, the expression for calculating core loss is the modified IGSE. The formula for IGSE before modification is: in, Based on the range of values ​​for α and curve fitting, we obtain: The rate of change of B within one period is: The revised expression for IGSE is as follows:

5. The electromagnetic structure optimization method for a high-frequency transformer based on an intelligent optimization algorithm according to claim 4, characterized in that, In step two, the winding loss calculation is based on the principle of area equivalence and linearization of complex functions, deriving an approximate Dowell model applicable to Litz wire windings. First, under the condition that the number of turns and layers of the Litz wire winding remains unchanged, square strands are used to replace round strands, introducing an equivalent square strand side length d. seq The relationship between the side length of the square strand and the diameter of the round strand is shown in equation (23): Then, keeping the number of layers of the Litz wire winding unchanged, the square strand winding is equivalent to an ideal foil winding. However, this equivalence changes the effective conductive cross-sectional area of ​​the winding. To ensure that the DC conductivity of the winding is the same, a porosity η is considered to correct the conductivity of the winding wire, as shown in equation (24): Since the copper foils in foil windings need to be evenly distributed, the interlayer insulation distance needs to be equivalent to the insulation distance d between the foils. i : The winding losses of a high-frequency transformer can be calculated as follows: P w =P w1 +P w2 F r,n R is the AC resistivity of the winding. dc1 R dc2 I represents the DC resistance of the primary and secondary winding conductors, respectively. rms,n This is the root mean square value of the primary excitation current of the transformer under the nth harmonic. In equation (27), Δ n ξ1 and ξ2 are the skin and proximity correction factors of the winding, respectively, and δ is the penetration rate of the winding. w The skin depth of the winding at the operating frequency; In equation (32), μ0 is the vacuum permeability; Due to the induction of eddy currents at high frequencies, the skin effect and proximity effect of the windings are enhanced, the current density is no longer uniform, and the AC resistivity F... r This also increases accordingly; to achieve more accurate calculation of square Litz wire windings at high frequencies, this application derives an approximate Dowell model suitable for square Litz wire windings based on area equivalence. By linearizing the hyperbolic and trigonometric functions in the Dowell model, the AC resistivity F is obtained. r The approximate expression is shown in equation (33):

6. The electromagnetic structure optimization method for a high-frequency transformer based on an intelligent optimization algorithm according to claim 5, characterized in that, In step two, the leakage inductance calculation model needs to introduce a Rogowski factor to correct the winding height by adjusting the magnetic field path length, as shown in equation (34): In the formula, K R For the Rogowski factor, h weq The equivalent height of the winding; Based on the magnetic field energy integral generated by the leakage magnetic field, a method considering the winding end effect and... The leakage inductance calculation model for structural effects is as follows: The calculation of leakage inductance is divided into two parts: one part is the frequency-dependent region, that is, the leakage inductance L generated in the region where the winding is located. σb The other part is the frequency-unrelated region, namely the leakage inductance L generated by the interlayer insulation region of the winding and the leakage magnetic channel region. σy ; The total leakage inductance L of the high-frequency transformer σ It can be calculated as: Lσ=Lσb+Lσy(35) For the leakage inductance in the frequency-dependent part, a frequency dependence factor k that takes into account the winding structure effect is introduced. f Then L σb The following can be calculated: k f =(2N s1 m 2 +1)ζ1+2(N s2 m 2 -1)ζ2(37) In the formula, Where γ is the conduction coefficient, γ=(1+j) / δ w For leakage inductance in the frequency-independent part, L σy The following can be calculated:

7. The electromagnetic structure optimization method for a high-frequency transformer based on an intelligent optimization algorithm according to claim 6, characterized in that, The improved non-dominated sorting genetic algorithm in step three is as follows: Arithmetic cross operator setting Let be the real-valued codes of the decision variables corresponding to the intersection point of the two individuals in generation t, respectively. Then, the decision variables corresponding to the two individuals after the intersection are as follows: Where a and b are random numbers uniformly distributed on [0,1]; and the dynamic clustering distance of individual i is calculated as follows: in, In the formula, I i Let M be the clustering distance of individual i, M be the target dimension, and I be the clustering distance of individual i. i,k The function value is the sorted value of the i-th individual on the k-th dimension target.

8. The electromagnetic structure optimization method for a high-frequency transformer based on an intelligent optimization algorithm according to claim 1, characterized in that, Step four involves performing 580,000 parameter scans across all decision variables using the free parameter scanning method, generating 260,000 effective design schemes within a specific range. This yields a distribution cloud map of volumetric power density and efficiency within the 10Hz-100kHz range, where each point represents a design scheme. This is then used as the initial population in the improved NSGA-II for iterative calculations. The improved NSGA-II is then used to globally optimize all design schemes obtained from the free parameter scanning, resulting in a globally optimal design scheme. This design scheme is then used to design and manufacture a high-frequency transformer prototype.

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