A robust optimization method for high-frequency transformer based on 6-sigma design

Abstract

The application discloses a high-frequency transformer robust optimization method based on 6 sigma design; comprising: determining a preliminary design scheme: combining system requirements and performance indicators, selecting core materials, structure types and winding types, and constructing a basic design framework of the high-frequency transformer; a mathematical analytical calculation model is established; a robust optimization model is established; a multi-objective iterative optimization is carried out to iteratively solve the robust optimization model; output design scheme: compare the performance parameters of all schemes, and screen out the optimal design scheme as the final design scheme of the high-frequency transformer under the corresponding application scene. The application establishes a multi-objective robust optimization model based on 6 sigma theory, realizes multi-physical field collaborative optimization and manufacturing uncertainty quantization of the high-frequency transformer, breaks through the limitations of traditional deterministic optimization, can significantly improve product consistency, development efficiency and mass production reliability, and has important industrial application value.

Description

Technical Field

[0001] This invention belongs to the field of electrical digital data processing technology, specifically a robust optimization method for high-frequency transformers based on 6σ design. Background Technology

[0002] Driven by the large-scale grid connection of renewable energy and the transformation of power grids towards power electronics, power systems are placing higher demands on the power density, dynamic response, and controllability of electrical equipment. As a core component of power electronic transformers, high-frequency transformers (HFTs) demonstrate irreplaceable value in areas such as new energy power collection and medium-voltage DC power distribution due to their small size and high power density. However, problems such as a surge in leakage inductance, uneven loss distribution, and thermal-noise coupling caused by high-frequency operating conditions severely restrict the reliability design and engineering application of HFTs. There is an urgent need to break through traditional experience-based design models and construct a systematic and intelligent design framework to improve design efficiency and performance.

[0003] The design of high-frequency transformers currently faces a dual challenge: First, traditional single-objective optimization methods based on empirical formulas struggle to achieve coordinated optimization of multiple physical field performance indicators such as leakage inductance, loss, temperature rise, and noise, and the iterative process relying on manual trial and error is inefficient. Second, existing multi-objective optimization algorithms generally ignore key uncertainties present in the actual manufacturing process, such as manufacturing tolerances caused by core and winding geometric errors, and material property deviations such as permeability fluctuations. These noise factors cause significant differences between actual performance and theoretical design values ​​during HFT mass production, increasing product failure rates. This design-manufacturing disconnect makes it difficult to meet the stringent requirements of modern power electronic equipment for lightweight, high reliability, and interference resistance. Therefore, establishing a robust optimization model that considers manufacturing uncertainties to achieve full-chain performance assurance from theoretical design to engineering implementation has significant engineering application value and promotional significance for improving product consistency, reducing development costs, and shortening the R&D cycle of high-frequency transformers. Summary of the Invention

[0004] To address the problems existing in the background technology, this invention provides a robust optimization method for high-frequency transformers based on 6σ design, aiming to solve the problems of insufficient multi-physics performance co-optimization and performance drift caused by manufacturing uncertainties in traditional design methods. This method, through a systematic and robust optimization process, balances performance improvement and reliability of high-frequency transformers. The technical solution includes:

[0005] Determine the preliminary design scheme;

[0006] Establish a mathematical analytical calculation model;

[0007] Establish a robust optimization model;

[0008] Multi-objective iterative optimization is performed to iteratively solve the robust optimization model;

[0009] The robust optimization model is as follows:

[0010]

[0011] Where, x r For design variables with uncertainty; μ x σ is the design value of the design variable. x The standard deviation of the design variable; x L As the lower bound of the design variable, x U The upper limit of the design variables; f r,1 (x r Let μ be the first objective function in the robust optimization model. Pm f is the mean power density. r,2 (x r ) represents the second objective function in the robust optimization model, μ η g represents the average efficiency. r,1 (x r ) represents the first constraint in the robust optimization model, μ Bm σ is the mean of the maximum operating magnetic flux density. Bm g is the variance of the maximum operating magnetic flux density. r,2 (x r ) represents the second constraint in the robust optimization model, μ Lk σ is the mean of the leakage inductance. Lk The variance of leakage inductance; g r,3 (x r ) represents the third constraint in the robust optimization model, μ THV σ is the average temperature of the high-voltage winding. THV The variance of the high-voltage winding temperature; g r,4 (x r ) represents the fourth constraint in the robust optimization model, μ TLV σ is the average temperature of the low-voltage winding. TLV The variance of the low-voltage winding temperature; g r,5 (x r ) represents the fifth constraint in the robust optimization model, μ Tcl σ is the average temperature of the core column. Tcl The variance of the core column temperature; g r,6 (x r ) represents the sixth constraint in the robust optimization model, σ Pm The variance of power density; g r,7 (x r ) represents the seventh constraint in the robust optimization model, σ ηLet Variance be the efficiency.

[0012] After iterative solution, the design scheme is output: the performance parameters of all schemes are compared, and the optimal design scheme is selected based on the actual situation, which is the final design scheme of the high-frequency transformer in the corresponding application scenario.

[0013] The steps for iteratively solving the robust optimization model are as follows:

[0014] Step 5.1, Population Initialization: Define the high-frequency transformer design variable x = (x1, x2, ..., x...). p ) T And randomly generate an initial population P0 of size N;

[0015] Step 5.2, Individual robustness assessment, considers the uncertainty distribution of performance parameters caused by design parameter fluctuations, and quantifies this distribution: Monte Carlo analysis is performed on each individual, and the performance output under noise disturbance is calculated based on the mathematical analytical calculation model; the mean, standard deviation, and constraint violation degree of the output objective function and performance index are used as input data for step 5.3, wherein the constraint violation degree is calculated as follows:

[0016]

[0017]

[0018] Among them, v g,j (x) represents the degree of violation of the j-th constraint; v total (x) represents the total degree of constraint violation; g r,j (x) is the robustness value of the j-th constraint; g r min,j For the minimum value of the j-th constraint, g r max,j The maximum value of the j-th constraint;

[0019] Step 5.3, Fast Non-Dominated Sort and Crowding Calculation: Calculate the mean μ of the objective function. f Standard deviation σ f Using the degree of constraint violation as input data, perform a fast non-dominated sort on population P0 and divide it into Pareto ranks F1, F2, ..., F k F1 is the first Pareto front;

[0020] For each layer of nondominated solution F i Sort by objective function value in ascending order and calculate the crowding distance of individuals:

[0021]

[0022] Among them, C d(i) represents the crowding distance of the i-th individual; p represents the number of objective functions; f i n-1 f represents the (n-1)th individual with the i-th objective function; i n+1 f represents the (n+1)th individual with the i-th objective function; i max f is the maximum value of the objective. i min This is the minimum value of the objective;

[0023] Step 5.4, Genetic Operations: When iterating to the kth iteration, genetic operators such as selection, crossover, and mutation are used to modify the parent population P. k Perform the operation to generate the offspring population Q. k and Q k Perform individual robustness assessments;

[0024] Step 5.5, Population Merging: Merge parent generations P k With offspring Q k A mixed population R of size 2N is formed. k ;

[0025] Step 5.6, Elite Retention and Selection: For R k Perform fast non-dominated sorting and crowding calculation, and select individuals to fill P according to Pareto level from low to high. k+1 When F i If the number of individuals in a layer exceeds the remaining capacity, then individuals in that layer are selected in descending order of crowding, up to P. k+1 The scale reaches N;

[0026] Step 5.7 Termination Judgment: If the termination condition is met, output the non-dominated solution of the current population as the Pareto front solution set for the robust optimization design of high-frequency transformers; otherwise, increment the iteration count by 1, i.e., let k = k + 1, and return to step 5.4 to continue iterating.

[0027] The preliminary design scheme includes: selecting core material, structural type and winding type based on system requirements and performance indicators, and constructing the basic design framework for high-frequency transformers.

[0028] Before determining the preliminary design scheme, the system-level design requirements of the high-frequency transformer should be clarified based on the technical specifications of the application scenario.

[0029] The steps for determining the preliminary design scheme are as follows:

[0030] Step 2.1: Select materials based on the power rating, operating frequency, and loss requirements of the high-frequency transformer;

[0031] Step 2.2: Select the core structure based on comprehensive leakage inductance control, heat dissipation requirements, and space constraints;

[0032] Step 2.3: Select the winding type based on current density, skin effect, and winding loss requirements.

[0033] The mathematical analytical calculation model includes: leakage inductance calculation, core loss calculation, temperature rise calculation, power density calculation, and efficiency calculation, wherein:

[0034] Leakage inductance calculation, leakage inductance L of high-frequency transformer referred to the primary side. k The calculation is as follows:

[0035]

[0036] Among them, W iso Leakage magnetic energy storage in the primary and secondary side main insulation layers; W pri_ins For energy storage of leakage flux between layers of the primary winding, W sec_ins For energy storage of leakage flux between layers of the secondary winding; W pri W is used for energy storage through leakage magnetic flux inside the primary winding conductor. sec Energy storage for leakage flux inside the secondary winding conductor; I p This represents the effective value of the primary winding current.

[0037] Core loss calculation:

[0038]

[0039] Among them, P c For core loss; B mr C represents the actual maximum operating magnetic flux density. m α, β are Steinmetz empirical coefficients; V c ρ is the volume of the iron core; core D is the core density; D is the duty cycle, taken as 1 for square wave; f s θ is the operating frequency; θ is the phase angle characterizing the periodic variation of magnetic flux.

[0040] Winding loss calculation:

[0041]

[0042] P w =F r R dc I 2 ;

[0043] Among them, R dc R is the DC resistance of the winding. ac F is the AC resistance of the winding. r I is the AC resistivity of the winding; I is the effective value of the current in each layer of the winding; P w For winding losses;

[0044] Temperature rise calculation:

[0045]

[0046] Among them, T tr G is a column vector of temperatures at the core and winding nodes of a high-frequency transformer; T G is the thermal conductivity matrix of the transformer thermal network model; Ta P represents the thermal conductivity matrix between the transformer and the environment. Ta Transformer thermal power and ambient temperature T a Column vectors;

[0047] Power density calculation: The power density of a high-frequency transformer is calculated as follows:

[0048] m w =ρ w (N p A xp l m_p +N s A xs l m_s );

[0049]

[0050] Where, m w ρ is the total weight of the winding; w The density of the material used in the winding; N p N represents the number of turns in the primary winding. s A is the number of turns in the secondary winding; xp A represents the total bare conductor area of ​​each turn of the primary winding. xs The total bare conductor area per turn of the secondary winding; l m_p l is the average turn length of the primary winding. m_s P is the average turn length of the secondary winding; m Power density; S n This refers to the rated capacity of the high-frequency transformer; m c This refers to the weight of the iron core;

[0051] Efficiency calculation: The efficiency of a high-frequency transformer is calculated as follows:

[0052] P t =P c +P w ;

[0053]

[0054] Among them, P t η represents total loss; η represents efficiency.

[0055] The beneficial effects of this invention are as follows:

[0056] 1. This invention addresses the problem of existing technologies failing to consider manufacturing uncertainties by incorporating parameter fluctuations into the optimization process. By introducing parameter uncertainty analysis and 6σ constraints, the impact of noise factors is quantified, reducing the interference of manufacturing deviations on performance and significantly enhancing the product's anti-interference capability and long-term operational reliability.

[0057] 2. Based on the 6σ theory, a multi-objective robust optimization model is established to achieve multi-physical field collaborative optimization and manufacturing uncertainty quantification of high-frequency transformers (specifically, the collaborative optimization of multi-physical field performance indicators such as leakage inductance, loss, and temperature rise of high-frequency transformers is realized). This breaks through the limitations of traditional deterministic optimization and can significantly improve product consistency, development efficiency, and mass production reliability, which has important industrial application value. This avoids performance conflicts caused by single indicator optimization and can effectively improve the overall performance of the product.

[0058] 3. By combining analytical models with multi-objective algorithms, an efficient design optimization process can be achieved, reducing the cost of manual trial and error, improving design efficiency, and providing technical support for the prototype manufacturing and mass production of large-capacity high-frequency transformers. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating an embodiment of a robust optimization method for high-frequency transformers based on 6σ design according to the present invention.

[0060] Figure 2 This is a schematic diagram of a high-frequency transformer structure provided in an embodiment of the present invention;

[0061] Figure 3 This is a flowchart illustrating the robust optimization model solution provided in this embodiment of the invention.

[0062] Figure 4 Pareto frontier for robust optimization design of high-frequency transformers provided in embodiments of the present invention;

[0063] Figure 5 The mean μ and standard deviation σ of the constraints corresponding to each design point on the Pareto front provided in this embodiment of the invention;

[0064] Figure 6 The σ level of the constraint corresponding to each design point on the Pareto front provided in the embodiments of the present invention. Detailed Implementation

[0065] The present invention will be further described in detail below with reference to the accompanying drawings.

[0066] like Figure 1 The embodiment of the present invention shown includes:

[0067] Step 1: Define system design requirements: Based on the technical specifications of the application scenario, define the system-level design requirements of the high-frequency transformer to provide a quantitative basis for subsequent design;

[0068] Step 2: Determine the preliminary design scheme: Based on system requirements and performance indicators, select the core material, structural type and winding type to construct the basic design framework of the high-frequency transformer;

[0069] Step 3: Establish a mathematical analytical calculation model: Establish a multi-physics analytical calculation model for the high-frequency transformer to quantify core performance parameters such as leakage inductance, loss, temperature rise, power density, and efficiency; clarify the mapping relationship between design parameters and performance indicators through theoretical calculations;

[0070] Step 4: Establish a robust optimization model: Based on the 6σ design (Design For Six-Sigma, DFSS) technique, define the optimization objective, design variables, constraints and their value ranges, and set the noise factor and its disturbance range in the high-frequency transformer manufacturing process to establish a robust optimization model that includes uncertainties.

[0071] Step 5: Multi-objective iterative optimization: Considering the uncertainty of parameters, a multi-objective optimization algorithm is used to iteratively solve the problem, dynamically optimize the design parameters, and obtain the Pareto front solution set;

[0072] Step 6: Output Design Scheme: Compare the performance parameters of all schemes, and select the optimal design scheme based on the actual situation, which will be the final design scheme of the high-frequency transformer for the corresponding application scenario.

[0073] In step 1, the system-level design requirements for the high-frequency transformer include: capacity, voltage / current rating, turns ratio, operating frequency, and temperature rise limit;

[0074] The specific system-level design requirements parameters for the high-frequency transformer in this embodiment are shown in Table 1.

[0075] Table 1 System-level design requirements for transformers

[0076]

[0077] The basic design framework for the high-frequency transformer is established by selecting the winding type in step 2. The specific execution steps for determining the preliminary design scheme in step 2 are as follows:

[0078] Step 2.1: Select materials based on the power rating, operating frequency, and loss requirements of the high-frequency transformer.

[0079] Ferrites are suitable for medium- and high-frequency applications, exhibiting high permeability and low eddy current loss characteristics. However, their saturation magnetic induction is relatively low, requiring control of magnetic flux density fluctuations. Amorphous alloys are suitable for medium- and high-frequency wide-temperature applications, offering excellent temperature stability and low iron loss. However, they are brittle and require special forming processes. Nanocrystalline materials are suitable for high-frequency, high-current applications, combining the advantages of high permeability and low loss. However, they are more expensive, and the magnetic circuit design must avoid hysteresis loop distortion.

[0080] Step 2.2: Selecting the core structure based on comprehensive leakage inductance control, heat dissipation requirements, and space constraints:

[0081] O-type cores have a compact structure and good magnetic circuit closure, but the winding process is complex, making them suitable for miniaturized high-frequency transformers. U-type core windings offer flexible arrangement and easy maintenance, making them suitable for high-power applications and scenarios with ample heat dissipation space. U-type shell core windings are encased in the core, providing excellent electromagnetic shielding and mechanical strength, making them suitable for vibration-resistant environments, but they have low space utilization.

[0082] Step 2.3: Select the winding type based on current density, skin effect, and winding loss requirements.

[0083] Copper foil windings have low DC resistance and uniform current distribution, which can significantly reduce winding losses in high-frequency transformers with high current and low voltage output; flat copper wire windings are suitable for medium current and compact high-frequency transformers and have good heat dissipation performance; Litz wire windings are made of multiple thin wires twisted together, which can effectively reduce skin effect and proximity effect losses at high frequencies and are suitable for high-frequency and high-efficiency transformers.

[0084] In this embodiment, step 2 is performed based on the system-level design requirements defined in step 1, to select the appropriate components for the core needs of high-frequency, high-power scenarios:

[0085] Core materials: Nanocrystalline materials have significant advantages over similar soft magnetic materials due to their extremely low high-frequency core loss density, high saturation magnetic induction intensity and excellent thermal stability, making them the preferred solution for high-frequency and high-power applications.

[0086] Core Structure: As shown in Table 2, the performance comparison of different core structures shows that the U-shaped core structure, with its larger window area and adaptability to winding process, can meet the design requirements of high-capacity and high-voltage levels for the number of winding turns and conductor specifications. Although it has relatively large leakage flux and leakage inductance, these can be effectively improved by optimizing the winding arrangement.

[0087] Winding type: Litz wire adopts a multi-strand stranded design, which effectively suppresses the skin effect and proximity effect, significantly reduces high-frequency loss, and its electrical characteristics are highly consistent with the low-loss design goal of high-frequency transformers.

[0088] Accordingly, the preliminary design scheme of this embodiment is determined as follows: the core material is nanocrystalline, the core structure is U-shaped, and the winding type is Litz wire, so as to achieve synergistic optimization of loss, heat dissipation and power density.

[0089] Table 2 Comparison of characteristics of different core structures

[0090]

[0091] In step 3, based on the basic design framework determined in step 2, a mathematical analytical calculation model for the leakage inductance, loss, temperature rise, power density, and efficiency of the high-frequency transformer is established, including: leakage inductance calculation, core loss calculation, temperature rise calculation, power density calculation, and efficiency calculation. Specifically:

[0092] Leakage inductance calculation, leakage inductance L of high-frequency transformer referred to the primary side. k The calculation is as follows:

[0093]

[0094] Among them, W iso Leakage magnetic energy storage in the primary and secondary side main insulation layers; W pri_ins For energy storage of leakage flux between layers of the primary winding, W sec_ins For energy storage of leakage flux between layers of the secondary winding; W pri W is used for energy storage through leakage magnetic flux inside the primary winding conductor. sec Energy storage for leakage flux inside the secondary winding conductor; I p This represents the effective value of the primary winding current.

[0095] For core loss calculation, a correction factor related only to D is introduced. Based on this, the core loss under different duty cycles can be calculated using the Steinmetz empirical coefficient. The generalized Steinmetz improved formula is selected for core loss calculation, as follows:

[0096]

[0097] Among them, P c For core loss; B mr C represents the actual maximum operating magnetic flux density. m α, β are Steinmetz empirical coefficients; V c ρ is the volume of the iron core; core D is the core density; D is the duty cycle, taken as 1 for square wave; f s θ is the operating frequency; θ is the phase angle characterizing the periodic variation of magnetic flux.

[0098] Winding loss calculation: Due to the skin effect and proximity effect, the equivalent AC resistance of the winding is greater than the DC resistance. The winding loss is calculated as follows:

[0099]

[0100] P w =F r R dc I 2

[0101] Among them, R dc R is the DC resistance of the winding. ac F is the AC resistance of the winding. r I is the AC resistivity of the winding; I is the effective value of the current in each layer of the winding; P w For winding losses;

[0102] Temperature rise calculations are performed under steady-state conditions, where internal heat conduction and external heat exchange within the transformer reach equilibrium. By solving the thermal network equations, the temperature distribution at each node inside the transformer can be calculated. First, the temperature vector T is initialized, typically set to the ambient temperature or empirically. Then, an iterative loop is entered, updating the thermal resistance in each iteration until a steady-state value is obtained. Finally, the temperature rise of different parts of the transformer is determined based on the results of the equation below:

[0103]

[0104] Among them, T tr G is a column vector of temperatures at the core and winding nodes of a high-frequency transformer; T G is the thermal conductivity matrix of the transformer thermal network model; Ta P represents the thermal conductivity matrix between the transformer and the environment. Ta Transformer thermal power and ambient temperature T a Column vectors;

[0105] Power density calculation: The power density of a high-frequency transformer is calculated as follows:

[0106] m w =ρ w (N p A xp l m_p +N s A xs l m_s )

[0107]

[0108] Where, m w ρ is the total weight of the winding; w The density of the material used in the winding; N p and N s These are the number of turns in the primary and secondary windings, respectively; A xp and A xs These represent the total bare conductor area per turn of the primary and secondary windings, respectively; lm_p and l m_s These are the average turn lengths of the primary and secondary windings, respectively; P m Power density; S n This refers to the rated capacity of the high-frequency transformer; m c This refers to the weight of the iron core;

[0109] Efficiency calculation: The efficiency of a high-frequency transformer is calculated as follows:

[0110] P t =P c +P w

[0111]

[0112] Among them, P t P represents total loss; η represents efficiency; c For core loss; P w This refers to winding losses.

[0113] The specific high-frequency transformer structure diagram provided in this embodiment is as follows: Figure 2 As shown, step 3, establishing the mathematical analytical calculation model for leakage inductance, loss, temperature rise, power density, and efficiency, specifically includes:

[0114] (1) Leakage inductance calculation: leakage inductance L of the high-frequency transformer referred to the primary side. k The calculation is as follows:

[0115]

[0116] Among them, W iso Leakage magnetic energy storage in the primary and secondary side main insulation layers; W pri_ins W sec_ins Interlayer leakage magnetic energy storage for the primary and secondary windings, respectively; W pri W sec These are the leakage magnetic energy storage components inside the primary and secondary winding conductors, respectively.

[0117] (2) Core loss calculation: The generalized Steinmetz modified formula is selected to calculate the core loss as follows:

[0118]

[0119] Among them, P c For core loss; B mr C represents the actual maximum operating magnetic flux density. m α, β are Steinmetz empirical coefficients; V c ρ is the volume of the iron core; core D is the core density; D is the duty cycle, taken as 1 for square wave; f sθ is the operating frequency; θ is the phase angle characterizing the periodic variation of magnetic flux.

[0120] (3) Winding loss calculation: For Litz wire windings, the Tourkhani formula is used for calculation. The primary and secondary winding losses are P and P, respectively. wp and P ws High-frequency transformer winding loss P w for:

[0121]

[0122] Among them, I p and I s These are the effective values ​​of the primary and secondary winding currents, respectively; F rp and F rs These are the AC resistivity coefficients of the primary and secondary windings, respectively; R dc_p and R dc_s These are the DC resistances of the primary and secondary windings, respectively.

[0123] (4) Temperature rise calculation: The high-frequency transformer thermal network model provided in this embodiment of the invention performs steady-state temperature rise calculation based on the equivalent thermal circuit model of the high-frequency transformer.

[0124]

[0125] Among them, T tr G is a column vector of temperatures at the core and winding nodes of a high-frequency transformer; T G is the thermal conductivity matrix of the transformer thermal network model; Ta P represents the thermal conductivity matrix between the transformer and the environment. Ta Transformer thermal power and ambient temperature T a Column vectors;

[0126] Since the convective and radiative heat transfer coefficients are temperature-dependent, the steady-state temperature of each node of the high-frequency transformer needs to be obtained by iteratively solving the above matrix equations. The initial temperature is set to the ambient temperature, and the thermal resistance value is updated in each iteration.

[0127] (5) Power density calculation: The power density of the high-frequency transformer is calculated as follows:

[0128] m w =ρ w (N p A xp l m_p +N s A xs l m_s )

[0129]

[0130] Where, mw ρ is the total weight of the winding; w The density of the material used in the winding; N p and N s These are the number of turns in the primary and secondary windings, respectively; A xp and A xs These represent the total bare conductor area per turn of the primary and secondary windings, respectively; l m_p and l m_s These are the average turn lengths of the primary and secondary windings, respectively; P m Power density; S n This refers to the rated capacity of the high-frequency transformer; m c This refers to the weight of the iron core;

[0131] (6) Efficiency calculation: The efficiency of the high-frequency transformer is calculated as follows:

[0132] P t =P c +P w

[0133]

[0134] Among them, P t P represents total loss; η represents efficiency; w For winding losses;

[0135] In step 4, within the 6σ design framework, all design parameters (covering material properties and geometric dimensions) are set to follow a normal distribution with a specific mean (μ) and standard deviation (σ) to quantify the random fluctuations in manufacturing tolerances and material properties. Based on this, the robust optimization model can be expressed as:

[0136] min f r,i [μ f (x r ),σ f (x r )], i = 1, 2, ... p

[0137] stg r,j [μ g (x r ),σ g (x r )]≤0,j=1,2,...m

[0138] x r =μ x ±nσ x

[0139] x L ≤x r ≤x U

[0140] LSL≤μ f ±nσ f ≤USL

[0141] Where, x r For design variables with uncertainty; μ x and σ x Design values ​​and standard deviations of the design variables respectively; x L and x U These are the lower and upper limits of the design variables, respectively, defining the boundary of the feasible design domain; f r,i Let g be the i-th objective function, used to measure design performance (such as power density, efficiency, etc.); r,j The j-th inequality constraint restricts the boundaries that the design must meet (such as limits for temperature rise, leakage inductance, etc.) to ensure design feasibility; LSL and USL are the lower and upper specification limits, respectively, representing the allowable boundaries of performance indicators to ensure that the design meets actual engineering requirements; n is the sigma level, corresponding to the confidence interval probability of the standard normal distribution; μ f and σ f These are the mean and standard deviation of the design objective, describing the "central tendency" and "dispersion" of the parameter, respectively, and are generally estimated using Monte Carlo simulation with equal probability methods; μ g and σ g These are the mean and standard deviation of the performance indicators, respectively.

[0142] The robust optimization model simultaneously controls the "mean (design target)" and the "standard deviation (fluctuation risk)" to pursue the optimal design indicators while meeting performance constraints, so that the high-frequency transformer can still maintain robust reliability under manufacturing fluctuations and material differences.

[0143] In robust optimization models, quantifying the fluctuation range of design parameters is a core aspect of the design process. Through statistical methods and engineering experience, the boundaries of the fluctuation range can be clearly defined, and its impact on system performance can be controlled through optimization. The following section, using typical parameters of high-frequency transformers (such as Litz wire diameter tolerance and core permeability fluctuation), specifically illustrates the numerical process of fluctuation quantification:

[0144] (1) Identification and distribution modeling of key fluctuation parameters

[0145] The manufacturing fluctuations and material differences in high-frequency transformers are mainly reflected in:

[0146] Leeds wire diameter: Due to the tolerance of the stranding equipment, assuming the design target diameter is d0, the actual wire diameter fluctuation follows a normal distribution d~N(d0,σ d 2 (e.g., wire diameter standard deviation σ) d =0.02d0, i.e., ±2% tolerance).

[0147] Core permeability: Assuming the target permeability is μ r,0 The actual permeability ranges from μ due to batch variations in materials. r ~μ(μ r,min ,μ r,max (e.g., minimum value μ) r,min =0.92μ r,0 Maximum value μ r,max =1.08μ r,0 (i.e., fluctuation of ±8%).

[0148] Other parameters: Core column thickness (e.g., a~N(a0,σ)) a 2 )), current density (e.g., J ~ N(J0,σ) J 2 )) etc., where a0 and σ a These represent the design value and standard deviation of the core thickness, respectively; J0 and σ J These represent the design value and standard deviation of the current density, respectively.

[0149] (2) Quantification of the impact of fluctuations on performance (taking efficiency and power density as examples)

[0150] The impact of fluctuation parameters on target performance was calculated using analytical models and Monte Carlo simulations.

[0151] Efficiency (η) fluctuation: Affected by copper loss (skin effect caused by wire diameter fluctuation) and iron loss (hysteresis loss caused by core thickness and permeability fluctuation), efficiency fluctuation can be expressed as: η=f(d,μ r ,a,J), that is, η~N(μ η ,σ η 2 ), where μ η It is the average efficiency, σ η It is the efficiency standard deviation (the core quantitative indicator of fluctuation range).

[0152] Power density (P) m Fluctuations: Affected by winding volume (wire diameter fluctuation) and core volume (core thickness fluctuation), power density fluctuations can be expressed as a probability constraint: P(P m ≥P m,min )≥0.997, that is, at a 99.7% confidence level, it has P m ~N(μ) Pm ,σ Pm 2 The power density of the distribution is not lower than its lower limit P. m,min , where μ Pm It is the average power density, σ Pm It is the standard deviation of power density.

[0153] Robust optimization transforms the abstract "fluctuation risk" into numerical boundaries (e.g., lower confidence limit of efficiency ≥ 0.995, lower confidence limit of power density ≥ 0.1 kW / kg) through "fluctuation parameter distribution modeling → performance impact quantification → probabilistic constraint embedding → multi-objective optimization solution". This is ultimately implemented in high-frequency transformer design.

[0154] Mean-optimal: The average values ​​of core indicators such as efficiency and power density approximate the theoretical optimum;

[0155] Controllable fluctuations: Under manufacturing deviations and material differences, performance fluctuations are strictly limited within acceptable probability boundaries;

[0156] Reliability improvement: Performance under extreme conditions is guaranteed by probabilistic constraints, significantly reducing the risk of failure.

[0157] The proposed method is particularly suitable for products such as high-frequency transformers that are sensitive to manufacturing tolerances and have complex multi-physical field coupling, enabling the design to move from "optimal under ideal operating conditions" to "robust and reliable under all operating conditions".

[0158] In statistics, σ measures the dispersion of individual data values ​​relative to the mean. In quality control scenarios, a higher σ level indicates less dispersion in the actual process, a closer product output to the target value, and a lower defect probability, signifying more stringent quality control. Table 3 shows the percentage of variation (the proportion of data falling within the mean ± σ range), the number of defects per million, and the number of defects per million after considering the 1.5σ offset commonly present in actual manufacturing, visually demonstrating the relationship between σ and quality level.

[0159] Table 3 Quality characteristics at different σ levels

[0160]

[0161] First, a traditional deterministic optimization model for high-frequency transformers is established, with the power density P... m And efficiency η as the optimization objective:

[0162] max f1(x)=P m (x)

[0163] f2(x)=η(x)

[0164] stg1(x)=B m (x)-0.9≤0

[0165] g2(x)=L k (x)-100≤0

[0166] g3(x)=T HV (x)-120≤0

[0167] g4(x)=T LV (x)-120≤0

[0168] g5(x)=T cl (x)-100≤0

[0169] g6(x)=P m (x)-0.1≥0

[0170] g7(x)=η(x)-0.995≥0

[0171] x L ≤x≤x U

[0172] Where x is the design variable, x L As the lower bound of the design variable, x U B represents the upper limit of the design variables; f(x) is the objective function in the traditional optimization model, and g(x) is the constraint condition in the traditional optimization model; m The maximum operating magnetic flux density; L k Leakage; T HV T represents the high-voltage winding temperature. LV T represents the low-voltage winding temperature. cl The core column temperature is [value missing].

[0173] Secondly, based on the deterministic optimization model and considering the uncertainties of various design parameters, a robust optimization model for high-frequency transformers based on 6σ design is established. In long-term manufacturing and industrial design, the 6σ quality level, through a preset 1.5σ process offset tolerance, controls the defect rate to within 3.4 per million products, thereby achieving a highly robust design goal. This is a widely adopted quality evaluation system in the high-end manufacturing field. The range of values ​​for design variables and their perturbation ranges are shown in Table 4 below; therefore, the robust optimization model is:

[0174] max f r,1 (x r )=μ Pm (x r )

[0175] f r,2 (x r )=μ η (x r )

[0176] stg r,1 (x r )=μ Bm (x r )+6σ Bm (x r -0.9≤0

[0177] g r,2 (x r )=μ Lk (x r )+6σ Lk (x r -100≤0

[0178] g r,3 (x r )=μ THV (x r )+6σ THV (x r -120≤0

[0179] g r,4 (x r )=μ TLV (x r )+6σ TLV (x r -120≤0

[0180] g r,5 (x r )=μ Tcl (x r )+6σ Tcl (x r -100≤0;

[0181] g r,6 (x r )=μ Pm (x r )-6σ Pm (x r -0.1≥0

[0182] g r,7 (x r )=μ η (x r )-6σ η (x r -0.995≥0

[0183] x r =μ x ±6σ x

[0184] x L ≤x r ≤x U

[0185] Where, x r For design variables with uncertainties, their value range and disturbance values ​​are shown in Table 4; μ x and σ x These are the design values ​​and standard deviations of the design variables, respectively; f r (x) and gr (x) represent the objective function and constraint condition (f) in the robust optimization model, respectively. r,1 (x r f is the first objective function in the robust optimization model. r,2 (x r ) represents the second objective function in the robust optimization model; g r,1 (x r ) represents the first constraint in the robust optimization model, g r,2 (x r ) represents the second constraint in the robust optimization model, g r,3 (x r ) represents the third constraint in the robust optimization model, g r,4 (x r ) represents the fourth constraint in the robust optimization model, g r,5 (x r ) represents the fifth constraint in the robust optimization model, g r,6 (x r (x is the sixth constraint in the robust optimization model); L and x U These are the lower and upper limits of the design variable, respectively; μ Pm and σ Pm These are the mean and variance of the power density, respectively; μ η and σ η These are the mean and variance of the efficiency, respectively; μ Bm and σ Bm These are the mean and variance of the maximum operating magnetic flux density, respectively; μ Lk and σ Lk These are the mean and variance of the leakage inductance, respectively; μ THV and σ THV These are the mean and variance of the high-voltage winding temperature, respectively; μ TLV and σ TLV These are the mean and variance of the low-voltage winding temperature, respectively; μ Tcl and σ Tcl The mean and variance of the core column temperature are given.

[0186] Table 4. Range of values ​​and disturbance values ​​for design variables with uncertainties

[0187]

[0188] Where a is the thickness of the core column; m s and n s These represent the number of layers and turns of the secondary winding on a single iron core column, respectively; d L1 d L2 , where are the diameters of the single-strand Litz wires selected for the primary and secondary sides, respectively; J is the current density.

[0189] In step 5, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to iteratively solve the robust optimization model. The specific execution steps are as follows:

[0190] Step 5.1, Population Initialization: Define the high-frequency transformer design variables as x = (x1, x2, ..., x...). p ) T , such as core cross-sectional area, number of winding turns, insulation spacing, etc., and randomly generate an initial population P0 of size N;

[0191] Step 5.2, Individual Robustness Assessment: Monte Carlo analysis is performed on each individual, and the performance output under noise disturbance is calculated based on the mathematical analytical calculation model in Step 3. The mean, standard deviation, and constraint violation degree of the output objective function and performance index are calculated. The proposed method considers the uncertainty distribution of performance parameters caused by design parameter fluctuations and quantifies this distribution, using it as input data for Step 5.3. This effectively avoids the potential risk that performance parameters may exceed constraint thresholds (such as power density and temperature rise limits) under parameter fluctuations, but may be misjudged as optimal solutions because the ranking mechanism does not consider fluctuation risks. The constraint violation degree is calculated as follows:

[0192]

[0193] Among them, v g,j (x) represents the degree of violation of the j-th constraint; v total (x) represents the total degree of constraint violation; g r,j (x) is the robustness value of the j-th constraint; g rmin,j and g rmax,j These are the minimum and maximum values ​​of the j-th constraint, respectively.

[0194] Step 5.3, Fast Non-Dominated Sort and Crowding Calculation: Calculate the mean μ of the objective function. f Standard deviation σ f Using the degree of constraint violation as input data, perform a fast non-dominated sort on population P0 and divide it into Pareto ranks F1, F2, ..., F k (F1 is the first-level Pareto front); for each level of non-dominated solution F i Sort by objective function value in ascending order and calculate the crowding distance of individuals:

[0195]

[0196] Among them, C d (i) represents the crowding distance of the i-th individual; p represents the number of objective functions; f i nf represents the nth individual of the i-th objective function. i n-1 f represents the (n-1)th individual with the i-th objective function; i n+1 f represents the (n+1)th individual with the i-th objective function; i max and f i min These are the maximum and minimum values ​​of the target, respectively.

[0197] Step 5.4, Genetic Operations: When iterating to the kth iteration, genetic operators such as selection, crossover, and mutation are used to modify the parent population P. k Perform the operation to generate the offspring population Q. k and Q k Perform individual robustness assessments;

[0198] Step 5.5, Population Merging: Merge parent generations P k With offspring Q k A mixed population R of size 2N is formed. k ;

[0199] Step 5.6, Elite Retention and Selection: For R k Perform fast non-dominated sorting and crowding calculation, and select individuals to fill P according to Pareto level from low to high. k+1 When F i If the number of individuals in a layer exceeds the remaining capacity, then individuals in that layer are selected in descending order of crowding, up to P. k+1 The scale reaches N;

[0200] Step 5.7 Termination Judgment: If the termination condition is met (such as the iteration number threshold or Pareto front convergence), output the non-dominated solution of the current population as the Pareto front solution set for the robust optimization design of high-frequency transformers; otherwise, increment the iteration number by 1, i.e., let k = k + 1, and return to step 5.4 to continue iterating.

[0201] In this embodiment, the NSGA-II algorithm is used to iteratively solve the robust optimization model. The flowchart of the specific algorithm execution in step 5 is as follows: Figure 3 As shown in Table 5, the parameter settings are for the iteration process, and the specific execution steps are as follows:

[0202] Step 5.1, Population Initialization. Define the high-frequency transformer design variables as x = (x1, x2, ..., x...). p ) T , such as core cross-sectional area, number of winding turns, insulation spacing, etc., and randomly generate an initial population P0 of size N;

[0203] Step 5.2, Individual Robustness Assessment. A Monte Carlo analysis is performed on each individual, and the performance output under noise perturbation is calculated based on the mathematical analytical model from Step 3; the mean, standard deviation, and constraint violation degree of the objective function and performance indicators are also calculated.

[0204] Step 5.3: Fast Non-Dominated Sort and Crowding Calculation. Perform fast non-dominated sorting on population P0 and divide it into Pareto ranks F1, F2, ..., F6. k (F1 is the first-level Pareto front); for each level of non-dominated solution F i Sort by objective function value in ascending order and calculate the crowding distance of individuals;

[0205] Step 5.4, Genetic Operations. When iterating to the kth iteration, genetic operators such as selection, crossover, and mutation are used to manipulate P. t Perform the operation to generate the offspring population Q. k and Q k Perform individual robustness assessments;

[0206] Step 5.5, Population Merging. Merge parent generations P. k With offspring Q k A mixed population R of size 2N is formed. k ;

[0207] Step 5.6, Elite Retention and Selection. For R... k Perform fast non-dominated sorting and crowding calculation, and select individuals to fill P according to Pareto level from low to high. k+1 When F i If the number of individuals in a layer exceeds the remaining capacity, then individuals in that layer are selected in descending order of crowding, up to P. k+1 The scale reaches N.

[0208] Step 5.7, Termination Judgment. If the termination condition is met (such as the iteration count threshold or Pareto front convergence), output the non-dominated solution of the current population as the Pareto front solution set for the robust optimization design of high-frequency transformers; otherwise, increment the iteration count by 1, i.e., let k = k + 1, and return to step 5.4 to continue iterating.

[0209] Table 5 Parameter settings during the iteration process

[0210]

[0211] Following the above solution steps, the power density and efficiency of each design scheme are obtained, such as... Figure 4 As shown, different dots represent different design schemes, with red dots representing the Pareto front, i.e., the optimal performance solution set. Based on the individual robustness assessment results, the mean μ and standard deviation σ of the constraints corresponding to each design point on the Pareto front are as follows: Figure 5As shown. Robustness analysis is performed on the Pareto front to obtain the σ level of the constraint corresponding to each design point on the front, as shown. Figure 6 As shown, the proposed robust optimization method for high-frequency transformers can ensure that all design solutions satisfy the constraints even when design parameters fluctuate.

[0212] In step 6, constraints such as process feasibility, material procurement costs, and manufacturing cycle in actual production should be considered to screen the theoretically optimal solution, so as to ensure that the final selected design scheme has the best practicality and promotion value.

[0213] In this embodiment, step 6 specifically involves: comprehensively considering engineering constraints such as process feasibility in actual production (e.g., winding accuracy), material procurement costs (e.g., price fluctuations of nanocrystalline ribbon), and manufacturing cycle (e.g., processing time of Litz wire), selecting the design scheme with the best overall performance from the Pareto front solution set as the final implementation scheme for the high-frequency transformer.

[0214] The above design process not only meets the robustness requirements of high-frequency transformers, but also achieves comprehensive optimization in terms of efficiency, cost-effectiveness and heat dissipation performance, which is conducive to the mass production of high-reliability high-frequency transformers in industrial scenarios.

Claims

1. A robust optimization method for high-frequency transformers based on 6σ design, characterized in that, include: Determine the preliminary design scheme; Establish a mathematical analytical calculation model; Establish a robust optimization model; Multi-objective iterative optimization is performed to iteratively solve the robust optimization model; The robust optimization model is as follows: max f r,1 (x r )=μ Pm (x r ) f r,2 (x r )=μ η (x r ) s.t.g r,1 (x r )=μ Bm (x r )+6σ Bm (x r )-0.9≤0 g r,2 (x r )=μ Lk (x r )+6σ Lk (x r )-100≤0 g r,3 (x r )=μ THV (x r )+6σ THV (x r )-120≤0 g r,4 (x r )=μ TLV (x r )+6σ TLV (x r )-120≤0 g r,5 (x r )=μ Tcl (x r )+6σ Tcl (x r )-100≤0; g r,6 (x r )=μ Pm (x r )-6σ Pm (x r )-0.1≥0 g r,7 (x r )=μ η (x r )-6σ η (x r )-0.995≥0 x r =μ x ±6σ x x L ≤x r ≤x U Where, x r For design variables with uncertainty; μ x σ is the design value of the design variable. x The standard deviation of the design variable; x L As the lower bound of the design variable, x U The upper limit for design variables; f r,1 (x r Let μ be the first objective function in the robust optimization model. Pm f is the mean power density. r,2 (x r ) represents the second objective function in the robust optimization model, μ η g represents the average efficiency. r,1 (x r ) represents the first constraint in the robust optimization model, μ Bm σ is the mean of the maximum operating magnetic flux density. Bm g is the variance of the maximum operating magnetic flux density. r,2 (x r ) represents the second constraint in the robust optimization model, μ Lk σ is the mean of the leakage inductance. Lk The variance of leakage inductance; g r,3 (x r ) represents the third constraint in the robust optimization model, μ THV σ is the average temperature of the high-voltage winding. THV The variance of the high-voltage winding temperature; g r,4 (x r ) represents the fourth constraint in the robust optimization model, μ TLV σ is the average temperature of the low-voltage winding. TLV The variance of the low-voltage winding temperature; g r,5 (x r ) represents the fifth constraint in the robust optimization model, μ Tcl σ is the average temperature of the core column. Tcl The variance of the core column temperature; g r,6 (x r ) represents the sixth constraint in the robust optimization model, σ Pm The variance of power density; g r,7 (x r ) represents the seventh constraint in the robust optimization model, σ η Let Variance be the efficiency.

2. The robust optimization method for high-frequency transformers based on 6σ design according to claim 1, characterized in that, After iterative solution, the design scheme is output: the performance parameters of all schemes are compared, and the optimal design scheme is selected based on the actual situation, which is the final design scheme of the high-frequency transformer in the corresponding application scenario.

3. The robust optimization method for high-frequency transformers based on 6σ design according to claim 1, characterized in that, The steps for iteratively solving the robust optimization model are as follows: Step 5.1, Population Initialization: Define the high-frequency transformer design variable x = (x1, x2, ..., x...). p ) T And randomly generate an initial population P0 of size N; Step 5.2, Individual robustness assessment, considers the uncertainty distribution of performance parameters caused by design parameter fluctuations, and quantifies this distribution: Monte Carlo analysis is performed on each individual, and the performance output under noise disturbance is calculated based on the mathematical analytical calculation model; the mean, standard deviation, and constraint violation degree of the output objective function and performance index are used as input data for step 5.3, wherein the constraint violation degree is calculated as follows: Among them, v g,j (x) represents the degree of violation of the j-th constraint; v total (x) represents the total degree of constraint violation; g r,j (x) is the robustness value of the j-th constraint; g r min,j For the minimum value of the j-th constraint, g r max,j The maximum value of the j-th constraint; Step 5.3, Fast Non-Dominated Sort and Crowding Calculation: Calculate the mean μ of the objective function. f Standard deviation σ f Using the degree of constraint violation as input data, perform a fast non-dominated sort on population P0 and divide it into Pareto ranks F1, F2, ..., F k F1 is the first Pareto front; For each layer of nondominated solution F i Sort by objective function value in ascending order and calculate the crowding distance of individuals: Among them, C d (i) represents the crowding distance of the i-th individual; p represents the number of objective functions; f i n-1 f represents the (n-1)th individual with the i-th objective function; i n+1 f represents the (n+1)th individual with the i-th objective function; i max f is the maximum value of the objective. i min This is the minimum value of the objective; Step 5.4, Genetic Operations: When iterating to the kth iteration, genetic operators such as selection, crossover, and mutation are used to modify the parent population P. k Perform the operation to generate the offspring population Q. k and Q k Perform individual robustness assessments; Step 5.5, Population Merging: Merge parent generations P k With offspring Q k A mixed population R of size 2N is formed. k ; Step 5.6, Elite Retention and Selection: For R k Perform fast non-dominated sorting and crowding calculation, and select individuals to fill P according to Pareto level from low to high. k+1 When F i If the number of individuals in a layer exceeds the remaining capacity, then individuals in that layer are selected in descending order of crowding, up to P. k+1 The scale reaches N; Step 5.7 Termination Judgment: If the termination condition is met, output the non-dominated solution of the current population as the Pareto front solution set for the robust optimization design of high-frequency transformers; otherwise, increment the iteration count by 1, i.e., let k = k + 1, and return to step 5.4 to continue iterating.

4. The robust optimization method for high-frequency transformers based on 6σ design according to claim 1, characterized in that, The preliminary design scheme includes: selecting core material, structural type and winding type based on system requirements and performance indicators, and constructing the basic design framework for high-frequency transformers.

5. A robust optimization method for high-frequency transformers based on 6σ design according to claim 1 or 4, characterized in that, Before determining the preliminary design scheme, the system-level design requirements of the high-frequency transformer should be clarified based on the technical specifications of the application scenario.

6. The robust optimization method for high-frequency transformers based on 6σ design according to claim 1, characterized in that, The steps for determining the preliminary design scheme are as follows: Step 2.1: Select materials based on the power rating, operating frequency, and loss requirements of the high-frequency transformer; Step 2.2: Select the core structure based on comprehensive leakage inductance control, heat dissipation requirements, and space constraints; Step 2.3: Select the winding type based on current density, skin effect, and winding loss requirements.

7. The robust optimization method for high-frequency transformers based on 6σ design according to claim 1, characterized in that, The mathematical analytical calculation model includes: leakage inductance calculation, core loss calculation, temperature rise calculation, power density calculation, and efficiency calculation, wherein: Leakage inductance calculation, leakage inductance L of high-frequency transformer referred to the primary side. k The calculation is as follows: Among them, W iso Leakage magnetic energy storage in the primary and secondary side main insulation layers; W pri_ins For energy storage of leakage flux between layers of the primary winding, W sec_ins For energy storage of leakage flux between layers of the secondary winding; W pri W is used for energy storage through leakage magnetic flux inside the primary winding conductor. sec Energy storage for leakage flux inside the secondary winding conductor; I p This represents the effective value of the primary winding current. Core loss calculation: Among them, P c For core loss; B mr C represents the actual maximum operating magnetic flux density. m α, β are Steinmetz empirical coefficients; V c ρ is the volume of the iron core; core D is the core density; D is the duty cycle, taken as 1 for square wave; f s θ is the operating frequency; θ is the phase angle characterizing the periodic variation of magnetic flux. Winding loss calculation: P w =F r R dc I 2 ; Among them, R dc R is the DC resistance of the winding. ac F is the AC resistance of the winding. r I is the AC resistivity of the winding; I is the effective value of the current in each layer of the winding; P w For winding losses; Temperature rise calculation: Among them, T tr G is a column vector of temperatures at the core and winding nodes of a high-frequency transformer; T G is the thermal conductivity matrix of the transformer thermal network model; Ta P represents the thermal conductivity matrix between the transformer and the environment. Ta Transformer thermal power and ambient temperature T a Column vectors; Power density calculation: The power density of a high-frequency transformer is calculated as follows: m w =ρ w (N p A xp l m_p +N s A xs l m_s ); Where, m w ρ is the total weight of the winding; w The density of the material used in the winding; N p N represents the number of turns in the primary winding. s A is the number of turns in the secondary winding; xp A represents the total bare conductor area of ​​each turn of the primary winding. xs The total bare conductor area per turn of the secondary winding; l m_p l is the average turn length of the primary winding. m_s P is the average turn length of the secondary winding; m Power density; S n This refers to the rated capacity of the high-frequency transformer; m c This refers to the weight of the iron core; Efficiency calculation: The efficiency of a high-frequency transformer is calculated as follows: P t =P c +P w ; Among them, P t η represents total loss; η represents efficiency.

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