Multi-objective optimization mathematical model of high-frequency high-power three-phase transformer

Abstract

The high-frequency high-power three-phase transformer multi-objective optimization mathematical model selects core stack layers n c , core thickness A, secondary winding layers m2, secondary winding turns N l2 , primary winding flat copper wire thickness d f1 , secondary winding flat copper wire thickness d f2 and maximum current density J max as scanning parameters. A multi-objective optimization mathematical model with efficiency η and power density P s as optimization targets, with maximum allowable temperature rise, insulation level and leakage inductance parameters as constraint conditions, and the above 7 scanning parameters as independent variables is established to realize transformer design through a free parameter scanning method. The present application can accurately control the leakage inductance parameters of the flat copper wire winding, improve the power density and efficiency of the transformer, and reduce the calculation amount and calculation time required for optimization design.

Description

[0001] This is a divisional application for the patent titled "A design method for a high-frequency, high-power three-phase transformer" (application number: 202010773025.0; application date: August 4, 2020). Technical Field

[0002] This invention belongs to the field of high-frequency transformer design, specifically involving a multi-objective optimization mathematical model for a high-frequency, high-power three-phase transformer. Background Technology

[0003] DC-DC converter stages of solid-state transformers are generally classified as non-isolated and isolated. While non-isolated DC / DC converters based on all-power electronic devices achieve bidirectional flow of high-power DC, they cannot achieve electrical isolation. To address this issue, isolated DC / DC converters with magnetically coupled high-frequency transformers have received widespread attention. Currently, single-phase or three-phase isolated dual active bridge (DAB) DC / DC converters suitable for high-power transmission and satisfying bidirectional free flow of power have been applied to the DC-DC converter stages of solid-state transformers. These converters use single-phase or three-phase high-frequency transformers to achieve electrical isolation, increasing system reliability. Compared to single-phase DC / DC converter topologies, three-phase DC / DC converters offer significant advantages. They can not only significantly reduce the number of components such as high-frequency transformers, switching devices, communication systems, and auxiliary power supplies, thus reducing the size, weight, and cost of solid-state transformers, but also reduce the capacitance used to filter DC current ripple, lower circulating current power, and improve the efficiency and power density of solid-state transformers. Research on high-voltage, high-power three-phase DC / DC transformers has significant scientific and application value, and also shows promising application prospects.

[0004] In recent years, domestic and international research institutions have conducted extensive research on the structural design of high-frequency, high-power single-phase transformers in single-phase DC / DC converters, achieving fruitful results. However, the core topology, winding connection methods, and operating modes of high-frequency, high-power three-phase transformers differ from those of previous designs, and their internal electromagnetic effects are more complex. Therefore, existing theoretical formulas and design methods for core losses, winding losses, and temperature rise cannot be directly applied to optimize the design of high-frequency, high-power three-phase transformers. Although there is considerable research on three-phase DC / DC converters both domestically and internationally, most studies focus on the converter's control strategies and topology.

[0005] For example, in 2012, Li Hui et al. from Florida State University proposed a current-driven three-phase DC / DC converter. The YY connection method used in the high-frequency three-phase transformer has better current sharing capability compared to other connection methods. In 2020, Hu Jingxin et al. from RWTH Aachen University proposed a dual-sided single-phase phase-shifting operation mode that can eliminate DC bias magnetism during load abrupt changes or even instantaneous power flow reversal. Currently, there are very few documents available on the design methods of high-frequency high-power three-phase transformers. In 2010, North Carolina State University designed high-frequency three-phase transformers for two types of solid-state transformer topologies, using a five-limb core structure to solve the problems of harmonic flux and stray flux generated by unbalanced voltage. In 2018, Mitsubishi Electric and RWTH Aachen University jointly developed a shell-type high-frequency high-power three-phase transformer test model with rated parameters of 1.55kHz, 200kW, 1kV / 1kV. The core material was Vitroperm500F nanocrystalline cut core, and the winding conductor was Litz wire with a current carrying density of 1.7A / mm². Auxiliary inductors are added at the three-phase winding ports on the inverter side to achieve soft switching of the switching transistors. The auxiliary inductor loss accounts for 20% of the total loss. In 2019, Hu Jingxin et al. from RWTH Aachen University proposed a three-phase DC / DC converter based on a maximum output power point tracking strategy to integrate large-scale photovoltaic power generation into a medium-voltage DC grid. By comprehensively considering the electrical characteristics of the photovoltaic panels and the zero-voltage switching characteristics of the three-phase DC / DC converter, the leakage inductance and turns ratio of the high-frequency three-phase transformer are rationally designed to form a soft-switching region to match the operating region of the photovoltaic electric field, thereby achieving higher efficiency. The core topology of the high-frequency three-phase transformer test model is a three-phase five-limb type, with rated parameters of 20kHz, 1.38kW, 54V / 380V. The core is made of ferrite, and the windings are made of Litz wire. There are no detailed reports on the design method and implementation of the high-frequency three-phase transformer.

[0006] Therefore, this paper proposes a design theory for high-frequency, high-power three-phase transformers for solid-state transformer topologies, which is of great significance for the development of smart distribution networks and large-scale distributed renewable energy grid integration in my country. Summary of the Invention

[0007] This invention provides a design method for high-frequency, high-power three-phase transformers. Based on relevant formula derivations and specific design data, it derives conclusions regarding the optimized design of high-frequency, high-power three-phase transformers, providing support for subsequent engineering applications. This method can precisely control the leakage inductance parameters of the flat copper wire windings, improving the transformer's power density and efficiency while reducing the computational load and time required for optimization design.

[0008] The technical solution adopted in this invention is as follows:

[0009] A design method for a high-frequency, high-power three-phase transformer includes the following steps:

[0010] Step 1: Derive the winding current i LA Valid value expression I LA(rms) Using the fundamental frequency analysis method, the winding current i is derived. LA Expressions for the amplitudes of harmonic current components of each order;

[0011] Step 2: Derive the high-frequency loss P of the iron core under a six-step voltage excitation. c The expression for the high-frequency loss P of the primary and secondary windings of flat copper wire. wp P ws ;

[0012] Step 3: Derive the leakage inductance L of the high-frequency transformer using flat copper wire. σ(pri) expression;

[0013] Step 4: Determine the parameters of the high-frequency three-phase transformer system;

[0014] Step 5: Establish a system based on efficiency η and power density P s To optimize the objectives, a multi-objective optimization mathematical model is used with the maximum allowable temperature rise, insulation level, and leakage inductance parameters as constraints, and the scanning parameters as independent variables. The transformer design is achieved through the free parameter scanning method.

[0015] In step one, based on the winding current i of the high-frequency three-phase transformer... LA For piecewise linear waveforms, derive the winding current i. LA Valid value expression I LA(rms) for:

[0016]

[0017] In the formula: T s For periodicity; L σ(pri) The leakage inductance is calculated to the original side; V in V out These are the voltages across the converter; This is the phase shift angle between the gate signals of the inverter and rectifier side three-arm converters.

[0018] Winding current i LA The expressions for the amplitudes of each order harmonic current component are:

[0019]

[0020] In the formula: For V in The amplitude of the nth harmonic of the output voltage of the full-bridge inverter. For V outThe output voltage of the full-bridge inverter is converted to V. in The amplitude of the nth harmonic at the side and rear; L σ(pri) This is the leakage inductance that is returned to the original side.

[0021] The amplitude of the nth harmonic voltage is:

[0022]

[0023]

[0024] In the formula, ω is the angular frequency, ω=2πf s .

[0025] In step two, the high-frequency loss P of the iron core c for:

[0026]

[0027] In the formula, B max and B min These represent the maximum and minimum values ​​of the magnetic flux density waveform curve, respectively; T s For periodicity; B i+1 t i+1 B represents the magnitude of the magnetic flux density and the time corresponding to the inflection point of the (i+1)th magnetic flux density curve, respectively; i t i C represents the magnitude of the magnetic flux density and the time corresponding to the inflection point of the i-th magnetic flux density curve, respectively; m α and β are loss coefficients; k i The expression is as follows:

[0028]

[0029] The expression for the high-frequency loss P of the primary and secondary windings of flat copper wire wp P ws for:

[0030]

[0031]

[0032] In the formula, R represents the AC resistivity of the primary and secondary windings under the nth current harmonic, respectively. wpDC R wsDC Here, represents the DC resistance of the primary winding and the secondary winding, respectively, and N is the highest order of harmonic convection; N w This represents the turns ratio of the primary winding to the secondary winding.

[0033] The calculation formula is as follows:

[0034] In the formula, σw N is the conductivity of the winding conductor. l1 and N l2 , respectively, represent the number of turns per layer of the primary and secondary windings; m1 and m2 represent the number of layers of the primary and secondary windings; MTL1 and MTL2 represent the average turn length of the primary and secondary windings; d f1 and d f2 h represents the thickness of the original secondary flat copper wire. f1 and h f2 This refers to the width of the original secondary flat copper wire.

[0035] The formulas for calculating the AC resistivity of the primary and secondary windings under the nth current harmonic are as follows:

[0036]

[0037]

[0038] In the formula, m1 and m2 are the number of layers in the primary and secondary windings, respectively; μ0 is the permeability of the winding material; R wpn and R wsn The primary and secondary windings at the nth harmonic frequency nf are respectively s The AC resistance below; R wpDC and R wsDC Δ1 and Δ2 are the DC resistances of the primary and secondary windings, respectively; Δ1 and Δ2 are the normalized thicknesses of the flat copper wire windings with respect to the skin depth at the fundamental frequency component, respectively, and their expressions are as follows:

[0039]

[0040]

[0041] In the formula, d f1 and d f2 h represents the thickness of the original secondary flat copper wire. f1 and h f2 N is the width of the original secondary flat copper wire; l1 and N l2 These represent the number of turns per layer of the primary and secondary windings, respectively; h w1 and h w2 These are the heights of the primary and secondary windings, respectively; σ w μ is the electrical conductivity of copper; μ0 is the magnetic permeability in vacuum, μ0 = 4π × 10⁻⁶. -7 H / m; f s The frequency of the sinusoidal alternating current is denoted as .

[0042] In step three, the leakage inductance L of the high-frequency transformer using flat copper wire is used. σ(pri) The expression is:

[0043]

[0044] In the formula, MTL is the average turn length of the winding;

[0045] γ is the complex propagation constant, γ=(1+j) / δ w δ w For skin depth, j represents the imaginary sign, j 2 =-1.

[0046] d ins1 and d ins2 d represents the interlayer insulation thickness of the primary and secondary windings. iso This is the isolation distance between the primary and secondary windings;

[0047] d f1 and d f2 The thickness of the original secondary side flat copper wire;

[0048] N l1 m1 represents the number of turns per layer of the primary winding; m2 and m1 represent the number of layers of the primary and secondary windings, respectively.

[0049] h w The height of the iron core window;

[0050] k p1 k p2 k s1 and k s2 The calculation formula is as follows:

[0051] k p1 =sinh(2d f1 γ)-2d f1 γ

[0052] k p2 =sinh(2d f2 γ)-2d f2 γ

[0053] k s1 =d f1 γcosh(d f1 γ)-sinh(d f1 γ)

[0054] k s2 =d f2 γcosh(d f2 γ)-sinh(d f2 γ)

[0055] Skin depth δ w The expression is:

[0056]

[0057] In the formula, ρ w The resistivity of copper; σ wμ is the electrical conductivity of copper; μ0 is the magnetic permeability in vacuum, μ0 = 4π × 10⁻⁶. -7 H / m; f s The frequency of the sinusoidal alternating current is denoted as .

[0058] In step four, based on the determined three-phase dual-active full-bridge DC-DC converter and phase-shift control strategy, the parameters of the high-frequency three-phase transformer system are determined, including the active power P transmitted by the converter. n DC voltage V of the three-bridge arm voltage source converter on both sides in and V out Transformer ratio N w Maximum permissible temperature rise T of high-frequency transformer rmax Operating frequency f s Leakage inductance parameter L σ(pri) Phase shift angle

[0059] In step five, the scanning parameters include: the number of core stacking layers n. c Core thickness A, number of secondary winding layers (m2), number of secondary winding turns (N) l2 d, thickness of flat copper wire in primary winding f1 d, thickness of flat copper wire in secondary winding f2 Maximum current carrying density J max .

[0060] In step five, the multi-objective optimization mathematical model with the scanning parameters as independent variables is as follows:

[0061]

[0062] In the formula, P c P represents the core loss of the transformer. wp and P ws For the losses of the primary and secondary windings; V box L represents the volume of the transformer. σ This is the actual value of the leakage inductance; L σt P is the target design value for leakage inductance. n Rated power;

[0063] The constraints are as follows:

[0064]

[0065] In the formula, x i Let x be the i-th variable to be optimized, with an upper limit value. imax The lower limit of the value is x imin ; △T r and △T max These are the maximum temperature rise and the maximum allowable temperature rise, respectively; d isoThe distance between the primary and secondary windings, considering the limitations of the withstand voltage level, cannot be less than the minimum isolation distance d between the primary and secondary windings. iso-min .

[0066] In step five, the calculation process of the free parameter scanning method is as follows:

[0067] Step (1): Enumerate all candidate solutions one by one and calculate the core and winding dimensions;

[0068] Step (2): Calculate the core loss and winding loss of the high-frequency, high-power three-phase transformer, as well as the maximum temperature rise;

[0069] Step (3): Calculate the leakage inductance parameters of the high-frequency, high-power three-phase transformer;

[0070] Step (4): Determine whether the candidate solution meets the requirements of maximum allowable temperature rise and insulation voltage withstand capability.

[0071] This process is iterated repeatedly until all candidate solutions have been enumerated, at which point the optimized design result of the three-phase transformer can be obtained. This invention provides a high-frequency, high-power three-phase transformer design method, with the following technical advantages:

[0072] 1. This invention aims to optimize maximum power density, maximum efficiency, and precise control of leakage inductance. It uses the number of core lamination layers, core thickness, number of secondary winding layers, number of turns in the secondary winding, thickness of the primary winding flat copper wire, thickness of the secondary winding flat copper wire, and maximum current carrying capacity of the high-frequency three-phase transformer as scanning parameters, with maximum allowable temperature rise and insulation level as constraints. This method can be applied to the optimized design of high-frequency three-phase transformers with a three-phase five-limb core topology and flat copper conductors. It can accurately control the leakage inductance parameters of the transformer, effectively reduce the amount of calculation, save calculation time, and is convenient and fast, thus benefiting engineering applications.

[0073] 2: This invention is applied to the optimization design of high-frequency high-power three-phase transformers in three-phase dual active bridge DC-DC converters in solid-state transformers. It can accurately calculate the high-frequency core loss and high-frequency winding loss under six-level stepped voltage wave excitation, and can precisely control the leakage inductance parameters of flat copper wire windings, thereby improving the power density and efficiency of high-frequency high-power three-phase transformers. It is convenient, fast, and beneficial for engineering applications. Attached Figure Description

[0074] Figure 1 It is a solid-state transformer based on a three-phase dual active full-bridge DC-DC converter.

[0075] Figure 2 This is a flowchart illustrating the optimized design of the high-frequency, high-power three-phase transformer of this invention.

[0076] Figure 3(a) is a front view of the design structure of a three-phase five-column high-frequency high-power three-phase transformer;

[0077] Figure 3(b) is a side view of the design structure of a three-phase five-column high-frequency high-power three-phase transformer;

[0078] Figure 3(c) is a top view of the design structure of a three-phase five-column high-frequency high-power three-phase transformer;

[0079] Figure 3(d) shows the structure of the flat copper wire in the primary winding;

[0080] Figure 3(e) is a diagram of the flat copper wire structure of the secondary winding.

[0081] Figure 4 The waveform of magnetic flux density under six-step voltage wave excitation is shown.

[0082] Figure 5 The steady-state voltage and current waveforms of the DAB3-IBDC converter are shown.

[0083] Figure 6(a) is a schematic diagram of the winding arrangement inside the core window;

[0084] Figure 6(b) shows the magnetic field intensity distribution inside the iron core window.

[0085] Figure 7 This is a scatter plot showing the power density, efficiency, and temperature rise of a high-frequency, high-power three-phase transformer.

[0086] Figure 8(a) is a cloud map of the magnetic flux density distribution in the core of a high-frequency, high-power three-phase transformer model;

[0087] Figure 8(b) is a cloud map showing the core loss density distribution of a high-frequency, high-power three-phase transformer model;

[0088] Figure 8(c) is a cloud map showing the leakage magnetic field intensity distribution in the conductor region of a high-frequency, high-power three-phase transformer model;

[0089] Figure 8(d) is a cloud map showing the winding loss density distribution of a high-frequency, high-power three-phase transformer model.

[0090] Figure 8(e) is a simulation diagram of the temperature rise of a high-frequency, high-power three-phase transformer model. Detailed Implementation

[0091] A solid-state transformer topology based on a three-phase dual-active full-bridge DC-DC converter as the basic module is as follows: Figure 1As shown, a series connection is used on the high-voltage side to increase the voltage level, and a parallel connection is used on the low-voltage side to increase the power level. The three-phase dual active full-bridge DC-DC converter consists of a high-frequency three-phase transformer T, an inductor L, three-leg voltage source inverters (3-leg VSLs) at both ends of the transformer, and DC filter capacitors C1 and C2. The switching transistors of the three-leg voltage source are all connected in parallel with Snubber capacitors to achieve zero-voltage turn-on and turn-off of the transistors. The phase shift angle between the gate signals of the inverter and rectifier side three-leg inverters is adjusted. Control the direction of power flow. V in and V out The voltage across the converter; u AS u BS u CS and i LA i LB and i LC V in The inverter output voltage and current of the A, B, and C phases of the three-bridge arm voltage source converter; u as u bs and u cs and i La i Lb and i Lc V out The inverter output voltage and current of the three phases (a, b, and c) of the side three-arm voltage source converter.

[0092] The optimization design process for high-frequency, high-power three-phase transformers is as follows: Figure 2 As shown in Figures 3(a), 3(b), 3(c), 3(d), and 3(e), the structural schematic diagrams of a high-frequency, high-power three-phase transformer are presented. Flat copper wire is selected for the primary and secondary windings because it has advantages such as high current-carrying capacity, large fill factor, low loss, and good heat dissipation performance.

[0093] Select the number of core stacking layers n c Core thickness A, number of secondary winding layers (m2), number of secondary winding turns (N) l2 d, thickness of flat copper wire in primary winding f1 d, thickness of flat copper wire in secondary winding f2 and maximum current carrying density J max As scanning parameters, establish the efficiency η and power density P. s To optimize the objectives, with the maximum allowable temperature rise, insulation level, and leakage inductance parameters as constraints, the following multi-objective optimization mathematical model is established with the above seven scanning parameters as independent variables:

[0094]

[0095] In the formula, f1, f2, and f3 are the three objective functions for efficiency, power density, and leakage inductance, respectively; P c P represents the core loss of the transformer. wp and P ws For the losses of the primary and secondary windings; P n Rated power; V box L represents the volume of the transformer. σ This is the actual value of the leakage inductance; L σt This is the target design value for leakage inductance.

[0096] The constraints are as follows:

[0097]

[0098] In the formula, x i Let x be the i-th variable to be optimized, with an upper limit value. imax The lower limit of the value is x imin ; △T r and △T max These are the maximum temperature rise and the maximum allowable temperature rise, respectively; d iso The distance between the primary and secondary windings, considering the limitations of the withstand voltage level, cannot be less than the minimum isolation distance d between the primary and secondary windings. iso-min .

[0099] First step: System parameter selection:

[0100] Based on the determined power electronic topology of the three-phase dual-active full-bridge DC-DC converter and the phase-shift control strategy, the system parameters are determined, mainly including the active power P transmitted by the converter. n DC voltage V of the three-bridge arm voltage source converter on both sides in and V out Transformer ratio N w Maximum permissible temperature rise T of high-frequency transformer rmax Operating frequency f s Leakage inductance parameter L σ(pri) Phase shift angle

[0101] To achieve zero-voltage switching of the switching transistors, the phase shift angle between the two high-frequency full-bridge sections is... It must be greater than the minimum phase shift angle. The minimum phase shift angle can be expressed as:

[0102]

[0103] In the formula, t is the DC-DC conversion ratio, which is the maximum deviation between the actual output voltage and the rated voltage.

[0104] To improve system power density, the leakage inductance of the windings can be precisely controlled during the design phase, replacing the auxiliary inductance required for soft switching by the switching transistor. This transforms the two discrete components of the transformer and inductor into a single integrated magnetic component. For the YY winding connection, the minimum leakage inductance required for soft switching is expressed as follows:

[0105]

[0106] In the formula, V in V is the DC voltage at the input side of the converter; o ′ ut This is the DC voltage at the output side, which is then referred to the input side. ω is the phase shift angle between the gated signals of the inverter and rectifier three-arm converters; ω is the angular frequency, ω=2πf s ;P n The active power transmitted by the converter.

[0107] Step 2: Calculation of core and winding dimensions:

[0108] Based on the parametric scanning method, numerous candidate solutions are enumerated and verified one by one to determine the optimal solution set that satisfies various constraints. Under six-level stepped voltage excitation, the cross-sectional area A of the core column of a high-frequency three-phase transformer is derived. c Frequency f s With B m Relationship:

[0109]

[0110] In the formula, V out k is the DC voltage on the output side. c m2 is the core fill factor; m2 is the number of layers in the secondary winding; N l2 B is the number of turns per layer of the secondary winding; m f is the peak magnetic flux density; s For frequency.

[0111] Based on the cross-sectional area of ​​the core post, the core width B can be obtained as follows:

[0112]

[0113] In the formula, A c Where A is the cross-sectional area of ​​the core column of a high-frequency three-phase transformer; n is the core thickness; c This represents the number of layers stacked on the iron core.

[0114] Width of the flat copper wire in the primary and secondary windings:

[0115]

[0116]

[0117] In the formula, h b1 and h b2 These represent the widths of the flat copper wires in the primary and secondary windings, respectively; d ins-int1 and d ins-int2 These are the self-insulation thicknesses of the primary and secondary windings, respectively; d f1 and d f2 These represent the thicknesses of the flat copper wires in the primary and secondary windings, respectively; I LA(rms)1 and I LA(rms)2 J represents the effective values ​​of the primary and secondary winding currents; max This represents the maximum current carrying capacity.

[0118] Based on the winding current i of the high-frequency three-phase transformer LA To derive the effective value I of the primary and secondary winding currents as a piecewise linear waveform. LA(rms)1 and I LA(rms)2 The expression:

[0119]

[0120] I LA(rms)2 =N w I LA(rms)1 (10)

[0121] In the formula, N w T is the turns ratio of the primary and secondary windings; s For periodicity; L σ(pri) The leakage inductance is calculated to the original side; V in and V out The voltage across the converter; This is the phase shift angle between the gate signals of the inverter and rectifier side three-arm converters.

[0122] The height of the iron core window is

[0123]

[0124] In the formula, d ins-int2 d is the self-insulation thickness of the secondary winding; ch h is the distance from the end of the secondary winding to the upper and lower yokes. w2 The height of the secondary winding is calculated using the following formula:

[0125] h w2 =(N l2 +1)h b2 +N l2 d t2 -2d ins-int2 (12)

[0126] In the formula, N l2 h is the number of turns per layer of the secondary winding.b2 d is the width of the secondary winding conductor; t2 d is the distance between the secondary winding conductors; ins-int2 This refers to the self-insulation thickness of the secondary winding.

[0127] Number of turns N per layer of primary winding l1 The number of floors and height are:

[0128]

[0129] In the formula, h w2 h is the height of the secondary winding. b1 d is the width of the primary winding conductor; t1 This represents the distance between the primary winding conductors.

[0130] The number of layers m1 in the primary winding is:

[0131]

[0132] In the formula, N w N is the turns ratio of the primary and secondary windings; l1 N represents the number of turns per layer of the primary winding. l2 m1 represents the number of turns per layer of the secondary winding; m2 represents the number of layers of the secondary winding.

[0133] The height h of the primary winding w1 for:

[0134] h w1 =(N l1 +1)h b1 +N l1 d t1 -2d ins-int1 (15)

[0135] In the formula, N l1 h is the number of turns per layer of the primary winding. b1 d is the width of the primary winding conductor; t1 d is the distance between the primary winding conductors; ins-int1 This is the self-insulation thickness of the primary winding.

[0136] Step 3: Calculation of Losses and Maximum Temperature Rise:

[0137] 1) Core loss:

[0138] against Figure 4 The flux density waveform under six-step voltage excitation is shown. The high-frequency loss P of the iron core under six-step voltage excitation is derived. c :

[0139]

[0140] In the formula, Bmax and B min These represent the maximum and minimum values ​​of the magnetic flux density waveform curve, respectively; T s For periodicity; (B) i ,t i ) represents the i-th inflection point of the piecewise linear magnetic flux density waveform; C m α and β are loss coefficients; k i The expression is as follows:

[0141]

[0142] 2) Winding losses:

[0143] High-frequency loss expression for flat copper wire P wp and P ws :

[0144]

[0145]

[0146] In the formula, R represents the AC resistivity of the primary and secondary windings under the nth current harmonic, respectively. wpDC R wsDC The DC resistances of the primary and secondary windings are respectively, and the calculation formulas are as follows:

[0147]

[0148]

[0149] In the formula, σ w N is the conductivity of the winding conductor. l1 and N l2 , respectively, represent the number of turns per layer of the primary and secondary windings; m1 and m2 represent the number of layers of the primary and secondary windings; MTL1 and MTL2 represent the average turn length of the primary and secondary windings; d f1 and d f2 h represents the thickness of the original secondary flat copper wire. f1 and h f2 This refers to the width of the original secondary flat copper wire.

[0150] Using fundamental frequency analysis method, for Figure 5 The non-sinusoidal current waveform shown is used to derive the winding current i. LA Expressions for the amplitudes of harmonic current components of each order;

[0151]

[0152] In the formula, For V in The amplitude of the nth harmonic of the output voltage of the full-bridge inverter. For V out The output voltage of the full-bridge inverter is converted to V. in The amplitude of the nth harmonic at the side and rear; L σ(pri) The leakage inductance is calculated to the original side; n is the order of the harmonic current.

[0153] The amplitude of the nth harmonic voltage is:

[0154]

[0155]

[0156] In the formula, V in V is the DC voltage at the input side of the converter; out N is the DC voltage at the output side of the converter. w The turns ratio of the primary and secondary windings; n is the order of the harmonic current; ω is the angular frequency, ω = 2πf s .

[0157] The formulas for calculating the AC resistivity of the primary and secondary windings under the nth current harmonic are as follows:

[0158]

[0159]

[0160] In the formula, m1 and m2 are the number of layers in the primary and secondary windings, respectively; R wpn and R wsn The primary and secondary windings at the nth harmonic frequency nf are respectively s The AC resistance below; R wpDC and R wsDC Δ1 and Δ2 are the DC resistances of the primary and secondary windings, respectively; Δ1 and Δ2 are the normalized thicknesses of the flat copper wire windings with respect to the skin depth at the fundamental frequency component, respectively, and their expressions are as follows:

[0161]

[0162]

[0163] In the formula, d f1 and d f2 h represents the thickness of the original secondary flat copper wire. f1 and h f2 N is the width of the original secondary flat copper wire; l1 and N l2 These represent the number of turns per layer of the primary and secondary windings, respectively; h w1 and h w2 These are the heights of the primary and secondary windings, respectively; σ w μ is the electrical conductivity of copper; μ0 is the magnetic permeability in vacuum, μ0 = 4π × 10⁻⁶. -7H / m; f s The frequency of the sinusoidal alternating current is denoted as .

[0164] 3) Maximum temperature rise:

[0165] Temperature rise T in °C r The calculation formula is as follows:

[0166]

[0167] In the formula, F Fe F is the scattering area of ​​the iron core; Cu P represents the heat dissipation area of ​​the coil. c P represents the core loss of the transformer. wp and P ws This refers to the losses in the primary and secondary windings.

[0168] Step 4: Leakage inductance calculation:

[0169] Based on the leakage magnetic field intensity distribution of the core window shown in Figure 6, the leakage magnetic field energy method was used to derive the leakage inductance L of the high-frequency transformer with flat wire. σp The expression is:

[0170]

[0171] In the formula, MTL is the average turn length of the winding; γ is the complex propagation constant, γ=(1+j) / δ w δ w For skin depth; d ins1 and d ins2 d represents the interlayer insulation thickness of the primary and secondary windings. iso d is the isolation distance between the primary and secondary windings; f1 and d f2 The thickness of the primary and secondary flat copper wire; N l1 m1 is the number of turns per layer of the primary winding; m2 and m1 are the number of layers of the primary and secondary windings, respectively; h w For the height of the iron core window; k p1 k p2 k s1 and k s2 The calculation formula is as follows:

[0172] k p1 =sinh(2d f1 γ)-2d f1 γ (31)

[0173] k p2 =sinh(2d f2 γ)-2d f2 γ (32)

[0174] k s1=d f1 γcosh(d f1 γ)-sinh(d f1 γ) (33)

[0175] k s2 =d f2 γcosh(d f2 γ)-sinh(d f2 γ) (34)

[0176] In the formula, d f1 and d f2 The thickness of the primary and secondary flat copper wires is γ; γ is the complex propagation constant, γ=(1+j) / δ w δ w For skin depth.

[0177] Skin depth δ w The expression is:

[0178]

[0179] In the formula, ρ w The resistivity of copper; σ w μ is the electrical conductivity of copper; μ0 is the magnetic permeability in vacuum, μ0 = 4π × 10⁻⁶. -7 H / m; f s The frequency of the sinusoidal alternating current is denoted as .

[0180] Using the above optimized design method, a high-frequency three-phase high-frequency transformer was designed and manufactured, with a rated active power of 15kW, an operating frequency of 5kHz, and a voltage rating of 500V / 500V. Ambient temperature T am The maximum allowable temperature rise is ΔT at 40℃. rmax

[0181] The temperature is 80℃. The minimum phase shift angle is 0.2618 rad, and the leakage inductance is 86.81 μH. The electrical parameters are shown in Table 1.

[0182] Table 1 Electrical Specifications

[0183] <![CDATA[Rated power P n / kW]]> 15 <![CDATA[Primary winding voltage U ac1 / V]]> 500 <![CDATA[Secondary winding voltage U ac2 / V]]> 500 <![CDATA[Leakage inductance L referred to the primary side σ1 / μH]]> 86.81 <![CDATA[Isolation voltage V iso / kV]]> 3.2 Operating frequency f / kHz 5

[0184] Following the optimization design process for high-frequency, high-power three-phase transformers, a design scheme that meets the constraints is obtained. Figure 7 The power density, efficiency, and temperature rise of each design scheme are shown in Table 2. Different points represent different design schemes, and colors represent the maximum temperature rise. Table 2 provides a set of design parameters for a high-frequency three-phase transformer model.

[0185] Table 2 Design parameters for high-frequency three-phase transformer model

[0186] <![CDATA[(A / B / C / D / D1) / mm]]> 18 / 40 / 43 / 68.28 / 36.64 <![CDATA[P c / W]]> 146.12 <![CDATA[n c ]]> 1 <![CDATA[P w1 / W]]> 43.9 <![CDATA[m1×N l1 ]]> 3×8 <![CDATA[P w2 / W]]> 23.74 <![CDATA[m2×N l2 ]]> 4×6 <![CDATA[B m / T]]> 0.97 <![CDATA[(d f1 ×h f1 ) / mm 2 ]]> 1×4 efficiency / % 98.6 <![CDATA[(d f2 ×h f2 ) / mm 2 ]]> 1×4 <![CDATA[Power Density / (MW / m 3 )]]> 8.29 <![CDATA[d iso / mm]]> 16.8 Maximum temperature / °C 97.34

[0187] The finite element method was used to perform transient electromagnetic field-temperature field coupling calculations on core losses and winding losses. Figure 8(a) shows the magnetic flux density distribution cloud map of the core of the high-frequency high-power three-phase transformer model. Figure 8(b) shows the core loss density distribution cloud map of the high-frequency high-power three-phase transformer model. Figure 8(c) shows the leakage magnetic field intensity distribution cloud map of the conductor region of the high-frequency high-power three-phase transformer model. Figure 8(d) shows the winding loss density distribution cloud map of the high-frequency high-power three-phase transformer model. Figure 8(e) shows the temperature rise simulation diagram of the high-frequency high-power three-phase transformer model. Table 3 compares the design values ​​and simulation values ​​of core losses, winding losses, and maximum temperature.

[0188] Table 3 Comparison of Core Loss and Winding Loss of High-Frequency Three-Phase Transformers

[0189] Core loss / W 146.12 149.45 2.23 Winding loss / W 67.64 77.62 12.85 Temperature / °C 97.34 98.85 1.53

[0190] This invention is particularly suitable for the optimized design of high-frequency, high-power three-phase transformers used in three-phase dual-active full-bridge DC-DC converters in solid-state transformers. The winding conductors use flat copper wire, and the core structure adopts a three-phase five-limb topology. Because this invention addresses the steady-state voltage and current waveforms under the power electronic topology and phase-shift control mode of the three-phase dual-active full-bridge DC-DC converter, it derives expressions for high-frequency core losses and high-frequency winding losses under six-step voltage excitation; for the flat copper wire windings, it derives the leakage inductance expression; and to avoid the influence of harmonic and stray magnetic flux on the magnetic flux density waveform, a three-phase five-limb core topology is chosen, with the side yokes on both sides serving as pathways for stray magnetic flux.

[0191] This invention enables precise control of leakage inductance, ensuring that the losses, efficiency, and temperature rise of high-frequency, high-power three-phase transformers meet the standards required by the project.

Claims

1. A modeling method for a multi-objective optimization mathematical model of a high-frequency, high-power three-phase transformer, characterized in that: Select the number of core layers Core thickness Number of layers in the secondary winding Number of turns in the secondary winding Primary winding flat copper wire thickness Thickness of flat copper wire in secondary winding and maximum current carrying density As a scanning parameter; establish efficiency and power density P s To optimize the objective, with the maximum allowable temperature rise, insulation level, and leakage inductance parameters as constraints, the following multi-objective optimization mathematical model is established with the above seven scanning parameters as independent variables: ； In the formula, This refers to the core loss of the transformer; and The losses are those of the primary and secondary windings; This refers to the volume of the transformer; This is the actual value of the leakage inductance; This is the target design value for leakage inductance; Rated power; The constraints are as follows: ； In the formula, For the first i There are 1 variable to be optimized, with an upper limit value of 1. The lower limit of the value is ; and These are the maximum temperature rise and the maximum permissible temperature rise, respectively. The distance between the primary and secondary windings, considering the limitations of the withstand voltage level, cannot be less than the minimum isolation distance between the primary and secondary windings. ; High-frequency loss of iron core for: ； In the formula, and These represent the maximum and minimum values ​​of the magnetic flux density waveform curve, respectively. For periodicity; The first piecewise linear magnetic flux density waveform i One turning point; , , This is the loss coefficient; Expressions for high-frequency losses of primary and secondary windings of flat copper wire , for: ； ； In the formula, , These are the primary winding and the secondary winding, respectively. n AC resistivity under sub-current harmonics; R wpDC , R wsDC These are the DC resistances of the primary winding and the secondary winding, respectively. This is the highest order of harmonic convection; This represents the turns ratio of the primary winding to the secondary winding.

2. The modeling method for a multi-objective optimization mathematical model of a high-frequency, high-power three-phase transformer according to claim 1, characterized in that: The expression is as follows: ； set up: The conductivity of the winding conductor; and These represent the number of turns per layer of the primary and secondary windings, respectively. and These represent the number of layers in the primary and secondary windings, respectively. and These are the average turn lengths of the primary and secondary windings, respectively. d f1 and d f2 The thickness of the original secondary side flat copper wire; and This refers to the width of the original secondary side flat copper wire; The primary and secondary windings in the first n The formulas for calculating the AC resistivity under sub-current harmonics are as follows: ； ； In the formula, and These represent the number of layers in the primary and secondary windings, respectively. μ 0 represents the permeability of the winding material; and The primary and secondary windings are respectively in the th n Subharmonic frequency AC resistance below; and These are the DC resistances of the primary and secondary windings, respectively; and These are the normalized thicknesses of the flat copper wire windings with respect to the skin depth at the fundamental frequency component, respectively, and are expressed as follows: ； ； In the formula, d f1 and d f2 The thickness of the original secondary side flat copper wire; and This refers to the width of the original secondary side flat copper wire; and These represent the number of turns per layer of the primary and secondary windings, respectively. and These are the heights of the primary and secondary windings, respectively; The conductivity of copper; Permeability in vacuum The frequency of the sinusoidal alternating current is denoted as .

3. The modeling method for a multi-objective optimization mathematical model of a high-frequency, high-power three-phase transformer according to claim 1, characterized in that: Leakage inductance of high-frequency transformers using flat copper wire The expression is: ； In the formula, MTL is the average turn length of the winding; Let be the complex propagation constant. γ= (1+j) / δ w , δ w For deeper skin penetration; d ins1 and d ins2 This refers to the interlayer insulation thickness of the primary and secondary windings; d iso This is the isolation distance between the primary and secondary windings; d f1 and d f2 The thickness of the original secondary side flat copper wire; N l1 This refers to the number of turns per layer of the primary winding; m 1 and m 2 represents the number of layers in the primary and secondary windings, respectively; h w The height of the iron core window; , , and The calculation formula is as follows: ； ； ； ； Skin depth The expression is: ； In the formula, The resistivity of copper; The conductivity of copper; Permeability in vacuum; The frequency of the sinusoidal alternating current is denoted as .

4. The modeling method for a multi-objective optimization mathematical model of a high-frequency, high-power three-phase transformer according to claim 1, characterized in that: The calculation process of the parameter scan method is as follows: Step (1): Enumerate all candidate solutions one by one and calculate the core and winding dimensions; Step (2): Calculate the core loss and winding loss of the high-frequency, high-power three-phase transformer, as well as the maximum temperature rise; Step (3): Calculate the leakage inductance parameters of the high-frequency, high-power three-phase transformer; Step (4): Determine whether the candidate solution meets the requirements of maximum allowable temperature rise and insulation voltage withstand capability; This process is repeated iteratively until all candidate solutions are enumerated, resulting in the optimized design of the three-phase transformer.

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