Optimization design method for high-power high-frequency magnetic resonance air-core transformer

Abstract

This high-power, high-frequency magnetic resonant air-core transformer optimization design method determines the optimal winding connection method and the relative current flow between the two coils of the air-core transformer (ACT). Using air as the insulating medium, the isolation distance between the primary and secondary windings is calculated, and NOMEX is placed between the two coils and between the layers. The design parameters of the air-core transformer (ACT) are determined, and the electromagnetic parameters normalized to a single turn for different structures are extracted. The system parameters of all air-core transformers (ACT) are calculated, and the high-frequency loss of the Litz wire is calculated. All obtained design results are optimized from the perspectives of frequency, loss, and heat dissipation. The appropriate air-core transformer (ACT) structure is selected based on the Parato multi-objective optimization design results. This design method can provide guidance and reference for key issues involved in the ACT design process, such as winding arrangement and connection method, insulation and cooling design, and magnetic shielding design.

Description

Technical Field

[0001] The present invention relates to the field of air-core transformer design, and in particular to an optimization design method for a high-power high-frequency magnetic resonance air-core transformer. Background Art

[0002] DC-DC converters play a vital role in a wide range of modern energy conversion systems and are widely used in renewable energy generation, powering large data centers, charging electric vehicles, and electric propulsion aircraft. Solid-state transformers (SSTs) are core components of DC-DC converters. To reduce transformer weight and improve converter compactness, SSTs are typically fabricated as medium- and high-frequency magnetic core transformers (MCTs). As MCT capacitance increases, frequencies rise, and magnetic circuit structures shrink, cooling and insulation issues arise, increasing the complexity of MCT design and processing. Furthermore, the mass of the magnetic core and insulation materials limits the power density of MCTs, hindering their potential in applications with stringent load requirements, such as aerospace. Compared to MCTs, air-core transformers (ACTs) offer numerous advantages. ACTs, consisting solely of primary and secondary windings, simplify heat dissipation and insulation design. They avoid core-induced hysteresis losses, eddy current losses, and vibration noise. They are lightweight, facilitating high weight-to-power density. These advantages make ACTs of significant research interest and offer significant potential for application.

[0003] There are two common types of ACT winding structures: disc coil and cylindrical coil.

[0004] (I) In terms of disc coils, the literature [1]: R. Bosshard, J. W. Kolar, and J. Muehlethaler, Modeling and η-α-Pareto Optimization of Inductive Power Transfer Coils for Electric Vehicles [J] IEEE Trans. Emerg. Sel. Topics Power Electron, 2015, 3(1), 50–64. proposed for the first time a multi-objective optimization design process for the inductive power transfer (IPT) system, and introduced in detail key issues such as the selection of resonance compensation methods and how to establish a planar coil parameterized simulation model. The feasibility of the design method was verified by building a 5kW IPT system.

[0005] Reference [2]: Bosshard R and Kolar JW, Multi-Objective Optimization of 50kW / 85kHz IPT System for Public Transport [J]. IEEE Journal of Emerging & Selected Topics in Power Electronics, 2016, 4(4), 1370-1382. A prototype design of an electric vehicle charging system with a transmission power of 50kW was realized, and the overall efficiency of the DC-DC converter reached 95.8%.

[0006] Reference [3]: Zhou H, Chen J, and Deng Q, Input-Series Output-Equivalent-Parallel Multi-Inverter System for High-Voltage and High-Power Wireless Power Transfer[J]. IEEE Transactions on Power Electronics, 2021, 36(1), 228-238. An input series output equivalent parallel multi-inverter system for IPT was designed. The system can achieve input side voltage balancing and 40kW transmission power, but the system efficiency is only 89.31%.

[0007] The commonality among the aforementioned papers is that they all employ a planar coil structure. This type of coil has only two degrees of freedom, and the effects of coil misalignment and low coupling coefficient on transmission efficiency must be considered. To improve transmission efficiency, planar coils often use ferromagnetic materials to guide the magnetic field, but this is not conducive to achieving high weight-to-power density. Without the use of any magnetic material, the efficiency achieved by planar coils is unsatisfactory.

[0008] (2) In terms of cylindrical coils, the literature [4]: ​​P. Czyz, T. Guillod, F. Krismer and J. W. Kolar, Exploration of the Design and Performance Space of a High Frequency 166 kW / 10 kV SiC Solid-State Air-Core Transformer [C] 2018 International Power Electronics Conference (IPEC-Niigata 2018-ECCE Asia), 2018, 396-403. proposed the use of two coaxial cylindrical windings to achieve energy transmission in high-frequency and high-power systems. This type of winding structure does not require any magnetic material to guide the magnetic field and can achieve an efficiency of more than 99% at a transmission power of 166 kW.

[0009] References [5]: P.Czyz, T.Guillod, and F.Krismer, Design and Experimental Analysis of 166kW Medium-Voltage Medium-Frequency Air-Core Transformer for 1:1-DCX Applications[J]in IEEE Journal of Emerging and Selected Topics in PowerElectronics, 2022, 10(4), 3541-3560. and [6] T.Guillod, P.Czyz and JWKolar, Geometrical Optimization of Medium-Frequency Air-Core Transformers for DCXApplications[J]in IEEE Journal of Emerging and Selected Topics in PowerElectronics, 2022, 10(4), 4319-4335. For cylindrical windings of different structures, weight power densities of up to 16.5kW / kg and 31kW / kg were achieved respectively through multi-objective optimization design, which is more than twice that of MCT with the same capacity. However, shielding designed to suppress magnetic leakage fields reduces the volumetric power density of the ACT. Furthermore, the complex magnetic field of the ACT is difficult to approximate using an accurate analytical model. Therefore, current ACT optimization design almost always relies on finite element analysis tools. Summary of the Invention

[0010] To further explore the design methods and performance space of high-power, high-frequency magnetic resonant ACTs, this paper proposes an optimization design method for high-power, high-frequency magnetic resonant ACTs based on a parametric sweep method and orthogonal experimental methods, targeting issues such as the crossing method of two sets of coaxial cylindrical windings, calculation of high-frequency losses of Litz wires, modeling and simulation, cooling and insulation design, and magnetic shielding design. This method can provide guidance and basis for the optimized design of high-power, high-frequency magnetic resonant ACTs.

[0011] The technical solution adopted by the present invention is:

[0012] The optimization design method of a high-power high-frequency magnetic resonance air-core transformer includes the following steps:

[0013] Step 1: Using an air-core transformer (ACT) consisting of two identical sets of multi-layer coaxial cylindrical coils, determine the optimal winding connection method and the relative flow direction of the two coil currents.

[0014] Step 2: Using air as the insulating medium, calculate the isolation distance between the primary and secondary sides using an analytical formula. Place NOMEX paper between the two sets of coils and between the layers to improve the withstand voltage level of the insulation layer.

[0015] Step 3: Determine the ACT design parameters for the air-core transformer. Based on the electromagnetic parameter scaling rule and the finite element parametric sweep method, set each layer of the model to a single turn and the current to 1A. This allows the extraction of electromagnetic parameters normalized to a single-turn winding under different structures.

[0016] Step 4: Based on the electromagnetic parameter extraction and scaling results of step 3, the system parameters of all air-core transformers ACT are calculated using analytical methods;

[0017] Step 5: Calculate the high-frequency loss of the Litz line using a combination of analytical methods and ANSYS / Maxwell-assisted calculations;

[0018] Step 6: Optimize all the obtained design results from the three aspects of frequency, loss and heat dissipation, and select the appropriate air-core transformer ACT structure based on the Parato multi-objective optimization design results.

[0019] Step 7: Based on the optimized design results of the ACT winding structure in step 6, the shielding cover is designed using the orthogonal experimental method.

[0020] Step 8: Use electromagnetic field-temperature field coupling simulation to verify the feasibility of temperature rise design.

[0021] In step 1, the primary and secondary windings of the air-core transformer ACT are connected by two identical coaxial cylindrical coils. The number of turns of the primary and secondary windings is the same: n1=n2, and each includes 4 layers of windings. A complete cross-commutation winding connection method is adopted, and the primary currents in the two sets of coaxial coils flow in opposite directions. Figure 3 shown.

[0022] In step 2, the air-core transformer ACT designed by the present invention works in the CLLC resonant converter, such as Figure 2 As shown, the two ends of the CLLC resonant converter are connected to the DC bus, so ACT must be able to withstand the DC bus voltage V on the higher voltage side. h ACT withstand voltage between primary and secondary windings V iso V h Considering the 10% fluctuation of DC bus voltage, the withstand voltage between the primary and secondary windings of the air-core transformer ACT is calculated as follows:

[0023] V iso =2V h (1+10%);

[0024] Due to the uneven distribution of the electric field in the air and the presence of a certain amount of air humidity, the conservative value of the maximum electric field that the air can withstand is E. When air is used as the insulating medium, the isolation distance between the primary and secondary sides can be calculated according to the following formula:

[0025]

[0026] Where q is the safety factor, 0 <q<1。

[0027] In order to further improve the reliability of air insulation, the present invention places NOMEX paper between the two sets of coils and between the primary and secondary windings to improve the voltage resistance of the insulation layer.

[0028] In step 3, the inner radius r1, winding height h, and winding width d w , number of turns n 1,2 and frequency f as design variables. Since the structures and electromagnetic parameters of the two sets of coaxial coils are symmetrical, a 2D rotationally symmetric model of a single coaxial coil can be used for parametric simulation calculations. Figure 5 shown. Figure 5 middle

[0029] The electromagnetic parameters of the above simulation model follow the scaling law: when the ACT structural parameters r1, h, d are kept w and d iso If the number of turns of the primary and secondary windings of ACT and the primary and secondary currents are increased by k1 and k2 times respectively, the self-inductance of the primary and secondary windings of ACT and the external magnetic field strength will be increased by k1 respectively.2 Therefore, in order to reduce the amount of computation, each layer of winding is set to a single turn, and the current is set to 1A. The electromagnetic parameters normalized to a single turn winding under each structure can be extracted. The electromagnetic parameters include self-inductance L1 and L2, external magnetic field strength H ext and coupling coefficient k.

[0030] In step 4, the system parameters include self-inductance L1, L2, external magnetic field strength H ext , coupling coefficient k, mutual inductance L m , resonant frequency f, resonant capacitance C r2 、C r2 , the original secondary current i1, i2;

[0031] According to the electromagnetic parameter scaling law, the self-inductance L1 and L2 of ACT and the external magnetic field strength H under different turns are obtained. ext and coupling coefficient k.

[0032] Mutual inductance L m The calculation formula is as follows:

[0033]

[0034] The resonant frequency f is calculated as follows:

[0035]

[0036] Where: P is the rated power of the CLLC converter; V 1,dc and V 2,dc are the rated voltages of the DC busbars connected to both ends of the converter. m is the mutual inductance of the original secondary winding.

[0037] Resonant capacitor C r2 and C r2 The calculation formula is as follows:

[0038]

[0039] Among them, L σ1 and L σ2 They are the leakage inductance of the primary and secondary sides of ACT respectively.

[0040] In Simulink, follow Figure 6 Build a simulation circuit and set the circuit parameters according to the calculation results of step 4. The primary and secondary currents i1 and i2 can be calculated based on Figure 6 The T-type equivalent circuit of the ACT shown is simulated and calculated.

[0041] In step 5, the number n of strands of the Litz wire is calculated as follows:

[0042]

[0043] Where: S is the effective conductive cross-sectional area of ​​the Litz wire; s is the cross-sectional area of ​​the single-strand conductor; d y is the height of a single turn conductor, calculated as d y =h / (n1 / 4); n1 is the number of turns of the primary or secondary winding; k Litz is the filling rate of Litz line; d s is the diameter of the single-strand conductor, d w is the winding width.

[0044] Because skin effect loss (including DC loss) and proximity effect loss are orthogonal, they can be calculated separately. Under the influence of skin effect, the Litz copper loss per unit length can be calculated as follows:

[0045]

[0046] Where: R dc is the DC resistance per unit length of a single Litz wire; I is the peak current flowing through the Litz wire, and the current can be calculated based on Figure 6 Calculation of T-type equivalent circuit of ACT in F R is the skin effect factor, which is expressed as:

[0047]

[0048] Where: γ is the normalized thickness of the circular conductor, and the expression is d s is the diameter of a single Litz line; δ is the skin depth; ber0, ber1, and bei1 represent the real part of the first-kind zero-order Bessel function, the real part of the first-kind first-order Bessel function, and the imaginary part of the first-kind first-order Bessel function, respectively.

[0049] The calculation formula for the internal and external proximity effect loss per unit length of Litz line is:

[0050]

[0051] Where: d a is the diameter of the Litz wire; H ext is the external magnetic field strength. The external magnetic field strength can be calculated according to the electromagnetic parameter scaling law; G R is the proximity effect factor, which is expressed as:

[0052]

[0053] ber2 and bei2 represent the real part and the imaginary part of the first-kind second-order Bessel function, respectively.

[0054] In step 6, in order to make the design results more reasonable and standardized, factors such as frequency, loss, and heat dissipation need to be considered. First, considering the high-frequency performance and loss characteristics of the switching devices, the operating frequency of the CLLC converter should not be too high. Therefore, the operating frequency range of the ACT is limited to below 200kHz;

[0055] Secondly, in order to reduce the impact of winding loss on the overall efficiency of ACT, the design results with efficiency lower than 99% were eliminated.

[0056] Finally, a fan is used to actively cool the ACT, and a simplified transformer thermal model is considered to limit the maximum temperature rise of the ACT under steady-state operation. That is, the winding current density exceeding 20A / mm is discarded. 2 Or the winding surface loss density exceeds 0.25W / cm 2 ACT design results.

[0057] After the optimization is completed, a Parato diagram similar to that shown in Figure 7(a) and Figure 7(b) can be obtained for efficiency, weight power density, and volume power density (the weight, volume, and loss of the fan and shield are not considered). The appropriate ACT structure can be selected based on the Parato diagram.

[0058] In step 7, since the conductive shield has little effect on the winding loss and coupling coefficient, the design of the shield layer and the ACT structure can be carried out separately. For the ACT structure obtained in step 6, an aluminum shield with holes is selected. The design process of the orthogonal experimental method is as follows:

[0059] The distance between the shield and the ACT winding in three different directions is used as a factor, and the reference direction is as follows: Figure 3 As shown in the figure, a three-dimensional ACT simulation model is established under different factors to analyze the ACT power density and self-inductance changes under different factors. While ensuring that the volume power density is as high as possible, an orthogonal experimental scheme with the smallest self-inductance change is selected.

[0060] In step 8, the electromagnetic field-temperature field coupling simulation method is used to load the loss calculation results in ANSYS / Maxwell as a load into the steady-state thermal solution module in ANSYS / Workbench for coupling simulation to determine whether the maximum allowable temperature limit conditions are met.

[0061] The present invention provides a method for optimizing the design of a high-power, high-frequency magnetic resonance air-core transformer, and the technical effects are as follows:

[0062] 1) Step 1 of the present invention proposes a new air-core transformer winding structure and adopts winding cross-transposition technology to reduce winding losses.

[0063] 2) Step 3 of the present invention proposes a two-dimensional simplified simulation model based on the electromagnetic parameter scaling law, which can effectively reduce the parametric scanning calculation time.

[0064] 3) Step 6 of the present invention describes the principles that should be considered and followed in the design of high-power high-frequency air-core transformers from multiple aspects such as efficiency, loss, and temperature rise, which can provide a reference for the optimization design of other air-core transformers.

[0065] 4) Step 7 of the present invention takes into account the shielding effect and heat dissipation effect while taking into account the influence of the shielding cover on the winding self-inductance and the power density of the air-core transformer, so that the designed shielding cover size has a small influence on the winding self-inductance while achieving a higher power density as much as possible.

[0066] 5) This paper details a design method for high-power, high-frequency, magnetically resonant ACTs, using efficiency, gravimetric power density, and volumetric power density as optimization targets. This method, based on parametric sweeps and orthogonal experimental methods, provides guidance and reference for key ACT design issues, including winding arrangement and connection, insulation and cooling design, and magnetic shielding. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 ACT optimization design flow chart of the present invention.

[0068] Figure 2 This is a circuit diagram of the CLLC resonant converter of the present invention.

[0069] Figure 3 This is a cross-sectional view of the ACT structure.

[0070] Figure 4 This is a diagram showing the influence of the relative direction of current on the magnetic field strength in space.

[0071] Figure 5 This is the 2D parametric scanning model diagram of ACT.

[0072] Figure 6 This is the T-type equivalent circuit diagram of ACT.

[0073] Figure 7(a) shows the relationship between the efficiency and weight power density of the air-core transformer;

[0074] Figure 7(b) shows the relationship between the efficiency and volume power density of the air-core transformer.

[0075] Figure 8(a) is the ACT diagram drawn according to the optimal design parameters;

[0076] Figure 8(b) is the ACT cross-section diagram drawn according to the optimal design parameters.

[0077] Figure 9 The figure shows the weight, volume and loss ratio of ACT.

[0078] Figure 10(a) is the ACT loss density distribution cloud map;

[0079] Figure 10(b) is the steady-state temperature field distribution cloud map. DETAILED DESCRIPTION

[0080] The multi-objective optimization design process of large-capacity high-frequency magnetic resonance ACT is as follows: Figure 1 As shown, the following steps are included:

[0081] Step 1: Using an ACT consisting of two identical multi-layer coaxial cylindrical coils, determine the optimal winding connection method and the relative flow direction of the current in the two coils.

[0082] The ACT primary and secondary windings designed in the present invention are formed by connecting two identical coaxial cylindrical coils. The primary and secondary windings have the same number of turns (n1=n2) and each contains 4 layers of windings. Figure 3 shown.

[0083] This invention proposes a method for symmetrically interconnecting two sets of coils. This symmetrical winding connection ensures equal self-inductance and leakage inductance on the primary and secondary sides, facilitating the construction of a resonant network using the same set of resonant capacitor modules. Specifically, A1B2A3B4 forms the primary winding, and B1A2B3A4 forms the secondary winding (completely cross-connected). This completely cross-connected winding connection improves coupling coefficients and reduces proximity effect losses, thereby enhancing ACT efficiency.

[0084] In the case of complete cross-transposition of the windings, the eddy current field analysis method is used to calculate the effect of the leakage magnetic field on the ACT when the relative flow direction of the current of the two sets of coaxial coils changes. Figure 4 (b)), the magnetic field strength in the middle of the coil is partially offset, which helps to reduce shielding loss. The winding connection method and the relative current flow direction are as follows Figure 3 shown.

[0085] Step 2: Using air as the insulating medium, calculate the isolation distance between the primary and secondary sides using an analytical formula. Place NOMEX paper between the two sets of coils and between the layers. NOMEX paper is a synthetic aromatic amide polymer insulating paper with high mechanical properties, flexibility, and good electrical properties. It can be used to improve the withstand voltage level of the insulation layer.

[0086] The ACT designed by the present invention works in a CLLC resonant converter, such as Figure 2 As shown, the two ends of the converter are connected to the DC bus, so ACT must be able to withstand the DC bus voltage V on the higher voltage side. h ACT withstand voltage between primary and secondary windings V iso Vh Considering the 10% fluctuation of DC bus voltage, the calculation formula of the withstand voltage between the primary and secondary windings of ACT is:

[0087] V iso =2V h (1+10%)

[0088] Due to the uneven distribution of electric fields in air and the presence of a certain amount of air humidity, the conservative value of the maximum electric field that air can withstand is E = 0.6kV / mm. When air is used as the insulating medium, the isolation distance between the primary and secondary sides can be calculated according to the following formula:

[0089]

[0090] Where q is the safety factor (0 <q<1)。

[0091] In order to further improve the reliability of air insulation, the present invention places NOMEX paper between the two sets of coils and between the primary and secondary windings to improve the voltage resistance of the insulation layer.

[0092] Step 3: Determine the ACT design parameters. Based on the electromagnetic parameter scaling rule and the finite element parametric scanning method, set each layer of the model's winding to a single turn and the current to 1A. Extract the electromagnetic parameters normalized to a single-turn winding under different structures.

[0093] The inner radius r1, winding height h, and winding width d of the winding are w , number of turns n 1,2 and frequency f as design variables. Since the structures and electromagnetic parameters of the two sets of coaxial coils are symmetrical, a 2D rotationally symmetric model can be used for simulation calculations. Figure 5 shown. Figure 5 The electromagnetic parameters of the simulation model follow the scaling law: when the ACT structural parameters r1, h, d are kept w and d iso If the number of turns of the primary and secondary windings of ACT and the primary and secondary currents are increased by k1 and k2 times respectively, the self-inductance of the primary and secondary windings of ACT and the external magnetic field strength will be increased by k1 respectively. 2 Therefore, in order to reduce the amount of computation, each layer of winding is set to a single turn and the current is set to 1A. The electromagnetic parameters of each structure normalized to a single turn winding can be extracted. The electromagnetic parameters include self-inductance L1 and L2, external magnetic field strength H ext and coupling coefficient k.

[0094] Step 4: Based on the electromagnetic parameter extraction results, the analytical method is used to calculate the system parameters of all ACTs.

[0095] System parameters include self-inductance L1 and L2, external magnetic field strength H ext , coupling coefficient k, mutual inductance L m , resonant frequency f, resonant capacitance C r2 and C r2 , primary and secondary currents i1 and i2.

[0096] According to the electromagnetic parameter scaling law, the self-inductance L1 and L2 of ACT and the external magnetic field strength H under different turns are obtained. ext and coupling coefficient k.

[0097] Mutual inductance L m The calculation formula is as follows:

[0098]

[0099] The resonant frequency f is calculated as follows:

[0100]

[0101] Where: p is the rated power of the CLLC converter; V 1,dc and V 1,dc are the rated voltages of the DC bus connected to both ends of the converter.

[0102] Resonant capacitor C r2 and C r2 The calculation formula is as follows:

[0103]

[0104] Among them, L σ1 and L σ2 are the leakage inductances of the primary and secondary sides of ACT respectively.

[0105] The primary and secondary currents i1 and i2 can be calculated based on Figure 6 The T-type equivalent circuit calculation of the ACT is shown.

[0106] Step 5: Calculate the high-frequency loss of the Litz line using a combination of analytical method and ANSYS / Maxwell assisted calculation.

[0107] The loss of ACT mainly comes from winding loss. Using Litz wire can improve the high-frequency performance of ACT and achieve the purpose of improving efficiency. The number of Litz wire strands n is calculated as:

[0108]

[0109] Where: S is the effective conductive cross-sectional area of ​​the Litz wire; s is the cross-sectional area of ​​the single-strand conductor; d y is the height of a single turn conductor, calculated as d y =h / (n1 / 4); kLitz is the filling rate of Litz line; d s is the diameter of a single-strand conductor.

[0110] Because skin effect loss (including DC loss) and proximity effect loss are orthogonal, they can be calculated separately. Under the influence of skin effect, the Litz copper loss per unit length can be calculated as follows:

[0111]

[0112] Where: R dc is the DC resistance per unit length of a single Litz wire; I is the peak current flowing through the Litz wire, and the current can be calculated based on Figure 6 Calculation of T-type equivalent circuit of ACT in F R is the skin effect factor, which is expressed as:

[0113]

[0114] Where: γ is the normalized thickness of the circular conductor, and the expression is d s is the diameter of a single Litz line; δ is the skin depth; ber and bei represent the real and imaginary parts of the first-kind Bessel function, respectively.

[0115] The calculation formula for the internal and external proximity effect loss per unit length of Litz line is:

[0116]

[0117] Where: d a is the diameter of the Litz wire; H ext is the external magnetic field strength. The external magnetic field strength is extracted in ANSYS / Maxwell and calculated according to the electromagnetic parameter scaling law. R is the proximity effect factor, which is expressed as:

[0118]

[0119] Step 6: Optimize all the obtained design results from the three aspects of frequency, loss and heat dissipation, and select the appropriate ACT structure based on the Parato multi-objective optimization design results.

[0120] In order to make the design results more reasonable and standardized, factors such as frequency, loss and heat dissipation need to be considered. First, considering the high-frequency performance and loss characteristics of the switching devices, the operating frequency of the CLLC converter should not be too high. Therefore, the operating frequency range of the ACT is limited to below 200kHz. Secondly, in order to reduce the impact of winding losses on the overall efficiency of the ACT, the design results with an efficiency of less than 99% are eliminated. Finally, a fan is used to actively cool the ACT, and a simplified transformer thermal model is considered to limit the maximum temperature rise under steady-state operation of the ACT. That is, the winding current density exceeding 20A / mm is discarded. 2 Or the winding surface loss density exceeds 0.25W / cm 2 ACT design results.

[0121] After the optimization is completed, a Parato diagram similar to that shown in Figure 7 can be obtained for efficiency, weight power density, and volume power density (the weight, volume, and loss of the fan and shield are not considered). The ACT structure is selected based on the Parato diagram.

[0122] Step 7: Based on the optimized design results of the ACT winding structure, the shielding cover is designed using the orthogonal experimental method.

[0123] For the ACT structure obtained in step 6, an aluminum shield with holes is selected. The calculation process of the orthogonal experimental method is as follows:

[0124] Taking the distance between the shield and the ACT winding in the xyz direction as a factor, the reference direction is as follows: Figure 3 As shown in the figure, a three-dimensional simulation model of ACT under different factors is established, and the changes in ACT power density and self-inductance under different factors are analyzed.

[0125] While ensuring that the volume power density is as high as possible, an orthogonal experimental scheme with the smallest change in self-inductance is selected.

[0126] Step 8: Use electromagnetic field-temperature field coupling simulation to verify the feasibility of temperature rise design.

[0127] Using electromagnetic field-temperature field coupling simulation, the loss calculation results in ANSYS / Maxwell are loaded as loads into the steady-state thermal solver module in ANSYS / Workbench for coupled simulation to determine whether the maximum allowable temperature limit conditions are met.

[0128] Example:

[0129] The technical solution of the present invention realizes the optimization design of high-power high-frequency magnetic resonance ACT based on parametric scanning and orthogonal experimental method. The design process first selects the winding structure and the relative flow direction of the current, then determines the isolation spacing, and then uses parametric scanning to extract the electromagnetic parameters under all structures for calculation and optimization, thereby selecting the best ACT, and finally using the orthogonal experimental method to design the shielding cover. The flowchart of the optimization design of high-power high-frequency magnetic resonance ACT proposed by the present invention is as follows: Figure 1 shown.

[0130] Assume that ACT works in a CLLC resonant converter with a rated power of 100kW and a DC bus rated voltage of 2kV at both ends. Figure 2 shown.

[0131] Step S1: Using an ACT consisting of two identical multi-layer coaxial cylindrical coils, determine the optimal winding connection method and the relative flow direction of the two coil currents.

[0132] The ACT primary and secondary windings designed in the present invention are formed by connecting two identical coaxial cylindrical coils. The primary and secondary windings have the same number of turns (n1=n2) and each contains 4 layers of windings. Figure 3 shown.

[0133] This invention proposes a method for symmetrically interconnecting two sets of coils. This symmetrical winding connection ensures equal self-inductance and leakage inductance on the primary and secondary sides, facilitating the construction of a resonant network using the same set of resonant capacitor modules. Specifically, A1B2A3B4 forms the primary winding, and B1A2B3A4 forms the secondary winding (completely cross-connected). This completely cross-connected winding connection improves coupling coefficients and reduces proximity effect losses, thereby enhancing ACT efficiency.

[0134] In the case of complete cross-transposition of the windings, the eddy current field analysis method is used to calculate the effect of the leakage magnetic field on the ACT when the relative flow direction of the current of the two sets of coaxial coils changes. Figure 4 (b)), the magnetic field strength in the middle of the coil is partially offset, which helps to reduce shielding loss. The winding connection method and the relative current flow direction are as follows Figure 3 shown.

[0135] Step S2: Using air as the insulating medium, an analytical formula is used to calculate the isolation distance between the primary and secondary sides, and NOMEX is placed between the two sets of coils and between the layers to improve the withstand voltage level of the insulation layer.

[0136] The ACT designed by the present invention works in a CLLC resonant converter, such as Figure 2 As shown, the two ends of the converter are connected to the DC bus, so ACT must be able to withstand the DC bus voltage V on the higher voltage side.h ACT withstand voltage between primary and secondary windings V iso V h Considering the 10% fluctuation of DC bus voltage, the calculation formula of the withstand voltage between the primary and secondary windings of ACT is:

[0137] V iso =2V h (1+10%)

[0138] Due to the uneven distribution of electric fields in air and the presence of a certain amount of air humidity, the conservative value of the maximum electric field that air can withstand is E = 0.6kV / mm. When air is used as the insulating medium, the isolation distance between the primary and secondary sides can be calculated according to the following formula:

[0139]

[0140] Where q is the safety factor (0 <q<1)。

[0141] In order to further improve the reliability of air insulation, the present invention places NOMEX paper between the two sets of coils and between the primary and secondary windings to improve the voltage resistance of the insulation layer.

[0142] Step S3: Determine the ACT design parameters. Based on the electromagnetic parameter scaling rule and the finite element parametric scanning method, set each layer of the model winding to a single turn and the current to 1 A. Extract the electromagnetic parameters normalized to a single-turn winding under different structures.

[0143] The inner radius r1, winding height h, and winding width d of the winding are w , number of turns n 1,2 and frequency f are used as design variables. The fixed parameters and scanning parameters of ACT are defined in Table 1. Since the structures and electromagnetic parameters of the two sets of coaxial coils are symmetrical, the 2D rotational symmetric model of a single set of coaxial coils can be used for simulation calculations. Figure 5 shown. Figure 5 The electromagnetic parameters of the simulation model follow the scaling law: when the ACT structural parameters r1, h, d are kept w and d iso If the number of turns of the primary and secondary windings of ACT and the primary and secondary currents are increased by k1 and k2 times respectively, the self-inductance of the primary and secondary windings of ACT and the external magnetic field strength will be increased by k1 respectively. 2 Therefore, in order to reduce the amount of computation, each layer of winding is set to a single turn and the current is set to 1A. The electromagnetic parameters of each structure normalized to a single turn winding can be extracted. The electromagnetic parameters include self-inductance L1 and L2, external magnetic field strength H ext and coupling coefficient k.

[0144] Table 1 Fixed parameters and design parameters of air-core transformer

[0145]

[0146] Step S4: Based on the electromagnetic parameter extraction results, the system parameters of all ACTs are calculated using an analytical method.

[0147] System parameters include self-inductance L1 and L2, external magnetic field strength H ext , coupling coefficient k, mutual inductance L m , resonant frequency f, resonant capacitance C r2 and C r2 , primary and secondary currents i1 and i2.

[0148] According to the electromagnetic parameter scaling law, the self-inductance L1 and L2 of ACT and the external magnetic field strength H under different turns are obtained. ext and coupling coefficient k.

[0149] Mutual inductance L m The calculation formula is as follows:

[0150]

[0151] The resonant frequency f is calculated as follows:

[0152]

[0153] Where: P is the rated power of the CLLC converter; V 1,dc and V 1,dc are the rated voltages of the DC bus connected to both ends of the converter.

[0154] Resonant capacitor C r2 and C r2 The calculation formula is as follows:

[0155]

[0156] Among them, L σ1 and L σ2 are the leakage inductances of the primary and secondary sides of ACT respectively.

[0157] The primary and secondary currents i1 and i2 can be calculated based on Figure 6 The T-type equivalent circuit calculation of the ACT is shown.

[0158] Step S5: Calculate the high-frequency loss of the Litz line using a combination of analytical method and ANSYS / Maxwell-assisted calculation.

[0159] The loss of ACT mainly comes from winding loss. Using Litz wire can improve the high-frequency performance of ACT and achieve the purpose of improving efficiency. The number of strands n of Litz wire is calculated as follows:

[0160]

[0161] Where: S is the effective conductive cross-sectional area of ​​the Litz wire; s is the cross-sectional area of ​​the single-strand conductor; d y is the height of a single turn conductor, calculated as d y =h / (n1 / 4); k Litz is the filling rate of Litz line; d s is the diameter of a single-strand conductor.

[0162] Because skin effect loss (including DC loss) and proximity effect loss are orthogonal, they can be calculated separately. Under the influence of skin effect, the Litz copper loss per unit length can be calculated as follows:

[0163]

[0164] Where: R dc is the DC resistance per unit length of a single Litz wire; I is the peak current flowing through the Litz wire, and the current can be calculated based on Figure 6 Calculation of T-type equivalent circuit of ACT in F R is the skin effect factor, which is expressed as:

[0165]

[0166] Where: γ is the normalized thickness of the circular conductor, and the expression is d s is the diameter of a single-strand wire; δ is the skin depth; ber and bei represent the real and imaginary parts of the first-kind Bessel function, respectively.

[0167] The calculation formula for the internal and external proximity effect loss per unit length of Litz line is:

[0168]

[0169] Where: d a is the diameter of the Litz wire; H ext is the external magnetic field strength. The external magnetic field strength is extracted in ANSYS / Maxwell and calculated according to the electromagnetic parameter scaling law. R is the proximity effect factor, which is expressed as:

[0170]

[0171] Step S6: Optimize all the obtained design results from the three aspects of frequency, loss and heat dissipation, and select the appropriate ACT structure based on the Parato multi-objective optimization design results.

[0172] In order to make the design results more reasonable and standardized, factors such as frequency, loss and heat dissipation need to be considered. First, considering the high-frequency performance and loss characteristics of the switching devices, the operating frequency of the CLLC converter should not be too high. Therefore, the operating frequency range of the ACT is limited to below 200kHz. Secondly, in order to reduce the impact of winding losses on the overall efficiency of the ACT, the design results with an efficiency of less than 99% are eliminated. Finally, a fan is used to actively cool the ACT, and a simplified transformer thermal model is considered to limit the maximum temperature rise under steady-state operation of the ACT. That is, the winding current density exceeding 20A / mm is discarded. 2 Or the winding surface loss density exceeds 0.25W / cm 2 ACT design results.

[0173] Figure 7 is a Parato diagram of efficiency, weight power density and volume power density after optimization (the weight, volume and loss of the fan and shielding cover are not considered). As can be seen from Figure 7, the efficiency, weight power density and volume power density of ACT increase with increasing frequency. However, the soft switching loss is positively correlated with the frequency. When the frequency exceeds 100kHz, the trend of the soft switching loss growth rate accelerating with increasing frequency is more obvious. The efficiency of the CLLC resonant converter may continue to decrease with increasing frequency. Therefore, the feasible design is best selected from the results with a frequency below 100kHz, so as to ensure that the entire system achieves a higher transmission efficiency. The design point marked with a red square in Figure 7 is the transformer structure design result selected by the present invention. Its resonant frequency, efficiency, weight power density and volume power density are 81.34kHz, 99.66%, 30.21kW / kg, 41.78kW / dm 3 .

[0174] Step S7: Based on the optimized design results of the ACT winding structure, an orthogonal experimental method is used to design a shielding cover.

[0175] Since the shielding cover made of conductive material has little effect on the winding loss and coupling coefficient, the design of the shielding layer and the design of the ACT structure can be carried out separately. For the ACT structure obtained in step S6, an aluminum shielding cover with holes is selected. The calculation process of the orthogonal experimental method is as follows:

[0176] This time, a three-factor, three-level orthogonal experimental scheme was used to study the effect of the distance between the shielding cover and the winding on the ACT power density and self-inductance. The orthogonal experimental table and experimental results are shown in Table 2. Among them, a, b, and c represent the distance between the shielding cover and the winding in the xyz direction respectively; G p and V p= represent the weight power density and volume power density after considering the fan and shield, respectively; τ represents the effect of adding a shield on the transformer's self-inductance. While ensuring the highest possible volume power density, an orthogonal experimental scheme was selected to minimize the change in self-inductance. When the spacing in the xyz directions was 35mm, 44mm, and 72mm, respectively, the change in transformer self-inductance was already less than 5%. Further increasing the shield spacing would, on the one hand, limit the reduction in self-inductance change, and on the other hand, further reduce V p Therefore, the seventh set of orthogonal experimental designs is the optimal combination result. Table 3 lists the optimal design parameters and performance indicators of ACT. Figure 8 shows the ACT model established according to the optimal design parameters. Figure 9 The weight, volume and loss of various structural components that make up the optimal ACT design are shown in the figure.

[0177] Table 2 Orthogonal experimental design and experimental results

[0178]

[0179] Table 3 Optimal design parameters of air-core transformer

[0180]

[0181] Step S8: Use electromagnetic field-temperature field coupling simulation to verify the feasibility of the temperature rise design.

[0182] Using a coupled electromagnetic and temperature field simulation method, the loss calculation results in ANSYS / Maxwell were loaded as a load into the steady-state thermal solver module in ANSYS / Workbench for coupled simulation. Figure 10 shows the loss density distribution and steady-state temperature field distribution of the ACT. The maximum winding temperature is lower than the maximum tolerance temperature of the Litz wire: 130°C, meeting the design requirements.

Claims

1. The optimization design method of high-power high-frequency magnetic resonance air-core transformer is characterized by It includes the following steps: Step 1: Use a hollow transformer ACT composed of two completely identical multi-layer coaxial cylindrical coils to determine the optimal winding connection method and the relative flow directions of the currents in the two coils; Step 2: Use air as the insulating medium, calculate the isolation distance between the primary and secondary sides, and place NOMEX paper between the two coils and between layers; Step 3: Determine the design parameters of the hollow transformer ACT. Based on the electromagnetic parameter scaling law and the finite element parametric scanning method, set each layer of the winding of the model to a single turn and the current to 1 A, so as to extract the electromagnetic parameters normalized to a single-turn winding under different structures; Step 4: Calculate the system parameters of all hollow transformers ACT according to the electromagnetic parameter extraction and scaling results in Step 3; Step 5: Calculate the high-frequency loss of the Litz wire; Step 6: Optimize all the obtained design results from three aspects of frequency, loss and heat dissipation, and select a suitable hollow transformer ACT structure according to the Parato multi-objective optimization design results; In step 3, the inner radius r1, winding height h, and winding width d w , number of turns n 1,2 The sum frequency f is used as the design variable; a 2D rotationally symmetric model of a single coaxial coil is used for parametric simulation calculation; The electromagnetic parameters of the above 2D rotationally symmetric model follow the scaling law: When maintaining the ACT structure parameters r1, h, d w and d iso If the number of turns of the primary and secondary windings of ACT and the primary and secondary currents are increased by k1 and k2 times respectively, the self-inductance of the primary and secondary windings of ACT and the external magnetic field strength will be increased by k1 respectively. 2 times and k1k2 times, the coupling coefficient remains unchanged; each layer of winding is set to a single turn, and the current is set to 1A, and the electromagnetic parameters normalized to a single turn winding under each structure can be extracted. The electromagnetic parameters include self-inductance L1 and L2, external magnetic field strength H ext and coupling coefficient k.

2. The high-power high-frequency magnetic resonance air-core transformer optimization design method according to claim 1, characterized in that: It also includes Step 7: For the optimized design results of the ACT winding structure in Step 6, use the orthogonal experiment method to design the shielding cover.

3. The high-power high-frequency magnetic resonance air-core transformer optimization design method according to claim 1 is characterized in that: In Step 1, the primary and secondary windings of the hollow transformer ACT are connected by two completely identical coaxial cylindrical coils. The number of turns of the primary and secondary windings is the same: n1 = n2, and each contains 4 layers of windings; Adopt a completely cross-connected winding connection method, and the relative flow directions of the primary currents in the two coaxial coils are opposite.

4. The high-power high-frequency magnetic resonance air-core transformer optimization design method according to claim 1 is characterized in that: In Step 2, the hollow transformer ACT operates in a CLLC resonant converter. The two ends of the CLLC resonant converter are connected to the DC bus. The calculation formula for the withstand voltage between the primary and secondary windings of the hollow transformer ACT is: V iso =2V h (1+10%); Among them, V iso is the withstand voltage between the primary and secondary windings of ACT, V h is the DC bus voltage; When using air as the insulating medium, the isolation distance between the primary and secondary sides can be calculated according to the following formula: Where, E is the maximum electric field value that air can withstand; q is the safety factor, 0 < q < 1; Place NOMEX paper between the two coils and between the primary and secondary windings to improve the withstand voltage ability of the insulating layer.

5. The high-power high-frequency magnetic resonance air-core transformer optimization design method according to claim 1 is characterized in that: In step 4, the system parameters include self-inductance L1, L2, external magnetic field strength H ext , coupling coefficient k, mutual inductance L m , resonant frequency f, resonant capacitance C r2 、C r2 , the original secondary current i1, i2; According to the electromagnetic parameter scaling law, the self-inductance L1 and L2 of ACT and the external magnetic field strength H under different turns are obtained. ext and coupling coefficient k; Mutual inductance L m The calculation formula is as follows: The calculation formula for the resonant frequency f is as follows: Where: P is the rated power of the CLLC converter; V 1,dc and V 2,dc are the rated voltages of the DC busbars connected to both ends of the converter; L m is the mutual inductance of the original secondary winding; Resonant capacitor C r2 and C r2 The calculation formula is as follows: Among them, L σ1 and L σ2 They are the leakage inductance of the primary and secondary sides of ACT respectively.

6. The high-power high-frequency magnetic resonance air-core transformer optimization design method according to claim 1, characterized in that: In Step 5, the calculation formula for the number of strands n of the Litz wire is: Where: S is the effective conductive cross-sectional area of ​​the Litz wire; s is the cross-sectional area of ​​the single-strand conductor; d y is the height of a single turn conductor, calculated as d y =h / (n1 / 4); n1 is the number of turns of the primary or secondary winding; k Litz is the filling rate of Litz line; d s is the diameter of the single-strand conductor, d w is the winding width; Under the influence of the skin effect, the copper loss of Litz per unit length can be calculated by the following formula: Where: R dc is the DC resistance per unit length of a single Litz wire; I is the peak current flowing through the Litz wire, which can be calculated based on the T-type equivalent circuit of ACT; F R is the skin effect factor, which is expressed as: Where: γ is the normalized thickness of the circular conductor, and the expression is d s is the diameter of a single Litz line; δ is the skin depth; ber0, ber1, and bei1 represent the real part of the first-kind zero-order Bessel function, the real part of the first-kind first-order Bessel function, and the imaginary part of the first-kind first-order Bessel function, respectively; The calculation formula for the internal and external proximity effect losses per unit length of the Litz wire is: Where: d a is the diameter of the Litz wire; H ext is the external magnetic field strength; the external magnetic field strength can be calculated according to the electromagnetic parameter scaling law; G R is the proximity effect factor, which is expressed as: ber2 and bei2 respectively represent the real part of the first kind of second-order Bessel function and the imaginary part of the first kind of second-order Bessel function.

7. The high-power high-frequency magnetic resonance air-core transformer optimization design method according to claim 1, characterized in that: In Step 6, first, considering the high-frequency performance and loss characteristics of the switching device, the operating frequency of the CLLC converter cannot be too high. Therefore, the operating frequency range of the ACT is limited to below 200 kHz; Secondly, in order to reduce the influence of winding loss on the overall efficiency of the ACT, eliminate the design results with an efficiency lower than 99%; Finally, use a fan to actively cool the ACT, and consider a simplified transformer thermal model to limit the maximum temperature rise under the steady-state operation of the ACT; After the optimization is completed, a Parato diagram of efficiency, weight power density and volume power density can be obtained, and the appropriate ACT structure can be selected according to the Parato diagram.

8. The high-power high-frequency magnetic resonance air-core transformer optimization design method according to claim 1, characterized in that: In step 7, for the ACT structure obtained in step 6, an aluminum shielding cover with holes is selected. The design process of the orthogonal experimental method is as follows: The distance between the shielding cover and the ACT winding in three different directions is used as a factor; a three-dimensional simulation model of the ACT under different factors is established, and the change in ACT power density and self-inductance under different factors is analyzed; while ensuring the highest possible volume power density, an orthogonal experimental scheme with the smallest change in self-inductance is selected.

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