Method for optimizing water cooling structure of high-frequency transformer assisted by heat flow coupling simulation

Abstract

The invention belongs to the technical field of cooling of high-frequency transformers. According to the method, the temperature rise and cooling liquid flow characteristics of an internal winding and an iron core of the transformer are simulated by constructing a multi-physical field simulation model considering the thermophysical property change of a material; establishing a response surface model based on transformer structure parameters, and selecting the outer diameter, the wall thickness, the number of turns and the spacing of a cooling pipe as design variables; an NSGA-II multi-objective optimization algorithm is adopted, and a Pareto optimal solution set is obtained by taking maximum temperature minimization and cooling material consumption minimization as objectives; and typical scheme optimization is realized in combination with an entropy weight-TOPSIS method. According to the invention, the design requirements under different cooling structures and operation conditions can be met, the hot-spot temperature rise is obviously reduced, the cooling efficiency is improved, and good structural safety and manufacturability are achieved.

Description

Technical Field

[0001] This invention belongs to the field of cooling technology for high-frequency transformers, and specifically relates to an optimization method for the water-cooling structure of high-frequency transformers assisted by thermal-fluid coupling simulation. It is particularly suitable for the optimization of heat dissipation structure and the construction of thermal management system for medium- and high-voltage, high-power-density high-frequency transformers. Background Technology

[0002] With the rapid development of power electronics technology, high-frequency transformers, due to their small size and high efficiency, have been widely used in many key scenarios such as distributed power sources, new energy storage systems, electric vehicles, and data centers. However, the trend towards higher frequencies in transformers has significantly increased their internal heat load density, making it difficult for traditional natural or forced air cooling methods to meet effective heat dissipation requirements under high heat power density conditions, severely restricting their long-term safe operation and further performance improvement. Especially in high-frequency transformers with epoxy resin potting insulation, the poor thermal conductivity of the insulation material makes it difficult to dissipate the heat generated by the windings and core in a timely manner, easily forming hot spots in local areas. This not only causes excessive temperature rise but also accelerates insulation aging and induces failure risks such as thermal breakdown. Therefore, how to improve the cooling efficiency of epoxy-encapsulated high-frequency transformers and achieve efficient and stable thermal control has become a key technical challenge in the design of this type of transformer.

[0003] In recent years, forced water cooling technology has become a research hotspot in the thermal management of high-frequency power equipment due to its high heat transfer efficiency and good adaptability to high heat flux density conditions. Currently, various water cooling structures have been proposed, including water-cooled plates, water-cooled pipes, double-wing finned water channels, and embedded microchannels. However, existing designs mostly focus on morphological innovation or topological configuration, lacking a systematic and optimizable embedded water cooling structure design method for solid-insulated high-frequency transformers. Furthermore, existing research often fails to fully consider the impact of coolant temperature changes on the flow field and material thermal properties in the cooling structure arrangement, making it difficult to simultaneously optimize the structure and improve heat dissipation performance. To address these shortcomings, a water cooling structure design method that integrates thermal-fluid coupling characteristic analysis and multi-parameter collaborative optimization is urgently needed to solve key problems such as high-temperature distribution and cooling non-uniformity within transformers. Summary of the Invention

[0004] To address the issues of low heat dissipation efficiency and localized temperature rise in epoxy-sealed high-frequency transformers during operation, this invention aims to provide an optimization method for the water-cooling structure of high-frequency transformers assisted by thermal-fluid coupling simulation. This method not only significantly reduces hot spot temperature rise and improves heat dissipation efficiency, but also effectively reduces the amount of cooling materials used, thus balancing operational safety and economy.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: an optimization method for a high-frequency transformer water-cooling structure assisted by heat-fluid coupling simulation, characterized by comprising the following steps: Step 1: Structural Integration Design In the insulation area between the core and secondary winding of the epoxy resin-encapsulated high-frequency transformer, a spiral copper cooling pipe is pre-embedded to form an embedded water-cooling structure; this cooling structure is integrated with the transformer, taking into account both heat exchange efficiency and electrical insulation safety. Step 2: Thermal-fluid coupling modeling Based on high-frequency excitation conditions, a multi-physics thermal-fluid coupling model is established, which includes heat conduction, convection, thermal radiation, and non-isothermal fluid flow. The model considers the influence of coolant flow on the temperature field distribution, and temperature changes also feed back to affect the flow field behavior, thus achieving bidirectional coupling. Step 3: Determine the boundary of the heat source Through no-load and short-circuit tests, heat dissipation data of the core and winding under actual operating conditions are obtained and used as heat source input for steady-state simulation to ensure that the heat source boundary of the model is consistent with the actual operating conditions. Step 4: Modeling the cooling structure parameters With the outer diameter of the cooling pipe D Wall thickness d Number of turns N Turn spacing s To design variables, a structural parameter space was constructed; and an ethylene glycol-water mixture, which has both thermal performance and electrical insulation properties, was selected as the cooling medium (the volume ratio of ethylene glycol to water in the mixture is 30:100). Step 5: Response Surface Modeling and Optimization Objective Setting A response surface model of the relationship between the maximum temperature of the high-frequency transformer and the parameters of each cooling structure was established using the central composite design method (CCD) combined with finite element simulation. Dual objective functions were set: ① minimizing the maximum temperature and ② minimizing the amount of cooling material used. Step 6: Multi-objective optimization solution The non-dominated sorting genetic algorithm (NSGA-II) was used to perform multi-objective optimization of the cooling structure, and the Pareto optimal solution set was obtained. Step 7: Optimize the decision-making process The entropy weight-TOPSIS method is introduced to sort and filter the multi-objective solution set according to different weight preferences, and output a representative optimal structural design scheme.

[0006] In step 1, the structural integration design method is as follows: In epoxy resin-encapsulated high-frequency transformers, there is a closed insulation gap between the core and the secondary winding. To improve the heat dissipation efficiency in this area, spiral copper cooling pipes are pre-embedded along the axial direction to form an embedded forced water cooling structure. This structure is integrally encapsulated with the winding and epoxy resin, and is connected to the external cooling circuit through a sealed external water inlet (i.e., coolant inlet) and outlet (i.e., coolant outlet) on the shell. This not only achieves close contact between the cooling pipes and the heat source, but also effectively improves heat dissipation efficiency and avoids the problems of weak insulation and loose structure caused by arranging cooling channels outside the encapsulation. In addition, to ensure the insulation safety of the pipes under high-voltage operation, both sides of the cooling pipes are covered with an insulating dielectric layer.

[0007] In step 2, the thermal-fluid coupling modeling is as follows: The constructed heat-fluid coupling model includes multi-physics processes such as steady-state heat conduction, non-isothermal flow, natural convection, and thermal radiation; heat conduction and thermal convection are described by Fourier's law, and its basic equations are: In the formula: Density; Heat capacity; Heat flux density; This is the thermal conductivity coefficient (its value varies with the material); The fluid velocity; This is the temperature gradient vector; The divergence of heat conduction flux; This represents the Laplace operation on spatial coordinates; Thermal radiation is described by the Stefan-Boltzmann law, as follows: In the formula: Surface emissivity; The Stefan-Boltzmann constant { = 5.67×10 -8 }; T amb The ambient temperature; T This is the surface temperature at the boundary. This is the unit normal vector pointing outside the computational domain.

[0008] The flow field is calculated using the Navier-Stokes equations, taking into account the viscous and inertial effects of the coolant flowing within the pipe: In the formula: This represents the Laplace operation on spatial coordinates; The fluid velocity; For dynamic viscosity, p For pressure, During the coupling process, the temperature of the coolant affects its viscosity, thermal conductivity, and density, thereby influencing the flow field distribution and achieving bidirectional coupling.

[0009] In step 3, the method for determining the heat source boundary is as follows: By conducting no-load excitation experiments on high-frequency transformers, the core loss and winding loss were measured, and then standardized to the rated operating state according to the conversion formula: In the formula: I , I exp These are the effective values ​​of the actual operating current and the test current, respectively. P exp To test short-circuit loss; K Temperature conversion factor for losses; R dcT0 The sum of the DC resistances of the primary and secondary windings at the measured temperature; T con , T 0 represents the reference temperature and the measured temperature, respectively.

[0010] In step 4, the modeling method for the cooling structure parameters is as follows: Select the outer diameter of the cooling copper pipe D Wall thickness d Number of turns N and pipe spacing s As design variables, and considering that the setting of these parameters is constrained by the structural dimensions of the transformer, the parameter space is defined as follows: In the formula, D min ，D max Indicates the lower and upper limits of the outer diameter of the cooling pipe; d min ，d max Indicates the lower and upper limits of wall thickness. ； N min ，N max Indicates the lower and upper limits of the number of turns. ；s min ，s max Indicates the lower and upper limits of the spacing. ； The set of integers represents the number of turns. N Integer value required 。

[0011] Meanwhile, the cooling medium was selected as a 30% (v / v) ethylene glycol-water mixture, with the following physical properties: In the formula, ( T ) represents density; k t ( T () represents thermal conductivity; ( T () represents dynamic viscosity; T For temperature; Ensure that the thermal-fluid properties of the medium change with temperature during the simulation process.

[0012] In step 5, the objective for response surface modeling and optimization is set as follows: The test points were arranged using the central composite design (CCD) method to analyze the response variable "maximum temperature". T "With design variables" D , d , n , s Establish a quadratic polynomial response surface model between them: In the formula, 0 represents the regression coefficient of the constant term; j Let be the linear regression coefficient, representing the th . j Linear effects of individual variables; jj Let be the regression coefficient of the quadratic term, representing the th term. j The secondary effect of each variable; ij The interaction regression coefficient represents the variable. x i and x j The interaction effect; x i , x j For experimental variables; m The number of experimental variables; Set up a dual objective function: in, In the formula, f 1 represents the objective function 1; f 2 represents the objective function 2;T max This is the highest temperature; V gauge Total volume of copper material ; L 0 represents the axial unfolding length of a single turn; W 0 represents the radial unfolding length of a single turn.

[0013] Therefore, the objective function and constraints of the constructed multi-objective optimization model are as follows: In step 6, the solution process for the multi-objective optimization is as follows: The above model was solved using the non-dominated sorting genetic algorithm NSGA-II, and the optimized parameters were: D , d , N , s The objective is to minimize simultaneously f 1, f 2; In each iteration, new solution sets are continuously evolved through elite retention, tournament selection, simulated binary crossover and Gaussian mutation operations, eventually converging to the Pareto optimal frontier; The parameters in the algorithm are set as follows: total population size is 100, maximum number of iterations is 1000, crossover probability is 0.9, crossover distribution index is 10, and mutation distribution index is 20.

[0014] In step 7, the decision-making and screening of optimization schemes are as follows: The entropy-weighted TOPSIS method is introduced to construct a decision matrix based on the Pareto front solution set. , i The number of solutions above the frontier solution. j To optimize the number of indicators, r ij For the first i The first scheme is in the j The original evaluation values ​​for each indicator were then normalized. In the formula: r j max , r j min The first j The maximum and minimum values ​​of an objective across all possible scenarios; Based on the weight of each indicator By weighting the standardized matrix, we obtain the weighted decision matrix: In the formula, v ij The weighted standardized index value; ω j For the first j Entropy weights of each indicator; z ij This is the weighted standardized index value.

[0015] Calculate the ideal optimal solution for each option. v + and worst solution v - Euclidean distance: And the proximity coefficient is obtained: In the formula, For the first j The ideal optimal value of each indicator; For the first j The ideal worst value for each indicator; v ij After weighted standardization, the first i The first scheme is in the j Evaluation values ​​on each indicator; For the first i A plan and an ideal; No. i The Euclidean distance between each solution and the ideal worst solution; C i For the first i The proximity coefficient of each scheme.

[0016] Based on this, multiple schemes were sorted and screened, and three representative optimal structural schemes were selected, corresponding to three design preferences: heat dissipation priority, material saving priority, and weight balance.

[0017] This invention simulates the temperature rise and coolant flow characteristics of the transformer's internal windings and core by constructing a multiphysics simulation model that considers changes in material thermal properties. A response surface model is established based on the transformer's structural parameters, selecting the outer diameter, wall thickness, number of turns, and spacing of the cooling pipes as design variables. The NSGA-II multi-objective optimization algorithm is employed, aiming to minimize the maximum temperature and the amount of cooling material used, to obtain the Pareto optimal solution set. The entropy-weighted TOPSIS method is then combined to optimize typical solutions. This invention can adapt to design requirements under different cooling structures and operating conditions, significantly reducing hotspot temperature rise, improving cooling efficiency, and possessing good structural safety and manufacturability. Compared with traditional structures, this method can conduct embedded water-cooled structure design for different spatial constraints and insulation requirements, providing an efficient thermal management solution for high-power-density transformers.

[0018] The beneficial effects of this invention are as follows: By pre-embedding spiral cooling pipes between the core and windings and establishing a heat-fluid coupling model, the distribution of internal heat sources, coolant flow characteristics, and material parameter variations can be considered simultaneously during simulation and optimization, enabling accurate prediction of temperature rise and cooling efficiency under different structural parameters. Furthermore, by combining multi-objective optimization and scheme selection, not only is the hot spot temperature rise significantly reduced and heat dissipation efficiency improved, but the amount of cooling material used is also effectively reduced, balancing operational safety and economy. This method can provide a theoretical basis and engineering guidance for the cooling structure design of high-power-density high-frequency transformers. Attached Figure Description

[0019] Figure 1 This is a basic flowchart of the present invention.

[0020] Figure 2(a) is a schematic diagram of a high-frequency transformer.

[0021] Figure 2(b) shows some structural parameters of the high-frequency transformer (the unit in the figure is mm).

[0022] Figure 3 This is a structural model and heat dissipation diagram for forced water cooling.

[0023] Figure 4(a) is a schematic diagram of laminar velocity distribution.

[0024] Figure 4(b) is a schematic diagram of the turbulent velocity distribution.

[0025] Figure 5 This is a schematic diagram of heat-fluid coupling.

[0026] Figure 6 This is a schematic diagram of an unloaded test.

[0027] Figure 7(a) shows the voltage and current waveforms of the additional winding.

[0028] Figure 7(b) shows the voltage and current waveforms of the secondary winding.

[0029] Figure 8 This is a schematic diagram of the structural model under forced water cooling.

[0030] Figure 9 A schematic diagram of the variables to be optimized under forced water cooling.

[0031] Figure 10 Flowchart for NSGA-II multi-objective optimization.

[0032] Figure 11 For Pareto front solution set.

[0033] Figure 12(a) shows the simulation cloud diagram of the initial design scheme.

[0034] Figure 12(b) is a simulation cloud map of optimization scheme one.

[0035] Figure 12(c) shows the simulation cloud map of optimization scheme two.

[0036] Figure 12(d) shows the simulation cloud map of optimization scheme three. Detailed Implementation

[0037] An optimization method for a high-frequency transformer water-cooling structure assisted by heat-fluid coupling simulation includes the following steps: Step 1: Structural Integration Design In the insulation area between the core and secondary winding of the epoxy resin-encapsulated high-frequency transformer, a spiral copper cooling pipe is pre-embedded to form an embedded water-cooling structure. This cooling structure is integrated with the transformer, taking into account both heat exchange efficiency and electrical insulation safety. It can achieve efficient heat exchange close to the heat-generating area while maintaining overall insulation strength and operational safety.

[0038] Step 2: Thermal-fluid coupling modeling Based on high-frequency excitation conditions, a multi-physics thermal-fluid coupling model is established, which includes heat conduction, convection, thermal radiation, and non-isothermal fluid flow. The model considers the influence of coolant flow on the temperature field distribution, and temperature changes also feed back to affect the flow field behavior, achieving bidirectional coupling. The model comprehensively considers the effects of heat conduction, convection, and thermal radiation, and introduces the non-isothermal flow characteristics of coolant in the pipe, thus accurately reflecting the interaction between the temperature field and the flow field.

[0039] Step 3: Determine the boundary of the heat source By conducting no-load and short-circuit tests, the heat dissipation data of the core and winding under actual operating conditions are obtained and used as the heat source input for steady-state simulation to ensure that the heat source boundary of the model is consistent with the actual operating conditions.

[0040] Step 4: Modeling the cooling structure parameters With the outer diameter of the cooling pipe D Wall thickness d Number of turns N Turn spacing s To design variables, a structural parameter space was constructed; and an ethylene glycol-water mixture, which combines thermal performance and electrical insulation, was selected as the cooling medium; this medium has good heat transfer performance, antifreeze ability and insulation performance.

[0041] Step 5: Response Surface Modeling and Optimization Objective Setting A response surface model was established between the maximum temperature of the high-frequency transformer and the parameters of each cooling structure using the central composite design method (CCD) combined with finite element simulation. Dual objective functions were set: ① minimizing the maximum temperature and ② minimizing the amount of cooling material used. The optimization objectives were set as minimizing the maximum temperature and minimizing the amount of cooling pipe material used.

[0042] Step 6: Multi-objective optimization solution The non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization of the cooling structure to obtain a series of Pareto optimal solution sets that meet different design requirements, thereby achieving a comprehensive trade-off between heat dissipation performance and structural economy.

[0043] Step 7: Optimize the decision-making process The entropy-weighted TOPSIS method is introduced to sort the Pareto solution set, and the optimal structural design scheme is selected according to different design preferences, including priority of temperature rise control, priority of material saving, and balanced weight. The results show that the optimized embedded water-cooling structure is superior to the traditional design in reducing hot spot temperature rise and reducing material usage, and significantly improves the heat dissipation efficiency and operational reliability of the high-frequency transformer.

[0044] Example 1: An optimization method for high-frequency transformer water-cooling structure assisted by heat-fluid coupling simulation is shown in the following basic flowchart. Figure 1 As shown.

[0045] Step 1: Structural Integration Design A simulation study was conducted on a high-frequency transformer with rated parameters of 10kHz and 200kVA. The schematic diagram and some structural parameters of the high-frequency transformer are shown in Figure 2. It mainly consists of an iron core, primary winding, secondary winding, aluminum plate (thermally conductive aluminum plate), and epoxy resin (cast epoxy resin) (including air ducts). Both the primary and secondary windings have one layer, and each layer contains 7 turns of square Litz wire. The Litz wire has 2128 strands, with a single strand diameter of 0.2mm. The Litz wire dimensions are 11.35mm × 11.35mm. Epoxy resin is cast around the coils, with a width of 33mm and a height of 153.6mm. A 10mm thick thermally conductive aluminum plate is installed between adjacent iron cores. The material properties of the high-frequency transformer are shown in Table 1.

[0046] In epoxy resin-encapsulated high-frequency transformers, a closed insulation gap exists between the core and the secondary winding. To improve heat dissipation efficiency in this area, spiral copper cooling pipes are pre-embedded axially in this region, forming an embedded forced water-cooling structure. This structure is integrally encapsulated with the winding and epoxy resin, and is connected to a sealed external water inlet (i.e., coolant inlet) and outlet (i.e., coolant outlet) on the casing. Figure 8 As shown, it is connected to the external cooling circuit, which not only achieves close contact between the cooling pipe and the heat source, but also effectively improves the heat dissipation efficiency and avoids the problems of weak insulation and loose structure caused by arranging cooling channels outside the package; in addition, to ensure the insulation safety of the pipe under high pressure, both sides of the cooling pipe are covered with an insulating medium layer.

[0047] Table 1 Material Properties of Transformers Step 2: Thermal-fluid coupling modeling This paper analyzes the heat dissipation of high-frequency transformers under water cooling conditions. The Joule heat generated by the windings and core of the high-frequency transformer is mainly transferred to the transformer surface via heat conduction through different heat transfer paths. Therefore, the efficiency of heat conduction is closely related to the thermal conductivity and size of different materials. Simultaneously, the surface of the high-frequency transformer is in contact with air, resulting in heat convection and radiation. Because the middle of the core column of the high-frequency transformer is far from the outer surface, heat is difficult to transfer to the surface, causing significant temperature rise in hot spots. If copper water pipes are embedded between the low-voltage winding and the core for forced water cooling, the water cooling system can remove internal heat through circulating water flow, greatly improving heat transfer efficiency and reducing local temperature rise. The structural model and heat dissipation diagram under forced water cooling are shown below. Figure 3 As shown.

[0048] Heat conduction and heat convection are described by Fourier's law: In the formula: Density; Heat capacity; Heat flux density; This is the thermal conductivity coefficient (its value varies with the material); The fluid velocity; This is the temperature gradient vector; The divergence of heat conduction flux; This represents the Laplace operation on spatial coordinates.

[0049] The first term is the transient energy storage term, which describes the cumulative change of heat capacity per unit volume over time; the second term is the heat conduction term, with the negative sign indicating that heat is conducted and diffused from the high-temperature region to the low-temperature region; and the third term is the heat convection term, which describes the heat transferred with the fluid when the medium flows.

[0050] Thermal radiation is described by the Stefan-Boltzmann law: In the formula: Surface emissivity; Stefan-Boltzmann constant ( = 5.67×10 -8 ); T amb The ambient temperature; T This is the surface temperature at the boundary. This is the unit normal vector pointing outside the computational domain.

[0051] Boundary conditions represent the influence of the surrounding environment on the entire research object, that is, the heat transfer relationship between the heat conduction system and the external environment. The first type of boundary condition directly specifies the boundary temperature and is used to describe a surface in contact with a constant-temperature heat source or a known temperature field; the second type of boundary condition gives the heat flux and is used to characterize a uniform or time-varying externally heated flux on the boundary; the third type of boundary condition connects the surface to the external environment through a convective heat transfer model. The boundary conditions are shown below: In the formula: , , These represent the first type of boundary, the second type of boundary, and the third type of boundary, respectively. This is the unit normal vector pointing to the outside of the boundary; This is a function of heat flux, which varies with location and temperature; The convective heat transfer coefficient; The ambient temperature; T The temperature at the boundary; t For time variables; ▽ T This is the temperature gradient vector; k t Let be the components of the anisotropic thermal conductivity tensor.

[0052] The flow of coolant in the transformer's internal cooling pipes is complex; therefore, the Reynolds number is initially used. R e The flow state of the coolant is determined. In circular pipe flow, the Reynolds number... R e The calculation formula is: In the formula: For fluid density; The average flow velocity across the circular pipe cross-section; l The characteristic length of the fluid, i.e., the pipe diameter; This represents the dynamic viscosity of the fluid.

[0053] The critical Reynolds number for the transition from laminar to turbulent flow is generally considered to be 2320. R e <2320 indicates laminar flow. R e =2320~4000 is a transitional state. R e A Reynolds number greater than 4000 indicates turbulent flow. When the Reynolds number is low, the flow is laminar, with a stable and orderly velocity distribution, as shown in Figure 4(a). As the Reynolds number increases, the flow gradually becomes unstable and enters a transitional state; when the Reynolds number further increases, the flow becomes completely turbulent, with violent fluctuations in velocity distribution and a large number of vortices, as shown in Figure 4(b), which depicts a typical velocity distribution in turbulent flow.

[0054] For laminar flow, the Navier-Stokes equations are used to solve for the fluid motion state, as shown below: In the formula: This represents the Laplace operation on spatial coordinates; For dynamic viscosity, p For pressure, During the coupling process, the temperature of the coolant affects its viscosity, thermal conductivity, and density, thereby influencing the flow field distribution and achieving bidirectional coupling.

[0055] For turbulent flow, considering that this study focuses on the flow of liquid in a narrow pipe, the flow characteristics are mainly affected by the wall effect; therefore, the standard... k - A turbulence model is used to solve the problem, providing a more accurate description of turbulent behavior near the wall. The turbulent kinetic energy per unit mass of fluid is... k With turbulent energy dissipation rate They are shown below: In the formula: v i ' For the first The velocity pulsation component in the component direction, that is, the deviation between the instantaneous velocity and its average value; Molecular viscosity; For the first l Spatial coordinate components in the direction of the component.

[0056] The turbulence model gives the eddy viscosity coefficient With turbulent pulsating kinetic energy and turbulence frequency The relationship is as follows: And there are In the formula: For fluid density; Frequency attenuation coefficient ( =0.09 ).

[0057] standard Turbulence models require solving two transport equations. equations and The equation is as follows: In the formula: xl Represents spatial coordinate components; P k For turbulent kinetic energy generation; For turbulence model constants ( =0.09); It is turbulent kinetic energy; Specific dissipation rate; , For turbulence model constants ( =0.5532, =0.075); the left side is the pair and The mass derivative; the first term on the right is the diffusion term, derived from the molecular kinetic viscosity. With turbulent viscosity Combined effect, coefficient , The Prandtl number determines the turbulence of each equation ( = =2.0), thereby adjusting the gradient diffusion intensity; the second term on the right is the generation term, representing the rate at which velocity shear generates turbulent kinetic energy; the third term on the right is the dissipation term, which respectively characterizes and The dissipation of energy cascades from large-scale turbulence to small-scale turbulence and is ultimately converted into internal energy.

[0058] In the liquid cooling process of high-frequency transformers, the coolant flows within the pipes and exchanges heat with the windings and core, forming a typical heat-fluid coupling process. This process is non-isothermal; while absorbing heat, the coolant's temperature changes spatially, leading to alterations in its physical properties (such as density and viscosity), which in turn affect the flow state, demonstrating a two-way coupling relationship between the temperature field and the flow field. Specifically, the velocity distribution and shear gradient in the flow field determine the intensity of convective heat transfer at various points, dominating the spatial evolution of the temperature field; while the temperature field further influences the flow behavior by regulating fluid properties. A schematic diagram of the coupling is shown below. Figure 5 As shown.

[0059] Step 3: Determining the heat source boundary To ensure that the simulated heat source is consistent with the actual operating conditions, this embodiment conducted an no-load test on the high-frequency transformer. The experimental platform consists of a signal generator, a power amplifier, and a power analyzer. A schematic diagram of the experiment is shown below. Figure 6As shown in Figure 7(a), due to the limited maximum output voltage of the power supply, in order to obtain the core loss measurement value under rated frequency and rated operating magnetic flux density, an additional winding needs to be wound around the middle column of the core. A square wave voltage with a frequency of 10kHz and an amplitude of 142.7V is applied to the additional winding, with the primary and secondary windings open-circuited. The core loss is read as 331.7W by the power analyzer. The voltage and current waveforms of the additional winding at this time are shown in Figure 7(a). In the winding loss measurement experiment, a sinusoidal current with a frequency of 10kHz and an effective value of 30A is applied to the secondary winding of the transformer, with the primary winding short-circuited. The voltage and current waveforms of the secondary winding at this time are shown in Figure 7(b). The winding loss measurement value is 17.26W, which is corrected to 604.12W at a rated current of 193A and a reference temperature of 120℃. The conversion formula is as follows: In the formula: I , I exp These are the effective values ​​of the actual operating current and the test current, respectively. P exp To test short-circuit loss; K Temperature conversion factor for losses; R dcT0 The sum of the DC resistances of the primary and secondary windings at the measured temperature; T con , T 0 represents the reference temperature and the measured temperature, respectively.

[0060] Experimental measurements revealed that the heat dissipation rates of the transformer's core, primary winding, and secondary winding under no-load conditions were 319.11 W, 338.49 W, and 222.20 W, respectively. These heat source data will be used as input for steady-state thermal simulation to analyze the temperature distribution characteristics under different cooling structures.

[0061] Step 4: Modeling Cooling Structure Parameters Structural model under forced liquid cooling as follows Figure 8 As shown, the axis of the cooling pipes is located on the perpendicular bisector between the iron core and the primary winding, and they are evenly arranged according to the pipe spacing. This structure facilitates uniform distribution of coolant, improves heat exchange efficiency, and avoids excessive local temperature rise. Simultaneously, since the cooling copper pipes are embedded in epoxy resin insulation material and located in the center of the insulator, with insulation layers covering both sides, the risk of insulation breakdown is effectively reduced, further improving the system's operational reliability and safety. Variables to be optimized are as follows: Figure 9 As shown, including the outer diameter of the cooling pipe D , cooling tube wall thickness d Number of cooling pipe turns N Cooling pipe spacing s .

[0062] An ethylene glycol-water mixture with a volume fraction of 30% was selected as the cooling medium. The material properties of this cooling medium are shown in Table 2.

[0063] Table 230% Ethylene Glycol-Water Mixture Material Parameters Step 5: Response Surface Modeling and Optimization Objective Setting A central composite design (CCD) was employed to construct a combination of structural parameters. Finite element simulations were then performed to obtain temperature rise results under different design parameter conditions, which were used as the basis for response surface modeling instead of experimental data. Subsequently, a response surface model between temperature rise and key dimensions of the liquid-cooled structure was established based on the simulation results. A quadratic polynomial form was chosen to balance model simplicity and fitting accuracy, and its expression is shown below: In the formula: The objective function is... 0 represents the regression coefficient of the constant term; j Let be the linear regression coefficient, representing the th . j Linear effects of individual variables; jj Let be the regression coefficient of the quadratic term, representing the th term. j The secondary effect of each variable; ij The interaction regression coefficient represents the variable. x i and x j The interaction effect; x i , x j For experimental variables; m This represents the number of experimental variables.

[0064] Since the number of optimization factors is 4, according to the CCD experimental design standard, each factor adopts a five-level coding, generating a total of 30 sets of simulation sample points. The experimental design scheme is shown in Table 3, and the simulation results are shown in Table 4.

[0065] Table 3. Four-factor, five-level test table Table 4 Response Surface Simulation Results Based on experimental data relating water-cooled structural parameters to the transformer's maximum temperature, a quadratic polynomial model can be fitted and constructed as shown below to simulate and predict the maximum temperature under different structural parameters.T max .

[0066] Step 6: Multi-objective optimization solution The NSGA-II algorithm is chosen to handle multi-objective optimization problems. The specific optimization process is as follows: Figure 10 As shown. The parameters in the algorithm are set as follows: total population size is 100, maximum number of iterations is 1000, crossover probability is 0.9, crossover distribution index is 10, and mutation distribution index is 20.

[0067] A multi-objective optimization was performed to determine the maximum temperature of the high-frequency transformer and the amount of copper cooling pipe material used. The objective function and constraints of the constructed multi-objective optimization model are shown below: Material usage of copper cooling pipes V Represented as: In the formula: and The length and width of the cooling pipe's surrounding path are 83.36 mm and 207.36 mm, respectively. f 1 represents the objective function 1; f 2 represents the objective function 2; T max V represents the highest temperature; V is the highest temperature; V represents the highest temperature. Total volume of copper material ; L 0 represents the axial unfolding length of a single turn; W 0 represents the radial unfolding length of a single turn; D min ，D max Indicates the lower and upper limits of the outer diameter of the cooling pipe; d min ，d max Indicates the lower and upper limits of wall thickness. ；N min ，N max Indicates the lower and upper limits of the number of turns. ；s min ，s max Indicates the lower and upper limits of the spacing. ； The set of integers represents the number of turns. N Integer value required 。

[0068] The range of values ​​for each structural parameter of the cooling structure is shown in Table 5. The setting of these parameters is constrained by the dimensions of the transformer structure. For example, the outer diameter of the cooling tube is limited by the effective installation spacing between the core and the secondary winding; while the spacing between the cooling tubes and the number of turns are limited by the epoxy resin casting height, requiring a balance between thermal performance and structural strength.

[0069] Table 5. Constraints for Structural Optimization Step 7: Optimization Solution Decision Screening The Pareto front set obtained by the NSGA-II algorithm is as follows: Figure 11 As shown, each dot on the Pareto front set represents a feasible optimal solution. Each optimal solution requires a trade-off between two objective functions; there is no solution that simultaneously optimizes both objectives. Therefore, the entropy-weighted TOPSIS method is used to further comprehensively evaluate and screen the Pareto front solutions. This method allows for manual setting of the weights of each objective function based on actual engineering needs, and sorts the solutions by calculating their proximity to the ideal solution, thereby selecting a representative optimal solution that considers multiple objectives and improving decision-making efficiency and rationality.

[0070] First, construct the decision matrix based on the Pareto front solution set. , i The number of solutions above the frontier solution. j To optimize the number of metrics and perform normalization, the following steps are taken: In the formula: r j max , r j min The first j The maximum and minimum values ​​of each objective across all possible scenarios. r ij For the first i The first scheme is in the j The original evaluation values ​​for each indicator.

[0071] Then, based on the weight of each indicator By weighting the standardized matrix, we obtain the weighted decision matrix: In the formula, v ij The weighted standardized index value; ω j For the first j Entropy weights of each indicator; z ijThese are the weighted, standardized index values. Based on the weighted decision matrix, calculate the Euclidean distances between each solution on the frontier and the optimal and worst solutions: Finally, calculate the relative proximity: In the formula, For the first j The ideal optimal value of each indicator; For the first j The ideal worst value for each indicator; v ij After weighted standardization, the first i The first scheme is in the j Evaluation values ​​on each indicator; For the first i A plan and an ideal; No. i The Euclidean distance between each solution and the ideal worst solution; C i For the first i The proximity coefficient of each scheme.

[0072] The solutions are then sorted according to their relative proximity; the larger the value, the closer the solution is to the ideal solution, thus selecting the optimal solution.

[0073] To reflect design preferences under different operating conditions, three representative weighting combinations were selected: one is that hotspot temperature and conductor quantity are equally important, i.e. Secondly, when thermal performance is given greater emphasis, the hot spot temperature is chosen with greater weight, i.e. Third, when material conservation is prioritized, the amount of conductor used carries significant weight, i.e. Three optimal solutions were selected under three sets of weights. To verify the actual effect of each optimization scheme, the three optimization results were compared with the initial design scheme through simulation. The simulation results are as follows: Figure 12a As shown in Figures b, c, and d, the structural parameters, response surface methodology results, and cooling material usage of the initial and optimized design schemes are presented in Table 6. Optimized scheme one reduced the maximum temperature rise and material usage by 11.57% and 25.65% respectively compared to the initial design, achieving a balance between temperature rise control and material conservation. Optimized scheme two showed more significant effects in suppressing temperature rise, with the maximum temperature rise reduced by 33.86% compared to the initial design. Optimized scheme three further improved material usage, reducing cooling material usage by 47.04%.

[0074] Table 6 Optimization Design Results

Claims

1. A method for optimizing the water-cooled structure of a high-frequency transformer using heat-fluid coupling simulation, characterized in that... Includes the following steps: Step 1: Structural Integration Design In the insulation area between the core and secondary winding of the epoxy resin-encapsulated high-frequency transformer, a spiral copper cooling pipe is pre-embedded to form an embedded water-cooling structure; this cooling structure is integrated with the transformer. Step 2: Thermal-fluid coupling modeling Based on high-frequency excitation conditions, a multi-physics thermal-fluid coupling model is established, which includes heat conduction, convection, thermal radiation, and non-isothermal fluid flow. The model considers the influence of coolant flow on the temperature field distribution, and temperature changes also feed back to affect the flow field behavior, thus achieving bidirectional coupling. Step 3: Determine the boundary of the heat source Through no-load and short-circuit tests, heat dissipation data of the core and winding under actual operating conditions are obtained and used as heat source input for steady-state simulation to ensure that the heat source boundary of the model is consistent with the actual operating conditions. Step 4: Modeling the cooling structure parameters With the outer diameter of the cooling pipe D Wall thickness d Number of turns N Turn spacing s To design variables, construct a structural parameter space; An ethylene glycol-water mixture, which combines thermal performance and electrical insulation, was selected as the cooling medium. Step 5: Response Surface Modeling and Optimization Objective Setting A response surface model of the relationship between the maximum temperature of the high-frequency transformer and the parameters of each cooling structure was established by using the central composite design method combined with finite element simulation. Dual objective functions were set: ① minimizing the maximum temperature, ② minimizing the amount of cooling material used. Step 6: Multi-objective optimization solution A non-dominated sorting genetic algorithm was used to perform multi-objective optimization of the cooling structure, and the Pareto optimal solution set was obtained. Step 7: Optimize the decision-making process The entropy weight-TOPSIS method is introduced to sort and filter the multi-objective solution set according to different weight preferences, and output a representative optimal structural design scheme.

2. The optimization method for a high-frequency transformer water-cooling structure assisted by heat-fluid coupling simulation according to claim 1, characterized in that, In step 1, the structural integration design method is as follows: In epoxy resin-encapsulated high-frequency transformers, there is a closed insulation gap between the core and the secondary winding. To improve the heat dissipation efficiency in this area, spiral copper cooling pipes are pre-embedded along the axial direction in this area to form an embedded forced water cooling structure. This structure is integrally encapsulated with the winding and epoxy resin, and is connected to the external cooling circuit through the sealed external water inlet and outlet on the shell. Both sides of the cooling pipe are covered with an insulating dielectric layer.

3. The optimization method for a high-frequency transformer water-cooling structure assisted by heat-fluid coupling simulation according to claim 1, characterized in that, In step 2, the thermal-fluid coupling modeling is as follows: The constructed heat-fluid coupling model includes multi-physics processes such as steady-state heat conduction, non-isothermal flow, natural convection, and thermal radiation; heat conduction and thermal convection are described by Fourier's law, and its basic equations are: In the formula: Density; Heat capacity; Heat flux density; The thermal conductivity coefficient; The fluid velocity; This is the temperature gradient vector; The divergence of heat conduction flux; This represents the Laplace operation on spatial coordinates; Thermal radiation is described by the Stefan-Boltzmann law, as follows: In the formula: Surface emissivity; This is the Stefan-Boltzmann constant. = 5.67×10 -8 ; T amb The ambient temperature; T This is the surface temperature at the boundary. This is the unit normal vector pointing outside the computational domain; The flow field is calculated using the Navier-Stokes equations, taking into account the viscous and inertial effects of the coolant flowing within the pipe: In the formula: This represents the Laplace operation on spatial coordinates; The fluid velocity; For dynamic viscosity, p For pressure, During the coupling process, the temperature of the coolant affects its viscosity, thermal conductivity, and density, thereby influencing the flow field distribution and achieving bidirectional coupling.

4. The optimization method for a high-frequency transformer water-cooling structure assisted by heat-fluid coupling simulation according to claim 1, characterized in that, In step 3, the method for determining the heat source boundary is as follows: By conducting no-load excitation experiments on high-frequency transformers, the core loss and winding loss were measured, and then standardized to the rated operating state according to the conversion formula: In the formula: I , I exp These are the effective values ​​of the actual operating current and the test current, respectively. P exp To test short-circuit loss; K Temperature conversion factor for losses; R dcT0 The sum of the DC resistances of the primary and secondary windings at the measured temperature; T con , T 0 represents the reference temperature and the measured temperature, respectively.

5. The optimization method for a high-frequency transformer water-cooling structure assisted by heat-fluid coupling simulation according to claim 1, characterized in that, In step 4, the modeling method for the cooling structure parameters is as follows: Select the outer diameter of the cooling copper pipe D Wall thickness d Number of turns N and pipe spacing s As design variables, and considering that the setting of these parameters is constrained by the structural dimensions of the transformer, the parameter space is defined as follows: In the formula, D min ，D max Indicates the lower and upper limits of the outer diameter of the cooling pipe; d min ，d max Indicates the lower and upper limits of wall thickness. ；N min ， N max Indicates the lower and upper limits of the number of turns. ；s min ，s max Indicates the lower and upper limits of the spacing. ； The set of integers represents the number of turns. N Integer value required ； Meanwhile, the cooling medium was selected as a 30% (v / v) ethylene glycol-water mixture, with the following physical properties: In the formula, ( T ) represents density; k t ( T () represents thermal conductivity; ( T () represents dynamic viscosity; T For temperature; Ensure that the thermal-fluid properties of the medium change with temperature during the simulation process.

6. The optimization method for a high-frequency transformer water-cooling structure assisted by heat-fluid coupling simulation according to claim 1, characterized in that, In step 5, the objective for response surface modeling and optimization is set as follows: The test points were arranged using a central composite design method, and the response variable "maximum temperature" was analyzed. T "With design variables" D , d , n , s Establish a quadratic polynomial response surface model between them: In the formula, 0 represents the regression coefficient of the constant term; j Let be the linear regression coefficient, representing the th . j Linear effects of individual variables; jj Let be the regression coefficient of the quadratic term, representing the th term. j The secondary effect of each variable; ij The interaction regression coefficient represents the variable. x i and x j The interaction effect; x i , x j For experimental variables; m The number of experimental variables; Set up a dual objective function: in, In the formula, f 1 represents the objective function 1; f 2 represents the objective function 2; T max This is the highest temperature; V gauge Total volume of copper material ; L 0 represents the axial unfolding length of a single turn; W 0 represents the radial unfolding length of a single turn; Therefore, the objective function and constraints of the constructed multi-objective optimization model are as follows: 。 7. The optimization method for a high-frequency transformer water-cooling structure assisted by heat-fluid coupling simulation according to claim 1, characterized in that, In step 6, the solution process for the multi-objective optimization is as follows: The above model was solved using the non-dominated sorting genetic algorithm NSGA-II, and the optimized parameters were: D , d , N , s The objective is to minimize simultaneously f 1, f 2; In each iteration, new solution sets are continuously evolved through elite retention, tournament selection, simulated binary crossover and Gaussian mutation operations, eventually converging to the Pareto optimal frontier; The parameters in the algorithm are set as follows: total population size is 100, maximum number of iterations is 1000, crossover probability is 0.9, crossover distribution index is 10, and mutation distribution index is 20.

8. The optimization method for a high-frequency transformer water-cooling structure assisted by heat-fluid coupling simulation according to claim 1, characterized in that, In step 7, the decision-making and screening of the optimization scheme is as follows: The entropy-weighted TOPSIS method is introduced to construct a decision matrix based on the Pareto front solution set. , i The number of solutions above the frontier solution. j To optimize the number of indicators, r ij For the first i The first scheme is in the j The original evaluation values ​​for each indicator were then normalized. In the formula: r j max , r j min The first j The maximum and minimum values ​​of the target across all possible scenarios; Based on the weight of each indicator By weighting the standardized matrix, we obtain the weighted decision matrix: In the formula, v ij The weighted standardized index value; ω j For the first j Entropy weights of each indicator; z ij The weighted standardized index value; Calculate the ideal optimal solution for each option. v + and worst solution v - Euclidean distance: And the proximity coefficient is obtained: In the formula, For the first j The ideal optimal value of each indicator; For the first j The ideal worst value for each indicator; v ij After weighted standardization, the first i The first scheme is in the j Evaluation values ​​on each indicator; For the first i A plan and an ideal; No. i The Euclidean distance between each solution and the ideal worst solution; C i For the first i The proximity coefficient of each solution; Based on this, multiple schemes were sorted and screened, and three representative optimal structural schemes were selected, corresponding to three design preferences: heat dissipation priority, material saving priority, and weight balance.

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