Modelica-based modeling and simulation method for fast calculation of multi-physical fields of oil-immersed transformer

Abstract

This invention discloses a modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica, belonging to the field of transformer simulation calculation technology. Leveraging Modelica's object-oriented multi-domain unified modeling advantages, a hybrid-dimensional computational architecture with field-circuit coupling is constructed. A refined finite element field model is built for key winding regions affecting heat flow distribution to ensure local calculation accuracy. A one-dimensional path model is built for external cooling oil paths that do not require detailed distribution information to ensure system-level computational efficiency. A cross-dimensional data mapping mechanism based on the integral averaging rule is used to achieve bidirectional conservation data interaction between the field and path models. Simultaneously, the numerical discretization scheme is optimized to adapt to the transformer's heat flow coupling characteristics to ensure computational stability and solution accuracy. Finally, modular encapsulation enables standardized model reuse and rapid co-simulation, solving the problems in existing technologies where simulation accuracy and computational efficiency cannot be simultaneously achieved, multiphysics coupling data interaction is difficult, and it is difficult to adapt to the real-time simulation requirements of digital twins.

Description

Technical Field

[0001] This invention relates to the field of transformer simulation calculation technology, specifically to a modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica. Background Technology

[0002] Oil-immersed power transformers are core hub equipment in AC / DC power systems, responsible for voltage transformation, power transmission, and grid isolation. Their operational reliability directly determines the power supply safety and stable operation level of the power system. The losses generated by the windings, core, and other components inside the transformer during electromagnetic energy conversion are transformed into heat. This heat is exchanged through the flow of insulating oil and conducted through the solid structure to achieve temperature equilibrium. The hot spot temperature of the windings and the internal oil flow distribution characteristics directly determine the aging rate of the insulation material, the remaining service life of the equipment, and the risk of operational failure. Therefore, accurate and efficient electromagnetic-thermal-fluid multiphysics coupling simulation calculations inside the transformer are the core technical support for transformer optimization design, condition assessment, operation and maintenance, and full life cycle management.

[0003] Current mainstream technologies for multiphysics simulation of oil-immersed transformers all have significant technical shortcomings, failing to simultaneously achieve both simulation accuracy and computational efficiency. For instance, the empirical formula method can only roughly estimate the average oil temperature and hot spot temperature of the transformer. Its empirical coefficients rely on extensive experimental calibration, resulting in a narrow applicability and low computational accuracy. It can only be used for preliminary verification in the early design stage and cannot meet the needs of refined analysis. The thermoelectric analogy method achieves rapid calculation of macroscopic temperature rise through lumped parameter equivalence, but it cannot output the spatial distribution details of internal winding temperature and oil flow, making it difficult to accurately locate local hot spots and predict risks. While traditional finite element numerical calculation methods can achieve refined multiphysics solutions for the entire model, their full-size 3D model mesh is enormous, and single-condition solutions can take hours or even days, placing extremely high demands on computational resources and completely failing to meet the real-time simulation requirements of digital twin scenarios. Existing improvement schemes for accelerating simulations mostly reduce computational load by reducing model dimensionality, simplifying structure, and ignoring nonlinear terms. However, this sacrifices the equivalent accuracy of microstructures such as oil baffles and winding pads, and fails to accurately capture the influence of local structures on oil flow distribution and hot spot formation. Furthermore, it does not solve the problem of real-time iteration of nonlinear physical property parameters of insulating oil, thus reducing the physical realism of simulation results. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies by providing a modeling and simulation method for rapid multi-physics calculation of oil-immersed transformers based on Modelica. Leveraging Modelica's object-oriented, multi-domain unified modeling advantages, a hybrid-dimensional computational architecture with field-circuit coupling is constructed. A refined finite element field model is built for key winding regions affecting heat flow distribution to ensure local computational accuracy. A one-dimensional path model is constructed for external cooling oil paths that do not require detailed distribution information to ensure system-level computational efficiency. A cross-dimensional data mapping mechanism based on the integral averaging rule is used to achieve bidirectional conservation data interaction between the field and path models. Simultaneously, the numerical discretization scheme is optimized to adapt to the transformer's thermal-fluid coupling characteristics to ensure computational stability and solution accuracy. Finally, modular encapsulation enables standardized model reuse and rapid co-simulation, solving the problems of existing technologies where simulation accuracy and computational efficiency cannot be simultaneously achieved, multi-physics coupling data interaction is difficult, and it is difficult to adapt to the real-time simulation requirements of digital twins.

[0005] To solve the above-mentioned technical problems, this invention provides the following technical solution: a modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica, the method comprising: S1: Construct a refined geometric model for the key winding region that affects heat flow distribution in an oil-immersed transformer, perform mesh generation on the geometric model, extract the mesh information matrix and node information matrix, and store them as a preset format file; S2: Construct a two-dimensional finite element field model of the key region in the Modelica environment, set the nonlinear material property parameters, establish the incompressible laminar flow control equation and the temperature field control equation, set the boundary conditions and complete the steady-state field solution to obtain the flow field and temperature field distribution data of the key region. S3: For the external cooling oil circuit of oil-immersed transformer, a one-dimensional circuit model is constructed in the Modelica environment; and a fluid connector containing potential variables and flow variables is defined to establish a cross-dimensional data mapping mechanism at the interface between the field model and the circuit model. The two-way conversion and conservation transfer of discrete physical quantities of the field model and macroscopic physical quantities of the circuit model are realized through the mapping equation system. S4: Modularly encapsulate the field model and the road model in the Modelica platform, establish bidirectional connectivity between the field model and the road model, and export them as standard functional model units after encapsulation. Then, realize the rapid joint simulation calculation of multiphysics fields of oil-immersed transformers through the solution platform.

[0006] Furthermore, in S1, taking the grid-side winding of the converter transformer prototype as the implementation object, a geometric entity including high-voltage, medium-voltage, low-voltage, and voltage-regulating windings is constructed; the model retains a refined structure that changes the oil flow distribution, including oil baffles, foot rings, winding pads, and winding washers; and the computational domain of the above geometric model is divided into structured meshes. In the finite element preprocessing stage, the mesh information matrix and node information matrix of the computational domain are extracted and saved as MAT file format.

[0007] Furthermore, in step S2, the nonlinear material property parameters are set as nonlinear functions of temperature T for the core properties of the insulating oil, specifically including: the density of the insulating oil. Specific heat capacity at constant pressure Thermal conductivity Dynamic viscosity Furthermore, the nonlinear parameters are iteratively updated in real time within the computing nodes.

[0008] Furthermore, in S2, the incompressible laminar flow governing equations include a steady-state fluid continuity equation based on the law of mass conservation: And the Navier-Stokes equations: ,in, , These are the velocity components in the x and y directions, respectively. It is a velocity vector. The density of the insulating oil, For volume forces, The static pressure of the fluid. It is the viscous stress tensor.

[0009] Furthermore, in S2, the temperature field control equation adopts the steady-state energy conservation equation: ,in To calculate the real-time temperature of the node, The specific heat capacity of insulating oil under real-time constant pressure. This refers to the real-time thermal conductivity of the corresponding medium. The heat source term in the winding region is used; for the numerical oscillation problem under high Peckley number conditions, an upwind finite element scheme is introduced, with the weighting function as follows: ,in, It is the first The weighted function of the finite element method for each element facing the wind. As a windward factor, For the element feature size, Let Galerkin's finite element basis functions be used. This is the velocity vector.

[0010] Furthermore, in S2, the boundary conditions are set by: setting the non-permeable wall as a no-slip wall condition, i.e., the velocity vector... Heat transfer from the winding washers and insulating cylinders is ignored; heat is assumed to be transferred only through the inlet and outlet interfaces of the oil flow in the field model.

[0011] Furthermore, in S2, a steady-state thermal-fluid coupling solution is performed in the Modelica environment. The solution process employs a bidirectional iterative strategy: first, the flow field is initialized to obtain the initial flow field distribution; then, the initial flow field is substituted into the temperature field control equation to obtain the initial temperature field distribution; based on the initial temperature field, the nonlinear physical property parameters of the insulating oil are updated and substituted into the flow field control equation again for solution. This iterative process is repeated until a preset convergence criterion is met. The convergence criterion is set as follows: the residual of the total temperature calculation is less than 1 × 10⁻⁶. -6 The residual for velocity calculation is less than 1×10 -5 The pressure calculation residual is less than 1×10 -4 After the solution is completed, the flow field distribution data and temperature field distribution data of the key region of the winding in the entire computational domain are output.

[0012] Furthermore, in S3, the one-dimensional path model includes an environmental model, a water pump model, and a heat-fluid coupling power input module; the environmental model is used to set the atmospheric pressure and ambient temperature, the water pump model is used to set a constant oil flow rate to ensure stable mass flow rate and enthalpy, and the heat-fluid coupling power input module is used to transmit winding loss power to the field model; a fluid connector containing potential variables and flow variables is defined in Modelica, where the potential variables include pressure and specific enthalpy, and the flow variables include mass flow rate and enthalpy flow rate.

[0013] Furthermore, in S3, the mapping equation system specifically includes: Mass flow mapping from field model outlet to road model: ; Mass flow mapping from the road model to the field model inlet: ; Interface pressure transmission constraints: ; in, It is the total mass flow rate transferred from the two-dimensional field model outlet to the one-dimensional path model. It is the total mass flow rate transferred from the one-dimensional path model to the inlet of the two-dimensional field model. The average normal velocity of the boundary elements at the interface of the field model. The unit boundary length, The density of the insulating oil, This represents the total number of boundary elements at the interface. It is the uniform pressure at the interface entrance of the one-dimensional road model. It is the uniform pressure at the interface exit of the one-dimensional road model. The total area of ​​the interface. This represents the pressure values ​​of each element at the interface of the field model.

[0014] Furthermore, the specific steps of S4 are as follows: The compiler is used to compile and link the underlying code of the flow field and temperature field algorithms and the sparse matrix solver library into dynamic link libraries or static library files; In Modelica, a unified Package is created. The Package reads the stored MAT format preprocessed files and resource class files, and establishes a bidirectional connection between the one-dimensional path model and the field model through a connector and mapping mechanism by calling external functions. The complete package is encapsulated as a functional model unit (FMU) and exported. The calculation of trigger events, variables, and parameters is completed in the solver platform, and the simulation results are output.

[0015] Beneficial effects Compared with existing technologies, this Modelica-based modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers has the following advantages: This invention innovatively proposes a multi-physics field-path coupling hybrid-dimensional computing architecture based on Modelica. It constructs a two-dimensional finite element field model for key areas of the winding that require finely distributed information, and a one-dimensional path model for external cooling oil paths that do not require detailed distribution. While fully preserving the high-precision distribution information of the flow field and temperature field in key areas, it significantly reduces the computational load of the model. Furthermore, it designs a seamless cross-dimensional field-path data mapping mechanism based on the integral averaging law. Through standardized Modelica connectors and mapping equations, it realizes the bidirectional conversion between discrete physical quantities of the field model and macroscopic physical quantities of the path model, ensuring the conservation of mass and energy in the cross-dimensional transfer process. This solves the technical problems of cumbersome data interaction, inconsistent interfaces, and easy errors in the serial coupling of existing heterogeneous software.

[0016] This invention optimizes the numerical discretization scheme for the physical characteristics of transformer thermal-fluid coupling. It adopts Taylor-Hood hybrid element method to handle flow field calculations to meet the LBB condition, and introduces the upwind finite element method to solve the numerical oscillation problem under high Peclet number conditions, which significantly improves the stability and convergence of matrix solutions. At the same time, it establishes a nonlinear mathematical model of the changes in insulating oil physical properties with temperature, and iterates and updates it in real time during the calculation process, which greatly improves the physical realism and calculation accuracy of thermal-fluid coupling simulation.

[0017] This invention achieves refined equivalent modeling of the complex internal structure of transformers. It accurately preserves the microstructures such as oil baffles, foot rings, and winding pads in the two-dimensional solution domain, and precisely defines the boundary conditions. It can accurately capture and reproduce the true distribution characteristics of the oil flow velocity in the transformer's internal channels, which decreases first and then increases. This solves the technical problem that existing simplified models cannot accurately describe the influence of microstructures on local flow fields and hot spots.

[0018] Other advantages, objectives and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination or study, or may be learned from the practice of the invention. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0020] Figure 1 The flowchart shows a modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica. Figure 2 This is a flowchart of step S3 of the modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica. Detailed Implementation

[0021] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0022] This invention provides a modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica. Leveraging Modelica's object-oriented, multi-domain unified modeling advantages, a hybrid-dimensional computational architecture with field-circuit coupling is constructed. A refined finite element field model is built for key winding regions affecting heat flow distribution to ensure local computational accuracy. A one-dimensional path model is constructed for external cooling oil paths that do not require detailed distribution information to ensure system-level computational efficiency. A cross-dimensional data mapping mechanism based on the integral averaging rule is used to achieve bidirectional conservation data interaction between the field and path models. Simultaneously, the numerical discretization scheme is optimized to adapt to the transformer's heat flow coupling characteristics to ensure computational stability and solution accuracy. Finally, modular encapsulation enables standardized model reuse and rapid co-simulation. This solves the problems in existing technologies where simulation accuracy and computational efficiency cannot be simultaneously achieved, multiphysics coupling data interaction is difficult, and it is difficult to adapt to the real-time simulation requirements of digital twins.

[0023] like Figure 1 As shown, S1: Construct a refined geometric model for the key winding region that affects the heat flow distribution in the oil-immersed transformer, perform meshing on the geometric model, extract the mesh information matrix and node information matrix and store them as a preset format file; In the specific implementation process, the grid-side winding of the oil-immersed converter transformer prototype was used as the core implementation object. Based on the rated parameters and structural dimensions of the transformer design drawings, a complete coaxial nested geometric solid model was constructed, including the high-voltage winding, medium-voltage winding, low-voltage winding, and voltage regulating winding. This model fully reproduced the radial layering and axial segmentation structure of the windings, and replicated the actual gap dimensions of the main oil passages and interlayer oil passages between each winding. During the geometric model construction process, all detailed structures that have a significant regulatory effect on oil flow distribution and temperature rise distribution were fully preserved, including but not limited to the oil baffles set in the axial segmentation of the windings, the foot rings at the winding ends, the winding pads between winding layers, the winding washers at the winding ends, and the insulating cylinders. The installation position, dimensional parameters, and spatial layout of each structural component were accurately reproduced, and the actual oil flow channel morphology, oil flow turning path, and structural constraint boundaries of the winding area were fully reproduced. This avoided the problems of oil flow distribution calculation deviation and winding hot spot temperature prediction distortion caused by excessive simplification of the structure.

[0024] After constructing the geometric solid model, the effective computational domain of the winding region is fully structured and meshed. A hierarchical mesh control strategy is implemented: for core regions with large flow field and temperature gradients, such as the main oil channels between windings, the deflection zone around the oil baffle, and the gaps between winding pads, local mesh refinement is performed, and boundary layer meshes are set to ensure that the number of mesh layers in the near-wall region is no less than 3, accurately capturing the velocity and temperature gradients near the wall. For solid regions such as winding conductors and insulators, a uniform structured mesh is used to balance computational accuracy and solution efficiency. After meshing, mesh quality verification is performed to ensure that the mesh orthogonality is greater than 0.7, the aspect ratio is less than 5, and the skewness is less than 0.3, ensuring that the mesh quality meets the convergence and accuracy requirements of finite element calculation.

[0025] In the finite element preprocessing stage, the extraction and standardized storage of all information in the computational domain are completed: the mesh information matrix and node information matrix corresponding to the computational domain are extracted, where the mesh information matrix includes the topological connection relationship of the mesh elements, element type, element size parameters, and material domain identifier of the element; the node information matrix includes the two-dimensional coordinate information of each node, the association information between the node and its element, and the boundary type identifier of the node; the node set and element set of the entrance boundary, exit boundary, wall boundary, and adiabatic boundary of the computational domain are extracted simultaneously to generate the boundary identifier matrix. The extracted mesh information matrix, node information matrix, and boundary identifier matrix are uniformly saved in MAT file format to complete the standardized and reusable storage of preprocessed data, realize the decoupling of the geometric model and subsequent simulation calculation, and facilitate the rapid iteration of the model under different winding structures and different working conditions.

[0026] S2: Construct a two-dimensional finite element field model of the key region in the Modelica environment, set the nonlinear material property parameters, establish the incompressible laminar flow control equation and the temperature field control equation, set the boundary conditions and complete the steady-state field solution to obtain the flow field and temperature field distribution data of the key region. In the specific implementation process, in the Modelica simulation environment, the stored MAT format preprocessed data is read through the external function interface, and the geometric topology, mesh structure and boundary markers of the computational domain are automatically restored to construct a two-dimensional finite element thermal-fluid coupling field model of the key area of ​​the winding. The model is divided into a fluid computational domain and a solid computational domain. The fluid computational domain is the region of insulating oil flow between windings, and the solid computational domain is the region of solid structures such as winding conductors, insulating pads, and oil baffles.

[0027] First, complete the full setting of material properties, setting corresponding properties for the solid and fluid domains respectively: For solid structures such as winding conductors and insulation components, set fixed thermal conductivity, density, and specific heat capacity at constant pressure; for the fluid domain of insulating oil inside the transformer, set its core properties as nonlinear functions that dynamically change with the real-time node temperature T, accurately reproducing the property changes of insulating oil at different operating temperatures. The specific nonlinear parameter settings are as follows: Insulating oil density: ; Specific heat capacity of insulating oil under constant pressure: ; Thermal conductivity of insulating oil: ; Insulating oil dynamic viscosity:

[0028] During the simulation iterative calculation process, a real-time iterative update mechanism for nonlinear parameters is established: In each coupled iteration step, the real-time temperature of each calculation node in the current iteration step is first obtained, and the insulating oil physical property parameters of the corresponding node are updated based on the above nonlinear function. Then, the updated physical property parameters are substituted into the flow field and temperature field control equations for solution, realizing bidirectional coupled iteration of physical property parameters and temperature field. This ensures that the material parameters are completely matched with the changes in insulating oil physical properties under actual working conditions during the calculation process, and greatly improves the accuracy of thermal flow field coupled calculation.

[0029] After setting the material parameters, the incompressible laminar flow control equations and temperature field control equations of the field model are constructed sequentially, forming a complete set of heat-fluid coupling control equations. Among them, the incompressible laminar flow control equations are constructed based on the laws of conservation of mass and momentum, and are adapted to the low flow rate and incompressible laminar flow characteristics of transformer insulating oil. Specifically, they include: Steady-state fluid continuity equation based on the law of conservation of mass: ; Based on the Navier-Stokes equations of the law of conservation of momentum: ; In the formula, u and v are the velocity components in the x and y directions, respectively. It is a velocity vector. The density of the insulating oil, For volume forces, The static pressure of the fluid. This is the viscous stress tensor, which is directly related to the fluid dynamic viscosity and velocity gradient.

[0030] The temperature field control equations are constructed based on the steady-state energy conservation law, covering three major heat transfer processes: fluid convection heat transfer, solid heat conduction, and heat generation from the winding heat source. The specific equations are as follows: In the formula, To calculate the real-time temperature of the node, The specific heat capacity of insulating oil under real-time constant pressure. This refers to the real-time thermal conductivity of the corresponding medium. The heat source term is the heat source term in the winding region. The heat source term originates from the load loss and no-load loss generated during the operation of the transformer winding. In the implementation process, the total loss power of the winding is calculated based on the rated operating parameters of the transformer. According to the volume distribution of the winding conductor, the total loss power is converted into a uniformly distributed volume heat generation rate and loaded into the finite element element corresponding to the winding conductor to achieve accurate allocation of the heat source term.

[0031] Meanwhile, to address the numerical oscillations and non-convergence issues caused by the dominance of the convection term under high Peckley number conditions, a stabilized upwind finite element scheme is introduced into the finite element solution process to numerically stabilize the convection term. The corresponding weighting function is set as follows: In the formula, The windward factor can be adaptively adjusted according to the Peckley number of the working conditions. The higher the Peckley number, the higher the windward factor value. For the element feature size, Let Galerkin's finite element basis functions be used. The velocity vector is the element. The upwind finite element method effectively suppresses numerical oscillations under high flow velocity and strong convection conditions, ensuring convergence of the solution process and stability of the calculation results across the entire working range.

[0032] After constructing the governing equations, the precise boundary conditions for the field model are set, specifically including: Flow boundary conditions: All non-permeable solid walls, such as the winding conductor surface, oil baffle surface, pad surface, and insulating cylinder surface, are set as no-slip wall conditions, i.e., the fluid velocity vector at the wall surface is determined. It accurately reproduces the viscous constraint effect of the solid wall on the oil flow; the axial inlet of the field model is set as the velocity inlet boundary and the outlet is set as the free flow outlet boundary, providing upstream and downstream constraints for the oil flow.

[0033] Thermal boundary conditions: For axial solid structures such as winding washers and insulating cylinders, the heat transfer due to axial heat conduction is ignored and set as an adiabatic boundary condition; the heat generated in the winding region is set to be transferred only through the convection heat transfer of insulating oil at the inlet and outlet interfaces of the field model, which simplifies the non-core heat transfer process while ensuring the accuracy of the core heat flow coupling calculation.

[0034] After setting the boundary conditions, a steady-state thermo-fluid coupling solution is performed in the Modelica environment. The solution process adopts a two-way iterative strategy: first, the flow field is initialized to obtain the initial flow field distribution; then, the initial flow field is substituted into the temperature field control equation to obtain the initial temperature field distribution; based on the initial temperature field, the nonlinear physical properties of the insulating oil are updated and substituted into the flow field control equation again for solution, repeating the above iterative process until the preset convergence criterion is met. The convergence criterion is set as follows: the residual of the total temperature calculation is less than 1 × 10⁻⁶. -6 The residual for velocity calculation is less than 1×10 -5 The pressure calculation residual is less than 1×10 -4 After the solution is completed, the flow field distribution data and temperature field distribution data of the key region of the winding in the entire computational domain are output, including discrete physical quantities such as flow velocity, pressure, temperature, and heat flux density of each computation node, and the hot spot location and temperature of the winding are accurately located.

[0035] S3: For the external cooling oil circuit of oil-immersed transformer, a one-dimensional circuit model is constructed in the Modelica environment; and a fluid connector containing potential variables and flow variables is defined to establish a cross-dimensional data mapping mechanism at the interface between the field model and the circuit model. The two-way conversion and conservation transfer of discrete physical quantities of the field model and macroscopic physical quantities of the circuit model are realized through the mapping equation system. In the specific implementation process, such as Figure 2 As shown, in the Modelica environment, a corresponding one-dimensional heat-fluid coupling circuit model is constructed based on the actual cooling oil circuit topology of the transformer. The one-dimensional circuit model includes an environment model, a water pump model, and a heat-fluid coupling power input module. The environment model is used to set the atmospheric pressure and ambient temperature corresponding to the simulation conditions, providing boundary reference parameters for the oil circuit system. The water pump model is used to set a constant flow rate of the insulating oil in the cooling oil circuit, ensuring the stability of the mass flow rate and fluid enthalpy within the oil circuit system, providing stable oil flow input conditions for the two-dimensional field model. The heat-fluid coupling power input module is used to convert the transformer winding loss power into a heat source term, transmitting the corresponding power input to the two-dimensional field model, realizing the coupling correlation between winding loss and oil flow temperature rise.

[0036] A standardized fluid connector is defined in the Modelica environment. This connector fully complies with the causal relationship specification for multi-domain modeling in Modelica. Two types of core physical quantities are defined within the connector: potential variables and flow variables. Potential variables include fluid pressure and specific enthalpy, while flow variables include fluid mass flow rate and enthalpy flow rate. Through this standardized fluid connector, the physical quantity interaction interface between modules of the one-dimensional path model and between the one-dimensional path model and the two-dimensional field model is completely unified, providing a standardized and unbiased interaction channel for cross-dimensional data transfer.

[0037] A cross-dimensional data mapping mechanism is established at the interface between the field model and the road model. Through a complete set of mapping equations, a bidirectional conversion is achieved between the discrete microscopic physical quantities at the inlet / outlet interface of the two-dimensional field model and the macroscopic lumped physical quantities at the corresponding interface of the one-dimensional road model. At the same time, the mass conservation, energy conservation, and pressure continuity at the interface are strictly guaranteed, realizing the conservation and transfer of physical quantities. The mapping equations specifically include: Mass flow mapping equation from field model outlet to road model: ; Mass flow mapping equation from the road model to the field model inlet: ; Interfacial pressure transmission constraint equation: ; In the formula, The average normal velocity of the boundary elements at the interface of the field model. The unit boundary length, The density of the insulating oil, This represents the total number of boundary elements at the interface. The total area of ​​the interface. This represents the pressure values ​​of each element at the interface of the field model.

[0038] The above mapping equations ensure the conservation of mass, energy, and pressure at the interface between the field model and the road model, enabling bidirectional coupling and transfer of the fine discrete calculation results of the two-dimensional field model and the macroscopic system calculation results of the one-dimensional road model. This solves the problems of non-conservation of physical quantities and data transfer deviation in cross-dimensional model joint simulation.

[0039] S4: Modularly encapsulate the field model and the road model in the Modelica platform, establish bidirectional connectivity between the field model and the road model, and export them as standard functional model units after encapsulation. Then, realize the rapid joint simulation calculation of multi-physics fields of oil-immersed transformers through the solution platform. The specific implementation process is divided into the following three stages: In the first stage, the underlying code for the finite element solution algorithm of the flow field and temperature field of the two-dimensional field model was written in C / C++. An efficient solution library adapted to solve large sparse linear equation systems was integrated, supporting various sparse matrix solution algorithms such as the conjugate gradient method and the GMRES method. The solution was optimized for the matrix characteristics of the transformer thermal-fluid coupling problem. The underlying solution code and sparse matrix solution library were compiled and linked by the compiler to generate a dynamic link library or static library file that conforms to the Modelica external function interface specification. This provides efficient and stable external solution support for the Modelica environment and greatly improves the solution efficiency of finite element calculation.

[0040] The second phase involves creating a unified Package within the Modelica environment. This Package employs a layered architecture, comprising four core layers: Interfaces, Models, Functions, and Resources. Specifically, the Interfaces layer stores definitions for standardized fluid connectors, boundary interfaces, and input / output interfaces; the Models layer stores one-dimensional road models; the Functions layer stores external function interfaces, physical property calculation functions, mapping equation solving functions, and data read / write functions; and the Resources layer stores stored MAT format preprocessed files, compiled link library files, and parameter configuration files.

[0041] The Package automatically reads the MAT format preprocessed file and parameter configuration file in the Resources layer through built-in read and write functions. It calls the compiled solver library file through the external function interface in the Functions layer to realize the solution call of the two-dimensional field model. Through the standardized fluid connector in the Interfaces layer, the one-dimensional path model and the two-dimensional field model establish bidirectional data communication through the field-path coupling mapping module, forming a complete and independently runnable field-path coupling multiphysics simulation model. During the model encapsulation process, the transformer rated parameters, material property parameters, boundary condition parameters, and solution control parameters are all set as modifiable input parameters to realize the full parameterization of the model, which facilitates the rapid adaptation of models of transformers with different capacities and structures.

[0042] The third stage involves standard model export and co-simulation calculation. The complete package integrated in the Modelica environment is packaged into a functional model unit (FMU) according to the FMI (Functional Model Interface) standard and exported. It supports FMI 2.0 and FMI 3.0 standards and is compatible with both model exchange and co-simulation modes, realizing the standardization, portability and reusability of simulation models.

[0043] Import the packaged FMU file into a solver platform that supports the FMI standard, and complete the simulation configuration: set the initialization configuration of simulation trigger events, state variables and parameters, select the appropriate differential-algebraic equation solver, including implicit Euler method, trapezoidal method, BDF method, etc., set the simulation step size and convergence threshold. After configuration, start the co-simulation calculation. The solver automatically completes the bidirectional coupled iterative solution of the one-dimensional road model and the two-dimensional field model. During the solution process, the conservation and transfer of cross-dimensional data and the real-time update of nonlinear parameters are automatically realized.

[0044] After the simulation calculation is completed, the system automatically outputs the full simulation results, including but not limited to: the temperature distribution and hot spot temperature of the entire winding, the oil flow velocity distribution in the winding oil channels, the pressure and flow distribution at each node of the oil circuit system, the oil flow temperature difference between the radiator inlet and outlet, and the balance data of winding losses and system heat dissipation. Simultaneously, the encapsulated FMU model can be directly embedded into transformer system simulation and power grid system simulation, enabling joint simulation of the transformer's multi-physics characteristics and power grid operating conditions, significantly improving simulation efficiency and model compatibility.

[0045] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica, characterized in that, The method includes: S1: Construct a refined geometric model for the key winding region that affects heat flow distribution in an oil-immersed transformer, perform mesh generation on the geometric model, extract the mesh information matrix and node information matrix, and store them as a preset format file; S2: Construct a two-dimensional finite element field model of the key region in the Modelica environment, set the nonlinear material property parameters, establish the incompressible laminar flow control equation and the temperature field control equation, set the boundary conditions and complete the steady-state field solution to obtain the flow field and temperature field distribution data of the key region. S3: For the external cooling oil circuit of oil-immersed transformer, a one-dimensional circuit model is constructed in the Modelica environment; and a fluid connector containing potential variables and flow variables is defined to establish a cross-dimensional data mapping mechanism at the interface between the field model and the circuit model. The two-way conversion and conservation transfer of discrete physical quantities of the field model and macroscopic physical quantities of the circuit model are realized through the mapping equation system. S4: Modularly encapsulate the field model and the road model in the Modelica platform, establish bidirectional connectivity between the field model and the road model, and export them as standard functional model units after encapsulation. Then, realize the rapid joint simulation calculation of multiphysics fields of oil-immersed transformers through the solution platform.

2. The modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica according to claim 1, characterized in that, In S1, the grid-side winding of the converter transformer prototype is used as the implementation object, and a geometric entity including high-voltage, medium-voltage, low-voltage and voltage-regulating windings is constructed. The model retains a refined structure that changes the oil flow distribution, including oil baffles, foot rings, winding pads and winding washers. The computational domain of the above geometric model is divided into structured meshes. In the finite element preprocessing stage, the mesh information matrix and node information matrix of the computational domain are extracted and saved as MAT file format.

3. The modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica according to claim 1, characterized in that, In step S2, the nonlinear material property parameters are set as nonlinear functions of temperature T for the core properties of the insulating oil, specifically including: insulating oil density. Specific heat capacity at constant pressure Thermal conductivity Dynamic viscosity Furthermore, the nonlinear parameters are updated iteratively in real time within the computing nodes.

4. The modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica according to claim 1, characterized in that, In S2, the incompressible laminar flow governing equations include a steady-state fluid continuity equation based on the law of mass conservation: And the Navier-Stokes equations: ,in, , These are the velocity components in the x and y directions, respectively. It is a velocity vector. The density of the insulating oil, For volume forces, The static pressure of the fluid. It is the viscous stress tensor.

5. The modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica according to claim 4, characterized in that, In S2, the temperature field control equation adopts the steady-state energy conservation equation: ,in To calculate the real-time temperature of the node, This refers to the real-time constant-pressure specific heat capacity of insulating oil. This refers to the real-time thermal conductivity of the corresponding medium. For the heat source term of the winding region; To address the numerical oscillation problem under high Peckley number conditions, an upwind finite element scheme is introduced, with the weighting function being: ,in, It is the first The weighted function of the finite element method for each element facing the wind. As a windward factor, For the element feature size, These are the Galerkin finite element basis functions.

6. The modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica according to claim 1, characterized in that, In S2, the boundary conditions are set as follows: the non-permeable wall is set as a no-slip wall condition, i.e., the velocity vector... Heat transfer from the winding washers and insulating cylinders is ignored; heat is assumed to be transferred only through the inlet and outlet interfaces of the oil flow in the field model.

7. The modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica according to claim 1, characterized in that, In S2, a steady-state thermal-fluid coupling solution is performed in the Modelica environment. The solution process adopts a two-way iterative strategy: first, the flow field is initialized to obtain the initial flow field distribution; The initial flow field is substituted into the temperature field control equation to obtain the initial temperature field distribution. Based on the initial temperature field, the nonlinear physical properties of the insulating oil are updated and substituted back into the flow field control equation for solution. This iterative process is repeated until a preset convergence criterion is met. The convergence criterion is set as follows: the residual of the total temperature calculation is less than 1 × 10⁻⁶. -6 The residual for velocity calculation is less than 1×10 -5 The pressure calculation residual is less than 1×10 -4 After the solution is completed, the flow field distribution data and temperature field distribution data of the key region of the winding in the entire computational domain are output.

8. The modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica according to claim 1, characterized in that, In S3, the one-dimensional path model includes an environmental model, a water pump model, and a heat-fluid coupling power input module. The environmental model is used to set the atmospheric pressure and ambient temperature, the water pump model is used to set a constant oil flow rate to ensure stable mass flow rate and enthalpy, and the heat-fluid coupling power input module is used to transmit winding loss power to the field model. In Modelica, a fluid connector containing potential variables and flow variables is defined. Potential variables include pressure and specific enthalpy, and flow variables include mass flow rate and enthalpy flow rate.

9. The modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica according to claim 4, characterized in that, In S3, the mapping equation set specifically includes: Mass flow mapping from field model outlet to road model: ; Mass flow mapping from the road model to the field model inlet: ; Interface pressure transmission constraints: ; in, It is the total mass flow rate transferred from the two-dimensional field model outlet to the one-dimensional path model. It is the total mass flow rate transferred from the one-dimensional path model to the inlet of the two-dimensional field model. The average normal velocity of the boundary elements at the interface of the field model. The unit boundary length, The density of the insulating oil, This represents the total number of boundary elements at the interface. It is the uniform pressure at the interface entrance of the one-dimensional road model. It is the uniform pressure at the interface exit of the one-dimensional road model. The total area of ​​the interface. This represents the pressure values ​​of each element at the interface of the field model.

10. The modeling and simulation method for rapid multiphysics calculation of oil-immersed transformers based on Modelica according to claim 1, characterized in that, The specific steps of S4 are as follows: The compiler is used to compile and link the underlying code of the flow field and temperature field algorithms and the sparse matrix solver library into dynamic link libraries or static library files; In Modelica, a unified Package is created. The Package reads the stored MAT format preprocessed files and resource class files, and establishes a bidirectional connection between the one-dimensional path model and the field model through a connector and mapping mechanism by calling external functions. The complete package is encapsulated as a functional model unit (FMU) and exported. The calculation of trigger events, variables, and parameters is completed in the solver platform, and the simulation results are output.

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