A transformer field-circuit coupling simulation method and device

Abstract

The application discloses a transformer field-circuit coupling simulation method and device, and relates to the technical field of power equipment simulation. The application first configures frequency domain external circuit excitation parameters corresponding to a nonlinear transformer simulation domain and winding initial induced electromotive force; a frequency domain circuit model is built by using Kirchhoff's voltage law, and winding current is obtained by combining parameter configuration and operation, so that frequency domain circuit simulation is completed; the winding current is used as excitation, the whole nonlinear electromagnetic field in the nonlinear transformer simulation domain is simulated by using a frequency domain decomposition physical information neural network, and nonlinear field domain simulation is realized; the winding induced electromotive force is updated by inversely calculating the electromagnetic field distribution by using the electromagnetic induction law, and field-circuit data interaction is completed; the above three types of simulation processes are iterated circularly by using the updated induced electromotive force, and after the winding current or the induced electromotive force meets the convergence index, the target winding current and the electromagnetic field distribution are output, and the five-step closed loop is used to build a complete frequency domain field-circuit coupling simulation link.

Description

Technical Field

[0001] This application relates to the field of power equipment simulation technology, and in particular to a transformer field-circuit coupling simulation method and device. Background Technology

[0002] Electromagnetic field numerical simulation is an indispensable key technology in the design, optimization, operation analysis, and fault diagnosis of modern power equipment. By accurately predicting the electromagnetic field distribution, losses, and interactions with external circuits within the equipment, engineers can significantly shorten development cycles, reduce manufacturing costs, and improve equipment performance.

[0003] At present, the Finite Element Method (FEM) is the mainstream implementation scheme for electromagnetic field simulation in the engineering field. This method is mature and reliable, and can solve high-precision field distribution results under given excitation and boundary conditions. However, it has inherent shortcomings in the field-circuit coupling simulation scenario of transformer system: when realizing the bidirectional coupling calculation of circuit and electromagnetic field, it is necessary to use multiple independent solvers to perform alternating calculations and cross-module data interaction, which makes the solution process complicated. The data interpolation process is prone to introducing additional calculation errors, and the convergence of coupling iteration is difficult to guarantee. Therefore, the industry has begun to explore new meshless solution ideas to avoid the inherent drawbacks of the Finite Element Method.

[0004] Currently, with the development of deep learning technology, Physics-Informed Neural Networks (PINN) has emerged as a novel technology for solving partial differential equations without mesh. This method embeds the residuals and boundary conditions of partial differential equations into the loss function and uses the automatic differentiation characteristics of neural networks to achieve the solution of electromagnetic fields without mesh, thus avoiding the defects of finite element method that rely on mesh partitioning and cross-module interpolation.

[0005] However, most existing PINN-related studies only focus on solving independent partial differential equations with fixed source terms and boundary conditions. They lack a system-level coupling architecture that can realize real-time data interaction between external circuits and electromagnetic fields, and still cannot handle the coupling problem of dynamic linkage between the field and the external excitation circuit. This makes it difficult to meet the engineering application requirements of high-precision nonlinear field-circuit coupling simulation of transformers. Summary of the Invention

[0006] This application provides a transformer field-circuit coupling simulation method and apparatus. The main purpose is to realize meshless nonlinear field simulation by using a frequency domain decomposition neural network, and to realize bidirectional dynamic coupling of field and circuit through a closed-loop iterative architecture of circuit-field-data interaction, so as to provide a reliable engineering implementation scheme for high-precision nonlinear frequency domain field-circuit coupling simulation of transformers.

[0007] To achieve the above objectives, this application mainly provides the following technical solutions: The first aspect of this application provides a transformer field-circuit coupling simulation method, the method comprising: Configure the frequency domain external circuit excitation parameters and the initial induced electromotive force of the winding corresponding to the nonlinear transformer simulation domain; wherein, the external circuit excitation parameters are a set of electrical parameters that provide frequency domain excitation conditions for transformer circuit simulation, and the initial induced electromotive force of the winding is the initial boundary condition when the field-circuit coupling simulation iteration starts; A frequency domain circuit model is constructed based on Kirchhoff's voltage law. The current winding current is calculated by combining the external circuit excitation parameters and the initial induced electromotive force of the winding, so as to complete a round of frequency domain circuit simulation. Using the current winding current as excitation, the nonlinear electromagnetic field in the nonlinear transformer simulation domain is simulated in its entirety through a frequency domain decomposition physical information neural network to obtain the current electromagnetic field distribution, thereby completing one round of nonlinear field simulation. Based on the current electromagnetic field distribution, the induced electromotive force of the winding is updated by inversion based on the law of electromagnetic induction, so as to complete a round of field-circuit data interaction operation; Using the updated winding induced electromotive force, a coupled simulation process consisting of the frequency domain circuit simulation operation, the nonlinear field domain simulation operation, and the field-circuit data interaction operation is executed iteratively until the winding current or induced electromotive force meets the preset convergence condition. Then, the target winding current and target electromagnetic field distribution are output for transformer operating condition and performance simulation evaluation.

[0008] A second aspect of this application provides a transformer field-circuit coupling simulation device, the device comprising: An initialization unit is used to configure the frequency domain external circuit excitation parameters and the initial induced electromotive force of the winding corresponding to the nonlinear transformer simulation domain; wherein, the external circuit excitation parameters are a set of electrical parameters that provide frequency domain excitation conditions for transformer circuit simulation, and the initial induced electromotive force of the winding is the initial boundary condition when the field-circuit coupling simulation iteration starts; The circuit simulation unit is used to construct a frequency domain circuit model based on Kirchhoff's voltage law. Combining the external circuit excitation parameters obtained by the initialization unit with the initial induced electromotive force of the winding, it calculates the current winding current to complete one round of frequency domain circuit simulation. The field simulation unit is used to simulate the nonlinear electromagnetic field in the nonlinear transformer simulation domain by using the current winding current obtained by the circuit simulation unit as excitation and through the frequency domain decomposition physical information neural network to obtain the current electromagnetic field distribution, so as to complete a round of nonlinear field simulation operation. The field-path data interaction unit is used to update the winding induced electromotive force based on the law of electromagnetic induction according to the current electromagnetic field distribution obtained by the field simulation unit, so as to complete one round of field-path data interaction operation. The iterative control unit is used to iteratively execute a coupled simulation process consisting of the frequency domain circuit simulation operation, the nonlinear field domain simulation operation, and the field-circuit data interaction operation using the updated winding induced electromotive force obtained by the field-circuit data interaction unit, until the winding current or induced electromotive force meets the preset convergence condition, and outputs the target winding current and target electromagnetic field distribution that conform to the actual operating state of the nonlinear transformer.

[0009] A third aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the transformer field-circuit coupling simulation method as described above.

[0010] A fourth aspect of this application provides an electronic device, the device including at least one processor, and at least one memory and bus connected to the processor; wherein the processor and the memory communicate with each other through the bus; the processor is used to call program instructions in the memory to execute the transformer field-circuit coupling simulation method as described above.

[0011] By employing the above-described technical solution, the technical solution provided in this application has at least the following advantages: This application provides a transformer field-circuit coupling simulation method and apparatus. This application focuses on simulating nonlinear transformers. First, it configures the frequency domain external circuit excitation parameters and the initial induced electromotive force (EMF) of the winding corresponding to the nonlinear transformer simulation domain. Then, it uses Kirchhoff's voltage law to build a frequency domain circuit model and calculates the winding current using the configured parameters to complete the frequency domain circuit simulation. Next, using the winding current as excitation, it employs a frequency domain decomposition physical information neural network to simulate the nonlinear electromagnetic field across the entire nonlinear transformer simulation domain, obtaining the electromagnetic field distribution to achieve nonlinear field domain simulation. Then, it uses the law of electromagnetic induction to update the winding induced EMF from the electromagnetic field distribution, completing the field-circuit data interaction. Finally, it iterates the above three simulation processes using the updated induced EMF until the winding current or induced EMF meets the convergence index, outputting the target winding current and electromagnetic field distribution that closely matches the actual operating state of the nonlinear transformer. A complete frequency domain field-circuit coupling simulation link is built using a five-step closed-loop process.

[0012] Compared to the shortcomings of existing PINN-based simulations, which cannot achieve dynamic field-circuit linkage and are difficult to adapt to high-precision nonlinear field-circuit coupling simulations of transformers, this application utilizes a frequency domain decomposition neural network to achieve meshless nonlinear field simulation. Through a closed-loop iterative architecture of circuit-field-data interaction, it achieves bidirectional dynamic coupling of the field and circuit, avoids computational errors caused by the docking of multiple solvers, improves the accuracy and iterative convergence stability of nonlinear transformer electromagnetic simulation, and provides a reliable engineering implementation solution for high-precision nonlinear frequency domain field-circuit coupling simulation of transformers.

[0013] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0014] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A flowchart of a transformer field-circuit coupling simulation method provided in this application embodiment; Figure 2 This is a 2D model diagram of a transformer provided in an embodiment of this application; Figure 3 A flowchart illustrating the detailed implementation process of the field simulation operation provided in the embodiments of this application; Figure 4 A schematic diagram of the subdomain partitioning of the Frequency Domain Decomposition Physical Information Neural Network (XPINN) provided in an embodiment of this application; Figure 5 A detailed flowchart of the iterative field-circuit coupling simulation method provided in the embodiments of this application; Figure 6 This is a schematic diagram of the system functional architecture for implementing the simulation method provided in the embodiments of this application; Figure 7 This is a block diagram of a transformer field-circuit coupling simulation device provided in an embodiment of this application. Detailed Implementation

[0015] Exemplary embodiments of the present application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0016] This application provides a transformer field-circuit coupling simulation method, such as... Figure 1 As shown, the following specific steps 100 to 500 are provided in this embodiment of the application: Step 100: Configure the frequency domain external circuit excitation parameters and the initial induced electromotive force of the winding corresponding to the nonlinear transformer simulation domain; wherein, the external circuit excitation parameters are a set of electrical parameters that provide frequency domain excitation conditions for transformer circuit simulation, and the initial induced electromotive force of the winding is the initial boundary condition when the field-circuit coupling simulation iteration starts.

[0017] Step 100 is the initialization step of the method in the embodiment of this application. Before formally carrying out the transformer field-circuit coupling iterative simulation, the basic simulation parameters are configured in advance. The main content of step 100 is to complete the setting of the external circuit excitation parameters and the initial induced electromotive force of the winding corresponding to the electromagnetic system.

[0018] In this application embodiment, the physical object used in the entire field-circuit coupling simulation is the nonlinear transformer simulation domain. It refers to the global computational space that includes all physical regions such as the iron core, windings, and surrounding air when performing electromagnetic simulation on a transformer. The materials (especially the iron core) in this domain have nonlinear magnetization characteristics.

[0019] For example, Figure 2 The provided 2D model of the transformer shows the following: The outer dark gray area represents the iron core, which, relying on the high permeability of its ferromagnetic material, constrains the alternating magnetic flux and serves as the magnetic circuit carrier for electromagnetic energy coupling and transfer. The iron core material exhibits nonlinear magnetization characteristics, with its permeability varying with magnetic flux density. The two sets of vertical bicolor stripes on the left and right represent the primary and secondary windings, respectively, which act as the carriers for the input and output of alternating electrical energy. The white cavity outside the windings represents the insulating air gap region, providing electrical isolation. The transformer's working principle is as follows: After an alternating voltage at power frequency is applied to the primary winding, the winding generates an alternating excitation current, which in turn excites the alternating main magnetic flux inside the iron core. Simultaneously, the alternating magnetic flux links the windings on both sides, inducing an alternating electromotive force in the secondary winding according to the law of electromagnetic induction. Utilizing this electromagnetic coupling mechanism, the transformer achieves voltage transformation and power transfer from the primary side to the secondary side.

[0020] Among them, the frequency domain external circuit excitation parameters refer to the frequency domain equivalent parameters of the transformer's external power supply circuit, including power supply voltage, impedance, load, etc., which are used to provide excitation conditions in the frequency domain steady state for transformer circuit simulation. Additionally, the initial induced electromotive force of the winding refers to the initial induced electromotive force value set for the winding before the field-circuit coupling simulation begins, serving as the initial boundary condition for the field-circuit coupling simulation and initiating the first round of iterations.

[0021] After the external circuit excitation parameters are configured, this embodiment can continuously provide predetermined excitation conditions for transformer circuit simulation in subsequent circuit simulation stages, forming an external input for solving the circuit model. The initial induced electromotive force of the winding serves as a preset parameter for the start of iteration, providing initial boundary conditions for the entire field-circuit coupling simulation system, thereby enabling the start of the first round of circuit simulation and providing a prerequisite for the closed-loop iterative process of subsequent circuit simulation, field simulation, and data interaction.

[0022] Furthermore, it should be noted that the field-circuit coupling simulation scheme provided in this application combines transformer circuit simulation with field simulation. Specifically: Transformer circuit simulation refers to the process of calculating the electrical quantities of the transformer windings and external power supply circuits in the frequency domain based on Kirchhoff's voltage law, obtaining electrical responses such as winding current and voltage, providing current excitation conditions for field simulation; Transformer field simulation refers to the process of simulating the electromagnetic field distribution within the nonlinear transformer simulation domain using the winding current as excitation and through a frequency domain decomposition physical information neural network, obtaining the magnetic field distribution and winding induced electromotive force, providing feedback and update basis for circuit simulation. The advantages achieved are: bidirectional closed-loop coupling of the circuit-side electrical response and the field-side electromagnetic characteristics overcomes the limitation of standalone circuit simulation in failing to reflect the influence of the nonlinear magnetization effect of the iron core, and also solves the problem of standalone field simulation being difficult to adapt to dynamic circuit conditions; through frequency domain iterative convergence, while taking into account nonlinear effects, it improves the accuracy and computational efficiency of the simulation results, and can more realistically reproduce the actual operating state of the transformer.

[0023] Step 200: Construct a frequency domain circuit model based on Kirchhoff's voltage law, and calculate the current winding current by combining the external circuit excitation parameters and the initial induced electromotive force of the winding, so as to complete a round of frequency domain circuit simulation.

[0024] Step 200 is the frequency domain circuit simulation stage in the entire field-circuit coupling iteration process. Its working principle includes: (1) Establish quantitative constraint relationship using frequency domain circuit model: Using Kirchhoff's voltage law, construct frequency domain circuit model of transformer winding and external power supply circuit to quantify the relationship between external circuit excitation, winding induced electromotive force and winding current. (2) Using initialization or previous field simulation results as input: The external circuit excitation parameters (voltage source phasor) configured in step 100 and the initial induced electromotive force of the winding (or the induced electromotive force phasor output by the previous iteration field simulation) are used as the solution input; (3) Combine circuit topology and laws to complete the current solution: Combine the external circuit topology and solve the winding current phasor by frequency domain circuit equation calculation to complete the frequency domain circuit simulation of this round and provide current excitation conditions for subsequent field simulation.

[0025] The strict progressive relationship between (1) and (3) above fully presents the logical chain from "principle construction" to "input preparation" and then to "execution and solution" implemented in step 200, and finally outputs the winding current of the current iteration.

[0026] In detail, this application uses a frequency domain circuit model to establish a quantitative correlation between external circuit excitation, winding induced electromotive force, and winding current, realizing a numerical mapping from circuit excitation parameters to winding current. For example, in the process of building the frequency domain circuit model in this step, Kirchhoff's voltage law is used to establish a frequency domain winding circuit model, thereby quantifying the quantitative constraint relationship between external circuit excitation, winding induced electromotive force, and winding current. The frequency domain circuit expressions corresponding to the primary winding and secondary winding are denoted as formula (1) and formula (2), respectively: (1); (2); in, Û p This represents the externally applied voltage source phasor, which corresponds to the external circuit excitation parameters input in this step. Î p , Î s The phasors are the primary winding current phasor and the secondary winding current phasor, respectively, which are the current winding currents to be solved in this step. R p , R s These are the resistances of the primary winding and the secondary winding, respectively. Z L The load impedance; Ê ind，p , Ê ind，s These correspond to the induced electromotive force phasors of the primary and secondary windings, respectively. Ê ind，p , Ê ind，s It can be uniformly abbreviated as Ê ind The phasor of the winding induced electromotive force is taken from the initial preset value or the output of the previous field simulation stage; through the above two sets of frequency domain circuit models, the numerical mapping from the circuit excitation condition to the winding current can be realized. Formulas (1) and (2) are the direct implementation of the working principle of this step 200. They use Kirchhoff's voltage law to clearly provide the quantitative correlation between the three: external circuit excitation, winding induced electromotive force and winding current.

[0027] After quantifying the relationship between external circuit excitation, winding induced electromotive force, and winding current, as shown in (2) and (3) of the above working principle, it can be seen that: from the perspective of input composition, the input required for circuit solution includes the externally applied voltage source phasor and the winding induced electromotive force phasor calculated by field simulation in the preceding iteration process. The circuit solution process combines the external circuit topology and Kirchhoff's laws, relying on the two types of input quantities, external voltage source phasor and winding induced electromotive force phasor, to complete the quantitative solution calculation of the winding current inside the circuit.

[0028] Step 300: Using the current winding current as excitation, the nonlinear electromagnetic field in the nonlinear transformer simulation domain is simulated in its entirety through a frequency domain decomposition physical information neural network to obtain the current electromagnetic field distribution, thus completing one round of nonlinear field simulation.

[0029] It should be noted that Extended Physics-Informed Neural Networks (XPINN) is an existing general model. However, this application embodiment utilizes its domain decomposition architecture and the basic theory of Physics-Informed Neural Networks (PINN) to introduce a frequency domain control model to reconstruct the model, forming a frequency domain decomposition Physics-Informed Neural Network. In this application embodiment, for the sake of brevity, the abbreviation "XPINN" is used to specifically refer to the frequency domain decomposition Physics-Informed Neural Network developed in this application, and the two correspond one-to-one in the description of this application.

[0030] The embodiments of this application utilize the Frequency Domain Decomposition Physical Information Neural Network (XPINN), which refers to dividing the entire transformer simulation domain into multiple independent sub-regions based on the physical material boundaries of the core, winding window, and air within the frequency domain computation framework, thereby enabling the partitioned solution of the transformer's nonlinear electromagnetic field.

[0031] Step 300 is the field simulation stage corresponding to the entire field-circuit coupling iteration process. It takes the current winding current output from the frequency domain circuit simulation in step 200 as the global electromagnetic excitation source, uses the frequency domain decomposition physical information neural network (XPINN) to complete the electromagnetic field numerical simulation of the nonlinear transformer simulation domain, and finally outputs the electromagnetic field distribution corresponding to the current iteration step, thus completing this round of field simulation.

[0032] Step 400: Based on the current electromagnetic field distribution, update the induced electromotive force of the winding by inversion based on the law of electromagnetic induction to complete one round of field-circuit data interaction.

[0033] In this embodiment of the application, the current global electromagnetic field distribution result output in step 300 is used to calculate the updated winding induced electromotive force according to Faraday's law of electromagnetic induction. The electromotive force is then sent back to the circuit simulation in step 200 to realize the data transfer from field to path and complete a round of field-path data interaction.

[0034] Step 500: Using the updated winding induced electromotive force, iteratively execute the coupled simulation process consisting of frequency domain circuit simulation, nonlinear field domain simulation, and field-circuit data interaction until the winding current or induced electromotive force meets the preset convergence condition, and output the target winding current and target electromagnetic field distribution that fit the actual operating state of the nonlinear transformer.

[0035] In this embodiment, the updated winding induced electromotive force obtained from the current round of field-circuit data interaction is used to replace the winding induced electromotive force used in the next round of frequency domain circuit simulation. The frequency domain circuit simulation, field domain simulation, and field-circuit data interaction are then repeatedly executed. After each iteration, a first change in the winding current compared to the previous round is calculated, and / or a second change in the winding induced electromotive force compared to the previous round is calculated. It is then determined whether the first change and / or the second change is less than a preset convergence threshold. If either the first or second change is less than the preset convergence threshold, the iteration operation is stopped. Alternatively, a preset upper limit for the number of iterations can be added as an additional constraint to avoid excessive iterations leading to resource waste. After determining to stop the iteration operation, the winding current and electromagnetic field distribution obtained from the current iteration are determined as the final target winding current and target electromagnetic field distribution and output for transformer operating condition simulation and performance evaluation.

[0036] Based on the explanation of steps 100 to 500 above, this application performs simulation solutions for nonlinear transformers. First, it configures the frequency domain external circuit excitation parameters and the initial induced electromotive force of the winding corresponding to the simulation domain of the nonlinear transformer. Then, it uses Kirchhoff's voltage law to build a frequency domain circuit model and calculates the winding current using the configured parameters to complete the frequency domain circuit simulation. Next, it uses the winding current as excitation and employs a frequency domain decomposition physical information neural network to simulate the nonlinear electromagnetic field in the simulation domain of the nonlinear transformer, obtaining the electromagnetic field distribution to achieve nonlinear field domain simulation. Then, it uses the law of electromagnetic induction to update the winding induced electromotive force from the electromagnetic field distribution, completing the field-circuit data interaction. Finally, it iterates the above three types of simulation processes with the updated induced electromotive force until the winding current or induced electromotive force meets the convergence index, outputting the target winding current and electromagnetic field distribution that closely matches the actual operating state of the nonlinear transformer. A complete frequency domain field-circuit coupling simulation link is built using a five-step closed-loop process.

[0037] This application utilizes a frequency domain decomposition neural network to achieve meshless nonlinear field simulation. Through a closed-loop iterative architecture of circuit-field-data interaction, it realizes bidirectional dynamic coupling of the field and circuit, avoids the calculation errors caused by the docking of multiple solvers, improves the accuracy and iterative convergence stability of nonlinear transformer electromagnetic simulation, and provides a reliable engineering implementation scheme for high-precision nonlinear frequency domain field-circuit coupling simulation of transformers.

[0038] Furthermore, the target winding current and target electromagnetic field distribution are obtained by solving the coupled simulation process disclosed in steps 100 to 500 above, and electromagnetic simulation results that can characterize the actual operating conditions of the nonlinear transformer are obtained; based on the simulation results, the embodiments of this application further perform post-processing analysis and engineering applications, specifically executing the following steps (1)-(2): (1) Based on the target winding current and target electromagnetic field distribution output in step 500, extract the electromagnetic characteristic information such as winding loss, core loss, core magnetic saturation region, and winding electromagnetic force corresponding to the nonlinear transformer.

[0039] The target winding current reflects the electrical load level of each branch of the transformer, while the target electromagnetic field distribution characterizes the global magnetic flux density distribution. Combining the two types of simulation results allows for the quantitative calculation of winding Joule losses, core hysteresis and eddy current losses, locating local magnetic saturation regions of the core, calculating the magnitude and distribution area of ​​electromagnetic forces acting on the winding, and extracting various electromagnetic characteristic information to provide quantitative data support for transformer performance analysis.

[0040] Compared to the limitations of existing PINN, which can only solve independent electromagnetic field equations with fixed boundary conditions and cannot achieve dynamic linkage between the field and the circuit, this application utilizes steps 100 to 500 to construct a closed-loop iterative link, continuously completing frequency domain circuit simulation, nonlinear field simulation, and field-circuit data interaction, realizing real-time bidirectional data transmission between the external excitation circuit and the electromagnetic field; at the same time, it adopts a frequency domain decomposition physical information neural network to achieve meshless field solution, avoiding the shortcomings of traditional finite element method that relies on multiple solvers for alternating calculations and introduces additional errors through cross-module interpolation, effectively solving the problem that existing technologies cannot meet the engineering requirements of high-precision nonlinear field-circuit coupling simulation of transformers, and ensuring that the extracted electromagnetic features have high reliability.

[0041] (2) Based on the extracted electromagnetic feature information, complete the optimization of transformer structural parameters, evaluation of steady-state operation performance, or analysis of internal potential fault prediction.

[0042] Exemplary application scenarios include: if the core is found to be saturated over a wide range and the loss exceeds the standard, the core size and winding arrangement structure are adjusted to achieve structural optimization design; the operating efficiency and temperature rise level of the transformer are evaluated by combining the loss values ​​under rated operating conditions; and potential fault risks such as winding deformation and core loosening are predicted based on the electromagnetic field distortion distribution characteristics, thereby providing a quantitative decision-making basis for transformer product development and online operation and maintenance.

[0043] At the engineering implementation level, the proposed solution forms a complete processing flow of coupled simulation solution, electromagnetic feature extraction, and engineering analysis application. It can carry out quantitative analysis based on high-precision, stable and convergent nonlinear field-circuit coupled simulation results, making up for the shortcomings of existing technology in terms of insufficient simulation accuracy and difficulty in supporting the fine design and condition assessment of transformers. It is applicable to various practical engineering scenarios such as transformer product development and operation analysis.

[0044] Furthermore, it should be noted that the transformer field-circuit coupling simulation method disclosed in this application constructs a general solution process for nonlinear transformers, which is not limited to transformer objects with specific structures or operating conditions. For various nonlinear transformers with different core material characteristics, winding arrangements, and operating conditions, only the simulation domain geometric model, frequency domain external circuit excitation parameters, and material electromagnetic parameters need to be adjusted accordingly. The entire simulation link from steps 100 to 500 can be reused, demonstrating good versatility and engineering adaptability.

[0045] In some alternative embodiments, such as Figure 3 As shown, the implementation process of this field simulation operation can be further refined to include the following steps 310 to 340. Steps 310 to 340 utilize a domain decomposition neural network architecture to complete the nonlinear field simulation, specifically addressing the challenge of nonlinear simulation of transformer core magnetization. Step 310 involves splitting the physical region according to the medium and geometry and configuring independent subnets to achieve block-based solution of the simulation space, avoiding the convergence difficulties caused by fitting complex structures with a single network across the entire domain. Step 320 embeds the nonlinear magnetic characteristics of core magnetization into the frequency domain control model, accurately reproducing the nonlinear physical laws of core magnetic saturation, thus implementing transformer nonlinear simulation from a physical constraint perspective. Step 330 utilizes boundaries, interfaces, and physical constraints to collaboratively train each subnet, generating a frequency domain decomposition physical information neural network field simulator adapted to the simulation requirements. Step 340 uses the trained simulator to predict the electromagnetic field distribution across the entire domain. The entire set of steps can take into account both spatial partitioning and material nonlinearity without mesh generation, ensuring the accuracy of nonlinear transformer electromagnetic field simulation while compressing the computational errors caused by the multi-module interaction of traditional finite element methods.

[0046] The following section provides a detailed explanation of each step.

[0047] Step 310: Based on the material properties and geometric structure of the nonlinear transformer simulation domain, divide the nonlinear transformer simulation domain into multiple independent physical regions, each physical region corresponding to an independent neural network sub-model.

[0048] The necessity of “dividing the nonlinear transformer simulation domain into multiple independent physical regions” in the embodiments of this application is as follows: (1) Adaptation to different physical properties: the permeability and magnetization nonlinearity of the core, winding window, and air domain are different. The corresponding mathematical constraints and magnetization nonlinear equations can be configured separately for each region to avoid model distortion caused by the unified equation of the whole domain; (2) Independent network construction in each domain: using the XPINN domain decomposition architecture, each physical region is configured with a dedicated neural network sub-model, and the region is trained separately to reduce the fitting difficulty of a single global network and adapt to the local nonlinear magnetic saturation characteristics of the transformer; (3) Pre-feature optimization: Fourier feature mapping layer is added independently at the input end of each sub-model, and the coordinate feature mapping is completed in a targeted manner in each region to accurately capture the details of the spatial field distribution in different regions; (4) Facilitating field-circuit iterative coupling: after solving the electromagnetic field of each region in the domain, data interaction is performed at the interface of the sub-region, and then the frequency domain circuit iterative calculation is linked to greatly improve the simulation accuracy and convergence efficiency of field-circuit coupling under nonlinear conditions.

[0049] Step 310 is used to implement simulation domain partitioning and sub-model configuration. Specifically, the simulation domain partitioning is implemented first: referring to the material properties and geometric structure corresponding to the nonlinear transformer simulation domain, the overall simulation space is divided into regions. Since there are multiple materials such as iron core, windings, and air in the transformer computational domain, the material properties (such as permeability and magnetization nonlinearity) of different regions are significantly different, and the geometric boundaries of each component are clear. Therefore, the overall simulation domain can be divided into multiple independent physical regions by combining material properties and geometric boundaries.

[0050] For example, embodiments of this application provide a schematic diagram of subdomain partitioning using a frequency domain decomposition physical information neural network (XPINN), such as... Figure 4 shown. Book Figure 4 Based on the material properties and geometric structure of the transformer, it is divided into four independent subdomains: the middle gray frame area is the core area (number 0), nested inside the outer air domain; the two rectangular blocks inside the core frame are the left winding window area (number 1) and the right winding window area (number 2) respectively; the outer full-domain area is the outer air domain (number 3), which is the range surrounded by the outermost large rectangle boundary; the dashed frame inside each winding window represents the winding layout boundary, and different subdomains are separated along the contour edge. This partitioned structure is used to realize the XPINN sub-regional field simulation.

[0051] After dividing the space into multiple independent physical regions, this embodiment matches a dedicated deep feedforward neural network sub-model to each physical region to achieve domain decomposition modeling of the transformer multi-dielectric simulation space; the input of each sub-model is defined as spatial coordinates (x, y), and the output is the complex magnetic vector potential at the corresponding coordinate position. Â zThe real and imaginary values ​​are used to decompose the global solution task at the network architecture level, providing an architectural basis for applying differentiated electromagnetic constraints to different regions and embedding nonlinear magnetic properties of materials in different regions.

[0052] Furthermore, after obtaining the independent neural network sub-model corresponding to each physical region, a Fourier feature mapping layer is added to the front end of the input layer of each neural network sub-model. This structure can map the input spatial coordinates to a high-dimensional feature space through the Fourier feature mapping layer, thereby overcoming the inherent spectral bias defect of neural networks, optimizing the feature expression effect of spatial coordinates, and ultimately improving the computational accuracy of electromagnetic field numerical prediction.

[0053] Step 320: Establish frequency domain nonlinear electromagnetic field control models for each physical region, and embed the nonlinear magnetic characteristics of the iron core into the permeability parameter of the frequency domain nonlinear electromagnetic field control model to form physical constraint equations.

[0054] Step 320 is a key step in realizing nonlinear field simulation. Frequency domain control models are built in each physical region and nonlinear magnetic properties of the iron core are embedded to generate physical equations with magnetization constraints. This provides a physical constraint basis for subsequent joint training of neural networks and realizes the effective characterization of the magnetic saturation characteristics of the transformer iron core in the simulation model.

[0055] Step 330: Using the current winding current as the excitation source, and combining the boundary conditions, interface continuity conditions and physical constraint equations of each physical region, perform joint training on each neural network sub-model to obtain the trained frequency domain decomposition physical information neural network (XPINN) field simulator.

[0056] Step 330 involves multi-constraint joint training to obtain the XPINN field simulator, specifically including: using the current winding current obtained in step 200 as the external excitation of the system, combining the Dirichlet boundary conditions and Neumann boundary conditions of the outer boundaries of each physical region, as well as the continuity of the magnetic vector potential and the tangential component of the magnetic field strength at the interface of different physical regions. H t The continuous interface continuity condition, combined with the global physical constraint equation obtained in step 320, constructs a multi-objective loss function containing a nonlinear PDE loss term (a network constraint loss term constructed using a nonlinear "partial differential equation" (PDE)), a boundary condition loss term, and a nonlinear interface loss term. Based on this loss function, joint iterative training is carried out on all neural network sub-models. After training, a finalized frequency domain decomposed physical information neural network XPINN field simulator is obtained.

[0057] Step 340: Using the trained frequency domain decomposition physical information neural network (XPINN) field simulator, predict the magnetic vector potential distribution in the entire nonlinear transformer simulation domain to obtain the corresponding frequency domain electromagnetic field distribution, which is used as the current electromagnetic field distribution obtained in this round.

[0058] Step 340 is to achieve global field quantity prediction and solve the electromagnetic field distribution. Specifically, it includes: calling the fully trained XPINN field simulator, inputting the global spatial coordinates of the nonlinear transformer simulation domain into the network, completing the numerical prediction of the magnetic vector potential distribution in the entire simulation domain, and further converting the magnetic vector potential to obtain the complete frequency domain electromagnetic field distribution data of the simulation domain. This completes all the work of this round of field simulation.

[0059] In some alternative embodiments, step 320 may include further implementation steps, such as steps A1-A3, for forming the physical constraint equations: Step A1: Obtain the curve data of the measured magnetization curve corresponding to the core material in the nonlinear transformer simulation domain; perform data continuity processing on the measured magnetization curve data through a differentiable interpolation function to obtain the nonlinear magnetization expression, which is used to characterize the mapping relationship between magnetic induction intensity and equivalent permeability.

[0060] In this embodiment of the application, the magnetization curve is a magnetic induction intensity-magnetic field intensity curve (referred to as the BH curve); where B represents magnetic induction intensity and H represents magnetic field intensity. This curve is used to characterize the nonlinear magnetization law of the iron core.

[0061] Step A2: Construct electromagnetic field control models corresponding to each physical region in the frequency domain system; embed the mapping relationship into the permeability parameter of the electromagnetic field control model.

[0062] Step A3: Combining the medium properties and frequency domain electromagnetic constraints of each physical region with the electromagnetic field control model corresponding to each physical region, integrate and generate physical constraint equations with nonlinear magnetization constraints of the iron core and regional settings.

[0063] In conjunction with steps A1-A3, the embodiments of this application provide illustrative explanations as follows: For each divided physical region, a frequency-domain nonlinear electromagnetic field control model is established, and the nonlinear variation law of the iron core permeability is characterized using the BH magnetization curve of the iron core; within the iron core region, a differentiable interpolation function is used to obtain the equivalent permeability in real time by looking up a table based on the magnetic induction intensity amplitude |B| output by the network. μ r Substituting (|B|) into the equation, and using a fixed permeability parameter for the remaining linear material regions, we finally integrate them to form a physical constraint equation that includes the nonlinear characteristics of the material.

[0064] Specifically, for example: a frequency-domain nonlinear electromagnetic field control model is established for each divided physical region. In this embodiment, the electromagnetic field distribution is characterized by complex magnetic vector potential under the premise of two-dimensional magnetic quasi-static conditions. For the sinusoidal excitation signal with angular frequency ω, the original time-domain nonlinear diffusion equation is transformed into a frequency-domain nonlinear Helmholtz control equation, and the corresponding expression is as follows: (3) Formula (3); in,  z Let be the complex magnetic vector potential phasor to be solved; The source current density phasor is obtained by converting the winding current; μ Represents the magnetic permeability of materials, and nonlinear material regions such as iron cores. μ With magnetic induction intensity amplitude Dynamic changes via  z The spatial derivative is obtained by solving for the nonlinear correlation. The model parameters are embedded using the BH curve of the iron core, while a fixed permeability is used in the linear material region. σ The electrical conductivity of the material in the corresponding physical region; j The imaginary unit; operator For Hamiltonian differential operators, For divergence operators; Represents complex magnetic vector potential  z gradient, This indicates that divergence operations are performed on the vectors within the brackets. The above equations are the mathematical expressions of the frequency-domain electromagnetic field control models for each physical region, and also the basis for calculating the residual terms of the frequency-domain electromagnetic field control models in subsequent steps.

[0065] Based on the above explanation of steps A1-A3, this embodiment of the application achieves precise embedding of the nonlinear magnetic characteristics of the iron core into the frequency domain electromagnetic field model by sequentially performing three steps: magnetization curve data processing, regional electromagnetic field model construction, and regional physical constraint equation integration, thus providing multiple technical benefits. First, step A1 uses a differentiable interpolation function to process the measured magnetization curve of the iron core material into a continuous model, generating a differentiable nonlinear magnetization expression. This not only fully preserves the true nonlinear magnetization law of the iron core but also adapts to the backpropagation differentiation operation requirements of the neural network, avoiding gradient interruption in model training caused by discrete measured data. Second, step A2 independently constructs frequency domain electromagnetic field control models for each region, matching the differentiated medium characteristics of each physical region to achieve independent configuration of nonlinear magnetic constraints for each region. Finally, step A3 integrates the regional medium properties, frequency domain electromagnetic boundary constraints, and regional electromagnetic field models to uniformly generate global regional physical constraint equations. The entire process achieves deep integration of nonlinear magnetic properties and domain decomposition simulation architecture, accurately reproducing the saturated nonlinear working condition of transformer core, significantly reducing simulation distortion caused by the unified global model, and providing complete and differentiable physical constraints for multi-subnet joint training, thereby improving the solution accuracy and iterative convergence stability of nonlinear electromagnetic fields.

[0066] In some optional embodiments, for the implementation process of obtaining the XPINN field simulator through multi-subnet joint training, step 330 may further include the following implementation steps B1-B3. Steps B1-B3 construct a multi-objective loss function and perform hierarchical optimization training, utilizing various error terms to constrain the network fitting accuracy. The multi-dimensional loss term can simultaneously consider the control model, regional boundaries, and interface continuity requirements, ensuring the continuity of field quantities at the regional junctions of the segmented subnets; iterative optimization of network parameters is achieved using the gradient descent algorithm, with automatic termination of training via a threshold determination mechanism. The entire process efficiently completes the convergence training of the frequency domain decomposition neural network, leveraging the advantages of domain decomposition and regional simulation while eliminating simulation biases caused by partitioning, thus improving the stability and computational accuracy of nonlinear transformer electromagnetic field simulation. The following provides a detailed explanation of each step.

[0067] Step B1: Construct a multi-objective loss function, which includes: the residual term of the frequency domain electromagnetic field control model corresponding to each physical region, the interface continuity error term, and the boundary condition error term.

[0068] In this embodiment, the residual term of the frequency domain electromagnetic field control model is set for each divided independent physical region, with the regional frequency domain electromagnetic field control model as the reference; the equivalent permeability of the nonlinear region of the iron core is dynamically obtained by querying the BH curve using the magnetic induction intensity amplitude |B|. μ r(|B|) In the linear region, a fixed magnetic permeability is used. The output field quantity of the neural network is substituted into the control model to obtain the equation calculation residual. The residual quantifies the degree of deviation of the network solution from the theoretical solution of the electromagnetic field partial differential equation, which constitutes the quantitative index corresponding to the PDE loss.

[0069] The interface continuity error term is set at the interface of physical regions with different material properties, to ensure the continuity of the interface magnetic vector potential and the tangential component of the magnetic field strength. H t Based on two consecutive physical criteria, the numerical deviation is calculated by comparing the output field quantities of adjacent sub-models at the interface to form an error term, which is used to constrain the physical continuity of the field quantities at the boundary of the region, corresponding to the nonlinear interface loss in the original text.

[0070] Among them, the boundary condition error term acts on the global outer boundary of the nonlinear transformer simulation domain. According to the pre-set Dirichlet boundary conditions and Neumann boundary conditions of the outer boundary, the error term is formed by comparing the difference between the network boundary output field quantity and the given boundary constraint value, thereby realizing the numerical quantization of the electromagnetic constraint of the solution domain boundary, corresponding to the boundary condition loss in the original text.

[0071] This application embodiment constructs a multi-objective loss function through the above three categories of sub-items, transforming the electromagnetic field control model, regional interface constraints, and global boundary constraints into numerically optimizable quantifiable losses, providing a unified optimization objective for the parameter iterative optimization in step B2 below.

[0072] Step B2: With minimizing the loss function as the convergence objective, the gradient descent algorithm is used to iteratively update the network parameters of the corresponding neural network sub-models for each physical region.

[0073] In this embodiment, global discrete spatial coordinates (x, y) can be input to each neural network sub-model, and the network forward operation outputs the complex magnetic vector potential at the corresponding position. Â z ; Combining the core region with the |B| lookup table BH curve, we obtain μ r (|B|) Using the rule of fixed permeability in the linear region, substitute the frequency domain electromagnetic field control model, boundary constraints, and interface continuity conditions to solve for the three types of loss terms in step B1 and sum them to obtain the total loss function; use the gradient descent algorithm to obtain the gradient value of the total loss function relative to the internal parameters of each sub-model, and correct the weights and bias parameters of each sub-model according to the preset update step size along the gradient in the reverse direction to complete a single round of parameter update; repeat the entire operation process of forward evaluation, loss calculation, gradient solution, and parameter correction in a loop to continuously carry out multiple rounds of iterative optimization.

[0074] This application embodiment utilizes such an iterative update operation to continuously adjust the internal parameters of the neural network, constantly reduce the deviation between the network output field quantity and the theoretical physical solution of the electromagnetic field, gradually reduce the overall value of the multi-objective loss function, and ensure that the output results of each sub-model synchronously satisfy three physical criteria: frequency domain PDE equation, outer boundary constraint, and cross-regional interface continuity, so that the XPINN network fits the global electromagnetic field distribution law of the nonlinear transformer.

[0075] Step B3: Based on whether the value of the loss function is less than a preset threshold, determine whether to stop the iterative update. After the iteration terminates, the trained frequency domain decomposition physical information neural network (XPINN) field simulator is obtained.

[0076] In this embodiment, a quantization convergence criterion is set to terminate the training process when the loss function meets the accuracy threshold, thereby avoiding overfitting or invalid iteration problems and finally completing the final output of the XPINN field simulator, ensuring that the field simulator meets the engineering simulation accuracy requirements.

[0077] Specifically, retrieve the convergence accuracy threshold corresponding to the quantization convergence criterion, and compare the total loss value of this round calculated in real time with the preset threshold: When the total loss is less than the preset threshold: the network output accuracy is determined to have reached the design target, the gradient descent iteration loop is stopped immediately, and the parameter update step in step B2 is no longer executed; when the total loss is greater than or equal to the preset threshold: the current network fitting accuracy is determined to have not met the target, and the process returns to step B2 to continue the next round of parameter iteration optimization.

[0078] The total loss value in this round is the overall quantitative value obtained by summing the three types of sub-losses specified in step B1 after a single iteration. The overall structure is as follows: L 总 = L PDE + L 边界 + L 界面 ;in, L PDE For the residual terms of the frequency domain electromagnetic field control model; L 边界 This refers to the boundary condition error term; L 界面 This represents the interface continuity error term. The smaller the total loss, the better the output field quantity of the XPINN submodel conforms to the physical laws of electromagnetic fields.

[0079] Furthermore, based on B1-B3 above, this application also proposes some preferred methods, such as: configuring differentiated learning rates for neural network sub-models in different physical regions, using an adaptive variable learning rate in the nonlinear region of the iron core, and using a fixed learning rate in the linear region of the winding and air; dynamically adjusting the learning step size on the iron core side during the training process based on the real-time loss of each partition. Specifically, the explanation includes the following: During the iterative optimization of parameters for each neural network sub-model, differentiated learning rate rules were set for different dielectric partitions within the simulation domain of the nonlinear transformer. Based on the electromagnetic characteristics of the regions, they were divided into three categories: the core nonlinear region, the winding region, and the air region. The core, being the only region containing BH magnetization nonlinearity, presented a higher challenge in fitting network parameters, and thus an adaptive variable learning rate was adopted. The winding and air regions, with their approximately constant permeability and linearly varying electromagnetic characteristics, were uniformly configured with a fixed learning rate.

[0080] During network training, the partition loss values ​​corresponding to each sub-model are collected in real time, and the magnitude of the partition loss change is used as the basis for adjustment: when the single-step loss decrease rate in the core region is too small, the learning rate of that sub-network is automatically and slightly increased to accelerate parameter convergence; if loss oscillates and rises, the learning rate is appropriately reduced to prevent the parameters from exceeding the optimal solution. The sub-networks corresponding to the windings and air maintain a fixed learning rate throughout the entire process and do not require dynamic adjustment.

[0081] This setup aligns with the electromagnetic field variation patterns in different regions, addressing the drawbacks of a uniform learning rate across the entire domain: a uniform learning rate can easily lead to slow convergence in the nonlinear core region or training oscillations in the linear region. By utilizing a partitioned learning strategy, it balances training stability across the entire region, effectively shortening the convergence cycle of the core subnet while maintaining the simulation accuracy of the winding and air regions. This reduces the overall simulation time for a single nonlinear field, improving the operational efficiency of the entire field-circuit coupled simulation.

[0082] In some optional embodiments, during the field-to-road data interaction operation in step 340, the first round of field-to-road data interaction executes steps C1-C2 as follows, and subsequent rounds of data interaction execute steps C1-C3 as follows. Specifically, the explanation includes the following: Step C1: Extract the magnetic vector potential data of the winding region from the current electromagnetic field distribution.

[0083] After reading the global frequency domain electromagnetic field distribution results output by the field simulation in step 300, the complex magnetic vector potential of the corresponding spatial region of the winding is extracted from it. Â z Numerical data is used to extract the field quantities required for subsequent integration calculations. Magnetic vector potentials at corresponding locations on the winding cross-sections are selected from the global field simulation results to provide raw calculation data for solving the induced electromotive force using integral formulas.

[0084] Step C2: Based on Faraday's law of electromagnetic induction, perform line integration on the magnetic vector potential of the winding region to obtain the first round of updated winding induced electromotive force, so as to complete the first round of field-circuit data interaction.

[0085] This step is the induced electromotive force inversion operation. In fact, it is the transformation of physical quantities on the ground. The induced electromotive force is generated by the field magnetic vector potential conversion circuit and the first round of iterative electromotive force input is sent to the circuit simulation in step 200.

[0086] Step C3: In any round of field-path data interaction after the first round of field-path data interaction, for the winding induced electromotive force obtained from the initial update of any round, a preset relaxation factor is introduced, and the winding induced electromotive force obtained from the initial update of this round and the winding induced electromotive force obtained from the previous iteration are weighted and averaged to generate the winding induced electromotive force of the final update of this round, thus completing the field-path data interaction of this round.

[0087] This step involves retrieving pre-configured relaxation factor parameters, performing a weighted average calculation on the induced electromotive force (EMF) of the winding in this iteration and the finalized EMF from the previous iteration, and then smoothing and correcting it to obtain the final effective induced EMF for this iteration, thus completing the full data interaction step for this round. This embodiment of the application utilizes relaxation weighting to suppress large fluctuations in the induced EMF value during iteration, optimizing the iteration convergence stability, and then feeding the weighted and smoothed induced EMF into the next step, step 200, for frequency domain circuit simulation.

[0088] Based on the above explanation of steps C1-C3, the field-road data interaction operation provided in this application embodiment is divided into two types of execution branches, which are adapted to two scenarios: the first round of coupling iteration (steps C1-C2) and the remaining iteration rounds after the first round (steps C1-C3). The technical effects of the two types of branches are as follows: For the initial field-circuit data interaction, this embodiment can accurately extract the magnetic vector potential data of the winding region from the global electromagnetic field distribution, eliminating data from irrelevant areas such as the iron core and air, reducing the amount of data required for subsequent calculations, and focusing on the core region of the winding electromagnetic coupling. Using Faraday's law of electromagnetic induction, a line integral is performed on the magnetic vector potential, directly and accurately inverting the induced electromotive force of the winding from the magnetic field quantity output by the field simulation, establishing a standardized physical quantity transfer channel between nonlinear field simulation and frequency domain circuit simulation. The first round of data interaction can achieve bidirectional information exchange between the field and circuit without the need for historical iteration data, providing an initial update value of the electromotive force with rigorous physical theoretical support for the first coupling iteration, ensuring that the first round of field-circuit coupling simulation has a reliable physical benchmark.

[0089] For the additional step after the first iteration (step C3), this embodiment locks the induced electromotive force (EMF) of the initial winding obtained in this round to determine the basic data to be processed for smoothing the correction calculation. Then, a preset relaxation factor is introduced to weight the initial EMF of this round with the EMF of the previous iteration, weakening the numerical abrupt changes caused by the fluctuations in the field solution of a single round. This step suppresses the oscillation and divergence problem of the induced EMF during the coupled iteration process, smooths the trend of iterative numerical changes, improves the overall convergence speed and computational stability of the field-circuit coupling, avoids iterative back-and-forth oscillations caused by the simulation error of a single nonlinear field, and reduces the total number of coupled iterations while ensuring the accuracy of the physical solution, thus significantly improving the computational efficiency of the entire nonlinear transformer simulation.

[0090] Furthermore, to explain this more clearly, for example, regarding the bidirectional data transfer between the circuit simulation stage and the field simulation stage, field quantities and path quantities are coupled and correlated using induced electromotive force and source current density, specifically divided into two types of data mapping relationships: field-to-path and path-to-field. (1) Field-to-circuit data mapping: The induced electromotive force of the winding is solved by the field simulation results.

[0091] The global complex magnetic vector potential is obtained through field simulation in step 300. Â z Then, the induced electromotive force phasor of the winding is solved by integrating at the corresponding cross section of the winding, using the following formula (4): Formula (4) ； In formula (4): The phasor of the induced electromotive force of the winding is expressed in V. j The imaginary unit satisfies j 2 = -1; ω ω is the electrical angular frequency, measured in rad / s. N This refers to the effective number of turns of the corresponding winding; S winding The region for integrating the cross-sectional area of ​​the winding is the distribution area of ​​the winding on the solution section, with units of m. 2 ; The component of the magnetic vector potential phasor in the z-direction is expressed in Wb / m. dS Let the area be a small element. By integrating the magnetic vector potential within the cross-sectional area of ​​the winding, and combining this with the number of turns and operating frequency, the induced electromotive force phasor of the corresponding winding can be obtained. .

[0092] The phasor of the winding induced electromotive force can be obtained from the field magnetic vector potential using the above formula. The induced electromotive force phasor is then fed back to the next iteration step 200 of the frequency domain circuit simulation as the input parameter of the frequency domain circuit model.

[0093] (2) Data mapping between circuit and field: source current density is calculated from circuit winding current.

[0094] Take the winding current phasor output from the circuit simulation in step 200. Î The source current density phasor is obtained by converting it according to the following relationship (formula (5) below). ; Formula (5) ； In formula (5): The equivalent source current density phasor is expressed in A / m. 2 ; N This refers to the effective number of turns of the corresponding winding; The winding current phasor output from the circuit simulation in step 200 is in A. S The equivalent cross-sectional area of ​​the winding conductor in the field model, in meters. 2 .

[0095] Calculated source current density It is passed down to step 300 field simulation as an excitation term in the frequency domain field control model, serving as an external excitation for field simulation.

[0096] Relying on the above two sets of coupled equations, the parameter closed-loop transfer between steps 200 and 300 is realized. Together with the frequency domain circuit model of step 200 and the frequency domain field control model of step 300, they constitute the highly coupled nonlinear equation set to be solved by the method of this application embodiment.

[0097] Furthermore, in some optional embodiments, the nonlinear field simulation process provided in step 300 also includes training the initial neural network of frequency domain decomposition physical information to obtain the frequency domain decomposition physical information neural network, and the next round of training of the initial neural network of frequency domain decomposition physical information adopts the network weights obtained from the previous round of training.

[0098] The above operation introduces a warm-start strategy into the neural network training process of each round of nonlinear field simulation. The network weights, obtained after the convergence of the previous round of frequency domain decomposition physical information neural network training, are directly used as the initial weights for the next round of network training, replacing the traditional cold-start mode of randomly initializing weights in each simulation round. In the field-circuit coupling iteration process of this application embodiment, the winding current excitation, core nonlinear magnetization state, and global electromagnetic field distribution only undergo small, gradual changes in adjacent iteration rounds, and the optimal weights of the network in the two rounds have a high degree of continuity and similarity. Reusing the weight parameters completed in the previous round of training can provide an initial parameter benchmark close to the optimal solution for the current round of multi-subnet joint training, significantly reducing the initial value of the network loss function, significantly reducing the number of training iterations required for a single round of field simulation, and shortening the time consumed in a single round of field simulation. At the same time, this warm-start method can avoid training oscillations and gradient divergence problems caused by random initialization, improve the convergence stability of the XPINN regional network training, and compress the total number of rounds of field-circuit coupling iteration. While ensuring that the accuracy of the nonlinear transformer electromagnetic field solution is not diminished, it effectively improves the overall computational efficiency of the entire field-circuit coupling simulation process.

[0099] Furthermore, in step 500, some preferred methods can be provided, such as: configuring coarse and fine two-level convergence thresholds; using a coarse threshold for fast iteration in the early stage of coupled iteration, switching to a fine threshold after the iteration data tends to stabilize, and terminating the overall simulation when the fine threshold condition is met. Specifically, the explanation includes the following: In the multi-round field-circuit coupling iterative process, two sets of judgment criteria are set: coarse convergence threshold and fine convergence threshold, which control the iteration termination conditions in stages. In the early stage of simulation iteration, the winding current and induced electromotive force values ​​have large deviations, so the coarse convergence threshold is used as the judgment criterion. This threshold value is relatively large, and the system can proceed to the next stage of calculation as long as the iteration error meets the coarse threshold condition. As the iteration continues, the winding electrical parameters gradually tend to stabilize, and the system automatically switches to the fine convergence threshold. The fine threshold value is set to a smaller value, and the judgment criteria are more stringent. The overall simulation calculation ends only when the current and electromotive force errors simultaneously reach the fine threshold requirements.

[0100] Furthermore, the tiered threshold design aligns with the iterative characteristics of field-circuit coupling. A lenient, coarse threshold in the early stages quickly filters out invalid iterations with significant deviations, greatly reducing the number of early iterations and saving unnecessary network training overhead. A high-precision threshold in the later stages rigorously controls the final result error, preventing insufficient simulation accuracy due to premature iteration termination. Compared to the conventional approach of using a single convergence threshold throughout, this method avoids computational redundancy and excessive time consumption caused by fine thresholds across the entire process, while also preventing insufficient simulation accuracy due to coarse thresholds. It achieves a balance between computational efficiency and accuracy in coupled simulation, optimizing the overall performance of nonlinear transformer field-circuit coupling simulation.

[0101] Below, this application provides an illustrative explanation of step 500. In this application embodiment, the induced electromotive force of the current winding after smoothing correction in step 400 is used to replace the original initial induced electromotive force of the winding. The frequency domain circuit simulation operation in step 200, the field domain simulation operation in step 300, and the field-circuit data interaction operation in step 400 are executed again in a cyclic iteration. The overall solution of field-circuit coupling is based on the Picard iteration mechanism in this application embodiment. The specific iteration operation rules are as follows (1)-(3); (1) Iterative initialization: In the 0th iteration at the beginning of the iteration, the induced electromotive force corresponding to all windings is initialized. Ê ind The default value is zero, which serves as the initial input condition for the circuit simulation in the first round, step 200.

[0102] (2) Single-round iterative loop, including the following (21)-(24): (21) Circuit solution stage (corresponding to step 200): During the k-th iteration, the known external voltage source phasor is used. Û src The induced electromotive force retained from the previous iteration Ê ind (k-1) The winding current is obtained by solving the problem using an analytical circuit. (22) Field solution stage (corresponding to step 300): The winding current calculated in this round is used as the external source excitation of the field. The frequency domain decomposition physical information neural network XPINN field simulator is trained and fine-tuned. The global complex magnetic vector potential is solved by minimizing the multi-objective total loss function.  z (k) The iterative process employs a hot-start optimization strategy, reusing the network weights from the previous training round after convergence to continue training, thereby accelerating the network convergence rate. (23) Field-path data exchange stage (corresponding to step 400): using the current round global magnetic vector potential  z (k) By integrating at the corresponding cross-section of the winding, the calculated value of the induced electromotive force without relaxation correction is obtained. Ê ind_calc (k) ; (24) Electromotive force relaxation update: Introduce a preset relaxation factor α According to the weighted formula, the following formula (6) is given: Formula (6); Complete the final induced electromotive force update for this round, with Ê ind (k) Replace the old value and jump to the next step 200 to start a new iteration.

[0103] (3) Convergence Termination Judgment: The above iterative cycle is repeated continuously. When the change amplitude of the winding current and the winding induced electromotive force obtained in two adjacent iterations is less than the preset convergence tolerance, it is determined that the preset convergence condition is met and all iterative calculations are terminated. The converged target winding current and global target electromagnetic field distribution data are output. The results are used for transformer actual working condition simulation analysis and device performance evaluation.

[0104] Furthermore, this application embodiment also provides a more specific example of an "iterative control process," such as... Figure 5 The detailed flowchart of the iterative field-circuit coupling simulation method shown includes the following steps D1-D5; In the specific implementation of the field-circuit coupling solution using Picard iteration in the embodiments of this application, the iteration process is detailed into five stages: initialization, circuit solution, field solution, data exchange and update, and convergence determination. Step D1 (Iterative Initialization): In the initial iteration phase when iteration number k=0, convert the induced electromotive force phasors corresponding to all windings... Ê ind (0) The value is set to zero as the initial input condition for the first round of circuit simulation.

[0105] Step D2 (Frequency Domain Circuit Simulation): For any iteration process with iteration number k≥1, substitute the known external voltage source phasor. Û p The winding induced electromotive force output from the previous iteration Ê ind (k-1) Using the frequency domain circuit model derived from equations (1) and (2) above, the phasor of the primary winding current in this cycle is obtained. Î p (k) Phasor of secondary winding current Î s (k) .

[0106] Step D3 (Field Simulation): This step is the core of the field-circuit coupling solution in the embodiment of this application. The winding current obtained in step B is used as the external source excitation of the field. The domain decomposition physical constraint XPINN neural network is trained to solve the frequency domain field control model (as shown in the above formula (3)).

[0107] The XPINN algorithm divides the entire solution domain into several independent subdomains, each of which is approximated and solved by a separate neural network sub-model. The network is trained to minimize the weighted total loss function. L total To optimize the objective, the total loss is expressed as formula (7): Formula (7); in, W pde 、W bc 、W iface These are the weighted coefficients for residual loss, boundary condition loss, and interface continuity constraint loss, respectively. L pde The residual loss corresponding to the frequency domain field control model within each subdomain is used to calculate the magnetic permeability μ in the nonlinear material region based on the real-time output magnetic induction intensity amplitude of the network. The value is dynamically obtained by using a preset differentiable BH interpolation function; L bc To solve for the boundary condition loss corresponding to the outer boundary; L iface The continuity constraint loss at the interface between adjacent subdomains is given by equation (8), which includes the continuity of the magnetic vector potential. Formula (8); In formula (8): Representative subdomain i The frequency domain complex axial magnetic vector potential at the same coordinate point at the interface between the two regions Representing adjacent subfields j The frequency domain complex axial magnetic vector potential at the coordinate points of the exact same interface; this formula (8) represents the adjacent subdomain i , j The continuous amplitude of the axial complex magnetic vector potential at the interface is a mathematical expression for the continuous normal component of the magnetic field, and the continuous tangential component of the magnetic field is expressed as in formula (9): Formula (9); In formula (9): μ i Representative is i The equivalent permeability corresponding to the subdomain is, if the subdomain is an iron core material, then it is a nonlinear equivalent permeability that is dynamically updated with the magnetic induction intensity; if it is a winding or air region, then it is a fixed linear permeability. μ j Representatives and subdomains i Adjacent and boundary subdomains j The corresponding equivalent permeability is determined according to the same rules. μ i ; This represents a partial differential operator used to calculate the rate of change of a multivariable function along a single coordinate direction. , Subdomainsi , subdomain j The complex magnetic vector potential along the interface normal n The partial derivative of is physically characterized as the gradient of the change in magnetic vector potential along the interface normal.

[0108] Formula (9) constrains the continuity of the tangential magnetic field strength on both sides of the interface between adjacent subdomains. It works in conjunction with the magnetic vector potential continuity constraint in Formula (8) to form the complete electromagnetic continuity condition of the interface for XPINN domain decomposition and solution. The interface loss is taken into account for network training, and the global magnetic vector potential distribution of this round is output after completion. Â z (k) .

[0109] Furthermore, preferably, a warm-start acceleration strategy is introduced in the on-site XPINN network training stage, which reuses the weights of each sub-neuron after the previous iteration as the initial parameters for the current training, eliminating the random initialization of weights. This reduces the number of network optimization iterations while ensuring the accuracy of the solution, and accelerates the overall field-path coupling iterative computation efficiency.

[0110] Specifically, for example: in the k-th round of field training, directly load all the sub-model weights that have been solidified after the (k-1)-th round of iteration training as the initial weights for this round, and then use the updated incentives for this round. Ĵ s Continue to make minor optimizations to the parameters.

[0111] Step D4 (Data Exchange and Electromotive Force Relaxation Update): The field solution converges and the current-cycle magnetic vector potential distribution is obtained. Â z (k) Then, according to the formula (4) above, a cross-sectional integral is performed on the region where the winding is located to obtain the calculated value of the induced electromotive force without smoothing. Ê ind_calc (k) To suppress iterative oscillations and ensure iterative stability, a preset relaxation factor α is introduced to perform weighted relaxation updates. The update formula is as follows: (10) Formula (10); The winding induced electromotive force that finally takes effect in this iteration is obtained by the above calculation. Ê ind (k) .

[0112] Step D5 (Convergence Determination): Compare the numerical deviations of circuit characteristic quantities such as winding current and winding induced electromotive force corresponding to two consecutive iterations. If the deviation is less than the preset convergence threshold, the iteration is determined to meet the convergence condition, the iteration process is terminated, and the final winding current and global electromagnetic field distribution results are output; if the convergence threshold is not met, then...Ê ind (k) Replace the original initial value of the induced electromotive force and return to step D2 to start a new round of iteration.

[0113] Below, based on the transformer nonlinear field-circuit coupling simulation method based on domain decomposition XPINN neural network provided in steps 100 to 500 above, this application embodiment further provides a system functional architecture for implementing the simulation method, and the corresponding overall functional block diagram is as follows. Figure 6 As shown.

[0114] Figure 6 The system's functional architecture consists of three main parts: front-end parameter configuration, mid-section iterative coupling simulation engine, and back-end result post-processing. (1) User input and parameter configuration on the left: Complete the pre-simulation data entry, including transformer geometry, core material BH magnetization characteristics, external circuit device parameters, simulation convergence control parameters, and provide all basic physical boundary conditions for back-end solution.

[0115] (2) Iterative field-circuit coupling simulation engine in the middle: The engine includes two core modules: analytical circuit solver and nonlinear XPINN field solver. The two modules rely on bidirectional iterative coupling of data to realize the interaction of field and circuit physical quantities. The circuit solver uses external electrical parameters to solve the winding electrical quantities, and the field solver uses device geometry and material parameters to solve the global electromagnetic field. Through repeated iterations, the steady-state solution that satisfies the electromagnetic coupling law is gradually approximated.

[0116] (3) Right-side post-processing and result visualization: After the intermediate engine converges iteratively, the simulation results of winding circuit response and spatial electromagnetic field distribution data are extracted and organized to complete the quantitative analysis and result display of nonlinear electromagnetic characteristics such as transformer core saturation.

[0117] Furthermore, as a response to the above Figure 1 , Figure 3 , Figure 5 To implement the method shown, this application provides a transformer field-circuit coupling simulation device. This device embodiment corresponds to the aforementioned method embodiment. For ease of reading, this device embodiment will not repeat the details of the aforementioned method embodiment, but it should be understood that the device in this embodiment can implement all the contents of the aforementioned method embodiment. This device is used to provide a reliable engineering implementation scheme for high-precision nonlinear frequency domain field-circuit coupling simulation of transformers, specifically as follows... Figure 7 As shown, the device includes: Initialization unit 61 is used to configure the frequency domain external circuit excitation parameters and the initial induced electromotive force of the winding corresponding to the nonlinear transformer simulation domain; wherein, the external circuit excitation parameters are a set of electrical parameters that provide frequency domain excitation conditions for transformer circuit simulation, and the initial induced electromotive force of the winding is the initial boundary condition when the field-circuit coupling simulation iteration starts. The circuit simulation unit 62 is used to construct a frequency domain circuit model based on Kirchhoff's voltage law, and calculate the current winding current by combining the external circuit excitation parameters obtained by the initialization unit 61 with the initial induced electromotive force of the winding, so as to complete a round of frequency domain circuit simulation. The field simulation unit 63 is used to use the current winding current obtained by the circuit simulation unit 62 as excitation, and to perform a full-domain simulation of the nonlinear electromagnetic field in the nonlinear transformer simulation domain through a frequency domain decomposition physical information neural network, so as to obtain the current electromagnetic field distribution and complete a round of nonlinear field simulation operation. The field-path data interaction unit 64 is used to update the winding induced electromotive force based on the law of electromagnetic induction according to the current electromagnetic field distribution obtained by the field simulation unit 63, so as to complete one round of field-path data interaction operation. The iterative control unit 65 is used to iteratively execute a coupled simulation process consisting of the frequency domain circuit simulation operation, the nonlinear field domain simulation operation and the field-circuit data interaction operation using the updated winding induced electromotive force obtained by the field-circuit data interaction unit 64, until the winding current or induced electromotive force meets the preset convergence condition, and outputs the target winding current and target electromagnetic field distribution that conform to the actual operating state of the nonlinear transformer.

[0118] In some specific embodiments, the field simulation unit 63 is further specifically used for: Based on the material properties and geometric structure of the nonlinear transformer simulation domain, the nonlinear transformer simulation domain is divided into multiple independent physical regions, each of which corresponds to an independent neural network sub-model. For each of the physical regions, a frequency-domain nonlinear electromagnetic field control model is established, and the nonlinear magnetic properties of the iron core are embedded into the permeability parameter of the frequency-domain nonlinear electromagnetic field control model to form a physical constraint equation. Using the current winding current as the excitation source, and combining the boundary conditions, interface continuity conditions, and physical constraint equations of each physical region, the neural network sub-models are jointly trained to obtain the trained frequency domain decomposition physical information neural network (XPINN) field simulator. Using the trained frequency domain decomposition physical information neural network (XPINN) field simulator, the magnetic vector potential distribution in the entire nonlinear transformer simulation domain is predicted to obtain the corresponding frequency domain electromagnetic field distribution, which is used as the current electromagnetic field distribution obtained in this round.

[0119] In some specific embodiments, the execution flow of the field simulation unit 63 further includes: after obtaining the independent neural network sub-model corresponding to each physical region, before jointly training each neural network sub-model, adding a Fourier feature mapping layer at the front end of the input layer of each neural network sub-model, for mapping the input spatial coordinates to a high-dimensional feature space via the Fourier feature mapping layer.

[0120] In some specific embodiments, in the execution flow of the field simulation unit 63, the step of establishing a frequency-domain nonlinear electromagnetic field control model for each physical region, embedding the nonlinear magnetic properties of the iron core into the permeability parameter of the frequency-domain nonlinear electromagnetic field control model to form physical constraint equations, includes: Obtain the measured BH curve data corresponding to the core material in the simulation domain of the nonlinear transformer; The measured BH curve data is processed to make the data continuous by a differentiable interpolation function to obtain a nonlinear magnetization expression, which is used to characterize the mapping relationship between magnetic induction intensity and equivalent permeability. An electromagnetic field control model corresponding to each physical region is constructed in the frequency domain system. The mapping relationship is embedded into the permeability parameter of the electromagnetic field control model; By combining the medium properties and frequency domain electromagnetic constraints of each physical region, and the electromagnetic field control model corresponding to each physical region, physical constraint equations with nonlinear magnetization constraints of the iron core and regional settings are generated.

[0121] In some specific embodiments, the execution flow of the field simulation unit 63 includes the step of using the current winding current as the excitation source, combining the boundary conditions, interface continuity conditions, and physical constraint equations of each physical region, to jointly train each neural network sub-model to obtain a trained frequency domain decomposition physical information neural network (XPINN) field simulator, which obtains the trained frequency domain decomposition physical information neural network (XPINN) field simulator. Construct a multi-objective loss function, which includes: frequency domain electromagnetic field control model residual terms, interface continuity error terms, and boundary condition error terms corresponding to each physical region; With minimizing the loss function as the convergence objective, the gradient descent algorithm is used to iteratively update the network parameters of the neural network sub-model corresponding to each physical region. Based on whether the value of the loss function is less than a preset threshold, it is determined whether to stop the iterative update. After the iteration terminates, a trained frequency domain decomposition physical information neural network (XPINN) field simulator is obtained.

[0122] In some specific embodiments, in the execution flow of the field-circuit data interaction unit 64, the step of updating the winding induced electromotive force based on the law of electromagnetic induction according to the current electromagnetic field distribution to complete one round of field-circuit data interaction includes: Extract the magnetic vector potential data of the winding region from the current electromagnetic field distribution; Based on Faraday's law of electromagnetic induction, the magnetic vector potential of the winding region is linearly integrated to obtain the updated winding induced electromotive force, thereby completing the field-circuit data interaction operation for this round.

[0123] Furthermore, in any subsequent round of field-road data interaction operations after the first round, the method further includes: determining the winding induced electromotive force obtained from the initial update of this round; introducing a preset relaxation factor, performing a weighted average of the winding induced electromotive force obtained from the initial update of this round and the winding induced electromotive force obtained from the previous iteration, generating the winding induced electromotive force of the final update of this round, and completing the field-road data interaction operation of this round.

[0124] In some specific embodiments, in the execution flow of the iterative control unit 65, the process of the nonlinear field simulation operation further includes: training the initial neural network of frequency domain decomposition physical information to obtain the frequency domain decomposition physical information neural network, and the next round of training the initial neural network of frequency domain decomposition physical information adopts the network weights obtained from the previous round of training the initial neural network of frequency domain decomposition physical information.

[0125] The transformer field-circuit coupling simulation device provided in this application includes a processor and a memory. The initialization unit, circuit simulation unit, field simulation unit, field-circuit data interaction unit and iterative control unit are all stored in the memory as program units. The processor executes the program units stored in the memory to realize the corresponding functions.

[0126] The processor contains a kernel, which retrieves the corresponding program units from memory. One or more kernels can be configured, and by adjusting kernel parameters, a meshless nonlinear field simulation can be achieved using a frequency domain decomposition neural network. A closed-loop iterative architecture of circuit-field-data interaction enables bidirectional dynamic coupling between the field and circuit, providing a reliable engineering implementation scheme for high-precision nonlinear frequency domain field-circuit coupling simulation of transformers.

[0127] This application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the transformer field-circuit coupling simulation method described above.

[0128] This application provides an electronic device, which includes at least one processor, at least one memory and a bus connected to the processor; wherein the processor and the memory communicate with each other through the bus; the processor is used to call program instructions in the memory to execute the transformer field-circuit coupling simulation method as described above.

[0129] This application also provides a computer program product that, when executed on a data processing device, is suitable for performing the initialization steps of a simulation method for field-circuit coupling of an upper transformer.

[0130] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0131] In a typical configuration, the device includes one or more processors (CPUs), memory, and a bus. The device may also include input / output interfaces, network interfaces, etc.

[0132] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, like read-only memory (ROM) or flash RAM, and memory includes at least one memory chip. Memory is an example of computer-readable media.

[0133] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0134] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0135] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0136] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A transformer field-circuit coupling simulation method, characterized in that, The method includes: Configure the frequency domain external circuit excitation parameters and the initial induced electromotive force of the winding corresponding to the nonlinear transformer simulation domain. The external circuit excitation parameters are a set of electrical parameters that provide frequency domain excitation conditions for transformer circuit simulation, and the initial induced electromotive force of the winding is the initial boundary condition when the field-circuit coupling simulation iteration starts. A frequency domain circuit model is constructed based on Kirchhoff's voltage law. The current winding current is calculated by combining the external circuit excitation parameters and the initial induced electromotive force of the winding, so as to complete a round of frequency domain circuit simulation. Using the current winding current as excitation, a frequency domain decomposition physical information neural network is used to simulate the nonlinear electromagnetic field within the nonlinear transformer simulation domain, obtaining the current electromagnetic field distribution to complete one round of nonlinear field simulation. This includes: dividing the nonlinear transformer simulation domain into multiple independent physical regions based on its material properties and geometry, with each physical region corresponding to an independent neural network sub-model; establishing frequency domain nonlinear electromagnetic field control models for each physical region, embedding the nonlinear magnetic properties of the iron core into the permeability parameter of the frequency domain nonlinear electromagnetic field control model to form physical constraint equations; using the current winding current as the excitation source, and combining the boundary conditions, interface continuity conditions, and physical constraint equations of each physical region, jointly training each neural network sub-model to obtain a trained frequency domain decomposition physical information neural network field simulator; and using the trained frequency domain decomposition physical information neural network field simulator to predict the magnetic vector potential distribution within the entire nonlinear transformer simulation domain, obtaining the corresponding frequency domain electromagnetic field distribution as the current electromagnetic field distribution obtained in this round. Based on the current electromagnetic field distribution, the induced electromotive force of the winding is updated by inversion based on the law of electromagnetic induction, so as to complete a round of field-circuit data interaction operation; Using the updated winding induced electromotive force, a coupled simulation process including the frequency domain circuit simulation operation, the nonlinear field domain simulation operation, and the field-circuit data interaction operation is executed iteratively until the winding current or induced electromotive force meets the preset convergence condition, and then the target winding current and target electromagnetic field distribution are output.

2. The method according to claim 1, characterized in that, After obtaining an independent neural network sub-model corresponding to each physical region, and before jointly training the neural network sub-models, the method further includes: A Fourier feature mapping layer is added at the front end of the input layer of each neural network sub-model to map the input space coordinates to a feature space of a specified dimension via the Fourier feature mapping layer.

3. The method according to claim 1, characterized in that, The process involves establishing frequency-domain nonlinear electromagnetic field control models for each of the aforementioned physical regions, embedding the nonlinear magnetic properties of the iron core into the permeability parameter term of the frequency-domain nonlinear electromagnetic field control model, and forming physical constraint equations, including: Obtain the curve data of the measured magnetization curve corresponding to the core material in the simulation domain of the nonlinear transformer; The measured magnetization curve data is processed by a differentiable interpolation function to make the data continuous, so as to obtain a nonlinear magnetization expression. The nonlinear magnetization expression is used to characterize the mapping relationship between magnetic induction intensity and equivalent permeability. An electromagnetic field control model corresponding to each physical region is constructed in the frequency domain system; The mapping relationship is embedded into the permeability parameter of the electromagnetic field control model; By combining the medium properties and frequency domain electromagnetic constraints of each physical region, and the electromagnetic field control model corresponding to each physical region, physical constraint equations with nonlinear magnetization constraints of the iron core and regional settings are generated.

4. The method according to claim 1, characterized in that, The method of using the current winding current as the excitation source, combined with the boundary conditions, interface continuity conditions, and physical constraint equations of each physical region, to jointly train each neural network sub-model to obtain a trained frequency domain decomposition physical information neural network field simulator includes: A multi-objective loss function is constructed, which includes: residual terms of the frequency domain electromagnetic field control model corresponding to each physical region, interface continuity error terms, and boundary condition error terms; With minimizing the loss function as the convergence objective, the gradient descent algorithm is used to iteratively update the network parameters of the neural network sub-model corresponding to each physical region. Based on whether the value of the loss function is less than a preset threshold, it is determined whether to stop the iterative update. After the iteration terminates, a frequency domain decomposition physical information neural network field simulator that has been trained is obtained.

5. The method according to claim 1, characterized in that, The step of updating the induced electromotive force of the winding based on the law of electromagnetic induction according to the current electromagnetic field distribution to complete one round of field-circuit data interaction includes: Extract the magnetic vector potential data of the winding region from the current electromagnetic field distribution; Based on Faraday's law of electromagnetic induction, the magnetic vector potential data of the winding region is subjected to line integration to obtain the updated winding induced electromotive force, thereby completing the field-circuit data interaction operation for this round.

6. The method according to claim 5, characterized in that, In any subsequent round of field-road data exchange operations following the first round, the method further includes: Determine the induced electromotive force of the winding obtained in the first update of this round; By introducing a preset relaxation factor, the winding induced electromotive force of the first update in this round and the winding induced electromotive force obtained in the previous iteration are weighted and averaged to generate the winding induced electromotive force of the final update in this round, thus completing the field-circuit data interaction operation of this round.

7. The method according to any one of claims 1 to 6, characterized in that, The process of the nonlinear field simulation operation also includes: training the initial neural network of frequency domain decomposition physical information to obtain the frequency domain decomposition physical information neural network, and the next round of training the initial neural network of frequency domain decomposition physical information adopts the network weights obtained from the previous round of training the initial neural network of frequency domain decomposition physical information.

8. A transformer field-circuit coupling simulation device, characterized in that, The device includes: An initialization unit is used to configure the frequency domain external circuit excitation parameters and the initial induced electromotive force of the winding corresponding to the nonlinear transformer simulation domain. The external circuit excitation parameters are a set of electrical parameters that provide frequency domain excitation conditions for transformer circuit simulation, and the initial induced electromotive force of the winding is the initial boundary condition when the field-circuit coupling simulation iteration starts. The circuit simulation unit is used to construct a frequency domain circuit model based on Kirchhoff's voltage law. Combining the external circuit excitation parameters obtained by the initialization unit with the initial induced electromotive force of the winding, it calculates the current winding current to complete one round of frequency domain circuit simulation. The field simulation unit is used to simulate the nonlinear electromagnetic field in the nonlinear transformer simulation domain by using the current winding current obtained by the circuit simulation unit as excitation and through the frequency domain decomposition physical information neural network to obtain the current electromagnetic field distribution, so as to complete a round of nonlinear field simulation operation. Specifically, the field simulation unit is further configured to: divide the nonlinear transformer simulation domain into multiple independent physical regions based on the material properties and geometric structure of the nonlinear transformer simulation domain, with each physical region corresponding to an independent neural network sub-model; establish a frequency-domain nonlinear electromagnetic field control model for each physical region, embedding the nonlinear magnetic properties of the iron core into the permeability parameter of the frequency-domain nonlinear electromagnetic field control model to form physical constraint equations; use the current winding current as the excitation source, and combine the boundary conditions, interface continuity conditions, and physical constraint equations of each physical region to jointly train each neural network sub-model to obtain a trained frequency-domain decomposition physical information neural network field simulator; and use the trained frequency-domain decomposition physical information neural network field simulator to predict the magnetic vector potential distribution within the entire nonlinear transformer simulation domain to obtain the corresponding frequency-domain electromagnetic field distribution, which is used as the current electromagnetic field distribution obtained in this round. The field-path data interaction unit is used to update the winding induced electromotive force based on the law of electromagnetic induction according to the current electromagnetic field distribution obtained by the field simulation unit, so as to complete one round of field-path data interaction operation. The iterative control unit is used to iteratively execute a coupled simulation process consisting of the frequency domain circuit simulation operation, the nonlinear field domain simulation operation, and the field-circuit data interaction operation using the updated winding induced electromotive force obtained by the field-circuit data interaction unit, until the winding current or induced electromotive force meets the preset convergence condition, and outputs the target winding current and target electromagnetic field distribution that conform to the actual operating state of the nonlinear transformer.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the transformer field-circuit coupling simulation method as described in any one of claims 1 to 7.

10. An electronic device, characterized in that, The device includes at least one processor, and at least one memory and bus connected to the processor; The processor and the memory communicate with each other via the bus. The processor is used to call program instructions in the memory to execute the transformer field-circuit coupling simulation method as described in any one of claims 1 to 7.

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