Method and system for rapidly extracting equivalent parameters of winding parameters of oil-immersed transformer

Abstract

The invention provides a method and a system for rapidly extracting equivalent parameters of winding parameters of an oil-immersed transformer, and the method comprises the steps: converting a winding structure containing a plurality of materials into an anisotropic solid model with an oil duct, so as to process the directivity difference of the materials; and secondly, the model structure containing the oil duct is further equivalent to a uniform entity without the oil duct, multiple groups of different equivalent parameters are set to carry out temperature field simulation, an artificial intelligence method is combined to carry out temperature matching, and a parameterized database and a machine learning model are constructed, so that the equivalent parameters of windings with various structural sizes are rapidly calculated, and the calculation efficiency is improved. And the problem of physical property directionality caused by the oil duct is solved. According to the invention, the winding which is composed of a plurality of materials and has a complex internal structure is equivalent to a homogeneous continuous entity with anisotropic thermophysical properties in the aspect of macroscopic thermal behavior. The method breaks through shackles of traditional empirical formulas and isotropic hypotheses, and normal form transformation from geometric structure driving to physical performance equivalence is achieved.

Description

Technical Field

[0001] This invention relates to the field of transformer parameter prediction technology, specifically to a method and system for rapid extraction of equivalent parameters of oil-immersed transformer windings. Background Technology

[0002] Oil-immersed transformers are an important type of electrical equipment in current power systems. They utilize the convection circulation of insulating oil to transfer heat generated by the internal windings and core to the outside of the tank, achieving uniform temperature distribution and heat dissipation to ensure stable operation under safe loads. The structure of an oil-immersed transformer mainly consists of a core, windings, insulating paper, and an oil tank. Compared to dry-type transformers, oil-immersed transformers can withstand higher loads and sudden short-circuit currents during power conversion, making them an indispensable component of large-capacity power generation and distribution systems. However, the operating environment of oil-immersed transformers is often complex and variable; factors such as temperature, humidity, and load variations can all affect their operating conditions. Temperature rise in transformers not only affects the performance of their insulation materials but can also lead to aging and failure. Therefore, accurately assessing the temperature rise of oil-immersed transformers is crucial. Traditional temperature rise calculation methods, such as empirical formulas and thermal network methods, are insufficient to meet the accuracy and efficiency requirements of practical applications due to the complex structure and variable operating conditions of oil-immersed transformers.

[0003] In recent years, with the continuous advancement of computing power and software technology, the finite element method and the finite volume method have gradually become two mainstream tools for calculating the temperature rise of oil-immersed transformers. These two methods can accurately model the geometric model of the transformer and consider the nonlinear and anisotropic characteristics of materials during the calculation process, thereby achieving more accurate temperature field prediction. Furthermore, due to the complex internal structure and material composition of oil-immersed transformers, appropriate equivalent modeling is required during simulation calculations. This equivalent modeling can reduce the consumption of computing resources and improve simulation efficiency while ensuring simulation accuracy, thus providing more reliable data support for transformer design and improvement. Currently, researchers have developed several related methods. From the perspective of two-dimensional finite element simulation, Chinese patent CN117172055A proposes a homogenized thermal simulation modeling method for dry-type transformers and reactors. This method simplifies the winding structure into a continuous solid structure of uniform material through equivalent processing, but it is limited to thermal simulation calculations of dry-type transformers or reactors. Focusing on the equivalent modeling of magnetically controlled distribution transformers, Chinese patent CN117574663A proposes an equivalent modeling method for magnetically controlled distribution transformers. This method establishes an equivalent model of the winding by applying a uniform multi-turn conductor model to the winding region. By constructing an equivalent model with varying parameters through function fitting, the transformer structure is simplified and boundary conditions are applied, improving the modeling accuracy of magnetically controlled distribution transformers. With the equivalent modeling of slot windings in external rotor permanent magnet synchronous motors as the core objective, Chinese patent CN120524726A proposes a method for establishing equivalent modeling of slot windings in external rotor permanent magnet synchronous motors. Based on the slot winding structure, an equivalent model is established using appropriate isotropic material parameters. However, the above method still has some core problems. In the process of equivalent simulation of oil-immersed transformer windings, the insulating oil in the oil channels inside the windings is a flowing liquid. If the solid components of the windings are only equivalent as a whole and the flow of oil inside the windings is ignored, the accuracy of the simulation results will be reduced to some extent. On the other hand, due to the diversity of oil-immersed transformer structures, every time the winding structure and size are changed, time-consuming simulation calculations need to be performed again to obtain the equivalent parameters, which is a cumbersome process. Summary of the Invention

[0004] Purpose of the invention: The first purpose of this invention is to provide a method for rapidly extracting equivalent parameters of oil-immersed transformer windings by using an equivalent homogeneous model to replace a complex model. The second purpose is to provide a system for rapidly extracting equivalent parameters of oil-immersed transformer windings.

[0005] Technical solution: A method for rapid extraction of equivalent parameters of oil-immersed transformer windings, comprising the following steps:

[0006] S1. Construct a three-dimensional winding coil structure model based on the winding design parameters of an oil-immersed transformer;

[0007] S2. Set the material properties and boundary conditions of the three-dimensional winding coil structure model;

[0008] S3. Perform thermal simulation calculations on the three-dimensional winding coil structure model to obtain the heat flux density value;

[0009] S4. Calculate the equivalent parameters of the three-dimensional winding coil structure model based on the heat flux density value;

[0010] S5. Perform thermal simulation calculations on oil-immersed transformers using equivalent parameters to obtain simulation results of the equivalent temperature field.

[0011] S6. Construct a homogeneous model of the winding coil. Generate several sets of parameters in the parameter space by sampling. Perform thermal simulation calculations on the homogeneous model of the winding coil under each set of parameters to obtain the corresponding homogeneous model temperature field simulation results. Establish a Gaussian process proxy model and iterate with the goal of minimizing the temperature matching loss between the homogeneous model temperature field simulation results and the equivalent temperature field simulation results until the temperature matching loss is less than the set threshold. Output the corresponding equivalent homogeneous parameters.

[0012] S7. Construct a parameterized database based on the winding design parameters and corresponding equivalent homogeneous parameters of different oil-immersed transformers;

[0013] S8. Construct a prediction model based on a deep neural network, and obtain an equivalent homogeneous parameter prediction model after training with a parameterized database.

[0014] S9. Input the winding design parameters of the oil-immersed transformer to be predicted into the equivalent homogeneous parameter prediction model to obtain the corresponding equivalent homogeneous parameters.

[0015] Specifically, step S2 includes: setting the density, specific heat capacity and thermal conductivity of each material in the three-dimensional winding coil structure model, and setting different temperatures on the upper and lower surfaces of the three-dimensional winding coil structure model respectively.

[0016] Specifically, the equivalent parameters include equivalent thermal conductivity, equivalent density, and equivalent heat capacity.

[0017] Specifically, the formula for calculating the equivalent thermal conductivity is:

[0018]

[0019] In the formula: This is the heat flux density value. The equivalent thermal conductivity of the material. and for Temperature at both boundaries in the direction, For heat in The distance of directional propagation;

[0020] The formula for calculating equivalent density is:

[0021]

[0022] In the formula: For equivalent density, For the first The quality of the material The total volume of the material;

[0023] The formula for calculating equivalent heat capacity is:

[0024]

[0025] In the formula: For equivalent heat capacity, Represents isobaric conditions. For the first The heat capacity of this material This represents the total mass of the material.

[0026] Specifically, step S4 also includes: correcting the equivalent thermal conductivity based on the measured winding thermal conductivity, using the following formula:

[0027]

[0028] In the formula: This is the corrected equivalent thermal conductivity. and For linear regression parameters, The measured thermal conductivity of the winding is given.

[0029] Specifically, the construction of the homogeneous model of the winding coil includes: removing the oil passage structure and replacing it with a homogeneous material based on the three-dimensional winding coil structure model.

[0030] Specifically, the temperature matching loss is the temperature-weighted root mean square error between the simulation results of the homogeneous model temperature field and the simulation results of the equivalent temperature field.

[0031] Specifically, the parameterized database includes: a basic material table, a design parameter table, an equivalent parameter table, an experimental verification table, and a metadata table. The basic material table includes the physical parameters of each material contained in the oil-immersed transformer winding; the design parameter table includes the structural design parameters of the oil-immersed transformer winding and is associated with the parameters in the basic material table; the equivalent parameter table includes the equivalent parameters of the three-dimensional winding coil structure model and the metadata of the thermal simulation calculation; the experimental verification table includes the experimental data of the measured thermal conductivity of the winding; and the metadata table includes the parameter information and log information of the parameterized database.

[0032] Specifically, step S8 includes: cleaning and standardizing the data in the parameterized database, constructing derived input features based on the original design parameters, building a prediction model based on a deep neural network, using weighted mean square error as the loss function and introducing the Adam optimizer, and simultaneously implementing five-fold cross-validation and early stopping strategies to optimize and train the prediction model, and selecting an equivalent homogeneous parameter prediction model through evaluation indicators combined with expert experience.

[0033] On the other hand, the present invention also provides a rapid extraction system for equivalent parameters of oil-immersed transformer windings, comprising:

[0034] 3D Winding Coil Structure Model Building Module: Used to build a 3D winding coil structure model based on the winding design parameters of an oil-immersed transformer;

[0035] Model parameter setting module: used to set the material properties and boundary conditions of the three-dimensional winding coil structure model;

[0036] Heat flux density calculation module: used to perform thermal simulation calculations on the three-dimensional winding coil structure model to obtain the heat flux density value;

[0037] Equivalent parameter calculation module: used to calculate the equivalent parameters of the three-dimensional winding coil structure model based on the heat flux density value;

[0038] Equivalent temperature field simulation module: used to perform thermal simulation calculations of oil-immersed transformers using equivalent parameters, and obtain the equivalent temperature field simulation results;

[0039] Equivalent homogeneous parameter calculation module: used to construct a homogeneous model of the winding coil. It generates several sets of parameters by sampling in the parameter space, performs thermal simulation calculations on the homogeneous model of the winding coil under each set of parameters, obtains the corresponding homogeneous model temperature field simulation results, establishes a Gaussian process surrogate model, and iterates with the goal of minimizing the temperature matching loss between the homogeneous model temperature field simulation results and the equivalent temperature field simulation results until the temperature matching loss is less than a set threshold, and outputs the corresponding equivalent homogeneous parameters.

[0040] Parametric database construction module: used to build a parametric database based on the winding design parameters and corresponding equivalent homogeneous parameters of different oil-immersed transformers;

[0041] Equivalent homogeneous parameter prediction model construction module: used to build a prediction model based on a deep neural network, and obtain the equivalent homogeneous parameter prediction model after training with a parameterized database;

[0042] The equivalent homogeneous parameter prediction model application module is used to input the winding design parameters of the oil-immersed transformer to be predicted into the equivalent homogeneous parameter prediction model to obtain the corresponding equivalent homogeneous parameters.

[0043] Beneficial effects: Compared with the prior art, the significant effects of the present invention are:

[0044] 1. This invention is based on a method for rapid extraction of winding equivalent parameters that combines three-dimensional thermal-fluid coupling simulation, experimentation, and artificial intelligence. It obtains anisotropic equivalent thermal conductivity, equivalent density, and equivalent specific heat capacity, fully considers the influence of insulating oil flow, and uses experimental verification for correction. Compared with the two-dimensional simulation or isotropic assumption of the prior art, it significantly improves the accuracy of the equivalent model.

[0045] 2. The parameterized database and prediction model constructed by this invention can instantly predict the equivalent parameters of the new winding structure, avoiding the problem of having to perform time-consuming simulations every time the design is changed, and greatly improving design efficiency.

[0046] 3. This invention integrates equivalent parameter prediction with multi-objective optimization algorithms to achieve automatic optimization of winding design, which can ensure thermal performance while taking into account multiple objectives such as cost and weight.

[0047] 4. This invention constructs a feedback learning mechanism, enabling the system to continuously learn from new design and usage data, thereby continuously improving prediction accuracy. Attached Figure Description

[0048] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention. Detailed Implementation

[0049] A preferred embodiment of the present invention will be further described below with reference to the accompanying drawings.

[0050] Example 1

[0051] Please see Figure 1 As shown in the figure, this embodiment provides a method for rapid extraction of equivalent parameters of oil-immersed transformer windings, including the following steps:

[0052] S1. Construct a three-dimensional winding coil structure model based on the winding design parameters of an oil-immersed transformer.

[0053] In this embodiment, a model is constructed based on the actual oil-immersed transformer winding structure and corresponding design parameters. Specifically, the model includes the precise dimensions, spatial arrangement, and interlayer relationships of material components such as insulating paper, resin varnish, copper wire, and air. A three-dimensional winding coil structure model containing all details is constructed using three-dimensional modeling software.

[0054] S2. Set the material properties and boundary conditions of the three-dimensional winding coil structure model.

[0055] Specifically, setting material properties includes assigning realistic physical parameters to each material (such as copper, insulating paper, resin paint, air, etc.) in the three-dimensional winding coil structure model, including density, specific heat capacity, and thermal conductivity. If the material is anisotropic (such as insulating paper), the thermal conductivity in three directions in three-dimensional space needs to be set separately.

[0056] Setting boundary conditions includes setting different temperatures on the upper and lower surfaces of the winding to create a temperature difference between them.

[0057] S3. Perform thermal simulation calculations on the three-dimensional winding coil structure model to obtain the heat flux density value.

[0058] In this embodiment, simulation software is used to perform thermal simulation calculations on the established three-dimensional winding coil structure model, calculate its temperature field distribution and heat density, and extract the heat flux density value.

[0059] S4. Calculate the equivalent parameters of the three-dimensional winding coil structure model based on the heat flux density value.

[0060] In this embodiment, the equivalent parameters include equivalent thermal conductivity, equivalent density, and equivalent heat capacity.

[0061] The formula for calculating the equivalent thermal conductivity is:

[0062]

[0063] In the formula: This is the heat flux density value. The equivalent thermal conductivity of the material. and for Temperature at both boundaries in the direction, For heat in The distance of directional propagation;

[0064] The formula for calculating equivalent density is:

[0065]

[0066] In the formula: For equivalent density, For the first The quality of the material The total volume of the material;

[0067] The formula for calculating equivalent heat capacity is:

[0068]

[0069] In the formula: For equivalent heat capacity, Represents isobaric conditions. For the first The heat capacity of this material This represents the total mass of the material.

[0070] The following provides further explanation of the principles of equivalent modeling. The physical basis of equivalent modeling is the law of conservation of energy and the fundamental principles of heat transfer. Heat conduction in the winding during operation is a complex three-dimensional anisotropic process. Along the x and y directions, heat flow must sequentially pass through the copper conductor, the insulating paper layer, and the oil channels. Its equivalent thermal conductivity is mainly limited by the low thermal conductivity of the insulating paper and oil channels, resulting in relatively low thermal conductivity coefficients. However, in the z direction, due to the excellent heat path provided by the copper conductor, its equivalent thermal conductivity is significantly stronger.

[0071] This invention utilizes high-precision three-dimensional finite element thermal simulation to accurately calculate the heat flux density passing through the winding model under defined boundary conditions (such as a constant temperature difference between the upper and lower surfaces). According to Fourier's law, this heat flux density is proportional to the product of the temperature gradient and the equivalent thermal conductivity; the equivalent thermal conductivity in that direction can be obtained through inversion calculation. The equivalent density and equivalent specific heat capacity strictly adhere to the principles of mass and energy conservation, and are obtained by calculating the ratio of the sum of the masses of all component materials representing the unit cell to the total volume, as well as the average specific heat capacity based on mass weighting.

[0072] However, equivalent parameters obtained solely through simulation may contain errors due to model simplification and inaccurate material properties. Therefore, experimental verification and calibration are crucial for ensuring model accuracy. Test samples with the same materials and processes as the actual windings are prepared, and their macroscopic thermal conductivity is measured using specialized equipment. The measured values ​​are then compared with the simulated values. If the deviation exceeds an acceptable range, the simulation model (e.g., material properties, contact thermal resistance) needs to be calibrated, and a quantitative correction relationship (e.g., a linear correction formula) must be established between the two to ensure the reliability of all equivalent parameter datasets obtained through simulation.

[0073] Specifically, based on extensive domestic and international literature review and preliminary experimental simulation results, the magnitude of the winding thermal conductivity has a far greater impact on the temperature field simulation of oil-immersed transformers than heat capacity and density parameters. Therefore, it is necessary to experimentally verify and correct the obtained equivalent thermal conductivity. A winding test sample with the same structure as the actual winding (e.g., a multi-layer copper foil and insulating paper laminate structure) is prepared. The winding sample is measured using a thermal conductivity meter, with each sample measured several times. The average value is taken as the final result to obtain the actual winding thermal conductivity. The measured value is compared with the equivalent thermal conductivity extracted from the simulation. If the deviation exceeds a set threshold (e.g., 5%), the material parameters and boundary conditions in the thermal simulation calculation are adjusted, and the thermal simulation calculation is repeated until the thermal simulation result matches the measured data. In this embodiment, the equivalent thermal conductivity is corrected based on the measured winding thermal conductivity, using the following formula:

[0074]

[0075] In the formula: This is the corrected equivalent thermal conductivity. and These are linear regression parameters used to correct all simulation data. The measured thermal conductivity of the winding is given.

[0076] S5. Perform thermal simulation calculations on oil-immersed transformers using equivalent parameters to obtain the simulation results of the equivalent temperature field, and extract the temperatures of key temperature measurement points (top oil temperature, highest winding temperature, etc.).

[0077] S6. Construct a homogeneous model of the winding coil. Generate several sets of parameters in the parameter space by sampling. Perform thermal simulation calculations on the homogeneous model of the winding coil under each set of parameters to obtain the corresponding homogeneous model temperature field simulation results. Establish a Gaussian process surrogate model and iterate with the goal of minimizing the temperature matching loss between the homogeneous model temperature field simulation results and the equivalent temperature field simulation results until the temperature matching loss is less than a set threshold. Output the corresponding equivalent homogeneous parameters.

[0078] First, the verified three-dimensional winding coil structure model containing oil channels is converted into a homogeneous winding coil model without oil channels, with uniform material but exhibiting anisotropic thermophysical properties on a macroscopic scale. The core purpose of this step is to ensure that the simplified homogeneous winding coil model and the original three-dimensional winding coil structure model containing oil channels maintain consistency in the steady-state temperature field under the same boundary conditions, especially in key areas such as the hot spot temperature of the core winding, the average temperature rise, and the top oil temperature of the transformer.

[0079] To achieve the above objectives, this embodiment employs an intelligent inverse adjustment strategy based on a Bayesian optimization framework to automatically search for the optimal combination of anisotropic equivalent parameters, including equivalent density, equivalent specific heat capacity, and equivalent thermal conductivity in three orthogonal directions.

[0080] The search objective of this method is defined as minimizing the root mean square error of temperature weighted at the global domain or key temperature measurement points between the homogeneous model of the winding coil and the three-dimensional winding coil structural model, thereby ensuring a high degree of approximation of the macroscopic thermal behavior. The optimization process includes: generating initial sample points within a reasonable parameter space using Latin hypercube sampling; performing three-dimensional steady-state thermal simulations on each set of parameters to construct an initial dataset; subsequently, establishing a Gaussian process surrogate model to characterize the complex nonlinear relationship between parameters and thermal error. In the iterative search phase, based on the mean and uncertainty predicted by the Gaussian process surrogate model, the most promising new parameter points are actively selected for simulation verification using a data acquisition function, and the surrogate model is dynamically updated to gradually improve its approximation accuracy. Through multiple iterations, the optimization process finally converges to a set of optimal anisotropic parameters, enabling the homogeneous winding coil model to accurately reproduce the thermal conductivity characteristics of the original winding. After verification simulation confirms that the matching degree meets the engineering requirements, the obtained equivalent parameters will be stored in the parameterized database as key inputs to the high-fidelity thermal model, providing a training basis for subsequent data-driven rapid prediction models, thereby completing the accurate conversion from multi-component complex structures to homogeneous macroscopic thermal models.

[0081] S7. Construct a parameterized database based on the winding design parameters and corresponding equivalent homogeneous parameters of different oil-immersed transformers.

[0082] Based on the data obtained from the above steps, this embodiment further constructs a specifically designed parametric database. As the core data hub of the equivalent modeling platform, the parametric database is not only responsible for storing and managing the mapping relationship between winding design parameters and equivalent homogeneous parameters, but also provides a high-quality training foundation for subsequent machine learning modeling and intelligent prediction.

[0083] The parameterized database consists of the following five main parts:

[0084] Basic Materials Table: Stores the physical parameters of various basic materials involved in the winding, including copper conductors, insulating paper, and transformer oil. Records cover key properties such as density, specific heat capacity, and thermal conductivity in all directions. The table structure fully considers the possible anisotropic characteristics of the materials.

[0085] Design Parameter Table: This table records detailed structural design information for the windings, such as winding type, number of layers, oil channel dimensions, conductor cross-sectional area ratio, insulation layer thickness, and number of support bars. It is linked to the base material table via foreign keys to ensure accurate correspondence between design parameters and material properties.

[0086] Equivalent Parameter Table: Corresponding one-to-one with the design parameter table, this table stores the equivalent thermal properties of the homogeneous model obtained through 3D thermal simulation. These primarily include equivalent density, equivalent specific heat capacity, and equivalent thermal conductivity in three directions. Additionally, it records simulation-related metadata, such as calculation temperature, mesh quality, solver settings, and computation time, to assess the reliability of the simulation results.

[0087] Experimental Validation Table: This table is specifically used to store the measured data obtained during the experimental validation process, including sample number, measured equivalent parameters, test environment, error range, applicable standards, and data correction coefficients. It records the differences between simulation and experiment and their correction relationships, providing support for model calibration and data quality tracking.

[0088] Metadata table: Records overall information at the database level, such as data version, model version, total number of samples, proportion of validated simulation parameter data, and overall quality score. It also stores database creation and update times, usage licenses, and maintenance logs.

[0089] S8. Construct a prediction model based on a deep neural network, and obtain an equivalent homogeneous parameter prediction model after training with a parameterized database.

[0090] To achieve rapid prediction, this invention introduces a data-driven artificial intelligence method. The underlying principle is that there exists a complex, implicit, nonlinear mapping relationship between the equivalent thermophysical properties of the winding and its design parameters (such as the number of layers, oil channel width, and copper ratio). Through systematic simulation and experimentation, a large, high-quality parameterized database can be constructed, which is essentially a collection of numerous discrete sample points representing this mapping relationship.

[0091] Based on the parameterized database from the previous step, this invention constructs and trains a targeted machine learning prediction model, aiming to establish an accurate and efficient nonlinear mapping relationship from winding design parameters to equivalent homogeneous parameters. Specifically, it includes the following steps:

[0092] Data preprocessing: The data cleaning stage employs a combination of automation and manual review to systematically handle potential missing and outlier values ​​in the dataset. Feature standardization uses the Z-score standardization method to unify the scale of all input features, eliminating the impact of dimensional differences on model training. This process not only accelerates the model convergence process but also improves the model's training stability. In particular, for the anisotropic thermal conductivity in the output parameters, due to its large numerical range variation, this invention also performs appropriate scaling transformation to ensure a relatively balanced loss contribution from each output target during training.

[0093] Furthermore, feature engineering is also a crucial step in improving the model's predictive performance. This embodiment leverages expertise in transformer winding design to construct derived features with clear physical meaning from the original design parameters. For example, a "copper content ratio" is introduced to characterize the proportion of conductor cross-sectional area in the total cross-section, a "fill factor" measures the space utilization of the winding structure, and an "interlayer bonding factor" describes the tightness of contact between the insulation material and the conductor. In addition, this embodiment also constructs cross-terms and higher-order combination features between parameters to capture the nonlinear correlations and interactions between different design variables. Through these feature construction methods, the model's ability to characterize complex physical mechanisms and its predictive accuracy are significantly enhanced.

[0094] This invention employs a deep neural network (DNN) as the core prediction model. This choice stems from the superior performance of DNNs in handling complex mapping relationships with high dimensionality and strong nonlinearity. As a powerful function approximation tool, a deep neural network (DNN) can learn and internalize this complex mapping relationship through training. During training, the network continuously reduces the error between the equivalent properties predicted based on design parameters and the true values ​​(simulation + experimental verification values) in the database by adjusting its millions of internal parameters. Ultimately, the trained model encapsulates the "knowledge" from design to equivalent parameters, enabling it to predict all equivalent parameters of any new, unseen winding design with high accuracy within milliseconds, eliminating the time-consuming physical simulation process.

[0095] The deep neural network structure was finalized after multiple rounds of optimization: the input layer has 8 nodes, corresponding to 8 key features: copper content ratio, number of layers, oil channel width, insulating paper thickness, number of support bars, oil channel cross-sectional area ratio, winding height, and winding inner and outer diameter ratio; the hidden part consists of three fully connected layers, each with 256 neurons, ensuring model expressiveness while controlling computational overhead; the output layer has 5 nodes, corresponding to equivalent density, equivalent isobaric specific heat capacity, and equivalent thermal conductivity in the x, y, and z directions. To improve generalization ability, a dropout layer is introduced after each hidden layer, with a dropout rate of 0.2, supplemented by L2 weight regularization to constrain model complexity.

[0096] During the model training and optimization phases, this embodiment employs weighted mean squared error as the loss function to balance the importance of different output parameters. It also introduces the Adam optimizer, which integrates momentum and adaptive learning rate, along with dynamic learning rate decay and gradient pruning mechanisms to ensure stable and efficient training. To enhance model generalization ability, five-fold cross-validation and early stopping strategies are implemented. Multiple rounds of data splitting and validation loss monitoring effectively prevent overfitting. Model performance is comprehensively evaluated using various metrics, including coefficient of determination, mean absolute error, relative error, and adjusted coefficient of determination. Finally, combining statistical quantification results with domain expert experience, the optimal model, possessing both prediction accuracy and physical plausibility, is selected as the equivalent homogeneous parameter prediction model.

[0097] S9. Input the winding design parameters of the oil-immersed transformer to be predicted into the equivalent homogeneous parameter prediction model to obtain the corresponding equivalent homogeneous parameters.

[0098] In practical applications, an intelligent prediction and engineering application system for equivalent parameters was built around the equivalent homogeneous parameter prediction model. The system deploys a REST API web service based on the model. After users input design parameters and initiate prediction requests, the equivalent homogeneous parameter prediction model outputs the equivalent parameters. Then, it integrates a multi-objective optimization NSGA-II model through design optimization. The principle is to find a series of optimal compromise solutions (Pareto optimal solution set) in the solution space formed by conflicting design objectives (such as temperature rise, cost, and volume). The system uses a trained machine learning model as a performance predictor to quickly evaluate the thermal performance of numerous candidate designs generated by the optimization algorithm, thereby efficiently guiding the search direction and ultimately providing users with a set of optimal design solutions for decision-making. The optimized design solution is output through the multi-objective optimization model, and new data generated is recorded in a parameterized database through a feedback learning mechanism. This new data is then used to retrain the model. The system organically integrates artificial intelligence technology into the transformer winding design and optimization process, forming a closed-loop application system that integrates intelligent prediction, automatic correction, and adaptive evolution, achieving efficient connection from model results to engineering practice.

[0099] In a specific scenario, the equivalent parameter rapid extraction method provided in this embodiment was applied to a 400kW oil-immersed transformer. The obtained equivalent homogeneous parameters and corresponding measured values ​​are shown in Table 1 below.

[0100] Table 1 Equivalent homogeneous parameters

[0101] parameter unit equivalent value Measured value error density kg / m³ 8788 8800 0.14% Constant pressure heat capacity J / (kg·K) 34 35 2.9% thermal conductivity in the x direction W / (m·K) 4.28 4.4 2.8% thermal conductivity in the y direction W / (m·K) 2.26 2.28 0.88% thermal conductivity in the z-direction W / (m·K) 57.8 55.25 4.6%

[0102] As can be seen from Table 1, the method provided in this embodiment achieves high accuracy in the calculation of all equivalent homogeneous parameters, with errors controlled within 5%, and can be well applied in practical scenarios.

[0103] This invention establishes an accurate and efficient equivalent modeling method for oil-immersed transformer windings by organically combining physical simulation, experimental verification, and data-driven approaches. The windings, composed of various heterogeneous materials (copper, insulating paper, resin varnish, and insulating oil) and possessing complex internal structures, are macroscopically equivalent to a homogeneous but anisotropic continuous entity in terms of thermal behavior. This method transcends traditional empirical formulas and isotropic assumptions, achieving a paradigm shift from "geometric structure-driven" to "physical performance equivalence."

[0104] Example 2

[0105] This embodiment provides a rapid extraction system for equivalent parameters of oil-immersed transformer windings, corresponding to the rapid extraction method for equivalent parameters of oil-immersed transformer windings described in Embodiment 1, including:

[0106] 3D Winding Coil Structure Model Building Module: Used to build a 3D winding coil structure model based on the winding design parameters of an oil-immersed transformer;

[0107] Model parameter setting module: used to set the material properties and boundary conditions of the three-dimensional winding coil structure model;

[0108] Heat flux density calculation module: used to perform thermal simulation calculations on the three-dimensional winding coil structure model to obtain the heat flux density value;

[0109] Equivalent parameter calculation module: used to calculate the equivalent parameters of the three-dimensional winding coil structure model based on the heat flux density value;

[0110] Equivalent temperature field simulation module: used to perform thermal simulation calculations of oil-immersed transformers using equivalent parameters, and obtain the equivalent temperature field simulation results;

[0111] Equivalent homogeneous parameter calculation module: used to construct a homogeneous model of the winding coil. It generates several sets of parameters by sampling in the parameter space, performs thermal simulation calculations on the homogeneous model of the winding coil under each set of parameters, obtains the corresponding homogeneous model temperature field simulation results, establishes a Gaussian process surrogate model, and iterates with the goal of minimizing the temperature matching loss between the homogeneous model temperature field simulation results and the equivalent temperature field simulation results until the temperature matching loss is less than a set threshold, and outputs the corresponding equivalent homogeneous parameters.

[0112] Parametric database construction module: used to build a parametric database based on the winding design parameters and corresponding equivalent homogeneous parameters of different oil-immersed transformers;

[0113] Equivalent homogeneous parameter prediction model construction module: used to build a prediction model based on a deep neural network, and obtain the equivalent homogeneous parameter prediction model after training with a parameterized database;

[0114] The equivalent homogeneous parameter prediction model application module is used to input the winding design parameters of the oil-immersed transformer to be predicted into the equivalent homogeneous parameter prediction model to obtain the corresponding equivalent homogeneous parameters.

Claims

1. A method for rapid extraction of equivalent parameters of oil-immersed transformer windings, characterized in that, Includes the following steps: S1. Construct a three-dimensional winding coil structure model based on the winding design parameters of an oil-immersed transformer; S2. Set the material properties and boundary conditions of the three-dimensional winding coil structure model; S3. Perform thermal simulation calculations on the three-dimensional winding coil structure model to obtain the heat flux density value; S4. Calculate the equivalent parameters of the three-dimensional winding coil structure model based on the heat flux density value; S5. Perform thermal simulation calculations on oil-immersed transformers using equivalent parameters to obtain simulation results of the equivalent temperature field. S6. Construct a homogeneous model of the winding coil. Generate several sets of parameters in the parameter space by sampling. Perform thermal simulation calculations on the homogeneous model of the winding coil under each set of parameters to obtain the corresponding homogeneous model temperature field simulation results. Establish a Gaussian process proxy model and iterate with the goal of minimizing the temperature matching loss between the homogeneous model temperature field simulation results and the equivalent temperature field simulation results until the temperature matching loss is less than the set threshold. Output the corresponding equivalent homogeneous parameters. S7. Construct a parameterized database based on the winding design parameters and corresponding equivalent homogeneous parameters of different oil-immersed transformers; S8. Construct a prediction model based on a deep neural network, and obtain an equivalent homogeneous parameter prediction model after training with a parameterized database. S9. Input the winding design parameters of the oil-immersed transformer to be predicted into the equivalent homogeneous parameter prediction model to obtain the corresponding equivalent homogeneous parameters.

2. The method for rapid extraction of equivalent parameters of oil-immersed transformer windings according to claim 1, characterized in that, Step S2 includes: setting the density, specific heat capacity and thermal conductivity of each material in the three-dimensional winding coil structure model, and setting different temperatures on the upper and lower surfaces of the three-dimensional winding coil structure model respectively.

3. The method for rapid extraction of equivalent parameters of oil-immersed transformer windings according to claim 1, characterized in that, The equivalent parameters include equivalent thermal conductivity, equivalent density, and equivalent heat capacity.

4. The method for rapid extraction of equivalent parameters of oil-immersed transformer windings according to claim 3, characterized in that, The formula for calculating the equivalent thermal conductivity is: In the formula: This is the heat flux density value. The equivalent thermal conductivity of the material. and for Temperature at both boundaries in the direction, For heat in The distance of directional propagation; The formula for calculating the equivalent density is: In the formula: For equivalent density, For the first The quality of the material The total volume of the material; The formula for calculating the equivalent heat capacity is: In the formula: For equivalent heat capacity, Represents isobaric conditions. For the first The heat capacity of this material This represents the total mass of the material.

5. The method for rapid extraction of equivalent parameters of oil-immersed transformer windings according to claim 3, characterized in that, Step S4 further includes: correcting the equivalent thermal conductivity based on the measured winding thermal conductivity, using the following formula: In the formula: This is the corrected equivalent thermal conductivity. and For linear regression parameters, The measured thermal conductivity of the winding is given.

6. The method for rapid extraction of equivalent parameters of oil-immersed transformer windings according to claim 1, characterized in that, The construction of the homogeneous model of the winding coil includes: removing the oil passage structure and replacing it with a homogeneous material based on the three-dimensional winding coil structure model.

7. The method for rapid extraction of equivalent parameters of oil-immersed transformer windings according to claim 1, characterized in that, The temperature matching loss is the temperature-weighted root mean square error between the simulation results of the homogeneous model temperature field and the simulation results of the equivalent temperature field.

8. The method for rapid extraction of equivalent parameters of oil-immersed transformer windings according to claim 5, characterized in that, The parameterized database includes: a basic material table, a design parameter table, an equivalent parameter table, an experimental verification table, and a metadata table. The basic material table includes the physical parameters of each material contained in the oil-immersed transformer winding; the design parameter table includes the structural design parameters of the oil-immersed transformer winding and is associated with the parameters in the basic material table; the equivalent parameter table includes the equivalent parameters of the three-dimensional winding coil structure model and metadata of the thermal simulation calculation; the experimental verification table includes experimental data of the measured thermal conductivity of the winding; and the metadata table includes parameter information and log information of the parameterized database.

9. The method for rapid extraction of equivalent parameters of oil-immersed transformer windings according to claim 1, characterized in that, Step S8 includes: cleaning and standardizing the data in the parameterized database, constructing derived input features based on the original design parameters, building a prediction model based on a deep neural network, using weighted mean square error as the loss function and introducing the Adam optimizer, and simultaneously implementing five-fold cross-validation and early stopping strategies to optimize and train the prediction model. An equivalent homogeneous parameter prediction model is selected by combining evaluation indicators with expert experience.

10. A rapid extraction system for equivalent parameters of oil-immersed transformer windings, characterized in that, include: 3D Winding Coil Structure Model Building Module: Used to build a 3D winding coil structure model based on the winding design parameters of an oil-immersed transformer; Model parameter setting module: used to set the material properties and boundary conditions of the three-dimensional winding coil structure model; Heat flux density calculation module: used to perform thermal simulation calculations on the three-dimensional winding coil structure model to obtain the heat flux density value; Equivalent parameter calculation module: used to calculate the equivalent parameters of the three-dimensional winding coil structure model based on the heat flux density value; Equivalent temperature field simulation module: used to perform thermal simulation calculations of oil-immersed transformers using equivalent parameters, and obtain the equivalent temperature field simulation results; Equivalent homogeneous parameter calculation module: used to construct a homogeneous model of the winding coil. It generates several sets of parameters by sampling in the parameter space, performs thermal simulation calculations on the homogeneous model of the winding coil under each set of parameters, obtains the corresponding homogeneous model temperature field simulation results, establishes a Gaussian process surrogate model, and iterates with the goal of minimizing the temperature matching loss between the homogeneous model temperature field simulation results and the equivalent temperature field simulation results until the temperature matching loss is less than a set threshold, and outputs the corresponding equivalent homogeneous parameters. Parametric database construction module: used to build a parametric database based on the winding design parameters and corresponding equivalent homogeneous parameters of different oil-immersed transformers; Equivalent homogeneous parameter prediction model construction module: used to build a prediction model based on a deep neural network, and obtain the equivalent homogeneous parameter prediction model after training with a parameterized database; Equivalent homogeneous parameter prediction model application module: used to input the winding design parameters of the oil-immersed transformer to be predicted into the equivalent homogeneous parameter prediction model to obtain the corresponding equivalent homogeneous parameters.

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