Transformer temperature field calculation method, device and equipment based on WPOD and enhanced BPNN

Abstract

This application relates to the field of transformer technology, and provides a method, apparatus, and device for calculating transformer temperature field based on WPOD and enhanced BPNN. The method includes acquiring transformer attribute data, a sample operating condition set, a finite element model, a maximum weight, and several real-time temperature data; simulating the finite element model based on each operating condition sample to obtain sample data and a sample dataset; determining a diagonal weight matrix based on each sample data and the maximum weight; performing dimensionality reduction processing on the matrix formed by the sample dataset using intrinsic orthogonal decomposition based on the diagonal weight matrix to obtain modal coefficients and a transformation matrix; training a fast calculation proxy model using the output of an enhanced backpropagation neural network; acquiring the operating data of the transformer to be calculated, inputting the operating data into the fast calculation proxy model for solution, and obtaining the global temperature field distribution corresponding to the transformer to be calculated, avoiding the omission of local overheating risk and improving the calculation accuracy of the model.

Description

Technical Field

[0001] This application relates to the field of transformer temperature field calculation technology, and in particular to a transformer temperature field calculation method, apparatus and equipment based on WPOD and enhanced BPNN. Background Technology

[0002] With sustained and rapid economic development, the demand for electricity across society continues to grow. As a crucial basic energy source, the safe, stable, and efficient supply of electricity is a vital guarantee for supporting economic and social operations. Against this backdrop, the load density of power systems is constantly increasing, placing higher demands on the performance and reliability of transmission and distribution equipment. Dry-type transformers, due to their advantages such as good fire resistance, strong environmental adaptability, and low maintenance costs, are widely used in scenarios with high requirements for safety and space utilization, such as urban distribution networks, high-rise buildings, rail transit, and data centers. However, during long-term high-load operation of the power system, dry-type transformers experience significant temperature rise due to electromagnetic losses and conductor heating. This temperature rise not only accelerates the aging of insulation materials and reduces equipment lifespan but can also lead to serious accidents such as localized overheating, insulation breakdown, and even fires. Therefore, temperature rise has become a key factor restricting the safe operation and capacity expansion of dry-type transformers. Accurately obtaining the temperature rise status during the operation of dry-type transformers is fundamental for conducting condition assessments, life predictions, and thermal management optimization. By monitoring temperature changes in key components in real time, anomalies can be detected promptly, risks can be warned, and a scientific basis can be provided for operation and maintenance, thereby ensuring the safe and stable operation of the power system.

[0003] Currently, methods for obtaining the temperature rise status of dry-type transformers can be mainly divided into four categories: direct measurement method, empirical formula method, thermal circuit model method, and numerical calculation method. Specifically:

[0004] Direct measurement methods acquire data directly from critical parts of the transformer (such as pre-embedded PT100 temperature sensors or infrared thermometry), providing reliable and accurate results. However, due to limitations in insulation structure and installation space, the number of measurement points is limited, making it difficult to reflect the overall temperature distribution. While existing direct measurement methods can theoretically obtain relatively accurate local temperature data, they face inherent limitations in engineering applications, such as severely restricted placement of measurement points and difficulty in achieving full coverage. Sensors are often unavailable in critical hot spots such as deep windings and core gaps inside the transformer, easily overlooking local overheating risks. Furthermore, sensors suffer from insulation aging and signal drift under long-term exposure to strong electromagnetic fields and high temperatures. The installation process itself may also damage the original insulation structure and heat dissipation path. Moreover, this method relies entirely on physical prototypes and cannot predict temperature rise characteristics in advance during the design phase.

[0005] The empirical formula method is simple to calculate and responds quickly, but it is essentially a statistical relationship obtained by fitting test data of a specific model and limited operating conditions. It has very poor universality. When the transformer structure, capacity, cooling method or operating boundary changes, the formula often fails. It is difficult to adapt to temperature rise prediction under non-rated operating conditions and complex load curves, and the error range is large. Therefore, the empirical formula method is only suitable for rough estimation in engineering field.

[0006] The thermal circuit model method uses lumped parameters to represent the internal thermal process of a transformer, which to some extent balances physical mechanisms and computational efficiency. However, its oversimplification of the temperature field makes it difficult to accurately capture the location of hot spots in the windings and the local non-uniform temperature distribution. The thermal resistance and thermal capacity parameters in the model often rely on experimental calibration and lack a unified parameter identification method. The modeling accuracy is limited by the refinement of the equivalent network and it is difficult to reflect the complex local spatial thermal response process.

[0007] Numerical calculation methods (such as the finite element method, FEM) can obtain high-precision global temperature distribution based on multi-physics coupling theory, but they require solving high-dimensional nonlinear equations, which is extremely time-consuming and cannot meet the needs of real-time monitoring and rapid evaluation of digital twin systems in engineering sites. For example, numerical calculation methods, represented by the finite element method and computational fluid dynamics, can achieve high-precision three-dimensional simulation of the internal temperature field of transformers through multi-physics coupling, and theoretically have the strongest predictive ability. However, the cost is huge consumption of computing resources and extremely long solution time. Complex factors such as three-dimensional fine mesh generation, nonlinear material properties, and fluid-structure interaction often cause a single simulation to take several hours or even days, which cannot meet the urgent needs of massive parameter evaluation and high-frequency rapid calculation in engineering design and multi-condition iteration.

[0008] To balance computational accuracy and efficiency, reduced-order surrogate models combining intrinsic orthogonal decomposition (POD) with traditional artificial neural networks (such as BPNN) have become a research hotspot for rapid temperature rise calculations in recent years. However, existing data-driven surrogate models still face the following technical shortcomings that urgently need to be addressed in practical applications under complex working conditions:

[0009] First, the dimensionality weighting of feature extraction is unreasonable: When the traditional intrinsic orthogonal decomposition (POD) method extracts basis functions by reducing the dimensionality of the high-dimensional temperature field snapshot matrix, it usually assigns the same weight to all sample snapshots. This fails to distinguish the differences in thermal dynamic contribution of transformers under different load stages, different heat dissipation conditions, or sudden short circuits and other specific operating conditions. It is very easy to lose local high-frequency thermal features, which results in insufficient precision in reflecting key local hot spots in the reconstructed temperature field and easy loss of important high-frequency thermal features.

[0010] Second, purely data-driven models lack physical constraints, resulting in poor generalization and robustness. Traditional backpropagation neural networks (BPNNs) are pure "black box" models, whose prediction accuracy highly depends on the completeness of the training set data and completely ignores the thermodynamic and heat transfer control equations inside the transformer. When actual operating conditions fluctuate drastically or when faced with unknown conditions outside the training set, the prediction results are prone to violating physical laws such as energy conservation, leading to poor generalization and robustness. For example, when the actual operating conditions of the transformer fluctuate drastically or when encountering unknown conditions outside the training set coverage, the prediction results of such models are prone to serious deviations that violate physical laws such as energy conservation, exhibiting extremely poor robustness.

[0011] Third, there is a disconnect between simulation data and actual physical measurement data: existing rapid computational models typically rely solely on theoretical simulation data for training and prediction, failing to effectively integrate real-world sensor monitoring data from the operating environment. Under complex electromagnetic interference and non-ideal heat dissipation conditions, the actual temperature of transformers fluctuates significantly. Pure computational models lacking anchored data from real physical measurement points cannot dynamically correct prediction deviations, making it difficult to guarantee high fidelity and reliability for long-term operational monitoring.

[0012] In summary, existing methods for obtaining the temperature field of dry-type transformers struggle to achieve a balance between accuracy, efficiency, physical interpretability, and adaptability to complex real-world environments. Summary of the Invention

[0013] This application provides a method, apparatus, and equipment for calculating the temperature field of a transformer based on WPOD and enhanced BPNN, which solves the technical problems of narrow applicability and low accuracy of existing methods for obtaining the temperature rise state of dry-type transformers.

[0014] To achieve the above objectives, this application provides the following technical solution:

[0015] On the one hand, a method for calculating the temperature field of a transformer based on WPOD and enhanced BPNN is provided, including the following steps:

[0016] The environmental parameters, attribute data, sample operating condition set, finite element model and several real-time temperature data of the transformer are obtained. The finite element model is simulated according to each operating condition sample of the sample operating condition set to obtain sample data of the transformer global temperature field corresponding to each operating condition sample. All the sample data are used to form a sample dataset.

[0017] Obtain the maximum weight of the mesh nodes in the finite element model, and determine the diagonal weight matrix corresponding to the number of mesh nodes in the finite element model based on each sample data in the sample dataset and the maximum weight.

[0018] The matrix formed by the sample dataset is reduced in dimensionality using intrinsic orthogonal decomposition based on the diagonal weight matrix to obtain modal coefficients and a transformation matrix; an enhanced backpropagation neural network is obtained, and the environmental parameters, the attribute data, the working condition samples of the sample working condition set, and all the real-time temperature data are used as inputs to the enhanced backpropagation neural network, and the modal coefficients are used as outputs to train the network to obtain a fast computation surrogate model;

[0019] The operating data of the transformer to be calculated is obtained, and the operating data is input into the fast calculation proxy model for solution to obtain the global temperature field distribution corresponding to the transformer to be calculated.

[0020] Optionally, obtaining an enhanced backpropagation neural network includes:

[0021] The global temperature field is reconstructed based on the modal coefficients and the transformation matrix; the node temperatures corresponding to the mesh nodes in the finite element model and the temperature data corresponding to each real-time temperature data are extracted from the global temperature field.

[0022] Obtain the fitting loss data and adaptive penalty weight coefficients of the backpropagation neural network; determine the temperature physical loss data based on the temperature of all nodes and the attribute data; determine the real-time correction loss data based on all the real-time temperature data and the corresponding temperature data; construct the joint loss function of the enhanced backpropagation neural network based on the fitting loss data, the adaptive penalty weight coefficients, the temperature physical loss data and the real-time correction loss data.

[0023] Optionally, the attribute data includes the material density, specific heat capacity, thermal conductivity, and internal heat source density of the core or winding of the transformer; obtaining the enhanced backpropagation neural network further includes: calculating temperature physical loss data using a partial differential equation residual formula based on all the node temperatures and the attribute data; and calculating real-time corrected loss data using a deviation correction formula based on all the real-time temperature data and the corresponding temperature data; the partial differential equation residual formula is:

[0024] ;

[0025] The deviation correction formula is:

[0026] ;

[0027] The joint loss function is:

[0028] ;

[0029] In the formula, Ldata To fit the loss data, and These are the adaptive penalty weight coefficients with different values, L. phy For temperature physical loss data, L sen To correct lost data in real time, N S This represents the total number of real-time temperature data points collected. This is the Sth real-time temperature data collected. Let M be the S-th temperature data point, and M be the number of mesh nodes in the finite element model. Let be the nodal temperature corresponding to the i-th grid node, and ∇ be the vector differential operator. The material density of the transformer, Let be the specific heat capacity of the transformer, and k be the thermal conductivity of the transformer. Let L be the internal heat source density corresponding to the i-th grid node, t be time, and L be the internal heat source density. total This represents the total loss.

[0030] Optionally, determining the diagonal weight matrix corresponding to the number of mesh nodes in the finite element model based on each sample data in the sample dataset and the maximum weight includes:

[0031] Based on the sample data of the sample dataset, determine the mean temperature, maximum temperature and minimum temperature corresponding to each grid node in the finite element model;

[0032] The weight coefficient corresponding to each grid node is calculated based on the maximum weight value, the average temperature, the maximum temperature, and the minimum temperature of each grid node.

[0033] Based on all the weighting coefficients, determine the diagonal weight matrix corresponding to the number of mesh nodes in the finite element model.

[0034] Optionally, calculating the weight coefficient corresponding to each grid node based on the maximum weight and the average temperature, maximum temperature, and minimum temperature of each grid node includes: calculating the weight coefficient corresponding to each grid node using a weight calculation formula based on the maximum weight and the average temperature, maximum temperature, and minimum temperature of each grid node; the weight calculation formula is:

[0035] ;

[0036] In the formula, w max T represents the maximum weight. min The minimum temperature, T max T represents the maximum temperature. iLet w be the average temperature of the i-th grid node. i is the weight coefficient of the i-th grid node.

[0037] Optionally, obtaining the finite element model of the transformer includes:

[0038] The actual structural parameters, boundary conditions, and thermal excitation of the transformer are obtained. A simplified three-dimensional model is constructed based on the actual structural parameters, boundary conditions, thermal excitation, and attribute data.

[0039] The simplified three-dimensional model is partitioned using a structured mapping mesh to obtain a finite element model.

[0040] Optionally, obtaining the sample operating condition set of the transformer includes: using orthogonal experimental design or Latin hypercube sampling to obtain samples of various operating conditions of the transformer under different ambient temperatures and different loads, thus obtaining the sample operating condition set.

[0041] On the other hand, a transformer temperature field calculation device based on WPOD and enhanced BPNN is provided, including a sample data acquisition module, a weight matrix construction module, a model construction module and a temperature field calculation module;

[0042] The sample data acquisition module is used to acquire the transformer's environmental parameters, attribute data, sample operating condition set, finite element model, and several real-time temperature data. It simulates the finite element model based on each operating condition sample in the sample operating condition set to obtain sample data of the transformer's global temperature field corresponding to each operating condition sample. All the sample data are then used to form a sample dataset.

[0043] The weight matrix construction module is used to obtain the maximum weight of the grid nodes in the finite element model, and determine the diagonal weight matrix corresponding to the number of grid nodes in the finite element model based on each sample data in the sample dataset and the maximum weight.

[0044] The model building module is used to perform dimensionality reduction processing on the matrix formed by the sample dataset based on the diagonal weight matrix using intrinsic orthogonal decomposition to obtain modal coefficients and transformation matrix; to obtain an enhanced backpropagation neural network, using the environmental parameters, the attribute data, the working condition samples of the sample working condition set and all the real-time temperature data as inputs to the enhanced backpropagation neural network, and using the modal coefficients as outputs to train the enhanced backpropagation neural network to obtain a fast computation surrogate model;

[0045] The temperature field calculation module is used to acquire the operating data of the transformer to be calculated, input the operating data into the fast calculation proxy model for solution, and obtain the global temperature field distribution corresponding to the transformer to be calculated.

[0046] Optionally, the model building module includes a data extraction submodule and a loss function construction submodule;

[0047] The data extraction submodule is used to reconstruct the global temperature field based on the modal coefficients and the transformation matrix; and to extract the node temperature corresponding to the mesh node in the finite element model and the temperature data corresponding to each real-time temperature data from the global temperature field.

[0048] The loss function construction submodule is used to obtain the fitting loss data and adaptive penalty weight coefficients of the backpropagation neural network; determine the temperature physical loss data based on the temperature of all nodes and the attribute data; determine the real-time correction loss data based on all the real-time temperature data and the corresponding temperature data; and construct the joint loss function of the enhanced backpropagation neural network based on the fitting loss data, the adaptive penalty weight coefficients, the temperature physical loss data and the real-time correction loss data.

[0049] On the other hand, a terminal device is provided, including a processor and a memory;

[0050] The memory is used to store program code and transmit the program code to the processor;

[0051] The processor is configured to execute the transformer temperature field calculation method based on WPOD and enhanced BPNN as described above, according to the instructions in the program code.

[0052] This invention discloses a method, apparatus, and equipment for calculating the transformer temperature field based on WPOD and enhanced BPNN. The method includes acquiring the transformer's environmental parameters, attribute data, a set of sample operating conditions, a finite element model, and several real-time temperature data points. It then simulates the finite element model based on each operating condition sample from the sample operating condition set, obtaining sample data of the transformer's global temperature field corresponding to each operating condition sample, and constructing a sample dataset from all sample data. Finally, it obtains the maximum weight of each mesh node in the finite element model and, based on the sample data and the maximum weight of each node in the sample dataset, determines the relationship between the finite element model and the temperature field of the transformer. The diagonal weight matrix corresponding to the number of grid nodes is used; based on the diagonal weight matrix, the matrix formed by the sample dataset is dimensionality reduced using intrinsic orthogonal decomposition to obtain the modal coefficients and transformation matrix; an enhanced backpropagation neural network is obtained, using environmental parameters, attribute data, working condition samples from the sample working condition set, and all real-time temperature data as inputs to the enhanced backpropagation neural network, and using the modal coefficients as the outputs of the enhanced backpropagation neural network for training, to obtain a fast computation surrogate model; the operating data of the transformer to be calculated is obtained, and the operating data is input into the fast computation surrogate model for solution, to obtain the global temperature field distribution corresponding to the transformer to be calculated.

[0053] As can be seen from the above technical solutions, this application has the following advantages: The transformer temperature field calculation method based on WPOD and enhanced BPNN introduces intrinsic orthogonal decomposition through a diagonal weight matrix, which accurately preserves the high-frequency abrupt change law and local thermodynamic details of the transformer temperature field. This enables the construction of a fast calculation proxy model to effectively avoid the omission of local overheating risk when facing extreme or transient conditions, improve the calculation accuracy of the fast calculation proxy model, and solve the technical problems of narrow applicability and low accuracy of existing methods for obtaining the temperature rise state of dry-type transformers.

[0054] This transformer temperature field calculation device based on WPOD and enhanced BPNN introduces intrinsic orthogonal decomposition into the diagonal weight matrix through sample data acquisition module, weight matrix construction module, model construction module, and temperature field calculation module. It accurately preserves the high-frequency abrupt change law and local thermodynamic details of the transformer temperature field, so that the constructed fast calculation proxy model can effectively avoid the omission of local overheating risk when facing extreme or transient conditions, and improve the calculation accuracy of the fast calculation proxy model. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart illustrating the steps of the transformer temperature field calculation method based on WPOD and enhanced BPNN described in the embodiments of this application.

[0057] Figure 2 This is a schematic diagram of singular value decomposition of the transformer temperature field calculation method based on WPOD and enhanced BPNN described in the embodiments of this application;

[0058] Figure 3 This is a comparison chart of the predicted hot spot temperatures of the transformer in the transformer temperature field calculation method based on WPOD and enhanced BPNN described in the embodiments of this application.

[0059] Figure 4 This is a schematic diagram of the frame of the transformer temperature field calculation device based on WPOD and enhanced BPNN as described in the embodiments of this application;

[0060] Figure 5 This is a schematic diagram of the terminal device described in an embodiment of this application. Detailed Implementation

[0061] To make the inventive objectives, features, and advantages of this application more apparent and understandable, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0062] In the description of the embodiments of this application, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0063] In the embodiments of this application, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of this application according to the specific circumstances.

[0064] Patent terminology used in this application:

[0065] BPNN (Back Propagation Neural Network) is a multi-layer feedforward neural network trained using the error backpropagation algorithm. It was proposed by Rumelhart et al. in 1986 and is one of the most widely used neural network models.

[0066] Weighted intrinsic orthogonal decomposition (WPOD) is a dimensionality reduction technique that extracts the dominant characteristic modes of a physical system. It constructs a set of optimal orthogonal basis functions, sorted by energy contribution rate from highest to lowest, by performing eigenvector decomposition on the system data. WPOD can be understood as a dimensionality reduction technique based on intrinsic orthogonal decomposition (POD) with temperature-guided weighting.

[0067] This application provides a method, apparatus, and device for calculating the temperature field of a transformer based on WPOD and enhanced BPNN, which solves the technical problems of narrow applicability and low accuracy of existing methods for obtaining the temperature rise state of dry-type transformers.

[0068] Example 1:

[0069] Figure 1 This is a flowchart illustrating the steps of the transformer temperature field calculation method based on WPOD and enhanced BPNN as described in the embodiments of this application.

[0070] like Figure 1 As shown in the figure, this application provides a method for calculating the transformer temperature field based on WPOD and enhanced BPNN, including the following steps:

[0071] S1. Obtain the transformer's environmental parameters, attribute data, sample operating condition set, finite element model, and several real-time temperature data. Simulate the finite element model based on each operating condition sample in the sample operating condition set to obtain sample data of the transformer's global temperature field corresponding to each operating condition sample. Construct a sample dataset from all sample data.

[0072] It should be noted that step S1 involves collecting transformer attribute data, different sample operating condition data, finite element models, and several real-time temperature data. For each operating condition sample in the sample operating condition set, a simulation operation is performed using the finite element model to obtain sample data of the transformer's global temperature field corresponding to each operating condition sample. Finally, all these sample data are integrated to form a sample dataset, providing basic data for subsequently building a rapid calculation proxy model. Attribute data may include the transformer's material density, specific heat capacity, thermal conductivity, and internal heat source density of the core or windings. In this embodiment, the sample dataset can be a sample matrix formed by defining different operating condition samples with parameters such as different load currents, ambient temperatures, voltage levels, and cooling medium flow rates. The generated operating condition samples can be, for example: the sample parameters for operating condition sample A are an ambient temperature of 20℃, a load rate of 80%, and a convective heat transfer coefficient corresponding to natural air cooling; the sample parameters for operating condition sample B are an ambient temperature of 40℃ (extreme high temperature), a load rate of 120% (overload operation), and a high convective heat transfer coefficient corresponding to forced air cooling. Among them, orthogonal experimental methods can be used to generate dozens to hundreds of similar and independent combinations of operating condition samples to form an operating condition sample set, with different ambient temperatures, load rates and convective heat transfer coefficients.

[0073] In this embodiment of the application, the real-time temperature data of the transformer can be obtained by setting several fiber Bragg grating sensors inside the transformer, and the data monitored in real time by the fiber Bragg grating sensors can be used as the real-time temperature data.

[0074] It should be noted that in other embodiments, real-time temperature data can also be obtained by acquiring the real-time temperature of the transformer during operation through a temperature sensor or a temperature acquisition element (such as a thermistor).

[0075] S2. Obtain the maximum weight of the mesh nodes in the finite element model. Based on the sample data and the maximum weight of each sample in the sample dataset, determine the diagonal weight matrix corresponding to the number of mesh nodes in the finite element model.

[0076] It should be noted that when using existing intrinsic orthogonal decomposition to reduce the order of the matrix formed by the sample dataset, the goal is to minimize the global reconstruction mean square error. In transformer temperature field data, the number of nodes related to low-temperature rises is the vast majority, while the number of nodes related to high-temperature rises, which have a greater impact on transformer lifespan, is relatively small. This leads to excessive attention being allocated to the low-temperature rise region by existing intrinsic orthogonal decomposition, increasing the reconstruction error in the high-temperature rise region. Therefore, this transformer temperature field calculation method based on WPOD and enhanced BPNN obtains a temperature-oriented diagonal weight matrix in step S2, assigning higher weights to the high-temperature rise region. This ensures that the reconstruction accuracy of the high-temperature region is prioritized during the subsequent step S3 when reducing the order of the matrix formed by the sample dataset. In this embodiment, step S2 first obtains the maximum weight, and then constructs a diagonal weight matrix with all sample data obtained in step S1. Higher weight coefficients are assigned to sample data under specific operating conditions (such as high load, sudden overload, or extreme ambient temperature), providing data for the subsequent step S3 to extract enhanced spatial basis functions that accurately characterize local hotspot changes and obtain the corresponding low-dimensional modal coefficients during the reduction of the matrix formed by the sample dataset.

[0077] For example, the maximum weight in step S2 can be calculated from the set of mesh nodes in the finite element model using simulation results (such as temperature field, electromagnetic loss distribution, etc.). The weight value of each mesh node is calculated (e.g., based on physical quantities such as thermal stress concentration factor and electromagnetic loss density), and the global maximum value is selected. This global maximum value serves as the benchmark for constructing the diagonal weight matrix. The diagonal weight matrix in step S2 can first use a sample dataset (containing simulation results of global temperature field, electromagnetic field, etc. under different operating conditions) to associate the physical field data (such as temperature data) of each operating condition sample with the weight of the mesh nodes. For example, the weight coefficient of a certain mesh node may be determined by the average temperature gradient, maximum loss value, or thermo-mechanical coupling effect strength of that mesh node under multiple operating condition samples. The diagonal weight matrix W is of size M×M (M is the total number of mesh nodes), with diagonal elements w... i It is composed of the weight data corresponding to the i-th grid node, that is .

[0078] S3. Based on the diagonal weight matrix, perform dimensionality reduction on the matrix formed by the sample dataset using eigenorthogonal decomposition to obtain the modal coefficients and transformation matrix; obtain the enhanced backpropagation neural network, and use environmental parameters, attribute data, working condition samples of the sample working condition set and all real-time temperature data as inputs to the enhanced backpropagation neural network, and use the modal coefficients as outputs to train the enhanced backpropagation neural network to obtain a fast computation surrogate model.

[0079] It should be noted that the matrix formed by the sample dataset is a snapshot matrix. Step S3 first uses Orthogonal Eigenvalue Decomposition (POD) to reduce the dimensionality of the snapshot matrix, extract the dominant modes, and calculate the mode coefficients corresponding to each operating condition sample. Then, an enhanced backpropagation neural network is constructed, using environmental parameters and operating conditions (such as attribute data, sample operating condition sets, and all real-time temperature data) as inputs and mode coefficients as outputs for training. This establishes a nonlinear mapping relationship between the input parameters and the temperature field, forming a fast computational proxy model, providing a computational model for subsequent calculations of the global temperature field distribution corresponding to the transformer. In this embodiment, the environmental parameters also include heat source excitation parameters, boundary environment parameters, and heat dissipation boundary parameters. The heat source excitation parameters are the heating power of the high-voltage winding and low-voltage winding, as well as the heating power of the core, derived from different load rates. The boundary environment parameters refer to the specific temperature values ​​corresponding to the ambient temperature. The heat dissipation boundary parameters refer to the surface convection heat transfer coefficient values ​​corresponding to the cooling method.

[0080] For example, based on the sample snapshot matrix X formed by the sample dataset obtained in step S1, the high-dimensional temperature field data is first subjected to feature dimensionality reduction using Weighted Eigenorthogonal Decomposition (WPOD). Specifically, by introducing a diagonal weight matrix, higher weights are assigned to snapshot data under specific operating conditions (such as high load, sudden overload, or extreme ambient temperature), thereby extracting enhanced spatial basis functions that can accurately characterize local hotspot changes and obtaining the corresponding low-dimensional modal coefficients. Subsequently, an enhanced backpropagation neural network (BPNN) architecture is constructed, using the transformer's operating conditions (such as current and load rate) and environmental parameters as network inputs, and the modal coefficients obtained from WPOD dimensionality reduction as the output target for training, until the required number of training iterations or training-test error is achieved, resulting in a fast computation surrogate model.

[0081] Figure 2 This is a schematic diagram of singular value decomposition of the transformer temperature field calculation method based on WPOD and enhanced BPNN described in the embodiments of this application. Figure 2 The paper demonstrates the changes in modal coefficients under different operating conditions, with the fundamental function remaining unchanged, using a sample snapshot matrix X of singular value decomposition as an example.

[0082] Intrinsic Orthogonal Decomposition (POD) is a classic dimensionality reduction technique for extracting dominant characteristic modes of a physical system. It constructs a set of optimal orthogonal basis functions, sorted by energy contribution rate from highest to lowest, by decomposing the system data into eigenvectors. Based on this, selecting the top few modes preserves the main features of the system, achieving low-dimensional reconstruction of high-dimensional data and significantly reducing computational complexity. In this embodiment, a sample snapshot matrix X is first constructed using the sample data from the sample dataset, i.e.:

[0083] ;

[0084] In the formula, X j Let x be the sample data under the j-th working condition. i，j Let be the temperature of the i-th mesh node in the finite element model under the j-th working condition sample; M be the total number of mesh nodes in the finite element model, which also represents the degrees of freedom in the finite element calculation; N be the total number of working condition samples, or the number of time steps under a single working condition. The intrinsic orthogonal decomposition (POD) aims to find an N-dimensional orthogonal basis Ψ to represent this data set, such that the error of the sample snapshot matrix X is minimized when projected onto the orthogonal basis Ψ. The expression for the first optimization problem is:

[0085] ;

[0086] In the formula, I is the identity matrix. For X j The data in each column. The first optimization problem can be transformed into solving a problem under unit orthogonal constraints. Next, solve for the correlation matrix XX. T The maximum projection variance. By introducing the Lagrange multiplier λ and constructing an auxiliary function, the auxiliary function is:

[0087] ;

[0088] By taking the partial derivative of the auxiliary function with respect to the basis function Ψ and setting it to zero, the variational problem in the auxiliary function can be transformed into solving the following eigenvalue decomposition equation, which is:

[0089] ;

[0090] The problem of finding the optimal orthogonal basis is transformed into the problem of finding the eigenvalues ​​of a matrix. Considering that the number of nodes in M ​​grids is much greater than the number of samples in N working conditions, and that XX... T ∈R M×M With XTX∈R N×N Since they have the same non-zero eigenvalues, and the latter has a lower computational order, we choose to calculate X. T The eigenvalues ​​and eigenvectors of X, i.e.:

[0091] ;

[0092] Then we obtain the orthogonal basis:

[0093] ;

[0094] ;

[0095] In the formula, It is a diagonal matrix, matrix The element λ on the main diagonal j These are the eigenvalues ​​corresponding to the j-th mode, and they are arranged in descending order, λ j A larger value indicates that the corresponding j-th mode represents more system features. Therefore, according to the energy accumulation principle (satisfying...), Choosing the first r-order modes, the expression for the energy accumulation principle is:

[0096] ;

[0097] The energy accumulation principle ensures that the reduced-order model can capture most of the feature information of the original system (such as the sample snapshot matrix X), and the transformation matrix Ψ is formed by taking the eigenvectors corresponding to the first r eigenvalues. r According to projection theory, the column vector X of the original data space can be transformed. M×1 Mapped to Ψ r ∈R M×r On the orthogonal subspace formed, the system order is compressed from N dimensions to r dimensions, that is:

[0098] ;

[0099] Unlike eigenvalue decomposition, which strictly requires the target matrix to be square, singular value decomposition (SVD) is applicable to matrices of different sizes. Performing SVD on a sample snapshot matrix X can quickly yield the transformation matrix Ψ of an orthogonal basis that meets the requirements. r The expression for singular value decomposition is:

[0100] ;

[0101] In the formula, U∈R M×M V∈R N×N These are the left and right singular value matrices, respectively; Σ∈R M×N The singular value matrix X is a matrix whose diagonal elements are the singular values ​​of the sample snapshot matrix X, arranged in descending order. The higher the order, the greater the matrix information represented by its eigenvectors. For example... Figure 2 As shown. The problem of solving the M-order temperature field finite element equation under the new working condition sample can be expressed by the first formula, which is:

[0102] ;

[0103] In the formula, K is the nonlinear finite element stiffness matrix, x is the degree of freedom of the finite element model, and F is the right-hand side matrix. Substituting the expression for singular value decomposition into the first formula, we obtain... Then project the original system (sample snapshot matrix X) onto the reduced-order subspace formed by the orthogonal basis matrices, that is: Among them, the stiffness matrix of the original system Approximately expressed by the POD-Galerkin method as follows: This reduces an M-order finite element system to an r-order system, which can improve the solution efficiency.

[0104] In this embodiment, based on the intrinsic orthogonal decomposition (POD), a diagonal weight matrix with temperature values ​​as the guiding weight is introduced to transform the singular value decomposition expression into a data matrix X', i.e. After singular value decomposition, the influence of the diagonal weight matrix is ​​eliminated, resulting in the weighted singular value decomposition expression, i.e. .

[0105] It should be noted that this transformer temperature field calculation method based on WPOD and enhanced BPNN redefines the error minimization objective by introducing a diagonal weight matrix oriented by the spatial node temperature. This tilts the extraction of orthogonal basis vectors towards high-weight regions, amplifies the data characteristics of the high-temperature rise region, reduces the reconstruction error of the high-temperature region, and provides more reliable reduced-order data for subsequent data learning.

[0106] S4. Obtain the operating data of the transformer to be calculated, input the operating data into the fast calculation proxy model for solution, and obtain the global temperature field distribution corresponding to the transformer to be calculated.

[0107] It should be noted that the operational data includes new environmental parameters, real-time operating conditions, and real-time temperature data monitored by sensors. Step S4 involves inputting the operational data into a fast computational proxy model constructed by combining the Weighted Eigenorthogonal Decomposition (WPOD) and the Enhanced Backpropagation Neural Network (BPNN) trained in Step S3. The Physically Enhanced Backpropagation Neural Network (BPNN) quickly outputs low-dimensional modal coefficients, which are then linearly mapped and reconstructed using the enhanced spatial basis functions extracted by the WPOD. Without relying on the time-consuming finite element solver, a full-domain three-dimensional temperature field distribution that conforms to the physical conservation laws of heat transfer and has strong anti-interference capabilities is obtained directly at millisecond speed. This enables online monitoring, rapid assessment, and high-fidelity prediction of the temperature rise status of dry-type transformers under complex operating conditions.

[0108] In other embodiments, before inputting the running data into the fast computation surrogate model in step S4, the running data can be standardized / normalized to match the requirements of the fast computation surrogate model for input data and improve the accuracy of the fast computation surrogate model's solution.

[0109] Figure 3 This is a comparison chart of the predicted hot spot temperatures of the transformer in the transformer temperature field calculation method based on WPOD and enhanced BPNN described in the embodiments of this application. Figure 3In the image, (a) represents WPOD hotspot prediction, and (b) represents POD hotspot prediction.

[0110] In this embodiment, Table 1 shows the time comparison for solving the global temperature field distribution of a transformer using the WPOD and enhanced BPNN-based transformer temperature field calculation method. Table 1 shows that the fast computation surrogate model of Weighted Eigenorthogonal Decomposition (WPOD) and Physically Enhanced Backpropagation Neural Network (BPNN) significantly reduces the calculation time of the transformer temperature field, increasing the speed by 7650 times, while also minimizing calculation errors. The deviation in hotspot calculation is verified using 50 sets of validation samples. Figure 3 As shown, the absolute and relative errors of the transformer hotspot temperature were calculated under 50 test conditions. A horizontal comparison was made between the prediction results of the WPOD method and the traditional POD method. Figure 3 As shown, the Weighted Intrinsic Orthogonal Decomposition (WPOD) method outperforms the Traditional Intrinsic Orthogonal Decomposition (POD) method in capturing hotspot temperatures. The maximum absolute error of the WPOD prediction results is only 0.26°C, and the corresponding maximum relative error is strictly controlled within 0.72%. In contrast, the Traditional Intrinsic Orthogonal Decomposition (POD) method exhibits greater prediction fluctuations, with a maximum absolute error of 0.85°C, approximately 3.2 times that of the WPOD method, and its maximum relative error also rises to 2.2%. Furthermore, the WPOD method shows a more compact error curve distribution and demonstrates good stability when processing different test samples. This proves that assigning higher weights to the high-temperature region at the upper end of the transformer winding can effectively compensate for the energy loss of the reduced-order model at key hotspots, thereby improving the ability of the fast-computing surrogate model to reconstruct the local high-temperature characteristics of the transformer. This further verifies the effectiveness of the weight optimization strategy in improving the accuracy of hotspot prediction.

[0111] Table 1 compares the computation time of finite element software and fast computation proxy model.

[0112] Finite element software calculation 1836s - Fast computation proxy model computation 0.24s 0.251%

[0113] In the embodiments of this application, addressing the technical problem that traditional intrinsic orthogonal decomposition (POD) assigns equal weights to each sample when processing multi-condition sample data, which easily leads to the loss of local high-frequency thermal features, this transformer temperature field calculation method based on WPOD and enhanced BPNN uses weighted intrinsic orthogonal decomposition (WPOD) to non-uniformly weight the extracted high-dimensional temperature field snapshot matrix according to the severity of the transformer's operating conditions (such as high load, sudden overload, or extreme heat dissipation deterioration). This can significantly reduce the dimensionality of the computational space while accurately capturing and preserving the local hot spot mutation patterns of dry-type transformers under transient or extreme operating conditions, effectively avoiding the smoothing and filtering of key physical features, and providing accurate enhanced spatial basis functions for the subsequent construction of a high-fidelity fast computational proxy model.

[0114] It should be noted that this transformer temperature field calculation method based on WPOD and enhanced BPNN uses a sample space (such as a sample snapshot matrix) constructed based on a full-order transformer finite element model. Weighted intrinsic orthogonal decomposition (WPOD) is then used to reduce the dimensionality of the sample space, enhancing the extraction of key operating condition samples and abrupt change features. This transforms the prediction of high-dimensional temperature data into the prediction of low-dimensional modal coefficients, significantly reducing the computational scale of the fast computation surrogate model. Simultaneously, to address the black-box limitations of traditional BPNNs, a customized network reconstruction is performed. The transformer heat transfer partial differential equation is introduced as a residual penalty term into the loss function of the BP neural network, forming a weight update criterion guided by a physical mechanism. This constructs an enhanced backpropagation neural network, which learns the nonlinear mapping relationship between operating conditions and modal coefficients. Furthermore, incorporating real-time temperature data as input into training and prediction significantly enhances the physical consistency and anti-interference capability of the neural network when facing operating condition fluctuations.

[0115] This application provides a method for calculating the temperature field of a transformer based on WPOD and an enhanced BPNN. The method includes acquiring environmental parameters, attribute data, a sample operating condition set, a finite element model, and several real-time temperature data points of the transformer; simulating the finite element model based on each operating condition sample in the sample operating condition set to obtain sample data of the transformer's global temperature field corresponding to each operating condition sample, and constructing a sample dataset from all sample data; obtaining the maximum weight of each grid node in the finite element model, and determining a diagonal weight matrix corresponding to the number of grid nodes in the finite element model based on each sample data point and the maximum weight of the sample dataset; performing dimensionality reduction on the matrix constructed from the sample dataset using intrinsic orthogonal decomposition based on the diagonal weight matrix to obtain modal coefficients and a transformation matrix; acquiring an enhanced backpropagation neural network, using environmental parameters, attribute data, operating condition samples from the sample operating condition set, and all real-time temperature data as inputs to the enhanced backpropagation neural network, and using the modal coefficients as the outputs of the enhanced backpropagation neural network for training to obtain a fast computation surrogate model; acquiring the operating data of the transformer to be calculated, inputting the operating data into the fast computation surrogate model for solution, and obtaining the global temperature field distribution corresponding to the transformer to be calculated. This transformer temperature field calculation method based on WPOD and enhanced BPNN introduces intrinsic orthogonal decomposition through a diagonal weight matrix, accurately preserving the high-frequency abrupt change patterns and local thermodynamic details of the transformer temperature field. This enables the construction of a fast calculation proxy model to effectively avoid missing the risk of local overheating when facing extreme or transient operating conditions, thereby improving the calculation accuracy of the fast calculation proxy model. It also solves the technical problems of narrow applicability and low accuracy of existing methods for obtaining the temperature rise state of dry-type transformers.

[0116] In one embodiment of this application, obtaining an enhanced backpropagation neural network includes:

[0117] The global temperature field is reconstructed based on the modal coefficients and transformation matrix; the node temperatures corresponding to the mesh nodes in the finite element model and the temperature data corresponding to each real-time temperature data are extracted from the global temperature field.

[0118] Obtain the fitting loss data and adaptive penalty weight coefficients of the backpropagation neural network; determine the temperature physical loss data based on the temperature and attribute data of all nodes; determine the real-time correction loss data based on all real-time temperature data and corresponding temperature data; construct the joint loss function of the enhanced backpropagation neural network based on the fitting loss data, adaptive penalty weight coefficients, temperature physical loss data and real-time correction loss data.

[0119] It should be noted that, at the same location on the transformer, real-time temperature data refers to the temperature value detected in real time by sensors, and temperature data refers to the temperature value extracted from the temperature field at the same location on the transformer.

[0120] In this embodiment, the enhanced backpropagation neural network overcomes the inherent limitation of traditional backpropagation neural networks (BPNNs), which rely on pure data-driven "black box" predictions and are prone to violating the law of conservation of energy. It establishes a nonlinear mapping relationship between operating conditions and modal coefficients. In constructing the joint loss function of the enhanced backpropagation neural network, not only is the traditional error between the simulation-based predicted value and the actual value introduced, but the residual of the transformer's heat transfer partial differential equation is innovatively used as a physical constraint term, and real-time monitoring data from field sensors is used as a dynamic correction term. This dual joint driving mechanism of physical laws and measured data fundamentally enhances the anti-interference capability of the constructed fast computational proxy model under complex electromagnetic interference and unknown extreme operating conditions, ensuring that the millisecond-level output of the three-dimensional temperature field strictly follows objective thermodynamic laws.

[0121] It should be noted that in the process of obtaining the enhanced backpropagation neural network, the training mode of the backpropagation neural network BPNN is not adopted by pure data-driven mode. Instead, the heat transfer partial differential equation is constructed as the physical loss term, and the real-time temperature value monitored by the actual transformer layout is used as the real-time correction term. Both are integrated into the loss function of the backpropagation neural network BPNN, so that the enhanced backpropagation neural network has the dual constraints of physical laws and measured data. This allows the constructed fast computation surrogate model to be trained into a surrogate model with nonlinear mapping ability and physical conservation characteristics.

[0122] In this embodiment, reconstructing the global temperature field based on the modal coefficients and the transformation matrix can be understood as reconstructing the global temperature field by multiplying the transformation matrix by the matrix of the modal coefficients, thus quickly generating the global temperature field. In other embodiments, the global temperature field is obtained by linearly weighting the modal coefficients and the orthogonal basis Ψ of the weighted eigenorthogonal decomposition POD as basis functions (multiplying the modal coefficients by the orthogonal basis Ψ).

[0123] In one embodiment of this application, the attribute data includes the transformer's material density, specific heat capacity, thermal conductivity, and internal heat source density of the core or windings; obtaining the enhanced backpropagation neural network further includes: calculating temperature physical loss data using the partial differential equation residual formula based on all node temperatures and attribute data; and calculating real-time corrected loss data using the deviation correction formula based on all real-time temperature data and corresponding temperature data; the partial differential equation residual formula is:

[0124] ;

[0125] The deviation correction formula is:

[0126] ;

[0127] The joint loss function is:

[0128] ;

[0129] In the formula, L data To fit the loss data, and These are the adaptive penalty weight coefficients with different values, L. phy For temperature physical loss data, L sen To correct lost data in real time, N S This represents the total number of real-time temperature data points collected. This is the Sth real-time temperature data collected. Let M be the S-th temperature data point, and M be the number of mesh nodes in the finite element model. Let be the nodal temperature corresponding to the i-th grid node, and ∇ be the vector differential operator. The material density of the transformer, Let be the specific heat capacity of the transformer, and k be the thermal conductivity of the transformer. Let L be the internal heat source density corresponding to the i-th grid node, t be time, and L be the internal heat source density. total This represents the total loss.

[0130] It should be noted that the fitting loss data L data This could be the mean square error between the predicted mode coefficients output by the network and the true mode coefficients of the weighted intrinsic orthogonal decomposition (WPOD). In this embodiment, the architecture of the enhanced backpropagation neural network (BPNN) is a customized reconstruction of the traditional loss function of BP neural networks, constructing a joint loss function that includes data loss, physical mechanism loss, and monitoring correction loss.

[0131] In this embodiment of the application, during the process of obtaining temperature physical loss data, the heat conduction and temperature rise process inside the transformer follows the law of conservation of energy, and its three-dimensional transient heat transfer partial differential equation can be expressed as:

[0132] ;

[0133] In the formula, Let L be the internal heat source density of the transformer core or winding, and T be the nodal temperature of the grid nodes. Substituting the nodal temperatures of each grid node in the reconstructed global temperature field into the three-dimensional transient heat transfer partial differential equation, the residuals of the equations at the spatially configured grid nodes are calculated to obtain the calculated temperature physical loss data L. phy The residual formula for partial differential equations.

[0134] In one embodiment of this application, to further improve the anti-interference capability of the fast computation proxy model under actual complex electromagnetic and thermal environments, real-time temperature data monitored at the actual fiber optic grating sensor locations inside the transformer are extracted. Predicted temperature data at the same spatial coordinate points corresponding to each real-time temperature data point is extracted from the global temperature field, and the deviation between the two is calculated using a deviation correction formula to obtain real-time corrected loss data.

[0135] It should be noted that in the process of obtaining the fast computational proxy model, the total loss calculated by the joint loss function is achieved through the backpropagation algorithm. Minimization not only ensures rapid dimensionality reduction and fitting of the surrogate model to theoretical high-dimensional data, but also utilizes temperature-based physical loss data. The heat transfer mechanism constraint was introduced, and the loss data was corrected in real time. Dynamic calibration based on real-world operating conditions was introduced. The resulting fast computational proxy model, when faced with fluctuations in unknown operating conditions outside the training set, can still output a high-fidelity global temperature field that conforms to thermodynamic laws and closely approximates the actual monitoring data.

[0136] In one embodiment of this application, determining the diagonal weight matrix corresponding to the number of mesh nodes in the finite element model based on the individual sample data and the maximum weight of the sample dataset includes:

[0137] Based on the sample data of each sample dataset, determine the mean temperature, maximum temperature and minimum temperature corresponding to each mesh node in the finite element model;

[0138] The weight coefficient corresponding to each grid node is calculated based on the maximum weight and the average, maximum, and minimum temperatures of each grid node.

[0139] Based on all weight coefficients, a diagonal weight matrix corresponding to the number of mesh nodes in the finite element model is determined. Specifically, the weight coefficient for each mesh node is calculated using the maximum weight value, the mean temperature, maximum temperature, and minimum temperature for each mesh node, according to the weight calculation formula:

[0140] ;

[0141] In the formula, w max T represents the maximum weight. min The minimum temperature, T max T represents the maximum temperature. i Let w be the average temperature of the i-th grid node. i is the weight coefficient of the i-th grid node.

[0142] It should be noted that in the weighted intrinsic orthogonal decomposition (WPOD) order reduction modeling, a non-uniform weight allocation strategy is introduced. Higher weight coefficients are applied to the high-temperature region nodes at the upper end of the transformer winding. The weight setting and calculation formula are shown in the figure, linearly mapping to the weight interval [1, w]. max This is to ensure that the error in the high-temperature region is reduced during the temperature field reconstruction process, and to obtain the hot spot temperature more accurately.

[0143] In one embodiment of this application, obtaining the finite element model of the transformer includes:

[0144] The actual structural parameters, boundary conditions, and thermal excitation of the transformer are obtained. Based on the actual structural parameters, boundary conditions, thermal excitation, and attribute data, a simplified three-dimensional model is constructed.

[0145] A structured mapping mesh is used to partition the simplified three-dimensional model to obtain a finite element model.

[0146] It should be noted that in constructing the simplified 3D model, a simplified 3D model is built based on the actual structural parameters of the transformer. This simplified model covers key components such as the core, low-voltage winding, high-voltage winding, and insulation layer, ensuring that the transformer's geometry accurately reflects the actual heat transfer path and heat source distribution characteristics, meeting the needs of subsequent batch simulations of multiple operating conditions and training of proxy models. Specifically, the simplified 3D model simplifies the transformer's windings and core. The transformer windings are equivalent to a homogeneous cylindrical body, and the composite characteristics of copper and insulation are characterized through equivalent material properties, while retaining the main structure of the heat dissipation channels. The transformer core is simplified to a continuous anisotropic medium, ignoring details such as lamination gaps and clamps, retaining only the outline of the core column and yoke, significantly reducing computational complexity while ensuring the accuracy of the heat transfer path. The actual structural parameters mainly refer to the geometric dimensions that determine the transformer's three-dimensional spatial dimensions and the distribution of heat dissipation channels. Specifically, these include:

[0147] Core parameters: core column diameter, core window height, window width, etc.;

[0148] Winding parameters: inner diameter, outer diameter, and physical height of the low-voltage winding and the high-voltage winding;

[0149] Air duct and insulation parameters: width of the main insulation air duct between high and low voltage windings, interlayer / air duct dimensions inside the windings, thickness of insulation cylinders and pads, etc.

[0150] In this embodiment, during the construction of the simplified 3D model, 3D parametric modeling technology (such as the geometry building module of multiphysics simulation software like SolidWorks or numerical simulation software) is used for solid modeling. To avoid excessively large finite element mesh generation leading to computational divergence or high time costs, simplification is necessary. In the 3D simplified model, the main structure of the transformer's heat dissipation channels is retained, and the transformer windings are equivalent to a homogeneous continuum with anisotropic thermal conductivity. This reduces the computational load per solution and ensures the stability of the spatial manifold structure under different parametric simulations, laying a foundation for extracting standardized temperature field data later. During the construction of the simplified 3D model, small structures such as chamfers, bolts, and clamps, which have minimal impact on the macroscopic temperature field distribution, are ignored. The transformer windings are homogenized during the construction of the simplified 3D model; instead of establishing solid entities for individual conductors and turns of insulation, the high- and low-voltage windings are treated as a single heating block, and the actual heat transfer characteristics are reflected by assigning an equivalent anisotropic thermal conductivity.

[0151] In this embodiment, during the construction of the simplified three-dimensional model, boundary conditions describing the electromagnetic-thermal coupling characteristics of the transformer are set based on the geometric model of the transformer. The aim is to reproduce the actual nonlinear heat transfer process of the transformer as accurately as possible, ensuring that the temperature distribution calculated by the finite element method has sufficient physical reference value, thereby providing accurate physical prior knowledge for the subsequent enhanced backpropagation neural network. Boundary conditions include contact thermal resistance between components, external convective heat dissipation boundaries, etc. Simultaneously, heat source excitations for the windings and core are defined based on the electromagnetic loss calculation results to accurately characterize the heat source distribution under different load rates and environmental conditions. In the material property settings, parameters such as thermal conductivity, specific heat capacity, and thermal conductivity are set for the windings and core.

[0152] It should be noted that in the heat transfer calculations of dry-type transformers, the heat generated internally must ultimately be dissipated to the surrounding environment through the surface. The external convective heat dissipation boundary refers to the interface where the solid outer surface of each heat-generating component of the transformer contacts the surrounding air and undergoes heat exchange.

[0153] In this embodiment, during the construction of the finite element model, a structured mapping mesh is used to partition the model, with a focus on refining the mesh in areas with large temperature gradients, such as the transformer winding region and insulation layer. The total number of mesh elements is controlled while ensuring computational accuracy, thereby improving the computational convergence and solution efficiency of the finite element simulation. Specifically, the structured mapping mesh uses regular hexahedral elements to discretize the simplified three-dimensional model, with a focus on refining the mesh in areas with large temperature gradients, such as the transformer winding region, insulation layer, and core surface. Based on strict constraints that keep the mesh node coordinates and the total number of nodes constant for all parametric simulation samples, and by using a region-based partitioning strategy to partition the simplified three-dimensional model, orthogonal arrangement of the mesh is achieved while ensuring geometric fitting accuracy. This effectively controls the total number of control elements and mesh distortion, improving the convergence speed and solution accuracy of the finite element calculation, balancing computational efficiency and temperature field reproduction accuracy. It also eliminates numerical errors caused by mesh variations, ensuring that the output temperature field results can be successfully combined into a regular data matrix.

[0154] It should be noted that the regional division strategy includes:

[0155] For the heat-generating physical areas of the transformer (the core and the interior of the homogenized winding): Since the heat inside the transformer is mainly conducted by solids and the temperature distribution is relatively continuous, a regular hexahedral grid of conventional size is used for uniform discretization in order to control the total number of grids.

[0156] For the thin-walled insulation area of ​​the transformer (interlayer insulation, air duct insulation cylinder): due to the extremely low thermal conductivity and extremely thin thickness of the insulation material, there is a huge temperature difference along the thickness direction. The swept grid technology is used to force the division into at least 3 to 5 grids in the extremely thin thickness direction.

[0157] For the fluid-structure interaction boundary region of the transformer (the surface of the winding and core in contact with the cooling air): strong convective heat transfer occurs in this fluid-structure interaction boundary region, and the temperature gradient changes most drastically. A boundary layer mesh is introduced in the normal direction of the solid surface at this point.

[0158] In one embodiment of this application, obtaining a sample set of transformer operating conditions includes: using orthogonal experimental design or Latin hypercube sampling to obtain samples of various operating conditions of the transformer under different ambient temperatures and different loads, thereby obtaining a sample set of operating conditions.

[0159] It should be noted that orthogonal experimental design was used to generate representative and balanced operating condition samples under multiple influencing factors such as ambient temperature, load rate, and convective heat transfer coefficient. Specifically, the orthogonal experimental design selects multiple influencing factors such as ambient temperature, load rate, and convective heat transfer coefficient, and sets several representative levels for each factor. Based on the orthogonal array, it generates operating condition combinations with balanced dispersion and comprehensive comparability, covering the entire parameter space with the minimum number of samples. The orthogonal experimental design can effectively avoid the massive simulation computation caused by full factorial experiments, ensuring that the sample dataset is uniformly and reasonably distributed in terms of factor levels, providing an efficient and information-complete data foundation for training a fast computational surrogate model. Multiple sets of operating condition samples were generated using the Latin hypercube sampling method, and batch calculations of the finite element model were performed. After the calculation was completed, the temperature data of the global grid nodes under each operating condition sample was extracted, these three-dimensional spatial temperature data were flattened into one-dimensional vectors, and then concatenated column by column. The resulting high-dimensional matrix is ​​the temperature field snapshot matrix, which contains the thermal dynamics of the transformer under various operating conditions. This snapshot matrix will directly serve as the original input data for subsequent weighted intrinsic orthogonal decomposition (WPOD) feature extraction and enhanced backpropagation neural network training. In this embodiment, the snapshot matrix is ​​the core data structure connecting the full-order finite element physical field and the dimensionality-reduced surrogate model. Essentially, the snapshot matrix is ​​a two-dimensional matrix of dimension M×N, where M represents the total number of grid nodes in the topologically consistent space of the transformer model, and N represents the total number of extracted operating condition samples. Each column of the snapshot matrix is ​​equivalent to a digital snapshot, recording the global spatial node temperature distribution state of the transformer under a specific operating condition parameter.

[0160] Example 2:

[0161] Figure 4 This is a schematic diagram of the framework of the transformer temperature field calculation device based on WPOD and enhanced BPNN described in the embodiments of this application.

[0162] like Figure 4 As shown, this application provides a transformer temperature field calculation device based on WPOD and enhanced BPNN, including a sample data acquisition module 10, a weight matrix construction module 20, a model construction module 30, and a temperature field calculation module 40.

[0163] The sample data acquisition module 10 is used to acquire the transformer's environmental parameters, attribute data, sample operating condition set, finite element model and several real-time temperature data. It simulates the finite element model according to each operating condition sample in the sample operating condition set to obtain sample data of the transformer's global temperature field corresponding to each operating condition sample, and constructs a sample dataset from all the sample data.

[0164] The weight matrix construction module 20 is used to obtain the maximum weight of the mesh nodes in the finite element model. Based on the sample data and the maximum weight of each sample in the sample dataset, the diagonal weight matrix corresponding to the number of mesh nodes in the finite element model is determined.

[0165] The model building module 30 is used to perform dimensionality reduction on the matrix composed of the sample dataset based on the diagonal weight matrix using intrinsic orthogonal decomposition to obtain modal coefficients and transformation matrix; to obtain an enhanced backpropagation neural network, using environmental parameters, attribute data, working condition samples of the sample working condition set and all real-time temperature data as inputs to the enhanced backpropagation neural network, and using modal coefficients as outputs to train the enhanced backpropagation neural network to obtain a fast computation surrogate model;

[0166] The temperature field calculation module 40 is used to obtain the operating data of the transformer to be calculated, input the operating data into the fast calculation proxy model for solution, and obtain the global temperature field distribution corresponding to the transformer to be calculated.

[0167] It should be noted that the modules in the device of Embodiment 2 correspond to the steps described in the method of Embodiment 1. Since the steps in the method of Embodiment 1 have already been described, the contents of the sample data acquisition module 10, weight matrix construction module 20, model construction module 30, and temperature field calculation module 40 in the transformer temperature field calculation device based on WPOD and enhanced BPNN will not be described again in this embodiment. This transformer temperature field calculation device based on WPOD and enhanced BPNN introduces intrinsic orthogonal decomposition through the diagonal weight matrix of the sample data acquisition module 10, weight matrix construction module 20, model construction module 30, and temperature field calculation module 40. This accurately preserves the high-frequency abrupt change law and local thermodynamic details of the transformer temperature field, enabling the construction of a fast calculation proxy model to effectively avoid the omission of local overheating risks when facing extreme or transient operating conditions, thereby improving the calculation accuracy of the fast calculation proxy model.

[0168] In one embodiment of this application, the model building module 30 includes a data extraction submodule and a loss function construction submodule;

[0169] The data extraction submodule is used to reconstruct the global temperature field based on the modal coefficients and transformation matrix; and to extract the nodal temperatures corresponding to the mesh nodes in the finite element model and the temperature data corresponding to each real-time temperature data from the global temperature field.

[0170] The loss function construction submodule is used to obtain the fitting loss data and adaptive penalty weight coefficients of the backpropagation neural network; determine the temperature physical loss data based on the temperature and attribute data of all nodes; determine the real-time correction loss data based on all real-time temperature data and corresponding temperature data; and construct the joint loss function of the enhanced backpropagation neural network based on the fitting loss data, adaptive penalty weight coefficients, temperature physical loss data and real-time correction loss data.

[0171] Example 3:

[0172] Figure 5 This is a schematic diagram of the terminal device described in an embodiment of this application.

[0173] like Figure 5 As shown, this application provides a terminal device, including a processor and a memory;

[0174] Memory is used to store program code and transfer the program code to the processor;

[0175] The processor is used to execute the above-mentioned transformer temperature field calculation method based on WPOD and enhanced BPNN according to the instructions in the program code.

[0176] It should be noted that the processor is used to execute the steps in the above embodiment of a transformer temperature field calculation method based on WPOD and enhanced BPNN according to the instructions in the program code. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the above system / device embodiments.

[0177] For example, a computer program can be divided into one or more modules / units, one or more of which are stored in memory and executed by a processor to complete this application. One or more modules / units can be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in a terminal device.

[0178] Terminal devices can be computing devices such as desktop computers, laptops, handheld computers, and cloud servers. Terminal devices may include, but are not limited to, processors and memory. Those skilled in the art will understand that this does not constitute a limitation on the terminal device, which may include more or fewer components than illustrated, or combinations of certain components, or different components. For example, a terminal device may also include input / output devices, network access devices, buses, etc.

[0179] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0180] Memory can be an internal storage unit of a terminal device, such as a hard drive or RAM. Memory can also be an external storage device, such as a plug-in hard drive, SmartMedia Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, memory can include both internal and external storage units. Memory is used to store computer programs and other programs and data required by the terminal device. Memory can also be used to temporarily store data that has been output or will be output.

[0181] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0182] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between apparatuses or units through some interfaces, and may be electrical, mechanical, or other forms.

[0183] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0184] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0185] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0186] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for calculating the temperature field of a transformer based on WPOD and enhanced BPNN, characterized in that, Includes the following steps: The environmental parameters, attribute data, sample operating condition set, finite element model and several real-time temperature data of the transformer are obtained. The finite element model is simulated according to each operating condition sample of the sample operating condition set to obtain sample data of the transformer global temperature field corresponding to each operating condition sample. All the sample data are used to form a sample dataset. Obtain the maximum weight of the mesh nodes in the finite element model, and determine the diagonal weight matrix corresponding to the number of mesh nodes in the finite element model based on each sample data in the sample dataset and the maximum weight. The matrix formed by the sample dataset is reduced in dimensionality using intrinsic orthogonal decomposition based on the diagonal weight matrix to obtain modal coefficients and a transformation matrix; an enhanced backpropagation neural network is obtained, and the environmental parameters, the attribute data, the working condition samples of the sample working condition set, and all the real-time temperature data are used as inputs to the enhanced backpropagation neural network, and the modal coefficients are used as outputs to train the network to obtain a fast computation surrogate model; The operating data of the transformer to be calculated is obtained, and the operating data is input into the fast calculation proxy model for solution to obtain the global temperature field distribution corresponding to the transformer to be calculated.

2. The transformer temperature field calculation method based on WPOD and enhanced BPNN according to claim 1, characterized in that, Obtaining an enhanced backpropagation neural network includes: The global temperature field is reconstructed based on the modal coefficients and the transformation matrix; the node temperatures corresponding to the mesh nodes in the finite element model and the temperature data corresponding to each real-time temperature data are extracted from the global temperature field. Obtain the fitting loss data and adaptive penalty weight coefficients of the backpropagation neural network; determine the temperature physical loss data based on the temperature of all nodes and the attribute data; determine the real-time correction loss data based on all the real-time temperature data and the corresponding temperature data; construct the joint loss function of the enhanced backpropagation neural network based on the fitting loss data, the adaptive penalty weight coefficients, the temperature physical loss data and the real-time correction loss data.

3. The transformer temperature field calculation method based on WPOD and enhanced BPNN according to claim 2, characterized in that, The attribute data includes the material density, specific heat capacity, thermal conductivity, and internal heat source density of the core or winding of the transformer. The acquisition of the enhanced backpropagation neural network also includes: calculating the temperature physical loss data using the partial differential equation residual formula based on the temperature of all the nodes and the attribute data; The real-time correction loss data is obtained by calculating the deviation correction formula based on all the real-time temperature data and the corresponding temperature data; the partial differential equation residual formula is: ； The deviation correction formula is: ； The joint loss function is: ； In the formula, L data To fit the loss data, and These are the adaptive penalty weight coefficients with different values, L. phy For temperature physical loss data, L sen To correct lost data in real time, N S This represents the total number of real-time temperature data points collected. This is the Sth real-time temperature data collected. Let M be the S-th temperature data point, and M be the number of mesh nodes in the finite element model. For the node temperature corresponding to the i-th grid node, For vector differential operators, The material density of the transformer, Let be the specific heat capacity of the transformer, and k be the thermal conductivity of the transformer. Let L be the internal heat source density corresponding to the i-th grid node, t be time, and L be the internal heat source density. total This represents the total loss.

4. The transformer temperature field calculation method based on WPOD and enhanced BPNN according to claim 1, characterized in that, Based on each sample data point in the sample dataset and the maximum weight value, the diagonal weight matrix corresponding to the number of mesh nodes in the finite element model is determined as follows: Based on the sample data of the sample dataset, determine the mean temperature, maximum temperature and minimum temperature corresponding to each grid node in the finite element model; The weight coefficient corresponding to each grid node is calculated based on the maximum weight value, the average temperature, the maximum temperature, and the minimum temperature of each grid node. Based on all the weighting coefficients, determine the diagonal weight matrix corresponding to the number of mesh nodes in the finite element model.

5. The transformer temperature field calculation method based on WPOD and enhanced BPNN according to claim 4, characterized in that, The weight coefficient corresponding to each grid node is calculated based on the maximum weight value and the average temperature, maximum temperature, and minimum temperature of each grid node using a weight calculation formula. ； In the formula, w max T represents the maximum weight. min The minimum temperature, T max T represents the maximum temperature. i Let w be the average temperature of the i-th grid node. i is the weight coefficient of the i-th grid node.

6. The transformer temperature field calculation method based on WPOD and enhanced BPNN according to any one of claims 1-5, characterized in that, Obtaining the finite element model of the transformer includes: The actual structural parameters, boundary conditions, and thermal excitation of the transformer are obtained. A simplified three-dimensional model is constructed based on the actual structural parameters, boundary conditions, thermal excitation, and attribute data. The simplified three-dimensional model is partitioned using a structured mapping mesh to obtain a finite element model.

7. The method for calculating the transformer temperature field based on WPOD and enhanced BPNN according to any one of claims 1-5, characterized in that, Obtaining the sample operating condition set of the transformer includes: using orthogonal experimental design or Latin hypercube sampling method to obtain samples of the transformer operating under different ambient temperatures and different loads, thus obtaining the sample operating condition set.

8. A transformer temperature field calculation device based on WPOD and enhanced BPNN, characterized in that, It includes a sample data acquisition module, a weight matrix construction module, a model construction module, and a temperature field calculation module; The sample data acquisition module is used to acquire the transformer's environmental parameters, attribute data, sample operating condition set, finite element model, and several real-time temperature data. It simulates the finite element model based on each operating condition sample in the sample operating condition set to obtain sample data of the transformer's global temperature field corresponding to each operating condition sample. All the sample data are then used to form a sample dataset. The weight matrix construction module is used to obtain the maximum weight of the grid nodes in the finite element model, and determine the diagonal weight matrix corresponding to the number of grid nodes in the finite element model based on each sample data in the sample dataset and the maximum weight. The model building module is used to perform dimensionality reduction processing on the matrix formed by the sample dataset based on the diagonal weight matrix using intrinsic orthogonal decomposition to obtain modal coefficients and transformation matrix; to obtain an enhanced backpropagation neural network, using the environmental parameters, the attribute data, the working condition samples of the sample working condition set and all the real-time temperature data as inputs to the enhanced backpropagation neural network, and using the modal coefficients as outputs to train the enhanced backpropagation neural network to obtain a fast computation surrogate model; The temperature field calculation module is used to acquire the operating data of the transformer to be calculated, input the operating data into the fast calculation proxy model for solution, and obtain the global temperature field distribution corresponding to the transformer to be calculated.

9. The transformer temperature field calculation device based on WPOD and enhanced BPNN according to claim 8, characterized in that, The model building module includes a data extraction submodule and a loss function construction submodule; The data extraction submodule is used to reconstruct the global temperature field based on the modal coefficients and the transformation matrix. Extract the node temperatures corresponding to the mesh nodes in the finite element model and the temperature data corresponding to each of the real-time temperature data from the global temperature field. The loss function construction submodule is used to obtain the fitting loss data and adaptive penalty weight coefficients of the backpropagation neural network; determine the temperature physical loss data based on the temperature of all nodes and the attribute data; determine the real-time correction loss data based on all the real-time temperature data and the corresponding temperature data; and construct the joint loss function of the enhanced backpropagation neural network based on the fitting loss data, the adaptive penalty weight coefficients, the temperature physical loss data and the real-time correction loss data.

10. A terminal device, characterized in that, Including the processor and memory; The memory is used to store program code and transmit the program code to the processor; The processor is configured to execute the transformer temperature field calculation method based on WPOD and enhanced BPNN as described in any one of claims 1-7 according to the instructions in the program code.

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