A method for inverting the temperature field distribution of power transformers with physical model support and reduced uncertainty.

Abstract

This invention proposes a method for inverting the temperature field distribution of power transformers, supported by a physical model and reducing the impact of uncertainties. It employs a reduced-order transformer model to preserve core physical characteristics and constructs an internal temperature field inversion model based on an artificial neural network. Furthermore, it proposes a temperature field compensation inversion model based on support vector regression to compensate for the deviation between measured and predicted temperature values ​​at external and internal measuring points of the transformer, eliminating the influence of potential factors. This invention combines the two models to obtain high-precision and highly robust inversion results.

Description

Technical Field

[0001] This falls under the field of intelligent operation and maintenance of power equipment, used for condition monitoring and fault diagnosis of electrical equipment and various electromagnetically related equipment; it also directly belongs to the field of industrial simulation software. In particular, it relates to a method for inverting the temperature field distribution of power transformers, supported by a physical model and reducing the influence of uncertainties. Background Technology

[0002] With the continuous increase in power grid load and the prolonged heavy-load operation of power transformers, it is necessary to accurately sense the internal temperature of transformers, accurately assess the operating status of equipment, predict overheating defects in a timely manner, avoid failures, and ensure the reliability of equipment operation. The traditional method is to install temperature sensors inside the windings for real-time monitoring, but this method is not only costly but also damages the internal structure and insulation materials of the transformer.

[0003] In recent years, inversion methods for predicting transformer hotspot temperatures have emerged as a new monitoring approach. This method involves measuring external parameters such as temperature and then using mathematical models and computer simulations to invert the temperature distribution within the transformer windings. Compared to traditional methods, this approach eliminates the need for sensors inside the windings, enabling non-destructive monitoring and prediction of internal winding temperatures. It also allows for the timely detection of potential problems, improving transformer safety and reliability. Inverting hotspot temperatures based on transformer operating data has become a hot research trend. Compared to empirical and thermal circuit models, artificial intelligence algorithms offer higher accuracy, stronger generalization ability, and non-destructive testing capabilities for predicting transformer hotspot temperatures.

[0004] In current conventional algorithms, predicting transformer hotspot temperatures typically relies solely on neural network learning. As a purely data-driven model, this approach inevitably has limitations. If only data on the relationship between the target quantity (e.g., winding temperature) and externally monitored temperatures, as well as operating conditions and environmental factors, is used for inversion—essentially employing a black-box approach—the model lacks information about the transformer's physical structure, focusing solely on the relationships between data. This results in poor interpretability and high requirements for training data quality. Black-box models often involve multiple layers and complex structures, demanding significant computational resources and time for training. Due to the complexity and black-box nature of deep learning models, ensuring model reliability is difficult. Overfitting or underfitting can lead to inaccurate predictions, and the models are difficult to scale and optimize, exhibiting poor generalization ability. Summary of the Invention

[0005] This paper proposes a method for inverting the temperature field distribution of power transformers, supported by a physical model and reducing the impact of uncertainties. The full physical field model of the transformer is reduced to an alternative model jointly described by a reduced-order basis and basis coefficients. The basis coefficients are predicted by inverting the temperature from external control points. Deep learning is used to output the basis coefficients of the reduced-order model instead of directly predicting the internal winding temperature. The temperature field of the transformer space is reconstructed using the predicted basis coefficients and the reduced-order basis obtained from the full model, thus obtaining the winding temperature information. This method fully considers the characteristics and physical principles of the transformer model and can predict the winding temperature distribution characteristics without constraining specific winding locations, thus exhibiting stronger inversion capabilities. Furthermore, this method introduces a temperature inversion result correction model to eliminate the influence of difficult-to-quantify factors such as systematic errors and process deviations, resulting in more reliable results.

[0006] This invention can predict the changing patterns of spatial temperature field distribution based on temperature change data from external measuring points of the transformer. Combined with anomaly distribution inversion identification methods, it can detect and identify the fault type at an early stage of the occurrence and development of typical overheating defects, realize early warning of overheating defects, buy more time for maintenance personnel to handle faults, and avoid the fault from expanding and causing serious damage to the transformer.

[0007] This invention proposes a method for inverting the temperature field distribution of power transformers with physical model support and reduced uncertainty factors. It includes two processes: establishing an inversion model and using the inversion model for prediction. It also includes two methods: inverting temperature information and inverting temperature compensation information.

[0008] For temperature inversion models, the process of establishing an inversion model first involves using model reduction methods to obtain a substitute model corresponding to the full transformer model. This yields a reduced-order basis and corresponding basis coefficients that characterize the transformer. Then, combining a series of data such as transformer operating conditions, environmental factors, external measuring point temperatures, and basis coefficients, an inversion network is constructed using artificial neural networks (ANNs) to predict the basis coefficients from the external measuring point temperatures. In applying the inversion model, using the transformer operating conditions, environmental factors, and external measuring point temperatures, the basis coefficients are predicted from the external measuring point temperatures. The substitute model is then used to reconstruct the temperature field and other physical fields, thus obtaining the target temperature distribution, which is often the temperature of a key area inside the transformer that is difficult to measure directly.

[0009] The temperature compensation inversion model is mainly designed for scenarios with a certain sample size of internal temperature measurement experimental data. However, this internal temperature measurement is only obtained during the pre-shipment testing process, and the internal measurement value cannot be obtained during the actual operation of the transformer. In the process of establishing the temperature compensation inversion model, the measured temperature of the external measuring point is used to reconstruct the field through the temperature inversion network, and the predicted external and internal measuring point temperatures are obtained. The temperature deviations of the external and internal measuring points are calculated. Using transformer operating conditions, environmental factors, external measuring point temperatures, external measuring point temperature deviations, and internal measuring point temperature deviations, and employing methods such as support vector regression (SVR), an inversion model that predicts the internal measuring point temperature deviation from the external measuring point temperature deviation is constructed.

[0010] By connecting the two inversion models, the temperature and temperature compensation are inverted separately, and the two are combined to obtain the target temperature field distribution.

[0011] In actual operation, only transformer operating conditions, environmental factors, and external measuring point temperature information can be obtained; internal measuring point temperature information cannot be obtained. The process of applying this integrated model is as follows: Based on the transformer operating conditions, environmental factors, and external measuring point temperatures, the basis coefficients of the transformer reduced-order model are obtained using a temperature inversion network. The temperature field of the transformer is reconstructed using the basis coefficients and the basis, i.e., the reconstructed values ​​of external and internal measuring point temperatures are obtained. The reconstructed values ​​of external measuring point temperatures are compared with the measured external measuring point temperatures to obtain the deviation value. Based on this deviation value, the deviation of the internal measuring point temperature is obtained using a temperature compensation inversion network. This deviation is accumulated and added to the internal measuring point reconstructed values ​​to obtain the final predicted value of the internal measuring point temperature.

[0012] Beneficial effects:

[0013] Reconstructing the physical field replaces the purely data-driven approach. Instead of directly predicting the target temperature, the internal winding temperature is calculated by reconstructing the temperature field after predicting the coefficients of the reduced-order model through a deep learning network. This reflects the main physical characteristics of the transformer, has more physical meaning, and overcomes the poor interpretability of traditional black-box models.

[0014] Temperature compensation model correction. Constructing a temperature compensation network eliminates computational biases caused by unquantifiable potential factors such as process deviations and system errors when constructing the full transformer model, resulting in more reliable results.

[0015] By reconstructing the physical field to obtain the overall spatial temperature field distribution of the transformer, richer winding temperature information can be obtained quickly in a short time.

[0016] This paper introduces the concept of model order reduction. A transformer neural network inversion model is trained based on sample data from the forward model, outputting the basis coefficients of the reduced-order transformer model. Then, the entire model is further reduced in order using the intrinsic orthogonal decomposition (POD) method combined with discrete empirical interpolation (DEIM) to obtain the low-order model basis. The transformer's spatial temperature field is reconstructed using the basis and basis coefficients, ultimately yielding the internal winding temperature. Compared to purely data-driven models, this approach preserves physical characteristics and offers higher reliability and interpretability. Attached Figure Description

[0017] Figure 1 : Temperature field inversion model construction process;

[0018] Figure 2 Transformer order reduction model construction;

[0019] Figure 3 Transformer temperature inversion model;

[0020] Figure 4 The process of using the transformer temperature inversion model;

[0021] Figure 5 A transformer temperature inversion method supported by a reduced-order physical model to eliminate potential factors;

[0022] Figure 6 Construction of temperature-compensated inversion model;

[0023] Figure 7 Application of temperature-compensated inversion model;

[0024] Figure 8 Schematic diagram of the integrated application of temperature inversion model and temperature compensation inversion model. Detailed Implementation

[0025] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0026] Currently, in transformer operation and maintenance, it is still difficult to directly obtain the temperature distribution at various points inside the windings of an operating transformer through measurement. While multiphysics finite element numerical calculations can obtain the winding temperature, the calculation accuracy and speed are still insufficient to meet the real-time monitoring and early warning needs of operation and maintenance personnel.

[0027] Generally speaking, transformers can obtain the current and voltage values ​​on the high and low voltage sides. Those with oil pumps can obtain the pump flow rate, and those with radiators can obtain the cooling airflow speed. Transformers usually have a top-level oil temperature sensor installed on the top. For environmental factors, they can obtain ambient temperature, wind speed, sunlight conditions, etc.

[0028] To address the challenge of real-time monitoring of transformer internal winding temperature, this invention proposes a method for inverting the temperature distribution of power transformers with physical model support and reduced uncertainty factors. The internal temperature field is reconstructed from the temperature measured at external points on the transformer, and a temperature deviation correction network model is introduced to predict the temperature distribution of the transformer internal windings.

[0029] 1.1 Construction of Temperature Field Inversion Model

[0030] The multi-parameter temperature field inversion model can be expressed as a convex programming optimization problem, which is the inverse problem of the forward simulation problem. The objective function and constraints of this optimization problem are as follows:

[0031] min f(x)

[0032] st h i (x)=0 i=1,2,...,m

[0033] g j (x)≥0 j=1,2,...,p

[0034] x∈D s

[0035] Where x is the design variable; f(x) is the objective function; h i (x) is a linear constraint; g j (x) represents a nonlinear constraint. D s To find the solution domain.

[0036] like Figure 1 As shown, for the construction of the temperature field inversion model, simulation data generated by the forward model is used as sample input, and a deep neural network is trained to obtain the inversion model.

[0037] For power transformers, forward models are divided into full finite element models and reduced-order models. Full models used for numerical calculations contain all details and physical properties, accurately simulating multiple physical fields of the transformer, including electromagnetic, thermal, and fluid fields. These models offer high precision and accuracy but require longer computation time and higher computational resources. Reduced-order models, on the other hand, retain the main characteristics of the physical fields, sacrificing some computational accuracy but significantly improving computational speed. Model reduction methods include model simplification (such as using sparse mesh calculations, adopting coarser tolerances in iterative solvers, and ignoring nonlinear terms), projection-based simplification models (such as intrinsic orthogonal decomposition (POD), data fitting interpolation, and regression models.

[0038] The data used to train the temperature field inversion model includes the reduced-order model basis coefficients, transformer operating conditions, environment, and external measurement point temperatures. The external measurement point temperatures can be obtained from either the full model or the reduced-order model. Obtaining training data through the transformer reduced-order model is faster, allowing for the acquisition of a large number of training samples in a short time. A balance between computational efficiency and accuracy can be achieved by selecting appropriate reduction basis and reduction coefficients, significantly reducing computation time while ensuring sample accuracy. The neural network is then trained using a large amount of sample data to ultimately obtain the temperature field inversion model.

[0039] The construction and application of temperature field inversion models mainly include the following steps:

[0040] 1.1.1 Transformer Model Order Reduction

[0041] A complete model of the transformer's electromagnetic, thermal, and fluid physical fields is established, using methods such as the finite element method. Based on the intrinsic orthogonal decomposition (POD) method, a reduced-order model of the target physical field distribution is then built, including the basis and corresponding coefficients of the reduced-order model. The construction of the transformer's reduced-order model is as follows: Figure 2 As shown.

[0042] The complete model of the original problem is defined in the region Ω, and after being discretized by numerical methods such as the finite element method, it can be expressed as an algebraic equation:

[0043]

[0044] Its degrees of freedom are N, For an N×N matrix, f μ For the right-hand term, u μ Let μ be the solution to the equation, and let μ represent a certain working condition or a certain parameter, belonging to the parameter space Λ. Let the order of the discrete approximation space of Λ be M.

[0045] The solution set is obtained by solving the finite element equations of the full model using m sample points selected in the discrete approximation space of space Λ. A snapshot matrix S can be constructed. SVD decomposition of the snapshot matrix S yields the dominant left singular matrix, which contains the principal modes φ1, φ2, ..., φ of the POD. p By projecting the full model onto the subspace formed by the obtained p principal modes of POD, a p-order reduced model can be obtained. The solution to the reduction problem is denoted as By using the principal mode matrix Φ=[φ1,φ2,…,φ p ]and Multiplying them yields an approximate solution to the entire model. By reducing the model order, the computational complexity is reduced from M*O(NlogN) to m*O(NlogN) (offline) or M*O(p 2 (Online).

[0046] For example, a reduced-order model of the temperature field can be expressed as the formula:

[0047]

[0048] Where t(x) represents the temperature field, n is the number of reduced-order bases, and φ i (x) is the i-th reduced basis, a i Let be the coefficient corresponding to the i-th basis.

[0049] This reduced-order model does not necessarily have to be built using the POD method; it can be constructed using projection class methods, etc.

[0050] The basis of the reduced-order model can reflect the main physical characteristics of the transformer.

[0051] Analyzing various operating conditions and environmental factors based on a full transformer model requires significant computation time and resources due to the transformer's complexity. A reduced-order model, however, offers a much shorter computation time and allows for efficient generation of large numbers of samples. Furthermore, during the generation of the reduced-order model, methods such as Discrete Empirical Interpolation (DEIM) and adaptive reduction can be employed to address transformer nonlinearity and ensure high accuracy.

[0052] 1.1.2 Temperature Field Inversion Model

[0053] The full transformer model and the reduced-order model are used to generate the internal and external temperature field distribution under various transformer operating conditions (including load, transformer oil pump flow rate, radiator wind speed, etc., as well as abnormal conditions) and environmental factors (such as air temperature, wind speed, sunshine, etc.), as well as the basis coefficients of the corresponding reduced-order model.

[0054] Based on methods such as artificial neural networks, a large number of samples containing the above information are input for training and validation to obtain an inversion neural network, i.e., an inversion model. A transformer temperature inversion model is shown below. Figure 3 As shown.

[0055] 1.1.3 Predicting temperature using a temperature field inversion model

[0056] By utilizing transformer operating conditions, environmental factors, and external measuring point temperatures, the transformer's reduced-order basis and basis coefficients can be predicted through a temperature field inversion model. Combined with the already constructed reduced-order basis, the physical field distribution, such as the temperature field distribution, can be reconstructed, thereby directly obtaining the predicted values ​​of the transformer's external measuring point temperatures and internal (such as winding) temperatures.

[0057] The physical field reconstruction based on the reduced-order model can be expressed by formula (1), where {a i} represents the predicted basis coefficients, and t(x) represents the reconstructed temperature field.

[0058] Reconstructing the transformer's physical field allows the results to reflect its key characteristics more accurately and with greater physical meaning. The process of using the transformer temperature inversion model is as follows: Figure 4 As shown.

[0059] 1.2 Transformer Temperature Inversion Method Supported by Physical Model to Eliminate Potential Factors

[0060] Transformers can undergo appropriate temperature tests. For example, fiber optic temperature sensors can be installed in the internal windings before the transformer leaves the factory to obtain relevant measurement values. However, because transformer temperature values ​​are greatly influenced by uncertainties and factors that cannot be precisely characterized, such potential factors need to be eliminated.

[0061] The model is constructed using deviation values, which require reference values. It uses the deviation between measured values ​​and theoretical values. This model is temporarily called the "temperature-compensated inversion model".

[0062] Therefore, the inversion method of this invention comprises two parts: a master inversion model (temperature inversion model) and an auxiliary inversion model (temperature-compensated inversion model). The master inversion model is a temperature field inversion model (which can be constructed based on artificial neural networks), introducing the idea of ​​model order reduction to predict the basis coefficients of the temperature field order reduction model and characterize the correlation dominated by the physical model. The auxiliary inversion model is a temperature field compensation inversion model based on support vector regression, used to correct the internal winding temperature predicted by the master inversion model, and to correct the differences, difficulties in quantification, and uncertainties caused by potential factors. The master and auxiliary inversion models and their relationship are as follows: Figure 5 As shown.

[0063] The main inversion model and auxiliary inversion model of the present invention will be described in detail below.

[0064] In the master inversion model section, considering the transformer's magnetic-thermal-fluid coupling, a complete model reflecting the transformer's physical field properties is constructed. Using a hybrid finite element-finite volume solution method and adaptive model order reduction for transformer material nonlinearity, a large number of simulation data samples are obtained for external and internal measuring point temperatures and reduced-order basis coefficients under different operating conditions, enabling rapid accumulation of multi-physics calculation samples for the transformer's multi-scale model. A deep neural network is trained using a series of data on transformer operating conditions, environment, external measuring point temperatures, and the reduced-order transformer model (using basis coefficients) to output the low-order basis coefficients for predicting the reduced-order physical fields.

[0065] In the auxiliary inversion model section, measured values ​​of external measuring point temperatures under different operating conditions are obtained through experiments. The predicted values ​​obtained from the temperature field inversion model are subtracted from the measured values ​​to obtain the external measuring point temperature deviation. Using this external temperature deviation as input, a temperature field compensation model based on support vector machine regression is trained, outputting the deviation in predicting the internal winding temperature. The internal winding deviation is then used to correct the internal measuring point temperature prediction values ​​obtained from the reconstructed physical field, yielding the final internal winding temperature inversion result. Constructing a temperature compensation network eliminates the influence of potential factors such as systematic errors, resulting in more accurate results.

[0066] 1.2.1 Establishment of Temperature Field Compensation Inversion Model

[0067] Since the measured data is usually small, support vector regression (SVR) is used to build the inversion model; if the data is large, artificial neural networks can also be used.

[0068] The dataset for the compensation inversion model includes: transformer operating conditions, environmental factors, temperatures corresponding to external transformer measuring points, transformer reduced-order basis coefficient, temperature deviations corresponding to external transformer measuring points, and temperature deviations of internal transformer measuring points.

[0069] Temperature deviation data can be generated using two methods:

[0070] (1) Based on actual transformer measurement data: The temperature field is reconstructed using the temperature field inversion model. The external and internal measuring point temperatures predicted by the temperature field are subtracted from the actual measured temperatures of the measuring points, and this value is used as the deviation data.

[0071] (2) Calculate using full model or reduced-order model: obtain the temperature of the transformer’s external and internal measuring points under various working conditions and environmental factors through simulation calculation, subtract the actual measured temperature of the measuring point from the calculated value, and use the calculated value as the deviation data.

[0072] The main consideration is method (1). The temperature compensation inversion model is constructed as follows: Figure 6 As shown.

[0073] Mode In this context, f(x) represents the predicted output of the input sample x, and α i Let α represent the predicted output for the i-th sample. i * α represents the true output of this sample point. i -α i * It is the Lagrange multiplier corresponding to the i-th sample, k(x) i x) is the kernel function, and b is the bias term.

[0074] 1.2.2 Application of Temperature Field Compensation Inversion Model

[0075] like Figure 7 As shown. In practical applications, obtaining the temperature deviation at external measuring points of the transformer and utilizing the internal temperature deviation of the transformer both require a reference, thus necessitating the combined action of two networks.

[0076] 1.2.3 Integrated Application of Temperature Field Inversion Model and Temperature Field Compensation Inversion Model

[0077] Figure 8 A schematic diagram illustrating the integrated application of the temperature inversion model and the temperature compensation inversion model is provided. After obtaining information on transformer operating conditions, environmental factors, and measured temperatures at external measuring points, the temperature inversion model is used to obtain the transformer's reduced-order basis coefficient, reconstruct the temperature field, and obtain predicted temperatures at external and internal measuring points. The deviation between the measured external temperature and the predicted external temperature is calculated. Using the temperature compensation inversion model, the internal measuring point temperature deviation is obtained by considering the transformer operating conditions, environmental factors, external measuring point temperatures, and the external measuring point temperature deviation. This deviation is then compensated for with the predicted internal temperature, yielding the final inverted value of the transformer's internal temperature.

[0078] This invention includes two temperature inversion and temperature compensation inversion processes. In practical applications, the temperature inversion process can be used alone or the two processes can be used in combination.

[0079] In constructing the main network temperature inversion model, this invention uses artificial neural network methods, but is not limited to deep neural networks (DNN) and recurrent neural networks (RNN), and can also use support vector regression methods;

[0080] In the auxiliary network temperature compensation inversion model, this invention uses a support vector regression-based method to train the model, but it can also be constructed using support vector regression variants, artificial neural networks, and other methods.

[0081] In constructing a reduced-order model of a transformer, the POD method is not the only option; various alternative modeling methods, including different projection methods, can be used.

[0082] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes will be obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A method for inverting the temperature field distribution of a power transformer, supported by a physical model and with reduced uncertainty, characterized in that, Includes the following steps: Step 1: Construction and application of the temperature field inversion model to predict the basis coefficients of the transformer reduced-order model and obtain the temperature reconstruction value of the transformer internal windings. Step 2, the construction and application of the temperature compensation inversion model, which is used to predict the temperature deviation of the transformer's internal windings based on the temperature deviation of the external measuring points of the transformer. Step 3: The combined application of the temperature field inversion model and the temperature field compensation inversion model is used to correct the obtained reconstructed value of the transformer internal winding temperature based on the temperature deviation of the transformer internal winding, and finally obtain the final inversion value of the transformer internal winding temperature. The specific implementation method of step 1 is as follows: The construction and application of the temperature field inversion model includes the following steps: Step 1.1: Construct a reduced-order temperature field model for the transformer model; A complete model of the electromagnetic-thermal-fluid physical field of the transformer is established, and a reduced-order model of the temperature field distribution is established based on the intrinsic orthogonal decomposition method, including the reduced-order basis and the corresponding basis coefficients of the reduced-order model. The reduced-order model of the temperature field is expressed by the formula: (1) in, Represents the temperature field. The number of reduced-order bases, For the first A reduced-order basis, For the first The basis coefficients corresponding to each basis; Step 1.2: Construct a temperature field inversion model; The internal and external temperature field distributions under various transformer operating conditions and environmental factors are generated using full transformer models and reduced-order models, and the basis coefficients of the corresponding reduced-order models are used to form sample data. The above sample data is input into an artificial neural network for training and validation to obtain an inversion neural network, i.e., a temperature field inversion model. Step 1.3: Predict the temperature using the temperature field inversion model; Using transformer operating conditions, environmental factors, and external measuring point temperatures, the basis coefficients of the transformer reduced-order model are predicted through a temperature field inversion model. Combining the reduced-order basis and basis coefficients, the temperature field distribution after the reduced-order model can be reconstructed, thus directly obtaining the predicted values ​​of the external measuring point temperatures and the internal winding temperatures of the transformer. The temperature field reconstruction based on the reduced-order model is expressed by formula (1), where, The predicted base coefficients, This represents the reconstructed temperature field; The specific implementation method of step 2 is to use support vector regression or artificial neural network to construct the inversion model. The dataset for constructing the compensation inversion model includes: transformer operating conditions, environmental factors, temperature corresponding to external measuring points of the transformer, transformer reduced-order basis coefficient, temperature deviation corresponding to external measuring points of the transformer, and temperature deviation of internal measuring points of the transformer. Temperature deviation data is generated by two methods: (1) Based on actual transformer measurement data: using the temperature field inversion model, the temperature field is reconstructed, and the external and internal measuring point temperatures predicted by the temperature field are subtracted from the actual measured temperature of the measuring point, and this value is used as the deviation data. (2) Calculate using full model or reduced-order model: obtain the temperature of the transformer’s external and internal measuring points under various working conditions and environmental factors through simulation calculation, subtract the actual measured temperature of the measuring point from the calculated value, and use the value as the deviation data.

2. The method according to claim 1, characterized in that, The specific implementation method of step 3 is as follows: After obtaining the measured values ​​of transformer operating conditions, environmental factors, and external measuring point temperatures, the basis coefficients of the transformer reduced-order model are obtained using a temperature inversion model. The temperature field is reconstructed to obtain the predicted values ​​of external measuring point and internal winding measuring point temperatures. The deviation between the measured external temperature and the predicted external measuring point temperature is calculated. The internal winding measuring point temperature deviation is obtained using a temperature compensation inversion model based on the transformer operating conditions, environmental factors, external measuring point temperatures, and external measuring point temperature deviations. The deviation is then compensated with the predicted internal winding temperature to obtain the final inversion value of the transformer internal winding temperature.

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