Transformer winding leakage magnetic field distribution calculation method and system

Abstract

The invention discloses a transformer winding leakage magnetic field distribution calculation method, which comprises the following steps of: establishing a transformer finite element model, and calculating a spatial distribution leakage magnetic field of a transformer winding; constructing a transformer winding leakage magnetic field calculation model through a recurrent neural network; training the transformer winding leakage magnetic field calculation model according to the calculation result of the spatial distribution leakage magnetic field to obtain a trained transformer winding leakage magnetic field calculation model; acquiring a space distribution leakage magnetic field actually measured at the selected position of the transformer winding; inputting the spatial distribution leakage magnetic field into a transformer winding leakage magnetic field calculation model, and outputting the spatial distribution leakage magnetic field of the target position of the transformer winding; and fitting the obtained spatial distribution leakage magnetic field distribution by adopting a least square method to obtain final transformer winding leakage magnetic field distribution. According to the method, the echo state network dynamic modeling and the least square optimization algorithm are fused, so that rapid and accurate calculation of the leakage magnetic field of the whole region of the transformer winding is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of transformer operation and discloses a calculation method and system for transformer winding leakage magnetic field distribution. Background Art

[0002] As the lifeblood of energy transmission in modern society, the state perception accuracy of the power system's core equipment directly affects the power supply network's fault warning capabilities. As the core carrier of power conversion, dynamic monitoring technology for the electromagnetic parameters within transformers has long attracted industry attention. According to electromagnetic field theory, the non-closed magnetic circuit formed by the magnetic potential difference between windings will generate a spatially diffuse magnetic field. The time-varying characteristics of this vector field will trigger the superposition of multiple secondary effects: the circulating current effect formed by alternating leakage magnetic flux on the surface of the winding conductor leads to local overheating. The mechanical stress generated by the sudden change in magnetic field intensity under transient short-circuit conditions may exceed the yield limit of the structural components. The coupling of high-frequency leakage magnetic harmonics with the insulating medium will cause abnormal deviations in the dielectric loss angle. The early identification of these hidden defects has important engineering significance for the management of the entire equipment life cycle.

[0003] The operating principle of a transformer is based on the principle of electromagnetic induction. When alternating current is applied to the primary winding of a transformer, an alternating magnetic flux is generated in the core. This flux passes through the secondary winding and induces a current therein. However, not all of this flux is fully transferred from one winding to another through the core. Some of this flux leaks out through the space outside the core, forming a so-called leakage magnetic field. This leakage magnetic field has a significant impact on transformer performance, causing additional losses such as eddy current losses and stray losses. It can also generate mechanical forces that threaten the transformer's insulation and mechanical structure. This is especially true during short-circuit faults, where transient short-circuit currents can generate significant mechanical forces. Therefore, studying the leakage magnetic field distribution of transformer windings is crucial for determining proper operation and the extent of damage. Summary of the Invention

[0004] The present invention provides a method for calculating the leakage magnetic field distribution of transformer windings based on machine learning and optimization algorithms. By integrating echo state network dynamic modeling and least squares optimization algorithms, it overcomes the limitations of traditional methods in balancing real-time performance and accuracy under complex dynamic working conditions. This technology uses an echo state network to learn and model the local magnetic field characteristics of the winding, effectively reducing the model's dependence on finite element simulation and precise structural parameters, and improving the ability to predict magnetic field distribution under dynamic conditions such as winding deformation; at the same time, by introducing an optimization layer to correct the spatial continuity of the network output, the local magnetic field measurement accuracy under sparse sensor distribution conditions is significantly improved. The present invention achieves rapid and accurate calculation of the leakage magnetic field of the entire transformer winding area, significantly improves the ability to capture magnetic field distortion characteristics under transient short-circuit conditions, and greatly accelerates the efficiency of winding stress analysis and insulation status assessment.

[0005] The technical solution provided by the present invention is a method for calculating the leakage magnetic field distribution of a transformer winding, comprising the following steps: Step 1: Establish a finite element model of the transformer and calculate the spatially distributed leakage magnetic field of the transformer winding based on the field-circuit coupling method; Step 1.1: Establish a transformer finite element model, wherein the transformer finite element model includes an iron core, a winding, and an oil tank; Step 1.2: Geometrically split the winding and generate the split surface as the input port for external excitation; Step 1.3: Assign material properties to the transformer components, including the core, windings, insulating oil, and tank, and set the number of winding turns, current direction, and electrical connection method. Step 1.4: Construct a circuit model of the transformer, wherein the circuit model includes a voltage source, a winding resistance, and a leakage inductance; Step 1.5: Mesh the transformer finite element model; Step 1.6: Configure the solver's step size, calculation time, and convergence error parameters; Step 1.7: Calculate the spatially distributed leakage magnetic field of the transformer winding through field-circuit coupling solution.

[0006] Step 2: A transformer winding leakage magnetic field calculation model is constructed using a recurrent neural network. The transformer winding is segmented in the height direction. The input of the recurrent neural network is defined as the spatially distributed leakage magnetic field at the endpoints and midpoints of each segment of the transformer winding, and the output is the spatially distributed leakage magnetic field at the quarter-division points of the transformer winding. Step 2.1: Setting echo state network parameters, including the number of neurons in the state reserve pool and the radius of the internal connection weight spectrum; Step 2.2: Determine the number of input and output units of the echo state network; Step 2.3: Randomly initialize the input connection weight matrix between the input and reservoir units , the sparse connection weight matrix between internal units of the reserve pool .

[0007] The recurrent neural network is an echo state network, and the structure of the echo state network includes an input layer, a reservoir and an output layer. The input signal of the input layer is connected to the reservoir composed of neurons through an input connection weight matrix. The neurons form the reservoir output through internal connection weights, constitute the internal state vector of the network, and connect it to the output layer through output connection weights.

[0008] Step 3: Train the transformer winding leakage magnetic field calculation model using the calculation results of the spatially distributed leakage magnetic field obtained in step 1, obtain the recurrent neural network output connection weight matrix, and obtain the trained transformer winding leakage magnetic field calculation model; The transformer winding leakage magnetic field calculation model determines the input of the training samples required by the echo state network and output ,in, , is the number of samples; Select the initial state of neurons in the network reserve pool ; The training input samples are added to the reserve pool through the input connection weights, and the echo state network completes the calculation of the reserve pool state and the corresponding network output in sequence Calculation and collection of The calculation formula of the internal state vector of the storage pool is: ; Where, is the activation function of the reserve pool neuron, is the input of the echo state network at the k+1th iteration; The calculation formula of the corresponding network output is: ; Where, is the output function, is the output connection weight matrix; The echo state network collects the system state from the mth iteration and stores it in the form of vector Construct matrix B and collect corresponding output samples Construct the matrix T; Using the actual output of the network Approximating expected output , that is, calculate the output connection weight matrix that minimizes the network mean square error , the calculation process can be transformed into solving the following optimization problem: ; The optimization problem is solved by linear regression method, and the calculation is ; described The expression is: ; Step 4: Obtaining the spatially distributed leakage magnetic field measured at the selected position of the transformer winding; Step 5: Use the spatially distributed leakage magnetic field obtained in step 4 as the input of the trained transformer winding leakage magnetic field calculation model, and output the spatially distributed leakage magnetic field at the target position of the transformer winding; Furthermore, an optical fiber leakage magnetic field sensor is used for measurement, and the sensor measurement point corresponds to the position of the input quantity described in step 2.

[0009] Step 6: Use the least squares method to fit the spatially distributed leakage magnetic field distribution obtained in step 5 to obtain the final transformer winding leakage magnetic field distribution.

[0010] For any target position of the transformer winding, the position coordinates of the known axial leakage magnetic field point at the target position are and the corresponding axial leakage magnetic field surface potential , construct orthogonal polynomials , and its recursive relationship is: ; Where, is a k-degree polynomial with the leading coefficient being 1; are the polynomial coefficients; according to The orthogonality of and The relationship is expressed as: ;Will Substitute the expression The recursive formula is gradually deduced to get Each term in , and then complete the construction of orthogonal polynomials; Calculate the fitting curve coefficients and gradually Add to the fitting curve function The axial leakage magnetic field distribution of the winding is obtained. The coefficient calculation formula and the expression of the axial leakage magnetic field distribution are as follows: ; Furthermore, for any target position of the transformer winding, the orthogonal polynomial fitting according to claim 8 is performed to calculate the axial leakage magnetic field distribution at the target position.

[0011] Furthermore, the spatially distributed leakage magnetic field includes an axial leakage magnetic field and a radial leakage magnetic field; A transformer winding leakage magnetic field distribution calculation system, comprising: Finite element calculation module, used to establish the finite element model of the transformer and calculate the winding spatially distributed leakage magnetic field through the field-circuit coupling method; A neural network module is used to construct and train an echo state network model, defining the input of the echo state network model as the spatially distributed leakage magnetic field at a selected position of the transformer winding, and the output as the spatially distributed leakage magnetic field at a target position of the transformer winding; a sensing acquisition module, comprising an optical fiber sensor array, for acquiring measured spatially distributed leakage magnetic field data at the selected position in real time; The data processing module is used to perform the following operations: 1) performing curve fitting by constructing an orthogonal polynomial based on the target position leakage magnetic field data output by the neural network; 2) Iterate the above fitting operation for all segments of the winding; 3) Generate the final transformer winding leakage magnetic field distribution.

[0012] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention uses the echo state network algorithm to train a calculation model for the leakage magnetic field distribution of a specific part of the transformer winding. By conducting targeted tests on the leakage magnetic field distribution of the transformer winding, a relatively accurate approximate distribution of the leakage magnetic field of the transformer winding can be obtained while significantly reducing the workload of on-site testing. At the same time, the leakage magnetic field distribution of the transformer winding is fitted using the least squares algorithm, which can obtain a more accurate distribution of the leakage magnetic field of the transformer winding.

[0013] (2) The present invention constructs a transformer winding leakage magnetic field calculation model through an echo state network. The model reduces the strong dependence of the model on finite element structural parameters through adaptive learning of the nonlinear time series characteristics of the winding magnetic field by the reserve pool neurons. Under non-steady-state conditions such as winding plastic deformation and core displacement, the accuracy of the magnetic field spatial distribution prediction is still maintained, providing a reliable data basis for dynamic fault diagnosis.

[0014] (3) The present invention adopts the least squares method and performs spatial continuity correction on the discrete points output by the neural network based on orthogonal polynomials, thereby solving the data fault problem caused by the sparse endpoints and midpoints of each section of the transformer winding, realizing the smooth reconstruction of the leakage magnetic field of the entire winding area, and significantly improving the restoration accuracy of the local high-gradient magnetic field. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The present invention will be further described below with reference to the accompanying drawings and examples.

[0016] Figure 1 Schematic diagram of the flow of the transformer winding leakage magnetic field distribution calculation method of this embodiment.

[0017] Figure 2 FIG. 4 is a schematic diagram of the structure of the echo state network of this embodiment. DETAILED DESCRIPTION

[0018] like Figure 1 and Figure 2 As shown, a method for calculating the leakage magnetic field distribution of a transformer winding is used for condition monitoring of a 110 kV transformer, including the following steps: Step 1: Establish a finite element model of the transformer and calculate the spatially distributed leakage magnetic field of the transformer winding based on the field-circuit coupling method; Step 1.1: Establish a finite element model of the transformer, which includes the core, winding and oil tank; Step 1.2: Geometrically split the winding and generate the split surface as the input port for external excitation; Step 1.3: Assign material properties to the transformer components, including the core, windings, insulating oil, and tank. Set the number of winding turns, current direction, and electrical connection method. Step 1.4: Construct a circuit model of the transformer. The circuit model includes the voltage source, winding resistance, and leakage inductance. Connect the transformer windings according to their actual connection relationships. The voltage source amplitude is the peak rated voltage of the transformer's primary side, and the winding resistance is calculated based on the transformer's nameplate parameters. Step 1.5: Mesh the transformer finite element model; Step 1.6: Configure the solver's step size, calculation time, and convergence error parameters; Step 1.7: Calculate the spatially distributed leakage magnetic field of the transformer winding through field-circuit coupling solution.

[0019] Step 2: Construct a transformer winding leakage magnetic field calculation model using a recurrent neural network. The transformer winding is segmented into n parts in the height direction. The input of the recurrent neural network is defined as the spatially distributed leakage magnetic field at the endpoints and midpoints of the n-th part of the transformer winding, and the output is the spatially distributed leakage magnetic field at the quarter-division points of the n-th part of the transformer winding. Step 2.1: Set the echo state network parameters, including the number of neurons in the state reserve pool and the radius of the internal connection weight spectrum; Step 2.2: Determine the number of input and output units of the echo state network; Step 2.3: Randomly initialize the input connection weight matrix between the input and reservoir units , the sparse connection weight matrix between internal units of the reserve pool .

[0020] The echo state network structure consists of three layers: input, reservoir, and output. The input signal of the input layer is connected to the reservoir composed of a large number of randomly arranged neurons through the input connection weight matrix. The neurons form the reservoir output through the internal connection weight, forming the internal state vector of the network, and are connected to the output layer through the output connection weight. Set the parameters of the echo state network, including the number of neurons in the state reserve pool, the radius of the internal connection weight spectrum, etc. Determine the number of input and output units of the echo state network based on the number of conductors and meshes of the specific grounding grid; Randomly initialize the connection weight matrix between the input and the reservoir unit , the sparse connection weight matrix between internal units of the reservoir ; Step 3: Train the transformer winding leakage magnetic field calculation model using the calculation results of the spatially distributed leakage magnetic field obtained in step 1, obtain the recurrent neural network output connection weight matrix, and obtain the trained transformer winding leakage magnetic field calculation model; Transformer winding leakage magnetic field calculation model to determine the input of training samples required by the echo state network and output ,in, , is the number of samples; Select the initial state of neurons in the network reserve pool ; The training input samples are added to the reserve pool through the input connection weights, and the echo state network completes the calculation of the reserve pool state and the corresponding network output in sequence Calculation and collection of The calculation formula of the internal state vector of the reserve pool is: ; Where, is the activation function of the reserve pool neuron, is the input of the echo state network at the k+1th iteration; The corresponding network output is calculated as: ; Where, is the output function, is the output connection weight matrix; The echo state network collects the system state from the mth iteration and stores it in the form of vector Construct matrix B and collect corresponding output samples Construct the matrix T; Using the actual output of the network Approximating expected output , that is, calculate the output connection weight matrix that minimizes the network mean square error , the calculation process can be transformed into solving the following optimization problem: ; Using linear regression method to solve the optimization problem, we can calculate ; The expression is: ; Step 4: Use the optical fiber leakage magnetic field sensor to test the leakage magnetic field distribution of the transformer winding, and select the n-segment conductor of the transformer winding and the midpoint of each conductor segment as the measurement points; Step 5: Use the spatially distributed leakage magnetic field obtained in step 4 as the input of the trained transformer winding leakage magnetic field calculation model, and output the spatially distributed leakage magnetic field at the target position of the transformer winding; The spatially distributed leakage magnetic field obtained in step 4 is used as the input of the trained echo state network, and the output value of the echo state network is calculated, which is the spatial leakage magnetic field at the quarter-division point of the nth part of the transformer winding; Step 6: Use the least squares method to fit the spatially distributed leakage magnetic field distribution obtained in step 5 to obtain the final transformer winding leakage magnetic field distribution.

[0021] For any target position of the transformer winding, according to the position coordinates of the known axial leakage magnetic field point at the target position and the corresponding axial leakage magnetic field surface potential , construct orthogonal polynomials , and its recursive relationship is: ; Where, is a k-degree polynomial with the leading coefficient being 1; are the polynomial coefficients; according to The orthogonality of and The relationship is expressed as: ; Will Substitute the expression The recursive formula is gradually deduced to get Each term in , and then complete the construction of orthogonal polynomials; Calculate the fitting curve coefficients and gradually Add to the fitting curve function The axial leakage magnetic field distribution of this part of the winding is obtained. The coefficient calculation formula and the expression of the axial leakage magnetic field distribution are: ; Calculate the axial leakage magnetic field distribution of all parts of the transformer winding according to the above method, thereby completing the calculation of the leakage magnetic field distribution of the transformer winding. The spatially distributed leakage magnetic field includes the axial leakage magnetic field and the radial leakage magnetic field.

[0022] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, each process of the above-mentioned embodiment of the method for calculating the leakage magnetic field distribution of a transformer winding is implemented.

[0023] The embodiment of the present application provides a transformer winding leakage magnetic field distribution calculation system, which specifically includes: Finite element calculation module, used to establish the finite element model of the transformer and calculate the winding spatially distributed leakage magnetic field through the field-circuit coupling method; A neural network module is used to construct and train an echo state network model, defining the input of the echo state network model as the spatially distributed leakage magnetic field at a selected position of the transformer winding, and the output as the spatially distributed leakage magnetic field at a target position of the transformer winding; A sensing acquisition module, comprising an optical fiber sensor array, for collecting measured spatially distributed leakage magnetic field data at selected locations in real time; The data processing module is used to perform the following operations: 1) Based on the target position leakage magnetic field data output by the neural network, curve fitting is performed by constructing an orthogonal polynomial; 2) Iterate the above fitting operation for all segments of the winding; 3) Generate the final transformer winding leakage magnetic field distribution.

Claims

1. A method for calculating the leakage magnetic field distribution of a transformer winding, characterized in that: The following steps are involved: Step 1: Establish a finite element model of the transformer and calculate the spatially distributed leakage magnetic field of the transformer winding based on the field-circuit coupling method; Step 2: Construct a transformer winding leakage magnetic field calculation model through a recurrent neural network. Define the input of the recurrent neural network as the spatially distributed leakage magnetic field at the selected position of the transformer winding, and the output as the spatially distributed leakage magnetic field at the target position of the transformer winding. Step 3: Train the transformer winding leakage magnetic field calculation model using the calculation results of the spatially distributed leakage magnetic field obtained in step 1, obtain the recurrent neural network output connection weight matrix, and obtain the trained transformer winding leakage magnetic field calculation model; Step 4: Obtaining the spatially distributed leakage magnetic field measured at the selected position of the transformer winding; Step 5: Use the spatially distributed leakage magnetic field obtained in step 4 as the input of the trained transformer winding leakage magnetic field calculation model, and output the spatially distributed leakage magnetic field at the target position of the transformer winding; Step 6: Use the least squares method to fit the spatially distributed leakage magnetic field distribution obtained in step 5 to obtain the final transformer winding leakage magnetic field distribution.

2. The method for calculating the distribution of leakage magnetic field of transformer windings according to claim 1, characterized in that: The spatially distributed leakage magnetic field includes an axial leakage magnetic field and a radial leakage magnetic field; The transformer winding is segmented in the height direction; The selected positions of the transformer windings include the spatial positions of the endpoints and midpoints of each winding segment; The transformer winding target position includes the spatial position of the quarter-division points of at least one winding segment.

3. The method for calculating the distribution of leakage magnetic field of transformer windings according to claim 2, characterized in that: The step 1 includes the following sub-steps: Step 1.1: Establish a transformer finite element model, wherein the transformer finite element model includes an iron core, a winding, and an oil tank; Step 1.2: Geometrically split the winding and generate the split surface as the input port for external excitation; Step 1.3: Assign material properties to the transformer components, including the core, windings, insulating oil, and tank, and set the number of winding turns, current direction, and electrical connection method. Step 1.4: Construct a circuit model of the transformer, wherein the circuit model includes a voltage source, a winding resistance, and a leakage inductance; Step 1.5: Mesh the transformer finite element model; Step 1.6: Configure the solver's step size, calculation time, and convergence error parameters; Step 1.7: Calculate the spatially distributed leakage magnetic field of the transformer winding through field-circuit coupling solution.

4. The method for calculating the distribution of leakage magnetic field of transformer windings according to claim 3, characterized in that: In step 2, the recurrent neural network is an echo state network, and the structure of the echo state network includes an input layer, a reservoir and an output layer. The input signal of the input layer is connected to the reservoir composed of neurons through an input connection weight matrix. The neurons form the reservoir output through internal connection weights, constitute the internal state vector of the network, and connect it to the output layer through output connection weights.

5. The method for calculating the distribution of leakage magnetic field of transformer windings according to claim 4, characterized in that: In step 2, the specific process of constructing the transformer winding leakage magnetic field calculation model includes: Step 2.1: Setting echo state network parameters, including the number of neurons in the state reserve pool and the radius of the internal connection weight spectrum; Step 2.2: Determine the number of input and output units of the echo state network; Step 2.3: Randomly initialize the input connection weight matrix between the input and reservoir units , the sparse connection weight matrix between internal units of the reserve pool .

6. The method for calculating the distribution of leakage magnetic field of transformer windings according to claim 4, characterized in that: The transformer winding leakage magnetic field calculation model determines the input of the training samples required by the echo state network and output ,in, , is the number of samples; Select the initial state of neurons in the network reserve pool ; The training input samples are added to the reserve pool through the input connection weights, and the echo state network completes the calculation of the reserve pool state and the corresponding network output in sequence Calculation and collection of The calculation formula of the internal state vector of the storage pool is: ； Where, is the activation function of the reserve pool neuron, is the input of the echo state network at the k+1th iteration; The calculation formula of the corresponding network output is: ； Where, is the output function, is the output connection weight matrix; The echo state network collects the system state from the mth iteration and stores it in the form of vector Construct matrix B and collect corresponding output samples Construct the matrix T; Using the actual output of the network Approximating expected output , that is, calculate the output connection weight matrix that minimizes the network mean square error , the calculation process can be transformed into solving the following optimization problem: ； The optimization problem is solved by linear regression method, and the calculation is ; described The expression is: ；。 7. The method for calculating the distribution of leakage magnetic field of transformer windings according to claim 6, characterized in that: Use an optical fiber leakage magnetic field sensor for measurement, and the sensor measurement point corresponds to the position of the input quantity described in step 2.

8. The method for calculating the distribution of leakage magnetic field of transformer windings according to claim 7, characterized in that: In step 6, for any target position of the transformer winding, the position coordinates of the known axial leakage magnetic field point at the target position are calculated. and the corresponding axial leakage magnetic field surface potential , construct orthogonal polynomials , and its recursive relationship is: ； Where, is a k-degree polynomial with the leading coefficient being 1; are the polynomial coefficients; according to The orthogonality of and The relationship is expressed as: ;Will Substitute the expression The recursive formula is gradually deduced to Each term in , and then complete the construction of orthogonal polynomials; Calculate the fitting curve coefficients and gradually Add to the fitting curve function The axial leakage magnetic field distribution of the winding is obtained. The coefficient calculation formula and the expression of the axial leakage magnetic field distribution are as follows: ；。 9. The method for calculating the transformer winding leakage magnetic field distribution according to claim 8, characterized in that: For any target position of the transformer winding, the orthogonal polynomial fitting according to claim 8 is performed to calculate the axial leakage magnetic field distribution at the target position.

10. A transformer winding leakage magnetic field distribution calculation system, characterized in that: include: Finite element calculation module, used to establish the finite element model of the transformer and calculate the winding spatially distributed leakage magnetic field through the field-circuit coupling method; A neural network module is used to construct and train an echo state network model, defining the input of the echo state network model as the spatially distributed leakage magnetic field at a selected position of the transformer winding, and the output as the spatially distributed leakage magnetic field at a target position of the transformer winding; a sensing acquisition module, comprising an optical fiber sensor array, for acquiring measured spatially distributed leakage magnetic field data at the selected position in real time; The data processing module is used to perform the following operations: 1) performing curve fitting by constructing an orthogonal polynomial based on the target position leakage magnetic field data output by the neural network; 2) Iterate the above fitting operation for all segments of the winding; 3) Generate the final transformer winding leakage magnetic field distribution.

Images