Oil-immersed transformer temperature field acquisition method and system based on reduced order localization

Abstract

The invention relates to an oil-immersed transformer temperature field acquisition method and system based on reduced order localization. The method comprises the following steps: firstly, based on a pre-constructed oil-immersed transformer temperature field calculation model, acquiring a plurality of flow velocity characteristic partitions by using a k-means clustering method; secondly, in each flow velocity characteristic partition, constructing an oil-immersed transformer temperature field reduced-order model by using an intrinsic orthogonal decomposition method; and finally, calculating the temperature field distribution of the oil-immersed transformer based on the temperature field reduced-order model of the oil-immersed transformer. Compared with the prior art, the method has the advantages that local feature deficiency caused by global order reduction is avoided, and the calculation precision is improved while the temperature field of the oil-immersed transformer is rapidly obtained and improved.

Description

Technical Field

[0001] The present invention relates to the technical field of fast calculation of multi-physical fields of oil-immersed transformers, and in particular to a method and system for acquiring a temperature field of an oil-immersed transformer based on reduced-order localization. Background Art

[0002] As the basic and key equipment for voltage conversion and power transmission, oil-immersed transformers still face severe challenges in their safe operation. As the key content of oil-immersed transformer condition monitoring and evaluation, the efficient and accurate acquisition of temperature field distribution characteristics has become an important research topic.

[0003] In order to improve the calculation speed of the temperature field distribution of oil-immersed transformers, the order reduction calculation method represented by intrinsic orthogonal decomposition is still one of the effective and feasible methods so far. According to whether the field equation is directly processed, it is divided into invasive and non-invasive order reduction methods. The basic principle is to decompose the matrix into the product of modes and modal coefficients, and reduce the matrix size by deleting some modes. However, due to the inherent nonlinear characteristics of the temperature field problem, the calculation results are highly dependent on the boundary conditions and show the characteristics of large differences in local temperature characteristics. The modal decomposition and order reduction matrix construction of the entire solution domain will lead to the loss of local features. However, the fluid and temperature distribution in the oil-immersed transformer are complex, the local differences in the flow velocity distribution are large, and it is difficult to maintain the fluid characteristics during the local solution domain division. Therefore, how to quickly obtain the temperature field of the oil-immersed transformer while ensuring the calculation accuracy and enhancing the adaptability to local characteristics has become a problem that needs to be solved in this field. Summary of the invention

[0004] The purpose of the present invention is to overcome the defect of the above-mentioned prior art that global order reduction leads to the loss of local features and to provide a method and system for acquiring the temperature field of an oil-immersed transformer based on order reduction localization.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] According to a first aspect of the present invention, there is provided a method for acquiring the temperature field of an oil-immersed transformer based on reduced-order localization, comprising the following steps: S1, based on a pre-constructed calculation model of the temperature field of the oil-immersed transformer, a plurality of velocity feature partitions are acquired using a k-means clustering method; S2, in each of the velocity feature partitions, a reduced-order model of the temperature field of the oil-immersed transformer is constructed using an intrinsic orthogonal decomposition method; S3, based on the reduced-order model of the temperature field of the oil-immersed transformer, the temperature field distribution of the oil-immersed transformer is calculated.

[0007] As an optimal technical solution, the specific process of obtaining multiple flow velocity characteristic partitions using the k-means clustering method includes: S11, selecting k initial cluster centers from the solution domain, and calculating the flow velocity difference from each finite element node to each cluster center respectively, and the solution domain is calculated using the oil-immersed transformer temperature field calculation model; S12, assigning each finite element node to the cluster center with the smallest corresponding flow velocity difference to obtain the current k flow velocity characteristic partitions; S13, calculating the current error value of each cluster center; S14, updating the position of each cluster center based on the current k flow velocity characteristic partitions and the error value; S15, recalculating the current error value of each cluster center, and judging whether the error value before and after the update has changed: if yes, returning to S12 to reallocate each finite element node, update the flow velocity characteristic partition, and continue to execute; if not, iterating and converging, and outputting the current flow velocity characteristic partition.

[0008] As a preferred technical solution, the velocity difference from each finite element node to each cluster center is expressed as:

[0009]

[0010] In the formula, d is the dimension, x is i and c j are the velocity values ​​at the i-th finite element node and the j-th cluster center, respectively, is and c js are the values ​​corresponding to the sth dimension respectively.

[0011] As a preferred technical solution, the error value is expressed as:

[0012]

[0013] Where k is the number of cluster centers, E is the sum of squares of velocity differences from all finite element nodes to cluster centers, and n is the number of unit nodes.

[0014] As a preferred technical solution, the number of grids in each of the velocity characteristic partitions is less than 200,000.

[0015] As an optimal technical solution, S2 specifically includes: S21, in each of the flow velocity characteristic partitions, obtaining a snapshot matrix, the snapshot matrix is ​​composed of finite element node temperature vectors obtained at different times using the oil-immersed transformer temperature field calculation model; S22, performing singular value decomposition and main eigenvalue selection on the snapshot matrix to obtain a reduced-order coefficient matrix; S23, based on the reduced-order coefficient matrix, reconstructing the stiffness matrix and the finite element right-hand side terms to obtain a reduced-order model of the oil-immersed transformer temperature field in each flow velocity characteristic partition.

[0016] As a preferred technical solution, the reduced-order model of the temperature field of the oil-immersed transformer is expressed as:

[0017] M T KMT=M T B

[0018] T=(M T KM -1 )M T B

[0019] Where M is the reduced-order coefficient matrix, K is the stiffness matrix, and B is the right-hand side term of the finite element.

[0020] As an optimal technical solution, the oil-immersed transformer temperature field calculation model is constructed based on a pre-acquired oil-immersed transformer geometric model, and the oil-immersed transformer geometric model includes a core model, a winding model, an oil tank model, a clamp model, a pull plate model and an insulating cardboard model.

[0021] As a preferred technical solution, the expression of the oil-immersed transformer temperature field calculation model is:

[0022] ▽·(ρCUT)-▽·λ▽T=Q

[0023] Where ρ is density, C is specific heat at constant pressure, U is fluid velocity, T is temperature, λ is thermal conductivity, and Q is heat source density.

[0024] According to a second aspect of the present invention, there is provided a system for acquiring a temperature field of an oil-immersed transformer based on reduced-order localization for implementing the method, comprising a velocity feature partition acquisition module, a reduced-order model construction module and a temperature field distribution calculation module, wherein: the velocity feature partition acquisition module acquires a plurality of velocity feature partitions based on a pre-constructed oil-immersed transformer temperature field calculation model by using a k-means clustering method; the reduced-order model construction module constructs a reduced-order model of the oil-immersed transformer temperature field in each of the velocity feature partitions by using an intrinsic orthogonal decomposition method; the temperature field distribution calculation module calculates the temperature field distribution of the oil-immersed transformer based on the reduced-order model of the oil-immersed transformer temperature field.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. The present invention divides the temperature field area of ​​the oil-immersed transformer into multiple local solution domains, introduces a reduced-order coefficient matrix for different flow field characteristics, realizes the localization of the reduced-order matrix, and can effectively improve the adaptability and accuracy of the reduced-order method for multi-feature problems of the temperature field, avoid the loss of local features caused by global reduced-order, and thus quickly obtain the oil-immersed transformer temperature field while improving the calculation accuracy;

[0027] 2. The present invention utilizes the k-means clustering method based on flow velocity characteristics to divide the local solution domain, which can effectively improve the integrity of temperature and flow field characteristics in the local characteristic partitions. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a schematic diagram of the method flow in Example 1 of the present invention;

[0029] Figure 2 Schematic diagram of the transformer model structure in Embodiment 1 of the present invention;

[0030] Figure 3 is a two-dimensional interface flow velocity distribution diagram of the transformer winding in Example 1 of the present invention;

[0031] Figure 4 is a two-dimensional cross-sectional temperature distribution diagram of the transformer winding in Example 1 of the present invention;

[0032] Figure 5 It is a flow velocity characteristic partition diagram of the transformer winding area in Example 1 of the present invention. DETAILED DESCRIPTION

[0033] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. The following embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes, but the protection scope of the present invention is not limited to the following embodiments.

[0034] Example 1

[0035] like Figure 1 As shown, this embodiment provides a method for acquiring the temperature field of an oil-immersed transformer based on reduced-order localization, which adopts a reduced-order localization technology, that is, dividing the entire solution domain into multiple local solution domains according to certain standards, and constructing a reduced-order matrix separately in each solution domain, which can effectively improve the calculation accuracy of the temperature field. Specifically, the method uses the k-means clustering method to realize local feature partitioning based on flow velocity, and constructs a corresponding intrinsic orthogonal decomposition reduced-order model based on each feature partition. While improving the calculation speed, it can solve the problem of local feature loss caused by global order reduction, and can realize high-accuracy and rapid calculation of the temperature field of the oil-immersed transformer. The specific steps include:

[0036] Step 1: Based on the previously acquired oil-immersed transformer geometric model, a temperature field calculation model of the oil-immersed transformer is constructed.

[0037] Specifically, the geometric model of the oil-immersed transformer includes a core model, a winding model, an oil tank model, a clamp model, a pull plate model and an insulating paperboard model.

[0038] In this embodiment, a 35kV ONAN single-phase transformer is used as the object for electromagnetic field calculation. The structure of the oil-immersed transformer model is as follows: Figure 2The structural parameters are shown in Table 1. Among them, the core of the oil-immersed transformer is made of B27P095 electrical steel, the pull plate, clamp and oil tank are made of A3 magnetic steel, the winding is made of copper, and the heat flow parameters of the transformer oil and insulating oil paper are shown in Table 2. In the electromagnetic field calculation, the high-voltage side current is rated at 11.43A, and the low-voltage side is short-circuited.

[0039] Table 1 Structural parameters of oil-immersed transformer

[0040]

[0041] Table 2 Thermal flow parameters of transformer oil and insulating oil paper

[0042]

[0043]

[0044] The mesh is divided into tetrahedral meshes, and the inner wall of the oil tank, the pull plate and the surface of the clamp are divided into boundary layers. There are 326,883 tetrahedral meshes and 142,774 prismatic elements. The cross section of the oil-immersed transformer winding is taken, which includes 59,136 triangular meshes and 17,606 quadrilateral elements.

[0045] The expression of the temperature field calculation model of oil-immersed transformer is:

[0046]

[0047] Where ρ is density, kg / m 3 ; C is the specific heat capacity at constant pressure, J / (kg·K); U is the fluid velocity, m / s; T is the temperature, K; λ is the thermal conductivity, W / (m·K); the right-hand term of the temperature field, Q, is the heat source density, W / m 3 .

[0048] Using the Galerkin format, it can be expressed as:

[0049]

[0050] In the formula, n is the number of unit nodes, n e is the number of units, W is the weight function, N j is the unit node shape function, Ω is the solution domain, Ω e For each finite element area, T j is the node temperature value.

[0051] And can be simplified as:

[0052] KT=B (3)

[0053] Where K is the finite element stiffness matrix, T is the temperature solution vector, and B is the right-hand side term of the finite element.

[0054] After the oil-immersed transformer temperature field calculation model is built, the transformer loss on the right side is input, including core loss 1100W, winding ohmic loss 11412W, and magnetic steel eddy current loss 2240W, and the solution domain can be calculated. The calculation results are as follows Figure 3 and Figure 4 As shown, the maximum flow rate is 6.22 cm / s and the maximum temperature is 87.2°C.

[0055] Step 2: Based on the constructed oil-immersed transformer temperature field calculation model, the k-means clustering method is used to obtain multiple flow velocity feature partitions.

[0056] The specific process of obtaining multiple velocity characteristic partitions includes:

[0057] 1) Randomly select k initial cluster centers from the solution domain calculated in step 1, and calculate the velocity difference dist(x) from each finite element node to each cluster center. i ,c j );

[0058] 2) Assign each finite element node to the cluster center with the smallest velocity difference, and obtain the current k cluster regions (i.e. velocity feature partitions) Ω k ; Among them, the selection criteria for the number of clustering regions k are: in general, the number of grids in each clustering region should be less than 200,000;

[0059] The velocity difference from each finite element node to each cluster center is defined as:

[0060]

[0061] In the formula, d is the dimension, x is i and c j are the velocity values ​​at the i-th finite element node and the j-th cluster center, respectively, is and c js are the values ​​corresponding to the sth dimension respectively.

[0062] 3) Calculate the current error value of each cluster center;

[0063] The error value is calculated using the mean square error criterion:

[0064]

[0065] Where k is the number of cluster centers, and E is the sum of squares of velocity differences from all finite element nodes to cluster centers.

[0066] 4) After completing the cluster area division and error value calculation, the position of each cluster center is updated according to the current k velocity feature partitions and error values, so that the new k cluster center positions are the geometric centers of each cluster area;

[0067] 5) Recalculate the current error value of each cluster center and determine whether the error value before and after the update has changed: if yes, return to 2) reallocate each finite element node, update the velocity feature partition, and continue execution; if no, iterate and converge, and output the current velocity feature partition.

[0068] In this embodiment, the k value is 10. After the iteration is completed, Figure 5 As shown, the winding area is included in 7 characteristic areas, and the statistics of the number of two-dimensional grids included in the winding area in each flow velocity characteristic area are shown in Table 3.

[0069] Table 3 Cluster centers and grid statistics of velocity characteristic regions

[0070]

[0071] Step 3: In each velocity feature partition, the temperature field reduced-order model of the oil-immersed transformer is constructed using the intrinsic orthogonal decomposition method. The specific process includes:

[0072] 1) In each velocity characteristic partition, a snapshot matrix X is obtained, where the snapshot matrix X is composed of finite element node temperature vectors obtained at different times using the oil-immersed transformer temperature field calculation model;

[0073] 2) Perform singular value decomposition and main eigenvalue selection on the snapshot matrix X to obtain the reduced-order coefficient matrix M;

[0074] 3) Based on the reduced-order coefficient matrix M, the stiffness matrix K and the right-hand side term B of the finite element are reconstructed to reduce the calculation scale and obtain the reduced-order model of the temperature field of the oil-immersed transformer in each velocity characteristic partition.

[0075] The specific definition of the snapshot matrix X is:

[0076] X=[x ij ] (6)

[0077] In the formula, x ij is the temperature value of the i-th finite element node at the j-th moment.

[0078] The snapshot matrix X is decomposed into singular values:

[0079] X=WΣV T (7)

[0080] Where W is a left singular matrix; Σ is an eigenvalue diagonal matrix, Σ=[λ jj ],λjj is the value of the j-th diagonal element; V is a right singular matrix.

[0081] Sum the first m eigenvalues ​​in the eigenvalue diagonal matrix. Generally, the first d eigenvalues ​​are taken to satisfy Σλ. i The orthogonal basis composed of orthogonal vectors with the number greater than 0.999 can meet the requirement. The first d columns of the left singular matrix W are taken to form the reduced-order coefficient matrix M.

[0082] The simplified form of the finite element is reconstructed to form a reduced-order model of the temperature field of the oil-immersed transformer in each velocity characteristic partition:

[0083] M T KMT=M T B (8)

[0084] T=(M T KM -1 )M T B (9)

[0085] Where M is the reduced-order coefficient matrix, K is the stiffness matrix, and B is the reduced-order right-hand side term.

[0086] Step 4: Based on the reduced-order model of the temperature field of the oil-immersed transformer, calculate the temperature field distribution of the oil-immersed transformer.

[0087] After obtaining the reduced-order model of the temperature field of the oil-immersed transformer through step 3, the reduced-order model effect is tested and verified through actual test data. The transformer loss is input, including core loss of 636W, winding ohmic loss of 4695W, and magnetic steel eddy current loss of 1687W, and the temperature field distribution is calculated. The maximum temperature measured under this condition is 45.6℃. Compared with the measured results, the accuracy and calculation time of the reduced-order model are shown in Table 4.

[0088] Table 4 Comparison of calculation time of reduced-order models

[0089]

[0090] Example 2

[0091] This embodiment provides a system for acquiring temperature field of an oil-immersed transformer based on reduced-order localization, which is used to implement the method provided in Embodiment 1. The system includes a velocity feature partition acquisition module, a reduced-order model construction module, and a temperature field distribution calculation module.

[0092] The velocity characteristic partition acquisition module is based on the pre-built oil-immersed transformer temperature field calculation model, and uses the k-means clustering method to obtain multiple velocity characteristic partitions. The oil-immersed transformer temperature field calculation model is established based on the pre-acquired oil-immersed transformer geometric model; the reduced-order model construction module uses the intrinsic orthogonal decomposition method to construct the oil-immersed transformer temperature field reduced-order model in each velocity characteristic partition; the temperature field distribution calculation module calculates the temperature field distribution of the oil-immersed transformer based on the oil-immersed transformer temperature field reduced-order model. The specific operation process of each module is the same as the method execution process in Example 1, and will not be repeated here.

[0093] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for acquiring temperature field of an oil-immersed transformer based on reduced-order localization, characterized in that: The following steps are involved: S1, based on the pre-built oil-immersed transformer temperature field calculation model, the k-means clustering method is used to obtain multiple velocity feature partitions; S2, in each of the velocity characteristic partitions, constructing a reduced-order model of the temperature field of the oil-immersed transformer using an intrinsic orthogonal decomposition method; S3, calculating the temperature field distribution of the oil-immersed transformer based on the reduced-order model of the temperature field of the oil-immersed transformer.

2. The method for obtaining the temperature field of an oil-immersed transformer based on reduced-order localization according to claim 1 is characterized in that: The specific process of obtaining multiple velocity feature partitions using the k-means clustering method includes: S11, selecting k initial cluster centers from a solution domain, and calculating the velocity difference from each finite element node to each cluster center, respectively, wherein the solution domain is calculated using the oil-immersed transformer temperature field calculation model; S12, assigning each finite element node to the cluster center with the smallest velocity difference, and obtaining the current k velocity characteristic partitions; S13, calculating the current error value of each cluster center; S14, based on the current k velocity feature partitions and error values, updating the position of each cluster center; S15, recalculate the current error value of each cluster center, and determine whether the error value before and after the update has changed: If yes, then return to S12 to reallocate each finite element node, update the velocity characteristic partition, and continue execution; If not, the iteration converges and the current velocity characteristic partition is output.

3. The method for acquiring the temperature field of an oil-immersed transformer based on reduced-order localization according to claim 2 is characterized in that: The velocity difference from each finite element node to each cluster center is expressed as: In the formula, d is the dimension, x is i and c j are the velocity values ​​at the i-th finite element node and the j-th cluster center, respectively, is and c js are the values ​​corresponding to the sth dimension respectively.

4. The method for acquiring the temperature field of an oil-immersed transformer based on reduced-order localization according to claim 3 is characterized in that: The error value is expressed as: Where k is the number of cluster centers, E is the sum of squares of velocity differences from all finite element nodes to cluster centers, and n is the number of unit nodes.

5. The method for acquiring the temperature field of an oil-immersed transformer based on reduced-order localization according to claim 2 is characterized in that: The number of grids in each of the velocity characteristic partitions is less than 200,000.

6. The method for acquiring the temperature field of an oil-immersed transformer based on reduced-order localization according to claim 1, characterized in that: The S2 specifically includes: S21, in each of the velocity characteristic partitions, obtaining a snapshot matrix, wherein the snapshot matrix is ​​composed of finite element node temperature vectors obtained at different times using a temperature field calculation model of an oil-immersed transformer; S22, performing singular value decomposition and main eigenvalue selection on the snapshot matrix to obtain a reduced-order coefficient matrix; S23, based on the reduced-order coefficient matrix, reconstruct the stiffness matrix and the right-hand side term of the finite element to obtain a reduced-order model of the temperature field of the oil-immersed transformer in each velocity characteristic partition.

7. The method for acquiring the temperature field of an oil-immersed transformer based on reduced-order localization according to claim 6 is characterized in that: The reduced-order model of the oil-immersed transformer temperature field is expressed as: M T KMT=M T B T=(M T KM -1 )M T B Where M is the reduced-order coefficient matrix, K is the stiffness matrix, and B is the right-hand side term of the finite element.

8. The method for acquiring the temperature field of an oil-immersed transformer based on reduced-order localization according to claim 1, characterized in that: The oil-immersed transformer temperature field calculation model is constructed according to a pre-acquired oil-immersed transformer geometric model, wherein the oil-immersed transformer geometric model includes a core model, a winding model, an oil tank model, a clamp model, a pull plate model and an insulating paperboard model.

9. The method for acquiring the temperature field of an oil-immersed transformer based on reduced-order localization according to claim 1, characterized in that: The expression of the oil-immersed transformer temperature field calculation model is: ▽·(ρCUT)-▽·λ▽T=Q Where ρ is density, C is specific heat at constant pressure, U is fluid velocity, T is temperature, λ is thermal conductivity, and Q is heat source density.

10. A system for acquiring temperature field of an oil-immersed transformer based on reduced-order localization for implementing the method according to any one of claims 1 to 9, characterized in that: It includes a velocity feature partition acquisition module, a reduced-order model construction module, and a temperature field distribution calculation module, among which: The velocity characteristic partition acquisition module acquires multiple velocity characteristic partitions using a k-means clustering method based on a pre-built oil-immersed transformer temperature field calculation model; The reduced-order model building module builds a reduced-order model of the temperature field of the oil-immersed transformer by using an intrinsic orthogonal decomposition method in each of the velocity characteristic partitions; The temperature field distribution calculation module calculates the temperature field distribution of the oil-immersed transformer based on the reduced-order model of the temperature field of the oil-immersed transformer.

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