Method for extracting transient temperature rise main mode of transformer winding by using mixed norm

Abstract

The invention belongs to the technical field of rapid calculation of a temperature field of a transformer winding, and particularly relates to a method for extracting a transient temperature rise main mode of the transformer winding by using a mixed norm. Comprising the following steps: S1, setting simulation step length and time, and determining a winding temperature rise sampling analysis point; s2, acquiring temperature rise distribution of a winding temperature field from the first sampling moment to the + 1th sampling moment, and constructing matrixes Tk and Tk + 1; s3, calculating D according to dynamic modal decomposition; s4, calculating an infinity-norm and a 2-norm of the matrix row vector, and defining a convex combination of the infinity-norm and the 2-norm as a norm of the matrix row vector; s5, simplifying a calculation formula of Tk; s6, calculating to obtain an instantaneous value of Tk, setting the instantaneous value to be equal to + 1, returning to the step S3, and carrying out winding temperature rise prediction at the next moment; according to the method, the overall and local characteristics of the modes are considered, the accuracy of main mode selection is improved, and the prediction precision of the instantaneous temperature rise of the winding temperature field is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of rapid calculation of transformer winding temperature field, and in particular relates to a method for extracting main modes of transient temperature rise of transformer winding by using a mixed norm. Background Art

[0002] At present, the transient temperature rise values ​​of transformer windings are mainly obtained through three methods, namely: numerical calculation method combined with physical equations, direct measurement method and data-driven prediction algorithm. As a traditional method, the numerical calculation method requires the winding to be meshed. When the winding scale is large, the calculation time of the winding temperature rise is long and the efficiency is low, which makes it difficult to meet the requirements of real-time and rapid response to thermal defects of the winding. The direct measurement method can only arrange sensors at limited points of the winding, and it is difficult to obtain the temperature rise data of the entire winding field. The data-driven algorithm uses the historical data of the winding temperature rise to realize the rapid calculation of the winding temperature rise.

[0003] Reference [1] Research on the fast calculation method of transient temperature rise of oil-immersed power transformer winding based on DMD-ATS [Transactions of China Electrotechnical Society] reduces the calculation time of winding temperature rise by dynamic mode decomposition. The main idea is to use the temperature rise T of all temperature rise analysis points of the transformer at the kth sampling moment. k Calculate the temperature rise T at the next moment of the temperature node, that is, the k+1 sampling moment k+1 , the calculation formula is T k+1 =AT k , and so on. We can get T k+1 =A K T 1 , where A is called the temperature rise analysis point change matrix of the winding temperature field, and its size is determined by the number of nodes. In order to obtain the temperature rise distribution of the entire field of the winding temperature field, the winding temperature field should be arranged with as many temperature rise analysis points as possible, which leads to a very large size of the matrix A, so that A K The calculation of T is very difficult. To solve this problem, the literature [2]A new method for transformer hot-spot temperature predictionbased on dynamic mode decomposition[J].Case Studies in Thermal Engineering 1 Perform singular value decomposition and obtain is the modal matrix, and D is the temperature rise distribution coefficient of the winding temperature field under modal characterization. Because only a few modes play a leading role in predicting temperature rise, which are called main modes, the energy ratio method is used to select the main modes, that is, the norm of each row of the matrix D is calculated. The larger the norm value, the higher the energy ratio, and the corresponding mode is selected as the main mode. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and to provide a method for extracting the main modes of transient temperature rise of transformer windings using a hybrid norm. The method is suitable for determining the main modes of windings when predicting the instantaneous temperature rise of the winding temperature field using a modal reduction method. The overall and local characteristics of the modes are fully considered, the accuracy of the main mode selection is improved, and the prediction accuracy of the instantaneous temperature rise of the winding temperature field is improved.

[0005] The object of the present invention is achieved by: a method for extracting the main modes of transient temperature rise of transformer windings using a mixed norm, which comprises the following steps:

[0006] S1. Set the simulation step size and time to determine the winding temperature rise sampling analysis point;

[0007] S2. Obtain the temperature rise distribution of the winding temperature field from the 1st sampling time to the k+1th sampling time, and construct the matrix T k , T k +1 ;

[0008] S3, Calculation based on dynamic mode decomposition D;

[0009] S4. Calculate the ∞-norm and 2-norm of the row vector of the matrix B, and define the convex combination of the ∞-norm and the 2-norm as the norm of the row vector of the matrix B;

[0010] S5. Select the main mode of winding temperature rise prediction according to the value of the row vector norm of matrix B, and simplify T k The calculation formula of

[0011] S6. Calculate T k , set k=k+1, return to step S3, and predict the winding temperature rise at the next moment.

[0012] Furthermore, in the step S1, the simulation step and time are set to determine the winding temperature rise sampling and analysis points. The simulation step is 0.02 seconds, the simulation time is 120,000 seconds, and the winding temperature rise sampling and analysis points are set at the low-voltage winding, with a number of 4,200.

[0013] Furthermore, the matrix T in step S2 k ,T k+1 The structure is as follows:

[0014] T k =[TT k TT k+1 ... TT 2k-1 ]

[0015] Tk+1 =[TT k+1 TT k+2 ... TT 2k ]

[0016] TT k It is a matrix of 4200 rows and 1 column, representing the temperature rise value of the winding temperature rise sampling analysis point at the kth moment.

[0017] Furthermore, step S3 is calculated according to the dynamic mode decomposition D includes the following steps:

[0018] S31, T 1 Perform singular value decomposition and let T 1 =UΨZ, where U and Z are singular value matrices, and Ψ is a diagonal matrix equal to the singular values ​​of A;

[0019] S32, let T 1 =ΓΣH, where Γ and H are matrices consisting of the first r rows and columns of U and Z, respectively, and Σ is a full-rank diagonal matrix with the same singular values ​​as A;

[0020] S33, calculate the similarity matrix of matrix A

[0021] S34, calculate the temperature rise of the winding temperature field at any time k,

[0022]

[0023] Furthermore, the ∞-norm and the 2-norm in step S4 are respectively in the following forms:

[0024]

[0025] ||X|| ∞ =max{|x1|,|x2|,…|x n |}

[0026] Let d i =[d i1 d i2 d i3 …]∈D represents the row vector of the matrix D, whose norm, i.e., the convex combination of the ∞-norm and the 2-norm, is defined as

[0027] ||d i ||=θ||d i ||2+(1-θ)||d i || ∞ ,θ∈(0,1)

[0028] The parameter θ in the formula is selected independently according to the on-site conditions.

[0029] Beneficial effects of the present invention: The method of extracting the main modes of transient temperature rise of transformer windings by using mixed norms is suitable for determining the main modes of windings when predicting the instantaneous temperature rise of winding temperature field by using modal reduction method, and according to the distribution model of the instantaneous temperature rise of winding temperature field at the kth sampling moment The 2-norm and ∞ norm of the row vector of the matrix D are convexly combined to form the norm of the row vector of the matrix D, where D represents the distribution coefficient of the temperature rise of the original temperature field under modal characterization, It is the temperature rise mode matrix. The norm of each row of the matrix is ​​taken as the energy ratio of the corresponding mode. The larger the value of the energy ratio, the more temperature rise information the corresponding mode contains in the temperature field, and the more important the mode is. The norm proposed in the present invention uses the 2-norm to characterize the total energy of a single mode and the ∞-norm to characterize the maximum energy of the elements in a single mode vector, which fully considers the overall and local characteristics of the mode, improves the accuracy of the selection of the main mode, and improves the prediction accuracy of the instantaneous temperature rise of the winding temperature field. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0031] Figure 1 It is a schematic diagram of the flow of calculating the transient temperature rise of the winding temperature field in an embodiment of the present invention.

[0032] Figure 2 Schematic diagram of a transformer model in an embodiment of the present invention.

[0033] Figure 3 Schematic diagram of comparison of winding temperature rise errors with different norms in an embodiment of the present invention. DETAILED DESCRIPTION

[0034] The present invention will be further described below in conjunction with the accompanying drawings.

[0035] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0036] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] The method of the present invention for extracting the main modes of transient temperature rise of transformer windings by using a mixed norm comprises the following steps:

[0038] S1. Set the simulation step size and time to determine the winding temperature rise sampling analysis point;

[0039] S2. Obtain the temperature rise distribution of the winding temperature field from the 1st sampling time to the k+1th sampling time, and construct the matrix T k , T k +1 ;

[0040] S3, Calculation based on dynamic mode decomposition D;

[0041] S4. Calculate the ∞-norm and 2-norm of the row vector of the matrix B, and define the convex combination of the ∞-norm and the 2-norm as the norm of the row vector of the matrix B;

[0042] S5. Select the main mode of winding temperature rise prediction according to the value of the row vector norm of matrix B, and simplify T k The calculation formula of

[0043] S6. Calculate T k , set k=k+1, return to step S3, and predict the winding temperature rise at the next moment.

[0044] Furthermore, in one embodiment, in the step S1, the simulation step and time are set to determine the winding temperature rise sampling and analysis points, the simulation step is 0.02 seconds, the simulation time is 120,000 seconds, and the winding temperature rise sampling and analysis points are set at the low-voltage winding, with a number of 4,200.

[0045] Furthermore, the matrix T in step S2 k ,T k+1 The structure is as follows:

[0046] T k =[TT k TT k+1 ... TT 2k-1 ]

[0047] T k+1 =[TT k+1 TT k+2 ... TT 2k ]

[0048] TT k It is a matrix of 4200 rows and 1 column, representing the temperature rise value of the winding temperature rise sampling analysis point at the kth moment.

[0049] Furthermore, step S3 is calculated according to the dynamic mode decomposition D includes the following steps:

[0050] S31, T 1 Perform singular value decomposition and let T 1 =UΨZ, where U and Z are singular value matrices, and Ψ is a diagonal matrix equal to the singular values ​​of A;

[0051] S32, let T 1 =ΓΣH, where Γ and H are matrices consisting of the first r rows and columns of U and Z, respectively, and Σ is a full-rank diagonal matrix with the same singular values ​​as A;

[0052] S33, calculate the similarity matrix of matrix A

[0053] S34, calculate the temperature rise of the winding temperature field at any time k,

[0054]

[0055] Furthermore, the ∞-norm and the 2-norm in step S4 are respectively in the following forms:

[0056]

[0057] ||X|| ∞ =max{|x1| , |x2|,…|x n |}

[0058] Let d i =[d i1 d i2 d i3 …]∈D represents the row vector of the matrix D, whose norm, i.e., the convex combination of the ∞-norm and the 2-norm, is defined as

[0059] ||d i ||=θ||d i ||2+(1-θ)||d i || ∞ ,θ∈(0,1)

[0060] The parameter θ in the formula is selected independently according to the on-site conditions.

[0061] Based on the literature [1-2], the present invention further studies the mode selection problem that plays a major role in predicting the temperature rise of the winding temperature field, and provides a selection strategy for the matrix D norm when selecting the main mode. The row vector of the matrix D is a finite-dimensional array, and the space formed by its row vectors is a finite-dimensional normed space. According to the definition of the norm, the norms of the finite-dimensional space mainly include the 2-norm, the p-norm, and the ∞-norm. Different choices of the matrix D norm will result in different main winding modes. The main winding temperature rise mode obtained by the norm selection strategy provided by the present invention is closer to the real main winding temperature rise mode, which improves the accuracy of the temperature rise value while improving the calculation speed of the winding temperature rise.

[0062] The present invention is described in detail below by taking a specific type of transformer as an example.

[0063] (1) Establish a digital model of the winding on the Comsol simulation platform, set appropriate simulation steps and simulation time, and obtain the temperature rise history data of the winding before k+1. In order to obtain the temperature distribution of the entire physical field of the winding, it is necessary to arrange a large number of temperature rise analysis points. The SSZ11-25000 / 110 transformer is taken as the research object. Its winding physical parameters refer to the literature [3] Transformer Winding Thermal Defect Temperature Evolution Law and Identification Method [High Voltage Technology]. The low-voltage winding of the transformer consists of 42 coils with an overall height of 830 mm. Each coil consists of 5 turns (each turn is composed of 5 wires wound in parallel) of wire, and the wire is wrapped with insulating paper. 20 temperature rise analysis points are set for each turn of wire, and the analysis points of each turn of wire are evenly distributed on the radial circumference. Each coil consists of 100 temperature rise analysis points, and the entire winding has 4200 temperature rise analysis points. The obtained temperature rise history data at k+1 moments are divided into two parts, T 1 and T 2 ,in

[0064] T 1 =[TT 1 TT 2 ... TT k ]

[0065] T 2 =[TT 2 TT 3 ... TT k+1 ]

[0066] Here T i It is a matrix with 4200 rows and 1 column, i = 1, 2, ..., representing the temperature rise value of each temperature rise analysis point at the i-th moment. When the data-driven intelligent algorithm calculates the winding temperature rise, it is defined as

[0067] T 2 =AT 1

[0068] You can use AT 1 To predict the instantaneous temperature rise of the winding at any time in the future, that is, T 1+p =A p T 1 , so we need to find A.

[0069] (2) Solve the matrix A. First, 1 Perform singular value decomposition to facilitate the calculation of A p Let T 1 =UΨZ

[0070] Where U and Z are singular value matrices, Ψ is equal to the singular value of A, and is a 4200-dimensional diagonal matrix. Assuming that the first r elements on its diagonal are not zero, T can be 1 Approximately expressed as T 1 =ΓΣH, where Γ and H are the matrices consisting of the first r rows of U and the first r columns of Z respectively, and Σ is a full rank diagonal matrix with the same singular values ​​as A, and its scale is much smaller than Ψ.

[0071] Let the similarity matrix of matrix A be according to It can be concluded that Assumption Matrix The eigenvalue and eigenvector of are Φ and Υ respectively, then we have Since the matrices A and Similar, so we can conclude that the eigenvalue and eigenvector of A are Φ and ΓΥ respectively, and the matrix A=ΓΥΦ(ΓΥ) is obtained. -1 , the eigenvector φ=ΓΥ is called the mode of the temperature rise of the winding temperature field, Φ is the corresponding eigenvalue matrix, and the elements λ on its diagonal are i is modal The characteristic value of The elements in the diagonal matrix Φ are transformed as follows: i =ln(λ i ) / Δt, we can get μ i The real part of represents the modal growth rate, μ i The imaginary part of represents the frequency of the mode.

[0072] When the matrices A and T 1 When known, according to T 2 =AT 1 The temperature rise of the winding temperature field at a future time can be predicted. Because A=ΓΥΦ(ΓΥ) -1 , the winding temperature field temperature rise at any time k in is called the mode matrix of the temperature rise of the winding temperature field, B is the distribution coefficient matrix of the winding temperature field, B is a column vector, B = [b1 b2 …] T ,b i Representing modality The initial amplitude can be deduced

[0073]

[0074] Although the above 1 When performing singular value decomposition, the rows and columns with zero eigenvalues ​​have been deleted, but at this time The scale is still large. In order to improve the calculation speed of the instantaneous temperature rise of the winding temperature field, it is necessary to further reduce The dimension of .

[0075] (3) Select the row vector norm of matrix B. Only a few modes play a decisive role in the temperature rise of the winding in the future, and these modes are called main modes. If only the main modes are used to predict the instantaneous temperature rise of the winding temperature field, the time cost of calculating the transient temperature rise can be greatly reduced and the efficiency of the operation can be improved. The present invention adopts the energy ratio method in the document [2] to select the main mode. The energy ratio method is to use the row norm of each row of the matrix D as the energy ratio of the corresponding mode. The higher the energy ratio, the more system change characteristics it reflects, and the more important the mode is.

[0076] Each row of the matrix D is an element of a finite-dimensional space. In a finite-dimensional normed space, common norms are the 2-norm and the ∞-norm. Let X = [x1 x2 … x n ], the 2-norm and ∞-norm are defined as follows:

[0077]

[0078] ||X|| ∞ =max{|x1|,|x2|,…|x n |}

[0079] References [1-2] use the 2-norm of a vector to calculate the energy ratio. According to the definition of the 2-norm, it represents the energy of the entire mode and cannot fully represent the modal information. For example, at a certain moment, the temperature rise of a certain temperature rise analysis point of the winding increases instantly due to short circuit shock, insulation breakdown, etc., while the temperature rise values ​​of the remaining temperature rise analysis points of the winding are very small. According to the definition of the 2-norm, the corresponding mode The energy ratio of will not be too large, and it will be considered as a non-main mode and eliminated to a large extent. However, the mode at this time can characterize the thermal defects of the winding, which is of great significance in the monitoring of the winding operation status. It is unreasonable to exclude it.

[0080] In view of the above situation, the present invention proposes a hybrid norm strategy, that is, the norm of each row of the matrix D is defined as a convex combination of the 2-norm and the ∞-norm, and let d i =[d i1 d i2 d i3 …]∈B represents the row vector of matrix B, whose norm is defined as

[0081] ||d i ||=θ||d i ||2+(1-θ)||d i || ∞ ,θ∈(0,1)

[0082] It can be seen intuitively that the norm defined above satisfies the non-negativity, homogeneity and triangular inequality of the norm. Its advantage is that it can characterize the overall energy of the instantaneous temperature rise mode of the winding temperature field through the 2-norm, and can characterize the local energy maximum of the instantaneous temperature rise mode of the winding temperature field through the ∞-norm. Compared with the simple use of the 2-norm, the hybrid norm proposed in the present invention can more completely and fully characterize the characteristics of the instantaneous temperature rise mode of the winding temperature field, improve the accuracy of the main mode selection, and thus improve the accuracy of the predicted temperature rise.

[0083] According to the definition of mixed norm, the norm of each row of matrix D is calculated, that is, the energy ratio of the corresponding mode. The norms are arranged from large to small, and the number of main modes is determined according to the needs. Assuming that the number of main modes is d, the instantaneous temperature rise mode of the winding temperature field corresponding to the first d norms is selected as the main mode, T k Approximately expressed as The scale relative to Much smaller, using To predict the instantaneous temperature rise of the winding temperature field at future moments will greatly improve the efficiency of temperature rise calculation.

[0084] In order to verify the feasibility and superiority of the hybrid norm proposed in the present invention in predicting the instantaneous temperature rise of the winding temperature field, the SSZ11-25000 / 110 transformer was used as the research object in the Comsol simulation software, and its physical parameters are shown in Table 1. The instantaneous temperature rise of the winding temperature field was predicted, and the predicted calculation results were compared with the calculation results of the Comsol built-in calculator. The simulation results show the superiority of the hybrid norm.

[0085] Table 1 Part of the physical parameters of the transformer

[0086]

[0087] In summary, the method of extracting the main modes of transient temperature rise of transformer windings using mixed norms is suitable for determining the main modes of windings when predicting the instantaneous temperature rise of winding temperature field using modal reduction method, and according to the distribution model of the instantaneous temperature rise of winding temperature field at the kth sampling moment The 2-norm and ∞ norm of the row vector of the matrix D are convexly combined to form the norm of the row vector of the matrix D, where D represents the distribution coefficient of the temperature rise of the original temperature field under modal characterization, It is the temperature rise mode matrix. The norm of each row of the matrix is ​​taken as the energy ratio of the corresponding mode. The larger the value of the energy ratio, the more temperature rise information the corresponding mode contains in the temperature field, and the more important the mode is. The norm proposed in the present invention uses the 2-norm to characterize the total energy of a single mode and the ∞-norm to characterize the maximum energy of the elements in a single mode vector, which fully considers the overall and local characteristics of the mode, improves the accuracy of the selection of the main mode, and improves the prediction accuracy of the instantaneous temperature rise of the winding temperature field.

[0088] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0089] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A method for extracting the main modes of transient temperature rise of transformer windings using a mixed norm, characterized in that: The following steps are involved: S1. Set the simulation step size and time to determine the winding temperature rise sampling analysis point; S2. Obtain the temperature rise distribution of the winding temperature field from the 1st sampling time to the k+1th sampling time, and construct the matrix T k , T k+1 ; S3, Calculation based on dynamic mode decomposition D; S4. Calculate the ∞-norm and 2-norm of the row vector of the matrix B, and define the convex combination of the ∞-norm and the 2-norm as the norm of the row vector of the matrix B; S5. Select the main mode of winding temperature rise prediction according to the value of the row vector norm of matrix B, and simplify T k The calculation formula of S6. Calculate T k , set k=k+1, return to step S3, and predict the winding temperature rise at the next moment.

2. The method for extracting the main modes of transient temperature rise of transformer windings using a mixed norm as claimed in claim 1 is characterized in that: In the step S1, the simulation step and time are set to determine the winding temperature rise sampling and analysis points. The simulation step is 0.02 seconds, the simulation time is 120,000 seconds, and the winding temperature rise sampling and analysis points are set at the low-voltage winding, with a number of 4,200.

3. The method for extracting the main modes of transient temperature rise of transformer windings using a mixed norm as claimed in claim 1, characterized in that: The matrix T in step S2 k ,T k+1 The structure is as follows: T k =[TT k TT k+1 … TT 2k-1 ] T k+1 =[TT k+1 TT k+2 … TT 2k ] TT k It is a matrix of 4200 rows and 1 column, representing the temperature rise value of the winding temperature rise sampling analysis point at the kth moment.

4. The method for extracting the main modes of transient temperature rise of transformer windings using a mixed norm as claimed in claim 1, characterized in that: The step S3 is calculated according to the dynamic mode decomposition D includes the following steps: S31, T 1 Perform singular value decomposition and let T 1 =UΨZ, where U and Z are singular value matrices, and Ψ is a diagonal matrix equal to the singular values ​​of A; S32, let T 1 =ΓΣH, where Γ and H are matrices consisting of the first r rows and columns of U and Z, respectively, and Σ is a full-rank diagonal matrix with the same singular values ​​as A; S33, calculate the similarity matrix of matrix A S34, calculate the temperature rise of the winding temperature field at any time k, 5. The method for extracting the main modes of transient temperature rise of transformer windings using a mixed norm as claimed in claim 1, characterized in that: The ∞-norm and the 2-norm in step S4 are respectively in the following forms: ||X|| ∞ =max{|x1|,|x2|,…|x n |} Let d i =[d i1 d i2 d i3 …]∈D represents the row vector of the matrix D, whose norm, i.e., the convex combination of the ∞-norm and the 2-norm, is defined as ||d i ||=θ||d i ||2+(1-θ)||d i || ∞ ,θ∈(0,1) The parameter θ in the formula is selected independently according to the on-site conditions.

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