A transformer physical field dynamic reduction model construction method
By dynamically updating the transformer physical field reduced-order model, the problem of decreased calculation accuracy caused by changes in the operating conditions of power equipment was solved, and high-precision physical field calculation and control were achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INNER MONGOLIA UNIV OF TECH
- Filing Date
- 2026-05-14
- Publication Date
- 2026-07-31
AI Technical Summary
In existing technologies, the operating conditions of power equipment are complex and varied, which makes it impossible for traditional constant mode reduced-order models to maintain high accuracy and adapt to changes in operating conditions, resulting in a decrease in calculation accuracy.
By acquiring the current operating conditions, a physical field reduced-order calculation model is established, and transient simulation is performed when the load rate changes. The physical field reduced-order model is updated, and the modes are dynamically updated using singular value decomposition and Schmitt orthogonalization to construct a dynamic reduced-order model of the transformer physical field.
It achieves high-precision physical field calculations under changing operating conditions, improving the accuracy and precision of transformer control and reducing computational costs.
Smart Images
Figure CN122490822A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of solvers for multiphysics simulation platforms for power equipment, and more specifically, to a method for constructing a dynamic reduced-order model of the physical field of a transformer. Background Technology
[0002] Industrial simulation software is a significant driving force for industrial development and a key element in accelerating the digital and intelligent transformation of industries. my country is a major industrial nation, but its industrial simulation software market is dominated by foreign products. Multiphysics simulation software such as ANSYS and COMSOL are rapidly developing and iterating; therefore, developing domestically produced multiphysics simulation software to break the foreign dominance in this field is of great importance.
[0003] For multiphysics simulation software, the core lies in the physics solution algorithm, and this field is currently quite mature. However, the commonly used method is to construct a reduced-order model using constant modes, and then keep the reduced-order model unchanged for continued use. However, the operating conditions of power equipment are complex and variable, which inevitably leads to changes in its modes. In this case, the reduced-order model constructed by traditional methods will inevitably become invalid, making it impossible to maintain the high accuracy of the reduced-order model calculation. Summary of the Invention
[0004] In view of this, the present invention discloses a method for constructing a dynamic order reduction model of the physical field of a transformer, which can at least enable the rapid updating of the dynamic order reduction model of the physical field when the operating conditions continue to change, thereby ensuring the continuous accuracy of the calculation results of the physical field of the transformer.
[0005] Specifically, the present invention is achieved through the following technical solutions:
[0006] This application proposes a method for constructing a dynamic order-reduced model of the physical field of a transformer, characterized by comprising:
[0007] Obtain the current operating status;
[0008] Based on the current operating conditions and the pre-established physical field simulation model, the physical field reduced-order calculation model of the transformer is determined, and the operation of the transformer is controlled according to the reduced-order calculation model.
[0009] Obtain the load rate of the transformer and determine whether the change in the load rate of the transformer is greater than a preset load rate change threshold.
[0010] If the change in the load rate of the transformer is greater than the preset load rate change threshold, the transformer is determined to enter the next operating condition, and a very short-term transient simulation is performed on the physical field simulation model of the transformer, and a small number of snapshots of the physical field of the transformer under the next operating condition are obtained.
[0011] Based on the transient simulation and a few snapshots of the physical field under the next operating condition, the reduced-order physical field model of the transformer is updated to obtain the updated reduced-order physical field calculation model, and the operation of the transformer is controlled according to the updated reduced-order physical field calculation model.
[0012] In some embodiments, based on the current operating conditions and a pre-established physical field simulation model, a reduced-order physical field calculation model for the transformer is determined, including:
[0013] The boundary conditions are set based on the current working condition, and transient calculations are performed to obtain the physical field calculation results at multiple times.
[0014] The physical field calculation results at each time step are represented as column vectors, and the column vectors are arranged according to equal time intervals to construct an initial snapshot matrix;
[0015] Singular value decomposition is performed on the initial snapshot matrix. The column vectors of the decomposed left singular matrix, i.e. the singular vectors, are taken as modes. The modes are truncated according to the magnitude of their corresponding singular values. The dominant modes are selected and these dominant modes are taken as the initial modes of the transformer physical field.
[0016] Using the initial mode as a basis vector, the control equations for calculating the physical field of the transformer are reduced in order to obtain a reduced-order calculation model of the physical field of the transformer.
[0017] In some embodiments, the reduced-order physical field model of the transformer is updated based on the transient simulation and a small number of snapshots of the physical field under the next operating condition, resulting in an updated reduced-order physical field calculation model, including:
[0018] A very short-term transient simulation of the transformer physical field simulation model is performed, and a small number of snapshots of the transformer physical field under the next operating condition are obtained.
[0019] Using a small number of snapshots of the transformer physical field under the next operating condition and the initial field mode of the transformer physical field, the next physical field mode of the transformer after taking into account the distribution characteristics of the physical field under the next operating condition is calculated.
[0020] The transformer physical field control equations are reprocessed using the next physical field mode of the transformer to obtain an updated physical field reduced-order calculation model.
[0021] In some embodiments, an initial snapshot matrix is constructed through the following steps:
[0022] The current operating conditions are set for the transformer simulation model. Based on these conditions, the boundary conditions of the simulation model are set, and transient simulation is performed. The transient simulation results at each time step are then converted into column vectors. The form;
[0023] Transform the transient simulation results at each time step into column vectors. Merge into an initial snapshot matrix , where n is the number of grid points corresponding to the simulation model, m is the number of snapshots in the snapshot matrix, and the m snapshots are at equal time intervals, and i represents the column number.
[0024] In some embodiments, the initial snapshot matrix X is calculated using the following formula. g0 Perform singular value decomposition.
[0025] ;
[0026] in, Represented as:
[0027] ;
[0028] Wherein, matrix U g0 The matrix S corresponding to each column vector g0 The elements in the diagonal, that is Singular values The corresponding singular vector;
[0029] The step of truncating it according to the magnitude of its corresponding singular value includes: based on matrix S g0 The elements on the diagonal of matrix S g0 The elements on the diagonal are truncated, and the matrix S is... g0 The elements on the middle diagonal are arranged in descending order;
[0030] The criterion for truncation is as follows:
[0031] ;
[0032] Where P is the cumulative modal energy percentage, r is the retained modal order, and σ i Let be the i-th singular value.
[0033] In some embodiments, the governing equations for calculating the physical field of a transformer are reduced in order, including:
[0034] The control equations of the transformer physics field are subjected to an invasive order reduction process using the initial snapshot matrix.
[0035] Among them, using U r0 An invasive order reduction process is applied to the governing equations of the transformer's physical field, including:
[0036] The first governing equation represents multiple physical fields in the transformer;
[0037] The state variables of the system corresponding to the first governing equation are expressed in mode U. g0 After the transformation, the first constraint equation is satisfied;
[0038] According to the first state variable in the first constraint equation Second state variable Determine the expression for the state variables;
[0039] Based on the state variable expression and the original high-dimensional control equation, determine the intermediate reduced-order equation;
[0040] The intermediate reduced-order equations are simplified to obtain the reduced-order calculation model of the transformer physical field.
[0041] In some embodiments, the first governing equation is:
[0042] ;
[0043] Where u(t) is the input of the dynamic system corresponding to the physical location of the transformer, y(t) is the output of the dynamic system corresponding to the physical location of the transformer, x(t) is the state variable at time t, and its rate of change with time can be represented by the function f(.). The output y(t) at time t can be represented by the function g(.).
[0044] The first restrictive equation is:
[0045] ;
[0046] in, It is r-dimensional. It is (nr)-dimensional, where r is the previously reserved modal order, n is the dimension of the state variables, Ur0 is the first r rows of Ug0, and Ud0 is the first d rows of Ug0;
[0047] Where, assuming The state variable is expressed as:
[0048] ;
[0049] The intermediate order reduction formula is as follows:
[0050] ;
[0051] The transformer physical field order reduction calculation model is as follows:
[0052] ;
[0053] in, Low-dimensional state variables The rate of change over time, Ur is the r-order left singular matrix of the aforementioned stage.
[0054] In some embodiments, the snapshot matrix for the next operating condition is obtained through the following steps:
[0055] Assuming a new snapshot is generated after performing a physics simulation under the new operating conditions. Then the initial snapshot set is updated in the following form;
[0056] By replacing the first element of the initial snapshot matrix, we can obtain the snapshot matrix for the next operating condition.
[0057] Based on the SVD results of the initial snapshot matrix and the new snapshot x new The SVD result of the snapshot matrix under the next working condition can be directly obtained;
[0058] The elements in the snapshot matrix under the next operating condition are obtained by Schmidt orthogonalization.
[0059] In some embodiments, the snapshot matrix X of the next operating condition g1 for:
[0060] ;
[0061] Among them, X g0 To X g1 The update is represented as:
[0062] ;
[0063] Where a = xnew - x1, Furthermore, its m-th element is 1, and the remaining elements are 0. Sg0 is the characteristic matrix, Vg0 is the right singular matrix, and X... g0 Let X be the initial snapshot matrix. g1 This is the snapshot matrix for the next operating condition;
[0064] Among them, the snapshot matrix X under the next working condition g1 The SVD results are as follows:
[0065] ;
[0066] The following equation is obtained after performing Schmitt orthogonalization on [Ug0,a]:
[0067] ;
[0068] Among them, [U g0 The columns of [M] are mutually orthogonal;
[0069] Among them, for [V] g0 ,e s1After performing Schmidt orthogonalization, we obtain the following equation:
[0070] ;
[0071] Among them, [V g0 The columns of [,N] are mutually orthogonal.
[0072] For matrix After performing singular value decomposition, we obtain the following equation:
[0073] ;
[0074] Among them, matrix , , These are the left singular matrix, characteristic matrix, and right singular matrix after the singular value decomposition of matrix K, respectively.
[0075] In some embodiments, the updated order reduction model is:
[0076] .
[0077] The method for constructing a dynamic reduced-order model of the transformer physical field proposed in this application can update the reduced-order calculation model of the physical field according to the changes in the transformer operating conditions, so that the updated reduced-order calculation model of the physical field is more compatible with the new operating conditions. As a result, the transformer physical field control data obtained by calculating through the updated reduced-order calculation model of the physical field can control the transformer under the new operating conditions more accurately, with higher precision and better control effect. Attached Figure Description
[0078] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:
[0079] Figure 1 A flowchart illustrating a method for constructing a dynamic order reduction model of a transformer's physical field, provided in an embodiment of this application;
[0080] Figure 2 A flowchart illustrating another method for constructing a dynamic reduced-order model of the physical field of a transformer provided in this application. Detailed Implementation
[0081] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of systems and methods consistent with some aspects of this disclosure as detailed in the appended claims.
[0082] The terminology used in this disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. The singular forms “a,” “the,” and “the” as used in this disclosure and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.
[0083] It should be understood that although the terms first, second, third, etc., may be used in this disclosure to describe various information, such information should not be limited to these terms. These terms are used only to distinguish information of the same type from one another. For example, without departing from the scope of this disclosure, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."
[0084] This application relates to the field of solvers for multiphysics simulation platforms for power equipment, and more specifically, to a method for constructing a dynamic reduced-order model of the physical field of a transformer.
[0085] Industrial simulation software is a significant driving force for industrial development and a key element in accelerating the digital and intelligent transformation of industries. my country is a major industrial nation, but its industrial simulation software market is dominated by foreign products. Multiphysics simulation software such as ANSYS and COMSOL are rapidly developing and iterating; therefore, developing domestically produced multiphysics simulation software to break the foreign dominance in this field is of great importance.
[0086] For multiphysics simulation software, the core lies in the physics solution algorithm, and this field is currently quite mature. With the increasing demands for computational speed from applications such as digital twins, fast physics solution algorithms have attracted widespread attention from software developers. For example, ANSYS launched the TwinBuilder module, which integrates a reduction-order algorithm, and Altair launched a product integrating both reduction-order and AI algorithms. However, the currently common method of using constant modes to construct the reduced-order model, and then keeping it unchanged for continued use, is problematic. The operating conditions of power equipment are complex and variable, inevitably leading to changes in its modes. In such cases, the reduced-order model constructed using traditional methods will inevitably become invalid, failing to maintain the high accuracy of the reduced-order model calculation.
[0087] Based on this, this application constructs a reduced-order model whose modalities can be dynamically updated according to operating conditions to maintain high computational accuracy. Achieving a technological breakthrough in the field of reduced-order algorithms, and subsequently realizing the independent development and upgrading of multiphysics simulation software, is of great value for promoting the digital and intelligent development of my country's industrial sector.
[0088] Specifically, this application proposes a method for constructing a dynamic order reduction model of the physical field of a transformer.
[0089] Please see Figures 1-2 Please see Figure 1 This application discloses a flowchart illustrating a method for constructing a dynamic order-reduction model of a transformer's physical field. Specifically, the method for constructing a dynamic order-reduction model of a transformer's physical field proposed in this application includes:
[0090] S101, obtain the current operating condition.
[0091] In some embodiments, the current operating condition may also be the initial operating condition.
[0092] S102, based on the current operating conditions and the pre-established physical field simulation model, determine the physical field reduced-order calculation model of the transformer, and control the operation of the transformer according to the reduced-order calculation model.
[0093] Among them, the control equation of the transformer magnetic field, its discretized finite element equation, is in the form of:
[0094] .
[0095] For example, under operating condition A, the initial snapshot matrix of the transformer's magnetic field, X, is obtained. A =[x 1a , x 2a ,…, x ma Then, singular value decomposition is performed on it to obtain the initial mode U. rA The governing equations are then reduced in order as follows:
[0096] ;
[0097] In the above equation, the field distribution X is represented by modes. The modal coefficients α were expressed, and both sides of the governing equation were left-multiplied by the modal coefficients α. .
[0098] At this point, the governing equations for calculating the transformer's magnetic field are... The nth order shown has become The r-order model shown forms the initial reduced-order model.
[0099] Specifically, based on the current operating conditions and the pre-established physical field simulation model, the physical field reduction calculation model of the transformer is determined, including:
[0100] The boundary conditions are set based on the current working condition, and transient calculations are performed to obtain the physical field calculation results at multiple times.
[0101] The physical field calculation results at each time step are represented as column vectors, and the column vectors are arranged according to equal time intervals to construct an initial snapshot matrix;
[0102] Singular value decomposition is performed on the initial snapshot matrix. The column vectors of the decomposed left singular matrix, i.e. the singular vectors, are taken as modes. The modes are truncated according to the magnitude of their corresponding singular values. The dominant modes are selected and these dominant modes are taken as the initial modes of the transformer physical field.
[0103] Using the initial mode as a basis vector, the control equations for calculating the physical field of the transformer are reduced in order to obtain a reduced-order calculation model of the physical field of the transformer.
[0104] In some embodiments, an initial snapshot matrix can be constructed using the following steps:
[0105] The current operating conditions are set for the transformer simulation model. Based on these conditions, the boundary conditions of the simulation model are set, and transient simulation is performed. The transient simulation results at each time step are then converted into column vectors. The form;
[0106] Transform the transient simulation results at each time step into column vectors. Merge into an initial snapshot matrix , where n is the number of grid points corresponding to the simulation model, m is the number of snapshots in the snapshot matrix, and the m snapshots are at equal time intervals, and i represents the column number.
[0107] Specifically, the initial snapshot matrix X can be calculated using the following formula. g0 Perform singular value decomposition:
[0108] ;
[0109] in, Represented as:
[0110] ;
[0111] Wherein, matrix U g0 The matrix S corresponding to each column vector g0 The elements in the diagonal, that is Singular values The corresponding singular vector;
[0112] The step of truncating it according to the magnitude of its corresponding singular value includes: based on matrix S g0 The elements on the diagonal of matrix S g0 The elements on the diagonal are truncated, and the matrix S is... g0 The elements on the middle diagonal are arranged in descending order;
[0113] The criterion for truncation is as follows:
[0114] ;
[0115] Where P is the cumulative modal energy percentage, r is the retained modal order, and σ i Let be the i-th singular value.
[0116] Specifically, the governing equations for calculating the physical fields of a transformer are reduced in order, including:
[0117] The control equations of the transformer physics field are subjected to an invasive order reduction process using the initial snapshot matrix.
[0118] Among them, using U r0 An invasive order reduction process is applied to the governing equations of the transformer's physical field, including:
[0119] The first governing equation represents multiple physical fields in the transformer;
[0120] The state variables of the system corresponding to the first governing equation are expressed in mode U. g0 After the transformation, the first constraint equation is satisfied;
[0121] According to the first state variable in the first constraint equation Second state variable Determine the expression for the state variables;
[0122] Based on the state variable expression and the original high-dimensional control equation, determine the intermediate reduced-order equation;
[0123] The intermediate reduced-order equations are simplified to obtain the reduced-order calculation model of the transformer physical field.
[0124] The first governing equation is:
[0125] ;
[0126] Where u(t) is the input of the dynamic system corresponding to the physical location of the transformer, y(t) is the output of the dynamic system corresponding to the physical location of the transformer, x(t) is the state variable at time t, and its rate of change with time can be represented by the function f(.). The output y(t) at time t can be represented by the function g(.).
[0127] The first restrictive equation is:
[0128] ;
[0129] in, It is r-dimensional. It is (nr)-dimensional, where r is the previously reserved modal order, n is the dimension of the state variables, Ur0 is the first r rows of Ug0, and Ud0 is the first d rows of Ug0;
[0130] Where, assuming The state variable is expressed as:
[0131] ;
[0132] The intermediate order reduction formula is as follows:
[0133] ;
[0134] The transformer physical field order reduction calculation model is as follows:
[0135] ;
[0136] in, Low-dimensional state variables The rate of change over time, Ur is the r-order left singular matrix of the aforementioned stage.
[0137] S103, obtain the load rate of the transformer, and determine whether the change value of the load rate of the transformer is greater than the preset load rate change threshold.
[0138] S104, if the change in the load rate of the transformer is greater than the preset load rate change threshold, then the transformer is determined to enter the next operating condition, and a very short-term transient simulation is performed on the physical field simulation model of the transformer, and a small number of snapshots of the physical field of the transformer under the next operating condition are obtained.
[0139] Specifically, the snapshot matrix for the next operating condition can be obtained through the following steps:
[0140] Assuming a new snapshot is generated after performing a physics simulation under the new operating conditions. Then the initial snapshot set is updated in the following form;
[0141] By replacing the first element of the initial snapshot matrix, we can obtain the snapshot matrix for the next operating condition.
[0142] Based on the SVD results of the initial snapshot matrix and the new snapshot x new The SVD result of the snapshot matrix under the next working condition can be directly obtained;
[0143] The elements in the snapshot matrix under the next operating condition are obtained by Schmidt orthogonalization.
[0144] Among them, the snapshot matrix X under the next working condition g1 for:
[0145] ;
[0146] Among them, X g0 To X g1 The update is represented as:
[0147] ;
[0148] Where a = xnew - x1, Furthermore, its m-th element is 1, and the remaining elements are 0. Sg0 is the characteristic matrix, Vg0 is the right singular matrix, and X... g0 Let X be the initial snapshot matrix. g1 This is the snapshot matrix for the next operating condition;
[0149] Among them, the snapshot matrix X under the next working condition g1 The SVD results are as follows:
[0150] ;
[0151] The following equation is obtained after performing Schmitt orthogonalization on [Ug0,a]:
[0152] ;
[0153] Among them, [U g0 The columns of [M] are mutually orthogonal;
[0154] Among them, for [V] g0 ,e s1 After performing Schmidt orthogonalization, we obtain the following equation:
[0155] ;
[0156] Among them, [V g0 The columns of [,N] are mutually orthogonal.
[0157] For matrix After performing singular value decomposition, we obtain the following equation:
[0158] ;
[0159] Among them, matrix , , These are the left singular matrix, characteristic matrix, and right singular matrix after the singular value decomposition of matrix K, respectively.
[0160] In this way, only one singular value decomposition of an r+1 dimensional matrix and two Schmitt orthogonalizations are needed to complete the mode update that takes the snapshot under the new operating condition into account, without having to perform singular value decomposition again on the n-dimensional snapshot set to solve and update the modes, which greatly reduces the computational cost.
[0161] S105, based on the transient simulation and a small number of snapshots of the physical field under the next operating condition, the reduced-order physical field model of the transformer is updated to obtain the updated reduced-order physical field calculation model, and the transformer is controlled to operate according to the updated reduced-order physical field calculation model.
[0162] Specifically, based on the transient simulation and a few snapshots of the physical field under the next operating condition, the reduced-order model of the transformer physical field is updated to obtain the updated reduced-order calculation model of the physical field, including:
[0163] A very short-term transient simulation of the transformer physical field simulation model is performed, and a small number of snapshots of the transformer physical field under the next operating condition are obtained.
[0164] Using a small number of snapshots of the transformer physical field under the next operating condition and the initial field mode of the transformer physical field, the next physical field mode of the transformer after taking into account the distribution characteristics of the physical field under the next operating condition is calculated.
[0165] The transformer physical field control equations are reprocessed using the next physical field mode of the transformer to obtain an updated physical field reduced-order calculation model.
[0166] Specifically, the updated order reduction model is as follows:
[0167]
[0168] Please see Figure 2 In one optional embodiment, the initial snapshot matrix of the transformer magnetic field, X, is obtained under operating condition A. A=[x 1a , x 2a ,…, x ma Then, singular value decomposition is performed on it to obtain the initial mode U. rA The governing equations are then reduced in order as follows:
[0169] ;
[0170] In the above equation, the field distribution X is represented by modes. The modal coefficients α were expressed, and both sides of the governing equation were left-multiplied by the modal coefficients α. .
[0171] At this point, the governing equations for calculating the transformer's magnetic field are... The nth order shown has become The r-order model shown forms the initial reduced-order model.
[0172] When the transformer's operating condition changes to condition B, the corresponding mode of its magnetic field distribution will inevitably change as well. If the mode is still used... Performing order reduction will inevitably result in a significant decrease in the computational accuracy of the reduced model. Therefore, the method presented in this patent is used to dynamically update the modes and update the reduced model.
[0173] First, perform an ultra-short-term transient simulation under condition B to obtain a snapshot of the field distribution x. b Then, based on the above calculation formula, the updated mode can be directly calculated. Then, the updated reduced-order model is obtained, as follows:
[0174] .
[0175] As the operating conditions continue to change, the aforementioned calculation method of obtaining a new snapshot and updating the mode based on the new snapshot is repeated to complete the mode update, thereby realizing the dynamic update of the reduced-order model.
[0176] The method for constructing a dynamic reduced-order model of the transformer physical field proposed in this application can update the reduced-order calculation model of the physical field according to the changes in the transformer operating conditions, so that the updated reduced-order calculation model of the physical field is more compatible with the new operating conditions. As a result, the transformer physical field control data obtained by calculating through the updated reduced-order calculation model of the physical field can control the transformer under the new operating conditions more accurately, with higher precision and better control effect.
[0177] Finally, it should be noted that although this specification contains many specific implementation details, these should not be construed as limiting the scope of any invention or the scope of the claims, but rather are primarily used to describe the features of specific embodiments of a particular invention. Certain features described in the various embodiments of this specification may also be implemented in combination in a single embodiment. On the other hand, various features described in a single embodiment may also be implemented separately in various embodiments or in any suitable sub-combination. Furthermore, while features may function in certain combinations as described above and even initially claimed in this way, one or more features from a claimed combination may be removed from that combination in some cases, and a claimed combination may refer to a sub-combination or a variation of a sub-combination.
[0178] Similarly, although the operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring these operations to be performed in the specific order shown or sequentially, or requiring all illustrated operations to be performed to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the above embodiments should not be construed as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.
[0179] Thus, specific embodiments of the subject matter have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims may be performed in a different order and still achieve the desired result. Furthermore, the processes depicted in the drawings are not necessarily shown in a specific order or sequence to achieve the desired result. In some implementations, multitasking and parallel processing may be advantageous.
[0180] The above description is merely a preferred embodiment of this disclosure and is not intended to limit this disclosure. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.
Claims
1. A method for constructing a dynamic order-reduced model of the physical field of a transformer, characterized in that, include: Obtain the current operating status; Based on the current operating conditions and the pre-established physical field simulation model, the physical field reduced-order calculation model of the transformer is determined, and the operation of the transformer is controlled according to the reduced-order calculation model. Obtain the load rate of the transformer and determine whether the change in the load rate of the transformer is greater than a preset load rate change threshold. If the change in the load rate of the transformer is greater than the preset load rate change threshold, the transformer is determined to enter the next operating condition, and a very short-term transient simulation is performed on the physical field simulation model of the transformer, and a small number of snapshots of the physical field of the transformer under the next operating condition are obtained. Based on the transient simulation and a few snapshots of the physical field under the next operating condition, the reduced-order physical field model of the transformer is updated to obtain the updated reduced-order physical field calculation model, and the operation of the transformer is controlled according to the updated reduced-order physical field calculation model.
2. The method for constructing a dynamic order-reduced model of the transformer physical field according to claim 1, characterized in that, Based on the current operating conditions and the pre-established physical field simulation model, the physical field reduction calculation model of the transformer is determined, including: The boundary conditions are set based on the current working condition, and transient calculations are performed to obtain the physical field calculation results at multiple times. The physical field calculation results at each time step are represented as column vectors, and the column vectors are arranged according to equal time intervals to construct an initial snapshot matrix; Singular value decomposition is performed on the initial snapshot matrix. The column vectors of the decomposed left singular matrix, i.e. the singular vectors, are taken as modes. The modes are truncated according to the magnitude of their corresponding singular values. The dominant modes are selected and these dominant modes are taken as the initial modes of the transformer physical field. Using the initial mode as a basis vector, the control equations for calculating the physical field of the transformer are reduced in order to obtain a reduced-order calculation model of the physical field of the transformer.
3. The method for constructing a dynamic order-reduced model of the transformer physical field according to claim 2, characterized in that, Based on the transient simulation and a few snapshots of the physical field under the next operating condition, the reduced-order physical field model of the transformer is updated to obtain the updated reduced-order physical field calculation model, including: A very short-term transient simulation of the transformer physical field simulation model is performed, and a small number of snapshots of the transformer physical field under the next operating condition are obtained. Using a small number of snapshots of the transformer physical field under the next operating condition and the initial field mode of the transformer physical field, the next physical field mode of the transformer after taking into account the distribution characteristics of the physical field under the next operating condition is calculated. The transformer physical field control equations are reprocessed using the next physical field mode of the transformer to obtain an updated physical field reduced-order calculation model.
4. The method for constructing a dynamic order-reduced model of the transformer physical field according to claim 3, characterized in that, The initial snapshot matrix is constructed using the following steps: The current operating conditions are set for the transformer simulation model. Based on these conditions, the boundary conditions of the simulation model are set, and transient simulation is performed. The transient simulation results at each time step are then converted into column vectors. The form; Transform the transient simulation results at each time step into column vectors. Merge into an initial snapshot matrix , where n is the number of grid points corresponding to the simulation model, m is the number of snapshots in the snapshot matrix, and the m snapshots are at equal time intervals, and i represents the column number.
5. The method for constructing a dynamic order-reduced model of the transformer physical field according to claim 4, characterized in that, The initial snapshot matrix X is obtained using the following formula. g0 Perform singular value decomposition. ； in, Represented as: ； Wherein, matrix U g0 The matrix S corresponding to each column vector g0 The elements in the diagonal, that is Singular values The corresponding singular vector; The step of truncating it according to the magnitude of its corresponding singular value includes: based on matrix S g0 The elements on the diagonal of matrix S g0 The elements on the diagonal are truncated, and the matrix S is... g0 The elements on the middle diagonal are arranged in descending order; The criterion for truncation is as follows: ； Where P is the cumulative modal energy percentage, r is the retained modal order, and σ i Let be the i-th singular value.
6. The method for constructing a dynamic order-reduced model of the transformer physical field according to claim 5, characterized in that, The governing equations for calculating the physical fields of a transformer are reduced in order, including: The control equations of the transformer physics field are subjected to an invasive order reduction process using the initial snapshot matrix. Among them, using U r0 An invasive order reduction process is applied to the governing equations of the transformer's physical field, including: The first governing equation represents multiple physical fields in the transformer; The state variables of the system corresponding to the first governing equation are expressed in mode U. g0 After the transformation, the first constraint equation is satisfied; According to the first state variable in the first constraint equation Second state variable Determine the expression for the state variables; Based on the state variable expression and the original high-dimensional control equation, determine the intermediate reduced-order equation; The intermediate reduced-order equations are simplified to obtain the reduced-order calculation model of the transformer physical field.
7. The method for constructing a dynamic order-reduced model of the transformer physical field according to claim 6, characterized in that, The first governing equation is: ； Where u(t) is the input of the dynamic system corresponding to the physical location of the transformer, y(t) is the output of the dynamic system corresponding to the physical location of the transformer, x(t) is the state variable at time t, and its rate of change with time can be represented by the function f(.). The output y(t) at time t can be represented by the function g(.). The first restrictive equation is: ； in, It is r-dimensional. It is (nr)-dimensional, where r is the previously reserved modal order, n is the dimension of the state variables, Ur0 is the first r rows of Ug0, and Ud0 is the first d rows of Ug0; Where, assuming The state variable is expressed as: ； The intermediate order reduction formula is as follows: ； The transformer physical field order reduction calculation model is as follows: ； in, Low-dimensional state variables The rate of change over time, Ur is the r-order left singular matrix of the aforementioned stage.
8. The method for constructing a dynamic reduced-order model of the transformer physical field according to claim 7, characterized in that, The snapshot matrix for the next operating condition is obtained through the following steps: Assuming a new snapshot is generated after performing a physics simulation under the new operating conditions. Then the initial snapshot set is updated in the following form; By replacing the first element of the initial snapshot matrix, we can obtain the snapshot matrix for the next operating condition. Based on the SVD results of the initial snapshot matrix and the new snapshot x new The SVD result of the snapshot matrix under the next working condition can be directly obtained; The elements in the snapshot matrix under the next operating condition are obtained by Schmidt orthogonalization.
9. The method for constructing a dynamic order-reduced model of the transformer physical field according to claim 8, characterized in that, Snapshot matrix X under the next operating condition g1 for: ； Among them, X g0 To X g1 The update is represented as: ； Where a = xnew - x1, Furthermore, its m-th element is 1, and the remaining elements are 0. Sg0 is the characteristic matrix, Vg0 is the right singular matrix, and X... g0 Let X be the initial snapshot matrix. g1 This is the snapshot matrix for the next operating condition; Among them, the snapshot matrix X under the next working condition g1 The SVD results are as follows: ； The following equation is obtained after performing Schmitt orthogonalization on [Ug0,a]: ； Among them, [U g0 The columns of [M] are mutually orthogonal; Among them, for [V] g0 ,e s1 After performing Schmidt orthogonalization, we obtain the following equation: ； Among them, [V g0 The columns of [,N] are mutually orthogonal; for the matrix After performing singular value decomposition, we obtain the following equation: ; where the matrix , , These are the left singular matrix, characteristic matrix, and right singular matrix after the singular value decomposition of matrix K, respectively.
10. The method for constructing a dynamic order-reduced model of the transformer physical field according to claim 9, characterized in that, The updated order reduction model is as follows: 。