A Krylov subspace-based method for reducing the order of the transformer temperature field model

Abstract

The present invention discloses a method for reducing the order of a transformer temperature field model based on the Krylov subspace, belonging to the technical field of temperature field simulation of oil-immersed three-phase transformers. The present invention includes: Step 1. According to the actual physical dimensions of the transformer, construct a simulation model of the oil-immersed three-phase transformer and appropriately simplify the model. Step 2. Establish an electromagnetic field simulation model, use an eddy current solver, and simulate to obtain the transformer loss distribution. Step 3. Take the obtained transformer loss distribution as the excitation source of the fluid field, establish a fluid field simulation model, realize the coupled analysis of the electromagnetic field and the fluid field, and obtain the temperature field distribution characteristics of the oil-immersed three-phase transformer. Step 4. Build a reduced-order model for the transformer temperature field based on the Krylov subspace method. The present invention realizes the rapid simulation calculation of the physical field, reduces the simulation time, and further constructs a digital twin model of the transformer.

Description

Technical Field

[0001] The present invention belongs to the technical field of temperature field simulation of oil-immersed three-phase transformers, and in particular relates to a method for reducing the order of a transformer temperature field model based on the Krylov subspace, and more specifically, a method for reducing the order of a digital twin model of a transformer temperature field based on the Krylov subspace. Background Art

[0002] Digital twin technology has gradually developed from the original aerospace field to various manufacturing industries and shows good application prospects in the field of intelligent manufacturing. The military, civilian and other fields attach more and more importance to digital twin technology and begin to gradually explore its core technology and development potential. As a bridge connecting the physical world and the virtual world, digital twin technology uses complex physical simulation, real-time data sharing and analysis, data processing, etc. as key technologies to construct digital twins of the physical world and the virtual world, and real-time display the physical state of the physical world. The digital twin can efficiently and accurately simulate the physical entity, analyze the state of the physical entity, give early warnings of faults, and assist in the decision-making of operators.

[0003] As an important part of a substation, the thermal characteristics of a transformer directly affect the safe and reliable operation of the equipment. During the operation of the transformer, eddy current losses will be generated in the windings and the iron core under the action of the leakage magnetic field, and ohmic losses will be generated by the interaction between the current inside the windings and the coil resistance. These losses are all converted into heat, and the heat is transferred to the external environment through the transformer oil. As the voltage level and capacity of the transformer increase, its losses and temperature will also gradually increase. When the transformer temperature rises, it will accelerate the aging of the insulation and reduce the life of the transformer. Therefore, the accuracy of measuring the hot spot temperature of the winding should be improved to ensure its safe and stable operation. Currently, the temperature measurement of the transformer is mainly on the wall surface and the oil temperature. The method for measuring the hot spot temperature of the winding is to bury optical fiber sensors inside the winding, but the hot spot position cannot be accurately located. Therefore, temperature field simulation of the transformer can accurately calculate the temperature values at each point. At present, although physical field simulation can accurately simulate the temperature of each part of the transformer, the simulation takes a long time and the calculation amount is large, which is not suitable for constructing a digital twin of the transformer.

[0004] For example: The existing patent number is 2021108220457, and the name is a method for constructing a temperature field model of a converter transformer. This application uses the dynamic mode decomposition method to build a reduced-order model for the temperature field, which is also based on the full-order model that has been calculated. However, further, an instantaneous image matrix needs to be constructed according to the discrete-time temperature data samples obtained by calculation. The selection requirements for the discrete-time points to construct the instantaneous image matrix have relevance, and the sample quantity also directly affects the calculation accuracy.

[0005] For another example: In the prior art, in "Computer Engineering and Applications" 2016(052)012: ARNOLDI Model Order Reduction Method Based on Krylov-schur Restart Technology, although this article also uses the Krylov subspace and the Arnoldi algorithm to achieve model order reduction, this article points out that there is a problem in the traditional Arnoldi algorithm that a stable reduced-order system cannot be obtained at one time in the reduction of complex dynamic systems.

[0006] Therefore, aiming at the deficiencies in the prior art, a reduced-order model for the physical field is constructed. By sacrificing part of the calculation accuracy within the range of satisfying the error, the calculation amount is reduced, and the calculation time is greatly reduced, which can solve the defects existing in the current physical field calculation. Summary of the Invention

[0007] Aiming at the deficiencies existing in the above-mentioned prior art, the present invention provides a method for reducing the order of a transformer temperature field model based on the Krylov subspace. Its purpose is to achieve the invention purpose of accelerating the simulation efficiency through the reduced-order model, reducing the simulation time-consuming, and being better applicable to the construction of digital twins.

[0008] The technical solution adopted by the present invention to achieve the above purpose is as follows:

[0009] A method for reducing the order of a transformer temperature field model based on the Krylov subspace, comprising the following steps:

[0010] Step 1: Establish a simulation physical model of an oil-immersed three-phase transformer. Subsequent physical field simulations are all completed based on the simplified simulation physical model. Specifically, according to the actual physical dimensions of the transformer, a 1:1 simulation model is constructed; since the internal structure of the actual transformer is complex, and the field simulation involved in the present invention is only related to the iron core winding components, the model is simplified, and the winding is equivalent to a circular ring according to the magnetic field invariance criterion.

[0011] Step 2: Based on the simplified simulation physical model in Step 1, select the Maxwell 3D analysis module to construct an electromagnetic field simulation model, and use an eddy current solver to obtain the transformer loss distribution.

[0012] Step 3: Use the obtained transformer loss distribution as the excitation of the fluid field, establish a fluid field simulation model, realize the coupled analysis of the electromagnetic field and the fluid field, and obtain the temperature field distribution characteristics of the oil-immersed three-phase transformer; based on the electromagnetic-fluid field simulation calculation of the transformer to obtain the temperature distribution, export the calculation results to the MATLAB Simulink platform to complete the subsequent construction of the temperature field reduced-order model.

[0013] Step 4: Reduce the order of the reduced-order model of the transformer temperature field based on the Krylov subspace method and verify it.

[0014] Further, the winding is equivalent to a circular ring according to the magnetic field invariance criterion. Specifically, the geometric dimensions of the transformer are calculated based on the transformer capacity and voltage parameters, a transformer simulation model is established, and according to the magnetic field invariance criterion, the winding is simplified and the circular ring is used to replace the winding.

[0015] Further, the constructed electromagnetic field simulation model is an electromagnetic-fluid multi-physics field coupling simulation model, including the following steps:

[0016] Step (1): Add the iron core, winding parameters, and magnetic permeability, construct an external equivalent circuit as the excitation source, select the eddy current solver, and obtain the loss distribution of the transformer through circuit and magnetic field coupling simulation;

[0017] Step (2): Import the electromagnetic field simulation model and the solution results into the fluid field, construct a fluid region in the fluid field, name the inlet and outlet and boundaries, and perform sub-grid meshing on the electromagnetic-fluid multi-physics field coupling simulation model to obtain good grids;

[0018] Step (3): Check in the fluid field whether the electromagnetic field simulation model meets the standards and whether the grid quality is good, select the energy field and the turbulence field as the solution models, use the winding as the excitation source of the fluid field, and establish a material library to set the parameters of the winding and the transformer oil;

[0019] Step (4): Design the boundary conditions, heat transfer surfaces, and fluid flow rates;

[0020] Step (5): Solve the electromagnetic-fluid multi-physics field coupling simulation model.

[0021] Further, the reduced-order model of the temperature field of the oil-immersed three-phase transformer obtained by the method based on the Krylov subspace is built, calculated on the MATLAB simulink platform, and compared with the electromagnetic-fluid field simulation results to verify the model error, including the following steps:

[0022] Step 41: Use the function command HBMAT in Fluent to make Fluent output the overall matrix in the Harwell-boeing format, and restore it to a full matrix through programming; use the command stream to extract the heat conduction matrix and the heat capacity matrix from the FULL file of ANSYS respectively and save them in the output file; in Matlab, use the file reading command to obtain the heat conduction matrix, the load column array, and the heat capacity matrix from the output file, so as to obtain the steady-state temperature field equation, as shown in Equation (1):

[0023]

[0024] In the formula: u(t) is the input variable, y(t) is the output variable, E, A, B, and C are all real matrices, and x(t) is the state variable. To take the first derivative of the state variables, the above is the state equation.

[0025] Perform a Laplace transform on the system to obtain the transfer function H (s) = C(sE - A) -1 B. Perform a Taylor expansion of the transfer function at s0, as shown in Equation (2):

[0026]

[0027] In the above equation: Starting from the second term, define C((A - s0E) -1 E) n (A - s0E) -1 B = M n , n = 1, 2,..., i is the nth moment of the system, and H(s) is the Taylor series expansion of the transfer function at s0;

[0028] Step 42. An r-dimensional Krylov subspace K r Consists of a positive definite matrix A and a vector b, that is, it is composed of a set of basis vectors. Define the subspace expression as follows: K r (A, b) = span{b, Ab,......A r-1 b}; For the normalized system, construct the following two subspaces, as shown in Equation (3):

[0029] K r1 ((A0 - s0E0) -1 E0; (A0 - s0E0) -1 B0), K r2 ((A0 - s0E0) -T E0 T ; (A0 - s0E0) -T C0 T ) (3)

[0030] In the above equation: K r1 and K r2 Are the constructed subspace 1 and subspace 2 respectively. E0, A0, B0, and C0 are all matrices of the system at s0, and T represents taking the transpose of the matrix;

[0031] Step 43. Construct their respective standard column orthogonal matrices according to the Arnoldi algorithm where q << n, as shown in Equation (4):

[0032]

[0033] In the equation: R n×qis an n×q real matrix, colspan{} represents obtaining an orthonormal basis. Based on the above V and W transformation matrices, a reduced-order model of the original system is obtained, as shown in Equation (5):

[0034]

[0035] In the formula: is the state variable, is the output variable, u(t) is the input vector, is the input matrix after reduction; the transfer function of the full-rank reduced-order models of V and W maintains the first r1 + r2 orders of the original system, and the model changes from n order to q order;

[0036] Step 44. Verify whether the model meets the requirements, including the following steps:

[0037] Deform the reduced-order equation to obtain the state-space equation, input the matrix into the state-space equation module in the MATLAB simulink platform, record the experimental data, and compare it with the calculation data of the full-order model before simulation. If the error is within 0.01%, it meets the requirements.

[0038] Furthermore, the constructed electromagnetic field simulation model is an electromagnetic-fluid multi-physics field coupling simulation model, which is to establish electromagnetic-fluid multi-physics field coupling analysis, set materials, boundary conditions, and solution domains in ANSYS software; including:

[0039] Step a. Implementation of obtaining the transformer loss through electromagnetic field simulation;

[0040] Step b. Implementation of obtaining the transformer temperature field distribution through electromagnetic field-fluid field.

[0041] Furthermore, the implementation of obtaining the transformer loss through electromagnetic field simulation includes:

[0042] ① Set parameters for the model iron core and winding, and set material properties;

[0043] ② Select the eddy current field solver, add windings on the circular cross-section according to the designed number of coil turns, and add an external circuit as the excitation source of the simulation model;

[0044] ③ Simulate the model to obtain the loss distribution of the model.

[0045] Furthermore, the implementation of obtaining the transformer temperature field distribution through electromagnetic field-fluid field includes:

[0046] ① Import the electromagnetic field model and its solution results into the fluid field, construct a fluid region in the fluid field, name the inlet, outlet, and boundaries, and perform subdomain mesh division on the model to obtain good meshes;

[0047] ② Check whether the model meets the standards and whether the grid quality is good in the fluid field, and select the energy field and the turbulence field as the solution models;

[0048] ③ The heat transfer inside the transformer is mainly carried out by heat conduction. For the eddy current loss solved by the electromagnetic field, select the winding as the excitation source of the fluid field, and establish a material library for the parameters of the winding and the transformer oil;

[0049] ④ Design the boundary conditions, heat transfer surfaces, and fluid flow velocities;

[0050] ⑤ Solve the model.

[0051] Furthermore, the setting of material properties includes: magnetic permeability and B-H curve.

[0052] A computer device includes a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor. When the processor executes the computer program, it implements the steps of any one of the above-mentioned methods for reducing the order of the transformer temperature field model based on the Krylov subspace.

[0053] A computer storage medium stores a computer program. When the computer program is executed by a processor, it implements the steps of any one of the above-mentioned methods for reducing the order of the transformer temperature field model based on the Krylov subspace.

[0054] The present invention has the following beneficial effects and advantages:

[0055] The present invention takes the winding as the research object, and obtains the temperature field distribution of the transformer winding through electromagnetic-fluid multi-physics field coupling analysis. The idea of model reduction is to project the large-scale state space of the physical model onto a low-dimensional space characterized by a set of basis vectors. For the above system, the present invention uses the method of Krylov subspace to reduce the order of the system, obtains the stiffness, mass, and damping matrices of the overall matrix of the system from the result file of Fluent, and constructs the state equation of the system based on the above matrices. Therefore, the problem of reducing the order of the system can be transformed into the problem of reducing the order of the state equation. For the reduction of this equation, the moments of the transfer functions of the two systems before and after reduction are kept maximally matched, and the Arnoldi algorithm well solves the problem of numerical instability in the direct moment matching method and better realizes the moment matching. Finally, the standard column orthogonal matrix of the above two subspaces is established through the Arnoldi algorithm, so as to obtain the reduced-order equation of the present state equation and realize the reduction of the model.

[0056] The present invention uses this reduced-order model to calculate the electromagnetic-fluid coupling field simulation, with significantly improved calculation efficiency, suitable for the rapid simulation calculation of the transformer temperature field, and further constructs a digital twin model of the transformer. Digital twin technology is an important means to realize the digital transformation of the power equipment industry. The method for reducing the order of the transformer temperature field model based on the Krylov subspace can achieve rapid simulation calculation of the physical field and further construct a digital twin model of the transformer.

[0057] The present invention accelerates the simulation efficiency and reduces the simulation time through the reduced-order model. This reduced-order model is better suitable for the construction of digital twins. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the following description of the embodiments in conjunction with the accompanying drawings, where:

[0059] Figure 1 is the flowchart for constructing the reduced-order model of the three-phase transformer temperature field based on the Krylov subspace of the present invention;

[0060] Figure 2 is the loss distribution diagram of the three-phase transformer of the present invention;

[0061] Figure 3 is the implementation diagram of the electromagnetic-fluid field of the present invention;

[0062] Figure 4 is the temperature field distribution diagram of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0063] In order to more clearly understand the above objects, features and advantages of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other.

[0064] Many specific details are set forth in the following description in order to fully understand the present invention. However, the present invention may be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0065] The following refers to Figures 1-4 to describe the technical solutions of some embodiments of the present invention.

[0066] Embodiment 1

[0067] The present invention provides an embodiment, which is a method for reducing the order of the transformer temperature field model based on the Krylov subspace. On the basis of the traditional finite element analysis simulation, the model of the system is reduced in order to achieve a faster response and be more suitable for the requirements of the digital twin for the model.

[0068] As shown Figure 1 in Figure 1 Figure

[0069] The present invention provides a method for reducing the order of a transformer temperature field model based on the Krylov subspace. Specifically, it includes the following steps:

[0070] Step 1: Establish a simulation physical model of an oil-immersed three-phase transformer. Subsequent physical field simulations are all completed based on the simplified simulation physical model. Specifically, according to the actual physical dimensions of the transformer, a 1:1 simulation model is constructed. Since the internal structure of the actual transformer is complex, and the field simulation involved in the present invention is only related to the iron core winding components, the model is simplified. According to the magnetic field invariance criterion, the winding is equivalent to a circular ring.

[0071] The specific method of equivalent the winding to a circular ring according to the magnetic field invariance criterion is to calculate the geometric dimensions of the transformer based on the transformer capacity and voltage parameters, establish a transformer simulation model, and simplify the winding according to the magnetic field invariance criterion, using a circular ring to replace the winding.

[0072] Step 2: Based on the simplified simulation physical model in Step 1, select the Maxwell 3D analysis module to construct an electromagnetic field simulation model, and use an eddy current solver to obtain the transformer loss distribution. As shown Figure 2 in Figure 2 Figure

[0073] The constructed electromagnetic field simulation model is an electromagnetic-fluid multi-physical field coupling simulation model, including the following steps:

[0074] Step (1): Add iron core and winding parameters, such as B-H curve and magnetic permeability, construct an external equivalent circuit as the excitation source, select an eddy current solver, and obtain the transformer loss distribution through circuit-magnetic field coupling simulation.

[0075] Step (2): Import the electromagnetic field simulation model and the solution results into the fluid field, and construct a fluid region in the fluid field to name the inlet, outlet, and boundaries. Perform sub-grid meshing on the electromagnetic-fluid multi-physical field coupling simulation model to obtain good meshes.

[0076] Step (3): Check whether the electromagnetic field simulation model meets the standards and whether the mesh quality is good in the fluid field. Select the energy field and turbulent field as the solution models, ignore the iron core, use the winding as the excitation source of the fluid field, establish a material library, and set the parameters of the winding and transformer oil, such as heat transfer coefficient and convective heat transfer coefficient, etc.

[0077] Step (4): Design the boundary conditions, heat transfer surface, and fluid flow rate.

[0078] Step (5): Finally, solve the electromagnetic-fluid multi-physics coupling simulation model.

[0079] Step 3: Use the obtained loss distribution as the excitation of the fluid field, establish a fluid field simulation model, realize the coupling analysis of the electromagnetic field and the fluid field, and obtain the temperature distribution of the oil-immersed three-phase transformer. As Figure 3 shown, Figure 3 is the implementation diagram of the electromagnetic-fluid field of the present invention. Based on the simulation calculation of the transformer electromagnetic-fluid field to obtain the temperature distribution, export the calculation results to the MATLAB Simulink platform to complete the subsequent construction of the reduced-order model of the temperature field.

[0080] Step 4: Build a reduced-order model for the temperature field of the obtained oil-immersed three-phase transformer based on the Krylov subspace method, calculate the reduced-order model on the MATLAB simulink platform, and compare it with the electromagnetic-fluid field simulation results to verify the model error. As Figure 4 shown, Figure 4 is the temperature field distribution diagram of the present invention.

[0081] Specifically, it includes the following steps:

[0082] Step 41. Using the function command HBMAT in Fluent, Fluent can output the global matrix in Harwell-boeing format, and restore it to a full matrix through programming. Then use the command stream to extract the heat conduction matrix and heat capacity matrix from the FULL file of ANSYS respectively, and save them in the corresponding output files Cond_File.dat and Cap_File.dat. In Matlab, using the file reading command, the heat conduction matrix and load column array can be obtained from the Cond_File.dat file, and the heat capacity matrix can be obtained from the Cap_File.dat file, so as to obtain the steady-state equation of the temperature field, as shown in Equation (1):

[0083]

[0084] In the formula: u(t) is the input variable, y(t) is the output variable, E, A, B, and C are all real matrices, x(t) is the state variable, is the first derivative of the state variable, and the above is the state equation.

[0085] Perform Laplace transform on the system to obtain the transfer function H(s) = C(sE - A) -1 B. Further perform Taylor expansion on the transfer function at s0, as shown in Equation (2):

[0086]

[0087] In the above formula: Starting from the second term, C((A - s0E) -1 E) n (A - s0E) -1 B = M n , n = 1, 2,..., i is the nth moment of the system, and H(s) is the Taylor series expansion of the transfer function at s0.

[0088] To better approximate the transfer functions of the reduced - order model system and the original system, it is necessary to match the first r moments of the reduced - order model system and the original system transfer function as much as possible. The Arnoldi algorithm obtains a standard column - orthogonal matrix, which can well solve the problem of numerical instability in the direct moment - matching method.

[0089] Step 42. An r - dimensional Krylov subspace K r is composed of a positive - definite matrix A and a vector b, and is also considered to be composed of a set of basis vectors. The subspace expression is defined as follows: K r (A, b) = span{b, Ab,......A r-1 b}. Correspondingly, for the normalized system of this example, the following two subspaces can be constructed, as shown in Equation (3):

[0090] K r1 ((A0 - s0E0) -1 E0; (A0 - s0E0) -1 B0), K r2 ((A0 - s0E0) -T E0 T ; (A0 - s0E0) -T C0 T ) (3)

[0091] In the above formula: K r1 and K r2 are the constructed subspace 1 and subspace 2 respectively. E0, A0, B0, and C0 are all matrices of the system at s0, and T represents the transpose of the matrix.

[0092] Step 43. Construct their respective standard column - orthogonal matrices according to the Arnoldi algorithm where q << n, as shown in Equation (4):

[0093]

[0094] In the formula: R n×q is an n×q real matrix, and colspan{} represents obtaining the standard orthogonal basis. Based on the above V and W transformation matrices, the reduced - order model of the original system can be obtained, as shown in Equation (5):

[0095]

[0096] Wherein: is the state variable, is the output variable, u(t) is the input vector, is the input matrix after order reduction. The transfer function of the full-rank reduced-order models of V and W maintains the first r1+r2 order moments of the original system, and the model changes from the nth order to the qth order.

[0097] Step 44. Verify whether the model meets the requirements, including the following steps:

[0098] Deform the equation after order reduction to obtain the state-space equation, input the matrix into the state-space equation module in the MATLAB simulink platform, record the experimental data, and compare it with the calculation data of the full-order model before simulation. If the error is within 0.01%, it meets the requirements.

[0099] Embodiment 2

[0100] The present invention provides an embodiment, which is a method for reducing the order of a transformer temperature field model based on the Krylov subspace, specifically including the following steps:

[0101] Step 1. Establish a simulation simplified model of an oil-immersed three-phase transformer, and equivalent the winding to a circular ring according to the magnetic field invariance criterion;

[0102] Establishing a simulation simplified model of an oil-immersed three-phase transformer, according to parameters such as the transformer capacity and voltage, the geometric dimensions of the transformer can be deduced, a transformer simulation model can be established, and according to the magnetic field invariance criterion, the winding is simplified, that is, the winding is replaced by a circular ring.

[0103] Step 2. Establish an electromagnetic-fluid multi-physics field coupling analysis in ANSYS software, and set materials, boundary conditions, solution domains, etc.;

[0104] Establish an electromagnetic-fluid multi-physics field coupling analysis in ANSYS software. The ANSYS workbench finite element analysis software has powerful functions for structural, fluid, thermal, electromagnetic and their mutual coupling analyses. Its project view function can combine the entire simulation process more closely, and complex multi-physics field analysis processes can be completed through simple steps, specifically including:

[0105] Step a. Realize the acquisition of transformer losses through electromagnetic field simulation.

[0106] ① Set parameters for the model iron core and winding, and set corresponding material properties, such as magnetic permeability, B-H curve, etc.

[0107] ② Select the eddy current field solver. According to the designed number of coil turns, add windings on the circular cross-section and add an external circuit as the excitation source of the simulation model.

[0108] ③ Simulate the model to obtain the loss distribution of the model.

[0109] Step b. Implementation of obtaining the temperature field distribution of the transformer through the electromagnetic field - fluid field.

[0110] ① Import the electromagnetic field model and its solution results into the fluid field, construct a fluid region in the fluid field, name the inlets and boundaries, and perform subdomain mesh division on the model to obtain good-quality meshes.

[0111] ② Check whether the model meets the standards and whether the mesh quality is good in the fluid field, and select the energy field and turbulent field as the solution models.

[0112] ③ The heat transfer inside the transformer is mainly carried out by heat conduction. Based on the eddy current loss solved by the electromagnetic field, select the windings as the excitation source of the fluid field, and establish a material library to set the parameters of the windings and transformer oil, such as the heat transfer coefficient and convective heat transfer coefficient.

[0113] ④ Design the boundary conditions, heat transfer surfaces, and fluid flow velocities.

[0114] ⑤ Finally, solve the model.

[0115] Step 3. Build a reduced-order model for the transformer temperature field based on the Krylov subspace method, reduce the order of the system model, and obtain a fast calculation method;

[0116] Building a reduced-order model for the transformer temperature field based on the Krylov subspace method includes:

[0117] The functional command HBMAT in the Fluent fluid flow analysis module can enable Fluent to output the global matrix in the Harwell-boeing file format, and it is a sparse matrix, which is restored to a full matrix through programming. Then use the command stream to extract the heat conduction matrix and heat capacity matrix from the. FULL file of ANSYS respectively, and save them in the corresponding output files Cond_File.dat and Cap_File.dat. In Matlab, using the file reading command, the heat conduction matrix and load column vector can be obtained from the Cond_File.dat file, and the heat capacity matrix can be obtained from the Cap_File.dat file, so as to obtain the steady-state equation of the temperature field, as shown in Equation (1).

[0118]

[0119] where: u(t) is the input variable, y(t) is the output variable, E, A, B, and C are all real matrices, and x(t) is the state variable. Taking the first derivative of the state variable, the above is the state equation.

[0120] Performing a Laplace transform on the system to obtain the transfer function H (s) = C(sE - A) -1 B. Further, perform a Taylor expansion of the transfer function at s0, as shown in Equation (2):

[0121]

[0122] In the above equation: starting from the second term, define C((A - s0E) -1 E) n (A - s0E) -1 B = M n , n = 1, 2,..., i is the nth moment of the system, and H(s) is the Taylor series expansion of the transfer function at s0.

[0123] To better approximate the transfer function of the reduced-order model system and the original system, it is necessary to match the first r moments of the transfer function of the reduced-order model system and the original system as much as possible. The Arnoldi algorithm (obtaining a standard column-orthogonal matrix) can well solve the problem of numerical instability in the direct moment matching method.

[0124] An r-dimensional Krylov subspace K r is composed of a positive definite matrix A and a vector b, and is also considered to be composed of a set of basis vectors. Define the subspace expression as follows: K r (A, b) = span{b, Ab,..., A r-1 b}. Correspondingly, for the normalized system of this example, the following two subspaces can be constructed, as shown in Equation (3):

[0125] K r1 ((A0 - s0E0) -1 E0; (A0 - s0E0) -1 B0), K r2 ((A0 - s0E0) -T E0 T ; (A0 - s0E0) -T C0 T ) (3)

[0126] In the above equation: K r1 and K r2 are the constructed subspace 1 and subspace 2 respectively, E0, A0, B0, and C0 are all matrices of the system at s0, and T represents taking the transpose of the matrix.

[0127] Their respective standard column orthogonal matrices can be constructed according to the Arnoldi algorithm where q << n, as shown in Equation (4):

[0128]

[0129] In the formula: R n×q is a real matrix of order n×q, colspan{} represents obtaining the standard orthogonal basis. Based on the above V and W transformation matrices, the reduced-order model of the original system can be obtained, as shown in Equation (5):

[0130]

[0131] In the formula: is the state variable, is the output variable, u(t) is the input vector, is the input matrix after reduction. The transfer function of the full-rank reduced-order models of V and W maintains the first r1 + r2 order distances of the original system, and the model changes from order n to order q.

[0132] Step 4. Verify the reduced-order model and propose a verification method for the reduced-order model, and determine whether the reduced-order model is reasonable by analyzing the error.

[0133] The specific verification method for the reduced-order model is to deform the reduced equation to obtain the state-space equation, input the matrix into the state-space equation module in the MATLAB simulink platform, record the experimental data, and compare it with the calculation data of the full-order model before simulation. If the error is within 0.01%, it meets the requirements.

[0134] Example 3

[0135] Based on the same inventive concept, an embodiment of the present invention further provides a computer device, including a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor. When the processor executes the computer program, the steps of any one of the reduced-order methods for the transformer temperature field model based on the Krylov subspace described in Embodiment 1 or 2 are implemented.

[0136] Example 4

[0137] Based on the same inventive concept, an embodiment of the present invention further provides a computer storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of any one of the reduced-order methods for the transformer temperature field model based on the Krylov subspace described in Embodiment 1 or 2 are implemented.

[0138] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) that contain computer-usable program code.

[0139] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate a means for implementing the functions specified in Figure 1 one or more of the flows Figure 1 or blocks or a combination of blocks.

[0140] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including an instruction means that implements the functions specified in Figure 1 one or more of the flows Figure 1 or blocks or a combination of blocks.

[0141] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are performed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one or more of the flows Figure 1 or blocks or a combination of blocks.

[0142] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent replacements can still be made to the specific embodiments of the present invention. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention shall be covered by the protection scope of the claims of the present invention.

Claims

1. A method for reducing the order of a transformer temperature field model based on the Krylov subspace, characterized in that: Including: Step 1: Establish a simulation physical model of an oil-immersed three-phase transformer. Subsequent physical field simulations are all completed based on the simplified simulation physical model. Specifically, according to the actual physical dimensions of the transformer, a 1:1 simulation model is constructed; the winding is equivalent to a circular ring according to the magnetic field invariance criterion; Step 2: Based on the simplified simulation physical model described in Step 1, select the Maxwell 3D analysis module to construct an electromagnetic field simulation model, and use the eddy current solver to obtain the transformer loss distribution; Step 3: Use the obtained transformer loss distribution as the excitation of the fluid field, establish a fluid field simulation model, realize the coupled analysis of the electromagnetic field and the fluid field, and obtain the temperature field distribution characteristics of the oil-immersed three-phase transformer; Based on the electromagnetic-fluid field simulation calculation of the transformer to obtain the temperature distribution, export the calculation results to the MATLAB Simulink platform to complete the subsequent construction of the reduced-order model of the temperature field; Step 4: Reduce the order of the reduced-order model of the transformer temperature field based on the Krylov subspace method and verify it; The method based on the Krylov subspace is used to construct a reduced-order model of the temperature field of the obtained oil-immersed three-phase transformer. Calculate the reduced-order model on the MATLAB simulink platform and compare it with the electromagnetic-fluid field simulation results to verify the model error, including: Step 41. Use the function command HBMAT in Fluent to make Fluent output the overall matrix in the Harwell-boeing format, and restore it to a full matrix through programming; Use the command stream to extract the heat conduction matrix and the heat capacity matrix from the FULL file of ANSYS respectively and save them in the corresponding output files; In Matlab, use the file reading command to obtain the heat conduction matrix, the load column matrix, and the heat capacity matrix from the output files, so as to obtain the steady-state equation of the temperature field, as shown in Equation (1): Where: u(t) is the input variable, y(t) is the output variable, E, A, B, and C are all real matrices, and x(t) is the state variable. Taking the first derivative of the state variable, the above is the state equation; performing a Laplace transform on the system to obtain the transfer function H (s) = C(sE - A) -1 ^(-1)B, performing a Taylor expansion of the transfer function at s0, as shown in Equation (2): In the above formula: Starting from the second term, \(C((A - s_0E)\) is defined successively -1 E) n (A - s_0E) -1 B = M n , n = 1, 2,..., i is the \(n\)th moment of the system, and \(H(s)\) is the Taylor series expansion of the transfer function at \(s_0\); Step 42. An \(r\)-dimensional Krylov subspace \(K\) r is composed of a positive definite matrix \(A\) and a vector \(b\), that is, it is defined by a set of basis vectors, and the subspace expression is: \(K\) r (A, b)=span{b, Ab,......A r-1 b}; For the normalized system, construct the following two subspaces, as shown in the following formula: K r1 ((A0 - s0E0) -1 E0; (A0 - s0E0) -1 B0), K r2 ((A0 - s0E0) -T E0 T ; (A0 - s0E0) -T C0 T )(3) In the above formula: K r1 and K r2 are respectively the constructed subspace 1 and subspace 2. E0, A0, B0, and C0 are all matrices of the system at s0. T represents taking the transpose of the matrix; Step 43. Construct their respective standard column orthogonal matrices V according to the Arnoldi algorithm, where q << n, as shown in the following formula: where: R n×q is an n×q real matrix, colspan{} represents obtaining an orthonormal basis. Based on the above V and W transformation matrices, a reduced-order model of the original system is obtained as shown in Equation (5): In the formula: is the state variable, is the output variable, u(t) is the input vector, is the input matrix after order reduction; The transfer functions of the full-rank reduced-order models V and W maintain the first r1 + r2 orders of the original system, and the model changes from the nth order to the qth order; Step 44. Verify whether the model meets the requirements, including: transforming the reduced-order equation into a state-space equation, inputting the matrix into the state-space equation module in the MATLAB simulink platform, recording the experimental data, and comparing it with the calculation data of the full-order model before simulation. If the error is within 0.01%, it meets the requirements.

2. A method for reducing the order of a transformer temperature field model based on the Krylov subspace according to claim 1, characterized in that: The specific method of equivalenting the winding to a circular ring according to the magnetic field invariance criterion is to calculate the geometric dimensions of the transformer based on the transformer capacity and voltage parameters, establish a transformer simulation model, and simplify the winding according to the magnetic field invariance criterion, and use a circular ring to replace the winding.

3. A method for reducing the order of a transformer temperature field model based on the Krylov subspace according to claim 1, characterized in that: The constructed electromagnetic field simulation model is an electromagnetic-fluid multi-physical field coupling simulation model, including the following steps: Step (1) Add the iron core, winding parameters, and magnetic permeability, construct an external equivalent circuit as the excitation source, select the eddy current solver, and obtain the transformer loss distribution through the coupled simulation of the circuit and the magnetic field; Step (2) Import the electromagnetic field simulation model and the solution results into the fluid field, construct a fluid region in the fluid field, name the inlet and outlet and the boundaries, and perform sub-grid meshing on the electromagnetic-fluid multi-physical field coupling simulation model to obtain good meshes; Step (3) Check whether the electromagnetic field simulation model meets the standards and whether the mesh quality is good in the fluid field, select the energy field and the turbulence field as the solution models, use the winding as the excitation source of the fluid field, and establish a material library to set the parameters of the winding and the transformer oil; Step (4) Design the boundary conditions, heat transfer surfaces, and fluid flow velocities; Step (5) Solve the electromagnetic-fluid multi-physical field coupling simulation model.

4. A method for reducing the order of a transformer temperature field model based on the Krylov subspace according to claim 1, characterized in that: The constructed electromagnetic field simulation model is an electromagnetic-fluid multi-physical field coupling simulation model, which is established in ANSYS software for electromagnetic-fluid multi-physical field coupling analysis, setting materials, boundary conditions, and solution domains. It includes the following steps: Step a. Realization of obtaining transformer losses through electromagnetic field simulation; Step b. Realization of obtaining the temperature field distribution of the transformer through electromagnetic field-fluid field.

5. A method for reducing the order of a transformer temperature field model based on the Krylov subspace according to claim 4, characterized in that: The realization of obtaining transformer losses through electromagnetic field simulation includes: ① Set parameters for the core and windings of the model and set material properties; ② Select the eddy current field solver, add windings on the circular cross-section according to the designed number of coil turns, and add an external circuit as the excitation source of the simulation model; ③ Simulate the model to obtain the loss distribution of the model.

6. A method for reducing the order of a transformer temperature field model based on the Krylov subspace according to claim 4, characterized in that: The realization of obtaining the temperature field distribution of the transformer through electromagnetic field-fluid field includes: ① Import the electromagnetic field model and its solution results into the fluid field, construct a fluid region in the fluid field, name the inlet, outlet, and boundaries, and perform sub-grid division on the model to obtain good grids; ② Check whether the model meets the standards and whether the grid quality is good in the fluid field, and select the energy field and turbulent field as the solution models; ③ The heat transfer inside the transformer is mainly carried out through heat conduction. Select the eddy current loss obtained by electromagnetic field solving, choose the winding as the excitation source of the fluid field, and establish a material library for the parameters of the winding and transformer oil; ④ Design boundary conditions, heat transfer surfaces, and fluid flow velocities; ⑤ Solve the model.

7. A method for reducing the order of a transformer temperature field model based on the Krylov subspace according to claim 5, characterized in that: The setting of material properties includes: magnetic permeability and B-H curve.

8. A computer device, comprising a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, characterized in that, When the processor executes the computer program, it realizes the steps of a method for reducing the order of a transformer temperature field model based on Krylov subspace according to any one of claims 1-7.

9. A computer storage medium, characterized in that: The computer storage medium stores a computer program, and when the computer program is executed by the processor, it realizes the steps of a method for reducing the order of a transformer temperature field model based on Krylov subspace according to any one of claims 1-7.

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