CN115422808A - Transformer temperature field model order reduction method based on Krylov subspace - Google Patents
Transformer temperature field model order reduction method based on Krylov subspace Download PDFInfo
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Abstract
The invention discloses a Krylov subspace-based transformer temperature field model reduction method, and belongs to the technical field of oil-immersed three-phase transformer temperature field simulation. The invention comprises the following steps: step 1, constructing an oil-immersed three-phase transformer simulation model according to the actual physical size of the transformer, and properly simplifying the model. And 2, establishing an electromagnetic field simulation model, and simulating to obtain transformer loss distribution by adopting an eddy current solver. And 3, taking the obtained transformer loss distribution as an excitation source of the fluid field, establishing a fluid field simulation model, realizing coupling analysis of the electromagnetic field and the fluid field, and obtaining the temperature field distribution characteristic of the oil-immersed three-phase transformer. And 4, building a reduced-order model for the temperature field of the transformer based on a Krylov subspace method. The method realizes the rapid simulation calculation of the physical field, reduces the simulation time consumption, and further constructs the digital twin model of the transformer.
Description
Technical Field
The invention belongs to the technical field of simulation of temperature fields of oil-immersed three-phase transformers, and particularly relates to a method for reducing the order of a temperature field model of a transformer based on a Krylov subspace, in particular to a method for reducing the order of a digital twin model of the temperature field of the transformer based on the Krylov subspace.
Background
The digital twin technology is gradually developed into various manufacturing industries from the original aerospace field, and shows good application prospect in the intelligent manufacturing field. The digital twin technology is used as a bridge to connect a physical world and a virtual world, and takes complex physical simulation, real-time data sharing and analysis, data processing and the like as key technologies to construct digital twin organisms of the physical world and the virtual world and display the physical state of the physical world in real time.
The transformer is used as an important component of a transformer substation, and the thermal characteristics of the transformer directly influence whether equipment can run safely and reliably. In the transformer operation process, winding and iron core all can produce eddy current loss under the effect of leakage magnetic field, and the inside electric current of winding and coil resistance interact produce ohmic loss, and these losses all turn into the heat to transmit the heat to external environment through transformer oil. As the grade and capacity of the transformer increase, its loss and temperature also gradually increase. The temperature of the transformer rises, the insulation aging is accelerated, the service life of the transformer is shortened, the accuracy of measuring the temperature of the winding hot point is improved, and the safe and stable operation of the transformer is ensured. The temperature of the current transformer is mainly measured on the wall surface and the oil temperature. The method for measuring the winding hot point temperature is to embed an optical fiber sensor in the winding, but the position of the hot point cannot be accurately positioned. Therefore, the temperature value of each point can be accurately calculated by carrying out temperature field simulation on the transformer. At present, although the temperature of each part of a transformer can be accurately simulated through physical field simulation, the simulation is long in time consumption and large in calculation amount, and is not suitable for constructing a digital twin body of the transformer.
For example: the existing patent number is 2021108220457, which is named as a converter transformer temperature field model construction method, a reduced-order model is constructed for a temperature field by adopting a dynamic modal decomposition method, the reduced-order model is also constructed on the basis of a calculated full-order model, but a snapshot matrix is further formed according to discrete time temperature data samples obtained through calculation, the selection requirement of the constructed snapshot matrix on discrete time points has relevance, and the number of the samples directly influences the calculation accuracy.
For another example: in the prior art, 2016 (052) 012: the ARNOLDI model order reduction method based on the Krylov-schur restarting technology is used for realizing model order reduction by adopting a Krylov subspace and an Arnoldi algorithm, but the ARNOLDI model order reduction method provides the problem that a stable order reduction system cannot be obtained at one time in the complex power system order reduction of the traditional Arnoldi algorithm.
Therefore, aiming at the defects in the prior art, a reduced-order model is constructed for the physical field, the calculated amount is reduced by sacrificing part of calculation precision within the range meeting the error, the calculation time is greatly reduced, and the defects in the conventional physical field calculation can be overcome.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a transformer temperature field model order reduction method based on a Krylov subspace. The method aims to achieve the invention aims of accelerating the simulation efficiency and reducing the simulation time consumption through a reduced-order model and being better suitable for building a digital twin body.
The technical scheme adopted by the invention for realizing the purpose is as follows:
a transformer temperature field model order reduction method based on a Krylov subspace comprises the following steps:
step 1: establishing a simulation physical model of the oil-immersed three-phase transformer, finishing calculation of subsequent physical field simulation based on the simplified simulation physical model, and specifically, establishing a 1:1 simulation model according to the actual physical size of the transformer; because the internal structure of the actual transformer is complex, the field simulation related to the invention is only related to the iron core winding component, so that the model is simplified, and the winding is equivalent to a circular ring according to the magnetic field invariance criterion;
and 2, step: based on the simplified simulation physical model in the step 1, selecting a Maxwell3D analysis module to construct an electromagnetic field simulation model, and obtaining transformer loss distribution by adopting an eddy current solver;
and 3, step 3: taking the obtained transformer loss distribution as the excitation of a fluid field, establishing a fluid field simulation model, realizing the coupling analysis of the electromagnetic field and the fluid field, and obtaining the temperature field distribution characteristic of the oil-immersed three-phase transformer; obtaining temperature distribution based on transformer electromagnetic-fluid field simulation calculation, and exporting the calculation result to a MATLABSimulink platform to complete subsequent temperature field reduced-order model building;
and 4, step 4: and (3) building a reduced order model for the transformer temperature field based on a Krylov subspace method, and reducing and verifying the order.
Furthermore, the winding is equivalent to a circular ring according to the magnetic field invariance criterion, specifically, the geometric size of the transformer is calculated according to the capacity and voltage parameters of the transformer, a transformer simulation model is established, the winding is simplified according to the magnetic field invariance criterion, and the circular ring is used for replacing the winding.
Furthermore, the constructed electromagnetic field simulation model is an electromagnetic-fluid multi-physical field coupling simulation model, and comprises the following steps:
adding iron cores, winding parameters and magnetic permeability, constructing an external equivalent circuit as an excitation source, selecting an eddy current solver, and obtaining loss distribution of the transformer through circuit and magnetic field coupling simulation;
step (2) introducing the electromagnetic field simulation model and the solving result into a fluid field, constructing a fluid region named inlet/outlet and a boundary in the fluid field, and performing fractional grid division on the electromagnetic-fluid multi-physical field coupling simulation model to obtain a good grid;
checking whether the electromagnetic field simulation model meets the standard and whether the grid quality is good in the fluid field, selecting an energy field and a turbulent flow field as solving models, taking a winding as an excitation source of the fluid field, and establishing a material library to set parameters of the winding and transformer oil;
designing boundary conditions, heat exchange surfaces and fluid flow rate;
and (5) solving the electromagnetic-fluid multi-physical-field coupling simulation model.
Furthermore, the method based on the Krylov subspace is used for building a reduced order model for the obtained temperature field of the oil-immersed three-phase transformer, the reduced order model is calculated on an MATLABstimulink platform, the comparison is carried out on the reduced order model and the simulation result of the electromagnetic-fluid field, and the model error is verified, and the method comprises the following steps:
step 41, utilizing a function command HBMAT in the Fluent to enable the Fluent to output an integral matrix in a Harwell-boeing format, and reducing the integral matrix into a full matrix through programming; respectively extracting a heat conduction matrix and a heat capacity matrix from a FULL file of ANSYS by using a command stream, and storing the heat conduction matrix and the heat capacity matrix in an output file; in Matlab, a file reading command is utilized to obtain a heat conduction matrix, a load array and a heat capacity matrix from an output file, so that a temperature field steady equation is obtained, wherein the equation is shown in formula (1):
in the formula: u (t) is an input variable, y (t) is an output variable, E, A, B, C are all real matrices, x (t) is a state variable,
to derive the first derivative of the state variable, the above is the state equation.
Performing Laplace transform on the system to obtain a transfer function H (s) ＝C(sE-A) -1 B at s 0 Taylor expansion is performed on the transfer function, as shown in equation (2):
in the above formula: c ((A-s) is defined in the order from the second item 0 E) -1 E) n (A-s 0 E) -1 B＝M n N =1,2, i is the nth moment of the system, and H(s) is the transfer function at s 0 Taylor series expansion of (1);
step 42. One r dimension Krylov subspace K r The subspace expression is defined by 1 positive definite matrix A and 1 vector b, namely a group of basis vectors as follows: k r (A,b)＝span{b,Ab,......A r-1 b }; the following two subspaces are constructed for the normalized system, as shown in equation (3):
K r1 ((A 0 -s 0 E 0 ) -1 E 0 ；(A 0 -s 0 E 0 ) -1 B 0 ),K r2 ((A 0 -s 0 E 0 ) -T E 0 T ；(A 0 -s 0 E 0 ) -T C 0 T ) (3)
in the above formula: k r1 And K r2 Subspace 1 and subspace 2,E, respectively, of construction 0 、A 0 、B 0 、C 0 Are all systems in s 0 T represents transposing the matrix;
step 43. Construct their respective standard columns according to Arnoldi's algorithmOrthogonal matrix
Wherein q is less than n, as shown in formula (4):
in the formula: r n×q The method is characterized in that the method is a real matrix of n × q orders, colspan { } represents obtaining a standard orthogonal base, and a reduced order model of an original system is obtained based on the V, W transformation matrix, as shown in formula (5):
in the formula:
is a variable of the state of the vehicle,
is the output variable, u (t) is the input vector,
the input matrix after the order reduction is obtained; the transfer function of the V and W full rank reduced model keeps the former r of the original system 1 +r 2 Step distance, the model is changed from n order to q order;
and 44, verifying whether the model meets the requirements, wherein the method comprises the following steps:
and (3) deforming the reduced equation to obtain a state space equation, inputting the matrix into a state space equation module in the MATLABstimulink platform, recording experimental data, comparing the experimental data with the calculated data of the full-order model before simulation, and meeting the requirement if the error is within 0.01%.
Furthermore, the constructed electromagnetic field simulation model is an electromagnetic-fluid multi-physical field coupling simulation model, and electromagnetic-fluid multi-physical field coupling analysis, material setting, boundary condition establishment and domain solving are established in ANSYS software; the method comprises the following steps:
step a, obtaining the implementation of the loss of a voltage device through electromagnetic field simulation;
and b, realizing the temperature field distribution of the voltage device by using the electromagnetic field-fluid field.
Further, the electromagnetic field simulation obtains the implementation of the loss of the voltage transformer, and comprises the following steps:
(1) setting parameters and material properties of the model iron core and the winding;
(2) selecting an eddy current field solver, adding a winding on the section of the circular ring according to the number of turns of the designed coil, and adding an external circuit as an excitation source of the simulation model;
(3) and (5) simulating the model to obtain the loss distribution of the model.
Further, the realization of the electromagnetic field-fluid field acquisition voltage device temperature field distribution comprises the following steps:
(1) introducing a model of an electromagnetic field and a solving result into a fluid field, constructing a fluid region in the fluid field, naming an entrance and an exit and a boundary, and performing fractional grid division on the model to obtain a good grid;
(2) checking whether the model meets the standard or not and whether the grid quality is good or not in the fluid field, and selecting an energy field and a turbulent flow field as solution models;
(3) the heat transfer in the transformer is mainly carried out in a heat conduction mode, the eddy current loss is solved through an electromagnetic field, a winding is selected as an excitation source of a fluid field, and parameters of a material library for the winding and transformer oil are established;
(4) designing boundary conditions, heat exchange surfaces and fluid flow rates;
(5) and solving the model.
Still further, the setting material properties include: permeability and B-H curve.
A computer device comprising a storage medium, a processor and a computer program stored on the storage medium and executable on the processor, the processor implementing any of the steps of the Krylov subspace-based transformer temperature field model reduction method when executing the computer program.
A computer storage medium having a computer program stored thereon, the computer program when executed by a processor implementing the steps of any of the above-described methods for Krylov subspace-based transformer temperature field model reduction.
The invention has the following beneficial effects and advantages:
the invention takes the winding as a research main body, and obtains the temperature field distribution of the transformer winding through electromagnetic-fluid multi-physical field coupling analysis. The idea of model order reduction is to project the large-scale state space of a physical model into a lower-dimensional space characterized by a set of basis vectors. Aiming at the system, the invention adopts a Krylov subspace method to reduce the order of the system, obtains the rigidity, the quality and the damping matrix of the whole matrix of the system from the Fluent result file, and can construct the state equation of the system based on the matrix. Thus, the problem of reducing the order of the system can be translated into reducing the order of the state equation. Aiming at the order reduction of the equation, the maximum matching of the moments of the transfer functions of the two systems before and after the order reduction is kept, and the Arnoldi algorithm well solves the problem of numerical instability in a direct moment matching mode and better realizes the matching of the moments. And finally, establishing the standard column orthogonal matrixes of the two subspaces through an Arnoldi algorithm, thereby obtaining a reduced order equation of the state equation and realizing the reduction of the model.
The invention uses the reduced-order model to calculate the electromagnetic-fluid coupling field simulation, the calculation efficiency is obviously improved, and the method is suitable for the rapid simulation calculation of the temperature field of the transformer so as to construct the digital twin model of the transformer. The digital twinning technology is an important means for realizing digital transformation in the power equipment industry, and the Krylov subspace-based transformer temperature field model order reduction method can realize rapid simulation calculation of a physical field and further construct a digital twinning model of a transformer.
According to the method, the simulation efficiency is accelerated through the reduced-order model, the simulation time consumption is reduced, and the reduced-order model can be better suitable for building a digital twin body.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of the construction of a Krylov subspace-based three-phase transformer temperature field reduced-order model according to the invention;
FIG. 2 is a graph of loss distribution for a three-phase transformer of the present invention;
FIG. 3 is a diagram of an implementation of the electromagnetic-fluid field of the present invention;
fig. 4 is a temperature field profile of the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
The solution of some embodiments of the invention is described below with reference to fig. 1-4.
Example 1
The invention provides an embodiment, in particular to a transformer temperature field model order reduction method based on a Krylov subspace, which is used for carrying out order reduction processing on a system model on the basis of traditional finite element analysis simulation, realizes faster response and is more suitable for requirements of a digital twin body on the model.
As shown in FIG. 1, FIG. 1 is a flow chart for constructing a reduced order model of a temperature field of a three-phase transformer based on a Krylov subspace.
The invention provides a transformer temperature field model order reduction method based on a Krylov subspace. The method specifically comprises the following steps:
step 1: establishing a simulation physical model of the oil-immersed three-phase transformer, finishing calculation of subsequent physical field simulation based on the simplified simulation physical model, and specifically, establishing a 1:1 simulation model according to the actual physical size of the transformer; because the internal structure of the actual transformer is complex, the field simulation related to the invention is only related to the iron core winding components, so that the model is simplified, and the winding is equivalent to a circular ring according to the magnetic field invariance criterion.
The winding is equivalent to a circular ring according to the magnetic field invariance criterion, specifically, the geometric dimension of the transformer is calculated according to the capacity and voltage parameters of the transformer, a transformer simulation model is established, the winding is simplified according to the magnetic field invariance criterion, and the circular ring replaces the winding.
Step 2: and (3) based on the simplified simulation physical model in the step (1), selecting a Maxwell3D analysis module to construct an electromagnetic field simulation model, and obtaining transformer loss distribution by adopting an eddy current solver. As shown in fig. 2, fig. 2 is a loss distribution diagram of the three-phase transformer of the present invention.
The constructed electromagnetic field simulation model is an electromagnetic-fluid multi-physical field coupling simulation model and comprises the following steps:
adding an iron core and winding parameters such as a B-H curve and magnetic permeability, constructing an external equivalent circuit as an excitation source, selecting an eddy current solver, and obtaining the loss distribution of the transformer through circuit and magnetic field coupling simulation.
And (2) introducing the electromagnetic field simulation model and the solution result into the fluid field, constructing a fluid region named inlet/outlet and a boundary in the fluid field, and performing fractional grid division on the electromagnetic-fluid multi-physical field coupling simulation model to obtain a good grid.
And (3) checking whether the electromagnetic field simulation model meets the standard or not and whether the grid quality is good or not in the fluid field, selecting an energy field and a turbulent flow field as solving models, neglecting an iron core, using a winding as an excitation source of the fluid field, and establishing a material library to set parameters of the winding and transformer oil, such as heat transfer coefficient, convection heat transfer coefficient and the like.
And (4) designing boundary conditions, heat exchange surfaces and fluid flow rate.
And (5) finally solving the electromagnetic-fluid multi-physical field coupling simulation model.
And step 3: and taking the obtained loss distribution as the excitation of the fluid field, establishing a fluid field simulation model, realizing the coupling analysis of the electromagnetic field and the fluid field and obtaining the temperature distribution of the oil-immersed three-phase transformer. Fig. 3 is a diagram showing an electromagnetic-fluid field implementation of the present invention, as shown in fig. 3. And obtaining temperature distribution based on the simulation calculation of the electromagnetic-fluid field of the transformer, and exporting the calculation result to a MATLABSimulink platform to complete the subsequent construction of a temperature field reduced-order model.
And 4, step 4: and (3) building a reduced-order model for the obtained oil-immersed three-phase transformer temperature field based on a Krylov subspace method, calculating the reduced-order model on an MATLABsimulink platform, comparing the reduced-order model with an electromagnetic-fluid field simulation result, and verifying a model error. Fig. 4 is a temperature field profile of the present invention, as shown in fig. 4.
The method specifically comprises the following steps:
and 41, outputting the whole matrix in a Harwell-boeing format by using the function command HBMAT in the Fluent, and restoring the Fluent to the full matrix through programming. And then, respectively extracting the heat conduction matrix and the heat capacity matrix from the FULL file of ANSYS by using a command stream, and storing the heat conduction matrix and the heat capacity matrix in corresponding output files Cond _ File. In Matlab, a read file command is used to obtain a heat conduction matrix and a load matrix from a Cond _ file.dat file, and a heat capacity matrix from a Cap _ file.dat file, so as to obtain a steady-state equation of a temperature field, as shown in equation (1):
in the formula: u (t) is an input variable, y (t) is an output variable, E, A, B, C are all real matrices, x (t) is a state variable,
to derive the first derivative of the state variable, the above is the state equation.
The system is subjected to Laplace transformation to obtain a transfer function H(s) = C (sE-A) -1 B further at s 0 Taylor expansion is performed on the transfer function, as shown in equation (2):
in the above formula: c ((A-s) is defined in the order from the second item 0 E) -1 E) n (A-s 0 E) -1 B＝M n N =1,2, i is the nth moment of the system, and H(s) is the transfer function at s 0 Is expanded by taylor series.
In order to better approximate the transfer function of the reduced-order model system to the original system, the front r-order moment of the transfer function of the reduced-order model system and the original system needs to be matched as much as possible. The Arnoldi algorithm obtains the standard column orthogonal matrix, and the problem of numerical instability of a direct moment matching mode can be well solved.
Step 42. One r dimension Krylov subspace K r Consisting of 1 positive definite matrix a and 1 vector b, also considered to consist of a set of basis vectors, the subspace expression is defined as follows: k r (A,b)＝span{b,Ab,......A r-1 b }. Accordingly, for this example, the normalization system may construct the following two subspaces, as shown in equation (3):
K r1 ((A 0 -s 0 E 0 ) -1 E 0 ；(A 0 -s 0 E 0 ) -1 B 0 ),K r2 ((A 0 -s 0 E 0 ) -T E 0 T ；(A 0 -s 0 E 0 ) -T C 0 T ) (3)
in the above formula: k r1 And K r2 Subspace 1 and subspace 2,E, respectively, of a construct 0 、A 0 、B 0 、C 0 Are all systems in s 0 T denotes transposing the matrix.
Step 43, constructing their respective standard column orthogonal matrixes according to Arnoldi algorithm
Wherein q < n, as shown in formula (4):
in the formula: r n×q The method is a real matrix of n × q orders, colspan { } represents obtaining a standard orthogonal base, and based on the V, W transformation matrix, a reduced order model of an original system can be obtained, as shown in formula (5):
in the formula:
is a variable of the state of the vehicle,
is the output variable, u (t) is the input vector,
is the input matrix after the reduction. The transfer function of the V and W full rank reduced model keeps the former r of the original system 1 +r 2 Step distance, the model changes from n order to q order.
And 44, verifying whether the model meets the requirements, wherein the method comprises the following steps:
and (3) deforming the reduced equation to obtain a state space equation, inputting the matrix into a state space equation module in the MATLABstimulink platform, recording experimental data, comparing the experimental data with the calculated data of the full-order model before simulation, and meeting the requirement if the error is within 0.01%.
Example 2
The invention provides an embodiment, and provides a transformer temperature field model order reduction method based on a Krylov subspace, which specifically comprises the following steps:
the method comprises the steps of establishing an oil-immersed three-phase transformer simulation simplified model, calculating the geometric size of a transformer according to parameters such as transformer capacity and voltage, establishing a transformer simulation model, and simplifying windings according to a magnetic field invariance criterion, namely replacing the windings with circular rings.
the method is characterized in that electromagnetic-fluid multi-physical field coupling analysis is established in ANSYS software, ANSYSworkbeam finite element analysis software has strong structure, fluid, heat, electromagnetism and mutual coupling analysis functions, and the project view function can more closely combine the whole simulation flow, and the complex multi-physical field analysis flow can be completed through simple steps, and the method specifically comprises the following steps:
and a, realizing the loss of the voltage transformer by electromagnetic field simulation.
(1) And setting parameters for the model iron core and the winding, and setting corresponding material attributes such as magnetic permeability, B-H curve and the like.
(2) And selecting an eddy current field solver, adding a winding on the section of the circular ring according to the number of turns of the designed coil, and adding an external circuit as an excitation source of the simulation model.
(3) And (5) simulating the model to obtain the loss distribution of the model.
And b, realizing the temperature field distribution of the voltage device by using the electromagnetic field-fluid field.
(1) And introducing the model of the electromagnetic field and the solving result into the fluid field, constructing a fluid region in the fluid field, naming an entrance and an exit and a boundary, and performing fractional grid division on the model to obtain a good grid.
(2) And checking whether the model meets the standard or not and whether the grid quality is good or not in the fluid field, and selecting an energy field and a turbulent flow field as solving models.
(3) The heat transfer in the transformer is mainly carried out in a heat conduction mode, the eddy current loss is solved through an electromagnetic field, a winding is selected as an excitation source of a fluid field, and a material library is established to set parameters of the winding and transformer oil, such as heat transfer coefficient and convection heat transfer coefficient.
(4) Design boundary conditions, heat exchange surfaces, and fluid flow rates.
(5) And finally solving the model.
a method based on a Krylov subspace is used for building a reduced order model for a transformer temperature field, and the method comprises the following steps:
the function command HBMAT in the Fluent fluid flow analysis module can enable Fluent to output an integral matrix in a Harwell-boeing file format, is a sparse matrix and is restored to a full matrix through programming. The heat conduction matrix and the heat capacity matrix are extracted from the FULL file of ANSYS by using the command stream, and stored in the corresponding output files Cond _ file. Using a read file command in Matlab, a heat conduction matrix and a load matrix can be obtained from the Cond _ file.
In the formula: u (t) is an input variable, y (t) is an output variable, E, A, B, C are all real matrices, x (t) is a state variable,
to derive the first derivative of the state variable, the above is the state equation.
Performing Laplace transform on the system to obtain a transfer function H (s) ＝C(sE-A) -1 B further at s 0 Taylor expansion is performed on the transfer function, as shown in equation (2):
in the above formula: sequentially defining C ((A-s) from the second item 0 E) -1 E) n (A-s 0 E) -1 B＝M n N =1,2, i is the nth moment of the system, and H(s) is the transfer function at s 0 Is expanded by taylor series.
In order to better approximate the transfer function of the reduced-order model system to the original system, the front r-order moment of the transfer function of the reduced-order model system and the original system needs to be matched as much as possible. The Arnoldi algorithm (obtaining a standard column orthogonal matrix) can well solve the problem of numerical instability of a direct moment matching mode.
One r dimension Krylov subspace K r Consisting of 1 positive definite matrix a and 1 vector b, also considered to consist of a set of basis vectors, the subspace expression is defined as follows: k r (A,b)＝span{b,Ab,......A r-1 b }. Accordingly, for this example, the normalization system may construct the following two subspaces, as shown in equation (3):
K r1 ((A 0 -s 0 E 0 ) -1 E 0 ；(A 0 -s 0 E 0 ) -1 B 0 ),K r2 ((A 0 -s 0 E 0 ) -T E 0 T ；(A 0 -s 0 E 0 ) -T C 0 T ) (3)
in the above formula: k r1 And K r2 Subspace 1 and subspace 2,E, respectively, of construction 0 、A 0 、B 0 、C 0 Are all systems in s 0 T denotes transposing the matrix.
Their respective orthonormal column orthogonal matrices can be constructed according to the Arnoldi algorithm
Wherein q < n, as shown in formula (4):
in the formula: r n×q The method is a real matrix of n × q orders, colspan { } represents obtaining a standard orthogonal base, and based on the V, W transformation matrix, a reduced order model of an original system can be obtained, as shown in formula (5):
in the formula:
is a variable of the state of the vehicle,
is the output variable, u (t) is the input vector,
is the input matrix after the reduction. The transfer function of the V and W full rank reduced model keeps the former r of the original system 1 +r 2 Step distance, the model changes from n order to q order.
And 4, verifying the reduced-order model, providing a verification method of the reduced-order model, and judging whether the reduced-order model is reasonable or not by analyzing errors.
The verification method of the reduced order model specifically comprises the steps of obtaining a state space equation through equation deformation after order reduction, inputting a matrix into a state space equation module in a MATLABsimulink platform, recording experimental data, comparing the experimental data with calculation data of the full order model before simulation, and meeting the requirement if the error is within 0.01%.
Example 3
Based on the same inventive concept, embodiments of the present invention also provide a computer device, which includes a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor. The processor, when executing the computer program, implements the steps of any one of the Krylov subspace-based transformer temperature field model order reduction methods described in embodiments 1 or 2.
Example 4
Based on the same inventive concept, an embodiment of the present invention further provides a computer storage medium, where a computer program is stored on the computer storage medium, and when the computer program is executed by a processor, the steps of the Krylov subspace-based transformer temperature field model reduction method described in embodiment 1 or 2 are implemented.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (10)
1. A transformer temperature field model order reduction method based on a Krylov subspace is characterized by comprising the following steps: the method comprises the following steps:
step 1: establishing a simulation physical model of the oil-immersed three-phase transformer, finishing calculation of subsequent physical field simulation based on a simplified simulation physical model, and specifically, establishing a 1:1 simulation model according to the actual physical size of the transformer; because the internal structure of the actual transformer is complex, the field simulation related to the invention is only related to the iron core winding component, so that the model is simplified, and the winding is equivalent to a circular ring according to the magnetic field invariance criterion;
step 2: based on the simplified simulation physical model in the step 1, selecting a Maxwell3D analysis module to construct an electromagnetic field simulation model, and obtaining transformer loss distribution by adopting an eddy current solver;
and step 3: taking the obtained transformer loss distribution as the excitation of a fluid field, establishing a fluid field simulation model, realizing the coupling analysis of the electromagnetic field and the fluid field, and obtaining the temperature field distribution characteristic of the oil-immersed three-phase transformer; obtaining temperature distribution based on transformer electromagnetic-fluid field simulation calculation, and exporting a calculation result to an MATLAB Simulink platform to complete subsequent temperature field reduced model building;
and 4, step 4: and (3) building a reduced order model for the transformer temperature field based on a Krylov subspace method, and reducing and verifying the order.
2. The Krylov subspace-based transformer temperature field model order reduction method as claimed in claim 1, wherein: the winding is equivalent to a circular ring according to the magnetic field invariance criterion, specifically, the geometric dimension of the transformer is calculated according to the capacity and voltage parameters of the transformer, a transformer simulation model is established, the winding is simplified according to the magnetic field invariance criterion, and the circular ring replaces the winding.
3. The Krylov subspace-based transformer temperature field model order reduction method as claimed in claim 1, wherein: the constructed electromagnetic field simulation model is an electromagnetic-fluid multi-physical field coupling simulation model and comprises the following steps:
adding iron cores, winding parameters and magnetic conductivity, constructing an external equivalent circuit as an excitation source, selecting an eddy current solver, and obtaining loss distribution of the transformer through circuit and magnetic field coupling simulation;
step (2) introducing the electromagnetic field simulation model and the solving result into a fluid field, constructing a fluid region named inlet/outlet and a boundary in the fluid field, and performing fractional grid division on the electromagnetic-fluid multi-physical field coupling simulation model to obtain a good grid;
checking whether the electromagnetic field simulation model meets the standard and whether the grid quality is good in the fluid field, selecting an energy field and a turbulent flow field as solving models, taking a winding as an excitation source of the fluid field, and establishing a material library to set parameters of the winding and transformer oil;
designing boundary conditions, heat exchange surfaces and fluid flow rate;
and (5) solving the electromagnetic-fluid multi-physical-field coupling simulation model.
4. The Krylov subspace-based transformer temperature field model order reduction method as claimed in claim 1, wherein: the method based on the Krylov subspace is used for building a reduced order model for the obtained temperature field of the oil-immersed three-phase transformer, calculating the reduced order model on an MATLAB simulink platform, comparing the reduced order model with an electromagnetic-fluid field simulation result, and verifying the model error, and comprises the following steps:
step 41, utilizing a function command HBMAT in the Fluent to enable the Fluent to output an integral matrix in a Harwell-boeing format, and reducing the integral matrix into a full matrix through programming; respectively extracting a heat conduction matrix and a heat capacity matrix from a FULL file of ANSYS by using a command stream, and storing the heat conduction matrix and the heat capacity matrix in corresponding output files; in Matlab, a file reading command is utilized to obtain a heat conduction matrix, a load array and a heat capacity matrix from an output file, so as to obtain a steady state equation of a temperature field, as shown in formula (1):
in the formula: u (t) is an input variable, y (t) is an output variable, E, A, B, C are all real matrices, x (t) is a state variable,
to solve the first derivative of the state variable, the above equation of state;
performing Laplace transform on the system to obtain a transfer function H (s) ＝C(sE-A) -1 B at s 0 Taylor expansion is performed on the transfer function, as shown in equation (2):
in the above formula: c ((A-s) is defined in the order from the second item 0 E) -1 E) n (A-s 0 E) -1 B＝M n N =1,2, i is the nth moment of the system, H(s) is the transfer function at s 0 Taylor series expansion of (1);
step 42One r-dimensional Krylov subspace K r The subspace expression is defined by 1 positive definite matrix A and 1 vector b, namely a group of basis vectors as follows: k r (A,b)＝span{b,Ab,......A r-1 b }; the following two subspaces are constructed for the normalized system, as shown in equation (3):
K r1 ((A 0 -s 0 E 0 ) -1 E 0 ；(A 0 -s 0 E 0 ) -1 B 0 ),K r2 ((A 0 -s 0 E 0 ) -T E 0 T ；(A 0 -s 0 E 0 ) -T C 0 T ) (3)
in the above formula: k r1 And K r2 Subspace 1 and subspace 2,E, respectively, of a construct 0 、A 0 、B 0 、C 0 Are all systems in s 0 T represents transposing the matrix;
step 43, constructing their respective orthonormal column orthogonal matrices V according to the Arnoldi algorithm,
wherein q < n, as shown in formula (4):
in the formula: r n×q The method is a real matrix of n × q order, colspan { } represents obtaining a standard orthogonal base, and based on the V, W transformation matrix, a reduced order model of an original system is obtained, as shown in formula (5):
in the formula:
is a variable of the state of the vehicle,
is the output variable, u (t) is the input vector,
the input matrix after the order reduction is obtained; the transfer function of the V and W full rank reduced model keeps the former r of the original system 1 +r 2 Step distance, the model is changed from n order to q order;
and 44, verifying whether the model meets the requirements, wherein the method comprises the following steps:
and (3) deforming the reduced equation to obtain a state space equation, inputting the matrix into a state space equation module in an MATLAB simulink platform, recording experimental data, comparing the experimental data with the calculated data of the full-order model before simulation, and meeting the requirement if the error is within 0.01%.
5. The Krylov subspace-based transformer temperature field model order reduction method as claimed in claim 1, wherein: the constructed electromagnetic field simulation model is an electromagnetic-fluid multi-physical field coupling simulation model, and is used for establishing electromagnetic-fluid multi-physical field coupling analysis, setting materials, boundary conditions and solving domains in ANSYS software; the method comprises the following steps:
step a, obtaining the implementation of the loss of a voltage device through electromagnetic field simulation;
and b, realizing the temperature field distribution of the voltage device by using the electromagnetic field-fluid field.
6. The Krylov subspace-based transformer temperature field model order reduction method according to claim 5, wherein: the implementation of obtaining the loss of the voltage device by electromagnetic field simulation comprises the following steps:
(1) setting parameters and material properties of the model iron core and the winding;
(2) selecting an eddy current field solver, adding a winding on the section of the circular ring according to the number of turns of the designed coil, and adding an external circuit as an excitation source of the simulation model;
(3) and (5) simulating the model to obtain the loss distribution of the model.
7. The Krylov subspace-based transformer temperature field model order reduction method according to claim 5, wherein: the realization of the electromagnetic field-fluid field acquisition voltage device temperature field distribution comprises the following steps:
(1) introducing a model of an electromagnetic field and a solving result into a fluid field, constructing a fluid region in the fluid field, naming an entrance and an exit and a boundary, and performing fractional grid division on the model to obtain a good grid;
(2) checking whether the model meets the standard and whether the grid quality is good in the fluid field, and selecting an energy field and a turbulent flow field as solving models;
(3) the heat transfer in the transformer is mainly carried out in a heat conduction mode, the eddy current loss is solved through an electromagnetic field, a winding is selected as an excitation source of a fluid field, and parameters of a material library for the winding and transformer oil are established;
(4) designing boundary conditions, heat exchange surfaces and fluid flow rates;
(5) and solving the model.
8. The Krylov subspace-based transformer temperature field model order reduction method as claimed in claim 6, wherein: the setting material properties include: permeability and B-H curve.
9. A computer device comprising a storage medium, a processor and a computer program stored on the storage medium and executable on the processor, wherein the processor when executing the computer program implements the steps of a Krylov subspace-based transformer temperature field model reduction method as claimed in any one of claims 1 to 8.
10. A computer storage medium, characterized by: the computer storage medium has a computer program stored thereon, which when executed by a processor implements the steps of a Krylov subspace-based transformer temperature field model reduction method as claimed in any one of claims 1 to 8.
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| CN117454805B (en) * | 2023-12-22 | 2024-03-19 | 浙江远算科技有限公司 | Fan wake influence calculation method and system based on fluid reduced-order simulation |
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