CN106570218A - Method for computing electromagnetic force of transformer iron core based on finite element method - Google Patents
Method for computing electromagnetic force of transformer iron core based on finite element method Download PDFInfo
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Abstract
The invention discloses a method for computing electromagnetic force of a transformer iron core based on a finite element method. The method comprises the steps that structural parameters of a winding, the iron core and a fuel tank of a transformer are collected, and then a three-dimensional geometric grid model of the transformer is established; the three-dimensional geometric grid model is input into software, sinusoidal currents with a phase different of 120 DEG are applied to the cross section of the three-phase low voltage winding respectively, and Dirichlet boundary conditions are applied to the outer side of the structural grid model; and an instant electromagnetic field is solved by a virtual displacement method, magnetic field energy is computed, a virtual work method is used to compute instant electromagnetic force borne by the transformer iron core and the winding, FFT is conducted to the instant electromagnetic force, and frequency domain distribution of the electromagnetic force of the iron core can be obtained. The computation method disclosed by the invention is direct and convenient; electromagnetic vibration and force bearing situations of the transformer iron core can be analyzed from the perspective of energy; each influential factor on force bearing of the iron core is considered comprehensively; and computation results are accurate and reliable.
Description
Technical field
The present invention relates to the analysis of transformer electromagnetic vibration noise and control technology field, and in particular to one kind is based on finite element
The transformer core electromagnetic force computational methods of method.
Background technology
Transformer core vibration is too big may to be caused iron core deformation, loosen, and temperature rise increase, these situations will have a strong impact on change
Depressor resists the ability of short-circuit current rush, affects transformer normally to run, in some instances it may even be possible to cause transformer damage, while also shadow
Ring the normal operation of AC network.Transformer noise is mainly derived from the electric and magnetic oscillation of transformer core, studies transformer core
Electromagnetism stress can be that transformer vibration control and Optimal Structure Designing provide foundation.
At present, the research of transformer core electric and magnetic oscillation mainly has the following aspects：
(1) research of transformer core Mode Shape
Transformer core is simulated in a large number, the mode resonance frequency of iron core is solved, so as to transformer can be made to avoid altogether
Shake, reduce transformer noise.Some scholars utilize impact of the finite element method analysis core lamination stack structural stratification to iron core, find to adopt
Lamination is simulated with different models affects very big to the result of calculation of transformer core mode of oscillation.Vibration-mode analysis are simultaneously
State of the power transformer product in actual moving process can not be reflected, in order to obtain more accurately and reliably simulation calculation, using having
The first method of limit obtains simulation of the large-scale power transformer in electromagnetism and the coupled vibrations of structure.But this aspect research is only limitted to transformer
The mode of oscillation of iron core, is not directed to the vibration of Transformer Winding.
(2) transformer core electricity magnet machine coupling numerical model
Analytical calculation has been carried out to transformer core magnetostriction and displacement.Consider magnetic and magnetostrictive anisotropy,
Set up transformer 3 D electromagnetic-structure close coupling numerical model.With reference to grain-oriented Si steel sheet magnetization, the measurement of Magnetostrictive Properties knot
Fruit carries out the FEM calculation of Distribution of Magnetic Field and vibration displacement to transformer core.The method only accounts for the mangneto of transformer and stretches
Contracting power and have ignored the impact to transformer core of reluctance force, not enough comprehensively.
(3) other researchs
Start with from the general principle of D.C. magnetic biasing mechanism and vibration noise, study a during transformer influenced by DC magnetic biasing
Specific research is carried out in a little groundwork states, the vibration and noise problem mainly for transformer core under D.C. magnetic biasing,
Electric field, magnetic field using finite element business software to transformer under D.C. magnetic biasing, the structure field of force, sound field carry out coupling calculating,
And Free Modal Analysis are carried out to transformer core, obtain intrinsic frequency and Mode Shape.The method mainly considers D.C. magnetic biasing
Impact to transformer core vibration, the other factors research to affecting core vibration is not comprehensive enough.
The content of the invention
The technical problem to be solved in the present invention is to provide a kind of transformer core electromagnetic force calculating side based on FInite Element
Method, the calculating of core vibration is more directly and convenient, from the angle analysis transformer core electric and magnetic oscillation stressing conditions of energy, entirely
Face considers each influence factor of iron core stress, and result of calculation is accurately and reliably.
In order to solve above-mentioned technical problem, the technical scheme that the present invention is provided is as follows：
A kind of transformer core electromagnetic force computational methods based on FInite Element, comprise the following steps：
1) structural parameters of the winding, iron core and fuel tank of transformer are gathered, transformer three-dimensional geometry grid model is built；
2) the three-dimensional geometry grid model of transformer is imported in Ansoft Maxwell softwares, setting transformer core,
Winding and transformer oil material properties；
3) the sine electricity of 120 degree of phase is applied on the three-phase low-voltage winding cross section in three-dimensional geometry grid model respectively
Stream, electric current is evenly distributed in winding cross section, and applies dirichlet series boundary condition to three-dimensional geometry grid model outside；Setting is treated
Electromagnetism force parameter, simulation time and dummy spacings time are asked, wink is solved using method of virtual displacement in Ansoft Maxwell softwares
State electromagnetic field, expression formula of the magnetic field energy in FEM calculation be：
Using method of virtual work calculating transformer iron core and electromagnetic force suffered by winding, the calculation expression of transient electromagnetic power is：
W is magnetic field energy in formula, and H is magnetic field intensity, and B is magnetic induction intensity, and Ω is derivation region, and μ is magnetic conductivity, and A is
Magnetic potential, x, y, z is respectively three directions of reference axis；F is transient electromagnetic power, and W (s, i) is the magnetic field energy of system, and i is foundation
The electric current in magnetic field, s is virtual displacement, and v is derivation space；
4) FFT is carried out to transient electromagnetic power, obtains the electromagnetic force frequency domain distribution of iron core.
The step 1) in structural parameters include internal diameter and external diameter, the radius of iron core, the iron of high pressure winding and low pressure winding
The length of pillar height degree, iron strategic point length and fuel tank.
The step 1) in build transformer three-dimensional geometry network model detailed process be：Build transformer three-dimensional geometry
Model, will winding be established as cylindrical tube shape, iron core is established as into entirety, ignore iron strategic point and iron prop between seam, by fuel tank letter
Turn to cuboid, fuel tank intersect with iron core, winding beyond part as transformer oil；Transformer 3-D geometric model is entered again
Row stress and strain model, completes transformer three-dimensional geometry network model structure.
The step 2) in material properties when arranging, iron core is set to into silicon steel material, and the stacking system of iron core is set
Number, density, magnetic conductivity, the magnetic conductivity of the setting iron core arranges iron core in rolling direction and the non-thread perpendicular to rolling direction
Property B-H magnetization curves；Winding is set to into copper product, and density of setting, electrical conductivity and setting high pressure winding and low pressure winding
The number of turn；Transformer oil is set to into insulating oil material, and relative conductivity, relative permeability are set.
According to below equation, the non-linear B-H magnetization curves of iron core are modified using interpolation iterative method：
Bσ=(μ+△ μ) H+ λ σ；
Wherein, △ μ represent magnetic conductivity correction value, λmFor the magnetostriction coefficient in the case of magnetic saturation, σ is stress, and μ is magnetic
Conductance, BmFor saturation induction density, BσFor the magnetic induction intensity under stress, H is magnetic field intensity, and λ is magnetostriction system
Number.
The step 4) in transient electromagnetic power is carried out to process transient electromagnetic force data before FFT, have
Body is：The transient electromagnetic force data for obtaining is removed into the oscillating part of beginning, stable state waveform is obtained, then stable state waveform is carried out
FFT.
The invention has the advantages that：
1st, computational methods are direct, simple and convenient, visual result；
2nd, from energy point of view, transformer core electric and magnetic oscillation stressing conditions are analyzed, iron core stress is considered comprehensively
Each influence factor, result of calculation is accurately and reliably；
3rd, can be used for the analysis of short circuit in winding vibration deformation, while alternatively the noise analysis of motor provides method and foundation.
Description of the drawings
Fig. 1 is transformer core X-direction stress oscillogram；
Fig. 2 is transformer core Y-direction stress oscillogram；
Fig. 3 is transformer core Z-direction stress oscillogram；
Fig. 4 is electromagnetic force frequency domain distribution of the transformer core in X-direction：Amplitude-frequency change；
Fig. 5 is electromagnetic force frequency domain distribution of the transformer core in X-direction：Phase angle-frequency change；
Fig. 6 is transformer core electromagnetic force frequency domain distribution in the Y direction：Amplitude-frequency change；
Fig. 7 is transformer core electromagnetic force frequency domain distribution in the Y direction：Phase angle-frequency change；
Fig. 8 is electromagnetic force frequency domain distribution of the transformer core in Z-direction：Amplitude-frequency change；
Fig. 9 is electromagnetic force frequency domain distribution of the transformer core in Z-direction：Phase angle-frequency change；
Specific embodiment
Below in conjunction with the accompanying drawings the invention will be further described with specific embodiment, so that those skilled in the art can be with
More fully understand the present invention and can be practiced, but illustrated embodiment is not as a limitation of the invention.
A kind of transformer core electromagnetic force computational methods based on FInite Element, with the change of 110kV oil immersed type three-phases double winding
Depressor as example, the electromagnetic force harmonic wave of calculating transformer iron core,
Step 1：Build the three-dimensional geometry grid model of transformer
The structural parameters of the winding, iron core and fuel tank of collection transformer, the structural parameters include high pressure winding and low pressure
The internal diameter and external diameter of winding, the radius of iron core, iron prop height, the length of iron strategic point length and fuel tank.First build three-dimensional several
What model, will winding be established as cylindrical tube shape；Iron core is made up of iron strategic point and iron prop, and iron core is established as into entirety, ignores iron strategic point
Seam and between iron prop；Fuel tank is reduced to into cuboid, the part beyond fuel tank intersects with iron core, winding is transformer oil；Again
Stress and strain model is carried out to transformer 3-D geometric model, transformer three-dimensional geometry network model structure is completed.
A diameter of 948mm～the 1111mm of the present embodiment mesohigh winding coil, low pressure winding coil diameter be 598mm～
710mm, the high 1216mm of winding coil, iron core diameter is 565mm, a height of 540mm of iron core yoke, and fuel tank volume is 5m*2m*3m, base
The 3-D geometric model of transformer is set up in said structure parameter.
Step 2：Transformer device structure parameter setting
This step is realized using FInite Element.The three-dimensional geometry grid model of transformer is imported into Ansoft Maxwell soft
In part, transformer core, winding and transformer oil material properties are set.
Iron core is set to silicon steel material, and arranges the material properties such as iron core stacking coefficient, density, magnetic conductivity, iron core
The setting of magnetic conductivity is：Iron core is set in rolling direction and the non-linear B-H magnetization curves perpendicular to rolling direction.Winding is arranged
For copper product, and the material properties such as density of setting, electrical conductivity and the number of turn of high pressure winding and low pressure winding is set.Transformer oil
Insulating oil material is set to, and the material properties such as relative conductivity, relative permeability are set.
To consider magnetostrictive effect, according to relative permeability and the electromagnetic relationship (formula 1-1) and stress and magnetic strength of stress
The relation (formula 1-2) of intensity is answered, using the non-linear B-H magnetization curves of interpolation iterative method amendment iron core：
Bσ=(μ+△ μ) H+ λ σ (1-2)
Wherein, △ μ represent magnetic conductivity correction value, λmFor the magnetostriction coefficient in the case of magnetic saturation, σ is stress, and μ is magnetic
Conductance, BmFor saturation induction density, BσFor the magnetic induction intensity under stress, H is magnetic field intensity, and λ is magnetostriction system
Number.
In the present embodiment, stacking coefficient takes 0.95, and it is 1 that stacking direction takes relative permeability, ignores the eddy current effect of iron core
Relative conductivity is taken as into 1, the relative permeability of Transformer Winding and transformer oil takes 1, transformer BH curve data such as table
1 and table 2 shown in.
The rolling direction B-H data of table 1
Table 2 is perpendicular to rolling direction B-H data
Step 3：Transient field analysis
Apply excitation and constraints, in three-dimensional geometry grid model, by 120 degree of sinusoidal current difference of phase
Three-phase low-voltage winding cross section is put on, electric current is evenly distributed in winding cross section；Because there is magnetic in high-power transformer oil tank wall inner side
Shielding, can regard boundary face as fuel tank magnetic cup body, apply dirichlet series boundary condition to three-dimensional geometry grid model outside, i.e.,
The magnetic line of force is parallel to structured grid model outer surface；
Electromagnetism force parameter to be asked, simulation time and dummy spacings time are set, are adopted in Ansoft Maxwell softwares
Method of virtual displacement solves transient electromagnetic field, and magnetic field energy is calculated by the potential function in magnetic field and obtained, and magnetic field energy is in FEM calculation
In expression formula be：
In formula：W is magnetic field energy, and H is magnetic field intensity, and B is magnetic induction intensity, and Ω is derivation region, and μ is magnetic conductivity, and A is
Magnetic potential, x, y, z are respectively three directions of reference axis.
Solution obtains magnetic density and energy storage and can further calculate the electromagnetic force with suffered by winding unshakable in one's determination, in calculating transformer
It is unshakable in one's determination and adopt the method for virtual work, the calculation expression of transient electromagnetic power to be suffered by winding during electromagnetic force：
In formula：H is magnetic field intensity, and B is magnetic induction intensity, and F is transient electromagnetic power, W (s, i) for system magnetic field energy, i
To set up the electric current in magnetic field, s is virtual displacement, and v is derivation space.
Calculating by more than can obtain each phase winding and iron core in the transient electromagnetic power suffered by X, Y, Z-direction.
In the present embodiment, apply the sinusoidal current of point 120 degree of phase, high pressure respectively on three-phase low-voltage winding cross section
Winding rated current is 165.3A, and low pressure winding rated current is 1818.7A, and high pressure winding is 737 circles per the phase number of turn, low pressure around
Group is 116 circles per the phase number of turn, and electric current is evenly distributed on section, and setting simulation time is 80mm, and every 0.2mm a number is calculated
Value, the electromagnetic force oscillogram after being stablized is as shown in Figure 1-Figure 3.
Step 4：Transient electromagnetic power FFT
The transient electromagnetic force data of step 3 gained iron core is exported as into .txt forms, importing MATLAB instruments carries out FFT changes
Change, obtain iron core electromagnetic force frequency domain distribution in the X, Y, Z direction.
Further, transient electromagnetic power is carried out being processed transient electromagnetic force data before FFT, will be obtained
To transient electromagnetic force data remove the oscillating part of beginning, obtain stable state waveform, then FFT is carried out to stable state waveform, most
Electromagnetic force frequency domain distribution situation is obtained eventually as shown in Fig. 4-Fig. 9.
The present embodiment is started with from transformer noise mechanism of production, the electric and magnetic oscillation stress of transformer core is analyzed, by wink
State electromagnetic field analysis, and the time domain waveform of electromagnetic force suffered by iron core is obtained based on method of virtual displacement, result is carried out using FFT
The major harmonic of electromagnetic force is obtained after process, from the angle of energy the electromagnetic force harmonic wave of transformer core is obtained, considered comprehensively
Each influence factor of iron core stress, result of calculation accurately and reliably, can provide foundation for the analysis of transformer electric and magnetic oscillation.
Embodiment described above is only the preferred embodiment lifted to absolutely prove the present invention, the protection model of the present invention
Enclose not limited to this.Equivalent substitute or conversion that those skilled in the art are made on the basis of the present invention, in the present invention
Protection domain within.Protection scope of the present invention is defined by claims.
Claims (6)
1. a kind of transformer core electromagnetic force computational methods based on FInite Element, is characterized in that, comprise the following steps：
1) structural parameters of the winding, iron core and fuel tank of transformer are gathered, transformer three-dimensional geometry grid model is built；
2) the three-dimensional geometry grid model of transformer is imported in Ansoft Maxwell softwares, transformer core, winding is set
With transformer oil material properties；
3) sinusoidal current of 120 degree of phase is applied on the three-phase low-voltage winding cross section in three-dimensional geometry grid model respectively,
Electric current is evenly distributed in winding cross section, and applies dirichlet series boundary condition to three-dimensional geometry grid model outside；Arrange and wait to ask
Electromagnetism force parameter, simulation time and dummy spacings time, transient state electricity is solved using method of virtual displacement in AnsoftMaxwell softwares
Magnetic field, expression formula of the magnetic field energy in FEM calculation be：
Using method of virtual work calculating transformer iron core and electromagnetic force suffered by winding, the calculation expression of transient electromagnetic power is：
W is magnetic field energy in formula, and H is magnetic field intensity, and B is magnetic induction intensity, and Ω is derivation region, and μ is magnetic conductivity, and A is magnetic potential,
X, y, z is respectively three directions of reference axis；F is transient electromagnetic power, and W (s, i) is the magnetic field energy of system, and i is to set up magnetic field
Electric current, s is virtual displacement, and v is derivation space；
4) FFT is carried out to transient electromagnetic power, obtains the electromagnetic force frequency domain distribution of iron core.
2. a kind of transformer core electromagnetic force computational methods based on FInite Element as claimed in claim 1, is characterized in that, institute
State step 1) in structural parameters include internal diameter and external diameter, the radius of iron core, iron prop height, the iron strategic point of high pressure winding and low pressure winding
The length of length and fuel tank.
3. a kind of transformer core electromagnetic force computational methods based on FInite Element as claimed in claim 1 or 2, its feature
Be, the step 1) in build transformer three-dimensional geometry network model detailed process be：Transformer 3-D geometric model is built,
Will winding be established as cylindrical tube shape, iron core is established as into entirety, ignore iron strategic point and iron prop between seam, by fuel tank be reduced to length
Cube, fuel tank intersect with iron core, winding beyond part as transformer oil；Again grid is carried out to transformer 3-D geometric model
Divide, complete transformer three-dimensional geometry network model structure.
4. a kind of transformer core electromagnetic force computational methods based on FInite Element as claimed in claim 1, is characterized in that, institute
State step 2) in material properties when arranging, iron core is set to into silicon steel material, and stacking coefficient, density, the magnetic of iron core are set
Conductance, the magnetic conductivity of the setting iron core arranges iron core and magnetizes in rolling direction and perpendicular to the non-linear B-H of rolling direction
Curve；Winding is set to into copper product, and the number of turn of density of setting, electrical conductivity and setting high pressure winding and low pressure winding；Will
Transformer oil is set to insulating oil material, and arranges relative conductivity, relative permeability.
5. a kind of transformer core electromagnetic force computational methods based on FInite Element as claimed in claim 4, is characterized in that, according to
Below equation, is modified using interpolation iterative method to the non-linear B-H magnetization curves of iron core：
Bσ=(μ+△ μ) H+ λ σ；
Wherein, △ μ represent magnetic conductivity correction value, λmFor the magnetostriction coefficient in the case of magnetic saturation, σ is stress, and μ is magnetic conductivity,
BmFor saturation induction density, BσFor the magnetic induction intensity under stress, H is magnetic field intensity, and λ is magnetostriction coefficient.
6. a kind of transformer core electromagnetic force computational methods based on FInite Element as claimed in claim 1, is characterized in that, described
Step 4) in transient electromagnetic power is carried out to process transient electromagnetic force data before FFT, specially：By what is obtained
Transient electromagnetic force data removes the oscillating part of beginning, obtains stable state waveform, then carries out FFT to stable state waveform.
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