CN111597681A - Three-phase group type transformer core vibration calculation method under direct-current magnetic biasing condition - Google Patents

Three-phase group type transformer core vibration calculation method under direct-current magnetic biasing condition Download PDF

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CN111597681A
CN111597681A CN202010272910.0A CN202010272910A CN111597681A CN 111597681 A CN111597681 A CN 111597681A CN 202010272910 A CN202010272910 A CN 202010272910A CN 111597681 A CN111597681 A CN 111597681A
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vibration
magnetic
magnetic field
transformer
direct current
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CN111597681B (en
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朱洪防
牛健飞
张凯
杨少辉
王恒
高涛
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Binzhou Power Supply Co of State Grid Shandong Electric Power Co Ltd
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F27/00—Details of transformers or inductances, in general
    • H01F27/24—Magnetic cores
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Abstract

The invention discloses a three-phase group type transformer core vibration calculation method under the condition of direct current magnetic biasing, which relates to the field of transformers and comprises the steps of establishing a magnetic field model and a vibration harmonic response model, wherein a vector magnetic potential A is calculated by using an edge finite element method, so that related parameters such as magnetic field intensity H and magnetic induction intensity B are obtained; calculating the vibration acceleration of the transformer core through vibration displacement by combining a dynamic equation met by the core during direct current intrusion; carrying out simulation calculation on the vibration conditions of typical test points of the transformer under different direct-current disturbances and summarizing rules; the method is helpful for analyzing the iron core vibration law of the transformer when suffering from direct current disturbance, and has the advantages of being scientific, reasonable, real, effective, accurate in calculation, high in practical value and the like.

Description

Three-phase group type transformer core vibration calculation method under direct-current magnetic biasing condition
Technical Field
The invention relates to the technical field of transformers, in particular to a method for calculating the vibration of a three-phase group type transformer core under a direct-current magnetic biasing condition, which is applied to fault operation and safety evaluation of a power transformer under direct-current disturbance.
Background
The power transformer is one of key devices of a power transmission system, and the safety and stability of the power transformer are very important for the operation of a power grid. Research shows that (quasi) direct current exists in a grounding transformer-power transmission line-ground loop of an alternating current power grid under the conditions of direct current transmission monopole ground loop operation and earth magnetic storm, and meanwhile, a certain direct current component possibly exists in the line due to application and popularization of a large-scale power electronic device, so that the alternating current power grid transformer operates in a special alternating current and direct current mixed environment. The (quasi-) direct current flowing into the transformer causes asymmetry of excitation of positive and negative half cycles of the iron core, and further produces serious magnetostriction effect, which leads to iron core saturation, aggravation of vibration, iron core looseness and winding deformation. Therefore, the research on the problem of the vibration of the transformer core in the alternating current and direct current mixed environment has important significance on the research on the fault operation and safety evaluation of the transformer.
Disclosure of Invention
Aiming at the defects, the technical problems to be solved by the invention are as follows: the method for calculating the vibration of the three-phase group type transformer core under the condition of scientific, reasonable, efficient, practical and accurate calculation can be provided, a transformer magnetic field model can be established according to actual parameters, a vector magnetic potential A is calculated by using an edge finite element method, and the magnetic field intensity H and the magnetic induction intensity B can be obtained on the basis; and calculating the vibration acceleration of the transformer core through vibration displacement by combining a dynamic equation satisfied by the core during the direct current intrusion.
In order to solve the technical problems, the technical scheme of the invention is as follows:
a method for calculating the vibration of a three-phase group type transformer core under the condition of direct current magnetic biasing comprises the following steps:
step one, establishing a magnetic field model:
the finite element method of the edge adopts a vector magnetic potential A, and obtains a nonlinear magnetic field equation according to Maxwell:
Figure BDA0002443751210000011
(1) in the formula, eta is magnetic conductivity, and J is excitation current density;
the degree of freedom of the edge unit is the loop quantity A of the field vector along the edge llUsing a vector shape function NlThe method comprises the following steps:
a unit:
Figure BDA0002443751210000021
integer of:
Figure BDA0002443751210000022
(2) wherein, MnN is 1,2, …, n is a sequence of basis functions, and is formed by a related unit shape function AlCorresponding superposition, n is the general number of the sequence of the basis functions, nnIs the total number of terms;
applying Green's theorem to equation (2) to obtain the Galerkin weighted margin equation:
Figure BDA0002443751210000023
(3) in the formula, MmIs a weight function sequence, and the weight function is the same as the basic function; the weight function of the edge element is taken into formula (3), the weighted residual equations are dispersed to form an algebraic equation set aiming at all the weight functions, and vector magnetic potential A on all the edges is obtained by solving; on the basis, the magnetic field intensity H and the magnetic induction intensity B can be obtained according to the satisfied boundary conditions;
step two, establishing a vibration harmonic response model:
in a magnetic field, the silicon steel sheets of the iron core of the power transformer are influenced by magnetostriction force to generate vibration; after the external magnetic field is removed, the magnetostrictive effect can be eliminated, the silicon steel sheet can recover the original shape and size, and the magnetostrictive force can be regarded as the problem of elastic mechanics; the problem of plane strain is seen when the deformation, stress, of each cross section of the elastomer is independent of the z direction, the relationship between stress and strain being:
e＝Ge(4)
(4) in the formula:eis the cell stress;eis the cell strain; g is an elastic matrix;
Figure BDA0002443751210000024
(5) wherein mu is Poisson's ratio; e is Young's modulus;
calculating the equivalent magnetostriction force F of the unit by combining with a magnetic field modele：
Fe＝∫J×Bdv (6)
Meanwhile, the vibration generated by the iron core during the direct current intrusion satisfies the following dynamic equation:
Figure BDA0002443751210000025
(7) in the formula: m is a model quality matrix; c is a model damping matrix; k is the unit mechanical stiffness; s is a unit displacement vector;
the vibration acceleration g can be calculated according to the vibration displacement:
Figure BDA0002443751210000031
after the technical scheme is adopted, the invention has the beneficial effects that:
the method for calculating the vibration of the iron core of the three-phase group type transformer under the direct-current magnetic biasing condition comprises the steps of establishing a magnetic field model and establishing a vibration harmonic response model, wherein on the basis of establishing a three-dimensional model of the three-phase group type transformer with the model size and the actual proportion of 1:1, the magnetic field model is used for calculating relevant parameters such as magnetic field intensity H and magnetic induction intensity B, and the vibration acceleration of the iron core is calculated by combining a dynamic equation of the transformer under direct-current disturbance; the method is helpful for analyzing the iron core vibration law of the transformer when suffering from direct current disturbance, and has the advantages of being scientific, reasonable, real, effective, accurate in calculation, high in practical value and the like.
Drawings
FIG. 1 is a three-phase transformer in an example embodiment;
fig. 2 is a circuit diagram of a three-phase transformer in a test case;
FIG. 3 is a schematic view of a test end in a test case;
fig. 4 is a wiring diagram of the experimental principle.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
A method for calculating the vibration of a three-phase group type transformer core under the condition of direct current magnetic biasing comprises the following steps:
step one, establishing a magnetic field model:
the finite element method of the edge adopts a vector magnetic potential A, and obtains a nonlinear magnetic field equation according to Maxwell (Maxwell equation):
Figure BDA0002443751210000032
(1) in the formula, eta is magnetic conductivity, and J is excitation current density;
the degree of freedom of the edge unit is the loop quantity A of the field vector along the edge llUsing a vector shape function NlThe method comprises the following steps:
a unit:
Figure BDA0002443751210000041
integer of:
Figure BDA0002443751210000042
(2) wherein, MnN is 1,2, …, n is a sequence of basis functions, and is formed by a related unit shape function AlCorresponding superposition, n is the general number of the sequence of the basis functions, nnTotal number of terms (number of edges);
applying Green's theorem to equation (2) to obtain the Galerkin weighted margin equation:
Figure BDA0002443751210000043
(3) in the formula, MmIs a weight function sequence, and the weight function is the same as the basic function; the weight function of the edge element is taken into formula (3), the weighted residual equations are dispersed to form an algebraic equation set aiming at all the weight functions, and vector magnetic potential A on all the edges is obtained by solving; on the basis, the magnetic field intensity H and the magnetic induction intensity B can be obtained according to the satisfied boundary conditions;
step two, establishing a vibration harmonic response model:
in a magnetic field, the silicon steel sheets of the iron core of the power transformer are influenced by magnetostriction force to generate vibration; after the external magnetic field is removed, the magnetostrictive effect can be eliminated, the silicon steel sheet can recover the original shape and size, and the magnetostrictive force can be regarded as the problem of elastic mechanics; the problem of plane strain is seen when the deformation, stress, of each cross section of the elastomer is independent of the z direction, the relationship between stress and strain being:
e＝Ge(4)
(4) in the formula:eis the cell stress;eis the cell strain; g is an elastic matrix;
Figure BDA0002443751210000044
(5) wherein mu is Poisson's ratio; e is Young's modulus;
calculating the equivalent magnetostriction force F of the unit by combining with a magnetic field modele：
Fe＝∫J×Bdv (6)
Meanwhile, the vibration generated by the iron core during the direct current intrusion satisfies the following dynamic equation:
Figure BDA0002443751210000045
(7) in the formula: m is a model quality matrix; c is a model damping matrix; k is the unit mechanical stiffness; s is a unit displacement vector;
the vibration acceleration g can be calculated according to the vibration displacement:
Figure BDA0002443751210000051
on the basis of establishing a three-phase combined transformer three-dimensional model with the model size and the actual ratio of 1:1, calculating relevant parameters such as magnetic field intensity H, magnetic induction intensity B and the like by using a magnetic field model, and calculating the vibration acceleration of an iron core by combining a power equation of the transformer under direct-current disturbance; the method is helpful for analyzing the iron core vibration law of the transformer when suffering from direct current disturbance, and has the advantages of being scientific, reasonable, real, effective, accurate in calculation, high in practical value and the like.
Test cases:
establishing a simulation model (parameters are shown in table 1) according to an actual 220V single-phase double-winding transformer, connecting a direct current source to a primary side to simulate direct current disturbance, calculating the electromagnetic property of the transformer, and generating a circuit model as shown in figure 2,
TABLE 1 Single-phase double-winding Transformer parameters
Data plate parameter Rated value Measured value
frequency/Hz 50 —
Total capacity SN/VA 1000 —
Voltage UN/V 220/110 —
No load current I0/A — 0.1
Single-phase iron core window/mm — 120×45×105
Single phase primary/secondary winding number 396/216 —
Single-phase primary/secondary side resistor/omega — 3.2/0.4
The DC current generated by the DC source connected to the primary side of the transformer is IDC(IDC＝αI0) The operation modes of the transformer under four direct-current disturbances of α ═ 0, 1.0, 2.0 and 3.0 are simulated respectively, the working mode of the transformer is full load, vibration simulation is performed on the iron core of the transformer, typical test points are selected and shown in figure 3 (taking phase A as an example), and the calculation results of the vibration acceleration under different direct-current disturbances are shown in table 2.
As can be seen from table 2, when the dc disturbance occurs, the vibration acceleration of each test point increases with the increase of the dc disturbance degree. The vibration amplitude of the test points 1, 3 and 4 is obviously larger than that of the test point 2, which shows that the vibration of the transformer core along the vertical direction of the main flux is larger than that along the parallel direction of the main flux.
TABLE 2 vibration acceleration under different DC disturbances
Figure BDA0002443751210000061
4. Experimental verification
In order to verify the correctness of the result obtained by simulation, a modularized moving die experiment platform is built, an experiment principle wiring diagram is shown in figure 4, and the specific experiment steps are as follows:
1) regulating a voltage regulator T1 in the voltage regulation module so that the voltage applied to the primary side of the transformer reaches a nominal value;
2) closing a direct current branch switch K at the direct current injection module, and changing the direct current injection size of a direct current voltage source Udc by adjusting a sliding rheostat Rd;
3) and a vibration monitoring module monitors the vibration condition of the iron core by adopting a piezoelectric acceleration sensor, and the selection of vibration measuring points is consistent with the distribution of test points in simulation calculation. During the experiment, the sensor contacts are adsorbed at different positions of the transformer core, and the vibration acceleration is monitored.
The vibration acceleration for each test point is shown in table 3.
TABLE 3 vibration acceleration under different DC disturbances
Figure BDA0002443751210000062
It can be seen that as the direct current level rises, the vibration acceleration of each test point of the iron core is gradually increased, and the vibration amplitudes of the test points 1, 3 and 4 are obviously greater than that of the test point 2, which shows that the vibration along the vertical direction of the main flux is more severe, the experimental result is consistent with the simulation result, and the correctness of the simulation result and the effectiveness of the method are verified.
According to the method for calculating the iron core vibration of the three-phase group type transformer under the direct-current magnetic biasing condition, simulation and experimental analysis results show that the method can be used for correctly calculating the iron core vibration acceleration of the transformer during normal operation and direct-current disturbance, so that the purpose of the invention is achieved and the effect is achieved.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention, and is not intended to limit the present invention, and any modifications made within the spirit and principle of the present invention, equivalent to the improvement of the method for calculating the vibration of the core of the three-phase transformer under the condition of dc magnetic bias, and the like, should be included in the scope of the present invention.

Claims (1)

1. A method for calculating the vibration of a three-phase group type transformer core under the condition of direct current magnetic biasing is characterized by comprising the following steps of:
step one, establishing a magnetic field model:
the finite element method of the edge adopts a vector magnetic potential A, and obtains a nonlinear magnetic field equation according to Maxwell:
Figure FDA0002443751200000011
(1) in the formula, eta is magnetic conductivity, and J is excitation current density;
the degree of freedom of the edge unit is the loop quantity A of the field vector along the edge llUsing a vector shape function NlThe method comprises the following steps:
a unit:
Figure FDA0002443751200000012
integer of:
Figure FDA0002443751200000013
(2) wherein, MnN is 1,2, …, n is a sequence of basis functions, and is formed by a related unit shape function AlCorresponding superposition, n is the general number of the sequence of the basis functions, nnIs the total number of terms;
applying Green's theorem to equation (2) to obtain the Galerkin weighted margin equation:
Figure FDA0002443751200000014
(3) in the formula, MmIs a weight function sequence, and the weight function is the same as the basic function; the weight function of the edge element is taken into formula (3), the weighted residual equations are dispersed to form an algebraic equation set aiming at all the weight functions, and vector magnetic potential A on all the edges is obtained by solving; on the basis, the magnetic field intensity H and the magnetic induction intensity B can be obtained according to the satisfied boundary conditions;
step two, establishing a vibration harmonic response model:
in a magnetic field, the silicon steel sheets of the iron core of the power transformer are influenced by magnetostriction force to generate vibration; after the external magnetic field is removed, the magnetostrictive effect can be eliminated, the silicon steel sheet can recover the original shape and size, and the magnetostrictive force can be regarded as the problem of elastic mechanics; the problem of plane strain is seen when the deformation, stress, of each cross section of the elastomer is independent of the z direction, the relationship between stress and strain being:
e＝Ge(4)
(4) in the formula:eis the cell stress;eis the cell strain; g is an elastic matrix;
Figure FDA0002443751200000021
(5) wherein mu is Poisson's ratio; e is Young's modulus;
calculating the equivalent magnetostriction force F of the unit by combining with a magnetic field modele：
Fe＝∫J×Bdv (6)
Meanwhile, the vibration generated by the iron core during the direct current intrusion satisfies the following dynamic equation:
Figure FDA0002443751200000022
(7) in the formula: m is a model quality matrix; c is a model damping matrix; k is the unit mechanical stiffness; s is a unit displacement vector;
the vibration acceleration g can be calculated according to the vibration displacement:
Figure FDA0002443751200000023
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Cited By (1)

* Cited by examiner, † Cited by third party
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CN113221397A (en) * 2021-03-23 2021-08-06 国网河北省电力有限公司沧州供电分公司 Method and device for calculating vibration displacement of iron core of electrical equipment and terminal equipment

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CN107317331A (en) * 2017-07-25 2017-11-03 华北电力大学 A kind of extra-high voltage transformer axial symmetry D.C. magnetic biasing simulation model
CN108629080A (en) * 2018-03-27 2018-10-09 东北电力大学 A kind of transformer core vibration calculating method under alternating current-direct current promiscuous mode
CN108984941A (en) * 2018-04-24 2018-12-11 国家电网公司 A kind of transformer winding vibration calculation method under alternating current-direct current promiscuous mode

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CN107317331A (en) * 2017-07-25 2017-11-03 华北电力大学 A kind of extra-high voltage transformer axial symmetry D.C. magnetic biasing simulation model
CN108629080A (en) * 2018-03-27 2018-10-09 东北电力大学 A kind of transformer core vibration calculating method under alternating current-direct current promiscuous mode
CN108984941A (en) * 2018-04-24 2018-12-11 国家电网公司 A kind of transformer winding vibration calculation method under alternating current-direct current promiscuous mode

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113221397A (en) * 2021-03-23 2021-08-06 国网河北省电力有限公司沧州供电分公司 Method and device for calculating vibration displacement of iron core of electrical equipment and terminal equipment
CN113221397B (en) * 2021-03-23 2023-10-31 国网河北省电力有限公司沧州供电分公司 Method and device for calculating vibration displacement of iron core of electrical equipment and terminal equipment

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