Transformer core and winding analysis method and system employing equivalent mechanical model

Abstract

The present invention relates to the technical field of electric power. Disclosed are a transformer core and winding analysis method and system employing an equivalent mechanical model. The method comprises: carrying out mathematical analysis of a transformer core and winding; by means of a linear magnetostrictive characteristic of a silicon steel sheet, analyzing a vibration mechanism of the transformer core; by means of winding mechanical stress and winding axial vibration, analyzing a vibration mechanism of the transformer winding; and on the basis of the analysis of the vibration mechanism of the transformer core and the analysis of the vibration mechanism of the winding, determining a transformer vibration propagation path, and determining the source of vibrational higher-order harmonics. According to the present invention, winding vibration displacement and the relationship between vibration acceleration and power supply current and working frequency are determined by performing equivalent mechanical model computation, a propagation path of transformer vibration signals is specified, and a comprehensive algorithm is formulated for transformer core vibration, laying a theoretical foundation for subsequent simulation research on transformer core vibration and winding vibration.

Description

Analysis method and system for transformer core and winding based on equivalent mechanical model Technical Field

[0001] The present invention relates to the field of electric power technology, and in particular to an analysis method and system for transformer cores and windings based on an equivalent mechanical model. Background Art

[0002] In recent years, with the construction of new power systems and the improvement of power grid intelligence, the safety and stability of transformers, as important electrical equipment for electromagnetic conversion and voltage transformation in power systems, are particularly important. As new power systems develop towards a high proportion of new energy, the number of newly operated transformers has increased sharply. Due to the complex structure, long working cycle, poor operating environment and other reasons, the large investment in transformers has brought huge safety hazards to the power grid. Ensuring the safe operation of transformers is one of the important tasks of power grid workers. In 2022, the State Council issued the "14th Five-Year Plan for a Modern Energy System", which further emphasized the need to coordinate the grid connection of a high proportion of new energy to fully ensure the safe and stable operation of the power system.

[0003] The vibration of the transformer mainly comes from the magnetostriction of the transformer core and the electromagnetic force acting on the winding. So far, although corresponding research results have been achieved in the study of transformer core vibration, a complete and feasible algorithm has not yet been formed. The electromagnetic and vibration characteristics of the transformer core still need to be further improved, and the vibration of the transformer core needs further research.

[0004] Summary of the Invention

[0005] In view of the problems existing in the existing analysis methods and systems for transformer cores and windings based on equivalent mechanical models, the present invention is proposed.

[0006] Therefore, the purpose of the present invention is to provide an analysis method and system for transformer core and winding based on an equivalent mechanical model, and to perform equivalent mechanical model calculation when a complete and feasible algorithm has not been developed for the vibration of the transformer core.

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0008] In a first aspect, an embodiment of the present invention provides an analysis method for transformer cores and windings based on an equivalent mechanical model, which includes performing mathematical analysis on the transformer core and windings, analyzing the vibration mechanism of the transformer core through the linear magnetostrictive characteristics of silicon steel sheets; analyzing the vibration mechanism of the transformer windings through mechanical force on the windings and axial vibration of the windings; determining the transformer vibration propagation path based on the analysis of the transformer core vibration mechanism and the winding vibration mechanism, and determining the source of the vibration higher harmonics.

[0009] As a preferred embodiment of the analysis method of the transformer core and winding based on the equivalent mechanical model described in the present invention, the mathematical analysis includes converting the transformer core and winding in an electromagnetic field and generating a vibration signal, and analyzing the transformer vibration propagation path and higher harmonics according to the characteristics of the vibration signal.

[0010] As a preferred embodiment of the method for analyzing transformer cores and windings based on an equivalent mechanical model described in the present invention, the analysis of the vibration mechanism of the transformer core includes laminating the transformer core using magnetically conductive silicon steel sheets and calculating the linear magnetostrictive characteristics of the silicon steel sheets. Laminating the transformer core means that the silicon steel sheets undergo a magnetostrictive effect under the action of an alternating magnetic flux, generating vibration noise. The spin motion of the extranuclear electrons within the silicon steel sheets generates a molecular current, and the direction of the molecular current is redirected by the action of an external magnetic field to align with the direction of the external magnetic field.

[0011] As a preferred solution of the analysis method of the transformer core and winding based on the equivalent mechanical model of the present invention, the linear magnetostrictive characteristics of the silicon steel sheet are calculated in the following specific steps:

[0012] When the transformer core is magnetized, the axial expansion and contraction of the core column can be expressed by the linear magnetostriction coefficient λ of the silicon steel sheet as follows: λ=Δl / l

[0013] Among them, Δl is the change in the axial expansion and contraction of the core column, l is the initial axial length of the core column, and λ is dimensionless and can be positive or negative. When λ>0, it indicates that the ferromagnetic material is elongated, and when λ<0, it indicates that the ferromagnetic material is contracted. The magnetostriction coefficient λ of the core in the alternating magnetic field will change with the change of the external magnetic field and is also affected by a certain ambient temperature. When the external magnetic field is too large, the ferromagnetic material will reach the saturation value λs during the magnetization process. The saturation magnetostriction coefficient λs is one of the important parameters of the core.

[0014] The unit volume force on the silicon steel sheet when the iron core is excited is:

[0015] Where f is the volume force density, J is the current density, B is the magnetic induction intensity, H is the magnetic field intensity, μ is the magnetic permeability, and τ is the volume density of the material;

[0016] When the iron core is in an unsaturated state, the unit volume force of the silicon steel sheet can be simplified to consider only the electromagnetic force caused by the magnetostrictive characteristics:

[0017] Among them, F mis the amplitude of the electromagnetic force caused by magnetostriction, ω is the frequency of the applied alternating electromagnetic field. Under an external AC electromagnetic field with a frequency of 50 Hz, the vibration caused by the magnetostriction of the iron core is based on a fundamental frequency of 100 Hz and is accompanied by higher harmonic frequency components.

[0018] As a preferred embodiment of the analysis method of the transformer core and winding based on the equivalent mechanical model described in the present invention, the analysis of the vibration mechanism of the transformer winding includes generating electromagnetic force under the action of leakage magnetic field when the current passes through the winding and calculating the equivalent mechanical model of the transformer winding, wherein the electromagnetic force refers to the decomposition of the leakage magnetic field of the transformer winding in three-dimensional space.

[0019] As a preferred solution of the analysis method of the transformer core and winding based on the equivalent mechanical model of the present invention, the equivalent mechanical model of the transformer winding is calculated, and the specific calculation process is:

[0020] The motion equation of the equivalent mechanical model is:

[0021] Among them, m i is the mass of the i-th coil, x i is the displacement of the i-th coil relative to the initial position, c i is the system friction coefficient of the i-th coil, k B 、k N K is the elastic coefficient of the insulation spacer at the winding end, i is the elastic coefficient of the i-th insulating spacer, F i is the axial electromagnetic force of the i-th coil under the action of the leakage flux, and g is the acceleration due to gravity;

[0022] The formula is simplified to:

[0023] in, is the friction force of the winding coil, Kx is the elastic force provided by the transformer pad, F is the magnitude of the winding electromagnetic force, and Mg is the gravity;

[0024] The formula for the electromagnetic force on the winding and the square of the current is: F=ai 2 =aI M 2 cos 2 ωt

[0025] Where ω is the power current frequency;

[0026] From the double angle formula 2cos2ωt=1+cos2ωt, we can get:

[0027] Where F is the magnitude of the electromagnetic force of the winding, Mg is the gravity, and the elastic coefficient of the pad changes with the compression state and is also affected by temperature. If the compression state and temperature are not considered, the elastic coefficient K is a constant. Then the motion equation can be regarded as a second-order linear ordinary differential equation, and its solution is the sum of the general solution of the corresponding homogeneous equation and the special solution of the inhomogeneous equation. The specific calculation process is:

[0028] Solving homogeneous equations:

[0029] Among them, A and θ are integration constants, is the natural frequency of the transformer winding. The natural frequency of the winding is related to the elastic modulus, mass and friction of the pad. That is, the natural frequency can be simplified to

[0030] The non-homogeneous equation can be decomposed into:

[0031] That is, the solution to the nonhomogeneous equation is:

[0032] Among them, the integral constants A and θ are the initial time t = 0, that is, x = 0, Winding vibration position

[0033] In the shift solution, the first term is the unsteady-state solution of the system, the decaying periodic component, the decay speed mainly depends on the friction and mass of the system, and the decay time constant is

[0034] Taking the second derivative of the winding vibration displacement solution, the winding acceleration signal is obtained as:

[0035] Among them, A is the integration constant, μ is the natural frequency of the transformer winding, ω is the frequency of the applied alternating electromagnetic field, the integration constant A and θ are at the initial moment t = 0, that is, x = 0,

[0036] As a preferred embodiment of the analysis method of the transformer core and winding based on the equivalent mechanical model described in the present invention, the method of determining the transformer vibration propagation path includes propagating the vibration through the rigid connector of the foot pad to the surface of the transformer box, the transformer core vibration is transmitted to the oil tank surface through the transformer oil, the transformer winding vibration is transmitted to the oil tank surface through the transformer oil, and the vibration between the winding and the core is transmitted to each other through the solid parts and the transformer oil. The method of determining the source of the vibration high harmonics includes determining it based on the generation of the vibration signal of the transformer body.

[0037] In the second aspect, an embodiment of the present invention provides a transformer core and winding analysis system based on an equivalent mechanical model, which includes: an analysis module, which performs mathematical analysis on the transformer core and winding, and analyzes the vibration mechanism of the transformer core through the linear magnetostrictive characteristics of silicon steel sheets; a path propagation module, which determines the transformer vibration propagation path based on the analysis of the transformer core vibration mechanism and the winding vibration mechanism, and determines the source of the vibration high-order harmonics.

[0038] In a third aspect, an embodiment of the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: when the processor executes the computer program, it implements any step of the above-mentioned analysis method of the transformer core and winding based on the equivalent mechanical model.

[0039] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, any step of the above-mentioned analysis method of the transformer core and winding based on the equivalent mechanical model is implemented.

[0040] The beneficial effects of the present invention are as follows: by utilizing the perspective of mathematical analysis to analyze the iron core and winding of the transformer, the vibration mechanism of the transformer core is analyzed through the expansion and contraction of the transformer iron core material; the vibration mechanism of the transformer winding is analyzed through the mechanical force of the winding and the axial vibration of the winding; based on the analysis of the vibration mechanism of the transformer iron core and the vibration mechanism of the winding, the vibration propagation path of the transformer is determined, and the source of the vibration high-order harmonics is determined; by calculating the equivalent mechanical model, the relationship between the winding vibration displacement and the vibration acceleration and the power supply current and the operating frequency is determined, the propagation path of the transformer vibration signal is clarified, and a complete algorithm is formulated for the vibration of the transformer iron core, which lays a theoretical foundation for subsequent simulation research on the vibration of the transformer iron core and the winding vibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive effort. Among them:

[0042] FIG1 is a flowchart of a transformer vibration propagation path of a transformer core and winding analysis method and system based on an equivalent mechanical model provided by an embodiment of the present invention.

[0043] FIG2 is a diagram of an equivalent mechanical model of a transformer winding according to a method and system for analyzing a transformer core and winding based on an equivalent mechanical model provided by an embodiment of the present invention.

[0044] FIG3 is a schematic diagram of electromagnetic forces acting on transformer windings according to a method and system for analyzing transformer core and windings based on an equivalent mechanical model provided by one embodiment of the present invention.

[0045] FIG4 is a diagram showing the magnetic flux leakage distribution of a transformer winding according to a method and system for analyzing a transformer core and winding based on an equivalent mechanical model provided by an embodiment of the present invention.

[0046] FIG5 is a diagram showing the internal structure of a computer device of a method and system for analyzing a transformer core and windings based on an equivalent mechanical model provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0047] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, the following detailed description of the specific embodiments of the present invention is given in conjunction with the accompanying drawings. It is obvious that the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in this field without creative work should fall within the scope of protection of the present invention.

[0048] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0049] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0050] The present invention is described in detail with reference to schematic diagrams. For ease of illustration, cross-sectional views of device structures may be partially enlarged and not to scale when describing embodiments of the present invention. Furthermore, the schematic diagrams are merely illustrative and should not limit the scope of the present invention. Furthermore, in actual production, the three-dimensional dimensions of length, width, and depth should be included.

[0051] In the description of the present invention, it should be noted that the terms "upper, lower, inner, and outer" and other references to orientations or positional relationships are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first, second, or third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0052] In this disclosure, unless otherwise specified or limited, the terms "mounted," "connected," and "connected" should be interpreted broadly. For example, they may refer to fixed, removable, or integral connections. They may also refer to mechanical, electrical, or direct connections, indirect connections through an intermediary, or internal communication between two components. Those skilled in the art will understand the specific meanings of these terms in this disclosure.

[0053] Example 1

[0054] 1 to 4 , which are the first embodiment of the present invention, provide a method for analyzing a transformer core and winding based on an equivalent mechanical model, including:

[0055] S1: Perform mathematical analysis on the transformer core and windings, and analyze the vibration mechanism of the transformer core through the linear magnetostrictive characteristics of silicon steel sheets.

[0056] Among them, the analysis of the transformer core and winding from the perspective of mathematical analysis includes converting the transformer core and winding in an electromagnetic field and generating vibration signals, and analyzing the transformer vibration propagation path and high-order harmonics based on the characteristics of the vibration signals.

[0057] Furthermore, the vibration mechanism of the transformer core is analyzed, including laminating the transformer core with magnetic silicon steel sheets and calculating the linear magnetostrictive characteristics of the silicon steel sheets. Laminating the transformer core means that the silicon steel sheets undergo magnetostrictive effect under the action of alternating magnetic flux, and generate vibration noise. The spin motion of the extranuclear electrons in the silicon steel sheets generates molecular current, and the direction of the molecular current is redirected by the action of the external magnetic field, and is consistent with the direction of the external magnetic field.

[0058] Furthermore, the linear magnetostrictive characteristics of the silicon steel sheet are calculated. The specific steps are as follows:

[0059] When the transformer core is magnetized, the axial expansion and contraction of the core column can be expressed by the linear magnetostriction coefficient λ of the silicon steel sheet as follows: λ=Δl / l

[0060] Among them, Δl is the change in the axial expansion and contraction of the core column, l is the initial axial length of the core column, and λ is dimensionless and can be positive or negative. When λ>0, it indicates that the ferromagnetic material is elongated, and when λ<0, it indicates that the ferromagnetic material is contracted. The magnetostriction coefficient λ of the core in the alternating magnetic field will change with the change of the external magnetic field and is also affected by a certain ambient temperature. When the external magnetic field is too large, the ferromagnetic material will reach the saturation value λs during the magnetization process. The saturation magnetostriction coefficient λs is one of the important parameters of the core.

[0061] The unit volume force on the silicon steel sheet when the iron core is excited is:

[0062] Where f is the volume force density, J is the current density, B is the magnetic induction intensity, H is the magnetic field intensity, μ is the magnetic permeability, and τ is the volume density of the material;

[0063] When the iron core is in an unsaturated state, the unit volume force of the silicon steel sheet can be simplified to consider only the electromagnetic force caused by the magnetostrictive characteristics:

[0064] Among them, F m is the amplitude of the electromagnetic force caused by magnetostriction, ω is the frequency of the applied alternating electromagnetic field. Under an external AC electromagnetic field with a frequency of 50 Hz, the vibration caused by the magnetostriction of the iron core is based on a fundamental frequency of 100 Hz and is accompanied by higher harmonic frequency components.

[0065] S2: Analyze the vibration mechanism of transformer winding through winding mechanical force and winding axial vibration.

[0066] Among them, the vibration mechanism of the transformer winding is analyzed through the mechanical force of the winding, including the electromagnetic force generated on the windings on both sides under the action of leakage magnetic field when the current passes through the winding. The electromagnetic force shows periodic changes with time. The leakage magnetic field of the transformer winding can be decomposed into horizontal and vertical components in three-dimensional space.

[0067] Furthermore, the vibration mechanism of the transformer winding is analyzed through the axial vibration of the winding, including the establishment of an equivalent mechanical model. The winding is composed of a coil and an insulating spacer. The calculation steps for establishing the equivalent mechanical model of the transformer winding are as follows:

[0068] The motion equation of the equivalent mechanical model is:

[0069] Among them, m i is the mass of the i-th coil, x i is the displacement of the i-th coil relative to the initial position, c i is the system friction coefficient of the i-th coil, k B 、k N K is the elastic coefficient of the insulation spacer at the winding end, i is the elastic coefficient of the i-th insulating spacer, F i is the axial electromagnetic force of the i-th coil under the action of the leakage flux, and g is the acceleration due to gravity;

[0070] The above formula can be simplified as follows:

[0071] in, is the friction force of the winding coil, Kx is the elastic force provided by the transformer pad, F is the magnitude of the electromagnetic force of the winding, and Mg is the gravity;

[0072] The formula for the electromagnetic force on the winding and the square of the current is: F=ai 2 =aI M 2 cos 2 ωt

[0073] Where ω is the power current frequency;

[0074] From the double angle formula 2cos2ωt=1+cos2ωt, we can get:

[0075] The elastic coefficient of the pad changes with the compression state and is also affected by temperature. If the compression state and temperature are not considered, and the elastic coefficient K is a constant, then the above motion equation can be regarded as a second-order linear ordinary differential equation, and its solution is the sum of the general solution of the corresponding homogeneous equation and the special solution of the inhomogeneous equation. The specific calculation process is:

[0076] Solving homogeneous equations:

[0077] Among them, A and θ are integration constants, is the natural frequency of the transformer winding. The natural frequency of the winding is related to the elastic modulus, mass and friction of the pad. That is, the natural frequency can be simplified to

[0078] The non-homogeneous equation can be decomposed into:

[0079] That is, the solution to the nonhomogeneous equation is:

[0080] Among them, the integral constants A and θ are at the initial time t = 0, that is, x = 0, In the above winding vibration displacement solution, the first term is the unsteady-state solution of the system, the decaying periodic component. The decay speed mainly depends on the friction and mass of the system. The decay time constant is From the first term, we can see that when the winding coil is heavier and the friction is smaller, the non-steady-state periodic component decays more slowly. Since the coil mass is larger and the inertia is greater, it is more difficult to return to a steady state. In oil-immersed transformers, the viscosity of the oil increases C, so the vibration of oil-immersed transformers is attenuated compared to dry-type transformers. The second term is the steady-state response of the system.

[0081] Taking the second derivative of the winding vibration displacement solution, the winding acceleration signal is obtained as:

[0082] Among them, A is the integration constant, μ is the natural frequency of the transformer winding, ω is the frequency of the applied alternating electromagnetic field, the integration constant A and θ are at the initial moment t = 0, that is, x = 0,

[0083] Winding vibration is affected by both natural vibration and forced vibration caused by electromagnetic force. The frequency of forced vibration caused by electromagnetic force is twice the frequency of excitation current. At the same time, the winding vibration acceleration is related to the elastic coefficient K of the pad. As mentioned above, the elastic coefficient is related to the compression state. Its value is affected by the winding preload and coil pressure, and the vibration situation is relatively complicated.

[0084] S4: Determine the transformer vibration propagation path and the source of the vibration high harmonics based on the analysis of the transformer core vibration mechanism and the winding vibration mechanism.

[0085] Among them, according to the analysis of the vibration mechanism of the transformer core and the winding, it is determined that the transformer vibration propagation path includes the transmission through the rigid connector of the foot pad to the surface of the transformer box, the transformer core vibration is transmitted to the oil tank surface through the transformer oil, and the transformer winding vibration is transmitted to the oil tank surface through the transformer oil. The vibration between the winding and the core can be transmitted to each other through solid parts and transformer oil. The source of the vibration high harmonics is determined to include the generation of the vibration signal of the transformer body.

[0086] Furthermore, the vibration signal of the transformer body will inevitably produce high-order harmonic components, which mainly come from the following aspects: the nonlinearity of the transformer core magnetostriction itself affects the change in the distance of the magnetic flux path; when the transformer core is saturated, it causes the change in magnetic permeability, and then the high-order harmonic content increases; there are high-order harmonic components in the transformer excitation current, and the high-order harmonic current components excite harmonic components in the magnetostriction of the silicon steel sheet and the vibration of the winding; the vibration caused by leakage magnetic field on the core, and the vibration of the oil tank wall caused by leakage magnetic field, etc.

[0087] In a preferred embodiment, a transformer core and winding analysis system based on an equivalent mechanical model includes an analysis module that analyzes the transformer winding vibration mechanism through winding mechanical force and winding axial vibration; a path propagation module that determines the transformer vibration propagation path based on the analysis of the transformer core vibration mechanism and the winding vibration mechanism, and determines the source of the vibration high-order harmonics.

[0088] The above-mentioned unit modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the corresponding operations of the above-mentioned modules.

[0089] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be shown in Figure 5. The computer device includes a processor, memory, communication interface, display screen, and input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner. The wireless manner may be achieved through WIFI, an operator network, NFC (near field communication), or other technologies. The display screen of the computer device may be a liquid crystal display or an electronic ink display screen. The input device of the computer device may be a touch layer covering the display screen, or may be a key, trackball, or touchpad provided on the computer device housing, or may be an external keyboard, touchpad, or mouse.

[0090] In summary, the present invention analyzes the core and winding of the transformer from the perspective of mathematical analysis, analyzes the vibration mechanism of the transformer core through the expansion and contraction of the transformer core material; analyzes the vibration mechanism of the transformer winding through the mechanical force of the winding and the axial vibration of the winding; determines the transformer vibration propagation path based on the analysis of the transformer core vibration mechanism and the winding vibration mechanism, and determines the source of the vibration high-order harmonics, determines the relationship between the winding vibration displacement and the vibration acceleration and the power supply current and the operating frequency by calculating the equivalent mechanical model, clarifies the propagation path of the transformer vibration signal, and formulates a complete algorithm for the vibration of the transformer core, laying a theoretical foundation for the subsequent simulation research of the transformer core vibration and the winding vibration.

[0091] Example 2

[0092] 1 to 4 , which are a second embodiment of the present invention, provide an analysis method for a transformer core and winding based on an equivalent mechanical model. To verify the beneficial effects of the present invention, a scientific demonstration is performed through simulation experiments.

[0093] The analysis of transformer winding vibration mechanisms through mechanical forces on the windings involves the electromagnetic force generated by the current flowing through the windings on both sides due to the effect of magnetic flux leakage. This electromagnetic force exhibits periodic variations over time, and the magnetic flux leakage of the transformer windings can be decomposed into horizontal and vertical components in three-dimensional space. In the two-dimensional leakage magnetic field distribution of a single-phase dual-winding system, the actual transformer winding can be approximately equivalent to a cylindrical structure. The magnetic flux leakage of the transformer windings can be decomposed into horizontal and vertical components in three-dimensional space. Since the horizontal component has the same effect on the transformer windings, the three-dimensional winding can be simplified to two dimensions for analysis, and the magnetic induction intensity B can be decomposed into B1 and B2 in the horizontal and vertical directions.

[0094] The vertical component B2 acts on the winding, generating a radial force F2 that expands the winding outward. Under long-term transformer loads or even short-circuit current shocks, this can cause the coils and spacers to shift, and even cause the winding to deform. The magnetic flux distribution shows that the B2 component reaches its maximum in the middle of the winding, generating a large radial force in the middle, where deformation is most severe. However, due to the relatively simple radial mechanical structure of the transformer, radial forces do not significantly affect the vibration of the winding. The horizontal component B1 acts on the winding, generating an axial force F1 that compresses and stretches the winding axis. The transformer's leakage flux is constantly changing, and the axial electromagnetic force on the winding changes with this flux change. The winding vibrates due to this dynamic electromagnetic force. Transformer windings are composed of coils and insulating spacers between them, and the two have significantly different mechanical characteristics, which complicates axial vibration.

[0095] Our technology is significantly different from existing technologies in terms of technical means, research objects, and research scope. The specific differences are shown in Table 1 below:

[0096] Table 1 Comparison with existing technology

[0097] In terms of transformer vibration analysis technology, existing technologies mainly use experimental testing to detect and predict vibration signals of the entire transformer. Its advantages are simple and intuitive operation and can be directly applied to equipment status detection. However, the sample size is limited, the results have large errors, and it is impossible to deeply study the inherent mechanism of vibration. In contrast, this patent uses mathematical analysis and computer simulation to distinguish and study the core and winding parts, and deeply analyze their vibration mechanisms and mutual influences. In terms of research content, this patent not only tests the vibration spectrum but also determines the propagation path and source of the vibration, with a more comprehensive research scope. Its innovation lies in the establishment of an equivalent mechanical model, which lays a theoretical foundation for calculation and provides possibilities for subsequent simulation research. Compared with simple experimental testing, this patent can achieve high fitting accuracy and more reliable results through calculation. This patent surpasses existing technologies in research ideas, technical means, and research scope. It is of great significance for in-depth understanding of transformer vibration mechanisms and the establishment of accurate prediction models. It lays a theoretical foundation and provides a new direction for subsequent research. Although the calculation is complex, its advantages and application prospects are clear.

[0098] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. An analysis method for transformer core and winding based on an equivalent mechanical model, characterized in that: include, Conduct mathematical analysis on the transformer core and windings, and analyze the transformer core vibration mechanism through the linear magnetostrictive characteristics of silicon steel sheets; The transformer winding vibration mechanism is analyzed through winding mechanical force and winding axial vibration; Based on the analysis of the transformer core vibration mechanism and the winding vibration mechanism, the transformer vibration propagation path is determined, and the source of the vibration high-order harmonics is identified.

2. The analysis method of transformer core and winding based on equivalent mechanical model as claimed in claim 1, characterized in that: The mathematical analysis includes converting the iron core and winding of the transformer in an electromagnetic field and generating a vibration signal, and analyzing the transformer vibration propagation path and high-order harmonics according to the characteristics of the vibration signal.

3. The analysis method of transformer core and winding based on equivalent mechanical model as claimed in claim 2, characterized in that: The analysis of the vibration mechanism of the transformer core includes laminating the transformer core with magnetic silicon steel sheets and calculating the linear magnetostrictive characteristics of the silicon steel sheets. Laminating the transformer core means that the silicon steel sheets produce a magnetostrictive effect under the action of an alternating magnetic flux and generate vibration noise. The spin motion of the extranuclear electrons in the silicon steel sheets generates a molecular current. The direction of the molecular current is turned by the action of an external magnetic field and is consistent with the direction of the external magnetic field.

4. The analysis method of transformer core and winding based on equivalent mechanical model as claimed in claim 3, characterized in that: The linear magnetostrictive characteristics of the silicon steel sheet are calculated in the following specific steps: When the transformer core is magnetized, the axial expansion and contraction of the core column can be expressed by the linear magnetostriction coefficient λ of the silicon steel sheet as follows: λ=Δl / l Among them, Δl is the change in the axial expansion and contraction of the core column, l is the initial axial length of the core column, λ is dimensionless and has positive and negative values. When λ>0, it indicates that the ferromagnetic material is elongated, and when λ<0, it indicates that the ferromagnetic material is contracted. The magnetostriction coefficient λ of the core in the alternating magnetic field will change with the change of the external magnetic field, and is also affected by a certain ambient temperature. When the external magnetic field is too large, the ferromagnetic material will reach the saturation value λs during the magnetization process. The saturation magnetostriction coefficient λs is one of the important parameters of the core. When the core is excited, the unit volume force on the silicon steel sheet is: Where f is the volume force density, J is the current density, B is the magnetic induction intensity, H is the magnetic field intensity, μ is the magnetic permeability, τ is the volume density of the material; When the iron core is in an unsaturated state, the unit volume force of the silicon steel sheet can be simplified to consider only the electromagnetic force caused by the magnetostrictive characteristics: Among them, F m is the amplitude of the electromagnetic force caused by magnetostriction, ω is the applied alternating electromagnetic field frequency. Under an applied alternating electromagnetic field with a frequency of 50 Hz, the vibration caused by magnetostriction of the iron core is based on a fundamental frequency of 100 Hz and is accompanied by high-order harmonic frequency components.

5. The analysis method of transformer core and winding based on equivalent mechanical model as claimed in claim 4, characterized in that: The analysis of the transformer winding vibration mechanism includes generating electromagnetic force under the action of magnetic leakage when the winding current passes through the winding and calculating the equivalent mechanical model of the transformer winding, wherein the electromagnetic force refers to the decomposition of the magnetic leakage of the transformer winding in three-dimensional space.

6. The analysis method of transformer core and winding based on equivalent mechanical model as claimed in claim 5, characterized in that: The transformer winding equivalent mechanical model is calculated, and the specific calculation process is as follows: The equation of motion of the equivalent mechanical model is: Among them, m i is the mass of the i-th coil, x i is the displacement of the ith coil relative to the initial position, c i is the system friction coefficient of the ith coil, k B , k N K is the elastic coefficient of the insulation spacer at the winding end, i is the elastic coefficient of the ith insulating spacer, F i is the axial electromagnetic force of the ith coil under the action of the leakage flux, and g is the gravitational acceleration; Simplify the formula to: in, is the friction force of the winding coil, Kx is the elastic force provided by the transformer pad, F is the magnitude of the winding electromagnetic force, and Mg is the gravity; The formula for the magnitude of the electromagnetic force on the winding and the square of the current is: You have 2 =aI M 2 Cart 2 ωt Where, ω is the power supply current frequency; From the double angle formula 2cos2ωt=1+cos2ωt we get: Among them, F is the magnitude of the electromagnetic force of the winding, Mg is the gravity, the elastic coefficient of the pad changes with the compression state, and is also affected by the temperature. If the compression state and temperature are not considered, the elastic coefficient K is a constant, then the motion equation can be regarded as a second-order linear ordinary differential equation, and its solution is the sum of the general solution of the corresponding homogeneous equation and the special solution of the non-homogeneous equation. The specific calculation process is: Solving homogeneous equations: Among them, A and θ are integration constants, is the natural frequency of the transformer winding. The natural frequency of the winding is related to the elastic modulus, mass and friction of the pad, that is, the natural frequency can be simplified to The non-homogeneous equation can be decomposed into: That is, the solution to the non-homogeneous equation is: Among them, the integral constants A and θ are the initial time t = 0, that is, x = 0, In the winding vibration displacement solution, the first term is the non-steady-state solution of the system, the decaying periodic component, the decay speed mainly depends on the friction and mass of the system, and the decay time constant is Taking the second derivative of the winding vibration displacement solution, the winding acceleration signal is obtained as follows: Among them, A is the integration constant, μ is the natural frequency of the transformer winding, ω is the frequency of the applied alternating electromagnetic field, the integration constant A and θ are at the initial time t = 0, that is, x = 0, 7. The analysis method of transformer core and winding based on equivalent mechanical model as claimed in claim 6, characterized in that: The method of determining the transformer vibration propagation path includes propagating the vibration through the rigid connector of the foot to the surface of the transformer box, the transformer core vibration is transmitted to the oil tank surface through the transformer oil, the transformer winding vibration is transmitted to the oil tank surface through the transformer oil, and the vibration between the winding and the core is transmitted to each other through the solid parts and the transformer oil. The method of determining the source of the vibration high-order harmonics includes determining it according to the generation of the transformer body vibration signal.

8. A transformer core and winding analysis system based on an equivalent mechanical model, based on the transformer core and winding analysis method based on an equivalent mechanical model according to any one of claims 1 to 7, characterized in that: include, The analysis module performs mathematical analysis on the transformer core and windings, and analyzes the transformer core vibration mechanism through the linear magnetostrictive characteristics of silicon steel sheets; The path propagation module determines the transformer vibration propagation path based on the analysis of the transformer core vibration mechanism and the winding vibration mechanism, and determines the source of the vibration high-order harmonics.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method for analyzing the transformer core and winding based on the equivalent mechanical model according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the analysis method of the transformer core and winding based on the equivalent mechanical model according to any one of claims 1 to 7 are implemented.

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