Method for determining the optimal measuring point of the sensor based on the vibration signal on the surface of the transformer box

Abstract

A method for determining the optimal measuring point of a sensor based on the vibration signal on the surface of a transformer box, and the technical field of transformer monitoring, determining the optimal installation position of a sensor based on the monitoring and analysis of the vibration signal of a transformer box. The method includes the following steps: (1) establishing a vibration characteristic model based on the vibration of the transformer core and winding; (2) calculating the attenuation coefficient of the transformer vibration sound in the medium according to the characteristics of the sound field propagation; (3) analyzing the vibration condition of the box when the vibration sound is transmitted to the box through the oil body according to the fluid-solid coupling model. Starting from the analysis of the vibration sound source, the present invention establishes a vibration sound propagation model, analyzes the propagation attenuation of the vibration sound in the medium, and theoretically calculates the attenuation coefficient of different measuring points. The present invention quantitatively calculates the response of different positions of the box to the actual vibration sound from the perspective of theoretical analysis; the present invention proposes to combine the sound signal propagation attenuation coefficient and the fluid-solid coupling model, and comprehensively considers the influence of the internal medium on the selection of measuring points.

Description

Technical Field

[0001] The invention relates to the technical field of transformer monitoring, in particular to a method for determining an optimal measuring point of a sensor based on a vibration signal on the surface of a transformer box. Background Art

[0002] Power transformers are very important power transmission and transformation equipment, and have always been the focus of monitoring and protection. 12% to 15% of all transformer faults are caused by deformation of windings and cores due to high electromotive force during short circuit. These geometric changes intensify the vibration of windings and cores, which will inevitably cause mechanical fatigue of solid insulation. As the running time increases, the solid insulation will gradually be damaged, causing phase-to-phase short circuits, turn-to-turn short circuits and ground short circuits between windings. The loss of proper insulation capacity is the main reason for the end of the life of most transformers. The vibration signal on the surface of the transformer oil tank is closely related to the compression, displacement and deformation state of the transformer windings and cores, which provides a basis for the selection of the location when installing the vibration sensor. Due to the different paths through which the vibration source inside the transformer propagates when generating vibration, different degrees of attenuation will occur, and the degree of attenuation will also vary depending on different propagation media and different propagation distances. In other words, the amplitude, phase and energy of the signals obtained at different measuring points on the transformer box are not the same. This provides the prerequisite for establishing different measuring point models. Actual measurements show that the vibration signals measured by the same vibration sensor at different locations on the transformer vary greatly, and the responses of each frequency band in the frequency domain also vary greatly. Therefore, to accurately identify faults, it is important to choose the optimal placement of the sensor to obtain more abundant vibration information.

[0003] At present, the experimental analysis and research on the selection of vibration measurement points on the transformer oil tank surface only considers relatively simple and superficial aspects such as the distribution of electromagnetic force, the strength of vibration signals, and signal-to-noise ratio, and has not conducted an in-depth analysis of the oil tank surface vibration signals and their monitoring. Summary of the invention

[0004] The object of the present invention is to provide a method for determining the optimal measuring point of a sensor based on a vibration signal on the surface of a transformer box, and to determine the optimal installation position of the sensor based on monitoring and analysis of the vibration signal of the transformer box.

[0005] The technical solution adopted by the present invention to solve the technical problem is: a method for determining the optimal measuring point of a sensor based on a vibration signal on the surface of a transformer box, comprising the following steps:

[0006] (1) Establish a vibration characteristic model based on the vibration of the transformer core and winding;

[0007] (2) Calculate the attenuation coefficient of transformer vibration sound in medium propagation based on the characteristics of sound field propagation;

[0008] (3) The vibration state when the vibration-acoustic sound propagates through the oil body to the box body is analyzed according to the fluid-solid coupling model. Furthermore, according to the transformer damping vibration equation Where m is the mass, γ is the damping, and k is the stiffness; Then formula (1) can be written as Among them, δ is the system damping coefficient, ω0 is the natural frequency; the solution of the equation is in Formula (3) indicates that the forced vibration under small damping is the superposition of damped vibration and simple harmonic motion. After a period of attenuation, the forced vibration enters a stable constant amplitude vibration. Formula (3) is X(ω)=H(ω)F(ω)(5), H(ω) is the complex response matrix of the system, which contains the characteristic information of the system, H(ω)=(K-ω 2 M+iωC) -1 ; When the frequency of the driving force is a certain value, the amplitude of the forced vibration reaches a maximum value and resonance occurs. The resonance frequency The vibration amplitude A changes with the frequency of the driving force. The vibration amplitude of the transformer core is proportional to the square of the no-load voltage. The electromagnetic force on the transformer winding is proportional to the square of the current, which is v. wind ∝(I 50 cos(2πft+φ u50,i50 )) 2 (6), v wind is the winding vibration amplitude. 50 is the maximum value of the power frequency current, and the initial phase of the load voltage is taken as the initial phase angle, v core ∝(U 50 cos(2πft+φ u50,i50 )) 2 (7), v core is the core vibration amplitude; U 50 is the maximum value of the power frequency voltage, i.e. A core ∝U s 2 (8), A wind ∝I m 2 (9); Ignoring the high-order harmonic components of the core vibration caused by the strong nonlinearity of the magnetostrictive phenomenon, the vibration model of the transformer box in the specified direction is simplified to v tank =c1v wind +c2v core (10) where v tank is the vibration amplitude of the box; c1 is the winding vibration coefficient; c2 is the core vibration coefficient.

[0009] Furthermore, ignoring the magnetizing current harmonic components and some redundant harmonic current components far less than 50Hz contained in the load current signal, ignoring the magnetizing voltage harmonic components and some redundant harmonic voltage components far less than 50Hz contained in the load voltage signal, the transformer box vibration amplitude is calculated using the following formula: where v tank is the vibration amplitude of the box, c1 is the winding vibration coefficient, c2 is the core vibration coefficient, I and U are the effective values ​​of the load current signal and the load voltage signal respectively; I N and U N They are the rated current and rated voltage of the corresponding transformer respectively.

[0010] Furthermore, according to the propagation equation of acoustic signals in the medium , p is the sound pressure (N / m 2 ), ρ c is the density (kg / m 3 ), ω is the angular frequency (rad / s), c c is the speed of sound (m / s), and the boundary load at the acoustic-structure boundary is defined as F = -n s p(13), F is the boundary load, n s is the unit direction outward from the solid domain; on the fluid side, the normal acceleration of the fluid is set equal to the normal acceleration of the solid, expressed as follows n a is the outward unit normal vector seen from the acoustic domain, a n is the normal acceleration; under the action of oil pressure, the expression of the transient structural sound intensity per unit area on the box surface is When the force F changes harmonically, the expression of the structural sound intensity per unit area is: Where ω is the circular frequency of the force and response; when a plane wave acts on the surface at a certain angle of incidence, I in , I out represents the boundary load and the acoustic effect at the measuring point, then The change in sound wave energy is the transmission loss and is expressed as

[0011] Furthermore, the damped vibration and the box vibration are combined to form a measurement point model. The vibration amplitude at time t1 is A0 and cos(ω f t1+φ) is a constant; δ is the damping coefficient, let B=A0 cos(ω f t1+φ), Define β as the attenuation coefficient of the measuring point model, then x = Bβ (21); use the following formula to calculate the attenuation coefficient of sound wave propagation: α is the air sound propagation attenuation coefficient, unit is m -1; K is the segment y1(t i ,i) The number of consecutive pairs of signals; A i , A i-1 is the peak amplitude value of the segmented signal corresponding to the i-th pair of front and back junctions; L i , L i-1 is the number of segmented data points of the i-th pair of segmented signals; f p is the sampling rate of the signal, in Hz; c is the speed of sound propagation in air, in m / s; B f is a coefficient related to the value of A. When A is the amplitude of the sound signal, then B f =1; when A is the absolute mean value and effective value of the signal segment, B is determined by calibration experiment f The value of; the amplitude of all vibrations on the box surface is The attenuation coefficient at different measuring points is α.

[0012] Furthermore, the attenuation coefficient α of different measuring points is obtained by the least squares identification method; the mathematical model of the least squares identification method is: The attenuation coefficients of the vibration signals at different measuring points of the box are calculated by the least squares identification method. The measuring points are numbered and sorted from small to large according to the corresponding attenuation coefficients. The measuring points with small attenuation coefficients are selected as the best measuring points for the vibration signals.

[0013] Furthermore, from the perspective of fluid-solid coupling analysis inside the transformer: M c is the mass matrix of the core, u c is the displacement matrix of the core, c is the damping matrix, K c is the stiffness matrix of the core, which is calculated from the material parameters and structural dimensions of the core, F is the external force causing vibration, and F max is the Maxwell force matrix, F mag is the magnetostrictive force matrix, and t is time. In the fluid-solid coupling effect, the force exerted by the fluid on the solid is divided into two parts, namely, the damping force and the inertial force. The inertial force refers to the additional mass of the fluid on the solid surface, and the damping force represents the damping effect of the fluid. Without considering other damping factors, the damping matrix c is only related to the damping force. The vibration frequency of the reactor core is mainly twice the operating voltage frequency, and the damping force is small and can be ignored. Formula (25) is simplified to M is the equivalent mass matrix of the core considering the additional mass and the core mass. The elastic dynamics equation under Lagrangian coordinates is used to describe its motion. The equilibrium equation of the initial configuration is: σ c is the deformation gradient tensor of the core, σ ca is the stress tensor, λ cis Lamé's first constant, μ c is the second Lamé constant, where is the shear modulus σ g is the strain tensor of the core ρ c is the density of the core material, g is the local gravitational acceleration, I is the unit tensor, and σ0 is σ c The determinant, E c and α c are Young's modulus and Poisson's ratio of the core material respectively; all components in the oil tank are immersed in transformer oil, which is an incompressible Newtonian fluid. The continuity equation in Lagrange-Euler coordinates is S is the surface area of ​​the core, μ0 is the velocity matrix of the transformer oil, n is the normal vector of the transformer core surface, μ g is the velocity matrix of the moving grid; when the attenuation coefficient is determined, combined with the internal fluid-solid coupling analysis, the optimal measuring point on the box surface is selected for vibration monitoring.

[0014] The beneficial effects of the present invention are:

[0015] (1) Starting from the analysis of the vibration and sound source, a vibration and sound propagation model is established to analyze the propagation attenuation of the vibration and sound in the medium, and the attenuation coefficients of different measuring points are theoretically calculated. The present invention quantitatively calculates the response of different positions of the box to the actual vibration and sound from the perspective of theoretical analysis;

[0016] (2) The present invention proposes to combine the sound signal propagation attenuation coefficient with the fluid-solid coupling model to comprehensively consider the influence of the internal medium on the selection of the measuring point;

[0017] (3) The accuracy of the measurement points selected by the present invention is relatively high, which has certain guiding significance for the operation and maintenance of transformers. The combined model can not only be used for the selection of transformer vibration measurement points, but also provide ideas for predictive modeling in other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic diagram of traditional damped vibration;

[0019] Figure 2 Schematic diagram of transformer damping vibration. DETAILED DESCRIPTION

[0020] The principle of the present invention is: first, analyze the vibration signal source and fixings of the transformer box under normal working conditions, including the iron core, winding, fixing clamps and box reinforcement ribs; then analyze the propagation attenuation process of the transformer vibration signal based on the vibration source and the sound wave propagation mechanism, and combine the influence of different media on the vibration signal to establish a vibration model of the vibration signal from the winding, iron core to the box; finally, comprehensively consider the propagation characteristics of different positions, select the minimum vibration signal propagation coefficient to determine the best box vibration signal monitoring position. The experimental and data analysis results show that this measuring point can effectively realize the collection of transformer vibration signals and the monitoring of operating status, which has certain guiding significance for the operation and maintenance of transformers.

[0021] 1. Establish a vibration characteristic model based on the vibration of the transformer core and winding

[0022] Transformer dynamic characteristics: The excitation of transformer winding and core vibration mainly comes from the Lorentz force, magnetostriction of silicon steel sheets and Maxwell stress of the air gap between silicon steel sheets. The vibration information of the winding is transmitted to the surface of the oil tank through the iron core and insulating oil; the vibration information of the iron core is indirectly transmitted to the surface of the oil tank through the solid connection between the iron core and the oil tank and the insulating oil. The transformer damped vibration equation is:

[0023]

[0024] Where m is mass, γ is damping, and k is stiffness;

[0025] make It can be written as

[0026]

[0027] Among them, δ is the system damping coefficient, ω0 is the natural frequency, and the solution of the equation is

[0028]

[0029] in

[0030] Equation (3) indicates that the forced vibration under small damping is the superposition of damped vibration (the first term on the right side of the equation) and simple harmonic motion (the second term on the right side of the equation). After a period of attenuation, the forced vibration enters a stable constant amplitude vibration.

[0031]

[0032] X(ω)=H(ω)F(ω) (5)

[0033] H(ω) is the complex response matrix of the system, which contains the characteristic information of the system. 2 M+iωC) -1When the frequency of the driving force is a certain value, the amplitude of the forced vibration will reach a maximum value and resonance will occur. The corresponding frequency is called the resonance frequency. The resonant frequency is generally not equal to the natural frequency. Only when the damping is very small, the resonant frequency is close to the natural frequency.

[0034] The vibration amplitude A changes with the frequency of the driving force. The vibration amplitude of the transformer core is proportional to the square of the no-load voltage, and the electromagnetic force on the transformer winding is proportional to the square of the current, which is:

[0035] v wind ∝(I 50 cos(2πft+φ u50,i50 )) 2 (6)

[0036] Among them, v wind is the winding vibration amplitude; I 50 is the maximum value of the power frequency current; φ 50 is the phase angle between the load current and the load voltage, and the initial phase of the load voltage is taken as the initial phase angle.

[0037] v core ∝(U 50 cos(2πft+φ u50,i50 )) 2 (7)

[0038] Where: v core is the core vibration amplitude; U 50 It is the maximum value of the power frequency voltage.

[0039] Right now

[0040] A core ∝U s 2 (8)

[0041] A wind ∝I m 2 (9)

[0042] Since only the fundamental frequency component of the transformer box vibration is studied, and the strong nonlinearity of the magnetostrictive phenomenon makes it difficult to express the high-order harmonic components of the core vibration, the above formula has no actual physical meaning for the high-order harmonic components. The vibration model in the specified direction can be simplified to

[0043] v tank =c1v wind +c2v core (10)

[0044] Where: v tank is the vibration amplitude of the box; c1 is the winding vibration coefficient; c2 is the core vibration coefficient.

[0045] Since the load current signal contains magnetizing current harmonic components and some redundant harmonic current components, but is much smaller than the 50Hz current component, the load voltage is similar, so the transformer box vibration amplitude is

[0046]

[0047] I and U are the effective values ​​of the load current signal and the load voltage signal respectively; I N and U N They are the rated current and rated voltage of the corresponding transformer respectively.

[0048] 2. Calculate the attenuation coefficient of transformer vibration sound in medium propagation based on the characteristics of sound field propagation

[0049] The transformer vibration signal is transmitted to the tank wall in the form of longitudinal waves in the insulating oil. Only the component of the vibration wave perpendicular to the tank wall contributes to the vibration of the tank wall. Considering factors such as propagation distance and vibration attenuation, the vibration acceleration of a point on the transformer tank wall can be approximated by the single longitudinal wave contribution of its vertical vibration source.

[0050] According to the Helmholtz equation, the propagation equation of the acoustic signal in the medium is:

[0051]

[0052] Where p is the sound pressure (N / m 2 ), ρ c is the density (kg / m 3 ), ω is the angular frequency (rad / s), c c is the speed of sound (m / s).

[0053] The boundary load at the acoustic-structure boundary is defined as

[0054] F=-n s p (13)

[0055] Where F is the boundary load, which is the magnetostrictive force applied to the core and the Lorentz force on the winding in the calculation of oil-immersed transformer; n s Is the unit direction outward as seen from the entity domain.

[0056] On the fluid side, the normal acceleration of the fluid is set equal to the normal acceleration of the solid, which is mathematically expressed as

[0057]

[0058] n a is the outward unit normal vector seen from the acoustic domain, a n is the normal acceleration.

[0059] The vibration and sound of the transformer are essentially mechanical waves, which appear as sound waves in fluid media and as vibration waves in solid media. Different from the transmission wave pattern of vibration in air and oil media, when vibration is transmitted in solid, it is transmitted simultaneously as two waves with different phases, namely transverse wave and longitudinal wave. In order to measure the energy distribution characteristics of the transformer surface and describe the surface acoustic effect of the transformer, the structural sound intensity on the surface of the oil tank wall of the oil-immersed transformer is calculated. Since the surface sound intensity of the transformer is always closely related to the structural parameters, the structural sound intensity of the oil tank wall can be calculated to analyze the power distribution on the surface of the oil tank, and then the layout of the transformer sound measurement points can be optimized. Under the action of oil pressure, the expression of the transient structural sound intensity per unit area is:

[0060]

[0061] When the force F changes harmonically, the general expression of the structural sound intensity per unit area is:

[0062]

[0063] where ω is the circular frequency of the force and response.

[0064] When a plane wave is incident on a surface at a certain angle, the effect of damping is not considered. in , I out represents the boundary load and the acoustic effect at the measuring point, then

[0065]

[0066]

[0067] The change in sound wave energy at this time is the transmission loss, which is expressed as

[0068]

[0069] 3. Selection of the best measuring point for the box

[0070] The vibration of the transformer is different from the actual damped vibration, that is, the attenuation of the transformer vibration will no longer decrease when it reaches the box. The energy change of the traditional damped vibration signal is as follows: Figure 1 As shown in Figure 2, when the vibration signal of the transformer propagates in the medium, the vibration continues to decay, as shown in Figure 2. Figure 2 As shown in the figure, the vibration at time t1 is transmitted to the box, and the signal is collected by the sensor, so the subsequent vibration is considered not to continue to decay. This is also the main basis for combining damped vibration and box vibration to form a measurement point model.

[0071] The vibration amplitude at time t1 is

[0072] In the formula, A0 and cos(ω f t1+φ) is a constant; δ is the damping coefficient.

[0073] Let B = A0cos(ω f t1+φ), Define β as the attenuation coefficient of the measurement point model,

[0074] Then x=Bβ. (21)

[0075] When the propagation speed of the sound signal in the transformer insulating oil is known to be c, the sound wave propagation attenuation coefficient is calculated using the following formula:

[0076]

[0077] Where α is the air sound propagation attenuation coefficient, unit is m -1 ; K is the segment y1(t i ,i) The number of consecutive pairs of signals; A i , A i-1 is the peak amplitude value of the segmented signal corresponding to the i-th pair of front and back junctions; L i , L i-1 is the number of segmented data points of the i-th pair of segmented signals; f p is the sampling rate of the signal, in Hz; c is the speed of sound propagation in air, in m / s; B f is a coefficient related to the value of A. If A is the amplitude of the sound signal, then B f =1; if A is the absolute mean value, effective value, etc. of the signal segment, then B needs to be determined through calibration experiments f The numerical value of .

[0078] For the transformer box, without considering the vibration propagation attenuation, the amplitude of all vibrations on the box surface is

[0079]

[0080] The attenuation coefficient α at different measuring points is different, and α can be obtained by least squares parameter identification. The least squares identification method is a method of identifying unknown parameters based on the minimum mean square error between experimental data and theoretical model. Its mathematical model is:

[0081]

[0082] The attenuation coefficients of the vibration signals at different measuring points of the box are calculated by the least squares identification method. The measuring points are numbered and sorted from small to large according to the corresponding attenuation coefficients. The measuring points with small attenuation coefficients are selected as the best measuring points for the vibration signals.

[0083] Going further, from the fluid-solid coupling analysis inside the transformer:

[0084]

[0085] Where: M c is the mass matrix of the core; u c is the displacement matrix of the core; c is the damping matrix. According to the assumption that other vibration damping other than fluid-solid coupling is ignored, it can be considered that the damping matrix is ​​only related to fluid-solid coupling; K c is the stiffness matrix of the core, which can be calculated from the material parameters and structural dimensions of the core; F is the external force causing vibration, F max is the Maxwell force matrix, F mag is the magnetostrictive force matrix; t is the time.

[0086] In the fluid-solid coupling effect, the force exerted by the fluid on the solid can be divided into two parts: damping force and inertial force. Among them, the inertial force refers to the additional mass of the fluid on the solid surface, which can be calculated in the finite element simulation software based on the fluid density, depth, vibration frequency, fluid-solid interface characteristics, etc.; the damping force represents the damping effect of the fluid. Without considering other damping conditions, the damping matrix c in the formula is only related to the damping force. The vibration frequency of the reactor core is mainly twice the operating voltage frequency (100Hz), which can be considered to be in the low frequency band. At this time, the damping force is extremely small and can be ignored. Therefore, equation (25) can be simplified to

[0087]

[0088] Where M is the core equivalent mass matrix taking into account the additional mass and core mass.

[0089] The iron core is a linear elastic material, and its motion is described by the elastic dynamics equation under Lagrangian coordinates. Among them, the equilibrium equation of the initial configuration is

[0090]

[0091] Where σ c is the deformation gradient tensor of the core, that is

[0092]

[0093] σ ca is the stress tensor:

[0094]

[0095] λ c is Lamé's first constant:

[0096]

[0097] μ c is the second Lamé constant, which is the shear modulus:

[0098]

[0099] σ g is the strain tensor of the core:

[0100]

[0101] where ρ c is the density of the core material; g is the local gravitational acceleration; I is the unit tensor; σ0 is σ c The determinant of E c and α c are Young’s modulus and Poisson’s ratio of the core material, respectively.

[0102] All components in the oil tank are immersed in transformer oil. Transformer oil is an incompressible Newtonian fluid. Its continuity equation in Lagrange-Euler coordinates is:

[0103]

[0104] Where: S is the surface area of ​​the core; μ0 is the velocity matrix of the transformer oil; n is the normal vector of the transformer core surface. The finite element simulation software is used to use the moving mesh method to deal with the deformation problem in fluid-solid coupling, μ g is the velocity matrix of the moving mesh.

[0105] Once the attenuation coefficient is determined, the optimal measuring point on the box surface is selected for vibration monitoring in combination with the internal fluid-solid coupling analysis.

[0106] The transformer measurement point model proposed in the present invention can be used to calculate the amplitude of the vibration signal of the measurement point under any load and loading voltage. By comparing the size and error of the measured value and the calculated value under a certain load and loading voltage, it is found that the measured value and the calculated value have a good degree of agreement. The location of the optimal measurement point can be calculated and determined by this model.

[0107] The beneficial effects of the present invention are:

[0108] (1) Starting from the analysis of the vibration and sound source, a vibration and sound propagation model is established to analyze the propagation attenuation of the vibration and sound in the medium, and the attenuation coefficients of different measuring points are theoretically calculated. The present invention quantitatively calculates the response of different positions of the box to the actual vibration and sound from the perspective of theoretical analysis;

[0109] (2) The present invention proposes to combine the sound signal propagation attenuation coefficient with the fluid-solid coupling model to comprehensively consider the influence of the internal medium on the selection of the measuring point;

[0110] (3) The measurement points selected by the present invention have a high accuracy rate, which has certain guiding significance for the operation and maintenance of the transformer; the combined model can not only be used for the selection of transformer vibration measurement points, but also provide ideas for predictive modeling in other fields.

Claims

1. A method for determining the optimal measuring point of a sensor based on a transformer box surface vibration signal, characterized in that: The following steps are involved: (1) Establish a vibration characteristic model based on the vibration of the transformer core and winding; (2) Calculate the attenuation coefficient of transformer vibration sound in medium propagation based on the characteristics of sound field propagation; (3) Analyze the vibration condition when the vibration sound is transmitted from the oil body to the box body according to the fluid-solid coupling model; The attenuation coefficient α of different measuring points is obtained by the least squares identification method; the mathematical model of the least squares identification method is: c1 is the winding vibration coefficient; c2 is the core vibration coefficient, I is the effective value of the load current signal, U is the effective value of the load voltage signal, I N is the rated current of the corresponding transformer, U N is the rated voltage of the corresponding transformer, a n is the normal acceleration, x n is the experimental data of the vibration signal at the nth measuring point, and x is the theoretical vibration signal value. The vibration signal attenuation coefficients corresponding to different measuring points of the box are calculated by the least squares identification method. The measuring points are numbered and sorted from small to large according to the corresponding attenuation coefficients, and the measuring points with small attenuation coefficients are selected as the best measuring points for the vibration signal.

2. The method for determining the optimal measuring point of the sensor based on the transformer box surface vibration signal according to claim 1 is characterized in that: According to the transformer damping vibration equation (2), m is mass, γ is damping, k is stiffness; let Then formula (1) can be written as δ is the system damping coefficient, ω0 is the natural frequency; the solution of the equation is After a period of attenuation, the forced vibration enters a stable constant amplitude vibration, and formula (3) is X(ω)=H(ω)F(ω)(6), H(ω) is the complex response matrix of the system, which contains the characteristic information of the system, H(ω)=(K-ω 2 M+iωC) -1 ; When the frequency of the driving force is a certain value, the amplitude of the forced vibration reaches a maximum value and resonance occurs. The resonance frequency The vibration amplitude A changes with the frequency of the driving force. The vibration amplitude of the transformer core is proportional to the square of the no-load voltage. The electromagnetic force on the transformer winding is proportional to the square of the current, which is v. wind ∝(I 50 cos(2πft+φ u50,i50 )) 2 (7), v wind is the winding vibration amplitude; I 50 is the maximum value of the power frequency current, and the initial phase of the load voltage is taken as the initial phase angle, v core ∝(U 50 cos(2πft+φ u50,i50 )) 2 (8), v core is the core vibration amplitude; U 50 is the maximum value of the power frequency voltage, i.e. A core ∝U s 2 (9), A wind ∝I m 2 (10); Ignoring the high-order harmonic components of the core vibration caused by the strong nonlinearity of the magnetostrictive phenomenon, the vibration model of the transformer box in the specified direction is simplified to v tank =c1v wind +c2v core (11) where v tank is the vibration amplitude of the box; c1 is the winding vibration coefficient; c2 is the core vibration coefficient.

3. The method for determining the optimal measuring point of the sensor based on the transformer box surface vibration signal according to claim 2 is characterized in that: Ignore the magnetizing current harmonic components and some redundant harmonic current components contained in the load current signal that are far less than 50Hz, and ignore the magnetizing voltage harmonic components and some redundant harmonic voltage components contained in the load voltage signal that are far less than 50Hz. The transformer box vibration amplitude is calculated using the following formula: where v tank is the vibration amplitude of the box, c1 is the winding vibration coefficient, c2 is the core vibration coefficient, I and U are the effective values ​​of the load current signal and the load voltage signal respectively; I N and U N They are the rated current and rated voltage of the corresponding transformer respectively.

4. The method for determining the optimal measuring point of the sensor based on the transformer box surface vibration signal according to claim 1, characterized in that: According to the propagation equation of acoustic signal in the medium p is the sound pressure in N / m 2 , ρ c is the density kg / m 3 , ω is the angular frequency rad / s, c c is the speed of sound m / s, and the boundary load at the sound-structure boundary is defined as F = -n s p(14), F is the boundary load, n s is the unit direction outward from the solid domain; on the fluid side, the normal acceleration of the fluid is set equal to the normal acceleration of the solid, expressed as follows n a is the outward unit normal vector seen from the acoustic domain, a n is the normal acceleration; under the action of oil pressure, the expression of the transient structural sound intensity per unit area on the box surface is When the force F changes harmonically, the expression of the structural sound intensity per unit area is: Where ω is the circular frequency of the force and response; when a plane wave acts on the surface at a certain angle of incidence, I in , I out represents the boundary load and the acoustic effect at the measuring point, then The change in sound wave energy is the transmission loss and is expressed as 5. The method for determining the optimal measuring point of the sensor based on the transformer box surface vibration signal according to claim 4 is characterized in that: Combine damped vibration and box vibration to form a measurement point model. The vibration amplitude at time t1 is A0 and cos(ω f t1+φ) is a constant; δ is the damping coefficient, let B = A0cos(ω f t1+φ), Define β as the attenuation coefficient of the measuring point model, then x = Bβ (22); use the following formula to calculate the attenuation coefficient of sound wave propagation: α is the air sound propagation attenuation coefficient, unit is m -1 ; K is the segment y1(t i ,i) The number of consecutive pairs of signals; A i , A i-1 is the peak amplitude value of the segmented signal corresponding to the i-th pair of front and back junctions; L i , L i-1 is the number of segmented data points of the i-th pair of segmented signals; f p is the sampling rate of the signal, in Hz; c is the speed of sound propagation in air, in m / s; B f is a coefficient related to the value of A. When A is the amplitude of the sound signal, then B f =1; when A is the absolute mean value and effective value of the signal segment, B is determined by calibration experiment f The value of; the amplitude of all vibrations on the box surface is The attenuation coefficient at different measuring points is α.

6. The method for determining the optimal measuring point of the sensor based on the transformer box surface vibration signal according to claim 1, characterized in that: From the fluid-solid coupling analysis inside the transformer, M c is the mass matrix of the core, u c is the displacement matrix of the core, c is the damping matrix, K c is the stiffness matrix of the core, which is calculated from the material parameters and structural dimensions of the core, F is the external force causing vibration, and F max is the Maxwell force matrix, F mag is the magnetostrictive force matrix, t is the time, in the fluid-solid coupling effect, the force exerted by the fluid on the solid is divided into two parts, namely, the damping force and the inertial force. The inertial force refers to the additional mass of the fluid on the solid surface, and the damping force represents the damping effect of the fluid. Without considering other damping factors, the damping matrix c is only related to the damping force. The vibration frequency of the reactor core is mainly twice the operating voltage frequency, and the damping force is small and can be ignored. Formula (25) is simplified to M is the equivalent mass matrix of the core considering the additional mass and the core mass. The elastic dynamics equation under Lagrangian coordinates is used to describe its motion. The equilibrium equation of the initial configuration is: σ c is the deformation gradient tensor of the core, σ ca is the stress tensor, λ c is Lamé's first constant, μ c is the second Lamé constant, where is the shear modulus σ g is the strain tensor of the core ρ c is the density of the core material, g is the local gravitational acceleration, I is the unit tensor, and σ0 is σ c The determinant, E c and α c are Young's modulus and Poisson's ratio of the core material respectively; all components in the oil tank are immersed in transformer oil, which is an incompressible Newtonian fluid. The continuity equation in Lagrange-Euler coordinates is S is the surface area of ​​the core, μ0 is the velocity matrix of the transformer oil, n is the normal vector of the transformer core surface, μ g is the velocity matrix of the moving grid; Once the attenuation coefficient is determined, the optimal measuring point on the box surface is selected for vibration monitoring in combination with the internal fluid-solid coupling analysis.

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