Modular analysis method and system for axial nonlinear vibration of pancake winding of transformer

Abstract

The invention discloses a modular analysis method and system for axial nonlinear vibration of a pancake winding of a transformer, and the method comprises the steps: constructing a winding dynamical model considering nonlinear factors, and guaranteeing that the model can reflect the influence of factors such as nonlinear characteristics of a material; meanwhile, balance between independent calculation and overall coupling of each layer of the winding needs to be solved, modular calculation of the pancake winding is achieved, accuracy and expansibility of calculation are improved, and the pancake winding vibration analysis method is suitable for winding vibration analysis under different conditions. The method can accurately analyze the axial nonlinear vibration characteristics of the pancake winding under complex working conditions.

Description

Technical Field

[0001] The present invention relates to the field of vibration analysis of power equipment, and particularly to a modular analysis method and system for axial nonlinear vibration of transformer disk windings. Background Art

[0002] As an important hub device in China's power system, the safe and stable operation of power transformers is an important prerequisite for ensuring the stability of the power system. Vibration signals, as an important part of the operation and maintenance of power transformers, can effectively reflect abnormalities in the internal mechanical structure of transformers. Currently, the existing technical means cannot batch monitor the vibration signals of the internal windings of transformers, and numerical and analytical algorithms still need to be relied on to calculate the vibration signals of transformer windings. Most of the existing calculation methods for transformer winding vibrations are based on linear assumptions and do not fully consider the nonlinear characteristics of the winding structure, resulting in insufficient calculation accuracy. Especially in the axial vibration analysis of disk windings, the existing calculation methods cannot quickly and effectively provide accurate models and results. A single calculation model is only applicable to the vibration calculation of transformer windings corresponding to its model, resulting in low calculation efficiency and accuracy.

[0003] CN112364443A discloses a method for quantitatively analyzing the axial natural vibration characteristics of transformer windings. Its technical features are: establishing a dynamic model for the axial vibration of transformer windings; determining the equivalent stiffness of the springs between the mass blocks in the dynamic model of the axial vibration of transformer windings; and analyzing the axial natural vibration characteristics of the windings based on the equivalent stiffness of the springs between the mass blocks in the dynamic model of the axial vibration of transformer windings. The present invention is reasonably designed. By establishing a mass-spring-damping model including clamping plates and winding disks, the modal frequencies and vibration modes of the windings can be obtained, thereby being able to quantitatively analyze the influence of different structural parameters on the natural vibration characteristics of the windings. This invention only adopts a linear vibration dynamics model, assuming that the stiffness and damping of the internal structure of the winding are equivalent constants, and does not consider the nonlinear effects in the actual structure of the winding. The structure of transformer windings usually has obvious nonlinear characteristics. Especially under high load or vibration impact conditions, the stiffness and damping coefficients of materials will change significantly with stress. Ignoring this nonlinear factor will lead to a large deviation in the analysis results of vibration characteristics and cannot accurately reflect the dynamic response of transformer windings under actual working conditions. Moreover, in this invention, the conductors of the winding disks are regarded as concentrated equivalent mass blocks, and the vibration characteristics of each part of the winding cannot be calculated separately. This processing method is difficult to perform modular calculations, that is, when facing changes in different structural parameters or layouts, it is impossible to flexibly adjust and analyze the vibration characteristics of the winding disks. The modular calculation of disk windings requires the ability to independently analyze and combine different disk layers, which is of great significance in complex winding designs. Obviously, the existing technology fails to meet this requirement.

[0004] To solve the above problems, it is of great significance to develop a modular calculation method that can accurately reflect the axial nonlinear vibration of the disk winding, which is applicable to the axial vibration calculation of disk windings of transformers with different voltage levels and different models, improving the calculation accuracy while reducing the labor and time costs. Summary of the Invention

[0005] To solve the problems in the prior art that the nonlinearity of the transformer winding structure is not considered and the modular calculation of the disk winding cannot be realized, the method proposed by the present invention can accurately analyze the axial nonlinear vibration characteristics of the disk winding under complex working conditions. The technical difficulties are concentrated on how to construct a winding dynamics model considering nonlinear factors to ensure that the model can reflect the influence of factors such as the nonlinear characteristics of materials. At the same time, it is also necessary to solve the balance between the independent calculation of each layer of the winding and the overall coupling to realize the modular calculation of the disk winding, so as to improve the calculation accuracy and expandability and adapt to the winding vibration analysis under different conditions.

[0006] To solve the above problems, the technical solution adopted by the present invention is: a modular analysis method for axial nonlinear vibration of a transformer disk winding, including the following steps:

[0007] Perform axial dynamics modeling on the transformer winding, and the constructed dynamics model is where M is the equivalent mass matrix of the disk coils of the transformer winding considering the gravity cumulative effect, Z is the winding axial vibration displacement matrix, C is the damping matrix considering the damping effect of transformer oil and the structure between the winding coils, K is the equivalent stiffness matrix considering the axial insulation pads and the structure of insulating paper between the winding coils, F m is the electromagnetic force matrix received by the winding coils, F c is the equivalent pre-tightening force matrix from the top pressing plate to the bottom pressing plate of the winding, M, C, and K are n-dimensional square matrices, n is the number of axial coils of the winding, is the winding axial vibration velocity matrix, is the winding axial vibration acceleration matrix;

[0008] Based on the above dynamics model, the nonlinear stiffness and nonlinear damping of the insulating pads are combined as the influencing factors on the vibration characteristics of the transformer winding. Specifically, the Bouc-Wen model including nonlinear stiffness and nonlinear damping is introduced to correct the nonlinear hysteresis characteristics of the winding insulating pads;

[0009] Considering the influence of the transformer insulating pads on strain and temperature, combining them with the stiffness and damping in the dynamics model, the equivalent stiffness is obtained as:

[0010]

[0011] A is the contact area between the pad and the winding, N is the number of pads between two layers of coils, Es (ε, T), E p (ε, T) are the elastic moduli of the spacer and the wire insulating paper respectively, L s , L s are the thicknesses of the insulating paper or the spacer after the winding is compacted respectively; In summary, the dynamic stiffness matrix K of the winding axial dynamic model can be constructed; Further, based on the Rayleigh damping formula C = ξ1M + ξ2K, the dynamic damping matrix C is obtained, where ξ1 represents the damping coefficient related to the mass matrix and ξ2 represents the damping coefficient related to the stiffness matrix;

[0012] Use Simulink to build modules, including the upper and lower end pressing plate modules of the winding, the calculation unit module of the single-layer winding pancake, and the non-linear dynamic damping and stiffness modules built based on the Bouc-Wen model;

[0013] Conduct axial analysis of the transformer pancake winding to be analyzed according to the modules built by Simulink.

[0014] Furthermore, the winding axial vibration displacement matrix is:

[0015] Z = diag(Z T , Z1, Z2, …, Z n-1 , Z n , Z B )

[0016] Z T represents the axial vibration displacement of the upper end pressing plate of the winding, Z n represents the axial vibration displacement of the winding pancake, Z B represents the axial vibration displacement of the lower end pressing plate of the winding;

[0017] The winding axial vibration velocity matrix is:

[0018]

[0019] Z T ′ represents the axial vibration velocity of the upper end pressing plate of the winding, Z n ′ represents the axial vibration velocity of the winding pancake, Z B ′ represents the axial vibration velocity of the lower end pressing plate of the winding;

[0020] The winding axial vibration acceleration matrix is:

[0021]

[0022] Z T ″ represents the axial vibration acceleration of the upper end pressing plate of the winding, Z n ″ represents the axial vibration acceleration of the winding pancake, Z B ″ represents the axial vibration acceleration of the lower end pressing plate of the winding.

[0023] More specifically, the equivalent mass matrix M of the winding disk is expressed as:

[0024] M = diag(M T , M1, M2, …, M n-1 , M n , M B )

[0025]

[0026] m T represents the weight of the upper end pressing plate of the winding, m n represents the weight of the middle winding disk, m D(n-1) represents the weight of the spacer between two winding disks, m B represents the weight of the lower end pressing plate of the winding, m DB represents the self-weight of the spacer group between the last layer of the winding disk and the bottom line plate of the winding, m Dn represents the self-weight of the interlayer spacer group, m DT represents the weight of the spacer between the top pressing plate of the winding and the first layer of the winding disk.

[0027] Furthermore, the Bouc-Wen model is expressed as

[0028]

[0029] where x(t) is the displacement of the mass block relative to the ground; z(t) is the hysteretic displacement; α is the ratio of the tangent stiffness at the peak of the hysteresis loop to the initial stiffness, represents the restoring force, k is the initial stiffness, A and β are non-dimensional parameters jointly describing the shape of the non-linear hysteresis curve, ψ, n are non-dimensional parameters describing the size and smoothness of the non-linear hysteresis curve, represents the shear displacement rate, represents the shear stress rate.

[0030] Furthermore, when considering the influence of strain and temperature on the transformer insulation spacer, the time-varying transformer oil temperature parameter T is introduced to affect the elastic modulus E s of the spacer. The fitting function of the elastic modulus E s of the spacer is: E s = -0.29T + 171.53.

[0031] Furthermore, the upper and lower end pressing plate modules of the winding include 4 interfaces. The two output interfaces are respectively the damping output of the top pressing plate of the winding and the stiffness output of the top pressing plate of the winding. The two input interfaces are respectively the stiffness input of the lower winding disk and the damping input of the lower winding disk;

[0032] The winding single-layer coil calculation unit module includes 8 interfaces. The four output interfaces are respectively the damping effect on the upper coil, the damping effect on the lower coil, the stiffness effect on the upper coil, and the stiffness effect on the lower coil. The four input interfaces are respectively the damping effect of the upper coil, the damping effect of the lower coil, the stiffness effect of the upper coil, and the stiffness effect of the lower coil.

[0033] The nonlinear dynamic damping and stiffness module constructed based on the Bouc-Wen model includes three interfaces. The two output interfaces are respectively the dynamic damping coefficient c i and the dynamic stiffness coefficient k i . The model input interface is the displacement difference between the upper and lower coils. Since the nonlinearity changes with time, the nonlinear dynamic damping and stiffness module calculates the strain between two winding single-layer calculation units equivalent strain l i is the initial equivalent spacer thickness, and finally uses the input variable to output the dynamic stiffness k i and damping c i .

[0034] The present invention also provides a modular analysis system for axial nonlinear vibration of transformer disc windings, including:

[0035] A transformer winding dynamic model unit for constructing a dynamic model, where M is the equivalent mass matrix of the disc windings of the transformer winding considering the gravity cumulative effect, Z is the winding axial vibration displacement matrix, C is the damping matrix considering the damping effect of transformer oil and the winding disc structure, K is the equivalent stiffness matrix considering the axial insulation spacer and insulation paper structure of the winding, F m is the electromagnetic force matrix received by the winding disc, F c is the equivalent pre-tightening force matrix from the top pressing plate to the bottom pressing plate of the winding. M, C, and K are n-dimensional square matrices, n is the number of winding axial discs, is the winding axial vibration velocity matrix, is the winding axial vibration acceleration matrix;

[0036] A Bouc-Wen model unit for, based on the dynamic model, combining the nonlinear stiffness and nonlinear damping of the insulation pads as influencing factors on the vibration characteristics of the transformer winding. Specifically, it modifies the nonlinear hysteresis characteristics of the winding insulation pads by introducing the Bouc-Wen model including nonlinear stiffness and nonlinear damping.

[0037] An equivalent stiffness unit is used to consider the influence of strain and temperature on the transformer insulation spacer, combine it with the stiffness and damping in the dynamic model, and obtain the equivalent stiffness as follows:

[0038]

[0039] A is the contact area between the spacer and the winding, N is the number of spacers between two layers of winding pancakes, E s (ε,T), E p (ε,T) are the elastic moduli of the spacer and the wire insulating paper respectively, L s 、L s are the thicknesses of the insulating paper or spacer after the winding is compressed; in summary, the dynamic stiffness matrix K of the winding axial dynamic model can be constructed; further, based on the Rayleigh damping formula C = ξ1M + ξ2K, the dynamic damping matrix C is obtained, where ξ1 represents the damping coefficient related to the mass matrix and ξ2 represents the damping coefficient related to the stiffness matrix;

[0040] A module construction unit is used to construct modules using Simulink, including upper and lower end pressing plate modules of the winding, a calculation unit module for a single-layer winding pancake of the winding, and non-linear dynamic damping and stiffness modules constructed based on the Bonc-Wen model;

[0041] An analysis unit is used to perform axial analysis of the transformer pancake winding of the transformer to be analyzed according to the modules constructed by Simulink.

[0042] The technical solution of the present invention has the following beneficial effects:

[0043] 1. By integrating the time-varying characteristics of the spacer material, the accuracy of calculating the axial vibration of the transformer winding is improved

[0044] In the present invention, the transformer winding spacer is equivalent to a Bonc-Wen non-linear hysteresis characteristic curve, and the optimal parameter curve is measured and fitted through experiments to describe the dynamic damping and stiffness characteristics of the transformer axial spacer. Further, an axial electromagnetic excitation is applied to the whole model to obtain the vibration displacement, velocity, and acceleration characteristics.

[0045] 2. By modularizing the winding pancake unit, the versatility of calculating the axial vibration of the transformer is improved

[0046] In the present invention, the transformer pancake winding pancakes are packaged through a modular program, and interfaces are reserved to simulate the elastic contact brought by the spacers between the winding pancakes. The method of the present invention is applicable to calculating the axial vibration characteristics of all known structural transformer pancake windings. Due to modular packaging and parameter reduction, the time and labor costs of calculating the vibration characteristics can be significantly reduced, which is of great significance for transformer checking and evaluation and condition diagnosis. Description of the Drawings

[0047] Figure 1 It is the bonc-wen model structure of the wire cake fusion;

[0048] Figure 2 It is the stress-strain curve of the insulating spacer;

[0049] Figure 3 It is the dynamic stiffness and damping surface interpolated according to strain;

[0050] Figure 4 It is the axial nonlinear dynamic model of the winding;

[0051] Figure 5 It is the logic diagram of the combination relationship of different calculation module units;

[0052] Figure 6 It is the schematic diagram of the combination of single-layer winding calculation units;

[0053] Figure 7 It is the amplitude distribution of the acceleration of the main body of the 44-cake winding;

[0054] Figure 8 It is the time-domain distribution of the acceleration of the calculation units of each layer of wire cakes in the 44-cake winding. Specific implementation manner

[0055] The present invention proposes a modular analysis method for the axial nonlinear vibration of the transformer disk-type winding. By introducing the material nonlinear model of the transformer winding spacer into the axial dynamic equation of the transformer and combining the program modular packaging method, the wire cakes and spacers of the winding are modularly equivalent, so that the technical solution is more suitable for the rapid modeling and calculation of the nonlinear vibration of the disk-type winding.

[0056] First, perform axial dynamic modeling on the transformer winding. Among them, M is the equivalent mass matrix of the wire cakes of the disk-type winding considering the gravity cumulative effect, Z is the axial vibration displacement matrix of the winding, the reference direction of which is opposite to the direction of the gravity acceleration, C is the damping matrix considering the damping effect of the transformer oil and the structure between the winding cakes, K is the equivalent stiffness matrix considering the axial insulation spacers and the insulation paper structure between the winding cakes, F m is the electromagnetic force matrix received by the wire cakes of the winding, F c is the equivalent pre-tightening force matrix from the top pressing plate to the bottom pressing plate of the winding. M, C, and K are n-dimensional square matrices, and n is the number of wire cakes in the axial direction of the winding. is the axial vibration velocity matrix of the winding. is the axial vibration acceleration matrix of the winding.

[0057] Furthermore, the axial vibration displacement matrix of the wire cakes of the winding can be expressed as:

[0058] Z = diag(Z T , Z1, Z2, …, Z n-1,Z n ,Z B ) (1)

[0059] Z T represents the axial vibration displacement of the upper end plate of the winding, Z n represents the axial vibration displacement of the winding disk, Z B represents the axial vibration displacement of the lower end plate of the winding.

[0060] Furthermore, the axial winding disk vibration velocity matrix can be expressed as:

[0061]

[0062] Z T ′ represents the axial vibration velocity of the upper end plate of the winding, Z n ′ represents the axial vibration velocity of the winding disk, Z B ′ represents the axial vibration velocity of the lower end plate of the winding.

[0063] Furthermore, the axial winding disk vibration acceleration matrix can be expressed as:

[0064]

[0065] [[ID=३७]]Z T ″ represents the axial vibration acceleration of the upper end plate of the winding, Z n ″ represents the axial vibration acceleration of the winding disk, Z B ″ represents the axial vibration acceleration of the lower end plate of the winding.

[0066] Furthermore, the self-weight m of the interlayer spacer group in the axial model cannot be ignored Dn for the vibration influence, where m DT represents the weight of the spacer between the top layer pressing plate of the winding and the first layer of winding disks, m DB represents the self-weight of the spacer group between the last layer of winding disks of the winding and the bottom plate of the winding. Therefore, in the static state of the winding, considering the mass of each layer of spacer groups, the equivalent mass matrix M of the winding disks can be expressed as:

[0067] M = diag(M T , M1, M2, …, M n-1 , M n , M B ) (4)

[0068]

[0069] m T represents the weight of the upper end plate of the winding, m n represents the weight of the middle winding disks of the winding, m D(n-1) represents the weight of the spacer between two winding disks of the winding, m BIndicates the weight of the lower end pressing plate of the winding.

[0070] Furthermore, through the research and analysis of the winding structure, it can be known that the mechanical properties of the insulating pads play an indispensable role in the winding vibration dynamics model. The insulating pads are under the action of high strain and high stress for a long time. Evaluating the mechanical properties of the insulating pads is of great significance for further studying the axial vibration of the winding. The changes in its equivalent stiffness and damping will have an important impact on the vibration characteristics of the winding. However, traditional research methods usually regard the equivalent stiffness and damping of the insulating pads as constants or ignore the damping effect, lacking the research on the nonlinear dynamic behavior of the winding insulating pads combined with the axial nonlinear dynamics model of the winding. The method of the present invention introduces the Bouc-Wen model including nonlinear stiffness and nonlinear damping (its structure is as Figure 1 shown) to correct the nonlinear hysteretic characteristics of the winding insulating pads in the calculation of the winding axial nonlinear dynamics model. Its simplicity, versatility and strong adaptability can meet the stress-strain nonlinear relationship of the insulating pads in the non-degraded state. Its theoretical model is a first-order nonlinear differential equation, and the general form is as follows:

[0071]

[0072] In the expression of the Bouc-Wen model, there are a linear restoring force akx(t) and a hysteretic restoring force (1-α)kz(t). In the formula, x(t) is the displacement of the mass relative to the ground; z(t) is the hysteretic displacement; α is the ratio of the nonlinear stiffness to the linear stiffness, indicating the restoring force. Analogous to the Bouc-Wen model, it is the ratio of the tangent stiffness at the peak of the hysteresis loop to the initial stiffness, ranging from 0 to 1, and k is the initial stiffness. In formula (7), α = k f / k i , k f = P y / ε y , A and β jointly describe the shape of the nonlinear hysteresis curve, and ψ, n are non-dimensional parameters describing the size and smoothness of the nonlinear hysteresis curve. k i is the stiffness at the initial moment, k f is the stiffness at a certain moment under the action of the cyclic external force, p y is the initial pre-tightening force, ε y is the initial displacement, represents the shear displacement rate, represents the shear stress rate, which are respectively obtained by material tests.

[0073] Furthermore, the stress-strain curve of the pads between windings measured by experiments is as Figure 2 shown.

[0074] Furthermore, the time-varying transformer oil temperature parameter T is further introduced to the elastic modulus E of the padss The influence is that since the ambient oil temperature of the transformer during normal operation does not exceed 140°C, according to relevant research, the elastic modulus E of the winding spacer s shows an approximately linear change in the temperature range of -40°C - 140°C, and the fitting function of the elastic modulus at different temperatures is:

[0075] E s = -0.29T + 171.53 (8)

[0076] Based on the above steps, a change surface of the transformer insulation spacer under the influence of strain and temperature is further established. The surface is as Figure 3 shown. Further, this surface is combined with the stiffness and damping quantities in the transformer axial dynamic equation by the plane search method. The equivalent stiffness is:

[0077]

[0078] A is the contact area between the spacer and the winding, N is the number of spacers between two layers of wire cakes, E s (ε, T), E p (ε, T) are the elastic moduli of the spacer and the wire insulation paper respectively, L s , L s are the thicknesses of the insulation paper or the spacer after the winding is compressed. In summary, the dynamic stiffness matrix K of the winding axial dynamic model can be constructed. Further, based on the Rayleigh damping formula C = ξ1M + ξ2K, the dynamic damping matrix C is obtained. ξ1 represents the damping coefficient related to the mass matrix, and ξ2 represents the damping coefficient related to the stiffness matrix.

[0079] Further, based on the above steps, a single - cake calculation unit, a non - linear spacer equivalent calculation unit of the transformer, and an interface for stiffness - damping mutual coupling between units are constructed.

[0080] Assume that the number of layers of the multi - layer wire - cake structure is n, and the numbers from top to bottom are as Figure 4 shown. The electromagnetic forces of the n - layer wire cakes calculated by finite element are {f1, f2,..., f n}}. For the top wire cake of the winding, its acceleration can be expressed as

[0081]

[0082] For the i - th wire cake in the middle of the winding, its acceleration can be expressed as

[0083]

[0084] For the bottom wire cake of the winding, its acceleration can be expressed as

[0085]

[0086] Some of the physical symbols in the previous step have been described in the foregoing steps. Among them, the letter c represents the damping coefficient, and c i represents the damping between the i-th layer winding disk and the (i + 1)-th layer winding disk. The letter k represents the stiffness coefficient, and k i represents the stiffness between the i-th layer winding disk and the (i + 1)-th layer winding disk; g is the acceleration due to gravity.

[0087] As Figure 4 shown, based on the upper and lower end-plate modules of the winding, the single-layer winding disk calculation unit module, and the non-linear dynamic damping and stiffness modules constructed in the above steps, the three types of modules are respectively encapsulated, and coupling interfaces for stiffness, damping output, and upper and lower winding disk stiffness and damping input are reserved. For windings with any known number of winding disks, the axial vibration model can be flexibly built. Specifically

[0088] First, the upper and lower end-plate module of the winding contains 4 interfaces. The two output interfaces are respectively the damping output of the top end-plate of the winding and the stiffness output of the top end-plate of the winding. The two input interfaces are respectively the stiffness input of the lower winding disk and the damping input of the lower winding disk. It corresponds to the mutual influence of damping and stiffness between the top end-plate and the spacer block between the first layer of the winding disk in the dynamic equation.

[0089] The single-layer winding disk calculation unit of the winding contains 8 interfaces. The four output interfaces are respectively the damping influence on the upper winding disk, the damping influence on the lower winding disk, the stiffness influence on the upper winding disk, and the stiffness influence on the lower winding disk; the four input interfaces are respectively the damping influence of the upper winding disk, the damping influence of the lower winding disk, the stiffness influence of the upper winding disk, and the stiffness influence of the lower winding disk.

[0090] The non-linear dynamic damping and stiffness module constructed based on the bonc-wen model contains three interfaces. The two output interfaces are respectively the dynamic damping coefficient c i and the dynamic stiffness coefficient k i described in the above steps. The model input interface is the displacement difference between the upper and lower winding disks Since the non-linearity changes with time, the non-linear dynamic damping and stiffness module passes the strain between two single-layer winding calculation units The equivalent strain of the present invention l i is the initial equivalent spacer block thickness, which is set before calculation. Finally, using the input variable the dynamic stiffness k i and damping c i are output through the surface interpolation method. To ensure the accuracy of the modular program calculation of the axial vibration of the winding considering non-linear factors, the time step is 0.001 s.

[0091] Among the three calculation modules, the single-layer winding pancake units are linked to the main winding area through the stiffness-damping interaction interface. The upper and lower end pressing plate areas are also linked to the main winding area through the stiffness-damping interaction interface. The non-linear and linear dynamic damping and stiffness modules are integrated into the single-layer winding pancake units. By means of time-varying strain, the dynamic damping and stiffness coefficients are output, thereby changing the damping and stiffness effects of different pancake calculation units and the upper and lower end winding pressing plates, so as to realize the axial vibration modular calculation method considering non-linear factors proposed by the present invention.

[0092] Furthermore, calculations are carried out based on a specific transformer model. Different modules are combined, and structural parameters are input. Then, the electromagnetic force obtained through finite element calculation is used as the excitation input to the model, and the axial vibration acceleration waveform and vibration displacement distribution of the transformer winding can be obtained under the influence of considering non-linear material characteristics as shown in Figure 6 .

[0093] To verify the rationality of the method proposed by the present invention, the axial vibration acceleration distribution and its time-domain variation of each layer of the winding pancake are calculated using the winding data in the literature. The winding under calculation has a 44-pancake structure, and the calculation results are as shown in Figure 7 , Figure 8 . After verification with the calculation results in the corresponding literature, the accuracy of the method proposed by the present invention is verified. Moreover, the axial vibration calculation considering modularization and non-linear damping and spacer factors can more realistically simulate the actual axial vibration situation of the transformer.

Claims

1. A modular analysis method for axial non-linear vibration of transformer disc windings, characterized in that, Including the following steps: Axially dynamic modeling is performed on the transformer winding, and the constructed dynamic model is where M is the equivalent mass matrix of the disk windings of the cake-type winding considering the cumulative effect of gravity, Z is the axial vibration displacement matrix of the winding, C is the damping matrix considering the damping effect of transformer oil and the structure between the winding disks, K is the equivalent stiffness matrix considering the axial insulation pads between the winding disks and the structure of insulating paper, F m is the electromagnetic force matrix received by the winding disks, F c is the equivalent pre-tightening force matrix from the top pressing plate to the bottom pressing plate of the winding. M, C, and K are n-dimensional square matrices, where n is the number of axial winding disks, is the axial vibration velocity matrix of the winding, is the axial vibration acceleration matrix of the winding; Based on the kinetic model, the non-linear stiffness and non-linear damping of the insulating pad are combined as influencing factors for the vibration characteristics of the transformer winding. Specifically, the non-linear hysteretic characteristics of the winding insulating pad are corrected by introducing the Bouc-Wen model including non-linear stiffness and non-linear damping; Considering the influence of strain and temperature on the transformer insulating pad, it is combined with the stiffness and damping in the kinetic model to obtain the equivalent stiffness as: A is the contact area between the spacer and the winding, N is the number of spacers between two layers of winding pancakes, E s (ε, T), E p (ε, T) are the elastic moduli of the spacer and the wire insulating paper respectively, L s 、L s are the thicknesses of the insulating paper or the spacer after the winding is compacted respectively; In summary, the dynamic stiffness matrix K of the winding axial dynamic model can be constructed; Further, based on the Rayleigh damping formula C = ξ1M + ξ2K, the dynamic damping matrix C is obtained, where ξ1 represents the damping coefficient related to the mass matrix, and ξ2 represents the damping coefficient related to the stiffness matrix; Use Simulink to build modules, including the upper and lower end pressing plate modules of the winding, the calculation unit module of the single-layer winding disk, and the non-linear dynamic damping and stiffness modules built based on the Bonc-Wen model; According to the modules built by Simulink, perform axial analysis on the transformer cake-type winding of the transformer to be analyzed.

2. The modular analysis method for axial non-linear vibration of a transformer disk winding according to claim 1, wherein: The axial vibration displacement matrix of the winding is: Z = diag(Z T , Z1, Z2, …, Z n-1 , Z n , Z B ) Z T represents the axial vibration displacement of the upper end plate of the winding, Z n represents the axial vibration displacement of the winding disk, Z B represents the axial vibration displacement of the lower end plate of the winding; The axial vibration velocity matrix of the winding is: Z T ' represents the axial vibration velocity of the upper end plate of the winding, Z n ' represents the axial vibration velocity of the winding disk, Z B ' represents the axial vibration velocity of the lower end plate of the winding; The axial vibration acceleration matrix of the winding is: Z T ″ represents the axial vibration acceleration of the upper end plate of the winding, Z n ″ represents the axial vibration acceleration of the winding disk, Z B ″ represents the axial vibration acceleration of the lower end plate of the winding.

3. The modular analysis method for axial non-linear vibration of a transformer disk winding according to claim 1, characterized in that: The equivalent mass matrix M of the winding disk is expressed as: M = diag(M T , M1, M2, …, M n-1 , M n , M B ) m T Represents the weight of the upper end plate of the winding, m n Represents the weight of the middle pancake of the winding, m D(n-1) Represents the weight of the spacer between two pancakes of the winding, m B Represents the weight of the lower end plate of the winding, m DB Represents the self-weight of the spacer group between the last pancake of the winding and the bottom plate of the winding, m Dn Represents the self-weight of the interlayer spacer group, m DT Represents the weight of the spacer between the top layer pressing plate of the winding and the first pancake.

4. The modular analysis method for axial non-linear vibration of a transformer disk winding according to claim 1, characterized in that: The Bouc-Wen model is expressed as where x(t) is the displacement of the mass relative to the ground; z(t) is the hysteretic displacement; α is the ratio of the tangent stiffness at the peak of the hysteresis loop to the initial stiffness, representing the restoring force, k is the initial stiffness, A and β are non-dimensional parameters jointly describing the shape of the non-linear hysteretic curve, ψ, n are non-dimensional parameters describing the size and smoothness of the non-linear hysteretic curve, representing the shear displacement rate, representing the shear stress rate.

5. The modular analysis method for axial non-linear vibration of a transformer disk winding according to claim 1, characterized in that: When considering the influence of strain and temperature on the insulating spacer of the transformer, the influence of the time-varying transformer oil temperature parameter T on the elastic modulus E of the spacer is introduced. s The elastic modulus E of the spacer s The fitting function is: E s = -0.29T + 171.

53.

6. The modular analysis method for axial non-linear vibration of a transformer cake-type winding according to claim 1, characterized in that: The upper and lower end pressing plate modules of the winding include 4 interfaces. The two output interfaces are respectively the damping output of the top pressing plate of the winding and the stiffness output of the top pressing plate of the winding. The two input interfaces are respectively the stiffness input of the lower winding disk and the damping input of the lower winding disk; The calculation unit module of the single-layer winding disk of the winding includes 8 interfaces. The four output interfaces are respectively the damping influence on the upper winding disk, the damping influence on the lower winding disk, the stiffness influence on the upper winding disk, and the stiffness influence on the lower winding disk; The four input interfaces are respectively the damping influence of the upper winding disk, the damping influence of the lower winding disk, the stiffness influence of the upper winding disk, and the stiffness influence of the lower winding disk; The non-linear dynamic damping and stiffness module constructed based on the bonc-wen model includes three interfaces. The two output interfaces are the dynamic damping coefficient c i and the dynamic stiffness coefficient k i . The model input interface is the displacement difference between the upper and lower line cakes Since the non-linearity varies with time, the non-linear dynamic damping and stiffness module calculates the strain between two single-layer winding units equivalent strain l i is the initial equivalent spacer thickness, and finally the input variable is used to output the dynamic stiffness k i and the damping c i .

7. A modular analysis system for axial non-linear vibration of a transformer disc winding, characterized in that: Including The transformer winding dynamic model unit is used to construct a dynamic model for where M is the equivalent mass matrix of the disk-type winding disks considering the gravity cumulative effect, Z is the winding axial vibration displacement matrix, C is the damping matrix considering the damping effects of transformer oil and the structure between the winding disks, K is the equivalent stiffness matrix considering the axial insulation pads between the winding disks and the structure of insulating paper, F m is the electromagnetic force matrix applied to the winding disks, F c is the equivalent pre-tightening force matrix from the top pressing plate to the bottom pressing plate of the winding. M, C, and K are n-dimensional square matrices, and n is the number of winding axial disks is the winding axial vibration velocity matrix, is the winding axial vibration acceleration matrix; The Bouc-Wen model unit is used to, based on the kinetic model, combine the non-linear stiffness and non-linear damping of the insulating pad as influencing factors for the vibration characteristics of the transformer winding. Specifically, the non-linear hysteretic characteristics of the winding insulating pad are corrected by introducing the Bouc-Wen model including non-linear stiffness and non-linear damping; The equivalent stiffness unit is used to consider the influence of strain and temperature on the transformer insulating pad, combine it with the stiffness and damping in the kinetic model, and obtain the equivalent stiffness as: A is the contact area between the spacer and the winding, N is the number of spacers between two layers of winding pancakes, and E s (ε, T), and E p (ε, T) are the elastic moduli of the spacer and the wire insulation paper respectively. L s and L s are the thicknesses of the insulation paper or the spacer after the winding is compacted respectively; In summary, the dynamic stiffness matrix K of the axial dynamics model of the winding can be constructed; Further, based on the Rayleigh damping formula C = ξ1M + ξ2K, the dynamic damping matrix C is obtained, where ξ1 represents the damping coefficient related to the mass matrix and ξ2 represents the damping coefficient related to the stiffness matrix; The module building unit is used to build modules using Simulink, including the upper and lower end pressing plate modules of the winding, the calculation unit module of the single-layer winding disk, and the non-linear dynamic damping and stiffness modules built based on the Bonc-Wen model; The analysis unit is used to perform axial analysis on the transformer cake-type winding of the transformer to be analyzed according to the modules built by Simulink.

8. The modular analysis system for axial non-linear vibration of a transformer cake-type winding according to claim 7, characterized in that: The axial vibration displacement matrix of the winding is: Z = diag(Z T , Z1, Z2, …, Z n-1 , Z n , Z B ) Z T represents the axial vibration displacement of the upper end plate of the winding, Z n represents the axial vibration displacement of the winding disk, Z B represents the axial vibration displacement of the lower end plate of the winding; The axial vibration velocity matrix of the winding is: Z T ' represents the axial vibration velocity of the upper end plate of the winding, Z n ' represents the axial vibration velocity of the winding disk, Z B ' represents the axial vibration velocity of the lower end plate of the winding; The axial vibration acceleration matrix of the winding is: Z T ″ represents the axial vibration acceleration of the upper end plate of the winding, Z n ″ represents the axial vibration acceleration of the winding disk, Z B ″ represents the axial vibration acceleration of the lower end plate of the winding; The equivalent mass matrix M of the winding disk is expressed as: M = diag(M T , M1, M2, …, M n-1 , M n , M B ) m T Denotes the weight of the upper end-plate of the winding, m n Denotes the weight of the middle disk of the winding, m D(n-1) Denotes the weight of the spacer between two disks of the winding, m B Denotes the weight of the lower end-plate of the winding, m DB Denotes the self-weight of the spacer group between the last disk of the winding and the bottom plate of the winding, m Dn Denotes the self-weight of the interlayer spacer group, m DT Denotes the weight of the spacer between the top plate of the winding and the first disk.

9. The modular analysis system for axial non-linear vibration of a transformer disc winding according to claim 7, wherein: The Bouc-Wen model is expressed as where x(t) is the displacement of the mass relative to the ground; z(t) is the hysteretic displacement; α is the ratio of the tangent stiffness at the peak of the hysteresis loop to the initial stiffness, denotes the restoring force, k is the initial stiffness, A and β are non-dimensional parameters jointly describing the shape of the non-linear hysteresis curve, and ψ, n are non-dimensional parameters describing the size and smoothness of the non-linear hysteresis curve, denotes the shear displacement rate, denotes the shear stress rate.

10. The modular analysis system for axial non-linear vibration of a transformer disc winding according to claim 7, characterized in that: The upper and lower clamping plate modules of the winding include 4 interfaces. The two output interfaces are respectively the damping output of the top clamping plate of the winding and the stiffness output of the top clamping plate of the winding. The two input interfaces are respectively the stiffness input of the lower coil pancake and the damping input of the lower coil pancake; The calculation unit module of the single-layer coil pancake of the winding includes 8 interfaces. The four output interfaces are respectively the damping influence on the upper coil pancake, the damping influence on the lower coil pancake, the stiffness influence on the upper coil pancake, and the stiffness influence on the lower coil pancake; The four input interfaces are respectively the damping influence of the upper coil pancake, the damping influence of the lower coil pancake, the stiffness influence of the upper coil pancake, and the stiffness influence of the lower coil pancake; The non-linear dynamic damping and stiffness module constructed based on the bonc-wen model includes three interfaces. The two output interfaces are the dynamic damping coefficient c i and the dynamic stiffness coefficient k i , and the model input interface is the displacement difference between the upper and lower line cakes Since the non-linearity varies with time, the non-linear dynamic damping and stiffness module calculates the strain between two single-layer winding units equivalent strain l i is the initial equivalent spacer thickness, and finally the input variable is used to output the dynamic stiffness k i and the damping c i .

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