CN114964474A - Method and device for detecting mechanical state of power transformer winding - Google Patents

Method and device for detecting mechanical state of power transformer winding Download PDF

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CN114964474A
CN114964474A CN202210574611.1A CN202210574611A CN114964474A CN 114964474 A CN114964474 A CN 114964474A CN 202210574611 A CN202210574611 A CN 202210574611A CN 114964474 A CN114964474 A CN 114964474A
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钱国超
王山
张家顺
代维菊
邹德旭
洪志湖
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Electric Power Research Institute of Yunnan Power Grid Co Ltd
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Abstract

The embodiment of the invention discloses a method and a device for detecting the mechanical state of a power transformer winding, wherein the method comprises the following steps: obtaining a transformer winding vibration characteristic curve obtained based on vibration characteristic test of a transformer; constructing a three-order non-negative tensor based on a transformer winding vibration characteristic curve, and calculating a non-negative core tensor of the three-order non-negative tensor based on a gradient descent method; acquiring an eigen transformation matrix of the non-negative core tensor, and calculating eigen parameters of the eigen transformation matrix based on the eigen transformation matrix; and comparing the characteristic parameters with the control limit value interval, and determining the mechanical state of the transformer winding according to the comparison result. The non-negative core tensor of the three-order non-negative tensor is calculated by adopting a gradient descent method, so that the obtained non-negative core tensor is optimized, the effectiveness of characteristic parameters obtained based on a characteristic transformation matrix of the non-negative core tensor is guaranteed, the mechanical state of the transformer winding is judged according to a comparison result of the characteristic parameters and the control limit value interval, and the method is efficient and simple.

Description

Method and device for detecting mechanical state of power transformer winding
Technical Field
The invention relates to the technical field of information monitoring, in particular to a method and a device for detecting the mechanical state of a power transformer winding.
Background
The method has low sensitivity and fault detection rate, can only give more accurate diagnosis results when the whole deformation of a transformer coil is serious, and can not provide any power for loosening the transformer winding. In the latter method, a transformer winding is taken as a distribution parameter network, the characteristics of the transformer winding are described by a transfer function in a frequency domain according to the change of the corresponding distribution parameters when the transformer winding is loosened or deformed, and the mechanical state of the winding is further judged, but the frequency response waveform of the method is more complex, particularly, high-frequency parameters are easily influenced by related interference, and the winding state needs abundant experience to be accurately judged. Because the transformer winding is mainly formed by winding electromagnetic wires according to a certain structure, if the transformer winding is regarded as a mechanical structure body consisting of a plurality of natural frequencies and corresponding modes, when any change occurs to the winding structure, the change can be reflected from the change of the mechanical characteristics of the winding. Therefore, the technology of how to efficiently and accurately monitor the mechanical state of the power transformer winding needs to be improved.
Disclosure of Invention
The invention mainly aims to provide a method and a device for detecting the mechanical state of a power transformer winding, which can solve the problem of inaccurate monitoring of the state of the transformer winding under short-circuit impact in the prior art.
In order to achieve the above object, a first aspect of the present invention provides a method for detecting a mechanical state of a winding of a power transformer, the method comprising:
obtaining a transformer winding vibration characteristic curve obtained based on vibration characteristic test of a transformer;
constructing a third-order non-negative tensor based on the transformer winding vibration characteristic curve, and calculating a non-negative core tensor of the third-order non-negative tensor based on a gradient descent method;
acquiring an eigen transformation matrix of the non-negative core tensor, and calculating eigen parameters of the eigen transformation matrix based on the eigen transformation matrix;
and comparing the characteristic parameters with the control limit value interval, and determining the mechanical state of the transformer winding according to the comparison result.
In the technical scheme, the vibration characteristic curve of the transformer winding can well reflect the mechanical vibration response characteristic, so that the mechanical state of the transformer winding is judged by processing the vibration characteristic curve of the transformer winding, and the sensitivity and the accuracy of monitoring the state of the transformer winding under short circuit impact are improved. Secondly, the non-negative core tensor of the three-order non-negative tensor is calculated by adopting a gradient descent method, so that the obtained non-negative core tensor is optimized, the effectiveness of characteristic parameters obtained based on a transformation matrix of the non-negative core tensor is guaranteed, and the accuracy of judging the mechanical state of the transformer winding is improved. And finally, judging the mechanical state of the transformer winding according to the comparison result of the obtained characteristic parameter and the control limit value interval, and being efficient and simple.
With reference to the first aspect, in one possible implementation manner, the calculating an nonnegative core tensor of the third-order nonnegative tensor based on the gradient descent method includes: establishing a solving model of a non-negative core tensor of the three-order non-negative tensor, and solving a 1-order projection tensor, a 2-order projection tensor and a 3-order projection tensor in the solving model by using a gradient descent method; calculating an non-negative core tensor based on the 1 st, 2 nd, and 3 rd order projection tensors.
With reference to the first aspect, in one possible implementation manner, the solving of the 1 st, 2 nd and 3 rd projection tensors in the solution model by using a gradient descent method includes: randomly initializing a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor in the solution model to obtain an initialized 1 st order projection tensor, an initialized 2 nd order projection tensor and an initialized 3 rd order projection tensor; and performing iterative computation on the 1 st order projection tensor, the 2 nd order projection tensor and the 3 rd order projection tensor based on the initialized 1 st order projection tensor, the initialized 2 nd order projection tensor and the initialized 3 rd order projection tensor until obtaining the non-negative core tensor meeting the convergence condition.
With reference to the first aspect, in one possible implementation manner, the solution model is as follows:
Figure BDA0003661583090000021
wherein A represents a third-order non-negative tensor; g denotes the non-negative core tensor; i A-G is produced 1 U (1) × 2 U (2) × 3 U (3) || F A Frobenius norm representing a matrix; u shape (1) 、U (2) And U (3) Respectively a 1 st, 2 nd and 3 rd order projection tensor.
With reference to the first aspect, in one possible implementation manner, the iteratively calculating the 1 st projection tensor, the 2 nd projection tensor and the 3 rd projection tensor based on the initialized 1 st projection tensor, the initialized 2 nd projection tensor and the initialized 3 rd projection tensor until obtaining the non-negative core tensor satisfying the convergence condition includes:
let k be k +1, where k is the number of iterations and the initial value of k is 0, and perform iterative update according to the following formula:
Figure BDA0003661583090000031
Figure BDA0003661583090000032
Figure BDA0003661583090000033
wherein the content of the first and second substances,
Figure BDA0003661583090000034
and
Figure BDA0003661583090000035
respectively 1 st, 2 nd and 3 rd order projection tensors, and when k is 0, U is 0 (1) 、U 0 (2) 、U 0 (3) Respectively initializing a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor;
Figure BDA0003661583090000036
1 is a 3 × 3 all 1 matrix;
Figure BDA0003661583090000037
representing element-wise multiplication; e represents division by element correspondence; t represents transposition;
the formula for calculating the non-negative core tensor is as follows:
Figure BDA0003661583090000038
wherein G is k Representing a non-negative core tensor; a represents a third order non-negative tensor;
Figure BDA0003661583090000039
and
Figure BDA00036615830900000310
respectively a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor; t represents transposition;
if the nonnegative core tensor satisfies the convergence condition | | G k -G k-1 And if the | | is less than the epsilon, stopping iteratively updating the 1 st order projection tensor, the 2 nd order projection tensor and the 3 rd order projection tensor, wherein the epsilon is an iteration convergence threshold value.
With reference to the first aspect, in a possible implementation manner, the obtaining an eigen transformation matrix of the non-negative core tensor includes: obtaining a first mode expansion matrix, a second mode expansion matrix and a third mode expansion matrix based on the non-negative core tensor; and calculating a corresponding first characteristic transformation matrix, a second characteristic transformation matrix and a third characteristic transformation matrix according to the first mode expansion matrix, the second mode expansion matrix and the third mode expansion matrix respectively.
With reference to the first aspect, in a possible implementation manner, the calculating the feature parameters of the feature transformation matrix based on the feature transformation matrix includes: performing singular value decomposition on the characteristic transformation matrix to obtain a diagonal matrix of the characteristic transformation matrix; and obtaining diagonal elements of the diagonal matrix, and calculating characteristic parameters of a characteristic transformation matrix according to the average value of the diagonal elements.
With reference to the first aspect, in a possible implementation manner, the above calculation formula for obtaining the diagonal matrix of the feature transformation matrix is as follows:
Figure BDA0003661583090000041
Figure BDA0003661583090000042
Figure BDA0003661583090000043
wherein E is 1 、E 2 、E 3 Respectively representing a first feature transformation matrix, a second feature transformation matrix and a third feature transformation matrix; q 1 、Q 2 And Q 3 A first singular matrix representing the first eigen transformation matrix, a second singular matrix representing the second eigen transformation matrix, and a third singular matrix representing the third eigentransformation matrix; lambda 1 、Λ 2 And Λ 3 Respectively representing a first diagonal matrix of the first feature transformation matrix, a second diagonal matrix of the second feature transformation matrix and a third diagonal matrix of the third feature transformation matrix;
the calculation formula for calculating the feature parameters of the feature transformation matrix according to the average value of the diagonal elements is as follows:
Figure BDA0003661583090000044
wherein η represents a characteristic parameter; alpha is alpha 1 、α 2 And alpha 3 Is a constant; c 1 、C 2 、C 3 Is dimension;
Figure BDA0003661583090000045
Figure BDA0003661583090000046
respectively expressed as the average value of the diagonal elements of the first diagonal matrix, the average value of the diagonal elements of the second diagonal matrix and the average value of the diagonal elements of the third diagonal matrix.
With reference to the first aspect, in one possible implementation manner, the determining the mechanical state of the transformer winding according to the comparison result includes: when the comparison result is that the characteristic parameter is not in the control limit value interval, judging that the transformer winding is deformed; and when the comparison result is that the characteristic parameter is within the control limit value interval, judging that the transformer winding is not deformed.
In order to achieve the above object, a second aspect of the present invention provides a power transformer winding mechanical state detection apparatus, the apparatus comprising:
a characteristic curve acquisition module: the method comprises the steps of obtaining a transformer winding vibration characteristic curve obtained based on vibration characteristic test of a transformer;
a non-negative core tensor computation module: the method comprises the steps of constructing a third-order non-negative tensor based on a transformer winding vibration characteristic curve, and calculating a non-negative core tensor of the third-order non-negative tensor based on a gradient descent method;
a characteristic parameter calculation module: the characteristic transformation matrix is used for acquiring a non-negative core tensor, and the characteristic parameters of the characteristic transformation matrix are calculated based on the characteristic transformation matrix;
a mechanical state determination module: and the characteristic parameter is used for comparing with the control limit value interval, and the mechanical state of the transformer winding is determined according to the comparison result.
By adopting the embodiment of the invention, the following beneficial effects are achieved: firstly, a three-order non-negative tensor is constructed through a transformer winding vibration characteristic curve, a gradient descent method is adopted to calculate the non-negative core tensor of the three-order non-negative tensor, then, a characteristic transformation matrix of the non-negative core tensor is obtained, characteristic parameters of the characteristic transformation matrix are calculated based on the characteristic transformation matrix, then, the characteristic parameters are compared with a control limit value interval, and finally, the mechanical state of a transformer winding is determined according to a comparison result. In the technical scheme, the vibration characteristic curve of the transformer winding can well reflect the mechanical vibration response characteristic, so that the mechanical state of the transformer winding is judged by processing the vibration characteristic curve of the transformer winding, and the sensitivity and the accuracy of monitoring the state of the transformer winding under short circuit impact are improved. Secondly, the non-negative core tensor of the three-order non-negative tensor is calculated by adopting a gradient descent method, so that the obtained non-negative core tensor is optimized, the effectiveness of characteristic parameters obtained based on a characteristic transformation matrix of the non-negative core tensor is ensured, and the accuracy of judging the mechanical state of the transformer winding is improved. And finally, the mechanical state of the transformer winding is judged according to the comparison result of the characteristic parameters and the control limit value interval, so that the method is efficient and simple.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Wherein:
FIG. 1 is a schematic flow chart illustrating a method for detecting a mechanical state of a winding of a power transformer according to an embodiment of the present invention;
FIG. 2 is a block diagram of a system for testing vibration characteristics of a transformer according to an embodiment of the present invention;
FIG. 3 is a block diagram of a device for detecting the mechanical state of a winding of a power transformer according to an embodiment of the present invention;
fig. 4 is a block diagram of a computer device according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a method for detecting the mechanical state of a winding of a power transformer, and the inventor of the application discovers through creative work that: under short-circuit impact, the vibration of the transformer box wall mainly consists of winding vibration under the action of short-circuit current, as long as the mechanical characteristics of the transformer winding are changed, the vibration can be reflected from the mechanical vibration response characteristics of the transformer winding, and the transformer vibration signal is easy to monitor on line, so that the sensitivity and the accuracy of monitoring the state of the transformer winding under the short-circuit impact are greatly improved, and the on-site implementation is extremely convenient.
Referring to fig. 1, fig. 1 is a schematic flow chart of a method for detecting a mechanical state of a winding of a power transformer according to an embodiment of the present invention, as shown in fig. 1, the method includes the following steps:
and S101, obtaining a transformer winding vibration characteristic curve obtained based on vibration characteristic test of the transformer.
Specifically, a transformer low-voltage winding is subjected to short circuit, M measuring points are obtained on the low-voltage side of the wall of the transformer box, and a vibration acceleration sensor is placed on each measuring point, namely M vibration acceleration sensors are placed on the low-voltage side of the wall of the transformer box. And injecting constant-current variable-frequency current into the high-voltage winding of the transformer by using the transformer vibration characteristic test system, and testing the transformer vibration characteristic to obtain a transformer winding vibration characteristic curve.
Referring to fig. 2, fig. 2 is a block diagram of a transformer vibration characteristic testing system according to an embodiment of the present invention, and as shown in fig. 2, the transformer vibration characteristic testing system includes a constant-current variable-frequency power supply, a step-up transformer, a signal acquisition module, a signal analysis module, and a signal display and control terminal, where the signal acquisition module is connected to a vibration acceleration sensor, acquires a transformer vibration signal, and outputs the transformer vibration signal to the signal analysis module; the signal analysis module analyzes the acquired transformer vibration signal and outputs an analysis result to the signal display and control terminal; the constant-current variable-frequency power supply is connected with the signal display and control terminal, wherein the signal display and control terminal is used for acquiring output parameters of the constant-current variable-frequency power supply, and the constant-current variable-frequency power supply outputs constant-current variable-frequency current to the step-up transformer based on the output parameters of the constant-current variable-frequency power supply acquired by the signal display and control terminal; the step-up transformer is connected with the transformer and applies the received constant-current variable-frequency current to a high-voltage winding of the transformer.
In the embodiment, the effective value of the constant-current variable-frequency current is 15A, the frequency variation range is 60 Hz-350 Hz, and the frequency point interval is 5 Hz. In addition, the signal display and control terminal is also used for judging whether the frequency of the constant-current variable-frequency current output by the constant-current variable-frequency power supply is greater than the termination frequency or not, if the signal display and control terminal judges that the frequency of the constant-current variable-frequency current output by the constant-current variable-frequency power supply is greater than the termination frequency, the frequency of the constant-current variable-frequency current is continuously increased for testing, and if the signal display and control terminal judges that the frequency of the constant-current variable-frequency current output by the constant-current variable-frequency power supply is not greater than the termination frequency, the testing is stopped. The signal analysis module calculates transformer winding vibration characteristic curves corresponding to the M measuring points according to the acquired transformer vibration signals, wherein the transformer winding vibration curve at the ith measuring point consists of Fourier transform calculation results of the transformer vibration signals at the ith measuring point, the Fourier transform is a common mathematical method in the field, and detailed description is omitted here.
In a possible implementation manner, the method for detecting the mechanical state of the power transformer winding may be applied to a signal analysis module, after the vibration characteristic curve of the transformer winding is obtained, the vibration characteristic curve of the transformer winding may be analyzed and processed by the signal analysis module to determine the mechanical state of the transformer winding, or may be applied to another signal analysis terminal, and the vibration characteristic curve of the transformer winding is analyzed and processed by the signal analysis terminal to determine the mechanical state of the transformer winding.
Step S102, a third-order non-negative tensor is constructed based on the transformer winding vibration characteristic curve, and a non-negative core tensor of the third-order non-negative tensor is calculated based on a gradient descent method.
After the vibration characteristic curve of the transformer winding is obtained, a third-order non-negative tensor is constructed based on the vibration characteristic curve of the transformer winding, and specifically, the third-order non-negative tensor constructed based on the vibration characteristic curve of the transformer winding
Figure BDA0003661583090000071
The frequency spectrum distribution of the transformer vibration signals corresponding to the frequency points of the constant current and variable frequency current and the frequency spectrum distribution of the transformer vibration signals corresponding to the frequency points are respectively three-dimensional.
And can further calculate the nonnegative core tensor of the third-order nonnegative tensor based on the gradient descent method, the concrete steps are as follows:
establishing a solving model of the non-negative core tensor of the three-order non-negative tensor, wherein the solving model is as follows:
Figure BDA0003661583090000081
in the formula: a represents the third-order non-negative tensor, A ≈ G- 1 U (1) × 2 U (2) × 3 U (3) (ii) a G is a non-negative core tensor; | A-G is prepared 1 U (1) × 2 U (2) × 3 U (3) || F Fro representing a matrixbenius norm; u shape (1) 、U (2) And U (3) Respectively a 1 st, 2 nd and 3 rd order projection tensor.
The method comprises the steps of solving a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor in a solved model by using a gradient descent method, calculating non-negative core tensors based on the 1 st order projection tensor, the 2 nd order projection tensor and the 3 rd order projection tensor, specifically, randomly initializing the 1 st order projection tensor, the 2 nd order projection tensor and the 3 rd order projection tensor in the solved model to obtain an initialized 1 st order projection tensor, an initialized 2 nd order projection tensor and an initialized 3 rd order projection tensor, and iteratively calculating the 1 st order projection tensor, the 2 nd order projection tensor and the 3 rd order projection tensor based on the initialized 1 st order projection tensor and the initialized 2 nd order projection tensor until the non-negative core tensor meeting convergence conditions is obtained.
The method comprises the following specific steps:
step 1) carrying out random initialization on 1-order projection tensor, 2-order projection tensor and 3-order projection tensor and respectively recording the initialization as initialization 1-order projection tensor
Figure BDA0003661583090000082
Initializing a 2 nd order projection tensor
Figure BDA0003661583090000083
And initializing a 3 rd order projection tensor
Figure BDA0003661583090000084
And ensure non-negative;
step 2) making k equal to k +1, where k is the iteration number, and the initial value of k is 0, and performing iteration updating according to the following formula:
Figure BDA0003661583090000085
Figure BDA0003661583090000086
Figure BDA0003661583090000087
in the formula:
Figure BDA0003661583090000088
and
Figure BDA0003661583090000089
respectively 1 st, 2 nd and 3 rd order projection tensors, and when k is 0, U is 0 (1) 、U 0 (2) 、U 0 (3) Respectively initializing a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor;
Figure BDA0003661583090000091
1 is a 3 × 3 all 1 matrix;
Figure BDA0003661583090000092
representing element-wise multiplication; e represents division by element correspondence; t represents transposition;
step 3) calculating the non-negative core tensor
Figure BDA0003661583090000093
Wherein G is k Representing a non-negative core tensor; a represents a third order non-negative tensor;
Figure BDA0003661583090000094
and
Figure BDA0003661583090000095
respectively a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor; t represents transposition;
step 4) if the nonnegative core tensor satisfies the convergence condition | | G k -G k-1 If | | < epsilon, performing step 5), otherwise, returning to the step 2) to continue iteration, wherein epsilon is an iteration convergence threshold;
step 5) outputting the non-negative core tensor G and the projection matrix U (1) 、U (2) And U (3) Here, the dimension of the non-negative core tensor G is C 1 ×C 2 ×C 3 And is provided with
Figure BDA0003661583090000096
C 1 、C 2 And C 3 Is not more than min { MD [) b ,MD s ,D c Where A has dimension MD b ×MD s ×D c ，MD b 、MD S 、D c The dimension of the third order non-negative tensor A.
And S103, acquiring an eigen transformation matrix of the non-negative core tensor, and calculating eigen parameters of the eigen transformation matrix based on the eigen transformation matrix.
The method comprises the following steps of obtaining an eigen transformation matrix of a non-negative core tensor G:
step S1031, obtaining a first mode expansion matrix, a second mode expansion matrix and a third mode expansion matrix based on the non-negative core tensor;
step S1032, a corresponding first feature transformation matrix, a corresponding second feature transformation matrix, and a corresponding third feature transformation matrix are calculated according to the first mode expansion matrix, the second mode expansion matrix, and the third mode expansion matrix, respectively.
Specifically, the nonnegative core tensor G is subjected to modulo 1, modulo 2 and modulo 3 expansion to respectively obtain a dimension C 1 ×C 2 C 3 、C 2 ×C 1 C 3 And C 3 ×C 1 C 2 First mode expansion matrix G 1 A second mode expansion matrix G 2 And a third mode expansion matrix G 3 。
Respectively calculating a first mode expansion matrix G of the non-negative core tensor 1 A second mode expansion matrix G 2 And a third mode expansion matrix G 3 Corresponding first feature transformation matrix E 1 A second eigen transformation matrix E 2 And a third eigen transformation matrix E 3 The corresponding calculation formula is as follows:
E 1 (i)＝G 1 (i) T G 1 (i) 0＜i＜C 2 C 3
E 2 (j)＝G 2 (j) T G 2 (j) 0＜j＜C 1 C 3
E 3 (k)＝G 3 (k) T G 3 (k) 0＜k＜C 1 C 2
in the formula: e 1 (i) And G 1 (i) Are respectively E 1 And G 1 Column i element of (1); e 2 (j) And G 2 (j) Are respectively E 2 And G 2 Column j of (1); e 3 (k) And G 3 (k) Are respectively E 3 And G 3 The kth column element of (1).
After the eigen transformation matrix of the non-negative core tensor is obtained, the eigen parameters of the eigen transformation matrix are calculated based on the eigen transformation matrix, and the method specifically comprises the following steps:
step S1033, singular value decomposition is carried out on the characteristic transformation matrix to obtain a diagonal matrix of the characteristic transformation matrix;
step S1034, diagonal elements of the diagonal matrix are obtained, and characteristic parameters of a characteristic transformation matrix are calculated according to the average value of the diagonal elements.
Specifically, singular value decomposition is performed on the feature transformation matrix to obtain a diagonal matrix thereof, and the corresponding calculation formula is as follows:
Figure BDA0003661583090000101
Figure BDA0003661583090000102
Figure BDA0003661583090000103
wherein, E 1 、E 2 、E 3 Respectively representing a first feature transformation matrix, a second feature transformation matrix and a third feature transformation matrix; q 1 、Q 2 And Q 3 Respectively represent first feature transformation matricesA singular matrix, a second singular matrix of the second eigen transformation matrix and a third singular matrix of the third eigentransformation matrix; lambda 1 、Λ 2 And Λ 3 Respectively representing a first diagonal matrix of the first eigen transformation matrix, a second diagonal matrix of the second eigentransformation matrix, and a third diagonal matrix of the third eigentransformation matrix.
Calculating the characteristic parameters of the characteristic transformation matrix according to the average value of the diagonal elements, wherein the calculation formula is as follows:
Figure BDA0003661583090000104
wherein η represents a characteristic parameter; alpha is alpha 1 、α 2 And alpha 3 Is a constant; c 1 、C 2 、C 3 Is dimension;
Figure BDA0003661583090000105
Figure BDA0003661583090000106
respectively expressed as the average value of the diagonal elements of the first diagonal matrix, the average value of the diagonal elements of the second diagonal matrix and the average value of the diagonal elements of the third diagonal matrix.
And step S104, comparing the characteristic parameters with the control limit value interval, and determining the mechanical state of the transformer winding according to the comparison result.
The control limit interval Ψ for the characteristic parameters of the characteristic transformation matrix is determined according to a 3 σ criterion, which is a mathematical method commonly used in the art and will not be described in detail herein. Judging the mechanical state of the transformer winding according to the control limit interval psi of the characteristic parameter eta of the characteristic transformation matrix, judging that the transformer winding is deformed if the characteristic parameter eta is not in the control limit interval psi, and timely processing the deformation if the deformation is required to avoid forming major faults; and when the characteristic parameter eta is within the control limit interval psi, judging that the transformer winding is not deformed.
Based on the method, the vibration characteristic curve of the transformer winding can well reflect the mechanical vibration response characteristic, so that the mechanical state of the transformer winding is judged by processing the vibration characteristic curve of the transformer winding, and the sensitivity and the accuracy of monitoring the state of the transformer winding under the short-circuit impact are improved. Secondly, the non-negative core tensor of the three-order non-negative tensor is calculated by adopting a gradient descent method, so that the obtained non-negative core tensor is optimized, the effectiveness of characteristic parameters obtained based on a characteristic transformation matrix of the non-negative core tensor is ensured, and the accuracy of judging the mechanical state of the transformer winding is improved. And finally, judging the mechanical state of the transformer winding according to the comparison result of the obtained characteristic parameter and the control limit value interval, and being efficient and simple.
In order to better implement the method, a device 30 for detecting a mechanical state of a winding of a power transformer according to an embodiment of the present invention is described below, referring to fig. 3, and fig. 3 is a block diagram of a structure of the device for detecting a mechanical state of a winding of a power transformer according to an embodiment of the present invention, and as shown in fig. 3, the device 30 includes:
the characteristic curve obtaining module 301: the method comprises the steps of obtaining a transformer winding vibration characteristic curve obtained based on vibration characteristic test of a transformer;
the non-negative core tensor calculation module 302: the method comprises the steps of constructing a third-order non-negative tensor based on a vibration characteristic curve of a transformer winding, and calculating a non-negative core tensor of the third-order non-negative tensor based on a gradient descent method;
the characteristic parameter calculation module 303: the characteristic transformation matrix is used for acquiring a non-negative core tensor, and the characteristic parameters of the characteristic transformation matrix are calculated based on the characteristic transformation matrix;
the mechanical state determination module 304: and the characteristic parameter is used for comparing with the control limit value interval, and the mechanical state of the transformer winding is determined according to the comparison result.
In a possible implementation manner, the non-negative core tensor calculation module 302 is specifically configured to: establishing a solving model of a non-negative core tensor of the three-order non-negative tensor, and solving a 1-order projection tensor, a 2-order projection tensor and a 3-order projection tensor in the solving model by using a gradient descent method; calculating an non-negative core tensor based on the 1 st, 2 nd, and 3 rd order projection tensors.
In a possible implementation manner, the non-negative core tensor calculation module 302 is specifically configured to: randomly initializing a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor in the solution model to obtain an initialized 1 st order projection tensor, an initialized 2 nd order projection tensor and an initialized 3 rd order projection tensor; and performing iterative computation on the 1 st order projection tensor, the 2 nd order projection tensor and the 3 rd order projection tensor based on the initialized 1 st order projection tensor, the initialized 2 nd order projection tensor and the initialized 3 rd order projection tensor until obtaining the non-negative core tensor meeting the convergence condition.
In a possible implementation manner, the non-negative core tensor calculation module 302 is specifically configured to:
Figure BDA0003661583090000121
wherein A represents a third-order non-negative tensor; g denotes the non-negative core tensor; | A-G is prepared 1 U (1) × 2 U (2) × 3 U(3)|| F A Frobenius norm representing a matrix; u shape (1) 、U (2) And U (3) Respectively a 1 st, 2 nd and 3 rd order projection tensor.
In a possible implementation manner, the non-negative core tensor calculation module 202 is specifically configured to: let k be k +1, where k is the number of iterations and the initial value of k is 0, and perform iterative update according to the following formula:
Figure BDA0003661583090000122
Figure BDA0003661583090000123
Figure BDA0003661583090000124
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003661583090000125
and
Figure BDA0003661583090000126
respectively 1 st, 2 nd and 3 rd order projection tensors, and when k is 0, U is 0 (1) 、U 0 (2) 、U 0 (3) Respectively initializing a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor;
Figure BDA0003661583090000127
1 is a 3 × 3 all 1 matrix;
Figure BDA0003661583090000128
representing element-wise multiplication; e represents division by element correspondence; t represents transposition;
the formula for calculating the non-negative core tensor is as follows:
Figure BDA0003661583090000131
wherein G is k Representing a non-negative core tensor; a represents a third order non-negative tensor;
Figure BDA0003661583090000132
and
Figure BDA0003661583090000133
respectively a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor; t represents transposition;
if the nonnegative core tensor satisfies the convergence condition | | G k -G k-1 And if the | | is less than the epsilon, stopping iteratively updating the 1 st order projection tensor, the 2 nd order projection tensor and the 3 rd order projection tensor, wherein the epsilon is an iteration convergence threshold value.
In a possible implementation manner, the characteristic parameter calculating module 303 is specifically configured to: obtaining a first mode expansion matrix, a second mode expansion matrix and a third mode expansion matrix based on the non-negative core tensor; and calculating a corresponding first characteristic transformation matrix, a second characteristic transformation matrix and a third characteristic transformation matrix according to the first mode expansion matrix, the second mode expansion matrix and the third mode expansion matrix respectively.
In a possible implementation manner, the characteristic parameter calculating module 303 is specifically configured to: performing singular value decomposition on the characteristic transformation matrix to obtain a diagonal matrix of the characteristic transformation matrix; and obtaining diagonal elements of the diagonal matrix, and calculating characteristic parameters of a characteristic transformation matrix according to the average value of the diagonal elements.
In a possible implementation manner, the mechanical state determination module 304 is specifically configured to: when the comparison result is that the characteristic parameter is not in the control limit value interval, judging that the transformer winding is deformed; and when the comparison result is that the characteristic parameter is within the control limit value interval, judging that the transformer winding is not deformed.
In the equipment, a three-order non-negative tensor is constructed through a transformer winding vibration characteristic curve, a gradient descent method is adopted to calculate the non-negative core tensor of the three-order non-negative tensor, then, a characteristic transformation matrix of the non-negative core tensor is obtained, characteristic parameters of the characteristic transformation matrix are calculated based on the characteristic transformation matrix, then, the characteristic parameters are compared with a control limit value interval, and finally, the mechanical state of the transformer winding is determined according to a comparison result. In the technical scheme, the vibration characteristic curve of the transformer winding can well reflect the mechanical vibration response characteristic, so that the mechanical state of the transformer winding is judged by processing the vibration characteristic curve of the transformer winding, and the sensitivity and the accuracy of monitoring the state of the transformer winding under short circuit impact are improved. Secondly, the non-negative core tensor of the three-order non-negative tensor is calculated by adopting a gradient descent method, so that the obtained non-negative core tensor is optimized, the effectiveness of characteristic parameters obtained based on a characteristic transformation matrix of the non-negative core tensor is ensured, and the accuracy of judging the mechanical state of the transformer winding is improved. And finally, judging the mechanical state of the transformer winding according to the comparison result of the characteristic parameter and the control limit value interval, and being efficient and simple.
FIG. 4 is a diagram illustrating an internal structure of a computer device in one embodiment. The computer device may specifically be a terminal, and may also be a server. As shown in fig. 4, the computer device includes a processor, a memory, and a network interface connected by a system bus. Wherein the memory includes a non-volatile storage medium and an internal memory. The non-volatile storage medium of the computer device stores an operating system and may also store a computer program, which, when executed by the processor, causes the processor to carry out the steps of the above-described method embodiments. The internal memory may also store a computer program, which, when executed by the processor, causes the processor to perform the steps of the above-described method embodiments. Those skilled in the art will appreciate that the architecture shown in fig. 4 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a non-volatile computer-readable storage medium, and can include the processes of the embodiments of the methods described above when the program is executed. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present application. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. A method of detecting a mechanical condition of a winding of a power transformer, the method comprising:
obtaining a transformer winding vibration characteristic curve obtained based on a vibration characteristic test of a transformer;
constructing a third-order non-negative tensor based on the transformer winding vibration characteristic curve, and calculating a non-negative core tensor of the third-order non-negative tensor based on a gradient descent method;
acquiring an eigen transformation matrix of the non-negative core tensor, and calculating eigen parameters of the eigen transformation matrix based on the eigen transformation matrix;
and comparing the characteristic parameters with the control limit value interval, and determining the mechanical state of the transformer winding according to the comparison result.
2. The method of claim 1, wherein the gradient descent based calculation of the non-negative core tensor of the third order non-negative tensor comprises:
establishing a solving model of a non-negative core tensor of the three-order non-negative tensor, and solving a 1-order projection tensor, a 2-order projection tensor and a 3-order projection tensor in the solving model by using a gradient descent method;
calculating an non-negative core tensor based on the 1 st, 2 nd, and 3 rd order projection tensors.
3. The method of claim 2, wherein solving the 1 st, 2 nd and 3 rd order projection tensors in the solution model using a gradient descent method comprises:
randomly initializing a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor in the solution model to obtain an initialized 1 st order projection tensor, an initialized 2 nd order projection tensor and an initialized 3 rd order projection tensor;
and performing iterative computation on the 1 st order projection tensor, the 2 nd order projection tensor and the 3 rd order projection tensor based on the initialized 1 st order projection tensor, the initialized 2 nd order projection tensor and the initialized 3 rd order projection tensor until obtaining the non-negative core tensor meeting the convergence condition.
4. The method of claim 2, wherein:
the solution model is as follows:
Figure FDA0003661583080000011
wherein A represents a third-order non-negative tensor; g denotes the non-negative core tensor; | A-G is prepared 1 U (1) × 2 U (2) × 3 U (3) || F A Frobenius norm representing a matrix; u shape (1) 、U (2) And U (3) Respectively a 1 st, 2 nd and 3 rd order projection tensor.
5. The method of claim 3, wherein iteratively calculating the 1 st, 2 nd and 3 rd order projection tensors based on the initialized 1 st, 2 nd and 3 rd order projection tensors until an unrenegative core tensor is obtained that satisfies a convergence condition comprises:
let k be k +1, where k is the number of iterations and the initial value of k is 0, and perform iterative update according to the following formula:
Figure FDA0003661583080000021
Figure FDA0003661583080000022
Figure FDA0003661583080000023
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003661583080000024
and
Figure FDA0003661583080000025
respectively 1 st, 2 nd and 3 rd order projection tensors, and when k is 0, U is 0 (1) 、U 0 (2) 、U 0 (3) Respectively initializing a 1 st order projection tensor, a 2 nd order projection tensor and a 3 rd order projection tensor;
Figure FDA0003661583080000026
1 is a 3 × 3 matrix of all 1's;
Figure FDA0003661583080000027
representing element-wise multiplication; e represents division by element correspondence; t represents transposition;
the formula for calculating the non-negative core tensor is as follows:
Figure FDA0003661583080000028
wherein G is k Representing a non-negative core tensor; a represents a third order non-negative tensor;
Figure FDA0003661583080000029
and
Figure FDA00036615830800000210
1, 2 and 3 projection tensors respectively; t represents transposition;
if the nonnegative core tensor satisfies the convergence condition | | G k -G k-1 And if the | | is less than the epsilon, stopping iteratively updating the 1 st order projection tensor, the 2 nd order projection tensor and the 3 rd order projection tensor, wherein the epsilon is an iteration convergence threshold value.
6. The method of claim 1, wherein obtaining the eigen transformation matrix for the non-negative core tensor comprises:
obtaining a first mode expansion matrix, a second mode expansion matrix and a third mode expansion matrix based on the non-negative core tensor;
and calculating a corresponding first characteristic transformation matrix, a second characteristic transformation matrix and a third characteristic transformation matrix according to the first mode expansion matrix, the second mode expansion matrix and the third mode expansion matrix respectively.
7. The method of claim 1, wherein the computing the feature parameters of the feature transformation matrix based on the feature transformation matrix comprises:
performing singular value decomposition on the characteristic transformation matrix to obtain a diagonal matrix of the characteristic transformation matrix;
and obtaining diagonal elements of the diagonal matrix, and calculating characteristic parameters of a characteristic transformation matrix according to the average value of the diagonal elements.
8. The method of claim 6, wherein:
the calculation formula for obtaining the diagonal matrix of the feature transformation matrix is as follows:
Figure FDA0003661583080000031
Figure FDA0003661583080000032
Figure FDA0003661583080000033
wherein E is 1 、E 2 、E 3 Respectively representing a first feature transformation matrix, a second feature transformation matrix and a third feature transformation matrix; q 1 、Q 2 And Q 3 A first singular matrix representing the first eigen transformation matrix, a second singular matrix representing the second eigen transformation matrix, and a third singular matrix representing the third eigentransformation matrix; lambda 1 、Λ 2 And Λ 3 Respectively representing a first diagonal matrix of the first feature transformation matrix, a second diagonal matrix of the second feature transformation matrix and a third diagonal matrix of the third feature transformation matrix;
the calculation formula for calculating the feature parameters of the feature transformation matrix according to the average value of the diagonal elements is as follows:
Figure FDA0003661583080000034
wherein η represents a characteristic parameter; alpha is alpha 1 、α 2 And alpha 3 Is a constant; c 1 、C 2 、C 3 Is dimension;
Figure FDA0003661583080000035
Figure FDA0003661583080000036
respectively expressed as an average value of diagonal elements of the first diagonal matrix, an average value of diagonal elements of the second diagonal matrix, and an average value of diagonal elements of the third diagonal matrix.
9. The method of claim 1, wherein determining the mechanical state of the transformer winding based on the comparison comprises:
when the comparison result is that the characteristic parameter is not in the control limit value interval, judging that the transformer winding is deformed;
and when the comparison result is that the characteristic parameter is within the control limit value interval, judging that the transformer winding is not deformed.
10. A device for detecting the mechanical condition of a winding of a power transformer, said device comprising:
a characteristic curve acquisition module: the method comprises the steps of obtaining a transformer winding vibration characteristic curve obtained based on vibration characteristic test of a transformer;
a non-negative core tensor computation module: the method comprises the steps of constructing a third-order non-negative tensor based on a transformer winding vibration characteristic curve, and calculating a non-negative core tensor of the third-order non-negative tensor based on a gradient descent method;
the characteristic parameter calculation module: the characteristic transformation matrix is used for acquiring a non-negative core tensor, and the characteristic parameters of the characteristic transformation matrix are calculated based on the characteristic transformation matrix;
a mechanical state determination module: and the characteristic parameter is used for comparing with the control limit value interval, and the mechanical state of the transformer winding is determined according to the comparison result.
CN202210574611.1A 2022-05-25 2022-05-25 Method and device for detecting mechanical state of power transformer winding Pending CN114964474A (en)

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