CN112926184A - Method for determining oil paper insulation failure probability of vehicle-mounted transformer - Google Patents

Method for determining oil paper insulation failure probability of vehicle-mounted transformer Download PDF

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CN112926184A
CN112926184A CN202110084619.5A CN202110084619A CN112926184A CN 112926184 A CN112926184 A CN 112926184A CN 202110084619 A CN202110084619 A CN 202110084619A CN 112926184 A CN112926184 A CN 112926184A
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mounted transformer
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CN112926184B (en
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贾步超
周平宇
张鹏
王治军
孙卫平
孙红梅
张冬梅
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CRRC Qingdao Sifang Co Ltd
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Abstract

The invention provides a method for determining the oil paper insulation failure probability of a vehicle-mounted transformer, which comprises the following steps: step S10, testing the moisture content, the organic acid content and the furfural content of the insulation failure of the oil paper insulation sample of the vehicle-mounted transformer after the oil paper insulation sample is in service at different kilometers, and establishing a fitting function of the service kilometers on the moisture content, the organic acid content and the furfural content; step S20, establishing a Weibull distribution probability density function of the vehicle-mounted transformer according to the fitting function, and determining an insulation accumulation failure probability model of the vehicle-mounted transformer according to the Weibull distribution probability density function; and step S30, combining the insulation accumulation failure probability model, the insulation failure probability of the vehicle-mounted transformer can be effectively predicted, and a guidance method is provided for the insulation state evaluation and the operation maintenance of the vehicle-mounted transformer in the actual engineering.

Description

Method for determining oil paper insulation failure probability of vehicle-mounted transformer
Technical Field
The invention relates to the technical field of power transformation equipment, in particular to a method for determining the oil paper insulation failure probability of a vehicle-mounted transformer.
Background
With the development of electrified railways, particularly the rapid development of high-speed railways, higher requirements are put on the safety and reliability of train operation. The vehicle-mounted transformer is used as an electric energy conversion distribution device of a high-speed motor train unit and a high-power electric locomotive, and the running state of the vehicle-mounted transformer is related to the running safety and reliability of the motor train unit and the electric locomotive. Because the vehicle-mounted transformer is different from the special structural design, the special operation working condition and the special working environment of the common power transformer, the internal oiled paper insulation failure probability of the vehicle-mounted transformer is also different from that of the common power transformer. The existing insulation failure probability model of the common power transformer cannot well evaluate the insulation loss state of the vehicle-mounted transformer, the oil paper insulation failure of the vehicle-mounted transformer can cause railway accidents and resource waste, and the accurate determination of the insulation failure of the vehicle-mounted transformer becomes a great challenge.
At present, a great deal of research is carried out on the moisture content, the organic acid content and the furfural content, the service life assessment result is quite abundant, but due to the characteristics of special working conditions and strong short-time load impact of the vehicle-mounted transformer, the existing insulation failure probability model cannot be applied. In addition, the existing research does not comprehensively consider the moisture content, the organic acid content, the furfural content and other factors, and the accurate evaluation of the insulation state of the vehicle-mounted transformer cannot be realized.
Disclosure of Invention
The invention mainly aims to provide a method for determining the oil paper insulation failure probability of a vehicle-mounted transformer, so as to solve the problem that the insulation state of the vehicle-mounted transformer cannot be accurately evaluated in the prior art.
In order to achieve the above object, according to an aspect of the present invention, there is provided a method for determining a failure probability of oil-paper insulation of an on-board transformer, the method specifically includes the following steps: step S10: testing the moisture content, the organic acid content and the furfural content of the vehicle-mounted transformer oil paper insulation sample subjected to insulation failure after service at different kilometers, and establishing a fitting function of the service kilometers on the moisture content, the organic acid content and the furfural content; step S20: establishing a Weibull distribution probability density function of the vehicle-mounted transformer according to the fitting function, and determining an insulation accumulation failure probability model of the vehicle-mounted transformer according to the Weibull distribution probability density function; step S30: and determining the failure probability of the oil paper of the vehicle-mounted transformer according to the number of kilometers of the actual service of the vehicle-mounted transformer by combining an insulation accumulation failure probability model.
Further, the step S10 includes the following steps: step S11: according to the principle that the insulation failure service kilometers of the vehicle-mounted transformer are from small to large, the corresponding moisture content, organic acid content and furfural content of the oil paper of the vehicle-mounted transformer under different insulation failure service kilometers are tested, and the fitting function is obtained through the following formula: f (t) ═ eWC9.75lnWO + WK, WC as moisture content, WO as organic acid content, WK as furfural content.
Further, the step S10 includes the following steps: step S12: and carrying out normalization processing on the fitting function to obtain a normalized first fitting curve, and establishing a Weibull distribution probability density function of the vehicle-mounted transformer according to the normalized first fitting curve.
Further, the normalized first fitted curve is obtained by the following formula:
Figure BDA0002910367280000021
f(tn) The maximum service kilometer number of the nth vehicle-mounted transformer when the oil paper insulation service life is invalid.
Further, the weibull distribution probability density function is obtained by the following formula:
Figure BDA0002910367280000022
alpha is a scale parameter, beta is a shape parameter, and gamma is a position parameter.
Further, step S20 includes the following stepsThe method comprises the following steps: step 21: determining a distribution function F (F (t)) based on a Weibull distribution probability density function, wherein,
Figure BDA0002910367280000023
alpha, beta and gamma are parameters; step 22: and performing parameter estimation on the parameters alpha, beta and gamma by utilizing maximum likelihood estimation to obtain a formula L (alpha, beta and gamma), wherein the unconstrained optimization model formula is as follows:
Figure BDA0002910367280000024
an estimate of the parameter α is obtained from the formula L (α, β, γ)
Figure BDA0002910367280000025
An estimate of the parameter β is
Figure BDA0002910367280000026
An estimate of the parameter gamma is
Figure BDA0002910367280000027
Step 23: according to
Figure BDA0002910367280000028
And
Figure BDA0002910367280000029
and determining an insulation cumulative failure probability model.
Further, the insulation cumulative failure probability model is obtained by the following formula:
Figure BDA00029103672800000210
or
Figure BDA00029103672800000211
fc(tx) K is f for actually testing the service kilometers of the vehicle-mounted transformerc(tx) The normalized coefficient, k is more than 0 and less than or equal to 1.
Further, in step S30, before determining the failure probability of the vehicle-mounted transformer paper, the method further includes the following steps: step S31: testing different clothes in practiceNumber of active kilometers fc(tx) Determining the corresponding moisture content, organic acid content and furfural content of the corresponding paper edge sample of the lower vehicle-mounted transformer oil paper by combining the normalized first fitting curvex) According to f (t)x) Different service kilometer number f of actual vehicle-mounted transformerc(tx) And performing normalization processing to obtain a normalized second fitted curve, and determining the actual insulation failure probability of the vehicle-mounted transformer oil paper according to the normalized second fitted curve.
Further, the second fitted curve is obtained by the following formula:
Figure BDA00029103672800000212
wherein k is fc(tx) The normalized coefficient, k is more than 0 and less than or equal to 1.
Further, in practice, the insulation failure probability of the oil paper of the vehicle-mounted transformer is obtained by the following formula:
Figure BDA0002910367280000031
by applying the technical scheme of the invention, a mathematical relation is established by testing the moisture content, the organic acid content and the furfural content of the oil paper insulation sample of the vehicle-mounted transformer under different service kilometers of insulation failure, the failure probability of the oil paper of the vehicle-mounted transformer is determined according to a Weibull distribution function of three parameters, and during engineering application, the insulation failure probability of the vehicle-mounted transformer can be effectively predicted by combining the failure probability of the oil paper of the vehicle-mounted transformer according to the moisture content, the organic acid content and the furfural content after the oil paper of the vehicle-mounted transformer is actually used for a certain kilometer, so that the accurate evaluation of the insulation state of the oil paper of the vehicle-mounted transformer is realized.
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The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 shows a schematic flow diagram according to a first embodiment of the invention;
fig. 2 shows a schematic flow diagram according to a second embodiment of the invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
It should be noted that the terms "first," "second," and the like in the description and claims of this application and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments of the application described herein are, for example, capable of operation in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Exemplary embodiments according to the present application will now be described in more detail with reference to the accompanying drawings. These exemplary embodiments may, however, be embodied in many different forms and should not be construed as limited to only the embodiments set forth herein. It is to be understood that these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art, in the drawings, it is possible to enlarge the thicknesses of layers and regions for clarity, and the same devices are denoted by the same reference numerals, and thus the description thereof will be omitted.
Referring to fig. 1 and 2, according to an embodiment of the present invention, a method for determining a paper-oil insulation failure probability of an on-board transformer is provided.
As shown in fig. 1, in this embodiment, the method includes the following specific steps: step S10: testing the moisture content, the organic acid content and the furfural content of the vehicle-mounted transformer oil paper insulation sample subjected to insulation failure after the service of the sample is different kilometers, and establishing a fitting function of the service kilometers on the moisture content, the organic acid content and the furfural content. Step S20: and establishing a Weibull distribution probability density function of the vehicle-mounted transformer according to the fitting function, and determining an insulation accumulation failure probability model of the vehicle-mounted transformer according to the Weibull distribution probability density function. Step S30: and determining the failure probability of the oil paper of the vehicle-mounted transformer according to the number of kilometers of the actual service of the vehicle-mounted transformer by combining an insulation accumulation failure probability model.
In the embodiment, a mathematical relation is established by testing the moisture content, the organic acid content and the furfural content of the vehicle-mounted transformer oil paper insulation sample under different service kilometers of insulation failure, the failure probability of the vehicle-mounted transformer oil paper is determined according to a three-parameter Weibull distribution function, and during engineering application, the insulation failure probability of the vehicle-mounted transformer can be effectively predicted according to the moisture content, the organic acid content and the furfural content after the vehicle-mounted transformer oil paper is actually used for a certain kilometer and in combination with the failure probability of the vehicle-mounted transformer oil paper, so that the accurate evaluation of the insulation state of the vehicle-mounted transformer oil paper is realized.
Wherein, the step 10 further comprises the following steps: step S11: according to the principle that the insulation failure service kilometers of the vehicle-mounted transformer are from small to large, the corresponding moisture content, organic acid content and furfural content of the oil paper of the vehicle-mounted transformer under different insulation failure service kilometers are tested, and the fitting function is obtained through the following formula:
f(t)＝eWC9.75lnWO + WK, WC as moisture content, WO as organic acid content, WK as furfural content.
Step S12: and carrying out normalization processing on the fitting function to obtain a normalized first fitting curve, and establishing a Weibull distribution probability density function of the vehicle-mounted transformer according to the normalized first fitting curve. The normalized first fit curve is obtained by the following equation:
Figure BDA0002910367280000041
f(tn) The maximum service kilometer number of the nth vehicle-mounted transformer when the oil paper insulation service life is invalid.
The weibull distribution probability density function is obtained by the following formula:
Figure BDA0002910367280000042
alpha is a scale parameter, beta is a shape parameter, and gamma is a position parameter.
The step 20 further comprises the following steps:
step 21: determining a distribution function F (F (t)) based on a Weibull distribution probability density function, wherein,
Figure BDA0002910367280000043
alpha, beta and gamma are parameters;
step 22: and performing parameter estimation on the parameters alpha, beta and gamma by utilizing maximum likelihood estimation to obtain a formula L (alpha, beta and gamma), wherein the unconstrained optimization model formula is as follows:
Figure BDA0002910367280000051
an estimate of the parameter α is obtained from the formula L (α, β, γ)
Figure BDA0002910367280000052
An estimate of the parameter β is
Figure BDA0002910367280000053
An estimate of the parameter gamma is
Figure BDA0002910367280000054
Step 23: according to
Figure BDA0002910367280000055
And
Figure BDA0002910367280000056
and determining an insulation cumulative failure probability model.
The insulation cumulative failure probability model is obtained by the following formula:
Figure BDA0002910367280000057
or
Figure BDA0002910367280000058
fc(tx) K is f for actually testing the service kilometers of the vehicle-mounted transformerc(tx) The normalized coefficient, k is more than 0 and less than or equal to 1.
The step 30 further comprises the following steps:
step S31: testing different service kilometers f in practicec(tx) Determining the corresponding moisture content, organic acid content and furfural content of the corresponding paper edge sample of the lower vehicle-mounted transformer oil paper by combining the normalized first fitting curvex) According to f (t)x) Different service kilometer number f of actual vehicle-mounted transformerc(tx) And performing normalization processing to obtain a normalized second fitted curve, and determining the actual insulation failure probability of the vehicle-mounted transformer oil paper according to the normalized second fitted curve.
The second fitted curve is obtained by the following formula:
Figure BDA0002910367280000059
wherein k is fc(tx) The normalized coefficient, k is more than 0 and less than or equal to 1.
In practice, the insulation failure probability of the vehicle-mounted transformer oilpaper is obtained by the following formula:
Figure BDA00029103672800000510
as shown in fig. 2, in another embodiment, the method comprises the following specific steps:
step S10: WCi in the oil paper insulation test sample of the vehicle-mounted transformer with the insulation failure is obtained as the moisture content, WOi is the organic acid content, and WKi is the furfural content.
Testing the moisture content WCi, the organic acid content WOi and the furfural content WKi in the insulation test sample of the vehicle-mounted transformer oil paper with insulation failure, and testing different insulation failure service kilometers f (t) according to the principle that the insulation failure service kilometers are from small to largei) The following corresponding moisture content WCi, organic acid content WOi, and furfural content WKi, i ═ 1,2,3n) The unit is ten thousand kilometers for the maximum operation kilometer number when the insulation service life is failed, and n is a serial number corresponding to the maximum operation kilometer number when the insulation service life is failed.
Step S20: and (3) normalizing the obtained WCi as the moisture content, WOi as the organic acid content and WKi as the furfural content.
The different service kilometers f (t) in the step S10i) Fitting with corresponding test data of moisture content WCi, organic acid content WOi and furfural content WKi to obtain the numerical relationship between service kilometers and moisture content WCi, organic acid content WOi and furfural content WKi, and giving by formula (1):
f(t)＝eWC-9.75lnWO+WK (1)
normalized to f (t)n) Sometimes:
Figure BDA0002910367280000061
step S30: establishing a probability model of insulation failure of a Weibull distribution vehicle-mounted transformer with three parameters of water content WCi, organic acid content WOi and furfural content WKi.
The weibull distribution probability density function is:
Figure BDA0002910367280000062
the distribution function relationship is:
Figure BDA0002910367280000063
wherein, F (F (t)) is the insulation accumulated failure probability when the service kilometer number is F (t), and represents the insulation failure probability when the service kilometer number is not more than F (t), alpha is a scale parameter, beta is a shape parameter, and gamma is a position parameter.
Step S40: fitting Weibull distribution parameters;
the service kilometer number f (t) obeys Weibull distribution, and the parameters of alpha, beta and gamma are estimated by maximum likelihood estimation, which is given by formula (5):
Figure BDA0002910367280000064
and (3) taking natural logarithm at two sides of the formula (5) simultaneously to obtain an unconstrained optimization model formula (6):
Figure BDA0002910367280000071
solving the parameter estimation value according to the formula (6)
Figure BDA0002910367280000072
And
Figure BDA0002910367280000073
obtaining a Weibull distribution vehicle-mounted transformer insulation failure probability model with known parameters:
Figure BDA0002910367280000074
step S50: applying a Weibull distribution vehicle-mounted transformer insulation failure probability model to engineering;
testing different service kilometers fc(tx) The moisture content WCx, the organic acid content WOx and the furfural content WKx corresponding to the lower vehicle-mounted transformer are combined with the formula (1) and the formula (2) to solve the calculated kilometer number f (t) under the conditions of the moisture content WCx, the organic acid content WOx and the furfural content WKxx)。
The normalized values are equal and satisfy formula (8):
Figure BDA0002910367280000075
wherein k is a normalization coefficient, and k is more than 0 and less than or equal to 1;
calculating the kilometer reading f (t)x) And (3) solving the insulation failure probability of the vehicle-mounted transformer by combining a formula (7) and a formula (8), wherein the insulation failure probability of the vehicle-mounted transformer is given by a formula (9), and the calculation of the insulation failure probability of the vehicle-mounted transformer is completed:
Figure BDA0002910367280000076
wherein f isc(tx) The number of service kilometers to be measured is arranged from small to large, x is an arrangement serial number, and 1,2,3, is taken as x, and m is the maximum value of the number of vehicle-mounted transformers to be measured.
Spatially relative terms, such as "above … …," "above … …," "above … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial relationship to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is turned over, devices described as "above" or "on" other devices or configurations would then be oriented "below" or "under" the other devices or configurations. Thus, the exemplary term "above … …" can include both an orientation of "above … …" and "below … …". The device may be otherwise variously oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
In addition to the foregoing, it should be noted that reference throughout this specification to "one embodiment," "another embodiment," "an embodiment," or the like, means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment described generally throughout this application. The appearances of the same phrase in various places in the specification are not necessarily all referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with any embodiment, it is submitted that it is within the scope of the invention to effect such feature, structure, or characteristic in connection with other embodiments.
In the foregoing embodiments, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. The method for determining the oil paper insulation failure probability of the vehicle-mounted transformer is characterized by comprising the following steps of:
step S10: testing the moisture content, the organic acid content and the furfural content of the vehicle-mounted transformer oil paper insulation sample subjected to insulation failure after being in service at different kilometers, and establishing a fitting function of the service kilometers on the moisture content, the organic acid content and the furfural content;
step S20: establishing a Weibull distribution probability density function of the vehicle-mounted transformer according to the fitting function, and determining an insulation accumulation failure probability model of the vehicle-mounted transformer according to the Weibull distribution probability density function;
step S30: and determining the failure probability of the vehicle-mounted transformer oilpaper according to the number of kilometers of the actual service of the vehicle-mounted transformer by combining the insulation cumulative failure probability model.
2. The method according to claim 1, wherein the step S10 further comprises the steps of:
step S11: testing the corresponding moisture content, organic acid content and furfural content of the vehicle-mounted transformer oilpaper under different insulation failure service kilometers according to the principle that the insulation failure service kilometer number of the vehicle-mounted transformer is from small to large, wherein the fitting function is obtained by the following formula:
f(t)＝eWC9.75lnWO + WK, WC as moisture content, WO as organic acid content, WK as furfural content.
3. The method according to claim 2, wherein the step S10 further comprises the steps of:
step S12: and carrying out normalization processing on the fitting function to obtain a normalized first fitting curve, and establishing a Weibull distribution probability density function of the vehicle-mounted transformer according to the normalized first fitting curve.
4. The method of claim 3, wherein the normalized first fit curve is obtained by the following equation:
Figure FDA0002910367270000011
f(tn) The maximum service kilometer number of the nth vehicle-mounted transformer when the oil paper insulation service life is invalid.
5. The method of claim 3, wherein the Weibull distribution probability density function is obtained by the following equation:
Figure FDA0002910367270000012
alpha is a scale parameter, beta is a shape parameter, and gamma is a position parameter.
6. The method according to claim 5, wherein the step S20 further comprises the steps of:
step 21: determining a distribution function F (F (t)) from the Weibull distribution probability density function, wherein,
Figure FDA0002910367270000013
alpha, beta and gamma are parameters;
step 22: and performing parameter estimation on the parameters alpha, beta and gamma by utilizing maximum likelihood estimation to obtain a formula L (alpha, beta and gamma), wherein the unconstrained optimization model formula is as follows:
Figure FDA0002910367270000021
an estimate of the parameter α is obtained from the formula L (α, β, γ)
Figure FDA0002910367270000022
An estimate of the parameter β is
Figure FDA0002910367270000023
An estimate of the parameter gamma is
Figure FDA0002910367270000024
Step 23: according to
Figure FDA0002910367270000025
And
Figure FDA0002910367270000026
determining the insulation cumulative failure probability model.
7. The method of claim 6, wherein the insulation cumulative failure probability model is obtained by the following equation:
Figure FDA0002910367270000027
or
Figure FDA0002910367270000028
fc(tx) K is f for actually testing the service kilometers of the vehicle-mounted transformerc(tx) The normalized coefficient, k is more than 0 and less than or equal to 1.
8. The method according to claim 4, wherein in the step S30, before determining the failure probability of the vehicle-mounted transformer oilpaper, the method further comprises the following steps:
step S31: testing different service kilometers f in practicec(tx) Determining the corresponding moisture content, organic acid content and furfural content of the corresponding paper margin sample of the vehicle-mounted transformer oil paper by combining the normalized first fitting curvex) According to f (t)x) For different service kilometers f of the vehicle-mounted transformer in practicec(tx) And carrying out normalization processing to obtain a normalized second fitted curve, and determining the actual insulation failure probability of the vehicle-mounted transformer oil paper according to the normalized second fitted curve.
9. The method of claim 8, wherein the second fitted curve is obtained by the following equation:
Figure FDA0002910367270000029
wherein k is fc(tx) The normalized coefficient, k is more than 0 and less than or equal to 1.
10. The method according to claim 8, wherein the insulation failure probability of the vehicle-mounted transformer paper is actually obtained by the following formula:
Figure FDA00029103672700000210
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