CN108919041B - Transformer winding state online monitoring method based on cluster analysis - Google Patents

Abstract

The invention discloses a transformer winding shape based on cluster analysisThe on-line monitoring method of state, it includes: acquiring vibration signals of the wall of the transformer tank, and carrying out standardized processing on the acquired vibration signals; intercepting the vibration signals after the standardization processing to obtain m groups of vibration signals; performing clustering analysis on the m groups of vibration signals of the transformer to obtain a transformer vibration characteristic curve; computing a cluster of classes as C_t ^(k)Vibration characteristic curve Z of various vibration signals relative to transformer_tCurve rate of change Y of_ciThe mean of the root mean square values of (2) is obtained as Y_cm(ii) a Calculating transformer vibration curve y 'to be detected'_cCharacteristic curve Z of vibration relative to transformer_tCurve change rate Y'_cOf (d) is Y'_cm(ii) a Prepared from Y'_cmAnd Y_cmFor comparison, Y'_cm≤Y_cmJudging that the running state of the transformer winding is normal; y'_cm＞Y_cmThe transformer winding becomes loose or deformed; the method can effectively and highly sensitively monitor the loosening and deformation conditions of the transformer winding on line.

Description

Transformer winding state online monitoring method based on cluster analysis

Technical Field

The invention relates to a transformer signal monitoring method, in particular to a transformer winding state online monitoring method based on cluster analysis.

Background

The transformer is one of the most important devices in the power system, and the stability of the operation of the transformer has a great influence on the safety of the power system. With the increasing capacity of power grids in China, the capacity of short circuits is also increased continuously, and the huge electromagnetic force generated by impact current formed by short circuit at the outlet of a transformer poses serious threat to the mechanical strength of windings. After a transformer is subjected to a sudden short circuit, its windings may first become loose or slightly deformed, and transformer winding deformation has a cumulative effect. Accordingly, if the looseness or deformation cannot be found and repaired in time, the short-circuit resistance of the transformer is greatly reduced after the looseness or deformation is accumulated to a certain extent, and a large accident is caused even when a small impact current is applied.

Therefore, in the conventional maintenance after the transformer is subjected to an external short-circuit accident or after the transformer is operated for a period of time in the operation process, how to effectively detect whether the transformer winding is loosened and deformed is important to judge whether the transformer needs to be maintained or not, and the method is an important means for ensuring the safe operation of the transformer. If the transformer winding is regarded as a mechanical structure, any change of the winding structure or stress can be reflected on the change of the mechanical vibration characteristic of the winding. The vibration of the winding is transmitted to the transformer box body through the internal structural connecting piece of the transformer, so that a vibration signal detected on the surface of the transformer box body has a close relation with the vibration characteristic of the winding of the transformer, and the vibration signal analysis on the surface of the transformer box body can be used as a way for diagnosing the fault of the winding of the transformer. The method obtains the vibration signal of the transformer through the vibration sensor attached to the wall of the transformer box, and accordingly, the change condition of the winding state is judged. As long as the mechanical characteristics (such as structural deformation, pretightening force looseness and the like) of the winding are changed, the mechanical vibration characteristics can be reflected, and therefore the detection sensitivity is greatly improved. In addition, the vibration detection of the vibration sensor on the box wall is not directly connected with the whole strong electric system, so that the normal operation of the whole electric system is not influenced, and the method is an accurate, convenient and safe online monitoring method. However, under the influence of various factors such as the mechanical structure of the transformer, the dispersion of the process, the operating environment of the transformer substation and the like, it has been a difficult point to research how to obtain a more accurate winding state monitoring method from a mass of vibration signals acquired by the transformer vibration online monitoring system.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the transformer winding state online monitoring method based on cluster analysis is improved, and the technical problems that in the prior art, vibration signal analysis on the surface of a transformer box body is adopted as transformer winding fault diagnosis, and accurate winding state monitoring cannot be obtained from mass vibration signals obtained by a transformer vibration online monitoring system efficiently and accurately due to the influence of various factors such as a mechanical structure of a transformer, process dispersibility and a transformer substation operation environment.

The technical scheme of the invention is as follows:

a transformer winding state online monitoring method based on cluster analysis comprises the following steps:

step 1, collecting vibration signals x (t) of the wall of a transformer tank, and carrying out standardization processing on the collected vibration signals x (t);

step 2, intercepting the vibration signal after the standardized processing, wherein the intercepting interval is delta t, and the intercepting length is N₁Taking the lowest point of the vibration signals as the starting point of each group of vibration signals to obtain m groups of vibration signals;

step 3, performing clustering analysis on the m groups of vibration signals of the transformer to obtain a transformer vibration characteristic curve;

step 4, calculating the cluster as C_t ^(k)Vibration characteristic curve Z of various vibration signals relative to transformer_tCurve rate of change Y of_ciRoot mean square value of_cmi(i 1, …, h) to obtain the root mean square value Y_cmiHas an average value of Y_cm；

Step 5, calculating a transformer vibration curve y 'to be detected'_cCharacteristic curve Z of vibration relative to transformer_tCurve change rate Y'_cOf (d) is Y'_cm；

Step 6, mixing Y'_cmAnd Y_cmComparing if Y 'is satisfied'_cm≤Y_cmJudging that the running state of the transformer winding is normal; if Y 'is satisfied'_cm＞Y_cmAnd judging that the transformer winding is loosened or deformed. The calculation formula of the vibration signal standardization processing in the step 1 is

In the formula (I), the compound is shown in the specification,

is the average of the vibration signal x (t); n is the length of the vibration signal x (t); and y (t) is the vibration signal after the normalization processing.

The method for calculating the vibration characteristic curve of the transformer in the step 3 comprises the following steps:

step 3.1, recording m groups of data as C₁ ⁽⁰⁾、C₂ ⁽⁰⁾、……、C_m ⁽⁰⁾And regarding each group of data as an independent class, calculating Euclidean distance between every two classes to obtain an m-order initial distance matrix D⁽⁰⁾；

Step 3.2, searching an initial distance matrix D⁽⁰⁾Minimum value of all elements in (1), denoted as d_0ijIn the formula: i ≠ j, which will be identical to d, …, m, j ≠ 1, …, m, and satisfies i ≠ j_0ijCorresponding two classes C_i ⁽⁰⁾And C_j ⁽⁰⁾Merging to obtain new cluster C_ij ⁽¹⁾＝{C_i ⁽⁰⁾,C_j ⁽⁰⁾}；

Step 3.3, new cluster C_ij ⁽¹⁾Regarding the non-merged class as new m-1 class data; calculating the distance between every two types in the m-1 type to obtain a new m-1 order distance matrix D⁽¹⁾Wherein the distance between each two non-merged classes is calculated using Euclidean distance, class cluster C_ij ⁽¹⁾The distance from the m-2 classes which are not merged is calculated by using an intermediate distance formula

In the formula, h is a cluster C_ij ⁽¹⁾The number of classes in (1); d_xpIs a cluster C_ij ⁽¹⁾Euclidean distance of the pth class to the xth unmerged class; d_xqIs a cluster C_ij ⁽¹⁾Euclidean distance of the qth class to the xth unmerged class; d_pqIs a cluster C_ij ⁽¹⁾The Euclidean distance between the pth class and the qth class;

step 3.4, finding a distance matrix D⁽¹⁾Minimum value of all elements in (1), denoted as d_1ijWhere i ≠ j, where i ≠ 1, …, m-1, j ≠ 1, …, m-1, and i ≠ j is to be associated with d_1ijCorresponding two classes C_i ⁽¹⁾And C_j ⁽¹⁾Merging to obtain new cluster C_ij ⁽²⁾＝{C_i ⁽¹⁾,C_j ⁽¹⁾And e, repeating the step 3.3 until a distance matrix D is obtained after k times of operation^(k)Minimum value d of all elements in_kijStopping calculation when the distance is less than the set threshold or the dimension of the distance matrix is 0, and converting the distance matrix D into the distance matrix D^(k)Each cluster of the corresponding class of each group of data in (1) is marked as C₁ ^(k)、C₂ ^(k)、……、C_b ^(k)；

Step 3.5, recording the cluster with the largest number of the included classes as C_t ^(k)T is more than or equal to 1 and less than or equal to b, and a cluster C is calculated_t ^(k)Center of mass Z_tAs a vibration characteristic curve of the transformer, the centroid Z_tIs calculated by the formula

In the formula, h is a cluster C_t ^(k)The number of classes contained in (a); y is_jkIs a cluster C_tThe j-th vibration signal curve in (1).

Step 4, the calculation cluster is C_t ^(k)Vibration characteristic curve Z of various vibration signals relative to transformer_tCurve rate of change Y of_ciIs calculated by the formula

In the formula, y_iIs a cluster C_tThe ith vibration signal curve of (1);

the mean value of the ith vibration signal curve is obtained;

the average value of the vibration characteristic curve of the transformer is shown.

Step 5, calculating a transformer vibration curve y 'to be detected'_cCharacteristic curve Z of vibration relative to transformer_tCurve change rate Y'_cIs calculated by the formula

The invention has the beneficial effects that:

the invention carries out cluster analysis on the vibration signals of the wall of the transformer box in a certain time period to obtain the vibration characteristic curve of the transformer and the mean value (namely Y) of the root mean square value of the curve change rate of various vibration signals in the cluster where the vibration characteristic curve of the transformer is relative to the vibration characteristic curve of the transformer_cm) And then comparing the root mean square value (Y ') of the variation rate of the transformer vibration curve to be detected relative to the transformer vibration characteristic curve'_cm) With the above average value (i.e. Y)_cm) And comparing the voltage and the current, and judging the working state of the transformer winding according to the change of the voltage and the current.

By adopting the technical scheme, the working state of the transformer winding can be directly judged by monitoring the vibration signal of the wall of the transformer tank in real time, the judging method is efficient and accurate, is easy to implement, and is convenient for operators to find the abnormity of the transformer winding in time, so that the transformer can be overhauled in time according to the abnormal condition, and the fault damage rate of the transformer is greatly reduced; the technical problems that in the prior art, vibration signal analysis on the surface of a transformer box body is adopted as fault diagnosis of a transformer winding, and due to the influence of various factors such as the mechanical structure of the transformer, the dispersion of the process, the operation environment of a transformer substation and the like, a large amount of vibration signals obtained from a transformer vibration online monitoring system cannot be efficiently and accurately monitored in the winding state, and the like are solved.

Drawings

FIG. 1 is a flow chart of a vibration signal cluster analysis method employed in an embodiment of the present invention;

FIG. 2 is a schematic diagram of a cluster analysis result obtained in this embodiment;

fig. 3 is a schematic diagram of a transformer vibration characteristic curve obtained in the embodiment of the present invention.

Detailed Description

The invention provides a transformer winding state online monitoring method based on cluster analysis, which comprises the following steps

(1) Collecting vibration signals x (t) of the transformer box wall, and carrying out standardization processing on the vibration signals x (t). The vibration signal standardization processing calculation formula is

In the formula (I), the compound is shown in the specification,

is the average of the vibration signal x (t); n is the length of the vibration signal x (t); and y (t) is the vibration signal after the normalization processing.

(2) Intercepting the vibration signal after the standardization processing, wherein the interception interval is delta t, and the interception length is N₁And taking the lowest point of the vibration signals as the starting point of each group of vibration signals to obtain m groups of vibration signals.

(3) And performing cluster analysis on the m groups of vibration signals of the transformer to obtain a transformer vibration characteristic curve. The method comprises the following specific steps:

recording m sets of data as C₁ ⁽⁰⁾、C₂ ⁽⁰⁾、……、C_m ⁽⁰⁾And regarding each group of data as an independent class, calculating Euclidean distance between every two classes to obtain an m-order initial distance matrix D⁽⁰⁾. The calculation method of the euclidean distance in this step is a mathematical method commonly used in the art, and therefore, the inventor does not describe in detail herein;

3b. find initial distance matrix D⁽⁰⁾Minimum value of all elements in (1), denoted as d_0ijWherein i ≠ j, …, m, j ≠ 1, …, m, and satisfies i ≠ j. Will be reacted with d_0ijCorresponding two classes C_i ⁽⁰⁾And C_j ⁽⁰⁾Merging to obtain new cluster C_ij ⁽¹⁾＝{C_i ⁽⁰⁾,C_j ⁽⁰⁾}；

Cluster C. New class_ij ⁽¹⁾Regarding the non-merged class as new m-1 class data, wherein the non-merged class means that the m groups of data in step 3a do not include class C_i ⁽⁰⁾And C_j ⁽⁰⁾And (3) data of (1), in m-2 classes. Inscription of m-1 as C₁ ⁽⁰⁾、C₂ ⁽⁰⁾、……、C_i-1 ⁽⁰⁾、C_ij ⁽¹⁾、C_j-1 ⁽⁰⁾、……、C_m-1 ⁽⁰⁾. Calculating the distance between every two types in the m-1 type to obtain a new m-1 order distance matrix D⁽¹⁾Wherein the distance between each two non-merged classes is calculated using Euclidean distance, class cluster C_ij ⁽¹⁾The distance from the m-2 classes which are not merged is calculated by using an intermediate distance formula

In the formula, h is a cluster C_ij ⁽¹⁾The number of classes in (1); d_xpIs a cluster C_ij ⁽¹⁾Euclidean distance of the pth class to the xth unmerged class; d_xqIs a cluster C_ij ⁽¹⁾Euclidean distance of the qth class to the xth unmerged class; d_pqIs a cluster C_ij ⁽¹⁾The Euclidean distance between the pth class and the qth class;

3d. find distance matrix D⁽¹⁾Minimum value of all elements in (1), denoted as d_1ijWherein i ≠ j, …, m-1, j ≠ 1, …, m-1, and i ≠ j is satisfied. Will be reacted with d_1ijCorresponding two classes C_i ⁽¹⁾And C_j ⁽¹⁾Merging to obtain new cluster C_ij ⁽²⁾＝{C_i ⁽¹⁾,C_j ⁽¹⁾}. Repeating the step 3c until the distance matrix D is obtained after k times of operation^(k)Minimum value d of all elements in_kijStopping calculation when the distance is less than the set threshold or the dimension of the distance matrix is 0, and converting the distance matrix D into the distance matrix D^(k)Each cluster of the corresponding class of each group of data in (1) is marked as C₁ ^(k)、C₂ ^(k)、……、C_b ^(k)；

3e, recording the cluster with the largest number of classes as C_t ^(k)Wherein t is more than or equal to 1 and less than or equal to b, calculating a cluster C_t ^(k)Center of mass Z_tAs a vibration characteristic curve of the transformer, wherein the center of mass Z_tIs calculated by the formula

In the formula, h is a cluster C_t ^(k)The number of classes contained in (a); y is_jkIs a cluster C_tThe j-th vibration signal curve in (1).

(4) Computing a cluster of classes as C_t ^(k)Vibration characteristic curve Z of various vibration signals relative to transformer_tCurve rate of change Y of_ciRoot mean square value of_cmi(i 1, …, h) to obtain the root mean square value Y_cmiHas an average value of Y_cm. The change rate Y of the curve_ciIs calculated by the formula

In the formula, y_iIs a cluster C_tThe ith vibration signal curve of (1);

the mean value of the ith vibration signal curve is obtained;

the average value of the vibration characteristic curve of the transformer is shown.

The calculation method of the root mean square in this step is a mathematical method commonly used in the art, and therefore, the inventor does not describe it in detail here.

(5) Calculating transformer vibration curve y 'to be detected'_cCharacteristic curve Z of vibration relative to transformer_tCurve change rate Y'_cOf (d) is Y'_cmThe curve change rate Y'_cIs calculated by the formula

(6) Prepared from Y'_cmAnd Y_cmComparing if Y 'is satisfied'_cm≤Y_cmJudging that the running state of the transformer winding is normal; if Y 'is satisfied'_cm＞Y_cmAnd judging that the transformer winding is loosened or deformed.

That is to say, the technical scheme is that the vibration signals of the wall of the transformer box in a certain time period are subjected to cluster analysis to obtain a transformer vibration characteristic curve and an average value (namely Y) of root mean square values of curve change rates of various vibration signals in a class cluster where the transformer vibration characteristic curve is relative to the transformer vibration characteristic curve_cm) And then comparing the root mean square value (Y ') of the variation rate of the transformer vibration curve to be detected relative to the transformer vibration characteristic curve'_cm) With the above average value (i.e. Y)_cm) Ratio of performanceAnd then, the working state of the transformer winding can be judged according to the change of the two.

The method comprises the following steps of carrying out online monitoring by taking a 500kV transformer of a certain transformer substation of a certain power company as a test object, and judging the working state of a transformer winding according to the following steps:

(1) collecting vibration signals x (t) of the wall of the transformer tank, and carrying out standardization processing on the vibration signals x (t), wherein the vibration signal standardization processing calculation formula is

In the formula (I), the compound is shown in the specification,

is the average of the vibration signal x (t); n is the length of the vibration signal x (t); and y (t) is the vibration signal after the normalization processing.

(2) Intercepting the vibration signal after the standardization processing, wherein the interception interval is delta t, and the interception length is N₁And taking the lowest point of the vibration signals as the starting point of each group of vibration signals to obtain m groups of vibration signals. Here, Δ t is 5 minutes; n is a radical of₁＝10000；m＝3000。

(3) Clustering analysis is carried out on the m groups of vibration signals of the transformer to obtain a transformer vibration characteristic curve, and a flow chart of a calculation process is shown in figure 1. The method comprises the following specific steps:

recording m sets of data as C₁ ⁽⁰⁾、C₂ ⁽⁰⁾、……、C_m ⁽⁰⁾And regarding each group of data as an independent class, calculating Euclidean distance between every two classes to obtain an m-order initial distance matrix D⁽⁰⁾. The calculation method of the euclidean distance in this step is a mathematical method commonly used in the art, and therefore, the inventor does not describe in detail herein;

3b. find initial distance matrix D⁽⁰⁾Minimum value of all elements in (1), denoted as d_0ijWherein i ≠ j, …, m, j ≠ 1, …, m, and satisfies i ≠ j. Will be reacted with d_0ijCorresponding two classes C_i ⁽⁰⁾And C_j ⁽⁰⁾Merging to obtain new cluster C_ij ⁽¹⁾＝{C_i ⁽⁰⁾,C_j ⁽⁰⁾}；

Cluster C. New class_ij ⁽¹⁾Regarding the non-merged class as new m-1 class data, wherein the non-merged class means that the m groups of data in step 3a do not include class C_i ⁽⁰⁾And C_j ⁽⁰⁾And (3) data of (1), in m-2 classes. Inscription of m-1 as C₁ ⁽⁰⁾、C₂ ⁽⁰⁾、……、C_i-1 ⁽⁰⁾、C_ij ⁽¹⁾、C_j-1 ⁽⁰⁾、……、C_m-1 ⁽⁰⁾. Calculating the distance between every two types in the m-1 type to obtain a new m-1 order distance matrix D⁽¹⁾Wherein the distance between each two non-merged classes is calculated using Euclidean distance, class cluster C_ij ⁽¹⁾The distance from the m-2 classes which are not merged is calculated by using an intermediate distance formula

In the formula, h is a cluster C_ij ⁽¹⁾The number of classes in (1); d_xpIs a cluster C_ij ⁽¹⁾Euclidean distance of the pth class to the xth unmerged class; d_xpIs a cluster C_ij ⁽¹⁾Euclidean distance of the qth class to the xth unmerged class; d_pqIs a cluster C_ij ⁽¹⁾The Euclidean distance between the pth class and the qth class;

3d. find distance matrix D⁽¹⁾Minimum value of all elements in (1), denoted as d_1ijWherein i ≠ j, …, m-1, j ≠ 1, …, m-1, and i ≠ j is satisfied. Will be reacted with d_1ijCorresponding two classes C_i ⁽¹⁾And C_j ⁽¹⁾Merging to obtain new cluster C_ij ⁽²⁾＝{C_i ⁽¹⁾,C_j ⁽¹⁾}. Repeating the step 3c until the distance matrix D is obtained after k times of operation^(k)Minimum value d of all elements in_kijStopping calculation when the distance is less than the set threshold or the dimension of the distance matrix is 0, and converting the distance matrix D into the distance matrix D^(k)Each cluster of the corresponding class of each group of data in (1) is marked as C₁ ^(k)、C₂ ^(k)、……、C_b ^(k). Here, the threshold is 1.0; k is 3. As shown in fig. 2;

3e, recording the cluster with the largest number of classes as C_t ^(k)Wherein t is more than or equal to 1 and less than or equal to b, calculating a cluster C_t ^(k)Center of mass Z_tFig. 3 shows the vibration characteristic curve of the transformer. Wherein the center of mass Z_tIs calculated by the formula

In the formula, h is a cluster C_t ^(k)The number of classes contained in (a); y is_jkIs a cluster C_tThe j-th vibration signal curve in (1). Here, t is 2.

(4) Computing a cluster of classes as C_t ^(k)Vibration characteristic curve Z of various vibration signals relative to transformer_tCurve rate of change Y of_ciRoot mean square value of_cmi(i 1, …, h) to obtain the root mean square value Y_cmiHas an average value of Y_cm. The change rate Y of the curve_ciIs calculated by the formula

In the formula, y_iIs a cluster C_tThe ith vibration signal curve of (1);

the mean value of the ith vibration signal curve is obtained;

the average value of the vibration characteristic curve of the transformer is shown.

The calculation method of the root mean square in this step is a mathematical method commonly used in the art, and therefore, the inventor does not describe it in detail here.

(5) Calculating transformer vibration curve y 'to be detected'_cCharacteristic curve Z of vibration relative to transformer_tCurve change rate Y'_cmOf (d) is Y'_cmThe rate of change Y of said curve_cThe calculation formula of is

(6) Prepared from Y'_cmAnd Y_cmComparing if Y 'is satisfied'_cm≤Y_cmJudging that the running state of the transformer winding is normal; if Y 'is satisfied'_cm＞Y_cmAnd judging that the transformer winding is loosened or deformed.

Table 1 shows the analysis results of the vibration signals of the group of transformers 5 obtained in this example over time according to the method described above. As can be seen from Table 1, the change rates of the 5 sets of vibration signals all satisfy Y'_cm≤Y_cmThe transformer winding is in a normal state at this time.

TABLE 1

Claims (2)

1. A transformer winding state online monitoring method based on cluster analysis comprises the following steps:

step 1, collecting vibration signals x (t) of the wall of a transformer tank, and carrying out standardization processing on the collected vibration signals x (t);

step 2, intercepting the vibration signal after the standardized processing, wherein the intercepting interval is delta t, and the intercepting length is N₁Taking the lowest point of the vibration signals as the starting point of each group of vibration signals to obtain m groups of vibration signals;

step 3, performing clustering analysis on the m groups of vibration signals of the transformer to obtain a transformer vibration characteristic curve;

the method for calculating the vibration characteristic curve of the transformer in the step 3 comprises the following steps:

step 3.1, recording m groups of data as C₁ ⁽⁰⁾、C₂ ⁽⁰⁾、……、C_m ⁽⁰⁾And regarding each group of data as an independent class, calculating Euclidean distance between every two classes to obtain an m-order initial distance matrix D⁽⁰⁾；

Step 3.2, searching an initial distance matrix D⁽⁰⁾Minimum value of all elements in (1), denoted as d_0ijIn the formula: i ≠ j, which will be identical to d, …, m, j ≠ 1, …, m, and satisfies i ≠ j_0ijCorresponding two classes C_i ⁽⁰⁾And C_j ⁽⁰⁾Merging to obtain new cluster C_ij ⁽¹⁾＝{C_i ⁽⁰⁾,C_j ⁽⁰⁾}；

Step 3.3, new cluster C_ij ⁽¹⁾Regarding the non-merged class as new m-1 class data; calculating the distance between every two types in the m-1 type to obtain a new m-1 order distance matrix D⁽¹⁾Wherein the distance between each two non-merged classes is calculated using Euclidean distance, class cluster C_ij ⁽¹⁾The distance from the m-2 classes which are not merged is calculated by using an intermediate distance formula

In the formula, h is a cluster C_ij ⁽¹⁾The number of classes in (1); d_xpIs a cluster C_ij ⁽¹⁾Euclidean distance of the pth class to the xth unmerged class; d_xqIs a cluster C_ij ⁽¹⁾Euclidean distance of the qth class to the xth unmerged class; d_pqIs a cluster C_ij ⁽¹⁾The Euclidean distance between the pth class and the qth class;

step 3.4, finding a distance matrix D⁽¹⁾Minimum value of all elements in (1), denoted as d_1ijWherein i ═1, …, m-1, j ≠ 1, …, m-1, and satisfies i ≠ j, as will d_1ijCorresponding two classes C_i ⁽¹⁾And C_j ⁽¹⁾Merging to obtain new cluster C_ij ⁽²⁾＝{C_i ⁽¹⁾,C_j ⁽¹⁾And e, repeating the step 3.3 until a distance matrix D is obtained after k times of operation^(k)Minimum value d of all elements in_kijStopping calculation when the distance is less than the set threshold or the dimension of the distance matrix is 0, and converting the distance matrix D into the distance matrix D^(k)Each cluster of the corresponding class of each group of data in (1) is marked as C₁ ^(k)、C₂ ^(k)、……、C_b ^(k)；

Step 3.5, recording the cluster with the largest number of the included classes as C_t ^(k)T is more than or equal to 1 and less than or equal to b, and a cluster C is calculated_t ^(k)Center of mass Z_tAs a vibration characteristic curve of the transformer, the centroid Z_tIs calculated by the formula

In the formula, h is a cluster C_t ^(k)The number of classes contained in (a); y is_jNIs a cluster C_t ^(k)The j-th vibration signal curve;

step 4, calculating the cluster as C_t ^(k)Vibration characteristic curve Z of various vibration signals relative to transformer_tCurve rate of change Y of_ciRoot mean square value of_cmi(i 1, …, h) to obtain the root mean square value Y_cmiHas an average value of Y_cm；

Step 4, the calculation cluster is C_t ^(k)Vibration characteristic curve Z of various vibration signals relative to transformer_tCurve rate of change Y of_ciIs calculated by the formula

In the formula, y_iIs a cluster C_t ^(k)The ith vibration signal curve of (1);

the mean value of the ith vibration signal curve is obtained;

the mean value of the vibration characteristic curve of the transformer is obtained;

step 5, calculating a transformer vibration curve y 'to be detected'_cCharacteristic curve Z of vibration relative to transformer_tCurve change rate Y'_cOf (d) is Y'_cm；

Step 5, calculating a transformer vibration curve y 'to be detected'_cCharacteristic curve Z of vibration relative to transformer_tCurve change rate Y'_cIs calculated by the formula

Step 6, mixing Y'_cmAnd Y_cmComparing if Y 'is satisfied'_cm≤Y_cmJudging that the running state of the transformer winding is normal; if Y 'is satisfied'_cm＞Y_cmAnd judging that the transformer winding is loosened or deformed.

2. The transformer winding state online monitoring method based on cluster analysis according to claim 1, wherein the calculation formula of the vibration signal standardization processing in step 1 is

In the formula (I), the compound is shown in the specification,

is the average of the vibration signal x (t);n is the length of the vibration signal x (t); and y (t) is the vibration signal after the normalization processing.

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