CN106324405A - Transformer fault diagnosis method based on improved principal component analysis - Google Patents

Abstract

The invention discloses a transformer fault diagnosis method based on improved principal component analysis, which belongs to the technical field of transformer fault diagnosis. The method adopts the sum of absolute values of sample indexes to carry out standardized treatment on sample index values, and thus, the difference of each sample index value in magnitude can be eliminated, and the information difference features between samples can also be kept; and sample principal components are selected according to cumulative contribution rates of the principal components, Euclidean distances among the sample principal components are clustered, and a transformer fault type is judged. The method of the invention can effectively improve the accuracy for diagnosing inner hidden fault of the transformer.

Description

A kind of based on the Diagnosis Method of Transformer Faults improving principal component analysis

Technical field

The present invention relates to a kind of Diagnosis Method of Transformer Faults based on improvement principal component analysis, belong to transformer fault and examine Disconnected technical field.

Background technology

Power transformer is the visual plant of power system, and the reliability of himself has become as the base of power grid operation Plinth.It is diagnosed to be the Hidden fault before transformer fault especially peril occurs, not only direct relation accurately and in time To electric energy conveying reliability and the safety of Operation of Electric Systems, it is also possible to avoid its because of fault spread, cause shutdown with And to system shock, burn out equipment and produce tremendous economic loss.Therefore, the accurate of latent transformer fault diagnosis is improved Rate, has very important Research Significance.

Current Gases Dissolved in Transformer Oil analysis (DGA) method has become power system and has judged power transformer interior fault character Main method.The most commonly used in DGA method is three ratio in judgement rules.Three ratio in judgement rule forms are simple, clear, make With convenient, but application be frequently found the shortcomings, even some ratio such as understaffed code, encoded boundary be the most absolute at the scene and also looked for Less than corresponding fault type, therefore the accuracy rate of its fault diagnosis need to improve.Along with the development of artificial intelligence technology, adopt Grinding of transformer fault diagnosis is carried out with neutral net, fuzzy clustering, gray theory and evidential reasoning and other intelligent methods Study carefully and become the theme that comparison is popular.But, although neural network possesses self-learning capability, but bigger to the dependency of sample； Fuzzy theory is easier to ignore the dependency of sample space；Gray theory is also easily affected by artificial subjective factor；Evidential reasoning Algorithm is the most complicated, and can have a certain degree of uncertainty and subjectivity in evaluation procedure.So, these artificial intelligence at present Can method maturity in transformer fault diagnosis is applied need to improve.

Inside transformer Hidden fault comprises the factor of various complexity, and these factors many times comprise repetition Information.These information are the most tediously long, are just less susceptible to correctly judge the law of development of fault.But grind in major part fault During studying carefully, the characteristic information of fault always has certain dependency.Therefore, being correlated with between characteristic information variable how is eliminated Property so that breakdown judge is more accurate, become an interesting problem.1933, the principal component analysis that Hotelling proposes PCA (Principal Component Analysis) method is one of effective way realizing this purpose.The present invention based on Transformator DGA is theoretical, proposes to use follow-on PCA directly to diagnose power transformer interior fault.By master The contribution rate of accumulative total threshold value of composition, chooses main constituent number and corresponding characteristic vector, sets up the main one-tenth of raw sample data Sub-model so that comprise the main constituent that information is the most overlapping and orthogonal, has the maximum comprehensive original sample variable information of energy Ability.So it is easier to catch the principal contradiction of things, makes problem be simplified, failure classes severe particularly with running environment For there is the Transformer Faults Analysis of the biggest ambiguity between type and malfunction characteristic quantity, put these nature of troubles in order and close Cording has obvious advantage.

Summary of the invention

It is an object of the invention to deficiency of the prior art, it is provided that a kind of based on the transformator event improving principal component analysis Barrier diagnostic method.

For solving above-mentioned technical problem, the technical solution used in the present invention is:

A kind of Diagnosis Method of Transformer Faults based on improvement principal component analysis, comprises the steps:

1) transformer fault state is analyzed；

2) sample initial matrix standardization is carried out；

3) set up correlation matrix, calculate eigenvalue and characteristic vector；

4) calculate principal component contributor rate and contribution rate of accumulative total, choose sample main constituent；

5) distance between sample to be tested and state feature samples main constituent is calculated, it is judged that sample to be tested state belongs to.

Aforesaid analysis transformer fault state refers to, five kinds of crucial hydrocarbon gas H in being tested by oil chromatography₂、CH₄、 C₂H₂、C₂H₄、C₂H₆As characteristic gas, transformer fault is divided into normally, shelf depreciation, low-yield electric discharge, high-energy discharge, Hot stall t 300 DEG C, 300 DEG C of t of hot stall 700 DEG C, hot stall t 700 DEG C and electric discharge and eight kinds of fault shapes of overheated mixed fault State.

Aforesaid carrying out sample initial matrix standardization, particularly as follows: be provided with n sample, each sample has p item to refer to Mark, obtains sample initial matrix X:

$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1p}\\ x_{21}& x_{22}& ...& x_{2p}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{n1}& x_{n2}& ...& x_{np}\end{array}\right]={\left[\begin{array}{cccc}{x}_1& x_2& ...& x_n\end{array}\right]}^T---\left(1\right)$

Wherein, x_ij, i=1,2 ... n, j=1,2 ... p, represent the jth item index of i-th sample,

x_i=[x_i1 x_i2 … x_ip], i=1,2 ... n；

Use following formula to be standardized processing, obtain sample standardization data matrix,

$x_{ij}^{*}=\frac{x_{ij}}{\underset{j=1}{\overset{p}{\mathrm{\Σ}}}\left|x_{ij}\right|}---\left(2\right)$

Wherein,For x_ijStandardized data.

Aforesaid correlation matrix R is:

$R=\left[\begin{array}{cccc}{r}_{11}& r_{12}& ...& r_{1p}\\ r_{21}& r_{22}& ...& r_{2p}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ r_{p1}& r_{p2}& ...& r_{pp}\end{array}\right]---\left(3\right)$

$r_{ij}=\frac{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}\[(x_{ki}-{\stackrel{\‾}{x}}_i)(x_{kj}-{\stackrel{\‾}{x}}_j)\]}{\sqrt{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{(x_{ki}-{\stackrel{\‾}{x}}_i)}^2\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{(x_{kj}-{\stackrel{\‾}{x}}_j)}^2}}---\left(4\right)$

Wherein, r_ij, i, j=1,2 ..., p is the correlation coefficient of sample standardization data matrix；r_ij=r_ji；For x_iMiddle unit The average of element；For x_jThe average of middle element；

Use Jacobi method | the λ I-R |=0 that solves characteristic equation, calculate the eigenvalue of R, and by eigenvalue order by size Arrangement:

λ₁≥λ₂≥…≥λ_p>=0, λ_i, i=1,2 ... p is the eigenvalue of R；

Try to achieve the characteristic vector corresponding with eigenvalue: a simultaneously₁、a₂、…、a_i、…、a_p,

a_i=[a_1i a_2i … a_pi]^T, i=1,2 ..., p.

Aforesaid calculating principal component contributor rate T_iAnd contribution rate of accumulative total M_C, formula is as follows:

$\left\{\begin{array}{cc}{T}_i=\frac{{\mathrm{\λ}}_i}{\underset{k=1}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\λ}}_k}& i=1,2,...,p\\ M_C=\frac{\underset{k=1}{\overset{C}{\mathrm{\Σ}}}{\mathrm{\λ}}_k}{\underset{k=1}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\λ}}_k}& C=1,2,...,p\end{array}\right.---\left(5\right)$

Described selection sample main constituent refers to, when contribution rate of accumulative total M_CWhen meeting following formula, front C main constituent is selected Sample main constituent,

$\left|\right|\frac{1-M_C}{M_C}\left|\right|\≤\mathrm{\ϵ}---\left(6\right)$

Wherein, 0 ＜ M_C≤ 1, threshold epsilon ＞ 0, and be positive minimum real number.

Aforesaid threshold epsilon=0.005.

Aforesaid step 5) in, the computing formula of sample main constituent is:

$F_i=\left[\begin{array}{c}{F}_{i1}\\ F_{i2}\\ .\\ .\\ .\\ F_{ip}\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{21}& ...& a_{p1}\\ a_{12}& a_{22}& ...& a_{p2}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ a_{1p}& a_{2p}& ...& a_{pp}\end{array}\right]x_i^T,i=1,2,...,p---\left(7\right)$

F_iFor sample x_iMain constituent,

The main constituent F of state feature samples is obtained according to formula (7)_MMain constituent with sample to be tested

F_M=(F₁ F₂ … F_m)

$F_f^{*}=\left(\begin{array}{cccc}{F}_{f1}^{*}& F_{f2}^{*}& ...& F_{fm}^{*}\end{array}\right)$

Wherein, f is the sequence number of transformer fault classification, and m is selected sample number of principal components,

Choose state feature samples main constituent F_MWith sample to be tested main constituentBetween Euclidean distance d_f, as sample to be tested And the overall similarity between state feature samples,

$d_f={\[\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{(F_k-F_{fk}^{*})}^2\]}^{1/2}---\left(8\right)$

Finding out the Euclidean distance of minimum, sample to be tested just belongs to the state feature samples institute corresponding to minimum Eustachian distance The class malfunction belonged to.

Beneficial effect: the present invention uses variable absolute value sum to be standardized variable processing, and has both eliminated each index Numerical value difference on the order of magnitude, maintains again the information gap feature between each variable；The variable of sample space contains DGA 5 kinds of characteristic gas and code of direct ratio, calculate the contribution rate of accumulative total threshold value of main constituent, choose pivot number, form main constituent Model, simplifies the information characteristics that transformator is lengthy and tedious；Analyze the distance between sample main constituent, it is judged that latent transformer fault State belongs to, and has obvious advantage for the Hidden fault character relation putting transformator in order complicated.

The inventive method can relatively accurately reflect the running status of transformator, has certain effectiveness, and necessarily In degree, the noise in sample being had stronger denoising and immunocompetence, it is by calculating the main constituent of sample, it is achieved right The feature extraction of complex information, eliminates the correlation properties between variable, thus improves the precision of cluster.

Accompanying drawing explanation

Fig. 1 is based on the Diagnosis Method of Transformer Faults flow chart improving principal component analysis；

Fig. 2 is that main constituent selects flow chart.

Detailed description of the invention

With embodiment, the present invention is further described below in conjunction with the accompanying drawings.

A kind of based on improvement principal component analysis the Diagnosis Method of Transformer Faults of the present invention, as it is shown in figure 1, include as follows Step:

Step one: analyze transformer fault state；

Step 2: sample initial matrix standardization；

Step 3: set up correlation matrix, calculates eigenvalue and characteristic vector；

Step 4: calculate principal component contributor rate and contribution rate of accumulative total, choose sample main constituent；

Step 5: calculate the distance between sample to be tested and state feature samples main constituent, it is judged that sample to be tested state is returned Belong to.

Specific implementation process is as follows:

High dimensional data is mainly projected to an orthogonal projector space of new characteristic vector by principal component analysis, real The now feature extraction to complex process data, in order to eliminate the associate feature between variable, so that primary process specificity analysis Complexity significantly simplified.Principal component model has given up part residual error, retains simultaneously and embodies the main of data characteristics Gene, thus reach extraction system information, the purpose of scavenging system interference.This is for processing and analyze information redundancy, feature letter The power transformer interior fault of number aliasing is highly effective.The present invention proposes a kind of transformer fault based on improvement principal component analysis and examines Disconnected method.Below with 30 groups through the transformator DGA data instance of pendant-core examination its fault type known, provide its fault diagnosis side Method.

1) transformer fault state is set up

Transformator DGA is present analysis power transformer interior fault most efficient method.Inventive algorithm is with DGA data as base Plinth, selects H₂、CH₄、C₂H₂、C₂H₄、C₂H₆The content of these 5 kinds of gases, as characteristic quantity, diagnoses transformer insulated fault.Substantial amounts of Research proves, the fault diagnosis of oil-filled electric equipment can not only depend on the constituent content of oil dissolved gas, should also depend on The relative amount of gas.Based on the three-ratio method on the basis of thermokinetics, the relative amount of gas can be reflected, and in reality It is widely accepted.So the present invention uses the coded combination of three-ratio method as input quantity, extract the state feature of sample.

" Gases Dissolved in Transformer Oil divides GB/T7252-2001 according to the existing promulgation of IEC60599 code and China Analyse and judge directive/guide ", latent transformer malfunction is divided into 8 kinds of states (wherein comprising normal condition), each number of state indexes It is followed successively by 1,2 ..., 8, it is shown in Table 1.

Table 1 transformer fault is classified

2) sample initial matrix standardization

Being provided with n sample, each sample has p item index (variable) X₁、X₂、…、X_p, obtain sample initial matrix X:

$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1p}\\ x_{21}& x_{22}& ...& x_{2p}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{n1}& x_{n2}& ...& x_{np}\end{array}\right]={\left[\begin{array}{cccc}{x}_1& x_2& ...& x_n\end{array}\right]}^T---\left(1\right)$

Wherein, x_ij, i=1,2 ... n, j=1,2 ... p, represent the jth item index of i-th sample,

x_i=[x_i1 x_i2 … x_ip], i=1,2 ... n.

In order to eliminate impact and each index difference on the order of magnitude of dimension, need to be standardized X processing.Often Rule standardisation process obtains divided by sample standard deviation generally by the difference of sample with sample average.But inventive algorithm Sample initial matrix is due to containing dissimilar, varying number level, the data of different implication, so in course of standardization process In, both to separate, and individually carries out.In order to retain the characteristic information of each index value in initial matrix to a greater degree, this Invention does not use the standardized method of tradition PCA, but uses following formula to be standardized processing, and has both eliminated each Index value difference on the order of magnitude, maintains again the information gap feature between each variable.

$x_{ij}^{*}=\frac{x_{ij}}{\underset{j=1}{\overset{p}{\mathrm{\Σ}}}\left|x_{ij}\right|}---\left(2\right)$

In formula,For x_ijStandardized data.

The present invention chooses 8 groups and has clear and definite conclusion through pendant-core examination, and malfunction type is single, multiplicity event does not occurs The transformator DGA data being diagnosed before barrier, generation catastrophe failure are as state feature samples, as shown in table 2, wherein, and bag Sample containing normal non-fault state；8th group of data contain electric discharge and overheating fault simultaneously, but its every kind trouble point (source) is all only Have at 1；Gas content be finger pressure be 101.3kPa, temperature is when being 20 DEG C, the microlitre number of contained each gas component in every liter of oil, Same afterwards.

Table 2 transformer state feature samples

Form sample initial matrix X according to table 2, see below formula.In matrix X, x₉For sample to be tested, and x₁、x₂、…、x₈For State feature samples.

$X={\left[\begin{array}{ccccccccc}{x}_1& x_2& x_3& x_4& x_5& x_6& x_7& x_8& x_9\end{array}\right]}^T=\left[\begin{array}{cccccccc}46.1& 21.5& 15.8& 61.5& 1.2& 0& 0& 0\\ 195.8& 14.5& 2.4& 11.6& 0.7& 1& 1& 0\\ 78& 20& 13& 11& 28& 1& 0& 1\\ 1570& 1110& 1780& 175& 1830& 1& 0& 2\\ 181& 262& 28& 41& 0& 0& 2& 0\\ 1270& 3450& 1390& 520& 8& 0& 2& 1\\ 6709& 10500& 17700& 1400& 750& 0& 2& 2\\ 109& 45& 40& 14& 5& 1& 0& 1\\ 1330& 10& 66& 20& 182& 1& 1& 2\end{array}\right]$

3) set up correlation matrix, calculate eigenvalue and characteristic vector,

Set up correlation matrix R, it may be assumed that

$R=\left[\begin{array}{cccc}{r}_{11}& r_{12}& ...& r_{1p}\\ r_{21}& r_{22}& ...& r_{2p}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ r_{p1}& r_{p2}& ...& r_{pp}\end{array}\right]---\left(3\right)$

Wherein,

$r_{ij}=\frac{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}\[(x_{ki}-{\stackrel{\‾}{x}}_i)(x_{kj}-{\stackrel{\‾}{x}}_j)\]}{\sqrt{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{(x_{ki}-{\stackrel{\‾}{x}}_i)}^2\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{(x_{kj}-{\stackrel{\‾}{x}}_j)}^2}}---\left(4\right)$

In formula, r_ij(i, j=1,2 ..., p) it is the correlation coefficient of sample standardization data matrix；r_ij=r_ji；For x_iIn The average of element；For x_jThe average of middle element.Try to achieve characteristic vector by calculating correlation matrix R, and then try to achieve sample Main constituent F_i, sample x can be deleted_iIndex little on result of calculation impact in index, simplifies and calculates, and therefore i value is 1,2 ..., p。

Jacobi method is used to solve characteristic equation λ I-R |=0, calculate the eigenvalue of R: λ₁≥λ₂≥…≥λ_p>=0, and make It sequentially arranges by size, λ_i, i=1,2 ... p is the eigenvalue of R.The most also can try to achieve the feature corresponding with eigenvalue to Amount a₁、a₂、…、a_i、…、a_p。a_i=[a_1i a_2i … a_pi]^TI=1,2 ..., p.

According to above formula, DGA data and code of direct ratio to X are standardized processing respectively, set up correlation matrix R.Then Jacobi method is used to calculate eigenvalue λ and the eigenvectors matrix a of R.

λ=[0.2857 0.2111 0.0948 0.0184 0.0068 0.0030 0.0002 0]=[λ₁ λ₂ … λ₈]

$a=\left[\begin{array}{cccccccc}0.2256& 0.1442& -0.7015& 0.2815& -0.0158& 0.2397& 0.3150& -0.4472\\ -0.2786& 0.0229& 0.1823& -0.5885& -0.1982& 0.5473& 0.0597& -0.4472\\ -0.0772& -0.2195& 0.2325& 0.0062& 0.8129& -0.1196& 0.1112& -0.4472\\ 0.0122& 0.1625& 0.2392& 0.4743& -0.2078& 0.0617& -0.6666& -0.4472\\ 0.1180& -0.1100& 0.0475& -0.2335& -0.3911& -0.7291& 0.1807& -0.4472\\ 0.4126& -0.0884& -0.3825& -0.5111& 0.2394& -0.0569& -0.5949& 0\\ -0.8146& -0.1562& -0.4634& 0.0151& 0.0129& -0.2077& -0.2318& 0\\ 0.1326& -0.9272& -0.0088& 0.1706& -0.2148& 0.2168& -0.0184& 0\end{array}\right]=\[\begin{array}{cccc}{a}_1& a_2& ...& a_8\end{array}\]$

4) calculate principal component contributor rate and contribution rate of accumulative total, choose sample main constituent

According to main constituent contribution rate of accumulative total and threshold epsilon, choose sample main constituent.Calculate principal component contributor rate T_iAnd front C Contribution rate of accumulative total M of individual main constituent_C。

$\left\{\begin{array}{cc}{T}_i=\frac{{\mathrm{\λ}}_i}{\underset{k=1}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\λ}}_k}& i=1,2,...,p\\ M_C=\frac{\underset{k=1}{\overset{C}{\mathrm{\Σ}}}{\mathrm{\λ}}_k}{\underset{k=1}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\λ}}_k}& C=1,2,...,p\end{array}\right.---\left(5\right)$

Select main constituent primarily to distinguish principal character information and the secondary feature information that sample is comprised.Main special Reference breath is reflected by main constituent subspace, available main constituent contribution rate of accumulative total M_CRepresent, and secondary feature information spinner to comprise and makes an uproar Sound, available 1-M_CRepresent.When meeting following formula, it may be determined that front C main constituent, i.e. can main with reflected sample matrix X Characteristic information.

$\left|\right|\frac{1-M_C}{M_C}\left|\right|\≤\mathrm{\ϵ}---\left(6\right)$

In formula, 0 ＜ M_C≤1；Threshold epsilon ＞ 0, and be positive minimum real number.

Main constituent contribution rate of accumulative total matrix M is calculated according to above formula.

M=[0.4608 0.8012 0.9541 0.9838 0.9950 0.9997 1.0000 1.0000]=[M₁ M₂ … M₈]

5) distance between sample to be tested and state feature samples main constituent is calculated, it is judged that sample to be tested state belongs to

Sample x_iMain constituent F_iFor:

$F_i=\left[\begin{array}{c}{F}_{i1}\\ F_{i2}\\ .\\ .\\ .\\ F_{ip}\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{21}& ...& a_{p1}\\ a_{12}& a_{22}& ...& a_{p2}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ a_{1p}& a_{2p}& ...& a_{pp}\end{array}\right]x_i^T,i=1,2,...,p---\left(7\right)$

Can be obtained in sample space by above formula, the main constituent of state feature samples and sample to be tested is respectively

F_M=(F₁ F₂ … F_m) and(f is the sequence number of transformer fault classification, and m is main Composition number).Owing to Euclidean distance is modal distance metric, measurement be in hyperspace each point between distance, And its effect in distance measure is extensively applied by every field, so the present invention utilizes above formula to calculate main constituent F_MWith Between Euclidean distance d_f, as the overall similarity between sample to be tested and state feature samples.Distance is the least, and both get over phase Seemingly.

$d_f={\[\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{(F_k-F_{fk}^{*})}^2\]}^{1/2}---\left(8\right)$

Find out the distance of minimum, so that it may judge which kind of malfunction sample to be tested belongs to and (include normal non-fault shape State).

In actual applications, M is typically worked as_CDuring ＞ 0.995, the main constituent of selection can guarantee that enough precision.This Bright take threshold epsilon=0.005.Work as M_CWhen >=0.995, according to contribution rate of accumulative total matrix M, it may be determined that the number of its main constituent be 6 (because of For M₆=0.995).Owing to the number of its main constituent is 6, therefore only selected characteristic vector a₁-a₆.Obtain sample main constituent expression formula F It is shown below.

$F={\left[\begin{array}{ccccc}{F}_1^{*}& F_2^{*}& ...& F_8^{*}& F_M\end{array}\right]}^T=\left[\begin{array}{cccccc}0.028& 0.093& -0.068& 0.207& -0.037& 0.163\\ -0.022& 0.010& -1.007& -0.017& 0.096& 0.111\\ 0.369& -0.457& -0.490& -0.105& -0.040& 0.136\\ 0.358& -1.020& -0.255& -0.153& -0.026& 0.103\\ -0.881& -0.093& -0.586& -0.145& -0.066& 0.156\\ -0.865& -0.614& -0.440& -0.101& -0.047& 0.210\\ -0.754& -1.152& -0.427& 0.115& 0.112& 0.138\\ 0.323& -0.462& -0.462& -0.103& 0.096& 0.278\\ 0.127& -0.950& -0.993& 0.134& -0.116& 0.199\end{array}\right]$

The main constituent F of sample to be tested is calculated according to above formula_MWith other sample main constituentsDistance d:

D=[d₁ d₂ d₃ d₄ d₅ d₆ d₇ d₈]

=[1.4014 1.0098 0.7883 0.8382 1.4132 1.2094 1.0927 0.8159]

Understand, d₃=0.7883 is minimum, i.e. sample to be tested x₉Belong to the 3rd class malfunction, be low-yield putting as shown in Table 1 Electric fault, diagnostic result is consistent with actual phenomenon.And use David's triangulation method and IEC60599 three-ratio method to be diagnosed as respectively , there is erroneous judgement in high-energy discharge and partial discharges fault.

In order to further illustrate accuracy and the reliability of the inventive method, choose the DGA of 30 groups of its malfunctions known Data, as sample to be tested, carry out Analysis on Fault Diagnosis to it, are shown in Table 3, the fault type sequence number in table and the sequence number one in table 1 Cause, represent the fault type of each sample.

3 30 groups of transformer fault samples of table

Use the inventive method that this 30 example DGA data sample is carried out diagnostic analysis.It addition, in order to carry out diagnosis effect pair Ratio, is respectively adopted David's triangulation method, IEC60599 three-ratio method, improvement three-ratio method, fuzzy C-mean algorithm (FCM) method in table 3 30 groups of transformer fault samples diagnose, and diagnostic result is as shown in table 4.In table 4, sample sequence number and number of state indexes and table 3 It is consistent.When the number of state indexes that every kind of diagnostic method is diagnosed to be is with when the number of state indexes of the 2nd row is consistent in table 4, illustrate that this is examined Disconnected method diagnosis is accurate, otherwise diagnostic error.Last 2 row of table 4 be respectively every kind of diagnostic method Accurate Diagnosis total sample number with And the accuracy rate of diagnosis.

As can be seen from Table 4: David's triangulation method, IEC60599 three-ratio method, improvement three-ratio method, FCM method and basis Inventive method, the total sample number of Accurate Diagnosis is 22,21,10,21,26 respectively, and the accuracy rate of diagnosis of its correspondence is respectively 73.33%, 70.00%, 33.30%, 70.00%, 86.67%.It can thus be seen that the accuracy rate of the inventive method diagnosis is Height, David's triangulation method, IEC60599 three-ratio method take second place, and improve three-ratio method minimum.This explanation the inventive method can be relatively Adequately reflect the running status of transformator, there is certain effectiveness, and to a certain extent the noise in sample is had Stronger denoising and immunocompetence, it is by calculating the main constituent of sample, it is achieved the feature extraction to complex information, eliminates and becomes Correlation properties between amount, thus improve the precision of cluster.

The diagnostic result of 45 kinds of methods of table

It addition, diagnose by choosing different feature samples, find to use the inventive method, different feature samples Little on sample evaluation result impact to be measured.Certainly, sample data accurately and accurately, more diagnosis can be produced impact.

The above is only the preferred embodiment of the present invention, it should be pointed out that: for the ordinary skill people of the art For Yuan, under the premise without departing from the principles of the invention, it is also possible to make some improvements and modifications, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (7)

1. a Diagnosis Method of Transformer Faults based on improvement principal component analysis, it is characterised in that comprise the steps:

1) transformer fault state is analyzed；

2) sample initial matrix standardization is carried out；

3) set up correlation matrix, calculate eigenvalue and characteristic vector；

4) calculate principal component contributor rate and contribution rate of accumulative total, choose sample main constituent；

5) distance between sample to be tested and state feature samples main constituent is calculated, it is judged that sample to be tested state belongs to.

A kind of Diagnosis Method of Transformer Faults based on improvement principal component analysis the most according to claim 1, its feature exists In: described analysis transformer fault state refers to, five kinds of crucial hydrocarbon gas H in being tested by oil chromatography₂、CH₄、C₂H₂、C₂H₄、 C₂H₆As characteristic gas, transformer fault is divided into normally, shelf depreciation, low-yield electric discharge, high-energy discharge, hot stall t 300 DEG C, 300 DEG C of t of hot stall 700 DEG C, hot stall t 700 DEG C and electric discharge and eight kinds of malfunctions of overheated mixed fault.

A kind of Diagnosis Method of Transformer Faults based on improvement principal component analysis the most according to claim 1, its feature exists In: described in carry out sample initial matrix standardization, particularly as follows: be provided with n sample, each sample has p item index, obtains sample This initial matrix X:

$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \mathrm{...}& x_{1p}\\ x_{21}& x_{22}& \mathrm{...}& x_{2p}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{n1}& x_{n2}& \mathrm{...}& x_{np}\end{array}\right]={\left[\begin{array}{cccc}{x}_1& x_2& \mathrm{...}& x_n\end{array}\right]}^T---\left(1\right)$

Wherein, x_ij, i=1,2 ... n, j=1,2 ... p, represent the jth item index of i-th sample,

x_i=[x_i1 x_i2 … x_ip], i=1,2 ... n；

Use following formula to be standardized processing, obtain sample standardization data matrix,

$x_{ij}^{*}=\frac{x_{ij}}{\underset{j=1}{\overset{p}{\Σ}}\left|x_{ij}\right|}---\left(2\right)$

Wherein,For x_ijStandardized data.

A kind of Diagnosis Method of Transformer Faults based on improvement principal component analysis the most according to claim 3, its feature exists In: described correlation matrix R is:

$R=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \mathrm{...}& r_{1p}\\ r_{21}& r_{22}& \mathrm{...}& r_{2p}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ r_{p1}& r_{p2}& \mathrm{...}& r_{pp}\end{array}\right]---\left(3\right)$

$r_{ij}=\frac{\underset{k=1}{\overset{n}{\Σ}}\[(x_{ki}-{\stackrel{\‾}{x}}_i)(x_{kj}-{\stackrel{\‾}{x}}_j)\]}{\sqrt{\underset{k=1}{\overset{n}{\Σ}}{(x_{ki}-{\stackrel{\‾}{x}}_i)}^2\underset{k=1}{\overset{n}{\Σ}}{(x_{kj}-{\stackrel{\‾}{x}}_j)}^2}}---\left(4\right)$

Wherein, r_ij, i, j=1,2 ..., p is the correlation coefficient of sample standardization data matrix；r_ij=r_ji；For x_iMiddle element Average；For x_jThe average of middle element；

Use Jacobi method | the λ I-R |=0 that solves characteristic equation, calculate the eigenvalue of R, and by eigenvalue order arrangement by size: λ₁≥λ₂≥…≥λ_p>=0, λ_i, i=1,2 ... p is the eigenvalue of R；

Try to achieve the characteristic vector corresponding with eigenvalue: a simultaneously₁、a₂、…、a_i、…、a_p, a_i=[a_1i a_2i … a_pi]^T, i= 1,2,…,p。

A kind of Diagnosis Method of Transformer Faults based on improvement principal component analysis the most according to claim 4, its feature exists In: described calculating principal component contributor rate T_iAnd contribution rate of accumulative total M_C, formula is as follows:

$\left\{\begin{array}{cc}{T}_i=\frac{{\mathrm{\λ}}_i}{\underset{k=1}{\overset{p}{\Σ}}{\mathrm{\λ}}_k}& i=1,2,\mathrm{...},p\\ M_C=\frac{\underset{k=1}{\overset{C}{\Σ}}{\mathrm{\λ}}_k}{\underset{k=1}{\overset{p}{\Σ}}{\mathrm{\λ}}_k}& C=1,2,\mathrm{...},p\end{array}\right.---\left(5\right)$

Described selection sample main constituent refers to, when contribution rate of accumulative total M_CWhen meeting following formula, front C main constituent is selected sample This main constituent,

$\left|\right|\frac{1-M_C}{M_C}\left|\right|\≤\mathrm{\ϵ}---\left(6\right)$

Wherein, 0 ＜ M_C≤ 1, threshold epsilon ＞ 0, and be positive minimum real number.

A kind of Diagnosis Method of Transformer Faults based on improvement principal component analysis the most according to claim 5, its feature exists In: described threshold epsilon=0.005.

A kind of Diagnosis Method of Transformer Faults based on improvement principal component analysis the most according to claim 4, its feature exists In: step 5) in, the computing formula of sample main constituent is:

$\begin{array}{cc}{F}_i=\left[\begin{array}{c}{F}_{i1}\\ F_{i2}\\ .\\ .\\ .\\ F_{ip}\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{21}& \mathrm{...}& a_{p1}\\ a_{12}& a_{22}& \mathrm{...}& a_{p2}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ a_{1p}& a_{2p}& \mathrm{...}& a_{pp}\end{array}\right]x_i^T& i=1,2,\mathrm{...},p\end{array}---\left(7\right)$

F_iFor sample x_iMain constituent,

The main constituent F of state feature samples is obtained according to formula (7)_MMain constituent with sample to be tested

F_M=(F₁ F₂ … F_m)

$F_f^{*}=\left(\begin{array}{cccc}{F}_{f1}^{*}& F_{f2}^{*}& \mathrm{...}& F_{fm}^{*}\end{array}\right)$

Wherein, f is the sequence number of transformer fault classification, and m is selected sample number of principal components,

Choose state feature samples main constituent F_MWith sample to be tested main constituentBetween Euclidean distance d_f, as sample to be tested and shape Overall similarity between state feature samples,

$d_f={\[\underset{k=1}{\overset{m}{\Σ}}{(F_k-F_{fk}^{*})}^2\]}^{1/2}---\left(8\right)$

Finding out the Euclidean distance of minimum, sample to be tested just belongs to belonging to the state feature samples corresponding to minimum Eustachian distance One class malfunction.