CN103941163B  Resonant earthed system fault line selection method utilizing fuzzy Kmeans clustering  Google Patents
Resonant earthed system fault line selection method utilizing fuzzy Kmeans clustering Download PDFInfo
 Publication number
 CN103941163B CN103941163B CN201410197442.XA CN201410197442A CN103941163B CN 103941163 B CN103941163 B CN 103941163B CN 201410197442 A CN201410197442 A CN 201410197442A CN 103941163 B CN103941163 B CN 103941163B
 Authority
 CN
 China
 Prior art keywords
 formula
 circuit
 sequence current
 line
 transient zero
 Prior art date
Links
 238000010187 selection method Methods 0.000 title claims abstract description 14
 238000003064 k means clustering Methods 0.000 title claims abstract description 8
 238000010606 normalization Methods 0.000 claims abstract description 17
 230000001052 transient Effects 0.000 claims description 119
 239000011159 matrix material Substances 0.000 claims description 35
 238000005070 sampling Methods 0.000 claims description 21
 238000000034 method Methods 0.000 claims description 15
 238000006243 chemical reaction Methods 0.000 claims description 10
 230000011218 segmentation Effects 0.000 claims description 10
 230000001629 suppression Effects 0.000 claims description 8
 238000010586 diagram Methods 0.000 claims description 5
 230000000875 corresponding Effects 0.000 claims description 4
 238000004364 calculation method Methods 0.000 claims description 3
 101700067964 andJ Proteins 0.000 claims 1
 230000001131 transforming Effects 0.000 abstract 2
 230000005611 electricity Effects 0.000 description 5
 235000006629 Prosopis spicigera Nutrition 0.000 description 2
 240000000037 Prosopis spicigera Species 0.000 description 2
 238000001514 detection method Methods 0.000 description 2
 230000000694 effects Effects 0.000 description 2
 238000005516 engineering process Methods 0.000 description 2
 239000007787 solid Substances 0.000 description 2
 238000004458 analytical method Methods 0.000 description 1
 230000005540 biological transmission Effects 0.000 description 1
 238000004891 communication Methods 0.000 description 1
 238000010219 correlation analysis Methods 0.000 description 1
 238000010192 crystallographic characterization Methods 0.000 description 1
 238000010891 electric arc Methods 0.000 description 1
 238000000605 extraction Methods 0.000 description 1
 230000001939 inductive effect Effects 0.000 description 1
 238000009413 insulation Methods 0.000 description 1
 230000000877 morphologic Effects 0.000 description 1
 230000001932 seasonal Effects 0.000 description 1
 230000002123 temporal effect Effects 0.000 description 1
Abstract
The invention relates to a resonant earthed system fault line selection method utilizing fuzzy Kmeans clustering. The resonant earthed system fault line selection method comprises the following steps of 1 performing stretching transformation treatment on transientstate zerosequence current of each line to improve similarities of transientstate zerosequence currents of nonfault lines; 2 dividing the transientstate zerosequence currents of all of lines according to a certain time period, performing subsection phase plane transformation to obtain Euclidean distances from all of phase points of the transientstate zerosequence current of each section to determinacy points x and y on a phase plane so as to extract local features of the transientstate zerosequence currents of all of subsections and obtain feature matrixes of global features of all of lines; 3 performing normalization processing on elements in the feature matrixes to improve comparability; 4 utilizing a fuzzy Kmeans clustering method to perform clustering on the normalized feature matrixes, dividing the transientstate zerosequence currents of all of lines into two categories and the lines independently included in one category are fault line. The method improves the automation degree and line selection margin.
Description
Technical field
The present invention relates to intelligent distribution system technical field of relay protection, particularly to a kind of based on waveform expansion and contraction conversion and
The malfunction route selection method for resonant grounded system of fuzzy kmeans cluster.
Background technology
Resonant earthed system has the power supply reliability of raising system, reduces lightning damage accident rate, anticommunication equipment electricity
The advantages of magnetic disturbance, it is widely used in medium voltage distribution network.The probability of resonant earthed system singlephase earth fault is very high, typically constitutes from total
More than the 80% of fault.If instantaneity earth fault, then fault can voluntarily eliminate；If permanent earth fault, it is then
System can continue to run with 1 ~ 2 hour by tape jam, does not affect the continued power of system.Because the earth current of resonant earthed system is relatively
Little, after there is singlephase earth fault, threephase voltage still keeps symmetrical relationss, does not interfere with the continued power to load, so one
Determine the power supply reliability of power system can be improved on degree.But after there is singlephase earth fault in system, the electricity of nonfaulting phase
Pressure rises to line voltage, that is,Phase voltage again, this is easy in line insulation more weakness induction second short circuit or shape
Become phase fault.If system is that intermittent arc grounding fault, overvoltage easily damage equipment or cause power equipment occur
New earth point occurs, so that fault coverage is expanded；And the fault current that overvoltage is formed is possible to promote trouble point from wink
When property earth fault develops into permanent earth fault.Therefore, accurate, reliable earth fault line selection technology, not only can and
When find out faulty line, remove a hidden danger, and can ensure that the safe and stable operation of whole electrical network, improve power system confession
Electric reliability.Because the situation of resonant earthed system generation singlephase earth fault is complicated and changeable, fault current is fainter, and normal companion
There is intermittent electric arc, its earthing wireselecting problem is solved not yet very well.
Carrying out fault line detection using the faultsignal transient of several times bigger than faultsignal steadystate quantity is this neck in recent years
The study hotspot in domain；The semaphore being adopted mainly has zerosequence current, residual voltage, traveling wave and phase current etc.；Characteristic quantity is main
There are energy, Sudden Changing Rate, amplitude, polarity and waveform etc.；Contain pole in the middle of the fault transient zerosequence current waveform of each circuit simultaneously
The information such as property, amplitude.Occur after singlephase earth fault using resonant earthed system, the transient zerosequence current waveform of nonfault line
Similar, and the faulty line transient zerosequence current waveform feature larger with nonfault line difference, to transient zerosequence current waveform
Or its feature band does correlation analysiss or grey correlation analysis, and then determine earth fault line, be that a good route selection is thought
Road.
The route selection criterion overwhelming majority that existing malfunction route selection method for resonant grounded system adopts takes threshold using artificial experience
Value method is it is impossible to accomplish Intelligent fault route selection；And accurate route selection is difficult to high resistance earthing fault, shortterm road fault, to power distribution network
When there is singlephase earth fault after accessing miscellaneous equipment, whether the route selection criterion of proposition still effectively also lacks research.
Content of the invention
It is an object of the invention to provide a kind of malfunction route selection method for resonant grounded system of utilization fuzzy kmeans cluster,
The method increase automaticity and the route selection nargin of failure line selection.
For achieving the above object, the technical scheme is that a kind of resonant earthed system of utilization fuzzy kmeans cluster
Faultline selecting method, comprises the following steps:
Step 1: stretching process is carried out to each circuit transient zerosequence current, to improve transient zerosequence between nonfault line
The similarity of electric current, reduces the impact that between nonfault line, transient zerosequence current amplitude difference is asked for similarity；
Step 2: each circuit transient zerosequence current is divided by certain period of time, makees the conversion of segmentation phase plane, ask
Take all phase points of each section of transient zerosequence current Euclidean distance determining point in phase plane, to extract each section of transient zerosequence electricity
The local feature of stream, obtains the eigenmatrix of each circuit global characteristics；
Step 3: normalized is made to the element in eigenmatrix, to strengthen comparability；
Step 4: using fuzzy kmeans clustering method, the eigenmatrix after normalization is clustered, by each circuit transient state
Zerosequence current is divided into two classes, then be individually divided into the circuit of a class to be faulty line.
Further, in step 1, as follows each circuit transient zerosequence current is carried out with stretching process:
Zerosequence network equivalent circuit during singlephase earthing is occurred for resonant earthed system, if thekBar circuit is fault wire
Road,u _{0}For trouble point zero sequence power supply,r _{0}For zero sequence loop equivalent resistance,l _{0}For arc suppression coil zero sequence inductance,c _{1},…,c _{ k1},c _{ k+1},…,c _{ n }For nonfaulting line three relatively equivalent capacity,u _{c}For the voltage at each feeder line directtoground capacitance two ends,i _{1},i _{2},…,i _{ n }For each feeder line zerosequence current,i _{l}For flowing through the electric current of arc suppression coil；Each feeder line transient zerosequence current is
(1)
(2)
Obtained by formula (1)
(3)
Whereini _{ j }、i _{ k }It is respectively nonfault linej, the transient zerosequence current of faulty line；
Introduce stretching coefficient and line translation is entered to transient zerosequence current waveform: with circuitbAs reference line, define
CircuitjStretching multiplep _{ j }For
(4)
In formulai _{ j }、i _{ b }It is respectively circuitjAnd circuitbTransient zerosequence current；
If reference linebFor nonfault line, that is,b≠k, then obtained by formula (3) and formula (4)
(5)
Convolution (1), formula (4) and formula (5) obtain the nonfault line transient zerosequence current after stretchingi ' _{ j }For
(6)
Convolution (2) and formula (4) obtain the faulty line transient zerosequence current after stretchingi ' _{ k }For
(7)
If reference linebFor faulty line, that is,b=k, then by formula (5), each nonfault line equivalent capacity over the groundc _{ j }
Use nonfault lineaEquivalent capacity over the groundc _{ a }It is expressed as
(8)
In formulaλ _{ j }For proportionality coefficient；Obtained by formula (1), formula (8)
(9)
Orderp _{ a }=i _{ a }/i _{ b }, then obtained by formula (2), formula (9)
(10)
Nonfault line transient zerosequence current after stretching is obtained by formula (9), formula (10)i ' _{ j }For
(11).
Further, in step 2, ask for the eigenmatrix of each circuit global characteristics as follows:
i ' _{ j }(n) for after stretching thejThe discretetime series of the transient zerosequence current waveform of bar circuit,nFor
Sampling period, the derivative of its corresponding point is asked for by formula (12)
(12)
In formulaf(i ' _{ j }(n)) bei ' _{ j }(n) derivative, δtFor sampling step length；
Transient zerosequence current after stretching is divided in time domainn _{1}Section, using least squares estimate matching
Do linearisation to each section, obtainn _{1}Individual straightway, then the derivative of point in the range of a straightway for the transient zerosequence current waveformf
(i ' _{ j }(n)) all represented with the slope of this straightway；
If the sampling number of transient zerosequence current head halfwave isl, by the transient zerosequence current after each circuit stretchingi ' _{ j }It is divided inton _{2}Section,n _{1}=bn _{2},b>=2, then each segmentation upsampling point number bel/n _{2}；Make equal paragraph by paragraph
Face converts, and the knock type (13) on each section of phaseplane diagram is normalized, and so that the data point in phase plane is all fallen
In interval [ 1,1]；
(13)
In formulai ' _{ jm }Representi ' _{ j }?mIndividual segmentation,i' _{ jm }(n) representi ' _{ jm }Discretetime series,m∈[1,n _{2}],n∈[1,l/n _{2}],f '(i ' _{ jm }(n)) bef(i ' _{ jm }(n)) sequence after normalization,i'' _{ jm }(n) bei ' _{ jm }
(n) sequence after normalization；
Determine in phase plane by the phase paths that formula (14) calculates the transient zerosequence current waveform after each section of stretching
Point (x,y) Euclidean distance:
(14)
In formular _{ m }Represent themSection phase paths arrive determination point (x,y) Euclidean distance；
Willr _{ m }As the local feature amount of one time period of transient zerosequence current waveform, the then transient state zero of any one circuit
The global characteristics amount of sequence current waveform is
(15)
ThennThe global characteristics amount of bar circuit constitutes onen×n _{2}Eigenmatrixs, as the formula (16)
(16)
In formulas _{ ji }Represent thejThe of article circuitiSection phase paths determine in phase plane point (x,y) Euclidean distance.
Further, in step 3, using if following formula (17) is to eigenmatrixsIn element do at normalization by row
Reason:
(17)
In formulas ' _{ ji }Represents _{ ji }By the value obtaining after row normalization.
Further, in step 4, as follows each circuit transient zerosequence current is classified and found fault wire
Road:
Input to be sorted firstnIndividual vectorx _{ j }And vectorkThe initially fuzzy subordinateddegree matrix of group classificationu ^{(1)}
(18)
In formulau _{ ij }Represent thejIndividual vector belongs toiThe degree of membership of class,And,j=1,
2,…,n；Ifv _{ i }ForiClass initial cluster center vector, then initial cluster center matrix is
(19)
Determine object functionj _{ m }(u,v), have
(20)
In formula,mIt is greater than 1 arbitrary real number,Forr ^{ p }Any one norm in space, using Lagrange's multiplier
Method proves to obtain
(21)
(22)
In formulaaFor iterationses enumerator；
Then determine cluster centre matrix according to the following stepsvAnd subordinateddegree matrixu:
Step 401: determine classification numberk, ordera=0, provide initial subordinateddegree matrix at randomu ^{(1)}；
Step 402: calculate the cluster centre vector of preliminary classification according to formula (22)v ^{(1)}；
Step 403: calculate subordinateddegree matrix according to formula (21)u ^{(a+1)}；
Step 404: the given condition of convergence, if the subordinateddegree matrix difference of iterative calculation gained is less than the condition of convergence twice
The threshold value setting, then iteration terminate, otherwise return to step 402 continues iteration, until it reaches the condition of convergence or reach set repeatedly
Till generation number；
Eigenmatrix by each line fault transient zerosequence current waveformsIt is divided into 2 classes, subordinateddegree matrix can be obtained
(23)
In formulau _{ ij }Represent thejArticle circuit belongs toiThe degree of membership of class；
By subordinateddegree matrixuEach circuit is divided into two classes, is individually divided into the circuit of a class to be faulty line.
Compared with prior art, the invention has the beneficial effects as follows: by fuzzy kmeans clustering algorithm introduce resonant earthed system
Failure line selection, it is to avoid artificial experience selected threshold is thus realize Intelligent fault route selection；Waveform is carried out to transient zerosequence current
Stretching, it is not of uniform size that stretching process preferably solves transient zerosequence current Numeric Attributes between nonfault line
Impact, improves the similarity of transient zerosequence current waveform between nonfault line, improves the nargin of route selection；Meanwhile, utilize and divide
Section phase plane conversion to extract the characteristic quantity of transient zerosequence current with Euclidean distance, thus the width of concentrated expression transient zerosequence current
Value and polarity information, more accurately depict faulty line and nonfault line transient zerosequence current feature.Additionally, the present invention
Method has stronger reliability, antiinterference and adaptability, has certain engineering application value.
Brief description
Fig. 1 is the zerosequence network equivalent circuit diagram that in the embodiment of the present invention, resonant earthed system occurs during singlephase earthing.
Fig. 2 is sine wave phase plane trajectory schematic diagram in the embodiment of the present invention.
Fig. 3 is resonant earthed system phantom figure in the embodiment of the present invention.
Fig. 4 is fault transient zerosequence current oscillogram in the embodiment of the present invention.
Fig. 5 is the flowchart of the embodiment of the present invention.
Specific embodiment
When there is singlephase earth fault in resonant earthed system, the variation tendency one of nonfault line transient zerosequence current waveform
Cause, it differs only in the difference of amplitude size, thus the transient zerosequence current waveform between nonfault line is similar；And it is right
In faulty line, faulty line transient zerosequence current, containing more DC component, nonfault line is practically free of direct current and divides
Amount, and the opposite in phase of faulty line and nonfault line transient zerosequence current high fdrequency components, therefore faulty line and nonfaulting
There is larger difference in the transient zerosequence current waveform of circuit.Therefore, the present invention utilizes transient zerosequence current waveform similarity to identify
Method carry out failure line selection.
Malfunction route selection method for resonant grounded system of the present invention, as shown in figure 5, comprising the following steps:
Step 1: stretching process is carried out to each circuit transient zerosequence current, to improve transient zerosequence between nonfault line
The similarity of electric current, reduces the impact that between nonfault line, transient zerosequence current amplitude difference is asked for similarity；
Step 2: each circuit transient zerosequence current is divided by certain period of time, makees the conversion of segmentation phase plane, ask
Take all phase points of each section of transient zerosequence current determine in phase plane point (x,y) Euclidean distance, to extract each section of transient state
The local feature of zerosequence current, obtains the eigenmatrix of each circuit global characteristics；
Step 3: by row, normalized is made to the element in eigenmatrix, to strengthen comparability；
Step 4: using fuzzy kmeans clustering method, the eigenmatrix after normalization is clustered, by each circuit transient state
Zerosequence current is divided into two classes, then be individually divided into the circuit of a class to be faulty line.
In step 1, as follows each circuit transient zerosequence current is carried out with stretching process:
There is zerosequence network equivalent circuit during singlephase earthing in resonant earthed system, as shown in figure 1, setting thekBar circuit is
Faulty line,u _{0}For trouble point zero sequence power supply,r _{0}For zero sequence loop equivalent resistance,l _{0}For arc suppression coil zero sequence inductance,c _{1}
,…,c _{ k1},c _{ k+1},…,c _{ n }For nonfaulting line three relatively equivalent capacity,u _{c}For the voltage at each feeder line directtoground capacitance two ends,i _{1},i _{2},…,i _{ n }For each feeder line zerosequence current,i _{l}For flowing through the electric current of arc suppression coil.Each feeder line transient state zero can be obtained by Fig. 1
Sequence electric current is
(1)
(2)
Obtained by formula (1)
(3)
Whereini _{ j }、i _{ k }It is respectively nonfault linej, the transient zerosequence current of faulty line.
From formula (3), ifjThe fault transient zerosequence current of bar circuit is divided by its equivalent capacity over the groundc _{ j }, then
Between nonfault line, the similarity of transient zerosequence current waveform will improve.Each linetoground equivalent capacityc _{ j }It is difficult to obtain, introduce
Stretching coefficient enters line translation to transient zerosequence current waveform.With circuitbAs reference line, define circuitjFlexible
Conversion multiplep _{ j }For
(4)
In formulai _{ j }、i _{ b }It is respectively circuitjAnd circuitbTransient zerosequence current.
In view of transient zerosequence current waveform, there is nonlinear and nonstationary feature, using during stable statei _{ j }Withi _{ b }Askp _{ j }.
For reducing the impact of the factor such as noise, with after fault theqThe average fold of individual 1/4 cycle sampled data is askedp _{ j }, transient process
1 ~ 2 cycle may be continued,qValue should be greater than 8.Hypothesis sample frequency is 20khz, then with the of zerosequence current after fault
(100(q 1)+1) individual sampled point is to the 100thqThe average fold of individual sampled point is askedp _{ j }:
1) if reference linebFor nonfault line, that is,b≠k, then obtained by formula (3) and formula (4)
(5)
Convolution (1), formula (4) and formula (5) obtain the nonfault line transient zerosequence current after stretchingi ' _{ j }For
(6)
Convolution (2) and formula (4) obtain the faulty line transient zerosequence current after stretchingi ' _{ k }For
(7)
In the case that reference line is for nonfault line, from formula (6), after processing through stretching, each nonfaulting
Circuit transient zerosequence current has identical expression formula, and stretching processes and improves transient zerosequence current ripple between nonfault line
The similarity of shape.Comparison expression (6) and formula (7) understand, after processing through stretching, faulty line and nonfault line transient zerosequence
Difference between current waveform is still larger.
2) if reference linebFor faulty line, that is,b=k, then by formula (5), each nonfault line equivalent capacity over the groundc _{ j }
Use nonfault lineaEquivalent capacity over the groundc _{ a }It is expressed as
(8)
In formulaλ _{ j }For proportionality coefficient；Obtained by formula (1), formula (8)
(9)
Orderp _{ a }=i _{ a }/i _{ b }, then obtained by formula (2), formula (9)
(10)
Nonfault line transient zerosequence current after stretching is obtained by formula (9), formula (10)i ' _{ j }For
(11)
When reference line is faulty line, faulty line transient zerosequence current waveform keeps constant.From formula (11), warp
After stretching is processed, the transient zerosequence current expression formula of each nonfault line is identical, has stronger similarity.Stretching
Process the similarity that improve between nonfault line transient zerosequence current waveform.Comparison expression (2) and formula (11) understand, become through flexible
After changing process, the difference of faulty line and nonfault line transient zerosequence current is still larger.
Phase plane analysis is the effective ways of time domain waveform feature extraction, divides in arc fault detection, electrical energy power quality disturbance
The field such as class and earth fault type classification is applied.Phase plane is with time seriesesx(t) it is transverse axis, seasonal effect in time series
Derivativex(t) plane that constituted by the longitudinal axis, it is with another kind of Morphological Characterization original waveform.As shown in Fig. 2 with SIN functiona
sinx(x∈[0, 2π]) as a example, whena=1、xIncrease to from 0πWhen, its phase plane trajectory as shown by curve 1, from a point
Along solid line to b point, phase paths are distributed in, quadrant；Whena=1、xFromπIncrease to 2πWhen, its phase plane trajectory such as curve 2
Shown, from b point along dotted line to a point, phase paths are distributed in, quadrant；Whena=1.5、xIncrease to from 0πWhen, its phase plane
As curve 3 illustrates, from c point along solid line to d point, phase paths are distributed in, quadrant for track.It follows that in a cycle
A certain section of specific sine wave, its phase plane trajectory is unique, and the amplitude of sine wave is bigger, its phase paths deviation from origin
Distance is also more remote.
In step 2, ask for the eigenmatrix of each circuit global characteristics as follows:
i ' _{ j }(n) for after stretching thejThe discretetime series of the transient zerosequence current waveform of bar circuit,nFor adopting
Sampling point number, the derivative of its corresponding point is asked for by formula (12)
(12)
In formulaf(i ' _{ j }(n)) bei ' _{ j }(n) derivative, δtFor sampling step length；
From formula (12),f(i ' _{ j }(n)) only and current sample valuesi ' _{ j }(n) and last sampled valuei ' _{ j }(n
1) relevant, and unrelated with other sampled values, it is vulnerable to random disturbances and effect of noise.By the transient zerosequence electricity after stretching
Stream is divided in time domainn _{1}Section, does linearisation using least squares estimate matching to each section, obtainsn _{1}Individual straightway,
The then derivative of point in the range of a straightway for the transient zerosequence current waveformf(i' _{ j }(n)) all with the slope table of this straightway
Show.
The transient process of barrier first half cycles of transient zerosequence current (first halfwave) substantially, contains polarity, amplitude for some reason
Etc. information, its temporal signatures matrix can be asked for for route selection.If the sampling number of transient zerosequence current head halfwave isl, Jiang Gexian
Transient zerosequence current after the stretching of roadi ' _{ j }It is divided inton _{2}Section,n _{1}=bn _{2},b>=2, then each segmentation upsampling
Point number bel/n _{2}；Make phase plane conversion paragraph by paragraph, and the knock type (13) on each section of phaseplane diagram is normalized
Process, so that the data point in phase plane is all fallen in interval [ 1,1].
(13)
In formulai ' _{ jm }Representi ' _{ j }?mIndividual segmentation,i ' _{ jm }(n) representi' _{ jm }Discretetime series,m∈[1,n _{2}],n∈[1,l/n _{2}],f '(i ' _{ jm }(n)) bef(i ' _{ jm }(n)) sequence after normalization,i'' _{ jm }(n) bei ' _{ jm }(n) sequence after normalization；
Amplitude and phase information for comprehensively utilizing fault transient zerosequence current carry out earthing wireselecting, take and determine in phase plane
Point is ( 1,0), and the phase paths calculating the transient zerosequence current waveform after each section of stretching by formula (14) are true in phase plane
The Euclidean distance of fixed point ( 1,0):
(14)
In formular _{ m }Represent themSection phase paths are to the Euclidean distance determining point ( 1,0)；
As shown in Figure 2, track in phase plane for the sine wave is ellipse, has axial symmetry relation.Calculated curve 1 and curve
2 Euclidean distances arriving initial point, can obtain identical distance value it is impossible to distinguish the positivenegative halfcycle of sine wave；But calculated curve 1 and song
Line 2 arrives the Euclidean distance determining point ( 1,0), then can be with the difference of resolution curve 1 and curve 2.If direct calculated curvey=
sinxWithy=sinx(x∈[0, 2π]) phase paths to determine point ( 1,0) Euclidean distance, also can obtain identical
Distance value is it is impossible to correctly distinguish two curves；Curve is divided into multistage, calculates every section of phase point respectively to the Europe determining point ( 1,0)
Family name's distance, then by the difference of distinguishable two curves of counted multiple Euclidean distance value.During in view of singlephase earthing, faulty line with
Phase paths relation between nonfault line transient zerosequence current waveform and the phase paths relation between curve 1 and curve 2 are similar, because
This adopts segmentation phase plane to convert, and calculates the Euclidean distance of the phase paths of each section of waveform to determination point ( 1,0), for differentiating
The transient zerosequence current waveform of faulty line and nonfault line.
Willr _{ m }As the local feature amount of one time period of transient zerosequence current waveform, the then transient state zero of any one circuit
The global characteristics amount of sequence current waveform is
(15)
ThennThe global characteristics amount of bar circuit constitutes onen×n _{2}Eigenmatrixs, as the formula (16)
(16)
In formulas _{ ji }Represent thejThe of article circuitiSection phase paths are to the Euclidean distance determining point ( 1,0).
In step 3, using if following formula (17) is to eigenmatrixsIn element by row do normalization process:
(17)
In formulas ' _{ ji }Represents _{ ji }By the value obtaining after row normalization.
In step 4, as follows eigenmatrix is clustered:
Fuzzy kmeans cluster is a kind of clustering method based on fuzzy division.The present invention inputs to be sorted firstnIndividual
Vectorx _{ j }And vectorkThe initially fuzzy subordinateddegree matrix of group classificationu ^{(1)}
(18)
In formulau _{ ij }Represent thejIndividual vector belongs toiThe degree of membership of class,And,j=1,
2,…,n；Ifv _{ i }ForiClass initial cluster center vector, then initial cluster center matrix is
(19)
Determine object functionj _{ m }(u,v), have
(20)
In formula,mIt is greater than 1 arbitrary real number,mValue relevant with the foglevel of final classification, for makingj _{ m }Final
Classification reaches local optimum, takesm=2,Forr ^{ p }Any one norm in space, proves to obtain using lagrange's method of multipliers
(21)
(22)
In formulaFor iterationses enumerator.
Then determine cluster centre matrix according to the following stepsvAnd subordinateddegree matrixu:
Step 401: determine classification numberk, ordera=0, provide initial subordinateddegree matrix at randomu ^{(1)}；
Step 402: calculate the cluster centre vector of preliminary classification according to formula (22)v ^{(1)}；
Step 403: calculate subordinateddegree matrix according to formula (21)u ^{(a+1)}；
Step 404: the given condition of convergence, if the subordinateddegree matrix difference of iterative calculation gained is less than the condition of convergence twice
The threshold value setting, then iteration terminate, otherwise return to step 402 continues iteration, until it reaches the condition of convergence or reach set repeatedly
Till generation number.
Clustered the eigenmatrix of each line fault transient zerosequence current waveform using fkmsIt is divided into 2 classes, degree of membership can be obtained
Matrix
(23)
In formulau _{ ij }Represent thejArticle circuit belongs toiThe degree of membership of class.By subordinateddegree matrixuEach circuit is divided into two
Class, that is, the circuit being under the jurisdiction of the 1st class and the circuit being under the jurisdiction of the 2nd class, are individually divided into the circuit of a class to be faulty line.
Transient zerosequence electricity between the similarity degree of transient zerosequence current is than nonfault line between faulty line and nonfault line
The similarity degree of stream is little, then shows as the eigenvalue difference very little between nonfault line in characteristic quantity, and faulty line and nonevent
Eigenvalue between barrier circuit is widely different, hence with subordinateddegree matrixuMay recognize that faulty line.
Below in conjunction with the accompanying drawings and specific embodiment the invention will be further described.
Build a resonant earthed system model containing 6 outlets using atp, as shown in Figure 3.In figure:o _{l}For aerial line
Road length；c _{l}For cable run length；r _{f}For earth resistance.The positive order parameter of the every km of overhead transmission line in model:r _{1}=0.17
ω,l _{1}=1.21mh,c _{1}=0.0097μf；Zero sequence parameter:r _{0}=0.23 ω,l _{0}=5.478mh,c _{0}=0.008μf.Cable
The positive order parameter of the every km of circuit:r _{1}=0.27 ω,l _{1}=0.255mh,c _{1}=0.339μf；Zero sequence parameter:r _{0}=2.7 ω,l _{0}
=1.019mh,c _{0}=0.28μf.System total capacitance electric currenti _{c}=3ωc _{σ} u _{n}=36a > 20a, should install arc suppression coil.Cancel arc
The overcompensation degree of coil is 5%, then inductancel=1/1.05×u _{n}/ωi _{c}=0.49h；The active loss of arc suppression coil is about to feel
Property loss 2.5% ~ 5%, take 3%, then resistancer _{l}=0.03ωl=4.58ω.
With circuit 3 break down at bus 5km switching angle be 60 °, the singlephase earth fault as 100w for the earth resistance
As a example, route selection process is described.Sample frequency is 20khz, the transient zerosequence current of faulty line and two of which nonfault line
Shown in first halfwave such as Fig. 4 (a).As reference line, each circuit transient zerosequence current presses conversion coefficient for access line 4p _{ k }=i _{ k }
/i _{4}Do stretching, after conversion shown in waveform such as Fig. 4 (b).As shown in Figure 4, after stretching, nonfault line transient state zero
Similarity between sequence current waveform is improved, and the similarity change between faulty line and nonfault line waveform is less.
The fault transient zerosequence current head halfwave of stretching gained is divided inton _{1}=20 sections, do piecewise linearization, with each
The slope of straightway represents the derivative of point in the range of this straightway for the transient zerosequence current waveform, obtains its phase plane trajectory；Taken _{2}=10, phase plane trajectory is divided into 10 sections and does normalized to each section.Ask for each every section of transient zerosequence current of circuit
Phase paths point, to the Euclidean distance determining point ( 1,0), forms eigenmatrixs, rightsProcessed and can be obtained by row normalization
RightsCarry out fkm cluster, obtain subordinateddegree matrix
Subordinateddegree matrixuRow represent status categories, 1 ~ 6 row represent 1 ~ 6 circuit respectively,uIn each train value maximum
Element be located row be the corresponding state of this circuit.By subordinateddegree matrixuUnderstand, circuit 3 belongs to a class, All other routes
Belong to another kind of, circuit 3 is individually classified as 1 class, thus can determine that circuit 3 is ground path.
If not doing stretching to each line fault transient zerosequence current waveform, other steps are constant, then eigenmatrixs ’
And subordinateddegree matrixu ’It is respectively
By subordinateddegree matrixu ’Also circuit 3 can be appropriately determined be grounded, but by comparing the eigenmatrix of the two and being subordinate to
Degree matrix understands, carries out stretching to transient zerosequence current waveform and can improve route selection nargin.
There is singlephase earthing event in different circuits in the case of different grounding resistance, different faults point and different faults switching angle
The route selection of barrier the results are shown in Table 1.In table: l_{ m }For faulty line；x _{f}Distance for trouble point to bus；r _{f}For earth resistance；θ
For fault close angle.
The adaptability checking of selection method:
1) arc fault
Show as intermittent arc fault more the singlephase earthing initial stage, arc fault emulation is carried out using mayr Arc Modelling.
Circuit l_{3}The results are shown in Table 2 there is the route selection of arcearth faults at bus 5km.
2) time windows
Circuit l_{4}The switching angle that breaks down at bus 2km be 90 °, earth resistance be 3k ω singlephase earthing therefore
Barrier, from different transient zerosequence current time windows, route selection the results are shown in Table 3.
3) engine noise
In engineer applied, the impact to selection method for the extraneous random noise disturbance need to be considered.Superposition signal to noise ratio is 20db's
White Gaussian noise disturbs, circuit l_{6}Route selection under 3 kinds of representative ground failure conditions the results are shown in Table 4.This line selection algorithm has relatively
Strong capacity of resisting disturbance.
4) asynchronous sampling
Earth fault occur after line selection apparatus the sampling of each circuit zerosequence current be there may be asynchronous.Consider circuit
l_{3}、l_{4}Delayed circuit l_{1}、l_{2}8 sampled points；Circuit l_{5}、l_{6}Delayed circuit l_{1}、l_{2}14 sampled points, circuit l_{3}End connects
Ground resistance is the singlephase earth fault of 3k ω, and its route selection the results are shown in Table 5.
It is more than presently preferred embodiments of the present invention, all changes made according to technical solution of the present invention, produced function is made
With without departing from technical solution of the present invention scope when, belong to protection scope of the present invention.
Claims (4)
1. a kind of malfunction route selection method for resonant grounded system of utilization fuzzy kmeans cluster is it is characterised in that include following walking
Rapid:
Step 1: stretching process is carried out to each circuit transient zerosequence current, to improve transient zerosequence current between nonfault line
Similarity, reduce transient zerosequence current amplitude difference impact that similarity is asked between nonfault line；
Step 2: each circuit transient zerosequence current is divided by certain period of time, makees the conversion of segmentation phase plane, ask for every
The all phase points of one section of transient zerosequence current Euclidean distance determining point in phase plane, to extract each section of transient zerosequence current
Local feature, obtains the eigenmatrix of each circuit global characteristics；
Step 3: normalized is made to the element in eigenmatrix, to strengthen comparability；
Step 4: using fuzzy kmeans clustering method, the eigenmatrix after normalization is clustered, by each circuit transient zerosequence
Electric current is divided into two classes, then be individually divided into the circuit of a class to be faulty line；
In step 1, as follows each circuit transient zerosequence current is carried out with stretching process:
Zerosequence network equivalent circuit during singlephase earthing is occurred for resonant earthed system, if kth bar circuit is faulty line, u_{0}
For trouble point zero sequence power supply, r_{0}For zero sequence loop equivalent resistance, l_{0}For arc suppression coil zero sequence inductance, c_{1},…,c_{k1},c_{k+1},…,c_{n}
For nonfaulting line three relatively equivalent capacity, u_{c}For the voltage at each feeder line directtoground capacitance two ends, i_{1},i_{2},…,i_{n}For each feeder line zero
Sequence electric current, i_{l}For flowing through the electric current of arc suppression coil；Each feeder line transient zerosequence current is
Obtained by formula (1)
Wherein i_{j}、i_{k}It is respectively nonfault line j, the transient zerosequence current of faulty line；
Introduce stretching coefficient and transient zerosequence current waveform is entered with line translation: using circuit b as reference line, define circuit j
Stretching multiple p_{j}For
I in formula_{j}、i_{b}It is respectively the transient zerosequence current of circuit j and circuit b；
If reference line b is nonfault line, i.e. b ≠ k is then obtained by formula (3) and formula (4)
c_{j}=p_{j}c_{b}(j ∈ [1, n], j ≠ k) (5)
Convolution (1), formula (4) and formula (5) obtain the nonfault line transient zerosequence current i ' after stretching_{j}For
Convolution (2) and formula (4) obtain the faulty line transient zerosequence current i ' after stretching_{k}For
If reference line b is faulty line, i.e. b=k, then by formula (5), each nonfault line equivalent capacity c over the ground_{j}Use nonfaulting
Circuit a equivalent capacity c over the ground_{a}It is expressed as
c_{j}=λ_{j}c_{a}(j ∈ [1, n], j ≠ k) (8)
λ in formula_{j}For proportionality coefficient；Obtained by formula (1), formula (8)
Make p_{a}=i_{a}/i_{b}, then obtained by formula (2), formula (9)
Obtain the nonfault line transient zerosequence current i ' after stretching by formula (9), formula (10)_{j}For
2. the malfunction route selection method for resonant grounded system of utilization fuzzy kmeans cluster according to claim 1, its feature exists
In in step 2, asking for the eigenmatrix of each circuit global characteristics as follows:
i′_{j}N () is the discretetime series of the transient zerosequence current waveform of jth strip circuit after stretching, n is sampling period, its
The derivative of corresponding point is asked for by formula (12)
F (i' in formula_{j}(n)) it is i'_{j}N the derivative of (), δ t is sampling step length；
Transient zerosequence current after stretching is divided into n in time domain_{1}Section, using least squares estimate matching to each section
Do linearisation, obtain n_{1}Individual straightway, then the derivative f (i' of point in the range of a straightway for the transient zerosequence current waveform_{j}(n))
All represented with the slope of this straightway；
If the sampling number of transient zerosequence current head halfwave is l, by the transient zerosequence current i' after each circuit stretching_{j}Averagely
It is divided into n_{2}Section, n_{1}=bn_{2}, b >=2, then the number of each segmentation upsampling point is l/n_{2}；Make phase plane conversion paragraph by paragraph, and to each
Knock type (13) on section phaseplane diagram is normalized, and so that the data point in phase plane is all fallen in interval [ 1,1]；
I' in formula_{jm}Represent i'_{j}Mth segmentation, i'_{jm}N () represents i'_{jm}Discretetime series, m ∈ [1, n_{2}], n ∈ [1, l/
n_{2}], f'(i'_{jm}(n)) it is f (i'_{jm}(n)) sequence after normalization, i "_{jm}N () is i'_{jm}Sequence after (n) normalization；
By formula (14) calculate each section of stretching after transient zerosequence current waveform phase paths determine in phase plane point (x,
Y) Euclidean distance:
R in formula_{m}Represent m section phase paths to the Euclidean distance determining point (x, y)；
By r_{m}As the local feature amount of one time period of transient zerosequence current waveform, the then transient zerosequence current of any one circuit
The global characteristics amount of waveform is
Then the global characteristics amount of n bar circuit constitutes a n × n_{2}Eigenmatrix s, as shown in formula (16)
S in formula_{ji}Represent that ith section of phase path of jth strip circuit determine the Euclidean distance of point (x, y) in phase plane.
3. the malfunction route selection method for resonant grounded system of utilization fuzzy kmeans cluster according to claim 2, its feature exists
In in step 3, employing such as following formula (17) is done normalization to the element in eigenmatrix s by row and processed:
S in formula_{ji}Represent that ith section of phase path of jth strip circuit determine the Euclidean distance of point (x, y), s' in phase plane_{ji}Represent
s_{ji}By the value obtaining after row normalization.
4. the malfunction route selection method for resonant grounded system of utilization fuzzy kmeans cluster according to claim 3, its feature exists
In in step 4, as follows each circuit transient zerosequence current being classified and is found with faulty line:
Input n vector x to be sorted first_{j}Initially fuzzy subordinateddegree matrix u with the classification of vectorial k group^{(1)}
U in formula_{ij}Represent that jth vector belongs to the degree of membership of the ith class, u_{ij}∈ [0,1] andJ=1,2 ..., n；If v_{i}
For the ith class initial cluster center vector, then initial cluster center matrix is
v^{(1)}=[v_{1}, v_{2}..., v_{k}] (19)
Determine object function j_{m}(u, v), has
In formula, m is greater than 1 arbitrary real number,     for r_{p}Any one norm in space, using lagrange's method of multipliers card
Ming Ke get
In formula, a is iterationses enumerator；
Then according to the following steps determine cluster centre matrix v and subordinateddegree matrix u:
Step 401: determine classification number k, make a=0, provide initial subordinateddegree matrix u at random^{(1)}；
Step 402: calculate the cluster centre vector v of preliminary classification according to formula (22)^{(1)}；
Step 403: calculate subordinateddegree matrix u according to formula (21)^{(a+1)}；
Step 404: the given condition of convergence, if the subordinateddegree matrix difference of iterative calculation gained is less than condition of convergence setting twice
Threshold value, then iteration terminate, otherwise return to step 402 continues iteration, until it reaches the condition of convergence or reach the iteration time setting
Till number；
The eigenmatrix s of each line fault transient zerosequence current waveform is divided into 2 classes, subordinateddegree matrix can be obtained
U in formula_{ij}Represent that jth vector in fuzzy kmeans clustering algorithm belongs to the degree of membership of the ith class, that is, jth strip circuit belongs to the
The degree of membership of i class；
Each circuit is divided into by two classes by subordinateddegree matrix u, is individually divided into the circuit of a class to be faulty line.
Priority Applications (1)
Application Number  Priority Date  Filing Date  Title 

CN201410197442.XA CN103941163B (en)  20140512  20140512  Resonant earthed system fault line selection method utilizing fuzzy Kmeans clustering 
Applications Claiming Priority (1)
Application Number  Priority Date  Filing Date  Title 

CN201410197442.XA CN103941163B (en)  20140512  20140512  Resonant earthed system fault line selection method utilizing fuzzy Kmeans clustering 
Publications (2)
Publication Number  Publication Date 

CN103941163A CN103941163A (en)  20140723 
CN103941163B true CN103941163B (en)  20170118 
Family
ID=51188912
Family Applications (1)
Application Number  Title  Priority Date  Filing Date 

CN201410197442.XA CN103941163B (en)  20140512  20140512  Resonant earthed system fault line selection method utilizing fuzzy Kmeans clustering 
Country Status (1)
Country  Link 

CN (1)  CN103941163B (en) 
Families Citing this family (10)
Publication number  Priority date  Publication date  Assignee  Title 

CN104898021B (en) *  20150525  20180306  昆明理工大学  A kind of distribution network fault line selection method based on k means cluster analyses 
CN105158612B (en) *  20150915  20180406  昆明理工大学  A kind of thunderbolt interference identification method adaptive using line voltage traveling wave 
CN105866631B (en) *  20160519  20190205  昆明理工大学  A kind of novel double end travelling wave ranging method based on fuzzy matching 
CN107064727B (en) *  20160918  20190412  昆明理工大学  A kind of distribution network fault line selection method based on transient state energy difference 
CN106370981B (en) *  20160930  20190326  中国石油化工股份有限公司  A kind of distribution network failure route selection method based on fuzzy cluster analysis 
CN109307824B (en) *  20180918  20201103  福州大学  Clusteringbased power distribution network singlephase earth fault section positioning method 
CN109541369A (en) *  20181109  20190329  国网甘肃省电力公司  A kind of power grid oneway earth fault detection system and its detection method 
CN110109446B (en) *  20190528  20200825  中南大学  Zinc flotation process fuzzy fault diagnosis method based on time series characteristics 
CN110609200B (en) *  20190920  20200724  长沙理工大学  Power distribution network earth fault protection method based on fuzzy metric fusion criterion 
CN111722055A (en) *  20200521  20200929  昆明理工大学  Singlepole grounding fault identification method for MMC direct current transmission line based on perceptual fuzzy identification 
Family Cites Families (6)
Publication number  Priority date  Publication date  Assignee  Title 

US6466030B2 (en) *  20001229  20021015  Abb Power Automation Ltd.  Systems and methods for locating faults on a transmission line with a single tapped load 
CN1180272C (en) *  20011128  20041215  淄博科汇电气有限公司  Smallcurrent earth fault switchselecting and sectioning method for power system 
CN100530884C (en) *  20071011  20090819  天津大学  Selfadaption route selection method for singlephase ground fault of power distribution network based on transient zero sequence current 
CN101242097B (en) *  20080311  20100929  昆明理工大学  Failure line selection method of small current ground system by using simulation after zero mode current measure 
CN102866326B (en) *  20120906  20150826  国家电网公司  Based on the distribution network fault line selection of zero sequence current variable quantity waveform correlation coefficient matrix 
CN103454562B (en) *  20130922  20160224  福州大学  The route selection of resonant earthed system singlephase earthing clustering procedure 

2014
 20140512 CN CN201410197442.XA patent/CN103941163B/en active IP Right Grant
Also Published As
Publication number  Publication date 

CN103941163A (en)  20140723 
Similar Documents
Publication  Publication Date  Title 

Lotfifard et al.  Voltage sag data utilization for distribution fault location  
CN103344875B (en)  Classification line selection method for singlephase earth fault of resonance earthing system  
Livani et al.  A fault classification and localization method for threeterminal circuits using machine learning  
CN103576048B (en)  A kind of possible breakdown sets of lines extracting method for voltage dip source electricity  
Wu et al.  Ultrahighspeed directional protection of transmission lines using mathematical morphology  
Valsan et al.  Wavelet transform based digital protection for transmission lines  
CN103675605B (en)  A kind of power distribution network earth fault line selection method based on the correlation analysis of faultsignal transient state  
CN104635114B (en)  A kind of power quality disturbance alignment system and localization method  
Ojaghi et al.  Use of clustering to reduce the number of different setting groups for adaptive coordination of overcurrent relays  
Gopakumar et al.  Adaptive fault identification and classification methodology for smart power grids using synchronous phasor angle measurements  
Khodadadi et al.  A noncommunication adaptive singlepole autoreclosure scheme based on the ACUSUM algorithm  
CN103424669B (en)  A kind of selection method utilizing fault feeder zerosequence current matrix principal component analysis (PCA) first principal component  
Yadav et al.  An overview of transmission line protection by artificial neural network: fault detection, fault classification, fault location, and fault direction discrimination  
Shah et al.  Fault discrimination scheme for power transformer using random forest technique  
Zhang et al.  Transmission line boundary protection using wavelet transform and neural network  
Kezunovic  A survey of neural net applications to protective relaying and fault analysis  
Wang et al.  Faulty feeder detection of single phaseearth fault using grey relation degree in resonant grounding system  
CN102854437B (en)  Fault line selection method of low current grounding system using timefrequency atom decomposition theory  
Zhang et al.  Fault localization in electrical power systems: A pattern recognition approach  
Saravanababu et al.  Transmission line faults detection, classification, and location using discrete wavelet transform  
Rathore et al.  Waveletalienation based transmission line protection scheme  
Costa et al.  Realtime classification of transmission line faults based on maximal overlap discrete wavelet transform  
CN105044560B (en)  A kind of distribution network failure decision method based on fault selfadapting technology  
CN105974264B (en)  A kind of faultline selecting method based on phase current transient characteristic  
Yao et al.  Impact evaluation of series dc arc faults in dc microgrids 
Legal Events
Date  Code  Title  Description 

PB01  Publication  
C06  Publication  
SE01  Entry into force of request for substantive examination  
C10  Entry into substantive examination  
GR01  Patent grant  
C14  Grant of patent or utility model 