CN103941163B - Resonant earthed system fault line selection method utilizing fuzzy K-means clustering - Google Patents

Resonant earthed system fault line selection method utilizing fuzzy K-means clustering Download PDF

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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
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formula
circuit
sequence current
line
transient zero
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CN103941163A (en
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郭谋发
郑新桃
杨耿杰
高伟
缪希仁
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福州大学
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Abstract

The invention relates to a resonant earthed system fault line selection method utilizing fuzzy K-means clustering. The resonant earthed system fault line selection method comprises the following steps of 1 performing stretching transformation treatment on transient-state zero-sequence current of each line to improve similarities of transient-state zero-sequence currents of non-fault lines; 2 dividing the transient-state zero-sequence 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 transient-state zero-sequence current of each section to determinacy points x and y on a phase plane so as to extract local features of the transient-state zero-sequence 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 K-means clustering method to perform clustering on the normalized feature matrixes, dividing the transient-state zero-sequence 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

Malfunction route selection method for resonant grounded system using fuzzy k-means cluster
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 k-means cluster.
Background technology
Resonant earthed system has the power supply reliability of raising system, reduces lightning damage accident rate, anti-communication 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, three-phase 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 non-faulting 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 wire-selecting problem is solved not yet very well.
Carrying out fault line detection using the fault-signal transient of several times bigger than fault-signal steady-state quantity is this neck in recent years The study hotspot in domain;The semaphore being adopted mainly has zero-sequence 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 zero-sequence current waveform of each circuit simultaneously The information such as property, amplitude.Occur after singlephase earth fault using resonant earthed system, the transient zero-sequence current waveform of non-fault line Similar, and the faulty line transient zero-sequence current waveform feature larger with non-fault line difference, to transient zero-sequence 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, short-term 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 k-means 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 k-means cluster Fault-line selecting method, comprises the following steps:
Step 1: stretching process is carried out to each circuit transient zero-sequence current, to improve transient zero-sequence between non-fault line The similarity of electric current, reduces the impact that between non-fault line, transient zero-sequence current amplitude difference is asked for similarity;
Step 2: each circuit transient zero-sequence 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 zero-sequence current Euclidean distance determining point in phase plane, to extract each section of transient zero-sequence 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 k-means clustering method, the eigenmatrix after normalization is clustered, by each circuit transient state Zero-sequence 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 zero-sequence current is carried out with stretching process:
Zero-sequence network equivalent circuit during single-phase earthing is occurred for resonant earthed system, if thekBar circuit is fault wire Road,u 0For trouble point zero sequence power supply,r 0For zero sequence loop equivalent resistance,l 0For arc suppression coil zero sequence inductance,c 1,…,c k-1,c k+1,…,c n For non-faulting line three relatively equivalent capacity,u cFor the voltage at each feeder line direct-to-ground capacitance two ends,i 1,i 2,…,i n For each feeder line zero-sequence current,i lFor flowing through the electric current of arc suppression coil;Each feeder line transient zero-sequence current is
(1)
(2)
Obtained by formula (1)
(3)
Whereini j i k It is respectively non-fault linej, the transient zero-sequence current of faulty line;
Introduce stretching coefficient and line translation is entered to transient zero-sequence current waveform: with circuitbAs reference line, define CircuitjStretching multiplep j For
(4)
In formulai j i b It is respectively circuitjAnd circuitbTransient zero-sequence current;
If reference linebFor non-fault line, that is,bk, then obtained by formula (3) and formula (4)
(5)
Convolution (1), formula (4) and formula (5) obtain the non-fault line transient zero-sequence current after stretchingi ' j For
(6)
Convolution (2) and formula (4) obtain the faulty line transient zero-sequence current after stretchingi ' k For
(7)
If reference linebFor faulty line, that is,b=k, then by formula (5), each non-fault line equivalent capacity over the groundc j Use non-fault 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)
Non-fault line transient zero-sequence 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 discrete-time series of the transient zero-sequence 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 zero-sequence current after stretching is divided in time domainn 1Section, using least squares estimate matching Do linearisation to each section, obtainn 1Individual straightway, then the derivative of point in the range of a straightway for the transient zero-sequence current waveformf (i ' j (n)) all represented with the slope of this straightway;
If the sampling number of transient zero-sequence current head half-wave isl, by the transient zero-sequence current after each circuit stretchingi ' j It is divided inton 2Section,n 1=bn 2,b>=2, then each segmentation up-sampling point number bel/n 2;Make equal paragraph by paragraph Face converts, and the knock type (13) on each section of phase-plane 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 Discrete-time 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 zero-sequence 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 zero-sequence 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 2Eigenmatrixs, 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 zero-sequence current is classified and found fault wire Road:
Input to be sorted firstnIndividual vectorx j And vectorkThe initially fuzzy subordinated-degree 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 subordinated-degree matrixu:
Step 401: determine classification numberk, ordera=0, provide initial subordinated-degree matrix at randomu (1)
Step 402: calculate the cluster centre vector of preliminary classification according to formula (22)v (1)
Step 403: calculate subordinated-degree matrix according to formula (21)u (a+1)
Step 404: the given condition of convergence, if the subordinated-degree 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 zero-sequence current waveformsIt is divided into 2 classes, subordinated-degree matrix can be obtained
(23)
In formulau ij Represent thejArticle circuit belongs toiThe degree of membership of class;
By subordinated-degree 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 k-means 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 zero-sequence current Stretching, it is not of uniform size that stretching process preferably solves transient zero-sequence current Numeric Attributes between non-fault line Impact, improves the similarity of transient zero-sequence current waveform between non-fault line, improves the nargin of route selection;Meanwhile, utilize and divide Section phase plane conversion to extract the characteristic quantity of transient zero-sequence current with Euclidean distance, thus the width of concentrated expression transient zero-sequence current Value and polarity information, more accurately depict faulty line and non-fault line transient zero-sequence current feature.Additionally, the present invention Method has stronger reliability, anti-interference and adaptability, has certain engineering application value.
Brief description
Fig. 1 is the zero-sequence network equivalent circuit diagram that in the embodiment of the present invention, resonant earthed system occurs during single-phase 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 zero-sequence 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 non-fault line transient zero-sequence current waveform Cause, it differs only in the difference of amplitude size, thus the transient zero-sequence current waveform between non-fault line is similar;And it is right In faulty line, faulty line transient zero-sequence current, containing more DC component, non-fault line is practically free of direct current and divides Amount, and the opposite in phase of faulty line and non-fault line transient zero-sequence current high fdrequency components, therefore faulty line and non-faulting There is larger difference in the transient zero-sequence current waveform of circuit.Therefore, the present invention utilizes transient zero-sequence current wave-form 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 zero-sequence current, to improve transient zero-sequence between non-fault line The similarity of electric current, reduces the impact that between non-fault line, transient zero-sequence current amplitude difference is asked for similarity;
Step 2: each circuit transient zero-sequence 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 zero-sequence current determine in phase plane point (x,y) Euclidean distance, to extract each section of transient state The local feature of zero-sequence 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 k-means clustering method, the eigenmatrix after normalization is clustered, by each circuit transient state Zero-sequence 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 zero-sequence current is carried out with stretching process:
There is zero-sequence network equivalent circuit during single-phase earthing in resonant earthed system, as shown in figure 1, setting thekBar circuit is Faulty line,u 0For trouble point zero sequence power supply,r 0For zero sequence loop equivalent resistance,l 0For arc suppression coil zero sequence inductance,c 1 ,…,c k-1,c k+1,…,c n For non-faulting line three relatively equivalent capacity,u cFor the voltage at each feeder line direct-to-ground capacitance two ends,i 1,i 2,…,i n For each feeder line zero-sequence current,i lFor 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 non-fault linej, the transient zero-sequence current of faulty line.
From formula (3), ifjThe fault transient zero-sequence current of bar circuit is divided by its equivalent capacity over the groundc j , then Between non-fault line, the similarity of transient zero-sequence current waveform will improve.Each line-to-ground equivalent capacityc j It is difficult to obtain, introduce Stretching coefficient enters line translation to transient zero-sequence current waveform.With circuitbAs reference line, define circuitjFlexible Conversion multiplep j For
(4)
In formulai j i b It is respectively circuitjAnd circuitbTransient zero-sequence current.
In view of transient zero-sequence 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 zero-sequence 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 non-fault line, that is,bk, then obtained by formula (3) and formula (4)
(5)
Convolution (1), formula (4) and formula (5) obtain the non-fault line transient zero-sequence current after stretchingi ' j For
(6)
Convolution (2) and formula (4) obtain the faulty line transient zero-sequence current after stretchingi ' k For
(7)
In the case that reference line is for non-fault line, from formula (6), after processing through stretching, each non-faulting Circuit transient zero-sequence current has identical expression formula, and stretching processes and improves transient zero-sequence current ripple between non-fault line The similarity of shape.Comparison expression (6) and formula (7) understand, after processing through stretching, faulty line and non-fault line transient zero-sequence Difference between current waveform is still larger.
2) if reference linebFor faulty line, that is,b=k, then by formula (5), each non-fault line equivalent capacity over the groundc j Use non-fault 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)
Non-fault line transient zero-sequence current after stretching is obtained by formula (9), formula (10)i ' j For
(11)
When reference line is faulty line, faulty line transient zero-sequence current waveform keeps constant.From formula (11), warp After stretching is processed, the transient zero-sequence current expression formula of each non-fault line is identical, has stronger similarity.Stretching Process the similarity that improve between non-fault line transient zero-sequence current waveform.Comparison expression (2) and formula (11) understand, become through flexible After changing process, the difference of faulty line and non-fault line transient zero-sequence 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 discrete-time series of the transient zero-sequence 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 zero-sequence electricity after stretching Stream is divided in time domainn 1Section, does linearisation using least squares estimate matching to each section, obtainsn 1Individual straightway, The then derivative of point in the range of a straightway for the transient zero-sequence current waveformf(i' j (n)) all with the slope table of this straightway Show.
The transient process of barrier first half cycles of transient zero-sequence current (first half-wave) 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 zero-sequence current head half-wave isl, Jiang Gexian Transient zero-sequence current after the stretching of roadi ' j It is divided inton 2Section,n 1=bn 2,b>=2, then each segmentation up-sampling Point number bel/n 2;Make phase plane conversion paragraph by paragraph, and the knock type (13) on each section of phase-plane 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 Discrete-time 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 zero-sequence current carry out earthing wire-selecting, take and determine in phase plane Point is (- 1,0), and the phase paths calculating the transient zero-sequence 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 positive-negative half-cycle 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 single-phase earthing, faulty line with Phase paths relation between non-fault line transient zero-sequence 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 zero-sequence current waveform of faulty line and non-fault line.
Willr m As the local feature amount of one time period of transient zero-sequence 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 2Eigenmatrixs, 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 k-means 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 subordinated-degree 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 fog-level 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 subordinated-degree matrixu:
Step 401: determine classification numberk, ordera=0, provide initial subordinated-degree matrix at randomu (1)
Step 402: calculate the cluster centre vector of preliminary classification according to formula (22)v (1)
Step 403: calculate subordinated-degree matrix according to formula (21)u (a+1)
Step 404: the given condition of convergence, if the subordinated-degree 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 zero-sequence 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 subordinated-degree 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 zero-sequence electricity between the similarity degree of transient zero-sequence current is than non-fault line between faulty line and non-fault line The similarity degree of stream is little, then shows as the eigenvalue difference very little between non-fault line in characteristic quantity, and faulty line and non-event Eigenvalue between barrier circuit is widely different, hence with subordinated-degree 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 lFor aerial line Road length;c lFor cable run length;r fFor 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 zero-sequence current of faulty line and two of which non-fault line Shown in first half-wave such as Fig. 4 (a).As reference line, each circuit transient zero-sequence current presses conversion coefficient for access line 4p k =i k /i 4Do stretching, after conversion shown in waveform such as Fig. 4 (b).As shown in Figure 4, after stretching, non-fault line transient state zero Similarity between sequence current waveform is improved, and the similarity change between faulty line and non-fault line waveform is less.
The fault transient zero-sequence current head half-wave of stretching gained is divided inton 1=20 sections, do piece-wise linearization, with each The slope of straightway represents the derivative of point in the range of this straightway for the transient zero-sequence 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 zero-sequence 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 subordinated-degree matrix
Subordinated-degree 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 subordinated-degree 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 zero-sequence current waveform, other steps are constant, then eigenmatrixs ’ And subordinated-degree matrixu ’It is respectively
By subordinated-degree 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 zero-sequence current waveform and can improve route selection nargin.
There is single-phase 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 fDistance for trouble point to bus;r fFor earth resistance;θ For fault close angle.
The adaptability checking of selection method:
1) arc fault
Show as intermittent arc fault more the single-phase earthing initial stage, arc fault emulation is carried out using mayr Arc Modelling. Circuit l3The results are shown in Table 2 there is the route selection of arc-earth faults at bus 5km.
2) time windows
Circuit l4The switching angle that breaks down at bus 2km be 90 °, earth resistance be 3k ω single-phase earthing therefore Barrier, from different transient zero-sequence 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 l6Route 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 zero-sequence current be there may be asynchronous.Consider circuit l3、l4Delayed circuit l1、l28 sampled points;Circuit l5、l6Delayed circuit l1、l214 sampled points, circuit l3End 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 k-means cluster is it is characterised in that include following walking Rapid:
Step 1: stretching process is carried out to each circuit transient zero-sequence current, to improve transient zero-sequence current between non-fault line Similarity, reduce transient zero-sequence current amplitude difference impact that similarity is asked between non-fault line;
Step 2: each circuit transient zero-sequence 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 zero-sequence current Euclidean distance determining point in phase plane, to extract each section of transient zero-sequence 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 k-means clustering method, the eigenmatrix after normalization is clustered, by each circuit transient zero-sequence 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 zero-sequence current is carried out with stretching process:
Zero-sequence network equivalent circuit during single-phase earthing is occurred for resonant earthed system, if kth bar circuit is faulty line, u0 For trouble point zero sequence power supply, r0For zero sequence loop equivalent resistance, l0For arc suppression coil zero sequence inductance, c1,…,ck-1,ck+1,…,cn For non-faulting line three relatively equivalent capacity, ucFor the voltage at each feeder line direct-to-ground capacitance two ends, i1,i2,…,inFor each feeder line zero Sequence electric current, ilFor flowing through the electric current of arc suppression coil;Each feeder line transient zero-sequence current is
Obtained by formula (1)
Wherein ij、ikIt is respectively non-fault line j, the transient zero-sequence current of faulty line;
Introduce stretching coefficient and transient zero-sequence current waveform is entered with line translation: using circuit b as reference line, define circuit j Stretching multiple pjFor
I in formulaj、ibIt is respectively the transient zero-sequence current of circuit j and circuit b;
If reference line b is non-fault line, i.e. b ≠ k is then obtained by formula (3) and formula (4)
cj=pjcb(j ∈ [1, n], j ≠ k) (5)
Convolution (1), formula (4) and formula (5) obtain the non-fault line transient zero-sequence current i ' after stretchingjFor
Convolution (2) and formula (4) obtain the faulty line transient zero-sequence current i ' after stretchingkFor
If reference line b is faulty line, i.e. b=k, then by formula (5), each non-fault line equivalent capacity c over the groundjUse non-faulting Circuit a equivalent capacity c over the groundaIt is expressed as
cjjca(j ∈ [1, n], j ≠ k) (8)
λ in formulajFor proportionality coefficient;Obtained by formula (1), formula (8)
Make pa=ia/ib, then obtained by formula (2), formula (9)
Obtain the non-fault line transient zero-sequence current i ' after stretching by formula (9), formula (10)jFor
2. the malfunction route selection method for resonant grounded system of utilization fuzzy k-means cluster according to claim 1, its feature exists In in step 2, asking for the eigenmatrix of each circuit global characteristics as follows:
i′jN () is the discrete-time series of the transient zero-sequence current waveform of j-th strip circuit after stretching, n is sampling period, its The derivative of corresponding point is asked for by formula (12)
F (i' in formulaj(n)) it is i'jN the derivative of (), δ t is sampling step length;
Transient zero-sequence current after stretching is divided into n in time domain1Section, using least squares estimate matching to each section Do linearisation, obtain n1Individual straightway, then the derivative f (i' of point in the range of a straightway for the transient zero-sequence current waveformj(n)) All represented with the slope of this straightway;
If the sampling number of transient zero-sequence current head half-wave is l, by the transient zero-sequence current i' after each circuit stretchingjAveragely It is divided into n2Section, n1=bn2, b >=2, then the number of each segmentation up-sampling point is l/n2;Make phase plane conversion paragraph by paragraph, and to each Knock type (13) on section phase-plane diagram is normalized, and so that the data point in phase plane is all fallen in interval [- 1,1];
I' in formulajmRepresent i'jM-th segmentation, i'jmN () represents i'jmDiscrete-time series, m ∈ [1, n2], n ∈ [1, l/ n2], f'(i'jm(n)) it is f (i'jm(n)) sequence after normalization, i "jmN () is i'jmSequence after (n) normalization;
By formula (14) calculate each section of stretching after transient zero-sequence current waveform phase paths determine in phase plane point (x, Y) Euclidean distance:
R in formulamRepresent m section phase paths to the Euclidean distance determining point (x, y);
By rmAs the local feature amount of one time period of transient zero-sequence current waveform, the then transient zero-sequence current of any one circuit The global characteristics amount of waveform is
Then the global characteristics amount of n bar circuit constitutes a n × n2Eigenmatrix s, as shown in formula (16)
S in formulajiRepresent that i-th section of phase path of j-th 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 k-means 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 formulajiRepresent that i-th section of phase path of j-th strip circuit determine the Euclidean distance of point (x, y), s' in phase planejiRepresent sjiBy the value obtaining after row normalization.
4. the malfunction route selection method for resonant grounded system of utilization fuzzy k-means cluster according to claim 3, its feature exists In in step 4, as follows each circuit transient zero-sequence current being classified and is found with faulty line:
Input n vector x to be sorted firstjInitially fuzzy subordinated-degree matrix u with the classification of vectorial k group(1)
U in formulaijRepresent that j-th vector belongs to the degree of membership of the i-th class, uij∈ [0,1] andJ=1,2 ..., n;If vi For the i-th class initial cluster center vector, then initial cluster center matrix is
v(1)=[v1, v2..., vk] (19)
Determine object function jm(u, v), has
In formula, m is greater than 1 arbitrary real number, | | | | for rpAny 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 subordinated-degree matrix u:
Step 401: determine classification number k, make a=0, provide initial subordinated-degree matrix u at random(1)
Step 402: calculate the cluster centre vector v of preliminary classification according to formula (22)(1)
Step 403: calculate subordinated-degree matrix u according to formula (21)(a+1)
Step 404: the given condition of convergence, if the subordinated-degree 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 zero-sequence current waveform is divided into 2 classes, subordinated-degree matrix can be obtained
U in formulaijRepresent that j-th vector in fuzzy k-means clustering algorithm belongs to the degree of membership of the i-th class, that is, j-th strip circuit belongs to the The degree of membership of i class;
Each circuit is divided into by two classes by subordinated-degree matrix u, is individually divided into the circuit of a class to be faulty line.
CN201410197442.XA 2014-05-12 2014-05-12 Resonant earthed system fault line selection method utilizing fuzzy K-means clustering CN103941163B (en)

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