CN103941163A - 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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CN103941163A
CN103941163A CN201410197442.XA CN201410197442A CN103941163A CN 103941163 A CN103941163 A CN 103941163A CN 201410197442 A CN201410197442 A CN 201410197442A CN 103941163 A CN103941163 A CN 103941163A
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formula
sequence current
circuit
transient zero
line
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CN103941163B (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

Utilize the malfunction route selection method for resonant grounded system of fuzzy K mean cluster
Technical field
The present invention relates to intelligent distribution system technical field of relay protection, particularly a kind of malfunction route selection method for resonant grounded system based on waveform expansion and contraction conversion and fuzzy K mean cluster.
Background technology
Resonant earthed system have raising system power supply reliability, reduce the advantages such as lightning damage accident rate, anti-communication facilities electromagnetic interference (EMI), be widely used in medium voltage distribution network.The probability of resonant earthed system singlephase earth fault is very high, generally accounts for the more than 80% of total failare.If instantaneity earth fault, fault can be eliminated voluntarily; If permanent earth fault, system can continue operation 1 ~ 2 hour by tape jam, does not affect the continued power of system.Because the ground current of resonant earthed system is less, after generation singlephase earth fault, three-phase voltage still keeps symmetric relation, can not affect the continued power to load, so can improve to a certain extent the power supply reliability of electric system.But after system generation singlephase earth fault, the voltage of healthy phases rises to line voltage, phase voltage doubly, this be easy to line insulation comparatively weakness bring out second short circuit or form phase fault.If system is that intermittent arc grounding fault occurs, very easily damage equipment or cause power equipment to occur new earth point of superpotential, expands fault coverage; And the fault current that superpotential forms likely impels trouble spot to develop into permanent earth fault from instantaneity earth fault.Therefore, accurate, reliable earth fault line selection technology, not only can find out faulty line in time, removes a hidden danger, and can ensure the safe and stable operation of whole electrical network, improves the power supply reliability of electric system.Because the situation of resonant earthed system generation singlephase earth fault is complicated and changeable, fault current is fainter, and often with intermittent electric arc, its earthing wire-selecting problem does not obtain fine solution yet.
Utilize that to carry out fault line detection than the fault-signal transient of the large several times of fault-signal steady-state quantity be the study hotspot in this field in recent years; The semaphore adopting mainly contains zero-sequence current, residual voltage, goes and involve phase current etc.; Characteristic quantity mainly contains energy, Sudden Changing Rate, amplitude, polarity and waveform etc.; In the middle of the fault transient zero-sequence current waveform of each circuit, comprised the information such as polarity, amplitude simultaneously.Utilize after resonant earthed system generation singlephase earth fault, the transient zero-sequence current waveform similarity of non-fault line, and the larger feature of faulty line transient zero-sequence current waveform and non-fault line difference, transient zero-sequence current waveform or its feature band are done to correlation analysis or grey correlation analysis, and then definite earth fault line, be a good route selection thinking.
The most artificial experience that adopt of route selection criterion that existing malfunction route selection method for resonant grounded system adopts are got threshold method, cannot accomplish Intelligent fault route selection; And high resistance earthing fault, short-term road fault are difficult to accurate route selection, and when there is singlephase earth fault after power distribution network access miscellaneous equipment, whether the route selection criterion of proposition still effectively also lacks research.
Summary of the invention
The object of the present invention is to provide a kind of malfunction route selection method for resonant grounded system that utilizes fuzzy K mean cluster, the method has improved automaticity and the route selection nargin of failure line selection.
For achieving the above object, technical scheme of the present invention is: a kind of malfunction route selection method for resonant grounded system that utilizes fuzzy K mean cluster, comprises the following steps:
Step 1: each circuit transient zero-sequence current is carried out to stretching processing, to improve the similarity of transient zero-sequence current between non-fault line, reduce 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 regular hour section, do the conversion of segmentation phase plane, ask for each section of all phase points of transient zero-sequence current to an Euclidean distance of determining point in phase plane, to extract the local feature of each section of transient zero-sequence current, obtain the eigenmatrix of each circuit global characteristics;
Step 3: the element in eigenmatrix is made to normalized, to strengthen comparability;
Step 4: the eigenmatrix after utilizing fuzzy K means clustering method to normalization carries out cluster, and each circuit transient zero-sequence current is divided into two classes, and the circuit that is divided into separately a class is faulty line.
Further, in step 1, as follows each circuit transient zero-sequence current is carried out to stretching processing:
Zero-sequence network equivalent electrical circuit during for resonant earthed system generation single-phase earthing, establishes kbar circuit is faulty line, u 0for trouble spot 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 relatively equivalent capacity of non-fault wire three, u cfor the voltage at each feeder line 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)
Wherein i j , i k be respectively non-fault line j, faulty line transient zero-sequence current;
Introducing stretching coefficient converts transient zero-sequence current waveform: with circuit bas with reference to circuit, define circuit jstretching multiple p j for
????(4)
In formula i j , i b be respectively circuit jand circuit btransient zero-sequence current;
If reference line bfor non-fault line, bk, 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 stretching i' j for
????(6)
Convolution (2) and formula (4) obtain the faulty line transient zero-sequence current after stretching i' k for
????(7)
If reference line bfor faulty line, b= k, by formula (5), each non-fault line equivalent capacity over the ground c j use non-fault line aequivalent capacity over the ground c a be expressed as
????(8)
In formula λ j for scale-up factor; Obtained by formula (1), formula (8)
????(9)
Order p a = i a / i b , obtained by formula (2), formula (9)
????(10)
Obtain the non-fault line transient zero-sequence current after stretching by formula (9), formula (10) i' j for
????(11)。
Further, in step 2, ask for as follows the eigenmatrix of each circuit global characteristics:
i' j ( n) be after stretching jthe 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 formula f( i' j ( n)) be i' j ( n) derivative, Δ tfor sampling step length;
Transient zero-sequence current after stretching is divided in time domain n 1section, adopts least squares estimate matching to do linearization to each section, obtains n 1individual straight-line segment, the derivative of the point of transient zero-sequence current waveform within the scope of a straight-line segment f( i' j ( n)) all represent with the slope of this straight-line segment;
If the sampling number of the first half-wave of transient zero-sequence current is l, by the transient zero-sequence current after each circuit stretching i' j be divided into n 2section, n 1= bN 2, b>=2, the number of each segmentation up-sampling point is l/ n 2; Do piecemeal phase plane conversion, and the knock type on each section of phase-plane diagram (13) is normalized, make the data point in phase plane all drop on interval [1,1];
????(13)
In formula i' jm represent i' j ? mindividual segmentation, i' jm ( n) represent i' jm discrete-time series, m∈ [1, n 2], n∈ [1, l/ n 2], f'( i' jm ( n)) be f( i' jm ( n)) sequence after normalization, i'' jm ( n) be i' jm ( n) sequence after normalization;
The phase path of calculating the transient zero-sequence current waveform after each section of stretching by formula (14) to determine in phase plane point ( x, y) Euclidean distance:
????(14)
In formula r m represent the msection phase path to determine point ( x, y) Euclidean distance;
Will r m as the local feature amount of one time period of transient zero-sequence current waveform, the global characteristics amount of the transient zero-sequence current waveform of any circuit is
????(15)
? nthe global characteristics amount of bar circuit forms one n× n 2eigenmatrix s , as the formula (16)
????(16)
In formula s ji represent the jof article circuit isection phase path to determine in phase plane point ( x, y) Euclidean distance.
Further, in step 3, adopt as shown in the formula (17) eigenmatrix s in element do normalization processing by row:
????(17)
In formula s' ji represent s ji by the value obtaining after row normalization.
Further, in step 4, as follows each circuit transient zero-sequence current is classified and is found faulty line:
First input to be sorted nindividual vector x j and vector kthe initial fuzzy membership matrix of group categories u (1)
????(18)
In formula u ij represent the jindividual vector belongs to ithe degree of membership of class, and , j=1,2 ..., n; If v i be iclass initial cluster center vector, initial cluster center matrix is
????(19)
Determine objective function j m ( u , v ), have
????(20)
In formula, mto be greater than arbitrary real number of 1, for r p any norm in space, utilizes lagrange's method of multipliers to prove to obtain
????(21)
????(22)
In formula afor iterations counter;
Then determine according to the following steps cluster centre matrix v with degree of membership matrix u :
Step 401: determine number of categories k, order a=0, provide at random initial degree of membership matrix u (1);
Step 402: the cluster centre vector that calculates preliminary classification according to formula (22) v (1);
Step 403: calculate degree of membership matrix according to formula (21) u ( a+ 1) ;
Step 404: the given condition of convergence, if the degree of membership matrix difference of twice iterative computation gained is less than the threshold value that the condition of convergence is set, iteration finishes, and continues iteration otherwise return to step 402, until reach the condition of convergence or arrive the iterations of setting;
By the eigenmatrix of each line fault transient zero-sequence current waveform s be divided into 2 classes, can obtain degree of membership matrix
????(23)
In formula u ij represent the jarticle circuit belongs to ithe degree of membership of class;
By degree of membership matrix u each circuit is divided into two classes, and the circuit that is divided into separately a class is faulty line.
Compared with prior art, the invention has the beneficial effects as follows: fuzzy K means clustering algorithm is introduced to resonant earthed system failure line selection, thereby avoided artificial experience selected threshold to realize Intelligent fault route selection; Transient zero-sequence current is carried out to waveform expansion and contraction conversion, stretching is processed and has been solved preferably transient zero-sequence current Numeric Attributes impact not of uniform size between non-fault line, improve the similarity of transient zero-sequence current waveform between non-fault line, improved the nargin of route selection; Meanwhile, utilize segmentation phase plane conversion and Euclidean distance to extract the characteristic quantity of transient zero-sequence current, thereby the amplitude of concentrated expression transient zero-sequence current and polarity information depict faulty line and non-fault line transient zero-sequence current feature more accurately.In addition, the inventive method has stronger reliability, anti-interference and adaptability, has certain engineering using value.
Brief description of the drawings
Fig. 1 is zero-sequence network equivalent circuit diagram when resonant earthed system generation single-phase earthing in the embodiment of the present invention.
Fig. 2 is sinusoidal wave phase plane trajectory schematic diagram in the embodiment of the present invention.
Fig. 3 is resonant earthed system realistic model 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 realization flow figure of the embodiment of the present invention.
Embodiment
When resonant earthed system generation singlephase earth fault, the variation tendency of non-fault line transient zero-sequence current waveform is consistent, and its difference is only the difference of amplitude size, thereby transient zero-sequence current waveform between non-fault line is similar; And for faulty line, in faulty line transient zero-sequence current, contain more DC component and non-fault line hardly containing DC component, and the single spin-echo of faulty line and non-fault line transient zero-sequence current high fdrequency component, there is larger difference in the transient zero-sequence current waveform of faulty line and non-fault line therefore.Therefore, the present invention utilizes transient zero-sequence current wave-form similarity knowledge method for distinguishing to carry out failure line selection.
Malfunction route selection method for resonant grounded system of the present invention, as shown in Figure 5, comprises the following steps:
Step 1: each circuit transient zero-sequence current is carried out to stretching processing, to improve the similarity of transient zero-sequence current between non-fault line, reduce 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 regular hour section, is done segmentation phase plane conversion, ask for each section of all phase points of transient zero-sequence current to determine in phase plane point ( x, y) Euclidean distance, to extract the local feature of each section of transient zero-sequence current, obtain the eigenmatrix of each circuit global characteristics;
Step 3: the element in eigenmatrix is made to normalized by row, to strengthen comparability;
Step 4: the eigenmatrix after utilizing fuzzy K means clustering method to normalization carries out cluster, and each circuit transient zero-sequence current is divided into two classes, and the circuit that is divided into separately a class is faulty line.
In step 1, as follows each circuit transient zero-sequence current is carried out to stretching processing:
Zero-sequence network equivalent electrical circuit when resonant earthed system generation single-phase earthing, as shown in Figure 1, establishes kbar circuit is faulty line, u 0for trouble spot 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 relatively equivalent capacity of non-fault wire three, u cfor the voltage at each feeder line 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.Can obtain each feeder line transient zero-sequence current by Fig. 1 is
????(1)
????(2)
Obtained by formula (1)
????(3)
Wherein i j , i k be respectively non-fault line j, faulty line transient zero-sequence current.
From formula (3), if jthe fault transient zero-sequence current of bar circuit is divided by its equivalent capacity over the ground c j , between non-fault line, the similarity of transient zero-sequence current waveform will improve.Each line-to-ground equivalent capacity c j be difficult to obtain, introduce stretching coefficient transient zero-sequence current waveform is converted.With circuit bas with reference to circuit, define circuit jstretching multiple p j for
????(4)
In formula i j , i b be respectively circuit jand circuit btransient zero-sequence current.
Consider that transient zero-sequence current waveform has nonlinear and nonstationary feature, while adopting stable state i j with i b ask p j .For reducing the impact of the factors such as noise, with after fault the qthe average multiple of individual 1/4 cycle sampled data is asked p j , transient state process may continue 1 ~ 2 cycle, qvalue should be greater than 8.Suppose that sample frequency is 20kHz, with zero-sequence current after fault (100 ( q-1)+1) individual sampled point to the 100 qthe average multiple of individual sampled point is asked p j :
1) if reference line bfor non-fault line, bk, 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 stretching i' j for
????(6)
Convolution (2) and formula (4) obtain the faulty line transient zero-sequence current after stretching i' k for
????(7)
In the situation that reference line is non-fault line, from formula (6), after stretching is processed, each non-fault line transient zero-sequence current has identical expression formula, and stretching processing has improved the similarity of transient zero-sequence current waveform between non-fault line.Comparison expression (6) and formula (7) are known, and after stretching is processed, the difference between faulty line and non-fault line transient zero-sequence current waveform is still larger.
2) if reference line bfor faulty line, b= k, by formula (5), each non-fault line equivalent capacity over the ground c j use non-fault line aequivalent capacity over the ground c a be expressed as
????(8)
In formula λ j for scale-up factor; Obtained by formula (1), formula (8)
????(9)
Order p a = i a / i b , obtained by formula (2), formula (9)
????(10)
Obtain the non-fault line transient zero-sequence current after stretching by formula (9), formula (10) i' j for
????(11)
When reference line is faulty line, faulty line transient zero-sequence current waveform remains unchanged.From formula (11), after stretching is processed, the transient zero-sequence current expression formula of each non-fault line is identical, has stronger similarity.Stretching processing has improved the similarity between non-fault line transient zero-sequence current waveform.Comparison expression (2) and formula (11) are known, and after stretching is processed, 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, is applied in fields such as arc fault detection, Classification of Power Quality Disturbances and earth fault type classification.Phase plane is with time series x( t) be transverse axis, seasonal effect in time series derivative x( t) be the plane that the longitudinal axis forms, it is with another kind of Morphological Characterization original waveform.As shown in Figure 2, with sine function asin x( x∈ [0,2 π]) be example, when a=1, xincrease to from 0 πtime, its phase plane trajectory as shown in curve 1, from A point along solid line to B point, phase path is distributed in I, IV quadrant; When a=1, xfrom πincrease to 2 πtime, its phase plane trajectory as shown in curve 2, from B point along dotted line to A point, phase path is distributed in II, III quadrant; When a=1.5, xincrease to from 0 πtime, its phase plane trajectory as shown in curve 3, from C point along solid line to D point, phase path is distributed in I, IV quadrant.Hence one can see that, and for a certain section of specific sine wave in one-period, its phase plane trajectory is unique, and sinusoidal wave amplitude is larger, and the distance of its phase path deviation from origin is also far away.
In step 2, ask for as follows the eigenmatrix of each circuit global characteristics:
i' j ( n) be after stretching jthe 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 formula f( i' j ( n)) be i' j ( n) derivative, Δ tfor sampling step length;
From formula (12), f( i' j ( n)) only with current sampled value i' j ( n) and last sampled value i' j ( n-1) relevant, and irrelevant with other sampled values, be vulnerable to the impact of random disturbance and noise.Transient zero-sequence current after stretching is divided in time domain n 1section, adopts least squares estimate matching to do linearization to each section, obtains n 1individual straight-line segment, the derivative of the point of transient zero-sequence current waveform within the scope of a straight-line segment f( i' j ( n)) all represent with the slope of this straight-line segment.
Because the transient state process of first half cycles of fault transient zero-sequence current (first half-wave) is obvious, comprise the information such as polarity, amplitude, can ask for its temporal signatures matrix for route selection.If the sampling number of the first half-wave of transient zero-sequence current is l, by the transient zero-sequence current after each circuit stretching i' j be divided into n 2section, n 1= bN 2, b>=2, the number of each segmentation up-sampling point is l/ n 2; Do piecemeal phase plane conversion, and the knock type on each section of phase-plane diagram (13) is normalized, make the data point in phase plane all drop on interval [1,1].
????(13)
In formula i' jm represent i' j ? mindividual segmentation, i' jm ( n) represent i' jm discrete-time series, m∈ [1, n 2], n∈ [1, l/ n 2], f'( i' jm ( n)) be f( i' jm ( n)) sequence after normalization, i'' jm ( n) be i' jm ( n) sequence after normalization;
For amplitude and the phase information of comprehensive utilization fault transient zero-sequence current are carried out earthing wire-selecting, get in phase plane and determine that point is for (1,0) phase path of, calculating the transient zero-sequence current waveform after each section of stretching by formula (14) is to the Euclidean distance of determining point (1,0) in phase plane:
????(14)
In formula r m represent the msection phase path is to the Euclidean distance of determining point (1,0);
As shown in Figure 2, sinusoidal wave track in phase plane is oval, has rotational symmetry relation.Calculated curve 1 and curve 2, to the Euclidean distance of initial point, can obtain identical distance value, cannot distinguish sinusoidal wave positive-negative half-cycle; But calculated curve 1 and curve 2 be to the Euclidean distance of determining point (1,0), can resolution curve 1 and the difference of curve 2.If directly calculated curve y=sin xwith y=-sin x( x∈ [0,2 π]) phase path to determining the Euclidean distance of point (1,0), also can obtain identical distance value, can not correctly distinguish two curves; Curve is divided into multistage, calculates respectively every section of phase point to determining the Euclidean distance of point (1,0), by calculate multiple Euclidean distances be worth the difference of distinguishable two curves.While considering single-phase earthing, phase path relation between phase path relation and curve 1 and curve 2 between faulty line and non-fault line transient zero-sequence current waveform is similar, therefore adopt the conversion of segmentation phase plane, calculate the phase path of each section of waveform to determining point (1,0) Euclidean distance, for the transient zero-sequence current waveform of Judging fault circuit and non-fault line.
Will r m as the local feature amount of one time period of transient zero-sequence current waveform, the global characteristics amount of the transient zero-sequence current waveform of any circuit is
????(15)
? nthe global characteristics amount of bar circuit forms one n× n 2eigenmatrix s , as the formula (16)
????(16)
In formula s ji represent the jof article circuit isection phase path is to the Euclidean distance of determining point (1,0).
In step 3, adopt as shown in the formula (17) eigenmatrix s in element do normalization processing by row:
????(17)
In formula s' ji represent s ji by the value obtaining after row normalization.
In step 4, as follows eigenmatrix is carried out to cluster:
Fuzzy K mean cluster is a kind of clustering method based on fuzzy division.First the present invention inputs to be sorted nindividual vector x j and vector kthe initial fuzzy membership matrix of group categories u (1)
????(18)
In formula u ij represent the jindividual vector belongs to ithe degree of membership of class, and , j=1,2 ..., n; If v i be iclass initial cluster center vector, initial cluster center matrix is
????(19)
Determine objective function j m ( u , v ), have
????(20)
In formula, mto be greater than arbitrary real number of 1, mvalue relevant with the fog-level of final classification, for making j m final classification reach local optimum, get m=2, for r p any norm in space, utilizes lagrange's method of multipliers to prove to obtain
????(21)
????(22)
In formula for iterations counter.
Then determine according to the following steps cluster centre matrix v with degree of membership matrix u :
Step 401: determine number of categories k, order a=0, provide at random initial degree of membership matrix u (1);
Step 402: the cluster centre vector that calculates preliminary classification according to formula (22) v (1);
Step 403: calculate degree of membership matrix according to formula (21) u ( a+ 1) ;
Step 404: the given condition of convergence, if the degree of membership matrix difference of twice iterative computation gained is less than the threshold value that the condition of convergence is set, iteration finishes, and continues iteration otherwise return to step 402, until reach the condition of convergence or arrive the iterations of setting.
Utilize FKM cluster by the eigenmatrix of each line fault transient zero-sequence current waveform s be divided into 2 classes, can obtain degree of membership matrix
????(23)
In formula u ij represent the jarticle circuit belongs to ithe degree of membership of class.By degree of membership matrix u each circuit is divided into two classes, is under the jurisdiction of the circuit and the circuit that is under the jurisdiction of the 2nd class of the 1st class, the circuit that is divided into separately a class is faulty line.
Between faulty line and non-fault line, the similarity degree of transient zero-sequence current is less than the similarity degree of transient zero-sequence current between non-fault line, show as eigenwert difference between non-fault line at characteristic quantity very little, and eigenwert between faulty line and non-fault line is widely different, therefore utilizes degree of membership matrix u can identify faulty line.
Below in conjunction with drawings and the specific embodiments, the invention will be further described.
Utilize ATP to build a resonant earthed system model containing 6 outlets, as shown in Figure 3.In figure: o lfor overhead transmission line length; c lfor cable line length; r ffor stake 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=0.0097 μ F; Zero sequence parameter: r 0=0.23 Ω, l 0=5.478mH, c 0=0.008 μ F.The positive order parameter of the every km of cable line: r 1=0.27 Ω, l 1=0.255mH, c 1=0.339 μ F; Zero sequence parameter: r 0=2.7 Ω, l 0=1.019mH, c 0=0.28 μ F.System total capacitance electric current i c=3 ω C Σ u n=36A>20A, should install arc suppression coil.The over-compensation degree of cancelling arc coil is 5%, inductance l=1/1.05 × u n/ ω I c=0.49H; The active loss of arc suppression coil is approximately 2.5% ~ 5% of perceptual loss, gets 3%, resistance r l=0.03 ω L=4.58 Ω.
Break down the singlephase earth fault of switching angle as 60 °, stake resistance as 100W as example taking circuit 3 apart from bus 5km place, route selection process is described.Sample frequency is 20kHz, and the first half-wave of transient zero-sequence current of faulty line and wherein two non-fault lines is as shown in Fig. 4 (a).Access line 4 conducts are with reference to circuit, and each circuit transient zero-sequence current is pressed conversion coefficient p k = i k / i 4do stretching, after conversion, waveform is as shown in Fig. 4 (b).As shown in Figure 4, after stretching, the similarity between non-fault line transient zero-sequence current waveform is improved, and the similarity between faulty line and non-fault line waveform changes less.
First the fault transient zero-sequence current of stretching gained half-wave is divided into n 1=20 sections, do piece-wise linearization, represent the derivative of the point of transient zero-sequence current waveform within the scope of this straight-line segment with the slope of each straight-line segment, obtain its phase plane trajectory; Get n 2=10, phase plane trajectory is divided into 10 sections and do normalized to each section.Ask for the phase path of every section of transient zero-sequence current of each circuit and put the Euclidean distance of determining point (1,0), form eigenmatrix s , right s can obtain by row normalized
Right s carry out FKM cluster, obtain degree of membership matrix
Degree of membership matrix u row represent status categories, 1 ~ 6 row represent respectively 1 ~ 6 circuit, u in the row at element place of each train value maximum be the state that this circuit is corresponding.By degree of membership matrix u known, circuit 3 belongs to a class, and it is another kind of that All other routes belong to, and circuit 3 is classified as separately 1 class, can judge that thus circuit 3 is as ground path.
If each line fault transient zero-sequence current waveform is not done to stretching, other steps are constant, eigenmatrix s 'with degree of membership matrix u 'be respectively
By degree of membership matrix u 'also can correctly judge circuit 3 ground connection, but by relatively the two eigenmatrix and degree of membership matrix is known, transient zero-sequence current waveform be carried out to stretching and can improve route selection nargin.
The route selection that singlephase earth fault occurs different circuits in different grounding resistance, different faults point and different faults switching angle situation the results are shown in Table 1.In table: L m for faulty line; x ffor trouble spot is to the distance of bus; r ffor stake resistance; θfor fault close angle.
The adaptability checking of selection method:
1) arc fault
The single-phase earthing initial stage shows as intermittent arc fault more, adopts mayr Arc Modelling to carry out arc fault emulation.Circuit L 3the results are shown in Table 2 in the route selection that arcing ground fault occurs apart from bus 5km place.
2) time windows
Circuit L 4be that 90 °, stake resistance are the singlephase earth fault of 3k Ω at the switching angle that breaks down apart from bus 2km place, select different transient zero-sequence current time windows, route selection the results are shown in Table 3.
3) engineering noise
In engineering application, need to consider the impact of extraneous random noise disturbance on selection method.The white Gaussian noise that stack signal to noise ratio (S/N ratio) is 20dB disturbs, circuit L 6route selection under 3 kinds of typical ground fault condition the results are shown in Table 4.This line selection algorithm has stronger antijamming capability.
4) asynchronous sampling
After earth fault occurs, line selection apparatus may exist asynchronous to the sampling of each circuit zero-sequence current.Consider circuit L 3, L 4hysteresis circuit L 1, L 28 sampled points; Circuit L 5, L 6hysteresis circuit L 1, L 214 sampled points, circuit L 3end generation stake resistance is the singlephase earth fault of 3k Ω, and its route selection the results are shown in Table 5.
Be more than preferred embodiment of the present invention, all changes of doing according to technical solution of the present invention, when the function producing does not exceed the scope of technical solution of the present invention, all belong to protection scope of the present invention.

Claims (5)

1. a malfunction route selection method for resonant grounded system that utilizes fuzzy K mean cluster, is characterized in that, comprises the following steps:
Step 1: each circuit transient zero-sequence current is carried out to stretching processing, to improve the similarity of transient zero-sequence current between non-fault line, reduce 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 regular hour section, do the conversion of segmentation phase plane, ask for each section of all phase points of transient zero-sequence current to an Euclidean distance of determining point in phase plane, to extract the local feature of each section of transient zero-sequence current, obtain the eigenmatrix of each circuit global characteristics;
Step 3: the element in eigenmatrix is made to normalized, to strengthen comparability;
Step 4: the eigenmatrix after utilizing fuzzy K means clustering method to normalization carries out cluster, and each circuit transient zero-sequence current is divided into two classes, and the circuit that is divided into separately a class is faulty line.
2. the malfunction route selection method for resonant grounded system that utilizes fuzzy K mean cluster according to claim 1, is characterized in that, in step 1, as follows each circuit transient zero-sequence current is carried out to stretching processing:
Zero-sequence network equivalent electrical circuit during for resonant earthed system generation single-phase earthing, establishes kbar circuit is faulty line, u 0for trouble spot 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 relatively equivalent capacity of non-fault wire three, u cfor the voltage at each feeder line 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)
Wherein i j , i k be respectively non-fault line j, faulty line transient zero-sequence current;
Introducing stretching coefficient converts transient zero-sequence current waveform: with circuit bas with reference to circuit, define circuit jstretching multiple p j for
????(4)
In formula i j , i b be respectively circuit jand circuit btransient zero-sequence current;
If reference line bfor non-fault line, bk, 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 stretching i' j for
????(6)
Convolution (2) and formula (4) obtain the faulty line transient zero-sequence current after stretching i' k for
????(7)
If reference line bfor faulty line, b= k, by formula (5), each non-fault line equivalent capacity over the ground c j use non-fault line aequivalent capacity over the ground c a be expressed as
????(8)
In formula λ j for scale-up factor; Obtained by formula (1), formula (8)
????(9)
Order p a = i a / i b , obtained by formula (2), formula (9)
????(10)
Obtain the non-fault line transient zero-sequence current after stretching by formula (9), formula (10) i' j for
????(11)。
3. the malfunction route selection method for resonant grounded system that utilizes fuzzy K mean cluster according to claim 1, is characterized in that, in step 2, asks for as follows the eigenmatrix of each circuit global characteristics:
i' j ( n) be after stretching jthe 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 formula f( i' j ( n)) be i' j ( n) derivative, Δ tfor sampling step length;
Transient zero-sequence current after stretching is divided in time domain n 1section, adopts least squares estimate matching to do linearization to each section, obtains n 1individual straight-line segment, the derivative of the point of transient zero-sequence current waveform within the scope of a straight-line segment f( i' j ( n)) all represent with the slope of this straight-line segment;
If the sampling number of the first half-wave of transient zero-sequence current is l, by the transient zero-sequence current after each circuit stretching i' j be divided into n 2section, n 1= bN 2, b>=2, the number of each segmentation up-sampling point is l/ n 2; Do piecemeal phase plane conversion, and the knock type on each section of phase-plane diagram (13) is normalized, make the data point in phase plane all drop on interval [1,1];
????(13)
In formula i' jm represent i' j ? mindividual segmentation, i' jm ( n) represent i' jm discrete-time series, m∈ [1, n 2], n∈ [1, l/ n 2], f'( i' jm ( n)) be f( i' jm ( n)) sequence after normalization, i'' jm ( n) be i' jm ( n) sequence after normalization;
The phase path of calculating the transient zero-sequence current waveform after each section of stretching by formula (14) to determine in phase plane point ( x, y) Euclidean distance:
????(14)
In formula r m represent the msection phase path to determine point ( x, y) Euclidean distance;
Will r m as the local feature amount of one time period of transient zero-sequence current waveform, the global characteristics amount of the transient zero-sequence current waveform of any circuit is
????(15)
? nthe global characteristics amount of bar circuit forms one n× n 2eigenmatrix s , as the formula (16)
????(16)
In formula s ji represent the jof article circuit isection phase path to determine in phase plane point ( x, y) Euclidean distance.
4. the malfunction route selection method for resonant grounded system that utilizes fuzzy K mean cluster according to claim 1, is characterized in that, in step 3, adopts as shown in the formula (17) eigenmatrix s in element do normalization processing by row:
????(17)
In formula s' ji represent s ji by the value obtaining after row normalization.
5. the malfunction route selection method for resonant grounded system that utilizes fuzzy K mean cluster according to claim 1, is characterized in that, in step 4, as follows each circuit transient zero-sequence current is classified and is found faulty line:
First input to be sorted nindividual vector x j and vector kthe initial fuzzy membership matrix of group categories u (1)
????(18)
In formula u ij represent the jindividual vector belongs to ithe degree of membership of class, and , j=1,2 ..., n; If v i be iclass initial cluster center vector, initial cluster center matrix is
????(19)
Determine objective function j m ( u , v ), have
????(20)
In formula, mto be greater than arbitrary real number of 1, for r p any norm in space, utilizes lagrange's method of multipliers to prove to obtain
????(21)
????(22)
In formula afor iterations counter;
Then determine according to the following steps cluster centre matrix v with degree of membership matrix u :
Step 401: determine number of categories k, order a=0, provide at random initial degree of membership matrix u (1);
Step 402: the cluster centre vector that calculates preliminary classification according to formula (22) v (1);
Step 403: calculate degree of membership matrix according to formula (21) u ( a+ 1) ;
Step 404: the given condition of convergence, if the degree of membership matrix difference of twice iterative computation gained is less than the threshold value that the condition of convergence is set, iteration finishes, and continues iteration otherwise return to step 402, until reach the condition of convergence or arrive the iterations of setting;
By the eigenmatrix of each line fault transient zero-sequence current waveform s be divided into 2 classes, can obtain degree of membership matrix
????(23)
In formula u ij represent the jarticle circuit belongs to ithe degree of membership of class;
By degree of membership matrix u each circuit is divided into two classes, and the circuit that is divided into separately a class is faulty line.
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