CN103424669B  A kind of selection method utilizing fault feeder zerosequence current matrix principal component analysis (PCA) first principal component  Google Patents
A kind of selection method utilizing fault feeder zerosequence current matrix principal component analysis (PCA) first principal component Download PDFInfo
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 CN103424669B CN103424669B CN201310336150.5A CN201310336150A CN103424669B CN 103424669 B CN103424669 B CN 103424669B CN 201310336150 A CN201310336150 A CN 201310336150A CN 103424669 B CN103424669 B CN 103424669B
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Abstract
The present invention relates to a kind of selection method utilizing fault feeder zerosequence current matrix principal component analysis (PCA) first principal component, belong to Relay Protection Technology in Power System field.The present invention is after the distribution network generation singlephase earth fault of neutral by arc extinction coil grounding, line selection apparatus starts, first calculate the absolute value of each feeder line zerosequence current sum in short timewindow after a failure, realize the judgement to busbar fault and feeder fault by this value and the magnitude relationship of setting threshold values; When being defined as feeder fault, then build each feeder line zerosequence current matrix and principal component analysis (PCA) is carried out to it, obtain each Principal component of zerosequence current matrix, and respectively the sign function of the sign function of each for first principal component element and first principal component each symbol of element function sum is taken advantage of; Finally reliably realize failure line selection according to the magnitude relationship of this value and null value.Invention increases accuracy and the reliability of route selection.
Description
Technical field
The present invention relates to a kind of selection method utilizing fault feeder zerosequence current matrix principal component analysis (PCA) first principal component, belong to Relay Protection Technology in Power System field.
Background technology
Power distribution network broad covered area, and directly in the face of user provides power supply service for it.80% of distribution network failure is accounted for according to statistics singlephase earth fault.Power distribution network resonant earthed system is neutral by arc extinction coil grounding system, belongs to small current neutral grounding system.Small current neutral grounding system breaks down and can affect healthy phases voltagetoground and cause it and raise, and voltage raises to produce the insulation of grid equipment and destroys; Particularly intermittent arcing ground, arc overvoltage can be caused, this voltage is by destroying system insulation and then developing into alternate or multipoint earthing short circuit, cause system overvoltage, thus damage equipment, destroy system safety operation, therefore must find faulty line accurately, fast and timely fault to be got rid of.
Distribution network failure mostly is singlephase earth fault, if fault applies power frequency steadystate quantity colony amplitude comparison phase comparing method after occurring carry out route selection, due to the impact by arc suppression coil compensation effect, ground current is faint, may cause route selection mistake.And after fault, fault transient state current amplitude, much larger than steadystate current, and not to affect by arc suppression coil, therefore utilizes the selection method of the selection method Billy steadystate quantity of transient to have more advantage.Recent domestic emerges in multitude based on the achievement in research of transient route selection, but it is to be solved and perfect to still have some problems to have, its main cause is: 1, failure boundary is complicated, random, as fault prima facies angle size, fault distance, transition resistance size etc., different faults condition, the distribution of transient zerosequence signal frequency composition, attenuation characteristic, spectrum energy has larger difference; When 2, there is singlephase earth fault near voltage over zero, the high fdrequency component caused is very little, and the sensitivity of high frequency transient amount selection method is declined greatly; 3, cable line and overhead transmission line electrical specification differ greatly, and perfect similarity between circuit zero sequence current waveform and reduce; 4, adopt traveling wave detector method, row velocity of wave propagation is very fast, and distribution network line is shorter, and power distribution network signal disturbing is more in addition, and row ripple Mintrop wave head not easily reliably catches.
Principal component analysis (PCA) (Principalcomponentsanalysis, PCA) is inferior to proposition in 1901 by Ka Er Pierre, for analyzing data and setting up mathematical model.Its method mainly by carrying out feature decomposition to covariance matrix, with the weights (i.e. eigenwert) of the major component (i.e. proper vector) drawing data with them.The method has been widely used in analysis and the simplification of data set.By the data set of principal component analysis (PCA), its dimension is reduced, but maintains data to the maximum feature of variance contribution.
After neutral by arc extinction coil grounding system generation singlephase earth fault, transient information dissimilar is in a large number contained in its fault transient zerosequence current, namely the dimension of data set is very large, if utilize PCA to extract zerosequence current major component, the feature of main signal is kept while reducing data dimension, realize failure line selection according to this, will effectively reduce the impact of undesired signal, improve the reliability of selection method.By this, a kind of selection method utilizing fault feeder zerosequence current matrix principal component analysis (PCA) first principal component is proposed.
Summary of the invention
Technical matters to be solved by this invention be overcome that traditional selection method is disturbed signal when ground current is faint affect the not high problem of route selection reliability, provide a kind of selection method utilizing fault feeder zerosequence current matrix principal component analysis (PCA) first principal component.
Technical scheme of the present invention is: a kind of selection method utilizing fault feeder zerosequence current matrix principal component analysis (PCA) first principal component, after the distribution network generation singlephase earth fault of neutral by arc extinction coil grounding, line selection apparatus starts, first calculate the absolute value of each feeder line zerosequence current sum in short timewindow after a failure, realize the judgement to busbar fault and feeder fault by this value and the magnitude relationship of setting threshold values; After being defined as feeder fault, then build each feeder line zerosequence current matrix and principal component analysis (PCA) is carried out to it, obtain each Principal component of zerosequence current matrix, and respectively the sign function of the sign function of each for first principal component element and first principal component each symbol of element function sum is taken advantage of; Finally reliably realize failure line selection according to the magnitude relationship of this value and null value.
The concrete steps of described selection method are as follows:
After A, generation singlephase earth fault, in short timewindow, calculate the absolute value of each feeder line zerosequence current sum
i _{∑}, and by this value and setting threshold values
i _{set}magnitude relationship realize to busbar fault and feeder fault judgement:
（1）
When
i _{∑}>
i _{set}time, be judged to be busbar fault;
When
i _{∑}<
i _{set}time, be judged to be feeder fault;
In formula:
i _{0
j }(
k) represent be numbered
jits zerosequence current of feeder line exist
kamplitude during sampled point,
j=1,2,3
nfor the numbering of feeder line,
nfor feeder line number;
k=1,2,3
kfor sampled point numbering,
kfor zerosequence current data sampled point quantity;
k<
n;
B, basis
nbar feeder line is abovementioned
kzerosequence current data on individual zerosequence current data sampled point, builds
n×
kzerosequence current matrix
i, and after principal component analysis (PCA) is carried out to it, the sign function of the sign function and first principal component each symbol of element function sum that obtain each element of first principal component be respectively sgn (
p _{1}(
j)), sgn (∑ sgn (
p _{1}(
j))); Wherein
p _{1}(
j) be the first principal component value after zerosequence current matrix principal component analysis (PCA),
j=1,2,3
nfor the numbering of feeder line,
nfor feeder line number:
（2）
C, according to sgn (
p _{1}(
j)) and sgn (∑ sgn (
p _{1}(
j))) magnitude relationship determination failure line selection between product between the two and null value:
When sgn (
p _{1}(
j)) × sgn (∑ sgn (
p _{1}(
j))) <0 time, judge the
jbar feeder line is fault feeder.
When calculating each feeder line zerosequence current sum, the length of short timewindow is 0.4ms.
Principle of work of the present invention is:
For the distribution network of resonance grounding, in the transient state process after fault occurs, its each bar feeder line zerosequence current is not by the impact of arc suppression coil compensation.If feeder line breaks down, each feeder line zerosequence current amplitude sum that perfects equals fault feeder zerosequence current, and namely all feeder line zerosequence current sums are close to zero; If bus breaks down, each feeder fault zerosequence current is changed direction unanimously in a timing window inwardly projecting, and its zerosequence current sum is much larger than zero.Therefore, when bus residual voltage instantaneous value is outoflimit, namely
u _{ n }(
t) >
k _{ u } u _{ n }time, (wherein:
u _{ n }(
t) be the instantaneous value of bus residual voltage,
u _{ n }for bus rated voltage,
k _{ u }=1.15), be considered as distribution network systems and break down, fault line selection device starts immediately and records ripple, obtains each bar feeder line zero sequence transient current, then can according to zerosequence current in each feeder line after a failure short timewindow and the size of absolute value
judge whether bus there occurs fault (in formula:
i _{0
j }(
k) represent be numbered
jits zerosequence current of feeder line exist
kamplitude during sampled point,
j=1,2,3
nfor the numbering of feeder line,
nfor feeder line number;
k=1,2,3
kfor sampled point numbering,
kfor zerosequence current data sampled point quantity.Consider the impact of outofbalance current, a threshold values is set for specific distribution system
i _{set},
i _{set}obtained by a large amount of emulation.According to the known busbar fault criterion of abovementioned analysis be: when
i _{Σ}>
i _{set}time, busbar fault; When
i _{Σ}<
i _{set}time, feeder fault).
After being judged to be feeder fault, need judging the numbering of fault feeder, thus realize failure line selection.Need to build zerosequence current matrix to carry out principal component analysis (PCA), due to the principal component analysis (PCA) requirement being greater than columns that usually requires analyzed matrix must meet line number, when therefore building matrix of elements, the number of zerosequence current sampled point must be less than the number of distribution network systems feeder line.
Principal component analysis (PCA) original sample data is projected in a new coordinate space, in new coordinate space, the dimension of sample data decreased more originally, the standard constructing new coordinate space is that the every one dimension variance making original sample data in new coordinate space all reaches maximal value, and the projection of each sample data in new coordinate axis is exactly the Principal component under the corresponding dimension of this coordinate axis.After principal component analysis (PCA), low order composition remains the most important information of data, and after therefore carrying out principal component analysis (PCA) to its zerosequence current during distribution network systems feeder fault, the spatial data under first principal component (lowestorder dimension) maintains the topmost feature of zerosequence current.First principal component value is then the projection value of zerosequence current data in new coordinate system in minimum dimension (coordinate axis).When distribution network systems feeder line breaks down, the polarity of fault feeder zerosequence current is contrary in a timing window with the polarity perfecting feeder line zerosequence current, therefore the projection of zerosequence current value under new coordinate must be reflected as wherein with other be distributed in the positive and negative both sides of new coordinate axis a little respectively.Therefore failure line selection can be realized according to this feature.Principal component analysis (PCA) follows these steps to carry out:
Step one: raw data standardization, supposes that the zerosequence current matrix be made up of each bar feeder line zerosequence current is
i _{ ij }, in order to eliminate the different and excessive impact brought of numerical value difference of dimension due to variable, by following formula, standardization is done to former variable:
（3）
Wherein:
;
;
In formula: subscript
ifor feeder line numbering (line label of matrix),
nfor feeder line number (line number of matrix); Subscript
jfor the sampled point of zerosequence current is numbered (matrix column label),
kfor zerosequence current data length (matrix column number).
Step 2: set up correlation matrix
, and calculate the proper vector of its eigenwert.
（4）
In formula:
i ^{*}for the data matrix after standardization, upper table
trepresent transpose operation,
nfor feeder line number (line number of matrix); Try to achieve
reigenwert be
>=
>=
with the unitization proper vector of its correspondence be
v _{1},
v _{2}...,
v _{ k },
k∈
z.
Step 3: determine major component number, first calculate variance contribution ratio:
（5）
In formula:
for correlation matrix
reigenwert,
i=1,2,3
k,
k∈
z.
Then accumulative variance contribution ratio is calculated:
（6）
Accumulative variance contribution ratio is depended in choosing of major component number, and accumulative variance contribution ratio should be greater than 85 ~ 90 usually, before corresponding
individual major component just comprises
most information that individual original variable can provide, therefore determine that the number of major component is
.
Step 4: solve the matrix obtaining major component and form,
pindividual major component characteristic of correspondence vector is
v _{m × p}, then
individual sample
pthe matrix that individual major component is formed
p _{n × p}for:
（7）
Wherein:
v _{k × p}=[
v _{1},
v _{2}...,
v _{ p }];
In formula:
i ^{*}for the data matrix after standardization,
pfor major component number,
m=1,2,3
k,
k∈
z,
for feeder line number,
kfor zerosequence current data length.
Build each feeder line zerosequence current matrix and after principal component analysis (PCA) is carried out to it (wherein first principal component can reflect the feature of zerosequence current), obtain each element of first principal component sign function sgn (
p _{1}(
j)) with the sign function sgn of first principal component each symbol of element function sum (∑ sgn (
p _{1}(
j))), then according to sgn (
p _{1}(
j)) and sgn (∑ sgn (
p _{1}(
j))) magnitude relationship determination failure line selection between product between the two and null value: when sgn (
p _{1}(
j)) × sgn (∑ sgn (
p _{1}(
j))) <0 time, judge the
jbar feeder line be fault feeder (wherein
p _{1}(
j) be the first principal component value after zerosequence current matrix principal component analysis (PCA),
j=1,2,3
nfor the numbering of feeder line,
nfor feeder line number).
The invention has the beneficial effects as follows:
1, this method is before carrying out route selection to fault feeder, has in fact carried out primary election to busbar fault, and specific aim carries out primary election to busbar fault, improves the reliability of route selection.
2, this method is using the element value symbol of first principal component as route selection criterion, reduces the interference of other signals, further increases route selection reliability.
3, the algorithm maturation of principal component analysis (PCA) makes the theory support of this method more solid, and realization rate is more convenient.
Accompanying drawing explanation
Fig. 1 is the distribution network systems realistic model of the neutral by arc extinction coil grounding of the embodiment of the present invention 1 and embodiment 2;
Fig. 2 is the route selection process flow diagram of the embodiment of the present invention 1 and embodiment 2;
Feeder line in window when Fig. 3 is 0.4ms after the embodiment of the present invention 1 fault occurs
l _{1}zerosequence current oscillogram;
Feeder line in window when Fig. 4 is 0.4ms after the embodiment of the present invention 1 fault occurs
l _{2}zerosequence current oscillogram;
Feeder line in window when Fig. 5 is 0.4ms after the embodiment of the present invention 1 fault occurs
l _{3}zerosequence current oscillogram;
Feeder line in window when Fig. 6 is 0.4ms after the embodiment of the present invention 1 fault occurs
l _{4}zerosequence current oscillogram;
Feeder line in window when Fig. 7 is 0.4ms after the embodiment of the present invention 1 fault occurs
l _{5}zerosequence current oscillogram;
Feeder line in window when Fig. 8 is 0.4ms after the embodiment of the present invention 1 fault occurs
l _{6}zerosequence current oscillogram;
Feeder line in window when Fig. 9 is 0.4ms after the embodiment of the present invention 2 fault occurs
l _{1}zerosequence current oscillogram;
Feeder line in window when Figure 10 is 0.4ms after the embodiment of the present invention 2 fault occurs
l _{2}zerosequence current oscillogram;
Feeder line in window when Figure 11 is 0.4ms after the embodiment of the present invention 2 fault occurs
l _{3}zerosequence current oscillogram;
Feeder line in window when Figure 12 is 0.4ms after the embodiment of the present invention 2 fault occurs
l _{4}zerosequence current oscillogram;
Feeder line in window when Figure 13 is 0.4ms after the embodiment of the present invention 2 fault occurs
l _{5}zerosequence current oscillogram;
Feeder line in window when Figure 14 is 0.4ms after the embodiment of the present invention 2 fault occurs
l _{6}zerosequence current oscillogram.
Embodiment
Embodiment 1: be illustrated in figure 1 the distribution that 6 feed out the 35kV neutral by arc extinction coil grounding of circuit composition, the G in this electrical network is infinitely great power supply; T is maintransformer, and noload voltage ratio is 110kV/35kV, and connection set is YN/d11; China's power distribution network maintransformer distribution voltage side is generally triangle junction, and system does not exist neutral point, need obtain for the neutral point of grounding through arc, can set up the way that grounding transformer is exactly the best, T herein when system adopts during resonance neutral grounding
_{z}for the special zigzag transformer of compensation network ground connection; L is arc suppression coil, and R is the damping resistance of arc suppression coil.Circuit adopts overhead transmission line, overhead linecable hybrid line and cable line three kinds of circuits, and the numbering of six feeder lines is followed successively by
l _{1},
l _{2},
l _{3}...
l _{6}, wherein,
l _{1}for pole line, length is 15km;
l _{2}for cable, length is 6km;
l _{3}for pole line, length is 18km;
l _{4}for cable joint line, cable length is 5km, and pole line length is 12km;
l _{5}for pole line, length is 30km;
l _{6}for cable, length is 8km.Load selects firm power load model, wherein
p=800
kW,
q=140
kVar.Now suppose feeder line
l _{1}there is singlephase earth fault, stake resistance 20 Ω in distance top 7 km A phase, fault angle is 90 °, and the moment occurs fault is 0.025s.The route selection flow process of fault feeder zerosequence current matrix principal component analysis (PCA) first principal component is utilized as shown in Figure 2 for this system.
When first intercepting 0.4ms after fault, the recorder data of each feeder line zerosequence current in window, as shown in figures 38, utilizes formula (1) to calculate the absolute value of each feeder line zerosequence current sum
i _{∑}=6.9A, for this system, determines threshold values by a large amount of emulation
i _{set}=100A is comparatively suitable.Cause
i _{∑}=6.9A<
i _{ set }=100A, therefore be judged to be feeder fault.
Then build zerosequence current matrix, the quantity due to system feeder line is 6, and therefore the data of zerosequence current sampled point mostly are 5 most.In zerosequence current recorder data as shown in figures 38, sample respectively in 0.0250s, 0.0251s, 0.0252s, 0.0253s and 0.0254s moment, obtaining zerosequence current matrix element structure zerosequence current matrix is:
Carry out principal component analysis (PCA) to abovementioned zerosequence current matrix using formula (3) to (7) again, each Principal component obtaining zerosequence current is as shown in table 1.
Wherein, in first principal component each element sign function value sgn (
p _{1}(
j))=(+111111),
j=1,2,3 ... 6.So, sgn (∑ sgn (
p _{1}(
j)))=(1).Obviously, sgn (
p _{1}(1)) × sgn (∑ sgn (
p _{1}(
j))) <0.So judgement feeder line
break down, consistent with hypothesis result, route selection is correct.
Embodiment 2: the distribution network systems of neutral by arc extinction coil grounding as shown in Figure 1, systematic parameter is identical with embodiment.Now suppose feeder line
l _{2}there is singlephase earth fault, stake resistance 20 Ω in distance top 5 km A phase, fault angle is 90 °, and the moment occurs fault is 0.025s.The route selection flow process of fault feeder zerosequence current matrix principal component analysis (PCA) first principal component is utilized still as shown in Figure 2 for this system.
When first intercepting 0.4ms after fault, the recorder data of each feeder line zerosequence current in window, as shown in Fig. 914, utilizes formula (1) to calculate the absolute value of each feeder line zerosequence current sum
i _{∑}=1.6A, and the threshold values of this system is set to by a large amount of emulation
i _{set}=100A.Because
i _{∑}=1.6A<
i _{ set }=100A, therefore be judged to be feeder fault.
Then build zerosequence current matrix, the quantity due to system feeder line is 6, and therefore the data of zerosequence current sampled point mostly are 5 most.In the zerosequence current recorder data such as shown in Fig. 914, sample respectively in 0.0250s, 0.0251s, 0.0252s, 0.0253s and 0.0254s moment, obtaining zerosequence current matrix element structure zerosequence current matrix is:
Carry out principal component analysis (PCA) to abovementioned zerosequence current matrix using formula (3) to (7) again, each Principal component obtaining zerosequence current is as shown in table 2.
Wherein, in first principal component each element sign function value sgn (
p _{1}(
j))=(+11+1+1+1+1),
j=1,2,3 ... 6.So, sgn (∑ sgn (
p _{1}(
j)))=(+1).Obviously, sgn (
p _{1}(2)) × sgn (∑ sgn (
p _{1}(
j))) <0.So judgement feeder line
break down, consistent with hypothesis result, route selection is correct.
By reference to the accompanying drawings the specific embodiment of the present invention is explained in detail above, but the present invention is not limited to abovementioned embodiment, in the ken that those of ordinary skill in the art possess, various change can also be made under the prerequisite not departing from present inventive concept.
Claims (3)
1. one kind utilizes the selection method of fault feeder zerosequence current matrix principal component analysis (PCA) first principal component, it is characterized in that: after the distribution network generation singlephase earth fault of neutral by arc extinction coil grounding, line selection apparatus starts, first calculate the absolute value of each feeder line zerosequence current sum in short timewindow after a failure, realize the judgement to busbar fault and feeder fault by this value and the magnitude relationship of setting threshold values; After being defined as feeder fault, then build each feeder line zerosequence current matrix and principal component analysis (PCA) is carried out to it, obtain each Principal component of zerosequence current matrix, and respectively the sign function of the sign function of each for first principal component element and first principal component each symbol of element function sum is taken advantage of; Finally reliably realize failure line selection according to the magnitude relationship making value and the null value taken advantage of.
2. the selection method utilizing fault feeder zerosequence current matrix principal component analysis (PCA) first principal component according to claim 1, is characterized in that: the concrete steps of described selection method are as follows:
After A, generation singlephase earth fault, in short timewindow, calculate the absolute value I of each feeder line zerosequence current sum
_{∑}, and by this value and setting threshold values I
_{set}magnitude relationship realize to busbar fault and feeder fault judgement:
Work as I
_{∑}>I
_{set}time, be judged to be busbar fault;
Work as I
_{∑}<I
_{set}time, be judged to be feeder fault;
In formula: i
_{0j}k () represents the amplitude of its zerosequence current of feeder line when k sampled point being numbered j, j=1,2,3 ... N is the numbering of feeder line, and N is feeder line number; K=1,2,3 ... K is sampled point numbering, and K is zerosequence current data sampled point quantity; K<N;
B, according to the zerosequence current data of N bar feeder line on abovementioned K zerosequence current data sampled point, build N × K zerosequence current matrix i, and after carrying out principal component analysis (PCA) to it, the sign function of the sign function and first principal component each symbol of element function sum that obtain each element of first principal component is respectively sgn (P
_{1}(j)), sgn (∑ sgn (P
_{1}(j))); Wherein P
_{1}j () is the first principal component value after zerosequence current matrix principal component analysis (PCA), j=1,2,3 ... N is the numbering of feeder line, and N is feeder line number:
C, according to sgn (P
_{1}(j)) and sgn (∑ sgn (P
_{1}(j))) magnitude relationship determination failure line selection between product between the two and null value:
As sgn (P
_{1}(j)) × sgn (∑ sgn (P
_{1}(j))) < 0 time, judge that jth bar feeder line is as fault feeder.
3. the selection method utilizing fault feeder zerosequence current matrix principal component analysis (PCA) first principal component according to claim 1 and 2, is characterized in that: when calculating each feeder line zerosequence current sum, the length of short timewindow is 0.4ms.
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