CN107704803A - A kind of leakage conductor action identifying method based on least square and correlation analysis - Google Patents
A kind of leakage conductor action identifying method based on least square and correlation analysis Download PDFInfo
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Abstract
The present invention relates to a kind of leakage conductor action identifying method based on least square and correlation analysis, belong to Relay Protection Technology in Power System field.When transmission line of electricity is by being struck by lightning, measuring end measures thunder-strike current waveform；The thunder-strike current waveform measured is converted using Wavelet Modulus Maxima, determines the initial traveling wave due in of failure；The not operating curve of arrester is gone out using least square fitting according to initial wavefront trailing edge；Window when selecting suitable, the thunder-strike current waveform that measuring end measures is drawn correlation analysis coefficient with fitting the not operating curve of arrester as correlation analysis, coefficient correlation threshold values is 0.9, if correlation analysis coefficient is more than 0.9, then leakage conductor is not operating, if correlation analysis coefficient is less than or equal to 0.9, leakage conductor action.The present invention is not influenceed by factors such as thunderbolt type, thunderbolt place on line, amplitude of lightning current sizes, and judged result is accurately and reliably.
Description
Technical field
The present invention relates to a kind of leakage conductor action identifying method based on least square and correlation analysis, belong to electric power
System relay protection technical field.
Background technology
Currently in order to the resistance to thunder for improving transmission line of electricity is horizontal, often taking reduces grounding resistance, reduces shielding angle, tower top installation
Lightning rod, strengthen line insulation, erection lightning conducter, set up coupling ground wire and the along the line lightning protection measures such as zinc oxide surge arresters, circuit
Arrester is mainly installed in shaft tower along transforming plant lead-in crossing or line outlet and part (physical features eminence, weight minefield, history hair
Gave birth to lightning stroke flashover position), arrester moves when thunderbolt causes overvoltage or the switching overvoltage to exceed the rated voltage of arrester
Make, wire is formed a current path with the earth, the amplitude of over-voltage, play and improve the resistance to voltage levels of line insulator string
With effect of the reduction lightning wave to power transformation station equipment invasion danger.
End arrester of standing monitors leakage current, action frequency in real time, and arrester does not install monitoring device generally along the line,
How to realize that leakage conductor acts using existing monitoring device is to be badly in need of.
The content of the invention
Moved the technical problem to be solved in the present invention is to provide a kind of based on least square and the leakage conductor of correlation analysis
Make discrimination method, condition monitoring etc. is acted for research travelling wave ranging factor to affect, leakage conductor.
The technical scheme is that：A kind of leakage conductor action identifying side based on least square and correlation analysis
Method, when transmission line of electricity is by being struck by lightning, measuring end measures thunder-strike current waveform；Small echo mould is utilized to the thunder-strike current waveform measured
Maximum converts, and determines the initial traveling wave due in of failure；Least square fitting is utilized according to initial wavefront trailing edge
Go out the not operating curve of arrester；Window when selecting suitable, the thunder-strike current waveform that measuring end measures and fit arrester
Not operating curve draws correlation analysis coefficient as correlation analysis, and coefficient correlation threshold values is 0.9, if correlation analysis coefficient is more than
0.9, then leakage conductor is not operating, if correlation analysis coefficient is less than or equal to 0.9, leakage conductor action.
Concretely comprise the following steps：
(1) when transmission line of electricity is struck by lightning, transmission line lightning stroke current waveform is measured in measuring end；
(2) the thunder-strike current waveform measured is converted using Wavelet Modulus Maxima and carries out continuous wavelet transform, it is determined that thunderbolt
At the time of the initial traveling wave of failure reaches measuring end, continuous wavelet transform formula is：
In formula (1), a is scale factor, a ∈ R and a ≠ 0；B is shift factor, center frequency corresponding to a certain decomposition scale a
The calculation formula of rate is：
In formula (2), fsFor the sample frequency of signal, fcFor the centre frequency of selected wavelet basis；
(3) carried out curve fitting, obtained corresponding using the least square method thunder-strike current traveling wave not operating to arrester
Matched curve, the least square method of curve matching is as follows：
Wherein,
Formula (3) is error sum of squares, yi=f (xi) (i=0,1 ..., m), wherein f (x) ∈ C [a, b], xi, i=0,
1 ..., m is one group of discrete point set；Y=S*(x) it is and data { (xi,yi), i=0,1 ..., m fitting function；δiFor by mistake
Poor δi=S*(xi)-yi, (i=0,1 ... m), δ=(δ0,δ1,...,δm)T；
In formula (4), S (x) is function after curve matching,It is linear independence family of functions on C [a, b], C
[a, b] represents continuous function on section [a, b]；a0,a1,...,an, (n ＜ m) is coefficient；
(4) window when selecting suitable, one is chosen compared with short time-window to be embodied with the difference of no lightning arrestor movement as far as possible, simultaneously
Only originated from the trailing edge of the initial traveling wave of failure, therefore select window during the initial traveling wave of failure follow-up 30 μ s；
The thunder-strike current waveform that measuring end the measures curve not operating with fitting arrester is drawn phase as correlation analysis
Coefficient of analysis is closed, using coefficient correlation to thunder-strike current waveform Δ u (k) and matched curveAnalysis, correlation analysis formula is such as
Under：
In formula (5), ρ represents the coefficient correlation of thunder-strike current waveform and matched curve, and ρ values are bigger, illustrates two recording letters
Number wave-form similarity is higher, and N is total number of sample points；
(6) it is 0.9 to determine coefficient correlation threshold values, and lightning arrestor movement differentiation is carried out by following condition：
If correlation analysis coefficient is more than 0.9, leakage conductor is not operating；
If correlation analysis coefficient is less than or equal to 0.9, leakage conductor action.
The present invention principle be：
First, least square curve fitting
When using least square fitting curve, fitting function f is determined according to initial wavefront trailing edge first
(x), determined according to the scatter plot distributions situation of data or physics law, but during the non-flashover of thunderbolt, under initial wavefront
Drop edge is not linear function, but can be converted into linear function, such as y=ae by conversionbx, i.e. f (x)=aebxFor index letter
Number, now coefficient a, b is not linear, but above formula both ends are taken the logarithm can obtain lny=lna+lnb, then makes y'=lny, m
=lna, above formula turn to y'=m+bx, as linear function, so as to obtain coefficient by linear fit.
Window when the 2nd, selecting suitable：
If when window selection comprising initial wavefront forward part or when window selection it is excessive, it is impossible to effectively depict lightning-arrest
Device acts the difference with the not operating waveform of arrester；One should be chosen compared with short time-window to be embodied with the difference of no lightning arrestor movement as far as possible
It is different, while only originated from the trailing edge of the initial traveling wave of failure, therefore select window during the initial traveling wave of failure follow-up 30 μ s.
3rd, correlation analysis：
Cross-correlation function is a kind of statistics characteristic described between two random signals, and two recording waveforms are used
Correlation analysis can know that similarity risen.Thunder-strike current waveform Δ u (k) and matched curveBetween phase relation
Number ρ is defined as：
ρ represents the coefficient correlation of thunder-strike current waveform and matched curve in formula, and N is total number of sample points.Determine coefficient correlation
Threshold values is 0.9, if correlation analysis coefficient is more than 0.9, leakage conductor is not operating, if correlation analysis coefficient is less than or equal to 0.9,
Then leakage conductor acts.
The beneficial effects of the invention are as follows：
1st, present invention foundation lightning arrestor movement is to the traveling wave effect characteristicses that are struck by lightning, using least square fitting and correlation analysis side
Method realizes the identification that the lightning fault traveling wave collected whether there is leakage conductor action；
2nd, the present invention is not influenceed by factors such as thunderbolt type, thunderbolt place on line, amplitude of lightning current sizes, judged result
Accurately and reliably.
Brief description of the drawings
Fig. 1 is the step flow chart of the present invention；
Fig. 2 is that the leakage conductor installation site of the embodiment of the present invention 2 is moved away from leakage conductor at insulator arc-over point 400m
Mapping；
Fig. 3 is that the leakage conductor installation site of the embodiment of the present invention 3 is moved away from leakage conductor at insulator arc-over point 900m
Mapping.
Embodiment
With reference to the accompanying drawings and detailed description, the invention will be further described.
Embodiment 1：As shown in figure 1, a kind of leakage conductor action identifying method based on least square and correlation analysis,
When transmission line of electricity is by being struck by lightning, measuring end measures thunder-strike current waveform；Small echo mould pole is utilized to the thunder-strike current waveform measured
Big value conversion, determines the initial traveling wave due in of failure；Gone out according to initial wavefront trailing edge using least square fitting
The not operating curve of arrester；Window when selecting suitable, the thunder-strike current waveform that measuring end measures and fit arrester not
The curve of action draws correlation analysis coefficient as correlation analysis, and coefficient correlation threshold values is 0.9, if correlation analysis coefficient is more than 0.9,
Then leakage conductor is not operating, if correlation analysis coefficient is less than or equal to 0.9, leakage conductor action.
Concretely comprise the following steps：
(1) when transmission line of electricity is struck by lightning, transmission line lightning stroke current waveform is measured in measuring end；
(2) the thunder-strike current waveform measured is converted using Wavelet Modulus Maxima and carries out continuous wavelet transform, it is determined that thunderbolt
At the time of the initial traveling wave of failure reaches measuring end, continuous wavelet transform formula is：
In formula (1), a is scale factor, a ∈ R and a ≠ 0；B is shift factor, center frequency corresponding to a certain decomposition scale a
The calculation formula of rate is：
In formula (2), fsFor the sample frequency of signal, fcFor the centre frequency of selected wavelet basis；
(3) carried out curve fitting, obtained corresponding using the least square method thunder-strike current traveling wave not operating to arrester
Matched curve, the least square method of curve matching is as follows：
Wherein,
Formula (3) is error sum of squares, yi=f (xi) (i=0,1 ..., m), wherein f (x) ∈ C [a, b], xi, i=0,
1 ..., m is one group of discrete point set；Y=S*(x) it is and data { (xi,yi), i=0,1 ..., m fitting function；δiFor by mistake
Poor δi=S*(xi)-yi, (i=0,1 ... m), δ=(δ0,δ1,...,δm)T；
In formula (4), S (x) is function after curve matching,It is linear independence family of functions on C [a, b], C
[a, b] represents continuous function on section [a, b]；a0,a1,...,an, (n ＜ m) is coefficient；
When using least square fitting curve, fitting function f is determined according to initial wavefront trailing edge first
(x), determined according to the scatter plot distributions situation of data or physics law, but during the non-flashover of thunderbolt, initial wavefront declines
Edge is not linear function, but can be converted into linear function, such as y=ae by conversionbx, i.e. f (x)=aebxFor exponential function,
Now coefficient a, b be not linear, but above formula both ends are taken the logarithm can obtain lny=lna+lnb, then makes y'=lny, m=
Lna, above formula turn to y'=m+bx, as linear function, so as to obtain coefficient by linear fit.
(4) window when selecting suitable：If when window selection comprising initial wavefront forward part or when window selection it is excessive, it is impossible to
Effectively depict the difference of lightning arrestor movement and the not operating waveform of arrester；One should be chosen compared with short time-window to be embodied with as far as possible
Difference without lightning arrestor movement, while only originated from the trailing edge of the initial traveling wave of failure, therefore select follow-up 30 μ of the initial traveling wave of failure
Window during s.
(5) correlation analysis：Cross-correlation function is a kind of statistics characteristic described between two random signals, to two
Recording waveform can know that similarity risen using correlation analysis.The thunder-strike current waveform that measuring end is measured and fitting
Go out the not operating curve of arrester and draw correlation analysis coefficient as correlation analysis, using coefficient correlation to thunder-strike current waveform Δ u
And matched curve (k)Analysis, correlation analysis formula are as follows：
In formula (5), ρ represents the coefficient correlation of thunder-strike current waveform and matched curve, and N is total number of sample points.
Formula (5) investigates the similarity of two signals with correlation analysis, and the scope of ρ values is [- 1 ,+1].+ 1 represents signal delta u
(k) andPhase is identical, waveform is completely the same, i.e. positive correlation；- 1 represent signal delta u (k) andWaveform shape one
Sample but be in inverse state, i.e., it is negatively correlated；0 represents that two recording signals are uncorrelated；ρ values are bigger, illustrate two recording signal waveforms
Similarity is higher.
(6) it is 0.9 to determine coefficient correlation threshold values, and lightning arrestor movement differentiation is carried out by following condition：
If correlation analysis coefficient is more than 0.9, leakage conductor is not operating；
If correlation analysis coefficient is less than or equal to 0.9, leakage conductor action.
Embodiment 2：As shown in Fig. 2 on the basis of embodiment 1, further, based on PSCAD/EMTDC electro-magnetic transients
Emulation platform establishes the simulation model of 220kV transmission lines of electricity, and transmission line of electricity uses frequency variable parameter model, emulation sampling step length 1 μ s；
Lightning models are injected using double exponential wave thunder and lightning flow models, insulation submodel discharge voltage U50%As criterion.Thunder and lightning attacks transmission of electricity directly
Flashover occurs for line insulator, and leakage conductor installation site is away from insulator arc-over point 400m and action.
Solid line during the lightning stroke flashover original waveform of measuring end collection is as shown in Figure 2, the dotted line in Fig. 2 is based on a most young waiter in a wineshop or an inn
Multiply the curve of fitting, correlation analysis is made to the solid line in Fig. 2 and dotted line by MATLAB softwares, it is 0.59 to obtain correlation coefficient ρ, i.e.,
Leakage conductor acts.
Embodiment 3：As shown in figure 3, on the basis of embodiment 1, further, based on PSCAD/EMTDC electro-magnetic transients
Emulation platform establishes the simulation model of 220kV transmission lines of electricity, and transmission line of electricity uses frequency variable parameter model, emulation sampling step length 1 μ s；
Lightning models are injected using double exponential wave thunder and lightning flow models, insulation submodel discharge voltage U50%As criterion.Thunder and lightning attacks transmission of electricity directly
Flashover occurs for line insulator, and leakage conductor installation site is away from insulator arc-over point 900m and action.
Solid line during the lightning stroke flashover original waveform of measuring end collection is as shown in Figure 3, the dotted line in Fig. 3 is based on a most young waiter in a wineshop or an inn
Multiply the curve of fitting, correlation analysis is made to the solid line in Fig. 3 and dotted line by MATLAB softwares, it is 0.51 to obtain correlation coefficient ρ, i.e.,
Leakage conductor acts.
Above in association with accompanying drawing to the present invention embodiment be explained in detail, but the present invention be not limited to it is above-mentioned
Embodiment, can also be before present inventive concept not be departed from those of ordinary skill in the art's possessed knowledge
Put that various changes can be made.
Claims (2)
- A kind of 1. leakage conductor action identifying method based on least square and correlation analysis, it is characterised in that：Work as power transmission line When road is by being struck by lightning, measuring end measures thunder-strike current waveform；The thunder-strike current waveform measured is converted using Wavelet Modulus Maxima, Determine the initial traveling wave due in of failure；Go out arrester using least square fitting according to initial wavefront trailing edge not move The curve of work；Window when selecting suitable, the thunder-strike current waveform that measuring end measures and fit the not operating curve of arrester Correlation analysis coefficient is drawn as correlation analysis, coefficient correlation threshold values is 0.9, if correlation analysis coefficient is more than 0.9, circuit is taken shelter from the thunder Device is not operating, if correlation analysis coefficient is less than or equal to 0.9, leakage conductor action.
- 2. the leakage conductor action identifying method according to claim 1 based on least square and correlation analysis, it is special Sign is to concretely comprise the following steps：(1) when transmission line of electricity is struck by lightning, transmission line lightning stroke current waveform is measured in measuring end；(2) the thunder-strike current waveform measured is converted using Wavelet Modulus Maxima and carries out continuous wavelet transform, determine lightning fault At the time of initial traveling wave reaches measuring end, continuous wavelet transform formula is：<mrow> <msub> <mi>W</mi> <mi>&psi;</mi> </msub> <mi>f</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mrow> <mo>|</mo> <mi>a</mi> <mo>|</mo> </mrow> </msqrt> </mfrac> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mrow> <mo>+</mo> <mi>&infin;</mi> </mrow> </msubsup> <mi>f</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mi>&psi;</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>t</mi> <mo>-</mo> <mi>b</mi> </mrow> <mi>a</mi> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>In formula (1), a is scale factor, a ∈ R and a ≠ 0；B is shift factor, centre frequency corresponding to a certain decomposition scale a Calculation formula is：<mrow> <msub> <mi>f</mi> <mrow> <mi>s</mi> <mi>c</mi> <mi>a</mi> <mi>l</mi> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>f</mi> <mi>c</mi> </msub> <mi>a</mi> </mfrac> <msub> <mi>f</mi> <mi>s</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>In formula (2), fsFor the sample frequency of signal, fcFor the centre frequency of selected wavelet basis；(3) carried out curve fitting using the least square method thunder-strike current traveling wave not operating to arrester, obtain corresponding plan Curve is closed, the least square method of curve matching is as follows：Wherein,Formula (3) is error sum of squares, yi=f (xi) (i=0,1 ..., m), wherein f (x) ∈ C [a, b], xi, i=0,1 ..., m For one group of discrete point set；Y=S*(x) it is and data { (xi,yi), i=0,1 ..., m fitting function；δiFor error deltai=S* (xi)-yi, (i=0,1 ... m), δ=(δ0,δ1,...,δm)T；In formula (4), S (x) is function after curve matching,It is linear independence family of functions on C [a, b], C [a, B] represent continuous function on section [a, b]；a0,a1,...,an, (n ＜ m) is coefficient；(4) window when selecting suitable, choose one compared with short time-window to be embodied with the difference of no lightning arrestor movement as far as possible, at the same only from The trailing edge starting of the initial traveling wave of failure, therefore select window during the initial traveling wave of failure follow-up 30 μ s；The thunder-strike current waveform that measuring end the measures curve not operating to fitting arrester is drawn related point as correlation analysis Coefficient is analysed, using coefficient correlation to thunder-strike current waveform Δ u (k) and matched curveAnalysis, correlation analysis formula are as follows：<mrow> <mi>&rho;</mi> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>&Delta;</mi> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mi>&Delta;</mi> <mover> <mi>u</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msup> <mi>&Delta;u</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>&Delta;</mi> <msup> <mover> <mi>u</mi> <mo>~</mo> </mover> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>In formula (5), ρ represents the coefficient correlation of thunder-strike current waveform and matched curve, and ρ values are bigger, illustrate two recording signal waves Shape similarity is higher, and N is total number of sample points；(6) it is 0.9 to determine coefficient correlation threshold values, and lightning arrestor movement differentiation is carried out by following condition：If correlation analysis coefficient is more than 0.9, leakage conductor is not operating；If correlation analysis coefficient is less than or equal to 0.9, leakage conductor action.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109766923A (en) * | 2018-12-20 | 2019-05-17 | 昆明理工大学 | A kind of lightning arrestor movement discrimination method based on Image Edge-Detection |
| CN111639554A (en) * | 2020-05-15 | 2020-09-08 | 神华包神铁路集团有限责任公司 | Lightning stroke identification method, device and equipment for traction power supply system |
| CN112684244A (en) * | 2020-11-10 | 2021-04-20 | 国网宁夏电力有限公司 | Method, medium and system for detecting action current type of lightning arrester |
| CN112730964A (en) * | 2020-12-23 | 2021-04-30 | 国网河南省电力公司洛阳供电公司 | Lightning overvoltage identification method based on overvoltage waveform characteristics |
| CN113740603A (en) * | 2021-08-13 | 2021-12-03 | 国网四川省电力公司电力科学研究院 | Method, device, equipment and medium for judging action of high-resistance neutral point lightning arrester |
| CN115577272A (en) * | 2022-12-06 | 2023-01-06 | 昆明理工大学 | Multiple lightning stroke discrimination method based on fault recording data |
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| CN109766923A (en) * | 2018-12-20 | 2019-05-17 | 昆明理工大学 | A kind of lightning arrestor movement discrimination method based on Image Edge-Detection |
| CN111639554A (en) * | 2020-05-15 | 2020-09-08 | 神华包神铁路集团有限责任公司 | Lightning stroke identification method, device and equipment for traction power supply system |
| CN112684244A (en) * | 2020-11-10 | 2021-04-20 | 国网宁夏电力有限公司 | Method, medium and system for detecting action current type of lightning arrester |
| CN112684244B (en) * | 2020-11-10 | 2022-08-30 | 国网宁夏电力有限公司 | Method, medium and system for detecting action current type of lightning arrester |
| CN112730964A (en) * | 2020-12-23 | 2021-04-30 | 国网河南省电力公司洛阳供电公司 | Lightning overvoltage identification method based on overvoltage waveform characteristics |
| CN113740603A (en) * | 2021-08-13 | 2021-12-03 | 国网四川省电力公司电力科学研究院 | Method, device, equipment and medium for judging action of high-resistance neutral point lightning arrester |
| CN113740603B (en) * | 2021-08-13 | 2023-05-23 | 国网四川省电力公司电力科学研究院 | High-resistance neutral point lightning arrester action discriminating method, device, equipment and medium |
| CN115577272A (en) * | 2022-12-06 | 2023-01-06 | 昆明理工大学 | Multiple lightning stroke discrimination method based on fault recording data |
| CN115577272B (en) * | 2022-12-06 | 2023-02-28 | 昆明理工大学 | Multiple lightning stroke discrimination method based on fault recording data |
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