CN102508115A - Identification method for faults in and out of area of high voltage direct current (HVDC) transmission line based on multi-fractal spectrum - Google Patents

Identification method for faults in and out of area of high voltage direct current (HVDC) transmission line based on multi-fractal spectrum Download PDF

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CN102508115A
CN102508115A CN2011103300659A CN201110330065A CN102508115A CN 102508115 A CN102508115 A CN 102508115A CN 2011103300659 A CN2011103300659 A CN 2011103300659A CN 201110330065 A CN201110330065 A CN 201110330065A CN 102508115 A CN102508115 A CN 102508115A
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fault
transmission line
singularity
voltage
mode voltage
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CN102508115B (en
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束洪春
安娜
董俊
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Kunming University of Science and Technology
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    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
    • Y04S10/52—Outage or fault management, e.g. fault detection or location

Abstract

The invention relates to an identification method for faults in and out of an area of a high voltage direct current (HVDC) transmission line based on a multi-fractal spectrum, which belongs to the technical field of relay protection of a power system. When a fault occurs in a direct current circuit, after a protective element is started, according to two-electrode direct voltage detected at a protective installation position, aerial mode voltage is obtained by utilizing the phase mode conversion theory. Fault component of the aerial mode voltage is obtained according to the superposition principle, probability density at different levels is obtained through the side length of a transform box, then partition function and quality factor are obtained, finally singularity exponent and growth rate k of the singularity exponent are obtained, and then faults in and out of the area are judged according to the k value. Sampling frequency is 20 kHz, time window is 1ms, the required data length is short, and effect of a control system is avoided. The identification method is capable of correctly identifying various types of faults within the range of the whole line and high in tolerance property for transition resistance, is not affected by interference and has high practical applicability.

Description

HVDC transmission line internal fault external fault recognition methods based on multifractal spectra
Technical field
The present invention relates to a kind of method of discerning the HVDC transmission line internal fault external fault, specifically a kind of HVDC transmission line internal fault external fault recognition methods based on multifractal spectra belongs to the relay protection of power system technical field.
Background technology
The HVDC transmission line through-put power is big, behind the line failure, requires the excision fault that line protective devices must be fast as far as possible, otherwise will cause very big impact to total system, and the safe and stable operation of system is constituted a threat to.General power frequency protection responsiveness is slow, consuming time longer, is difficult to satisfy the requirement of protection of direct current supply line.At present; Extensively adopt of the main protection of traveling-wave protection technology in the world as the HVDC transmission line protection; Its single-ended amount protection according to the sudden change amount of voltage traveling wave and rate of change and electric current variable gradient (voltage that instant of failure transmitted, current traveling wave change information) as criterion; Have the hypervelocity acting characteristic, do not receive that current transformer is saturated, advantage such as system oscillation and long line distributed capacitance influence.But related data shows; The DC line traveling-wave protection technology of using at present (mainly being provided by ABB and SIEMENS two companies) is in various degree problems such as existing easy malfunction, receive noise or receive that transition resistance influences all; When DC line during through high resistive fault; The voltage change ratio of traveling-wave protection reduces, and causes the tripping of traveling-wave protection device sometimes.Can the security and the reliability that how to improve the DC power transmission line operation have become urgent problem, propose new method based on the characteristic of border fault-signal, and DC line fault is made fast and correctly judged, be the key of DC line protection.
Summary of the invention
The purpose of this invention is to provide a kind of HVDC transmission line internal fault external fault recognition methods based on multifractal spectra; Utilize the single-ended hypervelocity protection philosophy of DC power transmission line of border high fdrequency component characteristic, realize, reliably identification quick the HVDC transmission line internal fault external fault.
The step of HVDC transmission line internal fault external fault recognition methods that the present invention is based on multifractal spectra is following:
(1) after DC line breaks down; According to anodal DC voltage
Figure 2011103300659100002DEST_PATH_IMAGE002
and the negative pole DC voltage
Figure 2011103300659100002DEST_PATH_IMAGE004
of protecting the installation place to record; Adopt the Karenbauer transformation matrix, obtain line mode voltage
Figure 2011103300659100002DEST_PATH_IMAGE006
:
Figure 2011103300659100002DEST_PATH_IMAGE008
?；
Again according to superposition principle; Through the line mode voltage
Figure 2011103300659100002DEST_PATH_IMAGE010
under line mode voltage
Figure 225222DEST_PATH_IMAGE006
and the non-malfunction, obtain the fault component
Figure 2011103300659100002DEST_PATH_IMAGE012
of line mode voltage:
Figure 2011103300659100002DEST_PATH_IMAGE014
；
(2) fault component
Figure 866550DEST_PATH_IMAGE012
to the line mode voltage is divided into the one dimension etui of
Figure 2011103300659100002DEST_PATH_IMAGE016
individual yardstick for
Figure 2011103300659100002DEST_PATH_IMAGE018
along time orientation; The difference of each dimension etui maximal value and minimum value is
Figure 2011103300659100002DEST_PATH_IMAGE020
;
Figure 2011103300659100002DEST_PATH_IMAGE022
=1,2,3 wherein;
Figure 2011103300659100002DEST_PATH_IMAGE024
=1;, ;
Get SF fBe 20kHz, sample sequence length is 20 points,
Figure 2011103300659100002DEST_PATH_IMAGE026
, ,
Figure 2011103300659100002DEST_PATH_IMAGE030
, obtain probability density
Figure 2011103300659100002DEST_PATH_IMAGE032
For:
Figure 2011103300659100002DEST_PATH_IMAGE034
；
(3) to probability
Figure 649272DEST_PATH_IMAGE032
Use qPower carries out weighted sum and obtains partition function
Figure 2011103300659100002DEST_PATH_IMAGE036
, partition function
Figure 721568DEST_PATH_IMAGE036
With yardstick
Figure 732249DEST_PATH_IMAGE018
Relation be:
Figure 2011103300659100002DEST_PATH_IMAGE038
，
Wherein,
Figure 2011103300659100002DEST_PATH_IMAGE040
,
Figure 2011103300659100002DEST_PATH_IMAGE042
is performance figure;
(4) try to achieve performance figure with least square fitting:
；
(5)
Figure 173168DEST_PATH_IMAGE042
differentiated, obtains singularity index
Figure 2011103300659100002DEST_PATH_IMAGE046
:
Figure 2011103300659100002DEST_PATH_IMAGE048
；
(6) according to performance figure
Figure 635505DEST_PATH_IMAGE042
, singularity index
Figure 500693DEST_PATH_IMAGE046
, obtain multifractal spectra
Figure 2011103300659100002DEST_PATH_IMAGE050
:
Figure 2011103300659100002DEST_PATH_IMAGE052
; Wherein,
Figure 390283DEST_PATH_IMAGE040
;
(7), obtain the minimum value and the maximal value
Figure 2011103300659100002DEST_PATH_IMAGE056
of singularity index according to multifractal spectra
Figure 973711DEST_PATH_IMAGE050
;
(8) according to the minimum value of singularity index
Figure 98793DEST_PATH_IMAGE054
And maximal value
Figure 959432DEST_PATH_IMAGE056
, obtain the rate of growth of singularity index k:
；
(9) according to the rate of growth of singularity index k, screen, judge the extra high voltage direct current transmission line internal fault external fault: when k≤1.5 o'clock is external area error, when k>1.5 the time be troubles inside the sample space.
Principle of the present invention is:
DC transmission system generally includes the smoothing reactor and the DC filter at DC power transmission line, DC line two ends, and smoothing reactor and DC filter have constituted " natural " physical boundary of DC power transmission line high frequency transient amount.When troubles inside the sample space or external area error take place, the spectral characteristic of the line mode voltage ripple of its two ends boundary element (smoothing reactor and DC filter) will have significant difference.This can be from the transport function of DC transmission system physical boundary element<i >H</i>(j ω) obtains reflection.<img file=" 2011103300659100002DEST_PATH_IMAGE060.GIF " he=" 38 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 162 " />; Wherein, Z1 (j ω) is the DC filter impedance, and Z2 (j ω) is the smoothing reactor impedance.The boundary element transport function<i >H</i>The amplitude versus frequency characte such as the Fig. 3 of (j ω); When<i >f</i><during 1000Hz, |<i >H</i>(j ω) | ≈ 0; Work as 1000Hz<<i >f</i><during 2000Hz,<i >H</i>(j ω) spectrum curve has vibration; When<i >F></i>During 2000Hz, |<i >H</i>(j ω) |>-30dB.Thus it is clear that, the detected high fdrequency component of troubles inside the sample space high 30dB during than external area error.The characteristic of detected high fdrequency component during based on fault can judge it is troubles inside the sample space, or external area error.
Fractally be meant one type of random, chaotic and complicated but its local and whole system that has similarity at aspects such as form, function and information.Multifractal is estimated research physical quantity or the distribution of other amount on geometry support.Each point to fractal surface is measured with mass distribution probability
Figure 2011103300659100002DEST_PATH_IMAGE062
; Use the zonule of many dimensions for to go to cover whole fractal surface, the mass distribution probability
Figure 2011103300659100002DEST_PATH_IMAGE068
on
Figure 2011103300659100002DEST_PATH_IMAGE066
individual zonule with the relation of dimension
Figure 895290DEST_PATH_IMAGE064
is:
Figure 2011103300659100002DEST_PATH_IMAGE070
Wherein,
Figure 966014DEST_PATH_IMAGE046
is called scaling exponent; What its reflected is that the unusual degree of each zonule is relevant in the fractal, therefore is called the singularity index again.
If in fractal; Zonule number with identical value is
Figure 2011103300659100002DEST_PATH_IMAGE072
, is defined as
Figure 609933DEST_PATH_IMAGE072
:
Figure 2011103300659100002DEST_PATH_IMAGE074
Wherein, The fractal dimension that
Figure 965959DEST_PATH_IMAGE050
expression has the subclass of identical value is called multifractal spectra.
Fractal for a complicacy; Its inside can be divided into the subclass of a series of different
Figure 115498DEST_PATH_IMAGE046
values, and identical
Figure 685150DEST_PATH_IMAGE046
value has identical unusual degree.According to the function that provides
Figure 257394DEST_PATH_IMAGE050
, just can provide the fractal property of these a series of subclass about
Figure 336712DEST_PATH_IMAGE046
.
For DC transmission system, during external area error, because boundary element is to the attenuation of high frequency; High fdrequency component in the line mode voltage ripple that the protection installation place records is less relatively; And the amplitude of high fdrequency component is relatively very little, and Fractal Set is simple relatively, and singularity exponential increase rate is lower.During troubles inside the sample space, high fdrequency component is not passed through boundary element, and high frequency content is more, and its amplitude is also much larger than the high fdrequency component amplitude of external area error, the Fractal Set relative complex, and singularity exponential increase rate is higher.
Therefore, carry out multifractal spectra through fault component and find the solution, obtain about the singularity index to the line mode voltage
Figure 652603DEST_PATH_IMAGE046
Function
Figure 201396DEST_PATH_IMAGE050
, according to
Figure 164804DEST_PATH_IMAGE046
Minimum value
Figure 431838DEST_PATH_IMAGE054
And maximal value , calculate the singularity index
Figure 909404DEST_PATH_IMAGE046
Rate of growth
Figure 43713DEST_PATH_IMAGE058
, basis again kThe size of value can be screened and judges troubles inside the sample space or external area error.In SF is after 20kHz, sampling time window length are fault under the 1ms condition, shows through macromethod research and simulation results: K≤1.5 the time, be external area error; K>1.5 the time, be troubles inside the sample space.
The present invention compared with prior art has following advantage:
1, this method SF is 20kHz, and time window is 1ms, and desired data length is shorter, has avoided the influence of control system.
2, this method is to all correct identification of ability of the various fault types in the total track length scope.
3, the performance of this method tolerance transition resistance is stronger, and interference-free influence has stronger practicality.A large amount of simulation results show that the present invention is respond well.
Description of drawings
Fig. 1 is the embodiment of the invention ± 800kV DC transmission system structural representation; Among the figure: F 2, F 3Be external area error, F 1, F 4Be troubles inside the sample space, M is the protection installation place;
Fig. 2 is the DC transmission system boundary element synoptic diagram that embodiment of the invention smoothing reactor and DC filter constitute; Among the figure: U 1Be the transient voltage outside distinguishing, U 2For U 1Fade to the voltage of DC line protection installation place through flank pass; B 1, B 2, B 3, B 4Be the DC filter lightning arrester; D 1Be smoothing reactor lightning arrester, D 2Be DC bus arrester; L 1, L 2, L 3, L 4Be inductance element; C 1, C 2, C 3, C 4Be capacity cell;
Fig. 3 is the spectral characteristic figure of DC transmission system boundary element of the present invention; Among the figure: fBe frequency, Hz is the unit of frequency, H(j ω) is the amplitude of frequency spectrum;
Line mode voltage fault component oscillogram when Fig. 4 is the embodiment of the invention 1 troubles inside the sample space; Among the figure t/ms be time/second, U/kV is voltage/kilovolt;
Line mode voltage fault component oscillogram when Fig. 5 is the embodiment of the invention 1 external area error; Among the figure t/ms be time/second, U/kV is voltage/kilovolt;
Figure 6 embodiment of the invention a fault zone on the singularity exponent
Figure 798042DEST_PATH_IMAGE046
multifractal spectrum ;
Figure 7 is an embodiment of the invention an external fault on the singularity exponent multifractal spectrum
Figure 363650DEST_PATH_IMAGE050
;
Fig. 8 is for the anodal one pole earth fault of generation in the district of the present invention, when stake resistance is respectively 1 Ω, 10 Ω, 100 Ω, 300 Ω, singularity exponential increase rate kDistribution plan, K>1.5 satisfy the criterion requirement; Among the figure: kBe the singularity rate of growth, l/ km is the distance (unit is a km) of fault occurrence positions distance protection installation place.
Embodiment
Below in conjunction with accompanying drawing and embodiment, the present invention is done further elaboration, but protection scope of the present invention is not limited to said content.
Embodiment 1: as shown in Figure 1, this based on the HVDC transmission line internal fault external fault recognition methods of multifractal spectra cloud wide ± use in the 800kV DC transmission system.System's power transmission capacity is 5000MW, and the reactive compensation capacity of rectification side and inversion side is respectively 3000Mvar and 3040Mvar; Every utmost point convertor unit is composed in series by 2 12 pulse transverters, and DC power transmission line is a six-multiple conductor, and total length is taken as 1500km, adopts J.R.Marti frequency dependence model; The smoothing reactor of 400mH is equipped with in the circuit both sides; F 2, F 3Be external area error, F 1, F 4Be troubles inside the sample space, M is the protection installation place.
As shown in Figure 2, this DC transmission system constitutes its physical boundary with smoothing reactor and DC filter.Wherein: U 1For distinguishing outer transient voltage, U 2For U 1Fade to the voltage of DC line protection installation place through flank pass; B 1, B 2, B 3, B 4Be DC filter lightning arrester, D 1Be smoothing reactor lightning arrester, D 2Be DC bus arrester, lightning arrester B 1, B 2, B 3, B 4, D 1, D 2Be referred to as the border lightning arrester.B 1, B 2Rated voltage is 150kV, B 3, B 4Rated voltage is 75kV, D 1, D 2Rated voltage is 824kV; L=400mH, L 1=39.09mH, L 2=26.06mH, L 3=19.545mH, L 4=34.75mH, C 1=0.9 μ F, C 2=0.9 μ F, C 3=1.8 μ F, C 4=0.675 μ F.
At 150km place, distance protection installation place, the plus earth fault takes place in 0.505s, transition resistance is 10 Ω.By following method, based on multifractal spectra, identification HVDC transmission line internal fault external fault:
(1) after DC line breaks down; Starting element starts immediately; According to anodal DC voltage
Figure 215062DEST_PATH_IMAGE002
and the negative pole DC voltage
Figure 755765DEST_PATH_IMAGE004
of protecting the installation place to record; Adopt the Karenbauer transformation matrix, obtain line mode voltage
Figure 399236DEST_PATH_IMAGE006
according to following formula:
Figure 609769DEST_PATH_IMAGE008
?；
Again according to formula
Figure 338690DEST_PATH_IMAGE014
; Utilize superposition principle; Through the line mode voltage
Figure 790848DEST_PATH_IMAGE010
under line mode voltage
Figure 292871DEST_PATH_IMAGE006
and the non-malfunction; Obtain the fault component of line mode voltage, waveform is as shown in Figure 4;
(2) fault component
Figure 388500DEST_PATH_IMAGE012
to the line mode voltage is divided into the one dimension etui of
Figure 271005DEST_PATH_IMAGE016
individual yardstick for
Figure 623489DEST_PATH_IMAGE018
along time orientation; The difference of each dimension etui maximal value and minimum value is
Figure 441404DEST_PATH_IMAGE020
;
Figure 879338DEST_PATH_IMAGE022
=1,2,3 wherein;
Figure 299955DEST_PATH_IMAGE024
=1;,
Figure 647891DEST_PATH_IMAGE016
;
Get SF fBe 20kHz, sampling time window length is got 1ms after the fault, and sample sequence length is 20 points,
Figure 495761DEST_PATH_IMAGE026
,
Figure 420992DEST_PATH_IMAGE028
,
Figure 520666DEST_PATH_IMAGE030
, probability density For:
Figure 132093DEST_PATH_IMAGE034
；
(3) to probability
Figure 419986DEST_PATH_IMAGE032
Use qPower carries out weighted sum and obtains partition function
Figure 182406DEST_PATH_IMAGE036
, partition function
Figure 215917DEST_PATH_IMAGE036
With yardstick
Figure 671169DEST_PATH_IMAGE018
Relation below existing:
Figure 570992DEST_PATH_IMAGE038
；
Wherein,
Figure 12469DEST_PATH_IMAGE040
,
Figure 48558DEST_PATH_IMAGE042
is performance figure;
(4) try to achieve performance figure with least square fitting:
Figure 937197DEST_PATH_IMAGE044
；
(5)
Figure 41419DEST_PATH_IMAGE042
differentiated, promptly obtains singularity index
Figure 72960DEST_PATH_IMAGE046
:
Figure 870015DEST_PATH_IMAGE048
；
(6) according to formula
Figure 478850DEST_PATH_IMAGE052
; Obtain the multifractal spectra
Figure 538390DEST_PATH_IMAGE050
of singularity index
Figure 527709DEST_PATH_IMAGE046
, as shown in Figure 6;
(7), obtain minimum value
Figure 477845DEST_PATH_IMAGE054
=0.3871, the maximal value
Figure 923869DEST_PATH_IMAGE056
=2.2247 of singularity index according to multifractal spectra
Figure 506346DEST_PATH_IMAGE050
;
(8) according to the minimum value of singularity index
Figure 930003DEST_PATH_IMAGE054
And maximal value
Figure 68860DEST_PATH_IMAGE056
, obtain the rate of growth of singularity index k:
Figure 527654DEST_PATH_IMAGE058
=4.747；
(9) gained singularity exponential increase rate K=4.747 numerical value higher, satisfy criterion K>1.5 condition judges that this fault is a troubles inside the sample space.
Embodiment 2: like Fig. 1, shown in 2, this based on the HVDC transmission line internal fault external fault recognition methods of multifractal spectra cloud wide ± carry out in the 800kV DC transmission system, the transmission system structure is with that related parameter is arranged is all identical with embodiment 1.
At 150km place, distance protection installation place, the plus earth fault takes place in 0.505s, transition resistance is 10 Ω.Press the identical method of embodiment 1, identical SF ,Sampling time window length and sample sequence length are obtained the fault component of line mode voltage
Figure 652736DEST_PATH_IMAGE012
Waveform is as shown in Figure 5, the singularity index
Figure 513376DEST_PATH_IMAGE046
Multifractal spectra
Figure 823135DEST_PATH_IMAGE050
As shown in Figure 7; Obtain the minimum value of singularity index
Figure 769225DEST_PATH_IMAGE054
=0.7902, maximal value =1.3230, singularity exponential increase rate k=0.6743.
Gained singularity exponential increase rate k=0.6743 numerical value is lower, satisfies criterion k≤1.5 conditions judge that this fault is an external area error.
The present invention has carried out simulating, verifying to different fault distances, different stake resistances, obtains result such as the following table of singularity exponential increase rate k:
Figure 2011103300659100002DEST_PATH_IMAGE076

Claims (3)

1. HVDC transmission line internal fault external fault recognition methods based on multifractal spectra is characterized in that carrying out according to the following steps:
(1) after DC line breaks down; According to anodal DC voltage
Figure 2011103300659100001DEST_PATH_IMAGE001
and the negative pole DC voltage
Figure 16297DEST_PATH_IMAGE002
of protecting the installation place to record; Adopt the Karenbauer transformation matrix, obtain line mode voltage
Figure 2011103300659100001DEST_PATH_IMAGE003
:
Figure 291421DEST_PATH_IMAGE004
?；
Again according to superposition principle; Through the line mode voltage
Figure 2011103300659100001DEST_PATH_IMAGE005
under line mode voltage and the non-malfunction, obtain the fault component
Figure 20791DEST_PATH_IMAGE006
of line mode voltage:
Figure 2011103300659100001DEST_PATH_IMAGE007
；
(2) fault component
Figure 625078DEST_PATH_IMAGE006
to the line mode voltage is divided into the one dimension etui of
Figure 703893DEST_PATH_IMAGE008
individual yardstick for
Figure 2011103300659100001DEST_PATH_IMAGE009
along time orientation; The difference of each dimension etui maximal value and minimum value is
Figure 77237DEST_PATH_IMAGE010
;
Figure 848884DEST_PATH_IMAGE012
=1,2,3 wherein;
Figure 2011103300659100001DEST_PATH_IMAGE013
=1;,
Figure 674888DEST_PATH_IMAGE008
;
Get SF fBe 20kHz, sample sequence length is 20 points,
Figure 432760DEST_PATH_IMAGE014
,
Figure 2011103300659100001DEST_PATH_IMAGE015
,
Figure 785244DEST_PATH_IMAGE016
, obtain probability density
Figure 2011103300659100001DEST_PATH_IMAGE017
For:
；
(3) to probability
Figure 916459DEST_PATH_IMAGE017
Use qPower carries out weighted sum and obtains partition function
Figure 2011103300659100001DEST_PATH_IMAGE019
, partition function
Figure 212442DEST_PATH_IMAGE019
With yardstick
Figure 685012DEST_PATH_IMAGE009
Relation be:
Figure 673828DEST_PATH_IMAGE020
；
Wherein,
Figure 2011103300659100001DEST_PATH_IMAGE021
,
Figure 599058DEST_PATH_IMAGE022
is performance figure;
(4) try to achieve performance figure
Figure 698732DEST_PATH_IMAGE022
with least square fitting:
Figure 2011103300659100001DEST_PATH_IMAGE023
；
(5)
Figure 635596DEST_PATH_IMAGE022
differentiated, obtains singularity index
Figure 919946DEST_PATH_IMAGE024
:
Figure 2011103300659100001DEST_PATH_IMAGE025
；
(6) according to performance figure
Figure 207839DEST_PATH_IMAGE022
, singularity index
Figure 235838DEST_PATH_IMAGE024
, obtain multifractal spectra
Figure 292787DEST_PATH_IMAGE026
:
; Wherein,
Figure 357826DEST_PATH_IMAGE021
;
(7), obtain the minimum value
Figure 823760DEST_PATH_IMAGE028
and the maximal value of singularity index according to multifractal spectra
Figure 257649DEST_PATH_IMAGE026
;
(8) according to the minimum value of singularity index
Figure 794DEST_PATH_IMAGE028
And maximal value
Figure 236735DEST_PATH_IMAGE029
, obtain the rate of growth of singularity index k:
Figure 623854DEST_PATH_IMAGE030
；
(9) according to the rate of growth of singularity index k, screen, judge the HVDC transmission line internal fault external fault.
2. the HVDC transmission line internal fault external fault recognition methods based on multifractal spectra according to claim 1 is characterized in that: when k≤1.5 o'clock is external area error, when k>1.5 the time be troubles inside the sample space.
3. the HVDC transmission line internal fault external fault recognition methods based on multifractal spectra according to claim 1 and 2, it is characterized in that: SF is 20kHz, sampling time window length is 1ms after the fault.
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CN111695089A (en) * 2020-06-12 2020-09-22 国网四川省电力公司电力科学研究院 Alternating current transmission line fault identification method based on multi-fractal spectrum
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CN113030653A (en) * 2021-05-06 2021-06-25 重庆大学 Fault identification method for single-end protection of direct-current power grid
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