CN109085457A - A kind of method of high-voltage line fault zero crossing quick predict - Google Patents
A kind of method of high-voltage line fault zero crossing quick predict Download PDFInfo
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- CN109085457A CN109085457A CN201810641043.6A CN201810641043A CN109085457A CN 109085457 A CN109085457 A CN 109085457A CN 201810641043 A CN201810641043 A CN 201810641043A CN 109085457 A CN109085457 A CN 109085457A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/08—Locating faults in cables, transmission lines, or networks
- G01R31/088—Aspects of digital computing
Abstract
The invention discloses a kind of method of high-voltage line fault zero crossing quick predict, S1 establishes fault-current signal i (t) model；S2 obtains discrete current signals i (n)；S3, it is discrete to discrete current signals i (n) progress to obtain sampled signal i ' (n): S4, discrete voltage signal u (n): S6 is constructed, the pseudoinverse of sampling matrix I is multiplied to obtain square matrix I+U with sampling matrix U；S7, to square matrix I+U carries out depression of order and seeks characteristic root；S8 obtains predicting the phase difference between power frequency component and reference voltage signal in sampled current signal | θ |；S9 by reference voltage signal delay Δ T, and obtains second of phase difference in sampled current signal between power frequency component and reference voltage signal | θ ' |；S10 determines the phase of sampled current signal；Whether the phase theta of S11, the sampled current signal judged match with zero point phase, carry out zero point fault alarm if matching.Precision of prediction of the present invention improves, and calculation amount is small, provides reliable information for the safe and stable operation of electric system.
Description
Technical field
The invention belongs to electric network fault detection technique fields, and in particular to a kind of high-voltage line fault zero crossing quick predict
Method.
Background technique
In the transient process after electric system is disturbed, whether breaker can reliably cut-off fault current to power train
System safe operation is most important.And maximally efficient drop-out current scheme is exactly to cut-off fault current in current over-zero.Because
There is inevitably delay in breaker mechanism operation, it is therefore desirable to predict the zero crossing of fault current, issue in advance
Trip command just can guarantee breaker actual act in current over-zero point moment.It is pre- for the current zero-crossing point under normal condition
It surveys, there are many method and are easily achieved.But for the zero passage point prediction of fault current, then rarely have suitable for the actual algorithm of engineering,
Main reason is that the zero passage point prediction of fault current is influenced by harmonic wave and attenuating dc component, measurement inaccuracy is caused,
And at present the method for most of failure zero-crossing examination all assume that system frequency stablize it is constant, and in real system, system frequency
It is time-varying.
Summary of the invention
It is influenced to solve existing zero passage prediction by harmonic wave and attenuating dc component, the technology for causing forecasting inaccuracy true is asked
Topic, a kind of method that the present invention proposes high-voltage line fault zero crossing quick predict, can eliminate integer time and non-integer time is humorous
The influence of wave, the influence for being attenuated DC component is small, and calculation amount is small, being capable of quick predict fault current zero crossing.
In order to solve the above technical problems, the technical solution adopted in the present invention is as follows:
A kind of method of high-voltage line fault zero crossing quick predict, steps are as follows: S1, establishes high-voltage line fault electric current
The mathematical models of signal i (t)；The model of the fault-current signal i (t) are as follows:
Wherein, AmFor amplitude；For phase；αm< 0 is decay factor；fmFor frequency, q is the number of signal component；
S2 carries out high precision collecting to fault-current signal i (t), obtains the current signal i (n) of discretization.
S3 carries out sliding-model control to the current signal i (n) that step S2 is obtained, obtains sampled current signal i ' (n):
zk=exp [(αk+j2πfk)Ts] (4)；
In formula, M=2q1+q2, and 2q before i ' (n)1A component represents decaying cosine, rear q2A component represents decaying dc；pk
It include amplitude and phase information for the multiple amplitude of k-th of component in signal；zkFor the amplitude and phase of k-th of component in signal
Variable quantity within a sampling interval；TsFor the sampling interval；And k≤2q1When, pkWith pk-1Conjugation, zkWith zk-1Conjugation；K >
2q1When, fk=0.
S4, construction have the discrete electrical of identical frequency component and decay factor with sampled current signal i ' (n) in step S3
It presses signal u (n):
S5 constructs sampling matrix I and R-matrix U；
I=Z1PZ2(6)；
U=Z1P′Z2(7)；
In formula,For p '1Conjugation.
The pseudoinverse of sampling matrix I is multiplied to obtain square matrix I with R-matrix U by S6+U；
Enabling the power frequency component in the discrete voltage signal u (n) of construction answer amplitude is 1, and the multiple amplitude of other components is 0,
And preceding 2 exponential components of discrete voltage signal u (n) and sampled signal i (n) represent power frequency, then have:
Formula 12 is brought into formula 11 and is obtained,
S7, to square matrix I+U carries out depression of order and seeks characteristic root.
S7.1 enables A=I+U, and similarity transformation is carried out to square matrix A, obtain transformation square matrix A '；
A '=R ' AR '-1=R ' QRR '-1=R ' Q Λ R ' R '-1=R ' Q Λ (14)；
In formula, R '1For 2 × 2 unit upper triangular matrix；R′2For the full battle array of 2 × (L-2)；E is (L-2) rank square matrix；And
S7.2 seeks the characteristic root λ of the 2 rank principal minor array of sequence of transformation square matrix A '1、λ2, obtained characteristic root λ1、λ2Just
It is the non-zero characteristics root for converting square matrix A '.
S7.3 obtains the power frequency phasor p of sampled current signal i ' (n) according to step S7.2 and step S61And p2。
S8 is obtained between prediction power frequency component and the reference voltage signal of sampled current signal i ' (n) according to step S7
Phase difference | θ |.
S9 by reference voltage signal delay Δ T, and repeats step S5-S8 and obtains the prediction work of sampled current signal i ' (n)
Second of phase difference between frequency component and reference voltage signal | θ ' |.
S10, by second of phase difference | θ ' | compared with pi/2, if | θ ' |≤pi/2, the prediction of sampled current signal i ' (n)
The phase of power frequency component be θ=| θ |, otherwise, θ=- | θ |.
Whether the phase theta of S11, the sampled current signal i ' (n) judged match with zero point phase, carry out if matching
Zero point fault alarm.
The present invention constitutes the side comprising power frequency phasor information using reference signal sampling battle array and measured signal sampling battle array
Battle array, by the way that square matrix depression of order is solved characteristic root, reduce calculation amount and completely eliminates the influence of integer time and non-integer harmonics,
And so that the influence of attenuating dc component is become smaller in calculating process, improve precision of prediction, be the safety and stability of electric system
Operation provides reliable information.
Specific embodiment
The following is a clear and complete description of the technical scheme in the embodiments of the invention, it is clear that described implementation
Example is only a part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, this field is general
Logical technical staff every other embodiment obtained under that premise of not paying creative labor, belongs to protection of the present invention
Range.
A kind of method of high-voltage line fault zero crossing quick predict, steps are as follows: S1, establishes high-voltage line fault electric current
The mathematical models of signal i (t)；The model of the fault-current signal i (t) are as follows:
Wherein, AmFor amplitude；For phase；αm< 0 is decay factor；fmFor frequency, q is the number of signal component；
S2 carries out high precision collecting to fault-current signal i (t), obtains the current signal i (n) of discretization.
S3 carries out sliding-model control to the current signal i (n) that step S2 is obtained, obtains sampled current signal i ' (n):
zk=exp [(αk+j2πfk)Ts] (4)；
In formula, M=2q1+q2, and 2q before i ' (n)1A component represents decaying cosine, rear q2A component represents decaying dc；pk
It include amplitude and phase information for the multiple amplitude of k-th of component in signal；zkFor the amplitude and phase of k-th of component in signal
Variable quantity within a sampling interval；TsFor the sampling interval；And k≤2q1When, pkWith pk-1Conjugation, zkWith zk-1Conjugation；K >
2q1When, fk=0.
S4, construction have the discrete electrical of identical frequency component and decay factor with sampled current signal i ' (n) in step S3
It presses signal u (n):
S5 constructs sampling matrix I and R-matrix U；
I=Z1PZ2(6)；
U=Z1P′Z2(7)；
In formula,For p '1Conjugation.
The pseudoinverse of sampling matrix I is multiplied to obtain square matrix I with R-matrix U by S6+U；
Enabling the power frequency component in the discrete voltage signal u (n) of construction answer amplitude is 1, and the multiple amplitude of other components is 0,
And preceding 2 exponential components of discrete voltage signal u (n) and sampled signal i (n) represent power frequency, then have:
Formula 12 is brought into formula 11 and is obtained,
S7, to square matrix I+U carries out depression of order and seeks characteristic root.
S7.1 enables A=I+U, and similarity transformation is carried out to square matrix A, obtain transformation square matrix A '；
A '=R ' AR '-1=R ' QRR '-1=R ' Q Λ R ' R '-1=R ' Q Λ (14)；
In formula, R '1For 2 × 2 unit upper triangular matrix；R′2For the full battle array of 2 × (L-2)；E is (L-2) rank square matrix；And
S7.2 seeks the characteristic root λ of the 2 rank principal minor array of sequence of transformation square matrix A '1、λ2, obtained characteristic root λ1、λ2Just
It is the non-zero characteristics root for converting square matrix A '.
S7.3 obtains the power frequency phasor p of sampled current signal i ' (n) according to step S7.2 and step S61And p2。
S8 is obtained between prediction power frequency component and the reference voltage signal of sampled current signal i ' (n) according to step S7
Phase difference | θ |.
S9 by reference voltage signal delay Δ T, and repeats step S5-S8 and obtains the prediction work of sampled current signal i ' (n)
Second of phase difference between frequency component and reference voltage signal | θ ' |.
S10, by second of phase difference | θ ' | compared with pi/2, if | θ ' |≤pi/2, the prediction of sampled current signal i ' (n)
The phase of power frequency component be θ=| θ |, otherwise, θ=- | θ |.
Whether the phase theta of S11, the sampled current signal i ' (n) judged match with zero point phase, carry out if matching
Zero point fault alarm.
Described above is only presently preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Within mind and principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (2)
1. a kind of method of high-voltage line fault zero crossing quick predict, which is characterized in that steps are as follows, and: S1 establishes high-voltage line
The mathematical models of road fault-current signal i (t)；The model of the fault-current signal i (t) are as follows:
Wherein, AmFor amplitude；For phase；αm< 0 is decay factor；fmFor frequency, q is the number of signal component；
S2 carries out high precision collecting to fault-current signal i (t), obtains the current signal i (n) of discretization；
S3 carries out sliding-model control to the current signal i (n) that step S2 is obtained, obtains sampled current signal i ' (n):
zk=exp [(αk+j2πfk)Ts] (4)；
In formula, M=2q1+q2, and 2q before i ' (n)1A component represents decaying cosine, rear q2A component represents decaying dc；pkFor letter
The multiple amplitude of k-th of component in number includes amplitude and phase information；zkFor k-th component in signal amplitude and phase one
Variable quantity in a sampling interval；TsFor the sampling interval；And k≤2q1When, pkWith pk-1Conjugation, zkWith zk-1Conjugation；K > 2q1When,
fk=0；
S4, construction with sampled current signal i ' (n) in step S3 there is the discrete voltage of identical frequency component and decay factor to believe
Number u (n):
S5 constructs sampling matrix I and R-matrix U；
I=Z1PZ2(6)；
U=Z1P′Z2(7)；
In formula,For p '1Conjugation；
The pseudoinverse of sampling matrix I is multiplied to obtain square matrix I with R-matrix U by S6+U；
Enabling the power frequency component in the discrete voltage signal u (n) of construction answer amplitude is 1, and the multiple amplitude of other components is 0, and from
Preceding 2 exponential components for dissipating voltage signal u (n) and sampled signal i (n) represent power frequency, then have:
Formula 12 is brought into formula 11 and is obtained,
S7, to square matrix I+U carries out depression of order and seeks characteristic root；
S8 obtains the phase between the prediction power frequency component of sampled current signal i ' (n) and reference voltage signal according to step S7
Difference | θ |；
S9 by reference voltage signal delay Δ T, and repeats step S5-S8 and obtains the prediction power frequency point of sampled current signal i ' (n)
Second of phase difference between amount and reference voltage signal | θ ' |；
S10, by second of phase difference | θ ' | compared with pi/2, if | θ ' |≤pi/2, the prediction power frequency of sampled current signal i ' (n)
The phase of component be θ=| θ |, otherwise, θ=- | θ |；
Whether the phase theta of S11, the sampled current signal i ' (n) judged match with zero point phase, carry out zero point if matching
Fault alarm.
2. the method for high-voltage line fault zero crossing quick predict according to claim 1, which is characterized in that in step S7
In, specific steps are as follows: S7.1 enables A=I+U, and similarity transformation is carried out to square matrix A, obtain transformation square matrix A '；
A '=R ' AR '-1=R ' QRR '-1=R ' Q Λ R ' R '-1=R ' Q Λ (14)；
In formula, R '1For 2 × 2 unit upper triangular matrix；R′2For the full battle array of 2 × (L-2)；E is (L-2) rank square matrix；And
S7.2 seeks the characteristic root λ of the 2 rank principal minor array of sequence of transformation square matrix A '1、λ2, obtained characteristic root λ1、λ2Exactly convert
The non-zero characteristics root of square matrix A '；
S7.3 obtains the power frequency phasor p of sampled current signal i ' (n) according to step S7.2 and step S61And p2。
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| CN113092847A (en) * | 2021-03-31 | 2021-07-09 | 武汉大学 | Method for predicting zero offset of fault current |
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Application publication date: 20181225 |