CN109884471A - Phasor product has works to judge failure phase and selection method - Google Patents
Phasor product has works to judge failure phase and selection method Download PDFInfo
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- CN109884471A CN109884471A CN201910223581.8A CN201910223581A CN109884471A CN 109884471 A CN109884471 A CN 109884471A CN 201910223581 A CN201910223581 A CN 201910223581A CN 109884471 A CN109884471 A CN 109884471A
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Abstract
The invention discloses a kind of phasor products to have works to judge failure phase and selection method, propose the average value of half of cycle of the active synchronized sampling value multiplication gained product for being equal to two phasors of phasor product, and it proposes according to the phase relation between the active size of phasor product and positive negative judgement phasor, the judgement and route selection of failure phase when to realize single-phase earthing, it is no longer rely on and accurately calculates the implementation judgement of each failure amount, failure amount is accurately calculated without Fourier transformation etc., the present invention has evaded the influence of various uncertain factors and transient, accurate judgement failure phase and route selection, ensure system safety operation.
Description
Technical field
The present invention relates to the identification of failure phase when neutral point of electric network non-effectively earthed system, specially singlephase earth fault with
Route selection.
Background technique
All the time, isolated neutral mode is China's power distribution network using a kind of most earthing modes, it is with low investment,
Power supply reliability is high.But when arc grounding occurs in the system, since the energy in direct-to-ground capacitance cannot be released effectively,
Arc grounding over-voltage or resonance overvoltage will be generated, the numerical value of the voltage is very high, can be to the insulation of electrical equipment in system
It threatens.
Currently, it is all defective to be mutually grounded extinguishing arc for arc suppression coil, failure, it has to are grounded using neutral point low values of resistors fast
Speed excision faulty line, but neutral point is grounded the failure when encountering fault point high resistance grounding through low values of resistors, can not also cut
Except faulty line.
It is simple, with low investment that failure is mutually grounded extinguishing arc, but failure phase difficult judgment, and being unable to judge accurately failure mutually will result in
Phase fault is not only unable to extinguishing arc and also causes bigger accident, and accurate judgement failure is mutually that failure is mutually grounded extinguishing arc and must have
Condition.
Single-phase earthing cannot accurate route selection be current all line selection apparatus common fault, accurate route selection and cannot judge failure
Phase is all because the process put out of arc grounding arc arcing is extremely complex, and current route selection and the algorithm for judging failure phase are from every
Accurately calculating for the value of one failure amount is started with, rational judgment failure and route selection, since to put out process not true for arc grounding arc arcing
Fixed factor is excessive, and half of cycle is often below during arcing, and the voltage during blow-out and arcing is phase voltage and over the ground respectively
Voltage, is not a voltage parameter, and Fourier transformation etc. accurately calculates that algorithm is lack scope for their abilities, along with the shadow of transient
It rings, prior art means are exhaustive to be also unable to get satisfied result.
Summary of the invention
The present invention be to avoid above-mentioned existing deficiencies in the technology, provide a kind of phasor product have works judgement therefore
Barrier phase and selection method qualitatively judge failure phase and route selection, rather than quantitative, are no longer rely on the accurate failure phasor that calculates and implement to sentence
It is disconnected, evade the influence of various uncertain factors and transient, overcomes the defect of current rational judgment failure phase and route selection, nothing
It needs Fourier transformation etc. to accurately calculate failure amount, realizes a hundred percent accurate judgement failure phase and route selection, it is ensured that system is transported safely
Row.
The present invention adopts the following technical scheme that in order to solve the technical problem
Phasor product of the present invention has the characteristics of works judge failure phase and selection method to be:
PhasorFunction expression uE(t) are as follows: uE(t)=Ksin (ω t+ α),
PhasorFunction expression uF(t) are as follows: uF(t)=Psin (ω t+ alpha+beta),
K and P is respectively phasorAnd phasorMould, α and alpha+beta are respectively phasorAnd phasorPhase angle, β is
PhasorAnd phasorAngle；
By phasorAnd phasorPhasor productIt is denoted asPhasor productPhasor product active be denoted as WE*F, phasor productFunction expression be denoted as g (t)；
WE*F=KPcos β
G (t)=WE*F-KPsin(2ωt+2α+β)
Phasor productThe active W of phasor productE*FSampling algorithm characterized by formula (1.1):
uE(ti)、uF(ti) and g (ti) it is respectively phasorPhasorAnd phasor productIn the synchronized sampling value at ti moment, n
For phasorAnd phasorHalf of cycle or half of cycle integral multiple number of samples, n is natural number not less than 2；
The criterion characterized by formula (1.2) is obtained according to formula (1.1):
It is active according to formula (1.1) calculating phasor product, according to formula (1.2) further according to the active size of phasor product and positive negative judgement
Phase relation between phasor, the judgement and route selection of failure phase when realizing single-phase earthing.
Phasor product of the present invention has the characteristics of works judge failure phase and selection method to lie also in:
For the network system with m outlet, when singlephase earth fault occurs for the network system,
WithWithThe phase voltage of leading phase, lag phase and failure phase is respectively indicated, and will be describedWithOne group of three-phase symmetrical is defined as referring to phasor；
WithWithIt respectively indicates advanced Relative fault phase, lag opposite leading phase and failure relatively lags behind phase
Line voltage, and will be describedWithIt is defined as another group of three-phase symmetrical reference phasor, it will be describedIt is defined as selecting
Line is referring to phasor；
WithWithThe phase-to-ground voltage of leading phase, lag phase and failure phase is respectively indicated, withIndicate neutral
Point voltage, will be describedWithWithIt is defined as failure phasor；
θ indicates phasorAnd phasorAngle；
WithIndicate that the capacitance current of i-th outlet, i=1,2 ..., m, m are the natural number not less than 1, withIndicate event
Hinder the capacitance current of route,WithFor failure phasor, then there are relational expression (2.1):
One group of three-phase symmetrical is constructed referring to phasorWithThe three-phase symmetrical is referring to phasorWithAdvanced three-phase phase voltageWithPhase beIt willAny value in (- 30 °, 60 °) section；Or it willNeutral point voltage is tracked by formula (2.1) and formula (2.2)Dynamic value, makesWithAngle be acute angle and minimum；
One group of three-phase symmetrical is constructed referring to phasorWithThe three-phase symmetrical is referring to phasorWithAdvanced three-phase phase voltageWithPhase beIt willAny value in (- 30.5 °, 59.5 °) section；
Or it willNeutral point voltage is tracked by formula (2.1) and formula (2.3)Dynamic value, makesWithAngle be acute angle and most
It is small；
A route selection is constructed referring to phasorThe reference phasorIn advancePhase isIt willAt (0 °, 90 °)
Any value in section；Or it willNeutral point voltage is tracked by formula (2.1) and formula (2.4)Dynamic value, makesWithFolder
Angle is acute angle and minimum；
For realizing the phasor product for thering are works to judge failure phase are as follows: failure phasor multiplies with failure phasor, or is failure phasor
It is multiplied with three-phase symmetrical referring to phasor；
For realizing the phasor product for having works route selection are as follows: the capacitance current of every outlet is multiplied with route selection referring to phasor, or
The capacitance current of every outlet is multiplied with failure phase-to-ground voltage；
Phasor product of the present invention has the characteristics of works judge failure phase and selection method to lie also in:
G phase singlephase earth fault occurs for system, carries out failure by following any criterion and mutually judges:
Criterion 1: failure phasor is multiplied with failure phasor, it may be assumed that willRespectively withWithIt is multiplied, obtains WithWherein,Phasor product it is active maximum and be positive；
Criterion 2: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willRespectively withWithIt is multiplied,
It obtainsWithWherein,Phasor product it is active maximum and be positive；
Criterion 3: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willRespectively withWithPhase
Multiply, obtainsWithWherein,Phasor product it is active maximum and be positive；
Criterion 4: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed thatWithRespectively with same famous prime minister's WithIt is multiplied, obtains:WithWherein,Phasor product it is active maximum and be positive；
Criterion 5: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willWithRespectively with same famous prime minister
's WithIt is multiplied, obtainsWithWherein,The active maximum of phasor product
And it is positive；
Criterion 6: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willRespectively withWithPhase
Multiply, obtain:WithWhereinPhasor product it is active maximum and be positive；
Criterion 7: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willWithRespectively with same famous prime minister
's WithIt is multiplied, obtains:WithWherein,Phasor product it is active maximum and
It is positive；
Phasor product of the present invention has the characteristics of works judge failure phase and selection method to lie also in:
G phase singlephase earth fault occurs for system, carries out event by any route selection criterion of following criterion one to criterion three
Hinder route selection:
Criterion one: failure phasor and route selection are multiplied referring to phasor, and it is active to obtain phasor product, it may be assumed that by every outletWithIt is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active maximum and is positive
Value；
Criterion two: it failure phasor is multiplied failure phasor and failure phasor and with route selection referring to phasor obtains phasor product
It is active:
IfFailure phasor is multiplied with failure phasor and obtains that phasor product is active, every outletWith
It is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active maximum and is positive value；
IfWhen, failure phasor and route selection are multiplied referring to phasor, and it is active to obtain phasor product, it may be assumed that goes out every
LineWithIt is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active most
It greatly and is positive value；
Criterion three: failure phasor and route selection are multiplied referring to phasor, and it is active to obtain phasor product, it may be assumed that by every outletWithIt is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active maximum and is positive
Value.
Phasor product of the present invention has the characteristics of works judge failure phase and selection method to lie also in:
When G phase single-phase earthing occurs for system, the phase voltage sampled value of three-phase is obtained by following any way:
Mode one: leading phase phase voltageLag phase phase voltageWith failure phase phase voltageSampled value be equal to it is of the same name
The sampled value of the phase-to-ground voltage of phase subtracts the synchronized sampling value of neutral point voltage, is characterized by formula (5.1)；
Mode two: being measured using voltage transformer, is sampled for the secondary side voltage of the voltage transformer
Obtain phase voltage sampled value, the primary side isolated neutral of the voltage transformer.
Mode three: leading phase phase voltageLag phase phase voltageWith failure phase phase voltageSampled value, according to three
Equipotential sampled value of the phase-to-ground voltage before singlephase earth fault obtains, and the equipotential sampled value refers to:
Implement sampling for the AC signal f (t) that the period is T, the AC signal f (t) when system is operated normally is denoted as
f1(t), by tτAC signal f (t) after moment system jam is denoted as f2(t), f1(t) t after the failure occurred2Moment adopts
Sample value f1(t2), and have:
K is not less than 1 natural number, f1(t1) it is f1(t2) the equipotential sampled value before failure, then:
f1(t2)=f1(t1) (5.3)
F (t) is in t2The fault increment at moment:
Δf(t2)=f2(t2)-f1(t2) (5.4)
Indicate the phase-to-ground voltage of system, with f (t) with f1(t) phase voltage of system is indicatedWithWith f2(t)
The phase-to-ground voltage of system after expression single-phase earthingWithF (t)=f when system operates normally1(t), single-phase to connect
F (t)=f behind ground2(t)。
Phasor product of the present invention has the characteristics of works judge failure phase and selection method to lie also in:
Advanced Relative fault phase lags opposite leading phase and failure relatively lags behind the line voltage of phaseWith's
Sampled value is obtained by following any way:
First way: according to formula (2.1),WithSampled value respectively by leading phase, lag mutually and therefore
Hinder the phase voltage of phaseWithSynchronized sampling value subtract each other acquisition；
The second way: according to formula (6.1),WithSampled value respectively by leading phase, lag mutually and therefore
Hinder the voltage-to-ground of phaseWithSynchronized sampling value subtract each other acquisition；
The difference of two phasors is equal to third phasor, then the synchronized sampling value of two phasors is subtracted each other equal to third phasor
Synchronized sampling value, and be suitable for vector additive operation.
Phasor product of the present invention has the characteristics of works judge failure phase and selection method to lie also in: the sampled value of neutral point voltage
It is the synchronized sampling value addition acquisition according to formula (2.1) by three phase-to-ground voltages, or by voltage transformer open delta voltage
Sampled value transformation obtains；
The sum of two phasors are equal to third phasor, then the synchronized sampling value of two phasors, which is added, is equal to third phasor
Synchronized sampling value, and be suitable for addition of vectors operation.
Phasor product of the present invention has the characteristics of works judge failure phase and selection method to lie also in: the route selection criterion is suitable for
The network system of neutral point resistor ground connection.
Phasor product of the present invention has the characteristics of works judge failure phase and selection method to lie also in: setting phasorAnd phasor
Phasor product it is active be WE1*F1, phasorAnd phasorPhasor product it is active be WE2*F2；
If WE1*F1≥WE2*F2, then have:
Or:
n1For the number of samples of greater than half cycle period, uE1(ti)、uF1(ti)、uE2(ti) and uF2(ti) be respectively WithIn tiThe sampled value at moment.
Compared with the prior art, the invention has the advantages that:
1, the phasor product that the present invention creates has works to judge failure phase and line selection apparatus, qualitatively judges failure phase and route selection,
Rather than rational judgment, it is no longer rely on and accurately calculates the implementation judgement of each failure amount, accurately calculated without Fourier transformation etc.
Therefore failure amount has cast aside the transient process changeable for being difficult to capture rule, excluded many and diverse Temporal Data and gone judgement event
Barrier phase and route selection, to realize absolutely accuracy rate.
2, the present invention proposes that phasor product has works, and algorithm simply only has arithmetical operation, in the time of half of cycle integral multiple
The average value of two phasor sampled value products, low to sample frequency requirement, the functional requirement of CPU is small.
3, the present invention proposes that phasor product has works, and two phasor angles, which are that acute angle is active, to be positive, and angle, which is that obtuse angle is active, is
It is negative, referring to phasor it is arranged according to the phase range that failure phasor is fallen into, keeps the angle referring to phasor and failure phasor any
In the case of all keep acute angle, provide reliable guarantee to qualitatively judge failure phase and route selection.
4, the active judgement failure of phasor product of the present invention mutually gives various features criterion, and a variety of criterions are mutually authenticated, effectively
Ground has ensured judgement failure phase of the invention absolutely accuracy, has captured the technical problem that failure is mutually difficult to accurate judgement.
5, the active route selection of phasor product of the present invention provides three kinds of characteristic criterions, and three kinds of criterions are mutually authenticated, and effectively ensures
Route selection of the present invention absolutely accuracy, has captured the technical problem of route selection.
6, the invention proposes the algorithms of phase voltage equipotential sampled value after a failure, select to mention for reference phasor of the invention
Basic condition is supplied, and equipotential sampling value-based algorithm of the invention is suitable for all vectors.
7, the sampled value of line voltage of the present invention directly subtracts each other acquisition by the sampled value of phase voltage, is vector sum, difference sampling
The calculating of value provides new method.
Detailed description of the invention
Fig. 1 is each phasor relation schematic diagram of single-phase earthing；
Fig. 2 is single-phase earthing blow-out moment schematic diagram；
Figure label:WithRespectively leading phase phase voltage, lag phase phase voltage and failure phase phase voltage, WithRespectively advanced phase-to-ground voltage, advanced phase-to-ground voltage, failure phase-to-ground voltage and neutral point electricity
Pressure, Q, H, G and O distinguish leading phase, lag phase, failure phase, neutral point symbol, θ be single-phase earthing when failure phase phase voltage
With neutral point voltageAngle,WithRespectively leading phase, lag phase, the line voltage of failure phase, ICiIt is
The capacitance current of i outlet,For the capacitance current of faulty line.
Specific embodiment
Phasor product has that works judge failure phase and selection method is in the present embodiment:
PhasorFunction expression uE(t) are as follows: uE(t)=Ksin (ω t+ α), phasorFunction expression uF(t)
Are as follows: uF(t)=Psin (ω t+ alpha+beta), K and P are respectively phasorAnd phasorMould, α and alpha+beta are respectively phasorAnd phase
AmountPhase angle, β is phasorAnd phasorAngle；
By phasorAnd phasorPhasor productIt is denoted asPhasor productPhasor product active be denoted as WE*F, phasor productFunction expression be denoted as g (t)；
WE*F=KPcos β
G (t)=WE*F-KPsin(2ωt+2α+β)
Phasor productPeriod be phasorAnd phasorHalf, therefore phasorAnd phasorHalf of cycle
It is phasor productOne cycle, so half of cycle or in half of cycle integral multiple time:
Therefore
Phasor productThe active W of phasor productE*FSampling algorithm characterized by formula (1.1):
uE(ti)、uF(ti) and g (ti) it is respectively phasorPhasorAnd phasor productIn tiThe synchronized sampling value at moment, n
For phasorAnd phasorHalf of cycle or half of cycle integral multiple number of samples, n is natural number not less than 2；
The criterion characterized by formula (1.2) is obtained according to formula (1.1):
It is active according to formula (1.1) calculating phasor product, according to formula (1.2) further according to the active size of phasor product and positive negative judgement
Phase relation between phasor, the judgement and route selection of failure phase when realizing single-phase earthing.
PhasorAngle β be acute angle when, active bigger, the phasor that is positive of the smaller phasor product of βAngle β be
When obtuse angle, β closer to 180 ° of phasor products it is active be negative it is bigger with regard to absolute value.The active judgement failure of phasor product is utilized in specific implementation
When mutually with route selection, phasor is generally usedAngle β be that acute angle is implemented, it is simple in this way convenient for analyzing.
The present invention proposes that phasor product has works, and algorithm simply only has arithmetical operation, two in the time of half of cycle integral multiple
The average value of a phasor sampled value product, low to sample frequency requirement, the functional requirement of CPU is small.
In specific implementation, for the network system with m outlet, when singlephase earth fault occurs for network system:
WithWithThe phase voltage of leading phase, lag phase and failure phase is respectively indicated, and willWithIt is fixed
Justice is one group of three-phase symmetrical referring to phasor；
WithWithIt respectively indicates advanced Relative fault phase, lag opposite leading phase and failure relatively lags behind phase
Line voltage, and willWithIt is defined as another group of three-phase symmetrical reference phasor, it willRoute selection is defined as referring to phase
Amount；
WithWithThe phase-to-ground voltage of leading phase, lag phase and failure phase is respectively indicated, withIndicate neutral
Point voltage, willWithWithIt is defined as failure phasor；
θ indicates phasorAnd phasorAngle；
WithIndicate that the capacitance current of i-th outlet, i=1,2 ..., m, m are the natural number not less than 1, withIndicate event
Hinder the capacitance current of route,WithFor failure phasor, then there are relational expression (2.1):
One group of three-phase symmetrical is constructed referring to phasorWithThree-phase symmetrical is referring to phasorWithIt is super
Three-phase phase voltageWithPhase beIt willAny value in (- 30 °, 60 °) section；Or it willBy formula
(2.1) and formula (2.2) tracks neutral point voltageDynamic value, makesWithAngle be acute angle and minimum；
Referring to Fig. 1, when single-phase earthing occurs, with the increase of impedance ground, θ is also increased with it,In advancePhase
Reduce therewith,In advancePhaseBetween -30 °~60 °, under metallic earthing,In advancePhaseIt is 60 °, when
When impedance ground infinity,In advancePhaseIt is -30 °.
In specific embodiment,Any value between -30 °~60 °, we can incite somebody to actionBest value be 15 °, therefore
When barrier point falls in any point on failure locus of points semicircle,Three-phase symmetrical with building is referring to phasorWithIn
'sAngle is both less than 45 °, most beneficial forThe active maximum of phasor product.
Certainly it can also allowTrack neutral point voltageDynamic value, such as Fig. 1,According to
Formula (2.2), then:In advanceIn this wayWithAngle be acute angle and close
0, then,Phasor product it is active more prominent, be more advantageous to failure and mutually judge.
One group of three-phase symmetrical is constructed referring to phasorWithThree-phase symmetrical is referring to phasorWithIt is super
Three-phase phase voltageWithPhase beIt willAny value in (- 30.5 °, 59.5 °) section；Or it willNeutral point voltage is tracked by formula (2.1) and formula (2.3)Dynamic value, makesWithAngle be acute angle and minimum；
Have in Δ OQJ referring to Fig. 1:
Formula (2.3) are derived by formula (2.3.1)~(2.3.3)
It is calculated by formula (2.3):In advancePhase between -3 °~30 °,Best value be 13.5 °, therefore
Barrier point falls in any point on failure locus of points semicircle,Three-phase symmetrical with building is referring to phasorWithInAngle is both less than 16.5 °, most beneficial forThe active maximum of phasor product.
Certainly it can also allowTrack neutral point voltageDynamic value, makesWithAngle be acute angle and close to 0,
So,Phasor product it is active more prominent, be more advantageous to failure and mutually judge.
A route selection is constructed referring to phasorReferring to phasorIn advancePhase isIt willIn (0 °, 90 °) section
In any value；Or it willNeutral point voltage is tracked by formula (2.1) and formula (2.4)Dynamic value, makesWithAngle
For acute angle and minimum；
Referring to Fig. 1,In advance90 °~180 ° of phase, the capacitance current of faulty lineLag90 ° of phase,It is super
Before0~90 ° of phase,Best value be 45 ° so thatWithAngle be acute angle under various Groundings,Phasor product it is active be allIn it is active maximum and be positive.
Certainly it can also allowTrack neutral point voltageDynamic value,Make
?WithAngle be acute angle and close to 0, then,Phasor product it is active be allIn it is active maximum and be
Just.
For realizing the phasor product for thering are works to judge failure phase are as follows: failure phasor multiplies with failure phasor, or is failure phasor
It is multiplied with three-phase symmetrical referring to phasor；
For realizing the phasor product for having works route selection are as follows: the capacitance current of every outlet is multiplied with route selection referring to phasor, or
The capacitance current of every outlet is multiplied with failure phase-to-ground voltage；
It is if the angle referring to phasor and failure phasor is obtuse angle, i.e., contrary with failure phasor referring to phasor, then
Phasor product referring to phasor and failure phasor is active for negative value maximum.
If A phase is failure phase in system, C phase is leading phase, and B phase is lag phase；If B phase is failure phase, A in system
It is mutually leading phase, C phase is lag phase；If system C phase is failure phase, B phase is leading phase, and A phase is lag phase.
The present invention proposes that phasor product has works, and two phasor angles, which are that acute angle is active, to be positive, and angle, which is that obtuse angle is active, to be negative,
Referring to phasor it is arranged according to the phase range that failure phasor is fallen into, makes any situation of angle referring to phasor and failure phasor
Under all keep acute angle, provide reliable guarantee to qualitatively judge failure phase and route selection.
The phasor product that the present invention creates has works to judge failure phase and line selection apparatus, qualitatively judges failure phase and route selection, and
It is not rational judgment, is no longer rely on and accurately calculates the implementation judgement of each failure amount, accurately calculate event without Fourier transformation etc.
Therefore barrier amount has cast aside the transient process changeable for being difficult to capture rule, has excluded many and diverse Temporal Data and gone to judge failure
Phase and route selection, to realize absolutely accuracy rate.
In specific implementation, G phase singlephase earth fault occurs for system, carries out failure by following any criterion and mutually judges:
Criterion 1: failure phasor is multiplied with failure phasor, it may be assumed that willRespectively withWithIt is multiplied, obtains WithWherein,Phasor product it is active maximum and be positive；
Referring to Fig. 1, no matter impedance ground is much, and fault point is all fallen on failure locus of points semicircle, in addition to metallic earthing,WithAngle is less thanWithAngle, andMould be greater thanMould, thereforePhasor product active be greater thanPhasor product it is active, it is equal both when metallic earthing；With90 ° of angle, soWithPhasor product have
Function is 0, soWith leading phasePhasor product it is active maximum and be positive.
Criterion 2: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willRespectively withWithIt is multiplied,
It obtainsWithWherein,Phasor product it is active maximum and be positive；
Referring to Fig. 1, no matter impedance ground is much, and fault point is all fallen on failure locus of points semicircle,In advancePhase
Between -30 °~60 °, the two angle is always that acute angle is up to 60 °, and when metallic earthing is 60 °, and other situations are both less than
60 °,Phasor product active be positive；In advancePhase is between 60 °~150 °, and metallic earthing is 60 °, other feelings
Condition is both greater than 60 °,WithMould is identical,Phasor product active be greater thanPhasor product it is active；WithAngle
At 90 °~180 °,Phasor product it is active be negative value.Therefore,Phasor product it is active maximum and be positive.
Criterion 3: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willRespectively withWithPhase
Multiply, obtainsWithWherein,Phasor product it is active maximum and be positive；
Referring to Fig. 1, no matter impedance ground is much, and fault point is all fallen on failure locus of points semicircle,In advancePhase
Between -60 °~30 °, the two angle is always that acute angle is up to 60 °, and when metallic earthing is 30 °, and other situations are both less than
60 °,Phasor product active be positive；In advanceFor phase between 90 °~180 °, metallic earthing is 90 °, other
Situation is both greater than 90 °,Phasor product it is active be negative value；WithAngle at 60 °~150 °,WithFolder
Angle is consistently greater than 60 °,Phasor product active be consistently less thanPhasor product it is active.Therefore,Phasor product
It is active maximum and be positive.
Criterion 4: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed thatWithRespectively with same famous prime minister's WithIt is multiplied, obtains:WithWherein,Phasor product it is active maximum and be positive；
Referring to Fig. 1, no matter impedance ground is much, and fault point is all fallen on failure locus of points semicircle,And it is same
Under impedance groundWithAngle is less thanWithAngle, so And under same impedance groundWithAngle is small
InWithAngle, so Phasor product it is active；Therefore,Phasor product
It is active maximum and be positive.
Criterion 5: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willWithRespectively with same famous prime minister
's WithIt is multiplied, obtainsWithWherein,The active maximum of phasor product
And it is positive；
Referring to Fig. 1, no matter impedance ground is much, and fault point is all fallen on failure locus of points semicircle,And it is same
Under impedance groundWithAngle is less thanWithAngle, so Therefore,Phasor product it is active maximum and be positive.
Criterion 6: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willRespectively withWithPhase
Multiply, obtain:WithWhereinPhasor product it is active maximum and be positive；
WithIt is one group of three-phase symmetrical of building referring to phasor, three-phase symmetrical is referring to phasorWithAdvanced three-phase phase voltageWithPhase beIt willAny value in (- 30 °, 60 °) section；Or it willNeutral point voltage is tracked by formula (2.1) and formula (2.2)Dynamic value, makesWithAngle be acute angle and minimum.
Referring to Fig. 1,In advancePhase between -30 °~60 °,Best value be 15 °, fault point falls in failure
Any point on locus of points semicircle,Three-phase symmetrical with building is referring to phasorWithInAngle is all small
In 45 °, most beneficial forThe active maximum of phasor product.
Certainly it can also allowTrack neutral point voltageDynamic value,In advanceMakeWithAngle be acute angle and close to 0, then,Phasor product have
Function is more prominent, is more advantageous to failure and mutually judges.
Criterion 7: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willWithRespectively with same famous prime minister
's WithIt is multiplied, obtains:WithWherein,Phasor product it is active maximum and
It is positive；WithIt is one group of three-phase symmetrical of building referring to phasor, the three-phase symmetrical is referring to phasorWithIn advance and three-phase phase voltageWithPhase beIt willIt is arbitrarily taken in (- 30.5 °, 59.5 °) section
Value；Or it willNeutral point voltage is tracked by formula (2.1) and formula (2.3)Dynamic value, makesWithAngle be acute angle and
It is minimum.
Referring to Fig. 1,In advancePhase between -3 °~30 °,Best value be 13.5 °, fault point fall in therefore
Hinder any point on locus of points semicircle,Three-phase symmetrical with building is referring to phasorWithInAngle is all
Less than 16.5 °, most beneficial forThe active maximum of phasor product.
Certainly it can also allowTrack neutral point voltageDynamic value, makesWithAngle be acute angle and close to 0,
So,Phasor product it is active more prominent, be more advantageous to failure and mutually judge.
For intermittent arc grounding, the criterion of failure phase of the present invention is still effective, and has higher accuracy:
Referring to fig. 2, the intermittent single-phase earthing of power frequency blow-out, at the blow-out moment,It is vertical with Y-axis,'sMaximum,WithIt is equidirectional i.e. with positive and negative, while being positive or be simultaneously negative value；The blow-out moment After blow-out,It is equal to the value at blow-out moment, leading phase phase-to-ground voltage for a constant value Until next fault point arc light is restriked,WithWith just
It is negative, then Phasor product active be still positive most
Greatly.
For the single-phase earthing of high-frequency extinguishing arc, high-frequency extinguishing arc moment and power frequency blow-out moment have the memory of same voltage special
Sign:WithIt is equidirectional i.e. with positive and negative, while being positive or be simultaneously negative value, therefore not influencing the accurate of this judgement not only
Property, also improve the accuracy of this judgement.
One feature of any of the above may determine that failure phase, can also two or two features above judge failure together
Phase.
The various features criterion that the active judgement failure of phasor product of the present invention mutually provides, a variety of criterions can be mutually authenticated, have
It has ensured to power judgement failure phase of the invention absolutely accuracy, has captured the technology hardly possible that failure is mutually difficult to accurate judgement
Topic.
In specific implementation, G phase singlephase earth fault, the capacitance current I of j-th strip non-fault line occurs for systemCjBy
Formula (3.1) is characterized:
The capacitance current of faulty lineIt is characterized by formula (3.2)
XCFor system capacitance to earth, the capacitance current of non-fault lineWith faulty line capacitance currentPhase difference be
180 °, faulty line capacitance currentWith failure phase-to-ground voltageSame-phase simultaneously lags neutral point voltage90 ° of phase,
WithIt is ahead of failure phase phase voltageBetween 0~90 °.
Failure line selection is carried out by any route selection criterion of following criterion one to criterion three:
Criterion one: failure phasor and route selection are multiplied referring to phasor, and it is active to obtain phasor product, it may be assumed that by every outletWithIt is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active maximum and is positive
Value.
Referring to Fig. 1, the capacitance current of faulty lineIn advanceAngle at -30 °~60 °, the two angle less than 60 °,
And non-faulting phase capacitance currentWith iC180 ° of phase difference,Phasor product it is active be positive,In it is active be negative, because
This,Phasor product it is active be allIn it is active maximum and be positive.
Criterion two: it failure phasor is multiplied failure phasor and failure phasor and with route selection referring to phasor obtains phasor product
It is active:
IfFailure phasor is multiplied with failure phasor and obtains that phasor product is active, every outletWith
It is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active maximum and is positive value；
IfWhen, failure phasor and route selection are multiplied referring to phasor, and it is active to obtain phasor product, it may be assumed that goes out every
LineWithIt is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active most
It greatly and is positive value；
Although the capacitance current of faulty line and failure phase-to-ground voltage same-phase, when metallic earthingIt connects
When nearly metallic earthingAlso very little, transient process are easy to produce adverse effect, are unfavorable for the active value of phasor product, therefore
Criterion settingThe single-phase earthing close to metallic earthing is avoided, failure phasor is multiplied with failure phasor, and every goes out
LineWithIt is multiplied,Phasor product it is active be allIn it is active maximum and be positive；For being connect close to metallicity
The single-phase earthing on ground, i.e.,When, then every outletWithIt is multiplied,Phasor product it is active be allIn it is active maximum and be positive.
Criterion three: failure phasor and route selection are multiplied referring to phasor, and it is active to obtain phasor product, it may be assumed that by every outletWithIt is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active maximum and is positive
Value.
Referring to Fig. 1,In advance90 °~180 ° of phase, the capacitance current of faulty lineLag90 ° of phase,It is super
Before0~90 ° of phase,Best value be 45 ° so thatWithAngle be acute angle under various Groundings,Phasor product it is active be allIn it is active maximum and be positive.
Certainly it can also allowTrack neutral point voltageDynamic value,Make
?WithAngle be acute angle and close to 0, then,Phasor product it is active be allIn it is active maximum and be
Just.
It is if the angle referring to phasor and failure phasor is obtuse angle, i.e., contrary with failure phasor referring to phasor, then
Phasor product referring to phasor and failure phasor is active for negative value maximum.
One feature of any of the above may determine that failure phase, can also two or two features above judge failure together
Phase.
The active route selection of phasor product of the present invention provides three kinds of characteristic criterions, and three kinds of criterions can be mutually authenticated, effectively ensure
Route selection of the present invention absolutely accuracy, has captured the technical problem of route selection.
In specific implementation, for example, by t1Moment phasorWithSampled value be denoted as a (t respectively1) and b (t1), if phasor
For phasorAnd phasorThe sum of, phasorFor phasorAnd phasorDifference, then t1Moment phasorSampled value c (t1) and phase
AmountSampled value d (τ) be respectively as follows:
Therefore, when G phase single-phase earthing occurs for system, the phase voltage sampled value of three-phase is obtained by following any way:
Mode one: leading phase phase voltageLag phase phase voltageWith failure phase phase voltageSampled value be equal to it is of the same name
The sampled value of the phase-to-ground voltage of phase subtracts the synchronized sampling value of neutral point voltage, is characterized by formula (5.1)；
Mode two: being measured using voltage transformer, carries out sampling acquisition for the secondary side voltage of voltage transformer
Phase voltage sampled value, the primary side isolated neutral of voltage transformer.
The isolated neutral of three voltage transformers, voltage transformer secondary side output is phase voltage, rather than phase
Single-phase earthing occurs for voltage-to-ground, system, and voltage transformer secondary side voltage output will not change, and not have transient state mistake
Journey.
Mode three: leading phase phase voltageLag phase phase voltageWith failure phase phase voltageSampled value, according to three
Equipotential sampled value of the phase-to-ground voltage before singlephase earth fault obtains, and equipotential sampled value refers to:
Implement sampling for the AC signal f (t) that the period is T, the AC signal f (t) when system is operated normally is denoted as
f1(t), by tτAC signal f (t) after moment system jam is denoted as f2(t), f1(t) t after the failure occurred2Moment adopts
Sample value f1(t2), and have:
K is not less than 1 natural number, f1(t1) it is f1(t2) the equipotential sampled value before failure, then:
f1(t2)=f1(t1) (5.3)
F (t) is in t2The fault increment at moment:
Δf(t2)=f2(t2)-f1(t2) (5.4)
Indicate the phase-to-ground voltage of system, with f (t) with f1(t) phase voltage of system is indicatedWithWith f2(t)
The phase-to-ground voltage of system after expression single-phase earthingWithF (t)=f when system operates normally1(t), single-phase earthing
F (t)=f afterwards2(t)。
The invention proposes the algorithms of phase voltage equipotential sampled value after a failure, provide for of the invention referring to phasor selection
Basic condition, and equipotential sampling value-based algorithm of the invention is suitable for all vectors.
The sampled value of system line voltage is to subtract each other acquisition by the synchronized sampling value of two phase voltages；Or system line voltage is adopted
Sample value is to subtract each other acquisition by the synchronized sampling value of two phase-to-ground voltages, and system line voltage refers to advanced phases line voltage in systemLag phases line voltageWith failure phases line voltage
In specific implementation, according to formula (5.1.1), the opposite leading phase of advanced Relative fault phase, lag and failure relatively lag behind
The line voltage of phaseWithSampled value obtained by following any way:
First way: according to formula (2.1),WithSampled value respectively by leading phase, lag mutually and therefore
Hinder the phase voltage of phaseWithSynchronized sampling value subtract each other acquisition；
The second way: according to formula (6.1),WithSampled value respectively by leading phase, lag mutually and therefore
Hinder the voltage-to-ground of phaseWithSynchronized sampling value subtract each other acquisition；
The difference of two phasors is equal to third phasor, then the synchronized sampling value of two phasors is subtracted each other equal to third phasor
Synchronized sampling value, and be suitable for vector additive operation.
In specific implementation, the sampled value of neutral point voltage is the synchronized sampling value according to formula (2.1) by three phase-to-ground voltages
It is added and obtains, or converted and obtained by the sampled value of voltage transformer open delta voltage；
The sum of two phasors are equal to third phasor, then the synchronized sampling value of two phasors, which is added, is equal to third phasor
Synchronized sampling value, and be suitable for addition of vectors operation.
The sampled value of line voltage of the present invention directly subtracts each other acquisition by the sampled value of phase voltage, is vector sum, poor sampled value
Calculating provide new method.
Phasor product of the present invention has works to judge that the route selection criterion in failure phase and selection method is suitable for neutral point resistor
The network system of ground connection.
When neutral point resistor is grounded single-phase earthing the electric current that generates substantially with faulted phase voltage same-phase, the electric current with
After capacitance current superposition, phase angular advance faulted phase voltage so not influencing the accuracy of route selection criterion of the present invention, and is helped
In the accuracy of route selection.
But the network system of neutral point grounding through arc, with the change of system operation mode, an arc suppression coil can
There can be two kinds of operating statuses of overcompensation and undercompensation, undercompensation is not on influencing route selection criterion accuracy of the invention, but overcompensation
Influence accuracy of the invention, it is necessary to the present invention is modified, arc suppression coil weakens the zero-sequence current of faulty line in a word,
Its may be made minimum, had an adverse effect to route selection.
When system G phase stable state is grounded, failure phase-to-ground voltageLag neutral point voltage90 ° of phase, the two is vertical,
So failure phase-to-ground voltageAnd neutral point voltageIt is multiplied, obtainsActive be equal to 0.
In specific implementation, if phasorAnd phasorPhasor product it is active be WE1*F1, phasorAnd phasorPhase
Active amount product is WE2*F2；If WE1*F1≥WE2*F2, then the accumulated value for having more than the phasor product of half of cycle also meets:
Or, the average value more than half of cycle equally also meets:
n1For the number of samples of greater than half cycle period, uE1(ti)、uF1(ti)、uE2(ti) and uF2(ti) be respectively WithIn tiThe sampled value at moment.
Formula (9.1) in practical applications, directly substitutes the active reality of phasor product with the accumulated value that phasor product is more than half of cycle
It applies and compares, it is possible to reduce calculate, be conducive to quickly judge failure.
Claims (9)
1. phasor product has works to judge failure phase and selection method, it is characterized in that:
PhasorFunction expression uE(t) are as follows: uE(t)=Ksin (ω t+ α),
PhasorFunction expression uF(t) are as follows: uF(t)=Psin (ω t+ alpha+beta),
K and P is respectively phasorAnd phasorMould, α and alpha+beta are respectively phasorAnd phasorPhase angle, β is phasorAnd phasorAngle；
By phasorAnd phasorPhasor productIt is denoted asPhasor productPhasor product active be denoted as WE*F, phasor productLetter
Number expression formula is denoted as g (t)；
WE*F=KPcos β
G (t)=WE*F-KPsin(2ωt+2α+β)
Phasor productThe active W of phasor productE*FSampling algorithm characterized by formula (1.1):
uE(ti)、uF(ti) and g (ti) it is respectively phasorPhasorAnd phasor productIn tiThe synchronized sampling value at moment, n are phase
AmountAnd phasorHalf of cycle or half of cycle integral multiple number of samples, n is natural number not less than 2；
The criterion characterized by formula (1.2) is obtained according to formula (1.1):
It is active according to formula (1.1) calculating phasor product, according to formula (1.2) further according to the active size of phasor product and positive negative judgement phasor
Between phase relation, realize single-phase earthing when failure phase judgement and route selection.
2. phasor product according to claim 1 has works to judge failure phase and selection method, it is characterized in that:
For the network system with m outlet, when singlephase earth fault occurs for the network system,
WithWithThe phase voltage of leading phase, lag phase and failure phase is respectively indicated, and will be describedWithDefinition
It is one group of three-phase symmetrical referring to phasor；
WithWithIt respectively indicates advanced Relative fault phase, lag opposite leading phase and failure relatively lags behind the line of phase
Voltage, and will be describedWithIt is defined as another group of three-phase symmetrical reference phasor, it will be describedIt is defined as route selection ginseng
Photograph amount；
WithWithThe phase-to-ground voltage of leading phase, lag phase and failure phase is respectively indicated, withIndicate neutral point electricity
Pressure will be describedWithWithIt is defined as failure phasor；
θ indicates phasorAnd phasorAngle；
WithIndicate that the capacitance current of i-th outlet, i=1,2 ..., m, m are the natural number not less than 1, withIndicate failure
The capacitance current of route,WithFor failure phasor, then there are relational expression (2.1):
One group of three-phase symmetrical is constructed referring to phasorWithThe three-phase symmetrical is referring to phasorWithIt is super
Three-phase phase voltageWithPhase beIt willAny value in (- 30 °, 60 °) section；Or it willBy formula
(2.1) and formula (2.2) tracks neutral point voltageDynamic value, makesWithAngle be acute angle and minimum；
One group of three-phase symmetrical is constructed referring to phasorWithThe three-phase symmetrical is referring to phasorWithIt is super
Three-phase phase voltageWithPhase beIt willAny value in (- 30.5 °, 59.5 °) section；Or it will
Neutral point voltage is tracked by formula (2.1) and formula (2.3)Dynamic value, makesWithAngle be acute angle and minimum；
A route selection is constructed referring to phasorThe reference phasorIn advancePhase isIt willIn (0 °, 90 °) section
In any value；Or it willNeutral point voltage is tracked by formula (2.1) and formula (2.4)Dynamic value, makesWithAngle be
Acute angle and minimum；
For realizing the phasor product for thering are works to judge failure phase are as follows: failure phasor multiplies with failure phasor, or is failure phasor and three
It is symmetrical to be multiplied referring to phasor；
For realizing the phasor product for having works route selection are as follows: the capacitance current of every outlet is multiplied with route selection referring to phasor or every
The capacitance current of outlet is multiplied with failure phase-to-ground voltage.
3. phasor product according to claim 2 has works to judge failure phase and selection method, it is characterized in that:
G phase singlephase earth fault occurs for system, carries out failure by following any criterion and mutually judges:
Criterion 1: failure phasor is multiplied with failure phasor, it may be assumed that willRespectively withWithIt is multiplied, obtains WithWherein,Phasor product it is active maximum and be positive；
Criterion 2: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willRespectively withWithIt is multiplied, obtainsWithWherein,Phasor product it is active maximum and be positive；
Criterion 3: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willRespectively withWithIt is multiplied, obtains
?WithWherein,Phasor product it is active maximum and be positive；
Criterion 4: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed thatWithRespectively with same famous prime minister's
WithIt is multiplied, obtains:WithWherein,Phasor product it is active maximum and be positive；
Criterion 5: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willWithRespectively with same famous prime minister's WithIt is multiplied, obtainsWithWherein,Phasor product it is active maximum and be
Just；
Criterion 6: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willRespectively withWithIt is multiplied, obtains
:WithWhereinPhasor product it is active maximum and be positive；
Criterion 7: failure phasor is multiplied with three-phase symmetrical referring to phasor, it may be assumed that willWithRespectively with same famous prime minister's WithIt is multiplied, obtains:WithWherein,Phasor product it is active maximum and be
Just.
4. phasor product according to claim 2 has works to judge failure phase and selection method, it is characterized in that:
G phase singlephase earth fault occurs for system, carries out failure choosing by any route selection criterion of following criterion one to criterion three
Line:
Criterion one: failure phasor and route selection are multiplied referring to phasor, and it is active to obtain phasor product, it may be assumed that by every outletWith
It is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active maximum and is positive value；
Criterion two: being multiplied referring to phasor by failure phasor and failure phasor and by failure phasor with route selection obtains phasor product and has
Function:
IfFailure phasor is multiplied with failure phasor and obtains that phasor product is active, every outletWithIt is multiplied
It obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active maximum and is positive value；
IfWhen, failure phasor and route selection are multiplied referring to phasor, and it is active to obtain phasor product, it may be assumed that by every outletWithIt is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product it is active maximum and
For positive value；
Criterion three: failure phasor and route selection are multiplied referring to phasor, and it is active to obtain phasor product, it may be assumed that by every outletWith
It is multiplied and obtainsThe phasor product of faulty line is activeIt is allMiddle phasor product is active maximum and is positive value.
5. phasor product according to claim 2 has works to judge failure phase and selection method, it is characterized in that:
When G phase single-phase earthing occurs for system, the phase voltage sampled value of three-phase is obtained by following any way:
Mode one: leading phase phase voltageLag phase phase voltageWith failure phase phase voltageSampled value be equal to famous prime minister's
The sampled value of phase-to-ground voltage subtracts the synchronized sampling value of neutral point voltage, is characterized by formula (5.1)；
Mode two: being measured using voltage transformer, carries out sampling acquisition for the secondary side voltage of the voltage transformer
Phase voltage sampled value, the primary side isolated neutral of the voltage transformer.
Mode three: leading phase phase voltageLag phase phase voltageWith failure phase phase voltageSampled value, according to three relatively
Equipotential sampled value of the voltage before singlephase earth fault obtains, and the equipotential sampled value refers to:
Implement sampling for the AC signal f (t) that the period is T, the AC signal f (t) when system is operated normally is denoted as f1(t),
By tτAC signal f (t) after moment system jam is denoted as f2(t), f1(t) t after the failure occurred2The sampled value f at moment1
(t2), and have:
K is not less than 1 natural number, f1(t1) it is f1(t2) the equipotential sampled value before failure, then:
f1(t2)=f1(t1) (5.3)
F (t) is in t2The fault increment at moment:
Δf(t2)=f2(t2)-f1(t2) (5.4)
Indicate the phase-to-ground voltage of system, with f (t) with f1(t) phase voltage of system is indicatedWithWith f2(t) indicate single
The phase-to-ground voltage of system after being mutually groundedWithF (t)=f when system operates normally1(t), f (t) after single-phase earthing
=f2(t)。
6. phasor product according to claim 2 has works to judge failure phase and selection method, it is characterized in that:
Advanced Relative fault phase lags opposite leading phase and failure relatively lags behind the line voltage of phaseWithSampling
Value is obtained by following any way:
First way: according to formula (2.1),WithSampled value respectively by leading phase, lag mutually and failure phase
Phase voltageWithSynchronized sampling value subtract each other acquisition；
The second way: according to formula (6.1),WithSampled value respectively by leading phase, lag mutually and failure phase
Voltage-to-groundWithSynchronized sampling value subtract each other acquisition；
The difference of two phasors is equal to third phasor, then the synchronized sampling value of two phasors is subtracted each other same equal to third phasor
Sampled value is walked, and is suitable for vector additive operation.
7. phasor product according to claim 2 has works to judge failure phase and selection method, it is characterized in that: neutral point voltage
Sampled value be according to formula (2.1) by three phase-to-ground voltages synchronized sampling value be added obtain, or by voltage transformer opening three
The sampled value of angle voltage, which converts, to be obtained；
The sum of two phasors are equal to third phasor, then the synchronized sampling value of two phasors, which is added, is equal to the same of third phasor
Sampled value is walked, and is suitable for addition of vectors operation.
8. phasor product according to claim 4 has works to judge failure phase and selection method, it is characterized in that: the route selection is sentenced
According to the network system for being suitable for neutral point resistor ground connection.
9. phasor product according to claim 1 has works to judge failure phase and selection method, it is characterized in that: setting phasor
And phasorPhasor product it is active be WE1*F1, phasorAnd phasorPhasor product it is active be WE2*F2；
If WE1*F1≥WE2*F2, then have:
Or:
n1For the number of samples of greater than half cycle period, uE1(ti)、uF1(ti)、uE2(ti) and uF2(ti) be respectively WithIn tiThe sampled value at moment.
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Application publication date: 20190614 Assignee: HEFEI YIXIN ELECTRIC POWER TECHNOLOGY Co.,Ltd. Assignor: Zhang Anbin Contract record no.: X2021340000010 Denomination of invention: Fault phase identification and line selection by phasor product power method Granted publication date: 20201211 License type: Common License Record date: 20210525 |
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