CN106483428A - A kind of IEC61850 substandard traveling wave fault detection and localization method - Google Patents

A kind of IEC61850 substandard traveling wave fault detection and localization method Download PDF

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Publication number
CN106483428A
CN106483428A CN201610965055.5A CN201610965055A CN106483428A CN 106483428 A CN106483428 A CN 106483428A CN 201610965055 A CN201610965055 A CN 201610965055A CN 106483428 A CN106483428 A CN 106483428A
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signal
iec61850
fault
travelling wave
substandard
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彭熹
梁勇超
潘飞来
李龙
谢培元
崔卓
侯备
刘烁
李俊堂
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State Grid Corp of China SGCC
State Grid Hunan Electric Power Co Ltd
Maintenance Co of State Grid Hunan Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Hunan Electric Power Co Ltd
Maintenance Co of State Grid Hunan Electric Power Co Ltd
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Priority to CN201610965055.5A priority Critical patent/CN106483428A/en
Publication of CN106483428A publication Critical patent/CN106483428A/en
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08Locating faults in cables, transmission lines, or networks
    • G01R31/081Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/086Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution networks, i.e. with interconnected conductors
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08Locating faults in cables, transmission lines, or networks
    • G01R31/088Aspects of digital computing
    • YGENERAL 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
    • Y04INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04SSYSTEMS 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
    • Y04S10/00Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
    • Y04S10/52Outage or fault management, e.g. fault detection or location

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Theoretical Computer Science (AREA)
  • Locating Faults (AREA)

Abstract

The invention discloses a kind of IEC61850 substandard traveling wave fault detection and localization method, implementation steps include:1) build IEC61850 substandard Travelling Wave Fault Location system model;2) travelling wave signal is gathered by described Travelling Wave Fault Location system model;3) travelling wave signal is carried out pretreatment;4) wavelet transformation is carried out to the signal obtaining after pretreatment and ask for modulus maximum, find out singular point position;5), after obtaining singular point position, fault distance is calculated by the opposite polarity spike position of two in waveform.The present invention has the advantages that alternating current-direct current fault alternating current-direct current fault is accurately reliable, fault location is accurate, safety and reliability is high, extensibility good.

Description

A kind of IEC61850 substandard traveling wave fault detection and localization method
Technical field
The present invention relates to the traveling wave fault detection of intelligent substation of electric power system with location technology and in particular to one kind The detection of IEC61850 substandard traveling wave fault and localization method.
Background technology
The scale of modern power systems is increasing, the electric pressure more and more higher of transmission line of electricity, and length is more and more longer, defeated Environment residing for electric line is also more complicated, and the probability therefore breaking down and number of times also inevitably roll up.For This problem, travelling wave ranging is maximally effective solution.The key technology point of Algorithms of Travelling Wave Based Fault Location is accurately to detect traveling wave Wave head time point.This algorithm, compared to impedance method, has and is difficult to be tied by system transition resistance, line short type, circuit Structure, voltage current transformer saturation etc. affect, and only in the velocity of wave of transmission line of electricity and reach the wave head time at bus with traveling wave Relevant.
In order to adapt to digital transformer substation and future substation automated system demand for development, in traveling wave fault location system In realize IEC61850 communication standard, the interoperability between intelligent electronic device in lifting transformer station that can be very big.It is expert at Realize IEC61850 communication standard in ripple fault location system, can be very big lifting they between interoperability, permissible Adapt to digital transformer substation and future substation automated system demand for development.One of feature of IEC61850 standard is exactly to use Object oriented designing thought, carries out unified Modeling to whole system.Therefore, according to IEC61850 standard to traveling wave harvester Carry out data modeling and function modeling, be the necessary requirement realizing this standard.
The detection of transmission line malfunction and positioning, have been proposed that multiple methods both at home and abroad now.In early days, impedance method is conventional Fault detect and localization method, that is, by measure impedance calculate fault distance.But the method is hindered by transition resistance, system Anti- asymmetric the problems such as, affects larger, is therefore gradually replaced by traveling wave method.Traveling wave method is not subject to trouble point transition resistance, line construction Etc. the impact of factor, range accuracy is high, applied widely.Traditional both-end traveling wave positioning is carried out based on a circuit, only The initial wave head reaching circuit two ends traveling wave need to be caught, do not affected by various echos and refracted wave, principle is relatively easy.But It is based on the Fault Locating Method of single bar circuit, time precision to be had high demands, under adverse circumstances, position error is likely to be breached 150 meters.Comparatively, network failure traveling wave positioning can utilize adjacent lines data, realizes accurately detecting 5300 km electric power Various classification faults on circuit.Additionally, around traveling wave method, having derived some other innovatory algorithm, including based on neutral net With the algorithm based on network path.Additionally, wavelet technique and morphology are also gradually applied in fault detection and location algorithm.
Content of the invention
The technical problem to be solved in the present invention:For the problems referred to above of prior art, a kind of alternating current-direct current fault is provided to hand over straight The substandard traveling wave of IEC61850 that stream fault is accurately reliable, fault location is accurate, safety and reliability is high, extensibility is good Fault detection and location method.
In order to solve above-mentioned technical problem, the technical solution used in the present invention is:
A kind of IEC61850 substandard traveling wave fault detection and localization method, implementation steps include:
1) build IEC61850 substandard Travelling Wave Fault Location system model;
2) travelling wave signal is gathered by described Travelling Wave Fault Location system model;
3) travelling wave signal is carried out pretreatment;
4) wavelet transformation is carried out to the signal obtaining after pretreatment and ask for modulus maximum, find out singular point position;
5), after obtaining singular point position, fault is calculated by the opposite polarity spike position of two in waveform Distance.
Preferably, step 1) in IEC61850 substandard Travelling Wave Fault Location system model from bottom to up successively include count According to collection terminal, server end, the client three-decker positioned at grid dispatching center, described data acquisition end Real-time Collection electrical network Traveling wave data and send server end to, described server end by the data collecting according to IEC61850 modeling method will Collection terminal be decomposed into corresponding logical node and and each logical node complete the data object that a certain concrete function needs, patrol Collect data exchange and process between node object, and described server end is entered to data collection terminal using IEC61850 modeling technique Row modeling, thus obtaining the OO information model data flow chart of data terminal, and modeling data is passed through IEC61850 agreement passes through the client to grid dispatching center for the network transmission after being packaged.
Preferably, step 3) in travelling wave signal is carried out pretreatment detailed step include:
3.1) travelling wave signal of each frame band being made an uproar asks discrete Fourier transform;
3.2) it is directed to the result signal calculated prior weight of discrete Fourier transform;
3.3) spectrum gain function is calculated according to signal prior weight;
3.4) enhanced signal frame is calculated according to spectrum gain function.
Preferably, step 3.1) in ask shown in the function expression such as formula (1) of discrete Fourier transform;
Y (m, k)=S (m, k)+N (m, k) (1)
In formula (1), Y (m, k) represents that m frame band travelling wave signal of making an uproar seeks the result of discrete Fourier transform, and S (m, k) represents The Fourier transformation of useful signal, N (m, k) represents the Fourier transformation of noise signal, and k represents frequency.
Preferably, step 3.2) in signal calculated prior weight function expression such as formula (2) shown in;
In formula (2), SNRprio(m, k) represents that m frame band is made an uproar travelling wave signal corresponding signal prior weight, and α is less than 1 Invariant,Represent the m-1 frame pure traveling wave power spectrum estimated,Represent the m frame noise work(estimated Rate is composed, SNRpost(m, k) represents posteriori SNR, posteriori SNR SNRpostShown in the function expression of (m, k) such as formula (3);
In formula (3), Y (m, k) represents that m frame band is made an uproar the Fourier transformation of travelling wave signal,Represent the noise estimated The Fourier transformation of signal.
Preferably, step 3.3) calculate shown in the function expression such as formula (4) composing gain function;
In formula (4), G (m, k) expression m frame band is made an uproar, and travelling wave signal is corresponding to compose gain function value, SNRprio(m, k) represents M frame band is made an uproar travelling wave signal corresponding signal prior weight.
Preferably, step 3.4) calculate enhanced signal frame function expression such as formula (5) shown in;
In formula (5),Represent that m frame band is made an uproar the corresponding enhanced signal frame of travelling wave signal, G (m, k) represents m Frame band is made an uproar travelling wave signal corresponding spectrum gain function value, and Y (m, k) represents that m frame band is made an uproar the Fourier transformation of travelling wave signal.
Preferably, step 5) calculate fault distance function expression such as formula (6) shown in;
XL=v Δ t/2 (6)
In formula (6), XLRepresent fault distance, Δ t represent from trouble point travel to rectification side m point initial wavefront and The again Distance Time between the wave head that trouble point reflects after the reflection of m bus, v represents wave velocity.
IEC61850 of the present invention substandard traveling wave fault detection is had with localization method and has the advantage that:
1st, the present invention builds IEC61850 substandard Travelling Wave Fault Location system model, by described Travelling Wave Fault Location System model gathers travelling wave signal, travelling wave signal is carried out pretreatment, carries out wavelet transformation to the signal obtaining after pretreatment and ask Delivery maximum, finds out singular point position, after obtaining singular point position, by two opposite polarity spikes in waveform Pulse position calculates fault distance, by carrying out pretreatment to travelling wave signal, can improve the accuracy of detection of fault-signal, The safety and reliability of raising system, have that alternating current-direct current fault alternating current-direct current fault is accurately reliable, fault location accurately, safety The advantage high with reliability.
2nd, the inventive method detection efficiency is high, and can be combined process with other algorithms, thus being applied to various distribution networks Or in other related application, have the advantages that extensibility is good.
Brief description
Fig. 1 is the basic procedure schematic diagram of present invention method.
Fig. 2 is the Travelling Wave Fault Location system model schematic diagram in the embodiment of the present invention.
Fig. 3 is the noise reduction comparison schematic diagram of present invention method.
Fig. 4 is the positioning precision comparison schematic diagram of present invention method.
Specific embodiment
As shown in figure 1, the implementation steps bag of the detection of the present embodiment IEC61850 substandard traveling wave fault and localization method Include:
1) build IEC61850 substandard Travelling Wave Fault Location system model;
2) travelling wave signal is gathered by described Travelling Wave Fault Location system model;
3) travelling wave signal is carried out pretreatment;
4) wavelet transformation is carried out to the signal obtaining after pretreatment and ask for modulus maximum, find out singular point position;
5), after obtaining singular point position, fault is calculated by the opposite polarity spike position of two in waveform Distance.
The detection of the present embodiment IEC61850 substandard traveling wave fault and localization method pass through to build under IEC61850 standard Travelling Wave Fault Location system model, by described Travelling Wave Fault Location system model gather travelling wave signal, travelling wave signal is entered Row pretreatment, carries out wavelet transformation to the signal obtaining after pretreatment and asks for modulus maximum, finds out singular point position, obtains Behind singular point position, fault distance is calculated by the opposite polarity spike position of two in waveform, by row Ripple signal carries out pretreatment, can improve the accuracy of detection of fault-signal, improves the safety and reliability of system, has friendship straight The advantage that stream fault alternating current-direct current fault is accurately reliable, fault location is accurate, safety and reliability is high;And, the present embodiment The detection of IEC61850 substandard traveling wave fault is high with localization method detection efficiency, and can be combined process with other algorithms, thus It is applied in various distribution networks or other related application, have the advantages that extensibility is good.
As shown in Fig. 2 step 1) in IEC61850 substandard Travelling Wave Fault Location system model wrap successively from bottom to up Include data acquisition end, server end, the client three-decker positioned at grid dispatching center, described data acquisition end Real-time Collection The traveling wave data of electrical network simultaneously sends server end to, described server end by the data collecting according to IEC61850 modeling side Method by collection terminal be decomposed into corresponding logical node and and each logical node complete the data pair that a certain concrete function needs As, data exchange and process between logical node object, and described server end adopted to data using IEC61850 modeling technique Collection end is modeled, thus obtaining the OO information model data flow chart of data terminal, and modeling data is passed through IEC61850 agreement passes through the client to grid dispatching center for the network transmission after being packaged.Referring to Fig. 2, Travelling Wave Fault Location System model is divided into three layers:The bottom is data acquisition end, and major function is Real-time Collection traveling wave data, then passes this data Give server end;The second layer is server end, and the data collecting is packaged by IEC61850 agreement, carries out network Transmission.This layer can also carry out Business Processing and drives terminal;Third layer is in the client of grid dispatching center, main realization Analysis to data, and fault message is positioned and finds range.For whole model, client is the pass of fault location Key, directly affects the precision of fault location.And server end is responsible for pretreatment and is collected traveling wave data, it is the core of whole model The heart.Server end carries out functional analyses, and the modeling method according to IEC61850 using Target-oriented thought to data collection terminal Collection terminal is decomposed into corresponding logical node, and and each logical node complete the data pair that a certain concrete function needs As data exchange and process between logical node object.Additionally, server end utilizes IEC61850 modeling technique to data acquisition End is modeled, thus obtaining the OO information model data flow chart of data terminal.
In the present embodiment, step 3) in travelling wave signal is carried out pretreatment detailed step include:
3.1) travelling wave signal of each frame band being made an uproar asks discrete Fourier transform;
3.2) it is directed to the result signal calculated prior weight of discrete Fourier transform;
3.3) spectrum gain function is calculated according to signal prior weight;
3.4) enhanced signal frame is calculated according to spectrum gain function.
In the present embodiment, step 3.1) in ask shown in the function expression such as formula (1) of discrete Fourier transform;
Y (m, k)=S (m, k)+N (m, k) (1)
In formula (1), Y (m, k) represents that m frame band travelling wave signal of making an uproar seeks the result of discrete Fourier transform, and S (m, k) represents The Fourier transformation of useful signal, N (m, k) represents the Fourier transformation of noise signal, and k represents frequency.
In the present embodiment, step 3.2) in signal calculated prior weight function expression such as formula (2) shown in;
In formula (2), SNRprio(m, k) represents that m frame band is made an uproar travelling wave signal corresponding signal prior weight, and α is less than 1 Invariant (typically taking 0.98),Represent the m-1 frame pure traveling wave power spectrum estimated,Show estimation M frame noise power spectrum, SNRpost(m, k) represents posteriori SNR, posteriori SNR SNRpostThe function expression of (m, k) is such as Shown in formula (3);
In formula (3), Y (m, k) represents that m frame band is made an uproar the Fourier transformation of travelling wave signal,Represent the noise estimated The Fourier transformation of signal.
In the present embodiment, step 3.3) calculate shown in the function expression such as formula (4) composing gain function;
In formula (4), G (m, k) expression m frame band is made an uproar, and travelling wave signal is corresponding to compose gain function value, SNRprio(m, k) represents M frame band is made an uproar travelling wave signal corresponding signal prior weight.
In the present embodiment, step 3.4) calculate shown in the function expression such as formula (5) of enhanced signal frame;
In formula (5),Represent that m frame band is made an uproar the corresponding enhanced signal frame of travelling wave signal, G (m, k) represents m Frame band is made an uproar travelling wave signal corresponding spectrum gain function value, and Y (m, k) represents that m frame band is made an uproar the Fourier transformation of travelling wave signal.
In the present embodiment, step 5) calculate shown in the function expression such as formula (6) of fault distance;
XL=v Δ t/2 (6)
In formula (6), XLRepresent fault distance, Δ t represent from trouble point travel to rectification side m point initial wavefront and The again Distance Time between the wave head that trouble point reflects after the reflection of m bus, v represents wave velocity (numerical value is 300m/ μ s).
Property for traveling wave fault detection substandard to the present embodiment IEC61850 and the preprocess method of localization method Can be detected, by the preprocess method of the detection of substandard for the present embodiment IEC61850 traveling wave fault and localization method and tradition Noise reduction under -10dB noise intensity for the wavelet filtering method.Referring to Fig. 3, obtain noisy signal by purified signal plus after making an uproar, By noisy signal respectively by traditional wavelet filtering method, the detection of the present embodiment IEC61850 substandard traveling wave fault and positioning The preprocess method of method carries out preprocessor, the waveform that " wavelet filtering " of in figure obtains for wavelet filtering method, " proposes to calculate Method " is the waveform that the substandard traveling wave fault of the present embodiment IEC61850 detects that the preprocess method with localization method obtains, by Figure contrast understands, what effect is the wavelet filtering method traditional in low signal-to-noise ratio almost do not have, and signal is submerged in white noise completely In, do not see the conversion of signal.And the pretreatment of the detection of the present embodiment IEC61850 substandard traveling wave fault and localization method Method in the case of low signal-to-noise ratio, still it can be seen that signal at 0.7 second mutation.
For traveling wave fault detection substandard to the present embodiment IEC61850 and the performance of localization method, detected, It is respectively provided with the fault under the interference of varying strength at different distance, and by substandard for the present embodiment IEC61850 traveling wave fault Detection has carried out positioning precision ratio with localization method and traditional wavelet method (wavelet filtering method), smoothing techniques (smothing filtering method) Relatively.Understand, with the reduction of signal to noise ratio, the fault location precision of three kinds of methods all constantly reduces referring to Fig. 4;From three kinds of methods Algorithm angle changing rate, the detection of the present embodiment IEC61850 substandard traveling wave fault is best with the effect of localization method, wavelet method Take second place, smoothing techniques are worst.But, with the rising of signal to noise ratio, the difference of three kinds of algorithms gradually decreases.Therefore contrast understands, this The detection of embodiment IEC61850 substandard traveling wave fault has preferable row with localization method in the case of Low SNR signal Ripple fault detection and location degree of accuracy.
The above is only the preferred embodiment of the present invention, and protection scope of the present invention is not limited merely to above-mentioned enforcement Example, all technical schemes belonging under thinking of the present invention belong to protection scope of the present invention.It should be pointed out that for the art Those of ordinary skill for, some improvements and modifications without departing from the principles of the present invention, these improvements and modifications Should be regarded as protection scope of the present invention.

Claims (8)

1. a kind of detection of IEC61850 substandard traveling wave fault with localization method it is characterised in that implementation steps include:
1) build IEC61850 substandard Travelling Wave Fault Location system model;
2) travelling wave signal is gathered by described Travelling Wave Fault Location system model;
3) travelling wave signal is carried out pretreatment;
4) wavelet transformation is carried out to the signal obtaining after pretreatment and ask for modulus maximum, find out singular point position;
5) obtain singular point position after, by the opposite polarity spike position of two in waveform calculate fault away from From.
2. the detection of IEC61850 according to claim 1 substandard traveling wave fault with localization method it is characterised in that step In rapid 1), IEC61850 substandard Travelling Wave Fault Location system model includes data acquisition end, server from bottom to up successively End, the client three-decker positioned at grid dispatching center, the traveling wave data of described data acquisition end Real-time Collection electrical network simultaneously passes Give server end, it is right that collection terminal is decomposed into by described server end by the data collecting according to the modeling method of IEC61850 The logical node answered and and each logical node complete the data object that a certain concrete function needs, between logical node object Data exchange and process, and described server end is modeled to data collection terminal using IEC61850 modeling technique, thus obtaining Fetch data the OO information model data flow chart at end, and modeling data is packaged by IEC61850 agreement Pass through the client to grid dispatching center for the network transmission afterwards.
3. the detection of IEC61850 according to claim 1 substandard traveling wave fault with localization method it is characterised in that step The detailed step in rapid 3), travelling wave signal being carried out pretreatment includes:
3.1) travelling wave signal of each frame band being made an uproar asks discrete Fourier transform;
3.2) it is directed to the result signal calculated prior weight of discrete Fourier transform;
3.3) spectrum gain function is calculated according to signal prior weight;
3.4) enhanced signal frame is calculated according to spectrum gain function.
4. the detection of IEC61850 according to claim 3 substandard traveling wave fault with localization method it is characterised in that step Ask in rapid 3.1) shown in the function expression such as formula (1) of discrete Fourier transform;
Y (m, k)=S (m, k)+N (m, k) (1)
In formula (1), Y (m, k) represents that m frame band travelling wave signal of making an uproar seeks the result of discrete Fourier transform, and S (m, k) represents useful The Fourier transformation of signal, N (m, k) represents the Fourier transformation of noise signal, and k represents frequency.
5. the detection of IEC61850 according to claim 3 substandard traveling wave fault with localization method it is characterised in that step In rapid 3.2) shown in the function expression of signal calculated prior weight such as formula (2);
SNR p r i o ( m , k ) = α · S 2 ^ ( m - 1 , k ) N 2 ^ ( m , k ) + ( 1 - α ) · m a x ( SNR p o s t ( m , k ) - 1 , 0 ) - - - ( 2 )
In formula (2), SNRprio(m, k) represents that m frame band is made an uproar travelling wave signal corresponding signal prior weight, and α is normal less than 1 The number factor,Represent the m-1 frame pure traveling wave power spectrum estimated,Represent the m frame noise power estimated Spectrum, SNRpost(m, k) represents posteriori SNR, posteriori SNR SNRpostShown in the function expression of (m, k) such as formula (3);
SNR p o s t ( m , k ) = | Y ( m , k ) | 2 | N ^ ( m , k ) | 2 - - - ( 3 )
In formula (3), Y (m, k) represents that m frame band is made an uproar the Fourier transformation of travelling wave signal,Represent the noise signal estimated Fourier transformation.
6. the detection of IEC61850 according to claim 3 substandard traveling wave fault with localization method it is characterised in that step Rapid 3.3) calculate shown in the function expression such as formula (4) of spectrum gain function;
G ( m , k ) = SNR p r i o ( m , k ) 1 + SNR p r i o ( m , k ) - - - ( 4 )
In formula (4), G (m, k) expression m frame band is made an uproar, and travelling wave signal is corresponding to compose gain function value, SNRprio(m, k) represents m frame Band is made an uproar travelling wave signal corresponding signal prior weight.
7. the detection of IEC61850 according to claim 3 substandard traveling wave fault with localization method it is characterised in that step Rapid 3.4) calculate shown in the function expression such as formula (5) of enhanced signal frame;
S ^ ( m , k ) = G ( m , k ) · Y ( m , k ) - - - ( 5 )
In formula (5),Represent that m frame band is made an uproar the corresponding enhanced signal frame of travelling wave signal, G (m, k) represents m frame band Travelling wave signal of making an uproar corresponding spectrum gain function value, Y (m, k) represents that m frame band is made an uproar the Fourier transformation of travelling wave signal.
8. the detection of the substandard traveling wave fault of the IEC61850 according to any one in claim 1~7 and localization method, It is characterized in that, step 5) calculate fault distance function expression such as formula (6) shown in;
XL=v △ t/2 (6)
In formula (6), XLRepresent fault distance, △ t represents and travels to the initial wavefront of rectification side m point and in m mother from trouble point The again Distance Time between the wave head that trouble point reflects after line reflection, v represents wave velocity.
CN201610965055.5A 2016-11-04 2016-11-04 A kind of IEC61850 substandard traveling wave fault detection and localization method Pending CN106483428A (en)

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