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Three terminal line protection based on asuperimposed component impedance relay

J.S. Daniel, PhDR.K. Aggarwal, PhD, MlEEA.T. Johns, PhD, FIEE

Indexing erms: Line protection, Impdance relay, Teed feeder. T rip time

~~ ~~

Abstract: The paper presents the application of anew impedance relaying principle to a Teed feeder.The relay design is immune from false trippingowing to power swings or prefault load condi-tions. This has been achieved by ext racting andusing prefault and superimposed components ofrelaying voltages and currents. Results are pre-sented for earth faults on a Teed feeder configu-ration. Relay trip t ime is typically in the range 11to 20ms and is plotted as a surface against pre-fault power angle and fault point on wave angle.

List of symbols

q x ) = line inductancer = relay reach distanceR x )= line resistanceR, = fault resistancet, = fault inception timet, = time at which relay is triggeredx = fault distanceZ o = zero phase sequence line impedance2 = positive phase sequence line impedanceZ, =positive phase sequence source impedance at

Z,, = positive phase sequence impedance of feeder PTZ,, = Thevenin equivalent source impedance at busbar

Z,, = Thevenin equivalent source impedance at Tee

busbar P

P

point

1 Introduction

Teed feeders present difficult protection problems [l],but can offer considerable economic advantages over twoended alternatives. Three protection methods exist.

1.1 Using di stance relaysProblems exist in protecting the region around the Teepoint, since, if relay reaches are set to cover this point,there can be a risk of overreaching past a remote busbar.

IEE, 1993Paper 9597C Pll), 6m.t received 2nd February 1993J.S. Daniel is with the Department of Elcdrical and Electronic Engin-

eering, University of Newcastle upon Tyne, Tyne and Wear NE1 7RU,United KingdomR.K. ggarwal and A.T. Johns arc with the Powex and Energy SyuemsGroup, School of Elearonic and Electrical Engineering, Un im it y ofBath, Claverton Down, Bath BA2 7AY, United Kingdom

IEE PROCEEDINGS-C, Vol. 140, No.6. NOVEMBER 1993

The technique cannot therefore be used on all Teedfeeder configurations.

1 2 Using differential protectionThis is feasible, but often requires fibreoptic or micro-wave communication links to achieve acceptable oper-ating times [2].

1.3 Using di rectionalproteetionThis offers a reasonably cheap solution, since convention-al power line carrier signalling can be &. Consider-ation needs to be given to coordinating relay sensitivities[3], but the major problem is the Yeed around effcct [2],which causes internal faults to be seen incorrectly asexternal to the Tee. In configurations such as Fig. 1 for

h 2 C WW

Fig. 1 Teed fadn co&uration

example, a directional relay at R would detect an internalfault on PT as external for fault distances up to at least

40 km from P. Hence under these conditions, any di rectional scheme would fail, despite the relays at P and Qcorrectly detecting the fault. The problem regions aresmaller when large source capacities are present (e.g. ifthe source capacity at P is increased to 20 GVA. a faulton PT up to 20 km from P would be seen as external bythe relay at R).

The gaps in the protection characteristic of the direc-tional scheme can be filled by adding extra relays with addined reach at each end, and intertripping if an in-zonefault is detected. If the signals are to be derived from con-ventional CTs and CVTs, measurement of the power fmquency impedances is the only feasible relaying principle.A stable reach characteristic is also desirable, since insome cases over half the feeder length to the Tee pointneeds to be protected, and, using the largest safe reachsetting, maximises fault resistance coverage.

Practical impedance measuring algorithms can showsignificant unwanted dependence on fault point on waveand prefault power flow. Under abnormal operating con-ditions (i.e. power swings) distance relays can producefalse trips [4], which are usually inhibitW by the scheme

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logic, which requires additional relays to detect the con-ditions. The more logical alternative of restraining thetrip within the originating relay, is achieved as follows.

(i) A reach algorithm is used to test whether the faultlies within a nondirectional protection characteristic.

(ii) A validity check ensures that large prefault currentsdo not prevent unambiguous determination of an in-zonefault (i.e. the trip characteristic shrinks during abnormalsystem conditions to prevent false tripping).

iii) A directional check ensures directionality.(iv) A third test is necessary to distinguish between

phase and earth faults.

2 Singl e phase relay princ iple

2.1 Reach algorithmIn a faulted single phase circuit shown in Fig. 2 4 thevoltage U and current i at a relay are assumed to berelated (in the time domain) by an equation such as

U = z(x)i R , if = 44 R x) i R , i (1)rThe inductance 44 esistance R x), and thereforeimpedance z(x) are all functions of the fault distance x. Ifthe quantities in Fig. 24 are considered as the s u m ofsteady state (Fig. 26) and superimposed quantities (Fig.a), qn. 1 becomes

(2)

(In Fig. 26 and Fig. 2c, the Thevenin equivalent imped-ance of the source side network terminating in busba r Phas been substituted. ) Also

0 = 0, + %p ( x b z(X)Ci, S ,C) R , if

e,=O t < t , (3)

e = -sI(x) t 2 , (4)

The superimposed components uaUp,is. re functions ofthe fault distance (x), whereas the prefault componentsare ndependent of it. A relay principle may be derived byconstructing and comparing estimates of the magnitudesof the steady-state fault point voltage and superimposedvoltage source [i.e. Isl(x) and Ie I]. Since the fault dis-tance x is not known, estimates are formed using thereach r (the distance to the far end of the protectionzone). Estimates s ) and sz r, x) are constructed:

(5)

(6)The variable sl r) is used in eqn. 5 to emphasise both thedependence of the estimate on reach setting and theequality of the estimate with sI(x) in Fig, 26 for r = x).The estimate s2 r,x) .will not, in general, equal the nega-tive of the fault point superimposed voltage source, (i.e.# -e,) owing to an unknown fault resistance term. Thetwo arguments emphasise the dependence of the estimateon both fault position and reach setting.

With reference to Fig. 26 and Fig. 2 he actu al valuesof fault point voltage componen ts are given in the follow-ing equations:

s,(x) = us (x)i,, (7)

e, = (x)i, p(x) - R , if (8)

e = -sz r, x) [z r )- (x)]i,&x) - R ,i,

(9)

e = -Isl r) Cz d tx)Ii,) (10)

sl r) = U, (r)i,

x) = -Usu&X) z(rPs&)

Substituting for uss&x) rom eqn. 6 gives

Using qns. 4,s. 7 givesI

448

Hence

sZ@ 4 = l(r) Cz(r) - (x)lCi, +bi..p(x)l R,i, (11)It can be Seen that, if the fault resistance term R, isneglected, the estimates sl(r) and s2 r, x) are equal when

P-

tRf

a

b

C

Fig. 2 I n t e r n o f f i ra toul quantiliab steady-suk quantitigE supaimpoled quantitk.

the fault is at the reach point. The reach algorithm uses aquantity e + x) which is defined:

ed*ff(r> x) = I 4 S l W I (12)

A trip condition may be defined:(13)

(i.e. if the magnitude of the superimposed voltage sourceestimate exceeds that of prefault estimate, a fault isinferred to be within the protected zone and a trip deci-sion is required).

2 2 External fault analysisFor an external fault, the technique of splitting the totalquantities network (Fig. 3 4 into steady state (Fig. 36)and superimposed (Fig. 3c) networks has been used again(with substitution of the Thevenin equivalent of thesystem to the right of the Tee point). When a fault m u mbehind the relay, the superimposed voltage and currentare related as follows (with reference to Fig. 3 4 :

This may be contrasted with the forward fault case (Fig.24, in which

if e,,&, x) > 0 then x < r : rip required

%,(X) = (ZPT + ZSTPmp(X)

u..p(x) = - SP mp(x)

(14)

(15)

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where arg [S2 r, x ) ] is the superimposed quantities esti-mate of the phase angle of the prefault voltage phasor atthe reach point. Hence an assumption can be made forthe angle of the prefault voltage phasor at the fault pointfrom superimposed quantities. If this assumption and cri-terion (i) are satisfied, Appendix 8.1 shows that a phasorcondition equivalent to criteria ii) and (iii) also beingsatisfied is

where S3 r, x ) is the phasor quantity corresponding o thefollowing time domain discriminant :

(20)Eqn. 19 shows that the phase angle between two(assumed) sinusoids can be used to determine whether toinhibit tripping br ovide d criterion (i) is satisfied]. Thecheck depends on the ra tio of fault to prefault currentmagnitudes, and is almost independent of reach setting.

2.7 Fault directi on checkIt is intended that the relay will be triggered by a direc-tional relay so that the signals it is presented with arealways consistent with a fault in front of the relay.However, checking that this is actually true, and inhibit-ing tripping if it is not, has two benefits:

(i) There will be no possibility of a false trip owing to a

closer reverse fault occurring after the relay has startedmeasuring.

ii) Tripping is inhibited for some out-of-zone faults forwhich the reach algorithm and validity checks are satis-fied, but cr iter ion (i) is not.

The terms in the phasor versions of eqns. 14, 15 satisfythe following relation:

s , x ) = z(r)Ci, sup(x)l

are ( Z S d = arg ( Z m Z S T = arg [ Z ( r l l (21)

s4(r* x ) = z(r)kp(x) (22)

Hence if a fourth time domain discriminant is defined:

A directional criterion may then be d e w which onlyforward faults satisfy):

- < arg [ 4(r, )S, r, x) ] < (23)2 2This is a reformulation of the directional criterion usedby Lanz et ql. [ S I in terms of the angle between two(assumed) sinusoids .

3 Three phase relay prin cip le

3.1 Reach algorithmThe extension of the single phase principle to three phasecircuits requires six relaying elements: three phase faultelements and three earth fault elements. A phase faultelement uses time domain quantities such as (U. - b)and(i,, - s), and an earth fault element use9 a phase voltageand a z ero sequence compensated phase current, e.g. forthe a phase:

(24)i,, + b ,

3i = ,, I2 - )io io =

3 2 E f f e c t sof power flowWhen the prefault power angle is large, problems canoccur owing to encroachments between relaying elements

450

(i.e. tripping of an earth fault element when a phase faultexists). Criterion (i) is not satisfied when a fault occurswhich does not correspond to the type of the detectingelement, yet cr iterion (i) is assumed in deriving the valid-ity check, which as a result is satisfied over an inapprop-riate range of prefault power angle (e.g. over the range- 20 < 8 c 60 , ather than -90 < < 90 ). Henceif the reach algorithm for the a-e element reached a falsepositive decision for an a 4 ault at a prefault powerangle within the range 60 < 8 < 90 . he a+ validitycheck would not restrain the relay and a false trip would

occur.

3.3 Phase selection checkEncroachment problems may be avoided if the earth faultdetectors are disabled when a phase fault is present.(Encroachments do not occur for earth faults.) If the timedomain discriminants for phase fault elements (e.g. s 3are scaled as follows, direct comparison of the magni-tudes of sl. and s m allow a-e and a-b faults to be distin-guished :

If eithe r of the following conditions are met, an k b ora-c fault is inferred t o be present, and tripping by the a-efault element should be inhibited :

I ~ 1 . I - I ~ ~ 1 < 0S 1 . l - i S z r . I < O (26)

These conditions are a consequence of the different ratiosof positive to negative sequence fault curren t for phasefaults as against earth faults. For double phase to earthand three phase faults, discrimination is less definite but,essentially, f a fault needs to be tripped by the a-e faultelement, neither con dition will be met.

4 Implementation

The implementations of the a lgorithms operate withinput signals which are either derived from simulationstudies or are pure power frequency sinusoids, but it ismuch easier to demons trate the motivation behind thedesigns assuming the latter .

Either phase or magnitude criteria may be used tocompare sinusoids. Magnitude comparison is used in the

design, owing to the difficulty of assessing the phase of asuperimposed component. The relay is triggered by thedirectional relay at the same end, so hat measurement isstarted only once a fault in front of the relay has beendetected. (Since the minimum operating time of the direc -tional relay is known, a bound is set on the latest pos-sible time of fault incidence.)

4.1 Initial signal processingThe relay is designed to use conventional CVTs and CTs.The CT urden is a transactor which provides phase shiftat power frequency and reduction of offset (for voltageminimum faults). Sampling for both voltages and cur-rents is carried out at a 2 kHz rate (in a 50 Hz system),and these are then converted into a digital form via a 12bit A D convertor. Low pass filtering (to attenua te trav-elling wave components) is applied using running averagefilters [6] and superimposed components are extractedusing a delay of one power frequency period as shown inFig. .

The time domain discriminants s1 and s2 are con-structed according to eqns. 5 and 6. Remultiplication of

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currents by the term z r) is avoided by defining

ki = z r)i (27)

Where i is proportional to the voltage developed by thecurrent i in the CT burden and mimic impedance z r),

one cycledelay

su

Fig. 6 Superimposed exnrrrionfilter

and k is a scalar factor proportional to the reach setting.Introducing delay between (digital) voltage and currentsignals will modify the phase of phasor Z r).

4 2 Magnitude cornperisonAn accurate estimate of a sinusoid 's magnitude may beachieved more quickly if a version of the signal delay bya quarter peiod is available. This may be seen by com-paring Fourier expansions of lsin ot)l and[sin o t ) l + co s (wt)l:

the size and frequency of the seond term, which, in thesecond expansion, is smaller and at a higher frequency(and may therefore be more easily further reduced by lowpass filtering).

If the relaying signals are considered to be power fre-quency sinusoids, an estimate of their magnitudes may beobtained by summing the modulus of a signal and thesame quantity delayed by a quarter of a power frequencyperiod (T/4). To obtain valid pairs of undelayed anddelayed superimposed component signals for magnitudecomparison of each algorithm quantities requires that the

start of measurement be delayed by T/4.

4.3 AlgorithmsIn the block diagram of the reach algorithm implementa-tion shown in Fig. 6a, he signals are bandpass filtered toreduce the effects of the CVT transients. This is not donein Fig. 66, since the accuracy of the validity and direc-tional checks is much less affected by the latter. Theoutput (y) as a function of input(s) (U) or the componentblocks in Fig. 6 is defined:

(30)ate: y = 0, t G t , ; y = U, t >Comparator: y = 0, u2 d U,; y = 1, U, Q u2 (31)

(28) Phase sensitive rectification: y = u2 sgn (U,) (32)2 2n 3 2

sin o t ) l =---cos ( 2 4 . . .

(29)The magnitude is proportional to the first term of eachexpansion, and estimation error is heavily dependent on

filter filter filter

modulus modulus modulus modulus

Fig. 6 Relay d g m th n ua Tc.Ehnlgorifhmb validity chcck

sensitiverectification

phase

rectification

phasesensitive

re cl i f c a l i m

'Q'

phosesensitive

reclif calion

9M - _ _ _ _ _ _ _ _ _ - - - _ _ _ - - - -- - - - -

low pass low passfilter filter

1 2

comporator comparator

or

I I

to counter (inhibit)

b

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The gating ensures that only postfault signals are used.Low pass filtering is used to reduce the ripple on thewaveform. It is essential that the processing of prefaultand superimposed fault voltage estimates be identical, toavoid additional fault point on wave dependency beingin t ro d ud . Equality of the frequency responses at powerfrequency is not a sulTiicient condition, since the fre-quency spectrum corresponding to the sudden applica-tion of a sinusoid in the time domain containscomponents at all frequencies.

Each fault element has a counter, which isincremented when its input is logical 1 (unless inhibitedby a validity or phase selection check). An extensiveseries of tests has indicated that the optimum trip thresh-old is six counts; a smaller number risks relay overreachfor some faults. A larger number can ead to an unneces-sary reduction in relay sensitivity owing to a decision notbeing reached witbin the maximum time allowed by thesuperimposed component extraction filtering character-istic (i.e. 20 ms after fault incidence).

6 Simulation studies

In the following studies, the configuration referred to isFig. 1; the power angle of busb ar R is held equal to thatof busbar P; e faults are simulated on feeder PT with

distances being measured from busbar P; time is mea-sured from fault incidence, and waveforms/characteristicsare those of the a-e element of the re lay at P.

5.1 Typical waveformsFig. 7 shows relay waveforms for a 50 km voltagemaximum solid fault, with a prefault power anglebetween busbar Q and P of 60 which would only occurunder abnormal condition s, but has been chosen to showthe interaction of the validity check and the reachalgorithm). The current signals have been multiplied bythe modulus of the power frequency impedance of a50 km length of transmission line.

In Fig. 7 4 he waveforms show the superimposedcomponents becoming invalid after 20 ms (owing to themethod of extraction). Since the change is not abrupt, itis unnecessary to rigorously exclude invalid signals, andmeasurement is terminated 2 ms after triggering, ratherthan 20 ms after fault incidence. The difference betweendiscriminants si, t is due to error in assumed line imped-ance, hence a relay setting of 65 km s required for trip-ping to occur, rather than the theore tical value (50 km).

Fig. 7e shows that counting would be inhibitedbetween 8 and 11 ms (since i; is greater than kiLup). Asthe power angle is increased above W, this intervalextends and tripping becomes less and less likely (since

0 5 IO I5 20 25 30 35 40

18 r

14 .

0 5 10 15 20 25 30 35 40b

2

,

I -:.. .. ..

IO

50

> Y. .... .. .. 0 '. .... .. .. .. .. .... ... .. ..

.I. ..5 .. ..

-10

-15-20- I

I

0 5 10 15 20 25 30 35 40t ime, ms

d

0

I6 -14 .12 .10.

8 -

6 -

4 -

2 -

C

2 4 6 8 10 12 I4 16 20tirne,ms

eFig. 7 Relay algorithm quantitiesa validity cbkk and Mch ignlla (at L in Fig. 6)b reach point dincrimiaants at M in Fig. 60)

452

c filtercd reach discriminants at N in F i g 60)d a-c ekmcnt checks (at M in Fig. ab)

e filtered kmmt checks (at N n Fig ab)

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measurement is terminated after 20 ms). Hence the trip-ping characteristic of the relay is reduced when abnormalsystem conditions exist.

5 2 Performance characteristi cThe UNIMAP [7] graphics package was used to gener-ate 3D plots of the following quantities against thepower angle between two busbars (Q and P) nd the faultpoint on wave: (i) operating time (which includes thedirectional relay operating time) for a relay setting of80 km (corresponding to the Tee point); ii) the minimum

setting for operation.The latter characteristic is generated by altering relayreach (with the fault position kept constant) until trippingjust occurs. It requires much less computation than theconventional characteristic, in which fault position isaltered (with the relay reach setting held constant). Whenthe minimum reach for operation is less than the faultdistance, either encroachment if the tripping elementdoes not correspond with fault type) or overreaching bythe correct fault element is indicated.

Fig. 8a shows that the minimum reach setting foroperation characteristic for a solid a-e fault at 50 km hasa distinct trend (i.e. it increases with power angle). This isdue to the 'average' value of line impedance being used toset up the relay, which cannot be accurate for all faults inan untransposed system. Since V, and Z I , are typicallyabout 90 out of phase, error arises principally in sl(r).and increases as prefault current magnitude (or powerangle modulus) increases. The truncation of the charac-teristic in Fig. Sa for power angle c - 20 is caused bythe validity check. The spread of conductor impedancesis small enough to ensure that overreaching due to theerror in the assumed impedance would only becomeevident at more negative power angles.

Fig. 86 shows a minimum operating time of 11 ms forvoltage maximum faults, increasing to a maximum of21 ms. Operating time is increased for faults at extreme

aFig. 8 Relay performance evaluationo variation in reach settingb operating lime for 80 hn each settingsolid p-c fault 50 km from P

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power angles (owing to the action of the validity check)and close to voltage minimum, owing to the increasedoperating time of the associated directional relay anderrors caused by the slowly decaying current offset.

5.3 Fault resistanceSince the reach algorithm is nondirectional, themaximum theoretical protection characteristic in thecomplex impedance plane is a circle centred at the origin.The relay approaches this characteristic for fault resist-ance (modelled as linear) GSf2, but significant errors

occur for resistances of the order of 20 Fig. 9a shows adefinite valley for near voltage maximum faults corre-sponding to operation at lower than theoreticalminimum reach settings. (The theoretical minimum reachfor operation for a 20 km, 20 R a-e fault is 72 km.)

When a high fault resistance is present, the rate ofcurrent offset decay and the resultant CT voltage com-ponents are larger and more significant. At most faultpoints on wave, these components increase the magni-tude of the estimate. s, , nd hence decrease the minimumreach for operation. Due to the action of the validitycheck, overreach past a remote busbar for a high resist-ance external fault does not occur, since, despite criterion(i) not being satisfied, tripping is inhibited for extremeprefault power angle cases (where the worst overreachwould occur).

6 Conclusions

The new relay principle improves on the performance ofconventional distance relays under abnormal system con-ditions. This is achieved by extracting additional infor-mation from the relaying signals (i.e. effectively the phaseangle of the prefault voltage at the fault point). Twoassumptions are made in the theory: (i) that fault reis-tance is zero; (ii) that the power system is homogeneous.

b

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p

d

0

Fis. 9a variation in rcach settingb operaling h e or 80 km ru c h setting20 fl M ault 20 km rom P

Relay performancefor II resistiw eorthfrrult

However, studies have shown that performance is notcritically dependent on these being satisfied. The mostsensitive design parameter is the phase shift of the CTtransactor burden a t power frequency. Failure to set thiscorrectly can result in the relay overreaching for faultswhere the prefault current is almost sufficient to cause thevalidity check to inhibit tripping.

Additional advantages of the design are: (i) good faultresistance coverage; (U) the reach characteristic is rela-tively insensitive to fault point on wave and prefaultsystem conditions; (iii) a relatively low sampling rate(2 kHz) is required.

The disadvantages are: (i) it requires triggering by adirectional relay; ii) the operating time is not fast (11-22ms on a 50Hz system); i ) the design is morecomplex than a conventional distance relay.

The design is particularly suited as an independentmode relay in a Teed f aader application, working in con-junction with a directional protection scheme. Its func-tion is then to trip when the directional scheme fails totrip an internal fault (e.g. due to the feed-round effect[2]). The relays advantages then most definitely out-weigh its disadvantages.

7 References

I IEEE Study Committee report on protection aspects of multi-terminal l i . IEEE rcport 79, THOOM2-PWR. 1979

2 AGGAR WAL , R.K., and JOHNS, AT.: he cvelopmmt of a newhigh speed %terminal line protection Ichaac: IEEE Trons., 1986,pwI1D-1, (1). pp. 125-133

3 DANIEL, J.S.: Independent mode protection of three ended powersyatcmd. WD thcsis, Univcmity of Bath, 1991

4 THORP, J.S., PHADKE, A.G., HOROWlTZ S.H., and BEGOVIC,M.M.: Some applications of pharor meadurcments to adaptive pro-tection. IEEE FICA. 1987

5 ENGLER, F., LAN Z O.E., HAENGGLI. M., and BACCHINI, G.:Transient sign& and their proassing in an ultra high s p e d direc-tional d a y for EHV/UHV line protection. IEEE Tram., 1985, PAS104. pp. 163-1473

454

b

6 JOHNS, A.T, M ARTIN, MA., BARKER, A., WALKER, E .P., andCROSSLEY. PA.: A new approach to EHV d imtiond comparisonpmktion usins s i p d Pr-g techniqw,IEEE PWRD1987, pp. 24-34

7 UNIRAS A/S, Gladsaxcvej 376,2860 SBborg, DcnmarL

8 Appendix

8.1 Derivation of validity checkDefining :

z.=dzor(33)

E = S, X, x) S,(x) (34)

The 6rst two terms of the Taylor expansion of Z r )

(35)

(36)

(37)

(Eqn. 34 s a consequence of criter ion (i) being met.)

about the point r = x are

where q = r - . Hence or small q :Z r ) U Z x ) qZ

S2 r, x ) = E @I )Sl r) N E ZI,

Hence substituting in eqn. 17 n Section 2.6:

Assuming that Z is a linear function of the reach r :

Z r ) = r Z (39)

E h c Re { S k ,x)z r)CI, + , )I) (40)Substituting eqns. 18,39 nto eqn. 38 gives

Eqn. 38 is therefore equivalent to eqn. 19.

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