Chapte14 Dist Static Design

8/2/2019 Chapte14 Dist Static Design

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CH AP TER 14 Distance protection: optimum dynamicdesign of static relay comparatorsBYL.JACKSON,J.B.PATRICKSON,ANDL.M. WEDEPOHL.

SYNOPSISThe ease with which transistor comparators for distancerelays can be designed for high-speed operation must betempered with consideration of overall performance andintegrity of operation. Operating speed must be definedover the whole of the working range of the relay, andneither the speed nor the measuring accuracy should beunduly affected by the severe transients generated bymodern e.h.v. networks. The comparator, as well asbeing proof against damag ing voltage surges, m ust oper-ate accurately in the presence of long-duration offsettransients ac centuated by low-loss modern-plant para-meters and the random point-on-wave inception offaults due to natural hazards and closure or reclosure ofmodern pressure-head circuit breakers. The attainmentof high-speed operation under these practical co nditionsprecludes the adoption of many, apparently practicaltransistor-comparator circuits and favours the adoptionof circuits w ith well defined dynamic performances.Extensive laboratory investigation has shown that theblock-average comparison principle is amenable to pre-cise design in all respects, and practical fast-operatingrelays can be designed with good transient-free charac-teristics. The results obtained on such a practical relayare presented in the paper for a phase compa rator with apolarised-mho characteristic. It is shown that aminimum inherent operating time of one halfcycle ofthe power frequency can be defined for this comparatorarrangement and that both the static and dynamicoperating characteristics are predictable over the wholeworking range. Equivalent performance for theamplitude-comp arator counterpart is justified in anappendix, and underlines earlier work.

Relays using the block-average comparison principlehave been used successfully in field trials since 19 57, andthis principle now forms the basis for various productiondesigns. Sufficient field experience is now available tojustify the theoretical analysis and laboratory test resultsgiven in the paper.

LIST OF PRINCIPAL SYMB OLSV1, V2 = input signals to a 2-input relaycomparator4 = phase displacement between Vi and

v2VL = phase-to-phase voltageI, = line currentVsl, Vs2 = level-detector voltage settingsSi = p.u. inp ut 1 related to setting

S2 = p.u. input 2 related to setting204

V,, V, = particular levels of voltage in a leveldetector, corresponding to timeintervals T, and T,, respectivelyV, = polarising voltageT = system periodic timed = phase-comparator angular setting

Z,_ = VL/IL = protected impedance of a section ofpower systemZa = relaying-system impedance setting

INTRODUCTIONUntil a decade ago, relay design was dominated by theuse of electromechanical elements. Such an element, ofwhatever basic characteristic; e.g. square-law inductionelement, has a dynamic behaviour special to that ele-ment, and design freedom is consequently restricted byfactors such as the conflicting requirements of sensitivityand mechanical robustness. The same period saw theemergence of a method for assessing the dynamic per-fomance of different relaying systems by displaying tim-ing contours under practical conditions of switching.5The relative deficiencies of several types of relay couldthus be exposed, and criteria for dynamic performancebe established. Furthermore, it became possible toestablish correlation between operating time, switchedmeasuring accuracy an d overall integrity und er practicaloperating conditions. Over the last ten years, relaysusing transistors have been shown to be practical alter-natives to relays using conventional componentsi andboth phase and amplitude comparators have been usedwith double and multiple inputs. A lthough the relation-ships of geometrical duality between phase- andamplitude-comparators in the steady state are wellestablished,7 the respective dy namic performances havenot been adequately rationalised.The transistor comparator affords great freedom ofdesign for specific laws of operation and/or characteris-tics; this has no counterpart in the electromechanicalrelay, where the basic characteristics are prescribed bythe behaviour of the element itself. This freedom ofdesign embraces both static characteristics and dynamicperformance. Rationalisation beyond elementaryreproduction of conventional dynamic performancebecomes possible, design procedure is clarified, and therelative assessment of comparators operating to differ-ent principles is faciliated.The transformation of input quantities defining iden-tical steady-state operating characteristics using phaseor amplitude comparators is shown below to have


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extended significance in rationalising comparator per-formance, especially in the case of circuits using transis-tors.

DESIGN PRINCIPLES OF TRANSISTOR DIS-TANCE RELAYSBasis for designA transistor relay m ay be designed to have a wide rangeof different characteristics. These include, on the onehand, a close approximation to an electromagneticsquare-law comp arator6 such as the induction cup orbalanced-beam type or, on the other ha nd, a characteris-tic not normally obtainable by conventional means, suchas an inverse relationship between operating time andcompa rator output. Equally, nonlinear timing relation-ships can be obtained. It is, in any case, illogical toemphasise the reproduction of conventional-relaycharacteristics without reconsideration based on thenewly available design freedom using transistors. Bothinverse and inverse-square timing characteristics arise inconventional relays, because they are inherent to theelectro-mechanical elements used and not because theyare necessarily desirable in a functional sense. Repro-duction of existing characteristics in this way can lead tounwarran ted circuit complexity, without leading to tim-ing or other ch aracteristics which are specially suited topower-system protection requirements. From broadconsideration of the protective requirements, it is theauthors opinion (and a view which appears to havemajority support amo ng those engineers intimately con-cerned with protection design and application), that adefinite time characteristic is the most desirable one.

Finally, however, it is necessary to assess a relaydesign beyond the philosophical factors discussedabove. Purely technological design aspects, such aslong-term circuit stability, susceptibility to damag ingtransient surges, economic feasibility and performanceunder nonideal system conditions have influences whichoften redirect design thinking away from the narrowrequirements of the laboratory prototype.

Phase-comparison and amplitude-comparisonNotwithstanding the fact that Ellis x8 established thatthere were no fundamen tal differences between these

two principles, unfounded comparisons have beenmade. For example, Mathews and Nellist presented ananalysis of the differential rectifier-bridge compa ratorand mentioned its inferior transient response relative tothe transistor phase comparator described by Adamsonand W edepohl. In order to clarify this point, it is estab-lished in Appendix 9 that with both a basic phase and anamplitude comparator, each with specified operatingcriteria, the output signals are identical, instant byinstant, provided that the correct input relationshipsspecified by Ellis are observed. Thus, the only way inwhich differences in dynamic performance in the twocases can occu r is if there are differences in the passivenetworks processing the input signals, o r in the circuitsconnected to the comparator output.

Useful characteristics obtained using transistor comparatorsThere is little do ubt that some of the past uncertaintiesconcerning electromechanical relays have resulted fromill-considered attempts to compare the inherent perfor-mance of phase comparators and amplitude com-parators with fundamen tally different output charac-teristics, e.g. a linear moving-coil element comparedwith a square-law induction-cup element. With transis-tor relays, similar misconceptions can arise, and it isimportant to recognise that the numbe r of basically dif-ferent methods of obtaining useful characteristics from acomparator circuit is confined to the following:

(4

Cc)

fc)

Block instantaneous comparison in which theduration of polarity coincidence determines theoutput. The tripping criterion is that the durationof the first coincidence should exceed a specifiedtime, usua lly one quarter of the power-frequencyperiod.Block average com parison, a development of (a),in which the duration of polarity coincidence ismeasured on both halfcycles of the input signals,and the average value is determined in an integ-rating circuit, a trip signal being produced if aspecified average value is maintained for morethan a prescribed duration. The principles of thisform of comparison have already beendescribed.2, 3, IPulse comparison, in which the polarity of onesignal is measured during a short interval in thecycle of the second signal, usu ally, but not neces-sarily, at the latters peak.

Whether a practical transistor comparator in categories(a) or (b) is based on phase or amplitude comparisonhas been shown to be immaterial. To date, practicalcomparators falling into category (c) are of the phase-comparison type only, even though equ ivalent amp-litude versions can be conceived. Thus, the relativemerits of practical comparators of each category areconveniently compared by considering phase-anglecomparators only, in detail. This choice has practicalsignificance in that the inherent characteristics of trans-istors lend themselves most readily to phase-comparatorprinciples.

Fundamental principles of operation of transistor comparator sConsidering phase comparators in the three

categories of Section 2.3, the operating criterion isexpressed in the equation:- d 5 4 2 + d . . . . . . . . . . . . . . . . . . . . . (1 )

where $I is the phase difference between the two inputsignals and a is the phase-angle setting, usually 7r/2. Forthe block comp arators of categories (a) and (b), theoperating limit 0~ may be preset between 0 and 7r to giveoverall characteristics comprising sectors of circles andstraight lines in the complex plane.3, 4 The case of anoperating limit of 7r/2 yields characteristics which com-prise either straight lines or circles. Thus , in the steadystate, there are no basic differences between the threecomparators, but it can be observed that the block-

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comparison principle allows for greater versatility.Consideration of relative dynamic performance dis-closes sharper contrasts, however. Comp arators in the

first and last category are inherently susceptible to sys-tem transients and other spurious signals by virtue oftheir near instantaneous operation., 2 Unless allunwanted surges and transients are effectively removedfrom the signal inputs, their measuring accuracy cannotbe maintained under dynamic conditions without sac-rifice in operating speed. A compromise solution hasbeen proposed* wherein two identical comparators arearranged to compare signals on alternate halfcycles, andtheir outputs are gated so that transient overreach in oneelement is blocked by the other. O ther arrangements usefirst-block-rejection circuits or gap-timing circuits.All such attempts to preserve dynamic measuring accu-racy sacrifice speed of operation, because the form ofcompa rator with which they are associated have noinheren t transient-free charac teristics.The block-average comparator, however, has usefulinherent transient-free characteristics, and it is shown inthe following Sections that a relay can be designed to atheoretical minimum operating time of one half of thepower-frequency period without incurring transientoverreach and without resorting to special filtering cir-cuits in the input signal paths. The operating time is notsignificantly affected by the instant of fault initiation ordegree of the d.c. offset transient in the input signals, andcan be precisely defined following the proceduredescribed in Section 3. Timing over the full workingrange approaches the ideal definite-time characteristic,but as the critical p hase angle d (usually n/2) isapproached, the timing tends to infinity at the bound aryof operation. This controlled timing-characteristic, andthe use of both halfcycles for measuremen t, contributemost significantly to the dynamic accuracy, and contrastswith the other two types of compa rator with their varia-tion in timing depending on the point-on-wave instant offault initiation and the uncontrolled timing characteris-tic at or near the boundary of operation. This latterproperty largely accounts for their poor dynamicmeasuring properties and for their susceptibility tomaloperation resulting from spurious su rges and trans-ient signals; the comparators in categories (a) and (c) areprobably of lowest merit in these respects.

BLOCK AVERAGE COMPARISONSpecification of design r equirementsThe following are the factors of most significance inrelating inherent comparator performance to the con-junctive performance of any practical distance-measuring relay and, as such, they are used as the basisfor specifying the block average system:

(a ) Measuring accuracy: The specified accuracyshould be maintained over the full working range whenmeasured under realistic dynam ic conditions with offsetd.c. transients and other spurious signals superimposedon the input quantities. Long-term stability of measuringaccuracy requires that the compa rator design levels besuch that all vectorial signal mixing shou ld be done in

passive circuits before the signals are compared.(b ) Timing characteristic: The timing characteristicshould be of the definite-minimum type for all faultswithin the protected zone, allowance being made forcontrolled performance in the immediate vicinity of theoperating bounda ry. An operating time of the order of 1cycle of power frequency is considered desirable overthe majority of the practical working range.

(c) Stability: The comparator should have inherentresistance to high-amplitude short-duration system-generated surges, both with regard to maloperation andto surge damage.

It is of fundamen tal importance in developing a soundrelaying philosophy to consider in close detail the inher-ent performance as set out above, bearing in mind thatmodern high-speed relays are required to operate cor-rectly in the presence of long-duration offset d.c. trans-ients. The major part of any discussion on performancemust thus centre on the dynamic response of the relayand on its operating mechanism in the presence of offsetd.c. components, with the clear understanding that thesteady-state response is merely a particular case of thedynamic response. It is on this basis that relays using theprinciple of block-average comparison are at an advan-tage over simpler and/or faster arrangements in whichdesign is based on steady-state considerations only.Basic considerations

Fig. 1 shows a schematic diagram of a basic relay usingthe phase-comparator principle; the definitive eq uations

1 L_ measuring r/2 and r#~7r/2, respectively. It is evident that the output signal fromthe integrator is sawtooth in nature, and that there is aneffective gain in output only for the condition $J < n/2.The rise and fall rates in the integrator are at thedesigners disposal, so that the critical phase angle maybe set to any desired value. Both the level-detector setand reset levels a re critical in relation to the total excur-

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(1)-_____---- ---- __--_-- ----(ii)__- - - - - _ - - - - - - - - - - - - - -

(iii)- - - - - __-- - - - _ - - - - - _

FIG. 2. RELAY WA~ORWS($ 3 42)a Inputi gna l s t o co inc i denc e c i r cu i tb Outpu t f r om co inc i dence c i r cu i t: ( i ) Upper imit (i i) Set level (i i i) Restlevel(' n teg ra to r ou tpu t

sion limits of integrator linearity and also to the slope ofthe output. Considering first the setting, it may be seenthat this should at least exceed a value w hich w ould bereached after one quarter of the system periodic time. Ifthis were not so, the output would switch at twice systemfrequency, even if the displacement between input sign-als was greater than the critical v alue. The differencebetween set and reset levels should also exceed the samevalue in order that cyclic switching does not occur formarginal phase displacements when the net rate ofchange of integrator output is very small; this is illus-trated in Fig. 4. Finally, the upper limit of linearityshould not be excessive, otherwise the reset time will bepoor.

If all these factors are taken into account, togetherwith the problem of designing a trigger circuit to operateto a specified level, it is found that the optimum level-detector setting is two thirds of the integrator excursionlimit and reset one third of the same limit, as indicated inFig. 4.

-- _ ---- -_---_--------

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Response TimeThe basic time-response characteristic is of funda-

mental importance. Since the response is directly relatedto the coincidence time, it is a simple matter to derive theequation relating this time (which, in turn, is propor-tional to the complement of phase displacement, r - 4,in the steady state) to the time of operation. Theresponse time is directly related to the time taken for theintegrator to produce a signal which actuates the leveldetector under conditions of continuous coincidence.

I I I I Ib

(I)--__-- _ -- - -_ _ /v - - -_

ma y operotlonc

F I G . 5 . R E L A Y W A VE F O R M S W I T H D . C . O F F S E T 1 N v ,* Inputsignalso co inc idence c i r cu i th O u t p u t f ro m c o i n c d e n c c & c u lt

(i) U p p e r l imt t(ii) S e t l r v e l

(i i i) R e w t l e v e lc I n t e g r a t o r Output

Under conditions of maxim um d.c. offset transient inone signal, operation can be delayed slightly as shown inFig. 5, where the time of positive coincidence has beenreduced, and of negative coincidence increased, over thetransient period. The compensatory action resultingfrom the use of an integrator responsive to bothpolarities is apparent.

It is clearly adva ntageous to have the response time asfast as poss ib le ; however, the minimum will be related tothe spurious output during conditions of maxim um d.c.offset transient. Under conditions of maxim um d.c. off-set transient in VZ, V, will, in the limit, h ave one p olarityonly, and it is possible to produce a coincidence pulse of

exactly one half of a system period in width, and this willbe independent of phase shift. It is essential that thisshould not actuate the level detector and hence possiblyinitiate a spurious tripping pulse. T his very simplestabilising criterion sets a limit on minimum operatingtime; from it the inherent operating characteristic maybe readily derived.This describes the performance of the relay with a d.c.offset in one input only to the comparator; the moregeneral case of transients in both inputs will be coveredlater.

t ime, msTX - T -

6. I N T E G R A T O R O U T P U T W A VE F O R M U S E D T OD E T E R M I N E O P E R A T I N G T IM E

Referring to Fig. 6, showing the relationship betweentime and integrator output, V, is the setting of the leveldetector which it is assumed, would be reached in T/2under conditions of continuous energisation, where T isthe power-system period. Using C#J or the phase dis-placement between input signals V, and VZ, the follow-ing basic equations apply:T, = (1 - ~$/7r)T/2.................... (2)

V, = 2V,T,/T . . . . . . . . . . (3 )V! = 2V,T ,/T . . . . . . . . . . . . . . . . . . . . . . . .T, + T, = T/2 . . . . . .

(4 )(5 )

For zero phase displacement between comparatorinputs, point a in Fig. 6 coincides with the trigger levelV,, i.e. V, = V, and the operating time is T/2. When thepoint b coincides with V,, the change in integrator out-put is given by

V, = 2V, - V, . . (6 )and this change takes place in time

t = T/2 + T, . (7 )If. however, point b falls just below V,,

t = T + T!giving rise to a discontinuity in the operating-timecharacteristic.The next discontinuity occurs when

v,= 3v, - 2v, . . . . . . . . . . . . . . . . . . . . . . (8 )and t=T +T \ ._...._...._.......,...... WIor 3T/2 + T,........................... (9b)

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01 1 I I 1 I f-90" -60 -3oO 0 3 0 " 6 0 " 9 0 "pha s e d l s p l o c emen t , #

FIG. 7. OPERATING TIME AS A FUNCTION OF PHASEDISPLACEMENT

a Minimum t imingb Maximum t im ing

Fig. 7 shows the theoretical response-time curve of thecomparator derived on this basis. Two curves are shown,the upper giving the uncertainty which occurs whenmeasuremen t starts during a noncoincidence period.The time delay due to the uncertainty is proportional tophase displacement and has a maxim um of T/2 at theoperating threshold $I = 7r/2. The operating time isvirtually constant for phase shifts of less than 60 .Thereafter, the time is delayed progressively until itbecomes infinite at the operating threshold.

The virtue of this type of characteristic is that it com-bines the advantages of very high speed of operationwith very accurate measureme nt at the threshold. Thischaracteristic is a direct consequence of the fact that thedesign is based on the transient response as discussedearlier. In the authors view, it is fundamen tal that, if thetransient response is to be satisfactory, a gradedresponse time is an inevitability.

PRACTICAL CONSIDERATIONSRelay sensitivityThe inherent dynamic response was derived a bove onthe assumption that the comparator was infinitely sensi-tive, since it was assumed that measureme nt took placeduring coincidence without regard to amplitude. This isundesirable in practice, since the condition of one, orboth, inputs being zero should be a positive restraintcondition. This is achieved in practice by arranging thatcoincidence outputs are only initiated when both inputsignals simultaneously exceed some minimum valueknown as the setting, which need no t necessarily be thesame for the two inputs.

The effect of setting on performance is readily takeninto account. It is merely necessary to compute theapparent phase shift as seen by the integrator, this beingrelated to the true phase shift and to the ratio of eachsignal input to its setting. For example, if the two, signalsare in phase, the peak v alue of each sho uld be v/2 timesthe setting in order that the apparent phase shift is 90 .

This provides the useful criterion that the r.m.s. input atthe threshold should be equal to the setting. Futher-more, for this in-phase condition, the smallest inputsignal will determine operation.

2kkJ& : 01 o1 2 5 1 0 20 5 0 foe

FIG. 8. CONSTANT PHASE ANGLE CURVES; DEGREE SINDICATED BETWEEN s1 AND sz

- theore t i ca l00 prac t i ca l

Fig. 8 shows the relationship between the ratios Si =Vi/V,i and S 2 = V2/Vs2 with $J as a parameter, where Vsland Vs2 are comparator voltage settings. The salientfeatures of the threshold characteristics are:

(a) For 4 = 0, the characteristic comprises twointersecting straight lines, Vi/V,i = 1 and VJV,z= 1.(b) For 0 < 4 < n/4, the characteristic is divided intothree regions; i.e. a straight line V1/Vsl = 1, acontinuous curve, an d a straight line V2/V,Z = 1.

It has been shown3 that transition points from thestraight lines to the curve are desribed by theequationV,lV,i = ll(V2 cos (4 + 7 r l 4 ) ) . ( 1 0 )The same expression applies for V2/V,Z becauseof the symmetry.

(c) For a/4 < + < n/2, the characteristic is a con-tinuous curve, the equation for which has beenshow? to beco? 4 = & + & + sin +/(S,S,) . . . . . (11)1 2

Eqn. 11 also describes the curved portion of thediscontinuous characteristic in Fig. 8 for the caseof +


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FIG. 9. P O L A R C H A R A C T E R IS T I C O F D I R E C T IO N A LRELAY

_ _ th eo re t i ca l00 pract ical

The discontinuities for cases (a) an d (b ) represent thetransition from the condition where one signal alonedetermines the characteristic (straight line) to the condi-tion where both signals determine the characteristic(continuous curve). In particular, these curves are usefulfor deriving the more familiar polar characteristic, afamily of which is shown in Fig. 9, drawn for constantvalues of S1 so that the curves relate Sz to 4. Again, boththeoretical and practical curves are shown a nd the effectof the comparator setting is evident, where it is shown toproduce a discontinuous characteristic made up ofstraight lines and the arc of a circle w ith radius S2 = 1 andcentre at the origin. The polar curves of Fig. 9 are usefulin assessing practical relay performance and applicationsuitability in a power system; in this context, the featuresof the directional characteristic are well known.

Fig. 10 illustrates the plain impedance characteristicobtained with the same kind of comparator using theappropriate input transformation. This characterisitic isdrawn using parameters of impedance in the complexplane, the broken line defining the high-level (ideal)characteristic. The full-line characteristic is obtained atlower signal levels; it can be shown that the two semicir-cular indents reduce in size at more practical input signallevels as the circle expands towards the broken-linecharacteristic.

The sensitivity attainable using transistors usuallyreduces such imperfections in characteristics to verysmall proportions, and, in any case, a fuller analyticaltreatment is warra.nted when compensation using non-linear elements is used.

i/--///lI_ I\\

\L -_-1.-c-t

-_ \--K \ \Y\

\b \\ \

\

+-

III

//

/I_A/ /----FIG. 10. I M P E D A N C E - R E L A YC H A R A C T E R I S T I C

a I d e a l m p e d a n c eh arac t e r i s t i cb Lo w-s ig n a l - l ev e lm p e d a n c eh arac t e r i s t i c

Practical derivation of the input quan tities of a comparatorInevitably the phase-shifting requirements in the

measuring and mixing circuit of Fig. 1 will influence thedynamic performance of the final scheme, and the trans-ient response of this circuit must b e carefully assessedeven when transient-free comparator circuits are beingused. Mimic impedances in the current circuit are gener-ally preferred, and two well known arrangements areillustrated in Figs. 1 la and b. Under ideal conditions, thetrue mimic-impedance arrangement of Fig. lla resultsin the offset d.c. transient components in the measuringinput to the comparator being eliminated. In practice,however, the not unusu al mismatch of angle between themimic and the protected line may result in transientcomponents of the same polarity on both inputs, and forthis reason the imperfect mimic impedance or transactorof Fig. 116 is preferred. The steady-state responses ofthe two arrangements in Fig. 11 are identical, but for allpractical line angles the transactor is a transient filter, sothat asymm etrical inputs to the compa rator are due tovoltage transients only. Thus , when transient compo-nents exist in both inpu ts to the comparator, they will beof opposite polarity and the critical m inimumoperating-time of 1 Oms can be preserved. Other practi-cal advantages of the transactor include the fact that onlyone iron-cored element is required and that the transientflux levels in the core are much less onerous than thoseencountered in the auxiliary cu rrent transformer of Fig.

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-i

%

III//Itb

F~c,.ll. ALTERNATIVE MIMICIMPEDANCEARRANGEMENTS

u True mimicb Transformer-reactor11~. All these po ints were fully exploited in thedevelopment of the practical p rototype relay discussedin Section 5. The practical aspects of design of themeasuring circuit include the requirement for goodsurge proofing, which is conveniently achieved byscreening the transactor and voltage transformer units;these units include the necessary means for adjusting thephase-angle and relay impedance settings.

DYNAMIC PERFORMANCE OF THEPRACTICAL PROTOTYPE RELAYDynam ic testing of a prototype relay was done und ercontrolled conditions on a test bench, one phase ofwhich is shown in schematic form in Fig. 12. The line

I_.-FIG 12 . SINGLE-PHASE REPRESENTATI ON OF TFST

BENCH

impedance of this apparatus is variable in magnitude.the X/R ratio being constant; the source imp edance isalso variable, with the X/R ratio being nom inally 30 butvarying somewhat with the magnitude setting. Thecharacteristics presented here were obtained from therelay arranged to give a polarised-mho characteristic,

with the well known vector-mixing relationships:v, = ILZR - VI_. . . . . . . . . . . (14)v2 = vi_ + v, . . . . . . . . . . . . . . . . . . . . . (15)

Characteristics were measured in order to confirm thehigh speed of operation and inherent accuracy of meas-urement under transient fault conditions; it wasarranged that the minimum oerating time of the com-parator under test should be 15ms. Fig. 13 shows relayaccuracy p lotted against system impedance ratio (s.i.r)with operating time as a parameter and for zero-offsetd.c. transient in the primary circuit; this curve therefore

1 5p41. 25% 10% 5%i I II I I1.0; I I I boundary of

operation

t/ _I

00 1 2 5 10 20 50 100 200system mpedance ratio

FIG. 13 . MEASURED TIMING AND ACCURACYCHARACTERISTIC OF

POLARISED-MHO RELAY;NO OFFSET D.C.TRANSlENT~ constant-timing contour\

constant-wltage cotOr\

describes the performance of both replica impedanceand transactor since their steady-state performances areidentical. In Fig. 13 accuracy is defined as the ratio

Zx=-L= impedance to point of faultZR impedance setting of relay

and s.i.r. is defined as

Fig. 14 shows the corresponding curves plotted formaxim um offset d.c. transient in the primary circuit;comparison of the curves defining the bounda ry of oper-ation in Figs. 13 and 14 shows there to be no transientoverreach and clearly illustrates the transient-freenature of the comparator. Inspection of these curvesshows that variation in operating time is not significantin the two extreme cases. As an alternative, the testresults are presented in the form of constant-voltagecontours superimposed on the constant-operating-timecontours. These are shown as broken-line curves in Fig.13. When these cu rves are plotted in the form of operat-

211


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boundary 31operation

system Impedance ratlo

FIG. 14. MEASURED TIMING AND ACCURACYCHARACTERlSTlC OF

POLARISED-MH O RELAY; MAXIMUM OFFSET D.C.TRANSIENT

ing time ag ainst relay accu racy, as in Fig. 15, thedefinite-time characteristic is clearly shown; i.e. thecharacteristic is flat over a high proportion of the linelength, even for low operating voltages.

OoL- J02 I0.4 0.6 08 10relay ccuracy,

FIG. 15. POLARISED-MHO CONSTANT-VOLTAGECONTOURS

Fig. 16 serves to illustrate dynamic performance interms of oscillograms of the output waveforms of theintegrator and level detector. The waveform at a definesthe inherent operating time, being for the close-in faultcondition. The waveforms at b and c are for operation2% inside and outside the operating boundary , respec-tively. The stability under the onerous test conditionsspecified is evident, the effects of the alternate wide andnarrow pulses driving the integrator during the transientperiod being apparent.

b

FIG. 16 . PRACTICAL RELAY INTEGRATOR AND TRIPWAVEFORMS; S.1.R.Y 10.

X/R = ZX.&GRATlCULE LINES ATZOMSINTERVA LSax=o b x = 0~98 c x = I.02

CONCLUSIONSFor comparators based on the principle of block com-parison, the generalised analysis given in the Appendix 9establishes the corresponding identity of outputwaveform from the basic measuring circuit for a giventransformation procedure. Thus , for particular charac-teristics, block-comparison comparators using eitherphase or amplitude comparison can be designed to haveidentical dynamic performance, and the significance ofclaims purporting to distinguish inherently betweenthem are shown to be unfounded.

The broad general requirements of static relays havebeen considered, and it is clear that there are a numberof firm reasons for using the principle of block-averagecomparison. The principal reasons are the following:

(4

(b)

Cc)

Such relaying systems are completely predict-able; desirable transient, and hence steady-state,characteristics can be defined, the equations for-mulated and practical circuits realised.The controlled time characteristic has the virtuethat minimum operating times approaching onehalf of the system period can be attained withoutsacrificing stability under marginal conditions.As a consequence of (b) transient, and steady-state, operating boundaries coincide so that thereis no tendency for transient overreach to occur.

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(d) Owing to the principle of averaging comparatorsignals on both half-cycles of the primarywaveform s, the degree o f primary transient d.c.offset has no significant effect on the speed ofoperation.Static and dynamic performance curves are presentedin this paper for a practical relay of a type w hich has seenconsiderab le field service; F igs. 13-1 6 a re in close

agreement with the performance originally specified.Further information on the performance of such systemsin the field is becom ing available, and all results to datejustify the confidence resulting from laborator y tests.

ACKNOWLEDGMENTSThe authors wish to acknowledge the facilities providedby the Powe r Systems Laboratory of the University ofManchester Institute of Science & Technology, to Prof.C. Adamson for discussions and helpful advice in pre-paring this paper and to A. Reyrolle & Co. Ltd. forpermission to publish this paper. The guidance and help-ful discussions with F. L. Hamilton and N. S. Ellis of A.Reyrolle & Co. Ltd. is acknowledge d.

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10.

11.

ADAM SON, C. and WED EPOHL , L. M .: Power sys-tem protection, with special reference to the appli-cation of junction transistors to distance relays,Proc. IEE, 1956, 103A, pp.379-388ADAM SON, C., and WED EPOHL , L. M.: A dual-com parato r mho -type distanc e relay, utilizing junc-tion transistors, ibid., 1956, 103A , pp.509-5 17WE DEP OH L, L. M.: Th e application of junctiontransistors to distance relays, Ph.D. thesis, VictoriaUniversity of Manch ester, May 1957HOEL , H., HUM PAGE, W. D., and CHAPM AN,C. P.:Compo site polar characteristics in multizone sys-tems of phase-comparison distance protection,Proc. ZEE, 1966, 113, (lo), pp.1631-1642HAMILTON,F. L., and EL LIS, N. S.: Performance ofdistance relays, Reyrolle Rev., 1956, 166, p.14(which is chapter 9).PEN ESCU , C.: Universal characteristic transistor-ised distance relay, CIGR& Paris, paper 31 7,1964ELLIS , N. S.: Distance protection of feeders,Reyrolle Rev., 1957, 168, p.16ELLIS , N. S.: Distance protection of feeders,lbid.,1957, 169, p.6 (which is chapter 11).MA THE WS, P., and NELL IST, B. D.: Transients indistance protection relays, Proc. ZEE, 1963, 110,(2), pp.407-418WEDEPOHL,L. M. : A transistor phase-angle com-parator experiment, J. Ins t . Elect. Engng. Educ.,1965, 3, p.215DEW EY, C. G., MATH EWS, C. A., and MORR IS, W.C.: Static mho -distance and pilot relaying princi-ples and circuits, IEEE Trans. Pow er ApparatusSyst., 1963, 72, 391-400

APPENDIXRelationship between amplitude and phase comparatorsConsider two relay devices indicated in Figs. 17a and b.The one indicated in Fig. 17a is a differential bridge inwhich

SOUt ( S,I - 1Sbl nstantaneously . . . . . . (15)The device in Fig. 17b is basically a coincidence circuit

and has the following operating law:S, , and S,/S, > 0S, , and S,/S, < 0S, , and S,/S, > 0 (16)S, , and S,/S, < 0The second device effectively pro duces an outputsignal which is equal in magnitude to the smaller of thetwo input signals, is positive in sign when the inputsignals have the same polarity, and is negative in thealternative case.If the following substitution is mad e in eqn. 15:

s, = (S, + S,)/2Sb = (S, - S&2and thus2S,, = Is, + s,I - Is, - s,( . . . . . . . . . . (17 )

then the four cases listed in eqns. 16, (a)-(d) inclusiveneed to be considered:fa) ) S,( > ) S,( and S,/S, > 0

thus 2S,,, = S, + S, - (SX - Sy)and S,,, = S,

(b) ( S,( > I S,l and WS, < 0thus 2S,,, = S, - S, - (SX + S,)and S,,, = - S,

(c) IS,I < JS,( and S,/S, > 0thus 2S,,, = S, + S, - (S, - SY.)and S,,, = S,

Cd) \S,\ < IS,\ and S,/S, < 0thus 2S,,, = S, - SX - (SX - S,)and S,,, = -S,It can be seen that the operating law of the arrange-ment in Fig. 17a is the same as that of Fig. 17b under thespecified transformation . The transformation is revers-ible, so that b would have the same characteristic as a if

s, = s, + Sbs, = s, - Sb

Since the equivalence is based on instantaneous val-ues, it follows tha t the result is perfectly general. Conse-quently, the performance of one device will be identicalwith that of the other, provided that the output signalsare subjected to the same constraints, i.e. amplitudelimiting, integration etc.It is well known that the device of Fig. 17a has a meanoutput voltage of zero w hen S1 and S2 are sinusoidal2 1 3


11/11

I I

SO---.

DI ISalL I II

sb

I Isx -----I coincidencesu _ 1 cirwit t-sou

IFIG. 17 . THEORETICALCOMPARATORBLOCK

SCHEMATICSa Amplitud e omparator6 Phase comparatorvoltages of equal amplitude irrespective of phase, whileb has a mean output voltage of zero when energised with

sinusoidal signals displaced in phase by 90 irrespectiveof amplitude. It follows tha t the former principle formsthe basis for amplitude comparison; the latter for blockphase comparison.

In practice, it is customary to introduce amplitudelimiting in a, i.e. the rectifier-bridge moving-coil system,and in b, i.e. the static phase-comparator, as described.

It is possible to repeat the argume nt for comparatorswith nonlinear operating criteria, e.g. a square-law beamrelay, and thereby derive the relations for equivalence.It is equally evident that it is not permissible to comparethe performance of devices which have nonequivalentlaws of operation. This includes ancillary devices such asvoltage limiters, integrators and so on. For example, theperformance of a rectifier/moving-coil system is mod-ified very considerably by the introduction of voltagelimiters.

The important conclusion to be drawn from theanalysis here is that, if amplitude and phase-comparators have identical operating laws, there is noneed to consider their dynamic characteristics sepa-rately; any remarks which ap ply to one apply to theother. This is particularly the case in this paper where adesired operating principle of signal processing isdefined and applies to both comparator principles.

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Chapte14 Dist Static Design