Method for Setting the Resistive Reach ofQuadrilateral Characteristics of Distance Relays

Elmer SorrentinoUniversidad Simon Bolivar, Venezuela

elmersor@usb.ve

Eliana RojasABB, Venezuela

eliana.rojas@gmail.com

Jesus HernandezSeneca, Venezuela

jesusr.hernandez@laedc.com.ve

Abstract-A new method for setting the resistive reach onquadrilateral characteristics of distance relays is proposed inthis article. The method is based on: a) analysis of theimpedances seen by the relay (apparent impedances); and b)explicit definition of the protection desirable attributes for eachanalyzed zone (selectivity, sensitivity). In the proposed method,the resistive reach setting is calculated assuming that thereactive reach setting has been previously defined. Theproposed method was applied in an example with 18 distancerelays and its solution was compared with a conventionalsimplified solution. The conventional simplified solutionconsists in setting the resistive reach by multiplying the reactivereach by a constant factor. The result obtained with theproposed method is different since there is not a constant factoramong the settings of the reactive and resistive reaches.

Index Terms-Distance relay setting, Quadrilateralcharacteristic.

I. INTRODUCTION

Traditionally, the distance relay zones have been setaccording to simple rules [1-4]. The non-traditional optionscan be grouped according to their conceptual basics: basedon expert systems, mathematical optimisation, adaptiveprotection or probabilistic methods [5]. The well-knowntraditional setting rules have been developed to have aspecific reactive reach for solid faults [1-5]. In the case ofrelays with quadrilateral characteristics, the reactive andresistive reaches can be set independently. For these relays,it is desirable to defme the resistive reach by an analysis offaults through impedance. Some traditional setting methodsconsider faults through impedance, but usually just a typicalresistance value is considered [1,2]. Such methods usuallydo not consider that the apparent impedances are affected bydiverse factors [6]. A still more simplistic option is to set theresistive reach by multiplying the reactive reach by aconstant factor [7].

The main purpose of this article is to present a newmethod for setting the resistive reach on quadrilateralcharacteristics of distance relays. The proposed method isbased on: a) analysis of the impedances seen by the relay(apparent impedances); and b) explicit definition of theprotection desirable attributes for each analyzed zone(selectivity and sensitivity).

II. PROPOSED SETIING CRITERIA

A. Preliminary basic considerations

-It is considered that the reactive setting (XR) has beenevaluated previously by traditional rules. Such rules are notuniversal, especially for the delayed zones; due to this fact,the rule used for each zone in this article will be specificallydescribed here.

-The time delays for zones 2, 3 and 4 are assumed to bepredefmed and fixed. Additionally, it is considered that thereare not teleprotection schemes (communication-assistedtrip), breaker-failure protection (50BF), line differentialprotection (87L), or other line protection functions. Theseconsiderations affect the criteria for setting the relay reaches.

-The proposed method for setting the resistive reach (R0can be adapted to the different ways of setting XR. Thecriteria used in this article for XR setting are relativelycomplex. This helps to better explain the proposed method.

B. Analyzed quadrilateral characteristics

The quadrilateral characteristics may have differentshapes; Fig. I shows the first quadrant for 3 cases. It will beassumed that the settings are defmed by the first quadrant inthe R-X plane. For the sake of simplicity, shape of Fig. lawill be used in this article. However, the techniquesdeveloped here can be applied to other characteristic shapes(such as those shown in Figures Ib and lc) by using anadaptation to the geometry of each particular characteristic.

Fig. I. Examples of different shapes for quadrilateral characteristics.

C. Setting the zone 1 resistive reach

C.l. Criterion used/or the reactive reachThe first criterion states that zone I only has to operate for

faults on the line since this zone is instantaneous. Zone Ishould not operate for faults at the remote bus, byselectivity. Zone 1 reactive reach (XR1) will be set to 80% ofthe reactance of the protected line (XL+): XR1= 0.8 XL+.

C.2. Criterion used/or the resistive reachAccording to the previous paragraph, zone 1 resistive

reach (RRI) must be set in a way that assures that the relayfirst zone will not trip for faults at the remote bus.Considering the effect of the fault resistances (~) on theapparent impedance (ZAP), there are 3 cases:

a) Faults at the remote bus whose ZAP tends to fall withinzone I (Fig. 2a). To have a safety margin, the resistivesetting will be limited to the value of the real part of ZAP(RRI-A) where the imaginary part of ZAP is 90% of XL+.

b) Faults at the remote bus whose ZAP tends to be parallelto XR1(Fig. 2b). It will be assumed that the possible error ofmeasurement of the relay is proportional to the ZAP module.For this reason, when the ZAP imaginary part minus 5% of

978-0-947649-44-9/09/$26.00 ©2009 IEEE

Faults within theprotected line

RZ.MIN.l

Zona I of the adja centline, as it is viewed by

the analyzed relay

R

RZ.MIN.Z

R =0 9R IFaults out of the IZ· MAX ' Z·RI·ADY .protected lme

R

RZ-RI-ADY

Fig. 3. Limits for the settingof the zone2 resistive reach.

ZL+,ADJIj)

setting for the zone 2 reactive reach (XZ-MIN-Z) will becomputed as 110% erx., (Xz_MIN_z=I ,IXL+)'-If XZ-AVG is greater than XZ-MIN-Z, there is not conflictbetween those values and the setting is: XR2=XZ-AVG.-IfXz-AVGis less than XZ-MIN-Z, it will be assumed that itis not possible to guaranty selectivity with that shortadjacent line and the setting will be: XR2=XZ-MIN-Z.Actually, the solution for these cases is to implement aunit protection scheme for the short adjacent line (linedifferential and/or a scheme with teleprotection) and/ora change in the zone 2 delay for the line in study . Theanalysis of such solutions is beyond the scope of thepresent work .

D.2. Criterion usedfor the resistive reachThe setting criterion of zone 2 resistive reach (RR2) is

similar to the criterion described for XR2. A desirablesensitivity will be defined to cover faults in 100% of theprotected line, with the typical fault resistance value (RF-TyP)multiplied by a safety factor (Fsl). An allowable minimumsensitivity will be defmed using a smaller safety factor (Fsz):Fsz<Fsl; RFI=(Fsl)RF_TYP; RFZ=(Fsz)RF-TYP (thus, RFZ< RFI).

The desirable and allowable minimum settings (RZ-MIN-Iand RZ-MIN-Z, respectively) correspond to the real part of theapparent impedance seen by the relay for faults at 100% ofthe protected line, with the fault resistances that consider theaforementioned safety factors (RFI and RFZ, Fig. 3a).

The desirable maximum setting for the zone 2 resistivereach (RZ-MAX) is evaluated with resistive faults at thebeginning of adjacent lines that are out of the zone I of theadjacent line. The maximum fault resistance (Rp-L1M-ADJ) thatis able to see the relay of the adjacent line at the beginningof its zone 1 will be found. With this fault resistance, the realpart of the apparent impedance seen by the relay of the linein study, for faults at 100% of the protected line (RZ-RI-ADY),will be computed: it will be considered that the desirablemaximum adjustment corresponds to 90% of this value (Rz_MAX=0.9 RZ-RI-ADY, Fig. 3b). The algorithm to set RR2 issimilar to the described one for XRZ:

-If RZ-MAX is greater than RZ-MIN-h then there is not conflictbetween those values and the setting will be: RR2=Rz-MIN-I.

-If RZ-MAX is less than RZ-MIN-" the desired sensitivity is notpossible without a lack of selectivity, and:

a

c

If .Im{ZAP}=0,9XL+,=> RR I .A=~e{ZA P }

RRI is not limited by ZAP

R

If [.Im{ZAP }-0,05IZAPI1=0,85XL+,=> RRI .B =~e{ZA P }

~::::::: " .': ') .------------~- - - - - - - - - - - - -- ,XR1=0,8XL+ :

IIII R

Fig. 2. Criteriausedfor settingthe zone 1 resistivereach.

D. Setting the zone 2 resistive reach

D.l. Criterion usedfor the reactive reachIt will be considered that the main objective of zone 2 is to

cover the sector of the line that is not covered by zone I .This implies that the reactive reach should be set to covermore than 100% of the protected line impedance, in order toguaranty sensitivity for internal faults . This criterion isfrequently used; however, it is usually necessary to takeprecautions that guaranty selectivity when there are adjacentshort lines at the remote bus . This is because the beginningof zone 2 of the relay of the adjacent short line could overlapwith the zone 2 of the relay in study . The setting of the zone2 reactive reach (Xd will be done thus:

-The desirable minimum setting for the zone 2 reactivereach (XZ-MIN-I) will be computed as 120% of the reactanceof the protected line: XZ-MIN-I = 1.2 XL+.

-The desirable maximum setting for the zone 2 reactivereach (XZ-MAX) will be computed as 80% of the totalreactance seen by the relay for a fault at the beginning ofzone 2 of the adjacent line protection at the remote bus(XL+,ADJ,SHORT). The case with the smaller additionalreactance will be used: XZ-MAX = 0.8 (XL++0,8XL+, ADJ,SHORT).

-If XZ-MAX is greater than XZ-MIN-" then there is not conflictbetween those values and the setting will be: XR2 = XZ-MIN-I .

-If XZ-MAX is less than XZ-MIN-" the desired sensitivity isnot possible without a lack of selectivity, and :

-The average of the previous values will be computed(XZ-AVG=[XZ-MIN-I+XZ-MAX]/2). The allowable minimum

ZAP module is 85% of XL+, the corresponding real part ofZAP limits the resistive setting (~I-B)'

c) Faults at the remote bus whose ZAP tends to separate ofXRI (Fig. 2c) : RRI is not limited by ZAP.

RRI setting will be the smaller value of ~I-A and RRI-B, ifboth situations can happen. If the RRI setting is not limitedby ZAP, RRI could be set to a very high value.

-If RZ-MAX is greater than RZ-MIN-Z, then there is notconflict between those values and the setting will be:RR2=Rz-MAX•

-If RZ-MAX is less than RZ-MIN-Z, then it is not possible toguaranty selectivity for some values of fault resistanceand the setting will be: RR2=Rz-MIN-Z.

of the apparent impedance (ZAP) seen by the relay in study is110% of XR3, or if the imaginary part of the apparentimpedance minus 5% of the ZAP module is 105% of XRJ, thecorresponding real part of ZAP will be the value of resistivereach (Rd. As zone 1, if the RR3 setting is not limited byZAP, then RRJ could be set to a very high value.

TABLE Ill' Loxn DATA

Fig. 5. Criteria used for setting the zone 3 resistive reach.

TABLE II ' EQUIVALENT GENERATOR DATA

If:(Im(ZAP}=I,IXR3)

OR([Im(ZAP} -O,051ZAPI]=I,05XR3),

~ RR3=>\'f(ZAP}R

jX (FINFEED)ZL+,AD.J I Z ( . R ) I~ AP varyIng F

XR3=O,8(XL++(f'INFEED)XR2-ADJ,SHORT)

III. SYSTEM USED AS EXAMPLE

B. Ground distance function description

The apparent impedance seen by ground distance function(ZPh-G) depends on its polarisation method [9]. It is assumedthat the relay uses the following form of polarisation:

ZPh-G = VPh-G / (IPh+KoI~ (I)VPh-G: Phase-to-earthvoltage of the faulted phase.Iph: Current of the faulted phase.IR: Residual current (IA + IB + Ie).Ko: Residual compensationfactor.It is assumed that Ko is set exactly to see the positive

sequence line impedancefor solid faults:Ko = (ZLO - ZL+) / (3 ZL+) (2)ZL+: Positive sequence line impedance.ZLO: Zero sequence line impedance.

LCA C I:3.37kmPLM

Fig. 6. Power system used as example (II5kV).

A. Power system description

Figure 6 shows the power system used as example and itsdata are in Tables I, II and III.

C I:26km

TABLE I: LINE PARAMETERS (r,x inQ/km; b in umho/km),r, x+ b+ ro Xo bo

Cl 0.1211 0.4959 3.347 0.3160 1.102 1,938C2 0.1714 0.4928 3.421 0.3630 1.151 1.860

X+=K(Q) Xo(Q) P(MW) Q(MVAR)LCA 7.3 3.3 Slack SlackGUA 15.9 15.9 120 74.37LM 120,0 53.0 20 12.39

LCA LM LA PMT LR PLM GUAP(MW) 73 48 31 38 56 38 30cos(<!» 0.900 0.900 0.900 0.900 0.936 0.900 0.850

RR2-MIN-2

ZL+,ADJ ~ I Zone I of the adjacent line Ij x XR2-CASE2

~~ ~~~~~~~~~~ -~ - ~ ~ ~ ~ ~ ~ ~B Increase erx, implies

~, XR2-CASEI : a lack of selectivity ifZL+ : Z . . h' .AP ISIn t ISregIon

eL+ i R

E.2. Criterion usedfor the resistive reachZone 3 resistive reach (RRJ, Fig. 5) is set similarly to RRI .

The resistive faults were computed at the end of the sameadjacent line used for the XR3 setting. If the imaginary part

Fig. 4. Example of a lack of selectivity by increasing XR2 sensitivity .

E. Setting the zone 3 resistive reach

£.1 . Criterion usedfor the reactive reachIt will be assumed that the main objective of zone 3 is to

operate as backup protection for faults in adjacent lines [8].However, selectivity between zones 3 of different lines willhave priority because zone 3 is the faster backup function.This criterion presupposes that the faults non-covered by azone 3 as backup will be covered by its zone 4, that is moresensitive (zone 4 has a greater reach or it is simply adirectional function).

Zone 3 reactive reach (XR3) should be set at 80% of thelowest total apparent reactance seen by the relay in study forfaults at the end of zone 2 of the relays that protect adjacentlines. Worst case combines the smaller zone 2 reactive reachof the relays of the adjacent lines (XR2-ADJ,SHORT) with thesmaller infeed (FINFEED, due to the current contributions atthe remote bus): XR3=0.8 (XL++ (FINFEED) XR2-ADJ,SHORT).

To fmd the previous value may not be simple. For the sakeof simplicity, XRJ was set to 75% of the smallest totalapparent reactance for faults at the end of the adjacent linesto the remote bus: XR3 = 0.75 (XL++XAP-ADJ-LOWEST). BaseCase of load flow was used; therefore, the FINFEED valuescorrespond to the Base Case.

D.3. Comments about both criteriaIn both setting criteria, if the first condition is satisfied

(XZ-MAX>XZ-MIN-" or RZ-MAX>Rz-MIN-I), then a different actioncould be taken, in order to increase still more the zone 2sensitivity. For example, in such cases the setting could bethe maximum value instead of the minimum, or an averageof both values. An analysis of those options is outside thescope of the present work; however, Fig. 4 helps to illustratethis concept. In the example of Fig. 4, it is assumed that theresistive setting (Rd has been limited by the allowableminimum sensitivity (RZ-MIN-Z)' In such case, an increase ofthe reactive reach sensitivity (to use XR2-CASEZ, instead ofXR2-CASEI) would imply a greater lack of selectivity forresistive faults in the adjacent line if the fault is out of thezone 1 of the adjacent line protection.

c. Pre-fault loadflow

With fault resistance (RF), apparent impedance depends onthe pre-fault load flow, measured in the relay locality [6],[9].The determination of the worst possible condition for eachzone of each relay is outside the scope of the present article.By simplicity, a simple preliminary analysis of the system instudy suggested the use of the following conditions of pre­fault load flow:

-Base Case: It is the system described in section III-A.-Case 1: It is the Base Case without one transmission line.

For the system in study, the approximated load flow valuesat the relay localities are in Table IV (QMAX).

-Case 2: This case is as Case 1 and, additionally, this casepresupposes that the system operators can control thereactive power flow. For the system in study, a half of theprevious reactive power value was assumed; the values arein Table IV (QMIN).

These cases were used thus: a) For setting zone 1, Case 1was used when the pre-fault load flow is positive and Case 2when it is negative; for the system in study, by coincidence,P and Q have the same sign in the simulated cases. b) Forsetting zones 2 and 3, Base Case was used.

D. Typical groundfault resistance value

The ground fault resistance value depends on multiplefactors. Each RF value has a probability of occurrence [10];however, a typical value is required in the present work inorder to compute the desirable zone 2 reach. Such value wassupposed arbitrarily (RF_TYP=50). Using safety factors, theresults are: RFl=(Fsl)RF-TYP=200; RF2=(Fs2)RF-TYP= 100.

IV. RESULTS FOR THE RELAY SETTINGS

The settings obtained for zone 1 are in Table V. The XR1values are identical to those obtained in another study [11]since the used criterion is exactly the same. However, in thatstudy a unique factor of RIJXRwas used (RIJXR=2). Table 5shows clearly that RIJXR is not constant with the developedmethod: RIJX Rvaries between 0.77 and 33.41.

On the other hand, the maximum value of fault resistance,at the remote bus, for which the adjustment of the RRI wasdefmed, varies between 0.970 and 17.390. However, thereare 5 cases where the resistive reach was limited by the linethermal capability and not by the apparent impedance locus.

The settings obtained for zone 2 are in Table VI. RR2 is, insome cases, less than RRI (it happens at bus 2 of the linesLM-LA, PLM-LR, LCA-PLM, LCA-LR). This result isillustrated in Fig. 7, it is not conventional and it happenssince RR2 must be limited to reduce the risk of lack ofselectivity (since XR2 is greater than XR1).

The settings obtained for zone 3 are in Table VII. RR3 is,in some cases, less than RR2 (it happens at bus 1 of the linesGUA-LM, LA-PMT, and at bus 2 of LA-PMT, LR-PMT).This result is similar to the result described for zone 2. If RR3is less than RR2' then zone 2 is more sensitive for faults withfault resistance. In such cases, as zone 3 is not so sensitive,the backup function for faults with a high value of faultresistance is the zone 4. By this reason, zone 4 would haveto be sufficiently sensitive in these cases.

In the cases where RR2 is less than RRI (or RR3 is less thanRR2), this nonconventional result could be avoided if thedesired condition were imposed. Such condition is: thegreater the value of the reactive setting, the greater must bethe value of the zone resistive reach. There are differentways for imposing such condition. Special care should betaken to update the resistance setting values since there aredependences among the reach settings; for example, Fig. 3bshows how the RR2 setting of a relay depends on the value ofRRI of the relay of an adjacent line.

TABLE IV: PRE-FAULTLOAD FLOW, AT THE LOCALITY OF THE RELAYS INSTUDY, FOR THE CASES 1 AND 2 (QMAX AND QMIN, RESPECTIVELY)

Line Line Prefault load flow (line in study)

in out of PandQ P OMAX OMIN

study service direction MW MVAR MVAR

GUA-LM PLM-LCA GUA->LM 90 56 28.0LM-LA PMT-LR LM->LA 70 33 16.5

LA-PMT PMT-LR LA->PMT 38 18 9.0LA-PMT LM-LA LA->PMT -31 -15 -7.5PMT-LR PMT-LR LR->PMT 70 33 16.5LR-PLM PLM-LCA PLM->LR 87 36 18.0LR-PLM LCA-LR PLM->LR -38 -18 -9.0

PLM-LCA LCA-LR LCA->PLM 125 54 27.0LCA-GUA GUA-LM LCA->GUA 90 56 28.0LCA-LM GUA-LM LCA->LM 68 33 16.5LCA-LR PLM-LCA LCA->LR 125 54 27.0

S.

(*): These values were only limited by the line thermal capability (Fig. 2c).

T: ONE SETTINGS. HE FAULT RESISTANCE THAT DEFINED THE RESISTIVE REACH SETTING (FIG. 2) IS SHOWN. VALUES IN PRIMARY OHM

Line Bus 1 Bus 2(Bus 1-Bus2J XR1 RRl R F MAX RR1/XRl XR1 RRl R F MAX RR1/XRlGUA-LM 10.31 12.11 3.86 1.17 10.31 18.06 5.56 1.75LM-LA 4.81 7.75 8.71 1.61 4.81 88* N/A 18.30

LA-PMT 2.41 4.39 4.98 1.82 2.41 5.06 5.92 2.10LR-PMT 2.71 4.95 5.67 1.83 2.71 88* N/A 32.49PLM-LR 1.34 2.98 2.70 2.23 1.34 104.79 17.39 78.38

LCA-PLM 3.95 8.30 8.62 2.10 3.95 132* N/A 33.41LCA-GUA 10.31 16.60 6.16 1.61 10.31 7.89 0.97 0.77LCA-LM 8.73 14.17 8.77 1.62 8.73 132* N/A 15.12LCA-LR 3.98 8.39 8.54 2.11 3.98 132* N/A 33.17

. .

TABLE V Z

TABLE VI: ZONE 2 SETIINGS (SEE FIG. 3). VALUES INPRlMARY OHMS.

Line Bus 1. Bus 2(Bus 1.-Bus2J XR2 RR2 XR2 RR2

GUA-LM 14.82 25.28 15.47 46.42LM-LA 6.98 15.75 7.21 40.39

LA-PMT 3.61 42.03 3.61 27.97LR-PMT 4.06 11.14 3.92 88*PLM-LR 2.01 19.34 2.01 31.33

LCA-PLM 5.47 13.77 5.93 42.20LCA-GUA 14.47 31.42 14.47 60.14LCA-LM 12.83 22.19 12.49 132*LCA-LR 5.51 14.62 5.97 76.59

(") : These values were only limited by the line thermal capability.

·x.I X R2i~: - - - - - - - - - - - - - - - - - - - - - - - - - - :

~- - - -x;~ - - - - - - - - - - - - - - - - - - - - t - - - - - - - - :

I II I

8L+ :: R

R R2 R RI

Fig. 7. Example of a nonconventional result: XR2 can be smaller than XRl.

TABLE VII: ZONE 3 SETIINGS(SEE FIG. 5), VALVES INPRlMARY OHMS.

Linea Ext. 1. Ext. 2(Ext.1.-Ext.2J XR3 RR3 XR3 RR3

GUA-LM 18.01 19.58 21.92(1) 132*LM-LA 7.55 19.88 44.89 88*

LA-PMT 5.18 11.32 7.36 15.32LR-PMT 5.33 14.28 4.39 39.25PLM-LR 8.26 43.46 4.19 132*

LCA-PLM 5.57 132* 8.43(1) 132*LCA-GUA 21.92(1) 50.24 33.16 132*LCA-LM 22.34 67.41 13.47(1) 132*LCA-LR 6.05 132* 8.43(1) 132*

(*): These values were only limited by the line thermal capability.(1): These values were not found by the criterion indicated insection Il-E, since it was not being possible (the reactances wouldbe negative). To find them, the smaller reactance ofadjacent lineswas added to XL+ and the total value was multiplied by O.75.

V. CONCLUSION

-A novel method for setting the resistive reach ofquadrilateral characteristics in distance relays was presented.The method is based on the analysis of the apparentimpedance seen by the relay, and the explicit definition ofthe protection desirable attributes for each analyzed zone.

-The proposed method was applied to an example with 18distance relays and the resistive reaches for 3 relay zoneswere calculated. The results obtained with the proposedmethod were compared with a conventional simplifiedsolution. The conventional simplified solution is to set theresistive reach by multiplying the reactive reach by aconstant factor . The results obtained with the proposedmethod are substantially different since there are particularsolutions for each relay location .

-In the future, this work could be complemented of diverseways. For example, an analysis of other criteria to set thereactive and resistive reaches could be done in order to study

the variations in the results. On the other hand, the effect ofthe inclusion of more cases for the pre-fault load flowsshould be studied.

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