Novel method for implementingthe mho characteristic into distance relays

Janne Altonen*, Ani Wahlroos**

ABB Oy Distribution Automation, Finland, janne.altonen @ f.abb.com-ABB Oy Distribution Automation, Finland, ari.wahlroos@fi.abb.com

Keywords: distance protection, impedance characteristic,polarization

Abstract

Traditionally the mho characteristic has been implemented byapplying torque-like algorithms using voltage phasors.Presenting and analyzing the behaviour of such algorithms inthe impedance plane are not straightforward. Protectionengineers, however, need to know the relationship betweenthe measured impedance and the operating characteristic ofthe protection during power system faults. A too] preferred bythe protection engineers is one that plots both the loopimpedance trajectory and the operating characteristic in theimpedance plane (R-X diagram). This paper describes a novelway of implementing the mho characteristic so that it can beanalyzed in the impedance plane in a similar way as thequadrilateral characteristic. The method enables the dynamicexpansion of the mho circle as a result of the healthy voltagepolarization during fault conditions. An additional advantageof this method is that it reduces the computational burden inthe relay terminal as the fault loop impedance can becalculated centrally and utilized in zone boundarycomparisons for both the mho and quadrilateralcharacteristics. This algorithm can be utilized in new distanceprotection designs applied in power distribution andsub-transmission networks.

1 Introduction

The distance protection functionality of modem feederterminals for global markets includes both mho andquadrilateral characteristics. For earth-fault protection thedesired shape of the protection characteristic is typicallyquadrilateral (polygonal), as it enables the fault resistancereach to be set independently of the reach in the reactivedirection. This is especially advantageous in the case of shortlines. For historical reasons, e.g. to enable fluent protectionco-ordination, short-circuit protection has been based on themho characteristic, notably in countries influenced by theANSI standards.

The traditional method of creating a distance protectionfunction with circular characteristic is to compare the anglebetween two voltage phasors: the operating voltage phasor S.,(also known as "the line drop compensated voltage") and the

polarizing voltage phasor S2. These voltage phasors can beexpressed as:

SýI -~.L + dir' Lt, + _Z&,'i -L,)

sL =u_'xl(1)(2)

where

U,= Voltage phasor of the faulted phase(s). For phase-to-earth impedance elements the voltage is UL, UI.2 orU1.3. For phase-to-phase impedance elements thevoltage is _UL12, UIL23 or UL31-

dir = -1, if operation direction is forward

+1, if operation direction is reverse

Zset

I,.

ZOset =

ZNset =

-Positive-sequence line impedance setting

-Current phasor of the faulted phase(s). For phase-to-earth impedance elements the current is IL, IL2 or 113.For phasc-to-phase impedance elements the currentis 1112, IJ 23 or IL-11*

Zero-sequence line impedance setting

Earth return-path impedance setting = (Zoe - ZIset)/ 3.

This term is zero for phase-to-phase impedanceelements.

IN. = Residual current phasor (= ILI + 11- + 1I13)

UP,= Polarization voltage

Figure 1 shows the forward-reaching self-polarized mhocharacteristic in two fault cases: fault inside the protectionzone (left) and fault outside the protection zone (right). Notethat the characteristics are drawn in the voltage plane.

As shown in Figure 1, the angle (x between the phasors S, andS2 indicates whether the measured impedance lies inside thecircle or not. If the angle ax becomes greater than 90 degrees,the measured impedance will lie inside the miho circle and anoperate signal should be activated. At the circumference, theangle a equals 90 degrees.

156

Lziset*kx + ~I (Z1 -L.

,S Re(ij))

a Re(M4

-1

the Equations (1) and (2) into the impedance plane. Theconversion is done by dividing the voltage equations with theappropriate current. The resulting impedance phasors aredenoted K, and jý, which correspond to the voltage phasorsSj and a,_. For reasons of simplicity, the current in the healthyphases is assumed to be zero.

tL ' +LL ( ,+ SF

Im(eU)U

-S,

Figure 1: Left: phasor diagram of forward-reaching self-polarized mho circle at a single phase-to-earth fault insidethe protection zone and right: outside the protection Zone.

Typically the angle comparison implementation is based on atorque-like algorithm utilizing either a cosine or a sine phasecomparator [1]. These phase comparators emulate thebehaviour of an induction cup clement, the amplituderepresenting the torque of the rotating cup and the signrepresenting the direction of rotation. Using the cosinecomparator, the torque-like equation will be:

S'UK•2 =2

(4)

(5)

To illustrate the composition of the impedance phasors Kjand K2, the analysis employs the theory of symmetricalcomponents. The effect of the selected polarization voltagecan be seen in the phasor K?.

2.1 Phase-to-phase fault

The following analysis is based on the symmetricalcomponent equivalent circuit of a two-phase short-circuitfault illustrated in Figure 2.

T~.= Re(S~j).Re(S2) + Im(S1)Im(S,.)

If T , < 0, then the impedance lies inside the mho circle.

In Figure 1 the polarizing phasor S? is assumed to be thevoltage of the faulty phase(s). Such a polarization method isknown as seblfpolarization. The drawback of self-polarizationis that, in the case of a close-in fault, the measured voltagemay become too small and the trip decision may be uncertainor delayed. Therefore the polarizing voltage is typicallyderived from the healthy phases. The most common types ofpolarization methods utilizing voltages from healthy phasesare cross- (or quadrature-) polarization and positive-sequence polarization. In addition, the polarization voltagemay include a memorized pre-fault voltage part to secure areliable handling of close-in three-phase faults.

An often undocumented feature of the mho characteristic isthat the selection of the polarization voltage affects the mhocircle during a fault: the circle expands. This feature will beanalyzed in the following chapters.

2 Conversion of mho equations from thevoltage plane into the impedance plane

A quadrilateral characteristic is typically implemented by first

calculating the fault loop impedance Z,,,O = R,.p+ j .XL,,and then comparing the result with the operation zoneboundaries in the impedance plane. To implement the mhoand quadrilateral characteristics in the same way, the dynamicexpansion caused by the polarization voltage has to beincluded in the method. This can be achieved by converting

Figure 2: Symmetrical component equivalent circuit for atwo-phase short-circuit fault.

The following notations are used in Figure 2:

El= Positive-sequence source voltageZs= Positive-sequence source impedance

ZIL = Positive-sequence line impedance from substation tofault point

7,2s = Negative-sequence source impedanceZQL = Negative-sequence line impedance from substation to

fault pointRF= Fault resistance between phases

U, = Positive-sequence voltage measured at the substationU,= Negative-sequence voltage measured at the substation11 = Positive-sequence current measured at the substation

1, = Negative-sequence current measured at the substation

We assume that there is a short-circuit fault between phase L2

and phase L3 and, for reasons of simplicity, that the current ofthe healthy phase LI equals zero. Figure 2 gives the followingequations:

(6)1L2J( =Z 1j)+R 1

157

(3)

2L3-2 (Z, + ZIL)+ R,

Current I123 = 1 L2-43

(7) IMQ~ mZ

tL23 =2- '12 = 2(4 1 .ZI)+R

Correspondingly for voltages:

(8)Re(U)

a * f,(a Zj + Z1,+ 2 -a -ZI,+ a R,) (9)

2( CZ 1,+_IL +R

Voltage UL23 = _UL2 - U

UL3-a-E 1 .( 2 -a -ZL - 2-_Z, +_a--R, -Re) (1

where a = phase shift operator = cos(1 20') + j~sin(1200).

Inserting the voltage and current Equations (6-11) intoEquation (4) for K1, gives:

K1 =ZKI ±RF /2Z (12)

The term ZIL + RF/2 represents the measured fault loopimpedance Zj.. = RLp+ j.~p where R1L,0p = RIL + RF/2and X,,p= XIL. The set positive-sequence impedance Zisetdefines the zone reach.

2.1.1 Self-polarization

In the case of self-polarization K2 is equal to !L13/41.23.Inserting the Equations (6-11) for the faulted phase currentsand phase voltages into Equation (5) for K?, gives thefollowing:

Difference between phasors K, and K1 :

K. ,~,,j_ -:Et =ZL ±J? / 2 -(ZIL + RF I2-Z1 l,,) =Zlse (14)

Figure 3 illustrates the phasors K, and K, in the impedanceplane (left). The phasor ZLR represents the line replicaimpedance. It is for phase-to-phase impedance elements:

ZLR1 = Ziset (15)

and for phase-to-earth impedance elements:

ZLR1 = ZIiset + ZNset = Ziset + (Zoslet - Ziset)/3

Figure 3: Phasor diagram illustrating phasors K~~ ~, &Zu Iand Zev Lf:Sl-polarized mho circle, right: healthyvoltage polarized mho circle. ZLR = Line replica impedance,Zseq, = Equivalent source impedance (see chapters 2.1.2,2.1.3 and 2.2.2, 2.2.3).

As the phasor difference Kz - K, is equal to Zl, theequivalent source impedance Zs,. ieqatozrin the caseof a self-polarized mho circle. This means that the mho circlewill not expand during the fault. The mho circle is fixed in theimpedance plane and is explicitly defined by the line replicaimpedance.

2.1.2 Cross-polarization

In the case of cross-polarization K? is equal to j3U1/U3When inserting Equations (6-11) for the phase currents of thefaulty phases and phase voltages into Equation (5), thefollowing is obtained:

K2 _--p.1ýK ZL + RFI/2 + Z, (17)

As the phasor difference Kz - K, is equal to Zie,+Z15s, theequivalent source impedance Zs,,q is equal to Zjs in the caseof a cross-polarized miho circle. The mho circle expands byZis during the fault as illustrated in Figure 3 (right).

2.1.3 Positive-sequence polarization

In the case of positive-sequence polarization K2 equals+4-j.U 1 411,23 - Inserting Equations (6-11) for the phase currentsof the faulty phases and phase voltage into Equation (5),gives:

AK2_p.-=q p. ýZII +R, / 2+Z, / 2 (18)

As the phasor difference K2 - K, is equal to Ziset+Zis/2, theequivalent source impedance Zseq, is equal to Zjs/2 in the caseof a cross-polarized mho circle. The mho circle expands byZjs/2 during the fault as illustrated in Figure 3 (right).

(16)

158

ReQ~

IMQ

2.2 Phase-to-earth fault

The following analysis is based on the symmetricalcomponent equivalent circuit of a single phase-to-earth faultillustrated in Figure 4.

L6 I ý; -

3,R,

and X 1,,, = XIL+XN. The set loop impedance ZiI,,+ZN,,defines the zone reach.

2.2.1 Self-polarization

In the case of self-polarization, K? is equal to !Iuf/LI.Inserting Equations (19-22) for the faulted phase current andphase voltage into Equation (5), gives:

(24)

Difference between phasors K,2 and:K

equivalent circuit for a

The following notations are used in Figure 4:

Zs= Zero-sequence source impedance

ZOL = Zero-sequence line impedance from substation to faultpoint

Z = Neutral earthing impedance10= Zero-sequence voltage measured at the substation

10 = Zero-sequence current measured at the substation4.= Fault component current at the fault point

RF = Fault resistance between phase and earth

We assume that there is a fault between phase LI and earthand, for reasons of simplicity, that the healthy phase currents(L2 and LU) are equal to zero.

Based on Figure 4 the faulted phase current is given by:

LI - _ fE (19)2-ZI, +ZOS +2.ZIL+-ZO, +3-RF +3-Z,

Similarly for the phase voltages:

2.4I+Zo+2 Z.+Z), ±3*R, ±3-ZE

f, (Z1, ±Zos ±2.I + Z,~ +3.R, 4-.Z, )a 2 n*-41 flE(UL2 ý I ~ .- 2- ZI,+ , +2.Z,, +Z,, +3.R, +

3.Z,

E, -(4I +Z., +2.4I +Z.1. +3R, +3-Z,)-a a'-. -ft +(-3.

tLL3 2-Z,, +Z,, +2.Z,, ±Z, +3.R, +3- Z

Inserting Equations (19-22) for the faulted phase cuphase voltage into Equation (4) for KI gives:

K, =Z,, Z, +R,. -(91,+Z,_

The term ZIL+ZN+RF represents the measured f,impedance ZLO = RLp+ j-Lp where RL,,, = R

2K2 _efp1 - KI ! ýIZL + ZNX + RF, (ý11. + 4Z + R, +( Z&,))

ý U,+ _ZN-, (25)

As the phasor difference K? - Ki is equal to Zl,, + Z~t theequivalent source impedance ZSeq, is equal to zero in the caseof a self-polarized mho circle. This means that the mho circlewill not expand due to the fault. The mho circle is fixed in theimpedance plane and is explicitly defined by the line replicaimpedance.

2.2.2 Cross-polarization

In the case of cross-polarization K, is equal to jK'jU-L3/(l3 .-LI).Inserting Equations (19-22) for the faulted phase current andphase voltage, gives the following:

K 2 -- _o, pot ý411 +ZN +R, +(Zý 1 1 +4

SN +-Z) (26)

As the phasor difference K2 - K, is equal to

-Zist+ZN.+Zls+Z~s+ZF, the equivalent source impedanceZseq, is equal to Zis+Z~s+ZF in the case of a cross-polarizedmho circle. The mho circle expands by Zjs+ Z~s Z duringthe fault, as illustrated in Figure 3 (right).

2.2.3 Positive-sequence polarization

In the case of positive-sequence polarizationfJ/IL. Inserting Equations (19-22) for the

(20) current and phase voltage gives the following:

2jK2_M-q._po=ZIL +ZN +RF +(--Z Is+sZ3-+N Z-E

faulted phase

(27)

(21) As the phasor difference K? - Kij is equal toZI.,ZNt+2/3+.Zls+Z~s+ZFe, the equivalent source impedance

Z4 0 )'El Zevis eult 2AZls+ZŽ4s+ZE in the case of positive-

(2) sequence polarized miho circle. As illustrated in Figure 3(2) (right), the mho circle expands by %*Zis+ZŽ4s+ZF during the

rrent and fut

Based on Figure 3 the mho circle can now be defined usingthe phasors K, and K?:

" Radius, r

* Midpoint, m!

r=I(K, -KI)/21 (28)

159

Figure 4: Symmetrical componentsingle-phase-to-earth fault.

L2_MfPW ý11. +ZN +RF

nt = dir -(Z, + (KI - K2) / 2) (29)

where dir = +1, if the operation direction is forward, -1, if theoperation direction is reverse.

In the case of a self-polarized mho circle, the equations arereduced to the form:

* Radius, r

* Midpoint, m

r = Z,,, /21

m=dir-Z,R1 12

E

0

(30)

(31)

3

2

1

0

-1The calculated fault ioop impedance ZL~ LO + j XL~will be inside the mho circle, if the following equation is true:

(L, - Re(g!))2 + (X" IM(aJ)2- r < 0 (32)

Fulfilment of the Equation (32) results in activation of theoperate signal. Calculation of the radius r and the midpoint mnshould not be released before the initial transients of the faulthave been decayed. Otherwise the calculation of radius andmidpoint will be affected, which results in fluctuation of thecharacteristic.

3 Simulation results

Next the behaviour of the Equations (28-32) was analyzedusing computer simulations. The PSCADIEMTDC transientsimulation program was used to generate test data for phase-to-phase faults. A 33 WV, 50 Hz, network with the followingparameters was simulated:

* Positive-sequence source impedance Zjs = l.5Z850 ohm* Zero-sequence source impedance Zos = 4.5-/85" ohm* Source impedance ratios SIR = s/L:

Case#l1: SIR = 10,Positive-sequence line impedance setting:ZLRI = ZIt= Zjs/1O = 0. 15Z85- ohm

Case #2: SIR = 0.5,Positive-sequence line impedance setting:Zu~u = Zise, = Zis/0.5 = 3/85' ohm

The results are shown in Figures 5 and 6. Also the activationof the operate signal is shown. This operate signal is theoutput of the algorithm itself and does not include the delayof the output relay of the actual feeder terminal. As can beseen from Figures 5 and 6, cross-polarization provides thegreatest expansion of the mho circle. This matches the theorypresented in Chapter 2. In this simulation example, theincrease of the SIR from 0.5 to 10 leads to a slightly longeroperate time. In order to further analyze the performance ofthe algorithm the authors will conduct full-scale tests in aplayback simulation environment (PSCAD/RTP), where e.g.isochronous contour curves will be determined.

.E20CL 0!ý-20

Self-pularization

-2 -1 0 1 2R (ohm, prim)

IL2

1- 7Operate0 0.4 0.42 0.44 0.46 0.48 0.5

Time (sec)Figure 5: Analysis of the mho circle in the R-X plane,SIR = 0.5, phase-to-phase fault,

E.

0L

E.

0.20

-0.2-0.4-0.6-0.8

-1-1.2-1.4

200

Selt polarization

.,oia ai o)

-0.8 -0.4 0 0.4 0.8R (ohm, prim)

ZL

1 Operate00.4 0.42 0.44 0.46 0.48 0.5

Time (sec)Figure 6: Analysis of mho circle in the R-X plane, SIR = 10,phase-to-phase fault.

4 Field testing and experience

In recent years, ABB Oy, Distribution Automation, Finlandhas made intensive field tests in co-operation with someFinnish power utilities to test and develop new protectionalgorithms and gather data from distribution networks.Below, one field test case was studied. The test was made inthe 20 kV, 50 Hz rural distribution network of the utility ofSuur-Savon Sdihk6 Oy, near the city of Juva in Finland.

160

110/20 kWSubstation

0 2

Feeder data:*Total length: 153 km*Length of the main line: 43 km*Number of distribution transformers: 123*Peak load: 1.1 MW*Z1,.. = 26.8 + j. 18.0 ohm

10 krn iKANTTA LA

Figure 7: Test feeder configuration.

Test case: L23 short-circuit fault at Kanttala, approximately42 km from the substation. The SIR equals to 0. 16.

The behaviour of the algorithm is shown in Figure 8. Theoperating speed is approximately 32 milliseconds.

25-~20

.- 15

Eý10 ?= 5 \ Self polalizationl

0 0t

-5-10

0 10 20 30R (ohm, prim)

The behaviour of the algorithm as a function of time has beenanalyzed in Figure 9. Both the radius r and the absolutedifference between the estimated fault loop impedance Zj.,,and the calculated midpoint in are presented. As can beenseen, the fault transients cause initial oscillations in thevariables. After about one cycle the variables are stabilized totheir final values and the dynamic expansion of the mhocharacteristic reaches its final form. It should be noted thatthe zone boundary comparison (Equation (32)) is started oncethe release signal from the starting function has beenactivated.

0.Q~7- 1 L2-7 -L3

~-500

24 ~ 2 3 a b s ( Z ,P-Mn )*c. 22

~ 21Calculated radius rfor-ro 20 cross-polarized mho circle

~190c: 18

17a)cL 16E 1

- 15

1 Release-signal

0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74Time (sec)

Figure 9: Calculation of variables of Equations (28-29) as afunction of time during a phase-to -phase fault.

5 Conclusions

-~500 -~*. 0 /1 L2[

_-500_Z

00.64 0.65 0.66 0.67 0.68 0.69 0.7Time (sec)

Figure 8: Analysis of mho circle in the R-X plane, phase-to-phase fault.

The source impedance can be estimated using phasors K, and

ZlS ý[i 2 _cross pot -11 -Ziset = 1.1 +j-5.0 ohm

This closely matches the value obtained from the networkdatabase of the utility's DMS.

This paper describes a novel way of implementing the mhocharacteristic so that it can be analyzed in the impedanceplane in a similar way as the quadrilateral characteristic. Themethod enables the dynamic expansion of the mho circle as aresult of the healthy voltage polarization during faultconditions. This has been validated through computersimulations and field tests. The algorithm will beimplemented in the next generation feeder terminals targetedto global power distribution and sub-transmission markets.

6 Acknowledgemnents

The authors thank the following persons for their support inthe performance of the valuable field tests: MarkkuViholainenlABB Oy, Hannu Rautio, Heikki Majanen/Suur-Savon Stibko Qy.

7 References

[1] "Modem distance protection functions and applications",Cigre working group B5. 15 - Draft 7.0, October 2007.

161