Issues and Solutions in Setting a Quadrilateral Distance Characteristic

Issues and Solutions in Setting a Quadrilateral Distance Characteristic

By Dr. Juergen Holbach ([email protected]) Vythahavya Vadlamani ([email protected]) Dr. Yuchen Lu ([email protected]) Siemens Power Transmission and Distribution, Inc Raleigh, North Carolina

Presented to the 61st Conference for Protective Relay Engineers College Station, Texas April 1-3, 2008 1st edition

978-1-4244-1949-4/08/$25.00 ©2008 IEEE

89

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Issues and Solutions in Setting a Quadrilateral Distance Characteristic Abstract The MHO characteristic is used very extensively in North America over the last decades in distance relaying. They are simple to design with electro mechanical components and simple to set. With the introduction of static and numerical relays other characteristics have been developed to overcome certain limitations of the MHO circle. More and more quadrilateral characteristics are used here in North America for ground faults on short lines in particular. The advantage is that the resistive reach can be selected via a setting and is not anymore limited by the characteristic of the MHO circle which particularly is a problem on short lines. This advantage of MHO circle becomes a challenge in quadrilateral characteristic for the setting engineer because he has to select an appropriate setting. This paper will discuss some of the guidelines to set the resistive reach on a quadrilateral characteristic. This paper also discusses the requirements for zone 3 settings from NERC. On the other side the advantage of the MHO circle, to be insensitive for arc faults in combination with heavy load, is a challenge for the quadrilateral characteristic and requires special attention for a secure functionality. The paper will discuss the source of the problem caused by load current in combination with arc faults and introduce some solutions. Guidelines will be outlined to set the quadrilateral characteristic accordingly to prevent an insecure operation. With the introduction of the quadrilateral characteristic it becomes possible to do the zero sequence compensation more effectively as the compensation with a complex ko factor used in the MHO circle. First the paper will show the limitations of the zero sequence compensation done with a complex ko factor and introduce some modern solutions and talk about their advantages. Calculated examples will demonstrate the benefit of this method. The paper will also give some guidelines and limitations in applying this new compensation method. Basics The distance protection function calculates out of the voltage and current measurements from one line terminal the loop impedance to the fault. The distance protection needs to calculate out of the loop impedance in the next step the line impedance because the setting is done in relation to the line impedance. For phase faults this can be simply archived by dividing the loop impedance by a factor of 2. On ground faults, information about the zero sequence impedance is needed and entered into the relay, so that the relay is able to calculate the line impedance out of the loop. By assuming that the impedance distribution along the line is constant, the location of the fault can be calculated and a trip decision can be issued by comparing the calculated line impedance to a setting inside the relay. For the trip decision on an overhead line normally only the reactance of the impedance needs to be considered because the measured resistance includes not only the line resistor but also an arc fault resistor and the footing tower resistor and can therefore not be used to determine the fault location. Several characteristics are developed which have all in common that the reactance is used for the tripping decision. However, the measured resistor is used to reduce the applicable reactance or block the tripping at all if the resistor is too high so that the

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measured impedance may be inside the load area or the expected error on the reactance calculation may be too high. The most common characteristics are the MHO circle and the quadrilateral characteristic. Quadrilateral characteristic is most preferred when protecting short transmission lines as this provides substantial resistive coverage and arc compensation than the traditional circular characteristics

X

R

Figure 1:Impedance characteristic Setting resistive reach for short lines in quadrilateral characteristic involves various factors which will be discussed in the following chapter. Fault Resistor Most of the faults on high voltage overhead lines result from isolator flash-overs. The short circuit current flows from the faulted conductor via the arc to the isolator and through the tower to the ground. This implies that at the fault location the arc resistance and tower footing resistance should be considered when calculating the fault resistance. In cable networks the fault resistor can normally be neglected. In the following discussion we are mainly concentrating on a fault resistor RF on an overhead line and the influencing factors. The fault resistor RF consists of an arc resistance and a tower footing resistance.

RF = RARC + RTF

Eq (1)

Where RF = Fault resistance RARC = Arc resistance RTF = Footing tower resistance The fault resistance for phase to phase and three phase short circuits mainly includes only an arc resistance. It need to be mentioned here that the calculation of a possible arc resistor is no an exact science and there is not a single but several formula to calculate arc fault resistance, according to the literature. Two of the most commonly used models are listed here for


our discussion. In order to arrive at the highest possible estimate for the fault resistance we consider Eq (2). By using this model, the arc resistance can be higher than the Warrington formula and there by avoiding any under reach.

The most commonly used formulas to arrive at the arc fault resistance are: 1.

Worst case formula

R ARC =

762.l ARC [:] I ARC

Eq (2)

lARC = Arc length in Feet IARC = arc current in Amps 2.

Warrington’s formula

R ARC =

8750.l ARC [:] .4 I 1ARC

Eq (3)

lARC = Arc length in Feets IARC = arc current in Amps The fault resistance calculated above is valid only for the first cycles because of the dynamics of an arc. Over time the arc tents to increase its diameter. The arc resistance varies with the fault current ,with time and with the wind velocity.

§ 5.v.t B R*ARC = ¨¨1 l ARC ©

· ¸¸ R ARC [:] ¹

Eq (4)

lARC = Arc length in Feet IARC = arc current in Amps v = wind velocity (feet/sec) tB = arc duration in sec Tower Footing resistance: The tower footing resistor depends very much on environmental conditions and may vary very much along the line. The actual value can normally only be obtained by measuring the resistor. It is important to know whether a ground wire is used on the


tower. If it is used, the tower footing resistance and ground wire on the overhead line can be represented as a T section connected in series [1] The effective tower footing impedance as derived by [1] is given as

Z ETF

1 RTF Z LNW 2 1 RTF Z LNW 2

Where Z LNW

Eq (5)

( Z 'GW I AS ) 2 1 Z 'GW l AS RTF Z 'GW l AS 2 4

Eq (6)

ZETF = Tower footing impedance RTF = Tower Footing resistance ZLNW = Equivalent impedance of tower footing resistances Z’GW = Ground wire impedance Neglecting ground wire impedance the equivalent tower footing impedance can be written as

Z ETF

1 RTF Z ' GW l AS 2

M 1 RTF Z ' GW l AS e j GW 2 2

Eq (7)

Example: Distance between the towers Ground wire resistanc Ground wire reactance Tower footing resistor

lAS = 0.15 miles, R’GW = 0.374 :/mile, X’GS = 1.2 :/mile, RTF = 10:

results in Z ETF = 0.54 + j 0.4 : On lines with ground wires the fault current flows through several parallel tower footing resistances and the resultant resistance is substantially reduced and hence often neglected. Furthermore, the effective ground impedance (ZETF) contains inductive component and this 0.4: would easily correspond to approx 1-1.5 mile line length on a HV transmission line and can result in under-reach situation. Where as if the ground wires are not present the resistance can go substantially higher and can be in order of hundreds of ohms. Setting the fault resistor If the total fault resistor is calculated it builds the basis for the relay setting. Normally a security factor of 1.2 is applied to assure that the relay will detect the maximum fault resistor. However it is important to understand, that the fault resistor becomes a part of the loop resistor what is calculated by the relay out of the voltage and current


measurement. The settings for the reactive reach and resistive reach are done as line settings. The following consideration helps to understand how the calculated fault resistor need to be considered inside the settings. a) Ph-Ph fault with fault resistance at the fault location IA

XL

RL

IF

V AB RL

RF

XL

IB Two phase short circuit with fault resistance

Figure 2: Two phase short circuit with fault resistance

Substituting

A

= -IB = IF

VAB = VA-VB = 2 IF (RL + j XL) + RF . IF

Eq (8)

V A V B 2 I F

Eq (9)

ZL

RF 2

On phase to phase faults, the measured fault resistance becomes divided by a factor of 2 by the relay to convert from a loop impedance to a line impedance. b) Ph-ground fault with fault resistance (single ended in feed) On phase to ground faults it is important to know how the zero sequence compensation in the relay is done. In the next example a zero sequence compensation method is used which is implemented in Siemens distance relays with quadrilateral characteristics.

IL

XL

RL

V ph G

RF

XG

RG

IG

Figure 3: A Fault Loop for a Single-Line-to-Ground Fault


The voltage at the relay location is given by

Vph-G = IL . (RL+j XL) – IG. (RG + j XG) + IL. RF

Eq (10)

With introducing the zero sequence compensation factors RG/RL and XG/XL which are settings inside the relay and the simplification L

= -IG = IF

we can write:

Z Loop

V ph G

R L calculated

IF

RLoop jX Loop

RLoop R 1 G RL

RL

RL (1

RF R 1 G RL

RG X ) RF jX L (1 G ) Eq (11) RL XL

Eq (12)

In this case, the fault resistance will not add to the calculated line resistor with half of its value like on phase to phase faults, but rather depending on the setting RG/RL. We can see that for the resistive reach setting on phase to phase faults we need to set only half of the calculated total fault resistor and for ground faults we need to take also the zero sequence compensation factor RG/RL in consideration. The setting for the resistive reach for ground faults is determined by the total fault resistor divide by a factor (1+RG/RL). Before selecting a setting, the way how the particular relay will perform the zero sequence compensation needs to be understood! The example shown here is only valid for Siemens relays with quadrilateral characteristic. Zero Sequence compensation The majority of the short circuits that occur in the transmission system are ground faults. In this case the accuracy of the distance protection depends also on the zero sequence compensation setting for the ground impedance. The exact value of this compensation factor is often not known. Even if the ground impedance of the line is determined by measuring the zero sequence impedance prior to commissioning – which is usually not done due to time and cost constraints – the actual effect of ground impedance during the short circuit may be severely dependent on the actual fault location. The effective ground impedance is often not proportionally distributed along the line length, as it may vary significantly depending on the consistency of the ground (sand, rocks, water, snow) and the type of grounding applied (tower grounding, parallel cable screens, metal pipes). Normally it is sufficient for the zone 1 distance protection function to know the zero sequence factors which is measured on the remote line terminal. For all other zones the relay should have a separate zero sequence compensation factor settable because in may cases the factor can change drastically on the adjacent line/cable.


We want to point out that modern numerical relays have as a standard function a fault recorder ability implemented inside the relay. The fault recorder data can be used to determine the real zero sequence factors on a transmission line. In the following to methods of zero sequence compensations are introduced and compared. The compensation with a complex Ko factor is common in many relays and is simple to implement. On a Mho circle this is actually the only way the zero sequence compensation can be performed. However, a quadrilateral characteristic offers better ways to do the compensation what becomes shown in the following. Setting of residual compensation factors k 0 and { K R Usually the positive sequence impedance of the line Z 1 impedance Z 0

RG XG , KX } RL XL R1 jX 1 and zero sequence

R0 jX 0 are available for setting the residual compensation factors.

The conventional residual compensation factor k 0 can be calculated as k 0

Z 0 Z1 . 3Z 1

Note that in general k 0 is a complex number. To calculate { K R , K X }, we need to first calculate the ground impedance Z G and line impedance Z L by the following equations:

ZG

RG jX G

Z 0 Z1 3

ZL

RL jX L

R1 jX 1

R0 R1 X X1 j 0 3 3

Eq (13) Eq (14)

Then, { K R , K X } can be calculated as

KR KX

RG RL XG XL

R0 R1 3R1 X 0 X1 3X 1

Eq (15a) Eq (15b)

Note that { K R , K X } are real numbers and generally k 0 z K R jK X . Impedance Calculation based on different compensation factors In the following we will show how the zero sequence compensation will effect the impedance calculation if a fault resistor is involved. For simplification we assume that the phase and ground currents are equal.


IF

XL

RL

V phG

RF

XG

RG IF

Figure 4: A Fault Loop for a Single-Line-to-Ground Fault The traditional impedance calculation method uses the following equations for calculating resistance and reactance of the phase-to-ground loops:

Z ph G

Where V

ph G

V ph G I F (1 k 0 )

,

R ph G

real{ Z ph G },

X ph G

imag{ Z ph G }

Eq (16)

is the measurement of phase-to-ground voltage for the faulted phase,

I F is the measurement of fault current for the faulted loop. With above measurements and the { K R , K X } residual compensation factors, the phaseto-ground impedance are calculated as:

R ph G

real{

V ph G I F (1 K R )

},

X ph G

imag{

V ph G I F (1 K X )

}

Eq (17)

The fault resistance is one of the factors which will cause an error in the impedance calculation. For bolted faults (fault resistance RF 0 ), both compensation methods can correctly calculate the fault impedance. However, if the fault resistance exists ( RF z 0 ), the traditional k 0 compensation method and the { K R , K X } compensation method will produce different impedance calculation errors. This is illustrated in the following Figure.


X

X RF 1 k0 Z ph G

ZL

ZL

RF 1 KR

Z ph G

R

R

(a) impedance calculation using traditional k0 compensation method

(b) impedance calculation using {Kr, Kx} compensation method

Figure 5: Comparison of different compensation methods The traditional k 0 compensation method will produce an impedance calculation error on both R-axis and X-axis, which is due to the factor that k 0 is generally a complex number. The { K R , K X } compensation method will produce impedance calculation error only on R-axis. Example: A ground fault with fault resistance

XG

IF

RL

XL

V ph G

RF

RG

XG

IF

Figure 6: Simple model for a ground fault Given line impedance data: Z1=R1+jX1=2+j10 (ohm) Z0=R0+jX0=32+j40 (ohm) Source reactance


XG= 10 Ohm Calculate RL, XL, RG, XG as RL = R1 = 2 (ohm) XL = X1 = 10 (ohm) RG = (R0-R1)/3 = 10 (ohm) XG = (X0-X1)/3 = 10 (ohm) Assume the generator phase to ground voltage as (secondary): V G fault resistance RF=5 (ohm)

69e j 0 (V) and

The resulting fault current is:

IF

VG = 0.986-j1.741(A) R L jX L RG jX G R F jX G

k0

ZG ZL

10 j10 2 j10

1.154 j 0.769

Measured voltage by the relay:

VR

V G I F jX G

69 (17.41 j 9.86)

(51.59 9.86)V

By the k 0 compensation method, we can obtain the calculated impedance:

Z ph _ G

VR I F (1 k 0 )

51.59 9.86 =4.067 + j10.75(ohm) (0.986 j1.741)(2.154 j 0.769)

R ph _ G

real{Z ph _ G } =4.067 (ohm)

X ph _ G

imag{Z ph _ G } = 10.75 (ohm)

By the { K R , K X } compensation method, we can obtain the calculated impedance:

R ph _ G X ph _ G

VR } =2.83 (ohm) I F (1 K R ) VR imag{ } = 10 (ohm) I F (1 K X )

real{

The results show that although the fault resistance causes significant calculation errors on the R ph _ G for both methods, only the { K R , K X } compensation method produces the correct X ph _ G value.


Setting of RG/RL As discussed earlier, by selecting a setting for the fault resistor reach on ground faults, the RG/RL factor set inside the relay need also to be taken in consideration. The setting should be the total fault loop resistor (RL+RG+Rarc+RTF) divided by a factor of 1+RG/RL. If the RG/RL factor, which results out of the line data is used as a setting in the relay, the line resistor calculation of the distance protection will only be correct for faults without a fault resistor as we saw above! On overhead lines many times an arc fault is involved and the calculated line resistor will therefore always be wrong. This is normally not a problem, because we set in the quadrilateral characteristic an additional resistor to compensate for this. Therefore the setting RG/RL which will only help to determine the line resistor for faults without an additional fault resistor is not of any importance. It is normally not recommended to set the calculated value which results out of the line data, which can in some cases result in factor >5 . The disadvantage of such a high factors is that any loop resistor gets divided by a (high factor +1) and therefore also load and unfaulty loops on long transmission lines can be seen inside of the trip zone! It is normally recommended to set RG/RL to a factor of 1, than the line resistor for ground faults gets calculated whit the same factor as for phase faults! Load influence on resistive faults Transmission of load across long transmission lines results in a phase displacement between the voltages V1 and V2 at the two line ends (Figure 7 and 8). In the event of a short circuit, the generator voltages (Figure 7) feeding onto the fault will therefore have different phase angles. In a first approximation, the short circuit currents from the two ends are also displaced by this angle. The short circuit current flowing from the two line ends through the ohmic fault resistance RF causes that the relays will see the fault resistor as resistive and inductive impedance due to this phase displacement.

Figure 7: Infeed from both ends


Figure 8: Phase shift between the sources voltages and fault currents

Figure 9: Influence on the measured impedance At the line end that is exporting the load, the measured reactance is reduced, the phasor (I2/I1)y RF is rotated downwards (Figure 9). At the line end that is importing load, the measured reactance is increased; the phasor (I2/I1)y RF is rotated upwards. The smaller the phase displacement between the currents I2 and I1 is, the smaller the influence on the measured reactance will be. In the case of an unloaded line, the generator voltages and the currents at both ends are in phase. This assumed that the angles of the fault impedance loop are equal on both sides of the fault, which is on transmission lines normally fulfilled. On faults without ground, the fault impedance will be measured only with an additional resistive part what can be considered in the distance protection settings. To measure higher reactance in a case of load import is normally acceptable; even so it can lead to an underfunction and higher fault clearing times. The reduced reactance measurement in the case of a load import can lead to an overreach and needs to be avoided. The characteristic of a MHO circle has for this situation an advantage because it automatically reduced the reactance reach for resistive faults. The user doesn’t need to set this behaviour but also has no influence on limit the amount of the reduction. This is particular on short line a problem because the MHO circle almost has no resistive reach. But also on long transmission lines with a large load angle the characteristic of the Mho circle get shifted and limits so the resistive reach.


Figure 10: Load effect on MHO circle The quadrilateral characteristic in many relays can be adjusted so that the distance protection function is stable for faults with load import. This put an additional burden to the setting engineer because he has now to find the appropriate setting for this additional tilt.

Figure 11: Example of quadrilateral characteristic In some relays this tilt of the characteristic is automatically done based on negative or zero sequence measurements. However, all this automatic adjusting algorithms normally are using some assumptions about the power system and the accuracy of this automatic adjustment depends on the degree in which the assumptions are confirmed by the real conditions. By manually adjusting the slope in the characteristic the protection engineer can find the worst case condition and adjust to it. However, this requires knowledge about the power system and in some cases simulations to find the worst case scenarios. In the following


a graph is presented which helps how much the quadrilateral characteristics needs to get tilt with the angle D to avoid an overreach based on the influence of load on an fault resistor.

Figure 12: Compensation setting for load influence [4] The Figure 12 uses the ratio of the of the reactive reach setting to the resistive reach setting and the max. load angle in the power system to determine the tilt. To determine accurately the effect of load on the fault resistor, several more parameters needs to be evaluated too, like the zero sequence system seen from both sides of the fault, the fault location etc. The shown graphic represents a solution for most of the usual grid conditions and is based on worst case scenarios. Summary The paper discussed the main factors which need to be considered when setting a quadrilateral characteristic. We presented formulas to calculate an arc resistor on an overhead line. We showed the effect of a ground wire and its influence when present. The ground wire will reduce the fault resistance in orders of few ohms versus up to few hundreds when not present. However we want to point out that the ground wire will add some inductive/reactance to the fault impedance. The zero sequence compensation is an important issue when setting a distance relay for ground faults. In the paper, we compared two kinds of compensation methods, the traditional k0 and the {RG/RL, XG/XL} method. We showed that both methods will correctly calculate the fault impedance in the case of bolted faults. However, in the case of unbolted faults, {RG/RL, XG/XL} compensation method will introduce a calculation error only on R-axis, while k0 will introduce calculation errors on both R-axis and X-axis. A simple calculation example for a single-line-to-ground fault is presented to show this difference. Also discussed was the influence of load on the impedance calculation if a fault resistor is present. A graphic was presented which helps to determine how much a quadrilateral characteristic needs to get tilt to avoid an overreach of the distance protection function.


References [1] Gerhard Ziegler, "Distance Measurement, Influencing quantities," chap. 3 in Numerical Distance Protection, 2nd ed., Publicis Corporate Publishing, Erlangen, Germany: 2006. [2] S.Ward, "Comparison of Quadrilateral and Mho distance characteristic," presented at 26th Annual Western Protective Relay Conference 1999, Spokane, Washington. October 26-29, 1999 [3] G. Swift, D.Fedirchuck, T. Ernst, “Arcing Fault ‘Resistance’ (it isn’t)” presented at 29th Annual Western Protective Relay Conference 2002, Spokane, Washington. October 22-24, 2002 [4] 7SA522 Manual V4.6, C53000-G1176-C155-4, page 89, Siemens 2004 [5] S. Kaiser, "Different Representations of the Earth Impedance Matching in Distance Protection Relays or What Impedance Does a Digital Distance Protection Relay Measure”, OMICRON Anwendertagung 2004


Issues and Solutions in Setting a Quadrilateral Distance Characteristic

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