18a) ground distance relays ppt

Ground Distance Relays – Understanding the Various Methods of Residual Compensation,

Setting the Resistive Reach of Polygon Characteristics, and Ways of Modeling and Testing the Relay

Jun VerzosaDoble Engineering Company

Watertown, Massachusetts, USA

Presented to Protection Testing User’s Group

Salt Lake City, Utah26-28 September 2005

Topics Covered

• Why this paper?• Residual compensation or Zero-sequence

current compensation• Typical Polygon characteristics and resistive

reach setting• Modeling and testing ground distance

characteristics and influence of residual compensation

Ground Distance Compensation Factors –Survey of Terminology (1)

Names• Residual compensation• Zero-sequence current

compensation• Ground (or earth) – return

compensation• Neutral (or earth or ground)

impedance correction

Ground Distance Compensation Factors –Survey of Terminology (2)

Symbols• KN• K0• KE• KG

• KZN, KZPh• Z0/Z1• RE/RL, XE/XL• Etc.

Some relays have no factor setting but internally calculate compensation from:• R1, X1, R0, X0• Z1 and Z0

Power system –Phase A to Ground Fault

n Es

Z1, Z0

21G A-N Fault

Z1S, Z0S

Ia .

VaR

FR

Symm. Component sequence circuit

E1

ZS1

nZ1

ZS2

nZ2 = nZ1

ZS0

nZ0

Pos. Seq.

Network

Neg. Seq.

Network

Zero. Seq.

Network

F1 F2 F0

Symmetrical Component Network for SLG fault at F

Relay Location R

Fault Location F, VF=0

I1 I0I2

V1R V2R V0R

N1 N0N2

I1 = I2 = I0 .

Residual Compensation (1)

The voltage at the fault point F is zero (assuming a bolted fault), and the sequence voltages are:

V1R = I1•n•Z1V2R = I2•n•Z1V0R = I0•n•Z0

And the PhA-N voltage at the relaying point is:

VaR = V1R + V2R + V0R= I1•n•Z1 + I2•n•Z1 + I0•n•Z0


The phase A current Ia at the relaying point is then

Ia = I1 + I2 + I0

and, since I1 = I2 = I0, the residual (neutral) current is

In = Ia + Ib + Ic = 3I0

I0 = In / 3 = Ia / 3


If we add and subtract I0•n•Z1 in the voltage equation, factor out n•Z1 and I0, and substitute the Ia and I0 equations

VaR = I1•n•Z1 + I2•n•Z1 + I0•n•Z1 – I0•n•Z1 + I0•n•Z0

= ( I1 + I 2 + I0 ) • n•Z1– I0•n•Z1 + I0•n•Z0

= Ia • n•Z1 + I0 • (Z0 – Z1) • n= Ia • n•Z1 + (Ia/3) • (Z0 – Z1) • n


If we use the voltage VaR and the current Ia directly for measurement the apparent impedance that is measured is

ZRapparent = VaR / Ia= n •Z1 + (Z0 – Z1)•n/3

The extra second term makes the result not very usable.

To make the relay easier to use, the objective in the design of most ground distance relays is to make the relay measure only the first term, n•Z1


If we substitute In/3 for I0 in the voltage equation and multiply the second term by Z1/Z1

VaR = Ia•n•Z1 +(In/3)•(Z0 – Z1)•n•Z1/Z1and simplify the equation to express the impedances as a factor of Z1, we obtain

VaR = [Ia + In• (Z0 – Z1)/(3Z1)] • n•Z1

If we define a constant KN= (Z0 – Z1)/(3Z1), VaR simplifies to

VaR = (Ia + KN•In) • n•Z1


Zrelay = VaR / (Ia + KN•In) = n•Z1where: KN = ( Z0 – Z1) / 3Z1

= ( Z0/Z1 – 1) / 3Residual Compensation is a technique that allows measurement of the fault impedance in terms of positive-sequence impedance, by adding a portion, KN, of the residual current In to the phase current.

KN = residual compensation factor

Ground-return Impedance (1)

Considering the previous voltage equation

VaR = [Ia + In• (Z0 – Z1)/(3Z1)] • n•Z1If we express the voltage drops in terms of Z1

VaR = Ia •n•Z1 + In• n•(Z0 – Z1)/3

This is the loop voltage from the relay terminal to the fault point and back, through a ground-return impedancen•ZN= n•(Z0-Z1)/3, to the neutral of the relay location.

Ground-return Impedance and Simplified Network Equivalent Circuit (2)

Hence, we can model the network as shown belowEA n*Z1Zs

EB n*Z1Zs

EC n*Z1Zs

n*ZNZNs

Relay Location IA

IC =0

IN

IB = 0

VaR

Ph A–NFault

F

=n*(Z0 - Z1)/3

Ground-return Impedance (3)

The impedance ZN is called the ground-return (or residual) impedance and is defined as

ZN = ( Z0 – Z1 ) / 3

Note also the relationships

ZN = KN • Z1Or

KN = ZN / Z1

Relay Implementation of Residual Compensation

Ia

In

Z1Z1

ZN

Z1Relay

Comparator Circuits

IA

A-N Fault

A

C

B

Van

Replica Circuits

Zero-sequence Current Compensation (1)

Considering the previous voltage equation and and if we replace In by 3•I0 we get

VaR = [Ia + 3•I0• (Z0 – Z1)/(3•Z1)] • n•Z1= [Ia + I0• (Z0 – Z1)/(Z1)] • n•Z1

We introduce K0 = (Z0-Z1)/Z1

VaR = (Ia + K0 •I0) •n•Z1

Zero-sequence Current Compensation (2)

Zrelay = VaR / (Ia + K0•I0) = n•Z1where: K0 = ( Z0 – Z1) / Z1

= Z0/Z1 – 1Zero-sequence Current Compensation is a technique that allows measurement of the fault impedance in terms of positive-sequence impedance, by adding a portion, K0, of the zero-sequence current I0 to the phase current.

K0 = residual compensation factor

Residual Compensation Factors –RE/RL and XE/XL (1)

xyzEA *ZLZs

EB ZLZs

EC *ZLZs

ZEZNs

Relay Location IA

IC =0

IN

IB = 0

VaR

Ph A–NFault

F

=(Z0 - Z1)/3

=RL + j XL

=RE + j XE


ZL =

Z1

ZE = ZN

XL=

X1

.

XE

RL=R1

RE

X

R

ZLoop

RLoop

XLo

op


ZE = ZN = (Z0 – Z1) / 3 = [ (R0 – j X0) – (R1 + j X1) ] / 3 = (R0 – R1)/3 + j (X0 – X1)/3= RE + j XE

ZL = R1 + j X1= RL + j XL


If we express ZLoop into its resistive and reactive components, and express them in terms of RL and XL, we can introduce ratio constants RE/RL and XE/XL

ZLoop = RLoop + j XLoopRLoop = RL + RE

= RL (1 + RE/RL)XLoop = XL + XE

= XL (1 + XE/XL)


The compensation constants can be derived from equations of RE, RL, XE and XL

RE/RL = [ (R0 – R1)/3 ] / R1 =

XE/XL = [ (X0 – X1)/3 ] / X1 =

⎟⎠⎞

⎜⎝⎛ −= 1

10

31

RR

RLRE

⎟⎠⎞

⎜⎝⎛ −= 1

10

31

XX

XLXE

Survey of Formulas, Names and Symbols

Common factors and formulas (1)

• KN = (Z0/Z1 – 1) / 3 magnitude & angle

• K0 = (Z0/Z1 – 1) magnitude & angle

• K0 = Z0/Z1 magnitude & angle

• K0ratio = Z0/Z1 magnitude and angles of Z1 & Z0

• K0x = (X0/X1 – 1) / 3 scalar

Common factors and formulas (2)

• RE/RL=(R0/R1-1)/3 & XE/XL=(X0/X1-1)/3• Some relays do not require a compensation factor

setting but internally calculate KN or K0 from from the positive- and zero-sequence impedance settings

- Z1 and Z0

- R1, X1, R0, X0

- ZN and Z1

Conversion from one form to another

Conversion from one form to another

Why Convert?• Test system does not support form of

compensation• Try testing with a different compensation form• Using existing relay setting on another relay• Replacing an existing relay

Spreadsheet (1) – mode selection

Spreadsheet (2) – data entry

Enter setting values

Spreadsheet (3) – converted values

Spreadsheet (6) – Z plot

Loop impedance diagramZ1

ZN

Z1angZLoopAng

ZNang

X1

RNR1

XN

RLoop

XLoop

ZLoop = Z1 + ZN

ZN = KN*Z1 = 1/3 (Z0/Z1 – 1)

K0 = (Z0/Z1 – 1)KN = K0 / 3

RL = R1XL =X1ZE = ZN

RE/RL = 1/3 (R0/R1 – 1)XE/XL = 1/3 (X0/X1 – 1)

Loop Impedance Calculation

Fault Resistance (1)Z1

Rtf

Rarc

VaR

IaR

AN fault

21

ZN

• Arc Resistance, Rarc• Tower Footing Resistance, Rtf

Fault Resistance (2)Z1

ZN

Z1angZLoopAng

ZNang

X1

RNR1

XN

RLoop

XLoop

ZLoopAng = Z1 + ZN

Rarc Rtf

RFLoop = Rarc + Rtg

RFLoop

VaR/Ia = Z1 + ZN + Rarc + Rtf

= ZLoop + RFLoop

Fault Resistance setting (1)

Z1

Rtf

Rarc

VaR

IaR

AN fault

21

ZN

RFLoop = (1.1 to 1.2) * (Rarc + Rtf)

Fault Resistance setting with Remote Infeed (2)

)(1)2.11.1( RtfRarcIaR

IremotetoRFLoop +⋅⎟⎠⎞

⎜⎝⎛ +⋅=

Characteristic Shapes, Residual Compensation and Resistive Reach (1)

No Resistive Reach SettingNo Resistive Reach Setting


( )RtfRarcIar

IremotetoRFLoop +⋅⎟⎠⎞

⎜⎝⎛ +⋅= 1)2.11.1(


( )

KNx

RtfRarcIar

Iremote

toRFph+

+⋅⎟⎠⎞

⎜⎝⎛ +⋅=

1

1)2.11.1(


( )

RLRE

RtfRarcIar

Iremote

toRFph+

+⋅⎟⎠⎞

⎜⎝⎛ +⋅=

1

1)2.11.1(


Regardless of the characteristic type the maximum resistive reach setting is affected by other factors

• Relay maximum resistive setting, • Maximum load• Use of load encroachment feature, • Relay current sensitivity, • Tilting effect of remote infeed current.

Fault Resistance Coverage (1)

RFLoopRFph

X1Z1

ZLoo

p

XLo

op

RFLoop = RFph*(1+KNx)

XLoop = X1 * (1+KNx)

Less fault resistance coverage

Fault Resistance Coverage (2)

RFLoop

Z1

ZLoo

pPhi1

PhiLoop

RFLoop

Z1

Phi1

X1

ZLoo

p

XLoo

p

PhiLoop

Characteristic Modeling & Testing (1)

Z1L

P4L

P2L

P3L

P3

Z1P2

P4

Per Phase Characteristic

Loop Characteristic

O

Per-phase modelConstant test current method

VaR = Ia * ZFault * (1+KN)Constant test voltage method

Ia = VaR / (ZFault * (1+KN))

KN = (Z0/Z1-1) / 3 ------ complex

Loop ModelConstant test current method

VaR = Ia * ZFltLoopConstant test voltage method

Ia = VaR / ZFltLoop


Z1L

P4L

P2L

P3L

P3

Z1P2

P4

Per Phase Characteristic

Loop Characteristic

O

Per-phase model looks more like actual setting.

Both models work well.

Loop model needs extra calculation of ZLoop reach and ZLoop angle.

KN = (Z0/Z1-1) / 3 ------ complex

Characteristic Modeling & Testing(2)K0x = (X0/X1-1) / 3 ------ Scalar

P2P5L

P4L

P3L

P2LP1L

P6

P5

P3

P4P1

P6LRFph

X1

Use Per-phase modelVa/Ia = Zfault (1+ KNx)

Per-phase model looks more like actual setting.

Both models work well.


Scalar factors -- RE/RL and XE/XLPer-phase model Loop Model


Scalar factors -- RE/RL and XE/XLPer-phase model Loop Model

• Per-phase model looks more like actual setting.

• Both models work well.• Loop model requires extra complex

calculations.

• If software supports RE/RL & XE/XL compensation, use per-phase model.

Characteristic Modeling & Testing(3)

KN = (Z0/Z1 – 1) / 3 & RFLoopZ1

RFLoopPhi1

Va

n*Z1*KN

n*Z1

RFLoop

Ia

Ia

+

Z1 is per-phase

is Loop

Characteristic does not include ground return impedance. It is included in the KN setting

Characteristic Modeling & Testing(4)Loop model

ZLoo

pZ1L

RFLoop

RFLoop

Z1

PhiLoopPhiLoop

Q

Resistive Reach is the same for per-phase and loop models and remains the same throughout.

Hence, we can model per-phase using separate fault resistance.

Loop model includes the ground return impedance.

Characteristic Modeling & Testing (5)Separate Fault Resistance –How to calculate loop impedance for testing

Start with P (Px,Pr)

Draw horizontal line to the Zline to intersect at P’P’x = Px

P’r = P’x/tan(Phi1)

RF = Pr – P’x

P’L = P’ *(1+KN)

PL = P’L + RF

Z1

P

Z1L

PL

RF

RF

P’

P’L

Phi1


ZN

Z1

P4

P3

P2

Z1L

P4L

P3L

P2L

RF4

RF5

RF2

RF3

RF4

RF3

RF2

P5 = P5L

P’2

P’2L


Allows testing using separate fault resistance for points -To the right of the line angle only-To the left of the line angle only- both left and right of line angle

If not checked,ZPLoop = ZP (1 + KN)


Loop Testing Per-Phase Testing

Characteristic Modeling & Testing (8a)

Loop Testing Per-Phase Testing• Per-phase model looks more like

actual setting. • Both models work well.• Loop model requires extra complex

calculations.

• If software supports complex KN compensation, use per-phase model,

• if reactance line tilt is small


If tilt angle is more than +/-3 deg using separate fault resistance is erroneous.

Use Loop Impedance model only.

P

RF

RFP’

PLP’L

Rs1Rs2

ZLoo

p

Tilt angle

Tilt angle


Angle of resistance blinder is different from loop angle, phiLoop.

Use Loop Impedance model only

RFloop

X1

phi1

XN

ZLoo

p

phiN

phi1

Per-phase

Loop

phiLoop


Some test software allow selection of several types of compensation factors.

Use these features if per-phase modeling and testing provides correct results for type of characteristic tested


User-interface helps in modeling using setting

Characteristic Modeling & Testing (12a)


Characteristic Modeling & Testing (12b)



Importing characteristics exported by relay software


Simultaneous testing of multiple zones with complex characteristics

•Load encroachment

•Directional Lines

Loop modeling and testing

Summary (1)

• Ground distance relays employ some form of compensation of the ground-return impedance in order to measure (and also to allow the relay to be set) in terms of positive-sequence impedance. A derivation these forms of compensation is presented.

Summary (2)

• The many names, symbols and formulas that are in use for residual or ground-return compensation pose a challenge to personnel who set and test the relays.

• Some forms of compensation that use different formulas are called by the same name and symbol. This can result in applying the wrong setting if one is not careful and may result in either relay misoperation or failure to trip.

Summary (3)

• The fault resistance reach, for polygon-shaped characteristics, is set in Ohms per phase in some relays while in other relays it is set in Ohms per loop. In some relay manuals this fact is not explicitly indicated.

• The ground-return compensation affects the fault resistance reach and the angle of the resistive blinder in different ways, depending on the design of the relay.

Summary (4)

• Each form of ground-return impedance compensation can be converted to another form. Formulas are derived to perform this conversion. These formulas are handy when a relay being tested has a compensation setting that is not supported by the relay test system.

• A spreadsheet that implements these formulas makes conversion easy and avoids calculation errors.

Summary (5)

• Testing the reactance line and résistance blinder of polygon characteristics can be done – Both in the per-phase impedance plane– Both in the loop impedance plane, – A 3rd test method models the reactance

line in per-phase and treats the fault resistance separately from the main impedance.

Summary (6)

• Selecting the most suitable model for testing depends on assessment of – How the angle of the resistive blinder is

affected by the residual compensation– Tilt angle of the reactance line. Testing

points for a reactance line that has a large tilt angle, using a separate fault resistance, will result in test errors.

Summary (7)

• Personnel who set relays and those who test them must have a good understanding of the methods of residual compensation, how the resistive reach is set and affected by the compensation and how the relay characteristics are modeled.

• Cooperation between these personnel is very important to actually verify their understanding of the settings and relay behavior and that the models are suitable.

Summary (8)

• The relay operation in the 2nd and 4th quadrants of polygon characteristics is affected by additional factors – including the

– behavior of the directional lines, – the type of characteristic lines (straight

lines or circular arcs), – and the source impedance.

Summary (9)

• Automated software allows easy modeling and correct testing of complex ground distance polygon characteristics with various forms of residual compensation factors.

Questions?

18a) ground distance relays ppt

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