18a) Ground Distance Relays PPT
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Transcript of 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
Residual Compensation (2)
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
Residual Compensation (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
Residual Compensation (4)
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
Residual Compensation (5)
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
Residual Compensation (6)
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
Residual Compensation Factors –RE/RL and XE/XL (2)
ZL =
Z1
ZE = ZN
XL=
X1
.
XE
RL=R1
RE
X
R
ZLoop
RLoop
XLo
op
Residual Compensation Factors –RE/RL and XE/XL (3)
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
Residual Compensation Factors –RE/RL and XE/XL (4)
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)
Residual Compensation Factors –RE/RL and XE/XL (5)
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 (4) – converted values
Spreadsheet (5) – 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
Characteristic Shapes, Residual Compensation and Resistive Reach (2)
Characteristic Shapes, Residual Compensation and Resistive Reach (2)
( )RtfRarcIar
IremotetoRFLoop +⋅⎟⎠⎞
⎜⎝⎛ +⋅= 1)2.11.1(
Characteristic Shapes, Residual Compensation and Resistive Reach (3)
( )
KNx
RtfRarcIar
Iremote
toRFph+
+⋅⎟⎠⎞
⎜⎝⎛ +⋅=
1
1)2.11.1(
Characteristic Shapes, Residual Compensation and Resistive Reach (4)
( )
RLRE
RtfRarcIar
Iremote
toRFph+
+⋅⎟⎠⎞
⎜⎝⎛ +⋅=
1
1)2.11.1(
Characteristic Shapes, Residual Compensation and Resistive Reach (5)
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
Characteristic Modeling & Testing (1)
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.
Characteristic Modeling & Testing (11)
Scalar factors -- RE/RL and XE/XLPer-phase model Loop Model
Characteristic Modeling & Testing (11)
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
Characteristic Modeling & Testing (6)
ZN
Z1
P4
P3
P2
Z1L
P4L
P3L
P2L
RF4
RF5
RF2
RF3
RF4
RF3
RF2
P5 = P5L
P’2
P’2L
Characteristic Modeling & Testing (7)
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)
Characteristic Modeling & Testing (8)
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
Characteristic Modeling & Testing (9)
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
Characteristic Modeling & Testing (10)
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
Characteristic Modeling & Testing (11)
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
Characteristic Modeling & Testing (12)
User-interface helps in modeling using setting
Characteristic Modeling & Testing (12a)
User-interface helps in modeling using setting
Characteristic Modeling & Testing (12b)
User-interface helps in modeling using setting
Characteristic Modeling & Testing (13)
Importing characteristics exported by relay software
Characteristic Modeling & Testing (14)
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?