46 calculation
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REL352AN-93L-02
Phase Comparison Relay REL352 Current Pickup Calculation
Introduction
This note describes how to calculate the current pick-up level for different types of faults.
IT current
REL352 uses sequence filters to obtain positive, negative and zero sequence currents. These currents arethen combined into one quantity:
021 021 ICICICIT ++=
The positive, negative and zero sequence current is computed from the phase currents by the use ofClarkes components based on sample currents that can mathematically be expressed as:
3
3
43.104983.043.134983.015966.0
3
43.134983.043.104983.015966.0
0
2
1
CBA
CBA
CBA
IIII
IIII
IIII
++=
++=
++=
The advantage of using Clarkes components is that they give a close approximation of symmetricalcomponents while not having the need of using complex numbers.
Note that all sequence component currents are referenced to phase A current.
General calculation of IT
Based on input currents and C-settings, the IT current is calculated as follows:
Settings
0
2
1
C
C
C
ABBApplication NoteSubstation Automation and Protection Division
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Phase Comparison Relay REL352 Current Pickup Calculation AN-93L-02
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Input currents
C
B
A
I
I
I
IT
3
)(
3
)43.104983.043.134983.015966.0(
3
)43.134983.043.104983.015966.0(
02
1
002211
CBACBA
CBA
T
T
IIICIIIC
IIICI
ICICICI
+++
+++
+++
=
=++=
Example 1a, phase A to ground fault
With settings
0.1
7.0
1.0
0
2
1
=
=
=
C
C
C
and input currents
0
0
00.5
=
=
=
C
B
A
I
I
AI
IT becomes:
ACCC
I
ICICICI
T
T
65.23
)0.5(
3
)15966.00.5(
3
)15966.00.5( 021
002211
=+
+
=
=++=
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Phase Comparison Relay REL352 Current Pickup Calculation AN-93L-02
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Example 1b, phase B to ground fault
With settings
0.1
7.0
1.0
0
2
1
=
=
=
C
C
C
and input currents
0
1200.5
0
=
=
=
C
B
A
I
I
I
IT becomes:
ACCC
I
ICICICI
T
T
33.13
)1200.5(
3
)12043.134983.00.5(
3
)12043.104983.00.5( 021
002211
=
+
+
=
=++=
That the IT current is different for a phase B to ground fault compared to phase A to ground is due to thefact that Clarkes symmetrical component computations are made referenced to phase A.
REL352 Trip Criterion
REL352 operates when the IT RMS current exceeds the LP setting, assuming that the relay is connected inloop-back or back-to-back (with the same current fed into the two relays):
thresholdoperatingset
currentcomposite
=
=
>
LP
I
where
LPI
T
T
It is also assumed that all other settings (IPL, IGL, ITA1, ITA2) are set so that they do not restrict tripping atthe set LP level.
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Phase Comparison Relay REL352 Current Pickup Calculation AN-93L-02
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Sometimes, ITA2 is the limiting threshold, and then the operating criterion will be:
thresholdoperatingset2
currentcomposite
2
=
=
>
ITA
I
where
ITAI
T
T
Pickup calculation
To determine the theoretical pickup current for different types of fault, we need to determine that the outputfrom the trip criterion exceeds the set operating threshold.
Set-up in loop-back or back-to-back is assumed so that IR= IL= IT, i.e. the infeed current from both ends areequal in magnitude and in phase. This represents an internal fault.
In order to determine the required current threshold for operation for different types of faults the expressionsabove for ITand sequence currents need to be entered into the formula, solving the phase current(s).
Phase A to ground fault
Input currents
0
0
0
=
=
=
C
B
aA
I
I
AII
Pickup current phase A
)15966.015966.0(
3
3
15966.015966.0
021
021
002211
CCCLPI
LPICICIC
LPICICIC
LPI
a
aaa
T
++>
>++
>++
>
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Phase Comparison Relay REL352 Current Pickup Calculation AN-93L-02
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Phase B to ground fault
Input currents
0
120
0
=
=
=
C
bB
A
I
II
I
Pickup current phase B
)12043.254983.057.15983.0(
3
3
12043.254983.057.15983.0
021
021
002211
++>
>++
>++
>
CCCLPI
LPICICIC
LPICICIC
LPI
b
bbb
T
Phase C to ground fault
Input currents
=
=
=
120
0
0
cC
B
A
II
I
I
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Phase Comparison Relay REL352 Current Pickup Calculation AN-93L-02
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Pickup current phase C
)12043.224983.043.14983.0(
3
3
12043.224983.043.14983.0
021
021
002211
++>
>++
>++
>
CCCLPI
LPICICIC
LPICICIC
LPI
c
ccc
T
Phase A to B fault
Input currents
0
180
0
=
=
=
C
abB
abA
I
II
II
Pickup current phases A and B
)]57.45983.015966.0()43.284983.015966.0([
3
3
)57.45983.015966.0()43.284983.015966.0(
21
21
002211
+++>
>+++
>++
>
CCLPI
LPIICIIC
LPICICIC
LPI
ab
abababab
T
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Phase Comparison Relay REL352 Current Pickup Calculation AN-93L-02
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Phase B to C fault
Input currents
=
=
=
60
120
0
bcC
bcB
A
II
II
I
Pickup current phases B and C
)]43.164983.043.254983.0()43.74983.057.15983.0([
3
3
)43.164983.043.254983.0()43.74983.057.15983.0(
21
21
002211
+++>
>+++
>++
>
CCLPI
LIICIIC
LPICICIC
LPI
bc
bcbcbcbc
T
Phase C to A fault
Input currents
=
=
=
120
0
60
caC
B
caA
II
I
II
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Phase Comparison Relay REL352 Current Pickup Calculation AN-93L-02
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Pickup current phases C and A
)]43.224983.075966.0()43.14983.075966.0([
3
3
)43.224983.075966.0()43.14983.075966.0(
21
21
002211
+++>
>+++
>++
>
CCLPI
LPIICIIC
LPICICIC
LPI
ca
cacacaca
T
Three phase ABC fault
Input currents
=
=
=
120
120
0
abcC
abcB
abcA
II
II
II
Pickup current phases A, B and C
43.224983.043.254983.015966.0()43.14983.057.15983.015966.0(
3
3
)43.224983.043.254983.015966.0(
3
)43.14983.057.15983.015966.0(
21
2
1
002211
+++++>
>++
+++
>++
>
CCLPI
LPIIIC
IIIC
LPICICIC
LPI
abc
abcabcabc
abcabcabc
T
Theoretically, there should be no negative sequence current for a three phase fault, but Clarke introduces asmall value. However, the formula for three phase fault pickup current can be simplified by removing the C2term. The error by doing so will result in less than 10% error. Note however, that the below formula gives a10% highertheoretical result (i.e. the actual test current required for operation is lower).
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Phase Comparison Relay REL352 Current Pickup Calculation AN-93L-02
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Example 2b, Phase B to ground fault
With input currents:
0
120
0
=
=
=
C
bB
A
I
II
I
and settings:
0.10
7.02
1.01
5.0
=
=
=
=
C
C
C
OTH
the required phase B current becomes:
63.5)1200.143.254983.07.057.15983.01.0(
3
3
1200.143.254983.07.057.15983.01.0
002211
=++
>
>++
>++
>
LPI
LPIII
LPICICIC
LPI
b
bbb
T
That the pickup current is higher for a phase B to ground fault compared to phase A to ground is due to thefact that the symmetrical component computations of IT are made referenced to phase A.
Contributed by:Solveig WardRevision 0, 03/25/02
ABB Inc.7036 Snowdrift RoadAllentown, PA 18106800-634-6005 Fax 610-395-1055Email: [email protected]: www.abb.com/substationautomation