a-eberle
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QU2 - ALGORITHM FOR DETECTING EARTH-FAULTS
Gernot DRUML
A.Eberle GmbH&CoKG – Germany
g.druml@ieee.org
INTRODUCTION
In many countries of the EC the "resonant grounding" is one
of the most important options in electrical network design to
obtain the optimal power supply quality. The first main
advantage of this treatment of the neutral point is the fact,
that in most cases the system is self-healing, as the arc
distinguishes without any intervention of the protection
system[1]. The second main advantage is the possibility of
continuing the network operation during a sustained earth
fault. As a consequence, the number of interruptions of the
power supply for the customer is reduced. But with this
improved power quality problems arise for the selective
detection of earth faults. The conventional relays are
designed only for non-intermittend low ohmic earth faults
and for non meshed grids.
With the new adaptive algorithm directional earth fault
detection from low ohmic up to some kOhm is possible in
non-meshed and meshed networks.
Up to now the preferred fields of application for transient
relays in the medium voltage were large unmeshed cable
networks. With the new adaptive algorithm the relay is also
applicable for rural networks, where the probability of a
high ohmic earth fault is much higher.
This new adaptive algorithm is now also able to suppress
crosstalk from the load current to the zero-sequence-system.
Therefore transient relays with this new adaptive algorithm
can be used successfully in meshed networks with non
negligible crosstalk.
The algorithm can also be used for the detection of
restriking earth faults in compensated cable networks and
intermittent earth faults in isolated networks.
BASICS OF THE EARTHFAULT
To explain the behavior of a single line earth fault, two
different processes can be superposed [3], [6], [9]. The
following two processes are starting at the same time, but
with different duration:


discharge of the faulty line over the earth
charging of the two healthy lines over the earth
The two processes are ending in the stationary state of the
earth fault. The explanation of the two processes will be
made by using a network with three feeders (A, B and C)
and an earth fault in line 1 of feeder A according to Fig. 1.
Druml Gernot
Fig. 1: Discharge of the faulty line over the earth
Discharge of the faulty line over the earth
The lines can be considered as a distributed lattice network,
consisting of a complex serial impedance ZLXX and a line-toground capacitance CXX .The greatest probability for the
first ignition is near the maximum of the line-to-ground
voltage u1G. At this time the line has about the maximum
charge. The discharge of the lattice network of line 1 will
start at the fault location and will propagate in both
directions to the ends of line 1. A reflection of the waves
occurs at the end of the line respectively at every change of
the image impedance of the line. These reflections can be
detected in form of oscillations at a high frequency in the
zero-sequence current and in the zero-sequence voltage.
Important parameters for the behavior of the discharge are:
 Capacity of line 1 to ground
 Charge of the line-to-ground capacity before the start
of the first ignition
 Serial line impedance Z L of line 1 in the faulty feeder
and in the healthy feeders
 Impedance Z F at the fault location, including the
grounding resistance
The lines of phase 1 of the healthy feeders can be
considered as a parallel connection of these lines, which
results in a lower impedance of the equivalent serial
impedance and a higher equivalent line-to-ground capacity
of the healthy feeders. The oscillation frequency essentially
depends on the serial impedance and the line-to ground
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capacity, which are in a first approximation proportional to
the length of the line. The frequency is higher for short
networks and it is lower for large networks. Usually the
oscillation-frequency is above 10 kHz.
Charge of the two healthy lines over the earth
As a result of the discharge of the faulty line the triangle of
the line-to-ground voltages is destroyed.
2"
2
3 2
V2"1'
3
V21' V31'
V2G V3G
3"
2
3
GND 1'
V1G
1
V3"1'
1
a)
b)
From Fig. 3 the following conclusion can be made:
c)
Fig. 2: Change of the voltages during charging process
As the supply-transformer is still delivering a symmetrical
three phase system, the two healthy lines will be charged to
the line-to-line voltage. This charging process for the
network with three feeders is shown in detail in Fig. 3 .
ZL2C
Load C
Feeder C
iSC
ZL3C
ZL1C
C1C C3C C2C
iC2C
iC3C
ZL2B
Load B
Feeder B
iSB
ZL3B
ZL1B
iC2B
iC3B
ZL2A iC2A
3 ZTr3
ZL3A
ZTr1
ZL1A
iC3A
Load A
Feeder A
iSA
ZTr2
N
u31
u21
u1G
uNG
LP
ZF
C1A C3A C2A
1
iC2A
iC3A
iP
iC2B
iC3B
iC2C
iC3C
Fig. 3: Charge of the healthy lines over the earth
Important parameters for the behavior of the charging are:




Capacity of line 2 and line 3 to ground
Charge of the line-to-ground capacities before the
start of the first ignition
Charge voltage V 21 and V 31
Leakage inductance of the supply transformer
Serial line impedance Z L of the lines
Impedance Z F at the fault location, including the
grounding resistance
Druml Gernot
2) All the capacitive charging currents of the healthy
feeders (B and C) have to flow over the fault location.
3) The charging currents of the faulty feeder (A) flow over
the fault location and back to the supplying transformer in
line 1. As a result, these currents cannot be measured in the
zero-sequence system. The summation of this four currents
is zero.
5) In a compensated network a superposition of the current
through the Petersen-Coil takes place. The effect of this
current is small at the beginning of ignition.
iF
GND


1) Two capacitive charging currents flow into a healthy
feeder. These charging currents can be measured as zerosequence current. The amount of this zero-sequence current
is proportional to the line-to-ground capacity of this feeder.
4) The zero-sequence current of the faulty feeder is the sum
of all charging currents of the healthy feeders, but with
inverse direction. Instead of a capacitive charging current
there is an "inductive" charging current.
C1B C3B C2B
2
The essential remaining inductive components for the
description of the charge oscillation are the relative low
ohmic leakage inductance of the supply transformer and for
earth faults, which are far away, the inductance from the
point of the supply transformer to the fault location.
The influence of the Petersen-Coil can be ignored, as the
impedance of the Petersen-Coil is much higher than the
leakage inductance of the transformer.
1'
GND
The distribution transformers respectively the loads are
comparatively high ohmic and can be neglected in the first
approximation. The resistive load results in an additional
damping of the charge oscillation. If the distribution
transformer has no load on the secondary side only the very
high ohmic magnetizing inductance takes effect.
The conclusion is, that the relay in the faulty feeder can
only measure the sum of the charging currents of the
healthy network in it´s back and that this current has an
inverse direction.
.
Stationary state of the earth fault
For the explanation of the stationary state also Fig. 3 can be
used. For an isolated network the whole capacitive current
of all feeders flows over the fault location. The relays of
healthy feeders measure a capacitive zero-sequence current
and the relay in the faulty feeder measures an inductive
zero-sequence-current. In the stationary state, the size of
this inductive current is , like in the previous section, the
sum of the healthy lines in the back of the relay.
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Using a Petersen-Coil, the current over the fault location
can be reduced to the small watt metric part, which is
usually in the range of 2 % to 3 % of the whole capacitive
line-to-ground current of the network.
500
100
ioA
uo
io /A
400
80
300
60
200
40
100
20
0
0
-100
-20
-200
-40
-300
-60
-400
-80
-500
0
5
-100
15
10
t /ms
Fig. 5: Faulty feeder at a low ohmic earth fault
Superposition
50
50
ioC
uo
ioB
ioA
40
With the first ignition all thwo processes start at the same
time.
io /A
30
40
30
20
20
10
10
0
0
-10
-10
-20
-20
-30
-30
-40
-40
-50
0
20
40
80
60
100
120
uo /%
In the following figures two different earth faults are
shown for a 20 kV compensated network with three feeders
and a capacitive current of 108 A and 5 A overcompensation. The network corresponds to fig. 3. The lowohmic earth fault has a value of 10 Ohm and the high
ohmic fault a value of 2000 Ohm. The sampling frequency
of the recording is 10 kHz.
uo /%
For compensated networks the situation is changed. In this
case, the current through the Petersen-Coil superposes and
reduces the capacitive current over the fault location [4]. In
a well tuned network the capacitive current over the fault
location is complete compensated. From fig. 3 it is
recognizable, that in this case the relay in the faulty feeder
measures also a capacitive zero-sequence current , as well
as the relays in the healthy feeders. Therefore, in
compensated networks the inductive character of the zerosequence current is no more an indication for a faulty line.
-50
140
t /ms
In the case of the low ohmic earth fault the high frequency
oscillation of the discharging is higher.
Fig. 6: High ohmic earth fault
In case of the high ohmic earth fault the zero-sequence
voltage reaches about 40% in the steady state.
500
100
ioC
uo
ioA
80
300
60
200
40
100
20
0
0
-100
-20
-200
-40
-300
-60
-400
-80
-500
0
5
10
uo /%
io /A
400
-100
15
t /ms
Fig. 4: Two healthy feeders at a low ohmic earth fault
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0.06
QU-ALGORITHM
0.04
The following considerations are based on the transient
definition of the zero-sequence-system according to the
space-vector-theory [5].
iS
0
-0.02
-0.04
ZL2
Load
ZL3
ZL1
u0
0.02
qo /As
For example, for the healthy feeder B or C, as shown in
Fig. 7, of our sample-network the charging can be described
with equation (1).
qoA
qoB
qoC
-0.06
-30
-20
-10
0
10
20
30
40
uo /%
C1 C3 C2
Fig. 9: qu-diagram of a high ohmic fault
iC2
iC3
Fig. 7: Charge of one healthy feeder
u=
(t ) u0 (t0 ) +
0
(t ) u0 (t0 ) +
u=
0
1
Ceq
∫
t
i (τ ) dτ
(1)
t0 S
qS (t )
(2)
Ceq
Starting the integration at a point where u0(t0) = 0 results in:
u0 (t ) =
qS (t )
(3)
Ceq
Drawing a diagram of this relation, with q0 on the ordinate
and the zero-sequence voltage u0 on the abscissa results in a
straight line with the gradient Ceq, which is the equivalent
zero-sequence capacitance of the feeder. Subsequently, this
diagram shown in Fig. 8 will be referred to as qu-diagram.
0.6
0.5
0.4
qo /As
0.3
0.2
qoA
qoB
qoC
0.1
0
-0.1
-0.2
-150
-100
-50
0
50
100
uo /%
Fig. 8: qu-diagram of the three feeders in case of a low
ohmic fault in feeder A
In the case of a faulty feeder this relation is no more valid.
The sum of the charging currents of all healthy feeders
flows out from the faulty feeder, it starts with a negative
gradient and in compensated networks it is not a straight
line. The last statement can be used as additional
information for the earthfault detection.
Therefore, the task for detecting a transient earth fault can
be solved by the decision whether the curve in the qudiagram is a straight line or not. It should be noticed, that
on-line versions of the least square algorithm and pattern
recognition algorithm are implemented in the relay, in order
to improve computational efficiency.
qu-Algorithm with restriking earth faults
In the case of restriking earth faults, which very often occur
in cable-networks, two new problems arise for conventional
relays:
 The zero-sequence voltage u0 doesn't always fall
below the preset trigger level
 The zero-sequence current doesn't have a steady state
The first item is a problem for the transient relays, because
they will not be retriggered.
The second item is a problem especially for relays working
on symmetrical components. Most of these relays are using
the FFT to calculate the components of the fundamental
frequency. During the decaying phase of u0 the frequency
of u0 is changing, depending on the tuning of the PetersenCoil. Both, the decaying and the restriking current
influence the calculation of the fundamental components.
The result of this is, with high probability, a complete
erroneous decision of the fault direction. This problem
doesn't only occur in the faulty feeder, but even in the
healthy ones.
Fig. 10 shows, that u0 doesn't fall below the trigger value.
The restriking starts above the preset value of 25%. In
addition it should be noticed, that the zero sequence current
is not zero during the "healthy time" of the faulty feeder.
For a correct calculation of the fault direction the direction
of the change of u0 compared to the direction of the change
of i0 should be used.
Conventional relays do not use this method.
Fig. 9 shows the qu-diagram for an earth fault with a fault
impedance of 2000 Ohm. The corresponding time diagram
of i0 and u0 is shown in Fig. 6
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500
80
300
60
200
40
100
20
0
0
-100
-20
-200
-40
-300
-60
-400
-80
Simple evaluation
No high speed sample rate is necessary. A sample rate
of about 2 kHz is sufficient
Influence of the discharge is reduced due to the
integration of i0
The integration and evaluation can be done over a half
period
The integration of i0 over a larger range before the
trigger-point enables the detection also of high ohmic
earth faults up to some kOhm
on-line versions of the least squares algorithm [8] and
pattern recognition algorithms (e.g. [4] ) improve the
computational efficiency




-100
100
80
60
40
20
0


uo /%
io /A
400
-500
The advantages of the qu-algorithm are:
100
ioA
uo
t /ms
Fig. 10: Faulty feeder at a restriking earth fault
500
60
200
40
100
20
0
0
-100
-20
-200
-40
-300
-60
-400
-80
0
20
40
60

uo /%
io /A
80
300
-500
The disadvantages of the standard qu-algorithm are:
100
ioC
uo
ioA
400
-100
100
80
t /ms
Fig. 11: Healthy feeders at a restriking earth fault
0.5
0.4
Sensitive to analog-digital-converter saturations, as the
straight line is modified to a curve
Sensitive to not negligible phase-splitting
Sensitive to crosstalk from parallel systems


The first disadvantage is only relevant in case of integration
over the complete half period of u0 and in combination with
testing of the feature "straight line" of healthy lines.
The sensitivity against phase-splitting is a general
problem of all relays, especially for cos(phi) relays.
Using Fig. 13 the reason of phase splitting in a healthy
meshed network will be explained.
Phase-splitting
qoA
qoB
qoC
ZL2 C
ZL3 C
ZL1C
ISC
qo /As
0.3
ISA
16.6 A
0.1
=> 0.5 Ω
ZL2 B 1Ω
ZL3 B 1Ω
ZL1 B 1Ω
ISB
16.6 A
I’W
0.2
I’W
=> 66.66 A
50 A
50 A
50 A
ISB
0 A => 16.6 A
0
-0.1
-0.2
-150
Load
U2N U3N
ZTr2
ZTr3
ZTr1
N
-100
-50
0
uo /%
50
100
150
Fig. 12: qu-diagram of a restriking fault
ISTr
U1N
UNG
=> 33.33 A
ZL2 A 1Ω
50 A
ZL3 A 1Ω
50 A
ZL1 A 1Ω
50 A
U2G
U3G
U1G
100 A
100 A
100 A
Load
ISA
0 A => 16.6 A
GND
Fig. 13: Phase-splitting in the healthy network
Fig. 12 shows the associated qu-diagram for the restriking
fault.
In a symmetrical situation the load current in each phase
will be splitted symmetrical to the feeders A and B. In this
situation the measured sum-current ( IS = 3 I0) at the
substation will be zero. Due to unbalances in the serial
impedances of the lines the distribution of the load current
will change. In the example the current in phase 2 is
changing from 50 A to 33.3 A respectively to 66.6 A.
Now the sum-currents of the feeders in the substation are no
longer zero. In our example the sum-current increases up to
16.6 A and the directions in the two feeders are opposite.
Druml Gernot
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We can find this behavior in any loop, in parallel lines and
in meshed networks.
The size of the phase-splitting current depends on:




load current
point of load on the loop
physical arrangement of the asymmetry of the serial
impedances [2]
number of meshes
The asymmetry of a line may be caused for example by the
kind of laying the cables, as shown in Fig. 14 a (for further
details the reader is referred to [5],[10],[11]). If the cables
are laid in a triangle (see Fig. 14 b) the mutual coupling of
the three phases and therefore the serial impedance is
obviously the same.
2
ZM13
ZM12
1
ZM23
2
ZM12
3
2r
a
ZM23
1
under normal operation, due to the small distances between
the three phases. But in case of an earth fault in the parallel
system, the currents through the three wires are no more
symmetrical, also in healthy feeders (see Fig. 3). The
asymmetric loading currents can be in the range of 100 A.
Therefore the magnetic coupling must be taken into
account.
A worse situation arises in case of a cross-country-fault in
the parallel system.
Also a phase-splitting in the parallel system can be the
reason for a crosstalk.
QU2-ALGORITHM
With the assumption of no change of the crosstalk from a
neighbor system and no change of load in the own system
during the few periods of interest, a linearization around the
working point combined with a nonlinear filtering solves
the major problem.
3
ZM13
a
For the explanation real measurements of an earthfault in
the 16.7 Hz 110 kV network of the railway will be used.
The network has about 1200 A capacitive current and is
compensated with several distributed Petersen-Coils.
a
a)
b)
Fig. 14: a) Single conductor cables in parallel
b) Single conductor cables in triangle
A similar situation can be found for overhead lines where
an improvement can be made, by transposing the phases.
The last two channels show two independent feeders.
FaultRec_N008_E1_00000361.csv E1: uo(t), ie(t)
100
uo1 / %
One possible way to compensate this influence in loops is to
measure the currents in all feeders and to add the currents of
the feeders, which are switched to a loop. But this version
needs a very high number of current measurements and, in
addition, always the actual information, which feeders are
switched to a loop. The requirements to such a SCADA
System would be enormous.
In the following figures the first channel shows the zerosequence voltage in the substation.
The next two channels are the sum-currents of two parallel
lines with a high current due to phase splitting. These two
currents are more or less opposite. These currents include
also the smaller zero-sequence currents due to the natural
asymmetry of the network.
Crosstalk from parallel systems
0
-100
0
100
200
300
400
500
600
0
100
200
300
400
500
600
0
100
200
300
400
500
600
0
100
200
300
400
500
600
0
100
200
300
t / ms
400
500
600
is1 / A
Systems switched to a loop are also very sensitive to the
magnetic coupling of galvanic isolated parallel systems.
prim
20
0
-20
ZL2
ZL3
ZL1
prim
Load
is2 / A
parallel System
20
ISC
magnetic coupling
0
-20
ZL2 B
ZL3 B
ZL1 B
is3 / A
prim
20
ISB
0
-20
N
ISTr
20
Load
ISA
U1N
UNG
prim
ZL2 A
ZL3 A
ZL1 A
U2G
U3G
U1G
is4 / A
U2N U3N
ZTr2
ZTr3
ZTr1
0
-20
GND
Fig. 15: Magnetic coupling of parallel systems
The influence of the parallel system may be negligible
Druml Gernot
Fig. 16: Zero-sequence-voltage and -currents of four
feeders with phase-splitting in feeder 1 and 2
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Fig. 16 shows, that the change of currents in the feeders 1
and 2 due to the earthfault is very small.
The parameter of the adaptive filter has an effect on the
maximal detectable high ohmic earthfault.
In Fig. 17 the corresponding standard qu-diagrams are
shown. Comparing to Fig. 8 or [3], a clear decision, which
feeder is the faulty feeder and which are the healthy feeders
is not easy, respectively impossible.
On the other side, the saturation of analog-digital-converter
and currents of cross-country faults are also modifying the
filter-parameters.
As long as the natural asymmetry of the net, represented by
u0, is very small, a linearization around the working point
0
0.1
-100
0.05
0
-50
0
uo / %
50
-0.05
-100
100
-50
0
uo / %
50
-10
0
0.02
-0.01
-20
-0.02
20
600
0
100
200
300
400
500
600
0
100
200
300
400
500
600
0
100
200
300
400
500
600
0
100
200
300
t / ms
400
500
600
is2 / A
prim
-50
0
uo / %
50
0
100
-20
Fig. 17: Standard qu-diagram for the four feeders without
correct identification of the faulty feeder
20
prim
-0.04
-100
100
is4 / A
50
500
0
is3 / A
-0.03
0
uo / %
400
prim
0.03
-50
300
20
E1: qu4
0
200
0
100
0.01
qo / As
qo / As
E1: qu3
-0.01
-100
100
10
0.04
0.01
0
20
is1 / A
-0.1
0
prim
-0.05
uo1 / %
0.15
-0.15
-100
FaultRec_N008_E1_00000361.csv E1: uo(t), ie(t)
100
E1: qu2
0.05
qo / As
qo / As
E1: qu1
The results of the adaptive nonlinear filtering of the lowohmic earthfault are shown in Fig. 19
0
-20
results in relative small inaccuracy of the equivalent model.
Fig. 18 shows the result of the linearization. The first
periods are zero and the following periods up to the
earthfault have only small variations due to variations in the
load.
Fig. 19: Zero-sequence- voltage and -currents after
adaptive nonlinear filtering. Influence of crosstalk,
phase-splitting is reduced and prefault values are
set to zero.
FaultRec_N008_E1_00000361.csv E1: uo(t), ie(t)
uo1 / %
100
0
-100
0
100
200
300
400
500
600
In Fig. 20 the results of this qu-algorithm with additional
nonlinear adaptive filtering are shown. Now it is no more a
problem to identify the feeder 2 as the faulty feeder.
10
E1: qu1 pfch
0
-10
0
100
200
300
400
500
600
is2 / A
prim
qo / As
20
0
0.04
0.1
0.02
0.05
0
-20
0
100
200
300
400
500
600
-0.05
-100
-50
50
-0.04
-100
100
-50
100
200
300
400
500
0
uo / %
50
100
50
100
E1: qu4 pfch
0.06
0.06
0.04
0.04
0.02
0.02
600
prim
20
qo / As
0
qo / As
is3 / A
0
uo / %
E1: qu3 pfch
0
-20
0
-0.02
prim
20
is4 / A
E1: qu2 pfch
0.15
qo / As
is1 / A
prim
20
0
0
0
-0.02
-20
0
100
200
300
t / ms
400
500
600
Fig. 18: Currents after linearization at working-point with
strong reduction of the phase-splitting in feeder 1
and feeder 2
-0.04
-100
-0.02
-50
0
uo / %
50
100
-0.04
-100
-50
0
uo / %
Fig. 20: qu2-diagram with correct identification of the
faulty feeder 2
With an adaptive nonlinear filtering from the first period up
to the earthfault, also these values can be reduced.
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REFERENCES
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