NEW METHOD FOR THE STATE EVALUATION OF THE

ZERO-SEQUENCE SYSTEM
Gernot DRUML Olaf SEIFERT
A. Eberle GmbH Dresden University of Technology
Germany Germany
g.druml@ieee.org seifert@ieeh.et.tu-dresden.de

Abstract – In this paper we present a new method for tem. With the decreasing zero-sequence voltage the
the evaluation of the zero-sequence network parameters controller must be set much more sensitive. Due to the
by injecting two frequencies in the zero-sequence system. crosstalk of the load current to the zero-sequence volt-
These parameters can be used for the decision to move a age, each change of the load current can release a tuning
Petersen-Coil and also for the high ohmic earth fault de-
operation, which is, in most of the actual algorithms,
tection in resonant grounded networks.
The major problems for the correct calculation of the combined with a physical movement of the Petersen-
line-to-ground capacity ,respectively of the resonant-point Coil. Due to the disturbances the state and parameter
are the missing or very low zero-sequence voltage and the estimation of the network is much more difficult and
non negligible crosstalk of the varying load currents to the results in a necessary movement of the Petersen-Coil
zero-sequence-voltage. As a consequence, the number of over a longer distance. Nevertheless, sometimes a cor-
tuning operations and non correct tuning operations in- rect tuning is impossible.
creases in today's networks.
The new method uses the injection of two currents with One problem arises because the motor-drive of the
frequencies unequal to 50 Hz into the zero-sequence sys-
Petersen-Coil is only designed for few tuning operations
tem for the calculation of the network parameters. There-
fore it is possible to supervise complete symmetrical net- per day. The other problem arises because of the longer
works and to suppress the 50 Hz crosstalk of the load detuning time. This is caused by the increase of tuning
current. In consequence, the number of coil movements cycles, respectively by wrong tuning positions.
and also the number of wrong tuning positions are drasti-
cally reduced. This new method can be extended for the Therefore it is necessary to find methods, which are
estimation of the parameters of each feeder, to detect also able to find the correct tuning position, even if the natu-
high ohmic earth faults. ral zero-sequence voltage is zero, respectively if the
disturbances in the zero-sequence voltage are not negli-
gible. Additionally, the number of necessary moving
Keywords: resonant grounded system, earth fault,
operations should be reduced.
high ohmic earthfault detection, current injection,
Petersen-Coil
2DISTURBANCES OF THE CONTROL
OPERATION
1 INTRODUCTION Using the standard simplified equivalent circuit for a
The tuning of the Petersen-Coil is a preventive op- resonant grounded system [3] , [1] as it is shown in Fig.
X X X X XT

eration already done in the healthy network. With the 1 it seems to be very easy to find the resonance point of
TX

existing methods it is not possible to determine the the sound network, even for very small neutral-to-earth
network parameters during a solid earthfault. The fault voltages.
location and the resistance at the fault location are un-
known and are not accessible for a measurement. In
case of a solid earthfault, the zero-sequence voltage is
impressed and the measurement of the zero-sequence
current at the fault location is impossible. The zero-
sequence current can only be measured at the substation Fig. 1:
T Standard equivalent circuit for a resonant grounded
or in some cases at some dedicated switching-stations. system

In the past, different control algorithms were devel- The problem becomes more difficult because several
oped. Most of these algorithms are based on the neces- disturbances generate an additional non-zero neutral-to-
sity to move the Petersen-Coil. The development of earth voltage U NE . Thus, it is very difficult for the con-
U UB B

today's distribution networks is characterized on one trol algorithm to distinguish between “real” resonance
side by an increase of symmetrical cables, which results points and “fictitious” resonance points, caused by the
in smaller usable zero-sequence-voltages and, on the disturbances.
other side, in an increase of the crosstalk of the positive
sequence of the load current to the zero-sequence sys-

15th PSCC, Liege, 22-26 August 2005 Session 39, Paper 2, Page 1
2.1 Description of the network changes of the residual voltage, due to the crosstalk,
become very large and are not more negligible.
The network under consideration consists of a trans-
former, the Petersen-Coil, a transmission line and a load 0.045
as depicted in Fig. 2 . XT TX

0.04
Transformer Line Load
0.035
U3N ZL3 U3 ZLoad3
0.03
U2N ZL2 Z ZM13 U2 ZLoad2
M23

abs(UEN / U1N)
N N2 0.025
U1N ZL1 Z U1 ZLoad1
M12
0.02
dU1
UNE YP 0.015
Y1 Y2 Y3
IP 0.01
I1 I2 I3
Earth 0.005

0
0 50 100 150 200 250 300
Fig. 2:
T Equivalent circuit for the investigation of distur- load current /A

bances on U NE U UB B

Fig. 3:
T Neutral-to-earth voltage due to the voltage drop
T

along the line T

For the sake of clarity, we further assume, without

restriction of generality, that unbalances of the trans-
0.035
mission line only occur in phase 1. Furthermore, the
mutual coupling of the transmission lines is neglected, 0.03

because if the network is symmetrical this only has

0.025
minor influence on the results. The case of asymmetri-
cal mutual coupling can be treated in a similar way as
abs(UNE / U1N)

0.02
an unbalance in the series reactance of one phase. It is
worth mentioning that the equations for a complete 0.015

description of the different coupling effects of networks 0.01

with asymmetrical components are very complex, and
cannot be simplified by using the classical symmetrical 0.005

component concept.
0
0 50 100 150 200 250 300
load current /A
The disturbances can be summarized to the following
Fig. 4: Neutral-to-earth voltage due to an unbalance of the
three main coupling effects [3] based on Fig. 2 :
T T

serial impedances in the line

X X XT TX

1. Unbalance of the voltage The asymmetry of a line may be caused for example
2. Unbalance of the line-to-earth capacitances by the kind of cable laying, as shown in Fig. 5 a (for XT TX

3. Coupling of the load current over the normally further details the reader is referred to [5] , [6] , [7] , X X X X X X

negligible series line resistances and reactances [9] ). If the cables are laid in a triangle like in Fig. 5 b
X X XT TX

the mutual coupling of the three phases is obviously the

The second item results in a natural unsymmetry, same. A similar situation can be found for overhead
which depends more or less on the natural capacitive lines where an improvement can be made by transpos-
unbalance of the network. Due to the voltage drop along ing the phases.
the line, the unbalance can change in a small range with 2
ZM13
the change of the load current (see Fig. 3 ). Also XT TX

changes of the load current in other feeders, not shown ZM12 ZM23
1 2 3 ZM12 ZM23
in Fig. 2 influence the residual voltage U NE ..
XT TX U UB B

1 3
The tap-change of the transformer also influences the 2r
ZM13
zero-sequence voltage, mainly by changing the size of a a
U 1N , but also by an additional unsymmetry.
U UB B
a

The most important result describes item 3. Due to a) b)

this behaviour, an additional phasor is added to the Fig. 5:
T a) Single conductor cables in parallel.
natural U NE and the size of this phasor depends on the
U UB B b) Single conductor cables in triangle
size of the load current (see Fig. 4 ). This phasor is XT TX

added in the complex plane to the natural unbalance and

can increase or decrease the residual voltage U NE . Es- U UB B

pecially in symmetrical networks the resulting relative

15th PSCC, Liege, 22-26 August 2005 Session 39, Paper 2, Page 2
 3 CONTROL ALGORITHMS 3.2 New Algorithm

3.1 Existing Algorithms Principle

All the existing algorithms are based on the fact, that
Up to now, mainly the following algorithms are used the residual voltage is generated either by the natural
to determine the network parameters respectively to unbalance of the network or by an artificial 50 Hz cur-
tune the Petersen-Coil. The relative change of the zero- rent injection. These methods are assuming, that there is
sequence voltage is normally used as the criterion for no change in the network respectively no change of the
the detection of a switching operation in the network. crosstalk of the load current during the calculation pe-
riod. Please pay attention that the calculation period can
1. Artificial Earthfault last from several seconds up to several minutes.
By measuring the current over the artificial earth-
fault location and searching for the minimum of the In reality there are a lot of situations where these as-
current by tuning the Petersen-Coil, the tuning point and sumptions are not valid, for example in the sphere of
the parameters of the equivalent network can be deter- heavy industry with symmetrical networks but heavy
mined. This method is actually only used to check the changes of load.
quality of a control algorithm.
The new CIF-algorithm ( C ontrol by I njecting F re-
U U U U U U

2. Search of max | U NE |
U UB B

quencies) suppresses the 50 Hz crosstalk from the load

This algorithm searches the maximum of the resid- current by using frequencies unequal to 50 Hz for the
ual voltage. Improved versions of this algorithm deter- measuring and for the parameter estimation.
mine additionally the network parameters by using the
2 method [3] . Alternative algorithms are using least-
X X

The simplified equivalent circuit with a current injec-

square techniques to estimate the network parameters tion according to Fig. 6 XT TX

already from a part of the resonance curve.

3. Least square based on | 1/ U NE | U UB B

A lower sensitivity against disturbances can be

reached by using an algorithm based on the inverse of
the resonance curve [1] [3] .
X XX X

Fig. 6:
T Simple equivalent circuit with current injection
4. Locus Diagram of U 0 U UB B

This method is based on the fact that a circle can be results for the frequencies unequal to 50 Hz to Fig. 7 XT TX

constructed with only three points. This method as-

sumes that the third point of the circle is the origin of
the complex plane. A short detuning can be achieved
for example by switching a capacity in parallel to the
Petersen-Coil. This switching results in a second point
of the locus diagram of U NE . Measuring the voltage
Fig. 7: Simple equivalent circuit with current injection
U UB B

with amplitude and angle it is possible to construct the unequal to 50 Hz

locus diagram.
For the frequency fn the admittance, seen from the
5. 50 Hz Current Injection current injection, can be described as:
This algorithm is based on the idea to inject an arti-
ficial current into the neutral point of the system if there I CI _ fn 1
is no unsymmetrical current from the natural unsym- Y CI _ fn = = Y U + YW + j (ωn C − ) (2)
metry. The influence of the natural unbalance can be U NE _ fn ωn L
partly compensated by using a differential measurement
from two time points. Eq. (1) in combination with the X X

For symmetrical networks with a small Y U this re- U UB B

coil position enables to determine the network parame- sults in

ters.
I CI _ fn 1
d I CI Y CI _ fn = ≈ YW + j (ωn C − ) (3)
Y CI = ≈ YW + j ( BC − BL ) (1) U NE _ fn ωn L
dU NE

Using two different frequencies f 1 and f 2 one gets

B B B B

two complex equations with three variables, which

leads to the following solution:

15th PSCC, Liege, 22-26 August 2005 Session 39, Paper 2, Page 3
 ⎧⎪ I f 1 ⎫⎪ accuracy of the parameter estimation is increased, espe-
Y W = real ⎨ ⎬ (4) cially for systems with a large standard detuning.
⎩⎪U NE _ f 1 ⎭⎪
Operation philosophy
imag (Y CI _ f 1 ) ω1 − imag (Y CI _ f 2 ) ω2
C= (5) Depending on the operation philosophy the current
ω12 − ω22 injection can be activated only for a short time after the
1 detection of an essential relative change of the zero-
L= (6) sequence voltage, to check if a new tuning of the Peter-
ω1 (−imag (Y CI _ f 1 ) + ω1C ) sen-Coil is necessary. In symmetrical networks the
current injection can be switched on continuously, to
Assuming a linear system enables the current injec- detect any switching operation in the network immedi-
tion of two frequencies and evaluation of the corre- ately. Combinations of these two philosophies are pos-
sponding Y CI_fn at the same time. This results in very
U UB B
sible, for example to check every 10 min the actual
fast measurement possibilities and depends more or less network parameters in symmetrical networks.
on the used frequencies and filter algorithms [8] . The X X

duration of the measurement is usually in the range of More Precise Models

240 ms. In Fig. 8 a connection of the Petersen-Coil to the
XT TX

neutral point of the transformer is shown. For a more

The following items list the main advantages of this accurate calculation of the network including a Petersen
new CIF-algorithm: coil, as shown in Fig. 8 , it is necessary to use a more
XT TX

precise equivalent circuit as depicted in Fig. 9 .XT TX

¾ Very fast measurement

¾ Suitable also for symmetrical networks
¾ Determination of the sum of all Petersen-Coils
including distributed fixed-coils in the compensated
area
¾ Insensitive to the 50 Hz open-delta VT error
¾ Suppression of 50 Hz crosstalk

Additional requirements
Depending on the resonance curve and the normal
operation philosophy of the network, there arise some
additional requirements for the current injection.

1) The injected current should be variable in the am-

plitude to enable adaptation to the losses of different
switching states of the network.
Fig. 8:
T Petersen-Coil with current injection (CI) and watt-
One of the most used criteria for the earthfault detection metric increase G W B B

is the zero-sequence voltage. In small networks the

losses in the network are smaller, so that only a reduced
current should be injected, not to exceed the threshold
level of the earthfault detection system, especially in the
resonance point.

On the other side, in case of situations with a large

detuning a small injected current will not deliver a reli-
able measurement of the residual voltage U NE_fn .In this
U UB B

case a higher injected current is recommended.

2) The injected frequencies should not include 50 Hz Fig. 9:

T Simple equivalent circuit with current injection (CI)
components. and wattmetric increase G W B B

3) Using a current injection with variable frequen-

cies, it is possible to select the injected frequencies in Using frequencies unequal to 50 Hz enables now an
such a way, that these frequencies are near to the reso- accurate measurement of the following components
nance of the network. In this case small injected cur- during normal operation of the network
rents result in large values of the residual voltage. The

15th PSCC, Liege, 22-26 August 2005 Session 39, Paper 2, Page 4
¾ Zero-sequence capacity of the network rent. The auxiliary winding of the Petersen-Coil is
¾ External Petersen Coils existing in the network usually designed for 500 V, which makes necessary, in
(distributed Petersen-Coils) these cases, an additional transformer for the adaptation.
¾ Zero-Sequence Impedance of the Transformer With this type of current injection two currents with
¾ Values of the fixed-coils in the substation individual amplitude, frequency and phase can be in-
¾ Detuning jected very easy. On the other side the physical realisa-
¾ Value of additional damping resistors tion is not the cheapest one.
¾ Calculation of the unsymmetry of the network

3.3 High Ohmic Earthfault Detection with the DIF-

algorithm ( D etection by I njecting F requencies )
U U U U U U

The parameter estimation of the network can be ex-

tended for each feeder by measuring the injected cur-
rents in each feeder of interest either with the Holm-
Fig. 11: Current injection using a Frequency-Converter(FC)
green-Circuit (summation CT) or with the core-balance T

with Power-Factor-Correction (PFC)

transformer.
IY2
If the requirement for variable frequencies is can-
celled, a much cheaper version to generate a current
BC2 BL2 YW2 with more frequencies is available, as shown in Fig. 12 XT TX

Z0Tr IY1
L1 I CI
U1
ICI _ f1,f2 UNE U2
YW BL U0 BC1 U3 Une LP
L2

IP

Fig. 12: Current injection with AC-switch for three frequen-

T

cies (AC-1)
Fig. 10 :
T T T Parameter estimation for each feeder TT

The following figure shows one possible pattern of

As the crosstalk from 50 Hz is suppressed, the meas-
pulses for the current injection.
urement of U 0D can be used for the calculation of the
U UB B

essential parameters for each line.

It is possible to calculate the capacitive part B Cx , the B B
1

0.8
losses Y Wx and the size of distributed coils B Lx seen on
B B B B

0.6
feeder x, with the same method as explained above. By
0.4
using additionally the 50 Hz components at the same 0.2
time, the actual unbalance of the network can be deter-
I/A

0
mined and supervised. -0.2
The advantage of this algorithm is, that all measure- -0.4

ments are made at the same time. The usual problem to -0.6

check for a switching operation is removed. The deter- -0.8

mination of the network parameter is included in the -1

algorithm directly. 0 50 100 150 200 250

t / ms

Fig. 13 : Sample pulse pattern for AC-1

T T T TT

3.4 Types of multi-frequency Current Injections (CI)

The corresponding frequency spectrum is shown in
The most simple way is to use a standard frequency XT Fig. 14 TX

converter (FC) in the mode of a current source as shown

in Fig. 11 . To reduce the disturbances on the 400 V
XT TX

side, a frequency converter with a power factor correc-

tion module (PFC) is recommended [4] . The coil L1 X X

respectively the parallel circuit L1//L2 is used to con-

vert the pulsed voltage to an impressed current. The size
of L1//L2 defines the maximum available injected cur-

15th PSCC, Liege, 22-26 August 2005 Session 39, Paper 2, Page 5
 41.67 : 0.34724 25.00 : 0.28292

0.6 50.00 : 0.50000 0.6 41.67 : 0.69448

58.33 : 0.29383 50.00 : 0.00000
58.33 : 0.58767
0.5 0.5

0.4 0.4
I/A

I/A
0.3 0.3

0.2 0.2

0.1 0.1

0 0
0 50 100 150 200 250 0 50 100 150 200 250
f / Hz f / Hz

Fig. 14: Frequency spectrum for AC-1

T Fig. 17 : Frequency spectrum for AC-2
T T T TT

The major disadvantage of this type of current injec-

tion is that the main spectrum of the injected current is 1
50 Hz. This can be avoided by the following type of 0.8

thyristor-switch, where it is possible to invert the direc- 0.6

tion of the current during the previous pause time. 0.4

0.2

I/A
0

-0.2

-0.4

-0.6

-0.8

-1

0 50 100 150 200 250

t / ms

Fig. 18 : Sample pulse pattern with AC-2 with phase-firing

T T T TT TT

Fig. 15 : Current injection with AC-switch for two frequen-

T T T TT

cies (AC-2) TT

4 RESULTS OF FIELD TESTS

The resulting pulse pattern is shown in Fig. 16
XT T X

In the meantime, the new algorithms have been im-

1
plemented in real hardware and they have shown their
0.8
advantages in real network configurations.
0.6

0.4

0.2
The following picture shows for example a 19” rack
with two controllers using the CIF-Algorithm for two
I/A

-0.2
Petersen-Coils and one earthfault monitoring and detec-
-0.4 tion system for up to 40 feeders using the DIF-
-0.6 Algorithm.
-0.8

-1

0 50 100 150 200 250

t / ms

Fig. 16 :
T T T Sample pulse pattern with AC-2 TT

with the corresponding frequency spectrum shown in

XT Fig. 17 T X

Depending on the pulse pattern and the number of

periods different frequencies are available. The previous
figures show a 100 % phase-firing. The amplitude can
be reduced by a reduced phase-firing, as for example
depicted in Fig. 18 . This AC-switch (AC-2) can also be
XT T X
Fig. 19 : EDCSys ( E arthfault D etection and C ontrol Sy-
T T T U U U U U U U

used to generate the pattern for three frequencies like s tem) U TT TT

shown in Fig. 13 . XT T X

15th PSCC, Liege, 22-26 August 2005 Session 39, Paper 2, Page 6
 The Current Injection, type AC-Switch, has been in- This results in a tuning of the Petersen-Coil with an
cluded directly in the enclosure of the motor-drive of essential reduced number of coil movements. Additional
the Petersen-Coil. functions, like the measurement of the zero-sequence
impedance of the transformer under normal operation
and the use of it for the correction of the measured ca-
pacitive earth-current, can be achieved with the new
CIF algorithm. With this algorithm it is possible for the
first time to measure also the value of distributed Peter-
sen-Coils.

With the new D etection by I njecting F requencies

U U U U U U

(DIF) algorithm, which is based on the same measure-

ment principles as the CIF algorithm, now a fast and
high sensitive earthfault detection system is available.

The field tests and the first practical experiences

have shown the effectiveness of this new concept for
the control of Petersen-Coils and detection of high oh-
mic earthfaults.

REFERENCES

[1] Druml G., "Resonanzregler REG-DP, Betriebs-

anleitung", A-Eberle GmbH&CoKG, 2002, Nürn-
berg, Germany
[2] Druml G., "EDCSys Operation Manual - E arth- U U

fault D etection and C ontrol Sys tem", A-Eberle

U U U U U U

GmbH&CoKG, 2004, Nürnberg, Germany

[3] Druml G., Kugi A., Parr B., "Control of Petersen
Coils", XI. International Symposium on Theoreti-
cal Electrical Engineering, 2001, Linz
[4] Hagmann G, "Leistungselektronik - Systematische
Darstellung und Anwendungen in der elektrischen
Fig. 20 : 375A – Petersen Coil with AC-Switch Current Injec-
T T T
Antriebstechnik", 2.Aufl, AULA-Verlag Wies-
tion and Resistor for Wattmetric-Increase TT TT

baden, 1998, Germany

This combination has been used for tests in a real [5] Heinhold L., Stubbe R., "Kabel und Leitungen für
network with different artificial high ohmic earthfaults Starkstrom Teil 2", 4.Aufl., Siemens, 1987, Berlin-
of 20kOhms in different phases. The estimation of the München,
20 kOhm unbalance was detected with an accuracy of [6] Heinhold L., Stubbe R., "Kabel und Leitungen für
1%. The calculation of the resonant-point under the Starkstrom Teil 1", 5.Aufl, Publicis MCD Verlag,
worse condition of 250 A overcompensation had an Erlangen, 1999, Germany
accuracy of about 2%.
[7] Herold Gerhard, "Elektrische Energieversorgung
This system was tested and approved by ENEL.
II", J.Schlembach Fachverlag, Weil der Stadt,
2002, Germany
5 CONCLUSION
[8] Stearns S.D., Hush D.R., "Digitale Verarbeitung
analoger Signale", 7. Aufl, Oldenbourg, Wien,
In this contribution we have discussed the effects of
1999, Austria
the crosstalk of the positive sequence load current to the
zero-sequence system and the consequences to existing [9] Weßnigk K., "Kraftwerkselektrotechnik", VDE
control algorithms. With the new C ontrol by I njecting
U U U U
Verlag, Berlin-Offenbach, 1993, Germany
F requencies (CIF) algorithm the crosstalk can be sup-
U U

pressed. With the CIF a faster and more accurate state

estimation of the zero-sequence system can be achieved.

15th PSCC, Liege, 22-26 August 2005 Session 39, Paper 2, Page 7