Recent Researches in Applications of Electrical and Computer Engineering
High Order Harmonics In Zero-Sequence Earth Fault Currents Of
Isolated Neutral MV Networks
HANI OBEID
Electrical & Computer Department
P.O.Box 950674, Amman 11195
JORDAN
Haniob@gmail.com www.asu.edu.jo
Abstract: - This paper investigates the effect of high-order harmonics on the value of earth fault current in isolated
neutral MV networks. The relay protection in these networks is intended to give an alarm in case of earth faults.
The selective protection of these networks requires the study of transient character of the current in order to
develop relays that are sensible to small impulses of current during intermittent earth faults.
Key-words:- Earth Fault Current, Zero Sequence, MV Network, Isolated Neutral.
configuration, the time of fault occurrence,
and the time of arc extension. Settings of the
relay protection that are based on steady state
condition have not been selected according to
real fault conditions. The same could be
applied to the directional relay, working zone
of which is defined based on current voltage
phasor diagrams in steady state condition;
however, this relay should operate in transient
condition when short term current impulses
occur. Filter of the basic frequency in the
input of some devices does not change the
situation; because there is no way that the
fault could be periodically at each instant.
c. The devices type HSS-3, ZM HSS, which are
widely used in city cable and industrial
networks, react on harmonics of high order,
which contradict the current compensation
principle by coil installed in the neutral. If
earth faults current contains high order
harmonics, capacitive compensation should
not be applied, because compensation is
applied for basic frequency and the harmonics
of high order will lead to opposite.
d. Protection of motors in networks with small
earth fault currents as usual lacks sensibility.
Not only because the earth faults are of small
currents, but also, because protection does not
operate during intermittent faults. Moreover,
protection can’t sense the fault if it is being
developed deep down in the winding.
1 Introduction
A large number of public utilities adopted the concept
of isolated networks to maintain availability and
safety. Distribution networks continue to expand,
however and so do zero-sequence fault current [1].
Single phase earth faults are the most frequent and
dangerous faults. The relay protection in these
networks is intended to give an alarm in case of earth
faults. Exception is the case of connecting motors to
these networks, where it is required to trip in case of
fault currents [2]. If the protection is non-selective the
network collapse is more possible.
There are major contradictions between current
practice of neutral earthing and methods of protection
in these networks [3]. These contradictions are:
The requirements of national codes state that
the capacitive currents should be decreased or
compensated. That leads to difficulties in
construction of efficient and cheap relays to
protect from earth faults.
b. Decrease of capacitive currents lead to a
situation when most of earth faults have
intermittent character [4]. In that case, the
duration of the fault could be a few
milliseconds (during the period of industrial
frequency), and current in faulty and sound
feeders has transient character. The value of
the fault current depends on the network
a.
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Recent Researches in Applications of Electrical and Computer Engineering
It should be taken into consideration that these
problems were discussed by relay protection
developers [5]. Developers also discussed the need for
protection during stable and intermittent faults. Some
of them offered relay protection that reacts on the
magnitude during transients. Others stated that relays
based on harmonics of high order could not be used
during short term intermittent faults.
Energy source that works as a system generates
only basic frequency. The no-load current of
transformer T2 could be changed. There is no
point to consider a large number of those
transformers in the network, because the result is
defined by an equivalent source of the high order
harmonics, specter of which is always changed
due to changes in the transformer load, changes in
phases between high order harmonics of the
transformers, and changes of the network
diagram. Only odd harmonics are presented in
magnetizing current of the transformer ( k=5, 7,
11) when phase windings are connected in delta
(if there is unsymmetrical magnet system, is, there
could be odd harmonics k=3,9 …). Maximum
values of harmonics in transformers current are in
over voltage modes when transformer load is
little. If we suppose that there is a symmetry of
phase parameters of the network and if all phase
currents of the network generate high order
harmonics with positive zero sequence,
current will be equal to zero until single phase
earth fault occurs. When fault occurs,
currents
could be detected by devices, however, these
currents are only a small part of the currents that
are generated by the source (a few amperes). That
is why if there is no resonant enhancing of these
currents, sensitivity of the protection will not be
good enough.
However, all devices that are based on transients are
not popular because they are expensive, complicated,
and there are doubts about their reliability.
Many experiments confirm that in networks of large
industrial facilities with dc convertors, selectivity of
protection devices that react on harmonics of high
order is very big. But those experiments do not answer
two important questions, namely: how these devices
(HSS-3, ZM HSS) operate in network without dc
convertors (source of harmonics of high order), and
why these devices are efficient only in networks with
large capacitive currents. This paper tries to answer
those questions.
2 MV network with isolated neutral
Basic analytical results that define currents of
high order harmonics when single phase earth
fault occurs are calculated from network diagram
Fig. 1.
Δ/Y
110/10
System
KV
The equivalent circuit of network shown in Fig. 1
is shown in Fig. 2.
KV
R
Coil
Δ/Y
10/0.4
KV
𝐼𝐼𝑒
𝑒
Fig. 1
The source of high order harmonics is transformer
T2 (10/0.4). All other elements of the network:
power transformer T1, current limitation coil P,
neutral coil are taken into account by their line
inductances.
ISBN: 978-1-61804-074-9
Fig. 2
The faulted cable is simulated by four line
capacitance diagram. The difference between
positive
and zero sequence
capacitances is
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Recent Researches in Applications of Electrical and Computer Engineering
considered by capacitance to neutral
that
could be calculated by the following formula:
(
)
The inductive connections between cables are
ignored. Earth fault current
and
in faulted
cable are defined in branches as shown in Fig. 2.
The same model is applied to sound cables with
capacitances and . Zero sequence current in
the sound feeder is
.
Solving these equations, yields the value of current at
place of short circuit and triple value of zero sequence
in faulted feeder (
).
) and in sound feeder (
( )
( )
(
If the source of harmonics of the order k is
( ) ( ) ( )
presented (
)
and based on
equivalent diagram in Fig.2, the following
equations may be used to determine the value of
earth fault current:
( )
)
(
)
(
( )
)
( )
( )
(
( )
( )
( )
(
( )
( )
( )
( )
( )
)
)
( )
( )
⁄
⁄
Where:
( )
– current of k-order harmonic in phase “a” of
transformer (current source).
- rotational speed of k-oreder harmonic.
– the sum of phase to earth and phase to
phase capacitances.
– zero-sequence capacitance of faulted and
sound feeders.
( )
( )
(
)
(
)
(
)
Where: S=1,2
Where:
are positive –sequence capacitances
respective feeders.
– inductance of the source network.
– number of sound feeders.
( )
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of
It is easy to show that the value of current calculated
by the first equation of equations system (1) may be
obtained from the following equivalent circuit (the
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Recent Researches in Applications of Electrical and Computer Engineering
shunt resistance which is shown as dashed line is not
included), which is shown in Fig. 3.
Current resonance will take place if
)
(
References
[1] A.A.Meer, M.Popov. Directional relay
coordination in ungrounded MV radial distribution
networks using RTDS. International conference on
power system transients (IPST 2009), Koyto, Japan.
2009.
(𝑘)
𝐼𝑒
[2] M.A. Shabad single phase earth fault protection in
6-35 KV networks. ПЭИПК, 2007. (Russian
Language).
[3] G.A.Evdokunen, S.S. Titenkof. The systems of
neutral earthing in MV networks (6-35KV).
Overvoltage and Reliability of Equipment. Collective
works: ПЭИПК, 2006.
Fig. 3
We can conclude from studying equivalent circuit
of Fig.3, that the increae of k-order harmonic of
( )
the current
in place of fault is possible when
the following condition is fulfilled – the total sum
of admittances of the branch with L inductance of
k-order harmonic is approximately equal the sum
). If their absolute
of admittances (
values are equal then the equivalent admittance of
parallel branches to the current source will be
equal to zero. That leads to current resonance,
when voltage of capacitance
will be increased
( )
to infinity and the harmonic current
will be
increased at place of fault.
[4] Jozef Lorenc, Kazimierz Musierowicz, and
Andrzej Kwapisz. Detection of the intermittent earth
fault in compensated MV networks. IEEE Power Tech
Conference, 2003, Bolonga-Italy.
[5] L.E. Dudarof, B.B. Zubkov. Problems of
protection against earth faults in 6-35 KV networks.
Electrechestvo, No.2, 1999. (Russian Language).
In real conditions this can not happen as the
elements of the network have active resistance
and admittance, and the active resistance of the
current source is connected in parallel.
3 Conclusions
The value of high-order harmonic of zero-sequence
earth fault current was obtained based on equivalent
circuit diagram shown in Fig. 3.
The currents
( )
in faulted and sound feeders may
be calculated as part of the total current
The value of current in faulted feeder
(
greater than current in sound feeder
ISBN: 978-1-61804-074-9
( )
.
( )
)
is always
by .
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