D
Journal of Energy and Power Engineering 6 (2012) 240-249
DAVID
PUBLISHING
A New Transient Impedance-Based Algorithm for Earth
Fault Detection in Medium Voltage Networks
Mohamed F. Abdel-Fattah1,2 and Matti Lehtonen1
1. Department of Electrical Engineering, School of Electrical Engineering, Aalto University, Espoo 00076, Finland
2. Department of Electrical Power and Machines Engineering, Faculty of Engineering, Zagazig University, Zagazig, Sharqia, PO
Box 44519, Egypt
Received: August 05, 2010 / Accepted: April 28, 2011 / Published: February 29, 2012.
Abstract: This paper presents a new earth-fault detection algorithm for unearthed (isolated) and compensated neutral medium voltage
(MV) networks. The proposed algorithm is based on capacitance calculation from transient impedance and dominant transient
frequency. The Discrete Fourier Transform (DFT) method is used to determine the dominant transient frequency. The values of voltage
and current earth modes are calculated in the period of the dominant transient frequency, then the transient impedance can be
determined, from which we can calculate the earth capacitance. The calculated capacitance gives an indication about if the feeder is
faulted or not. The algorithm is less dependent on the fault resistance and the faulted feeder parameters; it mainly depends on the
background network. The network is simulated by ATP/EMTP program. Several different fault conditions are covered in the
simulation process, different fault inception angles, fault locations and fault resistances.
Key words: Earth faults, earth capacitance, transient impedance, transient frequency, unearthed and compensated MV networks.
1. Introduction
In networks with an unearthed (isolated) neutral, the
currents of single phase to ground faults depend mostly
on the phase to ground capacitances of the lines. When
the fault happens, the capacitance of the faulty phase is
bypassed, leading to unsymmetrical system. The fault
current is composed of the currents flowing through the
earth capacitances of the two sound phases as shown in
Fig. 1. Therefore, the capacitance measurement gives
an indication if the feeder is faulted or healthy. The
main advantage of unearthed neutral in power systems
is small fault currents which does not require to shut
down immediately, but the main problem is the
over-voltage that resulted by charging of the system
Corresponding author: Mohamed F. Abdel-Fattah,
postdoctoral researcher/lecturer, research fields: earth-faults
detection, diagnosis and location using transient and fast
transient-based algorithms and the intelligent protection
systems for self-healing capability of the smart grids. E-mail:
mohamed.abdel-fattah@aalto.fi.
capacitance of the sound phases, which may lead to
flashover or breakdown. Also, it may establish a double
line to earth fault.
In earth faults, the transient components include
charge and discharge of the network capacitance and
consist of different frequencies. The voltage of the
faulty phase falls suddenly, giving rise to the discharge
transient while the charge transient is generated by the
E1
E2
E3
~
~
~
Z
L1
Z
L2
Z
L3
Ce
Fig. 1 Earth fault in unearthed neutral network.
RF
A New Transient Impedance-Based Algorithm for Earth Fault Detection in Medium Voltage Networks
voltage rise in sound phases during a single-phase to
ground fault. This means that a charge transient is
always a side effect of the ground fault.
Moreover, the charge component dominates the
amplitude of the composite transient and therefore it is
reasonable to be used for single-phase to ground fault
detection. The charge component has to flow through
the transformer winding and consequently its
frequencies are substantially lower than those of
discharge component. According to practical
experience, the frequencies of discharge and charge
components vary in the range 500-2500 Hz and
100-800 Hz respectively. The amplitude of the
discharge component is relatively small, typically only
about 5%-10% of the amplitude of the charge
component [1, 2]. The small fault currents may reduce
the sensitivity of conventional relays that normally are
based on the fundamental components of the current
and voltage at power frequency. The high fault
generated high frequencies should be filtered out in the
conventional protective schemes which only use the
power frequency, however, these high frequency
components contain more information about the fault
than power frequency that should be utilized, with the
rapid developments in microprocessor technology, in
new developed techniques called transient based
techniques. In contrast to present protection techniques
based on fault transient detection, such as traveling
wave based protection techniques, the transient based
techniques are not limited by the bandwidth of the
conventional transducers, and are able to accurately
separate and extract the high frequency information
required from the dominant power frequency signals [3].
Transient-based protective schemes can detect high
impedance as well as intermittent arcing faults, leading
to improvement in the power system reliability.
However, there are the hidden faults which involve
developing and self extinguished/arcing faults which
may not be detected by the conventional protection
system. In particular, high resistance arcing faults are
highly random as viewed from their current waveforms.
241
Many research works have been done in this area in the
last few years, for earth fault detection in unearthed and
compensated neutral networks, but the goal is still not
fulfilled. It is very important to validate the results from
the simulation process and to be satisfied that it can
represent the actual realistic conditions. In Ref. [4],
comparative investigations between real earth fault
field tests and the equivalent simulation data have been
presented. A simple powerful technique in Ref. [5] is
proposed to utilize the peak values of the superimposed
waveforms. In the same time, these peaks can be used to
synchronize the waveforms, supported by a suitable
secure manipulation within the algorithm. Another
efficient way is to use the probabilistic analysis as
proposed in Ref. [6]. The earth fault characteristics,
analysis and comparison, in medium voltage
distribution networks, 20 kV with high impedance
earthing, were presented in Ref. [7]; the presented
results are based on the evaluation of 465 real case data
recording, obtained from substations of distribution
networks with an unearthed or a compensated neutral
during the observations period of 3 years; continued
investigations were presented in Ref. [8]. The earth
fault location for different fault conditions, in these
networks, were also investigated in Refs. [9-14] and a
probabilistic-based method is proposed in Ref. [15].
Some work have been done to investigate the
intermittent earth fault; in Ref. [16] using the zero
sequence voltage and a sum current of phase currents,
the intermittent fault is identified if the amplitude of the
voltage and current exceed corresponding set values
and the phase difference is within preset set values, in
Ref. [17] the features of the intermittent fault were
identified to using wavelet analysis and in Ref. [18] the
wavelet analysis were applied using the phase
comparison between wavelet coefficients of zero
sequence voltage and currents. A residual equivalent
circuit for Peterson coil grounded distribution systems
have been presented in Ref. [19] and an extended zero
sequence equivalent circuit for compensated medium
voltage systems, with load current contribution
242
A New Transient Impedance-Based Algorithm for Earth Fault Detection in Medium Voltage Networks
accounted, is presented in Ref. [20] and the detection of
single line-to-ground fault in compensated networks
has been investigated in Refs. [21, 22].
The transient period features have been investigated
in Ref. [23], an algorithm for high impedance fault is
detected in compensated neutral grounded medium
voltage power systems, the calculation of the influence
of feeder admittance unbalance in neutral voltage is
presented in Ref. [24].
The three-phase line can be decomposed into three
separate and independent modal equivalent circuits. The
modal components are the transform of the instantaneous
(or time domain) phase quantities, using transformation
matrices, into zero, first and second modes. The zero
mode is also termed the “earth mode”, while the second
and third modes are termed “aerial modes”.
In protection applications, there are three modal
transformation matrices that have been widely used.
They are Wedepohl, Karrenbauer and Clark
transformations [25]. For all of these transformations,
the earth mode is the same; it is equal to one-third of
the summation of the instantaneous phase values
(voltages or currents) as given by Eqs. (1) and (2). The
values of the voltage and current earth modes are equal
to zero in normal operation and become meaningful in
fault condition. They are very sensitive for earth faults;
hence they are suggested to be used for fault detection.
The voltage and current earth modes are given by Eqs.
(1) and (2).
v (t ) 0  13 [v a (t )  v b (t )  v c (t )]
i (t ) 0  13 [ia (t )  ib (t )  ic (t )]
(1)
(2)
In this paper, a new earth-fault detection algorithm
for unearthed and compensated neutral medium
voltage networks is presented. The algorithm is
proposed to calculate the earth capacitance that can be
used as fault indication for the faulted feeder. The
capacitance can be calculated using the dominant
transient frequency and the transient impedance.
Different fault inception angles, fault locations and
resistances were simulated to check the validity of the
algorithm.
2. The Simulated Network
Based on a typical 20 kV medium voltage
distribution network configuration, a suitable network
model will be proposed for the required investigations.
A realistic network of the arrangement shown in Fig. 2
is proposed for the study.
A primary (110/20 kV) substation feeds a rural
overhead network consisting of five feeders of many
tens of kilometers length. The mathematical model of
the network has been implemented using the
alternative transient program. The alternative transient
program ATP/EMTP is a popular simulation software
package mainly intended for transient analysis
applications [26, 27].
ATPDraw, a graphical pre-processor to ATP, has
been used to construct the network elements using
suitable graphical blocks/symbols, to plot the required
figures and to write the required output data files in a
suitable form for further advanced analysis in Matlab
[28]. The transmission line frequency dependent model
(JMarti) is used for feeders simulation with sampling
time of 100 μs. The network data are given in the
appendix.
3. The Proposed Algorithm
For the simulated network shown in Fig. 2, the earth
modes of the bus voltage and feeder currents are
calculated at substation (measuring points).
Fig. 3 shows the waveforms of the voltage earth
mode at the bus and the current earth modes for each
feeder. The waveforms for all healthy feeders are
approximately the same but situation is different for
faulted feeder as shown. The transient period is the first
few milliseconds directly after fault incidence. From
investigations of the simulation results it is found that a
suitable transient window of 2.5 ms is adequate to
extract the transient frequencies in all different fault
conditions, different fault inception angles, fault
locations and fault resistances, hence it will be used
with DFT (Discrete Fourier Transform) method.
A New Transient Impedance-Based Algorithm for Earth Fault Detection in Medium Voltage Networks
The enlarged view of the transient period is shown in
Fig. 4. The DFT method will be used to extract the
dominant transient frequency (of higher amplitude)
from the charge transient component, from 0 to 1200
Hz. In Matlab, the discrete Fourier transform (DFT) is
computed with a fast Fourier transform (FFT) algorithm.
F5
F4
66/20 kV, ∆/Y
Substation
Transformer
F3
F2
CB F1
Measuring Point
Fault Point
Fig. 2 The simulated medium voltage distribution network.
20
Healthy
Current
(A)
15
Faulted
Current (A)
10
Voltage (kV)
5
0
-5
-10
-15
-20
0
4
8
12
16
20
24
28
Fig. 3 The waveforms of the voltage earth mode at the bus
and the current earth modes of faulted and healthy feeders,
for one period after the fault incidence at 8 ms incidence
time, 10 Ω fault resistance and 80% fault distance.
20
15
Healthy
Current (A)
Faulted
Current (A)
10
Voltage (kV)
5
0
-5
At the beginning of the research, a sampling frequency
of 100 kHz (10 μs) is used for investigation. From the
results, a practical low sampling frequency can be used
without affecting the accuracy. This can be
investigated from the frequency range of the transient
period which is very effective from 200 Hz to 1000 Hz.
Hence lower practical sampling frequencies around 10
kHz (100 μs) will be adequate hence the proposed
algorithm will be suitable for microprocessor based
relaying. The frequency domains for the currents are
quite similar but the magnitudes are different; the
higher magnitude is of course for the faulted feeder
current.
The frequency domain output from DFT of the
faulted current waveform, presented in Fig. 3, is shown
in Fig. 5. For this case, the dominant frequency is 318
Hz which is equivalent to about 3.15 ms period.
Within the transient period, of 3.15 ms, the values of
the voltage and current earth modes will be calculated,
after that the impedance can be calculated as a ratio of
the voltage to the current. All these values are at the
same transient frequency, which in this case is equal to
318 Hz.
As expected, the dominant transient frequency is
different from case to another, depending up on the
fault conditions, including the fault resistance,
incidence angle and the fault distance. The flow of the
fault current is presented in Fig. 6.
The average value of a sinusoidal waveform over the
period is equal to zero; hence it is suggested to use the
average value of the waveforms to eliminate the values
of higher frequencies contained as possible. For the
fundamental transient frequency, the average values
will be calculated in the first half of the period to ensure
the same polarity, as in Ref. [23], and can be calculated
using Eqs. (3)-(5).
N
-10
The average voltage is V0 
-15
-20
243
7
8
9
10
11
12
Fig. 4 The transient period (the first few milliseconds
directly after the fault incidence), for the waveforms shown
in Fig. 3.
v
0, k
k 1
N
(3)
N
The average current is I 0 
i
0,k
k 1
N
(4)
244
A New Transient Impedance-Based Algorithm for Earth Fault Detection in Medium Voltage Networks
14
the earth capacitance and can hence be neglected.
The earth capacitance of the network depends on the
Magnitude
12
10
types and lengths of the lines connected in the same
8
part of the galvanic connected network. In practice, for
6
radial medium voltage distribution networks, it is the
4
area supplied by one HV/MV substation transformer.
Therefore, for faulted feeder, the calculated
2
0
0
300
600
900
1200 1500 1800
Frequency (Hz)
2100
2400
2700
3000
Fig. 5 The frequency domain output from DFT of the
faulted current.
impedance will be the capacitive impedance of the
background network while for healthy feeder, it is the
capacitive impedance of the feeder itself, both defined
at the dominating transient frequencies. Also, from
Healthy Feeder
Fig. 6, the calculated capacitance for the faulted
feeder will be negative because its direction is opposite
to the measurement direction which verifies the
66/20 kV
∆/Y
66 kV
Supply
directionality technique. In Ref. [5], the technique is
based on the transient impedance which highly
Faulted Feeder
dependends on the transient frequency band, in the
Measuring Point
(V0, I0)
transient period. The proposed algorithm here is based
Fault
Point
on earth capacitance estimation which improves the
performance. The earth capacitance of the feeder
Fig. 6 The flow of the earth fault currents, during a
single-phase to ground fault, through the earth capacitance
of the healthy feeders of the network.
The average impedance is Z 0 
V0
I0
(5)
where v0,k is the instantaneous voltage earth mode at
sample k, calculated from Eq. (1), i0,k is the instantaneous
current earth mode at sample k, calculated from Eq. (2)
and N is the number of samples in the window. The rms
and average values are related to peak value by
constant factors, 0.707 and 0.636 respectively, and then
the rms value is related to the average value by a
constant factor of 1.111. The impedance is calculated
as a ratio of the voltage to the current, hence, no need
for other factors to be considered. The fault current is
composed of the currents flowing through the earth
capacitances of the sound lines (background network)
as presented in Fig. 6, and hence the calculated
impedance will depend mostly on the earth capacitance
of background network. The other impedances of the
network components are small compared to those of
depends on the type and length. From the dominant
transient frequency and calculated transient impedance,
the earth capacitance can be calculated from Eq. (6), as
follows:
Ce 
1
2 f tr Z 0
(6)
where ftr is the dominant transient frequency that
determined the frequency domain output from DFT
and Z0 is the average impedance calculated from Eq.
(5). For the case shown in Fig. 3, the calculated values
are:
The voltage Vo= -6.5251 kV
The dominant transient frequency ftr = 318.004 Hz
The faulted feeder current I0f = 7.9679 A
The faulted feeder impedance Z0f = -0.8184 kΩ
The faulted feeder capacitance Cef= -0.6113 μF
The healthy feeder current I0h = -1.9271 A
The healthy feeder impedance Z0h= 3.3840 kΩ
The healthy feeder capacitance Ceh= 0.1478 μF
It is found that the calculated capacitance is not
accurate due to the sources of error in this technique,
A New Transient Impedance-Based Algorithm for Earth Fault Detection in Medium Voltage Networks
that are the error from the DFT method which is highly
effected by the sampling frequency, the error due to
neglecting the network impedances which effect
increases with higher frequencies and the error due to
the effect of frequencies of higher magnitudes around
the dominant frequency, including the discharge
transient frequency. To overcome these errors, it is
proposed to use the ratio (Kc) of the calculated
capacitances (Ce,calc.) to the total network capacitance
(Ce,total) as a fault indicator as given by Eq. (7).
C
K c  e , calc.
(7)
Ce , total
The capacitance is directly proportional to the
lengths of the feeders which are 41, 35, 30, 33 and 45
km, total length of 184 km, hence we can determine the
values of these ratios in healthy and faulty conditions
for all feeders as follows:
For healthy condition:
For feeder (1), Kc1 = 0.22
For feeder (2), Kc2 = 0.19
For feeder (3), Kc3 = 0.16
For feeder (4), Kc4 = 0.18
For feeder (5), Kc5 = 0.25
For faulty condition:
For feeder (1), Kc1 = -0.78
For feeder (2), Kc2 = -0.81
For feeder (3), Kc3 = -0.84
For feeder (4), Kc4 = -0.82
For feeder (5), Kc5 = -0.75
For the same feeder, the summation of the ratio
magnitudes, or the magnitude of the difference, in
healthy and in faulty conditions, is equal to one. It must
be noted that the total earth capacitance must be scaled
to include the error in the calculated values. From the
calculated values, the average scaled value of the total
earth capacitance of the network is equal to 0.7818 μF.
By this technique, for the case shown in Fig. 3, the ratio
of the healthy feeder is equal to 0.1891 and the ratio of
the faulted feeder is equal to 0.78187, which is
comparable to the calculated values. From the
calculated values of the ratios, the average value of the
245
healthy condition is 0.20 and the average value of the
faulty condition is -0.80.
For compensated networks (Peterson coil/ resonance
grounded/earthing networks), the impedance of the
compensation coil is relatively high at transient
frequencies. Consequently, the transients are about
similar in both of unearthed and compensated neutral
networks. This is clearly investigated from the
simulation data that will be presented in the following
section, also the setting of the algorithm will be
proposed.
4. Results and Setting
Fig. 7 shows the variation of the ratios for healthy
and faulty conditions with the fault incidence time,
over the power frequency period (0-20 ms), Fig. 8
shows its variation with the fault distance and Fig. 9
shows its variation with the fault resistance. The values
of the ratios for healthy and faulty conditions for
unearthed network are presented by solid lines and for
compensated network are presented by dash lines.
The setting value of the ratio will be chosen at the
middle between the average ratio values of healthy and
faulty conditions to achieve maximum performance of
the algorithm operation. These values are 0.2 and -0.8,
and then the setting value will be -0.3. The limits of the
setting value will be from 0.0 (for network with two
feeders) to -0.5 (for network with very high number of
feeders), so its value always negative. In this section,
some discussion about Figs. 7-9 will be presented.
It is found that there is an adequate gap between the
healthy and faulty condition, and no overlapping
between the two conditions. This gap covers any sources
of error in the measurements, that may give incorrect
higher or lower ratios, and the proposed algorithm will
operate effectively. For the simulated system, the
magnitude of the average ratio of the faulty condition is
equal to four times the average value of the healthy
condition; this related to the number of the feeders and
its lengths. At faulted condition we have four healthy
feeders and one faulted feeder, hence, we can find the
246
A New Transient Impedance-Based Algorithm for Earth Fault Detection in Medium Voltage Networks
0.4
the healthy condition will be 0.10, the average value of
the faulty condition will be -0.90. By choosing a
suitable value of the setting, the performance of the
proposed algorithm will not be affected by number of
feeders in the network.
Healthy condition
0.2
0.0
Ratio
-0.2
Setting Value = -0.3
-0.4
-0.6
From the practical point of view the required
Faulty condition
sampling rate is an important factor. From the results of
-0.8
-1.0
different analysis at different frequencies, it shows that
0
2
4
6
8
10
12
14
Incidence time (ms)
16
18
20
Fig. 7 The variation of the ratios for healthy and faulty
conditions with the fault incidence time, over the power
frequency period (0-20 ms) at 80 Ω fault resistance and 80%
fault distance for unearthed (—) and compensated (---)
neutral networks.
0.4
Ratio
definitely the sensitivity is increased with higher
sampling rate. Therefore, the simulations were
after using a sub-sampling factor of 16.
-0.2
The lower sampling frequency of the proposed
Setting Value = -0.3
algorithm indicates the applicability and the suitability
-0.4
for microprocessor based relaying.
-0.6
Faulty condition
5. Conclusions
-0.8
0
10
20
30
40
50
60
70
Fault distance (%)
80
90
100
Fig. 8 The variation of the ratios for healthy and faulty
conditions with the fault distance at 8 ms incidence time and
80 Ω fault resistance.
A new transient-based algorithm for earth fault
detection for unearthed (isolated) and compensated
neutral medium voltage networks is proposed. It is
based on determining the dominant transient frequency
by using DFT method.
0.4
The dominant transient frequency will be used to
Healthy condition
0.2
calculate the transient impedance, in the transient
0.0
Ratio
selectivity and security of the proposed algorithm,
data were analyzed at sampling frequency of 6.25 kHz
0.0
-1.0
analysis is around 6 kHz without affecting much in the
performed at sampling frequency of 100 kHz and the
Healthy condition
0.2
the minimum sampling frequency that can be used for
period, from which the earth capacitance can be
-0.2
calculated. The earth capacitance gives a good
Setting Value = -0.3
-0.4
indication about the earth fault, as it equals to all the
-0.6
background network earth capacitance in faulty
condition but equal to line earth capacitance in healthy
-0.8
-1.0
Faulty condition
1
10
condition. To overcome the sources of errors in the
100
1000
10000
Fault Resistance (Ω)
100000 1000000
calculation, it is proposed to use the ratio of the
Fig. 9 The variation of the ratios for healthy and faulty
conditions with the fault resistance at 8 ms incidence time
and 80% fault distance.
calculated
capacitances
to
the
total
network
factor four. This is for comparable length feeders, as an
example if we have ten feeders network and then we
will find a factor nine. In this case, the average value of
method) has been done to investigate and validate the
capacitance as a fault indicator. Extensive simulations
by ATP/EMTP program and analysis by Matlab (DFT
performance of the proposed algorithm for different
fault conditions including different values of incidence
A New Transient Impedance-Based Algorithm for Earth Fault Detection in Medium Voltage Networks
time, fault resistance and fault location. There is an
adequate gap between the healthy and faulty condition,
and no overlapping between the two conditions. This
[8]
gap can cover any source of errors in the measurements
that may give incorrect higher or lower ratios. An
average setting value of -0.25 can be used as the default
[9]
setting value that can be used for different network
configuration.
The performance of the proposed algorithm is
promising and it can be more enhanced by choosing the
ratio setting value from 0.0 to -0.5, at the middle
between the average ratio values of healthy and faulty
conditions, depending on the network configuration.
The proposed algorithm is applicable with a lower
sampling frequency of 6.25 kHz and hence suitable for
microprocessor based relaying.
[10]
[11]
[12]
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Appendix
The simulated network data:
Substation transformer:
U1/U2 = 66/20 kV
Delta/Star connection
S = 10 MVA, x = 10.0%
Network:
Five 20 kV overhead line feeders
Total length = 184 km
Feeder 1 length = 41 km
Feeder 2 length = 35 km
Feeder 3 length = 30 km
Feeder 4 length = 33 km
Feeder 5 length = 45 km
Network positive sequence capacitance: 5.1 μF
Network zero sequence capacitance: 9.6 μF
Line average positive sequence inductance: 0.9 mH/km
Distribution transformers:
Five step-down transformers
U1/U2 = 20/0.4 kV
Delta/Star-earthed connection
Loads:
Five 0.4 kV loads
Total load = 5.5 MW
Load 1 rating = 1.5 MW
Load 2 rating = 1.5 MW
Load 3 rating = 0.5 MW
Load 4 rating = 1.5 MW
A New Transient Impedance-Based Algorithm for Earth Fault Detection in Medium Voltage Networks
Load 5 rating = 0.5 MW
Overhead line configuration [29]:
MV wooden pole with steel cross-arm
Bare conductors ACSR 54/9 Raven
Aluminum Conductor Steel Reinforced (ACSR)
Current rating (in air at 80 oC) = 280 A
Number of wires = 7 (6 Aluminum & 1 Steel)
Complete conductor diameter = 10.1 mm
Total cross-section area = 62.4 mm2
DC resistance (at 20 oC) = 0.536 /km
Conductor spacing = 1.1 m and 8.1 m height
249