International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
Apparent Impedance of Ground Distance Relay using Variable
Zero Sequence Current Compensation Factor
Renuka Jagdale1, Prof. Dr. G.A. Vaidya2
1
2
M.E.Student, P.V.G’s College of Engineering, Pune (India)
Head of Electrical Engineering Department, P.V.G’s College of Engineering, Pune (India)
Newer methods of settings calculations and application
of digital technology for perfect coordination between the
primary and backup relays are helping to lead the existing
power system towards reliable and efficient performance
[4]-[7]. The basis for adaptive transmission protection and
its implementation is introduced in [8]-[9].
This paper presents the new approach to calculate
apparent impedance seen by the ground distance relays by
varying the zero sequence current compensation factor.
The method is based on simulating L-G fault at various
locations along the whole length of UHV long
transmission line. The zero sequence current compensation
factor is also calculated at every fault location and thus
made variable.
With the implementation of adaptive protection system,
it is now possible to adjust the relay settings automatically
in response to continuously changing power system
conditions. Hence the zero sequence current compensation
factor can also be varied with the fault location. The
impedance calculated with this approach is compared with
those calculated with the conventional methods and it is
shown that the new approach offers maximum accuracy.
Abstract--- This paper compares the apparent impedance
of Ground distance relay calculated using fixed zero sequence
current compensation factor with the impedance calculated
using variable zero sequence current compensation factor.
The UHV long Transmission line under study is modeled in
MATLAB and the Phase-to-Ground fault is simulated at
various fault locations along the whole length of line. The zero
sequence current compensation factor is calculated at every
fault location. It is shown that the ground distance relay set
on the basis of this approach offers greater accuracy than
that by conventional method.
Keywords— Distance relays, Phase-Ground faults,
apparent impedance, overreaching, underreaching, Zero
sequence current compensation factor
I. INTRODUCTION
Transmission line protection plays a vital role in the
power system protection. Distance protection schemes are
universally used for protection of High Voltage AC
transmission lines by providing the primary protection
(Main protection) and Back-up protection to lines against
all the 10 faults i.e. 3 phase faults (L-L-L), phase to phase
faults (L-L), phase to ground faults (L-G) and phasephase-ground faults (L-L-G). Out of these, single phase to
ground fault (LG) is the least severe but the most common
fault. The working principle of this relay is that the
impedance measured by it is proportional to its distance
from the fault location.
The bulk of recent literature has been devoted to digital
protection of transmission lines for sensing the fault type
and its location correctly. Bin Su et al. have analysed the
effect of distributed capacitance and susceptance of shunt
reactor on apparent impedance and in turn relay setting of
long EHV/ UHV transmission lines [1]. Research is going
on increasing the reach of the relay to minimise the time
delay and enable fast tripping of the circuit breakers [2].
New method based on apparent impedance and composite
current assistance parameter for calculation of all the three
zones settings of ground distance relays has been proposed
in [3] by Zengli Yang et al.
II. METHODS OF COMPENSATION USED FOR GROUND
DISTANCE RELAYS
The distance relay is a dual input relay viz. voltage and
current and it operates such that it measures the positive
sequence impedance of the faulted line. This is because the
positive sequence component is the only common
sequence component in all the types of faults. Therefore,
the phase relays which locate phase faults (LL, LLG, LLL)
are energised by line-to-line voltages (delta voltage) and
difference in line currents (delta current)[10].
When a single phase to ground fault occurs on a
transmission line with neutral point of the system solidly
grounded, the impedance is derived from the formula Vph/
Iph, where Vph and Iph are phase voltage and phase current
of the faulted phase at the relaying point respectively. But
this ratio is not equal to the positive sequence impedance
of line because of unbalance condition caused due to
additional zero sequence current and zero sequence
impedance.
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
As a result, the ratio of system voltage to current does
not provide proper indication of the fault location and so
cannot be used.
Ground distance relays can also be energised by zero
sequence voltage drop and zero sequence current so that it
measures distance by measuring the zero sequence
impedance. But the profile of zero sequence voltage is
such that it is maximum at the fault point and decreases
toward the grounding point. Hence the ratio V0/I0 also
cannot be used for locating the fault [12].
Thus, variation in the distribution of zero phase
sequence current causes considerable errors in distance
measurement as compared to those by distribution of
positive and negative phase sequence current. Hence
adequate compensation is provided so that the relay
measures exact positive sequence impedance of line. As a
result, several methods of compensation are used for
phase-ground fault.
The most common method used for compensation of
impedance of ground relay involves modification of either
the voltage or current. Depending upon the modified
quantity the compensation factor is given its name.
Another method operates on the principle that at the
fault location the sum of all the sequence voltages is zero.
Let,
Z1 = Positive sequence impedance of line per km
Z0 = Zero sequence impedance of line per km
VA = Phase –ground voltage of phase A
IA = Phase current of phase A
IA0 = Zero sequence current of phase A
Zc1 = positive sequence characteristic impedance
Zc0 = zero sequence characteristic impedance
γ1 = Positive sequence propagation constant
γ0 = Zero sequence propagation constant
x = the distance of fault from relay in km
The data of the system is as shown in Table I.
TABLE I
SYSTEM DATA
Sr.
No.
1
2
3
4
5
6
7
8
9
10
11
V0F + V1F +V2F = 0
This relation is modified by compensators and
reproduced at the relay location. The modified V 0 is used
as the operating quantity and modified (V1 +V2) as
restraining one. For the ground faults within reach, the
relay operates because the operating quantity V0 is greater
than the restraint. On the contrary, for the faults outside the
set zone, the relay does not operate as the restraint quantity
is greater than the operating quantity [12].
Thus, for L-G faults, the voltage and the current to the
Ground fault measuring units are found to be phase voltage
and phase current, suitably compensated by the zero
sequence current.
Parameters
Value
Line Length (L)
Voltage(U)
Short Circuit capacity of G1
Short Circuit capacity of G2
Line Resistance (R1=R2)
Line Resistance (R0)
Line Inductance (L1=L2)
Line Inductance (L0)
Line Capacitance (C1=C2)
Line Capacitance (C0)
Zero sequence impedance of
equivalent system behind relay
(Zsm0max)
600 km
400kV
500 MVA
500 MVA
0.073 Ω/km
0.68 Ω /km
1.295mH/km
4.6 mH/km
8.9 nF/km
5.93 nF/km
320∠88.73° ohm
A. Conventional Method
For Phase-Ground fault (e.g. A-G), the impedance
sensed by relay is given by [10]
Z1 = VA / (IA + k.IA0)
(1)
k = (Z0 –Z1) / Z1
(2)
where,
The value of k calculated using (2) is fixed and
impedance calculated using (1) measures the positive
sequence impedance of line. This is the conventional
method of calculating the impedance of ground relay.
To carry out the analysis of the above system, k is set
using (2) and Ph-G fault (A-G) is simulated at every 50 km
along the whole length of line. The impedance calculated
using (1) is measured and plotted against fault location as
shown in Fig. 2. Also the positive sequence impedance of
line (Z1·x) is plotted on the same graph as a comparison
with impedance of relay.
III. VARIOUS APPROACHES OF CALCULATION OF GROUND
RELAY IMPEDANCES AND ZERO SEQUENCE CURRENT
COMPENSATION FACTOR
The EHV/ UHV long transmission line under study is
shown in Fig. 1.
Fig.1. EHV/ UHV Transmission Line
277
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
The comparison between positive sequence impedance
of line and the measured impedance using (1) is shown in
Fig. 2.
The error varies from 1% at 200 km to 16% at 600 km
which is definitely not a negligible one. It means the relay
underreaches with the apparent impedance considering
distributed capacitance. For example, if the relay is set for
540 km as per positive sequence impedance, the line length
protected by relay is only 500 km. It may be further
observed that the percentage of underreaching increases
with increase in the line length.
Fig.2. Comparison of positive sequence impedance of line and relay
impedance calculated with conventional k
It is observed that the impedance measured by relay
equals the positive sequence impedance for the smaller
distances up to 250 km while it is slightly smaller than the
later beyond 250 km causing error of maximum 3%. This
results in the negligibly small overreaching of relay. For
example, if the relay is set for 540 km as per positive
sequence impedance, the actual reach is 575 km,
overreaching by 6%.
The above method gives the desired results for the
transmission line lengths up to 250 km. because it is based
upon the positive sequence impedance only. It means the
distributed capacitance of line is not considered during
impedance calculation and while zone settings. Z0 and Z1
are calculated using only resistance and inductive
reactance of line. The distributed capacitance of line is
negligible up to 300 km. With the increase in the
transmission line length and voltage, the distributed
capacitance remains no more negligible and is required to
consider for the calculation of relay impedance [1]. In such
cases, the conventional formula of k may give erroneous
results.
Fig. 3. Comparison of positive sequence impedance of line, Relay
impedance calculated with conventional k and theoretical apparent
impedance
Thus, the positive sequence impedance shows
considerable difference with the actual impedance
measured by relay. Therefore, in order to avoid
maloperation of the relay, it is suggested to set the relay on
the basis of apparent impedance considering distributed
capacitance instead of that with positive sequence
impedance. To set the relay using apparent impedance it is
required to modify the zero sequence current compensation
factor such that the relay always measures the apparent
impedance given by (3).
C. Apparent Impedance with Zero Sequence Current
Compensation Factor corresponding to length of
protection zone
The theoretical apparent impedance sensed by the
distance relay for A-G fault is given by [1]
B. Apparent Impedance of Relay using Distributed
Capacitance:
For EHV/UHV Long Transmission line, the theoretical
apparent impedance of relay considering distributed
capacitance is given by [1]
Zapp  Zc1th 1x
VA
 Zc1th 1 x
IA  k  I 0
(4)
Zc 0 sh 0 x  Zc1sh 1x  Zsm0 ch 0 x  ch 1x 
Zc1sh 1x
(5)
ZappA 
Where
(3)
k
The comparison between positive sequence impedance
of line and the theoretical apparent impedance is shown in
Fig.3. The apparent impedance shows the remarkable rise
than that calculated with (1).
Here, it is observed that values of k given by (5) vary
with the fault location x and equivalent zero sequence
impedance of system behind relay, Zsm0. (Zsm0= (-V0/I0)).
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
The zero sequence impedance of the system varies with
different operation modes. Generally, it is suggested to set
the zero sequence current compensation factor according
to the maximum value of zero sequence impedances of the
equivalent system behind the relay (Zsm0max) and the length
of protection zone (Lset)[1] because amplitude of k varies
inversely with distance. Hence as the distance goes on
increasing, the value of k goes on decreasing.
Consequently, the apparent impedance calculated is greater
than its exact value at the respective fault location. This
avoids the overreaching of relay.
Thus, k can be theoretically set using following
equation [1].
kN 
Zc 0 sh 0 Lset  Zc1sh 1Lset  Zsm 0 max ch 0 Lset  ch 1Lset 
Zc1sh 1Lset
The calculated impedance of relay and the % error goes
on decreasing as the fault location approaches 540 km.
The above analysis clears that the calculated impedance
is correct for the fault at 540 km only. The relay
underreaches up to 540 km and shows a slight
overreaching from 540-600 km. For example, if the fault is
at distance 400 km, then the impedance measured by the
relay, being lesser than the calculated impedance,
corresponds to a lesser distance on the curve of calculated
impedance. The fault location indicated by relay will be
slightly lesser (nearly equal to 375 km), causing
underreaching by approximate 6%, sometimes even
negligible.
However, it is always desirable if the relay operates
with the maximum accuracy. The above results can also be
further modified if k is calculated accurately at the
respective fault locations using the actual Zsm0.
(6)
The theoretical values of k are calculated at every 50 km
along the line length. Let the protection zone of relay is set
to 540 km. The value of k corresponding to this distance is
found to be (2.732-1.002i). If ground fault is simulated at
every 50 km and apparent impedance is calculated using
this value of k then the results are obtained as shown in
Fig.4.
D. Apparent Impedance with variable Zero Sequence
Current Compensation Factor
The model for variable zero sequence current
compensation factor prepared in MATLAB is shown in
Fig. 5. Zsm0 is given as input to this model so that even the
minor variations in Zsm0 can reflect in the apparent
impedance measurement giving more accurate results.
However, all the results shown are corresponding to
Zsmomax. This model is prepared as a subsystem of apparent
impedance calculation model shown in Fig. 6.
Fig.4. Comparison of theoretical apparent impedance with the
impedance calculated corresponding to protection zone length
The graph shows that the % error in the impedances
calculated with earlier approaches is reduced to a great
extent using this approach. However, at the fault locations
lesser than 540 km, the value of k is greater than its precise
value at the respective locations. This results in the bigger
impedances than the actual impedance sensed by the relay
at the corresponding fault locations.
Fig.5. Variable zero sequence current compensation factor
279
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
The comparison between theoretical apparent
impedance and apparent impedance measured by the relay
using variable k is shown in Fig.8. It can be observed that
later is quite accurate and can indicate the correct fault
location if the relay is set on the basis of apparent
impedance.
Fig. 6. Apparent impedance model for A-G Fault
The real and imaginary values of k plotted against
distance of fault from relay location at maximum value of
Zsm0 are shown in Fig. 7(a) and 7(b).
Fig.8. Comparison between theoretical apparent impedance and the
impedance with variable zero sequence current compensation factor
The value of k given by (5) is independent of phase
voltage (VA) and phase current (IA) though it involves zero
sequence quantities V0 and I0 in terms of Zsm0. Hence actual
measurement of VA, IA, V0 and I0 can be used to verify the
values of k at different fault locations. Microprocessor
based relays can be given the continuous inputs of phase
voltages, currents and their sequence components and k
can be calculated at every location. The profile of k can
thus be obtained.
From (4), k is given by:
VA
 IA
Zc1th 1x
k
I0
Fig. 7(a). Real part of k
(7)
If A-G fault is simulated at every 50 km and respective
VA, IA and I0 are measured, then k at every fault location
can be calculated. It has been observed that these values of
k match exactly with the actual values of k shown in the
Fig. 7(a) and Fig. 7(b).
This approach of voltage and current measurement can
also be used for designing the Ground distance relay which
will measure positive sequence impedance instead of
apparent impedance. It means, the voltage and current
measurement of relay are corresponding to the actual
apparent impedance but the relay calculates the positive
sequence impedance using variable k.
Fig. 7(b). Imaginary part of k
280
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
This can be made possible by using following equation
of k derived from (1)
VA
 IA
Z
k  1 x
I0
This additional step improves the earlier results and
offers more accuracy. The values of k are also verified by
measuring phase voltage, phase current and zero sequence
current. It is shown this approach also gives the same
values of k.
(8)
REFERENCES
Thus the apparent impedance of relay can be converted
into positive sequence impedance measurement. This will
reduce the errors in the measurement even if the relay is
set conventionally on the basis of positive sequence
impedance using (1).
Bin Su, Ying Yang, Weising Gong, Yongsheng Xu, “Setting
considerations of distance relay for UHV/EHV long transmission
lines”, Paper presented at the IEEE Power Engineering Society
Meeting, June 2007, Page 1-7.
[2] T. S. Sidhu, D. S. Baltazar, R. M.Palomino and M. S. Sachdev, “A
new approach for calculating zone-2 setting of distance relays and
its use in an adaptive protection system,” IEEE Trans. Power Del.,
vol. 19, no. 1, pp. 70–77, Jan. 2004
[3] Zengli Yang, Xianzhong Duan, “A New approach for calculating
setting of distance relays considering mutual coupling effect ” Paper
presented in 41 st International Conference on Universities Power
Engineering conference, September 2006.
[4] M. M. Eissa and M. Masoud, “A novel digital distance relaying
technique for transmission line protection,” IEEE Trans. Power
Del., vol. 16, no. 3, pp. 380–384, July 2001.
[5] B. R. Bhalja and R. P. Maheshwari, “High-resistance faults on two
terminal parallel transmission Line: Analysis, simulation studies,
and an adaptive distance relaying scheme,” IEEE Trans. Power Del.,
vol. 22, no. 2, pp. 801–812, Apr. 2007.
[6] C.-H. Kim, J.-Y. Heo, and R. K. Aggarwal, “An enhanced zone 3
algorithm of a distance relay using transient components and state
diagram,” IEEE Trans. Power Del., vol. 20, no. 1, pp. 39–46, Jan.
2005.
[7] Mahmoud Gilany, Ahmed M. Al-Kandari, and Jamal Y. Madouh,
“A New Strategy for Determining Fault Zones in Distance Relays”
IEEE Trans. Power Del., vol. 23, no. 4, pp. 1857–1863, Oct. 2008.
[8] Vajira Pathirana, P.G. McLaren, “Improving relay reach and speed
through hybrid algorithm”, Bologna Power Tech Conference, June
23-26, 2003,Bologna, Italy.
[9] L. P. Singh, Digital protection, Protective Relaying from
Electromechanical to Microprocessor, II Edition, New Age
International
[10] Y. G. Paithankar, Transmission Network Protection, Theory and
Practice, Marcel Dekker, Inc.
[11] W. D. Stevenson, Jr., Elements of Power System Analysis,
McGraw-Hill International Editions
[12] J. L. J. Lewis Blackburn, Protective Relaying Principles and
Applications. New York: Marcel Dekker, 1987.
[1]
IV. SYSTEM STUDIES AND MATLAB SIMULATIONS
The above analysis is applied to the UHV system shown
in Fig. 1. The results of the simulations are plotted against
fault locations. These results show that the setting principle
of variable k ensure accuracy and the reliability of the
distance relay for EHV/ UHV transmission lines.
V. CONCLUSION
The impedances seen by the ground distance relay for
different values of current compensation factor are
compared. It is shown that the conventional formula is
suitable for the transmission lines of length up to 200 km
and it shows overreaching above 200 km because it does
not consider the distributed capacitance of line. Beyond
300 km, the distributed capacitance gains considerable
value and hence, it is suggested for a long transmission
lines, that the setting should be based on the apparent
impedance considering distributed capacitance. This
requires the zero sequence current compensation factor to
be varied in such a way that it measures the apparent
impedance instead of positive sequence impedance. k can
also be set corresponding to the length of protection zone
but the relay shows underreaching in the protection zone
and overreaching beyond the protection zone. Therefore it
is required to vary the zero sequence current compensation
factor along the whole length of line.
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