Calculation of apparent impedance and distance relay characteristics

International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 12, December 2014)
518
Calculation of Apparent Impedance and Distance Relay
Tripping Characteristics in Ehv/Uhv Transmission Line with
and Without Capacitance
Jayachandra S1
, Sivakumar G2
1,2
J.N.T.U.A
Abstract—EHV/UHV long transmission lines have large
distributed capacitance which has significant effect on the
operation of a distance relay. To set the distance relay without
considering the distributed capacitance will cause serious over
reaching or under reaching. This paper analyzes the effect of
distributed capacitance on the relay tripping characteristics
and the setting principal of distance relay for EHV/UHV long
transmission line is discussed.
Keywords— EHV/UHV long transmission line, distance
relay, distributed capacitance, relay tripping characteristics.
I. INTRODUCTION
Distance relays are widely used as primary or backup
protection for UHV/EHV lines, as they are independent of
communication channels, and their reaches are insensitive
to system condition[1]. A distance relay operates by
measuring the electrical circuit distance between the relay
location and the point of fault (apparent impedance) to
determine if a fault is in its protection zone. It is apparent
that the protection zones need to be set accurately to avoid
overreaching or under reaching, and ensure the reliability
and selectivity. Normally the protection zones can be set
without considering the distributed capacitance, as the
impedance of the distributed capacitance is too big
compared with the line impedance. With the transmission
distance increasing, however, the distributed capacitance of
the whole line increases correspondingly. Meanwhile, to
improve the economical and transmission efficiency over
long distance, higher voltage levels are adopted, which
brings higher distributed capacitance per unit of
transmission lines[8]. The impedance of the distributed
capacitance is comparable with the line impedance, thus its
effects on the distance relay need to be considered, to
ensure the distance relay‟s reliable operation [2].
II. APPARENT IMPEDANCE WITHOUT CONSIDERATION OF
LINE CAPACITANCE
In the case of zero fault resistance, the measured
impedance by distance relay is the exact impedance of the
line section between the fault and the relaying points.
From Fig.1., this impedance is equal to dZ1L, where d is
per unit length of the line section between the fault and the
relaying points and Z1L is the line positive sequence
impedance in ohms. For a non-zero fault resistance, the
measured impedance at the relaying point is not equal to
the mentioned magnitude. In this case, the structural and
operational conditions of the power system affect the
measured impedance. The operational conditions prior to
the fault instances can be represented by the load angle of
the line „δ‟ and the voltage magnitude ratio at the line ends
„h‟ or in general EN / EM= he-jδ. The structural conditions
are evaluated by the short circuit levels at the line ends.
Fig.1. phase -to-ground fault without consideration of line
capacitance
The measured impedance at the relaying point can be
expressed by the following equations[3],[4].
1M 1SM 1L
Z =Z +dZ (1)
1N 1SN 1L
Z =Z +(1-d)Z (2)
M NPREI =I -I (3)
PRE M PRE 1M
V =E -I Z (4)
PRE
1F 2F 0F
Σ F
V
I =I =I =
Z +3R
(5)
1M 1N 0M 0N
Σ
1M 1N 0M 0N
Z Z Z Z
Z =2 +
Z +Z Z +Z
   
   
   
(6)
PRE
1MF 2MF 1 1F 1
Σ F
V
I =I =C I =C
Z +3R
(7)

519
PRE
0MF 0 0F 0
Σ F
V
I =C I =C
Z +3R
(8)
AM PRE 1MF 2MF 0MF
I =I +(I +I +I ) (9)
AM
APP
AM 0L 0F
V
Z =
I +K I
(10)
 
F
APP 1L
F 1 0 0L
3R
Z =dZ +
Z +3R K +2C +C (1+K )
(11)
-jδ
δ -jδ
1N 1M
1-he
K =
Z +Z he
(12)
For zero fault resistance, the apparent impedance at the
relaying point is equal to the impedance of the line section
located between the relaying point and the fault point.
From equation (12) it is observed that, in the presence of
fault resistance the apparent impedance is affected by
power system conditions only.
III. APPARENT IMPEDANCE WITH CONSIDERATION OF
LINE CAPACITANCE
Long EHV/UHV transmission lines are highly affected
by the line capacitance. If the effect of line capacitance for
a fault with considerable value of fault resistance is
ignored, then there is a substantial error in the impedance
seen by a relay. Transmission line model including the line
capacitance is shown in fig.2. In this proposed method
double π model is utilized for considering the transmission
line capacitance with fault resistance as shown in fig.3. The
system of fig.3 includes four additional shunt branches.
compared to fig .3 the fault point divides the line into two π
sections. Each line section is modeled by a π model[8],[5].
Fig.2. Transmission line model including shunt capacitance
 
M
1SM
1SN 1CN 1L 1CM 1SM
E
I =
(((Z //Z )+Z ))//Z )))+Z )
(13)
1CM 1SN 1CN
1LM 1SM
1L 1CM 1SN 1CN 1SN 1CN
Z (Z +Z )
I =I
((Z +Z )(Z +Z )+Z Z )) (14)
 
N
1SN
1SM 1CM 1L 1CN 1SN
E
I =
(((Z //Z )+Z ))//Z )))+Z )
(15)
1CM
1NM 1LN
1CM 1SM
Z
I =I
(Z +Z )
(16)
IPRE= I1SM-I1NM (17)
I1L= I1LM-I1LN (18)
Fig..3. Line diagram for phase-to-ground fault with consideration of
line capacitance
1Meq 1Neq 0Meq 0Neq
1Meq 1Neq 0Meq 0Neq
2Z Z Z Z
Z = +
Z +Z Z +Z

(19)
PRE
1F 2F 0F
F
V
I =I =I =
Z +3R
(20)
PRE
1QF 2QF 11 1F
Σ F
V
I =I =C I =
Z +3R
(21)
PRE
0QF 01 0F
Σ F
V
I =C I =
Z +3R
(22)
PRE
1PQ 2PQ 12 1F 12
Σ F
V
I =I =C I =C
Z +3R
(23)
PRE
0PQ 02 0F 02
Σ F
V
I =C I =C
Z +3R
(24)
PRE
1MP 2MP 13 1F 13
Σ F
V
I =I =C I =C
Z +3R
(25)
PRE
0MP 03 0F 03
Σ F
V
I =C I =C
Z +3R
(26)

520
AM
APP
AM 0L 0F
V
Z =
I +K I
(27)
AM PRE 1MF 2MF 0MF
I =I +(I +I +I ) (28)
AM 1L
PRE PRE PRE
F 1L 11 12 1L 01 02 0L
F F F
V =3R I dZ +2C C dZ +C C dZ
V V V
+
Z +3R Z +3R Z +3R  
(29)
F
1L 1L F 11 12 1L 01 02 0L
PRE
APP
F
PRE 11 12 13 01 02 03 0L
PRE
Z +3R
I dZ +3R +2C C dZ +C C dZ
V
Z =
Z +3R
I +2C C C +C C C (1+K )
V


 
 
 
 
 
 
(30)
It can be seen from equation (30) that the fault resistance
is not only the factor causing the measured impedance
deviation, but also the line capacitance. The ZAPP is also
dependent on power system conditions and line length
IV. THE IDEAL TRIPPING CHARACTERISTICS
Knowing the structural and operational conditions, i.e.
the short circuit levels, the load angle, and the voltage
magnitude ratio, the distance relay ideal tripping
characteristic can be defined. This characteristic has four
boundaries. First boundary is the measured impedance for
zero fault resistance; fault location varies from near end up
to the far end of the line. In the second boundary, the fault
point is at the far end; fault resistance varies between 0 and
200 ohms. Third boundary is the result of the fault point
variation along the line for the fault resistance of 200 ohms.
Forth is achieved by variation of the fault resistance
between 0 and 200 ohms for the faults on the near end of
the line[6],[7].
V. FLOW CHART TO OBTAIN THE IDEAL TRIPPING
CHARACTERISTICS.
Fig.4 shows the flow chart for ideal tripping
characteristics for with considering line capacitance and
explains the procedure for R-X plot with considering line
capacitance
Fig .4 .Flowchart for R-X plot with considering capacitance
Simulations are performed for a 400 kV transmission
line length of 300km.The line parameters[4],[8] are given
in table A and table B.
Table .A
Source impedances
Source
Impedance
Bus M Bus N
Positive and
negative,sequenc
e impedance
1.7431+j
19.9238
0.0871+j0.99
61
Zero sequence
impedance
2.6146+j
29.8858
0.1307+j1.49
42

521
Table .B
Line parameters
Line
parameters
R
(Ω/Km)
L
(mH/
Km)
C
(µF/
Km
)
Positive and
negativesequenc
e impedance
0.0301 1.0 0
.011
2
Zero
sequence
impedance
0.2269 2.2 0
.009
4
The distance relay tripping characteristic at h=0.96 and
load angle is 160 shown in Fig.5,(I) first boundary line is
for zero fault resistance and fault location varies from relay
point to reach point (II) in the second boundary-line, the
fault is at reach point with fault resistance varying from 0
to 200 Ohm (III) third one refers to fault resistance of 200
Ohm with fault position varying from relay to reach point
and (IV) fourth line is for relay location with fault
resistance varying from zero to 200 Ohm.
The characteristic without considering the line
capacitance is also in the dotted form for comparison. In
the Fig.5 the other important thing observed in this plot is
that there is significant difference in trip characteristic
while considering line capacitance.
Fig .5. Distance relay tripping characteristic at h=0.96, δ=160
The percentage Relative error with and without consideration
of line capacitance is defined as
% 100APPC APP
APPC
Z Z
Error
Z

 
(31)
Table C:
Percentage error in R, X and ZAPP in transmission line at 95 %
distance with h=0.96, δ=160
RF
(Ω )
Without
Capacitance
With
Capacitance
% error in
Resistance
% error in
Reactance
% error in
Impedance
0 8.71 +j90.55 9.62
+j95.24
9.45 4.92 4.9
200 361.35 +j60.84 374.54+
j1.951
3.52 3018.8 16.11
Fig.6 shows the amount of increase in the measured
impedance for the various fault points, in the case of zero
fault resistance. Here, the increase in the measured
resistance, reactance, and impedance magnitude are shown
by dotted, dashed, and full curves, respectively. It can be
seen that the impedance deviation is a function of fault
location. Because of different deviation of the measured
resistance and reactance, the angle of the measured
impedance varies as well as its magnitude.
Fig .6 .Increase in measured resistance, reactance, and impedance
magnitude
VI. APPARENT IMPEDANCE VARIATION
Fig.7. Tripping characteristic variations with changes in power
system conditions

522
In Fig.7, curve (1) is the tripping characteristic of Fig.5.
When the load angle increases from160 to 220 and the
voltage ratio decreases from 0.96 to 0.94, curve (2) would
be resulted. On the other hand, when load decreases, curve
(3) is resulted for δ = 100 and h = 0.98.
Fig..8 .Tripping characteristic variations with changes in power
system operational conditions for h=0.96 and delta= -100
& h=0.9 and
delta=-300
Fig.9. Variation in amount of increase in measured resistance,
reactance and impedance magnitude, with changes in power system
conditions
A. Load Angle Variation
Once the load level of a transmission line increases, the
load angle also increases, and vice versa. If power flow
direction in a transmission line reversed, the sign of load
angle is inversed. Fig.10 shows the effect of the load angle
variation on the tripping characteristic. Here, load angle
takes the values 250, 150, 50, -50, -150 and -250.
Fig.10 .Tripping characteristic variations with changes in load angle.
It can be seen that as the load angles varies, the tripping
characteristic changes considerably. In the case of negative
load angles, the tripping characteristic is in crescent shape.
resistance, reactance, and impedance magnitude with
change in load angle.
Fig.11. Increase in measured resistance, reactance, and impedance
magnitude as load angle changes.
B. Voltage Ratio Variation
Variation of the voltage ratio of transmission line affects
the reactive power flow through the line. The amount of
reactive power flowing through the line increases as this
factor decreases (for ratios lower than 1).

523
If the ratio is higher than 1, it means that the reactive
power flow direction is inversed. Fig.12 shows the impact
of voltage ratio, the magnitudes of 0.95, 1.00 and 1.05 are
considered for this factor, while the other parameters are
the same as Fig. 5.
Fig .12 .Tripping characteristic variation, with change in voltage ratio
Fig 13 .Increase in measured resistance, reactance, and impedance
magnitude.
resistance, reactance, and impedance magnitude for voltage
ratios of 0.95, 1.00, and 1.05.
C. Line Length Variation
Fig.14 shows the tripping characteristic for the line
lengths of 100,200,300, and 400 km. It can be that as the
line length increases, the covered region by tripping
characteristic also increases in both resistance and
reactance axis. Fig.15 shows the amount of increase in the
measured resistance, reactance, and impedance magnitude
for the mentioned line lengths.
Fig. 14.Tripping characteristic variation as line length changes
Fig. 15. Increase in measured resistance, reactance, and impedance
magnitude, line length changes
VII. ADAPTIVE DISTANCE RELAY SETTING
A. Effect Of Z1SN & Z0SN Trip Boundary
From the equation. (31), it is clear that the change in trip
boundary is due to VPRE, IPRE. Further the VPRE, IPRE,
are function of factors δ, h, Z1L etc. The variation of
apparent impedance with change in Z1SN with zero fault
resistance is given in table D .
Z1SN Apparent Impedance
0
5 85 0
95.79 84.220
0
2.5 85 0
95.78 84.224

524
From table D, it is observed that the effect of remote
source impedance on apparent impedance is quite
negligible.
Fig 16. Trip boundaries for change in remote source impedance
Fig.16 shows trip boundaries with change in Z1SN &
Z0SN. From Fig.16 it is seen that even if we decrease the
Z1SN and Z0SN to half of its case-1 values, there is no
effect on boundaries of the trip characteristics. Hence, the
remote end side impedance values are kept fixed to
estimate the h and δ from the local information only. From
the voltage and current equations the following relation can
be obtained
S =
11
relayj
L
relay
I
h e Z
V

 
    
 
(32)
The h and δ values are estimated using equation (32).
The voltage and current phasors are estimated using Matlab
simulink model.
B. Proposed Adaptive Technique
The proposed scheme and see the validity of the
approach for Relay setting, a simulation study is carried out
for line-to-ground fault. With the same system data as time-
domain simulations were carried out by creating line to
ground faults at different locations and conditions. Phasors
are estimated using three phase voltage and current samples
from equation.(32).
VIII. RESULTS AND DISCUSSION
Simulations are performed for a 400 kV sub
transmission system that contains an overhead line of 300
km length. The line parameters of the source and
transmission line are given in table A and table B.
Fig.17 Simulink model for transmition line with considering line
capacitance
Fig.17 shows the MATLAB Simulation network. Here
transmission line contains capacitance is molded as
nominal double Pie model.
IX. CONCLUSIONS
An adaptive relay setting scheme for stand-alone digital
distance protection has been proposed[4]. Network
conditions are monitored and setting patterns are renewed
automatically according to network configuration changes
through a pre-fault calculation routine. When a fault occurs
the relay will operate with this ideal trip characteristic. This
scheme involves relatively little real-time digital
processing. Sensitivity, selectivity and speed have all been
improved by using this scheme in a digital distance relay.
REFERENCES
[1] Anderson P M., “Power system protection” McGraw-Hill IEEE
Press, 1999, New York.
[2] IEEE guide for protective relay applications to transmission
lines, standard C37,113-1999,Feb.29,2000
[3] Y. Q. Xia, K. K. Li, A. K. David, "Adaptive Relay Setting for
Stand-alone Digital Distance Protection", IEEE Trans. Power
Delivery, Vol. 9, No. 1, pp. 480-491, Jan. 1994.
[4] A. K. Pradhan, Geza Joos “Adaptive Distance Relay Setting for
Lines Connecting Wind Farms”, IEEE Trans. on Energy Conversion,
Vol. 22, No. 1, March. 2007.
[5] Bin Su, Jianping Wang, Ying Yang, Weixing Gong, and
Yongsheng Xu,“ Setting Considerations of Distance Relay for
UHV/EHV Long Transmission Lines”, 2007 IEEE Conference.
[6] K. K. Li, L. L. Lai, A. K. David, "Stand alone Intelligent Digital
Distance Relay", IEEE Trans. Power Systems, Vol. 15, No. 1, pp.
137-142, Feb. 2000.
[7] K.K Li and L.L. Lai, "ideal operating region of digital distance relay
under high resistance earth fault,” international journal of electric
power system research, Vol,43,no.3,pp.215-219, dec.1997.
…. Case 1. Z1SN = 5e85j
Ω, Z0SN = 7.5e85j
Ω
Case 2. Z1SN = 2.5e85j
Ω, Z0SN =3.754e85j
Ω

525
[8] S. Jamali ,H. Shateri, “Measured Impedance by Distance Relay
Considering Double Model of the Line Capacitance”, 2006
International Conference on Power System Technology.
[9] Dash, P. K. Pradhan, A. K. Panda, G. and Liew, A. C.“Digital
protection of power transmission lines in the presence of series
connected FACTS devices”, IEEE Trans. Power Delivery, 15(1): 38-
43 (2000).
[10] Dash, P. K. Pradhan, A. K. Panda, G. and Liew, A. C.“Adaptive
relay setting for flexible AC transmission systems (FACTS)”, in
Proc. IEEE Power Eng.

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