Effects of Transmission Line Modeling on Fault Location Eugeniusz Rosolowski, Jan Izykowski Wroclaw University of Technology, Poland
Murari Mohan Saha, Kent Wikström ABB Automation Products AB, Sweden
Institute of Electrical Power Engineering Wybrzeze Wyspianskiego 27 50-370 Wroclaw, Poland
[email protected],
[email protected]
Dept. TTA SE-721 59 Västerås, Sweden
[email protected]
Abstract This paper deals with the technique designated to location of faults in untransposed lines. The algorithm capable locating faults in both a single line and parallel lines arrangement has been presented. ATP-EMTP has been used to generate reliable fault data used for evaluation of fault location accuracy. It is shown that the derived fault location algorithm provides substantial improvement of fault location accuracy. Keywords: untransposed power transmission line, ATP-EMTP simulation, fault location.
1
Introduction
Variety of fault location algorithms for both protective relaying and fault locators has been developed so far. The algorithms for fault locators, which are considered in this paper, are designated to pinpoint accurately the position on the line at which a fault has occurred. This facilitates the line inspection and thus shortens the discontinuity of power supply. Fault location algorithms differ in many aspects, mainly in: - kind of a transmission network for which the algorithm is designated - the input data required, - the used model for representing a transmission line, - accuracy of fault location. This paper investigates accuracy of fault location in relation to asymmetry of a line. Unsymmetrical (untransposed) lines require its adequate representing [1] in the location algorithm itself. For this purpose the phase coordinates method, derived for both a single line and parallel lines arrangement, has been applied in the delivered fault location technique. The presented algorithm has been evaluated using ATP-EMTP generated fault data. K.C Lee model of untransposed line [2] has been used in simulation. The achieved accuracy with the presented fault location algorithm is compared with the case of using the standard symmetrical components approach to fault location.
2
Fault location technique for untransposed lines
The symmetrical components approach can be effectively used for locating faults in completely symmetrical transmission lines. However, the symmetry of a line can be substantially disturbed. This is the case when there are long segments of a line without transposition of the conductors. The other causes are related with installations like for example series compensating capacitors equipped with Metal-Oxide Varistors for overvoltage protection, which introduce the asymmetry under occurrence of unsymmetrical faults [5, 6]. In order to take into account the asymmetry of a line the phase coordinates approach has to be applied for representing a faulted line in the fault location algorithm [5, 6]. Derivation of the fault location algorithm utilizing such the approach follows. Voltage drop across a three phase element (vector of phase voltages: V ) can be expressed as a product of impedance matrix ( Z ) and a vector of phase currents ( I ): V = ZI where: V a V = V b V c
(1) I a I = I b I c
Z aa Z = Z ab Z ac
Z ab Z bb Z bc
Z ac Z bc Z cc
For a power line which is perfectly transposed the diagonal components of the impedance matrix Z (self impedances: subscript - s) as well as all the off-diagonal components (mutual impedances: subscript - m) are accordingly equal to each other: Z s = Z aa = Z bb = Z cc
(2)
Z m = Z ab = Z bc = Z ac
(3)
and one obtains the following relations in which impedances of a line for the positive and the zero sequence are involved: Zs
Z Z 1 L
Zm
/
Z Z 1 L /
(4)
Models of transmission grids with a single line are presented in Fig.1, 2 while for parallel lines arrangement in Fig. 3, 4. Parallel lines transmission network as more general circuit is taken further for deriving the fault location algorithm. Location is considered as performed in a faulted line A based on the currents and voltages picked at the terminal denoted as AA (Fig.3, 4). Z sA
$
ZL
%
Z sB
IA_pre
a
EA
EB
a
Fig.1. Model of a transmission grid with a single line for pre-fault conditions
$
Z sA
)
dZL
IA
(1-d)Z L I B
%
Z sB
I F =(1/R f )K F V F
a
EA
VA
EB
VF
a
Fig.2. Model of a transmission grid with a single line for fault conditions
%$%%
Z LB
(LINE B) EA
a
IBB_pre= - IAB_pre
IAB_pre
Z sA
Z sB
Zm IAA_pre ( L I N E A )
EB
a
I B A _ p r e =-I A A _ p r e Z LA
$$
%$
Fig.3. Model of a transmission grid with parallel lines for pre-fault conditions %%
%$d Z LB EA
IAB
Z sA
a
(1-d )Z L B
(LINE B)
dZm IAA
G
=P
IBB= - IAB
)
IBA
(LINE A) ) d Z LA
$$
Z sB
(1-d )Z L A
(%
a
%$
VF I F = ( 1/R f )K F V F
Fig.4. Model of a transmission grid with parallel lines for fault conditions
Model from Fig.4 can be described:
∆E E E $
%
(Z
V$
GZ
/$
)I
$$
(( G )Z Z /$
V%
)I
%$
(Z Z V$
V%
)I
%$Z I P
%$(5)
where impedance matrix for a line A ( Z LA ) and for mutual coupling between lines A, B ( Z m ):
Z LA
Z LA _ aa = Z LA _ ab Z LA _ ac
Z LA _ ab Z LA _ bb Z LA _ bc
Z LA _ ac Z LA _ bc Z LA _ cc
Z m _ aa Z m _ ab Z m _ ac Z m = Z m _ ab Z m _ bb Z m _ bc Z m _ ac Z m _ bc Z m _ cc
For completely symmetrical network the elements of the impedance matrix Z are determined as in (4) while all the components of the mutual coupling impedance Z are identical: /$
P
Z 0m 3
Z m _ aa = Z m _ bb = Z m _ cc = Z m _ ab = Z m _ ac = Z m _ bc =
(6)
where: = - mutual coupling impedance for the zero sequence. P
Assuming that EMFs of the sources do not change due to a fault the vector ∆E defined in (5) can be determined from the pre-fault model (Fig.4) as:
∆E E E V$
(Z
V%
V$
Z Z V%
/$
)I
$$BSUH
(Z Z Z V$
P
V%
)I
$%BSUH
(7)
Vector of currents from the remote substation B and the line A can be determined from (5) as: I
%$
(( G )Z
Z
/$
) ((Z
V%
V$
GZ
/$
)I
$$
(Z Z Z )I V$
V%
P
%$ ∆E )
(8)
Vectors of voltages across the fault path and fault currents are determined accordingly: V
V GZ I
I
I
)
)
$
$$
/$
I
$$
GZ I P
(9)
%$(10)
%$
Fig.5 presents a general fault model [2] which can be stated in matrix notation as: 1 K F VF RF R f - equivalent (aggregated) fault resistance.
IF =
V Fa
a b c
V Fb V Fc
IFc R bc R ac
IFb
IFa
The fault matrix KF is built upon the fault type:
R ab
Rc
Rb
(11)
1.
compute: − 1 if i and j involved in fault k ij = i , j = a , b , c (12a) otherwise 0
Ra
2. adjust the diagonal elements using the formula: k ii =
Fig.5. Three phase fault model
j=c
∑ kij i = a ,b,c
(12b)
j =a
For example for a-b and a-b-g faults one obtains: KF
1 − 1 0 = − 1 1 0 (a-b), 0 0 0
KF
2 − 1 0 = − 1 2 0 (a-b-g) 0 0 0
Taking into account the equations (9) – (12) one obtains: 1 K (V GZ I Rf )
$
/$
$$
GZ I P
%$)
I
$$
I
%$
(13)
Combining (8) and (13) the following matrix equation is obtained: A G B G C D where: A Z K Z I Z K Z I
F
F
F
B
F
C
F
F
/$
)
/$
$$
Z K (V Z I /$
(Z
(Z
D
)
/$
V$
D = D5 F
$
Z
V%
(14)
F
)K
Z Z /$
/$
)
V
V%
/$
$$
)
) Z
P
V%
K Z I
$
)(I
$$
−I
%$$$BSUH
)
/$
) (Z
V$
$$
Z K (Z Z P
)
Z + Z V%
/$
P
)(I
%$−I
V%
)I
%$$%BSUH
)
I
Transforming (14) to the scalar form one obtains: $G %G & 5 where:
$
PA
I
%
F
(15)
PB
F
&
7
PC
P
F
D D D 7
The scalar quadratic equation (15) can be resolved into real and imaginary parts: 5HDO ($)G 5HDO (% )G 5HDO (& ) 5
I
,PDJ ($)G ,PDJ (% )G ,PDJ (& )
(16) (17)
Fault resistance ( R f ) is not involved in (17) from which one calculates a distance to fault as: G
G JG\,PDJ $ ≥
G
G JG\,PDJ $
(18)
where: d 1( 2 ) =
Im ag (B ) #
(Im ag (B ))2 − 4 Im ag (A) Im ag (C ) 2 Imag (A)
Knowing a distance to fault (d=d1 or d=d2) an equivalent fault resistance can be calculated as: 5f
5HDO ($)G 5HDO (% )G 5HDO (& )
(19)
In case of parallel lines arrangement one ought to discriminate faults overreaching a total line length, i.e. occurring in a remote system (Fig.4 – fault F1). By analyzing the following vector: D 1 = (Z LA − Z m )I AA − (Z LB − Z m )I AB
(20)
which for such the faults has to posses all the components equal to zero, however, in practice, due to measurement errors, some threshold has to applied. Adaptation of such the algorithm to the case of a single line requires deleting all the components relevant to mutual coupling of the lines ( Z m ) as well as all the components containing the vectors of currents from the sound line ( I AB , I AB_pre ) only.
3
Evaluation of fault location accuracy
A 400 kV, 300 km single transmission line equipped with two overhead ground wires has been taken for the analysis. Different earthing modes of the overhead ground wires have been taken into account (Table 1); namely these wires are considered as: a) not earthen, b) connected with the towers. The line has been modeled in ATP-EMTP by dividing it into 6 segments of 50 km length and using the unsymmetrical model of K.C Lee [2]. Equivalent systems at the terminals: - substation A: Z 1sA = 15 ∠ 80 deg ; Z 0sA = 26.7 ∠ 80 deg - substation B: Z 1sB = 30 ∠ 80 deg ; Z 0sB = 53.4 ∠ 80 deg - EMFs from the substation B delayed by 30 deg with respect to the substation A. Table 1. Parameters of a line for different modes of earthing of the overhead ground wires Line
Impedance matrix: Z L [Ω/km]
Capacitance matrix: C L [nF/km]
a)
0.0738 + j 0.5710 0.0459 + j 0.2648 0.0459 + j 0.2216 0.0459 + j 0.2648 0.0739 + j 0.5712 0.0459 + j 0.2622 0.0459 + j 0.2216 0.0459 + j 0.2622 0.0739 + j 0.5708
9.3168 − 2.0636 − 0.8353 − 2.0636 9.6339 − 2.0636 − 0.8353 − 2.0636 9.3168
b)
0.0952 + j 0.4504 0.0668 + j 0.1411 0.0631 + j 0.1048 0.0668 + j 0.1411 0.0967 + j 0.4420 0.0669 + j 0.1412 0.0631 + j 0.1048 0.0669 + j 0.1412 0.0952 + j 0.4504
9.7734 − 1.6792 − 0.5795 − 1.6792 10.0490 − 1.6791 − 0.5795 − 1.6791 9.7734
Asymmetry of phase currents and voltages for both the lines [a) and b)] and at both the substations [A and B] under normal operating conditions is evaluated in Tables 2, 3. Table 2. Asymmetry of phase currents Amplitude [A] Line
Substation
Amplitude [p.u.]
|Ia|
|Ib|
|Ic|
|I|aver.
|Ia |
|Ib |
|Ic |
| I |aver.
| I |aver.
| I |aver.
a)
A B
475 411
487 472
435 464
465.7 449
1.020 0.915
1.046 1.051
0.934 1.033
b)
A B
484 417.5
497 476
445.5 468
475.5 453.8
1.0179 0.9198
1.0452 1.0489
0.9369 1.0313
Table 3. Asymmetry of phase voltages Amplitude [V]
Amplitude [p.u.]
Substation
|Va|
|Vb|
|Vc|
|V|aver.
|V a | | V |aver.
|V b | | V |aver.
|V c | | V |aver.
a)
A B
319230 321340
320980 319820
321220 320810
320480 320660
0.9961 1.0021
1.0016 0.9974
1.0023 1.0005
b)
A B
319430 321510
321200 319930
321420 320960
320680 320800
0.9961 1.0022
1.0016 0.9972
1.0023 1.0005
Line
Fault location in the considered transmission system has been performed in two different ways regarding taking into account the asymmetry of a line, namely: (1) without including the asymmetry in the fault location algorithm, (2) asymmetry of a line is reflected by using the developed fault location algorithm. The first way (1) is based on using the standard symmetrical components based location algorithm [3]. The input data (the positive and the zero sequence impedances of a line) in this case is obtained by taking the self and the mutual impedances (4) as the averages of the diagonal and off-diagonal elements of the actual impedance matrix respectively (Table 1): =V =P
(= DD + = EE + = FF ) 3 (= DE + = EF + = DF ) 3
(21) (22)
Thus, in the first way of fault location (1) the actual unsymmetrical line is reflected as certain “symmetrical line” with the averaged parameters obtained by mathematical manipulation [1]. Such the procedure is a source of some additional errors (Table 4) in comparison to the second way of the performed fault location (2) in which the fault location algorithm (18) presented in this paper is utilized. The proposed method improves fault location accuracy in majority of fault cases and the improvement can reach up to 2 % (see the example - Fig.6). Table 4. Improvement of fault location accuracy by using the developed fault location algorithm (2) in comparison to the case of not reflecting the asymmetry of a line (1) Fault specification Line Fault type
a)
b)
4
Fault resistance RF [Ω]
Fault distance [p.u.]
a-g a-g a-b a-b
10 10 0.1 0.1
0.167 0.833 0.167 0.833
a-g a-g a-b a-b
10 10 0.1 0.1
0.167 0.833 0.167 0.833
Fault location Error [%] (1) (2) Asymmetry not Asymmetry is included included 0.1 0.2 3.4 2.1 0.8 0.2 3.4 1.4 0.0 1.3 0.8 3.0
0.2 0.7 0.1 1.4
Improvement [%] (1) - (2) due to including asymmetry 1.3 0.6 2.0 0.6 0.7 1.6
CONCLUSIONS
The paper deals with location of faults in power transmission lines for inspection and repair purposes. Accuracy of fault location is investigated in relation to asymmetry of a line. Location is firstly considered as performed with using the standard symmetrical components based approach. Then, the developed fault location algorithm utilizing phase coordinates representation of a transmission system is applied. Quantitative evaluation of the fault location accuracy has been performed using ATP-EMTP generated fault data. It was shown for the studied transmission system that the algorithm presented in the paper allows improvement of fault location accuracy up to 2 %. This is worth to notice that asymmetry of the considered line is comparatively small. Thus, in case of larger asymmetry of a line the improvement can be expected as considerably higher.
[
3KDVH YROWDJHV >9@
a)
b)
3KDVH FXUUHQWV >$@
7LPH >V@
7LPH >V@
c)
'LVWDQFH WR IDXOW UHVXOW >SX@
d)
'LVWDQFH WR IDXOW UHVXOW >SX@
3RVWIDXOW WLPH >V@
3RVWIDXOW WLPH >V@
Fig.6. Fault location in untransposed line (specification of a fault: a-b type, d = 0.833 p.u., R F = 0.1 Ω): a) phase voltages, b) phase currents, c) fault location algorithm averages the diagonal and off-diagonal elements of matrix impedance of a line, d) asymmetry of a line is reflected in the fault location algorithm
5 [1] [2] [3]
[4] [5]
[6]
REFERENCES Anderson P.M.: Power system protection, McGraw-Hill, 1999. Dommel H.: Electromagnetic Transient Program, BPA, Portland, Oregon, 1986. Eriksson L., Saha M.M., Rockefeller G.D.: An accurate fault locator with compensation for apparent reactance in the fault resistance resulting from remote-end infeed, IEEE Trans. on PAS, Vol.PAS-104, No.2, February 1985, pp. 424-436. Hupfauer H., Schegner P., Simon R.: Distance protection of unsymmetrical lines, ETEP Vol.6, No.2, March/April 1996, pp. 91-96. Saha M.M., Izykowski J., Rosolowski, Kasztenny B.: A new accurate fault locating algorithm for series compensated lines, IEEE Transactions on Power Delivery, vol.14, no. 3, July 1999, pp. 789-797. Saha M.M., Wikstrom K., Izykowski J., Rosolowski E.: Fault location in uncompensated and series-compensated parallel lines, Proceedings of PES Winter Meeting, IEEE Catalog Number: 00CH37077C, CD-ROM: 0-7803-5938-0, 23-27.01.2000, Singapore, p. 6.
