tion for the fault data obtained from versatile ATP-EMTP simula- tion of both .... Rv. Xv. Fig. 2. Equivalenting of SC&MOV: a) the original scheme, b) the funda-.
Fault Location in Uncompensated and Series-Compensated Parallel Lines M.M. Saha Senior Member, IEEE
K. Wikström Non-Member
ABB Automation Products AB Substation Automation Division S-721 59, Västerås, Sweden
Abstract: Accurate and robust fault location algorithm for parallel lines compensated with one three-phase bank of series capacitors in each the line is presented. The algorithm is categorized as one-end fundamental frequency based technique which offsets the series compensation effect and the reactance effect resulting from the remote end infeed under resistive faults as well as takes the countermeasure for the mutual coupling between the lines. The applied phase coordinates approach allows to locate faults in untransposed lines too. Adaptation of the algorithm to locating faults in uncompensated parallel lines is provided. The sample cases of fault location for the fault data obtained from versatile ATP-EMTP simulation of both series-compensated and uncompensated parallel lines are included. Keywords: capacitor compensated transmission lines, coupled transmission lines, digital recording, distance measurement, algorithms, fault diagnosis, simulation.
I. INTRODUCTION Parallel series-compensated lines (Fig. 1) are very important links between power generation and energy consumption regions. All the advantages relevant for both the parallel arrangement and the series capacitor compensation [1] are the primary reasons for increased use of such the transmission links. However, installation of series capacitors (SCs), equipped with nonlinear Metal-Oxide Varistors (MOVs) for overvoltage protection, on transmission lines causes certain problems for protective relaying and fault location [1, 2]. Accurate fault location requires to offset the series compensation effect and the reactance effect resulting from the remote end infeed under resistive faults. The fault location algorithm dedicated for single series-compensated lines coping with these the effects has been developed and presented in [2]. This was an adaptation of the idea of the fault locator [3] to the specific conditions of a single series-compensated line. This paper presents further extension of the algorithm for locating faults in series-compensated parallel lines.
J. Izykowski Member, IEEE
E. Rosolowski Member, IEEE
Wroclaw University of Technology Wybrzeze Wyspianskiego 27 50-370 Wroclaw, Poland
• the computations are arranged in the phase coordinates allowing to locate faults in untransposed parallel lines too, • the SCs and MOVs are represented with the fundamental frequency equivalents having the current dependent resistance and reactance, • the faults occurring in the remote system are discriminated, thus, the countermeasure for the mutual coupling between the lines is limited to the whole line length only, • the algorithm is primarily derived for series-compensated parallel lines but after adequate setting it is capable of locating faults in uncompensated parallel lines as well. To explain the concept, the paper starts with description of the particular components of the transmission network (Section II). The algorithm for series-compensated parallel lines is introduced in Section III while its adaptation to the case of uncompensated parallel lines is presented in Section IV. The report on broad ATP-EMTP based testing and evaluating follows (Section V). The conclusions (Section VI) with respect to the basic features of the algorithm and its accuracy close the paper. II. DESCRIPTION OF THE TRANSMISSION SYSTEM ELEMENTS IN PHASE COORDINATES Let us consider series-compensated parallel lines as shown in Fig. 1. Both the lines are compensated with three phase banks of SCs equipped with MOVs installed at the distance p [pu] from the station A.
The advantages and distinctive features of the presented algorithm summarize as follows: • the one-end measurement is utilized,
The algorithm applies the phase coordinates approach [2]. Unless otherwise indicated, all the symbols stand for complex numbers, either impedances or phasors while the matrix quantities are bold-type written. The following assumptions were applied for deriving the algorithm: • the algorithm is presented for neglected shunt capacitances of the lines, however, to improve the location accuracy for long lines the capacitances may be accounted for,
• simultaneous countermeasures are applied for the reactance effect, the series compensation effect and the mutual coupling between the lines,
• the recorded voltage and current data cover the time window without firing the air-gaps (on the command of the overload protection of MOVs),
Air-gaps MOVs
IAB
where the self (s) and mutual (m) impedances of the line A can be obtained from the zero (0) and positive (1) sequence data:
IBB
Line B
F1b
SCs Zm
a
F2
System A
Air-gaps MOVs
Z LAs =
a
Zm F1a
System B
IA A
Z 0 m - mutual coupling zero sequence impedance.
IBA Line A
VA
1 ( Z LA0 + 2Z LA1 ), Z LAm = 1 ( Z LA0 − Z LA1 ) , 3 3
SCs
FL AA
FL BA
The vectors IAA, IAB in (4) are composed of the phase currents picked up at the station A from the considered faulted line A and from healthy parallel line B, respectively.
VB
Fig. 1. Arrangement of series-compensated parallel lines.
C. SCs and MOVs • the fault resistance, equivalent system impedances and electromotive forces are all constant during the considered time window, • information on the type of fault and the fault inception time is provided by a protective relay or separate procedures of the fault locator. A. Supplying systems The supplying system, say A, is represented by the vector composed of electromotive forces in particular phases:
A bank of a parallel connected SC and its MOV is represented for the fundamental frequency phasors by equivalent resistance and reactance [2, 10]. The equivalencing technique assumes that the fundamental frequency phasors in the original arrangement and in the equivalent branch match (Fig. 2a, 2b). The dependence of the equivalent resistance and reactance upon the amplitude of the current flowing through the compensating bank (Fig. 2c) has been determined using ATP-EMTP simulations [2].
(1)
The SCs and their MOVs are represented in the algorithm by the current dependent impedance matrix:
and the 3 by 3 matrix of self and mutual impedances. For a completely transposed system this matrix becomes:
(6)
ZA
Z As = Z Am Z Am
E Ab
E Ac ]
Z Am Z As Z Am
Z Am Z Am Z As
(2)
where the self (s) and mutual (m) impedances are obtained from the zero (0) and positive (1) sequence data using the well known relations: 1 1 Z As = ( Z A0 + 2Z A1 ), Z Am = ( Z A0 − Z A1 ) (3) 3 3 The supplying system B is represented analogously.
Neglecting the shunt capacitances the voltage drop across the segment of the length x [pu] of the line A (Fig. 1) is determined as:
∆VLAx = x( Z LA I AA + Z m I AB )
(4)
where the self (ZLA) and mutual coupling (Zm) matrix impedances could be of the unsymmetric form, however, for a completely transposed parallel lines holds:
Z LA
Z LAm Z LAs Z LAm
where Iva, Ivb, Ivc are the currents flowing through the banks in particular phases and by the amplitude is denoted. a)
Z LAm Z 0 m 1 Z LAm , Z m = Z 0 m 3 Z 0 m Z LAs
Z0m Z0m Z0m
Z0m Z 0 m (5) Z 0 m
b)
VV IV
VV
IV
SC MOV
X V ( | IV | )
R V ( | IV | )
40
c)
B. Transmission line
Z LAs = Z LAm Z LAm
ZV ( IVa ) 0 0 Z V ( IV ) = 0 0 ZV ( IVb ) 0 0 ZV ( IVc )
Resistance, Reactance (Ω)
E A = [ E Aa
T
20
Rv 0
-20
-40
Xv -60
-80 0
2000
4000
6000
8000
10000
Amplitude of Current Entering SC&MOV (A)
Fig. 2. Equivalenting of SC&MOV: a) the original scheme, b) the fundamental frequency equivalent circuit, c) the equivalent characteristic.
(
(
D. Fault resistance
VA − VF = xZ LA + Z V I AA
Fig. 3 presents a general fault model [2] capable of reflecting different fault types. The fault model is stated as: (7) I F = GVF
I F = I AA + I BA
where VF, IF are vectors of voltages and currents at fault. Introducing the aggreV a gated value of the fault reV b sistance RF (even for multiV c phase faults) and the fault I I I matrix KF [2] we define G R bc R ab as: R ac 1 G= KF (8) Rc Rb Ra RF Fa
Fb
Fb
The pre-fault network is described (note that the subscript pre stands for all the pre-fault quantities):
(
Fig. 3. A three phase fault model.
1.
compute:
−1 if i and j involved in fault k ij = i, j = a, b, c 0 otherwise 2. adjust the diagonal elements using the formula: k ii =
j=c
∑ k ij
i = a , b, c
(9a)
(9b)
j=a
For example for a-b and a-b-g faults one obtains: 1 −1 0 K F = −1 1 0 (a-b), 0 0 0
2 −1 0 K F = −1 2 0 (a-b-g) 0 0 0
III. FAULT LOCATION ALGORITHM Since the fault position with respect to the SCs is not known prior to the fault, the algorithm considers the following fault spots for the locator FLAA (Fig. 1): - behind the SCs (F1a, F1b), and - in front of the SCs (F2). Thus, the algorithm applies the two subroutines: • subroutine 1 for locating the faults behind the SCs&MOVs (fault F1a) with additional discrimination of the faults overreaching the line length (fault F1b), • subroutine 2 for locating the faults in front of the SCs&MOVs (fault F2). A separate selection algorithm is applied to single the correct estimate of the two conditional solutions. A. Subroutine 1 - faults behind SCs&MOVs In case of the faults behind the SCs&MOVs and not overreaching the line length (fault F1a in Fig. 1) holds:
(
(
))
E A − E B = Z A + xZ LA + Z V I AA I AA + − ( (1 − x )Z LA + Z B ) I BA + (Z A + Z B + Z m ) I AB
))
(
E A − E B = Z A + Z B + Z LA + Z V I AA _ pre I AA _ pre + + ( Z A + Z B + Z m ) I AB _ pre
Fa
The fault matrix KF is built upon the fault type using the method:
(10)
where x is the sought fault location [pu] (x>p).
Fc
Fc
))I AA + xZ m I AB
(11)
The above set of matrix equations ((10) - (11)) together with the fault model ((7) - (8)) is solved for x and R F what yields to the simple quadratic equation [2]:
Ax 2 − Bx + C − R F = 0
(12)
where A, B, C are the complex scalars depending on both the system parameters and local measurements (from the substation A in case of the considered fault locator FLAA). Faults occurring in the remote system which are also behind the SCs&MOVs can be discriminated by considering the following vector:
(
)
D = Z LA + Z v (| I AA |) − Z m I AA +
(
)
− Z LB + Z v (| I AB |) − Z m I AB
,
(13)
which in such the cases has all the components equal to zeroes (in practice certain threshold has to be applied for that). There are, certainly, two roots of (12), but one of them as constant (depending only on the system parameters) can be easily identified and rejected. Thus, eventually, the first subroutine delivers the solution ( x1 , RF1 ) assuming the fault as behind the SCs&MOVs. B. Subroutine 2 - faults in front of SCs&MOVs The case of a fault between the substation and the SCs (fault F2 in Fig. 1) is more involved because the current flowing through the SCs&MOVs is not directly available to the one-end locator and thus ought to be estimated. In this case the following applies to the faulty network: E A − E B = ( Z A + xZ LA ) I AA + (Z A + Z B + Z m ) I AB
(
(
+
))
− (1 − x )Z LA + Z B + Z V I BA I BA VA − VF = xZ LA I AA + xZ m I AB
(14)
I F = I AA + I BA but now the sought fault location [pu] is: 0 < x < p. The model of the pre-fault network (11) and the fault model ((7) - (8)) remain valid.
In this case, one also obtains the quadratic equation as (12), but an iterative numerical solution is required because its coefficients depend on the unknown current from the remote substation B (Fig. 4b). Eventually, the second subroutine assuming the fault as in front of the SCs&MOVs delivers the solution ( x 2 , RF 2 ) . C. Selecting algorithm Locating a fault with respect to the SCs in the system of Fig. 1 narrows to the selection of the correct pair ( x , RF ) out of two alternatives ( x1 , RF1 ) and ( x 2 , RF 2 ) . The reliable se-
lecting algorithm has been developed for that. It is based on appropriate aggregation of the following criteria values estimated with both the subroutines: • for all the fault types: the aggregated fault resistance R F - the smaller positive value of this resistance indicates the valid subroutine while its negative value means that the considered subroutine has to be rejected (certain safety margin was applied for that), • amplitudes of the currents from the healthy phases in the fault path (for all the fault types except three-phase symmetrical faults) - the subroutine which gives lower amplitudes (ideally zeroes) is taken as the adequate one. (a)
(b) Recorded Data
A s s u m e IB A Calculate Z V
Subroutine 1 (F1a)
Subroutine 2 (F2)
(x 1 , R F 1 )
(x 2 , R F 2 )
Calculate x 2 and R F 2 Calculate I B A
(x, R F )
Fig. 4. Two subroutines compute two conditional fault locations (a). Iterative solution applies to the subroutine 2 (b).
IV. ADAPTATION OF THE ALGORITHM TO THE CASE OF UNCOMPENSATED PARALLEL LINES In the case of the uncompensated parallel lines it is reasonable to apply the single procedure only, namely the subroutine 1 which was derived for faults behind the SCs&MOVs and is of noniterative nature (in contrast to the iterative subroutine 2). By setting zeroes at the diagonal of the SC&MOV equivalent (6) one makes possible to locate faults in uncompensated parallel lines as well. V. ALGORITHM TESTING AND EVALUATING The detailed ATP-EMTP models of both the seriescompensated (Fig. 1) and uncompensated transmission networks have been developed. The arrangement for the uncompensated parallel lines is the same as in Fig. 1 with the exception that the compensation banks are not present in this case.
The 300 km 400 kV parallel transmission lines were represented by the Clarke model. It was assumed for the seriescompensated network (Fig. 1) that the SCs are installed in the middle (p=0.5 pu) and the rate of compensation is 70%. The supplying systems were represented by coupled RL branches and ideal voltage sources. The MOVs with the common approximation of the v-i characteristic were taken: q
v (15) i= P V REF The model included both the Capacitive Voltage Transformers (CVTs) and the Current Transformers (CTs). The analog filters were also implemented using the 2nd order Butterworth model. The phasors were estimated with the use of the DFT algorithm working with 20 samples per cycle. Variety of fault cases have been generated and used in testing the fault location algorithm. Testing proved satisfactory accuracy of fault location in both uncompensated and series-compensated parallel lines. Example 1 (Fig. 5) - fault location in series-compensated parallel lines under the following conditions: • fault type: phase-to-phase-to-ground fault (a-b-g), • fault resistances (in the model of Fig. 3): 10 Ω, • fault location: fault in line A at 0.5 [pu] but just behind the SCs&MOVs as seen from the substation A (Fig. 1). • fault locator is installed in the substation A. Nature of the transients in the fault locator input signals (Fig. 5) is typical for the fault case when the SC and its MOV are included in the fault loop. The phase currents from the faulted line do not contain dc components while in the healthy line MOVs operate in the linear region resulting in the subsynchronous oscillations. The phase voltages undergo rather low reduction. The fault distance estimated by the two subroutines settles after completing the full cycle data window of the applied digital filters. The averaged values (within the span: 25 - 40 ms for the post-fault time) of the estimated quantities for the particular subroutines are: • subroutine 1 (for faults behind the SCs&MOVs): − fault distance: 0.4943 pu, − aggregated fault resistance: 24.19 Ω, − amplitude of current in the phase c (healthy phase) of the fault path: 121 A. • subroutine 2 (for faults in front of the SCs&MOVs): − fault distance: 0.2347 pu, − aggregated fault resistance: 73.32 Ω, − amplitude of current in the phase c (healthy phase) of the fault path: 983 A. Both the estimated fault resistance and the healthy phase current amplitude support the selection of the subroutine 1 as the valid one for this case - what is correct. Thus, the estimated fault distance is 0.4943 pu and exhibits quite small error which is less than 0.6 %.
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Example 2 (Fig. 6) - fault location in uncompensated parallel lines for the same fault specifications as in the example 1. Nature of the transients in the fault locator input signals (Fig. 6) differs from the case of Fig. 5 as for example the phase currents from the faulted line contain dc components. The estimated fault distance is now 0.4936 pu and the estimation error is small: around 0.6 %.
[5]
M.S. Sachdev (Coordinator), „Advancements in Microprocessor Based Protection and Communication”, IEEE Tutorial Course (coordinator:), IEEE Catalog Number: 97TP120-0, Piscataway, NJ, USA, 1997.
[6]
F. Ghassemi, A.T. Johns, J. Goddarzi, „A method for eliminating the effect of MOV operation on digital distance relays when used in series compensated lines”, Proceedings of 32nd Universities Power Engineering Conference - UPEC’97, Manchester, UK, 1997, pp. 113-116.
[7]
D. Novosel, A.G. Phadke, M.M. Saha, S. Lindahl, „Problems and solutions for microprocessor protection of series compensated lines”, Proceedings of Sixth International Conference on Developments in Power System Protection, IEE Conference Publication No.434, Nottingham, UK, 1997, pp. 18-23.
[8]
J.R. Lucas, P.G. McLaren, „A computationally efficient MOV model for series compensation studies”, IEEE Trans. on Power Delivery, vol. 9, 1994, pp. 501-509.
[9]
M. Kezunovic, M. Aganagic, S. McKernns, D. Hamai, „Computing responses of series compensation capacitors with MOV protection in real time”, IEEE Trans. on Power Delivery, vol. 10, no. 1, 1995, pp. 244-251.
V. CONCLUSIONS A new algorithm for locating faults in series-compensated parallel lines has been presented. The algorithm counterbalances the reactance effect, series compensation effect and mutual coupling between the lines. The technique uses the fundamental frequency model of the series-compensated lines including the SCs and MOVs. The phase coordinates approach is used enabling to locate faults in untransposed lines as well. For the series-compensated lines the algorithm applies two subroutines for estimation of the fault distance — one for faults behind the SCs, and another one for faults in front of the SCs. A special selecting procedure is proposed to pick-up the correct alternative. After adequate setting the algorithm is capable of locating faults in uncompensated parallel lines as well. In this case the single noniterative procedure is used. Thousands of analyzed fault cases prove the algorithm to be accurate. The average fault location errors is about 0.3% while the maximum error of the proposed algorithm does not exceed 2%. This is a significant improvement comparing with the traditional fault locators applied to series-compensated parallel lines that display an error even higher than 20%. The analysis has shown high robustness of the algorithm against the mismatch with respect to the remote system impedance (the locator does not trace the real source impedance but uses its representative value) and an inaccuracy in providing the MOV parameters.
VI. REFERENCES [1]
CIGRE SC-34 WG-04, „Application guide on protection of complex transmission network configurations”, CIGRE materials, August 1990.
[2]
M.M. Saha, J. Izykowski, E. Rosolowski, B. Kasztenny, „A new fault locating algorithm for series compensated lines”, paper PE-191PWRD-0-08-1998 approved for publication in the IEEE Transactions on Power Delivery.
[3]
L. Eriksson, M.M. Saha, G.D. Rockefeller, „An accurate fault locator with compensation for apparent reactance in the fault resistance resulting from remote-end infeed”, IEEE Trans. on Power Apparatus and Systems, vol. PAS-104, no.2, February 1985, pp. 424-436.
[4]
M.M. Saha et al. „Implementation of new fault locating technique for series-compensated transmission lines”, paper to be presented at CIGRE Colloquium, Rome 1999.
[10] D.L. Goldworthy, „A linearized model for MOV-protected series capacitors”, IEEE Trans. on PAS, vol. 2, no. 4, 1987, pp. 953-958. [11] H. Dommmel H., ElectroMagnetic Transient Program, BPA, Portland, Oregon, 1986.
VII. BIOGRAPHIES Murari Mohan Saha ( M´76, SM´87) was born in 1947 in Bangladesh. He received B.Sc.E.E. from Bangladesh University of Engineering and Technology (BUET), Dhaka in 1968 and completed M.Sc.E.E. in 1970. From 1969 to 1971 he was a lecturer at the department of Electrical Engineering at BUET, Dhaka. In 1972, he completed M.S.E.E. and in 1975 he was awarded with Ph.D. from the Technical University of Warsaw, Poland. He joined ASEA, Sweden, in 1975 as a Development Engineer and currently is a Senior Research and Development Engineer at ABB Automation Products AB, Västerås, Sweden. He is a Senior Member of IEEE and a Fellow of IEE(UK). He is a registered European Engineer (EUR ING) and a Chartered Engineer (CEng). His areas of interest are measuring transformers, power system analysis and simulation, and digital protective relays. Kent Wikström was born in 1960 in Sweden. He received his M.Sc.E.E. degree from the University of Uppsala, Sweden in 1985. He has been employed as a Development Engineer at ABB Relays AB, Västerås, Sweden, since 1985. He is now the Manager of the Application Group of Product Development at ABB Automation Products AB, Västerås, Sweden. His areas of interest are the development and design in the area of line protection. Jan Izykowski (M’97) was born in Poland in 1949. He received his M.Sc. and Ph.D. degrees from the Wroclaw University of Technology in 1973 and in 1976 respectively. In 1973 he joined Institute of Electrical Engineering of the Wroclaw University of Technology where he is presently an Assistant Professor. His research interest are in power system protection, fault locators and transient phenomena of instrument transformers. Eugeniusz Rosolowski (M’97) was born in 1947 in Poland. He received his M.Sc. degree in Electrical Engineering from the Wroclaw University of Technology (WUT) in 1972 where he is presently an Associate Professor. From 1974 to 1977, he studied in Kiev Politechnical Institute from which he received his Ph.D. in 1978. In 1993 he received D.Sc. from the Wroclaw University of Technology. His research interests are in power system analysis and microprocessor application in power systems. Currently he is a Director of the Institute of Electric Power Engineering of WUT.
