2010 IEEE/PES Transmission THIS IS FOR LEFT PAGES and Distribution Conference and Exposition: Latin America
1 803
Fault location method based on the determination of the minimum fault reactance for uncertainty loaded and unbalanced power distribution systems G. Morales-España, J. Mora-Flórez, Member, IEEE, H. Vargas-Torres
Abstract—One of the widely recognized and most important aspects of power quality is related to power continuity. The fault location in power distribution systems is normally a not simple task, considering the complexity associated to these circuits due to several characteristics such as single end measurements, the presence of different conductors and line configurations, uncertain load distribution, presence of single phase laterals, system and load unbalances, among others. In this paper, a novel fault location method is proposed considering the above mentioned characteristics. This method is based on a iterative approach to determine the minimum fault reactance and uses the line series impedance matrix, measurements of prefault and fault voltages and currents at the power substation. The performance of the proposed algorithm is here evaluated by an application example in a power distribution system, commonly referenced in fault location papers. The tests are performed considering several fault situations and including a sensibility analysis for load variations. As result, the absolute error in distance estimation, is lower than 3.5%. Index Terms—Fault location, fault reactance, power distribution systems, power quality, service continuity indexes, uncertain load distribution.
I. I NTRODUCTION
P
OOR continuity indexes in power distribution systems are widely associated to faults which cause supply interruptions. Then, it is widely recognized that fault locators helps to improve the SAIFI and SAIDI indexes as follows: a) Reduces the time of the restoration process, b) Gives adequate indications to perform switching operations aimed to reduce the faulted area, and c) The location of non permanent faults helps to identify the places where scheduled maintenance tasks have to be done to avoid future faults. Several applications of fault location have mainly been oriented to transmission lines, where high accuracy approaches have been proposed [1], [2], [3]. However, these algorithms are not useful in radial power distribution systems, due to some distinctive characteristics such as: a) voltage and current are typically available at the distribution substation; b) presence of single and double phase laterals; c) variable tapped loads; and d) lines with heterogeneous sections (different conductor
gauges, overhead lines and underground cables); among others. The problem of fault location has been addressed following different strategies, but there are two which have a remarkable importance, the impedance based methods and the knowledge discovering methods [4], [5]. Several fault location methods which estimate the equivalent distance based on the calculation of the equivalent impedance seen at the power distribution system during the fault, have been proposed [6], [5]. The pre-fault and fault effective values of the fundamental currents and voltages at one terminal line are used to estimate the fault impedance, as it is comparatively presented in [7]. The common drawback of those methods is the no consideration of uncertain load behavior in power distribution systems. On the other hand, the knowledge-discovering techniques are based on exploiting the information contained in fault databases to train a learning machine for locating the faulted zone [8]. This approach is commonly known as a black box model and it is normally difficult to establish good confidence indexes [4]. The most relevant disadvantages associated to the two previously referenced approaches are: a) The impedance based methods require high modeling effort to adequately represent the line and load impedances; b) The knowledge discovering approaches use the historical fault database to relate the voltage and current measurements to the fault location making this approach computationally expensive. Additionally, and as a consequence of the developing of the distribution feeders, the circuit response to the fault also changes, making obsolete some fault measurements used to adjust the fault locator; and c) Both methodologies assume a well known load distribution, ignoring the normal seasonal and daily load variations. In the paper here presented, a strategy that only uses the information contained in the single end measurements of the fundamental of current and voltage. Furthermore, the proposed approach has a low computational cost. The proposed method is based on the determination of the minimum fault reactance considering load uncertainties. The paper is presented in four sections. In section II, the proposed fault location approach is completely described. Next, in section III the test of the method is presented, considering a real power distribution system and variations in fault resistance and circuit load. Finally, section IV is devoted to conclude and summarize the main contributions of the proposed approach.
G. Morales-España is with the Institute for Research in Technology (IIT), Universidad Pontificia Comillas, Madrid, España (e-mail:
[email protected];
[email protected]). J. Mora-Florez is with the Universidad Tecnológica de Pereira, Pereira, Colombia (e-mail:
[email protected]). H. Vargas-Torres is with the Universidad Industrial de Santander, Bucaramanga, Colombia (e-mail:
[email protected]). 978-1-4577-0487-1/10/$26.00 ©2010 IEEE
804 2
2010 IEEE/PES Transmission and Distribution Conference THIS and Exposition: Latin America IS FOR LEFT PAGES
II. P ROPOSED FAULT LOCATION APPROACH The method here proposed is based on the initial assumption of a fault distance which is used to estimate the fault reactance at each assumed distance, and then a systematic variation of the assumed distance is performed to cover all of the feeder length. Considering that most of the faults have resistive nature, the fault location is obtained when the fault reactance is zero. Such reactance is calculated using the prefault and fault measurements of the three phase voltages and currents at the power distribution substation. The proposed fault location approach only requires: a) the fundamental currents and voltages obtained from the single end measurements during fault and prefault situations; and b) the series impedance for each homogeneous line sections. The approach here presented satisfies the distinctive characteristics of the power distribution systems, as described in the previous section. A. Fault location considering normal load variations From voltage and current measurements at the power substation, it is not easy to have an online load estimation for each one of the power system nodes. The only possible estimation is the total circuit load obtained from prefault conditions. To consider the effect of this variation, the estimated load is aggregated at the end of the analyzed feeder, as presented in the equivalent circuit depicted in Fig. 1. This approximation is suitable because the load impedance (ZC ) is normally bigger than the line impedance (ZL ). In real applications ZC ZL , mainly due to concerns related to voltage regulation and line loses. Several fault location impedance based approaches use a similar load aggregation [9], [10]. Z L1
(i+1)
ZC
From Fig. 1, IP and VP are the prefault currents and voltages, respectively [3×1], measured at the power substation. . ZLi , . . . ZLn are the line impedance matrices, where ZL1 , . . i=n ZL = i=1 ZLi is the total feeder impedance, as presented in (1).
ZL
=
Z C × IP = V P − Z L × IP
ZLab ZLbb ZLcb
⎤ ZLac ZLbc ⎦ ZLcc
(4)
then VP a ZLaa · IP a + ZLab · IP b + ZLac · IP c − IP a IP a VP b ZLba · IP a + ZLbb · IP b + ZLbc · IP c ZCb = − (5) IP b IP b VP c ZLca · IP a + ZLcb · IP b + ZLcc · IP c ZCc = − IP c IP c In the proposed approach, all the load is aggregated at the farthest node because of the difficulty to estimate the load for each node by just using single end measurements. This strategy is an economic an suitable alternative for most of the power distribution companies. However, this approach could be improved if there is enough information available to estimate the daily load variation for each power system node. ZCa
=
B. Fault distance estimation The equivalent system shown in Fig. 2 presents the case of a fault in a power distribution system considering a non homogeneous feeder. Z L1
(i)
mi Z Li
) Li (i+1) Vf (1 mi )Z
Zf
If
Z Ln
ZC
Fig. 2. Fault at the section i, node f , located at distance mi from the node i.
Fig. 1. Simplified power distribution system considering prefault conditions
ZLaa ⎣ ZLba ZLca
(3)
The load impedance (ZC ) can be determined from (3) and it is presented in (4) and (5).
Z Ln
VS , I S
⎡
(ZL + ZC ) × IP = VP
VS , I S
mi Z Li
(i)
The load impedance is then obtained from prefault conditions (see Fig. 1), using (3).
(1)
The total load impedance ZC is represented as shown in (2). ⎤ ⎡ 0 0 ZCa 0 ⎦ ZCb (2) ZC = ⎣ 0 0 0 ZCc
The distance from the power substation to the faulted node (f ) is then obtained as presented in (6), where Li is the length of the line section i. Lf =
j=i−1
L j + mi L i
(6)
j=1
The fault impedance is presented as given in (7). ⎤ ⎡ 0 0 ZF a 0 ⎦ ZF b ZF = ⎣ 0 0 0 ZF c
(7)
From (7) it is possible to consider unbalanced faults (ZF a = ZF b = ZF c ), and additionally form Fig. 2, equations (8) to (11) are then obtained. ⎞ ⎛ j=i−1 VF (mi ) = VS − ⎝ ZLj + mi ZLi ⎠ × IS (8) j=1
MORALES-ESPAÑA et al.:PAGES FAULT LOCATION METHOD AND THIS IS FOR RIGHT
IF (mi )
=
3 805
IS − YEQ (mi ) × VP
Substation
(9)
1
Zth
where ⎛ YEQ (mi ) = ⎝(1 − mi ) ZLi +
j=n
3
4
5
6
8
7
a
9
10 b
a
Vth
⎞−1 ZLj + ZC ⎠
2 a
11
12
c
13
V&I
(10) 19
18
16
20
24
22
15
j=i+1
23
25
then the fault impedance is ⎢ ZF (mi ) = ⎣
VF a (mi ) IF a (mi )
0
0
0
0
VF b (mi ) IF b (mi )
0
0
⎤
VF c (mi ) IF c (mi )
⎥ ⎦
(11)
The fault reactance is then obtained by using (11) and presented in (12). XF (mi ) = imag (ZF (mi ))
(12)
In the proposed fault location approach, the assumed fault distance in section i (mi ) is systematically incremented from zero to the line section length. The fault location is given by the distance where the fault reactance at the faulted phase(s) is zero, due the resistive nature of the fault. It is possible to obtain the fault measurements of current and voltage and also the fault type from the most commonly used relays. In addition, the fault type could be obtained using several approaches as those proposed in [9], [6]. To consider the fault type, the measurements of current and voltage required to obtain the fault reactance are presented in Table I. Matrix equations from (8) to (12) can be used to locate all kind of faults by using Table I. TABLE I VOLTAGE AND CURRENT SIGNALS MEASURED AT THE POWER SUBSTATION AND REQUIRED TO ESTIMATE THE FAULT REACTANCE FOR DIFFERENT KIND OF FAULTS .
Fig. 3. Power distribution system used for testing the proposed fault location approach.
B. Preliminary tests As previously explained, the variation of the fault reactance is obtained by a systematic variation of the supposed fault location, analyzing 200 different locations from node 1 to node 12 at the test power system. Fig. 4 presents the fault reactance curves for three fault types located at different nodes along the line length (single phase fault at 14.52 km, double phase fault at 18.41 km and three phase fault at 22.31 km). 20 18
14 12 10 8 6 4 2 0 0
Fault reactance XF (a) XF (b) XF (c) XF (a−b) XF (b−c) XF (c−a) XF (a−b)
Fault voltage (Vf ) VF a VF b VF c VF b -VF a VF c -VF b VF a -VF c VF b -VF a
Fault current (If ) IF a IF b IF c IF b -IF a IF c -IF b IF a -IF c IF b -ISa
III. P ROPOSED TESTS AND ANALYSIS OF THE RESULTS A. Test system The system selected for tests is a 25 kV power distribution feeder, from SaskPower in Canada presented in Fig. 3. This distribution system has been also used previously in several fault location papers [6], [4], [7]. The test circuit was simulated using ATP, and single phase, double phase to ground, phase to phase and three phase faults were performed, using several fault resistances from 0, 05Ω to 40Ω [11].
5
10
15
20
25
30
35
Line length [km]
Fig. 4. Fault type a-t b-t c-t a-b or a-b-t b-c or b-c-t c-a or c-a-t a-b-c
Xf(a) − single phase fault (a−t) Xf(a−b) − Phase to phase fault (a−b) Xf(a−b) − Three phase fault (a−b−c)
16
|Fault Reactance (Xf)| [ohms]
⎡
Fault reactance curves (absolute values) for different faults.
From Fig. 4, it is noticed how the fault reactance decreases from a positive initial value, as the supposed fault location is increased. Then the location is obtained at the line length where the reactance is zero or where the minimum of the absolute value of the reactance fault is located. Far from this distance, the reactance becomes negative. To reduce the number of tests, a simple interpolation strategy is suggested, assuming only two possible locations; the positive and negative fault reactances which are closest to zero. Therefore, the fault location (line length) is obtained using (13), where the fault reactance is closer to zero. Lf = L2 − Xf 2
L2 − L1 Xf 2 − Xf 1
(13)
where Xf 1 and Xf 2 are the estimated values of the fault reactance (positive and negative, respectively), L1 and L2 are the respective assumed fault lengths where Xf 1 and Xf 2 are found. Finally, the proposed technique gives multiple estimations of the fault location in the case of feeders composed by several
806 4
2010 IEEE/PES Transmission and Distribution Conference THIS and Exposition: Latin America IS FOR LEFT PAGES 1.4 1.2 1
0 ohms 10 ohms 20 ohms 30 ohms 40 ohms
0.8 0.6
Error (%)
laterals. The number of estimations depends on the system topology and the fault location. The multiple estimation is a common disadvantage of all impedance based fault location methods [7]. Several approaches also consider possible solutions of the multiple estimation problem, however these requires a complete characterization and an extensive fault simulation of the analyzed feeder, increasing the economical cost of the fault locator [5], [8]. Morales et al. [12] propose a concept to estimate the zone under fault and avoiding thus the multiple estimation, but this approach does not consider load variations because it is based on the reactance method.
0.4 0.2 0 −0.2 −0.4 −0.6 0
2.41
6.44
10.46
14.48
18.51
22.53
27.68 30.09
34.6 37.01
Length (km)
This section presents the performance of the proposed methodology under variations of fault resistance from 0.05 to 40 ohms for the case of single phase, phase to phase, double phase to ground and three phase faults, located at several distances along the main feeder (from node 1 to node 12 where 55 faults are analyzed for each one of the fault types). Figs. 5 to 8 present the error in the fault distance estimation for different fault types (considering all the 220 analyzed faults). The error in the estimation of the fault distance is computed using (14), where Lest is the estimated distance using the proposed fault location method, Lreal is the real distance to the faulted node and Ltotal is the total feeder length. Lest − Lreal × 100 %Error = Ltotal
Fig. 6. Error estimation of the fault location in the case of phase to phase faults (a-b). 0.9 0.8 0.7
0.5 0.4 0.3 0.2 0.1 0 −0.1 0
(14)
A positive error means an over estimation of the fault location.
0 ohms 10 ohms 20 ohms 30 ohms 40 ohms
0.6
Error (%)
C. Extensive tests considering fault resistance variations
2.41
6.44
10.46
14.48
18.51
22.53
27.68 30.09
34.6 37.01
Length (km)
Fig. 7. Error estimation of the fault location in the case of double phase to ground faults (b-c-g).
2.5
2
0 ohms 10 ohms 20 ohms 30 ohms 40 ohms
advantage of a simple implementation, as presented in Section II. Comparatively, the implementation of proposed method for real power systems is similar to the reactance method proposed by [16]. This particular situation make this approach easy to implement in most of the distribution companies.
Error (%)
1.5
1
0.5
D. Extensive tests considering system load variations 0
−0.5 0
As the previously presented tests, this section also considers the estimation of the distance from the power substation to 2.41
6.44
10.46
14.48
18.51
22.53
27.68 30.09
34.6 37.01
Length (km) 2
Fig. 5. Error estimation of the fault location in the case of single phase faults (a-g). 1.5
1
Error (%)
According to the obtained results of the extensive tests considering fault resistance variations, the maximum errors obtained are near to 2.5% for the case of single phase faults, 40Ω of fault resistance and a fault located at the farthest node. In the remaining fault cases the errors are lower than 1.8%, even for a fault located at the farthest node with high fault resistance. A comparison between the proposed fault location approach and 10 different impedance based methods, using the same test feeder [7], is given in Table II. According to Table II, the proposed method has comparative errors with the approaches presented in [7], having the
0 ohms 10 ohms 20 ohms 30 ohms 40 ohms
0.5
0
−0.5 0
2.41
6.44
10.46
14.48
18.51
22.53
27.68 30.09
34.6 37.01
Length (km)
Fig. 8. Error estimation of the fault location in the case of three phase faults (a-b-c).
MORALES-ESPAÑA et al.:PAGES FAULT LOCATION METHOD AND THIS IS FOR RIGHT
5 807
TABLE II C OMPARISON OF THE MAXIMUM ERRORS OBTAINED BETWEEN THE PROPOSED APPROACH AND THOSE OBTAINED USING 10 DIFFERENT IMPEDANCE BASED FAULT LOCATION APPROACHES .
Single phase to ground Phase to phase Double phase to ground Three phase
Best results in fault location Rf=25 ohms Method Max. error reference (%) [6] 0.35 [13] 1.00 [14] 4.20 [9] -1.35 [6] 1.90 [14] 1.95 [6] 0.85 [9] -1.10 [14] 1.95 [15] 0.25 [16] -0.28 [6] -0.85
Max. error (%) of the proposed method (Rf=30 ohms)
2
60% of the nominal load 80% of the nominal load 120% of the nominal load 140% of the nominal load 200% of the nominal load Nominal load
1.5
Error (%)
Fault type
2.5
1
1.75 0.5
1.04 0 0
2.41
6.44
10.46
14.48
18.51
22.53
27.68 30.09
34.6 37.01
Length (km)
0.72
Fig. 10. Error estimation of the fault location considering a fault resistance of 40Ω and phase to phase faults (a-b).
1.45
1.6
3
1.2
60% of the nominal load 80% of the nominal load 120% of the nominal load 140% of the nominal load 200% of the nominal load Nominal load
1 0.8 0.6 0.4 0.2 0 −0.2 0
2.41
6.44
10.46
14.48
18.51
22.53
27.68 30.09
34.6 37.01
Length (km)
Fig. 11. Error estimation of the fault location considering a fault resistance of 40Ω and double phase to ground faults (b-c-g).
4 3.5
1.4
Error (%)
the faulted node in the case of single phase, phase to phase, double phase to ground and three phase faults, located at several distances along the main feeder (from node 1 to node 12). Where variations of the 60%, 80%, 120%, 140% and 200% of the nominal load are also considered to test the sensitivity of the proposed approach to load variations. Additionally, the proposed fault location algorithm is tested under the less favorable conditions of fault resistance, therefore 40Ω is selected [11]. The extensive tests presented in this section consider 264 fault situations. The error is estimated using (14) and the results are graphically presented from Figs. 9 to 12. 60% of the nominal load 80% of the nominal load 120% of the nominal load 140% of the nominal load 200% of the nominal load Nominal load
Error (%)
2.5
by the proposed load aggregation approach (according to the results here presented) even in the case of high load variations. This demonstrates the capabilities of the proposed fault location method to effectively solve the fault location problem in power distribution systems.
2 1.5 1 0.5 0 −0.5 0
2.41
6.44
10.46
14.48
18.51
22.53
27.68 30.09
34.6 37.01
Length (km) 3.5
Fig. 9. Error estimation of the fault location considering a fault resistance of 40Ω and single phase faults (a-g).
2.5
Error (%)
According to Figs. 9 to 12, it is noticed how a reduction of the performance in fault location is obtained for high load levels. In general, error is about twice of the nominal error in such hypothetical load case when load increases to 200% of the nominal. From Figs. 9 to 12 it can be noticed that a lower performance is obtained for the case of single phase faults. In such cases, where the power system is overloaded to the 200% of the nominal condition, the maximum estimation error is 3.8% approximately. Considering an overloaded power circuit to the 140% of the nominal condition, the estimation error is near to 3.0%. It is important to remark the good performance obtained
3
60% of the nominal load 80% of the nominal load 120% of the nominal load 140% of the nominal load 200% of the nominal load Nominal load
2
1.5
1
0.5
0 0
2.41
6.44
10.46
14.48
18.51
22.53
27.68 30.09
34.6 37.01
Length (km)
Fig. 12. Error estimation of the fault location considering a fault resistance of 40Ω and three phase faults (a-b-c).
808 6
2010 IEEE/PES Transmission and Distribution Conference THIS and Exposition: Latin America IS FOR LEFT PAGES
E. Qualitative comparison between the proposed approach and several impedance based fault location methods A qualitative comparison with the most cited impedance fault location methods is presented in Table III considering the information required by the proposed fault location approach. According to this table, the proposed method satisfies most of the requirements for locating faults in power distribution systems avoiding the use of symmetrical components (because the consequent errors due the unbalanced nature of the power distribution systems [13]). Furthermore, the proposed approach is the only one with an strategy to deal with unknown distribution load which is usually the case for real distribution systems. IV. C ONCLUSIONS A novel method to locate faults in power distribution systems based on the determination of the fault reactance is here proposed. This method considers all of the singular characteristics of such power systems, specially the non homogeneity of the feeders and the lack of information related to the load variation at each one of the power system nodes and the fault resistance. The proposed approach is based on the determination of the reactance at the supposed fault location and only if the supposed faulted place corresponds to the real location, the reactance reaches the zero value. According to the sensitivity analysis, considering fault resistance and load variations, the proposed method presented a high performance. From the sensitivity test, 3.8% was the worst error magnitude for the distance estimation. Finally, the proposed fault location method only requires information related to the serial line impedance in each one of the homogeneous section lines, and the single end measurements of current and voltage. These requirements make easy to implement the proposed strategy in real power distribution systems.
[8] J. Mora-Florez, G. Morales-Espana, and S. Perez-Londono, “Learningbased strategy for reducing the multiple estimation problem of fault zone location in radial power systems,” IET Generation, Transmission & Distribution, vol. 3, no. 4, pp. 346–356, Apr. 2009. [Online]. Available: http://ieeexplore.ieee.org/xpls/abs_all.jsp? isnumber=4806229&arnumber=4806233&count=8&index=3 [9] D. Novosel, D. Hart, Y. Hu, and J. Myllymaki, System for locating faults and estimating fault resistence in distribution networks with tapped loads, 1998, no. US Patent number 5,839,093. [10] L. Yang, One terminal fault location system that corrects for fault resistance effects. US Patent number 5,773,980, 1998. [11] J. Dagenhart, “The 40-Ω ground-fault phenomenon,” Industry Applications, IEEE Transactions on, vol. 36, no. 1, pp. 30–32, Jan/Feb 2000. [12] G. Morales-Espana, J. Mora-Florez, and H. Vargas-Torres, “Elimination of multiple estimation for fault location in radial power systems by using fundamental Single-End measurements,” Power Delivery, IEEE Transactions on, vol. 24, no. 3, pp. 1382–1389, july 2009. [Online]. Available: http://ieeexplore.ieee.org/stamp/stamp.jsp? tp=&arnumber=5109866&isnumber=5109837 [13] M. Choi, S. Lee, D. Lee, and B. Jin, “A new fault location algorithm using direct circuit analysis for distribution systems,” IEEE Transactions on Power Delivery, vol. 19, no. 1, pp. 35–41, 2004. [14] A. Girgis, C. Fallon, and D. Lubkeman, “A fault location technique for rural distribution feeders,” IEEE Transactions on Industry and Applications, vol. 26, no. 6, pp. 1170–1175, 1993. [15] K. Srinivasan and A. St-Jacques, “A new fault location algorithm for radial transmission lines with loads,” IEEE Transactions on Power Delivery, vol. 4, no. 3, pp. 1676–1682, 1989. [16] A. van C. Warrington, Protective Relays Their Theory and Practice: Volume Two, 3rd ed. Springer, Apr. 1978. [17] J. Zhu, D. Lubkeman, and A. Girgis, “Automated fault location and diagnosis on electric power distribution feefers,” IEEE Transactions on Power Delivery, vol. 12, no. 2, pp. 801–809, 1997. [18] R. Aggarwal, Y. Aslan, and A. Johns, “New concept in fault location for overhead distribution systems usings superimposed components,” IEE Proceedings. Generation, Transmission and Distribution, vol. 144, no. 3, pp. 309–316, 1997. [19] M. Saha and E. Rosolowski, Method and device of fault location for distribution networks. US Patent number 6,483,435, 2002.
R EFERENCES [1] A. Warrington and C. Van, Protective relays. Their theory and practice. Chapman and Hall Ltd, London, 1968, vol. 1. [2] T. Takagi, Y. Yamakoshi, R. Kondow, and T. Matsushima, “Development of a new type fault locator using the one-terminal voltage and current data,” IEEE Transactions on Power Apparatus and Systems, vol. PAS101, no. 8, pp. 2892–2898, 1982. [3] IEEE Guide for Determining Fault Location on AC Transmission and Distribution Lines, IEEE Std 37.114, Power System Relaying Committee 2004. [4] J. J. Mora, “Localización de faltas en sistemas de distribución de energía eléctrica usando métodos basados en el modelo y métodos basados en el conocimiento,” Ph.D. dissertation, Universidad de Girona, Girona, España, 2006. [5] J. Mora, V. Barrera, and G. Carrillo, “Fault location in power distribution systems using a learning algorithm for multivariable data analysis,” IEEE Transactions on Power Delivery, vol. 22, no. 3, pp. 1715–1721, July 2007. [6] R. Das, “Determining the locations of faults in distribution systems,” Ph.D. dissertation, University of Saskatchewan, Saskatoon, Canada, 1998. [7] J. Mora-Florez, J. Melendez, and G. Carrillo-Caicedo, “Comparison of impedance based fault location methods for power distribution systems,” Electric Power Systems Research, vol. 78, no. 4, pp. 657–666, Apr. 2008.
Germán Morales-España received the B.Sc. degree in electrical engineering from the Industrial University of Santander (UIS), Colombia, in 2007; the M.Sc. degree in engineering and policy analysis from the Delft University of Technology (TUDelft), The Netherlands, in 2010; and he is pursuing the Erasmus Mundus Joint Ph.D. degree in Sustainable Energy Technologies and Strategies (SETS) delivered by the Universidad Pontificia Comillas (UPCO), Spain, the Royal Institute of Technology (KTH), Sweden, and TUDelft, The Netherlands. He is currently an Assistant Researcher at the Institute for Research in Technology (IIT) at the UPCO. His areas of interest are power quality, protective relaying, economy and regulation of electric sector, and policy analysis. Mr. Morales-España is a member of GISEL (Col) Research Group on Electric Power Systems.
MORALES-ESPAÑA et al.:PAGES FAULT LOCATION METHOD AND THIS IS FOR RIGHT
7 809
TABLE III Q UALITATIVE COMPARISON BETWEEN THE PROPOSED APPROACH AND THE MOST CITED IMPEDANCE BASED FAULT LOCATION METHODS .
Analyzed aspect Symmetrical components Phase components Line model Load model Non homogeneity Unbalanced Systems Laterals Load taps
PROP
[1] √ ×
×
×
Short
Short
Long Z=f(V)
Short Z=cte √
× √
Z=cte √ √ √ √
× × × × ×
[15] √
× × × √
[14] √
× √ √
Juan Mora-Flórez (M’ 2009) received the B.Sc. degree in electrical engineering from the Industrial University of Santander (UIS), Colombia, in 1996, the M.Sc. degree in electrical power from UIS in 2001, the M.Sc. degree in information technologies from the University of Girona (UdG), Spain, in 2003, and the Ph.D. degree in information technologies and electrical engineering from UdG in 2006. Currently, he is associated professor at the Electrical Engineering School at the Technological University of Pereira, Pereira, Colombia. His areas of interest are power quality, transient analysis, protective relaying and soft computing techniques. Mr. Mora-Florez is a member of ICE (Col) Research Group on Power Quality and System Stability.
Hermann Vargas-Torres received the B.Sc. degree in electrical engineering from the Industrial University of Santander (UIS), Colombia, in 1985. The M.Sc. degree in Electrical power from UIS in 1990, and the Ph.D. degree in Electrical Engineering from UPCO, Spain, in 2002. Currently, he is a Professor with the Electrical Engineering School at the Industrial University of Santander (UIS), Bucaramanga, Colombia. His areas of interest are power systems stability, transient analysis, power quality, protective relaying and policy analysis. Mr. Vargas-Torres is a member of GISEL (Col) Research Group on Electric Power Systems.
[18] × √
[6] √ ×
×
×
×
Short Z=f(V) √
Short Z=cte √
Long Z=f(V) √
Short Z=cte
Short I=cte
Short Z=cte √
√ √ √
√ √ √
× √ √
[9] √
[10] √
[17] × √
× × × √
× × × ×
[19] √
× √ √
[13] × √
Short Z=cte × √
× √
