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Comparison of impedance based fault location methods for power distribution systems
Available online at www.sciencedirect.com
Electric Power Systems Research 78 (2008) 657–666
Comparison of impedance based fault location methods for power distribution systems J. Mora-Fl`orez a,∗ , J. Mel´endez b,1 , G. Carrillo-Caicedo c,2 a
b
Electrical Engineering School, Technological University of Pereira (UTP), La Julita, Pereira, Colombia Electronics, Computer Engineering and Automatics Department, University of Girona (UdG), EPS, Campus Montilivi, 17071 Girona, Spain c Electrical Engineering School, Industrial University of Santander (UIS), Cra 27-Cll 9, Bucaramanga, Colombia Received 20 May 2006; received in revised form 1 March 2007; accepted 16 May 2007 Available online 20 July 2007
Abstract Performance of 10 fault location methods for power distribution systems has been compared. The analyzed methods use only measurements of voltage and current at the substation. Fundamental component during pre-fault and fault are used in these methods to estimate the apparent impedance viewed from the measurement point. Deviation between pre-fault and fault impedance together with the system parameters are used to estimate the distance to the fault point. Fundamental aspects of each method have been considered in the analysis. Power system topology, line and load models and the necessity of additional information are relevant aspects that differentiate one method from another. The 10 selected methods have been implemented, tested and compared in a simulated network. The paper reports the results for several scenarios defined by significant values of the fault location and impedance. The estimated error has been used as a performance index in the comparison. © 2007 Elsevier B.V. All rights reserved. Keywords: Fault location; Impedance based methods; Power distribution systems; Power quality
1. Introduction Power quality requirements resulting from the deregulated electrical markets have motivated the improvement of fault location methods in distribution systems to speed up the restoration process [1]. Faults and outages affect power quality in terms of service continuity and disturbance propagation. Utilities are forced to improve quality indexes associated to these phenomena in order to be competitive in the current electric open market [2,3]. With this aim, several strategies for fault location in distribution systems have been developed. Some methods have been adapted from of those proposed for fault location in transmission systems, i.e. high frequency component based methods (e.g. [4]) or those that analyze travelling waves (e.g. [5]), but considering the specificity of distribution systems (single end measurements, radial operation, etc.). ∗
Corresponding author. Tel.: +57 6 3137329; fax: +57 6 3137329/3137122. E-mail addresses: [email protected] (J. Mora-Fl`orez), [email protected] (J. Mel´endez), [email protected] (G. Carrillo-Caicedo). 1 Tel.: +34 972 418391; fax: +34 972 418391. 2 Tel.: +57 7 6344000; fax: +57 7 6344000. 0378-7796/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2007.05.010
For example in [6] high frequency components from travelling waves are analysed using wavelets in order to deduce the fault. In [7] correlation analysis between transmitted and reflected waveform is performed, whereas in [8] peak detection on the reflected waveform is used to identify possible fault locations base on the delays estimated. A drawback of these methods is the necessity of measuring devices with a very high sampling rate (MHz). On the other hand, impedance based methods works on steady states values of currents and voltages during the fault to estimate an apparent impedance (or reactance) that is directly associated to a distance to the fault. The main drawback of impedance-based methods is the multi-estimation due to the existence of multiple possible faulty points at the same distance. Difficulties in developing effective fault location methods in distribution systems are due to the radial topology, the existence of short and heterogeneous lines and also a lower degree of instrumentation of these systems. Therefore, the join exploitation of available information has to be considered. Registers of voltage and current at substation must be complemented with additional knowledge to assist fault location procedure in distribution. Three different, but complementary, sources of
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knowledge can be distinguished: system knowledge, data history and external information. System knowledge is necessary to build models. These models allow checking the consistency between the impedance calculated, from measured voltages and currents, and the nominal one. On the other hand, data history allows analyzing the relevance of waveform attributes and frequency of occurrence. The observation of, previously registered, similar behaviours may be used to infer possible location according to probabilistic models, e.g. [9,10]. Finally, external information as weather, existence of construction sites, consumer calls and so on, can be very useful to delimitate a searching area. Despite the benefit of dealing with these three complimentary views of the fault, in this paper we have focused on those methods that exploit system knowledge for fault location. Ten methods based on the impedance calculation from measures of voltage and current in a single point have been compared. The use of currents and voltages for fault location is described in the early literature as the reactive component method [11]. A simplified model of the feeder, equivalent to the voltage divider model used in [12], is used to explain the dependence of sag magnitude on the distance to the fault. These simple models differ in the availability of currents (in the reactive component method) or in the necessity of the source/transformer impedance (in the voltage divider model) to compute the equivalent impedance. The nine additional methods analyzed in this paper are improvements of this simple approach to cope with the complexity (radial topology, heterogeneity of lines and variety of loads) of distribution networks. Also the uncertainty, in the estimation of the distance to the fault, caused by the unknown value of fault resistance is treated in these models under different assumptions. Srinivasan and St-Jacques [13] proposed one of the first algorithms considering the existence of loads in a radial transmission system. Yang and Springs [14] propose a fault location method which corrects the fault resistance effects while Aggarwal et al. [15,16] propose a methodology based on the analysis of the superimposed components. The methodology proposed by Novosel et al. [17] focus on the idea applied for short transmission lines with loads and laterals represented by a lumped parameter impedance model placed behind the fault. Zhu et al. [10] model loads as an injected current and they analyze current patterns for fault location. In Das [18,19] first, the faulted section is located and next the distance to the fault in this section is calculated. It considers laterals and load taps. The method proposed by Saha and Rosolowski [20] estimates the fault location by comparing the measured impedance with the calculate feeder impedance assuming faults each section line. Finally, Choi et al. [21] differs from the previous approaches because refuses to apply the classical symmetrical component theory [22] to analyze unbalanced power systems. The paper presents in Section 2 the signal processing requirements of each method. Next, in Section 3, the power system assumptions required in the methods are compared. In Section 4 we analyze the requirements from the point of view of line section model. The load modelling and the necessity of additional information is reviewed in Sections 5 and 6, respectively.
Finally last two sections are devoted to test the algorithms in benchmark and conclude about its performance. 2. Fundamentals of the methods 2.1. General methodology The nominated methods use the distribution system parameters and combinations of pre-fault, fault and post-fault values of current and voltage, measured at fundamental frequency on a single line end; typically at the substation. Pre-fault values are used to estimate the initial conditions of the power circuit before the fault. Fault values are used as known values in a set of equations where both, the distance from the measurement point to the fault location and the fault resistance are the unknown variables. From the 10, only [10] uses post-fault values of current or voltage to reduce the multiple estimation problem induced by the existence of multiple fault points in the network with the same impedance. The method proposes the identification of patterns of the disturbance waveform with the operation of protective devices as well as changes in substation load. 2.2. Treatment of measurements All methods considered in this paper use the fundamental rms values of voltage and current measured at the substation. Pre-fault and fault values of these variables are used in [9,13,17,18,23] to estimate the load parameters while [14,16], only make use of the rate of change between pre-fault and fault voltage and current rms values. Others as the reactive component method [11] and a recent approach proposed in [21], do not use the pre-fault measurements. Faulted circuit analysis is performed by symmetrical component analysis in [13,14,17,18,23,24], while approaches presented in [10,14–16] use phase voltage and current vectors to perform a direct circuit analysis. 3. Distribution system topology The most important aspects considered by fault location methods are directly related to the characteristics of distribution systems: (a) Heterogeneity of feeders given by different size and length of cables, presence of overhead and underground lines, etc. (b) Unbalances due to the untransposed lines and by the presence of single, double and three phase loads. (c) Presence of laterals along the main feeder. (d) Presence of load taps along the main feeder and laterals. These aspects introduce errors in the estimation of the fault locations performed by means of a simplified model. Its reduction has motivated the majority of approaches compared in this paper. Heterogeneity of distribution lines could be considered in [10,14,15,17,18,23,24] since these algorithms consider the analysis of each section line independently.
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Fig. 1. Power distribution system.
VR IR,S
= T (x)
VS IS,R
⎡
⎤ −Zc sinh(λx) VS ⎦ IS,R −1
1 = ⎣ sinh(λx) Zc
Fig. 2. Faulted section line. Single phase to ground fault.
The methods presented in [10,15,18,23,24] consider the presence of laterals. In such methods loads on laterals are lumped at the node in the radial system. Thus, the system depicted in Fig. 1 (with a fault in F) will be modified by lumped loads in nodes X − 1 and N − 1. A detailed model between nodes X and X + 1 is presented in Fig. 2. The presence of load taps is considered in the majority of methods except in those that use simplified models as [11,14]. 4. Line section model The analyzed methods propose different line models according to its length, existence of mutual impedance and loads. Long line models are used in [13,18,19] while the others ([11,14–17,21,23,24]) assume short line models. A distributed parameter model is used in [13]. The classical transmission matrix T(x) is used to obtain the voltages and currents at the receiving end (VR and IR,S ), from the values at the sending end (VS and IS,R ) as it is represented in (1). A simplified version of this model is adopted by [18,19] to model short lines. This model, represented in (2), is used to perform an initial estimation of the distance to the fault in the method. VR VS = T (x) IR,S IS,R ⎡ ⎤ cosh(λx) −Zc sinh(λx) VS ⎦ = ⎣ sinh(λx) (1) IS,R − cosh(λx) Zc
(2)
Lumped parameters used in the short line models differ from one model to other. The method proposed in [15,16] considers the classical matrix impedance model (see (3)). The same model is used in [21] while in [11] only the series impedance of the line is considered. The approach of [14] also considers only the series impedance but it is decomposed on symmetrical components ⎡
VRa
⎤
⎡
VSa
⎤
⎡
Zs
⎢ ⎥ ⎢ ⎥ ⎢ ⎣ VRb ⎦ = ⎣ Vba ⎦ − ⎣ Zm VRc VSc Zm
Zm
Zm
⎤⎡
ISRa
⎤
Zs
⎥⎢ ⎥ Zm ⎦ ⎣ ISRb ⎦
Zm
Zs
(3)
ISRc
Resistance and reactance is needed to model each line section in the methods [18,19]. An impedance matrix, Zabc , allowing mutual coupling among phases, is considered in the iterative algorithm proposed in [10,23] (see Fig. 1). In a similar way the method proposed in [17] considers the matrix, Zabc , with mutual and self parameters to model the section line. A priori, the selection of an appropriate model seems to have influence on the fault location results. Thus, long lines have to be modelled by considering all the capacitive and inductive effects whereas simpler models (only serial parameters) could be used to describe short lines. However, the heterogeneity (multiple sections of different types of lines, gauges and lengths) of distribution lines makes inefficient to combine multiple models in the fault location strategy. In fact methods for fault location never consider combination of models and the election of one or another is directly tied to how the fault location method operates. Therefore, when a line typology can be clearly identified this could be used as criteria to select the fault location method based on the consideration that a better description of the system obtained. Instead of this, in this work we have compared all the algorithms, with the line model associated, in the same system and the results show no great differences that could be assigned to modelling errors.
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5. Load modelling Fault current is much greater than load current and its magnitude is limited by the transformer. Moreover loads vary and it is difficult to know its exact value at specific time (fault instant). These considerations are commonly argued to work with simplified models as the voltage divider. However, some location methods consider the presence of loads in its models in order to reduce uncertainty in the system and improve the location. The methods presented in [17,21,23,24] consider a constant impedance load model, obtained from steady state conditions. In [17] all loads, including tapped lines are modelled by lumpedparameter impedance placed behind the fault (Zload in (4)). This way of compensating tapped loads is accepted as tapped load impedances are much larger than feeder impedance. The method is based on the calculation of source and load impedance from voltages and current measured at substation and using the positive sequence values (Vpfl and Ipfl ) in pre-fault and considering the typology of the fault. Zl1 is the pre-fault positive sequence line impedance. Zload =
Vpfl − Zl1 Ipfl
(4)
Another proposal of constant load modeling is presented in [14] where it is used a matrix composed by constant impedances. The load impedance matrix Znabc at node N is given by (5). ⎤ ⎡ Znaa Znab Znac ⎥ ⎢ Znabc = ⎣ Znba Znbb Znbc ⎦ (5) Znca
Zncb
Zncc
Methods presented in [10,13,15,16,18,19] propose load models that vary according to the current and voltage, as presented below. Methods proposed in [13,18,19] perform a load flow to determine the constants of the static load model at node N resulting a model as Eq. (6). Vn is the voltage at node N; Yn is the load admittance; Gn , and Bn are the conductance and susceptance; and np and nq are constants for the active and reactive load components. In [15,16] load taps are considered by assuming a model which depends on the node voltage Vn , the power factor Pf and the load type (k = 1 for single phase loads and k = 3 for three phase loads). The load model is presented in (7). Yn = Gn |Vn |np−2 + jBn |Vn |nq−2
(6)
−1
(7)
Zn = kVn ∠cos
(Pf )
A similar load model is presented in [10], where the fault distance method calculates the remote-end current infeed using a radial power flow algorithm, which uses the current-injectionbased load model presented in (8).
Vn np−2
Vn nq−2
In = Irn
+ jIin
(8) V0n
V0n
where V0n is the nominal voltage, Irn and Iin are the active and reactive components at the nominal current at node N, respec-
tively. np and nq are the composite components, reflecting the dynamic response of the customer load at N. The same consideration made in the previous section is applicable with the load model. The more appropriate the load model we use the better the accuracy in the estimation of fault location. However, is difficult to know instantaneous load in the instant of faults. This is why the majority of fault location methods consider constant impedance models or impedance voltage dependent models. The last allows taking into account both, the level of load at the fault instant and the type of load, using appropriate exponents (np, nq). Consequently, the use of these second type of loaf model offers a major adaptability of fault location methods for lines operating with different loads through time (day/night, seasons and so on). 6. Additional information Method proposed by Zhu et al. [10] uses probabilistic modelling and analysis of current patterns to improve the selection of the fault regions. Based on the sequence of events extracted from the waveforms and its relation with protective device settings and actuation, it is possible to isolate the fault. This procedure is used to reduce the number of possible fault location; problem known as “multiple estimation problem”. Method proposed by Das in [18,19] considers the use of software-based fault indicators located at the beginning of each tap. These are used to detect downstream faults irrespective or their location and so to solve the multiple estimation problem. The solution proposed by these two methods could also be implemented, as a diagnosis improvement in the other methods. Methods not mentioned above only use the system parameters and the pre-fault and post-fault values of current and voltage. Finally, most of the considered methods need to know the involved phases and the fault type. However, the method proposed by Aggarwal et al. [15] performs the fault location without using this information. Table 1 summarizes the main aspects of the comparison. 7. Test of the fault location methods Considering that all methods use real measurements then the internal model used by each method to locate the fault should reflects the real behaviour of the power system to have high precision rates. According to, there are two aspects to be considered. One of them is related to the characteristics of the distribution system where simplified models are commonly accepted in steady state studies. Considering that a steady state estimator is used to determine the rms value of currents and voltages used in the analyzed fault location methods, a simplified line model used in distribution systems is not supposed to introduce considerable errors. The second aspect is related to the availability of data, because frequently at most of the distribution substations, it is only possible to obtain the characteristics of the conductors (self resistance and inductance), and the characteristics of the standard structures. So no much information is available and considering that
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Table 1 Summary of the main aspects of the analyzed fault location methods Analyzed aspect
Fault location method Warrington [11]
Fault detection and – identification Signal processing RMS of voltage and current Pre-fault – √ Fault Pos-fault – √ Symmetrical components Phase components –
Srinivasan et al. [13]
Girgins et al. [23]
Zhu et al. [10]
√
√
√ √
√ √
– √
– √
√ √ √
–
–
–
Aggarwal et al. [15,16] √
Das [18,19]
Novosel [17]
Yang and Springs [14]
Saha and Rosolowski [20]
Choi et al. [21]
√
√
–
–
–
√ √
√ √
√ √
√ √
√ √
– √
–
– √
– √
– √
– √
–
–
–
–
–
–
–
√
√
Short Z = f(V) √ √ √ √
Long Z = f(V) √ √ √ √
Short Z = cte – – – –
Short – – – – –
Short Z = cte √
–
SBFI
–
–
–
Distribution system Line model Load model Non homogeneity Unbalanced System Laterals Load taps
Short – – – – –
Long Z = f(V) – – – √
Short Z = cte √ – √ √
Short Z = f(V) √ √ √ √
Additional information
–
–
–
PM, CP
– √
– – √
Short – √ √ – √ –
PM: probabilistic modeling. CP: current patterns. SBFI: software based fault indicators.
there is a high number of power distributions substations, the development of a complex model is not a easy and low cost task for the utility. In the specific case of the impedance based fault location methods, several aspects are interrelated and these methods were tested as these are proposed by the authors. The consideration of the variation of only one of these aspects (line model, load model, line homogeneity, and so on), is out of the scope of this paper. That is the reason for testing the analyzed methods by using the same power distribution system as it is presented in this section. Tables reflect the behaviour of
each one of the fault location methods, considering the same comparison situations and the algorithms proposed in each approach. 7.1. Benchmark and scenarios The model of a 25 kV power distribution system from Saskpower, Canada, proposed in [17] has been used to test the fault location algorithms in order to compare its performance. The system is depicted in Fig. 3. It has a non homogeneous main feeder with laterals and load taps. Tables 2 and 3 present
Table 2 System line data Section
1–2 2–6 6–7 7–8 8–9 9–10 10–11 6–12 8–13 13–14 13–15 15–16 15–17 9–18 18–19 18–20 20–21
Length (km)
2.414 16.092 4.023 5.150 2.414 4.506 2.414 2.414 2.414 2.414 2.414 2.414 2.414 2.414 2.414 3.219 3.219
Series impedance (/km)
Shunt admittance (Mhos/km)
±sec
Zero sec
±sec
Zero sec
0.3480 + j0.5166 0.3480 + j0.5166 0.3480 + j0.5166 0.5519 + j0.5390 0.5519 + j0.5390 0.5519 + j0.5390 0.3480 + j0.5166 0.3480 + j0.5166 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998
0.5254 + j1.704 0.5254 + j1.704 0.5254 + j1.704 0.7290 + j1.727 0.7290 + j1.727 0.7290 + j1.727 0.7290 + j1.727 0.7290 + j1.727 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998
j3.74E−6 j3.74E−6 j3.74E−6 j3.59E−6 j3.59E−6 j3.59E−6 j3.74E−6 j3.74E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6
j2.49E−6 j2.49E−6 j2.49E−6 j2.39E−6 j2.39E−6 j2.39E−6 j2.49E−6 j2.49E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6
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Fig. 3. 25 kV power distribution system from Saskpower, Canada.
the system data. The system has been modelled using Alternative Transients Program—ATP [24,25]. The scenarios considered in this paper simulate faults at 10 nodes (from 2 to 11) of the main feeder with three different values of the fault resistance (0.05, 5, and 25 ). These are representative values commonly used in this type of tests [26]. For these situations performance of algorithms have been tested for both phase to phase faults and phase to ground faults involving one, two or three phases. In methods where mutual coupling is considered, as those presented in [10,15], the mutual impedance values were assumed equal to zero. Finally the multiple estimation problem was not considered in the test, since this paper is oriented to compare the distance estimation performance of the analyzed methods. Table 3 System load data Node number
1 2 6 11 12 14 15 16 17 18 19 21
Phase
A A B A,B,C A,B,C B B B B C C C
Connected size (kVA)
Composition [%] Heating
Lighting
Motor
15.0 15.0 15.0 1000.0 67.5 15.0 15.0 7.5 15.0 25.0 15.0 15.0
99.8 99.8 99.8 0.1 99.8 99.8 99.8 99.8 99.8 99.8 99.8 99.8
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.1 0.1 0.1 99.8 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
In Tables 4–6 the results for single phase to ground tests are presented. 7.2. Comparative results The distance estimation error, its dependency with the fault location and the fault resistance, has been used to compare the analysed methods. Distance estimation error is calculated according to (9) e (%) =
estimated location − actual location × 100 length of distribution feeder
(9)
For single phase to ground faults and according to Tables 3–5 the boundaries for the estimation errors are −13.63% and 10.89%. To have a good visualization only the four fault location techniques which have lowest error are presented in Fig. 4(a and b), for fault resistances of 0.05 and 25 . In the test of phase to phase faults, the methods perform quite similar with errors between −3.61% and 6.45%. In Fig. 5(a and b) the four best techniques are presented for fault resistance of 0.05 and 25 . The methods proposed by Srinivasan and St-Jacques [13], Zhu et al. [23] and Choi et al. [21] do not consider two phase to ground faults. The estimation errors are in the interval (−1.11%, 6.52%). In Fig. 6(a and b) the four best techniques are presented for fault resistance of 0.05 and 25 . Finally, in case of three phase faults, the methods proposed by Zhu et al. [10], Aggarwal et al. [15,16], Choi et al. [21] and Girgins et al. [23], analyse this type of faults. In addition the method proposed by Aggarwal et al. [15,16] is only suitable if
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Table 4 Test results—single phase fault location through Rf = 0.05 Method
Warrington [11] Srinivasan et al. [13] Girgins et al. [23] Zhu et al. [10] Aggarwal et al. [15,16] Das [18,19] Novosel [17] Yang and Springs [14] Saha and Rosolowski [20] Choi et al. [21]
Faulted node and real distance from distribution substation (Node 1) [km] Node 2 (2.414)
Node 3 (6.437)
Node 4 (10.460)
Node 5 (14.483)
Node 6 (18.506)
Node 7 (22.529)
Node 8 (27.679)
Node 9 (30.093)
Node 10 (34.599)
Node 11 (37.013)
2.3984 2.4138 2.4138 2.4203 2.4453 2.410 2.3921 2.3909 2.4513 2.4131
6.367 6.438 6.4384 6.4513 6.4467 6.430 6.3781 6.3732 6.5555 6.4372
10.296 10.462 10.462 10.482 10.485 10.451 10.36 10.35 10.657 10.461
14.185 14.486 14.486 14.513 14.487 14.474 14.337 14.322 14.755 14.484
18.035 18.508 18.510 18.539 19.192 18.501 18.311 18.288 18.850 18.507
21.847 22.53 22.531 22.547 23.119 22.525 22.281 22.251 22.934 22.528
26.666 27.684 27.684 27.701 28.158 27.675 27.481 27.463 27.919 27.683
28.884 30.096 30.092 30.091 30.085 30.090 29.906 29.895 30.265 30.096
33.215 34.596 34.616 34.576 37.013 34.566 34.443 34.449 34.73 34.595
35.161 36.998 36.992 36.585 37.013 37.006 36.824 36.826 37.013 37.003
Table 5 Test results—single phase fault location through Rf = 5 Method
Warrington [11] Srinivasan et al. [13] Girgins et al. [23] Zhu et al. [10] Aggarwal et al. [15,16] Das [18,19] Novosel [17] Yang and Springs [14] Saha and Rosolowski [20] Choi et al. [21]
Faulted node and real distance from distribution substation (Node 1) [km] Node 2 (2.414)
Node 3 (6.437)
Node 4 (10.460)
Node 5 (14.483)
Node 6 (18.506)
Node 7 (22.529)
Node 8 (27.679)
Node 9 (30.093)
Node 10 (34.599)
Node 11 (37.013)
2.410 2.473 2.491 2.626 2.445 2.434 2.395 2.447 1.344 2.411
6.317 6.473 6.520 6.812 6.447 6.447 6.334 6.395 5.415 6.392
9.719 10.007 10.088 10.571 10.485 10.462 9.799 9.872 8.862 9.899
14.138 14.600 14.703 15.483 14.487 14.447 14.327 14.397 13.711 14.489
17.970 18.632 18.775 19.781 19.155 18.539 18.296 18.371 17.830 18.517
21.480 22.400 22.556 23.904 23.119 22.562 21.975 22.063 21.566 22.256
26.552 28.034 27.996 29.880 28.121 27.704 27.435 27.542 26.996 27.706
28.760 30.229 30.374 32.673 30.085 30.135 29.853 29.975 29.367 30.124
32.858 34.755 34.904 37.029 37.013 34.611 34.382 34.534 33.901 34.642
34.998 37.162 37.317 37.270 37.013 37.047 36.754 36.908 36.461 37.045
there are one or more healthy-phases. According to this method, the superimposed components of those healthy phases have a minimum the distance where the fault is located. In case of three phase fault (no healthy phases) this method is not suitable. The test performed using the others methods give an estimation errors band between −1.48% and 1.97%. In Fig. 7(a and b) the four best techniques are presented for fault resistance of 0.05 and 25 .
7.3. Result analysis One of the first aspects related to the presented results, is related to the clear influence of the fault resistance and distance between fault and measurement point. The higher the fault resistance and the distance to the fault, the bigger the estimation error.
Table 6 Test results—single phase fault location through Rf = 25 Method
Warrington [11] Srinivasan et al. [13] Girgins et al. [23] Zhu et al. [10] Aggarwal et al. [15,16] Das [18,19] Novosel [17] Yang and Springs [14] Saha and Rosolowski [20] Choi et al. [21]
Faulted node and real distance from distribution substation (Node 1) [km] Node 2 (2.414)
Node 3 (6.437)
Node 4 (10.460)
Node 5 (14.483)
Node 6 (18.506)
Node 7 (22.529)
Node 8 (27.679)
Node 9 (30.093)
Node 10 (34.599)
Node 11 (37.013)
2.850 2.736 2.816 1.521 1.260 2.417 2.423 2.636 −2.630 2.320
6.725 6.820 7.088 6.112 6.447 6.543 6.369 6.670 1.560 6.353
10.558 10.942 11.346 10.714 10.485 10.471 10.328 10.678 5.766 10.410
14.354 15.015 15.607 15.514 14.487 14.426 14.280 14.681 9.980 14.480
18.113 19.069 19.873 20.078 19.155 18.381 18.227 18.677 14.195 18.601
21.830 23.375 23.975 24.875 23.082 22.479 22.169 22.668 18.402 22.689
26.515 29.634 29.278 30.991 28.158 27.707 27.269 27.857 23.729 27.941
28.683 30.707 31.389 34.126 30.085 30.075 29.662 30.293 26.168 30.405
32.695 35.289 36.144 35.564 37.013 34.622 34.135 34.800 30.870 34.984
34.793 37.759 38.649 38.044 37.013 37.074 36.497 37.244 33.544 37.421
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Fig. 4. Lowest error values for single phase to ground fault. Estimation error at fault resistance of (a) 0.05 and (b) 25 .
Fig. 6. Lowest error values for two phases to ground fault. Estimation error at fault resistance of (a) 0.05 and (b) 25 .
Fig. 5. Lowest error values for phase to phase fault. Estimation error at fault resistance of (a) 0.05 and (b) 25 .
Fig. 7. Lowest error values for three phase fault. Estimation error at fault resistance of (a) 0.05 and (b) 25 .
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Highest errors were obtained in single phase fault tests, where the best performance methods are the proposed by Das [18] and Choi et al. [21]. According to tests these methods are not strongly influenced by distance from the substation node. In case of two phase faults in the four test situations presented in Figs. 5 and 6, those methods proposed by Das [18] and Girgins et al. [23] show good performance. Methods proposed by Warrington [11], Srinivasan and StJacques [13] and Das [18], are included in the best four in the two test fault resistances, presented in case of three phase faults. All methods here presented are defined to locate single phase faults. The errors obtained for this type of faults are always bigger than the obtained from the other fault types. The method with the best global performance is the proposed by Das [18], however simple approaches as those proposed by Warrington [11] and Novosel et al. [17] are also well suited to solve the fault location problem. 8. Conclusions This paper presents some of the most cited impedance based methods for fault location in distribution systems. The methods use the fundamental component of voltage and current measured at one terminal (substation) of the distribution line. Those methods were analyzed and tested under the same situations by using a data of simulated power distribution system as a benchmark. According to the tests, the method with the best global performance is the one proposed by Das. The model used in this approach fits better the type of line and load of the substation (in fact the same author tested the algorithm in the same benchmark) and also takes into account the fact that tapped loads and laterals exist in the line. However, simple approaches as those proposed by Warrington and Novosel are also well suited to solve the fault location problem. On the other hand, from the point of view of the utility the development of complex models can be considered as drawback to deploy those methods in a real environment. The availability of data, i.e. frequently only serial parameters are available in the distribution substations, and the variability of operating conditions of those lines, i.e. loads, configuration, etc., make difficult to implement complex methods that depend on a set of variable parameters. It is also well known that simplified models are commonly accepted in steady state studies in distribution systems. Considering that a steady state estimator is used to determine the rms value of currents and voltages, a simplified line model used in distribution systems is not supposed to introduce considerable errors. This is also reflected in the low error rates obtained by the majority of the methods with independence of the type of model used. Since all the methods here considered are based on the same concept (impedance estimation) similar, and quite good, results are obtained. However, the main problem of these methods is the dependency with a model (line parameters and configuration is needed) and the multiple estimation problem of the fault location point, due to the presence of laterals that makes possible that the estimated reactance match with different nodes in those laterals.
665
Finally, recent research works present the advantages of the integration of these impedance-based methods with other knowledge-based techniques to reduce the model dependency and the multiple fault location estimation problem. This is a new research area, strongly motivated by the electric open market and the power continuity indexes. References [1] C. Gellings, Power delivery system of the future, IEEE Power Eng. Rev. 22 (12) (2002) 7–12. [2] C. Crozier, W. Wisdom, A power quality and reliability index based on customer interruption costs, IEEE Power Eng. Rev. 19 (4) (1999) 59–61. [3] R. Dugan, D. Brooks, T. McDermott, A. Sundaram, Using voltage sag and interruption indices in distribution planning, in: Power Engineering Society 1999 Winter Meeting, IEEE, vol. 2, 1999, pp. 1164–1169. [4] T. Takagi, Y. Yamakoshi, J. Baba, K. Uemura, T. Sakaguchi, A new algorithm of an accurate fault location for EHV/UHV transmission lines: Part—Fourier transform method, IEEE Trans. Power Syst. Apparatus 100 (1981) 1316–1323. [5] G.B. Ancell, N.C. Pahalawaththa, Maximum likelihood estimation of fault location on transmission lines using travelling waves, IEEE Trans. Power Deliv. 9 (1994) 680–689. [6] S. Lee, M. Choi, S. Kang, B. Jin, D. Lee, B. Ahn, An intelligent and efficient fault location and diagnosis scheme for radial distribution systems, IEEE Trans. Power Deliv. 19 (2) (2004) 524–531. [7] F.H. Magnago, A. Abur, A new fault location technique for radial distribution systems based on high frequency signals, in: Power Engineering Society Summer Meeting, 1999. [8] D.W. Thomas, R.J. Carvalho, E. Pereira, Fault location in distribution systems based on travelling waves, in: Power Tech Conference Proceedings, 2003. [9] X. Zeng, K.K. Li, Z. Liu, X. Yin, Fault location using travelling wave for power networks, in: Industry Applications Conference, 39th IAS Annual Meeting, 2004. [10] J. Zhu, D. Lubkeman, A. Girgis, Automated fault location and diagnosis on electric power distribution feeders, IEEE Trans. Power Deliv. (1997) 801–809. [11] A. Warrington, Protective relays, their theory and practice, Chapman and Hall, V2 London, 1968. [12] M.H. Bollen, Understanding Power Quality Problems, Voltage Sags and Interruptions, IEEE Press, NY, 2000. [13] K. Srinivasan, A. St-Jacques, A new fault location algorithm for radial transmission lines with loads, IEEE Trans. Power Deliv. (1989) 1676–1682. [14] L. Yang, C. Springs. One terminal fault location system that corrects for fault resistance effects, US Patent number 5,773,980 (1998). [15] R.K. Aggarwal, Y. Aslan, A.T. Johns, An interactive approach to fault location on overhead distribution lines with load taps, in: IEE Developments in Power System Protection, 1997, pp. 184–187 (Conference Publication No. 434). [16] M. Shadev, R. Agarwal, A technique for estimating transmission line fault locations from digital impedance relay measurements, IEEE Trans. Power Deliv. 3 (1) (1998) 121–129. [17] D. Novosel, D. Hart, J. Myllymaki, System for locating faults and estimating fault resistance in distribution networks with tapped loads, US Patent number 5,839,093 (1998). [18] R. Das, Determining the locations of faults in distribution systems, Doctoral thesis. University of Saskatchewan, Saskatoon, Canada, 1998, 206 p. [19] R. Das, M. Shadev, T. Shidu, A technique for estimating locations on shunt faults on distribution lines, in: Conference Proceedings. IEEE WESCANEX, vol. 1, 1995, pp. 6–11. [20] M. Saha, E. Rosolowski, Method and device of fault location for distribution networks, US Patent number 6,483,435 (2002). [21] M.S. Choi, S. Lee, D. Lee, B. Jin, A new fault location algorithm using direct circuit analysis for distribution systems, IEEE Trans. Power Syst. (2004) 35–41.
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[22] P. Anderson, Analysis of Faulted Power Systems, The Iowa State University Press, 1973. [23] A. Girgis, C. Fallon, D. Lubkerman, A fault location technique for rural distribution feeders, IEEE Trans. Ind. Appl. 26 (6) (1993) 1170– 1175. [24] A. Gole, J.A. Martinez-Velasco, A.J.F. Ken, Modelling and Analysis of System Transients Using Digital Programs, IEEE PES Special Publication, TP-133-0, January 1999. [25] H.W. Dommel, EMTP Theory Book, second ed., Microtran Power System Analysis Corporation, Vancouver, BC, 1992. [26] J.B. Dagenhart, The 40-ground-fault phenomenon, IEEE Trans. Ind. Appl. 36 (1) (2000) 30–32. J. Mora-Fl´orez received his B.Sc. in electrical engineering from Industrial University of Santander (UIS), Colombia in 1996, M.Sc. in electrical power from UIS in 2001, Ph.D. from University of Girona, Spain in 2006. He is currently professor of the Electrical Engineering School at the Technological University of Pereira, Colombia, member of ICE3 research group on Power Quality and
System Stability (Col) and eXit group of Control and Artificial Intelligence (Sp). Interest areas: power quality, transient analysis, protective relaying and artificial intelligence. J. Mel´endez obtained his BSc in Telecommunication Engineering at the Universitat Polit`ecnica de Catalunya (UPC, Spain) in 1991 and the Ph.D. degree in Engineering by the Universitat de Girona (UdG) in 1998. Titular professor UdG. Interest areas: power quality, knowledge-based techniques for fault detection, diagnosis and supervision of industrial processes and its application to real process. G. Carrillo-Caicedo received his B.Sc. in electrical engineering from Industrial University of Santander (UIS), Colombia in 1978; M.Sc. of engineering from Rensselaer Polytechnic Institute, USA in 1981; Research Specialist from Technological Investigation Institute of the Universidad Pontificia Comillas (UPCO), Spain in 1994; PhD from UPCO, Spain in 1995. Laureate Titular Professor UIS. Interest areas: electric energy markets, ancillary services, power quality and technological management.
Electric Power Systems Research 78 (2008) 657–666
Comparison of impedance based fault location methods for power distribution systems J. Mora-Fl`orez a,∗ , J. Mel´endez b,1 , G. Carrillo-Caicedo c,2 a
b
Electrical Engineering School, Technological University of Pereira (UTP), La Julita, Pereira, Colombia Electronics, Computer Engineering and Automatics Department, University of Girona (UdG), EPS, Campus Montilivi, 17071 Girona, Spain c Electrical Engineering School, Industrial University of Santander (UIS), Cra 27-Cll 9, Bucaramanga, Colombia Received 20 May 2006; received in revised form 1 March 2007; accepted 16 May 2007 Available online 20 July 2007
Abstract Performance of 10 fault location methods for power distribution systems has been compared. The analyzed methods use only measurements of voltage and current at the substation. Fundamental component during pre-fault and fault are used in these methods to estimate the apparent impedance viewed from the measurement point. Deviation between pre-fault and fault impedance together with the system parameters are used to estimate the distance to the fault point. Fundamental aspects of each method have been considered in the analysis. Power system topology, line and load models and the necessity of additional information are relevant aspects that differentiate one method from another. The 10 selected methods have been implemented, tested and compared in a simulated network. The paper reports the results for several scenarios defined by significant values of the fault location and impedance. The estimated error has been used as a performance index in the comparison. © 2007 Elsevier B.V. All rights reserved. Keywords: Fault location; Impedance based methods; Power distribution systems; Power quality
1. Introduction Power quality requirements resulting from the deregulated electrical markets have motivated the improvement of fault location methods in distribution systems to speed up the restoration process [1]. Faults and outages affect power quality in terms of service continuity and disturbance propagation. Utilities are forced to improve quality indexes associated to these phenomena in order to be competitive in the current electric open market [2,3]. With this aim, several strategies for fault location in distribution systems have been developed. Some methods have been adapted from of those proposed for fault location in transmission systems, i.e. high frequency component based methods (e.g. [4]) or those that analyze travelling waves (e.g. [5]), but considering the specificity of distribution systems (single end measurements, radial operation, etc.). ∗
Corresponding author. Tel.: +57 6 3137329; fax: +57 6 3137329/3137122. E-mail addresses: [email protected] (J. Mora-Fl`orez), [email protected] (J. Mel´endez), [email protected] (G. Carrillo-Caicedo). 1 Tel.: +34 972 418391; fax: +34 972 418391. 2 Tel.: +57 7 6344000; fax: +57 7 6344000. 0378-7796/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2007.05.010
For example in [6] high frequency components from travelling waves are analysed using wavelets in order to deduce the fault. In [7] correlation analysis between transmitted and reflected waveform is performed, whereas in [8] peak detection on the reflected waveform is used to identify possible fault locations base on the delays estimated. A drawback of these methods is the necessity of measuring devices with a very high sampling rate (MHz). On the other hand, impedance based methods works on steady states values of currents and voltages during the fault to estimate an apparent impedance (or reactance) that is directly associated to a distance to the fault. The main drawback of impedance-based methods is the multi-estimation due to the existence of multiple possible faulty points at the same distance. Difficulties in developing effective fault location methods in distribution systems are due to the radial topology, the existence of short and heterogeneous lines and also a lower degree of instrumentation of these systems. Therefore, the join exploitation of available information has to be considered. Registers of voltage and current at substation must be complemented with additional knowledge to assist fault location procedure in distribution. Three different, but complementary, sources of
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knowledge can be distinguished: system knowledge, data history and external information. System knowledge is necessary to build models. These models allow checking the consistency between the impedance calculated, from measured voltages and currents, and the nominal one. On the other hand, data history allows analyzing the relevance of waveform attributes and frequency of occurrence. The observation of, previously registered, similar behaviours may be used to infer possible location according to probabilistic models, e.g. [9,10]. Finally, external information as weather, existence of construction sites, consumer calls and so on, can be very useful to delimitate a searching area. Despite the benefit of dealing with these three complimentary views of the fault, in this paper we have focused on those methods that exploit system knowledge for fault location. Ten methods based on the impedance calculation from measures of voltage and current in a single point have been compared. The use of currents and voltages for fault location is described in the early literature as the reactive component method [11]. A simplified model of the feeder, equivalent to the voltage divider model used in [12], is used to explain the dependence of sag magnitude on the distance to the fault. These simple models differ in the availability of currents (in the reactive component method) or in the necessity of the source/transformer impedance (in the voltage divider model) to compute the equivalent impedance. The nine additional methods analyzed in this paper are improvements of this simple approach to cope with the complexity (radial topology, heterogeneity of lines and variety of loads) of distribution networks. Also the uncertainty, in the estimation of the distance to the fault, caused by the unknown value of fault resistance is treated in these models under different assumptions. Srinivasan and St-Jacques [13] proposed one of the first algorithms considering the existence of loads in a radial transmission system. Yang and Springs [14] propose a fault location method which corrects the fault resistance effects while Aggarwal et al. [15,16] propose a methodology based on the analysis of the superimposed components. The methodology proposed by Novosel et al. [17] focus on the idea applied for short transmission lines with loads and laterals represented by a lumped parameter impedance model placed behind the fault. Zhu et al. [10] model loads as an injected current and they analyze current patterns for fault location. In Das [18,19] first, the faulted section is located and next the distance to the fault in this section is calculated. It considers laterals and load taps. The method proposed by Saha and Rosolowski [20] estimates the fault location by comparing the measured impedance with the calculate feeder impedance assuming faults each section line. Finally, Choi et al. [21] differs from the previous approaches because refuses to apply the classical symmetrical component theory [22] to analyze unbalanced power systems. The paper presents in Section 2 the signal processing requirements of each method. Next, in Section 3, the power system assumptions required in the methods are compared. In Section 4 we analyze the requirements from the point of view of line section model. The load modelling and the necessity of additional information is reviewed in Sections 5 and 6, respectively.
Finally last two sections are devoted to test the algorithms in benchmark and conclude about its performance. 2. Fundamentals of the methods 2.1. General methodology The nominated methods use the distribution system parameters and combinations of pre-fault, fault and post-fault values of current and voltage, measured at fundamental frequency on a single line end; typically at the substation. Pre-fault values are used to estimate the initial conditions of the power circuit before the fault. Fault values are used as known values in a set of equations where both, the distance from the measurement point to the fault location and the fault resistance are the unknown variables. From the 10, only [10] uses post-fault values of current or voltage to reduce the multiple estimation problem induced by the existence of multiple fault points in the network with the same impedance. The method proposes the identification of patterns of the disturbance waveform with the operation of protective devices as well as changes in substation load. 2.2. Treatment of measurements All methods considered in this paper use the fundamental rms values of voltage and current measured at the substation. Pre-fault and fault values of these variables are used in [9,13,17,18,23] to estimate the load parameters while [14,16], only make use of the rate of change between pre-fault and fault voltage and current rms values. Others as the reactive component method [11] and a recent approach proposed in [21], do not use the pre-fault measurements. Faulted circuit analysis is performed by symmetrical component analysis in [13,14,17,18,23,24], while approaches presented in [10,14–16] use phase voltage and current vectors to perform a direct circuit analysis. 3. Distribution system topology The most important aspects considered by fault location methods are directly related to the characteristics of distribution systems: (a) Heterogeneity of feeders given by different size and length of cables, presence of overhead and underground lines, etc. (b) Unbalances due to the untransposed lines and by the presence of single, double and three phase loads. (c) Presence of laterals along the main feeder. (d) Presence of load taps along the main feeder and laterals. These aspects introduce errors in the estimation of the fault locations performed by means of a simplified model. Its reduction has motivated the majority of approaches compared in this paper. Heterogeneity of distribution lines could be considered in [10,14,15,17,18,23,24] since these algorithms consider the analysis of each section line independently.
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Fig. 1. Power distribution system.
VR IR,S
= T (x)
VS IS,R
⎡
⎤ −Zc sinh(λx) VS ⎦ IS,R −1
1 = ⎣ sinh(λx) Zc
Fig. 2. Faulted section line. Single phase to ground fault.
The methods presented in [10,15,18,23,24] consider the presence of laterals. In such methods loads on laterals are lumped at the node in the radial system. Thus, the system depicted in Fig. 1 (with a fault in F) will be modified by lumped loads in nodes X − 1 and N − 1. A detailed model between nodes X and X + 1 is presented in Fig. 2. The presence of load taps is considered in the majority of methods except in those that use simplified models as [11,14]. 4. Line section model The analyzed methods propose different line models according to its length, existence of mutual impedance and loads. Long line models are used in [13,18,19] while the others ([11,14–17,21,23,24]) assume short line models. A distributed parameter model is used in [13]. The classical transmission matrix T(x) is used to obtain the voltages and currents at the receiving end (VR and IR,S ), from the values at the sending end (VS and IS,R ) as it is represented in (1). A simplified version of this model is adopted by [18,19] to model short lines. This model, represented in (2), is used to perform an initial estimation of the distance to the fault in the method. VR VS = T (x) IR,S IS,R ⎡ ⎤ cosh(λx) −Zc sinh(λx) VS ⎦ = ⎣ sinh(λx) (1) IS,R − cosh(λx) Zc
(2)
Lumped parameters used in the short line models differ from one model to other. The method proposed in [15,16] considers the classical matrix impedance model (see (3)). The same model is used in [21] while in [11] only the series impedance of the line is considered. The approach of [14] also considers only the series impedance but it is decomposed on symmetrical components ⎡
VRa
⎤
⎡
VSa
⎤
⎡
Zs
⎢ ⎥ ⎢ ⎥ ⎢ ⎣ VRb ⎦ = ⎣ Vba ⎦ − ⎣ Zm VRc VSc Zm
Zm
Zm
⎤⎡
ISRa
⎤
Zs
⎥⎢ ⎥ Zm ⎦ ⎣ ISRb ⎦
Zm
Zs
(3)
ISRc
Resistance and reactance is needed to model each line section in the methods [18,19]. An impedance matrix, Zabc , allowing mutual coupling among phases, is considered in the iterative algorithm proposed in [10,23] (see Fig. 1). In a similar way the method proposed in [17] considers the matrix, Zabc , with mutual and self parameters to model the section line. A priori, the selection of an appropriate model seems to have influence on the fault location results. Thus, long lines have to be modelled by considering all the capacitive and inductive effects whereas simpler models (only serial parameters) could be used to describe short lines. However, the heterogeneity (multiple sections of different types of lines, gauges and lengths) of distribution lines makes inefficient to combine multiple models in the fault location strategy. In fact methods for fault location never consider combination of models and the election of one or another is directly tied to how the fault location method operates. Therefore, when a line typology can be clearly identified this could be used as criteria to select the fault location method based on the consideration that a better description of the system obtained. Instead of this, in this work we have compared all the algorithms, with the line model associated, in the same system and the results show no great differences that could be assigned to modelling errors.
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5. Load modelling Fault current is much greater than load current and its magnitude is limited by the transformer. Moreover loads vary and it is difficult to know its exact value at specific time (fault instant). These considerations are commonly argued to work with simplified models as the voltage divider. However, some location methods consider the presence of loads in its models in order to reduce uncertainty in the system and improve the location. The methods presented in [17,21,23,24] consider a constant impedance load model, obtained from steady state conditions. In [17] all loads, including tapped lines are modelled by lumpedparameter impedance placed behind the fault (Zload in (4)). This way of compensating tapped loads is accepted as tapped load impedances are much larger than feeder impedance. The method is based on the calculation of source and load impedance from voltages and current measured at substation and using the positive sequence values (Vpfl and Ipfl ) in pre-fault and considering the typology of the fault. Zl1 is the pre-fault positive sequence line impedance. Zload =
Vpfl − Zl1 Ipfl
(4)
Another proposal of constant load modeling is presented in [14] where it is used a matrix composed by constant impedances. The load impedance matrix Znabc at node N is given by (5). ⎤ ⎡ Znaa Znab Znac ⎥ ⎢ Znabc = ⎣ Znba Znbb Znbc ⎦ (5) Znca
Zncb
Zncc
Methods presented in [10,13,15,16,18,19] propose load models that vary according to the current and voltage, as presented below. Methods proposed in [13,18,19] perform a load flow to determine the constants of the static load model at node N resulting a model as Eq. (6). Vn is the voltage at node N; Yn is the load admittance; Gn , and Bn are the conductance and susceptance; and np and nq are constants for the active and reactive load components. In [15,16] load taps are considered by assuming a model which depends on the node voltage Vn , the power factor Pf and the load type (k = 1 for single phase loads and k = 3 for three phase loads). The load model is presented in (7). Yn = Gn |Vn |np−2 + jBn |Vn |nq−2
(6)
−1
(7)
Zn = kVn ∠cos
(Pf )
A similar load model is presented in [10], where the fault distance method calculates the remote-end current infeed using a radial power flow algorithm, which uses the current-injectionbased load model presented in (8).
Vn np−2
Vn nq−2
In = Irn
+ jIin
(8) V0n
V0n
where V0n is the nominal voltage, Irn and Iin are the active and reactive components at the nominal current at node N, respec-
tively. np and nq are the composite components, reflecting the dynamic response of the customer load at N. The same consideration made in the previous section is applicable with the load model. The more appropriate the load model we use the better the accuracy in the estimation of fault location. However, is difficult to know instantaneous load in the instant of faults. This is why the majority of fault location methods consider constant impedance models or impedance voltage dependent models. The last allows taking into account both, the level of load at the fault instant and the type of load, using appropriate exponents (np, nq). Consequently, the use of these second type of loaf model offers a major adaptability of fault location methods for lines operating with different loads through time (day/night, seasons and so on). 6. Additional information Method proposed by Zhu et al. [10] uses probabilistic modelling and analysis of current patterns to improve the selection of the fault regions. Based on the sequence of events extracted from the waveforms and its relation with protective device settings and actuation, it is possible to isolate the fault. This procedure is used to reduce the number of possible fault location; problem known as “multiple estimation problem”. Method proposed by Das in [18,19] considers the use of software-based fault indicators located at the beginning of each tap. These are used to detect downstream faults irrespective or their location and so to solve the multiple estimation problem. The solution proposed by these two methods could also be implemented, as a diagnosis improvement in the other methods. Methods not mentioned above only use the system parameters and the pre-fault and post-fault values of current and voltage. Finally, most of the considered methods need to know the involved phases and the fault type. However, the method proposed by Aggarwal et al. [15] performs the fault location without using this information. Table 1 summarizes the main aspects of the comparison. 7. Test of the fault location methods Considering that all methods use real measurements then the internal model used by each method to locate the fault should reflects the real behaviour of the power system to have high precision rates. According to, there are two aspects to be considered. One of them is related to the characteristics of the distribution system where simplified models are commonly accepted in steady state studies. Considering that a steady state estimator is used to determine the rms value of currents and voltages used in the analyzed fault location methods, a simplified line model used in distribution systems is not supposed to introduce considerable errors. The second aspect is related to the availability of data, because frequently at most of the distribution substations, it is only possible to obtain the characteristics of the conductors (self resistance and inductance), and the characteristics of the standard structures. So no much information is available and considering that
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Table 1 Summary of the main aspects of the analyzed fault location methods Analyzed aspect
Fault location method Warrington [11]
Fault detection and – identification Signal processing RMS of voltage and current Pre-fault – √ Fault Pos-fault – √ Symmetrical components Phase components –
Srinivasan et al. [13]
Girgins et al. [23]
Zhu et al. [10]
√
√
√ √
√ √
– √
– √
√ √ √
–
–
–
Aggarwal et al. [15,16] √
Das [18,19]
Novosel [17]
Yang and Springs [14]
Saha and Rosolowski [20]
Choi et al. [21]
√
√
–
–
–
√ √
√ √
√ √
√ √
√ √
– √
–
– √
– √
– √
– √
–
–
–
–
–
–
–
√
√
Short Z = f(V) √ √ √ √
Long Z = f(V) √ √ √ √
Short Z = cte – – – –
Short – – – – –
Short Z = cte √
–
SBFI
–
–
–
Distribution system Line model Load model Non homogeneity Unbalanced System Laterals Load taps
Short – – – – –
Long Z = f(V) – – – √
Short Z = cte √ – √ √
Short Z = f(V) √ √ √ √
Additional information
–
–
–
PM, CP
– √
– – √
Short – √ √ – √ –
PM: probabilistic modeling. CP: current patterns. SBFI: software based fault indicators.
there is a high number of power distributions substations, the development of a complex model is not a easy and low cost task for the utility. In the specific case of the impedance based fault location methods, several aspects are interrelated and these methods were tested as these are proposed by the authors. The consideration of the variation of only one of these aspects (line model, load model, line homogeneity, and so on), is out of the scope of this paper. That is the reason for testing the analyzed methods by using the same power distribution system as it is presented in this section. Tables reflect the behaviour of
each one of the fault location methods, considering the same comparison situations and the algorithms proposed in each approach. 7.1. Benchmark and scenarios The model of a 25 kV power distribution system from Saskpower, Canada, proposed in [17] has been used to test the fault location algorithms in order to compare its performance. The system is depicted in Fig. 3. It has a non homogeneous main feeder with laterals and load taps. Tables 2 and 3 present
Table 2 System line data Section
1–2 2–6 6–7 7–8 8–9 9–10 10–11 6–12 8–13 13–14 13–15 15–16 15–17 9–18 18–19 18–20 20–21
Length (km)
2.414 16.092 4.023 5.150 2.414 4.506 2.414 2.414 2.414 2.414 2.414 2.414 2.414 2.414 2.414 3.219 3.219
Series impedance (/km)
Shunt admittance (Mhos/km)
±sec
Zero sec
±sec
Zero sec
0.3480 + j0.5166 0.3480 + j0.5166 0.3480 + j0.5166 0.5519 + j0.5390 0.5519 + j0.5390 0.5519 + j0.5390 0.3480 + j0.5166 0.3480 + j0.5166 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998
0.5254 + j1.704 0.5254 + j1.704 0.5254 + j1.704 0.7290 + j1.727 0.7290 + j1.727 0.7290 + j1.727 0.7290 + j1.727 0.7290 + j1.727 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998 7.3977 + j0.8998
j3.74E−6 j3.74E−6 j3.74E−6 j3.59E−6 j3.59E−6 j3.59E−6 j3.74E−6 j3.74E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6
j2.49E−6 j2.49E−6 j2.49E−6 j2.39E−6 j2.39E−6 j2.39E−6 j2.49E−6 j2.49E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6 j2.51E−6
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Fig. 3. 25 kV power distribution system from Saskpower, Canada.
the system data. The system has been modelled using Alternative Transients Program—ATP [24,25]. The scenarios considered in this paper simulate faults at 10 nodes (from 2 to 11) of the main feeder with three different values of the fault resistance (0.05, 5, and 25 ). These are representative values commonly used in this type of tests [26]. For these situations performance of algorithms have been tested for both phase to phase faults and phase to ground faults involving one, two or three phases. In methods where mutual coupling is considered, as those presented in [10,15], the mutual impedance values were assumed equal to zero. Finally the multiple estimation problem was not considered in the test, since this paper is oriented to compare the distance estimation performance of the analyzed methods. Table 3 System load data Node number
1 2 6 11 12 14 15 16 17 18 19 21
Phase
A A B A,B,C A,B,C B B B B C C C
Connected size (kVA)
Composition [%] Heating
Lighting
Motor
15.0 15.0 15.0 1000.0 67.5 15.0 15.0 7.5 15.0 25.0 15.0 15.0
99.8 99.8 99.8 0.1 99.8 99.8 99.8 99.8 99.8 99.8 99.8 99.8
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.1 0.1 0.1 99.8 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
In Tables 4–6 the results for single phase to ground tests are presented. 7.2. Comparative results The distance estimation error, its dependency with the fault location and the fault resistance, has been used to compare the analysed methods. Distance estimation error is calculated according to (9) e (%) =
estimated location − actual location × 100 length of distribution feeder
(9)
For single phase to ground faults and according to Tables 3–5 the boundaries for the estimation errors are −13.63% and 10.89%. To have a good visualization only the four fault location techniques which have lowest error are presented in Fig. 4(a and b), for fault resistances of 0.05 and 25 . In the test of phase to phase faults, the methods perform quite similar with errors between −3.61% and 6.45%. In Fig. 5(a and b) the four best techniques are presented for fault resistance of 0.05 and 25 . The methods proposed by Srinivasan and St-Jacques [13], Zhu et al. [23] and Choi et al. [21] do not consider two phase to ground faults. The estimation errors are in the interval (−1.11%, 6.52%). In Fig. 6(a and b) the four best techniques are presented for fault resistance of 0.05 and 25 . Finally, in case of three phase faults, the methods proposed by Zhu et al. [10], Aggarwal et al. [15,16], Choi et al. [21] and Girgins et al. [23], analyse this type of faults. In addition the method proposed by Aggarwal et al. [15,16] is only suitable if
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Table 4 Test results—single phase fault location through Rf = 0.05 Method
Warrington [11] Srinivasan et al. [13] Girgins et al. [23] Zhu et al. [10] Aggarwal et al. [15,16] Das [18,19] Novosel [17] Yang and Springs [14] Saha and Rosolowski [20] Choi et al. [21]
Faulted node and real distance from distribution substation (Node 1) [km] Node 2 (2.414)
Node 3 (6.437)
Node 4 (10.460)
Node 5 (14.483)
Node 6 (18.506)
Node 7 (22.529)
Node 8 (27.679)
Node 9 (30.093)
Node 10 (34.599)
Node 11 (37.013)
2.3984 2.4138 2.4138 2.4203 2.4453 2.410 2.3921 2.3909 2.4513 2.4131
6.367 6.438 6.4384 6.4513 6.4467 6.430 6.3781 6.3732 6.5555 6.4372
10.296 10.462 10.462 10.482 10.485 10.451 10.36 10.35 10.657 10.461
14.185 14.486 14.486 14.513 14.487 14.474 14.337 14.322 14.755 14.484
18.035 18.508 18.510 18.539 19.192 18.501 18.311 18.288 18.850 18.507
21.847 22.53 22.531 22.547 23.119 22.525 22.281 22.251 22.934 22.528
26.666 27.684 27.684 27.701 28.158 27.675 27.481 27.463 27.919 27.683
28.884 30.096 30.092 30.091 30.085 30.090 29.906 29.895 30.265 30.096
33.215 34.596 34.616 34.576 37.013 34.566 34.443 34.449 34.73 34.595
35.161 36.998 36.992 36.585 37.013 37.006 36.824 36.826 37.013 37.003
Table 5 Test results—single phase fault location through Rf = 5 Method
Warrington [11] Srinivasan et al. [13] Girgins et al. [23] Zhu et al. [10] Aggarwal et al. [15,16] Das [18,19] Novosel [17] Yang and Springs [14] Saha and Rosolowski [20] Choi et al. [21]
Faulted node and real distance from distribution substation (Node 1) [km] Node 2 (2.414)
Node 3 (6.437)
Node 4 (10.460)
Node 5 (14.483)
Node 6 (18.506)
Node 7 (22.529)
Node 8 (27.679)
Node 9 (30.093)
Node 10 (34.599)
Node 11 (37.013)
2.410 2.473 2.491 2.626 2.445 2.434 2.395 2.447 1.344 2.411
6.317 6.473 6.520 6.812 6.447 6.447 6.334 6.395 5.415 6.392
9.719 10.007 10.088 10.571 10.485 10.462 9.799 9.872 8.862 9.899
14.138 14.600 14.703 15.483 14.487 14.447 14.327 14.397 13.711 14.489
17.970 18.632 18.775 19.781 19.155 18.539 18.296 18.371 17.830 18.517
21.480 22.400 22.556 23.904 23.119 22.562 21.975 22.063 21.566 22.256
26.552 28.034 27.996 29.880 28.121 27.704 27.435 27.542 26.996 27.706
28.760 30.229 30.374 32.673 30.085 30.135 29.853 29.975 29.367 30.124
32.858 34.755 34.904 37.029 37.013 34.611 34.382 34.534 33.901 34.642
34.998 37.162 37.317 37.270 37.013 37.047 36.754 36.908 36.461 37.045
there are one or more healthy-phases. According to this method, the superimposed components of those healthy phases have a minimum the distance where the fault is located. In case of three phase fault (no healthy phases) this method is not suitable. The test performed using the others methods give an estimation errors band between −1.48% and 1.97%. In Fig. 7(a and b) the four best techniques are presented for fault resistance of 0.05 and 25 .
7.3. Result analysis One of the first aspects related to the presented results, is related to the clear influence of the fault resistance and distance between fault and measurement point. The higher the fault resistance and the distance to the fault, the bigger the estimation error.
Table 6 Test results—single phase fault location through Rf = 25 Method
Warrington [11] Srinivasan et al. [13] Girgins et al. [23] Zhu et al. [10] Aggarwal et al. [15,16] Das [18,19] Novosel [17] Yang and Springs [14] Saha and Rosolowski [20] Choi et al. [21]
Faulted node and real distance from distribution substation (Node 1) [km] Node 2 (2.414)
Node 3 (6.437)
Node 4 (10.460)
Node 5 (14.483)
Node 6 (18.506)
Node 7 (22.529)
Node 8 (27.679)
Node 9 (30.093)
Node 10 (34.599)
Node 11 (37.013)
2.850 2.736 2.816 1.521 1.260 2.417 2.423 2.636 −2.630 2.320
6.725 6.820 7.088 6.112 6.447 6.543 6.369 6.670 1.560 6.353
10.558 10.942 11.346 10.714 10.485 10.471 10.328 10.678 5.766 10.410
14.354 15.015 15.607 15.514 14.487 14.426 14.280 14.681 9.980 14.480
18.113 19.069 19.873 20.078 19.155 18.381 18.227 18.677 14.195 18.601
21.830 23.375 23.975 24.875 23.082 22.479 22.169 22.668 18.402 22.689
26.515 29.634 29.278 30.991 28.158 27.707 27.269 27.857 23.729 27.941
28.683 30.707 31.389 34.126 30.085 30.075 29.662 30.293 26.168 30.405
32.695 35.289 36.144 35.564 37.013 34.622 34.135 34.800 30.870 34.984
34.793 37.759 38.649 38.044 37.013 37.074 36.497 37.244 33.544 37.421
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Fig. 4. Lowest error values for single phase to ground fault. Estimation error at fault resistance of (a) 0.05 and (b) 25 .
Fig. 6. Lowest error values for two phases to ground fault. Estimation error at fault resistance of (a) 0.05 and (b) 25 .
Fig. 5. Lowest error values for phase to phase fault. Estimation error at fault resistance of (a) 0.05 and (b) 25 .
Fig. 7. Lowest error values for three phase fault. Estimation error at fault resistance of (a) 0.05 and (b) 25 .
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Highest errors were obtained in single phase fault tests, where the best performance methods are the proposed by Das [18] and Choi et al. [21]. According to tests these methods are not strongly influenced by distance from the substation node. In case of two phase faults in the four test situations presented in Figs. 5 and 6, those methods proposed by Das [18] and Girgins et al. [23] show good performance. Methods proposed by Warrington [11], Srinivasan and StJacques [13] and Das [18], are included in the best four in the two test fault resistances, presented in case of three phase faults. All methods here presented are defined to locate single phase faults. The errors obtained for this type of faults are always bigger than the obtained from the other fault types. The method with the best global performance is the proposed by Das [18], however simple approaches as those proposed by Warrington [11] and Novosel et al. [17] are also well suited to solve the fault location problem. 8. Conclusions This paper presents some of the most cited impedance based methods for fault location in distribution systems. The methods use the fundamental component of voltage and current measured at one terminal (substation) of the distribution line. Those methods were analyzed and tested under the same situations by using a data of simulated power distribution system as a benchmark. According to the tests, the method with the best global performance is the one proposed by Das. The model used in this approach fits better the type of line and load of the substation (in fact the same author tested the algorithm in the same benchmark) and also takes into account the fact that tapped loads and laterals exist in the line. However, simple approaches as those proposed by Warrington and Novosel are also well suited to solve the fault location problem. On the other hand, from the point of view of the utility the development of complex models can be considered as drawback to deploy those methods in a real environment. The availability of data, i.e. frequently only serial parameters are available in the distribution substations, and the variability of operating conditions of those lines, i.e. loads, configuration, etc., make difficult to implement complex methods that depend on a set of variable parameters. It is also well known that simplified models are commonly accepted in steady state studies in distribution systems. Considering that a steady state estimator is used to determine the rms value of currents and voltages, a simplified line model used in distribution systems is not supposed to introduce considerable errors. This is also reflected in the low error rates obtained by the majority of the methods with independence of the type of model used. Since all the methods here considered are based on the same concept (impedance estimation) similar, and quite good, results are obtained. However, the main problem of these methods is the dependency with a model (line parameters and configuration is needed) and the multiple estimation problem of the fault location point, due to the presence of laterals that makes possible that the estimated reactance match with different nodes in those laterals.
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Finally, recent research works present the advantages of the integration of these impedance-based methods with other knowledge-based techniques to reduce the model dependency and the multiple fault location estimation problem. This is a new research area, strongly motivated by the electric open market and the power continuity indexes. References [1] C. Gellings, Power delivery system of the future, IEEE Power Eng. Rev. 22 (12) (2002) 7–12. [2] C. Crozier, W. Wisdom, A power quality and reliability index based on customer interruption costs, IEEE Power Eng. Rev. 19 (4) (1999) 59–61. [3] R. Dugan, D. Brooks, T. McDermott, A. Sundaram, Using voltage sag and interruption indices in distribution planning, in: Power Engineering Society 1999 Winter Meeting, IEEE, vol. 2, 1999, pp. 1164–1169. [4] T. Takagi, Y. Yamakoshi, J. Baba, K. Uemura, T. Sakaguchi, A new algorithm of an accurate fault location for EHV/UHV transmission lines: Part—Fourier transform method, IEEE Trans. Power Syst. Apparatus 100 (1981) 1316–1323. [5] G.B. Ancell, N.C. Pahalawaththa, Maximum likelihood estimation of fault location on transmission lines using travelling waves, IEEE Trans. Power Deliv. 9 (1994) 680–689. [6] S. Lee, M. Choi, S. Kang, B. Jin, D. Lee, B. Ahn, An intelligent and efficient fault location and diagnosis scheme for radial distribution systems, IEEE Trans. Power Deliv. 19 (2) (2004) 524–531. [7] F.H. Magnago, A. Abur, A new fault location technique for radial distribution systems based on high frequency signals, in: Power Engineering Society Summer Meeting, 1999. [8] D.W. Thomas, R.J. Carvalho, E. Pereira, Fault location in distribution systems based on travelling waves, in: Power Tech Conference Proceedings, 2003. [9] X. Zeng, K.K. Li, Z. Liu, X. Yin, Fault location using travelling wave for power networks, in: Industry Applications Conference, 39th IAS Annual Meeting, 2004. [10] J. Zhu, D. Lubkeman, A. Girgis, Automated fault location and diagnosis on electric power distribution feeders, IEEE Trans. Power Deliv. (1997) 801–809. [11] A. Warrington, Protective relays, their theory and practice, Chapman and Hall, V2 London, 1968. [12] M.H. Bollen, Understanding Power Quality Problems, Voltage Sags and Interruptions, IEEE Press, NY, 2000. [13] K. Srinivasan, A. St-Jacques, A new fault location algorithm for radial transmission lines with loads, IEEE Trans. Power Deliv. (1989) 1676–1682. [14] L. Yang, C. Springs. One terminal fault location system that corrects for fault resistance effects, US Patent number 5,773,980 (1998). [15] R.K. Aggarwal, Y. Aslan, A.T. Johns, An interactive approach to fault location on overhead distribution lines with load taps, in: IEE Developments in Power System Protection, 1997, pp. 184–187 (Conference Publication No. 434). [16] M. Shadev, R. Agarwal, A technique for estimating transmission line fault locations from digital impedance relay measurements, IEEE Trans. Power Deliv. 3 (1) (1998) 121–129. [17] D. Novosel, D. Hart, J. Myllymaki, System for locating faults and estimating fault resistance in distribution networks with tapped loads, US Patent number 5,839,093 (1998). [18] R. Das, Determining the locations of faults in distribution systems, Doctoral thesis. University of Saskatchewan, Saskatoon, Canada, 1998, 206 p. [19] R. Das, M. Shadev, T. Shidu, A technique for estimating locations on shunt faults on distribution lines, in: Conference Proceedings. IEEE WESCANEX, vol. 1, 1995, pp. 6–11. [20] M. Saha, E. Rosolowski, Method and device of fault location for distribution networks, US Patent number 6,483,435 (2002). [21] M.S. Choi, S. Lee, D. Lee, B. Jin, A new fault location algorithm using direct circuit analysis for distribution systems, IEEE Trans. Power Syst. (2004) 35–41.
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[22] P. Anderson, Analysis of Faulted Power Systems, The Iowa State University Press, 1973. [23] A. Girgis, C. Fallon, D. Lubkerman, A fault location technique for rural distribution feeders, IEEE Trans. Ind. Appl. 26 (6) (1993) 1170– 1175. [24] A. Gole, J.A. Martinez-Velasco, A.J.F. Ken, Modelling and Analysis of System Transients Using Digital Programs, IEEE PES Special Publication, TP-133-0, January 1999. [25] H.W. Dommel, EMTP Theory Book, second ed., Microtran Power System Analysis Corporation, Vancouver, BC, 1992. [26] J.B. Dagenhart, The 40-ground-fault phenomenon, IEEE Trans. Ind. Appl. 36 (1) (2000) 30–32. J. Mora-Fl´orez received his B.Sc. in electrical engineering from Industrial University of Santander (UIS), Colombia in 1996, M.Sc. in electrical power from UIS in 2001, Ph.D. from University of Girona, Spain in 2006. He is currently professor of the Electrical Engineering School at the Technological University of Pereira, Colombia, member of ICE3 research group on Power Quality and
System Stability (Col) and eXit group of Control and Artificial Intelligence (Sp). Interest areas: power quality, transient analysis, protective relaying and artificial intelligence. J. Mel´endez obtained his BSc in Telecommunication Engineering at the Universitat Polit`ecnica de Catalunya (UPC, Spain) in 1991 and the Ph.D. degree in Engineering by the Universitat de Girona (UdG) in 1998. Titular professor UdG. Interest areas: power quality, knowledge-based techniques for fault detection, diagnosis and supervision of industrial processes and its application to real process. G. Carrillo-Caicedo received his B.Sc. in electrical engineering from Industrial University of Santander (UIS), Colombia in 1978; M.Sc. of engineering from Rensselaer Polytechnic Institute, USA in 1981; Research Specialist from Technological Investigation Institute of the Universidad Pontificia Comillas (UPCO), Spain in 1994; PhD from UPCO, Spain in 1995. Laureate Titular Professor UIS. Interest areas: electric energy markets, ancillary services, power quality and technological management.