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Fault Location in Distribution Systems Based on Smart Feeder Meters Fernanda C. L. Trindade, Student Member, IEEE, Walmir Freitas, Member, IEEE, José C. M. Vieira, Member, IEEE
Abstract--This paper proposes a fault location method based on smart feeder meters with voltage sag monitoring capability. The main idea is to explore voltage measurements from monitors placed in different buses of distribution systems to estimate the fault location. The estimation is achieved by relating the voltage deviation measured by each meter to the fault current calculated based on the bus impedance matrix, considering the fault in different points. In order to improve the method accuracy, the loads are represented by constant impedance models and included into the bus impedance matrix. The performance of the proposed method is demonstrated by using a real distribution system. Sensitivity studies results show that the method is robust since it has good performance for different values of fault resistance, quantity and location of smart meters. Index Terms--Fault location, power distribution, smart feeder meter, voltage measurement.
I. INTRODUCTION OTIVATED by the recent advances in communication and measurement systems, utilities have been seeking efficient solutions for improving distribution systems monitoring and automation. These advances include two-way communication of the meter, data management system and real-time access to information such as consumption, voltage sags, power outages etc [1], [2]. As a result, smart feeder and consumer meters can achieve potential applications beyond meter reading for billing purposes. For example, in [3], it is discussed the usage of feeder meters, which are installed in primary networks, as a cost effective solution for distribution monitoring and automation. An important potential application of those meters is related to fault management, since faults result in outages and lead to reliability and power quality problems such as voltage sags, temporary and sustained interruptions, and high operational costs. In this context, one of the main issues related to fault management are the fault location techniques [4] since reasonably high accuracy fault location schemes allow reducing costs and time for energy supply restoration. Traditionally, in distribution systems, fault location techniques are based on manual outage mapping using consumers calls, fundamental voltage and current components measured only at the substation and network electrical parameters. However, several methods have been recently proposed to take advantage of advanced metering systems. There are methods based on automated outage mapping [5], [6] or voltage sag source detection [7]-[10], which indicate a probable area (region) that may contain the faulted bus instead of pointing out a strict fault location. There are also invasive
M
This work was supported by FAPESP, CNPq and CAPES, Brazil. F. C. L. Trindade and W. Freitas are with the Department of Electrical Energy Systems, University of Campinas (UNICAMP), 13083-852, Brazil (e-mails:
[email protected],
[email protected]). J. C. M Vieira is with the Department of Electrical Engineering, Sao Carlos School of Engineering/USP, São Carlos 13566-590, Brazil (e-mail:
[email protected]).
methods, for instance in [11] the fault location method requires the injection of sinusoidal signals with two different frequencies into the faulted distribution line. Thus by using signal extraction techniques and mathematical processing, permanent single phase to ground faults can be located. Another class of methods uses the voltage and current measured at the substation, sparse voltage measurements and the network electrical parameters to estimate the fault location [12]-[14]. Their performance can be considerably affected by the fault resistance, and additional solutions are necessary in order to deal with this uncertainty. For instance, an iterative process dedicated to fault resistance estimation is used in [13]. Such additional techniques can increase the complexity of the fault location methods. In order to overcome some of the drawbacks observed in previous fault location methods and aggregate value to the smart feeder meters, this work proposes a robust fault location technique that explores the voltage sag measurement capability of these devices and fundamentals of the short circuit theory. Once a fault is detected and classified, the proposed method can be used to locate faults at the distribution system by using measurements from smart meters installed at the primary network. These smart feeder meters, which will be referred simply as "feeder meters" in this work, can be polled (triggered) every time a fault is detected to provide the information demanded by the proposed method under request [15]. Sensitivity study results have shown that the proposed method presents good performance for different values of fault resistance, quantity and location of feeder meters as well as measurement and load estimation errors. This paper is organized as follows. Section II presents the proposed method as well as a general view of how the feeder meters can be used to improve the fault location methods. Sections III to V provide simulation results and sensitivity analyses, respectively, to evaluate the performance of the proposed method. The method performance considering the presence of dynamic loads is presented in Section VI. Discussions about the proposed method compared to other related methods are shown in Section VII. Conclusions are given in Section VIII. II. PROPOSED FAULT LOCATION METHOD The proposed fault location method is based on the monitoring capability of feeder meters and short circuit theory. According to [15], several smart meter models are able to report outages as well as to measure voltage with an accuracy class that typically ranges from 0.1 to 0.5%. The main idea of the proposed method for fault location is to exploit such capability, so that the voltage sag information can be processed to calculate a fault location index, which indicates the bus closest to the fault point. Every time a fault is detected, the meters are polled to provide the voltage rms value just before and during the fault occurrence. In addition, in the results presented here,
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the voltage rms value was calculated by using a sampling rate 64 samples/cycle. The theoretical background of the method is presented as follows. By using the voltage magnitude measured by a feeder meter, it is possible to obtain the voltage deviation (V) as follows: Vi ( abc ) Vi
( abc ) p
Vi
( abc ) f
(1)
where the subscript i is related to a feeder meter installed at bus ( abc)
( abc)
f p i, Vi and Vi are the voltage magnitudes measured during and before the fault (pre-fault), respectively, and superscript abc represents each phase, so that one has the voltage deviation on phase a, b and c. If the bus k is under fault, one can estimate the fault current at each phase by using the voltage deviation determined by meter i based on the following expression:
abc ) Iˆ (fault Z ik( abc) ik
1
Vˆi ( abc)
(for i k )
(2)
where Z ik(abc ) is the ik 3x3 submatrix from the system three(abc ) phase bus impedance matrix Z bus , as discussed in the ( abc ) Appendix A, and Iˆ faultik is the fault current calculated by using
voltage measurement from meter i and considering a fault at bus k. Note that the loads, represented by constant impedance models, must be included into the bus impedance matrix to improve the method accuracy. In order to include the loads in the bus impedance matrix, all the loads are represented by constant impedance models. Then the equivalent shunt impedances associated to the bus are included at the matrix elements [16]. The load estimation can be done by using typical load curves or based on the information provided by smart consumer meters. The influence of the loads in method performance is analyzed in Section IV.A and in Appendix A. Therefore, if one has Nfm meters, there are Nfm estimated fault currents based on the assumption that the bus under fault is bus k. If the fault really occurred at bus k, all the estimated currents must have practically the same value, which is close to the real value. On the other hand, if the fault occurred at any other bus, there will be an error on the fault current estimated based on measurements from each meter i. In addition, the error obtained based on different meters will be distinct from each others. Based on the aforementioned explanation, a fault-location index δk can be used to identify the actual bus under fault. This index is given by the sum of the differences between the Nfm estimated fault current values taking into consideration that bus k is under fault and their average value (each difference is referred as dik), as shown in (3) and Fig. 1.
k
a ,b ,c N fm
Iˆ ph Iˆ ph faultik fault k ph i 1
ph where Iˆ fault
ik
a ,b ,c N fm
d ph i 1
ph ik
(3)
is the fault current calculated for phase ph with
measurements from the feeder meter at bus i using (2), and is the average of all the fault current values calculated Iˆ ph fault k
using the voltage measured at each feeder meter for bus k. As mentioned, if the bus under analysis is the faulted bus, all the
estimated currents will be practically the same. Thus, the bus associated with the minimum δk is selected as the faulted bus. Typically feeder meters supply only voltage magnitudes, however, in (2) and (3), currents are written as phasor quantities. In order to numerically calculate these expressions, it was assumed that phases a, b and c are simply shifted by 120°, although distribution systems are unbalanced. Note that such assumption was used only for calculation purposes. In the results presented in this paper, the system was unbalanced so that the phase currents are not really shifted by 120°, even so the proposed method shows good performance. The influence of this assumption is investigated in Section V. When only voltage magnitude is used, there is no need of synchronization; since all meters are simultaneously polled by the same fault event, decreasing the costs and complexity. For certain situations, numerically, the minimum δ may be associated with more than one bus k, indicating multiple estimation. In order to deal with such cases and improve the method performance, automated outage mapping can be used, as described in the following section. Iˆ fault2 k ˆI fault1 k d2
Iˆ faultk
d1
d4 d3
Iˆ fault4 k
Iˆ fault3 k Fig. 1 Illustration of the index δk meaning (Nfm = 4).
A. Automated Outage Mapping The communication among the feeder and consumer meters and the control center allows monitoring de-energized meters and, consequently, determining the part of the network that is de-energized. By incorporating data from the Geographic Information System (GIS), the outage mapping can speed up and automate the typical manual process of fault location, which depends on consumer calls. With smart meters one can automatically build the outage mapping by monitoring de-energized transponders. As a result, the chances of indicating a wrong bus as the faulted bus and multiple estimation occurrences can be minimized or even eliminated. An example of such application can be observed in the feeder of Fig. 2. In this system, if a fault occurs downstream the recloser R1 (fault 1), it will cause its opening and the feeder meters M3 to M6 would report the outage in Zone 1. Therefore, the fault location method could consider this information in order to decrease the search space as well as the chances of indicating the wrong bus as the faulted bus. In case of fault 2, if the fuse F3 blows, outage mapping would indicate a fault occurrence in an even reduced zone (Zone 2), since M3 would be the only meter to report the outage. The outage mapping can be combined with the proposed fault location method using two different approaches as follows: The first option consists in exploring the outage mapping to decrease the search space in fault location process. In
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this case, the computing demand is reduced. However, this alternative requires polling several meters in order to identify the affected zone, increasing the data traffic. The second option is based on applying outage mapping only in cases of multiple estimation, so that specific meters are polled in order to support the decision of which local refers to the affected one. In comparison to the first option, even though the whole feeder is used as the search space of the fault location method (increasing the computational effort), the data traffic is reduced. Regardless computational effort and data traffic, both options give the same results, and, in the following sections, the first option will be employed.
fault 2
M3
M6 Zone 2
F1 M1
F3
R1
F5
F2
F4
M5
fault 1 M4 M2 Zone 1
load update, for example, each 1 hour, or online each time a fault is detected by using the correspondent information. III. SIMULATION RESULTS In this section, base case results are presented to further explain and test the proposed method and the influence of the outage mapping. In the next section, a complete sensitivity study will be discussed to evaluate the method performance taking into consideration the impact of inaccurate load estimation, unknown fault resistance, inaccurate voltage measurements and variation of feeder meter quantity and location. The proposed fault location scheme was tested in a real, 13.8-kV distribution system shown in Fig. 3, which was obtained from [12] and [17]. All the data and distances are presented in Appendix B, including the impedance associated to each conductor. The voltage measurements at each feeder meter were obtained by using the Alternative Transients Program (ATP) simulations [18]. Each line section was modeled in ATP by using phase impedance matrices. Initially, the feeder meters were placed at the following buses: 3, 20, 30, 45, 51, 60, 100, 111, 118, 121, 127, 129, 134 (as shown in Fig. 3). This allocation was done arbitrarily without previous studies. In order to assess the results, an error index was defined as shown in (4), where the distances are obtained in relation to the substation. Error real fault distance calculated fault distance
Fig. 2 Distribution feeder outage mapping.
B. Method Guidelines The steps below summarize the method application after a fault has been detected: Step 1: Construct the bus impedance matrix (Zbus) (this step can be done offline). Step 2: Read the voltage deviation measurements from the feeder meters. abc) Step 3: Estimate the fault current Iˆ (fault of every bus in the ik
system by using the feeder meters measurements, the matrix Zbus and formula (2). abc) Step 4: Calculate the average fault current Iˆ (fault . k
Step 5: Calculate the fault current index δk for each bus k in the system by using formula (3). Step 6: Indicate the bus associated with the lowest δk value as the faulted bus. Step 7: If more than one bus (region) is pointed faulted bus, automated outage mapping can be used to solve the problem of multiple estimation. In Step 1, as discussed previously, it is necessary to include the loads represented by constant impedance models in the bus impedance matrix. This can be done by using typical loads curves, which give information about the load behavior in the time, or smart consumer meters, which report active and reactive powers each time interval. The bus impedance matrix can be built offline taking into consideration the interval of
(4)
The tests were conducted considering single-phase (phase A-to-ground) and three-phase faults. In case of single-phase faults, only the short circuit current of the faulted phase was used in the method. In addition, it was assumed that the fault has been already detected and classified since the proposed approach is related only with the fault location process. Unless otherwise specified, all the loads were modeled as constant impedances (in ATP simulations as well as in the proposed method). The faults were applied at each bus of the circuit, and the errors were calculated and grouped into classes, in order to simplify the results analyses. These error classes were divided from 0 to 400 m into intervals of 100 m, resulting in four classes. In addition, if the distance error is higher than 400 m, it is considered that the method has failed to locate the fault region. A. Results without Outage Mapping The results of the proposed method without the usage of outage mapping are presented in Table I. Single-phase and three-phase faults were considered, assuming fault resistance (Rf) values of 0.5 Ω and 10.0 Ω. The results show how many faulted buses could be grouped within each error class. For instance, in case of three-phase faults with fault resistance of 0.5 Ω, 82 buses selected as the buses under faulted ones were located within distance errors from 0 to 100 m, 38 buses were located from 100 to 200 m, 12 buses were located from 200 to 300 m and only 1 bus was located with distance error higher than 400 m. Moreover, the method has shown good performance since most of the errors are concentrated in the range from 0 to 100 m.
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Legend Symbols Meters (base case) Circuit Breaker Recloser Sectionalizer Fuse
Legend Conductor Type Blue #4/0 Green #1/0 Black #4 Red #2
Fig. 3 Distribution test feeder used for evaluating the fault-location algorithm (data are given in Appendix B). TABLE I In the next section, the fault location method robustness will NUMBER OF BUSES WITHIN EACH ERROR CLASS WITHOUT CONSIDERING be assessed by running several sensitivity studies. Unless OUTAGE MAPPING Error Classes 0-100 m 100-200 m 200-300 m 300-400 m > 400 m
Single-phase faults Rf = 0.5 Ω 62 57 12 2 -
Rf = 10.0 Ω 110 18 4 1 -
Three-phase faults Rf = 0.5 Ω 82 38 12 1
Rf = 10.0 Ω 109 18 5 1 -
B. Results with Outage Mapping The same cases presented in the previous subsection were analyzed in this subsection taking into consideration the outage mapping. As a result, the search space was reduced, decreasing the computing demand and also the chances of multiple estimation. For example, without using outage mapping, for a three-phase fault at bus 40 (Fig. 3), the algorithm indicates the bus 36 (120 m of distance from bus 40), while when outage mapping is considered, bus 40 was indicated correctly as the faulted bus. This happens because the search space is reduced to buses 40 to 45. The analysis of the results in Table II allows concluding that the results can be improved by using outage mapping. TABLE II NUMBER OF BUSES WITHIN EACH ERROR CLASS CONSIDERING OUTAGE MAPPING Error Classes 0-100 m 100-200 m 200-300 m 300-400 m > 400 m
Single-phase faults Rf = 0.5 Ω 85 41 6 1 -
Rf = 10.0 Ω 112 18 2 1 -
Three-phase faults Rf = 0.5 Ω 98 29 5 1 -
Rf = 10.0 Ω 110 19 3 1 -
otherwise specified, all the results are obtained using outage mapping and considering a fault resistance of 10.0 Ω as the base case. IV. SENSITIVITY STUDIES In this section several parameters and conditions were varied to further evaluate the proposed method. The sensitivity studies took into consideration: load estimation uncertainties, fault resistance, voltage measurement accuracy, quantity and location of feeder meters. A. Load Estimation Accuracy In the proposed method, the loads represented by constant impedances are considered to build the bus impedance matrix. Therefore, it is necessary to assess the influence of the load estimation accuracy on the method performance. To reach such a goal, all the loads represented in the bus impedance matrix were simultaneously varied and in the same proportion to simulate errors in the load estimation. The real load impedance was used in ATP simulations (ZATP), and this was the benchmark case. Then, in the proposed method, the load impedances were varied by a load factor ZZbus/ZATP, which assumed the following values: 80, 95, 105 and 120% of error on the load value for all loads. The results are presented in Table III. By comparing Table III and Table II, it can be concluded that errors in load estimation does not have a major impact on the method performance. B. Fault Resistance Typically, fault location methods are affected by the fault resistance, which influences the fault current value. In order to determine this influence on the proposed method, Table IV
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presents the results considering different fault resistance values. For the fault resistance values tested in this work, it can be observed that the proposed method performance is not deeply affected by the range of fault resistance values. Therefore, fault resistance uncertainty does not have a deep impact on the method accuracy. TABLE III IMPACT OF LOAD VALUE ESTIMATION ERRORS Error Classes
ZZbus/ZATP (%) 80
95
Single-phase faults 114 112 15 18 3 2 1 1 Three-phase faults 110 110 19 19 3 3 1 1 -
0-100 m 100-200 m 200-300 m 300-400 m > 400 m 0-100 m 100-200 m 200-300 m 300-400 m > 400 m
105
120
112 18 2 1 -
115 15 2 1 -
110 19 3 1 -
110 19 3 1 -
TABLE V IMPACT OF MEASUREMENT ERRORS Error Classes
Fault Resistance (Ω) 0.5
0-100 m 100-200 m 200-300 m 300-400 m > 400 m
85 41 6 1 -
0-100 m 100-200 m 200-300 m 300-400 m > 400 m
98 29 5 1 -
5.0
10.0
Single-phase faults 95 112 32 18 5 2 1 1 Three-phase faults 114 110 16 19 2 3 1 1 -
50.0
100.0
95 34 3 1 -
94 33 4 2 -
86 39 6 2 -
86 35 8 4 -
C. Voltage Measurement Accuracy Measurement errors may degrade the quality of the fault current estimation. Therefore it is necessary to analyze the method sensitivity to inaccuracies in voltage measurements. Errors can be caused by measurement noise or measurement device inaccuracy, and in this case the deviations are relatively small, lower than 1%, but likely to occur in all measurements. On the other hand, bad calibration can cause higher errors in a few devices. Thus, three cases were defined in order to study the impact of measurement errors in the proposed fault location method. These cases are described below and the results are presented in Table V. Case 1: addition of random noise (errors) to all measurements. As the noise addition is a random process, it is not possible to affirm that the presented result is unique. The noise is applied as follows. For each measured value, a random value RV is generated following a normal distribution with mean equal to zero and standard deviation of 0.5%. Then, the measured voltage value is multiplied by (RV + 1.0); Case 2: same situation of Case 1, but also considering that the voltage deviations measured by the feeder meters at buses 20 and 100 are multiplied by a factor of 1.15,
Case 1
Case 2
Single-phase faults 59 60 25 28 13 10 10 9 26 26 Three-phase faults 0-100 m 62 65 100-200 m 31 27 200-300 m 17 17 300-400 m 8 7 > 400 m 15 17 0-100 m 100-200 m 200-300 m 300-400 m > 400 m
TABLE IV IMPACT OF FAULT RESISTANCE VARIATION Error Classes
simulating bad calibration situations; Case 3: same situation of Case 1, but also considering that the voltage deviations measured by the feeder meters at buses 20 and 100 are multiplied by a factor of 0.85, simulating bad calibration situations; By comparing Table V and Table II (ideal condition without measurement errors) it is possible to conclude that errors in voltage measurement can decrease the method performance. However, the results are still acceptable since for most of the presented cases, the buses were located with distance errors equal or lower than 400 m. As a result, it must be pointed out that: the more accurate the voltage measurements, the better the method performance. This finding can be used to support the definition of the technical requirements of smart feeder meters and their communication system infrastructure.
Case 3 54 25 15 11 28 56 31 20 9 17
D. Feeder Meters Quantity and Location All the previous results had considered that voltage measurements were available from feeder meters installed in 13 out of the 134 buses of distribution system (i.e., about 10% of the total number of buses). The feeder meters quantity and location were chosen without previous studies. Since the proposed formulation is dedicated to the fault location through voltage measurements, it is reasonable to conclude that if more feeder meters are installed, more accurate results can be achieved. On the other hand, it is necessary to consider that the costs and the amount of data grow if the quantity of measurements increases. In this context, the method performance was assessed by using 10 and 5 feeder meters in the system of Fig. 3. For the case with 10 feeder meters, their respective locations are buses: 3, 20, 30, 60, 100, 111, 118, 127, 129 and 134; and for the case with 5 buses, they are: 3, 30, 100, 129 and 134. The results are presented in Table VI, where 13 feeder meters refer to the base case (Section III.B). It can be observed that the use of 5 meters did not degrade the quality of the solution significantly, since most of the buses were located with distance errors lower than 100 m. Therefore, the method is robust enough to cope with a reduced number of meters. This is an important characteristic since economical factors may limit the installation of feeder meters with voltage sag monitoring capability in distribution systems. The influence of the feeder meters placement was analyzed as well. The results for three scenarios considering different locations of 10 feeder meters are shown in Table VII. These
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scenarios are arbitrarily divided in: Case 1: feeder meters installed at buses 3, 20, 30, 60, 100, 111, 118, 127, 129 and 134; Case 2: feeder meters installed at buses 15, 25, 44, 56, 66, 85, 89, 102, 112 and 131; Case 3: feeder meters installed at buses 7, 36, 47, 66, 76, 84, 91, 104, 112 and 125. TABLE VI IMPACT OF DIFFERENT QUANTITIES OF VOLTAGE MEASUREMENTS Error Classes
Quantity of Smart Feeder Meters 13
10
5
Single-phase faults 0-100 m 100-200 m 200-300 m 300-400 m > 400 m 0-100 m 100-200 m 200-300 m 300-400 m > 400 m
112 114 18 16 2 2 1 1 Three-phase faults 110 107 19 22 3 3 1 1 -
92 30 1 4 6 61 32 16 12 12
It is possible to observe that the allocation of the meters has impact on the method performance, however, the performance is still acceptable. By analyzing the feeder meters location, preliminarily, one can conclude that when the voltage measurements are obtained at buses located at the end of the branches, such as in Case 1, the method presents better performance than when they are located in the main feeder and some main branches. Although it was not possible to find an analytical explanation for this, when the meters are located at the end of the branches, the voltage magnitude sensed by the meter is affected by the fault occurrence in different points of the system, since these faults will occur upstream from the meter location. Thus, the method will be sensitive to a higher number of fault locations.
Smart meters capable of measuring both voltage magnitude and phase angle are more complex and expensive due to the need of synchronization. However, in the future, this can be more common, thus, in this section, it is evaluated how the usage of angle information can improve the method performance. Therefore, considering that the feeder meters are capable of dealing with voltage phasors (magnitude and angle), instead of only magnitude, this section presents the performance of the proposed method considering such characteristic. The results are presented in Table VIII, where it can be observed that the algorithm performance was improved in comparison with Table II. Moreover, the performance was not affected by the different fault resistances: 0.5, 5.0, 10.0, 50.0 and 100.0 Ω. In this scenario, the immunity against fault resistance values represents an important advantage of the proposed method. It happens because all the indices δk vary with fault resistance practically with the same proportion. For instance, for a fault at bus 5 (Fig. 3), the values of δk for buses 1 to 10 are shown in Fig. 4 considering different fault resistance values. It can be observed that they change in the same proportion from one bus to another and as a result, the minimum is always associated to the same bus. TABLE VIII IMPACT OF VOLTAGE MAGNITUDE AND ANGLE MEASUREMENTS Without outage mapping
ThreeSingleThreeSinglephase phase phase phase faults faults faults faults 0-100 m 115 120 121 121 100-200 m 15 12 11 11 200-300 m 2 1 1 1 300-400 m 1 > 400 m Note: in this table, the results were the same for all the tested fault resistances. 0.2
0-100 m 100-200 m 200-300 m 300-400 m > 400 m
114 93 16 22 2 10 1 1 7 Three-phase faults 107 95 22 21 3 9 1 1 7
Rf =50.0
93 25 11 2 2
0.1 0.08 0.06 0.04 0.02 0
92 28 9 2 2
V. METHOD PERFORMANCE USING VOLTAGE PHASOR MEASUREMENTS The results presented in the previous sections have considered only the usage of voltage magnitude values to process the calculations in the proposed fault location method. The results have shown that the proposed method has a good performance even without information about the phase angles.
Rf =100.0
0.12 k
Case 3
Single-phase faults 0-100 m 100-200 m 200-300 m 300-400 m > 400 m
Rf =10.0
0.14
Indices
Case 2
Rf =5.00
0.16
Smart Feeder Meters Location Case 1
Rf =0.50
0.18
TABLE VII IMPACT OF FEEDER METERS ALLOCATION Error Classes
With outage mapping
Error Classes
1
2
3
4
5 6 Buses
7
8
9
10
Fig. 4 Values of the indices δk for a short-circuit in bus 5 and different fault resistances.
A. Sensibility to Voltage Measurement Accuracy The results from Section IV show that one of main factors affecting the method performance is the accuracy of voltage measurement. Therefore, Table IX presents the results considering voltage phasor measurements with outage mapping and random noise (errors) addition to all measurements according to Case 1, as described in IV.C. In addition, the random noises were included simultaneously in the voltage magnitude and angle. Again, one can see this is an
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important factor affecting the method performance. VI. METHOD PERFORMANCE CONSIDERING DYNAMIC LOADS Since all the loads are represented by constant impedance model, in this section, the method performance was studied considering the presence of an induction motor connected to bus 30. Table X shows the results for an induction motor of 100 HP and Table XI shows the results for an induction motor of 200 HP. Both set of results use voltage magnitude measurement. Table XII shows the results for an induction motor of 100 HP connected at bus 30 exploring phasor measurements. The results in this section show that the method performance is good even in presence of dynamic loads. TABLE IX IMPACT OF ERRORS IN PHASOR MEASUREMENTS Error Classes 0-100 m 100-200 m 200-300 m 300-400 m > 400 m
Single-phase faults Rf = 0.5 Ω 84 27 16 5 1
Rf = 10.0 Ω 73 40 17 2 1
Three-phase faults Rf = 0.5 Ω 103 21 6 3 -
Rf = 10.0 Ω 86 28 17 2 -
TABLE X NUMBER OF BUSES WITHIN EACH ERROR CLASS CONSIDERING OUTAGE MAPPING – MOTOR LOAD OF 100 HP Error Classes 0-100 m 100-200 m 200-300 m 300-400 m > 400 m
Single-phase faults Rf = 0.5 Ω 95 31 6 1 -
Rf = 10.0 Ω 103 25 4 1 -
Three-phase faults Rf = 0.5 Ω 99 28 5 1 -
Rf = 10.0 Ω 109 20 3 1 -
TABLE XI NUMBER OF BUSES WITHIN EACH ERROR CLASS CONSIDERING OUTAGE MAPPING – MOTOR LOAD OF 200 HP Error Classes 0-100 m 100-200 m 200-300 m 300-400 m > 400 m
Single-phase faults Rf = 0.5 Ω 99 26 5 3 -
Rf = 10.0 Ω 103 25 4 1 -
Three-phase faults Rf = 0.5 Ω 99 28 5 1 -
Rf = 10.0 Ω 109 20 3 1 -
TABLE XII NUMBER OF BUSES WITHIN EACH ERROR CLASS CONSIDERING OUTAGE MAPPING – MOTOR LOAD OF 100 HP – PHASOR MEASUREMENTS Error Classes 0-100 m 100-200 m 200-300 m 300-400 m > 400 m
Single-phase faults Rf = 0.5 Ω 114 17 2 -
Rf = 10.0 Ω 114 17 2 -
Three-phase faults Rf = 0.5 Ω 119 13 1 -
Rf = 10.0 Ω 119 13 1 -
VII. DISCUSSIONS In the Introduction, several methods of fault location based on automated metering systems were mentioned. They can be grouped into three main classes: (a) methods based on outage mapping; (b) methods based on voltage sag source detection; and (c) methods based on measurements at the substation and along the feeder. The methods presented in [12]-[14] and the method proposed in this paper can be classified as (c) methods
based on measurements at the substation and along the feeder. Thus, in this section, a short discussion is presented to compare the proposed method with the previous ones. For the proposed method, once the impedance matrix of the system is built, the computational effort is considerably lower than the method proposed in [12] since the proposed method is not iterative. Both methods require system parameters, however, the method proposed in [12] runs several load flows while the proposed one applies a simple equation. On the other hand, the advantage of the method proposed in [12] is that typically fewer meters are needed. The fault location method from [13] uses voltage phasors from sparse measurements along the feeder to locate the fault in distribution systems. The fault location process explores a short-circuit program, a technique for fault resistance estimation and another for load estimation. According to the authors, the method can precisely indicate the fault location and does not suffer from multiple fault location estimation imprecision. Because this method needs a stage for the estimation of fault resistance before its application, it is expected that the computational effort be higher and that the fault resistance values have more influence on the results than the proposed method. In addition, the method presented in [13] demands the usage of GPS information, which is not typically available in distribution systems. Finally, the method from reference [14] uses a formulation similar to the method proposed here, however in [14], it is proposed to estimate the fault current by measuring all the phasors of the currents injected in the system (substation and distributed generation, for example) and the total sum of the measured currents is assumed to be the fault current. After the estimation of the fault current value, the voltage deviation measured is compared to the calculated voltage deviation. The disadvantage of this method is that it needs synchronized measurements of voltage and current phasors at every distributed generator and at the substation, increasing the costs and complexities. VIII. CONCLUSIONS In this paper, the voltage measurement capability of feeder meters and the system bus impedance matrix were used to develop a robust fault location method. The main findings of this research are summarized below: If feeder meters with voltage sag measurement capability are available, the proposed fault location method can be easily applied due to its simplicity, increasing the aggregated value of such devices; The results have shown that the method is robust since it presented good performance when several parameters were varied, even for different fault resistance values; Automated outage mapping can improve the method performance by reducing the search space and the possibility of multiple estimation; The sensitivity studies showed that the method performance was satisfactory even with a reduced number of meters. This is an important finding since it may not be economically feasible to install many feeder meters in the distribution system. Some topics related to the proposed method require further investigation, such as the possibility of optimal placement of
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the feeder meters dedicated to the proposed fault location method, and the possibility of considering distributed generators, based on their representation in the bus impedance matrix. IX. APPENDIX A Different from traditional short circuit analysis, the proposed fault location method considers the loads in the construction of the bus impedance matrix. If the load is ignored in the proposed fault location method, the fault location index δk calculated for many different buses could assume the same value. Consequently, it would be challenging to identify the faulted bus. One illustrative example of this multiple estimation problem is shown below, based on a simple single phase distribution system presented in Fig. 5. 3 0
2
1 Z1
Z2
Z3
0
4
Z4 Z2
5 Z5
Fig. 5 Example of distribution system without representing the loads.
The bus impedance matrix Zbus, without considering the load impedances of the circuit shown in Fig. 5 is given by: Z1 Z1 Z bus Z1 Z1 Z1
Z1
Z1
Z1 Z 2 Z1 Z 2 Z1 Z 2 Z1 Z 2 Z 3 Z1 Z 2
Z1 Z 2
Z1 Z 2
Z1 Z 2
Z1 Z 2 Z 4 Z1 Z 2 Z 4 Z1 Z 2 Z 4 Z1 Z 2 Z 4 Z 5 Z1
Z1
Z1 Z 2 Z1 Z 2
Z1 Z 2 Z1 Z 2
Considering the illustrative case with two feeder meters: one at bus 3 and another at bus 5, and a fault at bus 1, the indices δ1 and δ2 are the same if the loads impedances are neglected, as shown below. Therefore, the algorithm would not be able to distinguish the actual bus under fault. Following the proposed algorithm, the bus associated with the minimum δk is selected as the faulted bus. And δk is given by the total sum of di,k (as shown in (3)), where i is associated to the feeder meters and k with the candidate bus. The indices calculated using voltage measurements from feeder meters at buses 3 and 5 for a short circuit at buses 1 and 2 (not simultaneously) are given below. Firstly, for bus 1 and exploring the measurements from smart feeder meters 3 and 5: Vˆ Vˆ Vˆ5 d 3,1 3 3 Z1 2 Z1 Vˆ Vˆ Vˆ5 d 5,1 5 3 Z1 2 Z1 Vˆ Vˆ5 Vˆ3 Vˆ5 0 1 d 3,1 d 5,1 3 Z1 Z1 Then, for bus 2 and feeder meters 3 and 5: Vˆ3 Vˆ5 Vˆ3 d 3, 2 Z1 Z 2 2 Z1 Z 2
d 5, 2
Vˆ3 Vˆ5 Vˆ5 Z1 Z 2 2 Z1 Z 2
Vˆ3 Vˆ5 Vˆ3 Vˆ5 0 Z1 Z 2 Z1 Z 2 The indices δ1 and δ2 have the same value, consequently yielding multiple identification. However, in the proposed fault location method, the inclusion of loads in the bus impedance matrix turns possible to differ one bus from the other, as the elements in the matrix become different from each other. However, it is important mention that accurate information about the load is not necessary as discussed in subsection IV. A.
2 d 3, 2 d 5, 2
X. APPENDIX B The different conductor types of the system in Fig. 3 were represented by different colors. The impedance associated to each conductor type is presented below and Zequivalent is the impedance of the external Thevenin equivalent connected to bus 1. 0.2900 i 1.9200 Z equivalent 0.1960 i 0.5300 0.1960 i 0.5300
0.1960 i 0.5300
0.1960 i 0.5300 0.1960 i 0.5300 0.2900 i 1.9200
0.2900 i 1.9200 0.1960 i 0.5300
0.4272 i 0.9609 Z #4 / 0 (in blue) 0.0600 i 0.4780 0.0600 i 0.4500
0.0600 i 0.4780
0.7567 i 1.0067 Z #1 / 0 (in green) 0.0600 i 0.4780 0.0600 i 0.4500
0.0600 i 0.4780
1.6440 i 1.0060 Z #4 (in black) 0.0600 i 0.4780 0.0600 i 0.4500
0.4272 i 0.9609 0.0600 i 0.5360
0.7567 i 1.0067 0.0600 i 0.5360
0.0600 i 0.4780 1.6440 i 1.0060 0.0600 i 0.5360
1.0840 i 0.9980 0.0600 i 0.4780 Z # 2 (in red) 0.0600 i 0.4780 1.0840 i 0.9980 0.0600 i 0.4500 0.0600 i 0.5360
0.0600 i 0.4500 0.0600 i 0.5360 / km 0.4272 i 0.9609 0.0600 i 0.4500 0.0600 i 0.5360 / km 0.7567 i 1.0067
0.0600 i 0.4500 0.0600 i 0.5360 / km 1.6440 i 1.0060 0.0600 i 0.4500 0.0600 i 0.5360 / km 1.0840 i 0.9980
The test system data is presented in Table XIII where k and m represent the initial and the final bus of each branch, respectively, and the loads are always connected to the final bus and the loads power factor is 0.92.
k
m
1 2 2 4 5 6 7 8 9 10 11
2 3 4 5 6 7 8 9 10 11 12
TABLE XIII TEST SYSTEM DATA Dist. Sload k (m) (kVA) 900 0 67 50 45 69 100 0 67 40 75 71 200 75 72 200 112.5 73 200 75 74 10 75 63 50 0 76 100 0 77 60 8.6 78
m 69 70 71 72 73 74 75 76 77 78 79
Dist. (m) 20 20 50 40 40 20 110 20 30 50 70
Sload (kVA)
7 112.5 75 8.5 1.9 112.5 112.5 112.5 5.9 0 75
9 k
m
12 13 11 15 16 17 18 19 18 10 22 23 24 25 26 27 28 29 28 26 32 33 23 35 36 37 38 38 40 40 42 40 44 38 46 47 48 49 50 48 52 53 54 52 56 57 57 59 48 61 62 63 64 65 66 67
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
Dist. (m) 30 160 30 10 20 40 40 50 150 30 70 50 20 30 60 40 20 120 20 20 5 25 10 70 10 10 70 100 60 50 10 30 40 60 20 120 50 20 170 100 60 30 130 20 80 50 60 20 40 10 50 30 20 30 20 30
Sload (kVA)
75 75 112.5 45 112.5 0 75 112.5 112.5 112.5 0 3 45 0 112.5 0 75 112.5 112.5 112.5 112.5 112.5 0 12.4 112.5 0 3 0 75 75 75 112.5 45 1 112.5 0 112.5 75 112.5 0 1.2 112.5 75 75 0 10 112.5 3.8 3 5.5 0 75 75 3.5 0 112.5
k
m
79 80 81 82 82 84 85 128 86 78 78 89 90 91 92 92 92 95 95 97 98 98 100 95 102 103 103 105 106 107 108 109 110 107 112 113 113 115 116 117 90 119 120 119 122 123 123 125 126 128 104 130 130 132 133
80 81 82 83 84 85 128 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 129 130 131 132 133 134
Dist. (m) 70 30 30 50 50 30 20 30 20 130 50 50 180 20 30 70 100 40 50 60 110 40 110 60 40 30 150 210 30 100 100 30 20 170 110 110 200 200 200 200 110 70 70 70 130 20 20 40 40 60 70 20 100 40 40
XI. REFERENCES
Sload (kVA)
112.5 112.5 0 75 75 112.5 0 15.5 75 75 75 0 45 0 112.5 23.5 0 75 6 0 23.5 75 112.5 112.5 0 75 75 108.5 0 0 108.5 112.5 112.5 75 0 0 30 30 30 30 0 0 30 55 0 15.5 15.5 45 112.5 45 0 112.5 0 112.5 112.5
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XII. BIOGRAPHIES Fernanda C. L. Trindade (S’09) received the M.Sc. degree in electrical engineering from the University of Campinas, Brazil in 2009. Currently, she is a Ph.D. student at University of Campinas, Brazil. Her research interests are power system automation, monitoring and protection. Walmir Freitas (M’02) received the Ph.D. degree in electrical engineering from the University of Campinas, Campinas, Brazil, in 2001. Currently, he is an Associate Professor with the University of Campinas, Campinas, Brazil. His research interests are analysis of distribution systems, distributed generation and power quality. Jose C. M. Vieira (S’98–M’07) received the M.Sc. and Ph.D. degrees in electrical engineering from the University of Campinas, Campinas, Brazil, in 1999 and 2006, respectively. Currently, he is an Assistant Professor at the São Carlos School of Engineering, São Carlos, Brazil. His research interests are distributed generation, power system control, dynamics, and protection.
