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2010 International Conference on Power System Technology
Impedance-Based Fault Location Formulation for Unbalanced Primary Distribution Systems
with Distributed Generation J. U. N. Nunes, Student Member, IEEE, and A. S. Bretas, Member, IEEE
Abstract- State-of-the-art impedance-based fault location formulations for power distribution systems suppose that the system is radial. However, the introduction of new generation technologies in distribution systems, such as distributed generation, changes the direction of the system load flow from unidirectional to multi-directional. Therefore, it is necessary to extended current impedance-based fault location formulations to
take into account the presence of generation units in the distribution system. Moreover, the distribution feeders are inherently unbalanced. This characteristic decreases accuracy of current fault location estimates that are based on sequence or
modal phasor quantities. In this paper it is presented an extended impedance-based fault location formulation using phase coordinates. Computational simulations test on a typical unbalanced deregulated distribution system are presented and
compared with state-of-the art techniques. The extended formulation is implemented numerically and a case study is
presented to demonstrate the methods accuracy.
Index Terms- Distributed generation, Fault location, Power distribution systems.
I. INTRO DUCTION
POWER distribution networks are essential for the
continuity of consumer electricity supply. The constant
exposure to environmental and climatic conditions increases
their vulnerability to possible faults that could interrupt the
power supply. Among the events that can cause system
disturbances are: load abrupt changes, network maneuvers,
human being contact, objects or vegetation and lightning,
among others. Currently, the digital relays technology,
through its fault location function, provides estimates that
improve maintenance by allowing faster system restoration.
Several techniques for fault location [1]-[4] based on
impedance measurement have been propped in recent years.
These techniques are suitable for radial distribution systems.
However, the presence of generation within the power
distribution system (PDS) affects considerably the accuracy of
these methods, requiring the study and proposals for new
methodologies. With the changes in the market for generation,
transmission and distribution of energy, has emerged in recent
This work was supported by CAPES (Coordenayiio de Aperfeiyoamento
de Pessoal de Nivel Superior). J. U. N. Nunes and A. S. Bretas are with the Electrical Engineering
Department, Federal University of Rio Grande do Sui (UFRGS), Porto
Alegre, RS, Brazil (e-mail: nunes!a>.ece.uttgs.br; abretas!a>.ece.uttgs.br).
978-1-4244-5940-7/1 01$26.00©20 1 0 IEEE
years a considerable interest in developing new generation
technologies such as distributed generation (DG), which is
characterized by being directly connected to the distribution
network [5]. However, the introduction of DG changes the
direction of power flow from unidirectional for multi
directional, affecting the coordination between fuses and
relays, while the fault occurrence [6]. In other words, the
presence of generators in the distribution system modifies the
magnitudes and directions of the fault currents, so that all the
coordination and adjustment of protective equipment should
be re-calculated [7]. The fault location algorithms based on
impedance present errors in the estimate when the insertion of
DG, since they use the fault current estimate. Currently, an
impedance-based fault location technique has been developed
to contemplate the presence of DG in PDS [8]. This
methodology proved to be very effective for balanced
systems; however it was not tested for unbalanced systems.
Given this limitation of current state-of-the art fault location
formulations, this paper presents an extended impedance
formulation for three-phase unbalanced systems. Test
computational simulations are performed using the
ATP/EMTP software [11] in order to compare the proposed
method with a recent proposed method [8]. The mathematical
formulation is numerically implemented in MATLAB [10]
and a case study is presented to demonstrate the formulation
accuracy. This paper is structured as follows: Section 2
describes the state-of-the-art impedance-based fault location
formulation for DG systems; Section 3 discusses the proposed
extensions for unbalanced systems; A case study is performed
in the Section 4; in Sections 5 and 6 illustrate the results and
conclusions, respectively.
II. FAULT LOCATION BASE D ON THE POSITIVE SEQUENCE
ApPARENT IMPE DANCE
Consider the system illustrated in Fig. 1. This on-line
diagram represents a deregulated distribution system.
Analyzing the following system, we found that this may be
subject to faults downstream or upstream of the generating
unit. If the failure occurs downstream of the generator, the
faulted system is represented by an equivalent impedance
(Zth) downstream to the fault, as illustrated in Fig. 2.
However, if the fault occurs upstream of the generator, there
will be a current contribution from the remote end to the fault.
In this case the faulted system is represented by an equivalent
impedance Zth and a source Vth, both located at the remote
end of the fault, as illustrated in Fig. 3. In both cases, the
equivalent impedance Zth is the result of all downstream loads
aggregated.
Substation 1 Z, k·1 Z, O+d---- ine_k+1
Fig. I. Distribution system ;ith distribut;d generation�
S R VSfa X VFa 1-x 111R � � ISfa Ila RF 11F Load Z'h
Fig. 2. Distribution system with fault downstream of the DG.
S R IR Vsfa X VFa 1-x 9 � � Isfa ILa
RF 11F
Fig. 3. Distribution system with fault upstream to the DG.
n
-1�,
Assuming that a three-phase fault occurs in the system
illustrated in Fig. 1, the estimated fault distance can be
obtained from the during fault single phase voltages and
currents obtained at the relay substation. Such consideration
can be made under the following assumptions: the system
equipment presents balanced operation, so that the impedances
do not interfere with each other in fault location formulation;
the fault current will be equal in all three phases, in order that
the three-phase fault is symmetrical. Thus, the equation used
for three-phase fault location can be obtained by line-to
ground fault in phase a, for example. Observing the equivalent
circuits of Fig. 2 and Fig. 3, the sending end voltage is
obtained by (1):
where:
Vsfa
Isfa
Zaa X VFa
IF RF
IR
Zth
Vth
Phase a terminal S voltage
Phase a term inal S current
Phase a self impedance [per km]
Fault distance
Phase a fault point voltage
Fault current
Fault resistance
Terminal R current
Terminal R equivalent impedance
Terminal R equivalent voltage
(1)
2
Multiplying both sides of Equation (1) by I; (fault current
complex conjugate), and knowing that the term IF· I; • RF results in a real number, we obtain the expression (2):
x = Im(vsfa·1;') Im(Zaa·1sfa·1;')
(2)
The pre-fault load current is considered equal to pre-fault
current at the local end, as (3):
(3)
The initial estimate of fault current is obtained by the
difference between the sending end during the fault current
and load current through (4):
(4)
With these equations, the following algorithm can be used
to estimate the fault location:
I. It is assumed ILa as the load current before the fault
occurrence, according to (3).
II. Using (4) an estimative of the fault current is
calculated.
III.
IV.
V.
VI.
Using (2), a fault location is estimated.
Using (5) the voltage at the estimated fault location is
calculated. This is done by considering system
topology.
(5)
Using the fault point voltage estimated in the
previous step, a Thevenin equivalent circuit is
determined of the all upstream system. If the fault
location estimate in step III is downstream of the DO,
as illustrated in Fig. 2, the equivalent circuit is the
parallel impedance of all the system (also considering
the line impedances) to upstream at the fault point.
After this calculation, the current in the remote end is
updated again with equation (6).
I - VFa
La - Ztha (6)
In the case of fault location being estimated
downstream of DO, the Thevenin equivalent will
have a generating source. In this case the current in
the remote end is obtained using equation (7):
(7)
VII. With the updated value of the load current, return to
the step II.
The routine is continued until the fault is located. If the
fault location estimate is located on the first section of the
feeder, the method is finished and it is obtain a final estimate
for the fault location. If the fault is estimated after the first
section of the system, the values of voltage and current
measured at the local terminal are upgraded to the next system
buses and the steps I to VI are run again. This update is
performed on until the fault is estimated within of the section.
A. Distributed generation model The electric model of distributed generation used is the
model of a synchronous generator in the subtransient time
period [12]. The model, shown in Fig. 4, consists of the
subtransient reactance X;, armature resistance R and the value
of its internal voltage E;. The generator internal voltage can
be obtained through a power flow program [9], which
determines the voltage on the bus of the generator and the
current injected by him.
E" 9
R X" S
Fig. 4. Electric model of distributed generation
As the time period studied is the subtransient corresponding
to the first few cycles after fault occurrence, it is considered
that the generator internal voltage remains constant during the
fault. Thus it is possible to estimate the contribution of current
supplied by the generator during the fault, according to (8):
(8)
where the variable k represents the bus in which the generator
is connected.
B. Downstream system bus voltages and currents estimates Considering the faulted system, and assuming the loads, the
line impedances and relay data known, the previous presented
algorithm for fault location is run for the first section of the
feeder. If the failure is not found within this section, an
estimate of downstream system bus voltages and currents is
calculated, as in equations (9) to (11).
v. =v. -L· Z· · 1 Sf k Sf k-l lmek_l Sf k-l (9)
(lO)
(11)
If the line section in analysis is upstream the generator bus, the
short-circuit current in the bus during the fault must be
updated according to equation (12):
3
(12)
By the equation (12), it is verified that the presence of the
generator directly affects the process of fault current
estimation and therefore, the fault location estimation.
IIi. PROPOSE D FAULT LOCATION METHO D
The proposed formulation aims to extend the work
described in Section 2, by representing the lines of a typical
PDS by phase coordinates. This method also demonstrates the
development of a mathematical formulation, suitable for
unbalanced systems. The proposed method also obtains the
system downstream of the fault, however the operations are
done in a matrix format considering that the distribution
systems are three phase and unbalanced. The mathematical
formulation, the iterative algorithm, the model of distributed
generation and update process of the components of three
phase voltage and current are described below.
A. Mathematical formulation Consider the distribution system subject to a three-phase
fault, illustrated in Fig. 5.
5 R � ISfC VFc � ILc V Sfc 1-----'''''-----'-*-----'--''''-1
x
Fig. 5. Three-phase fault with distributed generation.
The voltages in phases a, b and c in the terminal S during
the fault period is estimated by:
(13)
The expression of equation (13) through its real and
imaginary components results in the set of expressions:
(14)
(15)
(16)
(17)
Vsfc(r) = x . Ts + RFc · IFC(r) (18)
(19)
where the parameters of lines are obtained by:
(20)
Tz = Lk={a,b,e}[Zak(r) • ISfk(i) + Zak(i) • Isfk(r)] (21)
Ts = Lk={a,b,e}[Zek(r) • Isfk(r) - Zek(i) .ISfk(i)] (24)
By the equations (14)-(19) verifies the presence of six
equations and four unknowns, which are the fault distance and
the fault resistance in the three phases. For the solution of this
system is sufficient to choose only four equations as shown in
(26):
o o
IFb(r)
o
o ]_1 [Vsfa(r)]
o VSfa(i)
o . VSfb(r) IFe(r) VSfe(i)
(26)
The solution of equation (26) results in the estimate of the
fault distance.
B. Iterative algorithm The algorithm starts considering the possibility of fault
location at the beginning of the feeder, in the first section of
line after the bus of the substation, as follows:
I.
II.
III.
IV.
It is assumed that the vector of phase currents is
equal to the vector of the S end currents, in the pre
fault period, according to (27):
(27)
It is estimated initially the fault current using
equation (28):
(28)
Calculate the initial estimate of the fault distance,
using equation (26).
Once estimated the distance, is made the analysis of
convergence of the algorithm, by equation (29):
VI.
4
Zael [ISfa]
Zbe • ISfb (30)
Zee ISfe
With the three-phase voltages at the fault point,
obtained in step V, it is necessary to determine an
equivalent circuit of the entire system downstream of
the fault. Since of the data of equivalent circuit and of
the three-phase voltages at the fault location are
calculated the load three phase currents. The
equivalent circuit downstream of the fault is obtained
by observing the location of the first fault distance
estimate. If the fault location as estimated in step III,
is the upstream of DG, an equivalent impedance
matrix and a vector of the equivalent three-phase
voltages, seen from the remote end faulted section
must be determined. Representing the rest of the
system downstream of the fault taking into account
the contribution of DG to the fault, and from these,
an estimated three-phase load currents, according to
(31):
[I Lal [Yaa Yab Yael [VFa - Vthal
I Lb = Yba Ybb Ybe • VFb - Vthb I Le Yea Yeb Yee VFe - Vthe
(31)
If the location estimate in step III is downstream of
the DG, it means that the circuit downstream of the
fault is entirely passive in this case the three-phase
load currents are obtained simply by (32):
(32)
VII. With the updated value of the load current vector IL,
returns to the step II.
This algorithm runs until convergence, where it is obtained
an estimate of the fault location. If the fault is located on the
first section of the feeder, the method is finished and we have
a final estimate for the fault location. If the fault is estimated
after the first section or the distance found is negative, it is
necessary to estimate the voltage and current vectors for the
downstream system bus and the proposed algorithm is run
again, from the steps I to VII, until a new estimate of the
distance fault. This process is repeated while the fault distance
estimation is not found in the section corresponding to the
updated voltage and current vectors.
C. Distributed generation model [x(n) - x(n - 1)] < 0.0001 * L (29) The electrical circuit of the DG used in the fault location
V.
where n represents the number of iterations of the
algorithm and L is the length of line section analyzed.
The three-phase voltages at the fault point are
determined by equation (30):
algorithm is the circuit of a three phase synchronous
generator, connected in Y and with neutral solidly grounded.
The model assumes that concatenated flows in each phase of
the rotor are constants in subtransient period, eliminating only
the differential equation associated with the electrical
characteristics of the machine. Thus, each phase can be
represented simply by the subtransient reactance of the
generator X;, by its armor resistance R and for their internal
voltages E;, as shown in Fig. 6.
x " Sa
x " Sc
L-_---lII/I \I'�- a
'--_--11111 \I'�- b
L-_---lII/I \I'�- c
Fig. 6. Model ing of distributed generation for unbalanced systems.
The model used in the proposed method is similar to that
described in Section 2, which is suitable for programs of short
circuit in which you want to compute the value of the
fundamental frequency component of short circuit currents
[12]. However, in the proposed method, the modeling of the
generator was made for the three phases, while in the method
discussed in the previous section the modeling of the generator
was made only for one phase. As the rotor concatenated flows
do not vary instantaneously, the internal voltage generator
remains constant during the fault. With this consideration and
with the three-phase voltages during the fault at the terminal
of DG, it is possible to determine the contribution of current
from the generator to the system during the fault, according to
equation (33):
(33)
where the variable k represents the bus in which DG is
connected. The generator internal voltage in the pre-fault is
obtained through a program of three-phase power flow based
in the Ladder technique [9], with some modifications in the
algorithm to include the DG system.
D. Downstream system bus voltages and currents estimates Consider the PDS with the presence of DG, illustrated in
Fig. 1. It appears that the system can be divided into two parts:
the circuit upstream and downstream of the generator circuit.
As can be seen in Fig. 1, the circuit upstream of the generator
corresponds to the buses 1 to k - 1, and the circuit
downstream of the generator corresponds to the buses k + 1 to
n. If the fault location is not estimated within the first section
of the feeder referred to the voltage and current vectors of the
substation, it is necessary to estimate the vectors of voltages
and currents for the downstream system bus, according to the
following equations (34) and (35), respectively:
v =V -L · Z · ·1 st k st k-l lme k-l St k-l
1st = 1st - Yloadk • Vst k k-l k
5
(34)
(35)
Therefore, the fault location algorithm is run again until a
new distance between the local bus and the fault point is
obtained. This process is performed on until the fault is
estimated in the section corresponding to the vectors Vst and
1st updated. Equation (35), used to update the vector of
currents at the faulted period, is used in almost all sections of
the system except for the section that precedes the generator
bus. lf the line section in the previous analysis is the generator
bus, the vector of currents during the fault on the generator
bus should be updated as (36):
1st k = 1st k-l - Yloadk • Vst k + IBt (36)
The update of vector Vst and 1st may be better understood
through the simplified algorithm flow chart presented in Fig.
7. Through this algorithm it is clear that the presence of the
generator contributes to the fault current, with direct effect in
the fault location estimate.
Fault location
algorithm
(steps I to VII)
Update of faulted
voltages
at the knode,
using eq. 34
Update of faulted
currents
at the knode,
using eq. 35
Determining
of fault
distance
Update of faulted
currents
at the knode,
using eq. 36
Fig. 7. Simplified algorithm to update the voltages and currents.
IV. CASE STUDY
In order to analyze the performance of the proposed fault
location methodology, a 12 buses distribution feeder was
simulated in the software A TP/EMTP [11]. For
implementation of the algorithm, the software used was
MA TLAB [10]. The 12 buses system consists of 11 line
sections, 10 load buses and a generator interconnected at half
the system, as illustrated in Fig. 8. This system was based on a
distribution feeder, obtained from the literature [8], in which
some modifications were necessary to validate the
methodology, among which the reduction of the total three
phase system loading and the inclusion of lines asymmetries.
The system has a three-phase total power of 7,36 MVA, and
DO contributed 0,67 MV A of that. The generator has an
output voltage of 440 V and is connected to the distribution
network through a transformer V-V, 440113,8 kY. The
distribution feeder has an overall length of 27.6 km and the
generator was connected at km 11.86.
Fig. 8. 12 buses system with distributed generation.
A. Datafeeder To validate the methodology, the line model used was a RL
four-wire grounded neutral. The feeder configuration presents
an unequal spacing between phases and non-transposed lines,
resulting in an unbalanced line impedance matrix [10]. Line
impedance matrix was generated from a computational routine
built in MA TLAB, using Carson's equations [8]. The 12 buses
system is composed by 11 different line sections, whose
lengths are shown in Table I.
TABLE 1 12 BUSES DATA FEEDER
Bus Bus Distance From To IKml
1 2 4.1843 2 3 1.2633 3 4 1.2633 4 5 2.1887 5 6 2.9612 6 7 3.1640 7 8 1.5530 8 9 6.2040 9 10 2.1726
10 11 0.8851 11 12 1.8025
The conductor used in each line segment was 447,000 2617
ACSR, obtained from [8].
B. Load data The system loads are balanced three-phase, connected in Y
and with the neutral solidly grounded. The phases were
modeled as constant impedance, and their values are shown in
Table II.
TABLElI LOAD DATA OF 12 BUSES SYSTEM
C. Generator data
Bus Impedance (0) R+ ·X
1 64.8 + j21.6 2 328.3 + j 1 09.4 3 538.8 + j 109.4 4 183.0+j61.0 5 906.9 + j302.3 6 646.5 + j131.3 7 114.0 + j38.0 8 605.8 + j21O.5 9 194.9+j31.6
10 708.0 + j460.0 11 740.7 + ·279.8
6
The distributed generation system was interconnected to 12
buses through a three-phase Y -Y transformer of 440113,8 kV,
as shown in Fig. 8. The generator provides to the system 0,67
MV A, contributing approximately with 7,6% of the total
three-phase power of the system. The electrical circuit of DO
is a three phase synchronous generator connected in Y and
with neutral solidly grounded, in which the model, described
in Section III is the simplified model for short-circuit
calculate.
V. RESULTS
Simulations were made through solid three-phase faults in
the ATP/EMTP in 65 different points of the 12 bus system, as
described in Section 4. The estimated error in percentage of
the distance is calculated based on the total length of the
feeder, as illustrated by (37):
(37)
where xest is the estimated fault distance, xreal is the real fault
distance, and LT is the total length of the line, which in this
case is 27640 meters. In this section, the results are analyzed
by comparing the proposed method and a classical method of
fault location for systems with distributed generation [8]. The
results for the classical methodology are illustrated in Fig. 9,
and the results for the proposed methodology are illustrated in
Fig. 10. The results of the conventional method show that the
estimated error increases linearly with the distance between
the energy source to the fault location. In this system, we
verified the presence of two energy sources: one is the
substation, located at the beginning of the feeder and the other
is distributed generation, located at km 11.86 of the feeder.
For the graphic shown in Fig. 9, we find that the error tends to
increase from the substation to the point where DO is situated,
where the error is near zero. From this point the error tends to
increase again in proportion to fault distance. The average and
maximum errors for this method are approximately 15% and
40% of the length of the feeder, respectively, proving the
inefficiency of this technique when applied to unbalanced
systems and with line length above of 2 km.
45,0
./ ./
/' /"
40,0
35,0
30,0
25,0
20,0
15,0
10,0
5,0
0,0
A /' ./" .....-
.;' ./ � Y
Distance (km]
Fig. 9. Results of the Bretas and Salim methodology.
0,7
0,6
0,5
� 0,4 !. ]
0,3
0,2
0,1
0,0
. ...-... /
/ /
/ /
/'
Distance [kmJ
Fig. 10. Results of the proposed methodology.
The test results of the proposed methodology, illustrated in
Fig. 10, show that this also affected by distributed generation,
however the maximum error is approximately 0.7% and the
average error is around 0.2% of the total length of 12 buses
feeder. Comparing the results of conventional method with the
proposed method, it can be verified that the methodology
described here is more appropriate for the three-phase fault
location in distribution systems with the presence of
distributed generation.
VI. CONCLUSIONS
This paper proposes an extended methodology for fault
location based on apparent impedance for distribution systems
using only local terminal data. The equations described were
developed for three-phase faults in systems with distributed
generation. The methodology is suitable for distribution
systems, balanced and unbalanced, with high accuracy
compared with a traditional technique for fault location. The
implementation of the proposed method helps energy
companies reduce the time of restoration of systems,
improving their services to consumers.
VII. ACKNOWLE DGMENT
This work was supported by CAPES (Coordena9ao de
Aperfei90amento de Pessoal de Nfvel Superior).
7
vm. REFERENCES
[I] J. Zhu, D. L. Lubkeman, and A. A. Girgis, "Automated Fault Location and Diagnosis on Electric Power Distribution Feeders", IEEE Transactions on Power Delivery, Vol. 12, No. 2, pp. 801-809, April 1997 .
[2] M. S. Choi, S. J. Lee and D. S. Lee, "A New Fault Location Algorithm Using Direct Circuit Analysis for Distribution Systems", IEEE Transactions on Power Delivery, Vol. 19, No. I, January 2004.
[3] S. J. Lee, M. S. Choi and S. H. Kang, "An Intelligent and Efficient Fault Location and Diagnosis Scheme for Radial Distribution Systems", IEEE Transactions on Power Delivery, Vol. 19, No. 2, pp. 524-532, April 2004.
[4] R. H. Salim, M. Resener and A. D. Filomena, "Extended Fault-Location Formulation for Power Distribution Systems", IEEE Transactions on Power Delivery, Vol. 24, No. 2, pp. 508-516, April 2009.
[5] T. Ackerman, G. Anderson and L. Soder, "Distributed Generation: A definition", on Electric Power System Research, Vol. 57, No. 3, pp. 195-204, June, 200 I.
[6] R. C. Dugan and D. T. Rizy, "Electric Distribution Protection Problems Associated with the [nterconection of Small, Dispersed Generation Devices." IEEE Transactions on Power Apparatus and Systems, Vol.
PAS- I 03, No. 6, pp. 1121-1127,June 1984. [7] A. Girgis and S. Brahma, "Effect of Distributed Generation on
Protective Device Coordination in Distribution System", In: Large Engineering Systems Conference, pp. 115-119, July 2001.
[8] A. S. Bretas and R. H. Salim, "Fault Location in Unbalanced DG Systems using the Positive Sequence Apparent [mpedance", IEEE Transmission and Distribution Conference and Exposition, August 2006.
[9] W. H. Kersting, Distribution System Modeling and Analysis, Boca Raton, FL: CRC, 2002.
[10] Mathworks Matlab. Natick, MA, 2009. [Online]. Available: http://www.mathworks.coml.
[I I] Alternative Transient Program: ATP/EMTP, Bonneville Power Administration, 2002. [Online]. Available: http://www.emtp.org/.
[12] P. Kundur, Power Systems Stability and Control, New York: MacGrawHill, 1994.
[13] Distribution System Analysis Subcommittee, IEEE 4 Node Test Feeder.
[Online]. Available: http://ewh.ieee.org/soc/pes/dsacom/testfeeders.html, September 2006.
IX. B[OGRAPHIES
Jose Ubirajara Nunez de Nunes (S'09) was born in Arroio Grande, Rio Grande do SuI, Brazil, on July 5, 1980. He received the E.E. degree from the Catolic University of Pelotas (UCPel), Pelotas, Brazil, in 2005. Currently he is working in M. Eng. degree in power systems at Federal University of Rio Grande do SuI (UFRGS), Porto Alegre, Brazil. His research interests include power system protection, modeling and distributed generation.
Arturo Suman Bretas (M'98) was born in Baum, Sao Paulo, Brazil, on July 5, 1972. He received the E. E. and M. Eng. degrees from the University of Sao Paulo, Brazil, in 1995 and 1998, respectively, and the Ph. D. degree in electrical engineering from Virginia Polytechnic Institute and State University, Blacksburg, in 200 I. Currently, he is an Associate Professor of the Federal University of Rio Grande do SuI (UFRGS), Porto Alegre. His research interests include power system protection, control and restoration.
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