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.