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Optimum Fault Current Limiter Placement

Jen-Hao Teng Chan-Nan Lu

Abstract: Due to the difficulty in power network reinforcement

and the interconnection of more distributed generations, fault

current level has become a serious problem in transmission and

distribution system operations. The utilization of fault current

limiters (FCLs) in power system provides an effective way to

suppress fault currents and result in considerable saving in the

investment of high capacity circuit breakers. In a loop power

system, the advantages would depend on the numbers and

locations of FCL installations. This paper presents a method to

determine optimum numbers and locations for FCL placement

in terms of installing smallest FCL parameters to restrain

short-circuit currents under circuit breakers’ interrupting ratings.

In the proposed approach, sensitivity factors of bus fault

current reduction due to changes in the branch parameters are

derived and used to choose candidates for FCL installations. A

genetic-algorithm-based method is then designed to include the

sensitivity information in searching for best locations and

parameters of FCL to meet the requirements. Test results

demonstrate the efficiency and accuracy of the proposed

method..

Keywords: Short-Circuit Current, Circuit Breaker, Fault

Current Limiter, Sensitivity Analysis, Genetic Algorithm

I. INTRODUCTION

ith the increasing demand for power, electric

power systems have become greater and are

interconnected. Generation units of independent power

producers (IPPs) and renewable energy have been

interconnected to power systems to support the rising

demands. As a result, faults in power networks incur

large short-circuit currents flowing in the network and in

some cases may exceed the ratings of existing circuit

breakers (CB) and damage system equipment The

problems of inadequate CB short-circuit ratings have

become more serious than before since in many locations,

the highest rating of the CB available in the market has

been used. To deal with the problem, fault current

limiters (FCLs) are often used in the situations where

insufficient fault current interrupting capability exists

[1-10].

Active FCL is a variable-impedance device

connected in series with a CB to limit the current under

fault conditions. It has very low impedance under normal

operating conditions and high impedance under fault

conditions. Active FCLs with different operation

mechanism such as based on superconductor, power

electronics, polymer positive temperature coefficient

resistors and techniques of arc control [1-10] have been

introduced. Depending on the location of installation,

FCL could offer other advantages such as 1) increasing

the interconnection of renewable energy and independent

power units; 2) increasing the energy transmission

This work was sponsored by Taiwan Power Company under contract

TPC-023-95-C94080002Z.

Jen-Hao Teng is with Department of Electrical Engineering, I-Shou

University, Kaohsiung, Taiwan.

Chan-Nan Lu is with Department of Electrical Engineering, National

Sun Yat-Sen University, Kaohsiung, Taiwan.

capacity over longer distances; 3) reducing the voltage

sag caused by the fault; 4) improving the system stability,

and 5) improving the system security and reliability.

In radial power systems, the placement of FCL is

not difficult, but in loop power system, FCL placement

becomes much more complex when more than one

location that have high fault current problems. In such a

system, short-circuit currents could come from many

directions and are not easily blocked by a single FCL.

Therefore, from power system operation and planning

points of view, a technique that can choose optimum

number and locations for FCL placement with smallest

circuit parameters changes to constrain fault currents

under CB rating is becoming necessary. For this purpose,

rectifier-type superconducting FCL model has been

included in short-circuit current analysis and a method to

find FCL locations suitable for short-circuit current

reduction was proposed in [11]. Refs. [12, 13] used a

hierarchical genetic algorithm combined with a

micro-genetic algorithm to search for the optimal

locations and smallest

simultaneously.

This paper proposes a new method to find the

optimum numbers and locations for FCL placement. For

large loop system applications, in order to reduce the

search space in finding the optimum FCL locations, a

sensitivity analysis is first conducted to find better

candidate locations for

genetic-algorithm-based method is then designed and

used to solve the optimum FCL placement problem. Test

results demonstrate the efficiency and accuracy of the

proposed method.

II. FAULT CURRENT REDUCTION AND IMPEDANCE

REQUIRED

Although, most power

unsymmetrical, balanced three-phase faults are often the

worst and are used to determine the CB capacity. For a

balanced three-phase fault at bus i, the short-circuit

current can be calculated by

E

I*

=

FCL circuit parameters

FCL placement. A

system faults are

b

ii

i

sc

i

I

Z

(1)

where

i.

sc

iI

is the three phase short-circuit current at bus

i E is the voltage before the fault at bus i. Commonly,

i E can be set as 1.0 p.u.

impedance at bus i, it can be obtained from diagonal

entries of the impedance matrix (Zbus).

current.

In the Zbus building algorithm, when adding a line with

impedance

b

Z between bus j and k, the original

element of Zxy will be modified as

ii

Z

is the Thevenin

bI is the base

W

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b jkkkjj

ky

Z

jy

Z

xkxj

xy

new

xy

ZZ

Z

+

Z

2

ZZ

ZZ

−+

−−

−=

) )((

(2)

where

new

xy

Z

and

xy

Z

are the modified and original

elements of Zbus , respectively.

Fig. 1: Thevenin equivalent circuit of adding a line between two

existing buses

Fig. 1 shows the Thevenin equivalent circuit by looking

into the system from two existing buses. If a FCL with

impedance

FCL

Z

were installed on line between bus k

and j and fired after the faults, then Thevenin equivalent

circuit can be expressed as Fig. 2.

Fig. 2: Thevenin equivalent circuit with FCL fired up

The total effect of inserting

can be considered as adding a new branch with the

following impedance to the system:

FCL

Z

into the system

FCL

FCLb

Z

b

FCLbbP

ZZZ

ZZZZ

)(

) //()(

+

−=+−=

(3)

Therefore, the modification to the diagonal entries of Zbus

after FCL is fired up at a branch between bus j and k is

ZZ

Z

+−+

2

The fault current deviation at a bus after FCL is fired up

can be written as

PP jkkk jj

ik

Z

ij

ii

ZC

C

+

ZZZ

=

−

−=∆

1

2

2

)(

(4)

ii

i

iiii

i

∆

Fi

Z

V

ZZ

V

+

I

−=∆

,

(5)

Substituting (4) into (5), (5) can be rewritten as

C

Z

P ii

+

If the FCL is used to constrain the fault current from

original

N

to

F

calculated by (6) and expressed as [7]

C

II

iiFiNi

−

Substituting (7) into (3), the FCL impedance required is

Z

Z

+

III. PROBLEM FORMULATION

If the location for FCL placement has been decided,

the FCL impedance required to constrain the fault current

to acceptable level could be easily calculated by (8).

However, in a large power system, it could be difficult to

determine optimal number,

parameters when fault currents calculated at several

locations are approaching and/or have exceeded the

ratings of existing CBs. Therefore, the objective is to

find a minimum number of FCLs and/or the smallest

circuit FCL parameters that are more economical while

keeping fault currents within CBs’ ratings. The problem

can be formulated as follows:

N

FCL

* min

1

=

t s

. .

21

2

)

,

(CZZC

V

I

ii

i

Fi

+

−=∆

(6)

iI,iI, , then

P

Z required can be easily

1

2

,,

,

C

Z

I

Z

Fi

P

−=

(7)

P

FCL

ZZ

−=

2

(8)

locations and FCL

NwZJ

FCL

i

FCLi

,

+=∑

(9a)

N

sc

j

sc

j

FCL FCLi FCLi FCL

≤

i

B jII

N iZZZ

L

1

L

1

max,

max

,,

min

,

=

=≤≤

(9b)

where

is the number of installed FCL.

factor for trading off between the number of required

FCL and the summation of circuit parameters of FCLs.

w

is used to make sure that the minimum numbers

FCLi Z,

is the impedance of the i-th FCL.

FCL

N

FCL

w

is the weighting

FCL

of FCL can be achieved.

minimum and maximum impedance allowable for the

i-th FCL, respectively.

min

,FCLi Z

and

max

,FCLi Z

are the

sc

jI

and

max,

sc

jI

is the

short-circuit current and maximum allowable CB rating

for bus j, respectively.

N

B is the number of buses that

have dangerous fault current levels.

To minimize the solution time, in this paper, a

sensitivity analysis technique is used to find the better

candidate locations for FCL placement. Eqs. (3)-(5) are

T h e 1 4 t h I n t e r n a t i o n a l C o n f e r e n c e o n I n t e l l i g e n t S y s t e m A p p l i c a t i o n s t o P o w e r S y s t e m s , I S A P 2 0 0 7 N o v e m b e r 4 - 8 , 2 0 0 7 , K a o h s i u n g , T a i w a n

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used to build the sensitivity relation of bus fault current

reductions with respect to FCL impedance addition. For

a FCL with impedance

FCL

Z

between bus j and k, the fault current reduction for each

bus after the FCL is activated can be expressed in vector

form as

[

FFFF

III

∆∆∆=∆

L

I

where

B

N is the number of bus in the power system. It

is assumed that

FCL

Z

is 1.0 p.u. in the following

derivation.

From (10), for each bus, the largest bus fault

current reductions achieved due to branch impedance

changes can be obtained. If only

for fault level mitigation, buses are arranged into a vector

based on decreasing order of the fault current level

reduction and expressed as

( )) 1 (, ( [

2 , 1 ,

FFF

I BNI

−∆

−

where

)(i BN

is the bus number for the i-th largest

sa

that is added to branch l

]

l

FN

l

N

lll

BB

I

,1,

∆

−

(10)

sa

C

F

N buses are required

] ))(,( ))1(,(

)) 2 (,

,1,

C

F

l

FN

C

F

l

FN

lll

N BNIN BNI

BN

c

F

c

F

∆

∆∆=

L

S

(11)

short-circuit current reduction.

reduction due to impedance change at branch l.

Therefore, the sensitivity matrix between FCL placement

and bus fault current reduction can be expressed as

[

F

FF

F

SSSS

=

L

where

L

N is the number of line in the power system.

The best candidate locations for FCL placement can be

sought for by using

F

S .

l

Fi

I

,

∆

is the current

]

T

N

F

N

LL

S

1

21

−

(12)

Fig. 3: A six-bus test system [15]

Using the six-bus system shown in Fig. 3 as an

example [15], the

F

S is shown in (13), in this case

C

F

N is 3. From (13), for example, if bus 2 fault current

has exceeded CB rating, then it can be found that line 5

is the best location to install FCL. If the system planner

intends to find two candidate locations for bus 2, then

line 5 and line 7 are better choices for FCL placement.

11

10

9

8

7

6

5

4

3

2

1

) 3 ,012 . 0 ( ) 6 , 118. 0 () 5 , 120. 0 (

) 2 ,005 . 0 () 5 , 060. 0 () 4 ,076. 0 (

) 5 , 001. 0 () 6 , 422. 0 ( ) 3 ,490 . 0 (

) 6 ,018 . 0 ( ) 5 ,138 . 0 () 3 , 147 . 0 (

) 4 , 066 . 0 () 2 ,186. 0 () 6 ,225 . 0 (

) 4 ,010 . 0 ( ) 2 ,080 . 0 () 5 ,101 . 0 (

) 6 , 055. 0 () 2 ,257 . 0 () 4 , 541. 0 (

) 4 ,046 . 0 () 2 , 132. 0 () 3 , 176. 0 (

) 4 , 035 . 0 () 5 , 063. 0 ( ) 1 , 197 . 0 (

) 5 ,020 . 0 () 4 , 091 . 0 ( ) 1 .292 . 0 (

) 4 ,013 . 0 ( ) 2 ,042 . 0 ( ) 1 , 298. 0 (

=

l

F

S

(13)

For a large loop power system the problem

formulation becomes a combinatorial constrained

problem with a non-linear and non-differential objective

function. In this study a genetic algorithm (GA) is used

to solve the problem. Main steps of the GA used in this

study are:

1. Coding: representing the problem by bit strings. Each

possible parameters and candidate locations for FCL

placement needs to be integrated into each population.

For each candidate location, the FCL parameters or

types should be coded. For example, if we have six

types of FCL that are available in the market; three

bits can be used to code FCL type choices. In this case,

“000” means no FCL will be installed in this location

and “111” has no meaning. FCL parameters are also

coded. If maximum available parameter for FCL is

max

FCL

Z

and the variation between two adjacent

parameter is

FCL

Z

∆

, the relation between

Z

∆

can be expressed as

max

FCL

Z

and

FCL

12

max

FCL

−

=∆

n

FCL

Z

Z

(14)

n bits can be used to code FCL parameters.

2. Initialization: initializing the population. GA operates

with a set of populations. The populations go through

the process of evaluation to produce new generation.

To begin with, the initial populations could be seeded

with heuristically chosen strings or at random. In our

test systems, all initial populations are randomly

generated.

3. Evaluation: determining which population is better

and deciding who mates. The evaluation is a procedure

to determine the fitness value of each population and

is very much application oriented. Since the GA

proceeds in the direction of better-fit strings and the

fitness value is the only information available to the

GA algorithm, the performance of the algorithm is

highly sensitive to the fitness value. In the proposed

T h e 1 4 t h I n t e r n a t i o n a l C o n f e r e n c e o n I n t e l l i g e n t S y s t e m A p p l i c a t i o n s t o P o w e r S y s t e m s , I S A P 2 0 0 7 N o v e m b e r 4 - 8 , 2 0 0 7 , K a o h s i u n g , T a i w a n

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optimization problem, the fitness value is the objective

function as described in (9). The fitness function with

constraints can be expressed as

∑

=

i

1

∑

=

j

∑

=

i

+++=

N FCLFCL

B

qj

N

piFCL

N

FCLi

KKNwZf

1

,

1

,,

*

(15)

where

pi

K, and

qj

K, are the penalty values and

are defined in (16).

,

≤

FCLi

K then

1000

0

500

0

,

,

max,

,

,

max

,

FCLi

,

min

=

=

≤

=

=

≤

qj

qj

sc

i

sc

j

pi

pi

FCLi

K else

K then

II if

K else

ZZZ if

(16)

4. Crossover: exchanging information between two

mates. Mating is a probabilistic selection process in

which populations are selected to produce offspring

based on their fitness values. Populations with high

fitness values should have a higher probability of

generating offspring and are simply copied into the

next generation.

5. Mutation: integrating random information into GA.

Mutation is the process of randomly modifying the

value of a string position with a small probability. It

ensures that the probability of searching any region in

the problem space is never zero and prevents complete

loss of genetic material through mate and crossover.

Fig. 4: Flowchart of the Proposed Optimum FCL Placement

Genetic parameters are the entities that help to tune

the performance of the FCL placement. The following

parameters are used in this study:

?

Population Size: 190

?

Crossover Rate: 0.5

?

Fig. 4 shows the flowchart of the proposed procedure.

IV. TEST RESULTS

Mutation Rate: 0.05

Fig. 5: The IEEE 30-bus Test System [18]

The proposed algorithm was implemented with

Borland C++ on a Windows based PC. IEEE 30-bus [18]

as shown in Fig. 5 is used in the following tests. The line

data for IEEE 30-bus test system is listed in the

Appendix; other data used in the test can be found in [18].

The S/N transition-type superconducting FCLs are used

in the following test. Using the proposed sensitivity

technique,

F

S can be built and Table 1 shows the bus

numbers correspond to entries in

is 5. From Table 1, it can be seen that if a FCL is

installed in line 1, then the five largest bus fault current

reductions in decreasing order are at buses 1, 3, 2, 4 and

12. These buses are marked in Fig. 5. Thus, the candidate

locations for FCL placement can be arranged and is

shown in Table 2. Using the information shown in Table

2, if the bus 16 fault current exceeds or near its CB rating;

good locations for installing FCL in order to constrain

the bus fault current would be at line 19, 21 and 26.

F

S . In this case

C

F

N

Table 1: Bus Number of

Line

Number

1 1

2 1

3 2

4 3

5 5

6 2

7 4

8 5

9 7

10 8

11 9

12 10

13 11

14 9

15 12

16 13

17 14

18 15

19 16

20 14

F

S

while

C

F

N

is 3

Bus Number

3

3

4

1

2

6

3

7

6

28

10

21

9

10

4

12

15

12

17

15

2

2

1

4

1

1

6

6

5

27

6

22

10

21

15

15

12

23

12

23

4

4

3

2

4

8

8

8

8

6

11

6

6

22

3

4

13

18

10

18

12

12

6

6

3

28

28

28

28

4

21

17

4

11

13

6

23

19

13

19

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21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

16

18

18

19

20

17

21

22

22

23

24

23

25

26

25

27

29

30

30

28

28

17

19

19

20

19

16

22

21

21

24

22

24

27

25

27

25

30

29

29

8

27

12

20

20

18

18

10

24

24

24

15

21

15

24

27

24

29

27

27

27

27

25

10

15

15

10

10

21

10

10

23

12

10

12

26

24

26

30

6

6

6

25

29

21

12

12

15

21

22

17

17

25

14

23

22

29

6

29

28

28

28

28

29

30

Fig. 6: The Candidate Locations for Bus 16

Table 2: The Candidate Locations for FCL Placement

Bus

Number

1

2

3 1,2,3,4,5,7,15

4 1,2,3,4,5,7,10,13,15,16

5

6 3,4,6,7,8,9,10,11,12,13,16,34,37,38,39

7

8 6,7,8,9,10,40

9

10 11,12,13,14,19,21,24,25,26,27,28,31

11

12 1,2,15,16,17,18,19,21,22,23,30,32

13

14

15 15,16,17,18,20,22,23,24,30,32

16

17 12,19,21,26,27,28

18 18,20,22,23,24,25

19 18,20,22,23,24,25

20

21 11,12,14,21,25,26,27,28,29,31

22 12,14,26,27,28,29,31,32

23 17,18,20,29,30,31,32

24 27,28,29,30,31,32,33,34,35

25 29,33,34,35,36,40,41

26

27 10,33,34,35,36,37,38,39,40,41

28 6,7,8,9,10,36,37,38,39,40,41

29 33,35,36,37,38,39,40,41

30 36,37,38,39,41

Candidate Locations (Line Number)

1,2,3,4,5,6

1,2,3,4,5,6

5,8,9

8,9

11,13,14

11,13,14

15,16,17,19

17,20,30

19,21,26

22,23,24,25

33,34,35

To show the effectiveness of the proposed method

for solving more complex problems, in the following

example, three buses fault currents already exceed their

CB ratings, they are

?

Bus 10 with short-circuit current 10.11551kA;

?

Bus 11 with short-circuit current 15.82295kA;

?

Bus 13 with short-circuit current 19.99105kA.

The CB rating in this test case is assumed to be 10 kA.

From Table 2, the candidate locations for FCL placement

are

?

for bus 10, good candidate locations are lines 11,

12, 13, 14, 19, 21, 24, 25, 26, 27, 28, 31;

?

for bus 11, good candidate locations are lines 11,

13, 14; and

?

for bus 13 good candidate locations are lines 15, 16,

17, 19.

With the help from sensitivity analysis the total

number of candidate location is reduced from 41 to 15.

This minimizes the computational efforts in searching for

optimal locations and FCL parameters to resolve

simultaneously the fault current problems at buses 10, 11

and 13.

0

1000

2000

3000

4000

5000

6000

7000

8000

0 50 100150 200

Iteration No.

Fitness Value

Fig. 7: Fitness Value for Each Iteration

Fig. 7 shows the fitness value variations of GA

iterations. The optimal solution obtained for this case is

?

A FCL with an impedance of 0.400 p.u. should be

installed on line 13;

A FCL with an impedance of 0.800 p.u. should be

installed on line 16.

?

The short-circuit currents at buses 10, 11 and 13

after FCLs installations are reduced to 9.75256kA,

9.81937kA and 9.78321kA, respectively. Note that only

two FCLs are required to suppress fault currents at three

buses. Using the proposed GA technique to solve the

optimization problem, the computational times required

when with and without the proposed sensitivity analysis

are 43s and 3599s, respectively.

V. CONCLUSIONS AND DISCUSSIONS

The integration of FCLs into power system

provides an effective way to suppress large fault currents

T h e 1 4 t h I n t e r n a t i o n a l C o n f e r e n c e o n I n t e l l i g e n t S y s t e m A p p l i c a t i o n s t o P o w e r S y s t e m s , I S A P 2 0 0 7 N o v e m b e r 4 - 8 , 2 0 0 7 , K a o h s i u n g , T a i w a n

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